Regional models for the evaluation of streamflow series in ungauged basins

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1 Regional models for the evaluation of streamflow series in ungauged basins P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Department of Civil and Environmental Engineering, University of Catania, Italy Abstract: The assessment of water resources in a region usually must cope with a general lack of data, both in time (short observed series) as well as in space (ungauged basins). Therefore regionalization techniques have to be adopted in order to transfer information to sites without or with short available observed series. The present paper aims to analyze applicability and limitations of two regionalization procedures respectively based on a two-steps and on a one-step approach, for the evaluation of monthly streamflow series in ungauged basins. In particular, a two-steps and a one-step approaches based on multiple regression equations and a one-step approach based on neural networks are presented. The two-steps approach requires as a first step the estimation of the model parameters for each gauged basin, and as a second step the determination of regional relations between the parameters and the geomorphological characteristics of the basins. On the other hand, according to the one-step approach, hydrological and geomorphological characteristics of the sub-basins are directly considered as model inputs to derive streamflow series. An application of the proposed regional models to a Sicilian river basin is reported. For the investigated region, results indicate that models based on the one-step approach appear to be robust and adequate for evaluating the streamflows in ungauged basins. Key words: regional models - regression equations - neural networks - streamflows 1

2 2 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi 1. INTRODUCTION Although the importance of the use of complex hydrological models for water resources planning and management is widely recognized, experience has often shown that simple models may result more adequate for the needs of the water agencies in assessing the water resources available in a region. Assessment of water resources basically requires the use of streamflow data at adequate time scales (daily, monthly, yearly) (Alley, 1984; Xu and Singh, 1998) and space scales (river basin, regional, national and international). These data are often scarce both in time as well as in space and, depending on the specific adopted model, regionalization procedures have to be introduced in order to transfer information to ungauged basins or to basins with short available observed series. Lumped models that need the preliminary calibration of one or more parameters on the basis of observed streamflows (Klemes, 1986) have been largely adopted by several authors (Xu and Singh, 4). Their application to ungauged basins however requires the application of regionalization procedures of the parameters estimated on gauged basins. The simplest regionalization procedure is based on the direct transfer of parameters to ungauged basins from nearby hydrologically similar basins. Following this approach, Vandewiele and Elias (1995) derived the parameters of a monthly water balance model for 75 basins in Belgium from neighbouring basins. Other regionalization procedures are based on a two-steps approach. In the first step the model parameters are estimated separately for each gauged basin of the region; in the second step, the parameter values are expressed, usually by means of multiple regressions, as a function of the geomorphological characteristics of the examined basins. This approach has been implemented in several hydrological models such as the Sacramento model (Weeks and Ashkanasy, 1985), the HBV model (Braun and Renner, 1992) and in TOPMODEL (Franchini et al., 1996). Recently Fernandez et al. () have adopted a different regionalization procedure based on a one-step approach. This approach is based on the development of a single regional model calibrated using hydrological, climatical and geomorphological data derived from all the gauged basins of the region. Thus, the resulting model can be directly applied to ungauged basins within the region. The present paper aims to analyze applicability and limitations of two regionalization procedures respectively based on a two-steps and on a one-step approach, for the evaluation of monthly streamflow series in ungauged basins. The adopted regionalization procedures are presented in section 2. In particular a regionalization procedure based on a two-steps approach is derived for regression models, while a regionalization procedure based on

3 Regional models for the evaluation of streamflow series in ungauged basins 3 a one-step approach is developed both for regression and neural network models. An application of the regional models to a Sicilian river basin is also reported; in particular, the description of the basin is presented in section 3 while in section 4 the results derived by the application of the different regionalization procedures are illustrated. Finally, in section 5 some final remarks are drawn. 2. ADOPTED REGIONALIZATION PROCEDURES 2.1 Procedure based on the two-steps approach The regionalization procedure based on the two-steps approach has been developed using regression models. The approach (figure 1) requires a first step consisting in the preliminary definition of simple regressionbased rainfall-streamflow models for all the gauged basins of the region. In particular, for each basin k the following model has been considered: Q k [ a,..., a ] () t f P () t, T () t, Q ( t 1) = (1) k k k 1,k where the streamflow Q k () t [mm] at month t depends on the precipitation P k () t [mm], on the average temperature T k () t [ C] in the same month and on the streamflow in the previous month Q k ( t 1) [mm] through the set of n parameters a 1,k,..., an, k. The second step of the regionalization procedure consists in the determination of n regional relations between the parameters a 1,..., an and the geomorphological characteristics g i of the gauged basins (average altitude, soil permeability, stream length, etc): a = [ g,g,...,g,..., a,..., ] 1 f 1 2 i 1,1 α1,m... (2) [ g, g,..., g,..., a α ] an = f 1 2 i n,1,..., n,m being α 1,1,...,α n, m the parameters to be estimated. Equations (1) and (2) determine the two-steps regional regression model. The regionalization procedure has to be completed validating the model on l gauged basins that have not been previously taken into account in the calibration phase. n,k

