Comparison of reference evapotranspiration models for the agro-ecological zones of Nigeria

Irrigation practices are best done by estimating the crop water requirement in order to avoid over or under irrigation which may negatively affect crop yields. In this study, weather data (2004-2015) were collected and analyzed. The weather data include; minimum and maximum temperature (°C), relative humidity (%), wind speed (km/day), sunshine (hr/day) and radiation (MJ/m2/day). FAO Penman-Monteith model is a universal standard model used with other five evapotranspiration models such as; Priestley-Taylor model, Thornth-Waite model, Hargreaves model, ASCE-Penman Monteith model and Blaney-Criddle model to compute the mean monthly reference evapotranspiration (ET°) for the six agro-ecological zones of Nigeria. Statistic regressions were performed to examine the relationship of the reference ET° estimates from the five models with the estimates by FAO Penman-Monteith model. The results of the analyses show that the mean monthly average ETo estimates by the FAO Penman-Monteith model, Priestley-Taylor model, Thornth-Waite model, Hargreaves model, ASCE-Penman Monteith model and Blaney-Criddle model across the six weather stations are; 6.48, 7.66, 14.14, 11.16, 5.57, and 3.70 mm/day, respectively. The best predictor is the ASCE-Penman Monteith model which correlated well with the FAO Penman-Monteith model while, the Priestley-Taylor model is the second-best model. Thornth-Waite model and Hargreaves model produced underestimated ET values while, Blaney-Criddle model greatly over-estimated the FAO Penman-Monteith model. Therefore, this study is useful to the precise agricultural water management and regional water resources planning.


Introduction
The continuing growth of world population places new demands on water resources every day. Improved management and planning of water resources are needed to ensure proper use and distribution of water among competing users. Understanding the crop water requirement, use and consumption in irrigated agriculture is a prerequisite for better management and conservation of agricultural land [1]. Estimating crop water requirement by computing crop evapotranspiration is a widely used method [2]. The estimation of evapotranspiration and its components has been a key issue in hydrological studies and to enhance water use efficiency [3]. In practice, the estimation of ETc requires first calculating reference evapotranspiration (ETo) and then applying the proper crop coefficient (Kc) to estimate actual crop evapotranspiration (ETa) [4]. The Kc is defined as the ratio of ETc to ETo and is used to scale the ET model to a specific crop. This Consequently, different crops will have different Kc coefficients [5].
There are several models to calculate ETo, but their performance in different environment is diverse, since all of them have some empirical background The FAO Penman-Monteith model has been considered as a universal standard to estimate ETo for more than a decade [6]. This model accounts for aerodynamic as well as physiological parameters which requires several meteorological parameters such as net radiation, air temperature, vapour pressure deficit, relative humidity, sunshine, and wind speed [7]; [8].
The number of meteorological stations where reliable data for these parameters exist is an even smaller subset. This is especially true in developing countries where reliable collection of wind speed, humidity and radiation is limited [9]. However, the problem of over or under irrigation will be minimized if ETo is accurately estimated. Too much or too little water at the wrong stage of crop development can damage the crop and reduce yield.
It is in the light of the above that this study aimed at comparing reference evapotranspiration models with F.A.O Penman-Monteith model, using available climatic data for the agro-ecological zones of Nigeria. Figure 1 is a map of Nigeria showing agro-ecological zones. The study area is located at the tropical zone of West Africa within Africa continent of the world, between latitudes 4°N and 14°N and longitudes 2°2'E and 14°30'E,and has a total area of 923,768 km 2 . Approximately 13,000 km 2 of the land is covered by water (1.4%) and the remaining 98.6% of the land cover ranges from thick mangrove forests and dense rain forests in the south to a near -desert condition in the north-eastern corner of the country [10].   [11] Although the model was originally developed to compute ET on a monthly basis, it can be modified to estimate daily values of ET with mean daily temperature. As temperature models tend to underestimate ET in arid regions while overestimating ET in humid regions, local calibration of the empirical coefficients is required to produce reliable estimates of ET [12]. The advantage of this model is the simplicity and disadvantage is that it underestimates ET grossly compared to the measured ET values [13].

Thornth-Waite Model.
In 1948, Thornth-Waite and Penman both developed potential evapotranspiration model independently. The Thornth-Waite model is simpler than Penman's model because the model requires less climatic data.

ASCE-EWRI Standardized Penman Monteith Evapotranspiration Model. The ASCE Standardized
Reference Evapotranspiration Equation is based on the Penman-Monteith model, with some simplification and standardization on the aerodynamic and surface resistances. This model is applicable for both tall (Alfalfa) and short (grass) reference surfaces. A grass reference crop is defined as an extensive, uniform surface of dense, actively growing, cool-season grass with a height of 0.12 m, and not short of soil water; whereas a full cover alfalfa reference crop is defined as an extensive, uniform surface of dense, actively growing alfalfa with a height of 0.50 m, and not short of soil water [14]. [15] Found a good correlation between the ASCE Standardized ETo equation results and the FAO 56 PM ETo results calculated on hourly time steps. However, the FAO 56 PM method estimated 5% to 8% lower ETo compared to the ASCE Standardized ETo. According to [15] the results may be due to the higher surface resistance values during daytime periods in the FAO 56 PM equation.

