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A deterministic optimization approach for solving the rainfall disaggregation problem
Debora Cores, Lelys Guenni, Lisbeth Torres

One of the main problems in hydrology is  the time scale of the historical rainfall data, available from many meteorological data bases. Most of the rainfall data is given at a time scale coarser than the one needed for  many applications in hydrology and environmental sciences, as the estimation of spatially continuous rainfall at finer time scales, for drainage systems design and extreme rainfall analysis. A method to disaggregate monthly rainfall to daily or finer temporal scale is very important in many applications. Many authors have addressed this  problem  by using some stochastic methods including several stochastic rainfall models. The lowering resolution methods must be low-cost and low-storage  since the amount of rainfall data is large. The purpose of this work is to formulate this problem as a constrained optimization problem and solve it with a low-cost and low-storage deterministic optimization method. We modify the objective function proposed by  Guenni and Bárdossy for solving the disaggregation rainfall problem and  we use the low-cost spectral projected gradient (SPG) method. In contrast with the stochastic method, a deterministic approach will take into account important information, as for example the gradient  of the objective function. The proposed method was applied to a data set from a rainfall network of the central plains of Venezuela, in which rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. The numerical results show that the SPG method for solving the disaggregation rainfall problem avoids  daily precipitations outliers that might occur as an artifact of the simulation procedure and accurately reproduces the probability distribution. Also, the proposed model and methodology outperforms the one proposed by Guenni and Bárdossy (2002) in the sense that it reduces the absolute  error value  for the statistical  properties from the observed data.

Keywords: Rainfall disaggregation, spectral projected gradient, simulated annealing CompAMa-2015-001-CoresGuenniTorres-Acepted20151003.pdf

Cite this paper:
Cores D., Guenni L., Torres L., A deterministic optimization approach for solving the rainfall disaggregation problem
Bull. Comput. Appl. Math. (Bull CompAMa),
Vol. 3, No. 2, Jul-Dec, pp.7-29, 2015