Simulation and analysis of runoff from a partly glaciated meso-scale catchment area in Patagonia...

HYDROLOGICAL PROCESSESHydrol. Process. 23, 1019–1030 (2009)Published online 15 December 2008 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/hyp.7210

Simulation and analysis of runoff from a partly glaciatedmeso-scale catchment area in Patagonia using an

artificial neural network

Tobias Sauter,1* Christoph Schneider,1 Rolf Kilian2 and Michael Moritz3

1 Department of Geography, RWTH Aachen University, D-52056 Aachen, Germany2 Department of Geology FB VI, D-54286 Trier, Germany

3 Department of Physical Geography, Werthmannstrasse 4, D-79085 Freiburg i. Br. Germany

Abstract:

In this study, a model based on an artificial neural network (ANN) was developed to forecast the runoff of a meso-scale,partly glaciated (40%), Alpine catchment area in the southernmost Andes in Patagonia, Chile. The study area is located in amaritime climate with a mean annual air temperature of C5Ð7 °C and about 5500 mm of precipitation per year at sea level.

The multilayer feed-forward network is designed to make use of the Levenberg-Marquardt algorithm to increase the speedof computation (convergence). Using climate data recorded at an automatic weather station nearby as well as water levelrecords measured simultaneously, the ANN model was trained and verified using independent training and validation datasets.Parameters and the corresponding time lags were determined by statistical methods such as partial, cross- and autocorrelation.The results of the simulation confirm that the proposed model was able to identify the underlying non-linear relationshipsbetween the input parameters and the observed discharge. The correlation during validation shows a significant correlationcoefficient of 0Ð98, and an RMSE of 0Ð02 m respectively. However, it is almost impossible to decipher the internal behaviourof ANN due to its black-box character. Nevertheless, valuable insights were gained in the complex input–output relationships,and the occurrence of dependencies between different input variables were detected using global sensitivity analysis (GSA).The results of the GSA were compared with those of multiple linear regression (MLR). While the performance of the ANNis much better than the MLR, both models return similar results in terms of the dependency of the discharge upon inputvariables. It was found that despite the large proportion of glaciated surface area within the catchment, discharge is mainlycontrolled by precipitation (49%). Furthermore, the runoff is slightly influenced by temperature (19%), global radiation (15%)and wind speed (16%).

While the ANN proves to be a very efficient tool for simulating runoff in glacerized, Alpine catchments from meteorologicaldata, the GSA method, as outlined and used in this paper, offers a useful approach of analysing ANN output. Copyright 2008 John Wiley & Sons, Ltd.

KEY WORDS artificial neural network; stream-flow forecasting; rainfall-runoff modelling; Patagonia; South America; GlobalSensitivity Analysis

Received 13 May 2008; Accepted 20 October 2008

INTRODUCTION

During the last decade, informatic tools, such as artifi-cial neural networks (ANNs), have gradually been intro-duced into geophysical sciences and engineering. Sincethen, ANNs have been successfully applied in hydrolog-ical sciences to a wide range of application areas suchas classification, sediment transport, forecasting devicesand submodels of complex processes. A good review ondifferent applications of ANN used for various hydro-logical problems has been given by Minns and Hall(2004) and the American Society of Civil Engineers(ASCE) Task Committee (ASCE, 2000a,b). The conceptof neuronal computing thereby offers an important alter-native to the existing traditional, more well established,‘hard computing’ paradigms (Kecman, 2001; Soloma-tine, 2005). Decisive advantages of the ANN approach

* Correspondence to: Tobias Sauter, Department of Geography, RWTHAachen University, D-52056 Aachen, Germany.E-mail: [email protected]

mainly arise from its universal ability to approximateany multivariate function, which allows its applicationto unknown complex systems or processes (Hsu et al.,1995; Tsoukalas et al., 1997; Zell, 2003). Recently, suchapproaches have become more important in hydrologi-cal sciences as research questions often address complexsystems that are mostly controlled by non-linear pro-cesses. These non-linearities induce small uncertaintiesand unpredictable variations of the system behaviour intime (chaotic behaviour) and cannot be described byclassical statistical procedures (Poddig and Sidorovitch,2001). Adaptation of computation rules through learningeven makes networks insensitive to changes in modelassumptions and fluctuating boundary conditions so thatnetworks can easily be applied to various problems(Kasabov, 1998; Kecman, 2001). However, despite themultiplicity of so-called data-driven methods and theirracy development, a certain reluctance to apply themhas been revealed (Maier and Dandy, 2000; Dawson andWilby, 2001; Jain et al., 2004; Minns and Hall, 2005).

Copyright 2008 John Wiley & Sons, Ltd.

