**1. Introduction**

In many countries, agricultural production relies heavily on water resources [1]. Most of the cropland is irrigated and some traditionally rain-fed agriculture systems have seen growing irrigation to increase production and mitigate climate risks. Accounting for more than 80–90% of the total water withdrawals, irrigated agriculture needs to contribute an increasing share of food production to meet the growing demands of a rising population [2]. Faced with the dramatic impacts of climate change, many arid and semiarid areas are suffering from severe water shortages, for instance, the Western U.S. [3] and Northwestern China [4]. At the same time, some areas that were not facing water deficiencies are experiencing more, frequent droughts, for instance, the Midwestern U.S. [5,6], thus, increasing the stress on current water resources. In addition, in many areas, the water demand from other sectors is expected to grow faster. Though a large proportion of water demand could be satisfied through new investments in water supply and irrigation systems, and the expansion of water supply could be met with some non-traditional sources, the shrinking water availability increases both economic and environmental costs of developing new water supplies [2,7,8]. Therefore, investments in water systems and developing new water sources to meet growing demands will not be a sufficient solution.

As a more practical path to achieve the sustainability of water resources, water can be saved in current uses through increasing the irrigation water use efficiency (total yield per unit of land divided by irrigation water applied) in agricultural production [9]. The traditional flood (also called furrow or gravity) irrigation systems have been reported to lose 50–70% of the water applied as soil evaporation, seepage, and deep drainage [10,11]. Potential improvements in irrigation water use efficiency can be realized by adopting enhanced pressure irrigation systems.

Most of the studies on irrigation water use efficiency are conducted at the field level based on experiments [12,13]. Two foci of field experiments include the comparison of irrigation water use efficiency at different water application levels and utilizing various irrigation methods, and the interaction and compatibility of improved irrigation systems and other farm-related management practices that are considered the best (e.g., film or straw mulching, irrigation scheduling, and soil testing) [14–17]. Previous studies on irrigation water use efficiency (IWUE) typically used experimental data in one field, collected over multiple years. Because of limited research funding, heterogeneity of experimental fields, and the diversity of cropping systems and farming structures, the available farm-level data are limited. As a result, the evaluation of crop IWUE in multiple fields is very challenging. At the farm level, producers usually plant two or more crops in one growing season. In addition to making adoption decisions regarding different irrigation systems, farmers also need to make decisions on land allocation and irrigation water application for each crop that they choose to plant. These decisions can determine whether the water is used efficiently or not.

The farm-level irrigation and production decisions to improve irrigation efficiency in a multi-crop system are understudied, in particular, across regions with different cropping patterns and climatic conditions [18]. In addition, production decisions in irrigated agriculture may be affected by other factors like water sources, input costs, and the farming area [19]. Analysis of irrigation decisions and crop irrigation water use efficiency, as affected by these and other factors, could help farmers and policymakers adapt to potential climate risks, better manage the irrigation water application, and achieve the sustainable use of limited water resources. Furthermore, given the heterogeneity of farms and states, multi-level models (MLMs) can be readily utilized to deal with the hierarchical nature of the farm-level data and to extract the percentage of variability in each response accounted for by farmand state-level factors. The multilevel model has been applied in social science research [20,21] and agricultural sciences. To analyze the hierarchically structured data, Neumann et al. [22] adopted the multilevel model to investigate the global irrigation patterns using country-level data, and Giannakis and Bruggeman [23] studied the labor productivity in agricultural system in Europe. However, MLMs have never been used to analyze crop production decisions or farm irrigation efficiency. Given the data structure of the United States Department of Agriculture Farm and Ranch Irrigation Survey (USDA FRIS)—i.e., farms are embedded in states—we explore the applicability of the MLMs to multiple equations relating to production decisions in irrigated multi-crop agriculture.

Therefore, the objective of this study is to better understand the production decisions for irrigated agriculture and economic irrigation water use efficiency of major crops in the U.S., as well as the effects of water costs, the adoption of pressure irrigation systems, and the climatic determinants in a multi-crop production system.

Specifically, this research aims to answer the following fundamental questions:


The layout of the analyses in this paper is presented in Figure 1. Focusing on irrigated farms in a multi-crop production system, four equations on land allocation, water application, crop yield, and economic irrigation water use efficiency are estimated using multilevel models. Intensive and extensive margins of water use to water price and energy costs are calculated. Intraclass correlation coefficients (ICC) as defined later are calculated to find out the proportion of variability in each response is accounted for by each level. Econometric results from the multilevel models are provided to show the effects of exogenous variables on each response variable.

**Figure 1.** An analytical structure of irrigated multi-crop farming decisions.

## **2. Literature Review**
