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Page 1: Background           Introduction           Methodology           Results

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Hydrometeorological Prediction CenterNational Centers for Environmental Prediction

(Current affiliation: Meteorological Development Laboratory)

Jung-Sun ImFebruary 21, 2007

Background

Introduction

Methodology

Results

Verification

Upgrade Status

Confidence Interval Forecastsfor NCEP/HPC QPF

Using Short Range Ensemble Forecasts

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Objectives

The HPC at the NCEP has produced a suite of deterministic QPFs for over 40 years. While the operational forecasts have proven to be useful in their present form, they offer no information concerning the uncertainties of individual forecasts. Many users (including RFCs) have expressed a need for an objective way of assessing the likely success of a particular forecast.

The purpose of this study is to develop a methodology to quantify the uncertainty in manually produced 6-h HPC QPF using NCEP short-range ensemble forecasts (SREFs).

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Benefits1) This research produces probabilistic error

forecasts as well as deterministic error forecasts by applying confidence interval (CI) statistics .

2) The method developed from this study is efficient yielding a reasonably simple end product for operational use and cost effective to develop and implement on an inexpensive computing platform.

3) This study is also the first attempt to relate model produced ensemble forecasts with manually derived QPFs, and its operational application eventually could aid in increasing the forecast lead-time and accuracy of RFC streamflow model forecasts.

4) The methodology developed for QPF could have broader applicability and perhaps could be applied to other meteorological parameters.

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Timeline– Work begun August 2003

– Prototype CI Forecasts Available – December 2003

– Real-time CI Forecasts using 15 QPF Cat. Reg. Available – March 2004

– Real-time CI Forecasts for 12h QPF Available – July 2004

– Upgrade (Two method combination) – September 2004

– Start providing point or grid data products to several RFCs from diverse geographic and hydrologic areas of the country

1) ABRFC – starting July 2004

2) NCRFC – starting December 2004

2006 AMS Presentation by John Halquist: “Use of HPC QPF CI forecasts to produce a hydrologic ensemble of river

forecasts”

3) LMRFC – starting May 2005

4) MBRFC – starting October 2006

– Publication in Wea. Forecasting – February 2006

– New scheme implementation - December 2006

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Introduction

The quality of manual QPF forecasts, especially beyond 12 hrs,

varies considerably from forecast to forecast.

: This can be related directly to the inherent uncertainty

in model predictions.

Basis for all HPC Forecasts

* One of the possible ways to quantify the uncertainty is the use of ensemble forecasts (SREF).

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Early Ensemble StudiesMany of the early ensemble studies tried to address whether the

ensemble really can “forecast the forecast skill”- that is,

“forecast the uncertainty of forecasts”.

Traditionally, the ability has been measured in terms of a linear correlation between ensemble spread and ensemble mean skill.

The correlation between spread and skill has been shown to be positive for forecast lead-times of short-range and mesoscale forecasts, however, generally less than 0.5 (Barker 1991; Hamill and Colucci 1998; Whitaker and Loughe 1998; Stensrude et al., 1999).

While many studies report very little correlation (e.g., Hamill and Colucci 1998; Stensrude et al., 1999), considerably higher possibility to predict forecast skill is shown in more recent studies (Grimit and Mass 2002; Stensrud and Yussouf 2003).

Using more recent and improved ensemble data sets, the spread-error correlations have been increased up to 0.8 (Grimit and Mass 2002; Stensrud and Yussouf 2003).

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Hypothesis used in this approach

The larger spread in SREF,

the greater uncertainty in HPC QPF

: To test this hypothesis,

Investigate the relationship

between

HPC QPF Absolute Error (AE)

& Several parameters available from the SREF

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Spread / forecast error relationships

• Investigate relationship between HPC QPF AE and SREF spread for 500mb heights: Result: Low correlation ( -0.2 < cc < 0.2 )

• Investigate relationship between HPC QPF AE and SREF spread for 850mb RH: Result: Low correlation ( -0.2 < cc < 0.2 )

• Investigate relationship between HPC QPF AE and SREF QPF spread: Result: Higher correlation

-compute cc for various regression types (e.g., simple linear, logarithmic, power, exponential, polynomial, and multiple regressions…)

-best fit was found in the simple linear regression

- test the null hypothesis (Ho: slope=0)

: rejected at the 0.001 error rate (99.9% confidence level)

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Correlation Coefficient between HPC QPF AE and ENS QPF Spread

cc 0.5 at most US grid points (90.5%)

cc 0.8 at many grid points (10.5%)

This indicates the SREF can be used to predict the uncertainties of the HPC QPFs. The cc is greater than those previously reported in works (e.g., Grimit and Mass 2002; Stensrud and Yussouf 2003).

