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Neurocomputing ( ) –www.elsevier.com/locate/neucom

River �ow forecast for reservoir managementthrough neural networks

R. Barattia ;∗ , B. Cannasb , A. Fannib , M. Pintusc , G.M. Sechic ,N. Torenoa

aDepartment of Chemical Engineering, University of Cagliari, Cagliari, ItalybDepartment of Electrical and Electronic Engineering, University of Cagliari, Cagliari, Italy

cDepartment of Land Engineering, University of Cagliari, Cagliari, Italy

Abstract

River �ow forecasts are required to provide basic information for reservoir management ina multipurpose water system optimisation framework. An accurate prediction of �ow rates intributary streams is crucial to optimise the management of water resources considering extendedtime horizons. Moreover, runo, prediction is crucial in protection from water shortage andpossible �ood damages.In this paper, a neural approach is used to model the rainfall-runo, process when di,erent

time step durations have to be considered in reservoir management. Numerical comparisons withobserved data are provided for runo, prediction in the Tirso basin at the S.Chiara section inSardinia (Italy).c© 2003 Elsevier Science B.V. All rights reserved.

Keywords: Neural networks; Rainfall-runo, process; Flow prediction

1. Introduction

The rainfall-runo, process represents a complex nonlinear problem and there areseveral approaches to solve it. Traditionally, hydrological simulation modeling systemsare classi5ed into three main groups, namely, empirical black box, lumped conceptual,and distributed physically-based models.The last two are important in understanding hydrological processes, but their cal-

ibration is costly, time consuming and requires a deep knowledge of the underlying

∗ Corresponding author. Tel.: +39-0706-7550-56 fax: +39-0706-7550-67.E-mail address: baratti@dicm.unica.it (R. Baratti).

0925-2312/03/$ - see front matter c© 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0925-2312(03)00387-4

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physics. On the contrary, black-box modeling does not require, in principle, any apriori knowledge of the underlying physics, but the model parameters are not directlyrelated to the physical conditions of the catchments. Indeed, alternative parameter setsor di,erent model architectures can give very similar behaviors. This may be a prob-lem if relationships between parameter values and measurable catchment characteristicsare required. Moreover, black-box model applicability may be expected to be limitedto areas where runo, has been measured for several years and where no signi5cantchanges in catchment conditions have occurred.In any case, when the main concern is to make accurate predictions at speci5c

watershed locations, though this may be a rough simpli5cation of the real problem,mathematical models have to be used to represent this complex system.In this work a black-box model approach using arti5cial neural networks (ANNs)

was considered.Recently, ANNs have been widely accepted as a potentially useful way of modelling

complex non-linear systems with a large amount of data, at times noisy. They areparticularly useful in situations where the underlying physical process relationshipsare not fully understood, both as substitutes for more conventional mathematical andstatistical models, and in association with them.In recent years ANNs have been increasingly used for prediction and forecasting

of variables involved in hydrologic processes [12]. Despite of the general tendencyamong users to throw a problem blindly at an ANN in the hope that it will formulatean acceptable solution [9], it is essential to investigate di,erent aspects of the ANNapproach in order to improve prediction accuracy of the hydrologic processes, such asnetwork architecture, modelling process, and eEciency estimation for model validation.In this work a black-box model approach using Arti5cial Neural Networks (ANNs)

was considered. Despite of the main methodology is not new in the plethora of pub-lished works before, this paper contributes to test the neural approach in a particularclimate environment, the Mediterranean one, whose hydrological regime is character-ized by a general tendency to the draw, thus resulting in strongly non stationary data.In particular, the neural approach will be utilized to model the rainfall-runo, processes,i.e., to predict river levels for the Tirso catchment at the S.Chiara section in Sardinia(Italy), with two di,erent tasks related, respectively, with water management problemsand �ood forecasting. Due to the non stationarity of rainfall data in the Tirso area, notoutstanding results are expected if compared to those of most of the published papersand eEciencies less than 92%, indicated in [15] as very satisfactory, will be very far.In this sense, the neural approach will be tested in this work, rather severely.

