Research Article Improving Regional Dynamic Downscaling ...

Research ArticleImproving Regional Dynamic Downscaling withMultiple Linear Regression Model Using Components PrincipalAnalysis Precipitation over Amazon and Northeast Brazil

Aline Gomes da Silva12 and Claudio Moises Santos e Silva23

1 Instituto Federal do Rio Grande do Norte Brazil2 Programa de Pos-Graduacao em Ciencias Climaticas Rio Grande do Norte Brazil3 Universidade Federal do Rio Grande do Norte Brazil

Correspondence should be addressed to Aline Gomes da Silva alinegomesifrnedubr

Received 16 April 2014 Accepted 21 June 2014 Published 10 July 2014

Academic Editor Hann-Ming H Juang

Copyright copy 2014 A G da Silva and C M S e Silva This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In the current context of climate change discussions predictions of future scenarios of weather and climate are crucial for thegeneration of information of interest to the global community Due to the atmosphere being a chaotic system errors in predictionsof future scenarios are systematically observedTherefore numerous techniques have been tested in order to generate more reliablepredictions and two techniques have excelled in science dynamic downscaling through regionalmodels and ensemble predictioncombining different outputs of climate models through the arithmetic average in other words a postprocessing of the output dataspecies Thus this paper proposes a method of postprocessing outputs of regional climate models This method consists in usingthe statistical tool multiple linear regression by principal components for combining different simulations obtained by dynamicdownscaling with the regional climate model (RegCM4) Tests for the Amazon and Northeast region of Brazil (South America)showed that the method provided a more realistic prediction in terms of average daily rainfall for the analyzed period prescribedafter comparing with the prediction made by set through the arithmetic averages of the simulations This method photographedthe extreme events (outlier) that the prediction by averaging failed Data from the Tropical Rainfall Measuring Mission (TRMM)were used to evaluate the method

1 Introduction

General circulation models (GCM) have been used for cli-mate prediction over Brazil [1 2] Although these modelsrepresent the influence of synoptic scale weather systems andaspects of the general circulation that have limitations inrepresentingmesoscale processes such as squall linesmeteo-rological systems formed by complex topography watershedand others [3] Thus due to the large size and complexity ofterrain and biomes covering the Brazilian territory the GCMare limited to representation of regional aspects of the climateon Brazil

A solution to this problem is use of downscaling tech-nique through regional climate models (MCR) Over South

America several studies [1 4ndash7] showed the RCM skillrelatively to GCM The effectiveness and suitability of thistechnique are due to the possibility of usingmore appropriatephysical parameterizations for mesoscale due the increasingof the spatial resolution These characteristics are importantbecause in regions such as Brazil forcing mesoscale regulatesthe spatial and temporal distribution of atmospheric vari-ables reducing errors in GCMs that are performed with lowspatial resolution [8]

An important regional model is the regional climatemodel (RegCM) which was originally developed at theNational Center for Atmospheric Research (NCAR) duringthe 80s decade [9 10] Due to the contribution of manyresearchers to the RegCM there are six versions RegCM1

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2014 Article ID 928729 9 pageshttpdxdoiorg1011552014928729

2 Advances in Meteorology

RegCM2 RegCM25 RegCM3 RegCM4 and RegCM41 Itis widely used because it is public and open source codemoreover it has a good computational performance

Despite progress achieved in modeling regional in recentyears there are still many aspects to be explored evaluatedand improved to a substantial improvement of climate repre-sentation through the RCM compared to the representationsthrough the GCMs

Systematic errors that regional models exhibit includingthe RegCM in different regions especially over tropicalregion are due to a lack of fit in the physical parameteriza-tions especially in parameterizations of convective cumulusand precipitation in grid scale [11 12]

The most used technique to overcome the lack of adjust-ment in the parameterization and reduce forecasting errorsis called ensemble prediction which consists of combinationof the multiple simulations performed with different initialconditions or parameterization for the same period andregion Studies have shown that this method produces moreconsistent results with observation

For South America (SA) consequently to Brazil thesituation is no different there is a need of studies thataim to enhance regional and technical treatment models tooutput models However several studies have focused onsimulation with the standard model configuration [3 8 15ndash17] and for the ensemble prediction technique using thearithmetic meanTherefore this paper investigates the possi-bility of improvement of regionalmodel simulationsRegCM4through proper adjustment of physical parameterizations andusing appropriate statistical methods to combine multiplesimulations In this sense we use the technique of multiplelinear regression using principal components in order tocombine different simulations with the RegCM4 To test themethod we apply this technique of combination in the periodfrom February to June 1998This year was an atypical year ElNino

The work is organized as follows Section 2 will show abrief presentation of the physical parameters of the regionalclimate model RegCM4 that most influence the simulatedrainfall together with the input data of this model and thedata that are used to verify themethod proposed in this workIn Section 3 the method multiple linear regression usingprincipal components to combine different simulations willbe presented In Section 4 the results are present Finally inSection 5 the conclusions and discussions are drawn

2 Model Used and NumericalExperiments Performed

21 Regional Climate Model (RegCM4) The RegCM4 [18]is the fifth version of RegCM originally developed by theNational Center for Atmospheric Research NCAR [19] andbased on mesoscale model (MM5)This is a model of limitedarea discretized into grid points (Arakawa B) In the verticalsystem sigma coordinates are used The primitive equationswhich correspond to the core of the dynamic model are for acompressible hydrostatic fluid [20]

The physical processes are represented in the model bya series of parameterizations The radiative transfer scheme

is the same used in the global model Community ClimateModel version 3 (CCM3) This scheme calculates the inter-action of gases (H

