Jordan recurrent neural network versus IHACRES in modelling daily streamflows

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Jordan recurrent neural network versus IHACRESin modelling daily streamflows

Elena Carla Carcano a,*, Paolo Bartolini a,1, Marco Muselli b,2, Luigi Piroddi c,3

a Dipartimento di Ingegneria Ambientale, Facolta di Ingegneria Via Montallegro 1, 16145 Genova, Italyb Istituto di Elettronica ed Ingegneria dell’Informazione e delle Telecomunicazioni, Consiglio Nazionale delle Ricerche diGenova – Via De Marini 6, 16149 Genova, Italyc Dipartimento di Elettronica e Informazione, Politecnico di Milano – Via Ponzio 3415, 20133 Milano, Italy

Received 18 April 2007; received in revised form 12 August 2008; accepted 30 August 2008

KEYWORDSFeedforward neuralnetwork;Recurrent neuralnetwork;Tapped delayed line;Memory effect;Temporal dependence

Summary A study of possible scenarios for modelling streamflow data from daily timeseries, using artificial neural networks (ANNs), is presented. Particular emphasis isdevoted to the reconstruction of drought periods where water resource managementand control are most critical. This paper considers two connectionist models: a feedfor-ward multilayer perceptron (MLP) and a Jordan recurrent neural network (JNN), compar-ing network performance on real world data from two small catchments (192 and 69 km2

in size) with irregular and torrential regimes. Several network configurations are tested toensure a good combination of input features (rainfall and previous streamflow data) thatcapture the variability of the physical processes at work. Tapped delayed line (TDL) andmemory effect techniques are introduced to recognize and reproduce temporal depen-dence. Results show a poor agreement when using TDL only, but a remarkable improve-ment can be obtained with JNN and its memory effect procedures, which are able toreproduce the system memory over a catchment in a more effective way. Furthermore,the IHACRES conceptual model, which relies on both rainfall and temperature input data,is introduced for comparative study. The results suggest that when good input data isunavailable, metric models perform better than conceptual ones and, in general, it is dif-ficult to justify substantial conceptualization of complex processes.ª 2008 Elsevier B.V. All rights reserved.

0022-1694/$ - see front matter ª 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.jhydrol.2008.08.026

* Corresponding author. Tel.: +39 010 3532472; fax: +39 010 3532546.E-mail addresses: [email protected] (E.C. Carcano), [email protected] (P. Bartolini), [email protected] (M. Muselli),

[email protected] (L. Piroddi).1 Tel.: +39 010 3532472; fax: +39 010 3532546.2 Tel.: +39 010 6475213; fax: +39 010 6475200.3 Tel.: +39 02 23993556; fax: +39 02 23993412.

Journal of Hydrology (2008) 362, 291–307

ava i lab le a t www.sc iencedi rec t . com

journal homepage: www.elsevier .com/ locate / jhydrol


Introduction

Modelling of the rainfall–streamflow (R–R) transformationat any time scale has been a primary concern of hydrologicalresearch for several decades and has resulted in plenty ofmodels proposed in literature. Following Beck (1991), thesemodels can be divided into three categories: metric (empir-ical), conceptual and physics-based. Metric models are dee-ply observation-based: they pursue the system response byextrapolating information from available data. These mod-els are founded on the mathematical link between inputand output series (e.g. rainfall and streamflow data) consid-ering the catchment as a lumped unit, with no explorationof the spatial inhomogeneities of the basin. Besides ANNs,examples of this type of model include classical ARMA, ini-tially developed by Box and Jenkins (1976) and all its exten-sions, and transfer function models (Hipel and McLeod,1994).

The second category of models, on the other hand, de-scribes all the relevant components of hydrological pro-cesses through simplified conceptualisations. A furtherstep towards complexity is represented in physics-basedmodels, as they use a theoretical equation for each processconsidered, e.g. the Saint Venant equation for simulation offlow WHERE. Examples include: IHDM (Beven et al., 1987),SWATCH (Morel-Seytoux and Al Hassoun, 1989). Despitetheir ambition to use spatially-distributed parameters whichreflect the heterogeneity of the catchment, they are of lim-ited practicality in most contexts use due to their complex-ity and data availability requirements. Herein ANNs andIHACRES are introduced for a comparative study.

IHACRES (Jakeman et al., 1990; Littlewood et al., 1997)is an example of a hybrid conceptual-metric model as it usesa conceptual module to estimate the effective rainfall and atransfer function module to convert effective rainfall intostreamflow. ANNs are an example of black-box models.

In black-box models, unfortunately, no physical insight ispossible and the structure of the model is generally chosenfrom a family that shows good flexibility and has been suc-cessfully employed in a similar situation elsewhere (Sjoberget al., 1995). ANNs, in general, have been proved to provideuseful solutions when applied to (1) complex systems that,otherwise, may be poorly reproduced, (2) problems taintedby noise, and (3) circumstances where input is incompleteor ambiguous by nature. ANNs are suited for modelling theR–R relationship due to their ability to synthesize a reliablemodel without needing any prior knowledge of the func-tional relationship between dependent and independentvariables and to treat difficult issues such as the high non-linearity involved in such a processes.

It has been proven (Cybenko, 1989) that ANNs are able toapproximate with arbitrary accuracy (by increasing thenumber of neurones) any function with a finite number ofdiscontinuities.

Although feedforward ANNs were introduced in 1986,mainly through the book of Rumelhart, Hinton and McClel-land, their application in hydrological modelling began onlyin the middle of 1990s. Pioneer researches by Zhu and Fujita(1994) compared the performance of a feedforward ANN tofuzzy logic in predicting a 3 h lead runoff. Runoff depen-dence was expressed by using a window of previous rainfall

inputs. Later, Campolo et al. (1999) made use of a feedfor-ward network to predict the occurrence of flood eventsfrom distributed rainfall and hydrometer data on an hourlytime scale.

Recurrent neural networks (RNNs) have also been used inhydrology and related fields. Connor et al. (1994) high-lighted the advantages of recurrent over feedforward neuralnetworks for forecasting time series that include movingaverage components. Anomala et al. (2000) found out thatRNNs perform better when compared to other ANN architec-tures for predicting watershed streamflows. Recent workdone by Kumar et al. (2004) compares the traditional feed-forward approach to RNNs (trained with ordered partialderivatives), to forecast monthly river flows.