1020 T. SAUTER ET AL.

This attitude could be ascribed to the general problemsof interpreting ANNs, in particular, their internal func-tional behaviour. This implies that it is often not possibleto reveal why an ANN produces the answer it does. The‘knowledge’ of the network is distributed over the mul-titude of neuron weights (associative memory) and ishard to reconstruct (Minns and Hall, 2005). The needfor explanation triggered several studies dealing with thesubject in the last few years. An attempt has been madeto derive rules by comparing weight values with parame-ters of conceptual (Jain et al., 2004) and physical modelsas well as by heuristic approaches (Wilby et al., 2003;Sudheer and Jain, 2004).

This study not only deals with the prediction of runoffby ANN but also tries to point out existing input–outputrelations by analysing the complex structure of neuronlinkages as an entity by a Global Sensitivity Analysis(GSA), and thus, provides an alternative approach toidentify model properties. Consciously, assignments ofprocesses to specific hidden neurons have not beenconducted since the distributed information is difficult, ifnot almost impossible to decipher, and therefore, it is hardto allocate physical processes to neurons and weights.As the results in this paper show, this method can beuseful for the interpretation and comprehension of themodel behaviour. Based on this information, conclusionsof characteristic features of the basin can be drawn.The suggested methodology has been exemplified by theapplication of the procedure to a glaciated river basin. Tothe knowledge of the authors, no further studies have yetinvestigated the ability of ANNs to predict discharge inglaciated river basins.

METHODS

ANN

There is a category of problems that depends on a hugenumber of subtle factors which cannot be described bylinear algorithms (Freeman and Skapura, 1991; Kasabov,1998; Kecman, 2001). The human brain has the abil-ity to process such information dynamically and learnfrom it by reorganizing its structure during cerebration.Similar to biological nervous systems, the artificial neu-ral network is a data processing system composed of alarge number of simple, highly interconnected elements(nodes) operating in parallel (Tsoukalas et al., 1997).Each node consists of two parts: the propagation functionthat sums the weighted inputs and, to a certain extent, anon-linear filter, the so-called activation function (transferfunction), through which the activation signal is passed(Equation (1)). Usually, this activation function is a dif-ferentiable sigmoid logistic function with values between�1 and 1 (Freeman and Skapura, 1991; Tsoukalas et al.,1997; Kasabov, 1998; Kecman, 2001; Zell, 2003; Demuthet al., 2005). Mathematically, the activation function isgiven by

ϑ�netj� D 1

1 C e�˛nPetj�1�

Sum of theweighted

inputsTransferfunction

x0

x1

x2

xn

netj=Σwijxii=1

n

w0j

w1j

w2j

wnj

oj=ϕ(netj)oj

Output

Figure 1. Schematic illustration of an artificial neuron

where ˛ defines the slope of the function and netj thesum of the weighted inputs of the node j (Figure 1). Thenodes are mostly arranged in three-layer architecture, asshown in Figure 2. Information is mainly processed inthe hidden layer, which at the same time, represents themost important unit within the network. The ability ofgeneralization is basically affected by the right choiceof nodes in the hidden layer (Uvo et al., 2000; Dawsonand Wilby, 2001). Depending on the given input, the out-put layer finally provides the network result. In addition,some authors (e.g. Tsoukalas et al., 1997; Kasabov, 1998;Kecman, 2001) refer to the inputs, where the data areintroduced to the network as another layer even thoughthey are not real nodes. Besides the network topology,the applied learning algorithms which adapt the connec-tion weights are essential differences between individualnetworks. This process is accomplished by means of twofunctions: learning and recall (Tsoukalas et al., 1997).The learning phase adapts the weights with the object ofgenerating the desired output based on the input signal,whereas the recall phase compares the constructed outputvector, oj, with the desired vector, tj, by calculating thenetwork performance function, ε (Equation (2)). Duringtraining, the weights are iteratively adjusted so that theerror is minimized. ε is usually equal to the mean squarederror (MSE) (Demuth et al., 2005), e.g.

ε D 1

n

n∑jD1

�tj � oj�2 �2�

The way of adjusting the weights in order to minimizethe performance function is given by learning rules. Oneof the most common rules used for training feed-forwardnetworks is called backpropagation, a supervised learningtechnique which computes the gradient of the error withrespect to the modifiable weights backwards through thenetwork. Instead of using the basic gradient descent meth-ods, the high-performance Levenberg-Marquardt algo-rithm was applied for fast optimization (minimization)(Demuth et al., 2005). The supervised training processrequires an adequate set of learning examples in order toabstract learned data patterns and apply them to unseenexamples properly. After successful training (adaptationof weights) the network is able to solve similar problemsof the same class that have not been trained explicitly.