2O CO

2 O3 CH4 N2O and CFC) and

aerosols with radiation in the infrared and ultraviolet Forthe soil-vegetation-atmosphere interaction RegCM4uses thebiosphere-atmosphere transfer scheme (BATS) and commu-nity land model (CLM version 35) The full description ofthe model as well as the parameterization options are shownin [18]

The model has three options of convective schemes (i)Kuo scheme the most simplified and that is activated whenthe moisture convergence exceeds a threshold value and(ii) the convective schemes of Grell [20] which considersthe cloud as a plume entrainment model composed by adowndraft and updraft The interaction via entrainment ofair with the atmosphere occurs only in the top and in thebase of the cloud The convective activity is activated whenthe updraft reaches the moist adiabatic This scheme is moresensitive to precipitation efficiency (PEFF) parameter Thisparameter quantifies the portion of precipitation that willevaporate before reaching the ground Therefore high PEFFvalues decrease precipitation Two types of closures can beused Arakawa and Schubert (all potential energy availablefor convection is adjusted for each time step [13]) and Fritsch-Chappell (1980) (scale convective adjustment in the order of30 minutes [14]) (iii) parameterization MIT-emanuel [21]which characterizes the convection trigger when the level offree convection is higher than the cloud base

For stratiform precipitation the RegCM4 use the subgridexplicit moisture (SUBEX) which was developed by [22]The formulation for the auto conversion of cloud water intoprecipitation is as follows

119875 = 119862ppt (119876119888

FCminus 119876

th119888) FC (1)

119862ppt is the conversion rate119876119888 is the amount of water present119876

th119888is the minimum amount of water that must remain in

the cloud and FC is the conversion factor of water presentin precipitation FC value depends on the minimum relativehumidity (RHmin) for cloud formation according to theequation

FC = radic RH minus RHminRHmax minus RHmin

(2)

The RHmax value is 101 RHmin may vary between 1 and100 and RH is local relative humidity The thresholdamount of water in the cloud is given by

119876th119888= 119862acs10

minus049 + 0013119879 (3)

119879 is the temperature in degrees Celsius and 119862acs is scalingfactor

22 Numerical Experiments

221 Data The initial and boundary conditions of theatmosphere (wind temperature surface pressure and water

Advances in Meteorology 3

9N6N3NEQ3S6S9S12S15S18S21S

85W 75W 65W 55W 45W 35W 25W 15W

0 200 400 600 800 1000 1200 1400 1600 1800 2000

AMNE

Figure 1 Topography in meters (m) of the domain used to runthe simulations Amazon region (AM) and Northeast (NE) of Brazilindicated by black boxes

vapor) used in the simulation conditions are of the ERA-Interim reanalysisThe ERA-Interim is a global dataset of theatmosphere produced by the European Centre for Medium-Range Weather Forecast (ECMWF) with a horizontal gridspacing of 15∘ by 15∘ and frequency of six hours (0000 06001200 and 1800 UTC) [23] The topography and groundcover are from the United States Geological Survey (USGS)and Global Land Cover Characterization (GLCC) with 60minutes of horizontal grid spacing [24]

The dataset of sea surface temperature (SST) used wereproduced by the National Oceanic and Atmospheric Admin-istration (NOAA) using in situ data and satellite throughoptimal interpolation (OI) [25] The data are weekly andavailable from 1989 to the present day centered on Wednes-day with a resolution of 10∘ by 10∘

The simulated precipitation data will be compared withdata Tropical Rainfall Measuring Mission (TRMM) product3B42-V7 These data are obtained by using satellite infraredchannels with 025∘ by 025∘ resolution latitude versus longi-tude [26]

222 Configuration of the Experiments Seven simulationtests were performed during the Austral autumn beginningat 0000 UTC on February 15th 1998 and ending at 0000UTC on June 1th in the same year February was discardedbecause this is the time adjustment (spin-up) of the model

The model grid spacing is 50 km and 18 vertical levelswith the top at 5 hPa The domain and the topography areshown in Figure 1 Two regions will be analyzed Amazon(AM) and Northeast (NE) region of Brazil as indicated inFigure 1 Table 1 summarizes the settings of the experimentsthat varied according to the convective scheme (Grell andMIT-Emanuel) minimum relative humidity for formationof cloud in scale grid (RHmin) and the dynamic control(closure) of Grell model (Arakawa-Schubert or Fritsch-Chappell) in addition different PEFF are used if the schemewas the Grell convective

Table 1 Configuration of the seven simulations

SimulationPrecipitationEfficiency(PEFF)

SUBEX(RHmin)

Dynamiccontrol (closure)

GR PD SD 025ndash100 065Arakawa andSchubert (1974)

[13]

GR PD SW 025ndash100 090Arakawa andSchubert (1974)

[13]EM SD 065EM SW 090

GR PW SD 025ndash050 065Arakawa andSchubert (1974)

[13]

GR PW SW 025ndash050 090Arakawa andSchubert (1974)

[13]

GR PW SW FC 025ndash050 090Fritsch and

Chappell (1980)[14]

GR parameterization of cumulus Grell MS parameterization of cumulusMIT-Emanuel PD PEFF dry (high evaporation rate of the raindroptherefore decreases precipitation) PW PEFF wet (low evaporation rate ofthe raindrop therefore increases the precipitation) SD SUBEX dry (lowminimum relative humidity for cloud formation) SW SUBEX wet (highminimum relative humidity for cloud formation) FC closure cloud Fritschand Chappell (1980) [14]

3 Multiple Linear Regression UsingPrincipal Components

To minimize the error in climate forecasts predictions withseveral different configurations are generated and combinedThis method is called ensemble prediction [27] Usually theensemble prediction is made via a simple arithmetic average(AA) from different simulations or models or weighting bymeasures of dispersion

