Table 1 shows the climate types with mean annual precipitation P_ma and corresponding P_ma /P_agt ratios. To determine suitable E_ap /P_ma ratios, the writers have approximately estimated potential evapotranspiration across the climatic spectrum, for subtropical and midlatitudinal regions. For instance, the writers estimate E_ap = 3,000 mm at the limit between superarid and hyperarid regions. Corresponding estimates for other regions led to the E_ap /P_ma ratios shown in Table 1.

3.  GLOBAL DATA ON DROUGHTS AND CLIMATE

Droughts in the United States have a tendency to be more persistent in the interior of the country than in areas farther east or west, with durations for moderate and severe droughts varying between 3 and 5 years (Karl 1983). The greater drought persistence in the Great Plains of central North America than in any other part of the United States has been documented by Karl et al. (1987) and Laird et al. (1996). Johnson and Kohne (1993) have shown that drought persistence is greater in the interior of the United States, including the states of Wyoming, Colorado, North Dakota, and Montana. Horn (1989) studied the spatial variability of droughts in Idaho, where the mean annual precipitation varies between 250 and 1,500 mm, with an average of about 800 mm. He concluded that the median drought durations varied between 5.6 and 6.4 years throughout the state.

Klugman (1978) has studied droughts in the Upper Midwest of the United States from 1931 to 1969. His analysis showed that while the 30s and the 50s were decades of drought, the 40s and 60s were wet periods. This indicates a recurrence interval of 20 years for this subhumid region, with a mean annual precipitation of 1,500 mm. Karl and Young (1987) have reported drought recurrence intervals ranging from 20 to 60 years in the southeastern United Slates. This location includes North Carolina, Georgia and Tennessee, which have humid climates.

The Indian subcontinent, the northern half of which lies above the tropic of Cancer, has a wide variability of climatic regimes, from superarid to superhumid. High rates of evapotranspiration prevail over hyperarid Rajastan, in western India, with annual rate exceeding 2,500 mm and reaching 3,500 mm in some regions of northwest Rajastan. Conversely, low rates of evapotranspiration prevail over hyperhumid Assam and the Himalayan Bengal, in northeastern India, with annual rates in the range of 1,200-1,500 mm. Over central India, which is semiarid, evapotranspiration rates vary in the range of 1,400-1,800 mm (Abbi 1974). Gregory (1989) has reported that droughts in hyperhumid regions of India such as Assam are very infrequent, with the last documented drought in the region dating to 1900.

The Australian continent, more than half of which lies below the tropic of Capricorn, has a wide variability in climatic regimes. For instance, in hyperarid William Creek, in South Australia, precipitation is 127 mm and potential evapotranspiration is more than 2,540 mm and potential evapotranspiration is 2,460 mm. In semiarid/subhumid Perth, in Western Australia, precipitation is 890 mm and potential evapotranspiration is 1,670 mm. In subhumid Sydney, in New South Wales, precipitation is 1,200 mm, and evapotranspiration exceeds 1,020 mm (Kendrew 1961). French (1987) has analyzed long-term series of annual rainfall for semiarid Georgetown, in north central South Australia, where the mean annual rainfall is 475 mm. Records from 1874 to 1985 show 20 drought events, i.e., a mean recurrence interval of 5.6 years.

Russian experience shows that over the past 1,000 years, catastrophic droughts have occurred with a frequency of 8-12 per century (every 10 years on the average). In Kazakhstan which is mostly hyperarid and arid (Zonn et al. 1994), around 35 severe droughts have occurred in the last 100 years, i.e., every 3 years on the average. In the Ukraine, where climate and soils are more favorable for agricultural production, droughts affect the area every 4-5 years (Kogan 1997).

Ponce (1995a) hes documented the drought events in the drought polygon of northeastern Brazil during the twentieth century. The polygon contains a diversity of biogeographical regions, ranging from arid to semiarid to subhumid to humid. The data suggests a recurrence interval from 4 to 12 years, with an average value of about 10 years. The drought duration varied between 1 and 5 years.