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CC Seasonal Variations

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CC Variations with Forecast Hours(CC averaged for US)

0.40

0.45

0.50

0.55

0.60

0.65

0.70

00-06h 06-12h 12-18h 18-24h 24-30h 30-36h 36-42h 42-48h 48-54h 54-60hForecast hrs

cc

2002 Spring 2002 Summer 2002 Fall 2002 Winter

2002 2003

0.40

0.45

0.50

0.55

0.60

0.65

0.70

00-06h 06-12h 12-18h 18-24h 24-30h 30-36h 36-42h 42-48h 48-54h 54-60hForecast hrs

cc

2003 Spring2003 Summer2003 Fall2003 Winter

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Linear Regression of HPC QPF AE on ENS QPF Spread

|RFC_QPEij – HPC_QPFij | = b0ij + b1ij SPij

“AE ij”

• RFC_QPE: observed precipitation (i.e., ground truth)

• HPC_QPF:HPC precipitation forecast

• b0:intercept

• b1:slope

• SP:ensemble QPF spread

• i, j : horizontal position of each grid point

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Schematic illustration of Confidence Interval (CI) for df=

y = 2x + 1

0

10

20

30

40

0 5 10 15 20

X

Y

50% CI

95% CI

Linear regression fit line

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Confidence Interval (CI) for the Predicted AE at SP

(1) b0: Intercept(2) b1: Slope(3) SPo: SP value for the individual point we are trying to predict(4) t: appropriate percentile of the t distribution(5) MSE: Mean Squared Error (estimate of the true variance of residuals)(6) n: Number of data points(7) SS(SP): Sum of Squares for SP

When we compute the minimum (i.e., b0 + b1*SPo t ) and maximum (i.e., b0 + b1*SPo + t ), we can say we are 95% confident that HPC QPF with SP=SPo will have AE between the minimum value and the maximum value.

ij

ijij

ijijijijijijijij SPSS

SPSPo

nMSEtSPobbatSPoAEpredCI

)(

)(1110).(

2

(1) (3)(2) (6)(5)(4) (7)

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MSE (Estimate of the true variance of residuals )

In order to construct the CI, we usually assume the deviations of the observed AE’s from the true fit line (i.e., true errors, ) satisfy the following assumptions

1. They all have mean 0.2. They all have the same variance 2.3. They are uncorrelated.4. They are normally distributed.

To test our data sets satisfy the above assumptions, the estimates of were computed and examined. First, it was demonstrated that the methodology used for the first step approach satisfy the assumptions 1 and 4. Second, all the MSEs (estimates of the ’s variance) computed for HPC_QPF categorized subsets were not the same. Especially, the MSEs computed for the wet QPF categorized subsets were much greater than the MSE for dry QPF subset.

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Scatterplots of HPC QPF AE vs ENS QPF SP for observed precip. subsets & for HPC QPF subsets

y = 1.6325x + 0.0054

R2 = 0.5767

0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread (inch)

HP

C Q

PF

AE

(inc

h)

0 < obs precip. < 0.010.01 < obs precip. < 0.10.1 < obs precip. < 1.0

y = 0.2312x + 0.0003

R2 = 0.2588

y = 1.6325x + 0.0054

R2 = 0.5767

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20

Ensemble QPF Spread (inch)

HP

C Q

PF

AE

(inc

h)

0 < HPC QPF < 0.010.01 < HPC QPF < 0.10.1 < HPC QPF < 1.0

y = 1.3019x + 0.0003

R2 = 0.4988

0.0

0.2

0.4

0.6

0.8

1.0

0 0.1 0.2 0.3 0.4

Ensemble QPF Spread (inch)

HP

C Q

PF

AE

(inc

h)

0 < obs precip. < 0.010.01 < obs precip. < 0.10.1 < obs precip. < 1.0

y = 1.3019x + 0.0003

R2 = 0.4988

y = 0.0101x + 0.0007

R2 = 8E-050.0

0.2

0.4

0.6

0.8

1.0

0 0.1 0.2 0.3 0.4Ensemble QPF Spread (inch)

HP

C Q

PF

AE

(inc

h)

0 < HPC QPF < 0.010.01 < HPC QPF < 0.10.1 < HPC QPF < 1.0

Northwest (NW) Southeast (SE)

a

b

c

d

Page 17: Background           Introduction           Methodology           Results

