Title: Estimating ecosystem evaporation response to aridity with theory and causality
Description: This thesis estimates the ecosystem evaporation response to two forms of aridity: (1) atmospheric aridity in the form of vapor pressure deficit (Chapter 2), and (2) soil moisture aridity (Chapter 4). We also develop new methods to estimate the ecosystem response to aridity. For the response to atmospheric aridity (Chapter 2), we build a theoretical framework that allows us to derive an analytical expression for the ecosystem evaporation response to vapor pressure deficit with all environmental conditions held fixed (Chapter 2). For the response to soil moisture aridity, we develop a method to estimate the response of evaporation to interventions on soil moisture using only passive data generated in a simulated reality (Chapter 4). To guide the development of this data-driven approach, we review and analyze causal inference’s applications in the Earth system, considering generic scenarios that are applicable to the land-atmosphere system as well as many other subdomains of the Earth system (Chapter 3).

The subsections below elaborate more on the contents of each Chapter. Chapter 2: When does vapor pressure deficit drive or reduce evaporation? Increasingvapor pressure deficit increases atmospheric demand for water. While increased evaporation in response to increased atmospheric demand seems intuitive, plants are capable of reducing evaporation in response to increased vapor pressure deficit by closing their stomata. We examine which effect dominates the response to increasing vapor pressure deficit: atmospheric demand and increases in evaporation, or plant response (stomata closure) and decreases in evaporation. We use Penman-Monteith, combined with semi-empirical optimal stomatal regulation theory and underlying water use efficiency, to develop a theoretical framework for assessing evaporation response to vapor pressure deficit. The theory suggests that depending on the environment and plant characteristics, evaporation response to increasing vapor pressure deficit can vary from strongly decreasing to increasing, highlighting the diversity of plant water regulation strategies.

The evaporation response varies due to: 1) climate, with tropical and temperate climates more likely to exhibit a positive evaporation response to increasing vapor pressure deficit than boreal and arctic climates; 2) photosynthesis strategy, with C3 plants more likely to exhibit a positive evaporation response than C4 plants; and 3) plant type, with crops more likely to exhibit a positive evaporation response, and shrubs and gymniosperm trees more likely to exhibit a negative evaporation response. These results, derived from previous literature connecting plant parameters to plant and climate characteristics, highlight the utility of our simplified framework for understanding complex land atmosphere systems in terms of idealized scenarios in which evaporation responds to vapor pressure deficit only. This response is otherwise challenging to assess in an environment where many processes co-evolve together. Chapter 3: Causal inference for process understanding in Earth sciences There is growinginterest in the study of causal methods in the Earth sciences.

However, most applications have focused on causal discovery, i.e. inferring the causal relationships and causal structure from data. This paper instead examines causality through the lens of causal inference and how expert-defined causal graphs, a fundamental from causal theory, can be used to clarify assumptions, identify tractable problems, and aid interpretation of results and their causality in Earth science research. We apply causal theory to generic graphs of the Earth system to identify where causal inference may be most tractable and useful to address problems in Earth science, and avoid potentially incorrect conclusions. Specifically, causal inference may be useful when: (1) the effect of interest is only causally affected by the observed portion of the state space; or: (2) the cause of interest can be assumed to be independent of the evolution of the system’s state; or: (3) the state space of the system is reconstructable from lagged observations of the system. However, we also highlight through examples that causal graphs can be used to explicitly define and communicate assumptions and hypotheses, and help to structure analyses, even if causal inference is ultimately challenging given the data availability, limitations and uncertainties.

Chapter 4: Estimating the ecosystem evaporation response to interventions on soilmoisture: confounding and causal modeling in a simulated world We build a simulated reality using a numerical model designed to represent feedbacks in the land atmosphere system, and observational boundary conditions that are confounded by the real world’s underlying climate state. Although no simulation can reproduce the real land-atmosphere system’s complexity and any simulation’s predictions will deviate from the real world, this simulated reality does share the same characteristics of the real world that make causal inference challenging: it contains feedbacks, non-linearity, and the real world’s confounding-induced covariations between boundary conditions. We use this simulated reality to estimate confounding’s impact on relationships between soil moisture and ecosystem evaporation, and also to validate a method for calculating ecosystem evaporation response to interventions on soil moisture from passive observations.

We repeat this analysis at 12 sites spanning a range of humid and arid climates in western North American and Europe, and find that: • Confounding bias is largest at the more humid sites, and lower at the more arid sites where soil moisture limits evaporation and decouples the response from other environmental factors (Section 4.3.1). • At the more humid sites, bias due to confounding is of a larger magnitude than model specification bias, even when the specified model is a linear model applied to a known non-linear process. This highlights the importance of accounting for confounding. (Section4.3.1). • Statistically adjusting for potential sources of confounding improves causal estimates at the highly confounded sites without degrading causal estimates at arid, soil moisture-limited sites characterized by less confounding bias (Section 4.3.2). • The estimated causal effects appear to differentiate true variations in the causal effects across climates and ecosystems. (Section 4.3.2).