.. • We~'fern Region

SALT LAKE CITY,

UTAH

September 1973

NOAA TM NWS WR89

.,

NOAA Technical Memorandum NWS WR89 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Weather Service

Objective Forecast of Precipitation over the Western United States

Region of the

JULIA N. PAEGLE AND LAWRENCE P. KIERULFF

NOAA TECI:INICAL MEMORANDA National Weather Service, Western Region Subserles

The National Weather Service (NWSJ .Western Reglc;>n (WRJ Subserles provides an Informal medlu~ tor the documentation and ·quick dissemination of results not appropriate, or not yet ready, tor formal publication. The series Is used. to report on work In· progress, to describe technical ·procedures and practices, or· to relate progress to a limited audience •. These Technical Memoranda will report on Investigations devoted primarily to regional and local problems ot Interest mainly to ·personnel, and hence.wll I not be widely distributed. . . . .

Papers I ·to 23 are in the former sarles, ESSA Technical Memoranda, Western Region Technical Memoranda CWRTMJ; papers 24 to 59 are In th.e termer serl.es, ESSA Technical Memoranda, Weather Bureau Technical Memoranda (WBTMJ. Beginning with 60, .the p;:~pers are part of the series, NOAA Technical Memoranda NWS •.

Papers l·to 23, except. tor 5 <revised. edl.tlonl and 10, are ava.llable trcim the National Weather Service Western Region, Scientific Services Division, p, 0. Box 11188, Federal Building, 125 South State Street, Salt Lake City, Utah 84111. Papers.5 (revised edition), 10, and all c;>thers beg.lnnlng with 24 are available from the National Technical Information Service, U.S. Department of Commerce, Sills Bldg., 5285 Port Royal Road, Sprlngfla·ld, Va. · 22151. Price: $3.00 paper' .copy; $0.95 microfiche. Order by accession number shown In parentheses at end of each entry.

WRTM I WRTM 2 WRTM 3

WRTM 4 WRTM 5

WRTM 6 WRTM 7 WRTM 8 WRTM 9 WRTM 10 WRTM II WRTM 12

WRTM 13

WRTM 14

WRTM 15

WRTM 16 WRTM 17

WRTM 18 WRTM 19

WRTM 20

WRTM 21

WRTM 22 WRTM 23

WBTM 24

WBTM 25 ·

WBTM 26 WBTM 27 WBTM 28 WBTM 29 WBTM 30

WBTM 31

WBTM 32

WBTM 33 WBTM 34. WBTM 35

WBTM 36

WBTM 37 WBTM 38

WBTM 39 WBTM 40 WBTM 41 WBTM 42

WBTM 43 WBTM 44

WBTM 45/1

ESSA Technical Memoranda

Some Notes on Probability Forecasting. Edward D. Diemer, September 1965. COut of print.) Cl lmatologlcal Precipitation Probabl lltles. Campi led by Lucianna Ml I ler, December 1965. Western Region Pre- and Post-FP-3.Program, December I, 1965 to February 20, ·t966. Edward D. Diemer, March 1966. . . Use of Meteorological Sate! I Ita Data. March 1966. Station Descriptions of Local Effects on Synoptic Weather Patterns. Philip Williams, Jr., Apri I 1966 (revised November 1967, October 1969). CPB-178000) Improvement of Forecast Wording and Format. C. L. Glenn, May 1966 •.. Final. Report on Precipitation Probability Test Programs. Edward D. Diemer., May 1966. Interpreting the·RAREP. Herbert P. Benner, May 1966 (revised January 1967). COut of print.) A Collection of Papers Re.lated to the 1966 NMC Primitive-Equation Model. June 1966. Sonic Boom. Loren.Crow (6thWeather Wing, USAF, Pamphlet), June 1966. (Out of print.) (AD-479366) Some Electrical Process.es in the Atmosphere. J ;. Latham, June 1966. A. Comparison of Fog Incidence at Missoula, Montana, with Surrounding Locations. Richard A. Dlghtman, August 1966. (Out ot print.) · A Col taction of Technical Attachments on the 1966 .. NMC Primltlve-Equatlon.Model. Leonard W. Snellman, August 1966. (Out ·at prl nt. l . . · Application of Net Radiometer Measurements to Short-Range Fog and Stratus Forecasting at Los Angeles. Frederick Thomas, September 1966. The. Use of the Mean as an Estlmate·ot "Normal" Precipitation In an Arid Region. Paul C. Kangleser,

. November r966 •. Some Notes on Acclimatization In Man. Edited by Leonard W. Snellman, November 1966. A Digitalized Summary of Radar Echqes Within 100 Miles of Sacramento, Cal itornla. J, A. Youngberg and L. B. Overaas, December 1966. Limitations of Selected Meteorological Data. December 1966. A GrId Method .for EstImatIng PrecIpitatIon Amounts by UsIng the WSR-57 Radar. R. Granger, December 1966. (Out of print.) Transmitting Radar Echo Locations to Local Fire Control Agencies for Lightning Fire Detection. Robert R. Peterson, March 1967. (Out of print.) . . An Objective Aid tor Forecasting the End of East Winds rn the Columbia Gorge,· July thrciugb October. D. John Coparanl s, Apr(! 1967. · · · Derivation of Radar- Horizons In Mountainous Terrain. Roger G. Pappas, April 1967, "K" Chart Applications to Thunderstorm Forecasts Over the Western United States. Richard E. Hambidge May 1967. . ,

ESSA Techn I ca I Memoranda, Weather. Bureau Techn lea 1· Memoranda CWBTMJ

Historical ahd Cllmatol.oglcal Study at Grinnell Glacier, Montana. Richard A •. Dightman, July 1967. CPB-178071) VerifiCation of Operational Probability at Precipitation Forecasts, April 1966-March 1967. w. W. Dickey, October 1967. CPB-176240) A Study ot Winds in the Lake Mead Recreation Area. R. P. Augul is, January 1968. (PB-177830) ObjectJve Minimum Temperature Forecasting for Helena, Montana. D. E. Olsen, February 1968. CPB-177827) Weatber Extremes. R. J. Schmid! I, April 1968 (revised July 1968). CPB-178928) Smal !-Scale Analysis and Prediction. Phi I lp Wi I I lams, Jr., May 1968. CPB-178425) Numerical Weather Prediction and Synoptic Meteorology. Capt. Thomas D. Murphy U.S.A.F. May 1968. CAD-673365) ' ' Precipitation Detection Probabil !ties by Salt Lake ARTC Radars. Robert K. Belesky, July 1968. CPB-179084) " Probabli ity ·Forecasting--A Problem Analysis with Reference to the Portland Fire Weather District. Harold s. Ayer, July 1968. CPB-179289) Objective Forecasting. -Philip Williams, Jr., August 1968. CAD-680425) The WSR-57 Radar Program at MissouLa, Montana. R. Granger, October 1968. (PB-180292) Joint ESSA/FAA ARTC Radar Weather Surveillance Program. Herbert P. Benner and DeVon B. Smith, December 1968 (revised June 1970). CAD-681857) Temperature Trends in Sacramento--Another Heat Is I and. Anthony D. Lent in 1, February 1969. (Out of pr 1 nt.) (PB-183055) Disposal of Logging Residues Without Damage to Air Qual lty. Owen p, Cramer, March 1969. (PB-183057) Climate of Phoenix, Arizona. R. J. Schmid! i, P. C."Kangieser, and R. S. Ingram. Apri 1 1969, (Out at print,) ( PB-184295) Upper-Air Lows Over Northwestern United States. A. L. Jacobson, Apri 1 1969. CPB-184296) The Man-Machine Mix In Appl led Weather Forecasting in the 1970s. L. W. Snel I man, August 1969. CPB-185068) High Resolution Radiosonde Observations. W. s. Johnson, August 1969. CPB-18~673) ·Ana I ys is at the Southern C<l II torn I a Santa Ana of January 15-17, 1966. Barry B. Aronov i.tch, August 1969. CPB-185670) ' Forecasting Maximum Temperatures at Helena, Montana. David E. Olsen, October 1969. CPB-185762) Estimated Return Periods tor Short-Duration Precipitation in Arizona. Paul c. Kangieser, October 1969. (PB-187763) Precipitation Probabll !ties in the Western Region Associated with Winter 500-mb Map Types, Richard A. Augulls, December 1969. CPB-188248)

U. S. DEPARTMENT OF COMMERCE NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION

NATIONAL WEATHER SERVICE

NOAA Technical Memorandum NWSTM WR-89

OBJECTIVE FORECAST OF PRECIPITATION OVER THE WESTERN REGION OF THE UNITED STATES

J u I i a N. Paeg I e Assistant Professor of Meteorology

University of Utah Salt Lake City, Utah

Lawrence P, Kierulff i/ Scientific Services Division Western Region Headquarters

Salt Lake City, Utah

1/ Now at Weather Service Forecast Office, Los Angeles, California.

WESTERN REGION. TECHNICAL MEMORANDUM NO. 89

SALT LAKE CITY, UTAH SEPTEMBER 1973

TABLE OF CONTENTS

List of Tables

List of Figures

Abstract

I. Synoptic Climatology of 500-mb Winter Types*

A. Introduction

B. Typing Method

c. Atmospheric Variables

D. C I imato I ogy of Types

E. Characteristics of Types

I I. Regression Analysis and Related Statistics**

A. Introduction

B. Development of Method

C. Regression Analysis on Binary Predictand

D. Discussion of Results

I I I. Summary and Recommendations

IV. Appendix A

V. Acknowledgments

V I . 8 i b I i og rap h.y

*Chapter I -Authors: J. N. Paegle and L. P. Kierulff

**Chapter I I -Author: J. N. Paegle

i i

iii

iv-v

vi

1-2

2-3

3-4

4-5

5-7

7

7-9

9-11

11-15

15-16

16

17

17-18

2

3

4

5

6

7

8

9

10

II

12

13

14

15

16

17

18

19

20

21

22

LIST OF TABLES

Numerical Information Regarding Typing Procedure

Predictor Fields - Units and Constants

Station Code for Tables 5 through I I

Station Code for Predictor 20

First Two Predictors Selected in Preliminary Screening of Predictor Fields for Nonstratified Data

Same as Table 5 for Type Data

Same as Table 5 for Type 2 Data

Same as Table 5 for Type 3 Data

Same as Table 5 for Type 4 Data

Same as Table 5 for Type 5 Data

Same as Table 5 for Type 6 Data

Number of Cases in Nonstratified and Stratified Samples for Final Regression Analysis

Predictor Code for Final Regression Equations

Frequency of Precipitation for 12-Estimate Intervals for Nonstratified Developmental Sample

Same as Table 14 for Type and Type 2

Same as Table 14 for Type 3 and Type 4

Same as Table 14 for Type 5 and Type 6

Number of Times Each Predictor Field is Selected as the First or Second Predictor in the Final Equations for a I I Stations.

Reduction of Variance

Standard Error of Estimate

Root Mean Square Errors for Independent Nonstratified Sample

Root Mean Square Errors for Independent Sample, Types I, 2, and 3

iii

19

19

20

20

21

22

23

24

25

26

27

28

28

29

30

31

32

33

34

35

36

37

LIST OF FIGURES

Figure Page

Station Network and 43-Point Grid 38

2 Precipitation Frequencies 39

3 Means and Standard Deviation tor 850-mb Heights 40

4 Same as Figure 3 for 500-mb Heights 41

5 Same as Figure 3 tor 300-mb Heights 42

6 Same as Figure 3 for 500- 850-mb Thickness 43

7 Same as Figure 3 for 300- 500-mb Thickness 44

8 Same as Figure 3 tor 850-mb Dew-Point Depression 45

9 Same as Figure 3 for 700-mb Dew-Point Depression 46

10 Same as Figure 3 for Absolute Vorticity 47

II Same as Figure 3 tor Thickness Advection 48

12 Same as Figure 3 tor Vertical Velocities (Tota I) 49

13 Same as Figure 3 for Vertical Velocities Due to Vorticity Advection 50

14 Same as Figure 3 for Vertical Velocities Due to Thickness Advection 51

15 F Statistics 52

16 z Statistics 53

17 Final Regress ion Equations for Nonstratified Data 54

18 Same as Figure 17 including Dew-Point Depression Fields 55

19 Same as Figure 17 for Type 56

20 Same as Figure 17 for Type 2 57

21 Same as Figure 17 tor Type 3 58

22 Same as Figure 17 tor Type 4 59

iv

List of Figures (Continued)

Figure

23 Same as Figure 17 for Type 5

24 Same as Figure 17 for Type 6

25 Correlation Coefficients for Salt Lake City and

26

27

Phoenix

Correlation Coefficients for Los Angeles and Astoria

Predictors in Final Regression Equation for Astoria, Los Angeles, Salt Lake City, and Phoenix

v

60

61

62

63

64

This research was sponsored by the Techniques Development Laboratory, System~ Development Office, National Weather Service, and supported by the National Oceanic and Atmospheric Adminis­tration under Contract I I 1-35372.

Pub! ication of this technical report does not constitute official Government approval of the report's findings or conclusions. Its contents reflect the views of the Contractor who is responsible for the facts and accuracy of the results presented herein, and do not necessarily reflect the views or pol icy of the Government.

vi

l --·--····---

OBJECTIVE FORECAST OF PRECIPITATION OVER THE WESTERN REGION OF THE UNITED STATES

ABSTRACT

The case classification by 500~mb flow types described in the first chapter represents an objective synthesis of synoptic information which has swbjecfively and successfully been used by experienced forecasters in predicting the weather.

This information is presented in the form of a climatology of 500-mb winter flow patterns. It consists of the frequency of occurrences of seven tharacteristic 500-mb height configurations and associated patterns of vorticity, vertical velocity, higher and lower pressure levels, dew-point depressions, frequency of precipitation, etc. This stratification of probabi I ity of precipitation represents a refine­ment in the forecast of precipitation probabilities over simple· climatology.

The type classification is used as a stratification criterion in the second chapter to obtain predictive equations for precipitation probabi ~ity. Different predictive variables are stressed within the d i fferen·t types. Based on the reduction of variance and the Brier P-score, it appears that the stratification leads to signigicant improvement in the regression equations. In effect, the stratifica­tion includes a pattern comparison which could never be included in finite regressio~ equations. The results are promising and the method can presently be appl led in operational forecasting at very minimal computer cost.

I. SYNOPTIC CLIMATOLOGY OF 500-MB WINTER TYPES

A. Introduction

Precipitation forecasting is I imited by several basic problems. One of the most serious is the specification of the exact location of the mesoscale precipitation bands even if a perfect synoptic scale forecast is available. This problem can. be alleviated by experienced forecasters who give satisfactory subjective local predictions based on their knowledge of the flow characteristics and precipitation occurrence. Objective predictions can be useful to satisfy users' demands and to implement numerical forecasts at the local level.

It is the purpose of this chapter to present an objective correlation method of classification of 500-mb heights and associated precipita­tion occurrence. Some similar methods are reported in References I, 2, 3, and 4. The results are easy to interpret synaptically and provid~ quant~tative justification to complement ~uch of what is already intuitively clear.

In Section B the typing. method i~f pre·sented; atriiospherTC variables useful to describe the. different types are .presented Jn·section C; the climatology of the types is presented in Section D; and the distinctness of the types is further discussed in Section E.

B. Typing Method

The original intention was to use mented by Augul is (Reference-3). not sufficiently distinct for the with a relatively large number of that: ·

types already selected·and docu­These types were too numerous and present invest i gat 'ion, Few types, cases in each, are required, so

I ) The regression equations tan be obtained.

2) The estimates are statistically. stable.

3) The computational task of screening predictors for each type and for each station is feasible.

The various types to be used are obtained in the following way:

a) The 500-mb height fi~lds at the grtd points presented· in Reference 3 are used. This height field is chosen .since it is satisfactorily pr~dicted by Num~rical Weather Prediction CNWP).and is known to be a good aid to forecast meteorolog.lcal phenomena. In this investigation we :try to extract tne large"'-scale character­istics of the flow as they relate to precipitation occurrence. Therefore~ the heights at a relatively .few g~~d· pofnts are neces~ sary and the selected 52-point grid adequately describes this large scale. The data sample consists of I 176 sets of 500-mb heights at the 52 gr~d points. They cover the National Weather Service Western Region for,OOOO ahd 1200 GMT.durihg the riiohths December 1961-1967, January and February 1962-1968.

b) Each set of 52 points is correlated with alI other I 175 sets forming a correlation coefficient matrix R0

• An element ri+" of the matrix R0 is the correlation coefftcient between da es i and j. Cotumn i consists of the'correlations

·between case (date) i and.a1 I other I 175 oases. A count ofcthe number of correlations larger than 0.8 is made for each column. The case column with the most significant correlations n1 is chosen as Type I. AI I elements involving-these n1 significantly correlated cases are removed from the matrix .. The procedure is repeated to select alI successive types unti I either ten types are selected or the last type selected removes less than f1fteen cases.

c) On the basis of the original matrix R0, each case of

the data samp I e is pI aced in the typ.e with wh k:h it corre I ates most highly. Seven types are delineated by the descrioed method. Pertinent information is presented in Table I. The computer pro­gram used for typing is a modified version of a program borrowed

-2-

from Aerospace Science Division of the 4th Weather Wing, Air Weather Service, adapted to the University of Utah UNIVAC I 108.

C. Atmospheric Variables

The 850- 700-, 500~, and 300-mb height fields; the 850-, 700-, and 500-mb dew-point depressions for a 14 by 13 grid covering the region of interest; and precipitation amounts for 29 stations obtained from the Techniques Development Laboratory CTDL) data files are used in subsequent analysis. The precipitation files are extended to include a total of 42 stations.

The above data are used to obtain variables such as 850- 500-mb thicknesses, 500- 300-mb thicknesses, 500-mb absolute vorticities, thermal advections, vertical velocities, and partitioned vertical velocities due to vorticity and thermal advection. The absolute vorticities are computed considering geostrophic relative vortici­ties. ·The thermal advections consist of the 500- 850-mb thicknesses advected by the 500-mb geostrophic winds. A two-level quasi-geostro­phic model is used to obtain the vertical velocity fields. This model uses the height fields at 300 and 700mb to obtain the total omega and partial omegas due to laplacian of thermal advection and differential vorticity advection. Simi Jar models have been used in the past (Reference 5).

The vertical velocities at 500mb are obtained by integrating the finite difference form of the 11omegan equation:

3 <v 3~ = ;· -;:;- c 'Y • v~ ) - v2 c v · v _) 0 op a 3p

where o- is the static stability

w = ~ dt

p is the pressure

~ = g r is the geopotential height

;fo is the Corio! is parameter

~a is the absolute vorticity

Partitioned omegas w1 and w2 are obtained from:

-3-

(Reference 6)

v2 Cd- w ) + f2 2 0

Homogenous boundary conditions are used. Therefore:

The vertical velocity w = dz dt

is obtained by setting w

Some computational detai Is are given in Appendix A.

After the atmospheric variables are obtained for alI times. and for each of the ~4 x 13 grid points, values at 43 grid points are extracted for subsequent analysis. Figure I depicts this grid together w.ifh the 42 western stations considered for precipitation occurrence. The different atmospherfc variables are then grouped into the seven types described earlier.

D. Cl 'imatology of Types

Figure 2 depicts the probabi I ity of precipitation for the nonstrati1ied CALL) and the seven types. Figures 3 through 14 show the means and standard deviations for 850-, 500-, and 300-mb height fields, the 500-850-mb and 500 -300-mb thickness fields, dew-point depression at 850 and 700mb, 500-mb absolute vorticity, thickness advection and total and partitioned vertical veLocity fields. The mean values give a smoothed representation of the typical synoptic situation characteris­tic of the overal I and seven types.

I

The height fields show that the overal I configuration is characterized by a flat ridge with considerable variability over the Gulf of Alaska. Type I is similar to the overal I field as expected from the large number of cases included in this type. Types 2 and 4 are similar to each other in that the 43-point grid displays a ridge.near 140W and 120W, respectively. Types 3 and 5 each have a trough I ine off the coast near 140W and 120W, respectively. Types 6 and 7 contrast in the sense that 6 is a southwest-to-northeast ti !ted ridge, 7 a south­west-to-northeast tilted trough.

The standard deviations of the types are usually smaller than that of the overal I sample. This is expected if the method used is successful in discriminating among different flow configurations. Since the type variabi I ity at some grid points is sti I I quite large, the.distinctness of the types wi I I be discussed in the next section.

Figures 3, 4, 5, and 10 show large variabi I ities in regions with pro­nounced cyclonic activity, while smaller standard deviations are found near the semipermanent anticyclonic zones.

-.!].-

Figures 3 through 7 reveal that most of the atmospheric barocl inicity for alI types is concentrated in the lower layers. Figure I I gives a quantitative description of this barocl inicity. Here negative values represent positive thickness advections, and positive values negative thickness advections.

Figures 12, 13, and 14 reveal that the largest contribution to the total .vertical velocity is due to the vorticity advection forcing. This is expected because most of the thermal advection takes place at the lower levels and is not picked up at 500 mb. The average centers of rising and sinking motions correspond wei I with the average position of troughs and ridges. This indicates that the height corre­lations of deviations from the means are smal I compared to the products of mean values. The values of vertical velocities obtained with this model are comparable with daily values obtained by NMC using a primi­tive equation model.

Figures 8 and 12 compare wei I in the sense that dry regions are associated with sinking motions and moist regions with rising motions. The mean 700-mb dew-point depressions (Figure 9) are quite homogenous horizontally and I ittle can be concluded from them.

In Figure 2 the frequency of precipitation for alI stations for the developmental sample is given. The solid I ines represent fraction over normal. The vertical velocities and topographical effect seem to explain most of the frequency of precipitation patterns in the figures.

In general, then, the mean fields depict synaptically consistent situations for alI types. Since the averaged fields reproduce the general non I inear characteristics, vertical velocities, thermal advections, etc., of the individual situations, we might tentatively conclude that the variations within types are smal I, and therefore the typing is adequate. This is further explored in the next section.

E. Characteristics of Types

In this section statistics are presented to show that the separation by types results in a significant stratification of the atmospheric fields over most of the region considered.

First, the ratio of the variation between types to the variation within types at each grid point is considered. This is the F value generally used for the analysis of variance.

7

f_ (xi - x)2/ 6

F = i=l 7 n.

t I

i_cxti - x. )2 I (N -7) I

i= I t= I

-5-

7

where N = j_ Ni N. is the number of cases in Type i i=l I

N. I

x. = L Xt/Ni I

t=l

7 Ni

anq X = }_ z_ xti I N

i=l t=l

If it can be assumed that the seven types are random samples drawn from normal populations with the same variances, the hypothesis that the means of the populations are equal can be tested. Under th~ stated assumptions, if F> 2.80, this hypothesis can be rejected at the 1% confidence level; and it can be concluded that the samples come from different populatioris.

Figure 15 depicts the F values for three fields. The dashed regions indicate where F is less than 2.80. For almost alI the grid points for alI the fields conside~ed signi~icantly large F values are obtained. ·

Even if the above assumptions are not completely valid, the F values give an indication of the distinctness of the types. The highest values are expected and found at the 500-mb level. Maxima are found in regions of prevai I ihg cyclonlc activity, .with a 5° eastward shift of the 850-mb values relative to the 5.00-mb values. Thus the types seem to differentiate we I I in these reg Ions, in .· · spite of large variabi I ities within some of the types. Minimum values are found in the low latitudes of the Pacific area which are characterized by small fluctuations. The cold surface highs which dominate the winter pattern east of the Rockies cau;;e small F values for the 850-mb heights.

To test the distinctness between two types, the Z-statistics are used:

~I x2 z =

N· Na I x >2+ 2 L <Xtl f_ (Xt2 - X2) - I t= I (N I - I )N I t=l (N - I )N2 2

-6-

This statistic can be used to test the hypothesis that the samples drawn from populations I and 2 have equal means, if similar assump­tions as before are made. If I Zl~2.6 this hypothesis is rejected at the 1% probabi I ity level and therefore it is concluded that the samples have been drawn from two different populations.

Figure 16 depicts the Z-statistics for the 500-mb height between some selected types. The dashed region indicates again where IZI (2.6. The Z-statistics between Type I and Type 2 through 5 reveal the main characteristics of the first five types. Types 4 and 6 and 2 and 7 are qualitatively similar. Nevertheless the correspond­ing Z-statistics show that they are significantly different over most of the grid. The ridge and trough positions characteristic of each type can be easily seen. The intensity, though, is not comparable since the magnitude of the standard deviation is much smaller in ridge than in trough areas.

I I. REGRESSION ANALYSIS AND RELATED STATISTICS

A. lntrodtiction

In the first chapter the observed frequency of precipitation at 42 western stations associated with different 500-mb flow types were presented. These precipitation frequencies represent the probabi-1 ity of precipitation for each flow type forecast by climatology. This is already an improvement over climatological forecasts which do not consider flow types. Further improvement can be achieved by considering meaningful predictors within each type. This is commonly done in probabi I istic prediction in meteorology. This field has been extensively explored in the past; a comprehensive survey of main contributions up to 1969 is given in Reference 7. Recently, Klein (Reference 8) reported on probabi I ity of precipi­tation obtained for 108 stations in the U.S.A. using the perfect­prog method. Glahn and Lowry applied a similar approach using NMC forecast data (Reference 9).

A stepwise multiple regression analysis is used in this investigation to select the most meaningful predictors and to derive forecasting equations. Similar methods are presented and discussed in References 10 through 15. The present work differs from others in that a strati­fication based on flow types is used in the regression analysis.

The method that is used is presented in Section B; characteristics of the regression analysis considering a binary dependent variable are discussed in Section C; and the results obtained are discussed in Section D.

B. Development of Method

The twenty-one predictor fields considered are presented in Table 2. The heights considered are departures from the constants given in

-7-

this table. Predictors I ~hrough 19 and 21 are obtained at 43.grid points (Figure 1). Predictor 20 ts obtained at 43 ~tations (Table 4). Most of these fields have been drscussed .in the previous chap­ter (Section C). A smaller grid is considered here :tor computational economy. It is felt that the smal ~~~grid conveys ~I I the essential information included in the larger grid used to define the types.

The occurrence of precipitation at the 42 western stations is defined through a binary code. This code takes value 0 if there has been. l·es®4~1i1 O.~ches of ·precipitation in the next 12 hours; .and I if there has been 0. 0 I i nches,.f51 FA.~•·

Data for six winters (December 1961-1966, January and February 1962-1967) are considered to develop the predicting equations; while one winter (December 1967 through February 1968) fs used· to test the equations. ,

The twenty-one predictors are screened with respect to occurrence of precipitation at alI stations. The screening procedure consists of a multiple regression analysis computed in a step manner. At each step one variable is added to the regression equation. This variable is the one which gives the highest reduction in the variance of the predicted variable Cpredictand). When a selected predictor decreases this variance less than 1%· or there have been 10 predictors already chosen, the screening procedure is stopped.

For convenience and computational economy, the regression analysis is perform~d in the fo I I owing consecutive steps:

Step I: The means, standard deviations, ~u~s of cfoss­products of deviations from means, and correlation coeffi­cients were computed for alI predictor fields for non­stratified and stratified d~ta. The first thre~ quantities are stored in temporary files. In this way the surhs of cross...,.products of deviations from means for each predictor field are computed only once, thus·saving an appreciable amount of computer time.

Step 2: The ~recipitation codes for alI ~tations are regressed in the 21 predictor fi.elds one at a time, using a versidn of the stepwise multiple regression program from

'\

the. IBM Scientific Subroutine Package modi fled to suit our needs. At this time the two best grid points for predictors I through 19 and 21 and two best·stations for pr~dict6r 20 tor each station are selected. These grid points are depicted in Tables 5 through I I for nonstratifi~d data and for types one to six. A zero in these tables indicates a reduction for less than 1% of the variance of the predictand variable, and so the regression analysis is stopped before choosing the corresponding predictor. Due to the· smal I number of cases resulting in Type 7, these data are not inciuded in the present analysis.

-8-

At this point 42 x 7 = 294 new data files are created; Each file consists of the best two grid point time series from a I I predictors for one station. In the computation of these files any date for which any predictor is missing is discarded. Thus the total number of cases is considerably reduced. The data sample is significantly reduced when dew-point fields are considered since they are only avai !able for about half of the cases. Therefore, separate data files including and excluding dew-point depressio~s are created for the non-stratified data; while no dew-point depressions are considered for the stratified data. The total number of cases for the stratified and non­stratified data for the final regression analysis are given in Table 12.

Step 3: The regression analysis is now performed in the new data files for a! I stations. The resulting equations are depicted in Figures 17 through 24. The number in parenthesis indicates the predictor chosen. The corresponding code is shown in Table 13.

Step 4: Predlctand estimates are now obtained by applying the regression equations to the dependent samples. These estimates are divided Into 12 classes. The first class includes negative values, and the twelfth class values larger than one. Classes two through eleven are ten equally separated classes, at 0. I increments. The frequency of precipitation for each class Is then obtained. The results are shown in Tables 14, 15, 16 and 17.

Step 5: Independent data samples are used to test the nonstratified equations (with and without dew points) and the equations for Types I, 2, and 3. The number of cases involved are 123 for the nonstratified data and 30, 23, 32 for Type~ I, 2, and 3, respectively. The equations for Types 4, 5, and 6 are not tested since very few independent cases are avai !able.

C. Regression Analysis on Binary Predictand

The Imp! ications of applying the usual least-square. regression analysis to a binary dependent vairable are discussed in this section.

The customary estimate of the correlation coefficient between X and Y is:

N

I /

N z_ cx 1 - X) <Y i - Y) i= I

r = sx Sy

-9-.

where Sy =

and other quantities are defined below.

When Y is a binary vari~ble as previously defined, it can be easily shown that

r = ·.r-;­jTI7P) ( 3. I )

the so-cal led point biserial correlation coefficient (Reference 16) where:

N is the total number of cases

N

X = I t_ X X average - i , N i=l

XI is the X average for the cases for which Y =

xo same as above when Y = 0

p = Nl

N the freque~cy of precipitation

N1 is the number of cases with Y =

N

~ (Xi - X)2 is the standard deviation of X.

Thus, if p and Sx are·kn6wn (Figures 2 through I 1), r indicates the average spread of X for the cases with and without precipitation. Thu~, large~ indicates that the variable X discriminates we/ I the states of rain and no rain.

The regression equation of Yin M variables Xj (/~ j~m) gives:

M

j_ Bj Xm + ~ j = I

-10-

!·

where E denotes the expected value

;3 j and o< are the expected va I ues of the corresponding parameters estimated from the sample.

I

But E (Y/XI, x2 ... Xm) = i_ Yk f(Yk /X 1, x2 ... Xm) = f(Yk=I/X 1, X2 ... Xm) k=o

for the case when Y is a binary variable. Here f(Yk=l;x,, X2···Xm) denotes the probabi I ity that Y takes value one, for the given x 1, x2, ... Xm). In our case this wi I I correspond to the probabi I ity of precipitation. Nevertheless, the values obtained from the regression equation wi I I not necessarily be between 0 and I (Reference 17).