Problems in daily rainfall–streamflowmodelling

Recent severe droughts in many European countries (andelsewhere) have had a significant impact on water supplieswhich, in turn, has serious economic and social conse-quences. Hence, the need to find better tools for manage-ment and design of water resources has become a moreimportant issue than ever before. Despite considerableimprovements introduced into the catchment modellingfield, hydrologists are still limited by a number of factorsin rainfall–streamflow modelling. Inadequate data avail-ability and poor forecast/simulation capability of mostlyused models are two of the most significant.

Regarding data availability, it is known that the transfor-mation of inflow to watershed streamflow depends on aplethora of hydrological and climatic factors such as precip-itation, evapotranspiration, temperature, soil moisture andsnow water equivalence, and many more.

In a favourable scenario, where most of these variableshave actually been measured over a reasonable period oftime, conceptual and physics-based models produce differ-ent levels of understanding of the R–R process. Sophisti-cated conceptual models like TOPMODEL and MIKE SHE(Abbott et al., 1986) implement both climatic and catch-ment descriptive data (e.g., topography, vegetation, andsoil) and represent the inner mechanism of the R–R trans-formation in a detailed way. Thus the level of physical pro-cess understanding that can be gleaned from them is quitehigh. On the other hand, less data-demanding models, likeIHACRES, which require rainfall, streamflow and evapo-transpiration only, produce only the more practical resultsand understanding. When a poor level of information avail-able does not allow the conceptualization of complex phe-nomena, or in general, when data are collected only at afew specific sites in a catchment, empirical models becomethe best choice (Coulibaly et al., 2000). In many practicalcircumstances, where the main concern can only be to makeaccurate predictions with no insight on the internal struc-ture of the process involved, the authors believe black-box models can provide suitable and accurate solutions.

The authors believe that, aside from data requirements,the choice between conceptual and empirical modelsdepends on the temporal scale under consideration. Bothconceptual and physics-based models perform well in con-tinuous or short time scales (daily, sub-daily) where the

292 E.C. Carcano et al.


observations they rely on reflect the physical reality of theR–R process as encoded in the model. Conversely, black-box models, that disregard any conceptualization of the gi-ven phenomenon, may work well also on high scales: daily,monthly, etc.

Hence, daily scale modeling would appear to occupy theempirical and conceptual niches. This paper addresses thecomparison between a hybrid conceptual-metric ap-proaches (IHACRES) to a totally metric approach (ANNs),to model R–R process on a daily time scale. The comparisonbetween the two methodologies will focus on their ability tomodel mean daily discharges, particularly during non-rainydays which are known to make up the bulk of most dailyscale rainfall sequences.

ANNs and conceptual models seem to work in a comple-mentary way regarding rainfall heights as input stress. Whilethe latter have trouble when dealing with rainy days (notethat the exact duration of the precipitation event is un-known); the former perform poorly on non-rainy days. Con-ceptual models, in fact, link directly the given rainfallheight to the corresponding daily streamflow, consideringrainfall as the prime driver, despite the well known temporaldiscrepancy between the two categories. (Annali Idrologici).

As it has been pointed out in the literature (Minns andHall 1996; Campolo et al. 1999) R–R daily modelling is avery challenging benchmark for ANNs since long sequencesof non-rainy days make the reconstruction of the true hyd-rograph a hard task, especially at the start of the peak andduring the decay curve where contradictory information, ora non-unique mapping, occurs when the precipitation hasended and the flow is still decreasing. By this we mean thatnon-rainy days (zero values) are difficult to process becausethey render the input–output mapping non-unique: thesame (null) rainfall value must be associated with differentnon-zero flow values. To overcome this problem, it is essen-tial to determine the catchment memory length (s), or the‘precipitation influence history’, which is a crucial measureof the duration of antecedent precipitation on the currentstreamflow event (Muftuoglu, 1991).

Research’s objectives and paper organization

This work aims to demonstrate the ability of RNNs to solve asimulation task which consists in the reconstruction of dailystreamflow series starting only from rainfall and tempera-ture input data, conversely to the supposed inability re-ported in Hydrological literature (Minns and Hall, 1996;Campolo et al., 1999).

The primary goal is long range streamflow predictionstarting from minimal input information.

Hence, in the former part of the paper ANNs simulationabilities are challenged against a conceptual model requir-ing the same data. Simulations have been conducted overthe entire training set for the two approaches and modelperformances, abilities and shortcomings are discussed.

Further on, in order to focus on the reproduction of lowflows where our attention is mostly placed, data prefilteringtechniques (Ljung or Soderstrom–Stoica) are used to en-hance ANN accuracy in the low frequency range. Frequencyresponse plots show the increased model capability to de-scribe the low frequency dynamics.

The paper is organized as follows: first a detaileddescription of the two model approaches and the data is gi-ven, filtering techniques which focus on drought periods areprovided; the results are then discussed and some conclu-sions are drawn.

Conceptual vs. empirical rainfall–streamflowdaily modelling

The conceptual model: IHACRES

IHACRES is a lumped conceptual-metric rainfall–streamflowmodel originally developed by Jakeman et al. (1990). It is aparsimonious model which requires between 5 and 7 param-eters to be calibrated, and it has been shown to performwell on a broad variety of catchment sizes and temporalscales. It comprises two modules in series: the first moduleoperates non-linearly to calculate effective rainfall from to-tal rainfall and evapotranspiration (or temperature data as asurrogate). The remaining module operates linearly to con-vert effective rainfall to total streamflow, having parti-tioned it into quick and slow flow components.

Various versions of the non-linear loss module have beendeveloped by Ye et al. (1997), Post and Jakeman (1996), andothers. The catchment moisture deficit (CMD) version wasfirst introduced by Evans and Jakeman (1998), and revisedby Croke and Jakeman (2004). The Java-based version ofIHACRES_CMD (Croke et al. 2006) has been used in thisstudy, with the effective rainfall uk given by

uk ¼ ½cð/k � lÞ�prk ð1Þ

where rk is the observed rainfall, c, l and p are parameters(mass balance, soil moisture index threshold and non-linearresponse terms, respectively), and uk is a soil moisture in-dex changing according to

/k ¼ rk þ ð1� 1=skÞ/k�1 ð2Þ

The drying rate sk is given by

sk ¼ sw expð0:062fðTr � TkÞÞ ð3Þ

where Tk is the observed temperature, sw, f and Tr are fur-ther parameters (reference drying rate, temperature modu-lation and reference temperature, respectively). More indetail, f is a temperature modulation parameter whichtakes into account factors affecting seasonal variation ofevapotranspiration, like climate, land use, land cover. Soildrainage and infiltration rates should affect the variationof wetness decline, sw.

