Aridity indexes are quantitative indicators of the degree of water deficiency present at a given location. A variety of aridity indexes have been formulated, although the term Aridity Index specifically refers to the 1948 work of Thornthwaite. Aridity indexes have been applied at continental and subcontinental levels and are most commonly related to distributions of natural vegetation and crops. Critical values of the indexes have been derived from observed vegetation boundaries. For instance, Köppen’s 1918 classification defines the desert/steppe boundary as the 200-mm annual isohyet in regions where there is no seasonality of rainfall and the mean annual temperature is 5–10°C.

Formulation of aridity indexes is not straightforward due to the nature of aridity. First, aridity is a function of the interplay between rainfall, temperature, and evaporation. Use of mean annual rainfall as an index of aridity ignores the importance of temperature and evaporation. Aridity indexes that have gained widespread acceptance directly or indirectly take into account all three factors. Second, the arid regions generally have been recognized as having a paucity of climatological data. Given the temporal variability of precipitation inherent in arid regions, the lack of climatological data has been detrimental in attempts to quantitatively define the boundaries of aridity. Third, aridity indexes must be considered from the standpoint of their eventual use. For example, the 1968 US Army World Desert Classification defines aridity with respect to military operations; application to world vegetation patterns would be inappropriate. A particular aridity index may serve several purposes, but no one index is appropriate for all uses. However, aridity indexes are often mathematically related and to some extent have been used interchangeably on a global scale.

Identification of the arid zones of the Earth has roots that can be traced two millennia. Classical Greek thought identified the latitudinally controlled torrid, temperate, and frigid zones of the world. Implicit in their thought was the concept that the torrid, low-latitude climates were arid. Not until long-term instrumental records and reliable world vegetation maps became available could true aridity indexes be developed. Thus, aridity indexes are a product of the twentieth century. Table A27 outlines the major developments regarding aridity indexes. For additional information, see Dzerdzeevskii (1958), Hare (1977), and International Crops Research Institute for the Semi-Arid Tropics (1980).

In 1900 Köppen originally qualitatively classified as arid those places that had desert vegetation. V.V. Dokutchaev in 1900 and A. Penck in 1910 qualitatively defined arid regions as places where annual evaporation exceeds precipitation. In 1905 both E.N. Transeau and G.N. Vyssotsky quantified this relationship. Yet this approach was not totally satisfactory because of the lack of reliable, worldwide evaporation measurements. Köppen’s influential series of climatic classifications used mean annual temperature and precipitation combinations to define arid climates (1918, 1936). In a similar vein W. Lang’s 1920 Rain Factor Index was a ratio between mean annual precipitation and mean annual temperature. Lang’s index, and a modified version done by E. de Martonne in 1925, were widely used because their data requirements were minimal. However, their approach was limited in that the seasonality of temperature and precipitation were not addressed.

A. Meyer’s 1926 Precipitation-Saturation Deficit Ratio was an attempt to obviate the need for dependable evaporation data. Meyer assumed the evaporation rate to be a function of the saturation deficit (saturation vapor pressure minus actual vapor pressure at a particular temperature). The Precipitation- Saturation Deficit Ratio was calculated from long-term temperature, precipitation, and relative humidity data and was found to be more reliable than temperature/precipitation-based indexes. Data availability limited the application of Meyer’s ratio in that relative humidity data generally were not as available as were temperature and precipitation records.

Thornthwaite’s work had an immense influence on the quantitative calculation of aridity. His Precipitation Effectiveness Index of 1931 is computed as ten times the sum of the monthly precipitation to evaporation ratio at a given location. Of practical importance was his accompanying empirical formula for deriving the Precipitation Effectiveness Index for stations recording only mean monthly temperature and precipitation. In 1948, and in subsequent revisions of his climatic classification, Thornthwaite employed the Aridity Index, which relates annual moisture deficit to annual potential evapotranspiration (see Water Budget Analysis). Weighted by 0.6 and subtracted from Thornthwaite’s Humidity Index, the Aridity Index is a component of Thornthwaite’s Index of Moisture. On the basis of the Index of Moisture, Thornthwaite categorized the world into nine moisture zones ranging from arid to perhumid. Evapotranspiration prominently figured in Thornthwaite’s indexes, yet it was measured at only a handful of sites worldwide. So Thornthwaite devised a formula to estimate evapotranspiration through the use of a station’s latitude and temperature.

