Abstract

The guiding thread throughout this thesis work is data-driven modeling of Earth's climate. We investigate a variety of settings within the field of complex climate systems, such as gridded, high-resolution reanalysis data, lower-resolution climate indices, and incomplete paleoclimate records with missing values. We begin with reanalysis data of high spatial and temporal resolution, and use climate network analysis to uncover hidden trends in the data in regards to the Amazon rainforest and its changing role in the global climate system. We introduce a novel formulation of k-nearest neighbors climate networks to study changing trends at a local level, and apply graph diffusion and random walks to study the Amazon's changing connectivity structure. We then shift focus to making forecasts of the future state of Earth's climate rather than studying historical data, and introduce TreeDOX: a regression-tree-based approach to chaotic time series forecasting. TreeDOX features a variety of advantages, such as resilience to low training volume and automated hyperparameter tuning using statistical tests performed on the supplied training data. We use a variety of toy models to perform benchmarking of TreeDOX in comparison to state-of-the-art chaotic time series forecasting methods, and also demonstrate the efficacy of TreeDOX in a real-world setting by forecasting the Southern Oscillation Index (SOI)---a time series with strong ties to several critical climate phenomena. Next, we investigate empirical mode decomposition (EMD)---a data-driven method for decomposing nonlinear, nonstationary time series into a finite basis of orthogonal, stationary modes---as a method of automated TreeDOX preprocessing. We perform an extensive numerical experiment featuring 26 climate time series (including SOI) to establish that EMD-TreeDOX does forecast climate phenomena with higher accuracy than TreeDOX. Lastly, we adapt TreeDOX (and EMD-TreeDOX) to perform imputation of missing values (i.e., gap-filling) in time series. Missing values are common in many fields in the climate sciences (especially those that require remote sensing), but we wish to test TreeDOX gap-filling in perhaps the most challenging of settings: paleoclimate time series. Paleoclimate proxy records play an important role in the understanding of the current and future climate by establishing a baseline of extremely low-frequency trends in climate dynamics. Here, we use 14 real-world paleoclimatic time series that come in the form of speleothem (stalactite and stalagmite) oxygen isotope records from Asian caves, which have previously been shown to exhibit connections to Asian monsoon intensity. While leaving room for future improvement, we find TreeDOX and EMD-TreeDOX to be promising data-driven gap-filling techniques capable of using nonlinear, nonstationary dynamics to inform the imputation of missing values.

Library of Congress Subject Headings

Climatology--Mathematical models; System analysis; Rain forests--Amazon River Valley--Climate--Mathematical models

Publication Date

7-2025

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Department, Program, or Center

Mathematics and Statistics, School of

Advisor

Nishant Malik

Advisor/Committee Member

Kathleen Lamkin-Kennard

Advisor/Committee Member

Tamas Wiandt

Campus

RIT – Main Campus

Plan Codes

MATHML-PHD

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