In this paper we will compare the usual method with themethod of multiple linear regression using principal com-ponents (here we call PCR method) to produce a combina-tion of the seven experiments described in Section 222

The method of multiple linear regression is a multivari-ate technique that consists in finding a linear relationshipbetween a dependent variable (response variable) in thiscase the observed data and more than one independentvariable (predictors variables) that describe the system herethese are output of the climate model RegCM4

The following equation shows this relationship where119884119894is the variable to be estimated 119883

119898119894are the predictors

variables 1205720the intercept and 120572

119898the coefficients of multiple

linear regression to be estimated by least squaresmethod [28]This method consists in finding a solution that minimizes thesum of squared residuals which is the difference between theobserved and predicted (estimated)

119884119894= 1205720+ 12057211198831119894+ sdot sdot sdot + 120572

119898119883119898119894+ 120598119894 (4)


The problem of multiple linear regression is to find the120572119898coefficients that relate the independent variables and the

dependent variable this step can be called calibration ofthe regression model To find this solution we rewrite (4)in matrix form taking the 119884-matrix with the dependentvariable the119883-matrix with the independent variables the119860-matrix with 120572

119898coefficients and the 119864-matrix with errors 120598

119894

119884 =[[

[

1198841

119884119894

]]

]

119883 =[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

119860 =[[

[

1205720

120572119898

]]

]

119864 =[[

[

1205981

120598119894

]]

]

(5)

Rewriting the problem in matrix form we have

[[

[

1198841

119884119894

]]

]

=[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

sdot[[

[

1205720

120572119898

]]

]

+[[

[

1205981

120598119894

]]

]

(6)

Multiplying the 119860-matrix by 119883-matrix and adding the 120598-matrix we obtain the equation below but in matrix form

119884 = 119883119860 + 120598 (7)

The least squares method is used to find the coefficients ofmultiple linear regression with the condition that the sum ofthe squares of the errors be minimum For this isolate theerror in (4) getting

119884119894minus (1205720+ 12057211198831119894+ sdot sdot sdot + 120572

119898119883119898119894) = 120598119894 (8)

Then the sum of squared errors (SSE shown in (9) andin matrix form in (10)) is minimized through the derivativewith respect to 119860-matrix equaling to zero as shown in (11)By isolating 119860-matrix (step not shown) we have as thesolution of themultiple linear regression in (12) Consider thefollowing

SSE = sum(119910119894minus (1205720+12057211198831119894+ sdot sdot sdot + 120572

119898119883119898119894))2

(9)

SSE = 120598119879120598 = (119884 minus 119883119860)119879 (119884 minus 119883119860) (10)

120597 (SSE)120597119860

= 0 (11)

119860 = [119883119879119883]minus1

119883119879119884 (12)

A possible obstacle to find the solution of (12) is thatthe matrix 119883119879119883 cannot be inverted In other words itcan be a singular matrix where some predictors variablesare linear combinations of other so there is a correlationbetween the independent variables When this occurs thereis multicollinearity and there is no single least squares esti-mators for the parameters For climate ensemble predictionthe simulations with different configurations from a singleclimate model are correlatedThus to avoid multicollinearity

we will use the principal components of the simulationsThis technique aims to explain the structure of variance andcovariance of a random vector by constructing linear combi-nations of the original variables which are for this problemthe predictors variables of multiple linear regression Theselinear combinations are called principal components and arenot correlated [29] Therefore the principal components ofthe explanatory variables are a new set of variables withthe same information of the original variables but uncor-related eliminating multicollinearity The use of principalcomponents to fit a multiple linear regression model wasproposed initially by [30] This technique is called multiplelinear regression using principal components

The first step is to find the principal components (PCs)119885-matrix of the matrix of predictors variables 119883 where therelationship between them is given by

119885 = 1198751015840119883 (13)

119875 is the orthogonal matrix of dimension 119898 times 119898 (119898 is thenumber of predictors variables) consisting of eigenvectors ofthe covariance matrix or correlation matrix119883 Thus (7) and(12) can be rewritten in the forms

119884 = 119885119860 + 120598

119860 = [119885119879119885]minus1

119885119879119884

(14)

Finding 119875-matrix with the weights of each simulation andthe 119860-matrix with the regression coefficients the regressionmodel is calibrated this matrix should be used as setting fornew ensemble prediction The eigenvectors of the 119875-matrixthat provides the weights of each predictors variable are usedto find the newmatrix of principal components119885NEW of newsimulations119883NEW given by

119885nova = 1198751015840119883nova (15)

After to find the principal components using the coefficient119860-matrix the ensemble prediction 119885PRED is obtained by therelation

119884prev = 119885nova119860 (16)

The multiple linear regression using principal compo-nents can work with all PC obtained from the original dataor only to workwith components that have higher correlationwith the response variable [31] In the latter case the errorscan be minimized

For the analysis the results were calculated Bias meanerror (ME) mean absolute error (MAE) and root meansquare error (RMSE) according to (17) (18) (19) and (20)respectively 119875

119900119894is the observed precipitation 119875

119875119894is the

precipitation predicted and 119899 is the number of data

Bias = 119875119900119894minus 119875119875119894 (17)

ME =sum119899

119894=1(119875119900119894minus 119875119875119894)

119899 (18)


MAE =sum119899

119894=1

1003816100381610038161003816119875119900119894 minus 1198751198751198941003816100381610038161003816

119899 (19)

RMSE = radicsum119899

119894=1(119875119900119894minus 119875119875119894)2

119899

(20)