Table A27 Selected summary of aridity indexes
Full size table

His concepts have gained wide use because of the simplicity of their data requirements and their general agreement with world vegetation patterns. However, some engineers and agriculturalists have criticized his methods as too general for use in specific applications. The formulae have been found to produce unreliable results in certain tropical locales.

Budyko (1951) offered a new approach by considering the heat and water balance equations of the Earth’s surface. His Radiational Index of Dryness was the ratio of the mean annual net radiation (i.e. the radiation balance) to the product of the mean annual precipitation times the latent heat of vaporization for water. The warm dry conditions synonymous with arid regions are well characterized by Budyko’s index. In practical terms the Radiational Index of Dryness is the number of times the net radiative energy income at the surface can evaporate the mean annual precipitation. Although a number of writers have preferred Budyko’s method of calculating aridity, a major limitation in application is the lack of long-term radiation records at many observation stations.

Other indexes have tended to be refinements and hybridizations of the above notions. Of recent interest has been the use of aridity indexes to define the agricultural boundary between arid and semiarid climates. UNESCO, FAO, and WMO are in accord that the boundary should be drawn where lack of water makes dryland farming impossible. Thus, aridity indexes are gaining increased importance in the planning of water supplies for crops.

Meigs’s maps (1953, Meigs 1960) have been the most widely cited classification of aridity. Meigs used Thornthwaite’s Moisture Index to define aridity. The 1 : 2 500 000 Map of the World Distribution of Arid Regions (UNESCO, 1979) has been produced to refine Meigs’s maps. In this latter work approximately one-third of the world’s continental surface is classified as having some degree of aridity.

Although UNESCO’s 1979 map continued use of the ratio of precipitation to evapotranspiration, evapotranspiration was calculated by the more-favored Penman method. Calculation of aridity indices usually includes an input of evapotranspiration, The present international consensus is to estimate reference evapotranspiration using the Penman-Monteith formula (Allen et al., 1998). This formula is state-of-the-art but needs relatively esoteric atmospheric and soil input such as solar radiation and ground heat flux; if such data are not available locally, they can be estimated. An excellent explanation and commentary of operational drought-related aridity indices was compiled by Heim Jr. (2002).

Traditionally, climatologists and agriculturalists have used long-term weather data from standard weather shelters to create maps of aridity at Earth’s surface. The difficulties of interpolating between observation points have created profound uncertainties in areas where data are sparse. For instance, there has never been a worldwide map of Thornthwaite’s Moisture Index. The advent of satellites with continuous coverage of immense areas over a course of years has had a profound impact in the use of aridity indices. Recent advances in the archiving and collation of data have allowed worldwide monitoring of aridity as opposed to hindsight assessments.

The most commonly used satellite measure is the Normalized Difference Vegetation Index (NDVI). Derived from the Advanced Very High Resolution Radiometer (AVHRR) on the NOAA polar orbiter series, the NDVI at a location is closely related to the proportion of photosynthetically absorbed radiation that can be calculated from a ratio of reflectances in visible (0.58–0.68 μm) and near-infrared (0.725–1.1 μm). AVHRR channels:

Channel 1 (CH1) is the reflectance in the visible and Channel 2 (CH2) is the reflectance in the reflective infrared. CH1 is sensitive to chlorophyll’s absorption of incoming radiation, and CH2 is in a portion of the spectrum in which the mesophyll structure in leaves causes great reflectance (Tucker et al., 1991). As the NDVI values increase, this infers increasing amounts of biomass. Active biomass is largely controlled by climate, so NDVI is essentially an aridity index when time series of values are calculated over area. Multiyear data sets are needed so as to sort the phonological effects of green-up and senescence from atmospheric variability.

Near-real-time monitoring of aridity to assess drought is now possible. Surface and satellite measures of short-term drought/aridity can be combined to provide operational assessments. An example of this sort of work is given by Svoboda et al. (2002). By using a blend of the Palmer Drought Severity Index, CPC Soil Moisture Model Percentiles, USGS Daily Streamflow Percentiles, Percent of Normal Precipitation, the Standardized Precipitation Index, and the Satellite Vegetation Health Index, a weekly Drought Monitor index value is calculated for each US climate division. The results are mapped and widely distributed.

As latter-day aridity monitoring and research continues, the climatological prospects are exciting — “intellectual descendants” of the aridity indices of the early 1900s are providing useful decision support to policymakers. As time progresses and time-series of these products achieve climatological proportions, academic analyses should offer unprecedented dynamism to our concepts of aridity.