This version is based on the non-linear module of Yeet al. (1997), modified to enable the gain of the transferfunction to be directly related to the value of the parameterc, thus simplifying model calibration. The l and p parame-ters are typically only necessary for ephemeral catchments(default values are 0 and 1 respectively). The Tr parameteris correlated with the sw parameter, and is redundant in thenew version of IHACRES (though a value must be input). It isincluded to enable parameter sets derived using the previ-ous version of IHACRES to be adopted (the original IHACRESmodel used the Tr parameter primarily to adjust the dy-namic range of the f parameter, necessary due to the useof integer parameter values).

Jordan recurrent neural network versus IHACRES in modelling daily streamflows 293


The linear module uses a transfer function approach

Qk ¼b0 þ b1 � z�1 þ � � � þ bm � z�m1þ a1 � z�1 þ � � � þ an � z�n

uk�d ð4Þ

Here, Qk is streamflow, d is the delay between rainfall andstreamflow response, z is the time shift operatorz�nuk ¼ uk�n and ai and bi are parameters (see Jakemanet al. (1990) and references therein). The structure of thetransfer function is given by the numbers n and m. Five pos-sibilities are considered: (1,0) corresponds to a single expo-nential store; (1,1) to an instantaneous and an exponentialstore in parallel; (2,0) to a pair of exponential stores in ser-ies; (2,1) two exponential stores in parallel and (2,2) to aninstantaneous store with two exponential stores in parallel.

Artificial neural networks

ANNs are essentially parametric models, whose generality isensured by precise theoretical results. An empirical itera-tive calibration procedure allows the user to find appropri-ate values for the parameters of an ANN by from anarbitrary starting point. There are two major ANNs learningparadigms: supervised and unsupervised learning. In super-vised learning, network outputs are compared to given tar-gets and error feedbacks are employed to train the ANN.Examples are MLP (multiLayer perceptron) and RBF (radialbasis function) networks. In unsupervised learning there isno set target to achieve, and the network must discoverinteresting categories or features in the input data. Koho-nen self-organizing maps belong to this category. In thiswork supervised learning will be adopted.

The multilayer perceptronA MLP network is formed by a set of sensory units that con-stitute the input layer (set of input variables), one or morehidden layers of computational nodes (neurons), and an out-put layer of computational nodes. MLP training is the mostwidely used example of supervised learning, by which thenetwork outputs are compared with known answers andfeedback about the errors incurred is generated. A teacher

(e.g. data relating to physical reality) tells the networkwhat the right answers are; and through an inductive learn-ing approach the network is able to generate rules from gi-ven examples and then generalize its predictive ability witha different data set during the validation phase.

Within this framework, ANNs fall into two categories. In afeedforward neural network, knowledge is acquired duringtraining, which consists of a forward pass (1st phase) anda backward pass (2nd phase). In the first phase informationtravels from each layer to the subsequent one, throughweighted sums and activation functions of the hidden units;and at the end of each forward pass modelled outputs arecompared to given targets, and the mean square error(MSE) is evaluated (Fig. 1).

If the MSE value is higher than a certain value (tolerance)the backward pass modifies the weights through a selectedoptimization technique and the procedure is repeated untilthe desired tolerance is reached.

In Fig. 1 the following notation has been employed. Wewill use it throughout the remainder of this discussion.

• Yi output values,• fi target values,• Vi computational nodes in the hidden layers,• Xk input nodes,• wj,k weights between hidden layers and between inputand the first hidden layer,

• Wi,k weights between the last hidden and the outputlayer,

• g hidden layer activation function,• g1 output layer activation function.

In the case of a single hidden layer, if the pattern l ispresented at the input layer, the jth hidden unit receivesa net input of

hlj ¼

Xk

wj;k � xlk ð5Þ

where xlk is the value of the kth input in the pattern l, and

produces the output

Figure 1 A standard feedforward neural network scheme.



Vlj ¼ gðhl

j Þ ¼ gXk

wj;k � xlk

!ð6Þ

The ith output unit thus receives

hlj ¼

Xj

Wi;j � Vlj ¼

Xj

Wi;jgXk

wj;k � xlk

!ð7Þ

and produces the final output

Yli ¼ g1ðhl

i Þ ¼ g1Xj

Wi;j � Vlj

!

¼ g1Xj

Wi;j � gXk

wj;k � xlk

! !ð8Þ

The error function, depending only on the weights w,(where w is the set of all the weights used in the network)is given by

K½w� ¼ 1

2

Xl;i

½1li � Yl

i �2 ð9Þ

Weights are updated according to gradient rule of the type

Dwnewi;j ¼ �g

@k

@wi;jþ a � Dwold

i;j ð10Þ

where g and a are the Learning Rate and Momentum param-eters. The number of iterations necessary to reach final con-vergence is referred to as the number of Epochs.

The backpropagation algorithm, proposed by Werbos(1974), Parker (1985) and (Rumelhart and McClelland,1986) independently, provides a procedure for updatingthe weights wi,j and Wj,k in any feedforward network givena set of input–output pairs fxl

k ; 1li g.

This paper considers a regression problem (modelled out-puts y should 2 Rþ), therefore g1 is a linear unboundedfunction while g is non-linear bounded (generally: a tanhfunction or sigmoidal function is employed, as suggestedin ASCEE (2000)), and varies within the limits [�1,1].

Even though ANNs are very attractive to hydrologists,they do not provide any kind of description that would helpthe modeller to develop and train the network in a system-atic way, i.e. no process understanding is gained. WhileANNs are considered black-box models, some preliminarychoices must be made manually when creating a network.These involve network topology, network architecture,training algorithm and input selection. No hard and fastrules regarding these options exist for the general case,and in most circumstances, decisions relating to these fac-tors are left to the modeller’s experience and judgment.

In this paper, network topology is considered via thechoice of traditional over recurrent neural networks. Con-cerning network architecture, two or three layered percep-tron with one or two hidden sigmoid layer/s and a linearoutput layer are the most commonly used network typesin water resources (Coulibaly et al., 1999; Maier and Dandy,2000). We also seek a parametrically parsimonious modelable to perform well on different data and preserve gener-alization ability; so also network size is a concern. Inputsshall be selected taking into account the number and com-bination of antecedent data best able to reproduce ob-served behaviour without overly increasing complexity.

