1. Introduction 

Irrigation is essential to sustain crop production, especially in arid and semi-arid regions where crop growth is limited by water \cite{Elliott2014}. Crops benefit from irrigation in several aspects. With irrigation, crops are generally more productive than those under rainfed conditions, with increased leaf area/biomass, evapotranspiration, and higher water use efficiency \cite{Payero_2008,Grassini_2009,Oweis_2000}, which collectively translate into higher crop yield. Further, irrigation essentially decouples crop yield from climate, buffering yield variability due to climate fluctuation \cite{Troy_2015,Li_2019a,Shaw_2014}. Irrigation also improves crop resilience by partially offsetting the negative impacts from water stress under extreme drought and warming conditions \cite{Troy_2015,Tack_2017}
These various benefits of irrigation are underpinned by two key mechanisms, water supply and cooling, which reduce the effects of drought and heat stress on crop growth. The primary goal of irrigation is to supply an adequate amount of water when rainfall is not sufficient or timely to meet crops’ water demands. Such water supply effect is not limited to dry regions. Even in relatively humid regions with sufficient total precipitation, irrigation increases yield relative to rainfed crops as it compensates for intra-seasonal rainfall variability \cite{Grassini_2009} or supplements precipitation during sensitive crop growth stages \cite{Katerji_2008}
Irrigation also increases soil evaporation and crops' transpiration, and thus creates a cooling effect \cite{Siebert_2017,Lobell_2008,Szilagyi_2018}. Several empirical and modeling studies have found significant cooling over intensively irrigated areas such as the West \cite{Kueppers_2007} and Midwest United States \cite{MAHMOOD_2006,Huber_2014}, the North China \cite{Wu_2018} and Northeast China \cite{Zhu_2012}, and India \cite{Douglas_2009}. The cooling effect is particularly strong in reducing maximum temperature \cite{Bonfils_2007} and becomes more pronounced during hot days \cite{Thiery_2017}. Since crop yield is highly sensitive to high temperature and vapor pressure deficit (VPD), this cooling effect benefits crops by reducing heat stress \cite{Siebert_2017,Siebert_2014} and evaporative demand \cite{Nocco_2019}, and mitigating the impacts of extreme heat \cite{Vogel_2019}. In particular, cooling can shift the high temperature thresholds of crops beyond which yield declines so that crops become more tolerant to extreme weather \cite{Troy_2015,Carter_2016,Schlenker2009,Lobell_2013}
Irrigation effects on crops have been extensively studied in previous studies \cite{Payero_2008,Butler_2018,Tack_2017,Troy_2015,Carter_2016,Oweis_2000}, however, much attention has been paid to the water supply aspect of irrigation \cite{Szilagyi_2018}, while the cooling effect of irrigation on crop yield has not been in the focus. Although it is well-known that water supply and cooling are two key mechanisms responsible for yield gains of irrigation \cite{walker1989}, their effects on crop yield benefits have not been separately quantified. 
In this study, we aim to quantify the irrigation effects from multiple observation data and to disentangle the contribution of water supply and irrigation cooling on crop yield benefits. We first analyzed the irrigation effects on crop growth and their spatial and temporal variations with satellite remote sensing and yield observation data. Irrigation effects (including cooling and biomass/yield changes) were quantified by comparing land surface temperature (LST), enhanced vegetation index (EVI), and yields between irrigated and rainfed maize in Nebraska. Next we proposed a statistical method to quantify the separate contribution of water supply and cooling in yield benefits of irrigation. Our analysis focused on maize for the state of Nebraska, USA. Nebraska was selected as the study region because it is a major maize-producing state in the United States with an extensive irrigation/precipitation gradient \cite{Szilagyi_2018}. During the study period (2003-2016), irrigated maize accounted for 56% of the total maize harvest area and 65% of maize production in Nebraska.