2. On the rainfall-runo� problem

The aim of the 5rst neural application is to evaluate surface water resources dealingwith water management problems. Therefore, the time step has been established inmonthly lags. Using this extended time-step, disregarding the rainfall kinematics of thesingle storm event is possible and the more classical problem of mean area precipi-tation estimation on an extended time period has to be considered. Consequently, thereconstructed hydrologic behavior of the runo,, by using the monthly time unit, will be

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only suitable for water resource studies where storage-yield sequences are frequentlyrelated to monthly periods and will be inadequate to deal with other proposals such asthose related to �ood �ow problems.With regard to the second time-step, the neural network is trained to forecast the

1-day ahead runo,. River �ow forecasting is one of the earlier forecasting problemsthat attracted the interest of scientists as it can help in predicting demand supply,hydroelectric power generation or potential �ood damages.In both cases only time series of basic input variables are available, i.e., the rainfall

and temperature in several gauging stations in the basin area and the runo, in theconsidered section.Since the actual rainfall over an area is a termination stage of a number of di,erent

processes occurring on di,erent scales, the derivation of area estimations over thebasin from point observations remains one of the most diEcult issues in hydrology[4]. The space and time scale of precipitation (as well as other hydrological variables)are related to the resolution of measurements and extensions of watersheds as well asto the type of underlying general hydrologic problem.With regard to the runo, evaluation, as we are treating on reservoir management,

it can be possible to make direct runo, measures on incoming rivers or, alternatively,to make a reservoir volumes balance to estimate the global �ow contributing to thereservoir storage in each time step.

3. Neural networks for rainfall-runo� processes

In this paper traditional feedforward, multiLayer perceptron (MLP) networks areused. Even though in recent works [5,6] alternative architectures, such as locally recur-rent neural networks (LRNNs), have been proposed for rainfall-runo, processes, theresults showed no signi5cant improvement compared to the MLP approach, probablydue to the limited time-dependency of the process. Thus, even though di,erent networkarchitectures have been tested, the considered ANN refers to the classical MLP.In a previous paper [11] the rainfall-runo, process was modeled using MLP for the

Araxisi watershed in Sardinia (Italy). The examined ANNs to model the hydrologicprocess were built considering mean area values of rainfall and temperature over thebasin and also taking into account point rainfall and temperature values.The authors showed that ANN gained in eEciency when point data inputs were

considered. Moreover, the results obtained with ANN were signi5cantly better thanthose reached using the conceptual model to simulate the rainfall-runo, process andmultivariate AR models.In this paper we considered the Tirso basin in Sardinia (Italy) in the S.Chiara section.Tirso basin is of particular interest because of its geographic con5guration and water

resource management as a dam was built in the S.Chiara section in 1924, providingwater resources for central-western Sardinia. The basin area is 2082:01 km2 and ischaracterized by the availability of detailed data from several rainfall gauges. Recently,the new “Cantoniera Tirso” dam was built a few kilometers down the river, creatinga reservoir of a storage volume of 780 Mm3, one of the greatest in Europe.

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Because of the large number of rainfall gauge stations, in order to menage datadimensionality, several procedures considering both point and averaged variables havebeen tested. Most procedures to evaluate the mean area precipitation LPi over the i-timeperiod can be expressed as a linear combination of the observations Pi;j at the gaugesj = 1; : : : ; n.

LPi =n∑j=1

ajPi; j ; (1)

where the station weights aj, j = 1; : : : ; n are non-negative, constantly varying thei-period, and sum to 1. In this application we refer to mean area rainfall evaluationsas obtained in [7] by modifying a procedure originally exposed by [3]. The methodrequires the determination of a reference triangle network of the gauge stations in thebasin with vertices in the measurement locations. Using this approach, the baricentricalvalue Pi;j of the j-element rainfall triangle plane takes place in (1) of the vertex Pi;jobserved value; the areas of the triangle reference network are the weights aj in (1).Moreover, using the daily time step, we also compute a weighted precipitation for thecurrent day using the inverse-distance method to evaluate aj in (1).

4. Model performances

As suggested in [8], in order to evaluate the ANN performance, several error mea-surements have been used in this study, and reported below for the sake of clarity.Considering yi(simulated) as the model output in the ith period and yi(observed) the

observed data, the usual expression of

E =1N

∑i=1;N

(yi(observed) − yi(simulated))2 (2)

is used to 5nd the best ANN con5guration to 5t the observed data. It is the mostcommon objective criterion used in 5tting and testing models. The result is weightedin favour of signi5cant errors associated with high �ow events.Nevertheless the E index cannot easily be used to obtain a 5tness criterion to be used

to compare both model performances for the same watershed in di,erent time stages andthe reliability of model forecasting in di,erent watersheds. To overcome this limitation,we consider the model eEciency R according to the coeEcient of determination in theregression theory:

R=E0 − EE0

= 1− EE0; (3)

where

E0 =1N

∑i=1;N

(yi(observed) − Ly)2 (4)

and Ly is the mean of observed data.