Unfortunately, themajor shortcoming in applying the stan-dard feedforward ANN to R–R modelling is that the networkdoes not consider storage elements, and, therefore, temporalconsequentiality. In the feedforward architecture the outputat a particular time t depends on the input at that instant,which is not the best case forR–Rmodelling. Toovercomethislimitation, temporal dependence can be introduced by using

• A feedforward network with the Tapped Delay Line tech-nique (Mozer and Smolensky, 1989).

• Complete Recurrent Networks, whose connections areallowed both ways between a pair of units and even froma unit to itself (Almeida, 1988).

• Partially Recurrent Networks that have mainly feedfor-ward connections, but include a reduced set of feedbackconnections, too. In this architecture, recurrence letsthenetwork remember cues fromthe recent past, but doesnot significantly complicate the training process. A com-plete recurrent network involves a high computationalcost and can lead to stability problems; Elman (1990),Kohonen (1982), Jordan (1986), Jordan (1989) have pro-posed simplified models of this type, which can be trainedby conventional backpropagation (Hertz et al., 1991).

ANN methodology: tapped delayed lines and partiallyrecurrent neural networksThe simplest and most common way to deal with temporalseries is to convert it into an additional pattern on the inputlayer of a network. This process is known as the tapped de-layed line or TDL procedure. In a practical network, addi-tional input values can be obtained by feeding the inputsignal into a delay line that has been tapped at various inter-vals, extracting input data from the past to help estimatethe state of the system at the current time step. The TDLcreates a dynamic element in an otherwise static andmemoryless model. The resulting architecture is sometimescalled a time delay neural network.

The sliding window method of capturing delayedinput data has been widely used in the literature (e.g.Campolo et al., 1999; Tokar and Johnson, 1999;Zealand et al., 1999; Tingsanchali and Gautam, 2000;Coulibaly et al., 2000). Some results (see for exampleCampolo et al., 1999, or Minns and Hall, 1996) have shownthat in order to introduce temporal dependence in aneffective way and reproduce system memory over the basin,rainfall data alone is not sufficient to reproduce flows in aneffective way. Instead, a TDL of prior streamflow values canbe combined with a TDL built on prior rainfall data.

Nevertheless, the TDL procedure is restricted to intro-ducing a limited amount of information, since an increasingnumber of inputs involve a troublesome growth in the num-ber of model parameters (weights) and thus an increase inmodel complexity. A more synthetic way to deal with tem-poral sequences consists of using partially recurrent NNs,which we shall use for their ability to model a sort of systemmemory by feeding cues from the recent past back into theinput layer. Partially recurrent neural networks use a set ofcontext (or ancillatory) units Ci to accumulate a weightedmoving average of all previous information. In this waythe state of the network depends on an aggregate sum ofall previous states as well as on the current input.



Fig. 2 shows the general network methodology used inthis study. It comprises three TDL sections (Td1, Td2 andTd3) and two partially recurrent networks derived fromthe forerunner scheme proposed by Jordan (JNN1 andJNN2). Td1, Td2, and Td3 are based, respectively, on rain-fall, streamflow and temperature data; JNN1 and JNN2are based on rainfall and streamflow data.

In Fig. 2, the input layer is divided in two parts: the trueinput unit and the context units (C1 and C2). The contextunits are fed by the network output y(t) at the previous timestep for the Td2 and JNN2 cases; and also by an aggregatedsum of all previous rainfall values x(t) for JNN1. The true in-put unit is loaded with the current temperature and rainfalldata and by TDL values.

The networks were calibrated using observed rainfall,temperature and streamflow data. Once the weights weredetermined, system performance was tested using mea-sured rainfall, temperature and, at certain points, previ-ously calculated discharges as input.

When discussing the system in depth, we shall use thefollowing notation:

• r(t) observed rainfall height at time t,• Q(t) average calculated streamflow value at time t,

• T(t) average temperature value introduced at time t,• l number of layers employed in the network,• hi number of units in the ith layer,• s number of previous rainfall values considered,• z number of previous streamflow values considered,• d number of previous temperature values considered,• b rainfall memory effect coefficient,• a streamflow memory effect coefficient,• u rainfall memory effect counter, which takes a value of0 or 1,

• w streamflow memory effect counter, which takes avalue of 0 or 1.

We have, in the most basic case and where temperatureis not used, a total of s + z + 1 inputs x

xi ¼ rðt� iþ 1Þ for i ¼ 1; 2; :::; sþ 1 ðTd1Þ ð11Þxi ¼ Qðt� iþ sþ 1Þ for i ¼ sþ 2; :::; sþ zþ 1 ðTd2Þ ð12Þ

Under the most complex regime we have a total ofs + z + d + u + w + 2 inputs. Temperature is considered, aswell as delayed input. The set of variables becomes

xi¼Xt�1k¼1

ak�1 �Qðt�kÞ for i¼ sþzþuþ1 ðJNN2Þ ð13Þ

xi¼Xt�1k¼0

bk � rðt�kÞ for i¼ sþzþuþwþ1 ðJNN1Þ ð14Þ

xi¼Tðt� iþ sþzþ2Þfor i¼ sþzþuþwþ2; . . . ;sþzþdþuþwþ2 ðTd3Þ

ð15Þ

ANN methodology: modelling proceduresThe assessment of ANN input variables require some care. Alack of useful information can impair the learning processseverely, because ANNs do not use any a priori mathemati-cal description that encodes structural information andmust extract this directly from the input data. Trivial andunnecessary inputs may also impede learning for the samereason. Although ANNs are black-box models, any availablephysical insight or existing system knowledge should be usedwhen selecting inputs, in the data pre-processing phase.

Generally, in R–R modelling, the most useful input vari-ables are streamflow and rainfall series because they di-rectly influence the fast response of the catchment. Inmountainous regions where snowmelt must also be ac-counted for, temperature stress may also be a very strongdriver. Delayed streamflow sequences have been demon-strated to greatly enhance ANN performance, especially inforecasting tasks. Other time series have also been consid-ered as input candidates, but no strong consensus hasemerged in the literature (see Tokar and Johnson, 1999).

