SPI & SPEI: Drought Indices Explained with Calculations

Differences and Similarities Between SPI and SPEI

While SPI and SPEI share a standardized approach, they differ in their inputs and applications. Here’s a detailed comparison:

Similarities:

• Standardized to a normal distribution for comparability.
• Support multiple time scales (1, 3, 6, 12 months).
• Used for drought and wet period assessment.
• Implemented in Python, R, MATLAB, or Excel.
• Applied in climate research and water management.

Example Calculations for SPI and SPEI

Below are simplified examples for a 3-month time scale using hypothetical data. Full calculations require extensive historical data and statistical software.

Python Example (SPI and SPEI)

# Simplified SPI/SPEI calculation using SciPy
import numpy as np
from scipy.stats import gamma, norm, genlogistic
import pandas as pd

# Sample data: 3-month precipitation (mm) and temperature (°C)
data = pd.DataFrame({
    'precip': [50, 70, 30, 90, 20],  # Example precipitation
    'temp': [20, 22, 18, 25, 19]     # Example temperature
})
mean_precip = data['precip'].mean()  # Historical mean

# SPI Calculation
def calculate_spi(precip, mean_precip, timescale=3):
    precip_sum = precip.rolling(timescale).sum().dropna()
    shape, loc, scale = gamma.fit(precip_sum, floc=0)
    cdf = gamma.cdf(precip_sum - mean_precip, shape, loc, scale)
    spi = norm.ppf(cdf)
    return spi

# Simplified Thornthwaite PET (mm/month)
def calculate_pet(temp):
    return 16 * (10 * temp / 25)**1.5  # Approximation

# SPEI Calculation
def calculate_spei(precip, temp, mean_precip, timescale=3):
    pet = calculate_pet(temp)
    water_balance = precip - pet
    wb_sum = water_balance.rolling(timescale).sum().dropna()
    params = genlogistic.fit(wb_sum - mean_precip)
    cdf = genlogistic.cdf(wb_sum, *params)
    spei = norm.ppf(cdf)
    return spei

spi_values = calculate_spi(data['precip'], mean_precip)
spei_values = calculate_spei(data['precip'], data['temp'], mean_precip)
print("SPI:", spi_values)
print("SPEI:", spei_values)
                

R Example (SPI and SPEI)

# Using SPEI package in R
library(SPEI)

# Sample data
precip <- c(50, 70, 30, 90, 20)
temp <- c(20, 22, 18, 25, 19)
mean_precip <- mean(precip)

# SPI calculation
spi_3 <- spi(precip - mean_precip, scale=3)

# SPEI calculation (requires PET)
pet <- thornthwaite(temp, lat=40)  # Example latitude
spei_3 <- spei(precip - pet - mean_precip, scale=3)

print(spi_3)
print(spei_3)
                

Excel Example (SPI)

In Excel, SPI can be approximated:

1. Enter monthly precipitation in a column (e.g., A1:A360 for 30 years).
2. Calculate mean precipitation: =AVERAGE(A1:A360).
3. Calculate 3-month sums: =SUM(A1:A3), drag down.
4. Fit gamma distribution using add-ins (e.g., XLSTAT).
5. Use =NORM.S.INV to standardize CDF values.

Note: SPEI in Excel is complex due to PET calculations, requiring add-ins or external tools.

Frequently Asked Questions