Methodology
The daily weather data collected were summed and averaged to obtain the mean monthly values. Similarly, the mean daily values across the period of record were averaged to obtain the mean annual values. Six different ET models; two combination-based models (FAO Penman-Monteith and ASCE-Penman Monteith), two temperature-based models (Thornth-Waite and Blaney-Criddle) and two radiation-based model (Priestley-Taylor and Hargreaves) were used to estimate mean monthly reference evapotranspiration (ETo) for six agro-ecological zones of Nigeria. An Excel computer program was developed to calculate ETo for the six ET models on monthly basis, using the mean monthly weather data for the twenty three weather stations. Linear statistic regressions were performed to examine the relationship of the reference ETo estimates from the five ET models with the estimate by the standard FAO Penman-Monteith model for the six agro-ecological zones of Nigeria. The regression model is of the form: Where, Y = FAO Penman-Monteith monthly reference ETo X = Mean monthly reference ETo estimated from each of the other two models, and M and C = Slope and intercept, respectively. The values estimated from the mean monthly ETo for each of the five models were plotted against the mean monthly estimate by the standard FAO Penmen-Monteith model. The deviations on the graph in the respect of FAO Penman-Monteith were adjusted. Parmele and McGuiness in 1974 recommended that the best model is the one with the lowest absolute deviation, C value closest to Zero, M value closest to 1.0, the smallest RMSE, and highest R 2 . The mean monthly correction factors for the potential use of some models in the study area were also computed as the ratio of the monthly total FAO Penman-Monteith reference ETo to the monthly total for each model averaged over the record period.

Results and Comparison of ET models
The computed mean monthly reference evapotranspiration (ETo) for each model in each zone are shown in tables 2, 3, 4, 5, 6 and 7.The FAO Penman-Monteith's mean monthly ETo estimates ranged from           Table 9. With regards to regression equations, ASCE-Penman Monteith model resulted in a slope (M) slightly more than unity (1.7209) and an intercept (C) close to zero (0.1133), given the best predicted values. The second-best values were those obtained by the Priestley-Taylor model (M = 0.1890) and (C = 6.4404). The Thornth-Waite model produced the greatest underestimates (by as much as 16%), while the Hargreaves model yielded the least underestimated values (7%). Hence, the Blaney-Criddle model over-estimated by as much as 24%, given the worst estimates among all the tested models. A correlation coefficient (R 2 ) is used to reflect how the estimated ETo best matches with the FAO Penman-Monteith model estimation. Root mean square error (RMSE) and Absolute average deviation (ADD) also represent the deviation of estimated ETo from the FAO Penman-Monteith model estimation, and it does so in a more comprehensive manner [16]. It revealed that the most acceptable model of computing ETo is ASCE-Penman Monteith model (R 2 = 0.9992 %) which requires many parameters viz. monthly radiation, mean temperature, wind speed and vapour pressure data. RMSE and ADD values ranged from -5.43 to 0.92 mm/day and from 0.025 to 1.740 mm/day respectively, for all the five models. The ASCE-Penman Monteith model showed its superiority over the other models studied with a smallest RMSE value of -5.43 mm/day and the Blaney-Criddle model was the one that demonstrated the worst performance with RMSE of 0.92 mm/day. Similarly, the ASCE-Penman Monteith model showed the best performance over the other models with the lowest ADD value of 0.025 mm/day and Blaney-Criddle model was the least effective model with ADD value of 1.740 mm/day.
The mean monthly correction factors that can be used for adjusting the Blaney-Criddle, Hargreaves and Thornth-Waite model for their potential use at each agro-ecological zone are shown in Table 10.

Conclusions
The FAO Penman-Monteith model is well established as the accurate and robust model to estimate ETo. The mean monthly average ETc estimates by the FAO Penman-Monteith model for twenty three weather stations ranged from 2.58 mm/day for South-West to 15.03 mm/day for North-West. Similarly, the mean monthly average ETo estimates by the FAO Penman-Monteith, Priestley-Taylor, Thornth-Waite, Hargreaves, ASCE-Penman Monteith and Blaney-Criddle model are found to be 6.48, 14.14, 7.66, 11.16, 5.57 and 3.70 respectively. The results show considerable variability among the models, in addition, the relationship among models depends on location. The best predictor is the ASCE-Penman Monteith model which correlated well with the FAO Penman-Monteith model while, the Priestley-Taylor model remains the second-best model. Thornth-Waite and Hargreaves model produced the underestimated values while, Blaney-Criddle model greatly overestimated the FAO Penman-Monteith model.

Recommendations
The following recommendations were drawn from this study: