Sensitivity Analysis of the Penman-Monteith Reference Evapotranspiration to Climatic Variables : Case of Burkina Faso

Sensitivity analysis is important in understanding the effect of each climatic input variable on the variation of the evapotranspiration which is a significant element for hydrological modelling, irrigation programs, and water resources management. This study investigates the responses of evapotranspiration to the variation of maximum and minimum temperature, solar radiation, wind speed and maximum and minimum relative humidity. Daily data from 1998 to 2012 of eight stations are used. For each climatic variable, a variation of 5% up to ±25% was performed in order to evaluate the sensitivity of the evapotranspiration to the input variables. Results show that evapotranspiration is more sensitive to the variation of solar radiation, maximal temperature and wind speed, respectively.


Introduction
Climate change issues have become a major concern in recent years [1] because it may have significant impact on the different components of water cycle: precipitation, runoff and evapotranspiration [1] [2] [3].Also, it may exacerbate the dry conditions of arid regions by increasing evapotranspiration; thus aggravating the processes of desertification [3].Among the component of water cycle, the evapotranspiration is a key element for agricultural programs, irrigation scheduling, water management and planning [4]- [10].Several methods have been developed under different climatic conditions to estimate the reference evapotranspiration (ET 0 ).Among the various existing methods, Penman-Monteith (ET 0_FAO-PM ) was recommended by FAO as a standard method because its performance under different types of climate [6] [11] [12].
The FAO-Penman-Monteith method integrates climatic variables such temperature, solar radiation, relative humidity and wind speed which may be affected by climate change [13].Therefore, it is very important to know the sensitivity of ET 0_FAO-PM to the variation of each of these climatic variables.The sensitivity analysis is a way that allows improving understanding not only on the relationships between climatic conditions and ET 0 variability but also on the identification of the dominant climatic variables in estimating evapotranspiration [13] [14] [15].
Several studies have investigated the sensitivity analysis of ET 0_FAO-PM to the variation of climatic variables [1] [2] [13] [16] [17] [18].A sensitivity analysis of ET 0 to climatic variables in the different climatic regions of USA is conducted by [13].They used daily time scales and their results showed that ET 0 was most sensitive to vapor pressure.In a semi-arid climate in China, [2] used monthly and annual data from fifteen stations over the period 1961-2003 to analyze the sensitivity of ET 0_FAO-PM to maximum temperature, minimum temperature, mean temperature, wind speed, sunshine duration and relative humidity in the Tao watershed.They showed that the ET 0_FAO-PM was more sensitive to variation in relative humidity followed by sunshine duration, wind speed and air temperature.[16] studied the sensitivity of ET 0_FAO-PM to temperature, solar radiation, relative humidity and wind speed in a semi-arid climate of southern Spain.They concluded that relative humidity, temperature and radiation were the main climatic variables that influence ET 0_FAO-PM .[17] developed a sensitivity coefficient to drive sensitivity analysis of evapotranspiration to temperature, solar radiation and relative humidity at Greece.They concluded that evapotranspiration is more sensitive to the variation of solar radiation and temperature.[1] analyzed the sensitivity of ET 0_FAO-PM to temperature, and duration sunshine under four climatic conditions: humid, semi-arid hot, semi-arid cold and arid in Iran.They concluded that ET 0_FAO-PM is more sensitive to temperature and wind speed in the arid climate, wind speed in the semi-arid climate, and duration of sunshine in wet climate.In West Africa, [18] focused on the sensitivity analysis of ET 0_FAO-PM to climatic variables.They found that maximum temperature and solar radiation are the two variables that have more influence on ET 0_FAO-PM at Saint-Louis weather station in the Senegal River Delta.In Burkina Faso, there is no study which focuses on the sensitivity analysis of ET 0_FAO-PM to climatic variables.This research analyzes the sensitivity of ET 0_FAO-PM to maximum and minimum temperature, solar radiation, wind speed and minimum and maximum relative humidity in Burkina Faso.[19].From the Sahelian to the Sudanian zone the average annual rainfall increases from 600 to more than 1000 mm and evapotranspiration is ranging from 500 to more than 1500 mm.
The full daily data of eight weather stations of Burkina Faso over the period 1998-2012 were used.Some characteristics of these stations and their location are presented in Table 1 and Figure 1.The data used in this study are minimum and maximum temperature, solar radiation, wind speed and relative humidity.They come from the Africa Rice database (Africa Rice Center).Temperatures are expressed in degrees Celsius (˚C), relative humidity in percent (%), wind speed at a height of 2 m is expressed in meter by second (m −1 •s) and the radiation in mega joule (MJ•m −2 ). Figure 2 shows the annual evolution of wind speed (a), solar radiation (b), maximal and minimal temperature (c) (d) and maximal and minimal relative humidity (e) (f) at the stations of Bobo Dioulasso, Bur Dedougou and Dori.These stations are used to illustrate the fluctuation of climatic variable during the year.It is to be noticed that the trend remains the same for the other stations.

