The cooling on LST shown in our study is also an indication of how vegetation actively regulates their thermal environment at the plant scale. Also, the cooling was found on air temperature from flux tower comparisons. This further confirms that irrigation changes the microclimate surrounding irrigated crops. However, it should be clarified the irrigation cooling found in our study at small-scale is not the same as the regional cooling reported in studies that focus on irrigation impact on local and regional climate through land-atmosphere interaction \cite{Kueppers_2007,Sacks_2008,Thiery_2017,Lu_2017,Lobell_2008,Santanello_2011} (Figure \ref{141459}). The cooling effect in our study is quantified by a spatial comparison approach, which assumes that irrigated and rainfed crops are located in the same background climate conditions, and their differences reflect the irrigation effect. This assumption means irrigation would not trigger significant changes in background climate state, thereby excluding the atmosphere feedback that may cause non-local impact in remote regions \cite{Winckler_2019}. This is the key difference regarding the irrigation cooling effect between small- and large-scale studies. In fact, the irrigation cooling effect on climate could go beyond the scope of micro and local climate and affect precipitation pattern if irrigation area becomes sufficiently large, which seems to be already the case in many intensive agriculture areas (e.g., US Corn Belt) \cite{DeAngelis_2010,Szilagyi_2018,Huber_2014,Mueller_2015}. As a result, irrigation could become a climate forcing that not only drives regional climate change \cite{MAHMOOD_2006,Mueller_2015,Kueppers_2007} but also could have global climate consequences \cite{Sacks_2008}. These agricultural practice will interact with climate and then influence crop growth and yields \cite{Butler_2018}.

The separation of cooling and water supply relies on satellite remote sensing data and statistical model, as a result, the quantification results would inherit uncertainties from data and method we used. First, there are uncertainties in the thematic classification accuracy of the maize pixels of CDL and the 2005 irrigation facility map which were used to identify the location of irrigated and rainfed maize fields. In addition, our assumption that the field-level irrigation map made for 2005 is also valid for other years could result in some misclassified irrigated and rainfed fields, because some irrigated lands may have been retired, while other areas may have experienced irrigation expansion. Moreover, irrigated and rainfed crop fields on the ground may not be fully distinguished by the coarser spatial resolution of MODIS. The mixed pixel may confound the extracted crop properties of irrigated and rainfed maize, which could be more of an issue for LST (1km) than EVI (250m). To mitigate this issue, we only selected MODIS-scale pixel with the majority of its area composed of 30m irrigated or rainfed maize for analysis. All these factors add up to uncertainty in the extracted signals from satellite remote sensing data for irrigated and rainfed maize. Nevertheless, irrigation effects identified on LST and EVI are unlikely to be significantly altered by these uncertainties, as validation showed reasonable performance (Figs \ref{848838} and \ref{947083}) and the extracted signals such as LST cooing and EVI increase generally agree with our expectation.

The irrigation benefits on yield are separated into cooling and water supply with statistical models. Since this quantification relies on statistical models, the estimated specific contributions will likely to be different with different model configurations, but the relative importance of cooling and water supply is robust and is not affected by model selection. While the cooling effect on yield is quantified as the yield change due to temperature difference imposed by irrigation, the water supply effect is quantified as the yield difference between irrigated and rainfed crops if they had the same temperature. Our results showed that water supply effect, unsurprisingly, dominated the yield gain from irrigation. It should be noted that the water supply effect might be overestimated with this method, because the yield difference between irrigated and rainfed crops under the same temperature condition is all attributed to water supply. In fact, irrigated and rainfed crops could be different in other aspects such as crop variety \cite{Tack_2017}, management practices, and these factors may also contribute to their yield differences. Therefore, the water supply effect identified here actually includes contributions from water supply and other related factors.

Some important factors of irrigation are not taken into account in our analysis due to lack of data, for example, the amount, timing, and duration of irrigation. In our case, irrigation is considered as a binary situation. As for the actual irrigation practice, we assume that producers would make sensible decisions of their irrigation strategy to maximize their crop yields while being cost-effective. The effects of these granular factors require further investigation. 

Our study provides observational evidence of how irrigation changes crop growth and crop properties with satellite remote sensing data (LST, EVI), and disentangle two key processes by which irrigation increases crop yield: irrigation cooling and water supply. While results showed that water supply dominates the irrigation yield increase as it reduces water stress, we also found that irrigation cooling has a non-negligible contribution to yield as it reduces heat stress, and the latter was not well-recognized in previous studies. The spatiotemporal variations in the irrigation effect found in our results highlight the strong influence of climate condition. With projected shifting precipitation patterns, and more frequent droughts and heatwaves in the future \cite{2017,Huang_2017}, a large expansion of irrigation would be required to sustain current maize yield trend in the US \cite{DeLucia_2019,McDonald2013}, and the irrigation effects will also be intensified. Therefore, the interaction between irrigation effect and climate, as well as the different contributions from cooling and water supply, becomes more essential to understand the consequences of future expanded irrigation on crop production and regional climate. 

Y.L. acknowledges support from the State Key Laboratory of Earth Surface Processes and Resource Ecology. K.G. acknowledge the support from USDA NIFA projects (2017‐67013‐26253, 2017‐68002‐26789, 2017‐67003‐28703) and NSF CAREER award (#). T.F. acknowledges the support from USDA NIFA project (#???? New project number) and Hatch Project #1009760. The authors declare no conflict of interest for this work.

Y.L. and K.G. conceived and designed the study; T.F. and B.W. provided the 2005 Nebraska irrigation map data. Y.L. performed the data analysis; Y.L. and K.G. analyzed the results; Y.L. and K.G. wrote the manuscript with contributions from B.P., T.F., B.W. and M.P.