For example, for a one-dimensional case only for those values of X such that:

X+ < 1-e) s~ ~ X ~x s~

p cx1- X) (X,- X)

wi II ~ Y~O

Clearly then, it isn't known if the probabi I ities obtained from the regression equations are good estimates of the probabi I ity of precipi­tation to be determined. Step 4 of Section B is designed to avoid these difficulties. A similar approach is suggested by Morrison (Reference 18) and has been applied before when categorical variables are involved (References 12 and 15).

The method selected to obtain the regression equations (Section B) is of practical convenience, but which statistics are appropriate to test the rei iabi I ity of the estimated parameters is not clear. To do this, the multivariate probabi I ity distributions should be known (References 16, 20, and 21) and the effect of the stepwise method (Miller, Reference 19) and of the selections in Step 2 and 3 (Section B) should be considered. Here the results wi I I be presented without attempting to place confidence bands in the estimated parameters.

D. Discussion of Results

Figures 25 and 26 show the correlation coefficients between occurrence of precipitation at· fo~r selected stations and the grid-point 500-mb. heights, vorticities, and vertical velocities for the nonstratified data. The stations are Los Angeles, Astoria, Phoenix and Salt Lake City, chosen to represent coastal, desertic and intermountain regions. This correlation coefficient r is defined in (3. !). For any one map in these figures, p is constant and is given in Figure 2. The sx for 500-mb heights, vorticity and vertical velocity at a! I grid points are given in Figures 4, 10, and 12. The standard deviations of vorticity and vertical velocity present I ittle horizontal variation, while

-1 1-

the standard deviations of the 500-mb heights present a maximum in the Gulf of Alaska. According to (3,1), this maxjmumwould tend to decrease r in this region.

Figures 25 and 26 show that lower-than-normal heights at 500 mb over or to the west of the station favors precip.itation. Thus, precipita­tion in Salt Lake City is frequent when the high-level trough is almost overhead; implying that the surface front has already passed and the wind at the lower levels is from the west or the northwest. This type of configuration is empirically known to cause precipita­tion at this location. It can also be deduced that stronger than norma I southwester I y f I ow over the coasta I sta.t ions and south, south­easterl.y flow over Phoenix favors preci~itat~on in these. stations (References 12 and 22). Furthermore, the relative position with respect to the stations for stronger than normal vorticity and verti­cal velocities which favor precipitations can be easily determined from the other correlation fields. Thus, quite complete weather models, similar to those pr~sented by Klein (Ref~rence 12), can be obtained for each station. In these models the optimum regions for precipitation in alI of the atmospheric variables considered can be determined from the respective correlation fields.

Table 18 shows the number of times each field is selected as the first or second predictor for alI stations. As expected, previous 12-hour precipitation is by far the most frequently chosen p~edic­tor for the nonstratified d~ta. There are two ~ain justifications for this. *irst, winter precipitation occurrsnc~s at nearby stations are highly correlated; combining the effect of persist~n~e and up­stream weather (Reference 8 and others); ·Second, previous 12-hour precipitation is a binary predictor and as such wi I I tend to predict better a binary predictand .when a I inear regression analysis is done; From the definition of r equation (3.1 ), it is clear that r=l is only; possible when X is a binary ~ariable identical toY; and therefore:

X( I; X = p ; Sx = J p C 1-p)

If X is a continous variable, r=l wi II only be accidentally obtained.

The three first columns of Table 18 indicate that a height field is the next most frequently chosen predictor. For Types 2 to 6, predic­tors chosen more than 8 times follow:

Type 2. 500-mb vor+icity, vertical velocity due to vorticity advection, 850-mb height, and thickness advection.

Type 3. 850- and 700-mb height and 500-mb vorticity.

Type 4. thickness advection, 500-mb vorticity, and vertical velocities.

-12-

--,

Type 5. 500-mb vorticity.

Type 6. 850-mb height and thickness advection.

Figure 27 depicts the chosen predictors for the four stations discussed above. As expected from the strong correlation values (Figures 25 and 26), the 500-mb height at grid points to the northwest and the vertical velocity at the nearest grid point are chosen. AI I stations pick up previous precipitation at the same or nearby stations accounting for persistence or upstream weather. Los Angeles and Salt Lake City also choose 300- and 850-mb heights to the west and east of the stations, respectively, and vertical velocity and vorticity at 500 mb, respec­tively. Since the precipitation frequency in Phoenix is low, the best predictors of precipitatiqn are the previous 12-hour precipitation occurrence at Flagstaff and Yuma. The information synthesized numeri­cally in these equations is known to local forecasters.

Table .19 gives the percentage of the total variance of the predictand explained by the considered predictors or reduction of variance CRY). Table 20 gives the standard error of estimate S. For a binary variable it can be easily shown that:

RV = p p ( 1-p)

where P = s2 is the Brier P-score

p (1-p) gives the sample variance of the binary predictand. Thus, stations with very high and very low precipitation frequencies present smal I variabi I ities; while the largest variations would be expected at stations with p = .5.

Tables 19 and 20 compare the RV and S for the nonstratified and strati­fied cases. In general, the RV is higher in the stratified than in the nonstratified data. However, there are some exceptions to this general conclusion. We may expect the RV of the stratified data to be smaller than the RV of the nonstratified data if:

Pnonstratified ) stratified Pstratified

nonstratified

This may occur if:

a) Pstrat >Pnonst

. pstrat >pnonst

or

-13-

b) Pstrat <Pnonst

pstrat <pnonst

or

c) Pstrat >Pnonst

pstrat <pnonst

a) applies to those stations that have precipitation frequencies over normal (Figure 2) in the stratified data. If climatology is used as a forecast P = p(l-p) indicating that it is harder to forecast at sta­tions with larger variabi I ities, Thus, we may expect a decrease in ski II (higher P) for larger p (up top= 0.5). Similarly with a decrease of p we may expect an increase in ski I I and lower P. This corresponds to case b).

Both cases a) and b) could lead to larger or smaller values of RV, depending upon the relative increase or decrease of P and p. If the increase or decrease is of the order of a few percent, it is diffi­cult to assess if a decrease of RV means a real decrease in ski I I.

Table 19 shows that the RV for the nonstratified data is larger than the RV obtained in Type I in 20 stations, in Types 2 and 3 in I I stations. AI I of these cases except for two fa I I in categories a) or b). The two exceptions are for Eugene and Portland in Type 2 for which decreases in p are accompanied by increase in Pas indicated in c), indicating a definite decrease in ski I I.

In general, these results tend to indicate that the stratification leads to significant improvement in the regression equations. Caution should be exercised in this interpretation since the samples for the stratified cases are much smaller than the nonstrat)fied cases.

Table 19 also shows that inclusion of dew-point depressions leads to larger RV.

The root-mean-square: errors (RMSE) for the nonstratifie.d data and Types I, 2, ahd 3 for the independent sample are presented in Tables 21 and 22.

The RMSE are obtained using the probabi I ity estimate given by the predictive equations (first and second rows of numbers) and the proba­bi I ity estimate given by the relative frequency of the corresponding probability category. (Method explained in Section 2, Step 4; results presented in third and fourth rows of numbers, Tables 21 and 22, for nonstratified data and Types I, 2, and 3.)

As previously indlcated, the independent sample consisted only of 123, 30, 23, and 32 cases for the nonstratified sample and types I, 2, and

-14-

3, respectively. These samples are very smal I and any conclusions to be drawn from them are very tentative. The Scientific Services Divi­sion of the Western Region Headquarters of the National Weather Service wi I I be testing the equations further and their results wi I I be reported in the future.

Tables 21 and 22 show no appreciable systematic differences in the RMSE obtained from both methods described above, indicating no appreciable bias in the predictive equations.

The RMSE of the probabi I ity estimate given by the predictive equations is smaller for the stratified than for the nonstratified data except for:

Type I: Boise, Pendleton, and Kal ispel 1.

Type 2: Bi I I ings, Salt Lake City, Boise, Great Fa! Is, Missoula, Seattle, Kal ispel I, Havre, Mi !ford, Pocatello, Glasgow, Lewiston, and Portland.

Type 3: Burns, Pendleton, San Francisco, Spokane, Wa I I a Wa I I a, Ka I i spe I I , Lewiston, Winnemucca.

Most of these stations are located in regions of high variabi I ity of precipitation occurrence. It is tentatively concluded from the test in the independent data that stratification leads to improvement of verification in a large majority of the stations tested.

To implement these equations for forecasts longer than 12 hours, data obtained from the numerical forecast charts wi I I have to be used. In this case the equations wi I I probably not behave as wei I as when real data are used, since errors which are inherent to the numerical prog­nosis have not been bui It into the predictive equations. If the numerical models predict the future fields perfectly (perfect prog approach), the equations obtained in this investigation should hold as wei I as when real data are used. The main advantage of the perfect prog assumption used to develop the equations in this study is that they are physically realistic; that is, the physics implied or des­cribed by the equations correspond to characteristics of the real atmosphere and are not inherent to the numerical model used. Of secondary importance is the fact that once the equations are derived using a statistically stable sample, they should hold for all future forecasts. If the equations are derived using the output of the numerical models as· predictors, whenever the models are modified, alI of the equations would have to be recomputed.

I I I. SUMMARY AND RECOMMENDATIONS

The present investigation gives numerical and objective relationships between synoptic scale flows and precipitation occurrence suitable to

-15-

incorporate in Numer i ca I ·weather Prediction. Many of +bese reI a.t ion-' ships are empirically. known to experienced forecasters who apply them in a subjective manner.

In the first chapter an objective correlation method is used to classify 500-mb ~inter flows. The characteristics, cl imatolog~ and distinctn~ss of the seven types del ineatSd by this method are discussed and described by a variety of atmbspheric Variables.

This classification is used as a stratification criterion for the regression analysis applied in Chapter II. Predictive equations for the nonstratified sample, including and excluding dew-point fields,. and for six types, for 42 western stations are obtained, The equat)ons are tested in the developmental sample and in an independent sample for the nonstratified data and for Types I, 2, and 3.

The stratifications by 500-mb flow types appears to improve the fore­cast of precipitation probability. Different predictor variables are stressed within the different types. In effect, the stratification includes a pattern comparison which could never be incl~ded. in finite regression equations. The results are promi;;ing and the method can presently be applied in operational forecasting a·t'very minimal computer costs.

It is recommended that the predictive equations be tested further qs more data are collected. Then, it wi I I be possible to adequately compare the predictions bbtalned from the equa~ion~ developed in the present investigation with other existing equations.

IV. APPENDIX A

The partitioning of the vertical velocities requires homogeneous lateral boundary conditions. Since the grid 4s~d is rather smal I (14 ~ 13 grid points)1 the results in the interior of the grid may be affected by. the boundary values. This is tested 'by exp~rimentlng with nonzero boundaty conditio~s. ·The ~~stilts obtained differ in a smal I percentage in the regions of strong vertical velocities close. to the bodndaries. Within 2 grid points away from the boundaries, the resu Its are pract i ca I I y identical. to those obtai ned using homo­geneou~ boundary conditions.

Several tests were run to obtain the best relaxation coefficient for. thr~ grid. This is found to. be I .35, in agreement with ~ther results in the I i terature for He I mho I tz-type equations (I ike the omega equa­tion) for a grid of this size.

Whenever1the residual err6r fa I Is below the prescribed value of lo-17

m-1 sec- the relaxation is assumed to have converged, Tests run with prescribed values five times as large prove to leave the results unaffected. Therefore, it is felt that this is a ~tiitable value for the upper bound of the residual error.

-16-

V. ACKNOWLEDGMENTS

The cooperation of the Scientific Services Division (SSD) of the Western Region Headquarters and the Techniques Development Labora­tory (TDL) of the National Weather Service is greatly appreciated. Special thanks is given to Dr. Wi I I iam Klein (TDL), Mr. Woodrow Dickey (SSD), and Mr.' Leonard.Snellman (SSD) for many helpful indi­cations and discussions.

V I . B I BL I OGF~APHY

I. LUND, I. A. Map-Pattern Classification by Statistical Methods., JAM, 2, p. 56, 1963.

2. GODSKE, C. L. Statistics of Meteorological Variables. Geofysisk lnstitutt, Universiter I Bergen, Final ~eport, CRL, No. AF 61(052) 416, 1965.

3. AUGU L I S, R. P. Precipitation Probabilities in the Ties. tern Region Associated with Winter 500-mb Types., ESSA Tech. Memo, WBTM WR 45-1, 91 pp, 1969.

4. LUND, I. A. Climatology as a Function of Map Type. AFCRL-72-0173. Environmental Research Papers~ No. 391, 15 pp, 1972.

5. KRISHNAMURTI, T. N. Diagnostic Studies for Weather Systems of Low and High Latitides (Roseby ~Jumber ·I), AFCRL-67-0 128, 1967.

6. GATES, W. L. Static Stability Measures in the Atmosphere., JAM, Vol. 18, p. 526, 1961.

7. MURPHY, AI ian H. and R. A. ALLEN. Meteorology., A Bibliography. WBTM TDL 35, 60 pp, 1970.

Probabilistic Frediction in ESSA Technical Memorandum

8. KLEIN, W. H. Corrrputer Predic.tion of Precipitation Probability in the United States., JAM, Vol. 10, No. 5, p. 903, 1971.

9. GLAHN, N. R. and D. A. LOWRY. An Operational Method for Objec­tively Forecasting Probability of Preicpitation. ESSA Tech. Memo, WBTM TDL 27, 24 pp, 1969.

10. KLEIN, W. H., B. M. LEWIS, and I. ENGER. Objective Prediction of Five-Day Mean Temperature During Winter., JAM, Vol. 16, No. 6, p. 672, 1959.

I I. KLEIN, W. H. Specification of Precipitation from the ?DO­Millibar Correlation., MWR, Vol. 91, p 527, 1963.

12. KLEIN, W. H., C. W. CROCKETT, and J. F. ANDREWS. Objective Prediction of Daily Precipitation and Cloudiness, Journal of Geophsyical Research, Vol. 70, No. 4, p 801, 1965.

-17-

- --,--·-----------------------·------------------------------

13. KLEIN, W. H. An Objective Method of Predicting Quantitative Precipitation in the Tennessee and CumberZand VaZZeys, Proceadings of the First Nation~! Conference on Statistical MeteoroLogy, Hartford, Connecticut; May 27-29, 1968.

14. KLEIN,, W. H. The Precipitation Program of the Techniques DeveZop­ment Laboratory. ,Bu I I et in of the AMS, Vo I. 48, No. 12, p 890, 1967.

15. AUBERT, E. J., I. A. LUND, and A. THOMASELL, JR. Some Objective Six-Hour Predictions Prepared by StatisticaZ Methods 3 JAM, Vol. 16, p 436, 1959.

16. TATE, R. F. AppZications of CorreZation ModeZs for BiseriaZ'Data. American Statistical Association J., p 1078, 1955.

17. NETER, J . and E. S. MAYNES. On the Appropriateness of the Carre­- lation Coefficient with a 0 3 1 Dependent VariabZ,e. American

Statistical Association J._, Vol. 65, No. 330, p 501, 1970.

18. MORRISON, Q. G. Upper Bounds for CorreZations Between Binary Outerness and ProbabiUstic PredictiC?ns. -Arper: i can Stat is­tical Association J., Vol. 67, No. 337, p 68, 1972.

19. MILLER, R. G. StatisticaZ· Predic#on by Discriminant AnaZysis. Meteorological Monograph, No, 25, Vol. 4, Pub! ished by the AMS, 54 pp, 1962.

20. WARNER, S. L. MUitivariate Regression of Dummy Variqtes Under Nor,maZity Assumptions. American Statistical Association J .. , p 1056, 1963.~

21. TATE, R. F. ConditionaZ-Nor,maZ Regression ModeZs. American Statistical Association J,, p 477, June 1966~

22. STIDD, C. K. The Use of CorreZation FfeZds in Reiating Preci­pitation to CircuZation3 Journal of Meteorology, Vol. I I, p_ 202, 1954.

-18-

If

..

/

) ..

Type No.

Predictor Number

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

21

2

3

4

5

6

7

8

TA6LE. 1

NUMERICAL .INFORMATION REGARDING TYPING PROCEDURE

No. of No. of Cases in Date of Significant Final Selected

.Correlations Assignment Column

693 411 1-lZ-67, 12Z

172 178··· 2-13-66, ooz 102 206 1-28-67, 12Z

54 133 12-31-61 ~ 12Z

37 79 12-30-64, 12Z

26 74 12-16-65, 12'z

18 31 2-26-62, ooz

11 1-31-63, ooz

TABLE 2

PREDICTOR FIELDS - UNITS AND CONSTANTS

Predictor Field

Height at 850 mb Height at 700 mb Height at 500 mb Height at 300 mb .Dewpoint depression at 850 mb Dewpoint depression at 700 mb Dewpoint depression at 500 mb Height tendency at 850 mb Height tendency at 700 mb Height tendency at 500mb Thickness of 300-500 mb layer Thickness tendency of 300-500 mb layer Thickness of' 850-500 mb layer Absolute vorticity at 500 mb Thickness tendency of 850-500 mb layer Vorticity tendency at 500 mb Vertical velocity at 500mb (Total) Vertical velocity at 500 mb (Thickness) Vertical velocity at 500 mb (Vorticity) Previous 12-hour precipitation indicator

• Temperature advections

-19-

Units

meters meters meters meters 10-3 °C 10-3 oc 10-3 °C meters/12 hours meters/12 hours meters/12 hours meters meters/12 hours meters 10-6 sec-1

meters/12 hours 10-6 sec-1/12 hrs mm sec -l

mm sec -1

mm sec-1

Dichotomous Variable (0-1) 10-2 °C/12 hrs

Additive Constant

1457 3011 5572 9159

3587

4115

TABLE 3

STATION CODE FOR TABLES 5 THROUGH 11

1. Ely 15. Pendleton 29. Portland ,.

2. Bakersfield 16. Eureka 30. Olympia

3. Tucson 17. Medford 31. Wall a-.W.all a

4. Las Vegas 18. Seattle 32. Astoria

5. Phoenix 19. Fresno 33. Salem

6. Yuma 20. Los Angeles 34. Eugene

7. Sacramento 21. Milford 35. Kalispell

8. Santa Maria 22. Reno 36. Havre·

9. Bi 11 i ngs 23. San Diego 37. Helena

10. Salt Lake City 24. Winslow 38. Glasgow

11. Boise 25. San Francisco 39. Lewiston

12. Burns 26. Pocatello 40. Elko

13. Great Falls 27. Spokane 41. Winnemucca

14. Missoula 28. Red Bluff 42. Flagstaff

TABLE 4

STATION CODE FOR PREDICTOR 20

(Previous 12-hour Precipitation I~dicator)

. t--1. .Ely~O ~5 • Billings ~0 1.--29. Fresno~O

2. Bakersfield \...-46. Salt Lake Cit~ ~o. Olympia~O

3. Tucson \, • .-17. Boise-%f 0 31. Walla-Walla

~4. Las Vegas.)J;f-0 18. Burns k--32. As tori a .l!fJ<J)

v-s· Los AngeleJ!I.O l,.-t9. Great Fall~O 33. Salem I 6. Mi 1 fbrd 1,...-20. Missoula ¥0 34. Eugene

J---7. Phoenix ~0 ~1. Pendleton ... () 35. Kalispell

VS· Reno ~0 ~2. Pocatello~(:) 36. Havre

~· San Diego40 \,....o-23. Spokane ~\ }...--"'37. Helena J(-0

1 o. Winslow \,...--£4. Eureka ~0 t,...-38. Glasgow~ 0 11. Yuma 25. Red Bluff 39. Idaho Falls

1.--12. Sacramento f'$.0 k-26. Medford "'I 0 40. Lewiston

~13. San Francisco~ ~7. Portland lf. 0 41. El ko 14. Santa Maria \,.-28. Seattle ~0 4$. Wi nrlemucca

.. L---ifr. Flagstaff~O

-20-

TABLE 5 FIRST ThiJ PREDICTORS SELECTED IN PIR!Mitli\RY SCREENING OF PREDICTOR FIELDS FOR NONSTFATIFIED rATA

VARIABLES CORRESPONDING TO PREDICTORS 1 T!ROLGH 21 ARE GIVEN IN TABLE 2, FOR ALL PREDICTORS (EXCEPT Nl.MBER 20) STATION NLMBERS (TABLE 3) ARE GIVEN ON THE FIRST LINE, BEST IOOJ NEXT-To-BEST GRID-POINTS (FIGURE 1) ON THE S}COND IOOJ THIRD LINES, ~~rJ7LY, THE SECOND IOOJ THIRD LINES FOR PREDICTOR 20 (PREVIOUS 12-HOUR.PRECIPITATION INDICATOR ARE STATION Nl.MBE.~S

PREOH;TOR

1 '3 4-5 b 7 8 91Ull·t213141516J.718!92C.212223242526272829"031..,23334353637363o40414: ~6 30::. 43 37 1+0 "+1 21 27 l 39 25 2.6 35 25 20 15 15 10 27 27 36 27 3.3 41 21 31 15 16 15 6 11 6 11 11 10 25 31 25 1!" 26 26 37 ~3 4j '1-2 39 0 39 43 43 31 4~ 38 33 5 5 41 43 34 33 41 1+3 32 t•l 29 29 43 ttl 27 Lt-3 28 28 23 17 23 28 29 5 5 5 2P. 38 41 42

PREUICTOR

l 2 3 4 5 c 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2, 2'+ 25 26 27 28 29 30 31 32 33 31,j. 35 36 37 38 3Q 40 tl-1 42 32 27 43 33 1+1 '+l 22 27 1 36 20 15 31 20 10 21 15 6 27 33 36 2.7 33 40 16 26 10 16 10 6 11 6 6 11 10 25 25 25 Pi 21 21 37 4.3 0 2 30 u .,g 't3 43 25 '+3 41 29 1 37 41 ~.tl .)8 33 43 43 30 41 29 35 27 38 36 43 38 27 29 17 29 29 27 36 39 32 27 29 38 :39

PR"OICTOR

1 2. :3 4 5 b 7 8 9 1u 11 12 13 14- 15 16 17 18 19 20 21 22. 23 2.4 2.5 26 27 2.8 29 30 :31 32 :33 34 :35 36 37 38 3CI 40 41 42· j2 27 4:3 33 37 '+1 16 27 19 :32 20 15 25 1'lo 15 16 15 6 27 27 32 22. 33 40 16 26 6 16 6 2 6 6 6 11 10 14 11+ 111- 10 21 21 37 4:3 0 3G 30 35 jS '1-3 4.3 1 .38 '1-0 29 1 4-0 37 29 4-l 37 43 42 20 29 29 39 43 '1-0 29 1.1-3 29 6 0 23 29 28 27 0 1 7 37 29 41 39

PH.EOICTOR

1 z 3 l.j. 5 b 7 8 9 11.,) 11 12 13 14- 15 16 17 16 19 20 21 22 2.3 2tj. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 3<;1 40 41 42 26 27 1.1-0 3~ 37 '1-1 1b 27 19 20 15 15 19 1'1- 15 16 J.5 6 22 22 32 22 33 40 16 20 6 16 6 2 6 6 6 11 5 14 1'+ 1'1- 6 21 21 37 .30 L\-j 35 30 35 .)5 42 43 1 29 29 2q 1 30 37 38 j7 37 'l-3 33 38 29 29 39 43 29 29 1.1-0 29 18 29 28 29 28 0. 31 1 12 2CJ 33 38 39

PHEOICTOR S 12 3 4 56 7 8 91U1112131415161718.1920212223242526272829 ... 031.~23334353637383CI4 41,.2 ~7 37 '+3 37 43 4-0 33 37 25 31 .2.0 21 25 22 21 22 2.7 21 37 37 43 37 '+1 40 33 37 16 27 21 15 21. 11 16 16 15 14 21 11.1. 21 22 21 37 31 3f> "'1 20 40 j9 13 35 15 41 21 20 6 11.j. 20 21 2.1 4.3 .35 a 25 "'2 '+U 42 21 26 20 33 43 16 23 21 5 5 20 21 19 :59 4~ 26 :53' 43

PREDICTOR

1 ' 3 4 5 b 7 8 9 1U 11 12. 13 14 15 16 17 18 19 20 · 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 3t;~ 40 41 42 42 3t) 29 3tr 6 :)8 38 38 23 36 o 4 26 3 o :sa 2 25 34 26 33 22 26 4 2 33 26 2 12 15 26 41 19 19 12 16 o 29 1n 25 13 11 21 20 39 39 29 c 2 20 o ~3 o D o 11 .. o 2 .1.1 1 o 25 36 o 22 37 :sa o 3o ·o 19 o .3 19 1s 10 o 13 o 1o o 29 o 25

PREDICTOR

1 0:! 3 1 5 0 0 34 0

·5 6 7 a 9 10 11 12 13 " 15 16 l7 1a 19 2o 21 22 23 24 25 26 21 2a 29 30 31 32 33 34 35 36 37 3a 39 •o 41 42 19 ~a 5 10 29 l 1 s o 37 33 5 o7 12 5 5 1 37 27 38 5 5 33 o 11 o 2a 2 11 1 19 9 36 u 1 37 19 1

0 0 37 4 0 '+3 33 37 0 ~ 0 0 6 2~ 0 0 0 1 ~ 0 :37 0 5 0 0 0 7 19 5 0 12 0 33 21 36 3~ 0 9

PREOICTOR

l 2 3 4 5 o 7 8 9 lO 11 12 13 l'+ 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 ~6 37 38 39 40 41 42 42 21 37 27 v 31 16 25 26 31 31 15 35 31 12 31 20 16 17 26 16 42 32 31 39 25 26 7 10 15 12 20 15 20 31 31 25 26 31 "112 40 21 40 'f.2 42 0 12 3"6 39 42 21 11 39 15 7 32 16 7 36 41 39 3.3 28 42 17 21 11 16 31 23 23 15 23 23 41 0 10 21 (I 17 13 27

PREDI,TOR 9

1 2 3 4 s 6 7 a 9 1~ 11 12 13 14 15 16 11 16 19 20 21 22 2.3 ·24 25 26 21 28 29 :so .31 32 :s:s 34 35 36 37 38 39 Q.O .. 1 q.z 1+0 40 3b 34 42 '+U 32 16 10 15 ~1 31 39 31 26 32 26 2U 36 17 1.1.2 32 '+0 1.1.2 32 35 20 32 7 10 15 15 15 15 15 25 31 25 15 26 32 40 212Z.'f.24034 (J22373942161110151612.L6 71641261b2737172111122533 0~7 0 0 0 0 221016 027

PREDICTOR 10

1 2. :3 4 5 b 7 8 9 10 11 12 13 1"1- 15 16 17 18 19 20 21 22 2~ 2'f. 25 26 27 2.8 29 30 31 32 33 3Q. 35 36 37 :38 39 40 41 Q.2 36 40 38 40 42 43 32 37 35 39 26 26 31 25 26 26 26 15 37 37 39 32 40 42 32 31 20 27 20 11 15 10 15 15 15 2 20 14 15 26 27 40 Z117422828 U1222102116!110 0121212 717172112273212163128 712 013 011019122 0 0 017

PREDICTOR 11

1 C. 3 4 5 6 7 8 9 1D 11 i2 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ~1 32 33 3Lf. 35 36 37 38 39 40 41 4~ 26 21 40 2.7 37 ~7 11 21 19 2b 15 15 19 14 10 11 6 1 21 27 32 16 27 40 11 20 6 11 6 2 6 1 6 6 5 5 l't 1'4 5 15 15 3 .. 42 39 ::55 35 29 35 39 39 1 28 11 1a 30 39 29 39 '1-0 :su 39 39 "~-1 42 35 42 :59 39 31 39 23 1a 29 25 29 29 20 o 31 a 31 33 38 35

PREDICTOR 12

1 2 3 4 5 6 7 8 9 lu 11 12 13 14 15 16 l7 18 19 2v 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 36 16 39 40 40 40 26 32 30 36 26. 7 25 25 20 26 26 15 32 32 35 2i 36 40 26 31 15 21 20 6 0 10 10 11 36 0 14 30 0 26 26 36

o 32 37 o o c o 22 o 35 · o o o o o o o o o 16 37 o 41 32 o ~ o o o o o o o o 19 o 1 o o o n 37

PREDLCTOR 13

1 2 3 4 5 6 7 8 9 1u 11 12 13 14 15 16 l7 18 19 20 21 22 23 2Lf. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 27 22 1+3 33 41 41 12 27 19 26 21 11 1Lt 14 6 16 11 2 22 22 32 22 33 43 16 21 6 12 11 2 2 2 2 7 5 5 14 5 1 21 16 37 ~9 39 39 39 29 j9 <t2 36 35 35.37 9 35 31 40 4U J.8 25 29 39 39 29 39 1.1.2 36 29 31 36 37 25 29 1 29 29 20 9 31 9 !FI 32 29 39

PREDICTOR 14

1 2 3 4 5 6 7 8 g 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2'1- 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 l.j.Q '1-1 42 32 22 43 37 43 ~7 21 27 19 32 20 15 20 20 15 21 21 11 21 22 32 21 37 40 21 26 15 1-6 15 11 11 6 11 11 6 10 15 10 1~ 21 21 37 16 37 Ll-2 22 37 'tJ 17 16 26 31 21 21 19 14 6 11 l1 6 27 33 'f.O 22 38 41 22 15 b 17 6 7 i2 7 6 0 15 20 lot 20 fl il .LO c.r

PREDICTOR 15

l J. 3 4 50 7 8 91Vlll2131!.!-15!6.1718192Q.21222321.j.25262728293031323334353637383<;14Q4142 32 37 '+2 43 4C "t.:l 21 32 2.5 .H 26 7 25 20 21 21 2.1 15 37 37 36 27 t;.3 40 27 26 15 21 15 11 16 11 11 11 .25 14 14 35 0 21 21 32 22 17 37 o 33 o o 12 30 21 o9 21 1 o o a o 41 9 12 22 13 lo 37 8 22 31 o 40 33 o 4 o 30 o ·a 35 o o o 11 43

PREDICTOR 16

1 2 3 4 5 c 7 8 9 lG 11 12 13 l'f. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 3CI 40 41 42 .)6 37 37 '+0 21 '+C 7 16 ·1 2.1 26 26 31 25 26 32 ·.?.6 15 16 17 36 16 41 42 27 31 20 21 15 11 21 1~ 11 11 11 0 20 0 15 26 21 37 2.1 40 38 Li 33 1.: 32 37 10 30 25 7 1 20 7 20 i.1 14 7 16 '+2 33 'f.O 43 12 32 21 27 26 0 0 ·11 10 21 10 0 7 0 0 21 ,26 'f.O

PREDII.:TDR 17

1 2 3 4 5 0 7 0 9 lU 11 12 13 14 15 16 17 18 19 20 21 2.2 2j 24 25 26 27 26 29 30 31 32 33 3lt 35 36 37 38 3CI 40 41 42 ~s 4o 37 3~+ ~+2 ~.t:.J .j2 37 to 35 .31 26 3u 25 26 26 2o zv :n 37 35 37 43 42 32 3o 20 26 2o 1s 21 1"' 1"' 21 10 2s 25 25 1"5 26 26 ~+o 40 'f.1 'f.2 36 26 ~8 21 30 35 .30 0 3'S 10 2~ 25 3& .:.0 1.1.3 25 1.!-3 27 36 34 37 21 31 19 38 21 11 0 19 26 10 20 15 20 32 25 30 36 28