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How to Handle Different MSEs for Dry and Wet Precipitation…

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Stratification Methodology

(1)  Method 0 (Dry/All Regressions) For Dry HPC QPF (QPF=0) CI forecast: Apply regression model equation

parameters derived using previous year data of 0QPF<0.01 inch

For Wet HPC QPF (QPF>0) CI forecast: Apply regression model equation parameters derived using previous year data of QPF0

(2)  Method 1 (Dry/Wet Regressions) Dry QPF (QPF=0): Apply Reg. Parm. derived from 0QPF<0.01

Wet QPF (QPF>0): Apply Reg. Parm. derived from QPF>0

(3)  Method 2 (Dry/Light/ModerateHeavy Regressions) Dry QPF (QPF=0): Apply Reg. Parm. derived from 0QPF<0.01

Light QPF (0<QPF<0.1): Apply Reg. Parm. derived from 0<QPF<0.1

Moderate/Heavy QPF (QPF0.1): Apply Reg. Parm. derived from QPF0.1

(4)  Method 3 (Dry/Log-Log Regressions) Dry QPF (QPF=0): Apply Reg. Parm. derived from 0QPF<0.01

Wet QPF (QPF>0): Apply Reg. Parm. obtained from the logarithmically transformed data (both AE and SP) of QPF > 0

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Stratification Methodology (Cont.)

(5) Method 4 (15 QPF Categorized Regressions)

Dry QPF (QPF=0): Apply regression model equation parameters derived using previous year data of 0QPF<0.01 inch

Wet QPF 1 (0<QPF<0.10): Apply regression model equation parameters derived using previous year data of 0<QPF<0.10 inch

Wet QPF 2 (0.10QPF<0.25): Apply Reg. Parm. derived from 0<QPF< 0.25 Wet QPF 3 (0.25QPF<0.50): Apply Reg. Parm. derived from 0<QPF<0.50 Wet QPF 4 (0.50QPF<0.75): Apply Reg. Parm. derived from 0<QPF<0.75 Wet QPF 5 (0.75QPF<1.00): Apply Reg. Parm. derived from 0<QPF<1.00 Wet QPF 6 (1.00QPF<1.25): Apply Reg. Parm. derived from 0<QPF<1.25 Wet QPF 7 (1.25QPF<1.50): Apply Reg. Parm. derived from 0<QPF<1.50 Wet QPF 8 (1.50QPF<1.75): Apply Reg. Parm. derived from 0<QPF<1.75 Wet QPF 9 (1.75QPF<2.00): Apply Reg. Parm. derived from 0<QPF<2.00 Wet QPF10 (2.00QPF<2.50): Apply Reg. Parm. derived from 0<QPF<2.50 Wet QPF11 (2.50QPF<3.00): Apply Reg. Parm. derived from 0<QPF<3.00 Wet QPF12 (3.00QPF<4.00): Apply Reg. Parm. derived from 0<QPF<4.00 Wet QPF13 (4.00QPF<5.00): Apply Reg. Parm. derived from 0<QPF<5.00 Wet QPF14 (5.00QPF< infinite): Apply Reg. Parm. derived from 0<QPF<infinite

Page 20: Background           Introduction           Methodology           Results

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Method Comparisons:Evaluation of CI forecasts for AE and HPC QPF for 5 methods

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread

HPC

QPF A

E

Observed AEExpected AELower CI_AEUpper CI_AE

NW

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread

HPC

QPF A

E

Observed AEExpected AELower CI_AEUpper CI_AE

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4HPC QPF (inch)

Prec

ipitat

ion (in

ch)

Observed precip.Lower CI_QPFUpper CI_QPF

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4HPC QPF (inch)

Prec

ipitat

ion (in

ch)

Observed precip.Lower CI_QPFUpper CI_QPF

Dry/All (M0)

Dry/Wet (M1)

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread (inch)

HPC

QPF A

E (inc

h)

Observed AE for 0<QPF<0.1Observed AE for QPF>0.1

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4HPC QPF (inch)

Prec

ipitat

ion (in

ch)

Observed precip.

Lower CI_QPF

Upper CI_QPF

3 QPF (M2)

0.0

0.3

0.6

0.9

1.2

1.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread

HPC

QPF A

E

Observed AEExpected AELower CI_AEUpper CI_AE

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.1 0.2 0.3 0.4HPC QPF (inch)

Prec

ipitat

ion (in

ch)

Observed precip.Lower CI_QPFUpper CI_QPF

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.00 0.05 0.10 0.15 0.20Ensemble QPF Spread

HPC

QPF A

E

Observed AE for0<QPF<0.1Observed AE for0.1<QPF<0.25Observed AE for0.25<QPF<0.5

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4HPC QPF

Prec

ipitat

ion

Observed precip.

