ABSTRACT Historical rainfall records are relevant in hydrometeorological studies because they provide information on the spatial features, frequency, and amount of precipitated water in a specific place, therefore, it is essential to make an adequate estimation of missing data. This study evaluated four methods for estimating missing monthly rainfall data at 46-gauge stations in southwestern Colombia covering 1983-2019. The performance of the Normal Ratio (NR), Principal Components Regression (PCR), Principal Least Square Regression (PLSR), and Artificial Neural Networks (ANN) methods were compared using three standardized error metrics: Root Mean Square Error (RMSE), Percent BIAS (PBIAS), and Mean Absolute Error (MAE). The results generally showed a better performance of the nonlinear ANN method. Regarding the linear methods, the best performance was registered by the PLSR, followed by the PCR. The results suggest the applicability of the ANN method in regions with a low density of stations and a high percentage of missing data, such as southwestern Colombia.

RESUMO Os registros históricos de precipitação são relevantes para os estudos hidrometeorológicos porque fornecem informações sobre as características espaciais, frequência e volume de precipitação de água em um local específico, portanto, é essencial realizar uma estimativa adequada dos dados faltantes. Esta pesquisa avaliou quatro métodos para estimativa de dados de precipitação faltantes mensalmente em 46 estações de medição no sudoeste da Colômbia, abrangendo os anos de 1983 à 2019. O desempenho dos métodos de Razão Normal (NR), Regressão de Componentes Principais (PCR), Regressão por Mínimos Quadrados Principais (RMQP) e Redes Neurais Artificiais (RNA) foram comparados usando três métricas padronizadas para os erros: Raiz do Erro Médio Quadrático (REMQ), Percentagem BIAS (PBIAS) e Erro Absoluto Médio (EMA). Os resultados com frequência mostraram um melhor desempenho do método ANN não-linear. Com relação aos métodos lineares, o melhor desempenho foi registrado pelo PLSR, seguido pelo PCR. Os resultados sugerem a aplicabilidade do método ANN em regiões com baixa densidade de estações de medição e alta porcentagem de dados faltantes, como o sudoeste da Colômbia.

Abstract The knowledge of rainfall regimes is a relevant requirement for many activities such as water resources planning, risk management, agriculture activities management, and other hydrologic applications. The present study has consisted of validating four techniques (one linear, one non-linear, and two hybrids) that allow identifying homogenous regions. We take the monthly rainfall in the Southwestern Colombia (Nariño), an area of 33,268 km2 characterized by complex topography and local factors that can influence the rainfall behavior, to test all techniques. The results showed overall the best performance for the approach related to non-linear principal component analysis and self-organizing map. However, in all mainly prevail two regions: the Andean Region and Pacific Region with a bimodal and unimodal regime, respectively. The bimodal one dominates over the Andes mountains range and the unimodal one the coastal zone. The application of non-linear approaches provided a better understanding of the seasonality of rainfall, and the results may be useful for water resource management.