2 FutureWater, Eksterstraat 7, 6823 DH Arnhem, The Netherlands. Email: p.droogers@futurewater.nl

1. Table 1. GA solution to the regional inverse problem: additive and multiplicative. Figure 4. Regional ET over Bata Minor derived by SEBAL. Figure 1. Framework of the stochastic data assimilation technique Figure 5. Fitted regional ET over Bata Minor using additive fitness. Stochastic variables Mean Standard deviation 0.0212 0.0252  (soil parameter) n (soil parameter) 1.4144 0.0381 Emergence date (Edate) November 22 7 days Depth to groundwater 435 cm 33.5 cm Irrigation scheduling (Ta /Tp) 0.72 0.28 Irrigation quality 0.74 dS m-1 2.4 dS m-1 Table 2. GA solution to the regional inverse problem: actual case study. Figure 2. Solution of GA to the regional inverse problem. Jan 19 Dec 22 Jan 19 Dec 22 Feb 16 Feb 16 Mar 16 Mar 16 Figure 3. Fitted regional ET using additive and multiplicative fitness functions. STOCHASTIC DATA ASSIMILATION TECHNIQUE IN REGIONAL HYDROLOGY Amor V.M. Ines1, Peter Droogers2, Kyoshi Honda1 and Ashim Das Gupta1 INTRODUCTION One major problem in regional hydrological modeling is the quantification of the regional data needed in model applications. The classical approach to derive these data is time consuming, labor intensive and costly to implement. For this reason, cost effective and efficient way to derive such regional hydrological properties is becoming important in this area of research. In line with this, the potential of remote sensing (RS) data to derive this information has been emphasized and explored in recent studies where regional inverse modeling can be adopted in the process (Feddes et al., 1993; Droogers and Bastiaanssen, 2000; Ines and Droogers, 2002). In this study, we would like to present a methodology that can be used to derive regional data for the applications of hydrological models at the regional scale using a stochastic data assimilation technique. METHODOLOGY There is a dependency between the system behavior and its properties. Exploring this dependency would allow the characterization of a hydrologic system using an inverse modeling approach. Figure 1 shows the schematic of the data assimilation technique developed in this study. Using a deterministic-stochastic model to represent a hydrologic domain, this can be steered to derive the regional hydrological properties of such system. In this study, regional evapotranspiration (ET) derived from RS data has been used to train the regional model to quantify some system characteristics such as soil hydraulic properties, crop and water management practices, water quality and depth to groundwater. These properties were considered stochastic and are represented by their means, standard deviations and probability density functions (pdfs). SEBAL was used to derive regional ET from RS data and the Extended SWAP model was applied to simulate the regional hydrological processes of the system. Genetic Algorithm (GA) was employed to steer the regional model to quantify the system properties. First, a numerical case study was conducted to verify if the technique works. Here, the pseudo-regional model was applied to simulate a base scenario with the known system properties; 1000 simulations were done to represent the total number of homogenous soil units in the hypothetical system. In the regional inverse modeling, only 10% of it was resampled. Two fitness functions were evaluated in this case, an additive (Eq. 1) and multiplicative function (Eq. 2). The soil hydraulic properties α and n (MVG parameters), crop and water management practices (represented by the emergence date (Edate) and irrigation scheduling criteria (Ta/Tp)) were set as the unknown parameters in the numerical case study. Second, an actual case study was conducted at Bata Minor, in Kaithal, Haryana, India during the 2000-2001 rabi season. Two Landsat 7ETM+ images (Feb 4 and Mar 8, 2001) were used in the analysis. Figure 2 shows the solution of GA to the hypothetical regional inverse problem. The figure shows the stochastic nature of the process. In the figure, the best points were selected and then averaged. The parameter values are shown in Table 1. It appears that applying the multiplicative fitness form has relatively improved the solution of GA. However, in our further study where an increased number of datasets was used, it did not prove to be true in such a case. Figure 3 shows also how the solutions fair with the base scenario. From these results, we can infer, that although we cannot exactly match the parameter values, we can have the opportunity to derive the regional properties of a system with reasonable accuracy using the proposed methodology. Actual Case Study: (1) (2) RESULTS AND DISCUSSIONS Numerical Case Study: Figure 4 shows the regional ET over Bata Minor from SEBAL analysis for Feb 4 and Mar 8, 2001. These were used to steer the regional model to derive some information about the Minor. In the process, only areas planted to wheat were considered. Figure 5 shows the solution of GA to the actual regional inverse problem (using the additive function) and Table 2 shows the values of the considered parameters corresponding to this solution. The values were verified with the measured data in the field and we found that they are reasonably close to the actual data. For instance, the mean and standard deviation of the emergence date is Nov 23 and 8 days, respectively; GA estimated it to be Nov 22 and 7 days; see Ines and Droogers (2002) for more details. CONCLUSIONS (1). The stochastic data assimilation technique works reasonably well to derive regional data for regional hydrological modeling. (2). RS derived data (e.g. ET) are promising to be used in regional inverse modeling. (3). Genetic Algorithm (GA) is promising in regional inverse problems. REFERENCES Droogers P. and W.G.M. Bastiaanssen. 2002. Irrigation performance using hydrological and remote sensing modeling. Journal of Irrigation and Drainage Engineering. 128:11-18. Feddes, R.A., Menenti, M., Kabat, P. and W.G.M. Bastiaanssen. 1993. Is large-scale inverse modeling of unsaturated flow with areal average evaporation and surface soil moisture as estimated by remote sensing feasible? Journal of Hydrology. 143:125-152. Ines, A.V.M. and P. Droogers. 2002. Inverse modeling to quantify irrigation system characteristics and operational management. Irrigation and Drainage Systems. 16 (3): 233-252. 2FutureWater, Eksterstraat 7, 6823 DH Arnhem, The Netherlands. Email: p.droogers@futurewater.nl 1Asian Institute of Technology, P.O. Box 4 Klong Luang 12120 Pathumthani, Thailand. Emails: avmines@ait.ac.th, honda@ait.ac.th, adg@ait.ac.th Contribution to the 2003: EGS-AGU-EUG Joint Assembly held in Nice, France. April 6-11, 2003 .