4 4 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Regional model calibration In k gauged basins Monthly streamflow data Monthly climatical data Geomorphological characteristics Regression models in k gauged basins Calibration of regional regression model Models parameters Regional model validation In l gauged basins Monthly streamflow data Monthly climatical data Geomorphological characteristics Validation of regional regression model Figure 1. Procedure based on a two-steps approach (regression model) 2.2 Procedure based on the one-step approach The regionalization procedure based on the one-step approach (figure 2) has been developed both for regression and neural network models. The approach using regression models can be obtained developing one regional model for all the k gauged basins in which to consider also geomorphological characteristics in addition to hydrological and climatological data: Q [, g, g,..., g,... a,..., ] () t f P() t, T () t, Q( t 1) = (3) 1 2 i 1 an Equation (3) represents the one-step regional regression model. Also in this case, the regionalization procedure has to be completed validating the model on l gauged basins that have not been taken into account in the calibration phase. The same regionalization procedure based on the one-step approach can be obtained developing neural network models. The artificial neural networks (ANNs) usually adopted for resources evaluation are characterized by one input layer, one hidden layer and one output layer of neurons (Minns, 1998; Lange, 1999, Govindaraju, ; Luk et al, ). Considering the high number of neural parameters and their poor physical significance, the proposed regionalization procedure for the model based on the use of ANNs, exclusively follows a one-step approach. Similarly to the approach used for the regressions, one regional

5 Regional models for the evaluation of streamflow series in ungauged basins 5 model for all the k gauged basins has been developed introducing at the same time hydrological, climatological and geomorphological data. The validation of the neural network regional model is then made as previously described for the models based on regressions. Regional model calibration In k gauged basins Monthly streamflow data Monthly climatical data Geomorphological characteristics Calibration of regional regression or ANN model Regional model validation In l gauged basins Monthly streamflow data Monthly climatical data Geomorphological characteristics Validation of regional regression or ANN model Figure 2. Procedure based on a one-step approach (regression and neural network models) 2.3 Evaluation of model performances Calibration and validation of the presented regional models have been carried out, both for the one-step and the two-steps approaches, following the methodology suggested by Klemes (1986). In particular, given a set of observed data relative to a group of basins, calibration is carried out by excluding data relative to one basin, which is used instead for the validation phase. The procedure is then repeated by excluding each time a different basin. For any calibration and validation process, the accuracy of the model has been tested by three different statistical criteria that assess the agreement between observed and simulated streamflows. In particular the mean error (ME), the root mean square error (RMSE) and the efficiency (E) have been considered: N i= 1 ME = ( Q Q ) obs,i N ev,i (4) RMSE = N i= 1 ( Q Q ) obs,i N ev,i 2 (5)

6 6 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi E = 1 N i = 1 N ( Q Q ) ( Qobs, i Qobs ) i = 1 obs, i 2 ev, i 2 (6) where Q obs represents the observed streamflow, Q obs the average observed streamflow, Q ev the evaluated streamflow and N the number of observations. The mean error ME and the root mean square error RMSE measure the average error between the observed and evaluated streamflows. When the ME and RMSE values are close to zero the model performs better.. The zero value indicates that no improvements are attained by the model with respect to evaluating streamflows each month by means of the respective long term average. Values less than zero indicate that the model performs worse than the long term average. The value E = 1 indicates the perfect fit of the model. The efficiency E statistic ranges between [,1] 3. THE CASE STUDY OF THE SIMETO RIVER BASIN The proposed regional models have been applied to several sub-basins of the Simeto river basin in Eastern Sicily (Italy) (figure 3). Nine gauged sub-basins with areas ranging between 19 Km 2 and 183 Km 2 and average altitudes between 414 m a.s.l. and 1479 m a.s.l. (figure 3) have been considered. The 9 examined sub-basins have been selected on the basis of the available years of streamflow observations. In particular 7 streamflow gauges operated by the Sicilian Regional Hydrographic Office (UIR) have been selected in order to dispose of streamflow series with at least 15 years of records. Two additional series of streamflow data, derived from the application of the Pozzillo and Ancipa reservoirs water balances, have been taken also into account. Monthly precipitations and average temperatures have been derived from observations at 2 rainfall stations and at 5 thermometric stations (UIR). The localization of rainfall, temperature and streamflow stations is reported in figure 4. The characteristics of the 9 selected sub-basins are also summarised in table 1. Geomorphological information (figures 5 and 6) have been derived from litological and soil maps (Fierotti, 1989). From the maps, a prevalence of poorly permeable soils can be recognized; furthermore remarkably extended areas with a high permeability and a significant thickness of the aquifer (such as in the specific zone of the Etna volcano) can be identified.