4 Results

41 The Regression Model via Principal Component TheTRMM data which will be the dependent variable 119884 wasobtained through average daily precipitation from March01 to May 31 for the Amazon region and Northeast regionof Figure 1 Similarly independent variables were obtainedwhich is simulated precipitation (119883-matrix) of the sevenexperiments Preliminary tests indicated that the largerthe number of simulations improves the ensemble predic-tion

First step was to find the seven principal componentsof the 119883-matrix which composes the 119885-matrix (Section 3)Despite the cumulative variance explained to be equal to 86e 96 in the fourth principal component (see Tables 2 and3) for AM e NE region respectively the implementation ofPCR method were considered all PCs (seven PCs not shownhere) because each one captures a different parameter ofthe configuration of the model RegCM4 except for the firstcomponent which is a measure of the intensity of the rainThe PC[2] split the effect of the different parameterizations ofcumulus used Grell and MIT-Emanuel PC[3] differentiatesPEFWet and PEFDry associated with the Grell schemePC[4] captures the difference SUBEXDry and SUBEXWetassociated with Grell scheme PC[5] distinguishes differentPEFF associated with different closure of the clouds PC[6]differentiates closure of the cloud used for parameterizationof Grell and PC[7] captures the difference between theassociation of Emanuel parameterization with SUBEXDryand SUBEXWet Finally to run the PCR the regressionequations (21) show the regression coefficients that associateeach component principal (PC) with the precipitation (Prec)for the Amazon (PrecAM) and Northeast (PrecNE) of theBrazil respectively This equation allows us to estimate theaverage daily precipitation for the period analyzed usingwiththe same coefficients

PrecAM = 715 minus 100 lowast PC [1] minus 080 lowast PC [2]

+ 017 lowast PC [3] minus 081 lowast PC [4] minus 066 lowast PC [5]

minus 057 lowast PC [6] + 16 lowast PC [7]

PrecNE = 203 minus 052 lowast PC [1] minus 026 lowast PC [2]

minus 020 lowast PC [3] + 024 lowast PC [4] minus 046 lowast PC [5]

+ 008 lowast PC [6] + 16 lowast PC [7] (21)

For the regression model to be appropriate one mustsatisfy three requirements (i) the residues must to presentrandom distribution around the mean zero (ii) the residuesmust have a normal distribution and (iii) the variance must

Table 2 Proportion of variance and cumulative proportion forAmazon region for each principal component (PC)

PC1 PC2 PC3 PC4 PC5 PC6 PC7Proportionof variance 048 017 012 009 007 006 001

Cumulativeproportion 048 065 077 086 093 099 100

Table 3 Proportion of variance and cumulative proportion forNortheast region for each principal component (PC)



to be homogeneousThe residues in the graphs of Figures 2(a)and 2(d) to Amazon andNortheast of the Brazil respectivelyapparently do not present any particular pattern or trendindication

The plots in Figures 2(b) and 2(e) show the quantiles ofthe residuals versus the quantiles of the normal distributioncalled QQ-plot for the Amazon and Northeast respectivelyThis is necessary to verify the assumption of normalityof residuals The closer to a line the residues are closeto a normal distribution Figures 2(c) and 2(f) show thesquare root of the normalized residual versus predictedvalues randomly distributed indicating the homogeneity ofvarianceTherefore we conclude thatmodel satisfies the threeconditions

42 The Performance of Regression Model For the AAmethod we calculated the arithmetic mean of the sevensimulationsWith the purpose of comparing the performanceof the PCR andAAmethods to represent the daily rainfall thegraphs in Figure 3 present data fromTRMMversus simulatedfor both methods and regionsThe results were compared forthe Amazon region and Northeast in Figure 3 with the PCRmethod in Figures 3(a) and 3(c) and AA method in Figures3(b) and 3(d) We concluded that the simulation through theensemble PCR shows a better correlation with the TRMMdata relatively to the AA ensemble especially in the Amazonregion

Despite theNorth andNortheast of Brazil being located inthe tropical region one has different responses in simulationsin climate models Overall the simulations for the Northeastconverge to the observed presenting a smaller bias comparedto the northern region bias This is due to the variation oftopography distance to the ocean the diversity of vegetationtypes and forms of land use and other factors Therefore theefficiency of the PCRmethod is sharper in the regionwith thelargest bias

From the boxplot of TRMM data PCR and AA ensem-bles in Figure 4 we find that the median and interquartilerange of the data obtained by AA ensemble diverges sig-nificantly from the TRMM data For the model obtained


0

10

4 6 8 10 12 14Fitted values

Resid

uals

Residuals versus Fitted

62

199

5

minus5

(a)

Theoretical quantiles

Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)

1 2 3 4 5Fitted values

Resid

uals

Residuals versus fitted

53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)

Figure 2 (a) and (d) residues (mmday) with zero mean (b) and (e) residues with normal distribution and (c) and (f) homogeneity ofvariance of the residue (a) (b) and (c) the Amazon region (d) (e) and (f) Northeast region


1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)

Figure 3 (a) and (c) average daily precipitation data for the PCR ensemble versus TRMM data for the Amazon region and Northeastrespectively (b) and (d) AA ensemble versus TRMM data for the Amazon region and Northeast respectively

with the PCR ensemble compared to data from TRMMthere is the similarity in median precipitation and varianceRegarding the PCRmethod there is a slight underestimationof the intense events and overestimation of the weak eventsMoreover this method is able to capture two extremes events(outliers) in accordance with the data TRMM