PREUII.:TOR

1 ~ 3 32 l.t1 43 1+1 20 0

PRE.U!CTOR

18

5 b 7 8 9 liJ ll 12 13 11+ 15 16 l7 18 19 20 21 22 23 21.1. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 3Cil 40 41 42 L;.j lt~ 38 3b 24 ~9. 16 36 31 31 Q.O 36 o:~6 2·0 38 38 32 38 43 43 38 j1 31 38 31 21 21 21 21 21 30 26 19 30 2!=. 36 36 43 34 t,; 36 3<t .39 il "'" 21 32 u 21 31 .a c 34 34 43 3q. 20 20 31 32 30 36 21 34 c o 38 32 22 20 6 32 3A t6 16 34

1~

1 <:! ~ 4 5 b 7 8 9:i..v.J.112131tt15161718192C21222324252627282930313233343536373830404142 ~c 40 37 34 42 '+~..: j?., 37 35 35 :::.1 26 3o 25 26 26 <:!6 20 37 37 35 37 4u 42 32 35 20 26 20 15 15 15 15 15 10 25 25 19 1:" 26 32 LtD j5 3.L 4-2 36 28 .)o '7 35 1J 27 32 31 .31 0 35 31 60 1v ,31 39 27 3J. 34 37 27 25 0 27 31 12 0 20 20 .31 7 15 20 7 25 30 8 39

PRE.lllClOR 20

l 2 3 4 5 o 7 8 9 1v 11 12 13 14 15 16 .1. 7 18 19 2V 21 22 23 24 25 26 27 28 29 30 31 32 33 :34 35 36 37 38 30 40 41 42 41 2':) 11 43 '1-3 l.L 12 29 19 1.1.1 41 '34 37 '.37 31 3't ..)4 :3~,~ 12 14 1 12. 5 43 13 41 31 25 33 '.30 33 32 33 33 35 36 37 :38 40 1.1.2 (!.2 43

s o :s 4 11 <tj 2u 13 37 10 .;1 tR 36 40 40 24, ;u. :)s a s 43 s t.~.j 11 2'~- 22 28 34 32 32 31 30 32 :so 30 35 35 36 33 33 3q. 29

PKE.UlCTOR 21

1 z 3 1.;. 5 c 7 0 9 1.J J.1 12 13 14 15 16 17 18 19 20 21 2' 23 2Lj. 25 26 27 28 29 30 31 3:> 33 31+ 35 36 37 38 30 40 41 42 .:.7 3'l- Lf1 34 Ji+ ,:,4- j6 34 3C 33. 37 30 19 39 36 36 36 32 31.1. 34 42 36 34 34 36 32 36 36 30 2.2 10 ~2 22 22 26 21 21 32 3fi 37 36 .4 34 itj C <2:b l.t-1 lt~ ~t) 38 :::.2 ttL 40 33 32 31 39 31 37 30 38 38 34 27 0 0 1G 36 24 10 10 36 36 37 36 36 21 19 19 30 39 36 37 26

-21-

------------- ------------------------------------------------·--------·--

TYPE TABLE 6

PREDICTOR Sl!/f AS TABLE 5 FOR 1YFE 1

1 2 3 'f. s 6 7 s 9 10 11 12 13 14 ts 16 t7 lA 19 20 21 22 23 24 2s 26 21 za zq 3D 3 1 32 33 34 35 36 37 3B 39 4o 4 1 42 3& 3& 41 37 40 41 21 2& 35 35 25 26 35 25 20 26 26 10 26 26 39 26 41 42 26 31 20 21 2u 6 11 6 U 15 15 25 20 20 15 26 26 37 ""•"•~"uun~RHUUMun"u"~~o"M•nMuna~nu5nsuu~n

PREDICTOR,

12~45&7a9WhUURUdUUU~U~~M6.UHRHUMUMg•nn~g"q 31 37. 43 33 41 41 21 27 35 35 2o 20 31 20 20 21 15 10 21 27 36 27 41 40 21 26 15 21 15 6 11 6 11 u 15 25 2o 25 15 15 21 37 HU2~M~UU9U~~9UHM6HOUMUUO""B"Hd~NH~U1HDH6Uu

PREDICTOR

1 2 3 4 5 ~ 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2a 29 30 31 32 33 34 35 36 37 3a 39 40 41 42 26 32 43 33 37 41 21 27 19 31 14 20 20 14 15 21 15 6 21 22 32 22 37 40 21 26 15 16 15 2 29 6 11 11 6 20 10 14 41 15 21 37 43 31 2 23 35 42 43 43 1 32 41 43 1 40 40 33 29 23 42 42 24 42 42 2 41 42 31 38 29 22 17 23 2a 29. 29 2 1 4 10 40 29 42

PREDICTOR

1~34567a9wtiuu~UdUUU~U~UM6HDHnHUMURHHDUHg"q 2& 32 40 33 37 41 21 26 19 26 14 15 14 14 39 15 15 6 21 27 32 21 37 40 21 20 15 16 29 2 29 6 6 11 6 14 39 14 29 15 15 37 43 24 35 23 35 42 43 39 1 29 36 29 5 36 15 43 23 3& 42 42 38 39 42 2 41 42 25 34 15 1a 2a 13 29 29 23 30 15 29 0 37 29 42

PREDICTOR

1234567a9UUUU14UdUUU~U~~MHHDH~HUMYMHHOUHg"q 41 37 43 37 43 43 37 37 25 31 21 27 25 22 21 27 27 21 37 37 43 37 37 42 33 37 20 37 21 15 21 11 21 21 5 14 39 14 21 22 33 41 24 30 24 39 27 5 24 20 20 33 14 14 6 19 33 21 21 41 35 43 5 42 5 5 37 25 16 27 41 38 0 2 24 24 20 41 2 2 24 2 21 5

PREDICTOR

1 2 3 4 6 7 a 9 10 11 12 13 14 15 16 17 1e 19 20 21 22 23 24 25 .26 27 28 29 3o 31 32 33 34 35 3& 37 38 39· 40 41 42 43 38 34 2 6 2 26 9 24 38 36 4 42 24 12 26 40 17 13 26 33 1 2 33 27 37 22 2 12 41 26 1 12 12 12 22 40 10 17 13 29 6 38 32 2 9 34 12 27 20 22 36 39 29 38 1 38 4 34 1 3 43 32 33 38 6 15 4 30 12 19 15 28 25 15 43 30 10 22 22 3 25 4 4

PREDICToR

1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 n 1a 19 20 21 22 23 24 25 26 27 2a 29 3o 31 32 33 34 35 36 37 3a 39 4o 41 42 41 34 9 2a 17 4 33 29 29 9 9 12 16 17 35 22 1 1 37 5 34 37 34 17 37 9 9 29 16 39 22 1 7 22 9 9 34 17 12 37 39 25 29 16 43 4 16 7 27 1 10 34 22 5 7 13 22 30 43 18 27 34 32 5 36 36 5 2 17 37 9 37 36 13 3a 3 14 13 27 9 9 9 32 40

PREDICTOR

1 2 3 4 s· 6 7' a 9 10 11 12 13 14 15 16 17 1a 19 20 21 22 23 24 25 26 27 2a 29 30 31 32 33 34 35 36 37 38 39 40 41 42 39 39 37 4 26 42 12 16 25 26 31 31 15 11 7 12 31 20 16 35 26 36 42 32 12 39 25 12 7 6 3 3 3 3 20 31 31 25 3 31 0 42 27 27 39 38 4o 3a 36 40 39 39 12 16 a 31 26 36 12 8 43 27 39 16 33 42 43 21 u 5 25 4 2 6 15 1s 27 9 21 26 0 0 0 27

PREDICTOR . 9

123456789UhUURUd17UU~U~~M6.DH~HUMYMH•nM~g"q 39 40 3a 29 34 40 12 22 20 21 31 31 15 11 12 '12 12 14 22 22 27 36 2a 33 12 39 14 12 7 6 6 3 15 15 15 25 25 25 4 26 26 40 22 28 42 37 42 3a 36. 36 39 39 16 16 35 31 26 ~6 26 4 43 41 39 16 43 42 7 22 11 6 31 33 8 6 42 3 0 5 4 27 0 18 20 34

PREDICTOR 10

1·234567a9UUUU~UdUUH~U~~M6.DH~HUMUMHHDU·g~q 36 40 38 41 33 34 32 22 10 39 26 26 10 25 26 26 26 15 36 36 39 32 28 33 12 22 20 12 7 6 1a 6 11 11 11 26 26 28 0 26 27 40 28 27 42 38 36 40 12 36 39 21 5 10 36 19 25 12 43 8 18 22 27 18 40 42 27 36 31 27 24 33 2 23 42 3 10 5 4 20 0 14 0 34

PREDICTOR 11

1' 2 3 4 5 6 7 8 9 10' '11 12 13 14 15 16 "·1a 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33. 34 35 36 37 38 39 40 41 42 26 32 40 32 37 37 21 26 19 26 37 15 14 17 39 15 15 25· ·21 21 26 39 32 40 2i 20 18 34 23 2 29 2 2 2 23 30 35 29 29 is 15 32 40 30 35 39 3a 39 39 39 40 27 19 18 38 15 '18 33 33 1 39 35 30 21 35 1 33 39 25 21 6 43 34 13 23 29 25 19.19 30 20 33 38 39

PREDICTOR 12

1.34~6789UUUURUdUU~~U~UMHH~HnHU~UR.~DHH-"U 31 22 38 43 40 33 26 22 '35 '35 29 26 31 20 20 26 3i 10 36 32 39 26 27 40 31 31 30 21 20 2 0 7 6 6 19 21 20 24 0 21 29 '36 19 36 0 17 38 40 0 32 43 31 39 0 22 0 12 37 34 29 26 22 31 0 36 32 0 22 l5 0 32 26 0 17 29 29 36 27 0 31 0 31 0. 22

PREDICTOR 13

1 2 3 4 5 · 6 7 a 9 10 11 12 13 14 1s 16 u 1a 19 2o· 21 22 ·23 24 25 26 27 2a 29 3o 31 32 33 34 35 36 37 3a 39 40 41 42 21.37 43 33 41 41 27 27 19 26 4o 21 14 10 36 21 18 25 27 27 '32 39 37 40 16 21 25 36 6 2 1a 2 2 2 20 5 36 5 26 21 21 37 42 24 39 1a 29 29 36 39 39 39 14 1a 9 40 2 40 21 6 36 36 39 27 39 39 29 39 1a 27 1a 15 24 3 1a 18 10 36 14 18 14 32 23 39

PREDICTOR 14

1234567a9UhUURUd17UU~U~UMHHUHnHUMUMHHDH~U"U 32 32 43'·37 "40 37 21 32 25 32 20 '21 14 14 40 21 21 6" 21 26 32 27 41 40 21 26 15 21 15 2 21 6 11 11 6 25 10 24 10 21 21 37 UDUUM~17UUh~~-UNPdUMU~UDUUUUUHUo~UHUNUU~11W~

PREDICTOR 15

1 2 3 4 5 6 1 a 9 10 11 12 13 14 15 16 11 1a 19 20 21 22 23 24 25 26 21 2a 29 30 31 32 33 3q 35 36 37 38 39 40 41 42 •"u""~uauuqaq~unuNHwuauuunnuu2U21111UUHHuuuu 2a 22 37 1a 33 34 15 23 41 22 3.6 10 5 19 10 14 10 21 1a 9 33 31 27 33 12 22 21 14 19 42 16 0 42 14 16 39 21 26 0 10 1 13

PREDICTOR 16

123456789UhUU~UHUUU~U~HM6HUH~~UMURgHD~Hg"g 21 27 37 37 33 40 7 16 39.21 26 26 10 25 26 26' 26 15 16 16 21 26 33 32 12 16 20 12 7 H 1a 6 11 11 11 5 26 24 o 26 21 33

9 16 3a 2 3& 34 37 22 31 39 33 33 26 33 7 12 12 10 22 8 39 27 16 33 3 22 21 3 26 4 3 0 42 30 10 25 4 39 0 16 31 16

PREDICTOR 17

1234567a9WhUURUdUWU~UM~M6HUH~NUMURH~DMHg~g 35 27 37 34 33 40 37 30 35 35 32 32 30 19 32 31 26 '20 40 43 35 37 43 37 32 35 20 26 25 11 21 10 10 21• 20 25 20 25 15 26 32 40 27 31 39 4Q 39 3a 17 40 25 27 34 25 24 32 10 11 30 19 38 24 27 39 33 39 30 30 19 s, 43 10 14 8 16 27 10 32 30 37 6 0 40" 33

PREDICTOR 1a

1234567a9UUU~RUd17WHMU~~d6HDURHUdUR.HDH~U~U ~ggggdgUH~"UUU"UUNUUUHUUHUHU~d~d~~~HH•~ugu 40 33 41 41 41 43 10 43 33 21 5 36 28 22 3a 6 6 40 27 21 21 40 38 15 38 39 41 36 22 27 40 19 2a 33 30 8 32 "30 40 22 16 34

PREDICTOR 19

123456789UUUURUd17U~~U~HMUHDU~~U~UR~HUHHg~g

dUUU~UDddd.UNU.UH~HUHUUDUd~~~11"UUdUH~UUHMM 36 36 40 40 42 33 8 8 31 27 40 32 0 32 0 26 30 10 41 41 27 :i9 40 42 33 23 19 8 40 10 27 5 0 40 7 15 30 24 6 16 32 33

PREDICTOR 20

1234567a9UhPURUd17WH~U~~M6HDUnHUMUM~HDH~g"q 41 a u 43 11 11 42 14 19 41 21 34 36 40 31 41 34 30 a 5 43 8 5 43 24 41 :i1 2s 33 32 31 32 33 33 30 36 37 36 4o 41 41 29 29 2 3 14 43 o 13 a 3a 16 41 41 37 23 4o 34 24 2a 12 12 1 25 u 9 13 21 35 31 34 30 33 30 29 31 4o 21 4o 35 30 42 29 43

PREDICTOR 21

1 2 3 4 5 6 1 a 9 10 11 12 13 ·14 15 16 11 18 19 20 21 22 23 24 25 26 21 2a 29 30 31 32 33 34 35 36 37 3B 39 4o 41 42 37 43 2 34 34 34 36 37 36 33 25 33 25 26 2 33 36 35 37 26 42 2a 3'4 21 33 37 21 36 30 16 10 7 22 22 25 21 21 32 29 33 41 34 22 33 39 12 39 33 37 12 25 42 14 29 14 22 36 36 37 36 4D 2 34 22 17 34 36 40 25 14 22 7 26 34 11 33 21 20 20 13 7 3!> 19 43

-22- .

TY'PE

PKEDlL TtJR

1 ;::: .3 18 ::ill 42 37 24 l4

Pr<ED!C ruH

1 ~ 3 18 jj '+0 32 4::: j2

PRCOIL.lOR

TABLE 7

SA'£ fJS TABLE 5 FOR TYPE 2

5 b 7 8 9 10 11 12 13 1Ll- 15 10 17 1d 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Ll-2 42 .30 3 37 5 36 26 26 35 38 26 21 15 41 13 35 36 0 41 42 10 36 22 0 23 6 20 10 1 15 10 10 5 19 15 26 26 40 1'~ 10 1C 42 31 3Ll- 28 39 5 5 1Ll- 34 43 15 7 33 21 0 35 14 26 17 15 0 15 16 28 22 8 31 31 11 14 40 13 9 28 24

5 b 7 8 9 10 11 12 13 1'+ 15 16 17 1~ 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 42 41 3 33 1 36 18 21 31 24 2o 21 15 2~ 1 33 3& 0 IH 42 6 31 23 0 15 2 15 6 1 15 6 27 36 19 15 26 21 37

6 30 34 l.f.O 10 ~4 15 33 37 28 32 38 13 1~ 13 40 21 0 43 1 '+ 27 12 !5 0 28 12 28 22 8 20 31 14 20 26 13 22 14 2'1-

1 2 3 4 5 6 7 u q 10 11 12 13 1 Lj. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 9 27 '+.3 l1 40 40 22 .33 19 32 18 21 19 24 21 21 21 30 1 33 32 0 33 40 27 26 43 0 15 6 10 6 6 11 31 37 35 26 15 26 21 32

32 ""( 41 0 3t;. 39 3 43 43 33 20 33 8 35 36 31 23 29 32 43 27 0 20 41 6 12 15 0 28 17 5 12 4 13 11 5 14 38 13 13 14 24

PkEOICTUR

1 2 3 9 27 Ll-0

10 11 ~7

4 5 6 7 8 9 10 11 12 13 14 15 16 17 ll:.i 19 20 21 22 ?.:3 2'+ 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 40 4!1 22 27 19 31 13 21 8 24 20 21 21 30 1 33 32 0 33 q.O 27 25 42 0 15 2 35 6 1 11 31 37 35 26 9 13 21 32 34 39 0 11 2 11 2Q 33 14 35 39 31 17 23 13 39 27 0 25 41 36 34 15 0 28 3 11 12 4 23 11 5 1 41 15 26 23 2"1-

Pf<EDICTUH ~

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 lti 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 £4.0 41 42 33 0 42 1+3 41 28 38 !5 15 21 2 15 3 3tt 27 26 2 0 38 29 0 37 42 27 9 28 0 8 26 29 27 9 16 42 5 27 14 26 26 27 43 29 0 j9 20 39 43 5 '1-'1 29 26 26 16 4 6 41 28 q 0 5 38 0 43 14 lf.3 38 37 0 16 27 7 7 26 43 36 6 6 q.2 9 29 7 28

PR,t::DlCTvH

1 2 3 21 u 13 36 0 29 0

PREP!CTUR.

5 b 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 29 19 13 10 38 32 18 28 32 17 21 !3 2 28 O· 28 18 0 27 26 9 28 18 0 14 26 7 5 8 5 29 18 5 29 38 5 18 9

9 1.5 41 j3 15 9 2 8 4 20 13 6 3 33 0 5 36 0 5 18 6 14 9 0 16 18 42 38 28 28 5 37 36 26 14 28 6 29

1 2 3 * 5 o 7 s 9 10 11 12 13 11+ 15 16 11 1~ 19 20 2 1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 q.o 41 42 1 u 13 0 29 j 5 36 q.2 42 33 43 35 28 41 21 33 31 0 36 5 0 28 9 38 43 27 0 26 37 14 8 9 18 27 27 42 6 42 36 9 6

41 u 31 (1 9 6 33 39 41 8 27 1.1-1 9 1 36 4 27 43 0 18 27 0 27 14 43 5 42 0 9 5 26 27 18 14 26 38 8 29 28 38 42 7

PKEOICTOR

1 2 3 q.o 13 37 21 37 42

PREDICTOR

1 2 3 33 12 27 21 7 '+2

PREDICTOR

1 2 3 21 37 37 32 3tl 39

PREDICTOR

1 2 3 10 32 39

3 11 24

PREOICTUR

1 2 3 24 23 36 1.1-2 22 39

PREDICTOR

1 2. 3 32 27 'J.3 39 2 38

PREDICTOR

1 2 3 32 37 43

1 22 42

PREDICTOR

1 2 3 21 2 'J.2 36 22 37

PREDICTOR

1 2 3 21 12 2 36 11 37

PREDICTOR.

1 2 3 35 22 42 15 38 40

PREDICTOR

1 2 3 27 16 42 38 34 17

PREDICTOR

1 2 3 4

35 16 'J.1 15 27 42

PREDICTOR

1 2 3 4 24 12 11 17 0 43

PREDICTOR

5 27 42

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 'J.O 41 42 16 41 25 42 11 11 10 31 36 16 11 2 9 9 21 0 41 37 38 15 6 0 26 11 1 1 11 1 19 15 5 25 37 10 32 42

3 28 1 26 26 26 36 25 12 32 26 t:) 13 32 38 0 28 42 16 39 29 0 6 16 11 10 12 42 2 11 7 5 33 19 16 27

5 6 7 8 9 10 11 12 13 14 15 16 17 1d 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38. 39 40 41 42 21 1~ 16 41 36 40 11 11 36 31 32 11 11 2 9 37 21 0 41 32 38 15 2 0 2 10 1 15 15 38 15 2 1 36 15 26 32 40 41 7 >.8 28 14 15 26 26 10 32 17 26 26 43 13 28 36 0 38 42 31 39 16 0 29 22 15 7 37 17 31 15 20 25 12 22 16 4

10

5 6 7 8 9 10 11 12 13 lq. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41.42 l.j.l 31T 12 37 31 36 11 11 31 25 26 11 11 2 9 37 36 0 35 42 33 15 2 0 2 10 1 10 32 2 10 2 20 36 12 23 26 40 39 38 28 28 24 21 30 21 24 39 17 27 2 15 8 28 21 0 28 32 16 31 16 0 1 27 43 5 20 30 4 6 1 41 15 40 12 2.8

11

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 39 40 27 32 19 31 33 20 39 39 39 21 14 30 18 32 31 0 36 39 27 25 42 0 23 18 34 5 5 5 25 31 35 25 14 17 21 32 34 42 36 11 11 6 26 19 19 19 27 35 19 23 1 11 2 0 39 2q. 36 34 2 0 15 2 24 25 23 23 29 5 1 12 2 37 12 33

12

5 • 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 36 34 32 23 30 18 38 38 25 25 4 11 18 16 27 23 35 0 3 38 32 30 L 0 20 28 1 7 43 16 30 10 14 26 21 33 11 36 35 46 12 22 31 15 22 22 24 6 31 27 38 7 20 22 15 0 30 24 11 13 42 0 39 26 38 15 24 27 32 1 1 35 20 4 38 12

13

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2'+ 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 43 22 33 14 26 18 21 35 36 10 22 21 30 1 33 32 0 33 40 22 26 42 0 15 9 31 1 6 1 20 35 31 25 15 41 21 21 38 42 0 43 6 11 21 40 25 19 2 28 7 29 32 39 33 0 14 41 8 28 21 0 31 6 16 2,0 43 43 5 4 14 12 12 13 26 37

14

5 6 7 8 9 10 11 12 13 14 15 16 17 1d 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 1.1-0 41 42 43 40 6 37 15 32 20 21 8 24 25 21 21 15 32 37 32 Q, 37 40 9 32 15 0 ~5 2 10 6 6 1 31 35 10 26 15 38 21 32

2 4 22 27 14 2 28 20 24 35 26 22 20 28 13 33 18 0 25 12 7 26 16 0 ~3 41 19 24 17 15 20 25 19 36 17 20 16 40

15

5 6. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27'28 29 30 :31 32 33 34 35 36 37 38 39 40 41 42 6 43 8 2 25 32 11 27 25 20 26 27 11 15 32 37 32- 0 36 42 20 31 2 0 2 32 15 10 27 30 5 2 14 36 15 29 26 32

38 28 42 22 30 15 21 11 11 41 27 11 23 2 26 19 16 0 18 2 28 10 3 0 37 17 12 24 10 37 37 6 10 26 17 41 2 28

16

5 6 1 a 9 to 11 12 13 14 15 16 11 1a 19 20 21 22 23 24 2s 26 21 28 29 30 31 32 33 3L~- 35 36 37 38 39 ~.~oo 41 42 2 3b 28 28 6 32 26 11 31 31 26 11 26 2 9 28 32 0 36 2 28 32 2 0 2 32 15 10 32 2 37 2 20 16 15 20 26 22

18 34 16 12 32 7 3o 26 1 11 12 12 2 15 26 7 21 o 7 37 16 15 16 o 20 18 19 20 10 37 10 17 1 36 12 40 12. 4

17

5 6 7 8 9 10 11 12 13 1'J. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ·30 31 32 33 34 35 36 37 38 39 40 41 42 6 39 13 27 30 35 11 16 30 26 32 16 16 21 35 l.f.O 21 0 43 42 17 16 32 0 25 1lf. 8 15 33 21 15 14 20 36 25 33 36 33

37371138 621323213 54326261172435 03040113520 021.28201443121425241917262630

18

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19.20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 :55 36 37 38 39 'J.O 41 42 38 21 :53 3LI- 24 32 27 27 24 12 28 16 27 22 43 34 32 0 34 38 20 28 11 0 15 6 25 15 21 24 5 5 14 2q. 21 21 16 43 41 37 39 16 27 43 21 19 14 21 b 28 21 7 32 38 24 0 37 42 6 43 31 0 19 26 27 5 40 22 32 15 31 23 35 15 40 32

19

6789UUUU"U"DUUUUUUMBHnHnUMH~~~N~~M~UW

37 31 13 16 :so 35 3t 31 2'J. 24 32 16 16 21 15 21 21 o 27 :s7 11 16 32 o 26 28 a t£4- 33 2o 14 19 20 36 25 33 16 21 6 35 11 27 6 21 16 16 13 20 43 27 27 12 26 24 30 0 35 42 28 35 20 0 19 17 20 15 20 24 15 33 19 7 33 15 26 33

20

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 l.j.3 14 18 12 37 17 27 34 37 35 31 34 31.1- 32 29 12 22 0 12 43 24 41 31 0 33 32 32 32 1 33 35 36 35 38 34 30 34 26 11 7 Llo1 10 20 19 31 17 27 37 12 42 42 19 22 9 41 0 14 10 26 22 32 0 32 1 13 37 32 32 28 30 37 28 23 6 42 18

21

1 2 3 4 5 6 7 8 9 10 11 12.13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 '31 32 33 34 35 36 37 38 39 40 41 42 33 2~ 7 0 Ltl 3'+ 7 28 30 32 27 27 24 25 26 16 16 13 32 39 27 0 34 29 12 27 9 0 6 11 6 15 21 21 27 19 14- 22 34 1 28 27 41 41 34 0 2 41 29 7 10 3 34 32 35 41 41 23 4 19 37 7 q.l 0 40 40 38 5 11 0 11 36 13 10 42 32 15 40 25 42 14 36 16 17

-2}-

- - --------------------------------------------------------------------·-

TYPE 3 TABlE 8

PREDICTOR Sii"E flS TABlE 5 RlR T'IPE 3

123456 789UUUU"U"PUUUU·H~eanHRUMDUMMM~Y~~UU 36 36 41 41 40 41 26 26 42 39 25 15 35 25 20 t5 20 41 27 26 40 26 38 41 26 25 15 21 15 6 11 11 11 11 15 26 15 20 11 39 31 38 27 41 23 22 1 12 39 43 19 4 38 9 5 3 37 4 38 tO 4t 43 t 42 34 29 5 3 32 4 33 4t 37 41 38 38 37 32 27 33 23 42 38 34

PREDICTOR 2

3~ 3i ... ~ 4~ 4~. 4~ 2{2~ 3~ ~~ ~~ ~~· ~; ~~ ~~· ~~ ~t !~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ·~~ it ~~ i~ 3~ ~~ in~ i~ i~ ~~ ~~ ~g iU~ ~~ ;~ · 27 43 t3 22 42 8 42 43 10 4 38 24 19 4 37 4 34 10 41 3 43 39 0 34 43 41 36 4 33 4t 37 35 38 41 4 1 36 33 35 29 38 34

PREDICTOR 3

t.' 2. 3 4 5 ~ 7. 8 9 tO 11: t2 13 14 t5 t6 17 tB t9 20 2t 22 23 24 25 26 27 28 29 30 3t.32 33 34.35 36 37.38 39,40 41 42 3~. 32 41 41 4Q. ~1 21 ,26 24 31 2o. 15 20 20 14 u 15 43 27 26 40 21 37 tJ.l 21 20 6 21 15 11 1i ·11 11 11 10 26 15 1q. t5 26 26 37

3 43 23 2 42 3o 42 42 5· t 34 29 t5 36 34 43 34 to 4t 3 43 34 2 35 39 4t t 43 37 37 37 '2o 4t 4i 24 39 27 t7 32 4t 38 35

PREDICTOR

t23456789UUUU"U"UUHUU~H~e•nHRDH~HM~M~Y~~UU 26 26 4t 37 37, 41 2t 26 24 36 . 5 t5. 2o t4 t4 11 6 4o 2t 26 4o t5 37 37 2t 26 6 21 11 11 to tt 11 1i t9 t4 t5 to t5 2i 21 33

3 3o 13 '35 39 35 42 42 5 41 ·29 39 35 42 29 4t 34 6 43 43 43 39 43 29 39 38 29 42 41 37 38 20 37 4t 4o o 21 12 3t · 4 · 34 29

PREDICTOR

1· 2" 3 4 S 6 7 8 9 10 It 12 13 14 t5 16 17 tB t9 20 21 22 23 24 25 26 27 28 29 30 31 32 33.34 35 36 37 38 39 40 41 42

~~ 3~ i~ ~f i~ 4~ ~~ ~~ i~ ~~ ~~ ~~ ;~ ··~~ ~~ 2~ ~~ ~~ ;r ~~ ~; ~r ~~ ~~ ~~ ~~ ~~ ·~~ ~~ *; ~~ *~ 2~ 2~ ~~ ~~ ~~. ~~ 2~ ~~ • ~~ !~ PREDICTOR

1 2 3 4 5 6 7 8 9 10 11 t2 13 14 15 t6 t7 t8 t9 20 2t 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

=~~~==J~~~~J:g~J~~~J:J~:~9~~~~~JJJ~~~~JJ1: g PREDICTOR

t , 2 3 4 5 i/ 7 a 9 10 11 12 t3 t4 t5 t6 u t8 t9 20 21 22 23 24 25 26 21 2a 29 3o 3i 32 33 34 35 36 37 38 39. 4o 41 42 2342 217 t22t742t9t53433tatB34 4 4t340tB 527292916tB36 83636 a a a 814282943291616 5 t4 5 29 Hi 19 42 18 7 3 23 lt 5 24 11 42 7 37 34 7 5 26 28 9 9 29 t6 5 tB 5 37 26 28 27 5 29 43 tB tB 8 .36 8 42

PREDICTOR

t 2 3 4, 5 6 1. a 9 to 11 t2 t3 t4 t5 16 t7. 18 t9 2o 2t 22 23 24 2s 26 21 2a 29 3o 3~ 32 3~. 34 3s 36 37 3a 39 40 41 42 27 ·27 39 34 29 36 28 16 30 26 2t 11 4 15 8 17 26 20 31 9 34 31 25 29 28 35 25 22 7 17 23 t7 17 17 4l 4 22 21 5 32 32 36 41 36 3 40 26 37 36 3 17 42 3t 26 26 35 3t 13 37 7 28 27 42 24 30 tB 36 17 18 3 25 15 5 15 26 2i 22 27 4 33 32 37 18 26

PREDICTOR

i234567~9UUUU"U"l7UUU·H~H~PP~HB~·UDUMMM~~~qUU n ~~ ~~ ·;~ i~ ~~ ~~ ~~ ~:: 2~ ~~ g 2* i~ 2~ ~~ ~~ 1~ 2~ 2~ ;; ~~ ~: i~ ~~ ~~ ~~ ~g 2~ ~~ 3~ ~~ ~~ ~~ ~~ t: ~~ ~~ 2~ ~~ ~~ ~~

