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The unequal water distribution in the universe has resulted in more than 2 billion people living in water-stressed areas. Globally, withdrawals of water resources are still below the critical level. Pakistan is also affected by this serious problem. In the context of environmental evaluation, irrigation scheduling, and water resource management, evapotranspiration predictions are crucial. The evapotranspiration estimation methods may need to be evaluated daily or monthly to understand the climate change effects in the local areas. This paper investigates spatial-temporal interpolation of evapotranspiration data from 41 Pakistani meteorological stations. To estimate evapotranspiration, we have used the average time series data between 2006 and 2015 on temperature, relative humidity, wind speed, and solar radiation. We developed a new modified Hargreaves equation to estimate evapotranspiration and evaluate the performance of different models. We found that our modified Hargreaves model could perform better than the original Hargreaves model. To analyze trends in different seasons, such as rainy, dry, and annual, FAO-56 Penman-Monteith, Blaney-Criddle, and Hargreaves-Samani models are used. We used Ordinary Kriging for Functional Data to map and predict evapotranspiration spatially and temporally in various locations. [ABSTRACT FROM AUTHOR]