The variability of observation explained by simulations1198772 for the PCR ensemble was approximately 40 This value

is higher than that obtained with the AA method whichwas 28 (see Table 4) The 119865-test also shown in Table 4 ishigher than the tabulated 119865-value which for a confidencelevel of 95 is 2214 The probability of obtaining this resultis measured by the 119875 value which showed low values of theorder of 10minus7 for the PCR method

Table 4 119865-test 119875 value and 1198772 for PCR and AA methods to theNorth and Northeast domain

Region Method Estatıstica-119865 Valor-119875 1198772

Amazon PCR 7795 3279 sdot 10minus7 0399Amazon AA 3551 513 sdot 10minus8 0287Northeast PCR 1078 2552 sdot 10minus9 0501Northeast AA 6705 3195 sdot 10minus12 0452

Table 5 shows the mean error (ME) mean absolute error(MAE) and root mean square error (RMSE) calculatedaccording to (16) (17) and (18) respectively for PCR andAA ensembles As expected the ME was approximately zero


AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)

Figure 4 Boxplot of average daily precipitation (mmday) for the AA ensemble TRMM data and PCR ensemble in the (a) Amazon regionand (b) Northeast region

Table 5 ME (mmday) MAE (mmday) and RMSE (mmday) forPCR and AA methods to the North and Northeast domain

Region Method ME MAE RMSEAmazon PCR minus11 sdot 10minus4 214 276Amazon AA 494 495 589Northeast PCR minus36 sdot 10minus5 094 122Northeast AA 062 098 143

for the PCR method to the two regions once the graphof Figures 3(a) and 3(d) shows the uniform distribution ofresidue around zero This shows that there is a trend ofunderestimation or overestimation of the method The MAEindicates the magnitude of the error The MAE for the AAmethod was approximately twice the value obtained by thePCR method for Amazon region For Northeast region thevalue MAE was 8 less with PCR method The RMSE hadresults similar to MAE

5 Final Comments

Errors and uncertainties in weather and climate forecastingwill always exist due to several sources of errors present in asimulation and can be classified into two classes incompleteor erroneous atmospheric initial conditions and inadequacyof the numerical model

These errors in the initial conditions are due to instru-mental limitations for data collection discretized observa-tions and irregularly spaced increasing the difficulty ofinterpolation to the grid structure In the case of models oflimited area the artificial boundary condition increases theerrors and uncertainties

Inadequacy of the numerical model consists in difficultyto represent the influence of all physical-chemical-biologicalfactors in the state of the atmosphere and its evolution in time

With the ensemble prediction method by varying thephysical parameterization the error due to the inadequacyof the model is minimized since several possibilities ofrepresenting the state of the atmosphere are reproduced anda solution is generated from these Thus decreases in theprobability of observing extremes surprise that a particularsetting or parameter could not represent the forecast

By comparing the prediction method routinely per-formed (AA) together with the method presented here wefound that combination of simulations that are correlated inother words simulations that bring the same informationor contribution to the final solution does not improve theprediction A treatment is needed to remove redundantinformation from simulations that is a principal componentanalysis And from this assign specific weights to this new setof variables using multiple linear regression

The PCR method performed better in the Amazonregion where individual forecasts more diverged from theobservations For the Northeast region where the bias wasclose to zero the result was comparable to the average ofthe simulations A significant advantage of the PCR methodwas the ability to capture extreme events (outlier) for bothregions since the prediction of these events is of interest tothe community

Studies are still needed Besides to check the effectivenessof the methods to other regions and periods it is necessaryto take point to point of grid to obtain a spatial distributionof precipitation refining the process instead of using theaverage of a region as performed here with the purpose apreliminary analysis

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


References

[1] P Nobre A D Moura and L Sun ldquoDynamical downscaling ofseasonal climate prediction overNordeste Brazil with ECHAM3and NCEPrsquos regional spectral models at IRIrdquo Bulletin of theAmerican Meteorological Society vol 82 no 12 pp 2787ndash27962001

[2] B Liebmann S J Camargo A Seth et al ldquoOnset and end of therainy season in SouthAmerica in observations and the ECHAM45 atmospheric general circulation modelrdquo Journal of Climatevol 20 no 10 pp 2037ndash2050 2007

[3] J P R Fernandez S H Franchito and V B Rao ldquoSimulationof the summer circulation over South America by two regionalclimate models Part I mean climatologyrdquo Theoretical andApplied Climatology vol 86 no 1ndash4 pp 247ndash260 2006

[4] L Sun F H M Semazzi F Giorgi and L A Ogallo ldquoApplica-tion of the NCAR regional climate model to eastern Africamdash1 Simulation of the short rains in 1988rdquo Journal of GeophysicalResearch vol 104 pp 6529ndash6548 1999

[5] F Giorgi and L O Mearns ldquoIntroduction to especial sectionregional climate modeling revisitedrdquo Journal of GeophysicalResearch vol 104 no D6 pp 6335ndash6352 1999

[6] V Misra P A Dirmeyer and B P Kirtman ldquoDynamic down-scaling of seasonal simulations over South Americardquo Journal ofClimate vol 16 no 1 pp 103ndash117 2003

[7] L Sun D F Moncunill H Li A D Moura F D A D SFilho and S E Zebiak ldquoAn operational dynamical downscalingprediction system for Nordeste Brazil and the 2002ndash04 real-time forecast evaluationrdquo Journal of Climate vol 19 no 10 pp1990ndash2007 2006

[8] R D Machado and R P Rocha ldquoPrevisoes climaticas sazonaissobre o Brasil Avaliacao do RegCM3 aninhado no modeloglobal CPTECCOLArdquo Revista Brasileira de Meteorologia vol26 no 1 pp 121ndash136 2011

