Process-based models remain the gold standard in crop modeling as one is able to study the relationship between weather and all phases of crop growth in a range of weather possibilities, even those lying outside the historical record . California field crops have been modeled using DAYCENT . Both studies highlight resilience of alfalfa yield under A2 scenario by end of the century, whereas 5 other crops exhibit a decline. Jackson et al. also find alfalfa yield to be particularly resilient to early and repeated heat waves during May–July. Lee et al. also run climate projections with and without a CO2 fertilization effect on seven field crops in the Central Valley of California. They assume a CO2 increase of 350 ppmv from 1990 levels enhances net primary production by 10% for all crops except alfalfa andmaize. They find that CO2 fertilization increases crop yields 2–16% above the model without CO2 effects under the high-emissions scenario by the end of the 21st century. There is a much smaller yield increase under the low-emissions scenario. Lobell and Field use two estimation methods in studying the effects of temperature and precipitation on perennial crop yields. Their model includes 72 potential weather predictor variables for each crop, such as monthly averages for max and min temperature and their corresponding squares. They find that cherries and almonds are harmed by future warming out of a set of 20 perennial crops in their analysis.

Crop-level adaptations — such as adjusting the planting and harvesting date , vertical indoor hydroponic system and substituting between different crop varieties — have been included to a limited extent in crop models. However, these cannot account for the broad range of decision making at the farm-level under which many of the negative effects of climate change could be partially offset with input and output substitutions, improving information, and effective water institutions. Thus, economic models are necessary to capture a broader range of responsive decision-making as the climate changes.Recently, adaptations specific to California agriculture have been studied using three economic programming models: the Statewide Agricultural Production model, Central Valley Production Model , and the US Agricultural Resources Model .In programming models, the farmer’s decision is captured by the objective function. The main decision variable in these models is acres of land allocated to a region-specific crop mix. The farmer responds to reductions in water availability and yield by adjusting crop acreage. Exogenous adaptations include institutional , socioeconomic , and technological change . Calibration through positive mathematical programming also captures decision-making by preserving observed crop mix allocation decisions . SWAP employs a PMP cost function to the capture the decision of bringing an additional unit of land into production . Both CVPM and USARM have also been calibrated using PMP . CVPM studies have also generated synthetic crop share data from Monte Carlo runs using a base water supply and groundwater depth with random perturbations. Crop adaptation equations are then derived from a multinomial logit regression of this CVPM-generated synthetic crop share data . In order to represent climate-induced changes in water supply, many mathematical programming models are linked to hydrological management models, such as theCalifornia Value Integrated Network , Water Evaluation and Planning , CalSim-II, and C2VSim.

CALVIN is a generalized network flow-based optimization model that minimizes economic operating and scarcity costs of water supply, subject to water balance, capacity, and environmental constraints for a range of operational and hydrologic conditions . CALVIN has the potential to incorporate several basin-level adaptations to water allocation rules such as contract changes, markets and exchanges, water rights, pricing, and water scarcity levels. However, it has limited ability to represent important physical phenomena, such as stream-aquifer interactions and groundwater flow dynamics under different climate and water management scenarios . WEAP has many of the same water management features as CALVIN and CalSim-II. WEAP includes demand priorities and supply preferences in a linear programming framework to solve the water allocation problem as an alternative to multi-criteria weighting or rule-based logic. It is different because analysis in the WEAP framework comes directly from the future climate scenarios and not from a perturbation of historical hydrology as with the other models. Unlike CALVIN and CalSim-II, WEAP only has a simplified representation of the rules guiding the State Water Project and Central Valley Project systems . CalSim-II is also very similar to CALVIN and WEAP . C2VSim is a multi-layer, distributed integrated hydrologic model that could represent pumping from multiple aquifer layers, effects on groundwater flow dynamics, and stream-aquifer interaction . Recent programming studies focus on how certain adaptations may affect costs under relatively extreme cases of water scarcity. These studies thus assess how these adaptations may offset costs under worst-case-scenarios of water supply reductions. Given that reduction in statewide agricultural water use due to the current drought is estimated at 6% , studies on 40–70% flow reduction should be interpreted with caution. The subsequent studies are organized according to magnitude of water supply/flow reduction. Studies on 5–6% reduction in water supply reveal the heavy fallowing and groundwater use . Howitt et al. find that a 6.6 maf deficit in surface water caused by the current drought is largely substituted by 5.1 maf of additional groundwater.

