ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE March 2021. Vol. 17(1):91-102 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 91 ORIGINAL RESEARCH ARTICLE SENSITIVITIES OF SOME REFERENCE EVAPOTRANSPIRATION MODELS TO THE KEY CLIMATIC VARIABLES IN NORTHEASTERN NIGERIA J. M. Dibal1*, A. U. Bashir1, M. M. Haruna1 and N. A. Abubakar2 1Department of Agricultural and Environmental Resources Engineering, Faculty of Engineering, University of Maiduguri, Maiduguri, Borno State, Nigeria 2Department Agricultural and Bio-Resources Engineering Programme, Faculty of Engineering and Engineering Technology, Abubakar Tafawa Balewa University, PMB 0248, Bauchi, Nigeria. *Corresponding author’s email address: jibrinmd01@gmail.com 1.0 Introduction Mathematical models usually contain input variables, parameters and/or series of equations that express some course of actions under investigation. Quite often, some or all of the model inputs are subject to sources of uncertainties, including errors of measurement, lack of up-to-date information and poor or partial understanding of the driving forces and mechanisms. Furthermore, some models may be highly complex in structure, thereby posing obscurity in running it and in comprehending the input/output relationships of the model. Such uncertainties and quandaries inflict some limit on user’s confidence in model’s output (Bakhtiari and Liaghat, 2011). Also, some natural spacio-temporal variability of the input variables occurs in response to events such as climate change and geological actions, among others. Planas and Depoutot (2000) showed that a good model is expected to present minimal uncertainty and a high degree of confidence to its users. Weighing up the level of uncertainty in a model thus becomes an essential ingredient of model building and quality assurance. ARTICLE INFORMATION ABSTRACT Reference evapotranspiration (ETo) models are fundamental tools in decision-making in agricultural water management. They have potential spacio-temporal variations due to climatic variability that challenges their individual reliability in decision-making. The sensitivities of five ETo models were examined using the factor perturbation simulation approach (FPSA). The examined models were Penman-Monteith (PM), Hargreaves- Samanni (HS), Blaney-Criddle (BC), Jensen-Haise (JH) and Thornthwaite (TW) to alteration of climatic variables (wind speed (U2), maximum and minimum air temperatures (Tmax and Tmin), vapor pressure deficit (VPD), and Solar radiation (Rn). The study utilized ten years meteorological data obtained from Nigerian Meteorological Agency (NIMET) offices in Maiduguri between (2002-2011) for Borno State, Potiskum between (2005-2014) for Yobe State and from the Upper Benue River Basin Development Authority, Yola (UBRBDAY) between (2005-2014) for Adamawa, Taraba, Gombe, and Bauchi states respectively. Thus covering the entire northeastern region of Nigeria. The region was fractionalized in to three zones namely Borno State (zone A), Yobe State (zone B) and Adamawa, Taraba, Gombe, and Bauchi States (zone C). The results from zones A and B showed some distinctive similarities. Additionally, Blaney-Criddle, Hargreaves-Samanni and Jensen-Haise models outperformed Thorntwaite model, signifying that Thornwaite model is not suitable for application in this region. On an annual average, PM model was most sensitive to U2 and least sensitive to Tmean. BC model was highly sensitive to n/N with sensitivity coefficient (S.C.) of 3.640 in Borno and 3.611 in Yobe, and it was least sensitive to RH. The temperature difference (Tmax-Tmin) was found to have affected HS more than Ra. The Thorntwaite model was most sensitive to solar radiation. Similarly, it was observed that U greatly influenced the performances of the studied ETo models. For accurate and reliable output from any ETo model, emphases need to be placed on accurate measurement, documentation and systematic handling of the climatic variables and calibration © 2021 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. Submitted 20 Sept., 2020 Revised 22 February 2021 Accepted 27 February 2021 Keywords: Reference evapotranspiration models Sensitivity analysis climatic variables North east region Nigeria Dibal et al: Sensitivities of some Reference Evapotranspiration Models to the Key Climatic Variables in Northeastern Nigeria. AZOJETE, 17(1):91-102 ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 92 Sensitivity analysis (S.A.) is technique involving series of computational procedures that project the performance or the outcome of models as affected by changes in the assumptions or the values of the input variables of a model (Ambas and Baltas, 2011). It also weighs up how much each input is contributing to the output uncertainty. Among others, sensitivity analysis is often used to compare different scenarios and their potential outcomes based on changing condition and/or values of input variables and hence decisions become more effective. Furthermore, sensitivity analysis directs the study of how the uncertainty in the output of a model or system (numerical or otherwise) could be doled out to different sources of uncertainty in its variables; increase understanding of the relationships between input and output variables in a system or model. Sensitivity analysis also reduces uncertainty by identifying model inputs that cause significant uncertainty in the output; and be able to focus attention on variables that gravely impinge on the model (Gong et al., 2006). Additionally, it is used in identifying critical control points that will prioritize additional data collection or research, and in verifying and validating a model to reduce the its complexity by identifying and removing variables that least affects the final output of a model (Aydin and Keçecioğlu, 2009). Sensitivity analysis can be achieved by several approaches (Rana and Katerji, 1998; Saltelli, 2002; Irmak et al., 2006; Bormann, 2011), however, the factor perturbation simulation approach (FPSA) also referred to as one-at-a-time (OAT) approach is mostly preferred by modelers and analysts due to its straightforwardness and other practical reasons (Irmak et al., 2006; Bakhtiari and Liaghat, 2011). The factor perturbation simulation approach (FPSA) involves calculating the sensitivity of a model by monitoring changes in its output in response to changes in one factor at a time while all other factors are kept fixed to their central or baseline values. Thus, any change observed in the model output will unequivocally be due to the single variable changed. This method of analysis usually is accomplished using partial derivative or regression analysis. The quantitative value of changes in the model output due to changes in input variables is referred to as sensitivity coefficient (S.C) (Michael et al., 2000). Under FPSA, when there is any model malfunction, the modeler immediately knows which input factor is the source for the malfunction. S.A. generally enhances the comparability of models and minimize the probability of computer programme crashes that commonly happens when several input factors are changed simultaneously Evapotranspiration is the rate at which water, if readily available, would be removed from the soil and plant surfaces (James, 1993). The reference evapotranspiration (ETo) is the evapotranspiration from a reference surface, not short of water. Crop evapotranspiration (ETc) is the rate at which water, when readily available, would be removed from a specific crop and soil surfaces surrounding it (Hobbins et al., 2001). The most common procedure for estimating ETc is to adjust the ETo values with the crop coefficient (Kc), which in turn is a function crop’s stage of development. Water resources particularly in the arid and semi-arid regions commonly experience increasing pressure from competing users consequential to the usual limited availability of water resources. Efficient water use, especially in irrigated and other hydrological fields thus became a watch word (Hatfield et al., 1996). Precision estimation of ETc thus becomes practically crucial due to its close link to hydrology and agro-ecosystem design and management (Allen, 2000). Hobbins et al. (2001) stressed that ETo is one of the most important hydrological variables for scheduling irrigation systems, preparing input data to hydrological water-balance models, and calculating actual crop evapotranspiration (ETc) for a region and/or a basin and general field water management. The computation of reference evapotranspiration (ETo) using regularly recorded climatological data is Arid Zone Journal of Engineering, Technology and Environment, March, 2021; Vol. 17(1):91-102. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 93 usually the first step involved in estimating the ETc of agricultural crops. The term ETc is thus a very important parameter for accurate hydrology and agro-ecosystem design and management. Evapotranspiration being a quantitative measure of the evaporative demand of the atmosphere is independent of crop type and/or management practices, but is a function of climatic factors that can be computed from meteorological data (Allen, 2000). The success of the use of most ETo models lies in the transferability of the Kc from one location to another, a situation many researchers found to be nearly impractical (Bakhtiari and Liaghat, 2011). Tegos et al. (2013) provided a great number of methods for estimating ETo including the combination (Penman, 1948), mass transfer (Harbeck, 1962), energy budget (Fritschen, 1966), water budget (Guitjens, 1982) empirical (Kohler et al., 1995), and the FAO Standard Penman- Montieth method (Allens et al., 2000). Further, given the variability of the performances of different models with different local climatic conditions and the varieties of methods and/or equations that exist, adopting a specific method as a standardized model should become the central point of attention. For a reliable performance, it is expected that ETo should be calibrated, verified, and validated and this necessitate establishment of the sensitivity of ETo to the local climatic variables and evaluating is performance statistically (Steiner et al., 1991). The S.A. avails the model user the chance to gain understanding of the relative importance of each of the variables to the model solution. Bakhtiari and Liaghat (2011) performed the S.A. of Penman equation with respect to each climatic variable and concluded that the equation was most sensitive to net radiation. Piper (1989) showed that errors in measurement of sunshine hours, wind speed, and wet bulb temperature had the same relative effect on the estimated ETo. Ley et al. (1994) analyzed the sensitivity of the Penman-Wright ETo model to errors in parameters and weather data. They found that the model was most sensitive to error in the maximum and minimum air temperatures in Washington State. The sensitivity of the original Penman-Monteith equation to climatic and parametric factors in a semi-arid climate for a reference grass surface, grain sorghum, and sweet sorghum was analyzed in Italy (Rana and Katerji, 1998). They found that for grass, available energy and aerodynamic resistance played a major role. For sweet sorghum, the model was most sensitive to vapor pressure deficit. For grain sorghum under water stress, the most sensitive term was canopy resistance. Such works were also conducted on ASCE-Penman- Monteith equation in different climates of the United States. For ecosystem simulation and models uses, the required data for single-stand simulations are often available and possible to measure, but such functional data progressively became unavailable as spatial resolution increases. Sensitivity analysis would be needed by engineers, hydrologists, and agronomists to gain a better understanding of the meteorological systems in the Nigerian Northeastern region particularly to designate the physical meaning of each meteorological parameter used in the estimation of ETo and other related hydrological problems. Nevertheless, work done in this region on sensitivity analysis of FAO-56 Penman Montieth, Balney-Criddle, Thornwite, Jensen-Haise, and