Performance of Twelve Mass Transfer Based Reference Evapotranspiration Models under Humid Climate

Reference evapotranspiration is very important parameter in the hydrological, agricultural and environmental studies and is accurately estimated by the FAO Penman-Monteith equation (FAO-PM) under different climatic conditions. However, due to data requirement of the FAO-PM equation, there is a need to investigate the applicability of alternative ETo equations under limited data. The objectives of this study were to evaluate twelve mass transfer based reference evapotranspiration equations and determine the impact of ETo equation on long term water management sustainability in Tanzania and Kenya. The results showed that the Albrecht, Brockamp-Wenner, Dalto, Meyer, Rohwer and Oudin ETo equations systematically overestimated the daily ETo at all weather stations with relative errors that varied from 34% to 94% relative to the FAO-PM ETo estimates. The Penman, Mahringer, Trabert, and the Romanenko equations performed best across Tanzania and the South Western Kenya with root mean squared errors ranging from 0.98 to 1.48 mm/day, which are relatively high and mean bias error (MBE) varying from −0.33 to 0.02 mm/day and the absolute mean error (AME) from 0.79 to 1.16 mm/day. For sustainable water management, the Trabert equation could be adopted at Songea, the Mahringer equation at Tabora, the Dalton and/or the Rohwer equations at Eldoret, the Romanenko equation at Dodoma, Songea and Eldoret. However, regional calibration of the most performing equation could improve water management at regional level.


Introduction
Evapotranspiration is an important parameter for climatological and hydrological studies as well as for agricultural water resources management [1] [2]. The accuracy of reference evapotranspiration (ETo) estimates directly feeds into the decision making process for regional water resources planning and, especially under semi-arid and arid conditions. Different methods of ETo estimation have been developed ranging from direct measurements from a reference crop [3] to computation from weather data such as temperature based models [3] [4], radiation based models [3] [5], and combination-based energy balance models [6] [7].
Numerous worldwide studies have shown that the FAO- 56 Penman-Monteith (FAO-PM) model is the most accurate one under different climatic conditions across the world [6]- [13] and had been adopted and recommended for ETo estimation [6] [7]. However, FAO-PM model requires maximum and minimum temperature, minimum and maximum relative humidity, solar radiation, and wind speed data to be run and these weather datasets are usually incomplete and/or not available in most developing countries. This data demand is the main constraint of use of the FAO-PM in locations where climate data is limited [14]- [17]. Therefore, the application of ETo equations with fewer meteorological parameters requirements is necessary under situations where more complete weather data are lacking. However, the evaluation of the suitability for each of the alternative ETo equations to determine the most suitable for particular locations using FAO-PM model as reference is required for the East Africa Region prior to their application. [18] indicated that the Turc ETo equation is recommended for estimating ETo using measured maximum and minimum air temperature and estimated radiation in Florida. From a cross comparison of 31 ETo methods, [19] showed that the five best methods as compared to the FAO-PM model were the two radiation based developed by the authors, the temperature based Blaney-Criddle [20], the Hargreaves-M4 equations [5] and the Snyder pan evaporation based equation [21]. [22] reported that Hansen and Turc equations were the most useful with the least average monthly error from the evaluation of 13 empirical reference potential evapotranspiration equations in Greece. Regarding the importance of accurate estimation of ETo by the Penman-Monteith method in data-limiting conditions, the recent studies [23] [24] have managed to simplify the estimation method with good performance and accuracy, even when the available data is very limited. The applicability of several other different ETo methods has been evaluated under different climatic conditions depending on their complexity and the required climatic variables data and their availability [25]- [30]. [ [31]. [32] indicated that the Turc equation was the best in the Western Balkans in Europe. [22] reported that Hansen and Turc equations were the most useful for ETo estimation in Greece. [33] [36]. Similar results were reported by [37] using data from eight weather stations across Burkina Faso for the 1998-2012 period. Different sets of equations have been tested in different regions and sub-regions under different climatic conditions including Canada [38], Iran [28] [39] [40], China [41], Poland [42], Southeast Australia [43], Senegal [2], and in Burkina Faso [44].
While the aforementioned studies have been conducted at different parts of the world, extremely limited data and information is available on this very important topic in Eastern Africa, particularly in Tanzania and Kenya. Therefore, it is critical to assess the applicability of ETo models for sustainable water management. Thus, the objectives of this study were to: 1) evaluate twelve mass transfer based ETo equations with comparison to the FAO-PM method, and 2) determine the impact of ETo equation on long term water management sustainability in Tanzania and Kenya.

Data Source and Type
Climatic data required for evaluating the FAO-PM ETo equation and the se-
Twelve mass transfer ETo equations were selected based on their applicability to regions with similar characteristics and compared with the FAO-PM equation for their accuracy in estimating daily ETo and to determine the best performing equations at each weather station.
2) [49] ( )( ) 3) [50] ( ) where ETo is in mm/day, ems, ea and es in kPa, u in m/s, Tmean is mean daily Journal of Water Resource and Protection temperature in (˚C), RH is daily mean relative humidity in %.

ETo Method Evaluation Criteria
Comparisons were developed using graphics and simple linear regression. For further comparison, root mean squared error (RMSE), relative error (RE), mean bias error (MBE) and the absolute mean error (AME) were used to evaluate the simplified reference evapotranspiration models [61] [62]: where, Pi is the estimated ETo with the radiation based ETo models; and Oi is ETo estimated with FAO-PM model with full dataset, at the i th data point and n is the total number of data points.   [40]. [2] reported that the Romanenko equation showed better performance under dry and semiarid condition than under the humid semiarid conditions in the Senegal River Valley. Romanenko equation produced a 6% ETo underestimation and obtained a mean ratio of 1.0 and a regression slope of 0.92 [2]. Similarly in Iran, the Romanenko equation was reported as the best mass transfer equation [19]. The Trabert and Mahringer equations performed relatively well under the sahelian climatic conditions as reported by [2]. [19] reported that Trabert and Mahringer equations underestimated ETo with average error of 26% and 31%, respectively in Iran while [2] reported average ETo underestimation of 16% and 31% at Ndiaye (coastal area) and at Fanaye (inland area) in the Senegal River Valley and Delta, respectively. [64] reported the FAO24-Radiation method to be the best among twenty ETo equations evaluated in the sub-humid Udham Singh Nagar district of Uttarakhand (India). Adversely, poor performance of the Mahringer equation was reported in Poland [42]. [38] indicated reasonable performance of the Meyer, Dalton, and Rohwer equation for free water evaporation estimation from four weather stations in north-western Ontario, Canada. The results of this study showed the specificity of each ETo equation and this might have been due to the sensitivity of the models to the climatic variables used in each model [30].

ETo Equation Adoption for Sustainable Water Management across the Study Area
Reference evapotranspiration is a very important parameter for the hydrological,   could be used in place even under limited data conditions as proposed by [44] for the study area.
In cases of ETo overestimation, estimated irrigation water requirement becomes tremendously high and which will still increase when taking the low efficiency of the irrigation system into account.

Conclusion
Performance of twelve mass transfer based reference evapotranspiration equa- However, other reference evapotranspiration equations including the radiation based and the combination equations should tested to determine the best alternative ETo equation to the Penman-Monteith equation for sustainable water management in Tanzania and Kenya. Given the current status of weather station networks in the region, the results of this study can enhance crop water use estimation and thus feeds into the decision making process for regional water resources planning by irrigators, water managers and other agricultural professionals.