Regional Models for the Evaluation of Streamflow Series in Ungauged Basins
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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 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, 2004). 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. (2000) 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 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 regression- based rainfall-streamflow models for all the gauged basins of the region. In particular, for each basin k the following model has been considered: ()= [ () () (− ) ] Qk t f Pk t , Tk t , Qk t 1 a1,k ,...,an,k (1) where the streamflow Q ()t [mm] at month t depends on the precipitation () k () Pk t [mm], on the average temperature Tk t [°C] in the same month and ()− on the streamflow in the previous month Qk t 1 [mm] through the set of n parameters a1,k ,...,an,k . The second step of the regionalization procedure consists in the determination of n regional relations between the parameters a1 ,...,an and the geomorphological characteristics gi of the gauged basins (average altitude, soil permeability, stream length, etc): = [ ] a1 f g1,g2,...,gi,..., a1,1 ,...,α1,m ............................................. (2) = [ α ] an f g1 , g 2 ,...,g i ,..., an,1 ,..., n,m α α being 1,1 ,..., 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. 4 P. Cutore, G. Cristaudo, A. Campisano, C. Modica, A. Cancelliere, G. Rossi Regression Monthly streamflow data models in k gauged basins Models In k gauged Monthly climatical data basins parameters Calibration of regional Geomorphological characteristics regression model Regional calibration model Monthly streamflow data Validation of regional In l gauged Monthly climatical data basins regression model Geomorphological characteristics Regional validation 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 t f P t , T t , Q t 1 ,g1 ,g 2 ,..., g i ,... a1 ,...,an (3) 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, 2000; Luk et al, 2000). 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 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. Monthly streamflow data Calibration of In k gauged regional Monthly climatical data basins regression or ANN model Geomorphological characteristics Regional calibration model Monthly streamflow data Validation of In l gauged regional basins Monthly climatical data regression or ANN model Geomorphological characteristics Regional validation 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