Comparison of stochastic and deterministic methods for mapping groundwater level spatial variability in sparsely monitored basins

Abstract

In sparsely monitored basins, accurate mapping of the spatial variability of groundwater level requires the interpolation of scattered data. This paper presents a comparison of deterministic interpolation methods, i.e. inverse distance weight (IDW) and minimum curvature (MC), with stochastic methods, i.e. ordinary kriging (OK), universal kriging (UK) and kriging with Delaunay triangulation (DK). The study area is the Mires Basin of Mesara Valley in Crete (Greece). This sparsely sampled basin has limited groundwater resources which are vital for the island's economy; spatial variations of the groundwater level are important for developing management and monitoring strategies. We evaluate the performance of the interpolation methods with respect to different statistical measures. The Spartan variogram family is applied for the first time to hydrological data and is shown to be optimal with respect to stochastic interpolation of this dataset. The three stochastic methods (OK, DK and UK) perform overall better than the deterministic counterparts (IDW and MC). DK, which is herein for the first time applied to hydrological data, yields the most accurate cross-validation estimate for the lowest value in the dataset. OK and UK lead to smooth isolevel contours, whilst DK and IDW generate more edges. The stochastic methods deliver estimates of prediction uncertainty which becomes highest near the southeastern border of the basin.

Spatial Distribution and Mobility Assessment of Carcinogenic Heavy Metals in Soil Profiles Using Geostatistics and Random Forest, Boruta Algorithm

“…For this purpose, apart from the spatial variability of heavy metals at large distances described by the lag distance, the practical interest of variability at short distances is also required for improved characterisation. The Matern constitutes a flexible variogram model with a behaviour of the smoothness and fits the semivariogram close to the origin, supporting the differentiability and continuity of the random variables and covering the local smoothness [26] to plot the sample concentration of soil parameters.…”

Comparison of deterministic and stochastic methods to predict spatial variation of groundwater depth

“…For mapping of water table depth, the approach of interpolation has either been deterministic, such as inverse distance weighting (IDW) (Gambolati and Volpi 1979;Buchanan and Triantafilis 2009;Sun et al 2009;Varouchakis and Hristopulos 2013;Arslan 2014) and radial basis function (RBF) (Sun et al 2009;Arslan 2014) or stochastic, such as ordinary kriging (OK) (Desbarats et al 2002;Kumar and Ramadevi 2006;Ahmadi and Sedghamiz 2008;Sun et al 2009;Varouchakis and Hristopulos 2013;Arslan 2014) and universal kriging (UK) (Reed et al 2000;Kumar and Ahmed 2003;Kumar 2007;Sun et al 2009, Varouchakis andHristopulos 2013).…”

“…Sun et al (2009) compared UK with other interpolation methods for assessment of depth to groundwater and its temporal and spatial variations in the Minqin oasis of northwest China. Varouchakis and Hristopulos (2013) also compared between UK and other stochastic and deterministic methods for mapping groundwater level spatial variability in sparsely monitored basins in Greece.…”

Creating a monthly time series of the potentiometric surface in the Upper Floridan aquifer, Northern Tampa Bay area, Florida, January 2000-December 2009

“…3). Theoretical semivariogram models have been optimized in other studies using visual adjustments (Walker and Loftis, 1997) and weighting schemes (Varouchakis and Hristopulos, 2013). Because the best-fit curve for each month was modeled individually, curve-fit parameters can be viewed as response variables over time.…”

“…The statistical basis of kriging is preferable to deterministic interpolation schemes because it allows the uncertainty in the interpolated values to be quantified. The associated uncertainty directly improves the meaningfulness of the results and can be used further to optimize the location of wells in groundwater monitoring networks (Olea, 1984;Olea and Davis, 1999;Fisher, 2013;Varouchakis and Hristopulos, 2013). In the United States, kriging techniques have been used to map the water-table elevation in the Ogallala Formation in western Kansas (Dunlap and Spinazola, 1984), to improve mapping of the High Plains aquifer in the south-central United States (Olea and Davis, 1999), and to map water levels in regional aquifers in Idaho (Fisher, 2013), Kansas, Arkansas, Oklahoma, and Missouri (Gillip and others, 2008).…”