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).

The semiarid region between the North African Savanna and Sahara Desert, known as the Sahel, experienced dramatic multidecadal precipitation variability in the 20th century that was unparalleled in the rest of the world, including devastating droughts and famine in the early 1970s and 80s. Accurate predictions of this region’s hydroclimate future are essential to avoid future disasters of this kind, yet simulations from state of the art general circulation models (GCMs) do a poor job of simulating past Sahel rainfall variability, and don’t even agree on whether future precipitation will increase or decrease under global warming. Furthermore, climate scientists are still not in agreement about whether anthropogenic emissions played an important role relative to natural variability in dictating past Sahel rainfall change. Because the climate system is complex and coupled, it is difficult to determine which processes should be considered causal drivers of circulation changes and which should be considered part of the climate response, and therefore many theories for monsoon rainfall variability coexist in the literature. It is difficult to evaluate these competing theories because observational studies generally cannot be interpreted causally, but simulated experiments may not represent the dynamics of the real world. The Coupled Model Intercomparison Project (CMIP) provides a wealth of data in which GCMs maintained at research institutions worldwide perform similar experiments, allowing the researcher to reach conclusions that are robust to differences in parameterization between GCMs. The scientific community has been using a wide range of statistical techniques to analyze this data, and each has notable limitations. This dissertation explores two statistical techniques for leveraging CMIP to explore the drivers and mechanisms of historical Sahel rainfall variability: analysis of ensemble-mean responses to prescribed variables, and causal inference. In ‎Chapter 1, we give an overview of the climatology and variability of Sahel rainfall and present relevant physical theory. In ‎Chapter 2, we examine the roles of various types of anthropogenic forcing in observations and coupled simulations, using a 3-tiered multi-model mean (MMM) to extract robust climate signals from CMIP phase 5 (CMIP5). We examine “20th century” historical and single-forcing simulations—which separate the influence of anthropogenic aerosols, greenhouse gases (GHG), and natural radiative forcing on global coupled ocean-atmosphere system, and were specifically designed for attribution studies—as well as pre-Industrial control simulations, which only contain unforced internal climate variability, to investigate the drivers of simulated Sahel precipitation variability. The comparison of single-forcing and historical simulations highlights the importance of anthropogenic and volcanic aerosols over GHG in generating forced Sahel rainfall variability that reinforces the observed pattern, with anthropogenic aerosols alone responsible for the low-frequency component of simulated variability. However, the forced MMM only accounts for a small fraction of observed variance. A residual consistency test shows that simulated internal variability cannot explain the residual observed multidecadal variability, and points to model deficiency in simulating multidecadal variability in the forced response, internal variability, or both. In ‎Chapter 3, we investigate the causes for discrepancies in low-frequency Sahel precipitation variability between these ensembles and for model deficiency in reproducing observations. In the most recent version of CMIP – phase 6 of the Coupled Model Intercomparison Project (CMIP6) – the differences between observed and simulated variability are amplified rather than reduced: CMIP6 still grossly underestimates the magnitude of low-frequency variability in Sahel rainfall, but unlike CMIP5, historical mean precipitation in CMIP6 does not even correlate with observed multi-decadal variability. We continue to use a MMM to extract robust climate signals from simulations, but now additionally include sea surface temperature (SST) as a mediating variable in order to test the proposed physical processes. This partitions all influences on Sahel precipitation variability into five components: (1) teleconnections to SST; (2) atmospheric and (3) oceanic variability internal to the climate system; (4) the SST response to external radiative forcing; and (5) the “fast” (not mediated by SST) precipitation response to forcing. Though the coupled simulations perform quite poorly, in a vast improvement from previous ensembles, the CMIP6 atmosphere-only ensemble is able to reproduce the full magnitude of observed low-frequency Sahel precipitation variance when observed SST is prescribed. The high performance is due entirely to the atmospheric response to observed global SST – the fast response to forcing has a relatively small impact on Sahel rainfall, and only lowers the performance of the