Copyright 2008 John Wiley & Sons, Ltd. Hydrol. Process. 23, 1019–1030 (2009)DOI: 10.1002/hyp

ANALYSING RUNOFF IN PATAGONIA USING ARTIFICIAL NEURAL NETWORK 1021

x1 x2 x3

Comparison

Desired output

Weight adjustmentalgorithm

o1 o2Error

Output-Layer

Hidden-Layer

Input-Layer

x4

w15 w47w16 w46

w17 w45w25 w37

w26 w36w27 w35

w58 w79

w78 w59

w68 w69

1 2

5 6 7

98

43

Figure 2. Architecture of a multilayer feed-forward network with supervised learning

The quality of simulations depends highly on both theinput variables and the architecture of ANNs. Unfortu-nately, capable procedures to determine optimum net-work architectures, especially to detect optimal numberof nodes in the hidden layer, could not be established sofar (Poddig and Sidorovitch, 2001). Basically, the size ofthe hidden layer just comes up to a fraction of the inputlayer. Indeed, comprehensive studies of Maier and Dandy(1998, 2000) have shown that the number of neurons canbe optimized effectively by simple trial-and-error tech-niques. Commencing with one neuron in the hidden layerthe number of neurons were increased gradually. Foreach network structure 10 simulation runs were carriedout and analysed in order to get a representative sample.The assessment of the models was undertaken by usingthe Akaike information criterion (AIC) (Akaike, 1974)and the Bayessche information criterion (BIC) (Rissa-nen, 1978). These information criteria are computedaccording to

BIC D m Ð ln�RMSE� C p Ð ln�m� and �3�

AIC D m Ð ln�RMSE� C 2 Ð p �4�

where m is the number of samples, p the number ofneurons in the hidden layer, and the root-mean-squarederror (RMSE) (Equation (12)). The information criteriaincorporate statistical performance indicators as well asthe complexity of the model, which is indicated bythe number of parameters (neurons), in the assessmentof the model. The number of parameters is taken intoaccount negatively as otherwise comprehensive modelswith many parameters are preferred. From Figure 3 itfollows that, as a result of the great number of inputvariables, the network requires 47 neurons in the hidden

0 20 40 60−1.6

−1.4

−1.2

−1

−0.8x 104

Hidden Nodes

Err

or

Sco

re

Figure 3. AIC and BIC scores for ANN using 1 to 58 hidden nodes

layer. Usually a great number of hidden units (weights)enhances the chance of overfitting. However, the bestnumber of units depends on many factors like the numberof input and output units, the number of training cases, theamount of statistical noise, the complexity of the functionto be learned and the ANN architecture. There are somerules of thumb which relate the total number of weightsof the network to the number of training cases. However,these recommendations do not apply if ‘early stopping’(see Section on Results) is used to avoid overfitting asapplied in this study. For the early stopping method itis essential to use many hidden units in order to avoidlocal optima ‘traps’. Therefore, no upper limit on thenumber of weights is evident until now. The final networkarchitecture consists of 89 neurons in the input layer, 47neurons in the hidden layer, and one neuron in the outputlayer. All computations were carried out using Matlabsoftware.



Global Sensitivity Analysis (GSA)

Sensitivity analysis provides information on how sen-sitive a model output is with respect to individual factorsof the model, which are usually subject to certain vari-ability or uncertainty (Beven, 2001; Ratto and Saltelli,2001; Saltelli et al., 2004). Factors can be distinct ele-ments of the model such as parameters or input variablessuch as in this case study. In contrast to local sensi-tive analysis which estimates the partial derivatives ofthe output caused by a factor, while nominal values areallocated for the remaining factors, the GSA considersthe caused output variability while factors are varied overtheir domain simultaneously (Saltelli et al., 2000; Saltelliet al., 2004). For this purpose, probability density distri-butions for each factor have to be defined, from whicha sample of factor values is subsequently generated andused for model runs. From these model runs, the effect ofeach factor on the model output can be estimated (Hom-mat and Saltelli, 1996; Ratto and Saltelli, 2001). Theseeffects are best estimated by a variance-based sensitiv-ity analysis since the GSA is neither bound to linear nornon-additive models and, therefore, particularly suitablefor studying ANNs (Hommat and Saltelli, 1996; Rattoand Saltelli, 2001; Sobol, 2001; Saltelli et al., 2004).Such methods decompose the output variance into fac-torial terms called importance measures in the form of

SY Ds∑

iD1

SYjXi C∑

i

∑i<j

SYjXij C SYjX1,...,s �5�

where s is the number of factors, SY the total variance ofthe model output, Y, and Xi denotes an input factor. Theassociated importance measures are defined as