This is estimated to cost an additional $454 million in pumping. In addition to over-pumping groundwater, farmers adjust by fallowing crop land. The overwhelming majority of the 428,000 acres estimated fallowed in 2014 are in the Central Valley, where the majority of fallowed acres belong to field crops. However, they project that fallowing will decrease by 43% by 2016, suggesting a trend toward stabilization. Frisvold and Konyar use USARM to examine the effects of a 5% reduction in irrigation water supply from the Colorado River on agricultural production in southern California. In particular, they are able to compare the potential value-added of additional adaptations that include changing the crop mix, deficit irrigation, and input substitution to a “fallowing only” model. They find that these additional adaptations have the potential to reduce costs of water shortages to producers by 66% compared to the “fallowing only” model.1 Medellin-Azuara et al. examine the extent to which more flexible2 versions of California water markets could reduce water scarcity costs under a 27% statewide reduction in annual stream flow. They compare agricultural water scarcity in the year 2050 under two scenarios: 1. Baseline: population growth and resulting levels of agriculture to urban land transfer, 2. Warm-dry: includes population pressure and climatic changes under GFDL CM2.1 A2). Under the warm-dry scenario,vertical farming tower for sale even with optimized operations, water scarcity and total operational costs increase by $490 million/year, and statewide agricultural water scarcity increases by 22%. If water markets are restricted to operate only within the four CALVIN sub-regions, statewide water scarcity costs increase by 45% and 70% for the baseline and warm-dry scenarios, respectively. Marginal opportunity costs of environmental flows increase under the warm-dry scenario, with particularly large percentage increases for the Delta Outflow and American River. Medellin-Azuara et al. conduct a similar analysis, adding the comparison with a warm-only 2050 scenario. The agricultural sector water scarcity costs rise by 3% from the baseline to warm-only scenario, versus an increase of 302% from the baseline to the warm-dry scenario.3 Indeed the greater hydrological impact of the warm-dry scenario results in significantly greater scarcity costs than the warm-only scenario. Using the CALVIN model runs from Medellin-Azuara et al. , MedellinAzuara et al. analyze adaptations at the farm-level, including adjustments in crop acreage , and to a more limited extent, yield-enhancing technology . Similar to the 2008 paper, the model compares economic losses between a baseline scenario and a warm-dry scenario . Results reveal an anticipated decline in acreage of low-value crops , which is particularly severe due to the large reduction in water availability. For example, pasture acreage is reduced by 90% across 3 out of 4 agricultural regions. The results also suggest that statewide agricultural revenues decline at a proportionately lower level than the reduction in water availability . Their model also captures the complexity between crop demand and climate-induced supply reduction. Although the demand for high-valued orchard crop increases, production decreases due to the negative impact on yield from temperature increases.The resulting price increase cannot compensate for the decrease in supply, and gross revenue still declines. Two studies examine the impacts of more extreme reductions in water supply . Harou et al. construct a synthetic drought in 2020 based on the paleo-record, rather than GCM projections. Their results regarding agricultural water scarcity and environmental flows are consistent with other CALVIN-SWAP studies. Environmental flows are also extremely restricted.

Marginal opportunity costs of environmental flows rise by one or more orders of magnitude with extreme drought as compared to the historic baseline, with the Trinity, Clear Creek, and Sacramento Rivers experiencing the highest increase. Average agricultural water scarcity increases 3900% across the entire state under extreme drought even under well-functioning water markets, which seems somewhat implausible and may result from an overly restrictive model. Although Dale et al. do not calculate scarcity costs, they find that a 60-year drought with 70% reduction in surface flows only moderately impacts the total amount of irrigated acreage in the Central Valley, which declines from 2.4 million hectares to 2.1 million. This suggests that Central Valley farmers tend to have a relatively inelastic groundwater demand, compensating for the loss in surface water with groundwater rather than fallowing. Within the Valley, they find that Tulare Basin has a greater increase in fallowing than the San Joaquin Basin since the former is historically more dependent on groundwater. Dale et al. are also able to capture the increase in aquifer subsidence due to increased withdrawals during the prolonged drought, suggesting that the quality of the aquifer will decline through time with excessive pumping. Joyce et al. use WEAP-CVPM to model climatic changes with 6 GCMs under B1 and A2 scenarios for 2006–2099. Unlike the CALVIN-SWAP studies, they model irrigation efficiency by assuming that vegetable and fruit and nut crops in the Central Valley will be entirely converted to drip irrigation, and half of field crops will be converted by mid-century. They find that these adaptations tend to offset increasing water demands caused by increasing temperatures and periods of drought. The model even projects a reduction in annual groundwater pumping compared to the historical period until mid-century under some scenarios. Unfortunately, this positive effect of switching to drip irrigation is lost toward the end of the century as higher temperatures drive up crop water demands.One of the earliest econometric evaluations on the impacts of human-induced climate change to US agriculture developed out of a reaction to the limited substitution options in earlier production function models . Given long-run production decisions, one could use a cross-section of county farm data to assess how climate could impact agricultural rents. The underlying assumption is that farmers have fully adapted to their environmental circumstances . While one cannot explicitly identify these decisions, these models are an improvement over older models because one could at least measure the consequences of adaptive decision-making . Other econometric models are able to capture annual decision-making using panel data. However, these models are unable to capture the idea of adaptation because farmers are very likely unresponsive to changes in weather from one year to the next. In their classic paper, Mendelsohn et al. evaluate the impact of climate variables on the expected present value of future rents in US agriculture, which they assume is proportional to farm land value under a few simplifying assumptions.4 They regress farm land values on climate, soil, and socioeconomic variables using cross-sectional data for 2933 US counties. Their results reveal the seasonality and nonlinearity in the relationship between climate variables and farm land value. Beyond this, both the direction and magnitude of their estimated climate parameters have been criticized and subsequently revised . One criticism with the original model, now obvious with hindsight, is the omission of ground and surface irrigation variables . Indeed, the negative effect of summer precipitation on land value in Mendelsohn et al. is potential evidence of omitted variable bias and, as Schlenker et al. suggest, misspecification. In response, Mendelsohn and Dinar include a surface water variable interacting it with annual temperature and precipitation. They find that the former is positive while the latter is negative, suggesting that counties with more surface water can tolerate higher annual temperatures and lower annual precipitation.