[9] R E Dickinson R M Errico F Giorgi and G T Bates ldquoAregional climate model for the Western United Statesrdquo ClimaticChange vol 15 no 3 pp 383ndash422 1989

[10] F Giorgi and G T Bates ldquoThe climatological skill of a regionalmodel over complex terrainrdquoMonthly Weather Review vol 117no 11 pp 2325ndash2347 1989

[11] F Giorgi X Bi and J S Pal ldquoMean interannual variability andtrends in a regional climate change experiment over Europe IPresent-day climate (1961-1990)rdquoClimate Dynamics vol 22 no6-7 pp 733ndash756 2004

[12] E B Souza M N Lopes E G Rocha et al ldquorecipitacao sazonalsobre Amazonia Oriental no perıodo chuvoso Observacoese simulacoes regionais com o RegCM3rdquo Revista Brasileira deMeteorologia vol 24 no 2 pp 111ndash124 2009

[13] AArakawa andWA Schubert ldquoInteraction of a cumulus cloudensemblewith the large scale environment part Irdquo Journal of theAtmospheric Sciences vol 31 pp 674ndash701 1974

[14] J M Fritsch and C F Chappell ldquoNumerical prediction of con-vectively driven mesoscale pressure systems Part I convectiveparameterizationrdquo Journal of the Atmospheric Sciences vol 37no 8 pp 1722ndash1733 1980

[15] A Seth and M Rojas ldquoSimulation and sensitivity in a nestedmodeling system for South Americanmdashpart I reanalysesboundary forcingrdquo Jornal of Climate vol 16 pp 2437ndash24532003

[16] A Seth S A Rauscher S J Camargo J-H Qian and J SPal ldquoRegCM3 regional climatologies for South America using

reanalysis and ECHAM global model driving fieldsrdquo ClimateDynamics vol 28 no 5 pp 461ndash480 2007

[17] CM Santos e Silva A Silva P Oliveira andK C Lima ldquoDyna-mical downscaling of the precipitation in Northeast Brazil witha regional climatemodel during contrasting yearsrdquoAtmosphericScience Letters vol 15 no 1 pp 50ndash57 2014

[18] F Giorgi E Coppola F Solmon et al ldquoRegCM4 Modeldescription and preliminary tests over multiple CORDEXdomainsrdquo Climate Research vol 52 no 1 pp 7ndash29 2012

[19] F Giorgi ldquoSimulation of regional climate using a limited areamodel nested in a general circulationmodelrdquo Journal of Climatevol 3 pp 941ndash963 1990

[20] G A Grell ldquoPrognostic evaluation of assumptions used bycumulus parameterizationsrdquoMonthly Weather Review vol 121no 3 pp 764ndash787 1993

[21] K A Emanuel and M Zivkovic-Rothman ldquoDevelopment andevaluation of a convection scheme for use in climate modelsrdquoJournal of the Atmospheric Sciences vol 56 no 11 pp 1766ndash17821999

[22] J S Pal E E Small and E A B Eltahir ldquoSimulation of regional-scale water and energy budgets representation of subgrid cloudand precipitation processes within RegCMrdquo Journal of Geophy-sical Research Atmospheres vol 105 no D24 pp 29579ndash295942000

[23] D P Dee S M Uppala A J Simmons et al ldquoThe ERA-Interimreanalysis configuration and performance of the data assim-ilation systemrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 137 no 656 pp 553ndash597 2011

[24] T R Loveland B C Reed J F Brown et al ldquoDevelopment of aglobal land cover characteristics database and IGBP DISCoverfrom 1 km AVHRR datardquo International Journal of Remote Sens-ing vol 21 no 6-7 pp 1303ndash1330 2000

[25] R W Reynolds N A Rayner T M Smith D C Stokes andW Wang ldquoAn improved in situ and satellite SST analysis forclimaterdquo Journal of Climate vol 15 no 13 pp 1609ndash1625 2002

[26] G J Huffman R F Adler D T Bolvin et al ldquoTheTRMMMulti-satellite PrecipitationAnalysis (TMPA) quasi-globalmultiyearcombined-sensor precipitation estimates at fine scalesrdquo Journalof Hydrometeorology vol 8 no 1 pp 38ndash55 2007

[27] E Kalnay ldquoAtmospheric modelling data assimilation andpredictabilityrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 129 no 592 p 2442 2003

[28] D Wilks Statistical Methods in the Atmospheric Sciences Aca-demic Press 1995

[29] S A Mingoti ldquoAnalise de dados atraves de metodos de esta-tıstica multivariada uma abordagem aplicadardquo Belo HorizonteEditora da UFMG 2005

[30] M G Kendall A Course in Multivariate Analysis GriffinLondon UK 1957

[31] R Mo and D M Straus ldquoStatistical-dynamical seasonal pre-diction based on principal component regression of GCMensemble integrationsrdquo Monthly Weather Review vol 130 no9 pp 2167ndash2187 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


RegCM2 RegCM25 RegCM3 RegCM4 and RegCM41 Itis widely used because it is public and open source codemoreover it has a good computational performance

Despite progress achieved in modeling regional in recentyears there are still many aspects to be explored evaluatedand improved to a substantial improvement of climate repre-sentation through the RCM compared to the representationsthrough the GCMs

Systematic errors that regional models exhibit includingthe RegCM in different regions especially over tropicalregion are due to a lack of fit in the physical parameteriza-tions especially in parameterizations of convective cumulusand precipitation in grid scale [11 12]

The most used technique to overcome the lack of adjust-ment in the parameterization and reduce forecasting errorsis called ensemble prediction which consists of combinationof the multiple simulations performed with different initialconditions or parameterization for the same period andregion Studies have shown that this method produces moreconsistent results with observation