In this study, the available data set consists of three vari-ables observed daily: streamflow, rainfall and temperature.Rainfall and temperature data are considered as inputs, andthe streamflow sequence as the ANNs target data to be usedfor calibration purposes. Measured streamflows are consid-ered also as inputs to the ANN but only in the training phase.Once the model is fully parametrized with a set of weightswhich enables the network to generalize well on a new setof given data, the streamflow input will no longer be re-quired. Streamflow data is used to test model performance

Figure 2 General scheme of proposed architecture.



(see Fig. 2) in the calibration stage, but since we are consid-ering a simulation problem, the series cannot be consideredas an input during the model validation phase.

At first, a very simple model was built, expressing thestreamflow at time t as a function of the precipitation att. Since a single rainfall value is completely inadequatefor modelling the R–R transformation, a collection of valuesfrom previous time steps needed to be introduced in orderto reproduce temporal dependence. This was accomplishedby Td1 and by JNN1 applied separately and then in combina-tion. When calibrating the TDL schemes, a growing numberof previous values were considered and each time an addi-tional input was added, the goodness of fit statistics wascomputed for the network and compared with the resultsobtained at the previous calibration step; the process wasthen carried out until no significant improvement arose.At the end of the process, the value of s which best repro-duced the streamflow represents the catchment precipita-tion memory length over the basin. With the memoryeffect technique, all values before time t are taken into ac-count. Subsequently, other two TDLs were included: Td2and Td3 and the memory lengths values s (related to rain-fall) and q (related to streamflow) were determined and ap-plied as explained above. For the sake of compactness, bestmodel performance containing JNN1, JNN2, Td1, Td2, and

Td3 have been reported and compared to IHACRES resultsfor both catchments.

Catchment and database description

The models outlined in the previous section were applied todata from two small Ligurian catchments: Argentina andImpero in north-western Italy, located near the Tirrenosea coast (Fig. 3).

Two sequences of 20 years (1952–1971) of daily stream-flow, measured at Merelli for the Argentina River and atPontedassio for the Impero River and rainfall series, ob-tained by applying the Thiessen method to data from atleast six measurement stations inside the catchment and se-ven nearby, were used. Temperature data measured at the‘‘Osservatorio Metereologico’’ in Porto Maurizio were con-sidered appropriate for use in both basins. The series weredivided in three parts for calibration, crossvalidation andvalidation, recalling a standard prescription which recom-mends a database split of 80% for total training and 20%for testing of ANNs (ASCEE, 2000). Crossvalidation has beenintroduced as an early stopping tool to prevent networktraining over fitting and, as a direct consequence, poor gen-eralization ability. A 16 year record was used to calibrateboth the empirical (of which 12 years for real calibration

Figure 3 Location of the two basins.



and 4 for crossvalidation) and the conceptual model, while a4 year record was set aside to test the model performancelevels. A summary of the observations is reported below(Table 1).

When dealing with ANNs, rainfall, streamflow and tem-perature data were normalised to lie in the range of[0,1]. Standardization was carried out through the formula

xnorm ¼x � xmin

xmax � xminð16Þ

The Argentina watershed (192 km2 in size) extends fromMonte Saccarello to Arma di Taggia, and its 39 km streamlength is dominated by a very high and rough course withsharp drops. Several tributaries join the watercourse, themajor ones being the Carpasina, Oxentina and Corte Rivers.Elevations vary from 2199 m at Monte Saccarello (which is

the highest Ligurian mountain), 1776 m at Collardente and1626 m at Monte Ceppo, to sea level at Taggia, which lieson the coast. The Argentina catchment has an overall meanslope of 5.56%.

The Impero watershed (69 km2 in size), originates fromMonte Grande and runs through the valley of the samename. The basin is dominated by rich olive woods over the20 km watercourse. The most important tributaries arethe Trexenda River and the San Bernardo River. Elevationsvary from 1418 m at Monte Grande, 1110 m at Croce di Passodel Maro and 812 m at Monte Arosio, to sea level at Imperiaon the coast. The overall mean elevation of the catchmentis of 464 m and the mean slope is 6%. Arma di Taggia andImperia, located on the deltas of the two rivers (of about100 km far from Genova), are the most populated towns ineach catchment and are about 9 km apart. Both catchments

Table 1 Statistical characteristics of the daily variables

Impero River Argentina River

Training Test Training Test

Period 1952–1967 1968–1971 1952–1967 1968–1971Min Q (m3/s) 0.02 0.03 0.17 0.4Mean Q (m3/s) 1.33 2.13 4.53 6.74Max Q (m3/s) 119 106 246 337Min r (mm) 0 0 0 0Mean r (mm) 3.11 2.93 3.36 2.93Max r (mm) 140.40 106.02 159.7 98.84Min T (�C) 0.8 2.3 0.8 2.3Mean T (�C) 16.14 16.29 16.14 16.29Max T (�C) 33.9 28.6 33.9 28.6

Crosscorrelation function between daily rainfall and streamflow data: Impero River

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Figure 4 Cross correlation between Impero River rainfall and streamflow data.



are based on sedimentary rocks (with a prevalence of flysch)and are marked by the irregular and torrential regimes typ-ical of small Appenninic basins.

Times of concentrations for both catchments are of theorder of few hours. Hence, even though considering dailyaverage flows appears to smoothen out the dynamic effectsinherent in the data, it must be noticed that hydrographrecession curves (our intend as describe in Problems in dailyrainfall–streamflow modelling) cover daily scale and more,as reported by Fig. 13. Moreover, for poorly monitored ba-sins, like ours, sub-daily data are not easily provided.

A simple technique for checking rainfall and streamflowlink is to examine cross correlation. Fig. 4 shows a sequenceof 90 cross correlation values for Impero River. The fairlyhigh peak (�0.6) obtained for a zero lag indicates the lackof delay between daily rainfall and streamflow. At a highertemporal resolution, a 15 h lag becomes apparent, corre-sponding to the delay between rainfall event and the corre-sponding response in streamflow. This is due to a structuralerror in the observed data, as reported in Annali Idrologici,sezione di Genova (Ministero dei Lavori Pubblici, 1952–1977).