PREDICTOR tO

1 2 ;: 4 5 6 7 B. 9101112 t3 1415 tG 17 18~t9.·20 2t 22 23 24 25 26 27 2B 29'3Q .. 3t 32 33 34 3R . .36 37 3& 39 40 4t 42 & .31 29.:39 28 40 11 20 2~ 21 tt 6 t5 11 11 2t 1 t5 32 26 39 26 39 2~·32 31 42 29 .t? t5.38

1t

8s

32

81

3t

85 4

323

'.18

6 33

82 t

22

271 .• 2t6

1 21 4o

39 23 39''22 46 34 32 3 20 3 32 39 37 27 tB t6 2t 33 4 28 34 4 24 39 t6 21 20 26 6 37 2t ,11 I

PREDICTOR 11

t 2' '3· .,. ·s & 7 8 9 til 11 12 t3 14 15 16 17 ta t9 2o 2t 22 2~ 24 25 2& 21 28' 29 3o 31 32 33.34 3s 36 37 38 39 40 4t 42 26:2;;· 37·: 37' 3:h57 1s 21 21i 20· s t5 to 14 to 11 s 37 2!' 26 20 ts 32 37 t5. 20 9 t5 n 1 5 s 11 11 s s s s 1o 1s ts 21 35 35• 30 35' 39 39 42 39 5 2 2 39 32 39 28 9 34· 6 39 43 2 39 39 39 39 39 6 4 38 37 34 t 33 38 24 19 11 9 35 4 33 35

PREDICTOR 12

-·~ 4~6789UUUU"UU17UUUU~H~Ud~HB~UD~M~M~M~~UU 39 2bt 42' 40 40' 40' 26 26 39 40 7 2 t7 26 11 27 36 37 26 16 39 21 31 42 26 1'2 t8 26 2t 11 26 22 t6 11 5 9 21 t2 43 ·1 39 37

3:15 t 4t 'l't 2 t2 24 t9 41 25 28 32 t9 tS 24 2t 43 2t' 27 25 12 39 24 t2 37 36 0 37 37 29 29 37 38 3t 3 7 19 3t 30 20 42

PREDICTOR 13

1 2 3 4 ·5 o 7 8 9 10 lt t2 13 14 ts t6 t7 ta· 19 20 2t 22 23 24 25. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 a: 21 43 41 37 41 t5 22 24 31 5 11 14 14 5 2t 11 4() 22 22 37 ·t6 37 37 21 26 9 21 11 7 5 1 11 11 s 14 5 t4 t5 21 21 22

26' 39 39 39 39 39 33 42 39 39 29 9 35 40 29 4t 29 1 29· 29 ·6 34 39 24 1"' 4o 5 9 4t 29 25· 24 24 43 t9 2s 3t 9 26 36 34 3o

PREDICTOR t4

t23 45678•~udu"uurruu~u~~~-·~•~uuunM~·~-~~uu 26 22 43 40. 40 40 15 32 3t '3 t5 t5 20 20 20· 15 t5 t5 32 32 40 20 37 40 27 3t 6 21 t5 11 16 U H 11 15 20 t5 tS tS 2t 2t 12

8 25' 37 37 36 22 32 t7 t3 40 26 6 31 t9 40 t6 6 27 2t 8 36 21 11 t2 tS 20 tS 15 11 4t tO 42 8 8 6 t9 6 21 t6 9 29 38

PREDICTOR tS

t234167a•unuu"nun~uua~~~-•~aRuuunM~•~•~ouu .. ~t· 41 23 '"' 3t 40 i 20 t4 3t 12 29 3t 20 42 21 21 25 37 31 39 2() 31 40 7 3t 40 42 15 25 20 25 22 t6 5 9 31 t2 38 20 2t 40 .~ft~PUdUHU~UUUt72RHUU~UU~P"HBU11U~~PHUDUU"5P

PREDICTOR t6

1234567BI011UU"UP17UUUU~H~UP~HR.HDUM~M~M~gug 4t 41> 2t 22 36 40 11 t6 20 26 7 4'3 3t t 11 15 2t is 7 25 28 20 2 22 7 21 11 2t t5 iS 23 tS 11 h 7 4 32 t2 2t 3U 27 12 25 25' 11 40 2fi 23 1 20 24 7· 6 4o 21 11 to 21 t8 14 36 36 39 t8 22 29 16 3! rs t2 11 n 42 16 38 1 33 9 3 2 18 27 1 40

PREDICTOR t7

t234$67B~~UdU~U"17UU~U~H~UP~H~HUDUM~M~MH~UU ~MUHHHM3BU~~~-H"P8UM3BHPUg3BUUU2tUUPUU~UU"~ddg t3 22 15 34 t7 34 38 38 24 36 t3 36 t6 f6 5 14 f6 34 38 22 37 22 39 39 20 36 t6 36 3t 23 6 20 t4 25 tO 20 22 16 13 32 23 39

PREDICTOR 18

t2345Si!iO~tiUU~Dd~UUdUD~~--~-~-~DUM~M~3B~~UU 38 4l i9 43 39 43 31 41 23 39 26 36 3t 31 36 36 36 37 38 13 43 38 35 43 3t 3t 5 31 36 36 37 7 5 5 t4 3t 31 31 14 36 36 43 PUU~UUM3BMMUUQHUUH6M3BMRMUPPU"SM~5MUUP~~~-HM

PREDICTOR t9

'1234s6j89Ul1db"UU17UU~uaD24Md~HBh"~UA~M~MMg~u

~~~·~UUHU~H~UU~PUUH~"U~~NU~~PUUPUUUU~U~d~~ 38 31 tS 38 28 34 37 20 14 39 19 37 t6 tt t,7 tS 20 t4 27 t6 32 20 24 34 27 32 6 36 3t 40 23 39 43 20 31 t6 39 35 t3 30 31 40

PREDICTOR 20

J~=J~6789UUPU"UP17UU~U~~~PP~UBHHDUM~M~3B~~UU

. t i• ii 4 . 4 t ~= a~ t~ !~ ~~ ~: ;~ ~~ ~~ ~: ~: 3g ~~ 1~ 4~ 1~ i~ 4~ ~~ 4~ ~~ ~~ ~~ ~~ ~~ gg ~~ ~~ ;~ 3~ ~~ 1~ ~~ 4~ . ; ~ PREDICTOR 2t

·1 2 3 4 5 & 1 a 9 10 it 12 't3 t4 t5 t6 t7 !s t9 20 2t 22 23 24 2s 26 27 28 29 3o 3t 32 33 34 35 36 '37 3a 39 4o 4t 42 32 32 2 34 43 34 40 32 9 33 32 36 3t 3t 36 36 36 36 32 32 25 27 34 43 40 37 t3 36 36 2 36 t4 5 5 14 3t 27 22 36 37 37 34 B 39 28·43 34 43 37 4t 6 39 22 10 25 36 37 t4 2t 29 t6 20 20 33 lit t7 37 33 l.O 14 21 38 t4 19 12 t2 39 25 22 35 t4 34 36 40

-24-

TYPE

I

PR~OICTOR

1 2 3 0 0 39 0 0 3

PREDICTOR

Tf>lll.E 9

Sill'£ A'i TABlE 5 FOR 1Yf£ 4

S6789U11UU"UUITUU.UUU"U-n~~HU·U~--n~M~QU 0 0 32 0 31 30 43 30 5 19 6 32 32 6 32 0 39 32 34 0 16 30 5 32 1 6 16 6 6 36 20 35 35 43 6 35 29 32 0 0 41 0 1 3 26 29 31 32 1 27 27 27 41 0 38 41 43 0 12 14 36 41 28 23 23 29 29 38 36 43 14 21 27 22 21 41

1 2 3 q. 5 0 0 2 0

6789U11Uu"uunuu•uua"u•n~~HunuM••n~M~Uu 0 21 0 30 3 43 31 31 25 10 21 31 10 21 0 39 21 34 0 16 31 10 21 1 6 16 1 15 21 14 19 39 43 6 '31 21 21 0 7 0 1 31 21 40 5 32 9 2 41 9 7 0 35 7 14 0 7 39 42 7 17 29 11 29 34 29 9 43 1 3 27 6 29 7 0 u '1-0 0

PREDICTOR

1 2 3 0 0 3 o o q.o

PREDICTOR

1 2 3 0 0 3 0 0 40

PREDICTOR

1 2 3 0 0 41 0 0 3

PREDICTOR

1 2 3

0 " 13 0 0 31

PREDICTOR.

1 2 3 0 0 11 0 0 12

PREDICTOR

1 2 3 0 0 37 0 0 42

PREDICTOR

1 2 3 0 0 37 0 0 42

4 0 0

4 0 0

7 21 25

9U11Uu"uunuu•uuu~u•u~~HunuM•MnHH~uu 24 :s q.;s 2S g 2S 1s 10 21 to 21 .o 2 21 s o 16 :s 24 21 1o 6 1& 6 26 16 14 q.:s 14 43 2 · 26 21 21 43 43 27 41 25 39 21 7 11 40 25 0 38 25 2.9 0 7 42 42 35 17 q.l 21 18 41 29 36 24 1 4 37 31 15 25

7 9U11Uu"uunuuuuuu~u•n~~HunnM••n~H~uu 9 24 3 43 20 24 24 3 16 21 5 9 0 11 9 5 0 16 4 24 16 10 6 41 2 39 16 19 43 14 41 2 20 16 9

21 43 42 11 41 6 ·12 12 7 7 3 21 0 20 21 18 0 18 q.3 42 39 17 40 17 18 37 41 36 2q. 1. 25 32 35 41 21

7 8 9 10 11 12 13 14 15 16 17 1~ 1.9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 21 0 0 32 34 21 21 '34 22 21 21 3 21 0 29 37 5 0 37 43 28 37 16 27 0 43 16 16 6 14 16 16 0 16 0 37 39 0 0 40 30 41 41 10 10 40 40 11 39 0 43 36 43 0. 36 7 37 36 18 43 0 27 9 9 37 42 18 14 0 18 0 36

4 5 0

6789U11Uu"uunuuuuua~u•v~~Hu•n~••n~M~Uu 0 39 0 0 13 12 39 39 3 19 39 39 30 39 0 6 37 7 0 37 28 36 37 8 38 0 43 37 43 5 26 8 6 0 8 0 37 o q.o o o q.o 1:s 19 19 40 39 22 22 19 4o o 42 9 :sa o 9 :58 9 9 3D :56 o a 43 38 29 28 3D 38 o 36 o 9 0

5 6 7 8 0 10 0 0 'I 0

9 10 11 12 13 lq. 15 '16 17 18 19 20 21 22 23 2q. 25 26 27 28 29 30 31 32 33 34 35 36 '37 38 39 40 41 42 11 12 13 13 41 3 13 13 23 10 0 18 14 37 . 0 14 27 26 14 18 37 0 9 28 9 u 6 18 6 0 18 0 14 12 1o 11 11 33 22 32 32 1 41 o 27 28 36 o 28 7 43 ·2a 8 7 o 27 9 28 42 5 8 5 o 8 o 28

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 14 0 10 32 30 14 19 32 14 40 3 40 14 0 2 14 43 0 14 32 5 14 12 7 3 12. 12 12 13 23 14.39 5 14 12 14

3 0 36 42 18 140 35 2 15 32 42 3 0 31 3 41 0 3 41 32 3 1 1 11 5 19 37 41 41 40 33 2 33 16 3

6789U11UU"~unuuuuuu~u•vanHu•nM••n~a~uu 0 37 0 11 21 31 11 31 11 lq. 37 37 33 37 0 38 37 30 0 37 21 1 37 11 27 3 12 17 37 23 20 10' 20 5 10 17 37 0 14 0 35 42 24 16 14 35 29 15 11 29 14 0 42 14 26 0 14 35 27 14 1 33 23 1 14 8 11 23 31 39 27 37 22 14

PREDICTOR 10

1 2 3 4 0 0 27 0 0 0 30 0

PREDICTOR

1 2 . 3 4 0 0 3 n 0 40

P~EOICTOR

1 2· 3 4 o o :so ·a 0 0 32 0

PREDICTOR

1 2 3 0 0 3 0 0 43

PREDICTOR

1 2 3 0 0 22 0 0 40

PREDICTOR

1 2 3 0 0 27 0 0 31

PREDICTOR

1 2 3 0 0 32 0 0 37

PREDICTOR

4 0 0

4 0 0

5 0 0

11

5

12

13

14

5 0 0

15

16

6 7 0 37

9 10 11 12 13 1Li- 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Li-2 10 27 25 11 30 11 29 37 39 40 37 0 32 37 24 0 37 27 23 37 11 20 3 12 14 4 2:3 37 6 20 36 6 2 37 30 40 1 39 6 9 15 11 11 13 7 0 40 7 0 0 7 36 18 7 17 32 23 1 32 31 16 39 22 4 14 39 12 7 0

6 0 0

7

7 29 17

9U11UU"~UUU~•uua"u•v~BHH9UM.MnHH~QU 14 8 38 10 5 2lj. 24 6 21 tt 29 0 6 29 36 0 18 16 36 16 41 2 41 2 39 7 5 q.o 14 40 41 15 16 29 31 42 11 17 6 7 41 18 40 36 17 0 '+2 17 28 0 6 35 24 40 lt2 12 43 38 37 38 12 12 1 4 g 35 41 17

6789U11UU"UUITUU.UUU~U-VRBHU.U34-MnMH~QU 0 37 . 0 !.i-3 39 ~4 42 6 6 14 9 4 18 37 0 24 37 43 0 ·37 31 29 37 14 21 7 27 16 16 11 6 6 4 39 42 40 37 0 40 0 8 2q. 1 40 3 27 20 37 41 39 40 0 1 40 42 0 40 41 36 40 11 15 36 14 37 42 18 38 21 34 42 1 21 40

789U11UU"~UITUU.UUU~U-V~~HUNUM•Mn~H~UU 9 0 19 8 35 12 19 25 20 16 21 14 9 0 2 9 5 0 16 11 24 16 39 2 41 35 26 16 5 43 14 41 41 16 16 9 6 0 36 30 27 14 6 11 6 42 40. 1 6 0 39 6 18 0 42 35 22 35 40 41 18 37 37 41 12 24 30 26 14 2 15 6

7 9 10 11 12 13 lq. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 11-1 42 21 30 39 21 39 26 38 39 16 21 3 21 0 40 21 1 0 16 32 38 21 39 19 16 6 7 16 14 5 39 19 12 26 21 21

6 35 27 11 21 24 25 42 26 26 12 6 0 15 6 18 0 6 15 27 33 15 41 39 15 6 26 28 19 14 9 39 5 22 6

6 7 8 9 10 11 12 13 lf.!. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 0 9 0 25 19 19 39 24 11 13 26 22 6 9 0 35 9 43 0 10 25 14 33 39 20 q.1 14 39 36 . 2 33 6 33 6 26 27 9 0 33 0 28 38 21 1 6 34 28 22 11 18 33 0 32 33 39 0 23 4 34 13 40 25 39 9 37 4 18 4 39 38 13 1 40 33

5 b 7 . 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 'H 42 0 0 7 0 10 41 10 22 4 14 39 16 26 31 7 0 32 7 22 0 16 10 23 18 39 20 41 12 16 16 13 37 4 33 39 26 12 7 0 0 37 0 28 10 21 26 24 13 31 26 22 42 37 0 18 37 9 0 17 37 7 33 22 35 16 16 20 4 41 15 11-1 111- 15 10 16 37

17

1 2 3 4 5 0 0 32 0 0 0 0 17 0 0

789U11Uu"~unuuuuua~u•uanuunuM•MnHaguu 12 0 10 32 32 15 3Q 10 13 19 15 7 12 0 39 12 32 0 19 36 35 12 15 35 19 42 11 16 38 24 35 37 7 35 21 12 23 0 15 q.O 35 21 6 28 39 8 21 14 23 0 36 23 0 0 8 32 8 21 20 14 24 31 15 12 11 14 6 25 19 15 22 23

PREDICTOR 18

1 2 3 tj. 5 & 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 11-0 41 42 0 0 22 0 0 10 0 25 32 25 21 19 41 15 36 22 15 10 0 37 10 35 0 10 25 . 6 10 15 32 8 25 33 '33 6 111- 39 20 15 25 25 10 0 0 27 0 0 13 0 33 24 11-1 34 31 21 11 34 21 16 13 0 42 13 30 0 15 32 17 25 28 25 13 23 31 '26 7 35 19 5 10 34 11-0 13

PREDICTOR 19

12345&789U11UU"UUUUU.UUU"U·V~~HUHUMHMn~HgQQ

0 0 37 0 0 12 0 10 30 25 15 6 28 15 25 32 7 12 0 39 12 27 0 8 25 35 12 15 42 19 8 11 35 11 37 6 33 20 25 21 12 0 0 7 0 0 23 0 15 39 6 32 28 10 20 8 15 26 23 0 36 23 21 0 19 20 13 25 20 25 24 25 15 32 38 25 30 37 11 20 38 23

PREDICTUR 20

1 2 3 q. 5 6 7 8 9 10 11 12 13 14 15 16 17 lts 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 11-1 42 0 0 3 0 0 0 '17 0 28 2 17 26 26 23 18 26 311- 30 17 0 22 17 0 0 17 2 23 17 34 32 0 32 33 26 23 36 26 26 10 26 0 17 0 0 20 0 0 0 34 0 23 3 34 34 37 20 30 34 26 20 34 0 26 34 0 0 34 0 10 34 10 24 0 17 22 17 18 28 37 21 40 0 0 34

PREDICTOR

2 3 0 16 0 27

21

5 b 7 8 9 10 11 12 13 1q. 15 16 17 18 19 20 21 22 23 211- 25 26 27 28 29 30 31 32 33 34 35 36 37 38 :59 40 41 42 0 3 0 30 24 24 30 25 20 15 33 35 15 3 0 38 3 38 0 10 211- 15 2.4 15 15 17 21 33 38 26 18 39 27 15 24 38 3 0 10 0 25 16 6 39 29 6 7 36 8 24 10 0 42 10 27 0 3 33 20 6 7 22 1 8 27 11 28 19 19 37 7 27 6 10

-25-

TYPE 5 TMlElO Sl'f£ Ni TI\B!E 5 RR 1'11£ 5

~~~4s6~i~uu~~"uuriu~•u~~~~•b~a•u~~M~•••~~~­•~M~u~~~-~~•M•Mn•B~~~~••n•Duuunu6uuMM~D~u~

2 19 33 11 19 11 32 4 31 20 34 39 31 10 22 39 34 33 4 36 19 40 33 14 38 5 20 14 27 13 21 37 5 ll 22 20 26 38 24 40 5 31

PREDICTOR,

12i~~&7~9utiu~~uuuUu~ti~~~~~N~M~~~~M•••~~-~• U~~u-Ma~UU~~MBMB·U~~HVHBVUD~UllVB611-·U~UV~~ 41 19 34 32 4 11 41 40 3 20 39 32 19 32 20 10 34 22 4 43 42 38 13 25 38 26 20 27 23 5 10 23 40 5 14 27 35 36 24 41 32 41

PREDICJOR. 3

123~s~~~9uuuu"uuriu~•u~~~~~ti~8•n~•~~•u•~·~• 32 22 30 32 32 30 22 22 31 31 21 13 20 10 34 21 20 21 22 27 31 21 33 27 21 31 32 19 11 11 27 21 6 11 25 14 24 14 23 24 41 22 19 20 40 23 31 11 41 32 33 20 11 19 21 33 10 13 31 22 41 13 33 41 34 28 43 39 20 5 35 5 36 23 43 5 36 17 34 33 1.1 43 21 16

PRED~CTO.R 4

123456789UhUU"UdUU~BU~~~--D~~-U~-M~HU~~~~-32 21 40 32 32 30 22 22 19 31 21 13 20 10 34 21 10 21 21 27 32 16 17 30 21 26 35 19 11 11 27 21 6 11 25 24 24 5 23 24 41 22 4o 39 31 23 3o 41 4i 41 33 39 3o 19 32 3o 10 13 23 10 39 43 43 41 32 19 43 43 32 13 22 5 4o 22 17 ~7 36 5 58 37 43 43 21 35

PREDICTOR 5

1 2 3 4. s 6. 7. 8 ·9 10 1i 12 i3 14 is 16 i7 1s 19 20 21 22 23 24 2s i& 27 28 2'9 3o 31 32 33 34 35 36 37 3B 39 40 41 42 31 41 40 31 40 19 33 41 22 31 20 39 20 20 20 22 22 33 41 37 43 37 37 42 28 37 37 26 5· 5 37 16 5 5 26 7 26 14 37 36 . 9 37 39 22 31 13 1, 41 40 22 20 19 'I 34 40 41 32 11 41 13 22 27 42 26 43 36 18 26 B 7 42 16 43 9 26 29 6 27 18 26 38 36 28 · 27

PREDicTOR 6

123 5678 30 34 30 39 39 30 34 1 34 30 31 34 23 23 2 41

PREDICTOR 7.

' . . '

9iliUu~"uuudn•u•~~•~v~ahu~~-~-u~~-~-31 23 34 12 22 2 3 23 3 22 1 14 18 43 9 37 38 43 18 7 9 5 36 42 8 18 37 37 28 42 18 42 9 26

1 39 40 40 32 3 2 1 34 39 12 26 7 38 16 14. 29 6 37 27 5 26 6 7 6 9 29 29 18 43 38 5 '7 4;

1 2 ·3 4 s 6 7 a 9 10 1!. 12 13 14 15 16 u. 1B 19 2o 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 iio Iii 42 31 31 13 39 22 20 41 13 33 1 34 22 23 10 33 2 21 30 31 5 5 28 5 36 5 6 14 36 14 14 28 37 16 8 26 42 37 29 37 37 42 5 ~MUaU•11u•uu~RMa~~UUB"MMB9B~D~UUB6U7V95BU~ri

PREDiC.TOR

1 '2 3 4 s 6 7 a 9 10 it 12 13 14 is 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3D 3i 32 33 34 35 36 37 3s 39 iio 41 42 M~UUM~UPU~~~---11·U~PM~R~UUV~~Ma66UUU-~UHDU 20 20 31 40 31 3 2 20 32 13 4o 31 13 34 3 30 11 20 33 20 19 u 35 36 36 7 19 a 24 16 32 42 25 16 35 21 43 4o 43 11 17 15

PREDi.CTOR

1 2 ·3 4 s '6 7 ·a ·9 10 11,12 l3 14' 1s i6 17 ui i9 2o 21 22 23 24 ~s 26 27 2a 29 3o 31 32 33 34 35 36 37 :is 39 iio 41 42 H•3RMUUP4R~-UUU1111U~PVM~~11·"~~Da6•ua~--UHVU 19 20 22 33 40 34 2 21 32 39 12 31 40 34 3 30 31 20 33 15 19 17 20 36 43 41 39 43 25 24 32 35 6 33 39 14 7 34 19 12 " 40

PREDICTOR , lO

1 2 .: 3 : .4 s 6 7 a 9 10 ·11 12 13 14 15 16 17 '18 19 20 21 .22 '23 24 2s 26 '2.7 ;2.s 29 30 31 ·32 ,:;3 34 35 36 37 36 39 '4o ."tj:1 42 40 23 3 23 40 40 19 23 4 39 12 40 19 19 12 31 11 12 30 40 39 19 40 36 17 31 10 26 33 5 10 30 . 6 40 22 25 19 31 15 32 21 40 ,, 19 21 19 34 20 4 30 21 20 21 20 12 34 10 11 20 34 13 17 20 10 til 40 32 27 37 42 10 43 33 26 5 s 23 30 7 34 26 24 30, 13

PREDICTOR ll

l . ? '.'3 . 5 .,i; , 7 .B 9 10 11 12 .13 14 '1s 16 17 IS 19 .20 .21 22 :23 24 ·~5 ,26 27 28 29 30 31 32 33 34 ·3~ ;36 .37 38 J9 40 ::~1 '42' 21 39 40 32 30 30 39 39 20 20 21 3 10 30 13 21 11 1 39 24 21 39 35 30 24 24 39 19 7 11 40 24 6 11 25 24 35 35 17 24 36 35 ~•u~19"11uu~aaMuMun11unu•nuua~u~uauuuuu•~M 5~•

PREDICTOR 12 I . , :0 ' , . '. ;,• , • ,, ; •J,'.

1 2 3 • 5 6 c 7 .a 9 ·to 11 12 13 14 15 16 17 18 19 20 21 22 .23 24:25.26 .27 ·2B 29 .3o 31 32 ,33 34 35 36 37 3B 39 •o ~~ ,42 . 32 32 3 32 32 13 1 30 21 32 20 11 20 20 13 '20 40 2 19 32 36 23 32 40 14 14 40 15 43 43 14 5 37 36 16 5 30 30 14 27 38 32 2124039 219. 13321101910114032'2019 172313 7384113132338164020 624244025 63219,8 7

PREDICTOR 13

1 · 2 3 • 4 , 5 6 1 a .. 9 .10 ·11 12 13 14 15 16 17 is 19. 20 21 22 23 24 25 '26 27 2s 29 30 31 32 ~3 34 35 36 37 3B '39 •o · ~l 42 39 39 4o 39 3o 3o 30 39 19 39 3o 13 10 3o 13 30 31 20 39 39 33 24 39 35' ·24 39 22 19 11 11 24 21 6 ·u 26 5 41 31 17 24 5 39 41 11 32 32 •o 11 12 22 39 31 2o 21 31 10 1 39 10 19 22 33 39 7 41 40 16 26 23 35 10 10 30 33 43 27 5 a 27 14 .7 15 19 40

PREDICTOR 1. 1 2 3 4 s 6 · .7 ·a· .. 9 io 11 12 .13 '{4 1s 16 11 1.s 19 20 21 22 ;!3 24 25 26 21 28 29 30 31. 3.2 .. 33 3• 35 36

137 3B 39 4o · .41 42

31 33 40 11 40 13 22 32 31 31 11 10 20 20 34 22 20 2 41 28 31 26 37 40 27 31 32 19 31 11 27 33 6 11 26 20 37 20 26 22 21 33 ~uau•uua3~~uunu•auuuuuuvu•~•~u•~~u•R~uuuna

PREDICTOR 15

1 ° 2 3 4 5 6 7 ·6 9 10 11 12 °13 14 15 !6•17 18 19 20 21 22 23 24 25 26 27 28 2,9 30,31 32 33 34 35.36:37 38'·.:39 40 ~~~42 37 25 3 5 40 .3 27 25 30 36 26 10 24 20 '17 20 42 24 19 37 36 19 37 40 20 .26 37 21 6 33 33 41 6 5 16 12 7 30 26 27 22 43

5 31 4o 32 29 2• 2 37 39 s 6 43 27 2• 37 1 20 a 13 2s 5 2s 7 34 19 21 12 42 3o 5 36 25 43 3o 21 3o 24 26 11 25,35 25.

PREDICTOR 16

1:2:3 ~4 56 7 6 9101112131.15161718192021222324·252627282930313233343536373839 •• 0,.142 27 19 7 36 40 5 10 21 27 27 25 40 25 25 7 25 25 7 17 17 36 10 15 32 17 25 13 42 10 5 36 30 5 33 22 16 7 26 15 27 21 28

9 21 39 2. 1 7 27 10 21 39 7 9 12 43 1. 27 26 30 37 40 20 19 40 39 26 30 10 8 6 33 37 37 21 35 11 38 19 25 22 35 40 40

PREDICTOR 17

1 • 2 ·3 4 5 '6 7 a 9 10 11 l2·:13 14 1s 16 17 1s 19 20 21 22 23 2• 25 26 27 28 29 3o 31 32 33 3• 35 36.37 38 39 '•o 4t 42 •~n~n•••••u6~PRU~7~~"~u•••"••~u~uun•~••~•n

5 16 7 35 28 37 37 26 27 5 35 1. 6 6 36 25 26 37 .3 37 35 27 35 42 37 15 27 36 35 14 17 37 35 5 5 6 26 43 27 15 . 8 35 .

PREDI,CTOR 18

1234567B9~11Uu"uuuuu•u•~~••v~a•u~uMaau•~•~• 37 25 36 36 43 3B 3s 38 2s 36 25 ·37 26 1 7 26 42 6 38 3B •2 25 37 43 3B 26 36 15 6 6 5 6 5 5 7 26 2B 26 5 15 17 3B 42 42 37 6 38 26 15 43 15 42 17 42 7 25 37 16 7 35 43 42 36 27 42 B 43 28 27 38 15 15 36 16 27 16 28 5 37 16 27 14 38 43

PREDICTOR 19

1 2 3 4 5. ·6 7 s 9 io 11 12 13. t4 15 16 .17 18 19 20 21 22 23 24 25 26 27 2B 29 30 ·31 32 33 34 35 36 37 38 39 40 41 42

HUHM~gnpvv~"~PRP~HQDRPHPPPMUUUU~USDU~BUUUU 5 36 7 28 38 & 36 1. 17 1. 6 6 6 14 36 26 25 25 36 .3 35 14 36 42 37 27 14 8 17 42 17 42 8 15 28 6 26 27 27 43 8 35

PREDICTOR 20

1• ·2 3 4 5 6 7 8 9 10 ·1112 13141516.17 1S 19 20'21 22 23 24 25 26 27 28 29 30 3!'32 33 34 35 36 37 38 39'40 41 •2 5 12 11 1 43 32 12 12 15 14 a 5 20 21 31 12 31 30 •2 to 1 42 5 7 12 t4 2a 25 3o 34 37 32 35 14 27 31 40 21 22 42 25 43

13 5 33 6 5 .3 11 41 37 6 18 32 7 28 40 40 20 18 43 12 41 12 29 11 23 41 7 8 34 7 25 11 43 1 21 20 42 38 25 15 31 14

PREOI<. TOR 21•

1 2. 3 4 ·6• 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2a 29 30 31 32 33 3• 35 36 37 .. 38 39 4o 4t 42 •o 25 38 40 32 36 38 37 36 36 31 40 24 24 22 26 26 23 32 •o •o 19 40 39 25 26 22 11 43 •o s 42 10 10 21 26 40 3o 31 11 17 40 31 •o 24 43 7 s 27 33 21 43.32 38 41 23 3o 35 28 34 3B 26 37 27 13 32 27 31 6 21 24 3• 21 43 21 34 20 22 32 23 7 1 o 41 38

-26-

TYPE TABLE ll

PREDICTOR SI\"E PS TABLE 5 FOR TYPE 6

1 2 3 l.j. 5 6 7 8 9 10 ll 12 13 1'+ 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31. 32 33 34 35 36 37 38 39 40 1+1 42 32 29 22 37 38 Lj.l 27 3LI- 19 31 26 15 5 28 15 25 25 29 2 28 36 32 33 22 25 26 15 9 15 6 6 10 15 15 6 20 35 [!.1 1 26 9 27 21 17 14 32 19 42 37 3 35 4 33 39 35 35 2 24 2.4 15 7 23 19 10 37 1 1 32 36 7 2.7 5 42 33 37 32 41 18 1 12 17 37 27 39

PREDICTOR

1 2 3 4 5 6 7 8 9 10 lt 12 13 11f. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 3/.t 35 36 37 36 39 40 1.1-1 42 32 12 '+3 '+3 38 4-l 17 28 39 31 26 15 35 30 15 2.6 21 18 33 28 36 32 33 41 25 25 15 16 15 6 6 6 15 15 6 20 35 41 1 20 21 37 21 q.:s 14 30 37 t7 43 43 5 4 22 33 5 33 2 40 Lj.Q 20 38 42 20 ll 2 1 .42 18 36 40 37 37 35 17 31 31 37 18 2 37 13 1 19 39

PREDICTOR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2:6 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 :sz 12 43 L~-3 ~+t 11 11 za zg 3t zo to :a :so ts zt' ta 9 :s:s 28 32 32 33 ~+1 11 20 10 16 20 6 1 6 15 11 6 26 2o 38 1 1s 2.1 ;,1

6 38 3 30 6 1 £!.3 42. 5 35 23 31 1 12 2 35 16 20 38 l.j.2 21 2 l.j.' 1 37 18 4 42 13 14 '+2 17 26 7 33 29 2 4 23 1 24 35

PREDICTOR !.;.