For South America (SA) consequently to Brazil thesituation is no different there is a need of studies thataim to enhance regional and technical treatment models tooutput models However several studies have focused onsimulation with the standard model configuration [3 8 15ndash17] and for the ensemble prediction technique using thearithmetic meanTherefore this paper investigates the possi-bility of improvement of regionalmodel simulationsRegCM4through proper adjustment of physical parameterizations andusing appropriate statistical methods to combine multiplesimulations In this sense we use the technique of multiplelinear regression using principal components in order tocombine different simulations with the RegCM4 To test themethod we apply this technique of combination in the periodfrom February to June 1998This year was an atypical year ElNino

The work is organized as follows Section 2 will show abrief presentation of the physical parameters of the regionalclimate model RegCM4 that most influence the simulatedrainfall together with the input data of this model and thedata that are used to verify themethod proposed in this workIn Section 3 the method multiple linear regression usingprincipal components to combine different simulations willbe presented In Section 4 the results are present Finally inSection 5 the conclusions and discussions are drawn

2 Model Used and NumericalExperiments Performed

21 Regional Climate Model (RegCM4) The RegCM4 [18]is the fifth version of RegCM originally developed by theNational Center for Atmospheric Research NCAR [19] andbased on mesoscale model (MM5)This is a model of limitedarea discretized into grid points (Arakawa B) In the verticalsystem sigma coordinates are used The primitive equationswhich correspond to the core of the dynamic model are for acompressible hydrostatic fluid [20]

The physical processes are represented in the model bya series of parameterizations The radiative transfer scheme

is the same used in the global model Community ClimateModel version 3 (CCM3) This scheme calculates the inter-action of gases (H

2O CO

2 O3 CH4 N2O and CFC) and

aerosols with radiation in the infrared and ultraviolet Forthe soil-vegetation-atmosphere interaction RegCM4uses thebiosphere-atmosphere transfer scheme (BATS) and commu-nity land model (CLM version 35) The full description ofthe model as well as the parameterization options are shownin [18]

The model has three options of convective schemes (i)Kuo scheme the most simplified and that is activated whenthe moisture convergence exceeds a threshold value and(ii) the convective schemes of Grell [20] which considersthe cloud as a plume entrainment model composed by adowndraft and updraft The interaction via entrainment ofair with the atmosphere occurs only in the top and in thebase of the cloud The convective activity is activated whenthe updraft reaches the moist adiabatic This scheme is moresensitive to precipitation efficiency (PEFF) parameter Thisparameter quantifies the portion of precipitation that willevaporate before reaching the ground Therefore high PEFFvalues decrease precipitation Two types of closures can beused Arakawa and Schubert (all potential energy availablefor convection is adjusted for each time step [13]) and Fritsch-Chappell (1980) (scale convective adjustment in the order of30 minutes [14]) (iii) parameterization MIT-emanuel [21]which characterizes the convection trigger when the level offree convection is higher than the cloud base

For stratiform precipitation the RegCM4 use the subgridexplicit moisture (SUBEX) which was developed by [22]The formulation for the auto conversion of cloud water intoprecipitation is as follows

119875 = 119862ppt (119876119888

FCminus 119876

th119888) FC (1)

119862ppt is the conversion rate119876119888 is the amount of water present119876

th119888is the minimum amount of water that must remain in

the cloud and FC is the conversion factor of water presentin precipitation FC value depends on the minimum relativehumidity (RHmin) for cloud formation according to theequation

FC = radic RH minus RHminRHmax minus RHmin

(2)

The RHmax value is 101 RHmin may vary between 1 and100 and RH is local relative humidity The thresholdamount of water in the cloud is given by

119876th119888= 119862acs10

minus049 + 0013119879 (3)

119879 is the temperature in degrees Celsius and 119862acs is scalingfactor

22 Numerical Experiments

221 Data The initial and boundary conditions of theatmosphere (wind temperature surface pressure and water



85W 75W 65W 55W 45W 35W 25W 15W

0 200 400 600 800 1000 1200 1400 1600 1800 2000

AMNE









SUBEX(RHmin)



[13]


[13]EM SD 065EM SW 090


[13]


[13]


Chappell (1980)[14]











119884119894= 1205720+ 12057211198831119894+ sdot sdot sdot + 120572

119898119883119898119894+ 120598119894 (4)





119894

119884 =[[

[

1198841

119884119894

]]

]

119883 =[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

119860 =[[

[

1205720

120572119898

]]

]

119864 =[[

[

1205981

120598119894

]]

]

(5)


[[

[

1198841

119884119894

]]

]

=[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

sdot[[

[

1205720

120572119898

]]

]

+[[

[

1205981

120598119894

]]

]

(6)


119884 = 119883119860 + 120598 (7)



119898119883119898119894) = 120598119894 (8)



119898119883119898119894))2

(9)

SSE = 120598119879120598 = (119884 minus 119883119860)119879 (119884 minus 119883119860) (10)

120597 (SSE)120597119860

= 0 (11)

119860 = [119883119879119883]minus1

119883119879119884 (12)




119885 = 1198751015840119883 (13)


119884 = 119885119860 + 120598

119860 = [119885119879119885]minus1

119885119879119884

(14)


119885nova = 1198751015840119883nova (15)


119884prev = 119885nova119860 (16)




119875119894is the


Bias = 119875119900119894minus 119875119875119894 (17)

ME =sum119899

119894=1(119875119900119894minus 119875119875119894)

119899 (18)


MAE =sum119899

119894=1

1003816100381610038161003816119875119900119894 minus 1198751198751198941003816100381610038161003816

