Gap filling based on a quantile perturbation factor technique

Abstract

The presence of gaps in hydro-meteorological series is a common problem at the moment of analyzing data series. That is the case of the Ecuadorian hydrological data series, presenting eventual gaps of short term duration. The Paute River Basin, located in the Southern Ecuadorian Andes, is one of the most monitored basins in Ecuador, with 25 rainfall observed sites during the period of 1963 till 1990. However, its data base suffers of about 20% of missing data. For this research, two techniques were evaluated comparing their efficiency in the filling of missing gaps. The first one is based on multiple linear regressions, which applies a logarithmic transformation to the data and then converts the data to normalized standard variables. The second one is a new proposed technique based on quantile perturbation approach after a classical prior gap filling. It is used to shelter estimations for high and low intensities based on: i. Identification of the station with the highest monthly correlation ii. Selection and ranking of the stations for which the correlation is significant, tested by the t-test, iii. Gap filling based on the stations with the highest significant correlation, and iv. the application of a correction factor to the filled value. For the evaluation, 3 un-interrupted daily rainfall data series were selected. Data series were deleted in a random way, simulating the 20% of missing data. The two filling techniques were applied separately. Finally, data series were evaluated by the different statistic criteria. Results indicate that the proposed technique performs an efficient filling of missing gaps. It supports the definition of gaps corresponding to high or low events and avoids, in a certain range, the averaging of the series. However, it might lead to double counting of high/low extremes events.