1 2 3 4 5 "6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32. 33 34 35 36 37 38 39 tj.O £!.1 42 32 1 43 40. 37 11 17 33 31 31 2o 10 2.5 2.5 15 20 9 15 27 28 32 32 33 2 10 20 10 12 20 10 16 1 15 11 10 26 20 38 · 6 15 27 37

6 3 30 26 11 1 41 43 5 18 1 25 1 12 12 30 15 Lj. 11 1+2 43 1+3 4 35 Q.Q 9 4 40 13 1.!-3 40 17 26 18 27 29 2. 4 11 1 24 35

PREDICTOR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 £!.1 42 33 2 43 40 37 40 2 37 3o 3o b 12 19 1o 8 3o 42 21 2 28 28 27 38 14 o 1o 2o o Io 1o 1o 7 8 8 7 o o 14 42 o 27 37 25 19 25 26 4o 35 32 9 19 18 26 18 6 32 2 5 IJ.O 38 32 9 26 38 26 31 28 8 5 2.8 37 11.1- 1 16 27 26 1.!-3 '+2 16 4-3 26 16 5 a

PRE.DICTOR

1 ~ 3 4 5 6 1 a 9 10 11 12 13 14 15 16 11 18 19 2.0 2 1 22 23 24 2s 26 2.1 2.8 29 30 31 32 33 3tt 35 36 37 38 39 40 41 42 1+3111111111117 tj.251523 325 3312.52.5381127 8 7 738 82916 8 52.6 5tt3 52626 7 61.i-2 527 916 17 29 20 22 5 10 32 30 20 29 25 11-0 14 11 6 18 18 Lj. 41 8 38 37 16 q.3 6 18 6 6 9 5 37 18 26 5 28 27 5 2.8 26 18 27 36

PREDICTOR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1~ 19 20 21 22 23 24 25 2.6 27 2.8 29 30 31 32 33 34 35 36 37 38 39 1+0 41 42 31+ 3 39 22 41 41 22. 19 30 40 33 23 39 32 39 34 22 34 34 42 9 37 8 29 28 5 37 28 38 29 18 16 37 29 26 43 37 38 36 38 18 8

4 30 20 30 23 22 34 4 22 32 23 4- 22 23 31 3 33 2. 22 2.6 38 8 29 37 18 9 42 18 37 26 :3& 27 14 8 38 36 38 27 37 28 29 5

PREDICTOR

1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 1o 17 18 19 20 21 22 23 24 25 2o 27 28 29 3o 31 32 33 34 35 3o 37 38 39 40 41 42 37 21 38 32 17 34 22 41 20 15 32 3o 20 42 2 11 15 2o 27 18 26 21 1 5 31 27 2o 9 3 23 38 8 20 23 14 10 0 19 10 2o 13 38 21 43 3 11-0 19 18 43 33 3 41 15 23 21 10 23 37 9 33 3!+ 34 28 26 20 7 41 3 2.3 41 23 18 22 10 29 15 23 24 11-2 39 17 3 Ll-0 23

PREDICTOR

1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2.6 27 28 29 30 31 32 33 34 35 36 37 38 39· 40 41 42 37 38 38 1B 28 3'+ 25 22 3 37 26 36 39 39 23 11 27 21 26 18 21 16 6 5 31 27 20 13 23 23 38 13 20 23 14 30 6 19 5 26 23 38 21 3o 43 3'+ 38 1'+ 38 41 10 15 2o 18 5 6 2 27 15 3S 14 34 34 33 23 40 41 3 23 24 6 10 22 10 23 15 23 29 43 28.11 4 33 23

PREDICTOR 10

1 2 3 '+ 5 6 7 8 9 10 11 12. 13 11+ 15 16 17 18 19 20 21 22 23 211- 25 26 27 2.8 29 30 31 32 33 34 35 36 37 38 39 40 41 lf.2 37 1b 38 18 28 3b 33 tj.l 3 37 26 18 5 39 23 11 27 2.1 31 41 21 17 If.! ~1 32 26 20 24 6 23 38 10 15 23 10 6 6 8 23 20 20 38 21 ::SCI 9 24- 29 43 14 9 15 10 29 32 39 6 39 27 15 35 37 30 38 33 30 42 23 7 23 37 23 38 14 42 29 15 23 5 43 14 6 23 17 1

PREDICTOR l:L

1 2 3 4 5 b 7 8 9 10 11 12 13 1't 15 tb 17 18 19 20 21 22 23 2.4 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 36 3o '+O 40 37 11 11 33 25 :n 20 43 19 27 1s 20 1s 10 19 21 36 32 33 2 10 20 43 23 20 41 22 43 21 15 10 26 20 38 22 21 23 32

6 40 35 43 34 29 38 39 42 18 16 3 1 20 12 2.5 11 3 32 39 43 41 32. 40 15 9 40 29 18 5 3:5 5 43 '+3 39 4 11 20 2'+ 16 29 31

PREDICTOR 12

1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2.5 26 27 28 29 30 :51 32 33 34 35 36 37 38 39 40 41 !!-2 37 10 37 4C:! 27 34 29 17 24 36 16 9 5 18 4 11 23 42 26 37 2 12 38 2.3 10 31 20 23 25 9 29 43 42 15 10 17 29 39 42 2.5 16 38 22 29 36 18 23 1 26 22 10 37 5 21 30 35 35 23 31 20 1+3 24 40 33 27 1 32 9 42 28 2 33 41 5 2.0 35 43 34 1 30 11 7 17 25

PH.EOH .. TUR 13

1 2 3 4 5 6 7 8 9 10 11 12 "13 14 15 16 17 18 19 20 21 22 2.3 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 32 3 '+3 ;, 41 41 17 33 25 26 21 1b 14 14 10 15 18 1!> 27 33 32 27 33 41 13 20 10 12 20 15 16 1 15 11 10 10 11+ 34 1 21 22 37

6 1 .:\b 10 42 l 43 42 24 5 17 7 1 12 11 36 16 4 11 1+2 39 12 23 1 37 18 4 4 3 7 21 40 11-3 18 39 9 2 29 36 2 34 36

PREOIC.. TOR 14

12 3 4 5 b 7 B 9101112131415.16171819202!22232425262728293031323334353637:3839401+142 32 17 43 37 43 41 17 .33 32 32 21 15 20 33 15 21 16 20 27 33 32 33 27 43 17 15 10 9 20 43 35 1 11 11 10 4 15 14 1 21 9 37 37 ':l4-21LI3717 91213131633 637 620201 516"37383837 9263135211511522.2242234118361516 4

PKEDl1,. TUR 1!:)

.t .a 3 4 5 o 1 e 9 10 l1 12 13 14 10 16 17 1a 19 2.0 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 '+2 37 21 .:\3 B 2a 2o 33 2.1 22 1 26 18 25 31 18 2.6 21 21 37 41 22 8 15 1 26 6 23 33 6 23 11 33 18 23 to a 20 39 33 23 12 12 22 2.:> 9 14- 1 17 29 37 32 40 5 32 19 12 27 27 15 29 31 30 24 37 22 43 23 37 10 18 30 4 31 15 15 11 33 27 40 12 36 20 13 19

PKEOlC. TOR 16

1 2 3 11- 5 . G 7 8 9 10 11 12 13 14 10 16 17 1t3 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 37 37 .38 1'+ 28 ., 22 22 :; 1 26 33 10 39 2 11 15 21 9 9 11 33 4 6 23 6 23 18 & 23 22 13 2 2 lo 6 a 42 1a 8 1 8 23

5 43 b 2b 19 4 37 20 2 20 1 20 39 27 23 25 27 34 37 41 21 17 22 42 26 18 36 28 23 12 2 38 23 23" 37 16 27 15 11 17 20 35

Pt{EOl CTOR 17

1 2 3 4- 5 b 7 ~ 9 10 11 12 13 14 10 16 17 18 19 20 21 22 23 2'-l 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 3b 31 17 38 '+2. ci 37 37 35 6 25 7 11+ 14 25 16 15 2b 27 37 35 37 28 tt2 6 6 26 37 26 17 28 38 26 2.6 37 17 25 42 15 26 26 28

b 4-3 6 4~ 28 4j 27 1+3 43 36 15 35 35 28 35 25 27 43 43 q.3 27 17 11-3 38 16 25 16 27 14 37 27 26 17 35 14 6 6 25 :35 37 36 38

PkCDIC TUR 18

1 2 .3 .. 5 b 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 :39 40 41 42 5 6 36 4.:\ 30 15 28 37 6 5 16 42 5 36 1-1-2 25 43 42 16 38 14 28 37 27 15 28 15 28 15 7 17 15 7 7 42 6 16 2.5 26 16 16 36

151o 7.1.4 4217281426 516 816164316 8252827 743q.2251616434227 642 8423515421528261743

PHEO.l.CTVR 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1~ 16 17 18 19 20 21 2.2 23 24 25 26 27 28 29'·30 31 32 3:3 34 35 36 37 38 39 40 41 42 31:1 .j7 .;)0 3(:) 42 d 37 43 35 6 15 7 5 14 35 25 4-3 7 43 4-3 14 37 43 l.i-2 6 6 26 37 25 17 28 38 26 7 37 17 25 25 17 26 26 28

6 2b b 7 27 3U 26 26 17 36 25 37 35 28 2b 15 6 4.3 28 37 16 17 28 38 15 37 37 38 37 37 42 17 37 :37 15 5 28 42 15 35 7 38

PR.EOI-.:TVR 2ll

'"'•5•7&9UU~~~w~nuwu~uu"e~vun~~9~ue9~HH~"" 41 1.:> 1 11 11 4.> 2!5 2 t<J 41 34- 20 37 37 31 34 34 3C a 14 1 21 9 4-3 42 23 40 25 33 3o 12. 32 3o 33 3o 36 37 33 31 33 41 25 42 lt.l SO 1 9 24 2 2b 34 22 10 34 2•) 43 35 2A 22 4-1 26 25 2.9 32 2 11 25 41 33 2 35 6 22 43 40 37 32 11 20 35 22 21 42 2

PH.EDII... TVR 21

1 ..::: 3 4 5 l) 7 8 g 10 11 12. 13 14 15 1& 17 1ti 19 20 21 22 23 24- 2.5 2.6 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 19 3(..·j7 1o 34 2.:> 34 3'1- 32 27 27 16 '+2 36 21 22 43 22 28 23 24 32 17 t3 31 22 16 13 12 21 17 26 21 32 29 4 20 43 12 21 28 36

3 ..;~+ t:l 1 17 41 13 13 11 10 32 3e 27 16 22. 31 22 21 6 34 27 33 34 12 13 3 38 8 25 6 39 24 32 21 7 21 33 24 11 22 6 11

-27-

---·--·---------- ----------

; r:

TABLE 12

NUMBER OF CASES IN NON-STRATIFIED AND STRATIFIED SAMPLES

FOR FINAL REGRESSION ANALYSIS

Predictor Number

1,2

3,4

5,6

7,8

9,10

11 '12

13,14

'15, 16

17' 18

19,20

21,22

23,24

25,26

27,28

29,30

31,32

33,34

35,36

37,38

39,40

41,42

'Noh-Strati·fied sample 769

Non-Stratified Sample with Dew-Points 408

Type 1 276

Type 2 124

~~ 3 1~

Type 4 75

Type 5 47

Type 6 67

TABLE 13

PREDICTOR CODE FOR FINAL REGRESSION EQUATIONS

First two grid-points for 850 mb heights.

for 700mb heights.

for 500 mb heights.

for 300,mb heights.

for 850 mb height tendencies.

for 700 mb height tendencies.

for 500mb height tendencies.

for 300-500 mb thi ckness·es.

for 300-500 mb thickness tendencies.

for 500-850 mb thicknesses.

for 500mb vorticities.

for 500-850 mb thickness tendencies.

for 500mb vorticity tendencies.

for 500 mb vertical velocities (Total)

for 500 mb vertical velocities due to thickness advection.

for 500 mb vertical velocities due to vorticity advection.

Previous precipitation seJecteq for first two stations.

Fi'rst two grid-points for thickness advections.

,,

for 850 mb dew-point depressions.

for 700 mb dew-point depressions.

for 500mb dew-point depressions.

-28-

E.LY ,f)n ,01 ,06 ,14 ,40 2•

,77 1,0n

,00 ,00 ,Of) .or.

KNO ,(10 ,01 .ns ol9 .33 ,:JO .so ;82

1.no 1. no

.no

.no

BFL .un .o1 ol7 ol2 ·4" ,jj

o7l .:,7 • .,o .uo ,(ll)

1•00

SAN

.no

.n1 ,06 ,).6 .24 .56 ,73 .77 ,86 .78

loOO .no

t:LY tlFL. 0 00 oldl ,f)ll ,(11) • 02 ,J.7 ,15 ,,2t1 ,32 e.:ll ,:05 .<;2 , B9 , ~o ,67 .t;d ,67 l•UII ,0!') .uu

1.0~ ,,,o ,01"1 .uo

i\l'~o

.no

.n1

.no

.21

.36

.32

.69

.b3 1.nn 1. no 1. no

,f.\0

"Ai'< .no ,01 ,(1!_)

,00 .1.5 .73 • rrJ ,40 .90

1.00 ,nQ .no

TPKE 14 Rm.OO' (f PI£CIPITATIOO Fffi 12-fSTif'A1E INTERVP(S Fffi ~-STAATIFIED lB8JlfENfAL s.oz.'PLE

TuS .no .nl .ne .29 o3l .50 o7l o83 ob9 .67 ob6

1.no

LAS ,no ,no ,10 ,45 .20 ,55 ,00 .no ,00 .no .no .no

J.N~> SFO .oo .oo ,01 .01 , Ob ,·07 .14 ,13 ,25 .30 ,L}oo ,44-

1.00 .59 ,83 .77 ,78 ,85 ,50 1.00 .00 1.00 .co 1.oo

.I.JS

,PO .nl .n2

o?7 ob7 d3 .9()

1,(1(1

,:,(1

1. no 1. no

INw .oo

O' .'30 • Qf) .2(, .~0 .. oo .co .(l~

.89 1. ~0

LAS .nn , QIJ ,O(J .41. • 7~)

J.,OO .no ,00 .rn .no ,'QO ,('10

SFu ,()Q • •}1 • ·)2 .c::~ ,32 • 52 oO!+

.74

.81 i•OO J.,,)Q

1.::o

PHi\ .oo .oo .oo .oo .34 ,20 .co .on .co .se .oo .ao

PIH ,QQ .02 .12 .18 .36 .56 .73 .67 .63 .75 ,QJ .oo

1.CO ,()7

,7G 1.00 .oo .co

PIH .oo .oo ,Q9

-.)5 ,6') .67 .b7 .o2 ,60 ,67

1, OJ

YUM SAC .oo .oo .01 ,02 .13 .04 .29 .20 • .L3 ,38 .58 ,48 .o3 ,39 .no .o2 • oo· ,92 .oo 1.00 .oo 1,00 .no 1.00

vEG ,01 ,03 .09 ,21 ,31 .sa .62 ,65 ,76 ,81

1,00 .vo

1<BL .oo .01 .~8 ,22 .41 .33 .70 .70 ,86 ,67 .co .oo

SMX .oo ,01 ,08 ,06 ,44 ,55 ,56 ,72 .86

1.00 1,00

.oo

PDX .01 .oc .oo ,19 ,()0 .oo .26 .oo .oo ,82 .oo .oo

3IL .oo ,Cl .oa .26 .30 .38 .6(!

loOO .ll9

loCO .oo .oo

OLM .o2 .oo .10 .17 .28 .42 ,52 ,79 ,87 ,90 .92 ,98

NON STRATIFIED CASES

SLC .Cl .01 ,Q7 .16 .29 .47 ,61 ,73

1.00 1.00

.oo

.oo

ALW ,02 ,Q7 .10 .18 ,38 ,L\.9 .52 .72

1.00 .oo .oo .oo

BOI ,Ql .03 ,11 ,23 ,29 ,54 ,52 ,64

1,00 ,91 .oo .oo

AST .oo .co ,(17 .14 .26 .57 .65 .71 .84 .91 .95 o99

BNO .oo ,04 ,02 ol'> ,L\.0 .41 .62 .63 ,75

1,00 .oo .oo

SLM .o1 .01 .10 ol6 .27 .42 o54 .83 .85 ,97 .92

1.00

GTF .oo

.• 02 .13 .27 .22 o34 o64 .74 .92 .67

loOO 1.oo

EUG .01 .03 .06 .oa .35 .41 .60 .75 ,89 .89 .97 .97

MSO o02 o03 o14 ol5 .30 o60 .53 ofll o76· o83. .so

lo00

FCA .10 ,06 .12 ,22 .27 ,45 ,64 ,65 ,80

1,00 1.00 1,00

POT .01 .04 .07 .21 .39 .37 ,56 ,65 ,79 .81 .oo .oo

EKA ,00 • 01 ,05 ,17 ,31 ,Ill ,64 .75 ,83 ,84 ,95

1,00

HVR HLN .01 .oo .02 ,05 ,12 ,08 ,27 ,23 ,35' ,39 .5o .49 .36 .76 • 73 ,64

1.00 .50 1.00 .60

.oo .co

.00 1.00

NON STRATIFIED CASES INCLUDING DEW POINT DEPRESSIONS

Yu;-1 .Jo .:o .D3 .13 • :O•J .no .so .Do

.S0

.Jo

.oo

.21

.:9

.SH ,:,3 .64 .·-..12

1...0') 1,00 1,00

.;EG RBL ,.'.)1 • 00 • :Qt~ • '0(1

,05 ,r:ib ,lL~ el9 ,33 .2b 'JL~ • 54-• 7~\ • 74 • 7J .59 ,86 • '11 ,85 l.C0

l,Ou 1.00 l.OC· .00

• }3 ,13 .29 ,Lf6 ,53 ,87

1. 30 1, ,),~ .Jo .oo

Pux .oo

r r,

"'' .w~ .10 .oo .oc .21 .oc .oo .83 .GC .00

!3 I L. • f:;J ,0(:!

• C·U oliJ .42 .so .!:;G

1.(0 .00 • C•J .oo .ov

OLM .oo .oo .07 ,13 ,34 ,34 ,59 ,71 ,85 ,91 .95

1,00

St...C ,)C .n .uo .13 .26 ,LfLf .sc .be ,1;6

1.00 l.OC .oo

ALW .oo .07 .o5 .15 .40 .40 ,64 .07

1.00 ,:;o

1,00 .co

~or

.oo

.02

.15

.19 ,37 ,39 ,65 ,56 ,88

1.oo 1,QO .oo

3NO ,02 ,02 .06 .23 o2'l .57 .63 ,58 ,92 ,75 .oo .oo

GTF .i.,..C' • ( 1 .(,7 .21 .36 .39 .b2 .sa .'::12

loCO 1.00 l,(,C

AS T SLM lUG .oo ,(10 .oo .10 ,r)7 .03 .13 ,1)8 ,07 oC7 o18 ,27 .13 .:;2 .20 o42 oL\5 ,57 .55 .53 .58 o90 o71 ,73 .77 .go .73 .96 ,g3 .96 .96 o97 ,95 .99 1.00 1,00

-29-

t~SO

.n2 ,('5 .tl ·11 .33 o41 o64 .()9 .92

1.00 1.oo 1.!)0

FCA ,02 ,oo ,05 ,20 ,33 ,44 ,50 ,7f'

1. 00 ,92

1.00 1,00

POT .oo .04 .10 .19 .oo .oo ,53 .52 .80 .93 .oo .oo

HVr< .C1 .C2 .C!5 .20 .41 .41 .65 ,71 ,88 .75 .oo .oo

E~.A

,00 ,00 .07 .10 ,28 .41 .!:>6 ,71 ,91

1,00 ,89

1,00

HLN .oo ,01 ,G9 ,22 ,43 ,56 ,40 ,80 .on

1.00 1,00 .co

MFR .01 .01 .07 .19 .26 .35 .56 ,77 ,95

1.00 .00

1.00

GGW .02 .04 .12 olfl .36 ,56 .60 .78 ,83 ,67 .oo .oo

i~FR

.01

.01

.02

.14

.21

.Lfl

.61)

.so ,'l3

1. 01)

.67 1.00

SEA .c1 ,C3 .09 ,36 ,20 .33 ,59 .64 .74 ,89 .91

1.00

LWS ,n2 ,n5 ,10 ,;>5 ,33 ,L\.5 .58 ,77 ,43

1,00 ,00 ,no

SEA ,C2 .C2 .10 .17 .5(, • '~5 .so .57 .82 .91 .94 .91

GGW L\oiS .~1 ,n3 ,06 .nG ,06 ,07 .2n .?3 .25 .2P ,5g ,u,7 ,67 ,59 .75 ,f\4

1.00 ,67 ,67 1.nu

1,oo .no .co 1.no

FAT .oo ,02 ,06 .15 .33 ,52 ,63 ,67

1,00 1,00 .oo .on

EKO ,00 ,02 ,09 ,21 ,34· .50 ,76 ,60 ,83 ,78

1.00 1,00

FAT .oo ,00 ,07 ,14 ,10 ,50 .57 ,93

1.on 1,00 1.0~ .on

EKO .02 .02 ,06 .1<1 ,37 .52 ,68 ,60 ,63 ,83

1,00 1,00

LAX ,011 ,01 ,05 ,26 ,23 ,47 ,25 ,83

1.08 1,00 1,00 1,00

M,_~

.uo ,[]2 .u7 ol9 .;:,6 .~'< .~;,

.c:.:.,

.75

.ou l .oo l•UO

WMC FLG ,01 .uo , 04 , OIJ .12 .uo ,17 .211 ,33 ,,:,1 • 58 • J.9 .6Q .~1.+

,67 ob1 1,00 .<,;0

.on 1.un , 00 1• Oil , on 1 ,u,J

LAX .o~

,01 ,Ob ,2n ,29 ,2n ,55 ,71 ,92

1,00 1. 00

.on

I~L..I·

• Cfl ,(1.1.

.12

.co

.2.7 • ~)Lt

• 7'::> • t!..S

l•U" •(...oU

1• (i(J

1oUil

WMC FLG ,01 .os ,08 ,211 ,25 ,.35 ,7r;; ,67

1,1)0 1,0n 1,0n

,on

.on

.uo

.u~

o1b ,J.7 • 7:; .:,o • '+o

l•Ull ,<,':)

1,un l•UO

-~---~-------------------------------·-

TABLE 15 SJ'i'£ AS TABLE 14 FOR TYFfS 1 J1ND 2

f..LY ,on ,n1 , flL!.

,2.t

·''~ ,!.Jn .7t>

1.n~ 1,nn

,()il

,on ,on

f<~IO ,on ,fln ,nq ,11 ,25 ,7b

).,(10

l,On ,on

,1_111

•1.'.1. ,i.J.)

,J.O .::>!.> ,Ufl

1•L•II , UIJ

l•Uf1 ,(111

,LJil I UIJ

fuS ,(I (I

• r. ~! • ntJ .~2 ..t~i thil .bn • 7~)

•• 110 1,nn

,po l •. !lt1

S~\1~ !,..,~·:

'~ u • r ~ n ,lJIJ • ill • ulJ .-n..; ,J.4 .f!7 .2~ .c~9 .lt> .71 • 7!..> J. no .uti , ~>II

• Q'l .till ,Jill

; A~) 1-'t-1·" YUf'/1 S,\C ~!'-1A llL SLC .cu ~. • oc, ,•)'1 ,{)3

,PO ,Ul '.UQ ,IJ".Q , {};J.

, Pfl , O~l • fl() • en '.1.4 • c _) .67 .:::.2

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TYPE 4

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TYPE 6

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,00 .uo ,no ,no .oo .oo .oo .oo .oo .od .oo .oo .oo .oo .oo ,00 ,14 ,oo .o.o' .oo· ,no ,13 .uu .no ,oo .oo .10 .oo ,0() .bo .14 .oo .io .oo o17 .oo ,17 ~13 .oo .oo, ,00 .oo

_,0(1 .oo ,(1{1 .no .oo .ao ,00 ,00 .-oo-, .20· .oo .oo .oo .oo .oo ,00 ,20, ,67 ,00, ,33 .33 1,00 .oo .2s .ad 1.00 1.00 1,00 1,00 ,29 1.00 ,25 1,00 • oo .so .. .oo ,50 .so 1,00 ,50 ,00, ,50 1,01) 1•00 1,00 ,1,00 , Olt .Jo .ao ,60 1.oo 1.0"0· t.oo, ,67 1.oo, 1e00 1.00 ,50 ,50 .oo 1,,00, 1,00, ,,Q,O 1,on l•UD 1,00 ,00 1,00 .oo .oo 1,00 7'' 1,00. 1.oo 1.-oo ,67. .67 1.00 ,67 l.Oo 1,00 1.-oo 1, 00, 1,•00 __ • 0

,oo loOO 1.oo ,00 .co 1.00 .OG 1,00 1,00 1,00 1,00 1.oo leOO 1.oo .oo 1,00 1.00 1,00 1,00 l,Op, 1.00 1,01) 1o0D 1.no ,flO 1.00 loCO .oo 1,00 t,oo 1,00 1,QO 1.oo. 1.oo leOO .oo .oo • oo .. .oo . • on 1,no.. i.oo .

,Of) 1o00 1.00 ,00 .oo .oa 1.oo 1,00 t.oo .oo 1,QO 1,00 1.oo 1.oo .oo 1, 00, 1.oo .oo 1. 0.0 ,OQ, 1,00, ,on 1o00 1,no .oo 1.00 .oo .oo 1,00 1.00 1,00 1.oo 1,oo •. co 1.oo .oo 1,00 .oo. !.oo .oo l.no. 1,00

-32-

TABLE 18

NUMBER OF TIMES EACH PREDICTOR FIELD IS SELECTED AS THE FIRST OR SECOND PREDICTOR

IN THE FINAL EQUATIONS FOR ALL STATIONS

Non-Stratified SamJ1e

. Wl th Dew-

Points 1 2

850 mb Height 10 13 8 9

700 mb Height h 3 12 5 ""

500 mb Height 7 3 2 2

300 mb Height 1 0 1 2

~50mb Height Tendencies 0 2 2 3

700 mb Height Tendencies 0 0 2 5

500 mb Height Tendencies 0 0 1 4

300-500 mb Thickness 0 0 0 2

300-500 mb Thickness Tendencies · 0 0 0 4

500-850 mb Thickness 1 1 1 2

500 mb Vorticity 1 3 1 12

500-850 mb Thickness Tendencies 0 0 0 3

500 mb Vorticity Tendenc~ 0 0 0 4

500 mb Vertical Velocity (Tota1l 2 3 , 3 I

500 mb Vertical Velocity (Thickness Adv.) 0 0 0 4

500 mb Vertical Velocity (Vorticity Adv.) 0 1 2 9

Previous Precipitation 57 50 c~s 2

Thickness Advection 0 0 6 9

850 mb Dew Point Depression 4

700 mb Dew Point Depression 1

500 mb Dew Point Depression 0

-33-- -- -----~-----~

Type

3 4 5 6

24 5 7 12

9 3 5 6

2 0 4 2

4 2 4 1

6 c 6 5

0 2 8 5

1 '3 2 3

1 3 2 4

1 6 4 4

3 4 5 7

8, 9 12 8

1 3 3 4

2 5 5 6

1 a 2 3 J

6 8 3 2

2 2 2 1

6 7 2 1

7 13 8 10

TABLE 19

REDUCTION OF VARIANCE ,' ,. ;

Non-Stratified Station Data Types

with Dew-: 1 2 3 4 5 6

Points '

ELY .357 .406 .381 .509 .439 .824 .555 BFL .350 .394 .422 .821 .368 .693 .538 TUS .445 .488 .561 .432 .402 .757 .694 .716 LAS .237 :266 .386 .521 .790 .537 PHX .510 .. 524 .644 .385 .523 .708 .692 YUM.

' .273 . 351 .474 .348 .483 .790 .655

SAC .463 .556 . 361. .394 .514 .720 .840 .694' SMX .485 .514 .437 .560 . 521 .798 .671 BIL . 319 .264 .310 .451 .399 .. 434 .789 . 581 SLC. .386 .270 .458 .590 .399 .793 .818 .634 BOI. .. 314 .320 .380 .505 .493 .562 .681 .725 BNO . . 313 .349 .471 .582 .461 .599 . 710 .647 GTF. ·.416 . 434 .353: . 551 . .558 .509 .67.9 . .623 MSO. . 319 .354 . 344 .413 .592 .594 . 721 .617 PDT ~ ..• 456 .497 .485 .462 .428 .623 .742 .. 656 EKA .506 .537 .437 .590 .550 .574 • 717 .606 MFR

; .416 .434 .408 .582 .586 .641 .767 .674

SEA .505 .504 .439 .446 .461 .644 .745 .634 FAT .400 . . 476 • 368 . .355 .503 .642. .812 . .649 LAX .511 .508 .316 .546 .443 .810 .757 MLF .. ;420 .486 .412 .552 .. .476 .690 .816 ·.637 RNO .383 .441 .465 .523 .720 .733 .560 SAN .. 508 .534 . 550 .• 448 .452 .447 .804 .808 . INW .455 .508 .399 .589 . 581 .672 .723 SFO .484 .550 .452 .533 .544 .681 .781 .548 PIH .373 .421 .428 .364 .542 .740 .722 .664 GEG .353 .429 .395 .524 .500 .654 .689 .649 RBL .380 .403 .316 .400 .673 .697 .723 POX .555 .332· .529 .464 . .467 .651 .840 .756

-J

OLM . 501 .356 .453 .390 .434 .594 .765 .643 ALW .208 . 381 .313 . .314 . 441. .• 486 .695. .533 . AST .467 .484 .284 .512 .294 .658 .778 .673 SLM . ;487 . .465 .419 . .478 .453 .564 .733· .701' EUG .497 .519 .472 .389 .493 .578 .625 ,. 711 FCA • 186 .297 . .360 . 437 .528 .. .633 .670 .577 HVR .250 .329 .307 .432 .587 .648 .842 .606 HLN .247 .256 . 331 .515 .448 .436 .526 .. 585 GGW .228 .284 .363 .476 .466 .569 .662 .426 LWS .235 .357 . 3T6 .360 .413 .692 .726 '.560 . EKO .359 .393 .439 .418 .535 .631 .822 .581 WMC .266 .298 .253 • 539 • 534 . .. 660 . . 700 .635 FLG .535 .245 .524 .575 .485 .720 .847 .763

..