119899 (19)


119894=1(119875119900119894minus 119875119875119894)2

119899

(20)

4 Results






















0

10


Resid

uals


62

199

5

minus5

(a)


Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)


Resid

uals


53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)



1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



85W 75W 65W 55W 45W 35W 25W 15W

0 200 400 600 800 1000 1200 1400 1600 1800 2000

AMNE









SUBEX(RHmin)



[13]


[13]EM SD 065EM SW 090


[13]


[13]


Chappell (1980)[14]











119884119894= 1205720+ 12057211198831119894+ sdot sdot sdot + 120572

119898119883119898119894+ 120598119894 (4)





119894

119884 =[[

[

1198841

119884119894

]]

]

119883 =[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

119860 =[[

[

1205720

120572119898

]]

]

119864 =[[

[

1205981

120598119894

]]

]

(5)


[[

[

1198841

119884119894

]]

]

=[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

sdot[[

[

1205720

120572119898

]]

]

+[[

[

1205981

120598119894

]]

]

(6)


119884 = 119883119860 + 120598 (7)



119898119883119898119894) = 120598119894 (8)



119898119883119898119894))2

(9)

SSE = 120598119879120598 = (119884 minus 119883119860)119879 (119884 minus 119883119860) (10)

120597 (SSE)120597119860

= 0 (11)

119860 = [119883119879119883]minus1

119883119879119884 (12)




119885 = 1198751015840119883 (13)


119884 = 119885119860 + 120598

119860 = [119885119879119885]minus1

119885119879119884

(14)


119885nova = 1198751015840119883nova (15)


119884prev = 119885nova119860 (16)




119875119894is the


Bias = 119875119900119894minus 119875119875119894 (17)

ME =sum119899

119894=1(119875119900119894minus 119875119875119894)

119899 (18)


MAE =sum119899

119894=1

1003816100381610038161003816119875119900119894 minus 1198751198751198941003816100381610038161003816

119899 (19)


119894=1(119875119900119894minus 119875119875119894)2

119899

(20)

4 Results






















0

10


Resid

uals


62

199

5

minus5

(a)


Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)


Resid

uals


53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)



1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





119894

119884 =[[

[

1198841

119884119894

]]

]

119883 =[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

119860 =[[

[

1205720

120572119898

]]

]

119864 =[[

[

1205981

120598119894

]]

]

(5)


[[

[

1198841

119884119894

]]

]

=[[

[

1 11988311sdot sdot sdot 119883

1198981

1 1198831119894sdot sdot sdot 119883

119898119894

]]

]

sdot[[

[

1205720

120572119898

]]

]

+[[

[

1205981

120598119894

]]

]

(6)


119884 = 119883119860 + 120598 (7)



119898119883119898119894) = 120598119894 (8)



119898119883119898119894))2

(9)

SSE = 120598119879120598 = (119884 minus 119883119860)119879 (119884 minus 119883119860) (10)

120597 (SSE)120597119860

= 0 (11)

119860 = [119883119879119883]minus1

119883119879119884 (12)




119885 = 1198751015840119883 (13)


119884 = 119885119860 + 120598

119860 = [119885119879119885]minus1

119885119879119884

(14)


119885nova = 1198751015840119883nova (15)


119884prev = 119885nova119860 (16)




119875119894is the


Bias = 119875119900119894minus 119875119875119894 (17)

ME =sum119899

119894=1(119875119900119894minus 119875119875119894)

119899 (18)


MAE =sum119899

119894=1

1003816100381610038161003816119875119900119894 minus 1198751198751198941003816100381610038161003816

119899 (19)


119894=1(119875119900119894minus 119875119875119894)2

119899

(20)

4 Results






















0

10


Resid

uals


62

199

5

minus5

(a)


Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)


Resid

uals


53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)



1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


MAE =sum119899

119894=1

1003816100381610038161003816119875119900119894 minus 1198751198751198941003816100381610038161003816

119899 (19)


119894=1(119875119900119894minus 119875119875119894)2

119899

(20)

4 Results






















0

10


Resid

uals


62

199

5

minus5

(a)


Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)


Resid

uals


53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)



1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0

10


Resid

uals


62

199

5

minus5

(a)


Stan

dard

ized

resid

uals

Normal Q-Q

62

19

17minus2

minus1

0

1

2

3

minus2 minus1 0 1 2

(b)

4 6 8 10 12 14

00

05

10

15

Fitted values

Scale location62

19 17

radic|S

tand

ardi

zed

resid

uals|

(c)


Resid

uals


53 14

4

minus2

0

2

4

(d)


Stan

dard

ized

resid

uals

Normal Q-Q

5314

4

3

2

1

0

minus1

minus2

210minus1minus2

(e)

5431 2

00

05

10

15

Fitted values

Scale location53 14

4

radic|S

tand

ardi

zed

resid

uals|

(f)



1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


1050 15 20

0

5

10

15

20Amazon

Ensemble PCR

TRM

M (m

md

ay)

(a)

1050 15 20

0

5

10

15

20Amazon

Ensemble AA

TRM

M (m

md

ay)

(b)

0 2 4 6 8 10 12

Northeast

Ensemble PCR

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(c)

0 2 4 6 8 10 12

Northeast

Ensemble AA

TRM

M (m

md

ay)

0

2

4

6

8

10

12

(d)










AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


AA TRMM PCR

10

5

0

15

Amazon(m

md

ay)

(a)

AA TRMM PCR

Northeast

4

2

0

6

(mm

day

)

(b)





5 Final Comments











References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


References










































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

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Research Article Improving Regional Dynamic Downscaling ...

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