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Obviously, as E0 is a known value for the considered learning series, maximizingthe model eEciency R is equivalent to minimize E. Moreover, R=1 means perfect cor-respondence between generated and tested series, meanwhile R¡ 0 means that averagevalues are generally better predictors for tested series compared with ANN generateddata.Furthermore, in dealing with hydrological regimes with marked seasonal variations,

model eEciency indexes were used. In such a climate, eEciency should be de5nedtaking into account the intrinsic variation of the estimated values from the generalclimate periodicity [5,11].Considering d=1; : : : ; D periods and Nd values in the dth period, we can de5ne the

square deviations of the observed runo, data within the d period:

Ed =1N

∑i=1;Nd

(yi(observed) − Lyd)2; (5)

where Lyd is the mean of the observed values in the dth period.The seasonal e'ciency Rd can be written as

Rd =(∑

d=1;D Ed)− E∑d=1;D Ed

; (6)

Rd is a standard hydrological statistic. As Ed are known values from the training series,the criterion of maximizing Rd is equivalent to minimizing the residual square error Ebetween observed and generated data. E, Ed, R and Rd are global evaluation statistics.Due to the lack of a unique criteria to evaluate the best model, more speci5c errormeasurements has been calculated, i.e., global goodness-of-5t statistics and �ood relatedevent speci5c indicators. Multiple global and �ood related evaluation performanceswere thus applied and a brief description of each one is given below [1].Mean 4th order error M4E

M4E =1N

∑i=1;N

(yi(observed) − yi(simulated))4: (7)

Although high �ow events will exert a strong in�uence on the E, particular emphasiscan also be placed on model 5t at peak �ows using a higher even power.Mean absolute error MAE

MAE =1N

∑i=1;N

|yi(observed) − yi(simulated)|: (8)

The MAE is a global statistic where in all deviations from the original data, be thesepositive or negative, are treated on an equal basis.Mean squared relative error MSRE

MSRE =1N

∑i=1;N

(yi(observed) − yi(simulated)

yi(observed)

)2:

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Low �ow events exert strong in�uence on the MSRE due to the presence of yi(observed)in the denominator of the expression.NaOPve predictors which use the current value as performance are also provided. The

comparison with the mean predictor and the seasonal mean predictor is embedded inthe R and Rd de5nitions.

5. Applications and results

5.1. Monthly time steps

Considering monthly time steps, several di,erent models have been produced, i.e.,the traditional rainfall-runo, model and two runo, forecasting models.As described in [11], potential evapotranspiration (PET) losses in the basin can

be easily modeled, if temperature values are available. As a matter of fact, even ifapproaches based on mass-transfer and energy balance methods are more detailed inestimating evapotranspiration, for the extended period and practical purpose when notall the data are available, empirical temperature-based equations, such as the Thornth-waite equations, can be used [17].This method requires mean monthly temperatures and the number of daylight hours

calculated the 15th day of each month:

PETi =

0; T ¡ 0◦C;

16(10TiI

)a; 06T ¡ 26:5◦C;

−415:85 + 32:24Ti − 0:43T 2i ; T¿ 26:6◦C;

(9)

where Ti is the mean air surface temperature on the ith month and I is the heat indexde5ned as

I =N∑i=1

(Ti=5)1:514: (10)

The exponent a is a function of the index I

a= 6:7× 10−7I 3 − 7:71× 10−5 × I 2 + 1:79× 10−2I + 0:49: (11)

The equation used to calculate the PET needs a correction because it has been formu-lated for a 30-days month and a daylight of 12 h. The 5nal equation is

PETi = PETi[(d=30)(h=12)]: (12)

As losses in previous months are globally represented by the behavior of rainfall andruno,, the model will incorporate only the present month temperature. It is worth tonote that when data on temperature or evapotranspiration have been supplied to thenetwork, no improvements have been obtained because calculated on monthly basis,i.e., averaged in a large time period. The authors think that the in�uence of suchvariables would have been relevant on hourly basis if temperature measurements weremade available.