Hargreaves-Samanni models are scarce. This limits their uses in resolution to many hydrologic and agro-ecosystem problems. In consequence, in this study, we conducted the sensitivity analysis of above-mentioned model This limits their uses in resolution to many hydrologic and agro-ecosystem problems. In consequence, in this study, we conducted the sensitivity analysis of above-mentioned models in Northeast Nigeria using wind speed, maximum and minimum air temperatures, vapor pressure deficit, and Solar radiation. Dibal et al: Sensitivities of some Reference Evapotranspiration Models to the Key Climatic Variables in Northeastern Nigeria. AZOJETE, 17(1):91-102 ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 94 2. Materials and Methods 2.1 Study Area The study utilized ten-years meteorological data obtained from Nigerian Meteorological Agency (NIMET) offices in Maiduguri (2002-2011) representing Borno State, Potiskum (2005-2014) representing Yobe State, and from the Upper Benue River Basin Development Authority, Yola (UBRBDAY) (2005-2014) representing Adamawa, Taraba, Gombe, and Bauchi States thus covering the entire Northeastern region of Nigeria. The region was fractionalized into three zones namely Borno State (zone A), Yobe State (zone B) and Adamawa, Taraba, Gombe, and Bauchi States (zone C). The meteorological data collected and used for the analysis were maximum (Tmax) and minimum (Tmin) air temperatures at 2 m height, wind speed measured at 2m height (U2), relative humidity (RH) and daily sunshine duration (SSH). The region domicile about nine Universities, many tertiary institutions and research institutes, thus it is heavily occupied with substantial academic and research activities. Agriculture generally dominates the area, but flood that occurs nearly every rainy season is one of the chief hydrological challenges of the area. The climate of the region is semi-arid characterized by a high inter-annual variability in rainfall. 2.2 Computation of Reference Evapotranspiration (ETo) 2.2.1 FAO-56 Penman-Monteith Model The FAO-56 Penman-Monteith Model is given in (Eqn 1). ( ) ( ) (1) where: ETo= reference evapotranspiration (mmday-1), Rn= net radiation at the crop surface (MJm-2day-1), G= soil heat flux (MJm-2day-1), T= mean daily air temperature at 2m height (oC), U2= wind speed at 2m height (ms-1), es= saturation vapor pressure (kPa), ea= actual vapor pressure (kPa), Δ= slope of vapor pressure curve (kPa oC-1), γ= psychrometric constant (kPa oC-1). The details of equations associated with the calculation of the required parameters in Eqn. (1) have been standardized and described in Allens et al. (2000). Table 1 presents the monthly mean daily meteorological data for the study area that was used in the study. Arid Zone Journal of Engineering, Technology and Environment, March, 2021; Vol. 17(1):91-102. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 95 Table 1: Monthly mean daily meteorological data for the study area Months of the Years Climatic variables Z o n e s Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Tmax ( oC) A 32.725 35.208 40.151 41.870 40.519 36.758 33.419 31.407 33.330 36.190 35.967 33.000 B 32.170 35.910 37.800 40.340 39.280 36.580 32.190 30.750 32.700 35.180 35.610 32.450 C 33.300 36.600 39.300 38.300 34.800 32.800 31.100 29.900 30.300 32.900 34.000 30.300 Tmin ( oC) A 13.402 17.829 20.068 25.171 26.489 25.474 23.989 23.124 23.567 22.161 16.826 13.355 B 13.770 17.480 20.790 24.700 26.050 24.630 23.050 22.020 22.420 22.380 16.490 13.880 C 17.500 22.200 25.300 27.100 25.100 23.700 22.500 22.000 22.600 22.500 20.800 15.400 Tmean ( oC) A 15.635 19.840 23.045 25.900 25.575 24.165 22.775 22.010 22.510 22.440 18.645 14.640 B 22.970 26.695 29.295 32.520 32.665 30.605 27.620 26.385 27.560 28.780 26.050 23.165 C 20.900 20.200 20.000 18.600 17.850 17.550 17.300 16.950 16.850 18.200 19.600 20.450 RH (%) A 31.800 24.800 19.600 26.800 40.700 57.800 70.000 78.300 72.400 50.600 36.200 33.800 B 23.940 19.000 20.670 28.330 41.820 55.630 71.220 78.900 71.940 55.910 32.980 28.370 C 