European Water 50: 35-42, 2015. © 2015 E.W. Publications
Evaluating a modified simple rainfall-runoff model in Mediterranean river basins S. Giakoumakis*, P. Stamouli and D. Tigkas School of Rural and Surveying Engineering, National Technical University of Athens, Greece * e-mail:
[email protected]
Abstract:
During the last decades, numerous rainfall-runoff models have been developed, incorporating various levels of complexity. However, the choice of the proper model remains a challenging task, especially in arid or semi-arid climates such as the Mediterranean, and in cases of limited data availability. In such cases, the use of simple rainfallrunoff models may be still the most suitable approach. In this study, a modified version of the well-known Simple Water Balance (SWB) model is presented. The modified SWB model comprises three calibration parameters instead of one, though it retains the simple structure of the original model. The model was evaluated in two regions of Greece with different Mediterranean climatic conditions (Acheloos and Pinios river basins). The available historic runoff series comprised 19 hydrologic years each, on a monthly basis. Thirteen among them were used for calibrating the model, whereas the six subsequent, for validating it. Two evaluation criteria were used as a measure of performance of the modified model. Their values were relatively high and close for both calibration and validation periods. The outcomes of the analysis indicate an overall satisfactory performance of the modified model. Keeping in mind the size and the complexity of the studied river basins, it can be concluded that the modified SWB model may provide reliable runoff simulation results on monthly scale, even in complex hydrological systems.
Key words:
Rainfall-runoff model; river basins; calibration; validation
1. INTRODUCTION Model is a simplified representation of a real-world system, defined as an abstraction of reality in the simplest way that is adequate for the purpose of the modelling (Mulligan 2004). According to the principle of parsimony, if more than one model can be used for a specific case, the less complex (with the fewer parameters) model should be selected (Box et al. 2013). Rainfall-runoff models are sets of mathematical relationships, correlating rainfall with runoff (Nalbantis 2007). They are useful for a wide range of applications, such as the formulation and testing of hypotheses related to the hydrological processes, the study of runoff response to management practices or land use changes, the assessment of climate change effects on runoff, etc. (Nandakumar and Mein 1997; Chowdhury and Eslamian 2014). Depending upon the kind of equations used, rainfall-runoff models are typically divided into three categories: black box, conceptual and physically-based. The physically-based models produce reliable estimates of runoff through the representation of the physical processes, however they are usually complex and data demanding (Brooks et al. 2013). The use of conceptual models is considered a balanced choice for practical applications, providing satisfactory outcomes with less data requirements (Tsakiris et al. 2006). Model parameterisation is always an issue that should be carefully examined in each case (Phanartzis 1972; Viessman et al. 1989; Kuczera and Franks 2002; Crooks et al. 2014). Increased complexity of a model does not necessarily lead to better performance. Several studies have shown that a hydrological system can be described adequately even by a small set of parameters (Refsgaard and Knudsen 1996; Young et al. 1996; Wagener et al. 2004). Although the majority of the models have good response in humid conditions, water balance models are more efficient in drier climates, such as the Mediterranean. Further, simple models are usually more reliable in cases where low-quality data are available (W.M.O. 1975; James and Burges 1982; Wagener et al. 2004).
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The well-known mono-parametric Simple Water Balance (SWB) model (Diskin et al. 1973) has been used in several studies for the assessment of the hydrological regime, mainly in small watersheds. The sole parameter of the model represents the total soil capacity of the upper soil zone. Despite its simple structure, the model is considered suitable for annual water budget estimates. In this study, a modified version of the SWB model is presented, aiming at providing a more comprehensive, yet parsimonious, model structure for monthly runoff estimation. For this purpose, two additional parameters are integrated into the original model, representing the principal hydrological components of deep percolation routing and groundwater storage. The modified SWB model is evaluated in hydrologically complex river systems, covering a range of Mediterranean climatic conditions. The study areas are in Acheloos river basin (western Greece) and in Pinios river basin (east-central Greece), upstream Kremasta dam site and Ali Efendi and Larissa hydrometric stations, respectively.
2. MATERIAL AND METHODS 2.1 Model structure The SWB model is based on the assumption that the water storage in the river basin takes place in the upper soil zone (i.e. root zone) (Giakoumakis et al. 1991). In this study, a modified threeparametric version of SWB model is proposed. The schematic representation of the modified model is presented in Figure 1. According to this figure, Si (mm) represents the available water for any month i (soil moisture) and Smax is a parameter representing the total soil storage capacity. The monthly soil moisture deficit is then represented by the difference Smax - Si, averaged over the river basin. The water depth Si in the soil increases by the monthly precipitation Pi and is depleted by both the monthly potential evapotranspiration Ei and the deep percolation losses Di.
