Köppen

At the turn of the 20th century, Wladimir Köppen and Rudolf Geiger developed the concept of a climate classification where arid regions were defined as those places where the annual rainfall accumulation (in centimetres) is less than ${\displaystyle R/2}$, where:

• ${\displaystyle R=2\times T}$ if rainfall occurs mainly in the cold season,
• ${\displaystyle R=2\times T+14}$ if rainfall is evenly distributed throughout the year, and
• ${\displaystyle R=2\times T+28}$ if rainfall occurs mainly in the hot season.

where ${\displaystyle T}$ is the mean annual temperature in Celsius.

This was one of the first attempts at defining an aridity index, one that reflects the effects of the thermal regime and the amount and distribution of precipitation in determining the native vegetation possible in an area. It recognizes the significance of temperature in allowing colder places such as northern Canada to be seen as humid with the same level of precipitation as some tropical deserts because of lower levels of potential evapotranspiration in colder places. In the subtropics, the allowance for the distribution of rainfall between warm and cold seasons recognizes that winter rainfall is more effective for plant growth that can flourish in the winter and go dormant in the summer than the same amount of summer rainfall during a warm-to-hot season. Thus a place like Athens, Greece that gets most of its rainfall in winter can be considered to have a humid climate (as attested in lush foliage) with roughly the same amount of rainfall that imposes semi-desert conditions in Midland, Texas, where rainfall largely occurs in the summer.

Thornthwaite

In 1948, C. W. Thornthwaite proposed an AI defined as:

$${\displaystyle AI_{T}=100\times {\frac {d}{n}}}$$

where the water deficiency ${\displaystyle d}$ is calculated as the sum of the monthly differences between precipitation and potential evapotranspiration for those months when the normal precipitation is less than the normal evapotranspiration; and where ${\displaystyle n}$ stands for the sum of monthly values of potential evapotranspiration for the deficient months (after Huschke, 1959). This AI was later used by Meigs (1961) to delineate the arid zones of the world in the context of the UNESCO Arid Zone Research programme.^[2]

United Nations Environment Programme

In the preparations leading to the 1977 UN Conference on Desertification (UNCOD), the United Nations Environment Programme (UNEP) issued a dryness map based on a different aridity index, proposed originally by Mikhail Ivanovich Budyko (1958)^[3] and defined as follows:^[4]

$${\displaystyle AI_{B}=100\times {\frac {R}{LP}}}$$

where ${\displaystyle R}$ is the mean annual net radiation (also known as the net radiation balance), ${\displaystyle P}$ is the mean annual precipitation, and ${\displaystyle L}$ is the latent heat of vaporization for water. Note that this index is dimensionless and that the variables ${\displaystyle R}$, ${\displaystyle L}$ and ${\displaystyle P}$ can be expressed in any system of units that is self-consistent.

More recently in 1992, the UNEP has adopted yet another index of aridity, defined as:^[5]

Global map of the aridity index, from the CGIAR, following UNEP's definition, AI = P/PET.

$${\displaystyle AI_{U}={\frac {P}{PET}}}$$

where ${\displaystyle PET}$ is the potential evapotranspiration and ${\displaystyle P}$ is the average annual precipitation (UNEP, 1992). Here also, ${\displaystyle PET}$ and ${\displaystyle P}$ must be expressed in the same units, e.g., in millimetres. In this latter case, the boundaries that define various degrees of aridity and the approximate areas involved are as follows:

As this index increases with wetter conditions, some hydrologists refer to this as a humidity index.