Thornthwaite Aridity Index Calculator

Thornthwaite aridity index (Ia)

The Thornthwaite aridity index measures how much of the atmosphere's yearly water demand goes unmet by the rain that actually falls. The definition is Ia = 100·DEF/PET. Here DEF stands for the annual water deficit, which you get by adding up the monthly shortfalls in every month where PET runs higher than the rainfall plus the water already stored in the soil. PET itself is the annual potential evapotranspiration, usually worked out with the Thornthwaite (1948) or Penman-Monteith (FAO 56) equations. Take DEF = 200 mm and PET = 1200 mm: that lands Ia at 16.7, which reads as moderate aridity.

Thornthwaite's own scheme reads the thresholds this way: 0-16.7 means little or no aridity, 16.7-33.3 is moderate, and anything past 33.3 counts as large. UNEP (1992) draws on related ratios but uses P/PET instead, sorting drylands into hyper-arid, arid, semi-arid and dry sub-humid bands. To get the moisture index Im = Ih - 0.6·Ia that anchors the wider Thornthwaite climate classification, you pair Ia with the humidity index (Ih).

Applications

EMBRAPA Climapest, INMET and IBGE lean on Ia to map out semi-arid zones, the Brazilian Northeast SUDENE polygon being the obvious case. Agronomy and Forestry courses bring it into irrigation and water-balance lessons, and environmental engineers use it when they size reservoirs or weigh desertification risk. The PET figures usually come straight from the Penman-Monteith tables in FAO Irrigation and Drainage Paper 56.

FAQ

What is the difference between DEF and PET? Picture PET as the most evapotranspiration you could ever get if water never ran short. DEF is the slice of that demand the soil-rainfall system fails to cover over the year, tallied up month by month.

Does Ia equal the UNEP aridity index? No. UNEP frames aridity as P/PET, where a lower number means drier conditions, whereas Thornthwaite Ia is 100·DEF/PET and a higher number means drier. People use both, so always check which one a source is quoting before you line up the values.

How do I obtain DEF without a full water balance? Your best bet is a Thornthwaite-Mather monthly book-keeping run, set up with a soil water-holding capacity, often taken as 100 mm. This calculator skips that step and expects you to bring DEF and PET in hand, so it can concentrate on the index alone.