Requerimientos hardware del diseño

A farmer can use any of numerous irrigation strategies to adapt to limited water availability. The most common adjustment is reduced demand for water irrigation through intensive margin, extensive margin, and crop switching (D. Martin et al. 1989). The irrigation strategy that a farmer will choose depends on the severity of the water availability limitation problem.

The optimization of water irrigation through irrigated area adjustment is called adjustment at the extensive margin. For example, in the early stage of a growing season, a farmer may decide a portion of land will be irrigated or kept for rainfed cropping depending on water availability. This assumption is based on a farmer not having dependable information about future weather and therefore water demand. In this case, the portion of irrigated acreage and well

capacity will determine the maximum instantaneous rate of application for a given period of time. A standard engineering formula can be used to calculate the upper bound of irrigation application rate for water use optimization research (Foster et al. 2014; Peterson and Ding 2005).

Adjustment in intensive margin is an irrigation strategy that optimizes water per acre of irrigated area. Reducing such irrigation water depends on water availability and precipitation.

For example, one of the adjustment intensive margins is deficit irrigation, which will use less water but avoid crop stress at critical growth stages (Geerts and Raes 2009; Pereira, Oweis and Zairi 2002). Deficit irrigation can be managed by using uniform intensive irrigation or non-uniform intensive irrigation, and both techniques can be triggered using soil moisture level, or Management Allowed Deficit (MAD) (Vico and Porporato 2011b). Vico and Porporato (2011a) mentioned that deficit irrigation is expected to increase water productivity without causing a severe drop in crop yield. This is because such irrigation considers a minimum soil moisture level that needs to be maintained to avoid severe crop water stress.

Uniform soil moisture applies the same MAD level for all crop growth stages while uniform soil moisture applies a different MAD level for each crop growth stage. In fact, the non-uniform soil moisture method is governed by most crops needing different water productivity for each growth stage. Consequently, limiting water supply in the drought-sensitive growth stage may maximize the water application and crop productivity and stabilize crop yield rather than maximize the yield (Geerts and Raes 2009)

Ultimately, a trade-off between adjustment in extensive and intensive margin exists, according to English (1990). Thus, the marginal benefit of increasing irrigation acreage must equal the marginal benefit of increasing irrigation intensity (Wang and Nair 2013). Wang and Nair (2013) also stated that the maximum water resource rent is acquired when the return is

equal for intensive and extensive margins. In the case of low water supply, shown by lower well capacity, the crop producer will change irrigated acreage to maintain a particular irrigation intensity that maximizes the marginal benefit of water. Likely, the crop producer will concentrate water into a fraction of farmland that can generate a maximum marginal benefit of water.

O’Brien et al. (2001) stated that in response to well capacity declining a crop producer typically reduces the irrigated acreage to the extent of being able to provide sufficient water for crop growth. A farmer may focus the strategy on adjustment in the extensive margin but still maintain adequate water for crop growth through adjustment in the intensive margin in response to the decrease in well capacity. Thus, limited water availability may yield optimal water allocation by reducing the irrigated acreage and focusing the available water on smaller irrigated acreages (D. Martin et al. 1989; Nair, Maas, et al. 2013). Baumhardt et al. (2009) stated that a farmer might concentrate available water on a portion of a field with a complementary non-irrigated area to maintain optimal water use efficiency. Moreover, evidence shows a farmer may optimize water for intensive irrigation by applying deficit irrigation when faced with limited water availability (Heeren et al. 2011; English 1990). Panda, Behera and Kashyap (2004) stated a minimum MAD level for irrigation schedules that a farmer should attain to avoid severe crop yield loss. Such a farmer may focus the available water for irrigation during the most productive (vegetative) growth stage (Heeren et al. 2011; Nair, Wang, et al. 2013). My study suggests that the non-uniform MAD is an intensive adjustment strategy to account for different crop water productivity at each growth stage. The non-uniform MAD may also work for a deficit irrigation strategy.

Previous studies used varied irrigation strategy choices in the optimization analysis (Baumhardt et al. 2009; Foster et al. 2014; Heeren et al. 2011; Nair, Wang, et al. 2013; Peterson

and Ding 2005). For example, Foster et al. (2014) applied uniform soil moisture level for all crop growth stages and assumed non-irrigated acreage do not have any value. Foster et al. (2014) also assumed that intensive margin decisions can be characterized by constant soil moisture level for the whole growing season. However, previous studies found that the optimal level of soil moisture is different for each growth stage (Doorenbos and Kassam 1979; Payero et al. 2009).

Meanwhile, Baumhardt et al. (2009) offered an even simpler strategy by using only fixed net irrigation application in their irrigation schedule. However, fixed net water application may cause irrigation water to have low marginal productivity. Meanwhile, Heeren et al. (2011) include both uniform and non-uniform soil moisture level as intensive irrigation choices. Earlier, Peterson and Ding (2005) found the optimal water allocation for different irrigation technologies by assuming the farmer does not change the irrigated acreage. Alternatively, my study will have adjustment in the extensive margin, the intensive margin with uniform soil moisture level, and the intensive margin with non-uniform soil moisture level in the decision model. The adjustment in intensive margin with non-uniform soil moisture level may enable the farmer to prioritize the allocation of groundwater irrigation based on crop growth stage. Consequently, my findings for the optimal irrigated acreage and profit may be larger than what previous studies found (Baumhardt et al. 2009; Foster et al. 2014). Notably, my study does not consider crop switching as an alternative choice to deal with limited water availability. D. Martin et al. (1989) stated that crop allocation is a viable option to deal with limited water supply when the farmer is facing a multi-year allocation system. However, I am not analyzing multi-year optimal allocation;

instead, I am basing my model on only a one-period decision.