-34-

TABLE 20

STANDARD ERROR OF ESTIMATE

Non-Stratified Station Sample Types

Wlth Dew- l 2 3 4 5 6

Points

ELY .216 . 231 . 192 .129 .145 .203 .280 BFL .203 .217 .181 .040 .202 .285 . 155 TUS .219 .207 .199 .240 .164 . 105 .095 .244 LAS . 155 . 152 .116 .146 .144 .178 PHX . 181 . 187 .148 . 179 . 133 .234 .242 YUM . 166 .. 172 .123 .132 .125 . 152 .198 SAC .256 .262 .241 . 074 .335 .068 . 231 .074 SMX . 210 .225 . 187 .088 .224 .250 .193 BIL .286 .283 .269 . 357 . 175 .189 .152 . 218 SLC .273 .270 .278 . 212 .116 .078 . 210 .295 BOI . 321 .320 .342 . 213 .258 .145 .304 .241 BNO .330 .349 .316 . 135 .335 .081 .290 .259 GTF .289 .289 .268 .340 .208 .153 .283 .275 ~so .346 .345 .332 .372 .277 . 160 .305 .265 PDT .294 .299 .309 .222 .348 .134 .268 .230 EKA . 315 .323 .337 • 140 .342 .118 .247 .244 MFR .309 .326 .328 .137 .299 • 108 .274 .180 SEA .347 .353 .378 .224 .370 . 235 .260 .271 FAT .224 . 231 .194 .1 06 . 241 .073 . 231 .155 LAX .1 90 . 210 .156 • 109 .224 .232 .194 MLF . 241 .247 .227 .208 .172 .070 .214 .294 RNO .208 .236 .146 .234 .068 . 272 .209 SAN . 197 .204 .172 .122 .169 .095 .233 .200 INW . 197 .195 .172 .194 .137 .210 .257 SFO .264 .271 .237 .092 .327 .072 .265 .126 PIH .293 . 291 .286 .318 .235 .065 .297 .237 GEG .349 . 339 .356 .232 .354 . 178 . 321 . 198 RBL .275 .293 .257 .386 . 071 .266 .099 POX .325 .332 .346 .288 .377 .129 .187 .249 OLM .355 .356 .350 .279 . 331 .239 .192 .274 ALW .370 . 381 .375 .226 .372 .092 .302 .268 AST .352 . 327 . 339 .354 . 316 .224 .113 .307 SLM .356 .369 .384 .236 .364 .184 .186 .250 EUG .343 .348 .367 .213 .362 .142 .226 .209 FCA .409 .374 .378 .381 .316 .247 .295 .299 HVR .298 . 313 .295 . 335 .218 . 149 .192 .143 HLN . 325 .322 .277 .333 .233 . 131 .363 .302 GGW .323 .326 .310 .336 .177 .144 .299 .320 LWS .368 .348 .380 .284 .366 I . 100 .276 .237 EKO .304 .306 .307 .174 . 231 .078 .242 .290 WMC . 301 .305 .310 . 197 .254 .074 .295 .204 FLG . 241 .245 .193 . 213 . 218 .068 .218 .263

I

-35-

Tfllli..E21 lffiT t£iV'l SlliAI£ ERroRS

('[)N..sTJlATIFlED S/WlE

tL. f BFL TU5 l.AS PHX YUM SAC SMX BlL st.c 801 eNO GTF MSO POT EKA MFR SEA F".T t.r,,' ~11 I='

,3<8 • .309 ,3S& .211 ,;no ,231 ,495 .360 ,406 .416 ,373 ,460 .465 .5tS 481 ,611 .5UtJ .~)~t) ,.~41 c .33'' .351-1-

RI.•O SAN .N~ SFO PlH GEG RBL PoX OI.M ALW AST SLM EUG ~CII HVR HLN GGW LWS EKO 'tlfAC FLG .360 •. !u-:~ .534 .40q ,588 ,563 ,6 02 .657 .531 .s&o ,&56 ,632 .49[) .381 ·'~76 ,4Q8 .526 ,h15 .34 2 ,'171

eLY BFL TUS LAS PHX YUM SAC ';•i(, :ill.. SLC 80! .:~!0 Gil' 1·1~\j p~.T n~ ''!-", srtt F'T I . ' I•'I.F

.1>:19 .316 ,359 .2!7 ,367 .227 ,514 .~b.J t lj L'~ .4~t\ ,3-% ,1.4-(,b ,4% .~u .4Hl ,017· . "~'\ ~ ,nc::2 ~ 111 i' .·"'•:! • 3 1-1-7

RNO SAN lNW '":t!""•! r ... , ~ ' . ~ ' • 1- 1\,.:., OL ., J.!.Lq A'; r ~LM [Uci FG1-1 HVI"{ I'Lf·l P.\,. ,_,_.·r; F1<0 FL"'

.3S? ,;5q6 ,268 • It Ot~ • ..J~J . ··"/') .r . ..... ,r)l.; ,!>32 .~<;7 ,1'--,72 ,bUO ,!.>u6 ,jhr:'l •'tft) .l:,j:. .'•""~() ·'~ 1 Fl ."<7 ·'~6;:> •. J").

('[)N-STMTIFIED SPWI£ INCWDING Ifl1 POINTS

f.LY bi'L TUS LA~ Pli-' 1'./ $/n;. S~1X 131L SI.C B<il hNO' GTF o4SO PIJT t-:KA r~F,-{ ~I=' A F~T I • X ~lLF

.J4~ .279 ,.'165 .211 ,310 ,c."'51 ,424 ,;;.9tl ,37;:; ,442 ,350 ,457 ,487 .~21 ,'184 • ~,i)2 ,?17 ,()71) .3.23 I•?A6 ,36~

1\IJU SAN ww SF II P.U1 u.·. r~ kiJI.- f'~, >- OL,v1 AL• AST SLM ELlG FC~ HVI< Oll.r... GGt• L\•'S EH> ~··~,c FLC• ,j•_,~ .362 .~>;fo ,•Pt~ ,3')1 .~7":1( ,5,c::5 ,f•Jl ,6vt'J ,488 ,45" ,nr~9 .6~6 ,!'>05 ,368 ,1192 .:~y<, ,'1?--7 ,4;30 .~c:::o ,q '17

~u ,I· I 'lv..J '-''~ r l1A , .. ·~.,~.; S'!X rJL SLC RO! HNO GTF MSO. PDT FKA MI-'"H. SFA FAT LhX ML.F • ~\~o .2() • :, 11 .;::2~ .3u~ u::.3.!. ,41;.~ ,..1,3 ,30G ,459 ,349 ,467 .'IL>4 ,b4~ ,484 ,':)23 ,519 ,(..,ftt. ,3% .~78 ,3711

rd•U .•• )11'• lol,. ..:.FCJ Pili l:ll_, .• k.IL. f"ll)A O~i·1 ALW AST 5LI~ EUG FCII HVR HLN G~~·J L\·'S ;e:~o .,.~,c FI.G • .l~O .3'17 .e:.'.:t.J. e 1i54 ,11 J.4 ,!>'1'·· ,5t:~J .6;1 ,62.1 ,495 ,48;1 ,n62 ,646 ,:Jl3 ,377 ,t::i-:;5 ,4ul ,5U2 ,427 •. ~1~4 ,436

-36-

EL-Y ,223

TYF£ 1

~FL. TUS ~~S PHX YUM SAC SMX BIL. SL.C 80! R'IO GTF 1~SO PDT EKA ~FR SEA FAT LAX MLF , 195 ,18s .oeo .c?z .o32 ,227 ,22 3 ,33o .268 ,4Dl ,400 .328 ,497 ,504 ,244 ,277 .~e1 ,235 .2•9 ,264

SAN INW SFv p lh ~E.G • l<bL POX OLI~ ALW AS 1 SLM EUG FCA HVR HLN GGW LWS EKO WMC FLG .191 ,13 2 .297 ,313 d34 ,l.lo ,6o9 ,586 .s1e ,41~ ,346 ,474 ,589 ,367 ,438 ,3b7 ,452 ,266 ,219 ,138

6FL TUS L.A.S Ph< YUN SAC SMX BlL. SLC BO! BNO GTF MSO PDT EKA ''FR SE"A FAT LAX MLF .221 ,lo:, .oo6 .001 .ooo ,17G .2<)5 ,347 .29G ,4C5 ,442 .323 ,486 ,515 ,?.23 .271 .5~1 ,229 ,250 ,266

~JiN l.~to .,FO P ,d-l v;-:G k.JL.. POX OL1•1 ALw AS r SLM EoJG FCA HVR HLN GGW L'f,!S EKO WMC FLG .2.24 .t:.·.d .• .:.c,:, .291 ,45q ,2l~ ,6oo ,594 ,ij.98 .41~:~ ,326 .4b4_ ,598 .:338 .482 .4u' ,466 ,21.1-7 .2ua ,o3n

,Q71

.ooo

S1\'N .ceo

L-AS

,10~

11'1"' ,167

1YPE 2

PHX

.2.77

1YPE 3

YUM

,Q79 :;,EC7

,.l66

,i.,..,.,1 ..

,.:,;7'

SAC • C~{;

llBL.

SMX

.o:. 7 Pox

Pox

BIL.

,496 OLM

,563

BlL. ,!56j

OLM

,601

,477

SLC

.725

AL.'ti

,'+42

BOI

,388 AST

.498

bOI

.so; .• AST

• so~

eND GTF

,32& .6(.9 SLM EUG

.611 .516

91'0 GTF

• 326 • 6J.3

SLM EUG

,649 .501

MSO

,707 FCA

.716

FCA

• 785

PDT

,435 HVR

,62v

PDT

,48v

HVR

.762.

EKA

.194

HLN

,372

EKA

,380

HLN

,650

SEA

,768

LWS

.5~2

I' AT

, 07B

EKO

,139

FAT

.ooo

F.KO

• 09u

LAX

,OM

WMC

.2n1

';LF

,3-b'i

I'LG ,281

~LF

,331

FLG .315

::.Ll' BFL. 1"1..1:_, U1::. PHX YVf\\ SAC. S~.X B:L SL.C <30! P.I·!O GlF rASO PDT [K.,1 MFR SE'A FAT LtX MLF .24-j .248 ,Z:.35 .140 .1:..~ ,i3:, ,S.JS .r::s7 ,;.>45 .~.34 ,367 ,606 ,2.::,1 ,446 ,573 ,1.qo ,SQo .~06 ,3C0 .311.4- ,185

r<LO SA~ LNW ::.Fu PHi v.:'; l:,~L Pi)X OLI"I AI..W AST !-:.U~ E'U!.:7 FCI1 HVR HLN <;(; 1..; L\o!S E!<O ~'.'''C FLG ,j(·:~ .1':>7 .160 e'::lfH ,3.J7 ,o-139 ,Sv"t .536 ,372 ,7JU ,20t~ ,442 .4cH ,::;,34 ,237 ,323 .10:1:! ,f:l?8 ,349 ,379 ,150

ELY BP~ TUS LeS f'll): Yll 11 ;..A, S::X blL SLC llOl HNO GTF "'Sl> PDT f-1(~ ~FK SFA FAT LOX MLF ,22::;, :3:50 .2.13 .oov ,000 .000 .'"~l.:i ,::uo ,2 ... 6 ,354 ,4-6~ .~48 ,2.Gl ,o.+95 ,570 .~G7 .~~~7 .::il9 ,299 ,271 ,113

RNU SAN lNW SFU f' !H GEG i~:1L P!_,X Oli·;, 1~1...~'./ AST ~LM tuG FC/'1. HVR HLN G\.,~1 L\'.'5 El-'0 !i~'C F'LG ,31l.t .2.2.0 .ooo .S6i. .3~'-r .12q .530 .5~8 .346 ,677 .27u • .389 .4=>b ,571 ,2.2.8 .312 ,Qjt.~. ,6?5 ,352 .3~9 .033

-37-

---·- ---···-·-- ·-·-----·----·-- -----·-----·-··---- ---

~-~ •s<t<~~:ocrsco FRESI()

• BAI<ERSF!ao

\~ARIA e .

~5~~,

~.38-

ElY •· n!LFORD

•

CllCAT 'ALLS •

Fl.AGST.AFF" • VINSLOV •

I'II:!EN!X •

BILLI\CS

•

FIGURE 2

PRECIPITATION FREQUENCIES. SOLID LINES REPRESENT FRACTION OVER NORMAL

NON STRATIFIED

TYPE 3

-39-

< • • •

\..:- :r~, 00/IATIC\'S FCR 850-lilHEI~ FI~. -'-'--..---, ·•. FlliJRE 3. 1'EPm PID ST~O _

- ---------- -------------- --~- -~------------ --- ------------

1.:-FJ(J.JRE 7, I'EANS Al'il STIID'IRD ilEVIATIOOS FOR 300- :oo-Ml Til,IOOiESS FJE!m, ' '" '·. • 'f""44- I I • I

FIBjRE 8, !'EMS AND STJl/llMD JJEVIATIONS FeR S:D-113 DEW-POINT DEPRESSIOO.

··--------~-----~~-- ~---~----------------

Flll.IJ£ 9. foEANS IWl STAf!li\JU DEVIAT!Il\B FOR 700fll DBHU!tlf DEP~IOOS,

-4(,-

----~-----~----~---- ----------------

--~-- ~-- -~--~

~-------- ---------------·---------------~---

_j..;-IDJ~ AMl Sf~ IIV!ATI!l'IS Fffi lrn!CAL VEl.OC!TlES !liE ID IIRI!CllY IUM:CTIOO.

-SC-

------------------------------

Fig. 15. F statistics.

-52-

...

Z - STATISTICS TYPE 1 I TYPE 2

I - ST,TIST!CS . . , O HPE 1 I lYPE 4

Figure 16. Z Statistics for 500-mb Heights Between Selected Types.

-53-

E~Y INT~RCEPT ,06804 ,2170hl331 -.oo089•< 11 .24021•1341 -.oo594*129l

BF~ INTERCEPT . ,06952 o24o79o(331 -.00047•,1 5) .20349o(341 -,00507*1301

TU5 INT~RCEPT . ,17249 .4589Sol33l -.o~oh•l s1 ,26o61ol341 .oo121o1131 -,o008ooC141

~AS · INTERCEPT -1,18366 .• 15!;;77*(33) .2Z306*~3"J\ .uOO~'"'~t(20} -,OQ07'1o*Cl7J

PHX INT~RCEPT ,00096 ,3564h(331 o47431ol34)

ruil INToRCEPT • oo2s1 o133750I341, 'o28390ol331 o00193o131l -.,oo2i80(321

SAC INTERCEPT ,10279 -.0006201 51 o32l550(33) o00324o(311 .146450(34) -.000350(36)

SMX INTERCEPT , 09844 o302290I33l -.00065ol 51 o16514o!34l .003160I27l .000830I141

BI~ INT~RCEPT 1,85752 ~.00114o(19l o156070I341 ,~6185o(331 -.OOI430127l o000700(20l .oo046oc 3)

s~c INT~RCEPT -,03137' -,0010001 1l. ,23725>(33) o00~98o( 9) o18188o(341 o001370I211 -.oo6010!29l

BOi INT~RC~PT ,-,06574 ,336530133) o22974o(34) -.oouoo(111 .00049*( 81 -,000730( 1)

BNO INT~RCEPT , 09748 · ,26043o(33) .24405•!341 -.oo094ol 11

GTF INT.RCEPT 3,16139 ,33518ol33l o29178o(34) -.oo~75ol191 -.0010!0(131 ,00033•1 6)

MSO INTERCEPT ,11549 o28~43ol33) ,o22559o(341 -.o0233o( 11 o00104iol 2) o00061*( 6)

PDT INTERCEPT , ,03195 ,44~7501331 o22937ol34) -.000480( 31

EKA INTERCEPT ,19226 -,00125o( 5) o230820(33) o00178o(121 .169830(341

MFR IT'ITERCEPr -4,15624 ,26840•133)' -.00092•< 1) .20774ol341 o000990(201 -,o012B0(111

SEA INT~RCEPT , 05378 ,52149,ol331 .~2113o(34l -,oo133oC13l

fAT INT~RCEPT -,03452• o22850o(331 -·00110*( 31 o00036ol 81 o16439* I 34 I ,o0086ol22l

~AX INTERCEPT , 07503 o30458*1331 -.000330( 7) o23114ol3~l .oo2:Soo<2il ,0090501291 -.o1313oc30l

M~F INTERCEPT -,09891 ,335280(331 0 00163*(21)_ o21323o(34) ,003310(271 ,000140135)

RNO INTERCEPT , 02497 o20151ol33) -•00116*1 31 o15950o(341 ,01013* 129) -,Q1712oi3QI .o.QQQ91oJ_.~J.

SAN INTERCEPT , ,13372 ,33453* 1,331 o215580(34') -, 000680 I 51 -,003550(28) ,000430116) o001280(2S)

INW INTERCEPT ,01193 ,3316501331 o3467h(341 o00242ol271 -.001960128)

5F0 iNTERCEPT , 08645 -o00212ol 1) o22862o(331 o00196o( 2) oOOOB2*1Hl ,001700(251 .109670(34)

;

P!H INTERCEPT -3,73669 ,34325ol33l -.001360( 1) o19136ol34l o000910(201

GEG INTERCEPT , 05899 o33499o 1331 •.263960 (341 o00507o (27) '

Ril: m!~!7~g~P~. 00126o < '!~54~0Q153o 12fil .002030(251

POX INT~RCEPT -,01869 o576220133) o243680(341

O~M INT~RCEPT , 14919 -.0015401 11 ,2755001341 ,.00346oi2Bl ,163410(33) ,o01760(25)

A~W INTERCEPT , 06469 . • 2158501331 .zosuo,l~41 o00348oi271

~ST INT~RCEPT ,14 739 -,0010601 5) o30714o(33) o00076oc'6l o003420(271 o00164•112)

5~M INTERCEPT ,11893 -.ooosoo1 S> .247240(33) .oo215ol25l -.oo197ol u ,00134ol 21

EUG , INTERCEPT , 00907 ~o00178o( 3) o31083o(331 -,o.Ol45ol14l o001370( 41

FCA INT~RCEPT , 07619 o004440(27l o233270I331 o00449o(2~1 ;oo_1280( 2l

HVR INTERCEPT . 0 10487 ,254230I33l ~·U01770I 11 .~o322o<271 .oo7290(301 -,oOB200(29l .ooOB3o< 4l ,ooos7oc 21

H~N INT~RCEPT 3,11022 o22090ol33l o003170(27) o00463ol28) -,0007301'91 o000260I 81 o093360(34)

GGW INTERCEPT , 08209 -,00150•1 11 o1b8910C331 o00645ol291 ,1749301341 ,000300( Bl

~WS INTERCEPT ·,05811 o28517~(331 oZ08810(341 ,00907•129) -,0014901111

EKO INT~RCEPT ,07467 -,OQol.480I ll o3U4920I331 o00476ol271 o00021o(35) o000890( 4)

WMC INTt:RCEPT -,06662 -o00041ol 3) o269U30(331 o00164o(211 o112910I341

F~G INT~RCEPT ,25671 -.003060( 3) o30588ol331 o00079o( 61 ,178840(341

Figure 17. Final Regression Equations for Non-Stratified Data.

-54-

ELY I1nC.1~CCPT -.17.:>71 • 221;159• ( jj l o0Ul42*{2l) .19979•<34) -.001"'8*(11) .oooo6•139l • OtJ016* (35l

BFL If,.ll:.t-.CEPT .120:.78 o23<::3U• (31+) olSbll*(jJ) -.uOOlO* (37) .onoo6•C38l o00022$(36)

TUS 11-lTt:.HCEPT .21000 .29lti9•(.)4) ·3780l*{j3) -. uolb4• t 3) -.onu96*(14l ·00195•(11) .00026*( 8)

LAS !NTl:.h.Ct:t-'T -·1U087 .14017•{.).3) .ooooo•<39> -. uooas• 111 > .onootpC&(40l .ooo32•<16l .00059•<21)

PHX lNTE:.hCEPT -. O~c15 .341)07•<.33) • 35386* ( J4) • tJ0314* ( 27) .ono07*139l .00065•116)

YUM Ir~TE!<CEPT • Oti309 .12bl6•{.!)4) •OU~l:.::•C.Hl ..L4789•<33l -.00242*(32) -.oooo:5•<36J .ooooe•c3eJ -.oaoos.cnl •0007,...( 2) -.00095•(

SAC INTEHCEPT .2~475

-.00155• ( 1) o22975*(;)3) • 00209• ( 2) -.00010*(37) -.00040*(36) • 00217* (12) -.001'+2•{11)

~MX INH-HCEPT .21415 -.OOUld•<37l ·2~0d7•<33) • U0216• ( 4) .00036*C35l -.0006R*( 5) .00084*<14}

BIL INTI:..t{CEPT 2o6!:l935 -.OOU0.3•<19l .ld!lU6*(33) -.u00l0•(37l .00009*(38) -.ooo70•(23l

SLC lNTt::I'\CEPT .-.0.:)646 -.oou7a•< 1) • 27 d53* ( ~3) .:!10219• (34-) .00112*( 9) .00229•(26) -.00592*129) • 00110• 1211

801 INTt.t~CEf>T o11+768 • 22b95• I 34) ·2b9d1* <.:S3) -.J0024~d37l .00377•132) o00170•( 2) -. 00080* ( 1)

E:INO IIH~RCEPT .2:;,064. .20584•(::,3) ol-1767*(34) .00193•<22} -.ooo1a•<39l -.ooo17•<3BJ -.00017•<41)

GTF lNTt.i\CEPT .3o50193 .30~27•<:!14) o3UG99*(.33) -.uOOti3•(19) -.00168*(13) .00107•( 2) -.00014*(35)

MSO INlt:.hCEPT -.00476 -.OOl~tl*( 1) .!7ulq.*(.34J .19751•<33) .00118*( 4) -.00131•< 3)

PDT INTCRCEPT oOl-.04 o4+9b2!l• (33) ol7111*(34) -. 00051• ( 3)

EKA INTt:kC6PT .2>952 -.00240•< 3) o0017J*( 4) -.ooou•<3~l -.00167*<171 ol4264• ( 33)

MFR lhiTC.RCEPT -E>.24331 .27124-•<33) -. 00115* ( I) .00263•(12) .00148*(20) -.00225>&d11) .13777*(34) -.00122•114)

SEA lNTEH.CEPT .28752 .55103•<3.3) -.00192*( 9) -. 00014• (39) .15760*(34) -.00018•<42)

FAT 1NT£1<CEPT o11776 .19920•(.33} -·00010•(37) .00125•<21> .QOU41*( 8) .01544*(29) -. 02205• (30)

LAX it<TERCEPT o21o81 .32'+85• (,!13) -. 00012* (37) .00393•131) .19701*134)

MLF 1!-.Ti:.RCEPT -·2o931 .22.303•<34} .~0315•<33) .00150•121) .00023*(35) .00293•125) .ooooa•<39> .00087•122) .oooo7•<4o>

RNO 1NTEkCEPT -. 0L(.097 .2670S•(33J -.00150*{ 1l -.u0156•<23l • 00080* ( 6) .17053•(34) .00748•<29)

SAN lNTi;.RCEPT o1U..336 .26>t4-l•t::i4) • .3!;)354* ( 33) -.uo114• < 3)

INW IIHC:t-<CEPT .Du186 .37b6'1-•(33) o41589*(34) oU0197•<2bl

SFO Irnt::t<CEPT .29140 -.00160•( 1) -· 0001~* (37) • 00081* ( 6) .00155*112) o17384•(33) • 00202* C 2SJ

PlH IIH~HCEPT -6.10b00 .29185•<..33) -.0011.3*( 1) .1 74'1-fl* ( 3L(.) .00148*(20) -·00483•129) -.00007•137)

GEG INTC:.HCEPT oli.t804 .26u8u•<33l -.oo.::o7•< 1) oU0187*( 2) -.00021*(38) ol5070•(34) .00139*(24)

RBL INTI::kCEPT oH868 .26blO•t~3l -·00092*( 1) -.uoo1o•<23l -.00007*L.Hl o00140*( 2) .00264•<25} .OQ654•(3Q) ·00131*<10)

POX 1NTt:.kCEPT -.01+583 .~OU55•<33l o2Lf960*(34),

OLM liHI:.H.CEPT .uoss -. 00128•' 1) o31Q45* (34) oU0104•( 41 -.00053*( 7) o00210•(25J -.00013•(371

ALW lNll:.t.:CEPT -·· 7!.l87

o189U.l* (.~3) -·U02.3b*( 9) -.00017•<37) -.00020*(Lt1) .OQ170•(20l -.00012•<38}

AST H.IT'-.hCEI-'T o3cl28 -. oouSu• < 51 .2.7'+52*(.33) -.voo;,n•<37l .00121*(14) o00157•(21)

SLM lNTL...HCEPT -. Ojo65 -.OOUSb*( t>l ol9258*(33J olr0214-3•(25) .13960*(34) -.0016'*' 1) .00158*( 4)

EUG Il~T~:.,<CEP r -.21U63 -.OOu'+U* ( 5) • .:::su7S,..t33J .uo236•< 2l -.(.10171*( 1) I 00207• (21)

FCA' llHt.J,C£::~T o37t.~76 .26.;,7'+•<.!1;;:,) oOQ~98*(27) -.u002'+•<~8l .Of'\156*<18) .ooo22•<36J -.00011*(37)

HVR 11\lli:..KCEPT -4.1'+u91 .22737• (.):3) •0UU7'+*(~7) -. uo007• t 37 > .13662*(3'+) -.00532•<31J .00095*(211 o0010h(2Q) o0022S*I2S) .ooue•<

HLt~ I•-.ITL:.kCS:PT <:::.51.355 -.001.1'+0•< 1) .0015'+•<21) • .22741•(33) -. 00207* ( 9) -.ooo63•t19J

GG'ri liHt:t<CEf-'T old959 -.0011~* ( 1) ol!:lU4'+*(.34) • u0026• t d) • on382* (291 -.oool2•<37l .15'+99*(331 -.00119•( 9)

LWS IIH~t<CEPT -.au 735 • 30.3't9* {,:,3) o0LJ1.3c::.·H27} -.U0011•<37l .ooaso•<.c9J -.OQ136*(11l .00169*( 2l -.00097•( 1) .00012*(42)

EKO !NT::::KCEI-'IT o2ll39 o31Y20•(.:.3) -.U0124*( II .00230•<20) .OI'JU32*<3Sl o00979•{27) -.00011*(38) -.00538•(31)

,-Me 1N1 r;.J~CEPT -.2So22 .VOC..3':i,..(.C::ll oi::9'+6U*(33) ol1723•(.34) oOfl013*(39) o00790•<29) -.00253*(28)

,FLG lho1e.KCEPT .37.1.23 -.0012~*( 3} o.3du37•C33) .~05.38•(27) -.00013*(37)

Fig. 18. Final regression equations for non-stratified data including depression fields.

-55-

1)

2) -·001050( 1)

ELY II<TERCEPT -.066I5 ,13838•(331 o00035*(351 ·15762*(34) ,Q0841*(30) ,00381•<27) .00096*(181 ,00033•( 81

8FL INTERCEPT ,07771 ,25754o(331 -·00248o( 31 o00053o(2ll .00012*( 8) .oo17oot 41 .15159*(34) -.00293•(27) .000440( 61

TUS INTE~CEPT .18397 ,33405o(341 .4a874ot331 -.oo157ot 31 ,Q0006*{35) ,Q016D•tt7J -. 00148* (25)

LAS INTERCEPT -.03lJ.9CJ • 00023• ( 35) ·19&35*(33) -.15885*(34) .00047o(221 • 00045•(26) .000900(251 -.oooo5ot361 .00033•<16) -,00233•<27)

PHX INTERCEPT ,QOb62. ,58129o(331 .32036*(34) .00166•<32)

YUM INTERCEPT • 00222 ,47068•(33) o000270(351 o00169*(27) o000730(17)

SAC INTERCEPT 3.22'1-23 -,00365•< 3) • 006220 ( 31) o16B12*(33) o001400(ll) ,Q0284•(30) .002090(211 o00222o( 5) -.00078o(20l

SMX INTERCEPT .05202 ,33o29ot34l - •. 00103*1 51 .20319•(33) o001410(ll) ,00111o( 4)

8!L INTERCEPT -.50975 ,26083•(33) -.00074•(19) .u0025•t351 • 00086•(20) .09776•(34) -.00052*( 4)

SLC INTERCEPT -.08467 -,00121•< ll ·28613*(34) t00181*(21) o17670o(33) -,00819o(29) .00320*(27)

801 INTERCEPT .047114 -,00155•( 1) o21767o (33) '28395* ( 34) .ool77o(181 -.00393•<32) -.00243*(171 -.oo013ot36l

8NO INTEI<CEPT -.05068 •,0015fi.•C 3) .19906*(33) .20866•<34) -.02099•(29) ,QQOS1•C36) .001250{12) o00ll5o(16)

GTF INTERCEPT -1.96049 ,19283•<33) .21394*1341 -.ooo4o•t191 o00183*(27) .oooaaot20l '00151• ( 21 -.oo160o( 11

MSO INTERCEPT -.09989 ,23685• (33) o000260( 1) .00187•< 2) .13143*(34) .00026•(35) -.00211*( 3) · o00133o(15)

PDT INTERCEPT 3.17146 ,40'+72• (33) ·284530(341 -.00075*(13) -.00077*(20) -,00124•(26)

EKA INTERCEPT ·15492 -.00353•< 3) • 00248• ( ll) .00192•< 4) o170410(33)

MFR INTERCEPT -7 .. 39576 -,OOl4h( 3) • 28004* ( 341 .20Q.74* (33) .00175*{20) .00202o(21l -.00152*(14) .ootD6•Ut>

SEA INTERCEPT .08867 ,39b64• (33) .23825•<341 -.oo1o2•<13l .002040(12) ... ,00098$( 1)

FAT INTERCEPT -.03295 .33748•<33) -,QQ063*( 1·l o00133*(2l) .12963• ( 34) -.00129o(25l .00253*(28)

LAX INTIORCEPT -2.12165 • 22322• ( 33) .t35B6*<34J -.ooo5s•< 7> ,00052*(20) • 00082• ( 2)

MLF INTERCEPT .06004 ,24003o(33l -·00078*( 11 • 003270 ( 271 .ooota•C35) ,00099•C211 • 000590 ( 4) o14543o ( 34)

RNO INTIORCEPT -2.94712 ,29259•(.3~) .ooosz•t35J .16488•(34) .00173*(27) -.00015•(36) • 000270 (24) o00102o(26)

SAN lNTiiRCEPT -.07137 ,56125• (33) o00123*(22) o000460(35) • 01157• (30) -.003670(28) -.00138*(25)

INW INTERCEPT -.00077 ,27716•(33) ·19840•<3'1-) -.00646•<29) -,00411*(31) -,o0093•1l3l

SFO INTERCEPT -.09606 -,003460( 3) o001530(ll) -.013830(29) .00037*( 6) .16399•(34) .00235*(21) o00154o( 5)

PIH INT~RCEPT o15908 ,00072•< 1) o002320U31 e1777a•<34) ·15169*(33) -.00528$( 3) .00227*( 5) -.oo5B7ot30l

GEG INTERCEPT .09294 ,33901$(33) .32166*(34) .004220(27) -.OOll6*U1l

R8L INTERCEPT -.07318 -.00139o( 11 o00191*( 9) .17057•<33) .00095•(24) .0005h( 8) .001100(22)

POX INTERCEPT .12057 ,41956.(331 • .360iJ.4*(3lf.) oU06410(291

OLM INTERCEPT .12164 -,0021b•< 1) .30905*(33) .00523*(27) .00108*( 2) -.00154•(161 -.00276*(26) -.00124•(24)

ALW INTIOHCEPT -.04986 .20o7S•t33l .t8936•t3'J.l -.ooota•<3S> .001910(151 .01131•(30) -.000240(36) .oot93•<13J

AST INTERCEPT ·22563 -. 00169• ( 3) o00170*( 41 .19175•<33) • 000850 ( 9) ,00319•(30)

SLM INTE.RCEPT -,05054 -,00070o( 31 o21B570(331 oU0207*( 4) -,0016l*U5) ,24473•(341 -,001880( 1)

EUG INT~RCEPT -,1.5475 -.OD15ts•< 31 .30335*(331 .u023S•<25l • 00189* c 4) -.00284o(261 .00957*(29) -.00106•{15)

FCA INTERCEPT 4, 60621 ,00537•(27) .t'l-981*(34) ,(JQ491•<28) • 000950 ( al .ool3aot10l -. 0037'1-* ( 1) •e00022•C35)

HVR INT~RCEPT . o12368 '· ,23U'+3•<33l .ooo34*C:55l -.uo_029•<36l -.on188•tlll • 001'1-3* ( 12) .10824*(3'1-) o00136• ( 18)

HLN II<TERCEPT -, 01613 ,23o5o•t3.3J .ooo2S•t35J -.uoo15*<36J e00160*(21) .ooo87ot22l • 00230* ( 2) -.oo195ot 11

GGW INTERCEPT 2o3B812 ,33484•(.33) -.00161*( 9) -·01251•<29) e13ti46• { 34) ,0016q.•(13) o005970(30) -.00062•(191

LWS INTEhCEPT -7, 7<752 ,28904$(33) •2U056*C34l .u091'1o*{29) o00189*tl91 -.00355•(32) -. 00081• ( 3)

EKO INT~HCEPT -.06564 -.00138o( 3l .265120(341 .u05220t27l .23979*(33) ,Q0182•C26) .00104* ( 41

WMC INTERCEPT o00658 -.oo1~J'ol 31 -.oo~eHt311 .20512•t331

FLG hNTtiHCEPT .19;;89 -,oci147•t SJ .ouu'+S•t 8> .C3'+15•t31+J

• 001710 (211

.onU2ot141 .oo323•t27l

Figure 19. Fl na I Regress! on Equnti.ons for. ,Type

-56-I ..

