Climatic data required for evaluating the FAO-PM ETo equation and the selected ETo models were collected at five weather stations across Tanzania and four weather stations in South-Western Kenya, for the period of 1998-2012. Maximum and minimum air temperature (Tmax and Tmin), maximum and minimum relative humidity (RHmax and RHmin), solar radiation (Rs) and wind speed (u2) were collected from Dodoma, Morogoro, Songea, Kilimanjaro, and Tabora in Tanzania; and Nakuru, Jomo Kenyatta, Kisumu, and Eldoret in Kenya with the geographic coordinates presented in Table 1. Tanzania is characterized by tropical climate with hot and humid coastal areas and cool and temperate

northwestern highlands. The northern and eastern areas of Tanzania experience two distinct rain seasons; the short occurring during October to December and the long rains from March to May. However, the southern, western, and central parts of the country experience one wet season that continues from October through to April or May. The central plateau in Tanzania tends to be dry and arid throughout the year. Kenya’s spatial extent lies astride the equator and thus characterized by a tropical climate. Similar to Tanzania, Kenya’s coastal zone is hot and humid, has a temperate inland, very dry in the north and northeastern areas and the western area is hot and wet throughout the year [45] [46] . Most of Kenya has a bimodal rainfall pattern, with the longer season occurring during March to May (MAM) and the shorter season during October to December (OND). Some areas in the western and central parts of the Kenyan Rift Valley experience a tri-modal rainfall pattern. The climate is influenced by systems such as the migration of Inter-Tropical Convergence Zone (ITCZ) from south to north and vice versa, Sub Tropical High Pressure systems (STHP), El Niño/Southern Oscillation(ENSO), Monsoon winds, tropical cyclones, the Indian Ocean, Lake Victoria circulation and the topography [46] [47] [48] .

1) Penman-Monteith model (FAO-PM)

Daily reference evapotranspiration was computed using the Penman-Monteith (FAO-PM) equation (ETo-Ref) [6] . The Penman-Monteith ETo equation with fixed stomatal resistance values for grass surface is:

ETo = 0.408 Δ ( R n − G ) + ( γ C n u 2 / ( T + 273 ) ) ( e s − e a ) Δ + γ ( 1 + C d u 2 ) (1)

where: ETo is the reference evapotranspiration (mm/day), Δ is the slope of saturation vapor pressure versus air temperature curve (kPa・˚C⁻¹), Rn = net radiation at the crop surface (MJ・m⁻²・d⁻¹), G = soil heat flux density at the soil surface (MJ・m⁻²・d⁻¹), T = mean daily air temperature at 1.5 - 2.5 m height (˚C), u2 = mean daily wind speed at 2 m height (m・s⁻¹), es = the saturation vapor pressure at 1.5 - 2.5 m height (kPa), ea = the actual vapor pressure at 1.5 - 2.5 m height (kPa), es − ea = saturation vapor pressure deficit (kPa), γ = psychrometric constant (kPa・˚C⁻¹), Cn = 900˚C・mm・s³・Mg⁻¹・d⁻¹, Cd = 0.34 s・m⁻¹ for grass, γ is the psychrometric constant (kPa・˚C⁻¹). All parameters necessary for computing ETo were computed according the procedure developed in FAO-56 by [6] .

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]

ETo = ( 3.648 + 0.7223 u ) ( e s − e a ) (2)

3) [50]

ETo = 3.075 u ( e s − e a ) (3)

4) [51]

ETo = ( 0.375 + 0.05026 u ) ( e s − e a ) (4)

5) [52]

ETo = ( 3.3 + 0.891 u ) ( e s − e a ) (5)

6) [53]

ETo = 0.35 ( 1 + 0.98 / 100 u ) ( e s − e a ) (6)

7) [54]

ETo = ( 0.1005 + 0.297 u ) ( e s − e a ) (7)

8) [55]

ETo = 0.0018 ( T a + 25 ) 2 ( 100 − R H ) (8)

9) [56]

ETo = 0.543 u 0.456 ( e s − e a ) (9)

10) [57]

ETo = ( 1.298 + 0.934 u ) ( e s − e a ) (10)

11) [58]

ETo = 2.5 ( e m s − e a ) (11)

12) [59]

ETo = 0.15072 ∗ 3.6 u ∗ ( e s − e a ) (12)

13) [60]

ETo = 4.5 ∗ [ 1 + ( T m e a n 25 ) ] 2 ∗ ( 1 − e a e s ) (13)

where ETo is in mm/day, ems, ea and es in kPa, u in m/s, Tmean is mean daily temperature in (˚C), RH is daily mean relative humidity in %.

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] :

RMSE = ∑ i = 0 n ( P i − O i ) 2 n (14)

RE = RMSE ETomean × 100 (15)

MBE = n − 1 ∑ 1 n ( P i − O i ) (16)

AME = n − 1 ∑ 1 n | P i − O i | (17)

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.

