SPEI - Standardized Precipitation Evapotranspiration Index

Note: This guide references “drought” in some sections due to SPEI’s historical use in agricultural drought monitoring, but SPEI is a bidirectional index that monitors both dry and wet extremes equally. All analysis functions work for both directions.

Overview

The Standardized Precipitation Evapotranspiration Index (SPEI) extends SPI by incorporating potential evapotranspiration (PET), making it sensitive to temperature changes and climate warming. Like SPI, it monitors both dry and wet conditions.

SPEI Values:

Negative values: Indicate dry conditions (drought)
Positive values: Indicate wet conditions (flooding/excess)

Key Differences from SPI:

Includes temperature effects via PET
More sensitive to climate change
Better for agricultural drought and water balance
Same interpretation as SPI (negative=dry, positive=wet)

Quick Start

import xarray as xr
from indices import spei

# Load data
precip = xr.open_dataset('input/precipitation.nc')['precip']
temp = xr.open_dataset('input/temperature.nc')['temp']
lat = xr.open_dataset('input/temperature.nc')['lat']

# Calculate SPEI-12 (auto-calculates PET from temperature via Thornthwaite)
spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12)

# Negative values = dry conditions (drought)
# Positive values = wet conditions (flooding/excess)

# Save
spei_12.to_netcdf('output/netcdf/spei_12.nc')

PET Methods

Option 1: Thornthwaite (Default)

Use when: Only mean temperature data available

from indices import spei

# Pass temperature and latitude — PET computed automatically using Thornthwaite
spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12)

Pros: Simple, only needs mean temperature and latitude Cons: Less accurate in arid/semi-arid regions

Option 2: Hargreaves-Samani (Recommended for Arid Regions)

Use when: You have min/max temperature data and need better accuracy in dry climates

from indices import spei

# Hargreaves method — requires mean, min, max temperature
spei_12 = spei(precip, temperature=temp_mean, latitude=lat, scale=12,
               pet_method='hargreaves', temp_min=tmin, temp_max=tmax)

Pros: Better accuracy in arid regions, based on radiation balance Cons: Requires min/max temperature data

Option 3: Pre-computed PET

Use when: You have PET from other sources (FAO-56, Penman-Monteith, etc.)

# Load your PET data
pet = xr.open_dataset('input/pet.nc')['pet']

# Calculate SPEI directly
spei_12 = spei(precip, pet=pet, scale=12)

Best option: Most accurate if PET quality is good

PET Method Comparison

Method	Inputs Required	Best For
Thornthwaite	T_mean, latitude	Humid regions, quick estimates
Hargreaves	T_mean, T_min, T_max, latitude	Arid/semi-arid regions
Pre-computed	External PET dataset	Highest accuracy when available

Parameters

Same as SPI, plus:

pet (xarray.DataArray): Potential evapotranspiration
- Same dimensions as precipitation
- Units: mm/month
- Required (no default)
pe_fitting_params (xarray.Dataset, optional): Pre-fitted parameters for operational use

Examples

Example 1: With Temperature (auto-PET)

import xarray as xr
from indices import spei

# Load data
precip = xr.open_dataset('input/chirps.nc')['precip']
temp = xr.open_dataset('input/temperature.nc')['temp']
lat = xr.open_dataset('input/temperature.nc')['lat']

# Calculate SPEI-12 (PET computed internally from temperature)
spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12,
               calibration_start_year=1991, calibration_end_year=2020)

# Save
spei_12.to_netcdf('output/netcdf/spei_12.nc')

# Preview
print(spei_12)
spei_12.isel(time=-1).plot(cmap='RdBu', vmin=-3, vmax=3)

Example 2: With Hargreaves PET (Better for Arid Regions)

import xarray as xr
from indices import spei

# Load temperature data (mean, min, max)
temp_mean = xr.open_dataset('input/tmean.nc')['tmean']
temp_min = xr.open_dataset('input/tmin.nc')['tmin']
temp_max = xr.open_dataset('input/tmax.nc')['tmax']
precip = xr.open_dataset('input/precip.nc')['precip']
lat = temp_mean.lat

# Calculate SPEI-12 using Hargreaves method
spei_12 = spei(precip, temperature=temp_mean, latitude=lat, scale=12,
               pet_method='hargreaves', temp_min=temp_min, temp_max=temp_max)

