The irrigation cooling identified from satellite remote sensing is based on LST, which is physically different from air temperature (Ta) although these two are correlated \cite{Jin_2010}. It is unclear whether irrigation cooling can be observed with air temperature. To investigate this matter, we analyzed air temperature measurements from two paired flux tower sites of irrigated and rainfed maize in Nebraska. Results showed that irrigation cooling on air temperature (denoted as \(\Delta Ta\)) can be clearly seen from two pairs of site comparison (Ne1-Ne3 and Ne2-Ne3). The effect on air temperature (\(\Delta Ta\)) exhibited seasonal patterns similar to that of \(\Delta LST\) at both sites, with the strongest cooling in July (-0.38 °C for Ne1 and -0.53 °C for Ne2), weak or no cooling effect in June and moderate cooling effect in August (the absence of cooling in June is probably because irrigation is minimal in June in Mead site). However, the magnitude of cooling on air temperature was smaller than LST (-1.63 °C in July). This difference could be caused by factors mentioned in \cite{Li_2015}: (1) the inherent differences between air temperature and LST, (2) the clear-sky only retrieval of LST, and (3) different temporal samplings (1:30PM for LST while daytime averages for air temperature).

4.2 Interactions among processes involved in irrigation effects

The irrigation cooling effect observed on LST reflects contributions from different factors, including increased soil moisture and enhanced vegetation growth (Figure \ref{141459}). On one hand, irrigation water directly increases soil moisture and strengthens evaporative cooling. On the other hand, irrigated crops grow significantly better with more leaf area and biomass, which increase plant transpiration and thus exert an even stronger cooling. Such cooling from transpiration partially explains why the largest irrigation cooling corresponded to the peak growing season (i.e., July in Figure \ref{699893}). In fact, these processes of moisture and evapotranspiration are intertwined in a way where irrigation cooling (through evaporation) promotes crop growth, and the more vigorously-grown crops, in turn, enhance the cooling (through transpiration). Although our statistical model separated cooling from water supply in the irrigation yield effect, what we observed in reality will always be the combined effect of these processes.  For process-based crop models, it is still challenging to capture all these interactive processes, as it requires crop models to include both canopy energy balance and biochemical photosynthesis components to simulate the LST cooling (for cropland in peak growing season, it is mainly canopy temperature cooling) and its effect on crop growth, which are still absent in many agronomy crop models \cite{Peng_2018}. To simulate the cooling effects on air temperature and crop growth, crop models have to be bi-directionally coupled with an atmosphere model \cite{Lu_2015,Harding_2015}.