Transaction A: Civil EngineeringVol. 16, No. 2, pp. 165{172c Sharif University of Technology, April 2009

Long Lead Rainfall PredictionUsing Statistical Downscaling and

Arti�cial Neural Network Modeling

M. Karamouz1;�, M. Fallahi2, S. Nazif1 and M. Rahimi Farahani2

Abstract. Long lead rainfall prediction is important in the management and operation of waterresources and many models have been developed for this purpose. Each of the developed models hasits special strengths and weaknesses that must be considered in real time applications. In this paper, �eldand General Circulation Models (GCM) data are used with the Statistical Downscaling Model (SDSM)and the Arti�cial Neural Network (ANN) model for long lead rainfall prediction. These models have beenused for the prediction of rainfall for 5 months (from December to April) in a study area in the southeastern part of Iran. The SDSM model considers climate change scenarios using the selected climateparameters in rainfall prediction, but the ANN models are driven by observed data and do not considerphysical relations between variables. The results show that SDSM outperforms the ANN model.

Keywords: Statistical Downscaling Model (SDSM); Arti�cial Neural Network (ANN); Precipitation;GCM.

INTRODUCTION

In recent years, many e�orts have been devoted toinvestigating the e�ects of large scale climate signalsand climate change on rainfall variability in di�erentparts of the world. Statistical methods in the formof multiple nonlinear regression methods are used forpredicting rainfall. These models can consider morethan one predictor for rainfall prediction.

Even though General Circulation Models (GCMs)can be run at high resolutions, still the results fromsuch models need to be downscaled for individual sitesor localities for impact studies. Downscaling enablesthe construction of climate change scenarios for indi-vidual sites at daily time-scales using grid resolutionGCM outputs. Wilby et al. [1] investigated the SDSMapplication for spatial and temporal downscaling ofthe long lead predictions of meteorological variables

1. School of Civil Engineering, University of Tehran, Tehran,P.O. Box 11163-4563, Iran.

2. School of Civil Engineering, Amirkabir University of Tech-nology, Tehran, P.O. Box 4413-15875, Iran.

*. Corresponding author. E-mail: Karamouz@ut.ac.ir

Received 17 March 2007; received in revised form 5 November2007; accepted 2 March 2008

as well as rain and temperature. Harpham andWilby [2] predicted the precipitation for di�erent partsof England using di�erent models, including SDSM, aradial neural network and a multilayer neural network.The results of their research show that all of thesemethods are capable of predicting precipitation; how-ever, in di�erent regions, their capabilities are di�erent.Massah [3] has downscaled long-lead predictions of rainand temperature in the Zayanderud River basin in Iranusing Kriging and inversed distance weighting methods.

As for the studies of variability and climatesignals, Nazemosadat [4] showed that variations inSea Surface Temperature (SST) in the Persian Gulfhave signi�cant e�ects on precipitation variability inthe southwestern part of Iran. Nazemosadat andCordery [5] also studied the e�ects of the EL Nino-Southern Index (ENSO) on precipitation variabilityrecorded on 41 rain gauges in di�erent parts of Iran.The results of their study have shown that there is alow correlation between the Southern Oscillation Index(SOI) and precipitation in Iran. Karamouz et al. [6]have studied the e�ects of the SST, SLP, �SLP, ENSOand SOI on precipitation variability in the westernparts of Iran and showed that there is considerablecorrelation between SST, SLP and �SLP of key areas

166 M. Karamouz, M. Fallahi, S. Nazif and M. Rahimi Farahani

in the Atlantic Ocean, the Mediterranean Sea and someother sea surface areas and precipitation in the westernpart of Iran.