SYjXi D V�E�YjXi D xŁi �� 6�

SYjXij D V�E�YjXi D xŁi , Xj D xŁ

j��

� V�E�YjXi D xŁi �� V�E�YjXj D xŁ

j�� 7�

and are analogous for higher-order terms. The expectationof Y in consequence of Xi having a fixed value, xŁ

i , isdescribed by the term E�YjXi D xŁ

i �, while V stands forthe variance over all possible values of Xi. Finally, thevariance-based sensitivity indices, Si, can be calculatedby dividing the importance measures by the total outputvariance

Si D SYjXi

SY. �8�

Sensitivity indices with indexes i D 1, 2, ..s are so-called first-order indices which describe the main effect ofeach factor on the model output variance (Saltelli et al.,2004). However, interaction effects and dependenciesamong factors are not taken into account by the first-order indices. Since interaction effects may have a stronginfluence on the output variance, in particular, with anincreasing number of factors, the total sensitivity indicesSTi should also be estimated (Ratto and Saltelli, 2001).The total sensitivity indices sum the main effect and all

effects of interaction with other factors where a givenfactor, Xi, is participating. The STi can be computed using

STi D SYjXi C SYjXi,¾i

SY, �9�

where SYjXi,¾i indicates all important measures involvingthe factor Xi. A method that estimates the main effectsas well as interactions between factors is the extendedFourier Amplitude Sensitivity Test (extended FAST) asproposed in Saltelli et al. (2000, 2004) and Ratto andSaltelli (2001). In addition, this method can treat a‘group’ of factors as one single factor, which offers someattractive advantages in application.

STUDY SITE AND DATA

The developed ANN was calibrated with the measureddischarge data of the small Rio Lengua in southernChilean Patagonia on the southern part of PenınsulaMunoz Gamero at 52°500S and 73°000W (Figure 4). RioLengua drains the Glaciar Lengua, a minor ice body thatis part of the Gran Campo Nevado (GCN) Ice Cap, thesouthernmost major glaciated area north of the Strait ofMagellan. The glacier takes in about 40% of the entirecatchment, which measures an area of approximately15 km2 (Schneider et al., 2007a). The basin is laterallybounded by steep flanks which are barely covered withvegetation and predominantly composed of metamorphicbedrock (Fischbach et al., 2000). Hence, the dischargehydrograph is subject to high variability and shows addi-tional peak discharges. Regional climate can be describedas super-humid with annual precipitation amounting to6500 mm at sea level and even exceeding 10 000 mmon higher ground (Schneider et al., 2003). With monthlymean air temperatures ranging from 1Ð8 °C to 9Ð0 °C atsea level, this climate supports heavy glaciations at alti-tudes above 900 m a.s.l., with fast-flowing outlet glaciersextending down to sea level. These extreme precipitationrates entail high mass-balance gradients (Moller et al.,2007). In the ablation area of Glaciar Lengua, at approx-imately 450 m a.s.l., annual negative mass-balance aver-ages to around 8 m/yr and 22 mm/d respectively (Schnei-der et al., 2007b).

Discharge was measured at four gauging stations bymeans of salt tracer dilution and current meter whereasdata from one gauging station have been used (Figures 4,5). In addition, meteorological data was gained from anautomatic weather station (AWS) located just off thecatchment (Figure 4) (Schneider et al., 2003). All vari-ables have been recorded with time resolution of 3 h overa 2-year period, which represents 5048 data points. Atfirst, significant variables were identified on closer exam-ination of the underlying hydrological processes in thecatchment causing the runoff. The choice of proper forc-ing is a critical issue as predictors extensively affect theaccuracy of the ANN result. Due to the large proportionof glacerized ground the energy balance should be con-sidered in the model besides precipitation and antecedent



Figure 4. Location of the study area and the outline of the drainage basin of Rıo Lengua in southernmost Patagonia. Coordinates correspond to UTMZone 18S. The contour lines in Figure 4(c) are placed at an equidistance of 100 m

runoff. The energy balance on the glacier is basicallyaffected by the sensible heat flux (54%), net radiation(35%) and latent heat flux (7%) (Schneider et al., 2007b).This behaviour can be particularly explained by high pre-cipitation rates and year-round mild temperatures associ-ated with advection of warm and moist air mass fromthe Pacific Ocean. Thus, it appears that besides precipita-tion, further predictors such as air temperature, incomingshortwave radiation and wind speed, which account forthe discharge from the glacier, should be added as inputvariables to the model. Adequate time lags of individualvariables have been ascertained by qualitative examina-tion of the autocorrelation function (ACF), partial auto-correlation function (PACF) and cross-correlation (CC)curves (Figure 6) between influencing variables and therunoff series according to the methodology outlined inSudheer et al. (2002) and Dawson and Wilby (2001).Basically, this method yields first appropriate estimations,as has been proved by other studies (Sudheer et al., 2002;Wilby et al., 2003; Jain et al., 2004). However, it must bementioned that classical statistical procedures are not ableto trace non-linear coherences between input and outputvariables (Poddig and Sidorovitch, 2001). Consequently,