.00188o( 26)

,Q019&f*C26)

.oooe4•C241 .00164o (25)

-.00564•(29) -,000610( 5)

.oo3o3ot28l

.ooos9•< sJ

o003880(321 -.o0315ot28l

.o0089•t 71 ":o00i.llot20l

.006630(29)

.oooa9ot23l

,00047•< 8)

o00072o(2Dl

·00219*( 2)

E~ Y INTERCEPT -.1~746 .ooo24•<3SJ -·D018'6*tlll -.uo233•<2S> -.oo025*(36J .oooao•< 3> -.ooo4s•nS> -.o684S•<34> -.oD312•<29J

8FL' INTERCEPT -,01780 .oooza.c5s> .ooo13*<36l .aoo:so•<16> -.ooo72*<17> -.ooo61*<2S> .ooo~s•na> .ooo3o•<23>. .ooo32•<1&~->

TUS INTERCEPT ,10927 -,OQ112•< 3) •00496*< 91 .30962•<34) -·00268*UO> ,Q087'"'*<29)

PHX INTERCEPT -4,6.634 .oooa~•<22> -.ooo33*<3S> .ooo74•< 3J .oo112*<20> -.oo1S3•< S> .oo162•<17> -.ooo93•<18> .oolo6•<1S> -.oo74'+-•<29> -.ooo67•<23l

TUM INTERCEPT .19166 .00218•<26) -.00161*( 3) ,QQ096•< '1-) .Q0099•(22) ,QQ081•(11) -.00123•(18) -.00241•<29) .00033•< 8) .00136•(14) -.00171•<24,)

SAC INTERCEPT , 04879 -.oo707•(j1l -.ooo~S*( 6l .ooo4~•(1~> -.oo074*(15l .ooo76•(~2l .ooo~~*(16l -.ooo6~•(26l .oooo6•(~6l .ooo26•(21l

SMX INTERCEPT -, 00674 .ooo15•<3S> -.ooq.os•czs> -.uo14S•<17> .o013S•ne> .o7514•!:5q.J -.oo17D•<31J -.oooos•<36J

8IL lNlERCEPT ~.25d16 -.oou75•<2~> .00162•< 11 -.ooo7s•<19J -.o0159*<24l -.oo~4'+•<2BJ .14172•<~'+> .oo9oh<~o>

SLC INTERCEPT -.15066 ,002'+2•<21> -.-00347•<171 -.llo136•<~1> -.oou9•t22> .oooeo•< 6J .oo211*126> -.oo224•< 9> .oo1~6•t24l .o91~5•<~4l .oo419•t27l

80I INTERCEPT ,06032 .00'+29•<1~) -.00151*(221 ·00119•<14), -.00411*(23) .00161*(21) -.01055*(29) .oo7'1-3•(30) .00192•<17) -.11628•<33) -·00047•136)

8NO INTERCEPT -, 09465 .D0101•<21l .oo22o•t111 -.uoo9s•I10l -.12638*(~31 -.oo766•129l .oo12e•< 21 -.oo2oo•< 31 .0014o•< 41 -.o0235•128l

GTF INTERCEPT -.15252 -,OOU38•<23J -.03105*132) -.00187•126) .Q0021*(36) .00235•1241 ,QQ280*(22) e006f.l.7•t27J -.00640•<30l -.00182•<18) e00074*( 7)

MSO INTERCEPT -,4875~ .00124•!211 -.ooll4*<11l .23224•<33) -.oo267*<1Bl .ooo4'+•C~&J -.oo203*t17l -.oo14B•< 91 -.00108*< s> ,00138•< 41 .oo256•t32l

PDT INTERCEPT 3,99962 -.ooz.D9•< 11 .0023'1-*<12> .ooo3a•<36l .oo1s2•< 21 .12502•<331 -.oo1S9•t17J -.oooss•<20J .ooo79•< 7> -.00121•< s> .ooos4•<15>

EKA INT~RCEPT 5, 022~7 -.ooS01•<3U -.oo278*<191 .l.l0161•<2o> .oooso•c2e> -.ooo3S•t3Sl .oo212•1111 -.oo161•<12> -.00248•<241 -.oo1e9•<25J

MFR INTERCEPT -.04398 .00120•(21) -.0003'+*(36) -.00036•<351 .00130*(11) -,Q0100•C10l e00135*( 9)

SEA INTERCEPT -4;12261 -.001B7•<17l .oo1o1•<191 .oo172•<t6l .oo204*<12i .oo130•<21> -.ooo62•t35l -.oo497•t32> .oo779•<31l -.00648•t27l

FAT INTt:.RCEPT -,05520 .oos67•<29l .oo153*t22l -.oo19s•t2.5l .ooo27•t211 -.ooo7~•t u .o3272•t34J .oooo6•<35> -.oot46•<2s> .ooo64•t 91 .ooo31•<24>

LAX INTERCEPT :,04049 -.Oo106•( 1> -.ooo15•(36> -.uo442•(25> .oo114*( 9> .ooo75•(22> -.ooo96*(17> .ooo79•(16>

MLF Ir<TERCEPT -.~1564 ,Oo2S9•t,1> .oo166*t221 -.uo18o•<3o> -.oo396*C29l -.ooo2B•t36J -.oo163•< 11 .oo133•< 21

SAN INTERCEPT , 0690~ -.00101•< 1> -.oo1oo•t17> -.ao38o•t 9l .oo183*<10> .o0184•t12l -.ooo2S•< 2l -.oot16•t2&~ol -.ooo6o•<13> .ooo59•C23l .18955•<33>

INW INTERCEPT 1. 0•211 ,0009.3•<2ll ,lJQ190*t251 -.Q0223•<17l •.00175*(16) -.Q0156*( '!-) -.00026*{20) .00053•(35) -.00247•< 3) ,QOJ.I.93•t27l •00237*( 6)

SFO lNTi:.RCEPT .10149 -.ooao2•t31l .Oo179*C32l .oo229•<28l -.ooo67*117l -.oooe8•t21J -.oo274*t29J .oo428•t3ol .00182•<25> -.ooo99•<26l -.ooosl•tt2>

PIH lNTC:KCEPT -6.2o839 -.ooo22•<3Sl .ool26*<l6l -.uoB12•<27> -.oooe&•tlSl -.oo325•t18l -.ootoo•n7> .oot82•<21J .00166•< 91 -.o1421•t29l .oo144•t2ol

GEG . INTERCEPT .32361 .oo1c3•<11> -.ooo4o•<:56l -.oo37o•<1o> -.oo218*<22> .oo493•t:51> -.ooo3o•t35J -.oo146•t24> .oo3o'l-•<32> .oo279•t12l -.1'1-651•133>

PUX lNTEHCEPT 3.87294 .ooo27•t13l ·12450*I34l .u0122•<2ll .oo332*t12> .oo761•t29J .oo18D*C15J -.oo1&~o5•< 9) -.oo1oo•<19l .0015o•< 11 .oot16•Ue>

OLM INTERCEPT -6.23149 -.ooo30•< 11 .ooo5s•<31l .oo111•<21l .oo1'94*t19l .oo15D•t22l .oo253•t27l .oo197•tl71 .o1741•<29l -.oooz2.$t36l .oo783•t3ol

ALW lNTC.RCEPT -.31079 ,01717•<2.7> .ooo79•tl3l -.ooese•<3o> .oot49*C22l .oo1s1•t211 -.o93eo•t33> -.oo120•t241

AST INTERCEPT .1670~

-,00370•< 1l .00304*< 21 ,Q.0595*(28J .00161*(141 .00437•t27) ,11708*<33>

SLM lhiTt.H.CEPT -·1"094 -.D01tiS•< 1l -.oo::568*t30l -.oo1a2•<1't-l -.oo2S2*<17> .ooo23•<361 .0010'7*< 21 .2754&•t33J -.00234•<32> .00124•121> -.ooo13•t35J.

EUG IN.Tt:.H.CEPT o17776 -.ooo21"'t 7> -.oo171•tl7J -.uo16&•<2SJ -.on018*<,5l ... oo1'1-6•t 11 .oo2oo•t111 .ooo&B•tlll-l

FCA li'lllt:::HCEPT , 71<;;79 ,OQj10•<3ll ·00186*t24l -.00338*(21J -,Q003~*(36l o194'+1*(33) .00724*(30) -,0036h(25l ... 00070•< 61 -.00909•(29) -·00116*( 9)

HVR lNTC.KCEPT -.0.3b40 .oot09•<13l .oo319*<27l .ooD18•<~5> .ooot7*C:56> -.oo9o3•t29l -.oou~•t21l -.oo1sa•< 41 .o0229•1 2> -.oo1s2•t 1> .ooo46•< 11

HLN lhiTLi{CEPT .41980 ~00484•( 9) ·00196•<10) ·00202.•<16) .0114-414*(27) .18187•<33) -.00094*(17)

GGW INT~RCEPT -t:,,aul67 .ool6l•<.L5l -·00197*< 3l .oo271•<17l -.onb5'1-•t32l .ooo40•t36l .oo2614•120l -.oo226•t22> .00126•<191 .oOI420•<29l -.oooe6•t Sl

LwS lt..Tt..~CEPT -.2:,678 -,00445•(~6) •00109*<21) oU008~*( 7) oOn470*(30) •00214*(17) -,00197*(2~) -,Q0098•(15) e00196*(12) -,13023•1341

EKO 11-.Tt:.R.CEPT -.O?t,>44 -.0036:!>•L31l ·OLI789•t.29l eu0145*(21) -,00006*(35l e00177•(28) -,00041*( 5) ,Q01l4•t2~l .00073•<15) .00086•126) -·00276•1301

wMC lNTi:.I-:CEPT -23.07(:)3~ -.oou24>t=l2ll ·Oll91*t29l -.u0130•<tll -.ooB20*< 51 .ool77•< 4) ,ao222•t 21 .oos&S•C19> .00255•<121 .oa.4S6•< 3l .oo177•t32l

FLG rt~ T Eh.CEPT .1 7 jSS -.iJOlU'+•< ll -.ov52S•t271 .uo1o7•< f.l.l -,1J0234*t12l .ooo2o•t35l -.oo26S•t25l -.oo153•t18l -.00144•<171 .oo235•t28l .ooo79•122l

Fig. 20. Final regression equations for Type 2.

-,-57-

ELY lNT!:.RCEPT 2t2~LJ19

-.0015o•t ll .00126•t 91 -.ooo53•od19l -.on3o2•(32.l ,oo273•t2~l- -.oo1as•t23J -.oo326~.t3o> .ooaoo•l29l · -.ooo32•1 6> •oo1ni".l 2>

BFL INTEkCEPT -,00004 •,00135ol 5) o0018ool 9) o00293•125) oOOJ~Ool .2l •,00369*( 1) o00280o! ~~ .00145•!22) ,113000I34l

TUS INTE:RCEPT o19398 -,00279•< 1> .oooz~•< 8J .27157•<34> .ooo72*<22> ,ooos1•Ct8J .oo121•t13J -.oo108•t25) -.ooopt•<ys> ,ooo49.t16l -.t56~:5.•d33l

LAS INTeRCEPT 3.98300 •,00253•! 1) o17055ot33l o005810131) .0003401 6) ,00115•1 9) o00122•ll6l •,00087•!20) o00221*130l ,00023•135)

PHX INTERCEPT o18289 ,00474•131) o228850(33) -.00334ot32) .00273*128) -.001530( 3) -.00186*(26) .ooo73ol 8) o00108*(. 9) -,00085•! 6)

YUM INToRCEPT .09103 -.00041•1 1) ··00128•!21) •00109•(16) .ooqo•l22) -,00187•1 3) .ooo5o•l 4) o00317•110,) -.001~901 _9) .14240*133)

SAC INTERCEPT .37265 -.00324•( 1) o00527•1 9) o00885•128) .00098*113) ,13835•134) .00643•127)

SMX INfERCEPT 7o47396 -,00018•1 5) .00419•1 2) -.00098•125) -.00186*(19) ,00034•!35) -.001000(14) .17(000(33) -·17749•134) ,00182*(21) o00129•!26)

BIL INT~RCEPT 2o25429 •,00107•(19) ~.·00135*(241 "o00152•( 1l o00060*!16l ,00065o(13l •o00081*!10l o00055•!20l. o002~8•!27l

SLC INTERCEPT •oO!>o14 •,00876•129) o00156•!22l o00169•(10l .00539*!28) •,00153o(25) •o003.260(27J o00030•(14l o00018*( 6)

BOI INT~RCEPT ··04421 ,00045•t35J .o0154•t17J .00283•<18l - •. 00162*( 3l ,00184•< 41 .oo1.53•C23l -.01456•t3ol -·00146*<14>

BNO INTERCEPT , 00451 -.,.00126'*( 3,) ,Q0669*C25J, uJ1019~(30l -,00088*(35} ,00242*( 4) -.00149*( 2) -,oo305•Cl8l t00158*( &) -,.00027*(36) t001,,8B•Ul)

GTF ltlTERCEPT 2, 9oJ21 •,Ol34.8•t29l ··00186•1 91 -.00069•119l -.01117*!3ol ,0009101 2> .14060*1341 -.oooF•t36J o00218*'1ll -.00171otl4l o00213•(32l

MSO INTERCEPT •, 72807 -,00458•< 3) -·OC561•t29l t20691*(33l .o0500*(21) ,00396*(22) -.00049*(35) .00234*( 5)

POT INTE"CEPT , Od527 ,OOu59ol 1) o00428*( 4) oU0150•t.l7) •,00365*'(28) ,00276*( 5) •,007510( 31 •o00294o(26) •o001_82•! 9) ,148630(33) •oO.ii253*(10l

EKA INTERCEPT -.3.!<85 -,00162•< 7) -.00185•< 2} -.u0414•<17J .00188*(11) ,00140$.( 6)

MFR INTERCEPT -:60107 -,00572•t ll •00285•t 2> .uo5o3ot25l .o0330*t21l .ooo97•t 81 -.oo1~8•t1SI .oo252•t 31 .00157•t22l

SEA INTERCEPT •, 23o60 ,00!>60>t!C. 3> .ooz3~•<2t> -.o1B94•1d29> .oo253.*C2't> -.oo2oa•t 9J .ao113•<1oJ -.oot1B•<22J -.oo1o~•c 2> -.oo353*U8J .oo~1o•C17l

FAT INTERCEPT So540B1 -,OQ036•t 7) •OU32l•t21J t00044•< 8) .00029*(35) -,008Q.5*C lJ ,QQ232*Ci,OJ ~00258*( 2) t00573•t 3) -,00110*(14) -.OQ142*(19J

LAX INTERCEPT ··21722 •,OOU24•1 3) •14978•(33) oU1004•t27l ,00135*(22) ,00267•(101 o00386•!32l •o00057•( 61

MLF INTERCEPT •,2oJ197 .~8107•(,34) -.00153•!13) •00182•(21) -.00059*(15) ,00153*(22)

RNO INTERCEPT •6, 74983 -,00122•< ll .oot7~*it21J ·17937•t3~> .oqos7•t35J .o.o157•t2q> -.ooo'+6•C36J .oo~B7•C27J .ooo97•Uo>

SAN INTERCEPT , 06186 •,00157•( 31 o2332l•t33J ·00249*(121 ··00129*(131 •,00076•(141 •o00081•!,24l •o00094 .• (25l o00059•! 8) •oOOQ44•(36l o00026•l3~)

INW INTERCEPT , 02336 ,288900(341 •ooD227~! ll "o00196•t25l .o0063.,t22l ,00167•(11) •,0003~•!351 o00037•t 8) o00009•!36l ,00~53*!31) o00215•!30l

SFO INTERCEPT , 09740 -.D0412•C 1> .oo~toa•< 9> .uo25t•< 21 .oo~2~*<,4> .oo26hC21J ~.a1t46*C29> .oote7•<1n

PIH IoHERCEPT o04372 ,00087•(35) ··01277•.(291 oU1632.(30l ,34070*(34) ,16442*(33) •,00117*t10l ··00248•(18) •o00331*132l

GEG lNTt::H.CEPT •'+.44669 oQ0362•12ll -·0049~•(25). ·o0135•(22) ·00159*!23) .00094~(,9) -.oo025•!36) -.oo335•t121 .qo362*( 21 -.oo3o1•(10) ··00211*! ll

RBL INTERCEPT •o0H63 -,00217•< 3J -.oo1oo•< 2l .oo337•t23l .oo.a&6*U3> ,oo230•C21J -.oo?13•tlt> .to!+55•C34J

POX INli:::RCEPT -7,92735 ,0032.0$(21) -·00162•< 1) t00495•( 2) -.00250*(15) .00180.,(;9> ·01002~.(28) .oo589•<27) .13352*(34)

OLM lNTEkCEPT ·1G.U3 ,.00139•t3ll _,p0484*1 ?l •u0189•t2ll •. on015*(35l ,0024.6•t 91 .oo638•t28l ··14954•t33l -.ooo95•t 1>

ALW INTJ:.f<CEPT -.22081 -,00181•< ll .o0.313*C 9J .uoo78•< 8J -.02156*C30J -.oo420•C26J -.02265*(291 -.oo39o•<25J .00252*<17) -.00215*UOJ -.oot04*C15)

AST INTI:::f,CEPT , 50027 .D0221•~2:1J .oo546•12~J .uo339•C 21 .o0747*C32) -.16543•<33) -.oo79~•C29J -.oa155•t22l

5LM INT~f<CEPT -.3*!89 -.ooz.17*~ .. 1J .otJJf;IS•< 2> .ll0287•' 9> .on221•C22> -,ooo26'id35J .oo162*(21>

EUG INTEHCEPT -.09~98

-,OO~lO•C 1} .oOtt17•C 2) •i.J0324•C 9l ,Q0344*C32) -.00296*(1!0) .00350•C1~J .00665•(2~)

FCA INTEkCEPT - o2d476 -,00019•CJ5) -·U0~07+C15J •I:J12BS•C3QJ eOlll.BS*C17l ,00301•ClOJ ,QQ062*( 81 .oott-79•< 9) ,1lf.385*(33) .12495•<31+) .ooc'H2*C29J

HVR IIHEHCEPT 10.37662 -,UO.:!.~Q$(191 -.01060+CC9) •Ul.074•(3U) •?3675*(33) ,00148•(23) .00210*(25) ,OQ072•< 71 ,00553•(28) ,00041•(35)

HLN Il'tTt.RCEPT -.2UJ.18 -,OOlUb*( .3J .00036*( 4) •eu1636•(30J dA924*(3f1.) ,Q0397f(32) ,oo306*{28J ,Q0154*(21l -.00813*(29) •,00131*<26) .•00065oll( 6)

GGW ll'.l<kCE~T o4%55 -,000H)•C35J -.00015•<19} ,uo17b•CUJ .15318*(34) ,00112*(27)• ,Q0346*(28) -.OQQ94•(26J ,00019*C56) ,OQ091•C18) ·00081+C21l

LWS X..nLhCEPT -, 0:j910 -.0013tl•< 11 · •. uU13tt•< .c:J -.ooo46•<35J -.on~11•< 9> .oo696•<23J ~.oo378•C17l .21125•<34) .00139*<16> -.ooo29•C36J -.oo2ll9*<1o>

EKO lNTI::.kCEPT .lu274 .ooua6•L~5J ·01742•<29> -.lJ0134•< 1> .oooa7•<21J -.oo397•< 9J .oo411•<1oJ .ooo73•U4J -.ooo70*Cl6>

WMC lNTC.:KCEPT -1~h9b106

.oouo6•C.3!.>J -.00(16q•C36J .u0216*C21J .o0328*C20J -.00455•< 3) -.2560&•C33J .oo307•< 1J -,0027'+•< 9) ,o0068•C14J

F~:oo3~~!~R~~Pr.oooa5•< ·~~'+ 0:uoo72•131J -.onua4•< 1> .oo1o7•<t6J' .ooo39•h6> .ooit'6~·c21> ,oo573•<27l .o:J~1S2•<12J" .otooa•t29J

Fig. 21. Final regression equations for Type 3. -58-

TUS INTERCEPT 1.19157 -.ooo32•d3SJ •00214•<22> -.ooo72*< 1> -.oo347*<26> -.o139S•t3o> .ootl'l-'41( 9> -.ooo'S9•Cl4> -.ool29•<25> -.ooo3l•U9>

SAC INTERCEPT ,18502 .22777•t33> -·00~+59*<27> -.oo07:5•< 3> -.19361*<34> -.ooo92•<11> -.ooo2.9*< 7> -.ooo4B•U2> -.oozso•<29> .ooo9o•<1B> -.ootot•n7>

BIL INTERCEPT -.132'2 ,QQQ19•(35) -•0069'1-*(31) el1648*C54) •00082*<:32) -,QQQ64*( 5) ,QQ062*t 4) -.Q1973•C~O) -.00452*(29) ,Q0609•t28) •DOOSB•H 6)

SLC INTERCEPT -.93180 .61962•133> -·00668*127> -.o1026•129l .oo082•116l -.ooo19•1 7> -.ooo•1•1 1> .ooo22•12ol

BOI INTERCEPT -,q9960 .00091•(15) -·00024*{13) -.oo132•tl'J) e00~81*(22) -.00161•t12) -.21633*(;33) .00236•(21) -.00204•(25) .00009•t35l .ooo3o•t e)'

BNO INTERCEPT ,14q37 -.ooo22•<27> ·00237*(26> .ooo94•< 9> -.ool56*tl7> -.oo592•<31l -.oo92S•t29> .oo317•<za> -.25240•<331 -.oo096•< 4l .oo3B4•t32>

GTF INTERCEPT o05877 -.oooo7•<3S> -·00192.*(25> -.oooz8•t36) .o1816*<30J .ooo99•t24J .oo428*t27> -.oo136•tlol -.24995•<331' .oo1o4•< 9> -.oo294•t29>

MSO INTERCEPT -.26181 .Do293•<21l -.ooo23*<36> -.ooo4B•<3Sl -.oo19S*<24l -.oo696•<27> .1o87o•cs4> .oo11h:tl4> -.oo192•<25> .ol466•<3ol .ooo&7•<16>

PDT INTERCEPT , 05J21 .oooo4•t29l -.oo1o3*t26l -.oo115•< '1-J -.ooeez•t31l -.oo15S•<U> .oo208*t17> -.oo231•UB> .oo47B•t30l .ooo11•C36l -.oao&~-2*<15>

EKA INTERCEPT o1091l .00093•122) -·00208•1241 -.uo178•128) ·00142*114) -.00346•1 ll .00052*116) .ooo87•117l o00257•1 2) -.00137•111) .00132•125)

MFR INTERCEPT -.04190 .oolD2•<22l .oo2so•t21> -.oo531•<32l .oo133*t17l -.oozsa•t23l -.oo337•< u .oo154•<12l -.oo157•<18l .oo268•t 2> .oo&2B•t27J

SEA INTERCEPT -.79895 -.00054•<35) ·00020*(201 .01377•(32) -.Q0253*{17) -.OQ859•t28l .00160*!231 -.00108•( 4) o0017B•<Ul -.00183•< 3) ,QQ180*( 21

FAT INTERCEPT .15568 .14673•<33> -·00368*1271 -.uo1oe•< 3> .ooo26*< 6) -.ooo91•<17l ,oo373•t32l -.oo279•(29l .00425•<3ol

MLF INTii:RCEPT 1.8728• .00128•121) -.ooo•7•1191 o00131•111l -.00172*125) -.00547•1301 .00045•1 9) -.00037•117) .00028•116)

RNO INTERCEPT .18502 .22777•<:331 -·00459*C27l -.oo073•< 31 -.19361•<341 -.ooo92•<11> -.oo029*< 71 -.oo04B•<12J -.oo250•<29l .ooo9o•<1Bl -.ootol•t17l

SAN INTERCEPT -, 00363 -,00228•(171 -.00026*(351 eU0012*(36) ,Q0555*CHJ -,0026'+•125) ,Q0100•<11J -.00519•C29) ,00293*(30) .00076•(18) e00050•C24)

SFO INTERCEPT oOE>2E>8 ,25716•<33) ~·00121*(11) -.18021•(3'1-) ,Q0099*(26l -.00023•t 7> -.00221*C28l -.00607•<29) ,Q0514*(3Q) •,0011D•t17l ,QQ081*U8l

PIH INTERCEPT -.03115 -.0!032•<3ol .oo290*<27l -.oo6q8•<2Bl -.ooo7e•t24J -.oou4•(15J .ooo4B•t16> -.23369•<33> -.oo176•<26J .ooo27•C 8> .oo016*t36l

GEG INTERCEPT - o17602 -,ooo6S•<35l .oo23l*<Zll -.uoo42•t36J -.oo260*<17l .ooo72•t 8> .oo411•t14l -.ooo14•< 7> -.oo226•C13l -.oo131•<22> -.ooo97•t 3J

RBL INTERCEPT o129q8 .1816~t-•<33J -.oo272*<27J -.ooo7o•t 3> -.ooo'I-0*<12l -.u4e5•t34J -.oo2B7•t29l -.oo157•t17> .ooo85•Us> -.oo252•t1U .oo148•C13J

PDX INTERCEPT -.22079 .oo&B3•t31l -.oo2&8*<3o> -.ooo79•<3S> .ool84*C25l .oo194•t11>· .oo121*<15l -.o1976•t27> .oo732•<32> .oOJ9q.•<21l .oool2•t36l

OLM INTERCEPT .036'1 -.oo243•< 11 •00129*t 21 -.oo517•t26> -.o2450*t29l .ooo36•<36> .oo733*<11l -.oo526•<12l -.oo511•U7> .o0289•U8l

ALW INTERCEPT .02036 .00182*130) .00097•112) -.00018•113) -.00033•110) -.00004•136) .00046•115) -.00020•1 81

AST INTERCEPT ... , 05ij.Z::;) -.ooos7•t 3l' -·O'I-087*t30> .42729•<:341 -.oo2B3*t 11 .oo190•t '1-l -.oo373•t25> -.oo4o7•<3U

SLM INTEkCEPT -.15127 -.0033hl17l ·00207*121) ·0009••112) .00165*111) -.001&8•114) .00134•110) -.oo288.id26) -.00573•132) .00225•118) -.02037•129)

EUG INTERCEPT ,1q349 -.00298•<26> -·00203*t17> .u0113•<12l -.oo249*<18l -.o0226•t10l .ooo71o:t35l ,ooa39•<32> .oo259•t31> .oo3o5•<11> -.ooo&~-9•< 1J

FCA INTERCEPT -q,30501 -.oo72o•<u> -.ooo56*t3S> ··0129~•<32> -.oooe&~-•t36> .oo319•<12> -.oo201•t 3> .oo372•<2'~-> -.oo372•<26l .oo112$t19> -.oo2o&~-•t22l

HVR INTERCEPT ,S3255 -.00198•< 7l ·00233*(23) •ll0820*(30l ,Q0232*(27l ,OO'I-66•(28} -.00121*{ ll ,Q0421•(29l ,QQ293•t15l .00127•C24) e00155•t11l

HLN INTERCEPT 2.sa:.22 ,QOU·78*('3) ••00152*(25) -,1,)1)072*(101 •,00294*128) -,00062*(19) ,QQ056•t 21 •,00138•(12) o00131•<26) •,20872•<33) •00072*(11)

GG• INTC:RCEPT .39316 .ooo29•115l .ooo91•11•> .oooa4•112l .o1o77*128l -.oo158•1 1> .oo2t7•113> -.oo217•124l .oo1•1•117l -.oo1&4•118l -.oo1o3•1 5l

L•S INTERCEPT ·,12123 o00969•t29) •00303*(17) oll03b9*(27l -,00635*(32) .00122*( 4) •,0011'1o*(ll) •,QQ152•(13J -.00185•(18) .00182*(12) ··00051•UOJ

EKO INTER.CEPT .3.46069 .ooo91•<21l .ooo61*t13) -.u01'1-2•<17l .ooo25*t36l -.oooa2•t19) .00191•t25J -.257'1-5•<33> .o0229•t27l .oo214•<32J -.coolS•< 8l

WMC Ii'HERCEPT .1,654 .00235•<,71 -·00152*!17) -·012BS•<30l -,00129*(25) -,00045*( 8) ,00068•tll> ,oo515•t31) ,002'1-6•<321 -.0005B•U8)

FLG. INTERCEPT .1o;,02 .22777•(331 -.oo~+S9*<27l -.ooo73•( 3·> -.19361*(341 -.ooo92•t11l -.ooo29•< 7> -.ooo~+e•<12> -.oo25o•<29l .ooo9o•UBJ -.oo1ol•t17l

Fig. 22. Final regression equations for Type 4.

