## 2 Materials and Methods
### Modelling Scheme
#### 2.2.1 Pre-Modelling
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable/Index** & **Index Calculation** & **Index Description** \\ \hline NDVI & NDVI = (NIR\(-\)Red)/(NIR\(+\)Red) & Predictor variable; sourced from MODIS, the average monthly NDVI quantifying the average monthly vegetation greenness (\(i=1,3\)) for each county (\(c\)) in the study areas. The 3-month aggregation of the VCI is predicted variable. \\ RFE & BOKU Rainfall estimate calculated from TAMSAT version 3 product (in mm) [38] & Predictor variable; average monthly rainfall estimate \\ RCI 1 & RCI\(i=100\times\)(RFE\(c,i-\)RFEmin \(c,i\))/(RFEmax \(c,i\)) [13] & Predictor variable; RFE values normalized in the 0–1 range (both end points included) for each extent (\(c\)) and for each time period (\(i\)). \\  & For each location, \(c\) and period \(i\), the long-term record of TAMSAT RFE was fitted to a probability distribution then transformed to a normal distribution so that (\(i=1,3\)) \\ SPI & \(c,i=0\)[39] & \\ \hline \hline \end{tabular}  
* The Vegetation Condition Index (VCI) and the Rainfall Condition Index (RCI) are relative range indices and are thus susceptible to effects from the occurrence of extreme values in the historical data. The confidence of their use in this approach lies on the fact that the indices are calculated at pixel level prior to aggregation. Moreover, in the case of RCI, the Standardised Precipitation Index (SPI) is an alternative transformation realized from the same base dataset—the Rainfall Estimate (RFE).  
\end{table} 
Table 1: A description of the index calculation formulas. NDVIi indicates the Normalized Difference Vegetation Index (NDVI) observed at time \(i\); NDVImin and NDVImax are minimum and maximum NDVI observed for each pixel for every dekad in the period 2003–2013. Near infrared (NIR) and Red are the spectral reflectances in near infrared and red spectral channels of MODIS satellite, respectively. Before use, the NDVI time series is smoothed and filtered to remove negative impacts of poor atmospheric conditions and undetected clouds [22]. The input data for this study could suffer various errors. Noise as a result of cloud cover and other atmospheric disturbances is one such source of error. The data pre-processing stage of the BOKU datasets as provided in [PERSON] et al. (2019) however mitigates this through Whittaker smoothing, which uses the vegetation indicator (VI) usefulness quality indicator in the data smoothing process. In addition, the BOKU vegetation input data are NRT and have an element of forecasting that makes the input prone to estimation errors. This is however mitigated by the use of a constrained NRT filtering approach. The precipitation data from TAMSAT potentially could suffer estimation errors arising from a limitation in the spatial distribution of in situ observation gauges at the point of historical calibration. Drought events are defined in-terms of VCI3M for each administrative unit. The variables, with the exception of the variable 'Month', were lagged at 1-3 month time steps for each county to ensure that the lagged variables conform to the time series data for each county. The non-lagged variables were then dropped from the study, with the exception of VCI3M, which is the dependent variable. The resultant dataset is as described in Table 2.  
Random sampling is used to partition the data into training and validation datasets. The partitions follow on the 70:30 rule for training and validation data sets, respectively. To support decision making processes, products of operational drought monitoring systems should be easy to interpret. For example, readability of maps is improved by reducing the real value outputs to a few classes. The classes are generally subjective and are adjusted in operational systems based on practical applications. This study adopts the drought classification in Table 3 as used in [PERSON] (2019); [PERSON] et al. (2019) and [PERSON] et al. (2019). Even though the classes might appear subjective, the process for realizing them as documented in [PERSON] et al.