7 Regional models for the evaluation of streamflow series in ungauged basins 7 The hydrological regime in impermeable areas is characterised by long dry periods interrupted by severe stormflow events mainly occurring during autumn and spring. Preliminarily, the Thiessen s method has been used to determine the areal average rainfall series for each sub-basin starting from the available local rainfall data series. Furthermore, the average temperature series for the 9 selected sub-basins have also been determined by weighted averages as a function of the station s altitude. Ancipa reservoir Troina river Simeto river ETNA Nicoletti reservoir Pozzillo reservoir Salso river Dittaino river Don Sturzo reservoir Gornalunga river Simeto river Figure 3 Simeto river basin. Map of altitudes Legend Temperature gauge Rain-Temperature gauge Rain gauge Hydrografic network Basin Sub-basin Reservoir 7 Gauging stations 1 Crisa a Case Carella 2 Dittaino a Bozzetta 3 Salso a Ponte Gagliano 4 Salso a Pozzillo 5 Saracena at Chiusitta 6 Simeto a Biscari 7 Simeto a Giarretta 8 Troina a Ancipa 9 Troina a Serravalle Figure 4 Simeto river basin and considered sub-basins

8 8 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Figure 5 Simeto river basin. Litological map Figure 6 Simeto river basin. Soil use map

9 Regional models for the evaluation of streamflow series in ungauged basins 9 Table 1 Characteristics of the selected sub-basins Sub-basin Area [Km 2 ] Average altitude [m a.s.l.] Record size [years] Record periods Crisa a Case Carella ; ; ; 1986 Dittaino a Bozzetta ; Salso a Ponte Gagliano ; Salso a Pozzillo a Saracena a Chiusitta Simeto a Biscari b ; 19; ; 1966; 1972; ; 1983; Simeto a Giarretta ; Troina a Ancipa a Troina a Serravalle ; a) streamflow time series reconstructed on the basis of the Pozzillo and Ancipa reservoirs water balances b) from 1975 to 1982 Simeto a Maccarone 4. APPLICATION OF THE REGIONALIZATION PROCEDURES TO THE CASE STUDY 4.1 The two-steps approach The two-steps approach making use of the following regressionbased rainfall-streamflow model (step 1): Q a2,k a3,k a4, k () t a P () t T () t Q ( t ) = (7) k 1,k k k k 1 For each of the 9 selected sub-basins, the parameters of a 1,k,..., a4, k (k=1,...,9) have been calibrated maximizing the value of the efficiency E presented in equation (6). The parameter values and the statistics of the 9 regressions are summarized in table II.

10 1 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Table II Application of the two-steps regression model for the 9 sub-basins. Parameter values and statistics (step 1) Sub-basin a1,k a2, k a3, k a 4, k ME [mm/month] RMSE [mm/month] E Crisa a Case Carella Dittaino a Bozzetta Salso a Ponte Gagliano Salso a Pozzillo Saracena a Chiusitta Simeto a Biscari Simeto a Giarretta Troina a Ancipa Troina a Serravalle The table shows that parameters a 2, k and a 4, k provide similar values for all the examined sub-basins; instead, higher differences have been found for the other parameters. As expected, negative values of a 3, k were also obtained for all the regressions, being temperature T () t inversely correlated to streamflows Q () t. Globally, good results have been obtained for all the sub-basins as confirmed by the high values of E ranging between.68 and.8; in addition the low values of ME ranging between and.99 [mm/month] indicate good model estimations of the average monthly streamflows. For the step 2 of the regionalization procedure, different linear and non-linear regressions for determining the regional relations between parameters a 1,k,..., a4, k and the geomorphological and climatical characteristics g i of the 9 gauged sub-basins have been attempted. In particular, considering the small number of sub-basins, simple relations (including only one independent variable) have been used, in order to have a reduced number of parameters in relation to the limited available data; in particular, attempts carried out with average altitude H 3 [ m 1 ], permeability p [%], and stream length L [m] have shown that the average altitude H provides better correlations in comparison to the other examined variables. Equation (8) shows the adopted relations. α 1,2 2, 2 a1 = α1, 1 H ; a2 α2, 1 H α 4, 2 = ; = α + H ; = α H (8) a3 3,1 α3, 2 a4 4, 1 In table III, the parameters of regressions (8) determined over the entire set of available data (all 9 sub-basins) are summarised and the performance of each regression is assessed by means of the efficiency E. From the table, relatively high values of E can be inferred only for the regression between the parameter a 2 and the average altitude H. α