-59-

ELY llHEkCEPT b, 9J564 .OOUY2•(-!ISJ -.0009(!*( ll -.02109*(29} .Q0019*(36} .00007*( 2J o00182•C22J .0'0269•(16) .Q0256•C 9) .Q04?9*(23) -.00163•,C~O)

bFL INTlrtCEPT -.2G379 -.oobl5•< u -.ou~77*< 61 .uo29S•<lll .aoJao•czs> .2o641•C33J .OQ274•t 3J .oo122•<23J

TU5 INTUkEPt u.o~912 -.uQ(IS!•C.J~) o0tl221J*(21) .u0240•C26J -.00215*(18J o00148•C 2) -.00059*(23J -.00041•C10l -.00196*C2Ql o00148*(16) e004f;>O*C29J

LAS 11"1 t:.I<Ci::PT -ij..9::~028 .OOu9LJ•CJu) otl0't33*C 91 -.u0292•C26) .00119*(19) .11638•(33) ,OQ13111d23J

PHX lNlt:.kCEPT .3.c:t:s70 .IJOoJ5•C 91 -.00306*(10) .u0286•<21) .Q0376*C.26) -.25557•(34) -,00411*( 3} -.0012q11d 4) .OOlOS•C 2)

YUI-1 !1'.1 r~r<CEPT -2a538 -,13od4•1J31 oU0310*1251 ,'J0109•1 51 ,0?413*1291 ,00305•1221 -.00234•1171 o00621•1301 -,0951801341 o000460I 61 ,00603•1271

SAC IIH~kCEPT -~07172 -.OlOOq.*( 3) ·OU310*(2U) -,UObbl*(l7) ,Q0007*C36) ,QQ396•C 4) -,52151•(34) ,QQ659•C 1J ,Q011711dlO) -.00048*(35) ,OQ17lf*( .9}

Sf-•X INT1:.t,;Ct::PT -7 .l~U86 •.OO.l6b•< 1) -·DU'I-4u•t25J -,IJ0177>~d17) ,()2372*(29) ,02125•<:50) ,Qol77*(19J ,QQ316•(24J ,QQ182*C13)

~1L iNi~hCEPT -ti,6!~33 -,OQJb~•CUJ •00.::7.3*(21) ,l)Q059•( ll ,Q027S*C22) ,QQ102•Ct8) ,QQ146*( 41 -,Q0106•(23) e00127*C2Q) -.00218*( 9) ,QQ208*C131

SLC UHl:.t<CEPT ,tU:>93 -.D0476•< o> -.ooJu~•ll7J .uo4Js•tll> .oot7o•cto> .oo4o9•C 6> .ooo64*t:56> -.2oD06•C3tJ.> -.oo3o7•t 41 -.127es•t331

~01 INTLKCEPT o2l745 .oo~t:s4•tc.!.l> .uaJ37*Cl2J .uotH7•ClbJ -.onseq.•c2q.J -.oo241•Ct5J -.oous•<21J -.oo53o•<to> -.oo42D•t29l - •. 17Ssa•<33J .oo147*C14J

ijNO INT~~CEPT o40967 o01U7l•{ll) o00d24*121J .u0091•(22) .00648*(26) .00499*(17) o0D25S•C 8) -.00683•(31) o00035*{36) .00309•(14) -,0.027~•(.12)

6TF INTCkCEPT -.8.~23 o000H9•(21) o00J43*122) -.o0035:td35) o00556*(18) ,QQ060*(36) -.00830*(29) t0195R•C32) -·01536*(28) -.00126*(14) -,QQ212*C17l

MS.O lNTEkCEPT -.79'1o84 o00651•CI:!l) o00u35*(25J .ll051i2*(12) .ooq47*(24l -.02288•(29) .26807*(34) oOOlBS•t 6) -,QQ298*C 3) -.,00561*(32) ,00211*( 9)

PUT lhilt:h.CEPT -q.Sl005 -,00675•1211 -.00111*1.551 .U0663•13ll -.00421*1251 o008200il71 -,00504*1231 -.00794ol281 -.0002401361 -.01857*1291 o00130•I201

£KA 11-l·fE.HCEPT , fi f0l .. H9 -.oo~s.:~.c Sl -·D023l*tlOJ .uOU33*C36J .oo096*C &l .oo304•C2&J -.oo7i4•C29J .to633•C34J

MFR INt~kCEPt · ~. d<!o63 -.00327•< 3J o00~24*C23) -.u0164*( 9) .QOOBS*C 21 .00362•0.1J -,OQ053*(36J -.ot75S•(;~Q) o00337*C17l .0,1147*(27) ,00316.*,(12)

SEA .INTolicf:h 1o3!4•6 .oo~eo•U!>J -.o1B31*C29J -.uo112•<35J -.oo233•<23> .oo655•<26J -.oo104•< 7> -.oo314•Uo> -.oot79*f22J -.oos1s•< 1> .oo1q3•.< 21

FAT Iro~'Tt:::nCEPT f0•3'fo06 -.D0272•< 11 -.00273*< 4J -.oo31a•<17l .oo34o•usJ .oo234•(24J .oo607•<28J .oo027•C35> -.oo243•U9l .oo37S•C26J

LAX IN'iCkCEPT .1.d10 -.00149•< 1) .00455•C21J .u0645•C26J -.00372*C22) -.00957•(32) .0146o•C29J -.00312•< 3)

MLF IllTEkCEPT 8oSJl32 -.OOo07•t 3) eOU38~j*(12) -,00617•<18) e00"'43*(~4) ,Q0595•C31l -,24679•(33) e00414•( 9) -,00200*(20) ,OQ334*C 4) ,00031*C35)

RNO INTEilCEPT -.2\1414 -.oouD2•t19> .ooo37•t35J .uooo9•< a> -.ooo9&•t 3> .oo4so•t 41 -.oo653•C17J .oo474•C 21 -·OOI+B3•C2BJ .o0324•C18) -.~04'+.6~}29)

~AN lNTC:RCEPT "9.18 .. 93 ~'' 1•

-.OOb84•1 11 -·0002J•I 71 -.0035401181 .o09460I261 -.00394•1 91 .0071701271 -,17689oC341 -·00196•1121 -·00204•1191 -.0032101~21

lNW Ir~f~RtEPT . 6.92331 e01113•Ci!9) -.00270*C31J eU0220•C13) e00~47*C15) -.00124*(16) -,02584*(30) -.00164•C20) ,Q0390*C24) ,QQ73B*C28) ,QQU3U22)

SFO INTERCEPT -7, 9•561 .00200•1191 ·01121*1121 -.oo3So•l 31 .oo•o3•1 91 -.002620I101 .0008301 81 .00269•1171 o00193•1211 "~00211*1161 o002DO*( 51

PIH lNlERCEPT .03413 -,OOb5D•t 3) -.00401*C18) -,UQ296•C17) .oo251*(11) .00242*(25) .00993•C2BJ .o0423•UOJ e00377*C 4) ~00291*( 9) •e01013,_(30)

GEG Ifo~TERCEPT 1 r • 66'930

-.oo.H9•<31> •00146*U8J .u0026•<36J -.oo044*C35l -.oo37D•C22l -.oo79o•<15J .oo74B•I281 • 00596* ( 32,

RBL INTEHCEPT 2o47128 -,00055•<19) ·00034*C3SJ ,IJ0417•C181 •.02226*(27) -,00510*(32) ,00174*( 3J -,00194•C 6) ,QQ162*( 7J ,00616*(28) ,0094Bt(30J

POX lNl ERC,EPT 1.12232 I

-,02050•(~7) e00334*( 9) •,00425t.(22) e00419*(1Q) .oo731h(28J -.ooo35•< 11 -.oo272•<13J .o0445•<3oJ -,.00376•<23) .oo213•U4>

OLM iNTERC'EPT , 65d36 -.00120•t 7) e00338*C23J -.00476•<22) ,00217*( 2> -.ooo45*(36J e00224*U2J .o0128•U8J -.00597•<32) ~.00259*U4J .00253~U7J

ALW INTC"CEPT i 3!>940 .oootj4•t<::7J -.13971*(34) .U0696*(25) -.o0516*C26> -.00128*(21) -.00486*U8J -.oo079•L'55J •00192*< U -,Q0034*C36J -,OQ301*Cl1J

AST li<TEHtEPT . S, 01137 -.oou:)2•t1.3J -.oo1.36*t21J -.oo1o6•< 3l -.ooa82•C32l .oo149•<17J -.oo19S•<1DJ -.oo097•t20l .oot6o•C23J .oo437•C27J -.oo2SS•<3ol

SLM li.JTtuCEPT .35133 -.ooo78•t 7J .oo44o•t11J -.uo173•t13J -.ooaas•t26> .oo1o&•C 6J .oo227•U4J .ooo42•t a> .o8S63*C34J .oo1so•U7J

EUG !NTI:.t(CEPT • 3"d43 .oo755•t 91 -.oo1o1•t 5J .o057o•< 1> .on265•C12l -.oo471•<30J

FCA ·hii"t:.ltCEPT .91.J128 -,00157•t"3J e0U251*( 7J -.u0031~d36J -,on344*U21 -.00153t( 8) ,Q0178t.C25J .oo174•t18J e00473•t26J ,Q02B6•C 9) •e00349*CUJ

HVK II<Tli,CE~T o44931 .00155•t.>SJ -·OU356•t15J eu2845•t29J -,o0066*C36) -,00266•C22J e00498•C17J ,Q0589${32) ••00559*(31) e00191*( SJ •e00138*(23J

HLN lhTt:.i<CEPT .33189 -,OO.Hl•<.c::ll -.U0134*t11J -.01275•(2~) -,00180*(2.2) .00319*{23) .oo369*U7J -.00268•<16) .00215*U5J

G6W 1NTlhCEtlT . -.9~2.44 -.U0394•tllJ •OIJ187*C22J eOO.:!b64d31) -,00424*(16) .00352*(15) -.00599*UOJ e00491•C12J .00419*< 2) -.00192*< 3l .000!1*t35l

LWS lNh.hCEPT .. , 0!Jd49 ,U24U7•t29J .ouz3o•t1eJ .uo43o•<2LJ.J -.ooLJ.48*C 9J -.oo44B•C10J .oo311•< 5J -.oo104•C SJ -.ooa57•C 21 .ooo3o•C36J -.00239•C15J

EKO !i-.TLIICEPT -24.8Uu81 .00122•<19J .ou~o9•C20) -.ooB&6•<26J -.on402~1( 9J .oo562•C 21 -.oo:53a•UaJ .ooo51~C3,5J -.oo~6.6*<3o> .oo145*( e> -.oo!so•c 4)

111M.: I Ill t.hC:EPT -, 7 J.~85 .oo;::dt•tcl> .outto7•C35J -.uo633•C27J .onlSS•t22l -.oo591•<17J .oo854•C 1J -.oo188•tt4J -.ooo62*C36J -.0179o•C29) -.00136•c 2)

t=LG If~lt.t<CEPT 13,3u981 -.ooY1*LJ.•< lJ -.ou~67*U3J .tr02b9•<22J -.on.na•<2o> ,oo4a4•< 4J .00484*<"25J .oooao.t35J .ooo94•<24J

Fig. 23. Final regression equations for Type 5. -60-

E:.L'f INli:.•~CEPT -l~o0..)589 -.00170•(1~) -.QQ:;)Lt7*(15l -.U0187•<20) .OOU2C*(3Cl -.01357•t:50l o00138*<10l o00252•<18) o00357•<19) o00233*(21) -.00346*(17)

1:1FL !1-JTC:kCEPT -.l'+tj47 ,u032.9•(~ll -·U0050*(23l .uOltl2•( 91 .QOQ19•C3Sl o00298*(25l -.00!:>01*(31) -.00144•(22) -.Q0213*(2ll-l .Q0024•(36l ·OOOq3*(12)

TUS Ii''<Ti:..r.CEPT ~·30867 -·00~9~•(l':d -•00~2~*(25) ouU,H6•<2.ol ~uO:S25*( 9) -.QQ334•C18l o01537*(2()) -·01223•<321 o02649*<30) o00205•<22l •00116*(21)

LA~ .LI>I'rt.:l\CEPT -~0::,113 o00LJlO*L36l .OO.i.22*(21J -.u01!:>3•<17) -.QOj99*tlll ~19560•(331 -.00148*(251 -.10508•(34) o00172*(12l -·002U•Cl8l -·00108*(10)

PHX !NTt;.1,CEPT ~. 5.L 74-2 o.32i.i90•l.34l ~oo:;,02.*( 91 -.v0159•<27l -.002:n•t24l ,00114*(17) o002ll-1*(22l -.OQ271•< 2) o00183•< 6) .01057•<31) -·00092*(20)

YUM J.NTU<C~PT Oo6-+707 -.OOoj9•<..:7) -.ll<.Jl57•( 1) -~u0341•(25) -.00418*( 9) -~OOll-17•(26) .00188*(131 -.OQ164•(2Ql o00160*(16l o00275•C28) -·00084*(1ll-)

SAC IlJTLi~CEr'l 7 •'H"l-88 -.00179,..\l':l) -·0Lll20*(~3l ou01U3*(1b) .OOU36*L30) .001~6•(28) -.00166*(24) -.13849>td33) o00069*( 3) -~00112*(10l o00100*(32)

S~lX H<~Tt..H.CEt'l • 00:.933 .OOU~+O•t;;.t>J -.ou.no•<17J .u0187*<27l -.UOl70*<13l .00116•< 2) .Qo240*(26l -.oo347•(2Sl -·Oll83•C3Ql o00157•<23l -·OOOfJ3•< Sl

tslL .LIHi:..r<CEPT 4o5cio.t21 -.OU4.:W•<'Sl -.OU.:!1b*Cl9J .v0214•<2ol -.2q498*(3'+) -.00330*(22) o00352*(28) .Oul&S•< 5) o00104*(20l o0010h( 1} o00033*(36)

SLC li~h.I<CEPT -.O.Jt.:~BO .uO~Oj•tG!d -.Uul&l*Cl5l oJ0413*(lbl -o(J('lb76*(1t:il -.29448•(34-l -.Oo380*(2bl oOll85•(30l -.00883*(11) .Q0418*(1Q) o00352*<13l

eOI INTt..RCEPT -l4o2V993 .00729•(..:!1) -.OOb67*<C2l -.u0725:•d1::1) .00;.)34*(19) -.00632•< 3l .OQ159*( 6) o01512•(29l •00259•( 7l o00366•(31) •0021ll-*( 2)

I:INO l!HUiCEPT ol4489 .OOUUh=l .3) .U0.<::75•ll7l -.v018b*l22) .QOj04*U8l -.00558*(311 -.00403*(26} .02567•(30) -.18935*(33) -.00094*( 7) ·00143*(16)

GTF INTt:.f,CEPT 3o44017 -.UOU7l•<l9l oOlJllS*< 1) .00032*(3!:>) .000?5*<.36) -.00668•<10l o00594*(32l -·00325•l31) -.05952*(30) -.00225•<22) -·00215*(21)

MSO l1'>il~•~CEPT • Oj.:!98 .002ci1•(1~) o00098•(13) .v2271•(3Jl ,()t'l227*(12) -.00111•( 5) -.01199•(29) 100350•(25) -.00287*(11)

POT 11\jT~:..kCEPT .0:;,~27 -.00127*( j) ·o001~0*{.l.7l .u0209•< I+) .00403*(13) o00696•t 9) .00595*(311 -.000&0•(35) -.00591•<12) o00756*(271 •00158*(22)

~f.A Il'llft;.HCEPT -·0'+261.4-.0QjQ?•t11l .OOU2.G*(.35l" -,•J0528*(18l -.00j07*(10) -.00102•(15) .00188*(171 .OQ207•(26l -.13532*C3l!-l el296:5*C53)

MFfo{ .Lt~Tt.hCEPT -!:> o2,:,230 -.OOu37•(.;)!;)) -.UU13<t*(j1) -.u0152•(2::)l -.on2.75*( 1) -.00277•(17) -.00172*(11) -.OQ982•(3Q) o00129*( 2) .00127*119) -•00257*(271

SEA lNH .. RCEPT -. 7:.;163 .OOj03•( .3) -.UU155•C13l -.J0254*(17) -.00373*(26) o067B8•(:501 -.OQ159*(12l .00044•(35) -~17898*(341 .00188*(22) o00277*C21l

FAT INTt::RCEPT o1o104 -.001+1+7•(;.;,5) o00CJ34*(20l oU0021·•d36l -.00133*(27) oOUSh(29) o00357•(· 9) e00170•<18l -·00198*(1'1-) o00435*(32) o00069*(15)

LAX INT~kCEPT ~21342 -.OOb!:>O•< 3) .00548*( 21 .u0152•< Ol -.01b51*C:50l -~00293•C17l ~00139*(14) -·001'1-6•(211 o31115•<34l o00155•<18l -·00194*(10)

MLF 11-ITc..t-.CEi"'T 17o5oo26 -.OO.I.b0•(21l .00291*( 91 .U037?•(22l -.00887*(10) -.00951•(25) -.00589*(311 -.OQ'I-34•(19) .35781*(34) ·00124*( 8) -·00151*( 2)

I·WO INTC:kCEPT o1:,)'+10 .00<::.30•(2.5) -.Ol.l.l.20*( 7l .00071*( 6) -.194-64*(33) -.00474*(261 .~00105*(16) .00207•<23) -~02125*(30) -.00018*(351 -·00127*(221

SAt'li ltH!:::f<CEPT o19734 -.OO<:::Oo•< ~~ oUli123*(.35J -.u01+57•<17) .00403*(18) -.00274*(121 .. 00121*( 4) -.0092h(29) -~00.337*(251 ,13736*(331

INW li'lTt£1-<CEPT -~. 3.3.)04 -~00195•< 1) o01U2S*(27l -.UOl70*( Ol -~00435*<171 -.00658•(31) o00331*(22l o00235•<10) o002S0•<2l) o00183*(19l -·00060*( 8)

SFO Ii4T~kCEPT I 3U::~28

-.002.\lo*USl -.ou~02.*(24l -~u014~*(12) -~00108*( 9) o00185*(16l -.00151•< 51 o00059•( 6l -•00076•<22) -.00196*<311 •00385*(281

PHI 11-Jlt..f<CEPT -7.0.:~~;:~55 -.U04ti9•t 91 o0i.l19U*l2ll -.u060b*t2ol -.on.Ul*C14l ~00158•<221 o00162*<20l ·00594•(281 -~00421*(27) •00211*(24) •00942•<301

GI:..G 1NTLRCEPT •1 lo59 -.OOo16•CG.'il -.uO~Ob*C11l -.U007B*(3Sl -·00043*(361 o00867•(28l -.01453*(30) -.OQ093•< 1) -·10715*(34) o00096*(21l

Hi.>L J:,\jTL-1-iCEPT ito0/132 .U01~b•< 9) -.ULJ()4U•t36l .vOuq.S•(3!)) o00358*(25l -~00044*(14) .00200*(26l -.00097•(191 o00049•( 61 -~00205•<31) -·OOOA9*C17l

PUX l1~1 t::KCEPT j:), 8ob33 oUOolC•< :0) •U2~90*(29l -.u081J8*(30l .0(1314*( 6) .00018*(26) .16901*(34) -.OQ876•<19l -·00559*( 1) -.00223*( 9) o0054S*C27l

OU.I Ihllt..r-.CEPT o 3<+j81 -.U027j•{ ll -.ouus:;,•cS6J -.024-93•<27) -.on:l99*(32l o0037R•< 21 .00331*(141 -~oo2SQ•(12l ·00338*<17> -·00350*<251 -•00135*C15l

AL.... 11-0't;.I<CE?T -.07723 .OUO~d*(~5l -.u0.::.98*t17l .J0014*<3t:d -~C0462•< 9) .Oo427•Cl2l -.00'+01*<151 o00295•<16l o0039:5*C32l ·00145*( 21 -•00058*< 5l

A5f !fll~r~CEPT oO'+vi+H -.U049~*( ll oUoJ130*( 4l o\.10345*( 9) -.U0257*(17l .00169•(21) .00281*( 21 o00023•(36) -·00489*(25)

SLM 1NTC..t~CEPT I 2-+266 -.DOCtio•< 1) oUU32!:>*( 2l .u0477*( I;) -.Q0j16*(17l .OQ252•C22l -.00111*( 81 o003UA•<23l

I:.UG IIH~KCEPT -. 2~'-1-28 ~-.Oci.24tJ.;:( .1.1 oUU244•t2ll .~30!:>3*C:33) o0fi196*(13) .00301•<22) o00224*( 2) o00615•<28l -·00024*(35) -.00506*(32)

FCA !ill ft.kCEPT -. Oc.c::23 oUU-2..51*1..!:1) -·OUi!Cio*( 1l -.v0039*(35) o0fl~22*( 4) o00926*(30l o00168*(2ll -~23854•(33) •14626*(34) -.00154*( 91 o00348*(12)

HVH tr.nC::hCEPT • .;.c::'!-39 -.UUU46•t35) -·UU2.32*t11J 1VUU0:!.2*(36l -.U04:::c;IO*( 2) -.OQ191*(21l -.(J06p•<27l -·00202•(12) -•14151*(33) -.00096*(15) -·00065*(14)

HLN lNTt.i{CEPT 11•4-+676 .OOu.37*{11) - .. uo..::78•t'19J .u2107•<29l .on.l.S7•t 61 o00344•C 9) .Oo308*(17l o00052•(36l -·00719•<251 -.ll!-972*(33) -·00206*(13)

Gli~ lNTt:.h.:EPT -Sl. 3.;)381 -.CJ0291•<1ll ·OJ22o:!""l19l -.;..0281*<2ol -.on~e9*{25l .oo248•<l~) o000~2*(35l •00116•<17l -800101*( 21 .oo072*< Bl ·00145•<211

L..ViS lNTt.I<CEPT -0.2 7 .1.69 -.00159•< .l.l -.OUUb8*{:!15) "':"'oVOL.H•< 91 -.00.::.39*(17) -.00217*(18) .QQ354*( 2) -·00213•(15) -.00180*<16) .o0114•(20) 100026*(36)

£1(0 ll'liTI:..kCEPT ~. 5oo46 -.U570~+•L::::7) -.o0.;:21*(19l oV016Lt*( 4l .o7730*(3Ql -~00814*(25) -.OQ179*(12l ·01114•{29) -·00375*(28) -.00405*(261 •06567*(31)

YiMC INH .. H.CEPT -. Oi.t278 .00-'79•< 9l •V1t.:~41•(29l -.u0194*(10l -.C0114*(1Sl .02335•<30) o0U.396*(22.l •OOI+88•{32l -·11254•<33) -.00135*(21) e00162*Clll

FLG H~TLI\t..:C:PT -~.6oo63

-.UO.:.dtt•t 31 o00L95*{ 21 -.v0260•<1.3l -.00138*<1Bl o00f+79•t 7) .35371*(341 -.0081+4*( 5) -.00212*<2.2) .00109*(20)

Fig. 24. Final regression equations for Type 6. -61-

I 0\ N I

Fig. 25. Correlation coefficients for Salt Lake City and Phoenix.

I

e; : J..~:~ I

"

:·.h·_.·~:--........ 1

If 11.,,,

. ... . ..

Fig. 26. Correlation coefficients for Los Angeles and Astoria.

(b)

(d)

Fig. 2.7. Predictors in final regression equations for As.toria (a), Los Angeles (b), Salt Lake City (c) and Phoenix (d). X - station location. H - height~ + - predictor location. TD - tendency. W - vertical velocity. WT - vertical velocity due to thermal advection. P.P. -.past precipitation over the previous 12 hours. The numbers in parenth~ses indicate the best predictor chosen in the preliminary analysis (l) or the second best (2). The single numbers indicate the order in which the predictors appear in the final regression equations.

-64-

West~rn Region Technical Memoranda: (Continued)

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Precipitation Probabilities in the Western Region Associated with Spring 500-mb Map Types. Richard P. Augul is. January 1970. (PB-189434) Precipitation Probabilities in the Western Region Associated with Summer 500-mb Map Types. Richard P. Augul is. January 1970. (PB-189414) Precipitation Probabil !ties in the Western Region Associated with Fa I I 500-mb Map Types. Richard P. Augul is. January 1970. (PB-189435) Appl !cations of the Net Radiometer to Short-Range Fog and Stratus Forecasting at Eugene, Oregon. L. Yee and E. Bates. December 1969. (PB-190476) Statist."ical Analysis 'as a Flood Routing Tool. Robert J. C. Burnash, December 1969. (PB-188744) Tsunami. Richard A. Augul is. February 1970. (PB-190157) Predicting Precipitation Type. Robert J. C. Burnash and Floyd E. Hug. March 1970. (PB-190962) Statistical Report of Aeroal Jergens (Pollens and Moldsl Fort Huachuca, Arizona 1969. Wayne s. Johnson. Apr! I 1970. <PB-191743) Western Region Sea State and Surf Forecaster's Manual. Gordon c. Shields and Gerald B. BurdweJI. July 1970. <PB-193102) Sacramento Weather Radar Climatology. R. G. Pappas and C. M. Valiquette. July 1970. CPB-193347) Experimental Air Quality Forecasts in the Sacramento Val ley. NormanS. Benes. August I 97 0. ( PB-1 94 I 28 l A Refinement of the Vorticity Field to Delineate Areas of Significant Precipitation. Barry B. Aronovitch. August 1970. Appl !cation of the SSARR Model to a Basin Without Discharge Record'. Vall Schermerhorn and Donald W. Kueh I. August 1970. (PB-194394). . Areal Coverage of Precipitation in Northwestern Utah. Philip Williams, Jr., and Werner J. Heck. September 1970. (PB-194389) Preliminary Report on Agricultural Field Burning vs. Atmospheric Visibility in the Willamette Valley of Oregon. Earl M. Bates arid David 0. Chilcote. September.J.97Q. (PB-194710) . Alr Pol Jution by Jet Aircraft at Seattle-Tacoma Airport.· Wallace R. Donaldson. October 1970. CCOM-71-00017) . Application of P.E. Model Forecast Parameters to Local-Area Forecasting. Leonard W. Snel lman. October 1970. (COM-71-00016)

NOAA Technical Memoranda NWS

An Aid for Forecasting the Minimum Temperature at Medford, Oregon. Arthur W •. Fritz, October 1970. (COM-71-00120) Relationship of Wind Velocity and Stab!! lty to so2 Concentrations at Salt Lake City, Utah. Werner J, Heck, January 1971, (COM-71-00232) Forecasting the Catalina Eddy. Arthur L. Eichelberger, February 1971. (COM-71-00223) 700-mb Warm Air Advection as a Forecasting Tool for Montana and Northern Idaho. Norris E. Woerner, February 1971. (COM-71-00349) Wind and Weather Regimes at Great Fa I Is, Montana. Warren B. Price, March 1971. CJ imate of Sacramento, California. Wilbur E. Figgins, June 1971. (COM-71-00764) A Pre! iminary Report on Correlation of ARTCC Radar Echoes and Precipitation. Wilbur K. Hall, June 1971. (COM-71-00829) Precipitation Detection Probabi I ities by- Los Angeles ARTC Radars. Dennis E. Ronne, July 1971. (COM-71-00925) A Survey of Marine Weather Requirements. Herbert P. Benner, July 1971. (COM-71-00889) National Weather Service Support to Soaring Activities. ElI is Burton, August 1971. (COM-71-00956) Predicting Inversion Depths and Temperature Influences in the Helena Val ley. David E. Olsen, October 1971. <COM-71-01037) Western Region Synoptic Analysis-Problems and Methods. Phi lip Wi I Iiams, Jr., February 1972. (COM-72-10433) A Paradox Principle in the Prediction of Precipitation Type. Thomas J. Weitz, February 1972. (COM-72-10432) A Synoptic Climatology for Snowstorms in Northwestern Nevada. Bert L. Nelson, Paul M. Fransiol i, and Clarence M. Sakamoto, February 1972. (COM-72-10338) Thunderstorms and Hai I Days Probabi I ities in Nevada. Clarence M. Sakamoto, Apri I 1972. (CQM-72-10554) A Study of the Low Level Jet Stream of the San Joaquin Val ley. Ronald A. Wi I I is and Philip Williams, Jr., May 1972. (COM-72-10707) Monthly Climatological Charts of the Behavior of Fog and Low Stratus at Los Angeles International Airport. Donald M. Gales, July 1972. <COM-72-1 I 140) A Study of Radar Echo Distribution in Arizona During July and August. John E. Hales, Jr., July 1972. (COM-72-11136) Forecasting Precipitation at Bakersfield, California, Using Pressure Gradient Vectors. Earl T. Riddiough, July 1972. (COM-72-11146) Climate of Stockton, California. Robert C. Nelson, July 1972. (COM-72-10920) Estimation of Number of Days Above or Below Selected Temperatures. Clarence M. Sakamoto, October 1972. <COM-72-10021) An Aid for Forecasting Summer Maximum Temperatures at Seattle, Washington. Edgar G. Johnson November 1972. <COM-73-10150) Flash Fiood Forecasting and Warning Program in the Western Region. Phi lip WII Iiams, Jr., Chester L. Glenn and Roland L. Raetz, December 1972. (COM-73-10251) A Comparison of Manual and Semiautomatic Methods of Digitizing Analog Wind Records. Glenn E. Rasch, March 1973. (COM-73-10669) . _ . .

7 Southwestern United States Summer- Monsoon Source--Gulf of Mex1co or Pac1f1c Ocean. John E. Hales, Jr., March 1973. (COM-73-10769) . . WSR 5-Range of Radar Detection Associated with Precipitation Echoes of G1ven He1ghts by the - 1

at Missoula, Montana. Raymond Granger, Apri I 1973. <COM-73:11030~ Conditional Probabilities for Sequences of Wet Days at Phoen1x, Ar1zona, Paul C. Kangieser, June 1973. (COM-73-1 1264) . · t d o A Refinement of the Use of K-Values in Forecasting Thunderstorms 1n Wash1ng on an regan. Robert Y. G. Lee, June 1973. (COM-73-1 1276) . A Surge of Maritime Tropical Air--Gulf of California to the Southwestern Un1ted States. Ira S. Brenner, July 1973.