Analysis of Spatiotemporal Features of Cassava Evapotranspiration in Benin Using Integrated FAO-56 Method and Terra/MODIS Data

This study analyzed the temporal and spatial features of cassava evapotranspiration from 1985 to 2015 in Benin using linear regression, Mann-Kendall trend test, Sen’s slope estimator, and interpolation. The study used basic meteorological data from the Met office of Benin and the Terra/MODIS vegetation index. The estimated crop coefficients (Kc) from FAO and NDVI have shown a strong and positive linear relationship with a correlation coefficient of r = 0.968, while NDVI-Kc presented values slightly lower than FAO-Kc. The rates of crop evapotranspiration (ETc) varied from 1.23 to 7.63 mm/day and 2.92 mm/day on average. At the local level, there were significant upward trends in the seasonal ETc for stations located in the bimodal rainfall pattern area (Cotonou, Bohicon, and Save) and non-significant for stations in the unimodal rainfall pattern area (Kandi, Parakou, and Natitingou). At the country level, both methods revealed a non-significant positive trend in cassava evapotranspiration in the study area while showing a strong and positive linear relationship in variations throughout the growing season, r = 0.956. Cassava’s growth in Benin may encounter in the future the risk of water deficit.


Introduction
Cassava is one of the major food crops in Benin both for its direct consumption and for processing into gari, tapioca, cassava chips, and lafun, as well as for its economic implications as an important trade product. Growth of cassava extends throughout the country except for the agro-ecological zone of the Far North covering Karimama, Malanville and North Kandi Municipalities where the climate characteristics are not suitable for the crop growth even though cassava is a drought-resistant crop. Since the warning of the Intergovernmental Panel on Climate Change about global increase in evapotranspiration as result of a warming climate (IPCC, 2014), and the recent study of (Ndehedehe et al., 2018) on evapotranspiration dynamics over Sub-Sahara Africa which indicated an increasing trend of evapotranspiration in Benin, much more attention are drawn on how this may affect major crops of the country including cassava. Evapotranspiration (ET) is the combination of the loss of water from soils by evaporation and from crops by transpiration. ET plays a crucial role in the heat and mass fluxes of global and regional atmospheric systems. Understanding the mechanism of evapotranspiration is vital in hydrological and agricultural studies at the global, regional, and local scales (Xu et al., 2014). Crop water requirement (CWR) should be equal to the ET under ideal crop growth conditions. The FAO-56 method has been the most widely and practical approach used for estimating crop water requirement and the operational monitoring of the soil-plant water balance. In this approach, crop evapotranspiration is estimated by the combination of reference evapotranspiration (ETo) and crop coefficients (Allen et al., 1998). ETo in some cases is referred to as potential evapotranspiration (PET), which is defined as the maximum rate at which water, if available, can be removed from soil and plant surfaces under no-stress condition. As a key process in land surface studies, the reference evapotranspiration (ETo) mainly depends on two parameters, water availability and incoming solar radiation, and then reflects the interactions between surface water processes and climate (Sobrino et al., 2007). Two different approaches were developed by FAO-56 to determine crop evapotranspiration: single and dual crop coefficients. In the single crop coefficient approach, both plant transpiration and soil evaporation are combined into a single crop coefficient (Kc), while the dual crop coefficient approach uses two coefficients to separate the respective contribution of plant transpiration (Kcb) and soil evaporation (Ke), each by individual values (Allen et al., 1998).
It is well established that canopy cover intercepts sunlight then making the ratio of crop coefficient to canopy declined with a higher amount of canopy cover and structure (Trout & Gartung, 2006). Due to that dependent character of Kc on the dynamics of the canopies (cover fraction, LAI, greenness), Remote sensing data can thus be used to estimate some key-variables related to vegetation phenology (Bastiaanssen et al., 2000), which offer opportunities for monitoring spatial and temporal variability of Kc (Farg et al., 2012). The remote sensed vegetation indices such as Normalized Difference Vegetation Index (NDVI) and the Soil Adjusted Vegetation Index (SAVI) have been successfully used and positively tested to predict crop coefficients at the field and regional scales (Duchemin et al., 1998;Huete, 1988).
In recent years, the increasing interest to understand global warming and its possible impacts on crop production has led many researchers to examine the variability and change of potential evapotranspiration and even to predict its future fluctuations based on the future climate state. Determination of the crop evapotranspiration (ETc), which is based on daily Kc, is a key requirement for the sound of agricultural management and irrigation (Bezerra et al., 2010). This study, therefore, aimed to obtain Kc for each growing stage from tabulated FAO-56 Kc values and numerical Kc calculation, and through a careful analysis of the temporal NDVI values from the Terra/MODIS vegetation index product (MOD13Q1) by determining cassava evapotranspiration over past three  decades and across different regions. This study is an attempt to contribute to the existing literature on the variability of cassava crop evapotranspiration in time and space in Benin.

