## 1 Introduction  
In the low desert of California, alfalfa (_Mediago sativa_ L) is the dominant water user due to its large-cultivated area and long growing season. alfalfa has a total hectarage of nearly 94,000 in the low deserts of the Palo Verde and Imperial Valley agricultural areas of California, accounting for more than 30% of the crop area [1; 2; 3]. This irrigated region is a part of the lower Colorado watershed where alfalfa and other forages account for a large component of agricultural water use. Due to recurring long-term droughts and water shortages in the Colorado River Basin, the main source of irrigation water, there are growing concerns on the yearly shortfall between water supply and demand. Limited water supplies impact alfalfa production as well as other crops and urban use. Therefore, implementing water conservation tools and practices, and efficient use of irrigation water is necessary to sustain agricultural system in the region. While nearly 95% of the desert alfalfa is currently irrigated by surface irrigation systems [1], various irrigation strategies and on-farm water conservation practices have already been adapted by the local farmers to enhance the efficiency of water use. This includes utilizing subsurface drip irrigation (SDI), overhead linear move irrigation, and automated surface irrigation, and management strategies of tailwater recovery systems and deficit irrigation strategies [1]. Accurate estimate of alfalfa water-use as well as yield impacts of water deficits are critical for efficient irrigation water management, drought strategies, water transfer planning, and hydrological analyses. Worldwide, alfalfa seasonal evapotranspiration (ETc) is estimated between 800 and 1600 mm depending on climate and length of growing period [4; 5]. According to a two-year measurement using eddy covariance (EC) method at a commercial field located in Northern California, a range of 1249 to 1381 mm was reported as alfalfa seasonal water use under surface irrigation over six harvest periods [6]. alfalfa actual ET was estimated 625 mm at the windy arid environment of Curlew Valley, Utah using the residual of energy balance calculations [7]. The average ET for 751 alfalfa fields in the Lower Rio Grande Valley, New Mexico, using three OPEC (One Propeller Eddy Covariance) towers was determined 901 mm, which ranged from 386 to 1241 mm [8]. The average crop coefficient values of alfalfa varied from 0.80 to 1.09 in the Sacramento Valley, with a range of 0.45-0.60 just after harvest and 1.10-1.20 just before harvest [6]. The experimental fields were under common farmer irrigation practices with border check surface irrigation. The range of alfalfa crop coefficient (fields under border check surface irrigation) was found 0.5 to 1.3 in saline and shallow water tables area of the Imperial Valley, California based on measurements of applied water and soil moisture depletion data [9]. A wide range of the seasonal alfalfa actual crop coefficient values for the 751 fields investigated in the Lower Rio Grande Valley, New Mexico was reported (varied from 0.2 to 0.8, with an average value of 0.59) [8], in which irrigation methods, improper irrigation scheduling, limited water supply, interference of harvesting schedule with the irrigation, and cultural practices were recognized as the reasons of crop coefficient variability. Thus, these ET measurements likely reflected under-irrigated crops. An average seasonal actual crop coefficient value of 0.84 was found using the surface renewal (SR) and eddy covariance measurements in four commercial alfalfa fields in the Palo Verde Valley [1]. These alfalfa fields were under border check surface irrigation and furrow irrigation. Alfalfa is an herbaceous crop with rapid growth characteristics, and its yield is considered to be linearly related to evapotranspiration [10], particularly within a growth period. A wide range of 10-34 kg ha\({}^{-1}\) mm\({}^{-1}\) alfalfa water productivity has been reported in earlier studies [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21].