Analysis of spatio-temporal droughts using order statistics of remotely sensed relative productivity index

At the annual scale, the long-term average of the ratio of actual to potential evapotranspiration, represents the so-called relative productivity index (k_v) which depends on climate, soil, and vegetation conditions. We aim to assess drought based on the analysis of the spatio-temporal variability of k_v. The study area is the governorate of Zaghouan, located northern Tunisia, between latitudes 36°00N and 36°40N and longitudes 9°35E and 10°25E, mainly occupied by cereal crops. It is composed by 48 administrative districts (Imadas) of size between 20 and 80 km². Field evidence of drought is obtained using the National reports on cereal crops drought assessment. Bank facilities are provided to farmers with crop lands reported as drought damaged areas. The study period is 2000-2001 to 2020-2021. During that period, 11 years out of 21 were declared drought in the national reports. The methodology adopts order statistics of the remote sensing k_v. The latter is estimated by imada, using MODIS data, considering the accumulation of evapotranspiration during the cereal growth period, from November to May (herein year by extension). Thus, a k_v matrix of N=21 columns (years) with n=48 raws (imadas) is analyzed. For a given year i, we consider the values of k_v arranged in increasing order of magnitudes (X_(i,1), X_(i,2), …, X_(i,n)) where n is the number of imadas. Four drought prognostics are evaluated. We see whether the droughts registered by the National reports are retrieved by the prognostic methods. The minimum of k_v (X_(i,1)) is evaluated in Methods 1 while the maximum X_(i,n) is tested for Method 2. In Method 1 the 25% percentile of X₍₁₎ is considered to filter drought years. In Method 2 and Method 3, the 75% percentile of X_(n) and 2.5% percentile of X_(n/2) are respectively considered. In Method 4, a quantile-quantile plot approach is adopted based on the minimization of mean absolute error, considering X_(10%), X_(25%), X_(50%) and X_(75%). Four categories of years are assumed in Method 4: severe drought; moderate drought; as well as mild humid and humid (no drought). Method 1 resulted in one single undetected drought year. Method 2 resulted in 2 false droughts and one drought not detected. In Method 3 one single drought is false. Method 4 resulted in three drought years that were classed as humid. Though, these results encourage the use of order statistics of satellite relative productivity index as a procedure for drought identification over large areas.