Calculation of Drought Indicator SPI in Hydrological Analysis

The Standardized Precipitation Index (SPI) is a widely used drought monitoring indicator in hydrological analysis that reflects drought conditions across different time scales by calculating the cumulative probability distribution of precipitation data. The key advantage of SPI lies in its adaptability to various climatic regions and its capability to compute drought conditions across multiple time scales (e.g., 1-month, 3-month, 12-month), facilitating both short-term and long-term drought characteristic analysis.

The core computational steps for SPI involve: First, performing cumulative processing of precipitation data at different time scales - for instance, 3-month SPI requires summing monthly precipitation with data from the preceding two months. In code implementation, this typically uses a sliding window function with parameters for window size and aggregation method. Next, probability distribution fitting is applied to the cumulative precipitation series, where Gamma distribution or Pearson Type III distribution are commonly employed to characterize the statistical properties of precipitation data. The distribution fitting process can be implemented using maximum likelihood estimation (MLE) functions with appropriate goodness-of-fit tests. Then, through normal standardization, the fitted probabilities are converted to a standard normal distribution, where the resulting Z-value represents the SPI value. Positive values indicate wet conditions while negative values signify drought, with the magnitude reflecting the deviation from the mean.

In multi-time-scale calculations, special attention must be paid to boundary handling of sliding windows and data completeness. For example, 12-month SPI will have 11 months of missing data at the beginning of the series, typically requiring interpolation or truncation handling through boundary condition parameters in the algorithm. Furthermore, long-term drought analysis (e.g., 24-month scale) holds significant importance for agricultural and water resource management, while short-term scales (e.g., 1-month) are more suitable for rapid meteorological drought assessment.

The MATLAB implementation of this indicator is typically packaged as a configurable function, allowing users to specify input precipitation sequences, time-scale parameters, and distribution fitting methods through function arguments. The computation results can be further utilized for drought event identification, duration and intensity analysis, providing quantitative basis for water resource planning and disaster early warning systems. A typical function prototype might be: spi_values = calculateSPI(precipitation_data, time_scale, distribution_type, handle_boundaries).