the results should be more or less considered as val-ues for orientation. In this context, values obtained fromthe statistical procedure were additionally compared withthe experiences of the modeller. The chosen time lagsfor the used variables as well as the appropriate modelinput vector are shown in Table I. The different rangesof the variables require rescaling so that their variabil-ity, relative to each other, reflects their importance andnot their absolute ranges. Therefore, the input and out-put variables have been scaled so that the values fallwithin the range [�1 to 1] (Hsu et al., 1995; Shamseldin,1997; Tsoukalas et al., 1997; Kecman, 2001; Zell, 2003;Demuth et al., 2005). This advancement leads to bettersimulation results of extreme peak flows, which are oftencaused by input values that are out of range (Dawson andWilby, 2001). To avoid the critical issue of overfitting,the dataset was subdivided into separate training, test andvalidation sets so that the widely used cross-validationtechnique (Dawson and Wilby, 2001; Minns and Hall,2005; Solomatine, 2005) could be applied (Table II). Inthis technique, the test set is used to monitor the general-ity of the model during training. Depending on the modelperformance, the training is stopped if there is no further



Figure 5. Time series of daily mean values and of water level, precipitation, temperature, incoming shortwave radiation and wind speed; dailyaverages

reduction of the squared error in the test set, while onthe other hand the network learns the specific trainingset. The validation set in contrast consists exclusively ofevaluation data and is not used for training at all. Usingthe available data, the three sets were constructed takinginto consideration the statistical similarity. In particular,this includes similar ranges and variability. Thereby, itwas attempted to incorporate all extreme values in thetraining set so that the whole domain of the predictorswas trained.

RESULTS AND DISCUSSION

Evaluation

In this section, the applicability of using ANN toforecast runoff of the Rio Lengua basin is assessed and

compared with a multiple linear regression (MLR) model.The performances of both models were assessed by modelefficiency (Reff) (Nash and Sutcliffe, 1970), RMSE andcoefficient of determination (r2) as follows

Reff D

n∑iD0

�yi � xi�2

n∑iD0

�xi � x�2

�10�

r2 D Cov�x, y�

Var�x� Ð Var�y��11�

RMSE D

√√√√√√n∑

iD0

�xi � yi�2

i�12�



Cro

ss C

orre

latio

n

0 5 10 15 20 25−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Lag

Cro

ss C

orre

latio

n

Cross Correlation Function betweenwater level and precipitation

95% confidence band

0 5 10 15 20 25−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Lag

Cross Correlation Function (XCF) betweenwater level and wind speed

95% confidence band

0 5 10 15 20 25−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Lag

Cro

ss C

orre

latio

n

Cross Correlation Function betweenwater level and temperature

95% confidence band

0 5 10 15 20−0.5

0

0.5

1

Lag

Par

tial A

utoc

orre

latio

ns

Partial Autocorrelation Function of water level

95% confidence band

0 5 10 15 20−0.2

0

0.2

0.4

0.6

0.8

Lag

Aut

ocor

rela

tion

Autocorrelation Function (ACF) of water level

95% confidence band

0 5 10 15 20 25−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Lag

Cro

ss C

orre

latio

n

Cross Correlation Function (XCF) betweenwater level and incoming shortwave radiation

95% confidence band

(a) (b)

(c) (d)

(e) (f)

Figure 6. Statistical analysis of the input variables: (a) autocorrelation plot of the flow series, (b) partial autocorrelation plot of the flow series,(c) cross-correlation plot of the runoff-precipitation series, (d) cross-correlation plot of the runoff-temperature series, (e) cross-correlation plot of the

runoff against incoming shortwave radiation series and (f) cross-correlation plot of the runoff against wind speed series

in which n is the number of data elements, xi andyi are the observed and computed flows at time step,i, respectively, and x the mean value of the observedflow. The MSEs between observed and modelled runoffin the course of the training are shown in Figure 7.While the error of the training subset decreases contin-uously, the test error increased several times. Accordingto the cross-validation criterion, the training stopped after9 iterations before the defined training goal (validationerror <0Ð001) could be reached. The results of the ANNforecast for the validation subset are shown in Figures 7and 8. In Figure 8, residuals between observed and fore-casted discharge are plotted against water level. It is

