## 3 Results and Discussions
### Rainfall and Reference Evapotranspiration Comparison  
One of the objectives of this study was to highlight the gap between ETo and rainfall in order to strategize the need for supplemental irrigation and sustainable agriculture. A comparison between the cumulative values of rainfall and ETo for the period 2011-2017 is displayed in Figure 6 to gauge the gap between the two variables. The results showed a high variability of rainfall in different months (of the growing season) during all years of the study period than variability in ETo. For the month of June, the rainfall ranged between 64.85-107.025 mm while FAO-56 ETo ranged between 83.82-112.47 mm with an average difference of 13.52 mm. The ETo clearly surpassed the rainfall values in the month of  
Figure 5: (a) Comparison of ETo predicted with LSTM and FAO-56, (b) with bidirectional LSTM and FAO-56 using combined data set of Prince Edward Island for the test period 2016–2017.  
June for periods 2011-2014 and 2016-2017. The highest gap between rainfall and ETo was observed in the month of July for year 2012-2017. In July, the recorded difference between ETo and rainfall was computed to be 3.66, \(-\)92.2, \(-\)56.1, \(-\)85.0, \(-\)73.4, \(-\)68.5, \(-\)98.7 mm for years 2011 through 2017, respectively. The negative values clearly show the higher ETo than the respective rainfall. In the month of August, the ETo surpassed rainfall in the years 2012, 2013, 2015 2016, and 2017 by 46.1, 30.0, 4.39, 15.8, and 39.6 mm, respectively. In the months of September, October, and November, rainfall clearly surpassed the ETo. These are the months of crop harvest when crops do not need rainfall and have no ETo phenomenon.  
The result of this analysis suggested that rainfall is highly variable in the same months of different years unlike ETo, which seems to be more consistent in different years. However, in order to fulfill the crop water requirements, careful monitoring of rainfall and ETo is required in the months of June, July, and August in Prince Edward Island for potential crop yield.  
Suitability of the modeling approach adopted in this study was further evaluated by comparing the FAO-56 cumulative ETo with the values simulated using LSTM and bidirectional LSTM in Figure 7, where cumulative rainfall has also been plotted for the test periods 2016 and 2017. A close agreement was found between ETo determined with FAO-56 and the two RNNs. Despite overestimation during the period July-October, yearly cumulative values of ETo determined with all the three methods were also in good agreement with cumulative rainfall during 2016 (Figure 7a).  
During the year 2017, higher cumulative gaps were observed between ETo and rainfall in comparison with 2016 (Figure 7b). The lower rainfall during the growing season (June-November) of 2017 (403.74 mm) than during 2016 (506.69 mm) were responsible for these gaps. There was no difference in the trends of RNNs and FAO-56 ETo for the two test years. The cumulative gaps between values of FAO-56 ETo and the values of ETo determined with LSTM and bidirectional LSTM depict the predictive errors of RNNs models. The error may be further reduced by adding more input variables in the RNNs. Furthermore, underestimations for drier months and overestimation for colder months may be removed by adding RMSE correction factors in order to obtain more accurate predictions. The results support the applicability of LSTM and bidirectional LSTM for sustainable water management with accurate estimation of ETo. In order to replenish the crop water requirements, supplemental irrigation might be the option for certain months of the growing season when ETo surpassed rainfall. The estimated ETo will be useful in irrigation scheduling for sustainable cultivation of potato on the island.  
Figure 6: A comparison of rainfall and FAO-56 ETo for the study period 2011–2017.