38.364 31.364 26.164 41.800 62.800 70.200 75.500 80.180 79.300 71.700 46.400 40.364 U2 (ms-1) A 2.023 2.162 2.237 2.407 2.526 2.493 2.476 2.301 1.879 1.832 1.773 1.771 B 1.502 1.548 1.636 1.636 1.579 1.574 1.466 1.307 1.528 1.379 1.512 1.523 C 1.419 1.313 1.711 2.101 2.272 1.761 1.578 1.337 1.248 1.471 1.108 1.052 SSH (hrs) A 7.770 8.640 9.650 9.850 9.140 8.250 7.640 6.900 8.350 8.340 8.420 7.690 B 7.201 8.071 9.081 9.281 8.571 7.681 7.071 6.331 7.781 7.771 7.851 7.121 C 8.791 7.557 7.996 7.714 7.680 6.954 6.610 5.009 6.381 8.457 10.029 9.049 2.2.2 Thornwaite Model The monthly ETo according to Thornthwaite (1948) were estimated using Equation (2) ( ) ( ) (2) where: ETo= reference evapotranspiration, N= maximum number of sunny hours as a function of the month and latitude, dm = number of days per month, ETosc= is the gross ET (without correction) and was calculated from Equation (3). (3) where: T = mean daily temperature (°C), a = an exponent as a function of the annual index defined by Equations (4) and (5). (4) where I is the annual heat index obtained from monthly heat indices from equation 5. (5) where: I is the annual heat index obtained from monthly heat indices and T is as defined above (James, 1993). Dibal et al: Sensitivities of some Reference Evapotranspiration Models to the Key Climatic Variables in Northeastern Nigeria. AZOJETE, 17(1):91-102 ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 96 2.2.3 The Hargreaves-Samani Model Equation (6) presents the Hargreaves-Samani’s model (Allen et al, 2000) ( )( ) (6) where: Ra= extraterrestial radiation (mm day-1), T= mean daily temperature (ºC), Tmax= mean dialy maximum temperature, Tmin= mean daily minimum temperature. The Ra from Penman calculation were in (MJ m-2 day-1), so they were multiplied by 0.408 convert them to (mm day-1), as provided by Allen et al. (2000). 2.2.4 Jensen-Haise Model The Jensen-Haise model takes the form of Equation (7) ( ) (7) where: CT = air temperature coefficient for the location being considered, T= mean daily air temperatures (oC), Tx= constant for the location being considered, Rs= total solar radiation for period (mmday-1). The coefficients CT and Tx were determined using the equations (8) and (9). Rs values from Penman calculations were also converted from (MJ m-2 day-1) to (mmday-1) by multiplying them with 0.408 (Allen et al., 1998). (8) (9) 2.2.4 Jensen-Haise Model The Jensen-Haise model takes the form of Equation (7) ( ) (7) (8) (9) where: CT = air temperature coefficient for the location being considered, T = mean daily air temperatures (oC), Tx = constant for the location being considered, Rs = total solar radiation for period (mmday-1). Rs values from Penman calculations were also converted from (MJ m-2 day-1) to (mmday-1) by multiplying them with 0.408 to have a uniform units (Allen et al., 2000). The coefficients CT and Tx in Equation (7) were determined using the Equations (8) and (9) in which h = attitude of the location (m), Tmax, and Tmin= saturation vapor pressure at the mean maximum and minimum air temperature during the warmest month of the year respectively (kPa). where: h= attitude of the location (m), oTmax, oTmin= saturation vapor pressure at the mean maximum and minimum air temperature during the warmest month of the year respectively (kPa). Arid Zone Journal of Engineering, Technology and Environment, March, 2021; Vol. 17(1):91-102. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 97 2.3 Sensitivity Analysis and Determination of Sensitivity Coefficients (S.C.s) The Sensitivity of the models to Tmeam , U2 , VPD and SSH , was analyzed using the factor perturbation simulation approach (Smajstrla et al., 1987; Irmak et al., 2006). Sensitivity coefficient for each climatic variable was derived from Equation (10) (10) where: S.C= sensitivity coefficient, CHETo= change in ETo with respect to change in climatic variable, and CHcv= the change in climatic variable. 