Figure 1. Schematic representation of the modified SWB model.
Initially, a trial depth of the soil moisture Si' is computed by: Si' = Si-1 + Pi - Ei (mm)
where: Si-1: soil moisture for the month i-1 (mm) Pi : precipitation for the month i (mm) Ei : potential evapotranspiration for the month i (mm)
(1)
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The monthly direct runoff Ri (excess water) depends on the value of Si' (Eq.1). Thus: If Si' > Smax Ri = (Si' - Smax) · Κ'
(2)
Di = (Si' - Smax) · Κ
(3)
Si = Smax
(4)
If 0 ≤ Si' ≤ Smax Ri = 0
(5)
S i = S i'
(6)
Di = 0
(7)
If Si' < 0 Ri = 0
(8)
Si = 0
(9)
Di = 0
(10)
where: Κ' = 1 – Κ Di : deep percolation losses for the month i (mm) K : deep percolation losses coefficient (0 ≤ Κ ≤1) The calculated runoff from the above procedure is mainly concentrated in the winter months, because the groundwater storage is not taken into account. In order to overcome this drawback, the following equation is proposed: Qi = a · Ri + (1-a) · Qi-1
(11)
where Qi is a second, more accurate, approximation of the runoff Ri and a is a delay parameter of the modified model (0 < a ≤ 1). This parameter expresses the lag time of rainfall conversion to runoff. Values close to 0 correspond to a long delay and, as a result, runoff is transposed to spring and summer months, whereas values close to 1 correspond to an instant response of the river basin and, thus, instant runoff formation. 2.2 Evaluation criteria The efficiency of each performed simulation, is evaluated by the NSE coefficient, given by the following equation (Nash and Sutcliffe 1970):
∑( y NSE =
oi
− y! o ) 2 − ∑ ( yoi − yci ) 2
∑( y
oi
− y! o ) 2
where: yoi: observed monthly runoff for the month i (mm) ỹo: mean value of observed monthly runoff (mm) yci: computed monthly runoff for the month i (mm)
(12)
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Additionally, the criterion of the ratio of the sum of the computed monthly runoff over the sum of the observed monthly runoff is also used (Mimikou et al. 1991):
r=
∑y ∑y
ci
(13)
oi
The closer the values of NSE and r are to unity, the better the suitability of the model for describing the rainfall-runoff process.
3. RESULTS AND DISCUSSION 3.1 Study areas The first case study area is in the Acheloos river basin, in western Greece, upstream Kremasta dam site (Figure 2a) (Stamouli 2012). The total basin area is 3572 km2, the mean annual areal precipitation equals 1673 mm and the mean annual inflow to the reservoir 936.5 mm. The region is mountainous with forest vegetation covering approximately the 70% of the area. It is constituted by 56% of permeable carbonate formations and by 44% of impervious rocks (flysch) (Tzouka 2007). Kremasta dam is the largest in Greece. The reservoir area at the spillway crest is 80.6 km2 and the total storage capacity is equal to 4495 hm³ (Zarris et al. 2002). The second case study area includes two sub-basins of Pinios river basin, located in Thessaly region (east-central Greece), upstream of two hydrometric stations, i.e. Ali Efendi of an upstream basin area of 2714.4 km2 and Larissa, of an upstream basin area of 6529.7 km2 (Figure 2b). Pinios river basin is a large flat plain surrounded by high mountains. The mean annual areal precipitation upstream Larissa hydrometric station is equal to 871.2 mm (Xanthopoulou et al. 1997). The geological formations of the Pinios river basin are mostly composed by flysch, limestone and alluvial deposits in lower altitude areas (Nalbantis and Koutsoyiannis 1997).
Figure 2. Study areas: (a) Acheloos river basin (upstream Kremasta dam) (b) Pinios river basin (upstream Ali Efendi and Larissa hydrometric stations).