Lower CI_QPF

Upper CI_QPF

15 QPF (M4)

LN trans. (M3)

Note: Reg. parms were obtained using previous year data (i.e., 2001 winter data) and then CIs were computed (predicted) for 2002 winter

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Method Comparison Results

The best CI forecasts satisfying

Narrow CI and High Hit Rate (Lower_CIOBSUpper_CI), are found in

Method 4 (15 QPF categorized regression approach).

Final competitors are

Method 0 and Method 4 in Probabilistic CI forecasts for HPC QPF and HPC QPF AE

Method 2 and Method 4 in Deterministic HPC QPF AE forecasts.

(Details are described in Im et al. (Wea. Forecasting, 2006)

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Confidence Interval Forecasts Using 15 QPF categorized regressions

(Real Time Data Processing)http://www.hpc.ncep.noaa.gov/qpfci/qpfci.shtml

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2004 Jan 17 00z Case(Predicted Precip. & Observed Precip.)

OBS Precip.

OBS AE

HPC QPF_95% CI forecast

AE_95% CI forecast

HPC QPF

AE forecast

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VERIFICATION

2002 Winter 2003 Spring 2003 Summer 2003 Fall(2002 Dec, 2003 Jan Feb) (2003 Mar Apr May) (2003 Jun Jul Aug) (2003 Sep Oct Nov)

fhrs QPF Dec. % AE Dec. % QPF Dec. % AE Dec. % QPF Dec. % AE Dec. % QPF Dec. % AE Dec. % 00-06hrs 96.68 ± 2.09 95.78 ± 2.34 95.26 ±3.19 94.29 ± 3.55 95.57 ± 3.95 94.92 ± 4.35 97.08 ± 2.28 95.11± 2.69

06-12hrs 96.58 ± 2.19 95.75 ± 2.44 95.48 ±3.06 94.52 ± 3.41 95.81 ± 3.94 95.15 ± 4.61 97.07 ± 2.32 96.08 ± 2.80

12-18hrs 96.70 ± 1.97 95.77 ± 2.31 95.37 ± 3.18 94.38 ± 3.53 95.86 ± 3.48 95.28 ± 3.98 97.15 ± 2.15 96.19 ± 2.56

18-24hrs 96.49 ± 2.15 95.67 ± 2.40 95.41 ± 3.16 94.66 ± 3.43 95.62 ± 4.65 94.97 ± 5.37 96.94 ± 2.24 96.04 ± 2.61

24-30hrs 96.38 ± 2.03 95.46 ± 2.42 95.13 ± 3.19 94.20 ± 3.52 96.70 ± 3.95 94.97 ± 4.70 97.08 ± 2.12 96.31 ± 2.45

30-36hrs 96.29 ± 2.06 95.57 ± 2.33 95.16 ± 3.09 94.38 ± 3.38 95.66 ± 4.44 94.89 ± 5.36 96.82 ± 2.24 96.17 ± 2.54

36-42hrs 96.18 ± 2.14 95.47 ± 2.43 95.10 ± 3.18 94.31 ± 3.57 95.73 ± 3.56 95.05 ± 4.59 96.75 ± 2.38 96.12 ± 2.66

42-48hrs 95.92 ± 2.39 95.25 ± 2.61 95.19 ± 3.09 94.50 ± 3.48 95.61 ± 3.83 94.98 ± 4.99 96.69 ± 2.29 96.08 ± 2.51

48-54hrs 96.15 ± 2.19 95.46 ± 2.48 94.95 ± 3.31 94.19 ± 3.60 95.09 ± 4.34 94.33 ± 5.40 96.30 ± 2.55 95.65 ± 2.84

54-60hrs 95.90 ± 2.34 95.29 ± 2.52 95.16 ± 3.01 94.58 ± 3.29 94.69 ± 4.77 93.97 ± 6.04 96.22 ± 2.61 95.62 ± 2.87

