Predicting intra-seasonal fluctuations of NDVI phenology from daily rainfall in the East Sahel: a simple linear reservoir model

Short-term predictive models are essential for understanding the temporal relationships between the variability of impulsive daily rainfall and the attendant dynamics of vegetation development in rangelands, particularly for the water-limited, semi-arid East Sahel. After identifying selected rain-dependent sites in southeast Sudan, this report applies a procedure to predict seasonal biomass development in response to impulse-like daily storm events using a simple linear reservoir model as an analogue for the coupled soil–plant–atmosphere ecosystem. Key parameters are the characteristic time () of the reservoir and the number (n) of elementary reservoirs in series. Surface vegetative biomass is represented by the normalized difference vegetation index (NDVI) provided by the MODIS satellite MOD13A2 16 day 1 × 1 km product. Our specific metric is the commonly used differential NDVI, or δNDVI, the difference between the actual NDVI value and its long-term fallow season baseline. We review the concept of the modelling method, with selected application to 15 years (2000−2014) of NDVI data from a 51 × 51 km study area in the East Sahel, centred on the standard WMO Gauge 62752 at Gedaref City in southeast Sudan. Results indicate that as few as four – even as few as two – model parameters might be used to describe intra-seasonal to multiple-year vegetation dynamics. Allowing for inter-annually variable parameters, the predicted results exhibit a coefficient of determination of 0.96. An alternative formulation using a single set of four, seasonally dependent model parameters, globally determined from 15 years of observed reference data, results in a coefficient of determination of 0.90; a version using only two, globally determined model parameters works almost as well for the type of phenology characteristic of this area. In addition to enabling a number of applications that would benefit from the availability of a synthetic phenological time series that is solely dependent on daily rainfall, one of the most important applications may be for infilling data gaps in the observed time series, which for this area of the Sahel are typically encountered during early-season green-up; a critical time for most NDVI studies. We found that the 1 year lagged autocorrelation coefficient, and some version of the conventional rain use efficiency (RUE) factor with its associated annual correlation coefficient, are essential adjunct screening parameters when identifying sites with the highest inter-annual variability in biomass production (typical of the most natural rain-fed sites in this area).