3.0 Results and Discussion 3.1 FAO-56 Penman-Monteith Model Tables 2 presents the average daily sensitivity coefficients (S.Cs) computed on a monthly basis for each of the climatic variable considered in the Northeast region of Nigeria. The trends of the S.Cs showed similarities in all climatic variables. In most cases the response of ETo to factor perturbation was linear on seasonal basis but the monthly basis, and both locations, the increase in each climatic variable resulted in a corresponding increase in ETo except in the case of Tmean. In zone A, the S.C. of Tmean increased somewhat linearly from January through May where it attained its peak value. The least SC was found in July. This shows that the ETo calculated from PM model in July will be least affected by Tmean. The SC of Rn raged between 0.318 in December to 0.352 in October, while the S.C. of U2 was highest (1.793) in March and least (0.299) in August. VPD got the highest SC (0.969) in July and least (0.354) in November. Generally, in zone A, the S.C. of U2 (1.793) in March signifies it had the greatest contribution to the accuracy of POM model, and thus the need to pay greater attention while measuring U2. Table 2: Average sensitivity coefficients of climatic variables for Penman Monteith model in zones A, B, and C Climatic variables Zone A JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Tmean( oC) -0.023 -0.039 -0.060 -0.080 -0.064 -0.028 -0.003 0.013 0.008 -0.012 -0.017 -0.013 Rn(MJ mm-1 day-1) 0.319 0.331 0.348 0.355 0.358 0.351 0.338 0.336 0.343 0.352 0.337 0.318 U2(ms-1) 1.295 1.480 1.793 1.661 1.294 0.805 0.484 0.299 0.434 0.983 1.299 1.193 VPD(kPa) 0.894 0.857 0.781 0.747 0.813 0.888 0.967 0.955 0.596 0.588 0.354 0.681 Zone B Tmean( oC) -0.029 0.078 -0.045 -0.062 -0.023 -0.003 0.009 0.017 0.017 0.006 -0.008 0.007 Rn(MJ mm-1 day-1) 0.212 0.351 0.270 0.343 0.224 0.137 0.095 0.071 0.068 0.108 0.157 0.128 U2(ms-1) 2.728 1.646 2.130 1.509 1.328 0.000 0.333 2.232 2.404 2.151 2.935 4.188 VPD(kPa) 0.601 0.529 0.541 0.676 0.695 0.569 0.485 0.380 0.369 0.476 0.451 0.478 Zone C Tmean( oC) 0.566 0.771 0.932 1.138 0.866 1.119 0.947 0.801 0.864 1.025 0.479 0.624 Rn(MJ mm-1 day-1) 0.300 0.364 0.431 0.423 0.280 0.341 0.372 0.211 0.220 0.350 0.207 0.304 U2(ms-1) 1.633 0.985 1.275 0.903 0.795 0.052 0.199 1.336 1.439 1.288 1.757 2.507 VPD(kPa) 1.727 2.257 1.788 2.124 2.577 4.315 4.576 4.396 4.556 4.889 1.519 2.146 Dibal et al: Sensitivities of some Reference Evapotranspiration Models to the Key Climatic Variables in Northeastern Nigeria. AZOJETE, 17(1):91-102 ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 98 The S.C. of the climatic variables with respect to Blaney-Criddle B.C. model is presented in Table 3. In zone B, the highest SC (4.188) is that of U2 in December and the least (0.003) came from Tmean in June. This means the magnitude of variability of PM’s ETo with respect to U2 would be greatest in the dry windy months of the year. It also points that Tmean would have the list influence on ETo. It thus implies that sufficient precaution need to be taken during the measurement and recording of U2 to avert faulty ETo results. Similar results were observed in zone C where the S.C. of U2 exhibited nearly linear trend from 1.336 in June to its highest value (2.507) in December. But the overall peak value of S.C. (4.889) is that of VPD in October. Bakhtiari and Liaghat (2011) showed that due to the behavior of the term 1/( γ +∆ ) in Equation (1), the effectiveness of vapor pressure deficit on evapotranspiration is greater in the low temperatures months because this term decreases as temperature increase. Thus, the divergence in ETo with respect to increase in VPD would be larger during wet months. This lowest S.Cs of Tmean in June and July tallies with the report of Audu et al. (2015). Table 3: Average S.Cs. of climatic variables to Blaney Criddle ET Model JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Zone A Tmean 0.160 0.182 0.196 0.193 0.170 0.147 0.129 0.111 0.124 0.144 0.157 0.157 RH - 0.038 - 0.045 - 0.053 - 0.061 - 0.057 - 0.053 - 0.048 - 0.043 - 0.047 - 0.047 - 0.043 - 0.036 U2 0.224 0.293 0.335 0.305 0.289 0.203 0.168 0.125 0.138 0.166 0.220 0.254 SSH 3.279 4.081 