observed that deviations are remarkably small (<0Ð22 m)over the whole domain of water levels. Although devi-ations increase with higher water levels, an RMSEvalue of 0Ð023 m (validation) indicates the ability of theANN model to predict high water flows with reason-able accuracy. Systematic errors such as overestimationof peak flows are not identifiable. In order to comparethe ANN model outcomes, an MLR model was devel-oped and applied to the same dataset. Temperature andprecipitation were included in the MLR as explanatoryvariables. The inclusion of further variables, e.g. windspeed and global radiation, do not lead to any improve-ment of the MLR results. The best result was obtained



using the present precipitation, precipitation with a 30-hlag, as well as temperature with a 9-h time lag (Figure 9).The residual plot of the identified MLR model is pre-sented in Figure 10. A comparison of the two modelsmakes it evident that the ANN model is much morepowerful than the MLR model (Figures 8 and 10). Asystematic overestimation of low flows as well as anunderestimation of high peak flows is clearly apparentin the MLR model (Figure 10). The poor efficiency ofthe MLR is also reflected in the goodness-of-fit values,as given in Table III. Both the systematic error and thepoor efficiency indicate that a large amount of varianceis unexplained. Besides residual plots, closer analysis ofthe hydrographs reveals more detailed information on themodel behaviour and quality. Figure 11 shows a shortperiod of the observed and the computed hydrographs,generated by both the ANN and the MLR, during val-idation. The ANN mapped precisely all ranges of thehydrograph. Since the increase in discharge and the grad-ual decay in flow have been mapped successfully it can beconcluded that the non-linear coherences of the systemhave been captured satisfactorily. This result also con-firms the right choice of predictors and their associatedtime lags (Minns and Hall, 2005). However, the forecastof the MLR model is subject to great fluctuations andis not able to predict future events with adequate accu-racy. It is obvious that the association between dischargeand predictors cannot be explained sufficiently by a linearmethod such as the MLR.

Attention must be paid to remarkable events suchas snowfall and flood events associated with infrequentweather patterns. The former can occur if the air temper-ature falls below 2 °C. Based on a temperature gradientof 0Ð63K/100m (Schneider et al., 2007b), snowfall has tobe expected on Glaciar Lengua when positive tempera-tures up to 4 °C are measured at the AWS. Consequently,runoff is reduced because of snow retention and discharge

Table I. Description and time lags of the predictors used in theANN model

Variable Description

runoff (t-1). . . runoff (t-17) Antecedent runoff up to 54 hwithout actual value

prec (t). . . prec (t-17) Antecedent precipitation up to54 h

temp (t). . . temp (t-17) Antecedent temperature up to54 h

rn (t). . . rn (t-17) Antecedent incoming shortwaveradiation up to 54 h

wind (t). . . wind (t-17) Antecedent wind speed up to54 h

0 2 4 6 8 1010−5

10−4

10−3

10−2

10−1

100

101

Mea

n s

qu

ared

err

or

Iterations

Training

Validation

Test

Figure 7. Error trajectory of training, test and validation

becomes relatively low. In contrast, with the onset ofsnow ablation a marked peak flow has to be expected.As Figure 5 shows, temperature temporarily falls belowthis threshold. Nevertheless, the ANN is capable of pro-viding very good forecast of the river flow also duringperiods with low temperatures (Figure 12). In this casethe MLR method shows significant limitations due to itslinear character. This leads to a systematical underestima-tion of the runoff during periods of low temperature in theMLR model. Indeed, the MLR model even predicts neg-ative water levels. The evaluation of flood events, whichoccur more frequently, reveals considerable weaknessesof the MLR (Figure 13). Although high water flows aregenerally underestimated (Figure 10), simulated extremefloods are far beyond the measured flow (Figure 13).Since specific flood events are mainly affected by pre-cipitation, they are subject to high variability. Generally,this makes great demands on the model since the sim-ulation of such events is crucial for the model quality.Unfortunately, these events are predominantly phenom-ena that are beyond the range of the training sample, andtherefore, require extrapolation of the model which isnotoriously unreliable for non-linear system behaviours.Nevertheless, the ANN model extrapolated untrainedflood events with extraordinary accuracy. The success-ful mapping of extreme values is probably the result ofrescaling the variables into a defined range during pre-processing as described in the previous section. All inall, the ANN model supplies a very good forecast for allparts of the hydrograph, whereas the MLR model resultsare extremely inadequate.