ensemble when it is included. Using the previously-established North Atlantic Relative Index (NARI) to approximate the role of global SST, we estimate that the strength of simulated teleconnections is consistent with observations. Applying the lessons of the atmosphere-only ensemble to coupled settings, we infer that both coupled CMIP ensembles fail to explain low-frequency historical Sahel rainfall variability mostly because they cannot explain the observed combination of forced and internal variability in SST. Though the fast response is small relative to the simulated response to observed SST variability, it is influential relative to simulated SST variability, and differences between CMIP5 and CMIP6 in the simulation of Sahel precipitation and its correlation with observations can be traced to differences in the simulated fast response to forcing or the role of other unexamined SST patterns. In this chapter, we use NARI to approximate the role of global SST because it is considered by some to be the best single index for estimating teleconnections to the Sahel. However, we show that NARI is only able to explain half of the high-performing simulated low-frequency Sahel precipitation variability in the atmospheric simulations with prescribed global SST. Statistical techniques commonly applied in the literature cannot distinguish between correlation and causality, so we cannot analyze the response of Sahel rainfall to global SST in more depth without atmospheric CMIP simulations targeted at every ocean basin of interest or a new method. In ‎Chapter 4, we turn to a novel technique called causal inference to qualify the notion that NARI can adequately represent the role of global SST in determining Sahel rainfall. We apply a causal discovery algorithm to CMIP6 pre-Industrial control simulations to determine which ocean basins influence Sahel rainfall in individual GCMs. Though we find that state of the art causal discovery algorithms for time series still struggle with data that isn’t generated specifically for algorithm evaluation, we robustly find that NARI does not mediate the full effect of global SST variability on Sahel rainfall in any of the climate simulations. This chapter lays the foundation for future work to fully-characterize the dependence of Sahel precipitation on individual ocean basins using the non-targeted simulations already available in CMIP – an approach which can be validated by comparing the composite results to the interventional historical simulations that are available. Furthermore, we hope this chapter will guide algorithm improvement efforts that are needed to increase the performance and usefulness of time series causal discovery algorithms on climate data.

Dissertation submitted to the Faculty of Science, University of the Witwatersrand, for completion of the Degree of' Master of Science / The atmospheric response of the Colorado State University Regional Atmospheric Modelling System (RAMS) to sea-surface temperature anomaliesis investigated. A period of four days was chosen from 21 to 24 January 1981, where focus was placed on the development and dissipation of a tropical-temperate trough across Southern Africa. Previous experimenting this mesoscalenumerical model have detemined the kinematic, moisture, and thermodynamic nature of these synoptic features. The research in this dissertation focuses specifically on the sensitivity of the numerical model's simulated responses to positive sea-surface temperature anomalies. Three separate experiments were devised, in which positive anomalous temperatures were added to the ocean surface north of Madagascar (in the tropical Indian Ocean), at the region of the Agulhas Current retroflection, and along the tropical African west coast (in the Northern Benguela and Angola currents). The circulation aspects of each sensitivity test were investigated through the comparison of simulated variables such as vapour and cloud mixing ratios, temperature, streamlines and vertical velocity, with the same variables created by a control simulation. The results indicate that for the first sensitivity test, (the Madagascar anomaly), cyclogenesis was initiated over the area of modified sea temperatures which resulted in a marginal decrease in continental precipitation. The second sensitivity test (over the Agulhas retroflection) produced a much smaller simulated response to the addition of anomalously warm sea temperatures than the tropical Indian Ocean anomaly. Instability and precipitation values increased over the anomalously warm retroflection region, and were slowly transferred along the westerly wave perturbation and the South African east coast. The third sensitivity experiment showed a predominantly localised simulated increase in precipitation over Gabon and the Congo, with the slow southward progression of other simulated circulation differences taking place. The small perturbations in each of the simulated meteorological responses are consistent with the expected climate response to anomalously warm sea-surface temperatures in those areas. / AC 2018