Paleo data-model comparison is the process of comparing output from model simulations of past periods with paleoenvironmental data. It enables us to understand both the paleoclimate mechanism and responses of the earth environment to the climate and to evaluate how models work. This dissertation has two parts that each involve the development and application of approaches for data-model comparisons. In part 1, which is focused on the understanding of both past and future climatic changes/variations, I compare paleoclimate and historical simulations with future climate projections exploiting the fact that climate-model configurations are exactly the same in the paleo and future simulations in the Coupled Model Intercomparison Project Phase 5. In practice, I investigated large-scale temperature responses (land-ocean contrast, high-latitude amplification, and change in temperature seasonality) in paleo and future simulations, found broadly consistent relationships across the climate states, and validated the responses using modern observations and paleoclimate reconstructions. Furthermore, I examined the possibility that a small set of common mechanisms controls the large-scale temperature responses using a simple energy-balance model to decompose the temperature changes shown in warm and cold climate simulations and found that the clear-sky longwave downward radiation is a key control of the robust responses. In part 2, I applied the equilibrium terrestrial biosphere models, BIOME4 and BIOME5 (developed from BIOME4 herein), for reconstructing paleoclimate. I applied inverse modeling through the iterative forward-modeling (IMIFM) approach that uses the North American vegetation data to infer the mid-Holocene (MH, 6000 years ago) and the Last Glacial Maximum (LGM, 21,000 years ago) climates that control vegetation distributions. The IMIFM approach has the potential to provide more accurate quantitative climate estimates from pollen records than statistical approaches. Reconstructed North American MH and LGM climate anomaly patterns are coherent and consistent between variables and between BIOME4 and BIOME5, and these patterns are also consistent with previous data synthesis. This dissertation includes previously published and unpublished coauthored material.

Interpreting particular climatic drivers of local and regional vegetation change from paleoecological records is complex. I explicitly simulated vegetation change from the late-Glacial period to the present on the Olympic Peninsula, WA and made formal comparisons to pollen records. A temporally continuous paleoclimate scenario drove the process-based vegetation model, LPJ-GUESS. Nine tree species and a grass type were parameterized, with special attention to species requirements for establishment as limited by snowpack. Simulations produced realistic present-day species composition in five forest zones and captured late-Glacial to late Holocene transitions in forest communities. Early Holocene fire-adapted communities were not simulated well by LPJ-GUESS. Scenarios with varying amounts of snow relative to rain showed the influence of snowpack on key bioclimatic variables and on species composition at a subalpine location. This study affirms the importance of exploring climate change with methods that consider species interactions, transient dynamics, and functional components of the climate.

abstract: The main objective of mathematical modeling is to connect mathematics with other scientific fields. Developing predictable models help to understand the behavior of biological systems. By testing models, one can relate mathematics and real-world experiments. To validate predictions numerically, one has to compare them with experimental data sets. Mathematical modeling can be split into two groups: microscopic and macroscopic models. Microscopic models described the motion of so-called agents (e.g. cells, ants) that interact with their surrounding neighbors. The interactions among these agents form at a large scale some special structures such as flocking and swarming. One of the key questions is to relate the particular interactions among agents with the overall emerging structures. Macroscopic models are precisely designed to describe the evolution of such large structures. They are usually given as partial differential equations describing the time evolution of a density distribution (instead of tracking each individual agent). For instance, reaction-diffusion equations are used to model glioma cells and are being used to predict tumor growth. This dissertation aims at developing such a framework to better understand the complex behavior of foraging ants and glioma cells. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2019