Table II. Periods of training, test and validation sets

Set Time period Points Remarks

Training set 11Ð04Ð2002–31Ð05Ð2003 18–3330 Every second data point (even points)Test set 11Ð04Ð2002–31Ð05Ð2003 18–3330 Every second data point (odd points)Validation set 03Ð06Ð2003–01Ð01Ð2004 3376–5048 All data



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Observed water level (m)

Dev

iatio

n (m

)Training

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2


Dev

iatio

n (m

)

Validation

Figure 8. Comparison of actual and predicted water levels of the ANN model for training and validation phases

0.58

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.62

0.62

0.62

0.62

0.62

0.62

0.64

0.64

0.64

0.64

0.64

0.64

0.66

0.660.66

0.66

Precipitation time lag (hours)

Tem

pera

ture

tim

e la

g (h

ours

)

0 6 12 18 24 30 36 42 48 540

6

12

18

24

30

36

42

48

54

Figure 9. Correlation coefficients of the MLR model for different timeand precipitation time lags

Sensitivity analysis

The GSA was computed using SIMLAB software(JRC, 2006). As stated before, density distributions foreach input factor must be defined, primarily based ona corresponding variable-set created for simulation. Thedecision regarding the choice of the probability distri-bution function (PDF) usually depends on the statisti-cal properties and can possibly be estimated empirically(Saltelli et al., 2004). Since this application is at anexploratory stage, a uniform distribution ranging betweentheir extreme values was assigned to each factor. Esti-mation of the main and total effects requires approxi-mately 100 ANN model runs (Saltelli et al., 2004) foreach input variable so that, in total, 8000 samples werecreated. Finally, this set of input vectors was appliedto the trained ANN model. The training tends to resultin different generalization patterns using the same ANNarchitecture because the weights of ANNs are initial-ized randomly (between �1 and 1). However, it has

been found that these generalization patterns are simi-lar in their structures, whereas small fluctuations occurin the rates of each input variable. In order to take intoaccount these fluctuations, 10 ANN networks with thearchitecture mentioned earlier and described in the meth-ods section were analysed. Consequently, the followingsensitivity indices represent the mean values of the sen-sitivity indices obtained by the analysed networks. Fourindices were combined to form a group for one time,each representing a period of 12 h. First-order effects(see Equation (8)) explain in total 96Ð2% of the outputvariance (SY), whereas the remaining 3Ð8% account foreffects of higher order (interaction) (see Equation (9)).This ratio demonstrates the strong non-additive charac-ter of the ANN and notably simplifies the assignment ofeffects on the runoff caused by individual variables. Itis obvious that antecedent water levels (60 h)—as repre-sented by the sum of corresponding Si values—are verymuch present (49Ð2%) in the computation of the simulatedrunoff. The percentage of the explained variance in runoffby the antecedent water levels can be associated with thewater retained in the catchment. Essentially, this is a func-tion of the catchment properties such as geology, glacierextent, soils and vegetation cover (Minns and Hall, 2005).During periods without precipitation, the runoff is justfed by retained water. Hence, antecedent water levels areindispensable for prudential current outflow predictions.Accordingly, the remaining 47Ð0% of SY are attributeddirectly to the main effects that are caused by the mete-orological input variables of precipitation, temperature,incoming shortwave radiation and wind speed. In the fur-ther course of this study we concentrate on the effectsof the meteorological factors only. Subsequently, per-centages presented below refer to this subset of SY.Accordingly, Figure 14 shows the results of the GSAwithout taking note of the antecedent water levels. Theantecedent 12 h (4 ð 3-h mean values) of precipitationexplain around 18Ð7% of the variance caused by meteoro-logical variables. This explained variance decreases whenlonger antecedent periods of precipitation are considered.This implies that a major part of the precipitation is added



0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−1

−0.5

0

0.5

1

1.5

2

2.5


Dev

iati

on

(m

)

Training

0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2


Dev

iatio

n (m

)

Validation

Figure 10. Comparison of actual and predicted water levels of the MLR model for training and validation phases. Note that the labelling of the axesdiffers from Figure 8

Table III. Model performance indices of the ANN and the MLRmodels for training and validation

Model Training Validation

RMSE Reff R2 RMSE Reff R2

ANN 0Ð017 0Ð997 0Ð997 0Ð023 0Ð992 0Ð992MLR 0Ð205 0Ð642 0Ð642 0Ð211 0Ð450 0Ð481

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

days

wat

er le

vel (

m)

measured

MLR

ANN

Figure 11. Observed and modelled hydrograph of ANN and MLR of asingle event (Days 24 Sep 2003 to 30 Sep 2003)

directly to the runoff. However, it must be pointed outthat the group for 48–60 h consists of only 2 Si values,while all the other groups consist of 4 values. This greatlydecreases the explanatory power of the indices of thelast group. Strong interactions between precipitation andother factors can be derived from the high total sensitivityindices of precipitation (Figure 15). During the first 12 h,interactions supposedly take place between precipitation

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17−0.2

0

0.2

0.4

0.6

0.8

1

days

wat

er le

vel (

m)

measured

MLR

ANN

Figure 12. Observed and modelled hydrograph of ANN and MLR duringa period of air temperature below freezing point (Days 15 Jun 2003 to

02 Jul 2003)

and wind speed. The result seems to be reasonable, sinceintensive precipitation in this area is mostly associatedwith high wind speed (Schneider et al., 2007a).

