Sun-induced chlorophyll fluorescence (SIF) is a direct indicator of plant photosynthetic activities and can potentially indicate plant physiological changes caused by water stress. However, the direct effect of water stress on the physiological SIF responses in crops at the field level still needs further research to clearly understand the involved mechanisms. To study this relationship, we made use of Unmanned Aerial Vehicles (UAVs), which are flexible and cost-effective to acquire SIF data at a high temporal resolution. We acquired near-infrared SIF (760 nm) and red SIF (687 nm) measurements using a UAV platform over irrigated and non-irrigated sugar beet plots. To represent physiological changes in crops, we calculated the apparent SIF yield (SIF normalized by the absorbed photosynthetically active radiation) at 760 and 687 nm (SIF760yield and SIF687yield), the fluorescence emission yield at 760 nm ($Φ$F760), and the SIFratio (the ratio between SIF687 and SIF760). $Φ$F760 was estimated using the recently developed NIRvH approach. For an improved interpretation of the response of these SIF indicators, we also acquired additional UAV-based hyperspectral and thermal data. We found that on June 28, when sugar beets were experiencing water stress, SIF687yield, $Φ$F760, and SIFratio all showed a significant response to the recovery of the irrigated sugar beets (p-value $<$ 0.05). On the other hand, on July 24 when both water stress and heat stress affected the crop, only $Φ$F760 and SIFratio weakly tracked the changes induced by the irrigation (p-value $<$ 0.1). $Φ$F760 had similar changes to SIF760yield in both June and July, but $Φ$F760 was more sensitive to irrigation. This indicates the importance of correcting for the structural effect when interpreting the SIF response. The findings suggest that SIF indicators can indicate water stress at the field level, but its value to detect the changes of photosynthetic activities under severe stress needs more investigation.