The rainfall–streamflow daily observations given in theAnnali Idrologici (which are the primary data source forhydrologists in Italy), hide a temporal discrepancy of 15 hin the date markers: when referring to a given day i, themean daily discharge for that day is measured from 0 A.M.to 0 A.M, while the corresponding rainfall value is measuredfrom 9 A.M. of the previous day to 9 A.M. of the current day.This time lag can be considered as a further advantage ofANN and black-box models in general, as they avoid havingto address the problems of spatial and temporal physicalityof inputs and model parameters; in other words, by relatingpattern of inputs to pattern of outputs, volume continuity isnot a constraint (Minns and Hall, 1996).

Fig. 5 shows the runoff coefficient of the Impero catch-ment derived from the annually averaged daily rainfalland streamflow data. It shows a clear trend in the runoffcoefficient, with considerable reduction during drier years(1964 and 1967).

Assessment criteria

Model performance was evaluated using the mean squareerror (MSE), Nash Sutcliffe statistic (E), the Nash Sutcliffestatistic on the squares of the discharge series E ffip and Mean

Relative Error (MRE) for each hydrograph. Indices 1 and 2 re-fer to calibration and validation performances, respec-tively. The first indicator of model performance, MSE,quantifies the difference between observed and simulatedrunoff in a pointwise fashion along the x axis. It is thus verysensitive to timing differences. MSE is defined as follows:

MSE ¼Pn

i¼1ðQ obsðiÞ � Q calcðiÞÞ2

nð17Þ

Here Qobs and Qcalc refer to observed and simulated hydro-graphs respectively. N is the total number of points mod-elled. For sake of simplicity, in order to have thediscrepancy between target and modelled hydrograph di-rectly expressed in m3/s the root of MSE has been, subse-quently, evaluated and reported herein.

The E statistic proposed by Nash and Sutcliffe (1970) isunity minus the sum of the squared differences betweenthe calculated and observed streamflow values normalizedby the variance of the observed runoff during the periodof investigation.

E ¼ 1�Pn

i¼1ðQ obsðiÞ � Q calðiÞÞ2Pni¼1ðQ obsðiÞ � �Q obsÞ2

!ð18Þ

E lies between one and �1. A value of unity implies thatthe model is exactly matching observations, zero impliesthat the model is no better than assuming the mean flow,and a value lower than zero indicates that the mean valuesof the observed time series would have been a better pre-dictor than the model. As reported by Krauser et al.(2005), the main disadvantage of this criterion is the factthat the differences between observed and simulated valuesare calculated as squares. As a consequence, large values inthe time series are strongly overweighted and lower valuesare underweighted. Keeping in mind our stated aim of pre-dicting flow in dry periods, this is a serious issue. Modifiedversions of E are widely used to overcome this problem.We shall use the E ffip form proposed by Perrin et al. (2001)

E ffip ¼ 1�

Pni¼1ðXobsðiÞ � XcalðiÞÞ2

Pni¼1ðXobsðiÞ � XobsÞ2

0BB@

1CCA ð19Þ

where XðiÞ ¼ffiffiffiffiffiffiffiffiffiQðiÞ

p.

Another criterion widely used in ANNs environment is theMRE defined as follows:

MRE ¼ 1

n

Xni¼1

Q obsðiÞ � Q calcðiÞQ obsðiÞ

�� ð20Þ

MRE tends to favour underestimation when used as a mea-sure of accuracy. In fact, in case of overestimation Qobs <Qcalc and MRE can be greater than 1; while in case of under-estimation Qobs > Qcalc and MRE can never be >1.

Results

IHACRES

The IHACRES model was calibrated over a period from 19/7/1952 to 31/12/1967 for both the Argentina and Impero data,allowing a 200 day warmup period. Preserving the same

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Figure 5 Runoff coefficient for the Impero catchment.



calibration period used for ANNs was intentional, in order tomake direct comparisons between the two approachespossible, even though a shorter period is usually used whencalibrating IHACRES models.

The more complex linear module structures ((2,1) and(2,2), see the conceptual model: IHACRES for details) werefound to be necessary for the reconstruction of the targethydrograph, as the simpler schemes did not adequatelyreproduce both the high and low flows. Concerning MSE(and after that, other performance criteria) the (2,2) runbetter fits calibration data over the two catchments, butmodel (2,1) performs slightly better during validation, sug-gesting that the inclusion of the additional instantaneousstore may not be warranted. The tables reported below(Tables 2, 3) list the two IHACRES model performancesand parameter values.

A detailed analysis of the results (Figs. 6 and 7) showsdiscrepancies in the behaviour of the two catchments start-ing from 1961, with the observed flow becoming systemati-cally greater than the modelled flow.

The results are affected by a gradual change in the re-sponse of both catchments, which can also be highlightedby a break in the double mass plot structure. This impliesthat the anomaly could probably be real and not just anartefact of the model. It could be attributed either to achange in land use or in the rainfall data series. An overallincrease of annual rainfall through the Appenninic regionduring such periods should be rejected, as shown by theanalysis carried out on several catchments located on theopposite coast from Argentina and Impero basins.

ANNs

Models have been run in Matlab environment. The R–Rtransformation was conducted with a three layered feedfor-ward neural network and varying numbers of computationalnodes depending on the amount of input data to be pro-cessed. A sigmoidal activation function was used, and theLevenberg Marquardt algorithm adopted to train the net-work. This second order optimization technique, developedby Hagan and Menhaj (1994), has been demonstrated to befaster and more reliable than other backpropagation vari-ants. The Learning Rate, Momentum and epoch ANN param-eters were set in accordance with the modelling consideredstarting from default values of 0.8, 0.9 and 100,respectively.

Beginning with the TDL technique based on the current aswell as on s antecedent rainfall values, the catchment pre-cipitation memory length s was set to 6 for The Impero Riverand 4 for the Argentina River since no additional inputseemed to appreciably enhance the model’s final accuracy.

It must be noticed that, for both catchments we foundout that the major shortcoming of the TDL models was ex-pressed as a series of persistent plateaus thickened in thelow values of the modelled signal as illustrated in Fig. 8.