Methode of FAO-Penman-Monteith (FAO-PM)
The FAO-Penman-Monteith (FAO-PM) is standardized method recognized by the Food Agriculture Organization for the estimation of reference evapotranspiration.It requires climatic variables such as temperature, radiation, wind speed and relative humidity [11].The reference surface is hypothetical grass crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s•m −1 and an albedo of 0.23 [11].The Penman-Monteith grass reference evapotranspiration equation is: where ET 0 = reference evapotranspiration (mm/day), Rn = computed according the procedure developed in FAO-56 by [11].

Sensitivity Analyses
The principle of sensitivity analysis consists in varying each climate variable (Tmax, Tmin, Sr, u2, RHmax and RHmin) in order to determine their impact on FAO-PM evapotranspiration.Previous studies reveal that there is no standard procedure for calculating the sensitivity coefficient [13].But a simple and practical way is to correlate the relative change of dependent variables against the relative change of independent one [2].In this way, the evapotranspiration calculated by the FAO-PM method is correlated against each climate variable.This comparison allows determining the impact of each climatic variable in ET 0_FAO-PM .The coefficient of determination was used as a criterion of evaluation.
Furthermore, an increase and decrease of 5%, 10%, 15%, 20% and 25% is made on each climatic variable.Each variation of a climatic variable is made individually by keeping constant the others.This increase and decrease allowed determining the variation of the ET 0_FAO-PM induced by each climatic variable.The new values of ET 0_FAO-PM after changing the climatic variable were used to determine the sensitivity coefficient (CS): where CS = sensitivity coefficient, ΔET 0 = change in ET 0_FAO-PM entrained by the change of a climate variable and ΔCS = the unit of change of each variable.

Results and Discussion
The mean daily monthly evapotranspiration of the eight stations over the period tends to fall to a minimum value of 3 mm/day in August.This decrease in evapotranspiration is explained by the increase in relative humidity during this period.

