One of the main problems in hydrology is the time scale of the rainfall data. Most of the rainfall data is given at a time scale coarser than the one needed for an estimation of spatially continuous rainfall, for drainage system design or many other applications in hydrology and environmental sciences. So, a method to disaggregate monthly rainfall to daily or lower temporal scale is very important in many applications. Many authors have addressed this problem by preserving some statistical properties of the rainfall series by using some stochastic methods including several stochastic rainfall models. The lowering resolution methods must be low cost and low storage methods 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 modified the objective function proposed by Guenni and Bardossy (2002) for solving the disaggregation rainfall problem and we use the spectral projected gradient (SPG) method. This method is a deterministic low cost and low storage method based on the projection of the negative gradient that uses a spectral choice of the steplength that makes the method very competitive and sometimes preferable than some other low cost optimization techniques. In contrast with the stochastic method, a deterministic method 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 where 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 takes into account typical features of the initial rainfall series used as initial iterate and avoid daily precipitations outliers that might occur as an artifact of the simulation procedure.