# A Machine Learning Method to Estimate Reference Evapotranspiration Using Soil Moisture Sensors
## 1 Introduction  
In agricultural sciences, the optimal determination of crop water needs over time is based on measuring the soil water balance and the evaporative demand of the plants. The use of soil moisture measurements was adopted as a suitable strategy for soil water balance estimation. Several methodsfor computing this balance were developed by different authors [1; 2; 3]. These techniques were applied in agriculture to obtain the water needs in conjunction with other methods based on remote image sensing. The ultimate objective is to provide farmers with information on the appropriate irrigation volumes to apply in every phenological period of the crop, depending on the desired levels of yield and other parameters. Different physical principles are applied to determine soil moisture, such as gamma-ray spectroscopy [4], synthetic aperture radar [5], and others [6]. Furthermore, there is a wide range of techniques for measuring soil moisture based on electricity, which are applied in geophysical prospecting [7; 8] and agronomy [9; 10], among other areas. In these measuring techniques, capacitive methods such as frequency-domain reflectometry (FDR) are included [11; 12; 13]. The accuracy of such sensors varies due to the employed techniques and working conditions. The key of these techniques is to model the relationships among soil water balance, crop yield, and water use efficiency (WUE) in order to develop better semiarid crops and water management practices [14]. In Mediterranean agriculture, particularly in the southeast of Spain, soil water availability is one of the main limitations for the practice of an economically sustainable agriculture. For this reason, using a suitable irrigation management is critical in the quantity and quality of the obtained harvests. This involves the determination of crop water needs and an optimal irrigation scheduling [15; 16; 17; 18; 19]. Although yield reduction is generally expected when crops are subject to limited irrigation, a well-designed limited irrigation system can minimize the impact on yield and still lead to grower profitability. On the other hand, according to the FAO (Food and Agriculture Organization)-56 methodology [20], crop evapotranspiration (ETc) can be obtained as the product of the reference crop evapotranspiration (ETo) and a crop coefficient (Kc). This Kc coefficient takes into account the development season of the cultivated species, the type of irrigation (by sprinkler, trickle, etc. ), and the cultivation techniques (plantation density, pruning, etc.) [21]. [PERSON] et al. [20] proposed Kc values for a great number of species, in standard crop conditions; an adjustment of Kc is necessary when the actual conditions are different from this standard scenario [22; 23]. The infrastructure required for a direct measurement of ETc involves high-cost equipment such as lysimeters and Bowen-ratio stations [24]. Therefore, this methodology is unacceptable for small farms. However, both ETo and ETc can also be estimated indirectly, through their relationship with the values obtained using other inexpensive sensors. For example, in the Penman-Monteith method [20], ETo is estimated based on solar radiation, air temperature, humidity, wind speed, atmospheric pressure, site elevation above sea level, Julian day, and latitude degree of the study site. Thus, the main parameters of the soil water state (water content, water potential, and water balance, among others) can be estimated in a cost-efficient way. This methodology is widely extended and used by farmers because of its simplicity. However, it has the disadvantage of giving isolated measurements; in some cases, the obtained parameters are not representative of the entire plot. To overcome this drawback, remote image capture systems offer a promising alternative to traditional water status measurements [25]. They can provide a snapshot of the whole crop over a reduced period.