This weakness renders the TDL technique on its own un-able to reproduce slow streamflow data where our interestis most placed. Fig. 8 expresses the fact that as the Td1 pro-cedure is by its nature constrained to a limited number ofinput data, as the number of computational nodes andparameters that can be introduced should be kept as low

Table 2 IHACRES parameters

C sw f T(s) T(q) V(s) V(q) V(3)

Model (2,1)Impero River 0.000737 154 2 11.666 0.395 0.617 0.383 –Argentina River 0.00079 164 2 7.627 0.519 0.442 0.558 –

Model (2,2)Impero River 0.001395 66 1.1 38.924 4.357 0.361 0.317 0.322Argentina River 0.002514 46 0.1 102.85 2.87 0.294 0.292 0.413

Table 3 Models results

RMSE1 RMSE2 E1 E2 E1ffip E1

ffip MRE1 MRE2

IHACRESModel (2,1)Impero River 2.502 5.363 0.46 0.31 0.63 0.60 1.015 1.030Argentina River 7.916 13.798 0.60 0.39 0.62 0.59 0.948 0.769

Model (2,2)Impero River 2.486 5.303 0.46 0.34 0.71 0.59 0.702 0.987Argentina River 7.172 14.107 0.67 0.40 0.75 0.59 0.706 0.552

ANNsImpero River 1.603 5.051 0.567 0.389 0.772 0.349 1.641 1.843Argentina River 5.562 11.710 0.789 0.523 0.482 0.565 1.578 1.160



as possible. As the number of input values increases, addi-tional weights become necessary at the expense of modelparsimony: a restricted number of weights (model parame-ters) are always recommended either in order to avoid over-fitting and the curse of dimensionality (see Bellman, 1957).

This problem can be overcome by the memory effecttechnique, which enables a smoother reproduction of targetdata especially on the low flows prior to events with verydry antecedent conditions. It differs from the previous tech-nique in that all prior input data within the specified windoware loaded instead of a sample taken at intervals. The betacoefficient was set to 0.87 for the Impero and 0.82 for theArgentina data (Figs. 9 and 10) (see below). Note that mak-ing beta closer to unity means that the memory effect ex-tends further back into the past at the expense of minorsensitivity to detail. Experiments show that very high valuesof beta (0.97–0.99) lead to instability problems, while val-ues of beta around 0.8 seem to be a good compromise andwork well for both catchments during training and testingphases. This methodology produces slightly better perfor-mances and it shows that the JNN1 model is adequately rep-resenting the behaviour of the catchments (see Fig. 8).

The heap on rainfall heights given in Context 2 (seeFig. 2) gives a dynamic behaviour to the network and en-ables a fairly good streamflow reconstruction, on condi-tion that input series is infinite (Minns and Hall, 1996).In the same way, the heap on previous streamflow datagiven in Context 1 (see Fig. 2) make the hydrographreproduction more accurate; still it has to be noticedthat when antecedent streamflow information is used asinput a big discrepancy arises between training and testset model performances. In the case of forecasting prob-lems where measured streamflows can be used also dur-ing validation period, an almost perfect reconstructionbetween modelled and target signals can be reached,

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Figure 6 Impero River cumulative rainfall, observed andmodelled flow.

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Figure 7 Argentina River cumulative rainfall, observed andmodelled flow.

Test set of River Argentina: Rainfall Memory effect vs. Td1 as ANN inputs

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Figure 8 Comparison between Td1 and JNN1: Argentina River.



but this is not the problem we set out to address. OurANN modelling follows the structure introduced before,with Td2 and Td3 limited to number of two for bothcatchments.

Following Table 4 below, MSE2 values are of 5.051 m3/sfor the Impero River against 11.710 m3/s for the ArgentinaRiver. Differences in the two model performance levelsare noted when using E2 and E2 ffip criteria, the Impero hav-

ing E2 equal to 0.389 and E2 ffip equal to 0.349, againstrespectively 0.523 and 0.565 for the Argentina. This meansthat MSE criterion is not, by itself, sufficient to expressmodel performances.

The following tables show final best results obtained withthe techniques expressed in Research’s objectives and pa-per organization using rainfall, streamflow and temperaturedata, where

Test set extract of measured/calculated streamflows using IHACRES, River Impero

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Figure 9 Test set extract showing Impero daily streamflow reconstruction using IHACRES.

Test set extract of measured/calculated streamflows; River Argentina

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Figure 10 Test set extract showing Argentina daily streamflow reconstruction using IHACRES.



• log is the logistic sigmoidal activation function,• line is the activation function,• L.M. is the Levenberg–Marquardt optimizationtechnique.

Figs. 11 and 12 show the two models best performancesobtained during validation phase, whose results have beenkept for the two approaches comparison.

Data filtering

In order to focus on drought/low flow periods several at-tempts have been made. At first, streamflow series havebeen skimmed out with different threshold lines while thecorresponding rainfall and temperature data remained un-changed in order to preserve the cause-effect of the processconsidered. Results (Fig. 13) demonstrate this one to be auseful technique in case of forecasting task, where theknowledge of previous measured streamflows seem to bethe prime contribute for a good hydrograph reconstruction.However, the same is not true in case of simulation wherethe training of R–R dynamics given at specific intervals isnot sufficient to guarantee good generalization ability overthe entire simulation data set. An alternative to streamflowthreshold is data filtering technique which allows to improvemodel accuracy in a specified frequency band by filteringboth input and output data with a suitable low-pass/high-

pass filter. The filtered data are, then, used for model’sidentification. In case of linear system data prefiltering isactually equivalent to a frequency weighting on the predic-tion error function. In case of non-linear system additionalattentions need to be paid; the reader is herein remandedto the theory explained in ‘On the role of prefiltering innon-linear system identification’ (Spinelli et al.,2005).

Comments

Simulating daily river flowdata under ordinary conditions is ofconsiderable interest for small and poorly monitored catch-ments, for the purposes of better planning and managementof water resources (for domestic, irrigation, and other uses).This problem is more difficult to tackle with ANNs than themore commonones discussed in literature, such as flood fore-casting or river flow prediction at shorter time scales. Weaimed to find a technique able to process the long sequencesof zero values (non-rainy days) which are known to dominatedaily scale rainfall observations. The results showed notice-able improvement gained fromJNNswith the rainfallmemoryeffect technique. These models, by allowing the network toremember the recent past, are able to reproduce target hyd-rograph drought periods and streamflow decay curves withsatisfactory accuracy.

JNNs have proven to overcome in an effective and parsi-monious way (in terms of parameters considered) the inabil-

Test set of River Impero; comparison between measured and calculated

streamflows as inputs to ANN

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Figure 11 ANN streamflow reconstruction: Impero River.

