In practice, geostatistical stochastic simulation is always combined with Monte Carlo method to quantify the uncertainty in spatial model simulations (Isaaks, 1990, Pachepsky and Acock, 1998, Finke et al., 1999, Goovaerts et al., 2001, Saito and Goovaerts, 2001, Van Meirvenne and Goovaerts, 2001, Viscarra Rossel et al., 2001). They do not show the smoothing effect characteristic of kriging interpolated map and looks more “realistic”. the data values at their location, sample histogram and spatial dependence of the attribute value) (Goovaerts, 1997). Instead of a map of local best estimates, geostatistical stochastic simulation algorithms provide multiple conditional realizations of the spatial distribution of attribute values reproducing statistics deemed consequential for the problem at hand (e.g. Thus, there emerges a set of geostatistical stochastic simulation algorithms. However, kriging interpolation algorithms produce maps of best local estimates and tend to smooth out local details of the spatial variation of the attribute (Goovaerts, 1997). Because kriging methods quantify the spatial autocorrelation among measured points and account for the spatial configuration of the sample points around the prediction location, they have been widely used in soil science and forest science (e.g. Geostatistical techniques include ordinary kriging, simple kriging, universal kriging, probability kriging, indicator kriging and disjunctive kriging. Deterministic techniques include polynomial, inverse distance weighted, and radial based functions for interpolation. There are two main groups of interpolation techniques: deterministic and geostatistical (ESRI, 2001). Thus, interpolation or extrapolation is often necessary to derive species and related data for cells where information is missing, based on the inventory data. This is especially true when the simulated area has millions of cells. However, forest inventory data is often sparsely distributed across the landscape and no forest inventory can provide all the information at the cell level. Each cell requires the input of dominant canopy tree species, secondary tree species and/or other species related information (e.g. Most of these models employ a raster data format and the forest landscape is conceptualized as a grid of equal-sized cells or sites. In the last decade many spatially explicit forest models have been developed to simulate forest landscape changes (e.g. This suggests that LANDIS can be used to predict the forest landscape change at broad spatial and temporal scales even if exhaustive species age cohort information at each cell is not available. Application results showed that LANDIS simulation results at the landscape level (species percent area and their spatial pattern measured by an aggregation index) is not sensitive to the uncertainty in species age cohort information at the cell level produced by geostatistical stochastic simulation algorithms. Results showed that Latin hypercube sampling can capture more variability in the sample space than simple random sampling especially when the number of simulations is small. Then it is applied to the investigation of uncertainty in the simulation results of a spatially explicit forest model, LANDIS. Latin hypercube sampling is first compared with a common sampling procedure (simple random sampling) in LU decomposition simulation. In this study, we introduced an effective sampling method (Latin hypercube sampling) into a stochastic simulation algorithm (LU decomposition simulation). Thus, it is of great importance to generate a relatively small set of conditional realizations capturing most of the spatial variability. However, due to the relatively long running time of spatially explicit forest models as a result of their complexity, it is always infeasible to generate hundreds or thousands of Monte Carlo simulations. Geostatistical stochastic simulation is always combined with Monte Carlo method to quantify the uncertainty in spatial model simulations.
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