Doctor of Philosophy / Department of Agricultural Economics / Nathan P. Hendricks / Risk averse farmers face a substantial challenge managing irrigation water when they face limited water availability. The two primary reasons for limited water availability in the High Plains Aquifer region of the United States are limited well capacity (i.e., the rate at which groundwater can be extracted) or a constraint imposed by a policy. In this dissertation, I study how risk averse farmers optimally manage limited water availability in the face of weather uncertainty and also the impact of limited water availability on farmer welfare. I use AquaCrop, a daily biophysical crop simulation model, to predict corn yield under alternative irrigation scenarios with historical weather. Since no simple functional form exists for the crop production function, I use discrete optimization and consider 234,256 potential irrigation strategies. I also account for risk preferences by using expected utility analysis to determine the optimal irrigation strategy. Using a daily biophysical model is important because water stress in a short period of the growing season can impact crop yield (even if average water availability throughout the growing season is sufficient) and well capacity is a constraint on daily water use. The daily biophysical crop simulation model accounts for the dynamic response of crop production to water availability. First, I examine how optimal irrigation strategies change due to limited water availability. I find that it is never optimal for irrigators to apply less than a particular minimum instantaneous rate per irrigated acre. An optimal required instantaneous rate implies that a farmer with a low well capacity focuses on adjustment at the extensive margin. On the other hand, farmers who initially have a high well capacity should adjust at the intensive margin in response to well capacity declining. I also find that total water use increases as the degree of risk aversion increases. More risk averse farmers increase water use by increasing irrigation intensity to reduce the variance in corn yields. Another important finding is that a higher well capacity could actually promote less water use because the higher well capacity allows a greater instantaneous rate of application that allows the farmer to decrease irrigation intensity while still maintaining or increasing corn yield. This finding may imply an accelerated rate of groundwater extraction when the groundwater depletion reaches a particular threshold. Second, I analyze the welfare loss due to limited water availability. The relationship between welfare loss and well capacity due to a policy constraint differs by soil type. I found the welfare loss from a water constraint policy does not always increase as well capacity increases. Farmers with very high well capacity may make small or no adjustment at the extensive margin due to a higher instantaneous rate and higher soil water holding capacity. However, that is not the case for a farmer with land that has lower soil water holding capacity as the increase in well capacity results in greater welfare loss. I also investigate the effect of risk averse behavior on the magnitude of welfare loss. I found that the welfare loss per unit of reduced water use is lower for the farmer with more risk aversion. Thus, economic models that ignore risk aversion misestimate the cost of reducing water use. Finally, I investigate the incentive for adopting drip irrigation and its effect on water use. I find that a decrease in well capacity increases the benefits of adopting drip irrigation but is not sufficient to overcome the high initial investment cost without government support. While subsidies of the magnitude offered by current U.S. programs are sufficient to induce drip irrigation adoption, I find that such subsidies have the unintended consequence of increasing total water use, particularly for small well capacities.