4.654 4.925 4.466 3.723 3.067 2.527 2.776 3.406 3.472 3.299 Zone B Tmean 0.165 0.172 0.149 0.154 0.128 0.120 0.110 0.103 0.103 0.118 0.154 0.164 RH - 0.041 - 0.046 - 0.046 - 0.052 - 0.048 - 0.045 - 0.041 - 0.038 - 0.039 - 0.044 - 0.046 - 0.039 U2 0.254 0.310 0.333 0.263 0.175 0.143 0.118 0.111 0.096 0.126 0.207 0.235 SSH 3.657 4.522 4.205 4.295 3.262 2.973 2.647 2.364 2.371 2.598 3.258 3.352 Zone C Tmean 0.478 0.310 0.268 0.277 0.231 0.216 0.198 0.185 0.185 0.213 0.277 0.296 RH - 0.075 - 0.082 - 0.083 - 0.093 - 0.086 - 0.081 - 0.074 - 0.069 - 0.070 - 0.079 - 0.083 - 0.069 U2 0.459 0.558 0.601 0.474 0.315 0.258 0.213 0.200 0.173 0.227 0.372 0.424 SSH 4.317 5.337 4.963 5.070 3.850 3.509 3.124 2.790 2.799 3.067 3.845 3.956 It is evident from the model that the S. C. of the studied variables took a sinusoidal trend with the lowest around the months August. The Table also shows that SSH of 4.925, 4.295 and 5.07 in zones A, B. and C respectively all occurring in the month of April has a dominant influence on the overall performance of the model in this region. The influence of R.H. on the performance of the model is apparently insignificant, not only due to is negative values of S.Cs, but also by the account of low S.C. values in the all the zones. Similar results were reported by Ambas and Baltas (2011) which showed low and negative S.Cs of R.H in Blaney Criddle model. The term R.H. can thus be safely be replaced with the energy terms that have greater influence on the model. Arid Zone Journal of Engineering, Technology and Environment, March, 2021; Vol. 17(1):91-102. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 99 Table 4 elucidates that the Thorn White (T.W) ET model was found to be more sensitive to sunshine hours (SSH) which is also one of the energy terms of the model. In zones A, B and C respectively, the highest S.C values of the SSH were 0.4155, 1.095 and 1.424. This call for cautious and accurate instrumentation of SSH term to arrive accurate ET values with T.W. model. It also points that minimal emphasis can be placed on temperature measurement. The Hargreave – Samani (H.S.) model as with other models, exhibited a non-linearity in its sensitivity to changes in its parameters (Table 5). The model is most sensitive to perturbation in temperature, especially in the rainy seasons irrespective of the zones. The highest S.C of 0.381 for Tmean was found in the month of September in zone C. Apparently, the response of this model to changes in its building parameters has no defined trend, however, Tmean should be prudently recorded for accurate ET computation with H.S. model. The Jensen Haise model exhibited greater sensitivity to vapor pressure deficit (VPD) irrespective of the zones (Table 6). This was followed by the solar radiation in equivalent depth of evaporation (Rs). (Table 6) In zone A, the highest S.C. (1.147) for VPD was found in the month of July. The least values were found in zone C. this means the effectiveness of J.H. model in predicting ET relies on the accuracy of VPD. The Table also showed that Tmean holds the least position in the performance of the model, this challenges the proclamation that the Jensen Haise model depends on solar radiation in equivalent depth of evaporation (James, 1993). This study shows that efficiency of J.H. model in ET prediction is a function of its building parameters that are also in turn a function of location. The result implies that in the dry season, greater emphasis should be on Ra than (Tmax - Tmean) while in the wet season reverse is the case. Although this result shows that the effects of both parameters on the model have no significant difference, both parameters requires greater emphasis in determining ETo if this model is to be used in such locations. Table 4: Average S.Cs. of climatic variables to Thorn White ET Model Zone A JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Tmean 0.0598 0.0754 0.1016 0.1205 0.1119 0.0913 0.0756 0.0646 0.045 0.084 0.0758 0.0587 N (SSH) 0.3629 0.3785 0.4155 0.4538 0.4497 0.4279 0.4018 0.3928 0.3952 0.4053 