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The main characteristics of each river basin at the sites of interest are presented in Table 1 (Xanthopoulou et al. 1997; Stamouli 2012). Table 1. Main characteristics of each study area. Area (km2) Mean elevation (m)
Kremasta 3572
Ali Efendi 2714.4
Larissa 6529.7
1054
539.7
414.9
3.2 Runoff simulation and evaluation Monthly data of a 19 hydrologic year period (areal precipitation, potential evapotranspiration and measured runoff values) were available for each case (Stamouli 2012, Nalbantis and Koutsoyiannis 1997). For the calibration of the modified SWB model, data of the first 13 hydrologic years were used, whereas the validation performed with the subsequent 6 hydrologic years. The calibration procedure was carried out by applying a trial and error approach (Tigkas and Tsakiris 2004, Tigkas et al. 2012). In Table 2 are presented the basic statistics on annual basis of the three historic runoff time series for Kremasta, Ali Efendi and Larissa, respectively. The important decrease in Mean Annual Runoff (M.A.R.) reflects the quite different climatic conditions between west (Kremasta) and east Greece (Ali Efendi and Larissa). Table 2. Basic statistics of the historic runoff time series on annual basis. M.A.R. (mm) STD (mm)
Kremasta 936.5 272.6
Ali Efendi 355.9 162.2
Larissa 420.9 195.7
In Table 3 the optimum set of values of the parameters of the modified model, determined during calibration, is presented for each case considered. Table 3. Optimum set of values of model’s parameters. Parameter Smax (mm) K a
Kremasta 108.9 0.68 0.60
Ali Efendi 130.0 0.05 0.45
Larissa 152.0 0.12 0.48
Both NSE and r values, for both calibration and validation periods, for the three study areas, are summarized in Table 4. Table 4. Values of NSE and r for calibration and validation periods. Validation NSE r Acheloos (Kremasta) 0.65 0.90 Pinios (Ali Efendi) 0.68 0.94 0.65* 0.89* Pinios (Larissa) 0.83 1.01 0.53 0.99 * ( ) without considering the extreme runoff value of March 1987 (Figure 3c) River basin
Calibration NSE r 0.69 1.05 0.81 1.01
The monthly runoff simulation results are presented in Figure 3, for: (a) Kremasta (b) Ali Efendi and (c) Larissa. It can be observed that simulated runoff follows the variations of the measured values for both calibration and validation periods, at all sites considered, with the exception of the extremely high runoff value of March for the hydrologic year 1986-87 (last validation year / case of Larissa).
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Figure 3. Monthly measured and simulated runoff for calibration and validation periods at: (a) Kremasta (b) Ali Efendi and (c) Larissa.
Figure 4. Variation of NSE as a function of the parameters of the modified model: (a) Smax (b) K and (c) a, respectively (Kremasta).
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3.3 Sensitivity analysis Indicatively, the sensitivity analysis for Kremasta case study is presented. For each trial, one among the three parameters of the modified model was changed, whereas the other two were kept constant, according to the optimal values referred in Table 3. The sensitivity analysis results (Figure 4) indicate that the model’s performance is almost insensitive to the variation of the parameter Smax (Figure 4a). On the contrary, the parameter K seems to affect significantly the simulation results, while the parameter a has also a considerable effect on the performance of the model (Figures 4b and 4c, respectively). Similar conclusions were made for the other two examined cases (i.e. Ali Efendi and Larissa hydrometric stations).
4. CONCLUDING REMARKS In this paper, a modified version of the SWB model was presented, including two additional calibration parameters. The modified model retains, to a large extent, the simplicity of the original model, while it represents in a more accurate way the hydrological system. The modified SWB model was evaluated in challenging case studies of complex and relatively large river basins, in regions of Greece with Mediterranean climatic conditions. The model calibration was performed using a 13-year runoff series on a monthly basis from Kremasta dam site of the Acheloos river basin (western Greece) and from Ali Efendi and Larissa hydrometric stations of the Pinios river basin (east-central Greece). The suitability of the model was checked by the evaluation criteria NSE and r. Model validation was carried out using monthly runoff data of the subsequent 6 hydrologic years of the available corresponding runoff series. It was shown that both NSE and r values were relatively high and close for both calibration and validation periods. Moreover, the performed sensitivity analysis indicated that among the three parameters of the modified model, principally K and, at a lesser degree, a, seem to affect significantly the simulation outcomes, whereas the modified model is almost insensitive to the variations of Smax parameter. The satisfactory performance of the modified SWB model indicates that it can be a useful tool for reliable hydrologic simulations on monthly scale, even in large and complex river basins.
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