Abstract
Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.
Highlights
As a traditional geostatistical tool, variograms have been well-utilized for rainfall purposes, showing attributes that quantify and model the correlation and the variability of spacial or time structures represented by the rainfall dataset [1,2,3,4]
Variograms have some limitations to their use, such as in the direct estimation of rainfall, which is why they are only a complementary tool for the geostatistical analysis of data; in turn, experimental variograms are calculated from recorded data, which commonly consist of small samples or big samples that lack information, which means extrapolations and/or interpolations are needed
In order to prove our model for our case of study, we performed curve fitting for the variogram of each rainfall station
Summary
As a traditional geostatistical tool, variograms have been well-utilized for rainfall purposes, showing attributes that quantify and model the correlation and the variability of spacial or time structures represented by the rainfall dataset [1,2,3,4]. There are a lot of advantages of using variograms to analyze rainfall or geostatistical time series, such as a correctly determined variogram that supports a reliable statistical estimation. It helps design and modify the sampling network; the entire study includes an essential amount of samples for the variogram to be feasible [7,8]. Variograms have some limitations to their use, such as in the direct estimation of rainfall, which is why they are only a complementary tool for the geostatistical analysis of data; in turn, experimental variograms are calculated from recorded data, which commonly consist of small samples or big samples that lack information, which means extrapolations and/or interpolations are needed
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