In this study, ANN models have been used aswell. ANNs have been proved an e�ective alternative toother methods of modeling water resource variables [7-11]. A successful application of ANN to rainfallforecasting has been done by French et al. [12] whoapplied a neural network to forecast one-hour-ahead,two-dimensional rainfall �elds on a regular grid. Tothet al. [13] investigated the capability of ANN in short-term rainfall forecasting using historical rainfall dataas the only input information. Another approachdealing with a temporal pattern is to introduce a cyclic(feedback) connection described by direct loops in thenetwork. Once feedback connections are included,a neural network is often called a Recurrent NeuralNetwork (RNN). Anmala et al. [14] reported thatrecurrent networks may perform better than standardfeed forward networks in predicting monthly runo�.Also the models established by Gowariker et al. [15],Tapliyal [16] and Sahai et al. [17] are categorizedas Walker's studies. Among these, the model ofSahai et al. [17], which links global SST with Indianmonsoon seasonal data, appears to include a successfulapproach.

The objective of this study is to comparetwo models, namely Statistical Down-Scaling Model(SDSM) and Arti�cial Neural Network (ANN) forrainfall prediction. Di�erent measures of error havebeen used for comparing model performances. TheNational Center for Environmental Prediction (NCEP)reanalyzed data sets and HadCM3 (Second HadleyCentre Coupled Ocean-Atmosphere AOGCM) is usedin the SDSM model and large scale climate signalssuch as SLP and SST in the ANN model for rainfallprediction. The remainder of this paper is organizedas follows.

A brief description of the study area and data isprovided in the next section, followed by a descriptionof two methods for rainfall prediction. Then, the re-sults are presented and compared. Finally, a summaryand conclusion are given.

STUDY AREA

The study area is the Kajoo River basin in the southBaloochestan region in the south-eastern part of Iran(Figure 1), which has an area of 3659 km2. Theavailable meteorological station inside the sub-basin,Ghasreghand, is used for downscaling and predictionexercises. The daily rainfall data of this station from1977 to 2000 has been used as a predictand. Observeddata of the e�ective signals in the same period as therainfall are received from the NCEP (1977-2000) website, named predictors.

Figure 1. Kajoo River in the South Baloochestanwatershed would indicate that the predictor-predictandcorrelation could be chance related.

LONG LEAD RAINFALL PREDICTIONMETHODS

Statistical Down-Scaling Model (SDSM)

The �rst downscaling model introduced here is amultiple regression based method, which is referred toas the Statistical Down-Scaling Model (SDSM). Theanalytical base of this model is formulated by Wilbyet al. [1]. The developed formulation consists of twosteps. In the �rst step, it is determined, whether ornot rainfall occurs on each day:

!i = �0 +iX

j=1

�j u(j)i ; (1)

where !i is the candidate in a random process generatorthat indicates a state of rainfall occurring or not;accruing on day i, ui is the normalized predictor onday i; and �j is the estimated regression coe�cient.Precipitation in day i occurs if !i � ri, where riis a stochastic output from a linear random- numbergenerator.

The value of rainfall on each rainy day is esti-mated in the second step, using the z-score as follows:

Zi = �0 +nXj=1

�j u(i)i + "; (2)

Zi = ��1[F (yi)]; (3)

Long Lead Rainfall Prediction 167

where Zi is the z score calculated from the estimatedregression coe�cients, �j , and the normally distributedstochastic error term, ". The rainfall value is thencalculated from the cumulative distribution function,�, of the empirical distribution function, F (yi), of thedaily rainfall occurrence and amounts. The predictorsare standardized by subtracting the climatologicalmean and dividing it with standard deviations overthe calibration period. During downscaling with theSDSM, a multiple linear regression model is developedbetween a few selected large-scale predictors and thelocal scale predictands such as rainfall.