Example 3: With Pre-computed PET

# Your high-quality PET from another source
pet = xr.open_dataset('input/pet_penman_monteith.nc')['pet']

# Ensure same dimensions as precipitation
assert precip.dims == pet.dims
assert precip.shape == pet.shape

# Calculate SPEI
spei_6 = spei(precip, pet=pet, scale=6)

Example 4: Multiple Scales

from indices import spei_multi_scale

# Calculate multiple scales (with temperature-based PET)
scales = [3, 6, 12]
spei_multi = spei_multi_scale(precip, temperature=temp, latitude=lat, scales=scales)

# Access different scales
spei_3 = spei_multi['spei_gamma_3_month']
spei_12 = spei_multi['spei_gamma_12_month']

SPEI vs SPI

Aspect	SPI	SPEI
Input	Precipitation only	Precipitation + PET
Temperature	Not considered	Included via PET
Climate change	Less sensitive	More sensitive
Best for	Meteorological dry/wet monitoring	Agricultural dry/wet monitoring
Data needs	Minimal	More data needed
Computation	Faster	Slower (PET calculation)

When to use SPEI:

Agricultural dry/wet monitoring
Climate change analysis
Temperature effects important
Have temperature data

When to use SPI:

Purely meteorological dry/wet monitoring
Only precipitation available
Simple, fast analysis
Standardized comparisons

Common Issues

Issue 1: PET Units Mismatch

Problem: SPEI values unrealistic
Cause: PET in different units than precipitation

# Check units
print(f"Precip: {precip.mean().values:.1f} mm/month")
print(f"PET: {pet.mean().values:.1f} mm/month")

# PET should be 30-200 mm/month typically
# If PET is 1-6, likely mm/day - convert
if pet.mean() < 10:
    pet = pet * 30  # Convert mm/day to mm/month (approx)

Issue 2: Negative P-PET Values

Problem: Many negative P-PET values in arid regions
Solution: This is expected! SPEI handles negative water balance

# Check water balance
water_balance = precip - pet
print(f"Mean P-PET: {water_balance.mean().values:.1f} mm/month")
# Negative is fine for arid regions

Issue 3: PET > Precipitation Always

Problem: In deserts, PET always exceeds precipitation Solution: SPEI is designed for this — shows persistent dry conditions

Issue 4: NaN in Arid Regions (Distribution Fitting Failure)

Problem: Hyper-arid grid cells return NaN even with valid data Cause: Pearson Type III requires sufficient non-zero values for L-moments computation. When >95% of water balance values cluster near zero or are identical, fitting fails.

Diagnosis:

from distributions import diagnose_data

# Check the water balance distribution
water_balance = (precip - pet).isel(lat=50, lon=100).values
diag = diagnose_data(water_balance)
print(f"Zero proportion: {diag.zero_proportion:.1%}")
print(f"Suitable for Pearson III: {diag.is_suitable_pearson3}")

Solutions:

Use Gamma distribution instead of Pearson III (more robust for extreme cases)
Use longer time scales (SPEI-12, SPEI-24)
Mask hyper-arid pixels where SPEI is not meaningful

See Data Model — Arid Regions for detailed guidance.

Visualization

from visualization import plot_index

# Single location
location_spei = spei_12.isel(lat=50, lon=100)
plot_index(location_spei, threshold=-1.2,
           title='SPEI-12 Time Series')

Best Practices

Match grids: PET and precipitation on the same spatial and temporal resolution
Quality PET: Use the best available method for your region
Units check: Verify both precipitation and PET are in mm/month

For full input requirements (dimensions, calibration period, missing data handling), see Data Model & Outputs.

Performance

PET calculation is the bottleneck:

# Auto-PET from temperature (Thornthwaite)
spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12)  # ~30 sec

# Pre-computed PET (faster — PET already available)
spei_12 = spei(precip, pet=pet, scale=12)  # ~10 sec

# Use Dask for large datasets
precip_chunked = xr.open_dataset('precip.nc', chunks={'time': 100})['precip']
spei_12 = spei(precip_chunked, pet=pet, scale=12)  # Parallel

References

Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I. (2010). A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index. Journal of Climate, 23(7), 1696-1718.
Beguería, S., Vicente-Serrano, S.M., Reig, F., Latorre, B. (2014). Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. International Journal of Climatology, 34(10), 3001-3023.