Table 4 ANNs parameters

Catchment Beta, alpha, Td1/Td2/Td3 Hidden layers and neurons Functions Epochs Learning rate and momentum

Impero 0.87, 0.89, 6/2/2 3 and 7/4/1 Log, log, line, LM 35 0.8 and 0.9Argentina 0.82, 0.83, 4/2/2 3 and 8/4/1 Log, log, line, LM 33 0.8 and 0.85



ity expressed by tapped delayed line processes, in whichtemporal dependence necessitates a growing number of in-put values, without the stability problems typical of totallyrecurrent networks. Good results were obtained for the twocatchments considered, showing that the JNN rainfall mem-ory effect (strengthened with the TDL procedure) is a validtool for processing the R–R transformation. Results can becompared to those of a conceptual model approach. Furtherimprovements to the ANN can be obtained by feeding in pre-vious streamflow data, which are generally not consideredas inputs to conceptual models, into the network. Eventhough this seems to unfairly favour the ANN approach,measured streamflow are considered by these models onlyduring training. Thus, a valid comparison between the twoapproaches is preserved.

Concerning the conceptual approach in detail, a rainfall–runoffmodel like IHACRESmay be able to reproduce the influ-ence of climatic drivers such as the reduction in runoff coef-ficient in dry years, but the background trend in runoffcoefficient is not associated with a corresponding trend inthe climate data. As such, the model could not be expectedto reproduce this trend unless an additional driver was in-cluded. There has been a gradual change in land use since1850, but this is unlikely to contribute at the scale consideredby daily R–R modelling. Closer examination of Figs. 5 and 6suggests that the trend in streamflow coefficient pre-1961may be driven by a general upward trend in rainfall. However,the post-1961 increase in streamflow coefficient is as yetunexplained. In 1970, the flow is approximately equal to theestimated areal rainfall, suggesting that there is an error inthe estimated rainfall depth and/or the streamflow volume.This in itself is not a problem for the IHACRESmodel as the er-ror caused would be compensated for by the mass balanceparameter. However, the trend in the streamflow coefficient

from 0.4 to 1 results in poor model performance. It should benoted that for regionalisation studies, errors in the areal esti-mate of rainfall are a significant problem and need to be re-duced as much as possible. Concerning the empiricalapproach in detail, results demonstrate that, if well trained,ANNs are able to gain enough information thus solving a sim-ulation task in an appropriate way. For this reason the earlystopping learning criterion introduced has demonstrated tobe essential to guarantee network’s simulation ability andto limit the troublesome noise in modelled signal which issometimes still present for obvious reasons. Referring tographs 11 and 12 it can be noticed that ANN give a good repro-duction of target hydrographs both in general and on stream-flow decay curves. This is most highlighted by the ArgentinaRiver plotwhereas ANN signal appearsmuch smoother againstthe sharp and intermittent behavior of IHACRES model, eventhough the two models have very close RMSE2 values.

A performance criterion expresses the model ability toperform over an entire data set; therefore results whichshow a good general streamflow reconstruction with verypoor performance on high flow peaks may result worse thanthose with a bad simulation anywhere! For this reasonauthors believe that models abilities should be based notonly on their performances criteria but also on the qualityof their resulting graphs.

Subsequently, in order to focus on low streamflow data,streamflow thresholds and low-pass filtered data have beenintroduced. Among the two, filtering out slow flow dynamicsended out to be the best choice since it enables the networkto an overall good streamflow reproduction whereas thethreshold approach gives up to a streamflow underestima-tion as shown by Fig. 13. The ability of data prefiltering toincrease model’s accuracy in a specified frequency band ishighlighted by the curves reported in Fig. 15 which repre-

ANN streamflow reconstruction: Argentina River

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Figure 12 ANN streamflow reconstruction: Argentina River.



sents the Power Spectral Densities of data of Fig. 14. Fol-lowing Fig. 15 it can be noticed that if original data wereused during model’s identification (continuous red line4

the data set prediction (dotted red line) has frequency error

distributed uniformly (the model has the same accuracy le-vel on low and high frequencies). In case of filtered data(continuous blue line), instead, whereas the attention is fo-cused on low frequency, the data set prediction (dottedblue line) becomes resolutely more accurate. In otherwords, in such frequencies band, the dotted blue line ismuch closer to the continuous red line than the correspond-

Test set of River Impero; ANN recosntruction using threshold on streamflows

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Figure 13 ANN streamflow reconstruction using thresholds: Impero River.

Test set of River Impero; ANN reconstruction using filtered streamflows

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Figure 14 ANN streamflow reconstruction using filtered data: Impero River.

4 For interpretation of colour in Figs. 8, 10–14, the reader isreferred to the web version of this article.



ing dotted red line. Herein the model identified using a low-pass filter is much more capable to reproduce the slow trendof the output signal.

Conclusions

This paper addressed the task of simulating daily river flowsfor water resource purposes, comparing conceptual meth-odologies to black-box ones. Two different neural networkapproaches, the traditional feedforward MLP and the JordanRecurrent Neural Network, were discussed and comparedwith a well-known conceptual model.

The purpose of this study was twofold: (1) we aimed tofind an effective ANN procedure able to reproduce meandaily streamflow data starting from minimal input informa-tion (only precipitation values), and (2) we highlighted mer-its and weaknesses of the two different modellingapproaches. Results confirm that ANNs are able to standthe comparison with a conceptual procedure, obtaininggood performances if correctly trained and supplied with asufficient amount of well-chosen information. Thus, theycan be considered a powerful tool for simulating flowevents, even allowing for their lack of physical interpret-ability. In fact, as long as the user is interested in simulatingthe flow (e.g. filling in missing data) ANNs seem to be thebest option; however, if a physical interpretation of the pro-cess is needed, or if there is limited data available, then theparsimonious conceptual/hybrid models would be pre-ferred, given also the less time necessary for calibration.

Acknowledgements

The authors would like to the thank Barry Croke and JessicaSpate of the Integrated Catchment Assessment and Manage-ment Centre (iCAM) and Department of Mathematics, of theAustralian National University, Canberra, ACT, for the con-stant and irreplaceable help in running and interpretingIHACRES model’s results, and would also like to thank Doc-tor Nicola Podesta for supplying temperature data and for

his devotion in running the Osservatorio Metereologico ofPorto Maurizio (Imperia). A special thank also addressed tothe unknown reviewers for their precious help.

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Figure 15 Power spectral density: Impero River.



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Jordan recurrent neural network versus IHACRES in modelling daily streamflows

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