The structure and operation of SDSM can bedivided into �ve distinct tasks, including:

1. Preliminary screening of potential downscaling pre-dictor variables;

2. Assembly and calibration of SDSM;

3. Synthesis of ensembles of current weather datausing observed predictor variables;

4. Generation of ensembles of future weather datausing GCM-derived predictor variables;

5. Diagnostic testing/analysis of observed data andclimate change scenarios (Figure 2).

In SDSM, the parameters of the regression modelare estimated using the e�cient dual simplex algo-rithm. Large-scale relevant predictors (among thosepresented in Table 1) are selected using correlation,partial correlation and P value analysis. Also, consid-ering physical sensitivity between selected predictorsand predictands for the site in question, the corre-lation statistics and P values indicate the strengthof association between the predictor and predictand.Higher correlation values imply a higher degree ofassociation and lower P values indicate a better chancefor association between variables. It is importantto know that the P values of less than 0.05 as athreshold do not necessarily mean that the result canbe statistically signi�cant. On the other hand, the highP value would indicate that the predictor-predictandcorrelation could be chance related.

As rainfall values cannot take negative amounts,they are modeled as a conditional process in which localrainfall amounts are correlated with the occurrence ofwet-days which in turn, are correlated with regional-scale atmospheric predictors. A wet day is de�ned as aday with rainfall more than 0.3 mm. During calibrationof the model, the mean of downscaled daily rainfall isadjusted by a bias correction and a variance in ationfactor to force the model to replicate the observed

Figure 2. SDSM climate scenario generation process [1].

168 M. Karamouz, M. Fallahi, S. Nazif and M. Rahimi Farahani

Table 1. Large-scale predictors for the meteorologicalprediction with SDSM.PredictorVariable

Description

Temp Mean temperature

Mslp Mean sea level pressure

p u Zonal velocity component near surface

p5 u Zonal velocity component at 500 hPa height

p8 u Zonal velocity component at 850 hPa height

p v Meridional velocity component near surface

p8 v Meridional velocity component at850 hPa height

p z Vorticity

p zh Divergence near surface

p5zh Divergence at 500 hPa height

p8zh Divergence at 850 hPa height

p500 500 hPa geopotential height

p850 850 hPa geopotential height

s500 Speci�c humidity at 500 hPa height

r850 Relative humidity at 850 hPa height

Shum Near surface speci�c humidity

Rhum Near Surface relative humidity

data. The amounts of these variables are determinedby trial and error. Bias correction compensates forany tendency to overestimate/underestimate the meanof downscaled variables. Variance uctuation changesthe variance of downscaled daily weather variables byadding or reducing the amount of `white noise' appliedto the regression model estimates of the local process,in order to better accord with observations. Use ofthis stochastic (random) component also enables theSDSM regression model to produce multiple ensemblesof downscaled weather variables.

Rainfall predictions must be tested. There areseveral indicators that can be used for this purpose.Here, two indicators, namely Root Mean Square Error(RMSE) and Mean Absolute Error (MAE) have beenused. These indicators are calculated as follows:

RMSE =

vuut nPm=1

(Xp �Xo)2

n; (4)

MAE =

nPm=1jXp �Xojn

; (5)

where XP is simulated data, Xo is observed data andn is the number of data.

Arti�cial Neural Network (ANN)

The second model for forecasting rainfall in this studyis the Arti�cial Neural Network (ANN). This modelis a non-linear regression type in which a relation-ship is developed between a few selected large-scaleatmospheric predictors and basin scale meteorologicalpredictands. An ANN that emulates a biological neuralnetwork structure distributes the computation to smalland simple processing units called arti�cial neuronsor nodes. Neurons with similar characteristics arearranged into a layer. A layer can be seen as a groupof neurons, which are connected to other layers or theexternal environment, which have no interconnections.

Arti�cial Neural Networks can be trained using aBack Propagation Algorithm (BPA) during supervisedlearning. The back propagation algorithm providesa way to calculate the gradient of the error func-tion e�ciently, using the chain rule of di�erentia-tion [18]. In this algorithm, network weights aremoved along the negative gradient of the performancefunction.