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1cos(t)

sin(t)

Fig. 1. Seasonal information components.

In order to model the rainfall-runo, process related to Mediterranean climate water-sheds, taking into account a month dependent general climate variable will be important.This variable could easily be associated with analytic periodic functions with periodsequal to one year. In particular, as suggested in [2], to highlight the di,erences betweenspring and autumn and between winter and summer, the seasonal inputs correspond tothe sine and cosine components of the annual month count (Fig. 1).We considered rainfall data from 61 rainfall stations and climate information from

2 temperature stations. The runo, has been measured at the S.Chiara section in theTirso basin.Sixty-nine years of monthly �ow data for the S.Chiara basin are available, i.e. from

1924 to 1992 for a total of 828 data values which were subdivided into two parts,the 5rst 49 years (588 monthly values) used as a training set, while the remaining 20years (240 monthly values) as a test set. Training was carried out considering 9 years(108 monthly values) for cross-validation.Fig. 2 shows the linear 5t for annual rainfall from which a general tendency to the

drought can be grasped. Infact, the annual mean rainfall is of 1660 Mm3 for the 5rst49 years while this is of 1550 Mm3 for the last 20 years, thus con5rming the high nonstationarity of input data.The data of the training and test sets were normalized using the following expression:

xi =xi −min + eps

max −min + 2× eps ; (13)

where min and max are, respectively, the minimum and the maximum values of thetraining data. The constant eps was introduced to avoid �at regions in the sigmoidalfunction and it was set equal to 0.1.

5.1.1. The rainfall-runo1 modelThe network input included current and previous rainfall, previous runo,, data on

temperature or evapotranspiration and the alternative seasonal modeling componentswhich allow for variation in network output according to time-of-year.

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1000

1500

2000

0 10 20 30 40 50 60 70

Mm

3

years (1924 -1992)

Annual rainfall in the Tirso basin and linear fit

Fig. 2. Annual rainfall for the Tirso basin and linear 5t.

The network output was the actual runo, at the basin expressed in millions ofm3 (Mm3).Some test with a pre-processing of input data has been used. In particular, the

seasonal average of the �ow has been subtracted in order to deseasonalize data andlet the network concentrate on deviations from the seasonal average. Results yieldeda somewhat surprising conclusion because, although the method seems intuitive byvirtue of the cyclic nature of the time series, the results produced by such intuitivepre-processing were worse than those obtained with the most basic method with nopre-processing.The network has been trained using the matlab neural network toolbox [13]. Leven-

berg Marquardt algorithm gave the best performances in terms of mean square error[10]. To ensure good out of sample generalization performances cross validation tech-nique has been used [16].The best results have been obtained with a network made up of 8 inputs and 6

hidden neurons. The 8 inputs were the current rainfall, 5 previous rainfall and the twocomponents of the annual month count.The number of previous rainfall is broadly related to the lag time of the drainage

area. For the S.Chiara basin, it is shown that there is no special advantage in takinginto account more than the data of 5 previous months. This value has been obtainedby a heuristic method that gets the best compromise between performance and struc-ture complexity of the neural model. The heuristic strategy consists of solving theoptimization problem for di,erent net structures, i.e., for di,erent number of laggedrainfall-inputs. The behavior, not reported for seek of brevity, of the selected perfor-mance index, R, as a function of number of lagged inputs, shows saturation when thenumber of inputs become greater than 5.

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Table 1Performance indexes for test set years (monthly step)

Model R Rd RMSE MSRE MAE E M4E(Mm3)1=2 (Mm3) (Mm3) (Mm3)4

Rainfall-runo, NN 0.90 0.84 12 1.57 8 152 1:7× 105

NM −0:03 −0:64 40 3.6 23 1544 1:7× 106

Runo,-runo, NN 0.42 0.08 29 19 19 869 5× 107

1 month ahead ARMAX 0.13 −0:38 36 130 21 1304 15× 107

forecasting

Rainfall-runo, NN 0.41 0.05 30 37 20 892 6× 106

1 month ahead ARMAX 0.13 −0:39 36 114 26 1304 10× 106

forecasting

The obtained network is of modest size and this result, as discussed in other relatedworks on rainfall-runo, modeling problem [2,14], agrees with the 5nding that minimalstructures usually o,er better generalization performance than more complex networks.The performances of the neural network (NN) have been compared with those pro-