Study Area
Benin is located on the West African coast, bordering Nigeria to the East, Niger to the North, Togo to the West, Burkina Faso to the Northwest and the Atlantic Ocean to the South, with a total surface area of 112, 622 sq. km. It lies between 6°10′ and 12°25′ North latitude and between 0°45′ and 3°55′ East longitude. The climate in Benin is influenced by the Inter-Tropical Conversion Zone (ITCZ), creating winds from the Ocean as well as from the Sahara region that are dustier and warmer (Mcsweeney et al., 2010). The resulting annual West African Monsoon from the two opposing wind directions causes a wet season in the North from May to November and two wet seasons from March to July and from September to November in the Southern regions (GOB, 2018;Mcsweeney et al., 2010). This highly influences the derived eight agro-ecological zones available to the agrarian economy of Benin. The current study covers the whole country by focusing on the six synoptic station areas of the country.

Data Sets
Observed weather data such as precipitation, maximum and minimum temperatures were obtained from Benin Meteorological Admiration on a daily basis for the six (06) synoptic stations over the period 1985-2015. Figure 1 shows the stations and their geographic distribution in the study area.
The NASA's Terra Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data was accessed from The Land Processes Distributes Active Archive Center (LP DAAC) https://lpdaac.usgs.gov/. The Vegetation Indices (MOD13Q1) Version 6 data are generated every 16 days at a 250-meter spatial resolution as a Level 3 product and provides two primary vegetation layers (Didan et al., 2015).

Trend Analysis and Spatial Distribution
The total seasonal ETc at each station was plotted in RStudio software and the linear regression fitted with the correlation coefficient. A simple linear regression of the form y = ax + b was used to compute the linear trend. x and y are the independent and dependent variable respectively, a and b are constants to be determined by minimizing the function: An assessment of the trend over time was done by computing Mann-Kendall statistical test with the associated two-sided p-values (Hipel & McLeod, 2005;Mann, 1945). Due to the limitation of Mann Kendall to provide information about the magnitude of the significant trends (Fuwape & Ogunjo, 2018), Sen's slope was used alongside. The Mann-Kendall test statistics S is based on the pair-wise comparison of each data points with all preceding data points (Khambhammettu, 2005).
Where, n is the length of the time series x 1 , ... x n , sgn(·) is a sign function while x j and x k are values in years and we have: A very high positive (low negative) value of S is an indicator of an increasing (decreasing) trend. The variance of S was computed by the formula: σ 2 S = 1 18 n n -1 2n + 5 -∑ tp(tp -1)(2tp + 5) q p=1 (8) Where, q and t p are respectively the number of tied groups and the number of data values in the p th group (Hipel and McLeod, 2005;Mann, 1945)The Z test statistics is as follows (Khambhammettu, 2005): The spatial distribution was assessed by interpolation in ArcMap 10.3.1 (ArcGIS software). A study has assessed three interpolation methods to interpolate regional ETc distribution by spline, ordinary kriging (OK), Ordinary Co-kriging (OC) and inverse distance weighting (IDW), using station data (Ashraf et al., 1997;Dalezios et al., 2002), the general finding was that the IDW method gave the lowest mean error among the three common interpolation methods (Chuanyan et al., 2005). Given this reason, the inverse distance weighting (IDW) technique was adopted in the course of this study as it is revealed to give the lowest mean error compared to others.

Crop Coefficients
The crop coefficients were estimated from FAO-56 default values and NDVI on daily basis over the length of the cropping cycle. There is a strong linear relationship with a correlation coefficient of r = 0.968 between both crop coefficients while the Root Mean Squared Error is RMSE = 0.079. The linear relationship between the Kc was also reflected within the seasonal ETc. The NDVI-Kc though presented values slightly different from those of FAO-Kc, showing very similar variation all through the cropping cycle including the growing stages. Generally, FAO-Kc is markedly higher than NDVI-Kc. However, NDVI-Kc tend to have a higher value at the end of the late-season stage (day 210) when compared with FAO-Kc for the same stage. It is also remarkable that Kc during the first 20 days of growth is not constant as suggested in FAO paper (Allen et al., 1998). Over the length of the growth cycle, even for the periods of the first 20 days and between day 60 and day 150, during which FAO-Kc has constant values, there is a slight variation in the NDVI-Kc. The crossing of the two Kc lines between the days 174 and 177 showed that the two sources Kc have the same values during those days, while the FAO-Kc decreased faster than the NDVI-Kc over the period laying between day 150 and day 210. jas.ccsenet.  As reveale analysis (T higher in t to reach th in the area decline of where high 200 to 500

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