Multilayer Perceptron NetworkMultilayer Perceptron (MLP), also called a feed for-ward network, implements mappings from the inputpattern space to the output space. MLP is a staticnetwork in which information is transmitted throughthe connections between its neurons, forward only, andthe network has no feedback or memory, which coversits initial and past states. MLP can be trained withthe standard back propagation algorithm. Figure 3shows a typical three layer MLP (without recurrentconnections) which, mathematically, can be expressedas:

a1j (t) = F

RXi=1

w1j;ipi(t) + b1j

!; 1 � j � S1; (6)

a2k(t) = G

0@ S1Xj=1

w2k;ja

1j (t) + b2k

1A ; 1 � k � S2;(7)

Figure 3. MLP model structure.

Long Lead Rainfall Prediction 169

where t denotes a discrete time, R is the number ofinput signals and S1 and S2; the numbers of hiddenand output neurons, respectively; w1

i;j and w2k;j are the

weight matrices of hidden and output layers; b1j and b2kare the bias vectors of hidden and output layers; pi(t) isthe input matrix; and a1 and a2 are the output vectorsof the hidden and output layers. F and G are theactivation functions of the hidden and output layers,respectively.

Temporal Neural NetworksStatic networks only process input patterns that arespatial in nature, i.e. input patterns that can bearranged along one or more spatial axes such as a vectoror an array. In many tasks, the input pattern comprisesone or more temporal signals, as in speech recognition,time series prediction and signal �ltering [18]. Thedynamic behavior of the system or the recurring (feed-back) connections, as recurrent neural networks, shouldbe considered.

RAINFALL PREDICTION RESULTS

SDSM

A combination of predictors has been selected forlong lead rainfall prediction because of their maximumcorrelation with daily rainfall. Correlation coe�cientsbetween selected predictors and daily rainfall have beenpresented in (Table 2). This table also reports the par-tial correlation and P value between the predictors andrainfall that help identify the amount of explanatorypower for each predictor.

As the distribution of daily rainfall is skewed, afourth root transformation is applied to the originalseries to convert them to a normal distribution, andthen they are used in regression analysis. The model isstructured as a monthly model for rainfall downscaling,in which case twelve regression equations are derivedfor twelve months. The model is calibrated andvalidated using 15 years (1976-1990) and 9 years (1991-1999) of daily data of predictors and predictands,respectively, and one ensemble of downscaled dailyrainfall has been generated.

The reason for choosing 24 years of one ensembledata for calibration and validation purposes is that

a longer data set is capable of representing the trueclimatic condition for the site in question, includingless frequent climate events. For this purpose, one ofthe predicted scenarios for future climate variation suchas HadCM3 (Second Hadley Centre Coupled Ocean-Atmosphere GCM) is used as a model input signal andthe rainfall is predicted. Figure 4 shows the observedrainfall in 5 months (December, January, February,March, April) and the predicted rainfall by usingdeveloped weather generator variables (HadCM3) forthe study area. The MAE and RMSE for the predictedrainfalls are 5 and 6 mm, respectively, which areacceptable considering the magnitude of the observedrainfall.

ANN Models

Climate signals that seem to be signi�cant on Iran'srainfall are shown in Figure 5. The correlation betweenthe SLP of each area with di�erent lags between 1 to12 months and the total 5 month precipitation of thestudy area have been computed. The results of the bestcorrelation are presented in Table 3.

Results show that the following indices can beconsidered as indicators of winter precipitation andruno� in the study area:

Figure 4. Summation of 5-month rainfall (Dec.-Apr.) atthe study area for downscaled data from GCM (HadCM3)predictors and the observed data (1991-1999).

Table 2. The results of selected predictors for the study area.

PredictorCorrelation Coe�cient Between

Weather-Variablesand Rainfall

Pv (P Value) Pr (Partial)

Relative humidity at 850 hPa height 0.42 0.002 0.48

Near surface speci�c humidity 0.45 0.000 0.5

Near surface relative humidity 0.40 0.000 0.44

170 M. Karamouz, M. Fallahi, S. Nazif and M. Rahimi Farahani

Figure 5. E�ective points on Iran climate variations [19].

Table 3. Best correlation for each studied climate signaland (December-April) rainfall.

