# Extreme Droughs in the Peruvian Amazon Region (2000-2024)
## 2 Materials and Methods
### Obtaining the MCWD Drought Index  
The \"Maximum Cumulative Water Deficit (MCWD)\" index is obtained after the calculation of the water deficit (WD), which is the difference at each grid point between monthly precipitation (Pr) and evapotranspiration (Et). Subsequently, for the hydrologic year (HY), which in Peru is considered from September to August, the cumulative deficit is calculated as the sum of the deficits of all the months when monthly evapotranspiration is greater than monthly precipitation. The monthly water deficit WD for month j (j = 1,... 12) is given by  
\[\text{WD}_{\text{j}}=\text{Et}_{\text{j}}-\text{Pr}_{\text{j}}\]  
If WD\({}_{\text{j}}\) is negative, it means that precipitation has been sufficient to meet the evapotranspiration demand and recharge the soil water. If WD\({}_{\text{j}}\) is positive, it indicates a water deficit, i.e., precipitation has not covered water demand, and the soil has experienced a period of water stress. Next, from the WD\({}_{\text{j}}\) values, the accumulated water deficit is calculated month by month. This accumulation considers the existing deficit in the soil and how it increases or decreases with each month based on precipitation and evapotranspiration. That is, for each j starting from j = 1:  
\[\text{CWD}_{\text{j}}=\sum_{\text{j=1}}^{\text{j}}\text{WD}_{\text{i}}\times \text{H}(\text{WD}_{\text{i}})\] \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multicolumn{1}{c}{**Study Area**} & \multicolumn{1}{c}{**Longitude**} & \multicolumn{1}{c}{**Latitude**} & \multicolumn{1}{c}{**Approximate Location**} & \multicolumn{1}{c}{**Acronym**} \\ \hline
1 & 72\({}^{\circ}\)–70\({}^{\circ}\) W & 4\({}^{\circ}\)–2\({}^{\circ}\) S & Loreto Northeast & LOR1 \\ \hline
2 & 76\({}^{\circ}\)–74\({}^{\circ}\) W & 4\({}^{\circ}\)–2\({}^{\circ}\) S & Loreto Northwest & LOR2 \\ \hline
3 & 75\({}^{\circ}\)–73 W & 7\({}^{\circ}\)–5\({}^{\circ}\) S & Loreto South & LOR3 \\ \hline
3 & 77\({}^{\circ}\)–75\({}^{\circ}\) W & 7\({}^{\circ}\)–5\({}^{\circ}\) S & Moyobamba & MOY \\ \hline
3 & 73\({}^{\circ}\)–75\({}^{\circ}\) W & 10\({}^{\circ}\)–8\({}^{\circ}\) S & Ucayali & UCA \\ \hline
4 & 69.5\({}^{\circ}\)–71.5\({}^{\circ}\) W & 13\({}^{\circ}\)–11\({}^{\circ}\) S & Madre de Dios & MD \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinates and acronyms of the study areas. Figure 1: Locations of the study areas in the Peruvian Amazon forest region. LOR1: Loreto Notheast; LOR2: Loreto Northwest; LOR3: Loreto South; MOY: Moyobamba; UCA: Ucayali; MD: Madre de Dios. where H is the Heaviside step function. Thus, if the water deficit value is negative (i.e., there is a surplus of water in the soil), it would be reset to zero, since the moisture in the soil is sufficient to cover the deficit. Otherwise, if the WD value is positive, it continues to accumulate to record the water deficit for the following month. After calculating the accumulated \(\text{CWD}_{\text{j}}\) balance for each month of the year or study period, the MCWD is defined as the maximum value reached by \(\text{CWD}_{\text{j}}\) during that period, which represents the greatest water deficit experienced by the soil in that period and, therefore, the point of greatest water stress for vegetation. \[\text{MCWD}=\text{max}(\text{CWD}_{\text{1}},\text{CWD}_{\text{2}},\,\ldots, \text{CWD}_{\text{12}})\]  
The larger the MCWD value, the more intense the accumulated water deficit and, therefore, the greater the stress experienced by the ecosystem. A high MCWD value (e.g., MCWD > 200 mm) indicates a significant water deficit, meaning that the soil has been under considerable water stress and vegetation may have had difficulties accessing sufficient water [26], so that, following [30], a rainforest would tend to become a seasonal forest, while MCWD > 300 mm would correspond to a savanna. MCWD values close to zero suggest that the water deficit was low, and vegetation did not experience significant stress.