duced with a naOPve model (NM). The NM considers as predicted value, the last avail-able value, e.g., a naive predictor of the runo, on February is the runo, on January.The naOPve predictor de5nes the lower performance required for the network to be ac-ceptable. Its main drawback is the phase lag.In Table 1, test set global statistics for the NN and for the NM are shown while the

observed and generated runo, values are reported in Fig. 3.The main result from this analysis is that the use of runo, as an input to the

network had no real impact on the 5nal results as, in fact, the performance variationsare negligible. This can be considered a general statement for drought regions where thecorrelation between current and previous runo, is negligible. These results suggest thatthis approach could provide a useful tool for synthetic stream-�ow series generation,which is particularly helpful when historical series are incomplete, as it often happensin Sardinian basins. Thus, this model can be recommended for long term time seriesgenerations.Table 2 shows some statistics i.e., the peak p, the mean � and the variance � for

the reconstructed and observed runo,, the largest over-prediction (OP) and the largestunder-prediction (UP).

5.1.2. The runo1-runo1 forecasting modelIn this case the rainfall information was omitted, i.e., the network has 8 input nodes

and 9 hidden neurons. The network input included the actual runo,, the 5 previousruno, and sine and cosine clock while the network output was the one step-aheadruno, at the basin.The performances of the neural network (NN) have been compared with those

produced with the ARMAX (auto-regressive moving average with exogenous inputs)

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0

50

100

150

200

250

0 50 100 150 200

Observed runoffSimulated runoff

Mm

3

1973 -1992

Fig. 3. Rainfall-runo, model: the observed and generated runo, (Monthly step) for test set years.

Table 2Statistics for test set years (monthly step)

Model P � � OP UP(Mm3) (Mm3) (Mm3)2 (Mm3) (Mm3)

Rainfall-runo, Real 224 31 1508 — —NN 192 30 1336 41 −57

Runo,-runo, NN 133 32 764 71 −1531 month ahead ARMAX 131 19 551 78 −189forecasting

Rainfall-runo, ANN 114 35 809 80 −1441 month ahead ARMAX 80 32 513 69 −157forecasting

model. However, this linear model, often used in basin modellisation for its develop-ment easiness [18], is not expected to have a good performance because of the strongsystem non linearity and non stationarity.The input number in the ARMAX model has been chosen equal to the one used for

the neural network. This is an acceptable simpli5cation only for comparison purposesbecause, in order to 5nd out the optimal input number for a more suitable output/inputrelationship modellisation, an iterative method should be applied.A comparison between the performance indexes of the neural and ARMAX model

is reported in Table 1, while observed runo, values and the ones generated by the NNare reported in Fig. 4.

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0

50

100

150

200

250

0 50 100 150 200

Observed runoffSimulated runoff

Mm

3

1973 - 1992

Fig. 4. Runo,-runo, model: the observed and generated runo, (Monthly step) for test set years.

From the same table how the neural network 5ts better the peaks while the ARMAXmodel tends to produce values closer to the real runo, mean can be grasped. This iscon5rmed by M4E (Table 1) and � (Table 2) bigger and smaller in the ARMAX thanin the NN model.

5.1.3. The rainfall-runo1 forecasting modelThe network output was the one step-ahead runo, at the basin while the input

included the actual rainfall and the alternative seasonal modeling components to allowfor variation in network output according to time-of-year while. No data on temperatureor evapotranspiration have been supplied to the network since, as in the previous case,no improvements have been detected.Repeating the heuristic methodology previously described the best results have been

obtained with a network made up of 8 inputs and 9 hidden neurons.In Table 1, test set global statistics for the NN are shown where the results have

also been compared to those of ARMAX model, while, the observed and generatedruno, values for ANN are reported in Fig. 5.Again, the same considerations take place as in the previous runo,-runo, case.

5.2. Daily time steps

Considering daily time steps, 10 years of daily rainfall and runo, data have beenexamined, from 1930 to 1939.We considered rainfall data from 30 rainfall stations and climate information from

2 temperature stations. The runo, has been measured at the S.Chiara section in theTirso basin.

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0

50

100

150

200

250

0 50 100 150 200

Observed dataSimulated data

Mm

3

1973 - 1992

Fig. 5. Rainfall-runo, 1-step ahead forecasting model: the observed and generated runo, (Monthly step) forthe test set years.

