Defense Date

2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Systems Modeling and Analysis

First Advisor

Indranil Sahoo

Second Advisor

Yanjun Qian

Abstract

Arid climate classifications are threshold-dependent and easily interpretable mappings that are widely used in ecological, agricultural, and climate-related studies. These classifications inform scientific understanding, support policy and land management decisions, and provide an intuitive summary of environmental conditions. Despite their usefulness, traditional arid climate classifications often fail to quantify uncertainty, incorporate spatial context, or account for complex relationships among relevant environmental variables. Existing approaches to uncertainty assessment have largely relied on comparing classifications across multiple datasets or alternative formulas, but these methods generally overlook important spatial dependence and latent structure in the data.

This dissertation develops three machine learning-based statistical frameworks to quantify uncertainty in arid climate estimation, account for spatial heterogeneity, and incorporate latent environmental structure into climate classification and prediction. In the first project, we develop a feedforward neural network model with spatio-temporal covariates to estimate probabilistic arid climate classifications across Africa and the Middle East. This framework yields classification-specific uncertainty measures and identifies regions of high climate fluctuation, particularly during periods of extreme drought. In the second project, we model semi-arid climate boundaries across Africa using a heteroskedastic Gaussian process regression framework, which enables spatial uncertainty quantification of the estimated boundaries. Building on this, we develop a Maximum Absolute Deviant Global Envelope Test (MAD GET) to assess significant shifts in boundary structure over time. In the final project, we propose the Spatial Jacobian Neural Network (SJNN), a unified deep learning framework that jointly models the aridity index and environmental covariates by treating the covariates as latent stochastic spatial processes. This approach induces a flexible nonstationary spatial covariance structure through the neural network Jacobian, allowing uncertainty in the predictors to propagate into both mean and covariance estimation and yielding spatially coherent prediction and uncertainty quantification.

Across all three projects, the proposed methods are designed for large spatial and spatio-temporal datasets and demonstrate strong scalability. Each of the projects demonstrate their capacity to process correlated and nonlinear environmental datasets in an efficient manner. The first two frameworks avoid the computational burden of large covariance matrix modeling, while the final framework uses matrix-free covariance propagation, making these methods computationally efficient and suitable for real-time analysis of continental-scale climate data.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

4-28-2026

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