Study Area R2

� SLP of Greenland-East of the 0.46Mediterranean

� SLP of Greenland-Azores 0.45

� SLP of Greenland-West of the 0.49Mediterranean

SLP of Black Sea 0.38

1. SLP di�erence between Greenland and the east ofthe Mediterranean Sea;

2. SLP di�erence between Greenland and Azores;

3. SLP di�erence between Greenland and the west ofthe Mediterranean Sea;

4. SLP of the Black Sea.

The time series of the selected SLP di�erences andSLP as winter rainfall predictors are used to developan ANN model for winter precipitation predictions inthe study area. Twenty years data from 1971 to 1990are used to calibrate and 9 years (1991-1999) are usedto validate the ANN model. Several ANN modelswith di�erent training steps and neurons and returns

have been developed and their performance has beencompared. To quantify the ANN performance, RMSEand MAE criteria have been calculated. Finally, a3-layer ELMAN model with 2 neurons and the leastRMSE and MAE has been selected (Table 4). Resultsof winter rainfall forecasting with selected MLP andELMAN models have been shown in Figure 6. It canbe observed that both of the models have a similarperformance and can predict rainfall fairly well.

COMPARING RESULTS

For a better understanding of the models' performanceand through comparing their results, an error toleranceis de�ned. Here, error means the di�erence betweenobserved and predicted values divided by the observedvalue as:

Errori =jobsi � preij

obsi; (8)

Table 4. Errors of di�erent ANN models used inpredicting rainfall as 5-month summation.

ANN Model Variable MAE(mm)

RMSE(mm)

MLP Winter rainfall 37.19 32.13

ELMAN Winter rainfall 32.87 25.71

Long Lead Rainfall Prediction 171

Figure 6. Comparative forecasted and observed rainfall.

where obsi and prei stand for observed and predictedrainfall, respectively. The percentages of predictedrainfall found in de�ned error tolerance ranges arecalculated and summarized in Table 5 for the selectedmodels.

As seen in Table 5, the performance of the SDSMmodel is much better than ANN models due to theconsideration of local signals in SDSM model, whichare more e�ective than large scale global signals. ANNmodels overestimated the amount of rainfall, as shownin Figure 7.

CONCLUSION

Long lead rainfall predictions can play an importantrole in water resources management and operation. Ithas been investigated that large scale signals can beused for long lead rainfall predictions. Many methodshave been developed for utilizing climate signals for theprediction of rainfall for di�erent time scales. One ofthe commonly used models in this �eld is the ANNmodel. In recent years, downscaling models havebeen developed to predict the amount of rainfall inlocal scales and in smaller time steps. One of themodels used to downscale rainfall prediction is SDSM,which has a statistical base. In this paper, these twomodels are applied for long lead rainfall prediction in

Table 5. Error tolerances for selected long lead rainfallprediction models (percentage of occurrence).

Percentage of PredictionsModels with Error (%) Less than

< 10 < 20 < 30

ELMAN 22 67 67

MLP 11 45 67

SDSM 75 100 100

Figure 7. Comparing results of long lead rainfallprediction models including SDSM and ANN Models.

southwestern Iran. In ANN models, SLP and �SLP,and in the SDSM model with relative humidity at850 hPa height, near surface speci�c humidity andnear surface relative humidity have been selected aspredictors for long-lead rainfall prediction. Theseclimate signals have been selected with the highest R-Squared values.

Comparing the results, we can conclude that theELMAN model is better than the MLP model. In thismodel, MAE is 33 mm and RMSE is 26 mm; 67% offorecast errors are within 30% of the observed values.In the SDSM model, these values are 5mm, 6 mm and100%, respectively. 75% of forecasts using the SDSMmodel are within 10% of the observed values. It isconcluded that the SDSM performance is better thanthe ANN model, even though, in comparison, it is amore data intensive model than ANN.

ACKNOWLEDGMENT

This study is a part of a ood management projectentitled \Flood plane zoning downstream of Kajoo nadKariani River basins and the design of ood warningsystem" sponsored by the Sistan and Baloochestanwater Authority.

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