--- title: "SPEI - Standardized Precipitation Evapotranspiration Index" --- > **Note:** This guide references "drought" in some sections due to SPEI's historical use in agricultural drought monitoring, but SPEI is a bidirectional index that monitors **both dry and wet extremes** equally. All analysis functions work for both directions. ## Overview The Standardized Precipitation Evapotranspiration Index (SPEI) extends SPI by incorporating potential evapotranspiration (PET), making it sensitive to temperature changes and climate warming. Like SPI, it monitors both dry and wet conditions. **SPEI Values:** - **Negative values:** Indicate dry conditions (drought) - **Positive values:** Indicate wet conditions (flooding/excess) **Key Differences from SPI:** - Includes temperature effects via PET - More sensitive to climate change - Better for agricultural drought and water balance - Same interpretation as SPI (negative=dry, positive=wet) ## Quick Start ```python import xarray as xr from indices import spei # Load data precip = xr.open_dataset('input/precipitation.nc')['precip'] temp = xr.open_dataset('input/temperature.nc')['temp'] lat = xr.open_dataset('input/temperature.nc')['lat'] # Calculate SPEI-12 (auto-calculates PET from temperature via Thornthwaite) spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12) # Negative values = dry conditions (drought) # Positive values = wet conditions (flooding/excess) # Save spei_12.to_netcdf('output/netcdf/spei_12.nc') ``` ## PET Methods ### Option 1: Thornthwaite (Default) **Use when:** Only mean temperature data available ```python from indices import spei # Pass temperature and latitude — PET computed automatically using Thornthwaite spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12) ``` **Pros:** Simple, only needs mean temperature and latitude **Cons:** Less accurate in arid/semi-arid regions ### Option 2: Hargreaves-Samani (Recommended for Arid Regions) **Use when:** You have min/max temperature data and need better accuracy in dry climates ```python from indices import spei # Hargreaves method — requires mean, min, max temperature spei_12 = spei(precip, temperature=temp_mean, latitude=lat, scale=12, pet_method='hargreaves', temp_min=tmin, temp_max=tmax) ``` **Pros:** Better accuracy in arid regions, based on radiation balance **Cons:** Requires min/max temperature data ### Option 3: Pre-computed PET **Use when:** You have PET from other sources (FAO-56, Penman-Monteith, etc.) ```python # Load your PET data pet = xr.open_dataset('input/pet.nc')['pet'] # Calculate SPEI directly spei_12 = spei(precip, pet=pet, scale=12) ``` **Best option:** Most accurate if PET quality is good ### PET Method Comparison | Method | Inputs Required | Best For | |--------|-----------------|----------| | **Thornthwaite** | T_mean, latitude | Humid regions, quick estimates | | **Hargreaves** | T_mean, T_min, T_max, latitude | Arid/semi-arid regions | | **Pre-computed** | External PET dataset | Highest accuracy when available | ## Parameters Same as SPI, plus: - **`pet`** (xarray.DataArray): Potential evapotranspiration - Same dimensions as precipitation - Units: mm/month - Required (no default) - **`pe_fitting_params`** (xarray.Dataset, optional): Pre-fitted parameters for operational use ## Examples ### Example 1: With Temperature (auto-PET) ```python import xarray as xr from indices import spei # Load data precip = xr.open_dataset('input/chirps.nc')['precip'] temp = xr.open_dataset('input/temperature.nc')['temp'] lat = xr.open_dataset('input/temperature.nc')['lat'] # Calculate SPEI-12 (PET computed internally from temperature) spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12, calibration_start_year=1991, calibration_end_year=2020) # Save spei_12.to_netcdf('output/netcdf/spei_12.nc') # Preview print(spei_12) spei_12.isel(time=-1).plot(cmap='RdBu', vmin=-3, vmax=3) ``` ### Example 2: With Hargreaves PET (Better for Arid Regions) ```python import xarray as xr from indices import spei # Load temperature data (mean, min, max) temp_mean = xr.open_dataset('input/tmean.nc')['tmean'] temp_min = xr.open_dataset('input/tmin.nc')['tmin'] temp_max = xr.open_dataset('input/tmax.nc')['tmax'] precip = xr.open_dataset('input/precip.nc')['precip'] lat = temp_mean.lat # Calculate SPEI-12 using Hargreaves method spei_12 = spei(precip, temperature=temp_mean, latitude=lat, scale=12, pet_method='hargreaves', temp_min=temp_min, temp_max=temp_max) ``` ### Example 3: With Pre-computed PET ```python # Your high-quality PET from another source pet = xr.open_dataset('input/pet_penman_monteith.nc')['pet'] # Ensure same dimensions as precipitation assert precip.dims == pet.dims assert