11 Regional models for the evaluation of streamflow series in ungauged basins 11 Table III Application of the two-steps regression model for the 9 sub-basins. Parameter values and statistics (step 2) α 1,1 α 1, 2 α 2, 1 α 2, 2 α 3, 1 α 3, 2 α 4, 1 α 4, E =.43 E =.82 E =.34 E =.59 As already mentioned, in order to assess the suitability of the presented model for the evaluation of the streamflows in the other ungauged subbasins of the region, equations (7) and (8) have been validated according to the methodology suggested by Klemes (1986). In particular, 9 different sets (specifically made of the data of 8 sub-basins) have been obtained excluding by rotation the data of each basin, for the calibration of the parameters of equations (8). The data of the excluded basin have been successively used for the validation of equation (7). The results of the validation are presented in table IV. Table IV Application of the two-steps regression model for the 9 sub-basins. Validation results ME RMSE E Excluded gauged sub-basin [mm/month] [mm/month] Crisa a Case Carella Dittaino a Bozzetta Salso a Ponte Gagliano Salso a Pozzillo Saracena a Chiusitta Simeto a Biscari Simeto a Giarretta Troina a Ancipa Troina a Serravalle As shown in the table, quite good values of the three statistics have been obtained for all the adopted data sets, except for the set considered for the validation of the Saracena a Chiusitta sub-basin; in fact, the high values of ME and RMSE in relation to the observed average monthly streamflow (69.6 mm/month) clearly show the bad model performance for this sub-basin (also confirmed by the value of E close to zero). 4.2 The one-step approach The one-step approach applied by using regression models takes into account the considered geomorphological variables H, p, L, according to the equation: Q a2 a3 a4 a5 a6 a7 () t a P() t T () t Q( t 1) H p = (9) 1 L

12 12 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi The values of the parameters a 1,..., a7, calibrated using the data of the 9 sub-basins are summarized in table V. For this regression a value of efficiency E =.72 has been found. Table V Application of the one-step regression model for the 9 sub-basins. Parameter values and statistics a 1 a 2 a 3 a 4 a 5 a 6 a Again, the validation phase has been carried out according to the methodology suggested by Klemes (1986). The results of the validation are summarised in table VI. Globally, the values of the statistics used for the model evaluation show, for the examined case, better performances of the model based on the one-step approach in comparison to the one based on the two-steps approach. In particular, even if a lower value of E has been obtained for the sub-basin of Dittaino a Bozzetta (.48 instead of.61), a significant improvement can be observed for the sub-basin of Saracena a Chiusitta (.71 instead of.5). However, for this basin, an high value of RMSE (45.63 mm/month) is still obtained also using the one-step regional regression model. Table VI Application of the one-step regression model for the 9 sub-basins. Validation results ME RMSE E Excluded gauged sub-basin [mm/month] [mm/month] Crisa a Case Carella Dittaino a Bozzetta Salso a Ponte Gagliano Salso a Pozzillo Saracena a Chiusitta Simeto a Biscari Simeto a Giarretta Troina a Ancipa Troina a Serravalle In analogy to the one-step model based on regressions, also for the neural networks one regional model for all the 9 gauged basins has been defined directly considering in input geomorphological characteristics in addition to hydrological and climatical data. The architecture of the neural network expressing the regional model is characterized by 6 neurons in the input layer (3 associated to the hydrological variables P () t, T () t and Q( t 1) and 3 associated to the

