## 1 Introduction
The LSTM neural networks were introduced to overcome the vanishing gradient problems of RNNs with capability of storing important information containing long sequences [18]. To further improve the performance of RNNs, more advance LSTMs were developed by [PERSON] and [PERSON] [19], named bidirectional LSTM. The LSTMs relate different past records in time series problems; however, in bidirectional LSTMs the enhanced learning mechanism enable them to relate the past as well as future records for better estimation of a variable. The LSTMs are used in a number of applications including speech recognition, time series predictions, and grammar learning. However, the application of LSTMs in the field of hydrology has not been widely reported in literature but can be used in estimation of hydrologic variables since several climatic variables used in hydrology exhibit time series behavior. Several studies have highlighted the potential of LSTMs in rainfall runoff modeling [20; 21] in which the performance of LSTMs was better than physically-based runoff models. [PERSON] et al. [22] used LSTMs for groundwater estimation and reported that they performed better than the multilayer perceptron model. They used the dropout effect in hidden layers of LSTMs to increase the model learning for better estimation of groundwater. However, based on the literature review, the use of advanced RNNs in ETo modeling is very limited and/or unpublished. Need for this study is based on the fact that out of 57 meteorological weather stations, installed in Prince Edward Island, less than 10 stations provide enough data for ETo estimation for the FAO-56 method. This leaves researchers and the government sectors, responsible to promote sustainable agriculture in the island, to look for other approaches of estimating ETo to guide farmers about making intelligent decisions for irrigating their crops including potatoes. Potato industry significantly promotes the economy of Prince Edward Island as it contributes about 10.8% to the GDP (gross domestic product) of this province with more than one billion dollars direct and indirect economic benefits, while engaging 12.1% of the total work force of the island [23]. Currently, Prince Edward Island produces approximately 20-25% of total potatoes grown in Canada each year [24]. The potato is a very sensitive crop in terms of both yield and quality under limited water conditions [25] and soil water should not be depleted by more than 30-50% for optimum potato yield [26; 27]. The findings of [PERSON] et al. [27] revealed the high risk of reduced potato yields under water shortage conditions. The majority of potato production in Prince Edward Island is rainfed and irregular rainfall patterns may affect potato yield. Furthermore, climate changes add severity to this problem as more hot days, less cold days, and changes in precipitation patterns have been predicted for this island during the next decades [28]. These challenges demand the correct quantification of plant water requirements, calculated from ETo, through the use of robust and accurate methods. The neural networks and analysis used in this study to estimate ETo have not been previously used and/or published for this region making this study novel and innovative for the scientific community and for government sectors involved in agricultural activities. Therefore, this study explores the performance of conventional LSTMs and bidirectional LSTMs in modeling ETo across Prince Edward Island, Canada with the specific objectives to (i) model ETo with high accuracy as well as with a reduced number of input variables and (ii) assess the need of supplemental irrigation by comparing the rainfall and estimated ETo for sustainable production of potatoes in Prince Edward Island.