The evaluation of the twelve mass transfer based ETo equations showed different degrees of performance of the equations with comparably reasonable coefficient of determination across the study area. The Brockamp-Wenner equation obtained the highest ETo overestimation with the RMSE ranging from 3.18 to 6.19 mm/day, an average relative error of 95% of ETo estimates and the highest AME range of 1.78 - 5.47 mm/day (Table 2). [30] indicated overestimation of ETo by mass transfer based equations, compared to the Penman-Monteith model similar to the results reported by [63] . [30] reported a maximum overestimate of 17.7 mm/day by the Albrecht equation in Iran. The Albrecht, Dalton, Meyer, Rohwer, and Oudin equations also systematically overestimated the daily ETo across the study area with an average regression slope of 1.323, 1.288, 1.218, 1.263 and 1.451, respectively, and average RE of 71%, 41%, 34%, 41%, and 52%, respectively. The WMO and the Papadakis equations systematically underestimated the daily ETo at all weather stations. The RMSE varied from 1.09 to 1.97 mm/day and from 1.20 to 2.27 mm/day for WMO and the Papadaki equations, respectively (Table 2). The Penman, Mahringer, Trabert, and Romanenko equations overall showed satisfactory performance with some site specificities. The regression slope varied from 0.749 to 1.106, 0.812 to 1.15, from 0.867 to 1.149, and from 0.849 to 1.188 for the Penman, Mahringer, Trabert, and Romanenko equations, respectively, and averaged 0.929, 0.957, 1.017, and 1.002 for the respective equations. The RMSE for these four equations averaged 0.98, 1.38, 1.48,

and 0.99 mm/day (Table 2), however, they had low corresponding magnitude of RE, MBE and AME compared to the Brockamp-Wenner, Albrecht, Dalton, Meyer, Rohwer, and Oudin equations.

The results indicate that there is site specific adaptability of the ETo equations under this study. The Albrecht equation showed the best performance at Morogoro. The Penman equation seems to be non-applicable only at Dodoma, Jomo Kenyatta and Eldoret weather stations, however with site calibration the performance of the Penman equation could be improved and the adjusted Penman equation may be applicable across the study area. The Dalton equation showed its best performance at Eldoret while the Mahringer equation is adapted to the Songea station and the Trabert equation could be used at Songea, Nakuru, Jomo Kenyatta, and Kisumu stations. The Rohwer equation showed the best performance at Eldoret and the Romanenko equation performed satisfactorily at all weather stations, except Tabora and Jomo Kenyatta weather stations. Overall, the best four ETo equations can be ranked as Romanenko, Penman, Trabert and Mahringer with a decreasing performance levels. The Romanenko and Penman equations had almost similar performance in terms of RMSE, MBE and AME (Table 2). The Trabert and Mahringer equations also showed similar performance. The Penman equation was the best performing equation among mass transfer equations across 15 provinces in Iran with the least ETo overestimate of 0.03 mm/day as the Papadakis equation [30] [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] .

Reference evapotranspiration is a very important parameter for the hydrological, environmental and agricultural water management and it is much critical under water scarcity and changing climate conditions under semiarid and arid climates. Crop actual evapotranspiration (ETa) is indirectly estimated by the two steps method as a product of daily ETo and the crop coefficients Kc that is dependent on crop type and growth stages, climate, soil type, crop and water management practices and other environmental conditions (ETa = Kc*ETo) [6] [65] [66] . The effectiveness of this procedure depends upon the accuracy of data collection and ETo estimation method used. Since crop water requirement is dependent on ETo it is necessary to evaluate the impact of the choice of ETo estimation method on water resources management at local scale. The impact of using each ETo equation for water management at all weather stations is presented in Figure 1 showing the large discrepancies between the ETo estimates by the FAO-PM equation and the mass transfer ETo equations during the period of 1998 to 2012. As a selection criterion for sustainable water management, the model showing the closest cumulative ETo estimate to the cumulative FAO-PM ETo estimate (Figure 1) should be adopted for that location. Average annual total ETo estimates difference of each mass transfer ETo equation at each weather station relative to the FAO-PM ETo estimates is presented in Table 3. At Dodoma, annual average ETo difference varied from −697 to 1997 mm with the highest overestimation by the Brockamp-Wenner equation while the lowest annual absolute difference of 29 mm representing ETo underestimation of 0.08

mm/day was obtained by the Romanenko ETo estimates. The original Romamenko mass transfer ETo equation can therefore be recommended for ETo estimation at Dodoma area for appropriate and sustainable water management. On the other hand our results suggest, that the Brockamp-Wenner, Albrecht, and the other ETo equations should be avoided when choosing ETo estimation method for the Dodoma area. The Penman equation provided the least annual ETo difference of 99 mm representing a reasonable daily ETo overestimation of 0.3 mm at Morogoro weather station and should be adopted for water management in Morogoro. Similarly, the Trabert and/or the Marhringer equations at Songea, the Marhinger, Penman at Kilimanjaro, the Mahringer equations at Tabora, the Meyer equation at Jomo Kenyatta and the Rohwer, Dalton and/or Romananko equations at Eldoret could be adopted at the respective locations with non-significant overestimation or underestimation of the annual ETo that could be detrimental to water resources management sustainability across Tanzania and the South Western Kenya. The least annual absolute ETo difference was 130 mm at Nakuru and 110 mm at Kisumu which represented 1300 and 1100 m³/ha. Site specific calibration of the best performing ETo equation (Trabert equation) should be performed to improve the performance of the equation under the Kisumu and Nakuru climate conditions. Moreover, other ETo estimation models should be investigated for accurate ETo estimation at Kisumu and Nakuru. Alternatively, the FAO-PM equation or the Valiantzas equation with complete data 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. The Albrecht, Brockamp-Wenner, Dalton, Meyer, Rohwer and Oudin equation should be carefully investigated and adjusted through proper calibration across Tanzania and Kenya for sustainable water management since considerable discrepancies are revealed under long term water management as presented in Figure 1. At an irrigation scheme level and basin level, water losses become considerable and the implications in terms of pumping cost, labor and time requirements result in economically unviable products due to high pricing level that is unaffordable for the majority of small household farmers. In the case of ETo underestimation, there is a risk to put crops under water stress that will impact the yield and the quality of the harvested products and environmental pollution particularly soil pollution by nitrates [67] . The best performing ETo equation that could be adopted at a site is as the Mahringer equation at Tabora, the Trabert equation at Songea, the Rohwer equation at Eldoret and the Romanenko ETo equation at Dodoma, Songea and Eldoret (Table 3).