Conditional Gaussian simulations

The purpose of this section is to use conditional Gaussian simulations (CGSs) to reproduce the spatial soil moisture patterns. CGSs are performed using the closest 40 measurement points and using soil moisture network B. Furthermore, CGSs are performed using the predictors that are used for EDKs as secondary data. Figure 6.17 shows the spatial soil moisture patterns obtained using CGSs including and excluding secondary data in the simulations and in comparison to GEOtop simulated soil moisture map (input), while figure 6.18 shows the frequency distributions of soil moisture maps of figure 6.17. Figure 6.17 shows that when using gradient as secondary data to CGSs produces spatial soil moisture patterns that are more close to the actual patterns. Using secondary data from only one source (e.g., cosine aspect) to the CGSs also somehow show soil moisture patterns (figures 6.17c – 6.17l). In addition, performing CGSs without considering any secondary data (figure 6.17b) also somehow show the patterns. When using secondary data from two sources to the CGSs (figure 6.17m) produce spatial soil moisture patterns worse than the patterns reproduced without including secondary data or including secondary data from one source to the CGSs. On the other hand, when secondary data from multi sources are used in the CGSs, produce the worst soil moisture patterns (figure 6.17n). Therefore, we conclude that the more the secondary data sources are incorporated in CGSs, the worse the reproduced the patterns. Therefore, care should be taken when incorporating secondary data in CGSs. In general, all CGSs reproduce spatial soil moisture patterns better than the soil moisture patterns reproduced by kriging algorithms.

Figure 6.18 shows that all CGSs produce bimodals soil moisture frequency distributions, similar to the frequency distribution of GEOtop simulated soil moisture map. This is due to the fact that in CGSs the data (input) is first transformed into normal score, then the CGSs are performed on the transformed data, and finally simulated normal scores are back-transformed into simulated soil moisture patterns (e.g., Goovaerts 1997). In the previous sections we show that kriging algorithms are poorly reproducing soil moisture frequency distribution of the input. In this section we show that all CGSs are well reproducing soil moisture frequency distribution of the input. As the soil moisture patterns reproduced by CGSs are much better than the soil moisture patterns reproduced by kriging algorithms, this indicates that reproducing the frequency

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distribution of the input is necessary to reproduce the actual spatial soil moisture patterns.

a) GEOtop simulated map b) No secondary data

c) Elevations d) Gradient

e) Cosine aspect f) Wetness index

g) Longitudinal curvature h) Soil depth

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i) Laplacian j) Coordinates

k) Hydraulic conductivity l) River network

m) Combination of gradient and cosine n) All predictors except river

aspect network, hydraulic conductivity

and coordinates

Figure 6.17: Soil moisture maps obtained using conditional Gaussian simulations and in comparison to the simulated soil moisture map (input).

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Figure 6.18: Frequency distribution of the top 5cm soil layer obtained using conditional Gaussian simulations in comparison to the simulated soil moistures: a) Simulated soil moisture, b) No secondary data is used, c) Elevations, d) Gradient, e) Cosine aspect, f) Wetness index, g) Longitudinal curvature, h) Soil depth, i) Laplacian, j) Coordinates, k) River network, l) Hydraulic conductivity, m) Combination of gradient and cosine aspect, n) All predictors except coordinates, river network and hydraulic conductivity.

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6.6 Conclusion

Soil moisture patterns are studied using OK, and external drift indicator kriging (EDIK). The soil type is used as indicator for krigings, while the following indices: DEM, gradient, cosine aspect, wetness index, longitudinal curvature, soil depth, laplacian, coordinates, river network, hydraulic conductivity, and their combinations are used as drifts (predictors) for EDIK. Furthermore, CGSs are used to reproduce soil moisture patterns.

Analysis of directional variogram of soil moisture shows that there is no anisotropy. Results show that all krigings reproduced unbiased soil moisture estimates. Although all krigings reproduced unbiased soil moisture estimates, OK, and UK reproduced very smoothed patterns and are very different from the actual patterns. The patterns reproduced using DEM, wetness index, soil depth, river network, hydraulic conductivity, and laplacian as predictors for EDIK, are similar to the patterns reproduced by the OK and UK. While using gradient and cosine aspect as predictors for EDIK have clearly showed the patterns. The combination of all predictors except river network, hydraulic conductivity, and coordinates for EDIK, reproduced the closest patterns to the actual patterns. The frequency distribution and the variogram of soil moisture of the selected 240 points are very similar to the frequency distribution and the variogram of the simulated soil moisture map, respectively. The frequency distribution of the simulated soil moisture somehow showed to have bimodal distribution, while the frequency distributions obtained using all kriging algorithms showed to have normal distributions. Result shows that the closer the frequency distribution to the simulated frequency distribution, the better the reproduced the soil moisture patterns. Nevertheless, none of the above krigings is able to capture the extreme values of soil moisture. The residual soil moisture maps, as obtained from kriging cross validation, and the frequency distributions of soil moisture show that the 240-soil moisture measurement points are reasonably enough to establish permanent soil moisture network in the watershed. On the other hand, CGSs show that when using gradient as secondary data, reproduced the best patterns (similar to the actual patterns). In general, all CGSs clearly show the spatial soil moisture patterns and all CGSs reproduce soil moisture histogram of the input. Therefore, CGSs are preferred than krigings in studying spatial patterns.

7. Utility of remotely-sensed precipitation products for hydrological simulations

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Utility of remotely-sensed precipitation products for