Evaluation of three Gap-Filling techniques for daily rainfall data sets: a case study in Portugal

In hydro meteorological temporal datasets, the lack of data is a common problem that can be
caused by a variety of factors, including sensor malfunction, errors in measurement, and faults in
data acquisition from the operators. Because complete time series are necessary for conducting
trustworthy analysis, finding efficient solutions to this issue is crucial. In this work, a gap-filling
approach using Kriging-based methods (Ordinary Kriging and Simple Cokriging) is presented and
compared to a linear regression approach proposed by the Food and Agriculture Organization
(FAO method). The proposed procedure consists of fitting semi-variogram models for each month
using the available daily rainfall collected at all stations and averaged for the specific month in the
reference period. The advantages are that only 12 monthly semi-variograms have to be built
rather than one for each missing day of the dataset and that a greater amount of data at a time
can be processed. Then, the Ordinary Kriging and Cokriging are used to estimate the daily
precipitation where it is missed using the semi-variograms of the month of interest. The Cokriging
method is applied considering the elevation data as the second variable. The FAO approach fills
the gaps in rainfall time series by means of a linear relationship between the station that presents
missing data and the best correlated station that has data gathered at the gap time. The
approaches were compared using daily rainfall data from 60 rain gauges from the Portuguese
case study of the InTheMED project for a 30-year reference period (1976-2005). To evaluate the
effectiveness of the proposed approaches, one year of data (1985) was removed from some
stations; missing precipitation data were estimated using data from the remaining precipitation
stations by applying the three procedures. A cross-validation process and an analysis of the error
statistics have been considered to determine the accuracy of the estimation for the three gapfilling
methods. The outcomes pointed out that the geostatistical approaches outperformed the
FAO method in daily estimation. The presented approach performed well in the study area,
especially for the Ordinary Kriging, which well-estimated the daily missing data with a low
computational effort. However, Cokriging did not significantly improve the estimates.
The work presented herein is supported by the PRIMA programme under grant agreement No.
1923, project Innovative and Sustainable Groundwater Management in the Mediterranean
(InTheMED). The PRIMA programme is supported by the European Union.