13 Regional models for the evaluation of streamflow series in ungauged basins 13 geomorphological variables H, p and L) and 1 neuron in the output layer associated to Q () t. Many attempts have been carried out to determine the proper number of neurons in the hidden layer. In fact, only limited literature information exists on the optimal dimension of the hidden layer in order to well approximate the transfer function. In particular, the use of few neurons may determine bad results in calibration while overfitting conditions can occur when a too large number of neurons is considered, as expected due to the increased number of parameters. According to Swingler, (1996) and Berry and Linoff (1997), the hidden layer dimension has been assumed to be minor than the double of the number of neurons in input. The Levenberg-Marquadt (Levenberg, 1944; Marquadt, 1963) algorithm has been adopted for the neural network training. The architecture of the neural network regional model is reported in table VII. The table also reports the values of the three adopted statistics which show a very good performance of the regional model in the calibration phase. Table VII Application of the neural network model for the 9 sub-basins. Model architecture and statistics input hidden output ME RMSE E neurons neurons neurons [mm/month] [mm/month] The results of the application of the validation methodology are summarised in table VIII. Table VIII Application of the neural network model for the 9 sub-basins. Validation results ME RMSE E Excluded gauged sub-basin [mm/month] [mm/month] Crisa a Case Carella Dittaino a Bozzetta Salso a Ponte Gagliano Salso a Pozzillo Saracena a Chiusitta Simeto a Biscari Simeto a Giarretta Troina a Ancipa Troina a Serravalle The table shows that in the validation phase, the neural network model based on this approach has provided, for 6 of the 9 sub-basins better results in comparison to the one-step regression model.

14 14 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Globally, the comparison between values of the statistics reported in tables IV, VI and VIII shows that, for the examined case, better results have been provided by the procedures based on the one-step approach. Some results of the validation of the three regional models are also presented in the graphs of figure 7; in particular, the figure shows the comparison between evaluated and observed streamflows for 3 of the 9 considered sub-basins showing different performances in the evaluation of streamflow series. 2 a) regression model "two-step" 2 a) regression model "one-step" 2 a) neural networks "one-step" b) regression model "two-step" 2 b) regression model "one-step" 2 b) neural networks "one-step" c) regression model "two-step" 2 c) regression model "one-step" 2 c) neural networks "one-step" Figure 7 Comparison between observed and simulated streamflows according to the different regionalization procedures (a - Dittaino a Bozzetta; b - Salso a Pozzillo; c - Simeto a Biscari) 5. CONCLUSIONS Applicability and limitations of two regionalization procedures respectively based on a two-steps approach and on a one-step approach for the evaluation of monthly streamflow series in ungauged basins were analyzed in the paper. A regionalization procedure based on the two-steps approach was derived using regression models, while a regionalization procedure based on the one-step approach was developed by using both regression and neural network models.

15 Regional models for the evaluation of streamflow series in ungauged basins 15 The regionalization procedures were applied to 9 gauged sub-basins of the Simeto river and were validated according to the methodology suggested by Klemes, excluding by rotation each sub-basin from the calibration phase and using it successively for the validation phase. The two-steps approach based on regression equations globally provided good results in step 1 for all the sub-basins, while in step 2 an high correlation between model parameters and sub-basin geomorphological characteristics was found only for one of the four considered parameters. Globally, the two-steps regression model resulted to be validated for all the sub-basins, except for one of them, showing a limited applicability for the evaluation of streamflows in the ungauged sub-basins of the examined region. The one-step approach based on regression equations globally led to better results in comparison to the previous two-steps approach with acceptable values of the statistics for all the sub-basins. Further improvements were obtained with the one-step approach based on neural networks which provided better results for 6 of the 9 sub-basins in comparison to regressions. Globally, for the investigated region, results indicate that the onestep approach appears to be robust and adequate for assessing the streamflows in sites without or with short available observed series. Further research is needed in order to verify the applicability of the proposed procedures to different basins also with reference to the number of available stations. ACKNOWLEDGMENTS The present research has been developed with the partial financial support of the Italian projects PON-AQUATEC Tecnologie innovative di controllo, trattamento e manutenzione per la soluzione dell emergenza idrica (MIUR) and GENESTO Gestione integrata e sostenibile delle risorse idriche in differenti contesti territoriali (MIUR-CNR, contract no. CU4.59). REFERENCES Alley, W. M. (1984) On the treatment of evapotranspiration, soil moisture accounting, and aquifer recharge in monthly water balance models. Water Resources Research, 2, 8, pp Berry, M. J..A., Linoff, G. (1997) Data Mining Techniques, New York, John Wiley & Sons. Braun, L.N., Renner, C.B. (1992) Application of a conceptual runoff model in different physiographic regions of Switzerland. Hydrologicalal Sciences Journal, 37, 3, pp

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