Specific attention must be paid to the influence of tem-perature on the runoff, as pro-glacial fluvial systems areusually driven by the diurnal temperature cycle. Despiteextensive glaciations, such discharge variations superim-posed on base flow are not registered. The small effect oftemperature is confirmed by minor main effects, whichvary between 5Ð3 and 5Ð1% up to a time lag of 24 h.This is in good accordance with the observed hydrograph.Hence, subglacial and supraglacial meltwater drainingfrom the ablation area of the glacier plays a secondaryrole in the discharge pattern. Furthermore, it must bepointed out that rainfall also contributes to snow andice ablation due to latent heat input from the atmo-sphere. This complicates the process of determining thedischarge percentage caused by glacial processes. Nev-ertheless, the importance of this discharge remains farbehind the impact of precipitation on the hydrograph.



0 1 2 3 4 5 6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

days

wat

er le

vel (

m)

measured

MLR

ANN

Figure 13. Observed and modelled hydrograph of ANN and MLR of anindividual flood event (Days 21 Jul 2003 to 03 Aug 2003)

Time (hours)

0-12 12-24 24-36 36-48 48-54

Mai

n ef

fect

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

PrecipitationTemperatureIncoming shortwaveradiationWind speed

Figure 14. Main effects of the meteorological predictors on the runoff(see Equation (8))

Time (hours)

0-12 12-24 24-36 36-48 48-54

Tot

al e

ffect

0.02

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0.06

0.08

0.10

0.12

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0.22

PrecipitationTemperatureIncoming shortwaveradiationWind speed

Figure 15. Total effects of the meteorological predictors on the runoff(see Equation (9))

According to the existing precipitation-temperature dis-tribution the runoff regime can clearly be indicated aspluvio-glacial. Relatively short time lags indicate thatchannel systems must also be well developed, despitethe fact that the pro-glacial lake diminishes the signal ofthe temperature.

The interpretation of the wind speed and incomingshortwave radiation indices turn out to be more diffi-cult. Despite the highly glaciated drainage basin thesevariables do not play a decisive role in the runoff forma-tion. Indeed, indices of incoming shortwave radiation arelow throughout the entire term although a noticeable peri-odic variation, which probably displays its daily cycle, isapparent (Figures 6(e) and 14). Although wind speed isalmost as important as temperature during the first 12 h(4Ð8%), the pattern seems rather arbitrary.

The knowledge gained from the GSA is qualitativelyin good agreement with the prevailing processes asobserved in the study area. In contrast, it is difficult torate the quantitative information obtained as it cannotbe evaluated properly. For this reason, a comparisonwith a calibrated physical model could probably providefurther detailed information. Since the ANN is able tocapture non-linear relations that the MLR is not able toreproduce, it is indicative that rising and falling flowsare differently composed by varying the impact of thedifferent input variables. Therefore, separate GSAs foreach limb of the hydrograph are advisable for furtherstudies.

CONCLUSION

This study shows that ANNs are useful tools for analy-sis and prediction of runoff time series in partly glaciatedbasins. Furthermore, the ANN model provides by far bet-ter results than a simple MLR model. Until recently, noguidelines for developing ANNs could be established,and comparisons and assessments of ANNs versus tradi-tional methods are not available in almost all geosciences.A comprehensive comparison with other studies is diffi-cult because of poor information on the datasets used inother studies and different choices of input parametersand network structure. Due to the black-box character ofANNs only the overall impact of driving variables canbe directly analysed within the system. Complex pro-cesses cannot be explained by ANNs, which makes themparticularly useful in application-oriented studies. Morestraightforward ways for better understanding of ANNsneed to be developed. The GSA proves to be a promis-ing technique in this direction. It is self-evident that theresults of the GSA must be judged critically even thoughthe results obtained appear to be realistic. Further inves-tigations on the application of ANNs on other drainagebasins are considered to be necessary.

ACKNOWLEDGEMENTS

This study was funded by Grant Nos. Schn-680 1/1 andKi-456/6-1 of the German Research Society (DeutscheForschungsgemeinschaft (DFG)). The authors wish tothank M. Stickling and T. Hanneforth for assistance dur-ing field work and S. Schneider for help with the trans-lation into concise English. The authors are grateful toA. Saltelli, S. Tarantola and co-workers for providing the



computational code (SIMLAB) of the GSA. Commentson an earlier version of the manuscript by two anonymousreviewers are gratefully acknowledged.

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Simulation and analysis of runoff from a partly glaciated meso-scale catchment area in Patagonia...

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