2003 Winter(2003 Dec, 2004 Jan Feb)

QPF Dec. % AE Dec. % 96.41 ± 2.43 95.15 ± 2.82

96.27 ± 2.59 95.00 ± 2.96

96.53 ± 2.39 95.48 ± 2.70

96.32 ± 2.52 95.22 ± 2.73

96.71 ± 2.39 95.74 ± 2.52

96.42 ± 2.44 95.40 ± 2.65

96.47 ± 2.55 95.57 ± 2.81

96.22 ± 2.66 95.40 ± 2.86

96.41 ± 2.58 95.63 ± 2.77

96.16 ± 2.56 95.40 ± 2.77

Detection % (Hit Rate x 100)for “HPC QPF 95% CI” and “HPC QPF AE 95% CI”

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Relative Frequency of Occurrence of QPF & CI forecast Hit / False rates versus QPF

1

10

100

1000

10000

100000

1000000

10000000

0.0 0.5 1.0 1.5 2.0 2.5 3.0HPC QPF (inch)

Fre

quen

cy0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0HPC QPF (Inch)

Relative Frequency of Occurrence of QPFHit Rate (lower_CI < OBS < upper_CI)Over-Forecast Rate (OBS < lower_CI)Under-Forecast Rate (OBS > upper_CI)

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Hit / Under-Forecast Rates versus QPFfor Forecast lead times

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0HQPF (inch)

Hit Rate_F00-06hrsHit Rate_F12-18hrsHit Rate_F24-30hrsHit Rate_F36-42hrsHit Rate_F54-60hrsUF Rate_F00-06hrsUF Rate_F12-18hrsUF Rate_F24-30hrsUF Rate_F36-42hrsUF Rate_F54-60hrs

Hit Rates

Under-Forecast (UF) Rates

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Two Method Combination (M4+M0)

The verification statistics indicates improvements in the CI sizes (significantly reduced CI size in light rain ranges), while showing ignorable changes in hit rates.

Since September 2004, this method has been implemented to the real-time CI forecasts.

0_

)(

4_

)(

2

max4

2

max4

Mvaluet

QPFMSE

Mvaluet

QPFMSE

M

M

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Use of HPC QPF CI forecaststo produce a hydrologic ensemble of river

forecasts at NCRFC

John Halquist, 2006: 20th Conf. on Hydrology

While HPC QPF and NCRFC traditional forecast are under forecast, the forecast using upper bound value of HPC QPF 95% CI indicates a significant rise and provides a reasonable upper limit for potential river stages.

95% CI Max

OBS

Traditional Forecast

HPC QPF

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Upgrade in December 2006 at HPC

Previous SchemeCompute Regression

parameters (i.e., b1,b0, MSE, n, mean

SP, SS for SP, etc) each season and apply to CI computations

Use 09z and 21z cycle SREF

New SchemeCompute Regression

parameters each day using most recent 3 month data and apply to CI computations

Use 03z and 15z cycle SREF

Benefits HPC 95% QPF CI Forecasts are delivered

approximately 6 hrs earlier than previously.

New scheme adapts more quickly to changes in the operational SREF.

New scheme uses information more relevant to the current weather regime.

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Summary The SREFs appear to predict the uncertainty of HPC QPFs with

high cc between the AE and SP.

On the basis of the high cc, the linear reg model eq needed to estimate the AE are derived in this study.

Using the reg. model eq params (i.e., b1, b0, MSE, n, mean SP, etc.) derived at each horizontal grid point for each season and individual forecast lead time, we predict an AE associated with an individual SP and the 95% CI of the AE.

Based on the AE CI forecast and the HPC QPF itself, we also predict the 95% CI of the HPC QPF.

The evaluation of reg for data categorized according to the forecasted precip amounts indicates that the MSEs (estimates of the variance of the residuals) for wet categorized subsets (QPF0.01 inch) are much greater than the MSE for the dry subset (0QPF<0.01 inch).

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Summary (Cont.) To address this issue, 5 different QPF stratification

methodologies are tested: The best CI forecasts satisfying the requirements of narrow CI with high hit rate are found in method 4.

Using the M4 & M0 combined reg params which is derived for 15 categorized ranges of HPC QPF, real-time CI forecasts for HPC QPF and the AE are produced for the CONUS and are now available online twice (00 and 12 UTC) a day.

The present study indicates that it is possible to predict the uncertainties of the QPFs using more recent ensemble forecasts. This is possibly due to improvements in operational ensemble forecasts (e.g., forecast skill, horizontal resolution, ensemble members, etc).

The method developed from this study is efficient, yielding a reasonably simple end product for operational use.

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AcknowledgmentsJim Hoke

Edwin Danaher

Keith Brill

Jun Du

Zoltan Toth

Chris Bailey

Tish Soulliard

Mark Klein

Mike Bodner

Peter Manousos

Joey Carr

John Schaake


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