The data set was split into two parts: the 5rst 2 years (1930–1931) were used fortest, the last 8 years (1932–1939) were used for training and validation.Moreover, we computed a weighted precipitation for the current day using the

inverse-distance method, by evaluating the distances between rainfall gauges and theruno, measurement station.The experiments have been carried out considering only rainfall 5rst and adding,

in the following runo,, temperature and climate information in the input layer (seeFig. 1).Several experiments have been done to de5ne the number of previous periods. Best

results have been obtained by considering a network with 9 inputs and 1 hidden layerwith 9 hidden neurons.The 9 inputs include 5 inputs for the rainfall from the previous 60 days, i.e., the

present day rainfall and cumulated rainfall from the current day to 60 previous days;3 inputs for runo, from the previous 3 days and 1 input for a climate cyclic variable.The output is the runo, 1-day later, i.e., in t + 1.No special advantage has been obtained taking into account temperature or evapo-

transpirations.The network has been trained using the matlab neural network toolbox [13]. Leven-

berg Marquardt algorithm gave the best performances in terms of mean square error[10]. To ensure good out of sample generalization performances cross validation tech-nique has been used [16].The performances of the neural predictor have been compared with those produced

with the naOPve predictor (NP). The naOPve predictor considers as predicted value, the

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Table 3Runo, forecasting (daily model, 1 step ahead) for test set years

R RMSE MSRE MAE E M4E(Mm3)1=2 (Mm3) (Mm3)2 (Mm3)4

NN 0.67 1.39 24.05 0.53 1.94 167NP 0.65 1.44 0.10 0.45 2.08 196

Table 4Runo, forecasting (daily model, 1 step ahead) for test set years

P � � OP UP(Mm3) (Mm3) (Mm3)2 (Mm3) (Mm3)

y(observed) 21 1.3 5.7 — —y(simulated) 18 1.4 5.2 9 −15

Table 5Runo, forecasting (daily model, 1 step ahead, K = 1) for test set years

K = 1 R RMSE MSRE MAE E M4E(Mm3)1=2 (Mm3) (Mm3)2 (Mm3)4

NN 0.57 2.49 0.17 1.27 6.2 546

NP 0.53 2.59 0.17 1.29 6.7 639

last available value, e.g., a naive predictor of the runo, on Sunday is the runo, onSaturday.In Table 3, tests set global statistics for the neural network (NN) and for the NP

are shown.Table 4 shows some statistics i.e., the peak p, the mean � and the variance � for

the reconstructed and observed runo,, the largest over-prediction (OP) and the largestunder-prediction (UP).In order to provide a more speci5c indication of model performance for �ood fore-

casting, some statistics for runo, greater than K times the mean runo, are reported.For the test years the mean runo, is 1:67 Mm3.As can be noted, the naOPve predictor has a better MSRE value. This is due to the

large number of low runo, in which there is no change over time; in this case thenaOPve predictor provides a prediction with zero error.Conversely, considering high order statistics, i.e., E and M4E, the neural network

shows a better performance. This re�ects the network ability to better approximate therising runo,.Table 5 shows the statistics in case of K =1, i.e., for runo, values greater than the

mean runo,.

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0

5

10

15

20

25

0 100 200 300 400 500 600

Observed runoffSimulated runoff

Mm

3

1930 -1931

Fig. 6. Observed and simulated runo, for the test years (prediction 1 day ahead).

In this case all the statistics clearly show a better behavior of the neural network.It is worth noting that the comparison between neural network and the mean value

predictor is embedded in the R de5nition.Finally, Fig. 6 shows the observed and the simulated daily runo, for the test years.