The Sensitivity of Evapotranspiration to the Variation of Climatic Variables
A simple linear regression was performed between ET 0_FAO-PM against solar radiation (Sr), maximum and minimum temperature (Tmax and Tmin), maximum and minimum relative humidity (RHmax and RHmin) and wind speed (u2), separately.Results showed that ET 0_FAO-PM was most sensitive to the variation of solar radiation in Burkina Faso with coefficient of determination of 0.67, 0.64, 0.63, 0.56, 0.56, 0.56, 0.53, and 0.45 at the stations of Fada Ngourma, Gaoua, Po, Dori, Bobo Dioulasso, Boromo, Bur Dedougou and Ouahigouya stations, respectively (Table 2).A positive and negative variation of solar radiation from 5% to 25% causes a variation of evapotranspiration from 12.9% to 64.58% (0.129 to 0.646 mm/day) at the weather station of Bobo Dioulasso (Figure 4(a)).Similarly, at the station of Fada Ngourma and Dori (Figures 4(e)-(g)) the increase in solar radiation from 5% to 25% leads to an increase ET 0_FAO-PM from 14.74% to 73.63% and from 14% to 70%, respectively.The maximum temperature was the second climatic variable that has more impact to the variation of evapotranspiration.According to the Figure 4, if Tmax increases by 5%, 10%, 15% and 25% ET 0_FAO-PM will increase by 11.56%, 3.71%, 36.49%,49.92% and 64.05%, respectively.Its decrease in 5% to 25% leads also a decrease of evapotranspiration from 10.1% to 49.1% at the station of Bobo Dioulasso.At Dori station, increase and decrease of maximum temperature by 5% to 25% favor a variation of ET 0 from 0.11 mm to 0.61 mm and from −0.10 to −0.47 mm (10% to 60% and −10 to −47%).These results show that evapotranspiration is more sensitive to the increase in maximum temperature than to its decrease.
Wind speed is the third climatic variable that has more influence on evapotranspiration with coefficients of determination ranging from 0.17 to 0.48.Thus, evapotranspiration increases from 7% to 36% when wind speed increases by 5% to 25% at the Bobo Dioulasso station.A decrease in wind speed from 5% to 25% favors a decrease in ET 0_FAO-PM from 7.57% to 38.80%.Contrary to maximum temperature, the decrease in wind speed has more influence on evapotranspiration than its increase.At the stations of Fada Ngourma and Dori, a decrease in wind speed from 5% to 25% favors also a decrease in ET 0_FAO-PM from 3.87 to 19.60 and from 4.6%7 to 23.61%.The minimum temperature has values closed to that of the wind speed with coefficients of determination ranging from 14% to 49% depending on the stations (Table 2).However, Figure 4 shows that the influence of wind speed on ET 0_FAO-PM is minimal compared to that of radiation, maximum temperature and wind speed.Indeed, the increase and decrease of Tmin from 5% to 25% also lead to an increase and decrease in ET 0_FAO-PM from 3 to 18% and from 2% to 11% at Bobo Dioulasso station.However, relative humidity has less influence on ET 0_FAO-PM because of the low coefficient of determination which varies only between 0% and 8% for maximum relative humidity and 1% and 10% for minimum relative humidity (Table 2).The relative humidity follows an opposite trend compared to the other variables because its increase of 5% to 25% causes a decrease of ET 0_FAO-PM from 0.029 to 0.147 mm (−2.89 to −14.68%) at the Bobo Dioulasso station.This observation allows noting that the increase in relative humidity causes a decrease in the rate of evapotranspiration and vice versa.In arid and semi-arid climate where temperature is high the rate of evapotranspiration may be important.
The results of this study are in agreement with those of [17] [18] and [20].In the Delta of the Senegal River, [18] showed that evapotranspiration was more sensitive to maximum temperature and wind speed.By studying the sensitivity of evapotranspiration computed by five methods (Fao 56 Penman-Monteith, Fao 24 Penman, Fao 24 Blaney-Criddle, Fao 24 Makking and Hargreaves), [17] concluded that solar radiation and temperature have more influence on evapotranspiration than wind speed and relative humidity.And [20] analyzed the sensitivity of maximum temperature, minimum temperature, wind speed and sunshine in Spain.Their results showed that ET 0_FAO-PM was less sensitive to minimum temperature even less at sunshine.But it is more sensitive to variation in maximum temperature and wind speed.However, contrary to our results where relative humidity is the variable that has less influence on ET 0_FAO-PM , [21] noted that evapotranspiration is more sensitive to changes in relative humidity, followed by radiation, temperature and wind speed in coastal and mountain regions of West Korea.

The Monthly Change in the Sensitivity of ET0_FAO-PM to Climatic Variables
The sensitivity coefficient for each climate variable was calculated to highlight the impact of each variable on ET 0_FAO-PM and to show its variation as a function of the months.Figure 5 shows the monthly variations and Table 2 gives the mean values of the sensitivity coefficients for each climatic variable over the study period as a function of climatic zones.
The results show that at Bobo Dioulasso station (Figure 5

Figure 1 .
Figure 1.Localization of burkina Faso and the selected weather stations.

Figure 4 .
Figure 4. Change of ET 0-FAO-PM function of the change of climatic variables.

Figure 5 .
Figure 5. Variation of daily average sensitivity coefficient at the different stations.

2. Material and Method 2.1. Study Area
in March, April and October and the lowest values (15 to 35) in November, December, January and February

Table 1 .
Characteristics of the weather stations.

Table 2 .
Simple linear regression of ET 0_FAO-PM against each climate variable.