0.3848 0.3615 Zone B Tmean 0.0669 0.0718 1.0723 0.085 0.073 0.0633 0.0541 0.0392 0.0525 0.0726 0.0872 0.06 N (SSH) 0.3741 0.4096 1.095 0.4444 0.415 0.4006 0.3853 0.3783 0.3842 0.394 0.391 0.355 Zone C Tmean 0.08697 0.09334 1.39399 0.1105 0.0949 0.08229 0.07033 0.05096 0.06825 0.09438 0.11336 0.078 N (SSH) 0.48633 0.53248 1.4235 0.57772 0.5395 0.52078 0.50089 0.49179 0.49946 0.5122 0.5083 0.4615 Dibal et al: Sensitivities of some Reference Evapotranspiration Models to the Key Climatic Variables in Northeastern Nigeria. AZOJETE, 17(1):91-102 ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 100 Table 5: Average S.Cs. of climatic variables to Hargreaves-Samani ET Model JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Zone A Ra 0.169 0.173 0.202 0.198 0.180 0.162 0.134 0.123 0.134 0.165 0.181 0.169 (Tmean) 0.132 0.164 0.181 0.220 0.237 0.263 0.262 0.272 0.252 0.212 0.158 0.131 zone B Ra 0.152 0.159 0.165 0.158 0.108 0.137 0.125 0.117 0.118 0.141 0.163 0.148 (Tmean) 0.151 0.182 0.214 0.261 0.203 0.270 0.260 0.266 0.281 0.245 0.194 0.158 zone C Ra 0.207 0.216 0.225 0.215 0.147 0.186 0.170 0.159 0.161 0.191 0.222 0.201 (Tmean) 0.206 0.247 0.290 0.354 0.276 0.367 0.354 0.361 0.381 0.333 0.264 0.215 Table 6: Average S.Cs. of climatic variables to Jansen-Haise ET Model Zone A JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Tmean 0.124 0.147 0.209 0.212 0.178 0.130 0.098 0.079 0.108 0.145 0.158 0.126 Rs 0.181 0.212 0.297 0.320 0.284 0.209 0.152 0.124 0.155 0.218 0.227 0.184 VPD 0.683 0.855 0.882 1.012 1.075 1.143 1.147 1.130 1.231 1.033 0.808 0.691 Zone B JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Tmean 0.122 0.131 0.166 0.100 0.101 0.085 0.073 0.066 0.068 0.104 0.135 0.108 Rs 0.187 0.230 0.296 0.227 0.175 0.147 0.126 0.110 0.112 0.157 0.187 0.147 VPD 0.853 0.913 0.910 1.160 1.143 1.088 1.045 1.057 1.108 1.154 1.126 0.872 Zone C JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Tmean 0.110 0.119 0.150 0.090 0.092 0.077 0.066 0.060 0.062 0.095 0.123 0.098 Rs 0.152 0.159 0.165 0.158 0.108 0.137 0.125 0.117 0.118 0.141 0.163 0.148 VPD 0.151 0.182 0.214 0.261 0.203 0.270 0.260 0.266 0.281 0.245 0.194 0.158 4. Conclusions Model sensitivity analysis in response to the perturbation to its building parameters is an essential element in the study of model’s performance and user’s confidence. This is only true when the output under consideration is a time dependent function of the input parameters. In all the models studied here, the energy and the aerodynamic terms played some major roles. However, in Jensen- Haise model, the VPD was found to be more fundamental. Whereas some of the results and interpretations appeared fairly straight- forward and logical from physiological perception, majority of the results were non-linear and may be artifact of model design or field data instrumentation. In all the zones studied, all the ET models would be recommended to be used in estimating ETo based on the availability of meteorological data, but adequate calibration of the models should be conducted to eliminate spacio-temporal errors. However, it is believed that accurate predictions of the spatial distribution of several key parameters would produce the greatest reduction in the uncertainty to a large-scale. Further, adequate, and salient attention should be given during instrumentation and documentation of the most sensitive meteorological parameters of any chosen model to ensure a great level of accuracy in estimating ETo. It is also recommended that the Arid Zone Journal of Engineering, Technology and Environment, March, 2021; Vol. 17(1):91-102. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: jibrinmd01@gmail.com 101 scarcity of meteorological data and stations need to be overcome to simplify and improve hydro- meteorological research that may be performed in all the zones. Further research on sensitivity analysis should be expanded to include representative climatic distribution of the agro-climatic zones of Nigeria. References Allen, RG. 2000. 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