Sensitivity of FAO Penman – Monteith reference evapotranspiration ( ETo ) to climatic variables under different climate types in Nigeria

Understanding the impact of changes in climatic variables on reference evapotranspiration (ETo) is important for predicting possible implications of climate change on the overall hydrology of an area. This study aimed to determine the effects of changes in ETo with respect to changes in climatic variables. In addition, the specific objective was to determine the sensitivity coefficients of ETo in seven different locations in Nigeria with distinct agroecology, namely Maiduguri (Sahel savannah), Sokoto (Sudan savannah), Kaduna (Guinea savannah), Jos (Montane), Enugu (Derived Savannah), Ibadan (tropical rainforest), and Port Harcourt (coastal). The results showed that ETo is most sensitive to changes in maximum temperature (Tmax) in Maiduguri, Sokoto, Kaduna, and Jos. In Enugu and Ibadan, ETo is most sensitive to changes in solar radiation (Rs), while in Port Harcourt, ETo is most sensitive to relative humidity (RH). Overall, based on the average annual sensitivity coefficients (SCs) of the study area, the SC is ranked in the order: RH> Rs> Tmax>U2> Tmin. Also, the results showed positive SCs of ETo to Rs, Tmax, U2, Tmin, and negative SC for RH. This study can serve as a baseline for sustainable water management in the context of climate change and adapted to areas with a similar climate.


GRAPHICAL ABSTRACT INTRODUCTION
To meet the food demand of the projected human population of 9 billion by 2050, the world is expected to produce more than 60% more food relative to its 2005 production (Lal ). Water is an indispensable resource for food production. However, available water is under immense pressure as about 70% of the total available freshwater is used for agricultural purposes (Pimentel et al. ; Hertel & Liu ). This is further worsened by climate change, water scarcity, and other water-related problems (Hertel & Liu ; Sadow et al. ). This has necessitated the need for efficient and effective management of water resources. Sustainable water management in agriculture requires an accurate estimate of the reference crop evapotranspiration (ET o ). This is the first step to satisfying the water requirement of crops.
ET o is one of the most important components of the hydrologic cycle. It is a combined term of evaporation through the soil surface and transpiration, a process where water is lost through the stomatal openings in the leaves.
It has been referred to as the second most important hydrologic variable after precipitation (Goyal ; Alexandris identifying the climatic variables most sensitive to ET o becomes imperative, so that emphasis is placed on the measurements of those variables which could be used for developing simple empirical ET o models. Identifying sensitive variables is also important in adapting and mitigating climate change impacts (Nouri et al. ). Observations around the world have revealed that the earth's climate has changed and is still changing (IPCC ; USGCRP ). Under arid and semi-arid climate, Sharif & Dinpashoh () reported that by increasing mean temperature and wind speed at 20%, while decreasing actual vapour pressure,

Study area
Locations within Nigeria were selected for this study ( Figure 1). The study area represents unique and different agro-ecological zones found in Nigeria. Nigeria is on the western coast of Africa, located on latitude 3-15 E and longitude 4-14 N, with a land area of 923,769 km 2 , which is about 14% of West Africa. The country is also the most populous nation in the African continent with a current population of about 200 million (World Bank ). Agriculture is the highest employer of labour, where about 20-50% of her citizens earn their living from agriculture. Although agriculture is small scale, it contributed about 24.44% to GDP (NBS ). Major crops produced in the country are broadly classified into root crops (cassava and yams), grains (millet, corn, and sorghum), and legumes (cowpea and beans). Others are industrial crops, which include oil palm, rubber, groundnut, and cocoa. The type of crop grown in an area is dictated by the climate and soil type. In general, tree crops are cultivated in the south, while grains, legumes, and groundnut are grown in the north (Anthony et al. ).
The climate of Nigeria is broadly classified into the tropical rainforest, tropical savannah, and montane climate (Iloeje ). Based on rainfall, temperature, elevation, and vegetation, Nigeria is classified into different agro-ecological zones. The tropical rainforest is subdivided into coastal (tropical wet) and tropical wet and dry, while the savannah includes Derived savannah, Guinea savannah, Sudan savannah, and Sahel savannah. The montane climate has a cool climate with highland areas that are more than 1,520 m above sea level (Iloeje ). The climate of Nigeria is influenced by three atmospheric air masses: maritime tropical (mT), continental tropical (cT), and equatorial easterlies (Eludoyin et al. ). The mT and cT air masses originate from the Atlantic Ocean and the Sahara Desert. The point where both air masses meet is called the intertropical discontinuity (ITD), which controls the rainfall pattern and season (Ugbah et al. ). Nigeria is marked by two distinct seasons: wet and dry season. Generally, the south has about 8-10 months of rainfall with an annual mean rainfall of about 1,200-3,000 mm, while rainfall in the north lasts for 2-4 months, with an annual mean rainfall amount of 400-1,100 mm. The wide difference in rainfall is due to the closeness of the Atlantic Ocean in the south and the Sahara Desert in the north. The south usually experiences bimodal peaks of rainfall in June and September, while the north has one rainfall peak in August. During the rainy and dry season, temperature ranges between 25-30 C and 20-30 C, respectively (Ugbah et al. ). Figure 1 shows the specific study areas, namely Port Harcourt, Ibadan, Enugu, Jos, Kaduna, Sokoto, and Maiduguri.
Each location represents a unique and agro-ecological zone.  Each study area was located on the GIS-enabled data viewer webpage and all the associated agroclimatology data, namely solar radiation (R s ), minimum temperature (T min ), maximum temperature (T max ), relative humidity (RH), and wind speed (U 2 ). The data were further screened and checked for inconsistency following the recommendation of Allen ().

