Browsing by Subject "Kriging"
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Item Analysis of Spatial Performance of Meteorological Drought Indices(2013-01-14) Patil, Sandeep 1986-Meteorological drought indices are commonly calculated from climatic stations that have long-term historical data and then converted to a regular grid using spatial interpolation methods. The gridded drought indices are mapped to aid decision making by policy makers and the general public. This study analyzes the spatial performance of interpolation methods for meteorological drought indices in the United States based on data from the Co-operative Observer Network (COOP) and United States Historical Climatology Network (USHCN) for different months, climatic regions and years. An error analysis was performed using cross-validation and the results were compared for the 9 climate regions that comprise the United States. Errors are generally higher in regions and months dominated by convective precipitation. Errors are also higher in regions like the western United States that are dominated by mountainous terrain. Higher errors are consistently observed in the southeastern U.S. especially in Florida. Interpolation errors are generally higher in the summer than winter. The accuracy of different drought indices was also compared. The Standardized Precipitation and Evapotranspiration Index (SPEI) tends to have lower errors than Standardized Precipitation Index (SPI) in seasons with significant convective precipitation. This is likely because SPEI uses both precipitation and temperature data in its calculation, whereas SPI is based solely on precipitation. There are also variations in interpolation accuracy based on the network that is used. In general, COOP is more accurate than USHCN because the COOP network has a higher density of stations. USHCN is a subset of the COOP network that is comprised of high quality stations that have a long and complete record. However the difference in accuracy is not as significant as the difference in spatial density between the two networks. For multiscalar SPI, USHCN performs better than COOP because the stations tend to have a longer record. The ordinary kriging method (with optimal function fitting) performed better than Inverse Distance Weighted (IDW) methods (power parameters 2.0 and 2.5) in all cases and therefore it is recommended for interpolating drought indices. However, ordinary kriging only provided a statistically significant improvement in accuracy for the Palmer Drought Severity Index (PDSI) with the COOP network. Therefore it can be concluded that IDW is a reasonable method for interpolating drought indices, but optimal ordinary kriging provides some improvement in accuracy. The most significant factor affecting the spatial accuracy of drought indices is seasonality (precipitation climatology) and this holds true for almost all the regions of U.S. for 1-month SPI and SPEI. The high-quality USHCN network gives better interpolation accuracy with 6-, 9- and 12-month SPI and variation in errors amongst the different SPI time scales is minimal. The difference between networks is also significant for PDSI. Although the absolute magnitude of the differences between interpolation with COOP and USHCN are small, the accuracy of interpolation with COOP is much more spatially variable than with USHCN.Item Bayesian Analysis for Large Spatial Data(2012-10-19) Park, JincheolThe Gaussian geostatistical model has been widely used in Bayesian modeling of spatial data. A core difficulty for this model is at inverting the n x n covariance matrix, where n is a sample size. The computational complexity of matrix inversion increases as O(n3). This difficulty is involved in almost all statistical inferences approaches of the model, such as Kriging and Bayesian modeling. In Bayesian inference, the inverse of covariance matrix needs to be evaluated at each iteration in posterior simulations, so Bayesian approach is infeasible for large sample size n due to the current computational power limit. In this dissertation, we propose two approaches to address this computational issue, namely, the auxiliary lattice model (ALM) approach and the Bayesian site selection (BSS) approach. The key feature of ALM is to introduce a latent regular lattice which links Gaussian Markov Random Field (GMRF) with Gaussian Field (GF) of the observations. The GMRF on the auxiliary lattice represents an approximation to the Gaussian process. The distinctive feature of ALM from other approximations lies in that ALM avoids completely the problem of the matrix inversion by using analytical likelihood of GMRF. The computational complexity of ALM is rather attractive, which increase linearly with sample size. The second approach, Bayesian site selection (BSS), attempts to reduce the dimension of data through a smart selection of a representative subset of the observations. The BSS method first split the observations into two parts, the observations near the target prediction sites (part I) and their remaining (part II). Then, by treating the observations in part I as response variable and those in part II as explanatory variables, BSS forms a regression model which relates all observations through a conditional likelihood derived from the original model. The dimension of the data can then be reduced by applying a stochastic variable selection procedure to the regression model, which selects only a subset of the part II data as explanatory data. BSS can provide us more understanding to the underlying true Gaussian process, as it directly works on the original process without any approximations involved. The practical performance of ALM and BSS will be illustrated with simulated data and real data sets.Item Resampling Methodology in Spatial Prediction and Repeated Measures Time Series(2012-02-14) Rister, Krista DianneIn recent years, the application of resampling methods to dependent data, such as time series or spatial data, has been a growing field in the study of statistics. In this dissertation, we discuss two such applications. In spatial statistics, the reliability of Kriging prediction methods relies on the observations coming from an underlying Gaussian process. When the observed data set is not from a multivariate Gaussian distribution, but rather is a transformation of Gaussian data, Kriging methods can produce biased predictions. Bootstrap resampling methods present a potential bias correction. We propose a parametric bootstrap methodology for the calculation of either a multiplicative or additive bias correction factor when dealing with Trans-Gaussian data. Furthermore, we investigate the asymptotic properties of the new bootstrap based predictors. Finally, we present the results for both simulated and real world data. In time series analysis, the estimation of covariance parameters is often of utmost importance. Furthermore, the understanding of the distributional behavior of parameter estimates, particularly the variance, is useful but often difficult. Block bootstrap methods have been particularly useful in such analyses. We introduce a new procedure for the estimation of covariance parameters for replicated time series data.