What is the method for computing the SPI and SPEI for every grid level?

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The method for computing the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI) for every grid level involves the following steps:

1. Collect meteorological data: Collect monthly precipitation data and monthly temperature data for the desired time period for each grid level.

2. Calculate the precipitation anomaly: Calculate the difference between monthly precipitation and its long-term average (e.g., 30-year average) for each grid level.

3. Calculate the potential evapotranspiration (PET): Calculate the PET using a suitable method (e.g., Thornthwaite, Hargreaves, Penman) based on monthly temperature data for each grid level.

4. Calculate the water balance: Calculate the difference between precipitation and PET for each month and grid level.

5. Calculate the cumulative water balance: Calculate the cumulative water balance over different time scales (e.g., 3-month, 6-month, 12-month) for each grid level.

6. Determine the probability distribution: Determine the probability distribution of the cumulative water balance values for each grid level.

7. Compute the SPI or SPEI: Compute the SPI or SPEI values for each grid level by transforming the cumulative water balance values to a standard normal distribution using the probability distribution.

8. Validate the results: Validate the SPI or SPEI values by comparing them with historical drought events, other drought indices, or other climatic variables (e.g., soil moisture).

9. Visualize the results: Visualize the SPI or SPEI values using maps, graphs, or other visualization tools to identify the spatial and temporal patterns of drought occurrence and severity.