Reference crop evapotranspiration
The FAO-56 PM equation is expressed as follows (Allen et al. ): where ET o is the reference crop evapotranspiration (mm/ day); R n is the net radiation (MJ/m 2 /day); G is the soil heat flux (MJ/m 2 /day); T is the average daily air temperature at a height of 2 m ( C); U 2 is the wind speed at a height of 2 m (m/s); e s is the saturation vapour pressure (kPa); e a is the actual vapour pressure (kPa); e s À e a is the VPD (kPa) Δ is the slope of the saturation vapour pressure-temperature curve (kPa/ C); and γ is the psychrometric constant (kPa/ C).

Sensitivity analysis and sensitivity coefficient
where SC i is the sensitivity coefficient and X i is the climate variable.
We adopted the procedure of Irmak et al.

RESULTS AND DISCUSSION
Climatological analysis     We also observed that across all locations, the impact of an increase in T max , RH, and T min on ET o was higher than their decrease. However, for wind speed, ET o was more sensitive to decrease in wind speed than increase. For example,     (Table 3). We observed the least variation of SC in Port Harcourt, with SC ranging between 0.00 and 0.07, with a mean average of 0.03. As a result of the seasonality of U 2 , the SC increased during the dry season for all locations but decreased during the wet season. This suggests that the effect of U 2 is felt more during the dry season than the wet season (Table 3). This also implies that small variations in wind speed during the dry season could result in larger variations in the ET o rate. The cool, dry, and dust-laden wind, usually referred to harmattan, from the Sahara Desert could be a contributing factor to the high SC of U 2 in the region, which increases ET o .
The dust haze from the north-easterly trade wind has also been reported to reduce radiation ( In Port Harcourt, Ibadan, and Enugu, a reverse trend was observed. The SC of ET o to T max and U 2 decreased from the north to south. This signifies the greater influence of T max and U 2 on ET o in the north as compared to the south. In contrast, the SCs of ET o to R s , RH, and T min increased from the south to north, implying the greater influence of R s , RH, and T min in the south compared to the north. This agrees with Tabari & Talaee () who reported that   We observed that Port Harcourt, Ibadan, and Enugu have bimodal peaks at the start (April) and end of the growing season (October), and depression in September. However, for locations in the north, they have a uni-modal peak coinciding with the month of September. Consequently, we observed that the period where the SC was maximum for T min in the north (savannah), it was minimum in the south (Figure 3(d)). For all locations in the north, we observed that the SCs of R s , T min , and RH reached peak values in July and August and were minimum at the start and end ending of the season. In contrast, the SCs for T max and U 2 were lowest in July and August. A similar trend was also observed by Gao  We also observed an almost constant SCs in some weather variables (Table 3) In summary and as shown in to adapt and conserve water through an efficient watersaving irrigation system. On the other hand, R s , RH, and T min have the largest SCs in the south. As one moves from the north to south, the variation of SCs of T max and U 2 decreased, while the SCs of RH,  to changes in solar radiation, while in Port Harcourt, ET o is most sensitive to relative humidity. The sensitivity coefficients of relative humidity, solar radiation, and minimum temperature were higher in the wet season than the dry season, while the sensitivity coefficients of maximum temperature and wind speed were higher in the dry season than the wet season for all locations. In general, based on the average annual sensitivity coefficients, ET o is most sensitive to relative humidity, followed by solar radiation, maximum temperature, wind speed, and minimum temperature.

Spatial distribution of sensitivity coefficient
Based on the results of the sensitivity analysis and sensitivity coefficients, we suggest the development of simple empirical ET o models that would require the most sensitive variables, i.e. RH, R s , and T max .
In conclusion, the results from this study showed that the climate change and climate variability could have significant impacts on the consumptive crop water use and increased crop water demand in the future in Nigeria.
Therefore, there is need for adopting appropriate water management through an effective irrigation method and efficient irrigation design system that conserves water and cope with predicted impacts of climate change in Nigeria, as the country continues to seek means to attain food security.