Sequential Simulation

Sequential Simulation

Copyright: © 2018 |Pages: 13
DOI: 10.4018/978-1-5225-3270-5.ch010


In this chapter, the first main section analyzed the Conditional Cumulative Gaussian Simulation (CCGS) of myGeoffice©. Section 2 examines the Conditional Indicator Simulation (CIS).
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Unlike Kriging, stochastic simulation does not aim to minimize the local error variance but, instead, focuses on the reproduction of statistics such as the sample mean, variance, histogram or variogram model (Negreiros, 2015). In other words, it preserves the spatial variation of the attribute studied. In addition, it honors observation data values. For Deutsch and Journel (1998), in simulation, the reproduction of global features (texture) and statistics (histogram, covariance) take precedence over local accuracy. According to Goovaerts (1997), a simulated map looks more realistic than the map of the statistically best Kriging estimates because it reproduces the spatial variability modeled from the original data sample. Thus, stochastic simulation is increasingly preferred to Kriging for applications, where spatial variation of the measured field must be preserved and the extreme behavior of the variable under study should not be overlooked.

The trade-off cost for this better reproduction of spatial features by simulation maps is that the local property of the Kriging minimum error variance is lost. A practical consequence is the mean prediction error tends to be larger for simulated values than for Kriging estimates. Another difference between stochastic simulation and Kriging is that many realizations, all of which match reasonably the same statistics (mean, variance, histogram, covariance structure), can be generated whereas there is only a single Kriging map that yields the minimum error variance at each location.

For these three authors, this set of equally-probable realizations is particularly useful for assessing the spatial uncertainty of the attribute under study and for investigating the performance of different scenarios (contamination of a water reservoir, for instance), where each realization may provide a different remediation/cleaning cost and, consequently, dissimilar decision-making. Hence, under this risk analysis perspective and based on 100 realizations, for instance, it is possible to quantify the common and extreme behaviors (minimum, average and maximum) for any spatial phenomenon or calculate the probability of how many of those realizations exceed a particular threshold.

A practical and remarkable example of stochastic geosimulation usage is given by Teixeira et al. (2012). Due the importance of sugarcane cultivation in the state of São Paulo, Brazil, and because of the uncertainty in the process of CO2 emission (FCO2) from agricultural soils, it is important to characterize this primary source of emissions for agriculture purposes, i.e., it plays a major role in global carbon and other cycling of nutrients and is also associated with positive feedback on global climate change.

The major aim of the study conducted by these researchers in Fazenda Santa Olga at Guariba was (1) to characterize the variability and spatial distribution of FCO2, (2) to compare the accuracy of the results of OK (Ordinary Kriging) and SGS (Sequential Gaussian Simulation) and (3) to determine the uncertainty in predicting the spatial variability of FCO2 (based on 141 data samples) using SGS (where the differences between the various outputs provide a measure of uncertainty for prediction purposes).

From the descriptive statistics perspective, the average CO2 soil emission (1.57±0.07µmol m-2s-1) was lower than reported in other studies of Oxisols for sugarcane areas during this evaluation period, a difference that may be related to a lack of rainfall in the days before the experiment (according to the researchers).

Three hundred realizations were computed while the 30th, 68th, 176th and 214th were randomly selected (Figure 1). Further, minimum, medium (E-type), maximum and standard deviation maps were produced by counting the simulated points at each location of the 300 realizations. The standard deviation layout represents the point variation in all simulated realizations. As expected, the deviations were zero at the points of the observed values due to the conditional characteristics of the Gaussian simulation. There is a predominance of high FCO2 values (>3.30µmol m-2s-1) in the upper-right and center of the map whereas low values (>1.80µmol m-2s-1) are distributed throughout the area but with greater consistency in the upper-left portion of the map.

Figure 1.

Gaussian simulation realization maps generated by Teixeira et al. (2012) of FCO2 emissions in Brazil

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