2. Materials and methods

2.1 Data

(1) MODIS remote sensing data
We used 8-day LST data (MYD11A2) at 1km spatial resolution and 16-day Enhanced Vegetation Index (EVI, MYD13Q1) data at 250m spatial resolution as proxies of crop temperature and biomass. The LST and EVI data were obtained from Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 from 2003 to 2016. The daytime and nighttime LSTs retrieved from the Aqua satellite approximate the maximum and minimum temperature of a day as the satellite has a local overpass time of 13:30/1:30. The LST data were used to quantify the irrigation cooling effect. 
(2) Irrigation map and crop classification data
The 2005 Nebraska irrigation map produced by the Center for Advanced Land Management Information Technologies (CALMIT) at the University of Nebraska-Lincoln provides a field-level inventory of center pivot and other irrigation systems (e.g., flood irrigation) in Nebraska for the growing season of 2005. The irrigation systems were identified using Landsat 5 Thematic Mapper 30m satellite imagery and Farm Service Agency 1m airborne orthoimagery (see more information at https://calmit.unl.edu/metadata-2005-nebraska-land-use-center-pivots-irrigation-systems). The irrigation map was used in conjunction with the 30m maize map extracted from Crop Data Layer (CDL) from 2003 to 2016 to determine the locations of irrigated and rainfed maize fields in Nebraska.
(3) Statistical crop yield data
The county-level crop yield and harvest area data in Nebraska were obtained from U.S. Department of Agriculture National Agricultural Statistics Service (NASS, https://quickstats.nass.usda.gov/), including yields for both irrigated and rainfed maize from 2003 to 2016. The unit of maize yield is bu/acre, and it can be converted to unit of t/ha by multiplying a factor of 0.0628.
(4) Gridded and flux tower climate data
The gridded daily PRISM climate data from 2003 to 2016 include maximum and minimum air temperature and precipitation (ftp://prism.oregonstate.edu/). The data originally had a spatial resolution of 4km and were averaged to county-level to reflect climate condition of each county. To verify the irrigation cooling at the field level, we used daytime air temperature measurements ("TA_F_MDS" variable) from three maize flux sites (US-Ne1, Ne2, and Ne3) from AmeriFlux in Nebraska from 2001 to 2013 \cite{Suyker_2012,Suyker_2005}. NE1 is an irrigated maize site. NE2 is also an irrigated site but maize and soybean are rotated (maize in odd years during 2001–2009 and all years from 2010 to 2013). NE3 is a rainfed site with maize and soybean rotated (maize in all odd years during 2001–2013). By assuming these three sites are close in distance to share similar large-scale climate signal, the paired differences between irrigated and rainfed sites such as Ne1−Ne3 and Ne2−Ne3 are indicative of the irrigation effect on air temperature.  

2.2 Method

2.2.1 Extracting crop properties of irrigated and rainfed maize from remote sensing 

In this study, irrigation effect is quantified as the county-level differences in crop properties (i.e., yield, LST, and EVI) between irrigated and rainfed maize. While irrigated and rainfed maize yields in each county are readily available from NASS, their LST and EVI in each county have to be extracted by the procedure implemented in Google Earth Engine described below (Figure \ref{191496}).
The irrigation map was first overlaid with CDL data in 2005 to extract irrigated and rainfed maize pixels at 30m resolution. These 30m pixels were then spatially aggregated to create irrigated and rainfed maize masks at MODIS resolutions with the majority method (1km for LST and 250 m for EVI 250m). The resulting masks were combined with MODIS data to extract LST/EVI of irrigated and rainfed maize so that their differences can be computed in each county. This only gives LST and EVI of irrigated and rainfed maize and their differences in 2005, because the irrigation map is developed only for for 2005. In order to make this method work for other years, we assumed that the irrigation map produced for 2005 also applies to other years. To test this assumption, we compared irrigated and rainfed maize area in other years derived under this assumption with statistics from NASS. If the assumption was not accurate, the derived maize harvest area would show a large bias against NASS statistics. We found high correlations between these two from our our validation results, which supported the validity of this assumption (r=0.99 and r=0.94 for irrigated and rainfed maize area from 2003 to 2016 respectively, see Figures \ref{848838} and \ref{947083}).

2.2.2 Separation of cooling and water supply in yield benefit due to irrigation