precip.shape == pet.shape # Calculate SPEI spei_6 = spei(precip, pet=pet, scale=6) ``` ### Example 4: Multiple Scales ```python from indices import spei_multi_scale # Calculate multiple scales (with temperature-based PET) scales = [3, 6, 12] spei_multi = spei_multi_scale(precip, temperature=temp, latitude=lat, scales=scales) # Access different scales spei_3 = spei_multi['spei_gamma_3_month'] spei_12 = spei_multi['spei_gamma_12_month'] ``` ## SPEI vs SPI | Aspect | SPI | SPEI | | ------ | --- | ---- | | **Input** | Precipitation only | Precipitation + PET | | **Temperature** | Not considered | Included via PET | | **Climate change** | Less sensitive | More sensitive | | **Best for** | Meteorological dry/wet monitoring | Agricultural dry/wet monitoring | | **Data needs** | Minimal | More data needed | | **Computation** | Faster | Slower (PET calculation) | **When to use SPEI:** - Agricultural dry/wet monitoring - Climate change analysis - Temperature effects important - Have temperature data **When to use SPI:** - Purely meteorological dry/wet monitoring - Only precipitation available - Simple, fast analysis - Standardized comparisons ## Common Issues ### Issue 1: PET Units Mismatch **Problem:** SPEI values unrealistic **Cause:** PET in different units than precipitation ```python # Check units print(f"Precip: {precip.mean().values:.1f} mm/month") print(f"PET: {pet.mean().values:.1f} mm/month") # PET should be 30-200 mm/month typically # If PET is 1-6, likely mm/day - convert if pet.mean() < 10: pet = pet * 30 # Convert mm/day to mm/month (approx) ``` ### Issue 2: Negative P-PET Values **Problem:** Many negative P-PET values in arid regions **Solution:** This is expected! SPEI handles negative water balance ```python # Check water balance water_balance = precip - pet print(f"Mean P-PET: {water_balance.mean().values:.1f} mm/month") # Negative is fine for arid regions ``` ### Issue 3: PET > Precipitation Always **Problem:** In deserts, PET always exceeds precipitation **Solution:** SPEI is designed for this — shows persistent dry conditions ### Issue 4: NaN in Arid Regions (Distribution Fitting Failure) **Problem:** Hyper-arid grid cells return NaN even with valid data **Cause:** Pearson Type III requires sufficient non-zero values for L-moments computation. When >95% of water balance values cluster near zero or are identical, fitting fails. **Diagnosis:** ```python from distributions import diagnose_data # Check the water balance distribution water_balance = (precip - pet).isel(lat=50, lon=100).values diag = diagnose_data(water_balance) print(f"Zero proportion: {diag.zero_proportion:.1%}") print(f"Suitable for Pearson III: {diag.is_suitable_pearson3}") ``` **Solutions:** - Use **Gamma distribution** instead of Pearson III (more robust for extreme cases) - Use longer time scales (SPEI-12, SPEI-24) - Mask hyper-arid pixels where SPEI is not meaningful See [Data Model — Arid Regions](../get-started/data-model.qmd#arid-regions-and-zero-precipitation) for detailed guidance. ## Visualization ```python from visualization import plot_index # Single location location_spei = spei_12.isel(lat=50, lon=100) plot_index(location_spei, threshold=-1.2, title='SPEI-12 Time Series') ``` ## Best Practices 1. **Match grids:** PET and precipitation on the same spatial and temporal resolution 2. **Quality PET:** Use the best available method for your region 3. **Units check:** Verify both precipitation and PET are in mm/month For full input requirements (dimensions, calibration period, missing data handling), see [Data Model & Outputs](../get-started/data-model.qmd). ## Performance PET calculation is the bottleneck: ```python # Auto-PET from temperature (Thornthwaite) spei_12 = spei(precip, temperature=temp, latitude=lat, scale=12) # ~30 sec # Pre-computed PET (faster — PET already available) spei_12 = spei(precip, pet=pet, scale=12) # ~10 sec # Use Dask for large datasets precip_chunked = xr.open_dataset('precip.nc', chunks={'time': 100})['precip'] spei_12 = spei(precip_chunked, pet=pet, scale=12) # Parallel ``` ## References - Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I. (2010). A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index. Journal of Climate, 23(7), 1696-1718. - Beguería, S., Vicente-Serrano, S.M., Reig, F., Latorre, B. (2014). Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. International Journal of Climatology, 34(10), 3001-3023. ## See Also - [SPI Guide](spi.qmd) - Precipitation-only dry/wet index - [Run Theory](runtheory.qmd) - Dry/wet event analysis - [Magnitude Explained](magnitude.qmd) - Cumulative vs instantaneous severity - [Visualization Guide](visualization.qmd) - Plotting options