6. Conclusion

The neural models applied to the rainfall-runo, transformation problem in Sardiniabasins, could provide a useful tool for the prediction of runo, to generate an ex-tended hydrologic framework for water resource system planning and managementproblems referred to monthly data. In this case, it has been shown in the paper thateven when only information about rainfall is available, the performance of ANN donot deteriorate. It has to be remarked, that the networks have been built for a stronglynon-linear input/output relationship and using non-stationary input data (general ten-dency to draught). The non stationarity in the input data causes the network to betrained with a data set which di,ers from that used in the test phase. This can bethe reason of the low performance indexes if compared with those of already pub-lished papers. Furthermore, a more traditional model like ARMAX showed even worsenumerical performances, thus encouraging the MLP approach.Referring to daily data, preliminary results show the necessity to utilize alternative

preprocessors than the simple mean-area evaluation to treat adequately rainfall data.Results obtained using ANNs for daily data seem promising in this direction. Whenshorter time-steps have to be managed in order to face �ood forecast in extendedwatersheds, more sophisticate preprocessing methods and network structures have to

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be developed in order to reduce data dimensionality. Nevertheless, ANNs can be usedsuccessfully in many practical engineering applications where the main aim would beto make accurate hydrologic predictions, in cases where a physically-based descriptionof the rainfall-runo, process is not possible.

Acknowledgements

This work has been partially supported by Hydrocontrol S.c.r.l., Research and Train-ing Center for Water Systems Control, Capoterra (CA), Italy.

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Roberto Baratti received the Laurea degree (summa cum laude) from Universityof Cagliari in 1982 and the Dottorato di Ricerca (Ph.D.) from University of Pisa in1986. He is Associate Professor of Process Dynamics and Control Design at Uni-versity of Cagliari in the Chemical Engineering and Material Science Department.

His research interests include development of process model for control, moni-toring and optimization purpose and development of control strategies using neuralnetwork models. He is member of the Scienti5c Committee of the InternationalConference EANN, since 1998 he is member of Thematic Network “Intelligentforecasting systems (IFS) for re5neries and power systems” funded by the EU andmember of IFAC, AIDIC and AIChE.

Barbara Cannas was born in Cagliari, Italy on December 24, 1971. She receivedthe Laurea degree (summa cum laude) in electric engineering in 1996 and the Ph.D.degree in electronics and informatics in 2000, both from the University of Cagliari,Italy.

Since March 2002 she is an Assistant Professor at the Department of Electricand Electronic Engineering, University of Cagliari, Cagliari, Italy. Her main researchinterests are in the area of non-linear circuit theory and applications, with emphasison neural networks, chaotic systems control and synchronization, and analog circuitsfault diagnosis.

Alessandra Fanni received the laurea degree in Electrical Engineering from Uni-versity of Cagliari, Italy, in 1981. She is presently full professor of electric circuittheory in the Department of Electrical and Electronic Engineering of the Univer-sity of Cagliari. She co-ordinates several research projects and she is the scienti5cresponsible of some research contracts for young researchers and PHD students.Her research interests includes the following main areas: Circuit Theory, Systemand Signal Theory, Combinatorial Optimisation Algorithms, Numerical methods forelectromagnetic 5elds and electromagnetic compatibility, Neural networks. She isthe author of several international papers, many of them in the 5eld of neuralnetworks. In this 5eld she contributed to the study of original algorithms and archi-tectures of neural networks for classi5cation and prediction of time series, and forthe application of the same to diagnosis of analog circuits, identi5cation problems,and analysis of mono and multidimensional data.

Mariano Pintus graduated in hydraulic engineering in the year 2000. His researchesand studies are in the following 5elds: river �ow forecast for reservoir managementusing neural networks; alternative neural network models for the rainfall-runo,process; neural networks models to forecast hydrological risk.He is currently working at the Sardinia Regional Administration, Environment andLand defense Department.

ARTICLE IN PRESSR. Baratti et al. / Neurocomputing ( ) – 17

Giovanni Sechi is Associate Professor at the University of Cagliari, Italy. Since1993 he is teaching Water Resources Management. His research current topics aremainly in the 5eld of Hydrology and Water Resources Planning and Management.His scienti5c activity is focused on in�ows-out�ows modeling, �ood stochasticmodels, control and mitigation of droughts and optimization techniques in multi-functional water resources planning and management.

Nicola Toreno received the B.Eng. degree in Mechanical and Manufacturing Engi-neering, SheEeld Hallam University in 1995 and the Laurea degree from Universityof Cagliari in 1998. After a stage at SARAS S.p.A, and having been IT tutor atCagliari University (Economics), he has conducted research on neural networksand wavelets for Hydrocontrol S.c.r.l. from October 2001 to November 2002. Theresearch has been accomplished in collaboration with the Chemical EngineeringDepartment of Cagliari University. Now he is a mechatronics designer at CAT99(TECNOSISTEMI GROUP).