Ponce (1995b) has reported that hydrological droughts in the Upper Paraguay river basin, in central western Brazil, recur every 28-30 years on the average and last 3-6 years. The mean annual precipitation in the Upper Paraguay river basin varies between 900 and 2,000 mm, with an average of 1,380 mm.

4.  CONCEPTUAL MODEL OF DROUGHT CHARACTERIZATION

Our conceptual model deals specifically with meteorological droughts lasting at least one year, with an emphasis on subtropical and midlatitudinal regions. Persistence is the property of a drought event to last more than one year. For a given drought event, intensity refers to the extent of the precipitation deficit. To determine drought intensity, the moisture deficiency is accumulated over the drought duration. Therefore, the longer the duration, the greater the intensity. Since dry periods are generally followed by corresponding wet periods, it follows that the recurrence interval is always greater than the duration. Thus, for meteorological droughts lasting at least one year, the recurrence interval is at least two years.

The preceding concepts of drought intensity and duration resemble those of Dracup et al.'s severity, duration, and magnitude, wherein magnitude is defined as the ratio of severity over duration (Dracup et al. 1980). In our case, intensity is akin to severity; therefore, intensity is equal to magnitude times duration.

A conceptual model works in the mean: i.e., it describes general trends and not necessarily specific events. It is meant to aggregate the deterministic and stochastic components of the precipitation anomalies. Its value is that it provides a conceptual framework for interpreting the regional variability of drought phenomena.

Given a drought year with precipitation P where P < P_ma, the precipitation deficiency may be classified into three types: (1) moderate, with P/P_ma = 0.75; (2) severe, with P/P_ma = 0.5; and (3) extreme, with P/P_ma = 0.25 (National Institute of Hydrology 1990). The writers define drought intensity as the ratio of the deficit (P_ma - P ) to the mean (P_ma). For a drought lasting more than one year, intensity is defined as the summation of the annual intensities:

Pma - P             I  =  ∑   __________                   Pma

(1)

in which I = drought-intensity index.

Therefore, average annual drought intensity is the total drought intensity divided by the duration. Average annual drought intensity has been referred to as drought magnitude by Dracup et al. (1980) and as run intensity by Frick et al. (1990).

The writers base their conceptual model of drought characterization on the following premises, amply supported by observations:

1. Drought duration varies across the climatic spectrum, reaching a maximum around the middle and decreasing toward the extremes.

2. Since drought intensity is directly related to duration, intensity also reaches a maximum around the middle of the climatic spectrum and decreases toward the extremes.

3. The drought recurrence interval increases gradually from the dry to the wet side of the climatic spectrum.

Table 1 summarizes the writers' conceptual model of drought characterization. For drought duration, the expected values vary between 1 and 6 years, with larger values toward the middle of the climatic spectrum (6 years), decreasing toward either extreme (1 year). The longer durations toward the middle of the climatic spectrum are due to greater interannual precipitation variability within the semiarid and subhumid regions. Within these regions, drought duration is likely to be the longest, approaching 4-6 years. The shorter durations toward both extremes of the climatic spectrum are justified because of smaller interannual precipitation variability. In superarid regions, variability is reduced because the precipitation amounts are small; in superhumid regions. variability is reduced because of the length of the rainy season, which approaches 12 months.

The drought recurrence interval varies between 2 years on the extreme dry side and about 100 years on the extreme wet side, increasing in an approximate geometric progression. Since recurrence interval decreases from wet to dry climates, and since it must always exceed duration, it follows that duration must decrease toward the dry side of the climatic spectrum (Table 1). Thus, in hyperarid regions, droughts are short and recur once every 2-3 years; in semiarid and subhumid regions, droughts are long and recur once every 6-25 years; in hyperhumid regions, droughts are short and recur once every 50-100 years.

5.  SUMMARY

The writers have formulated a conceptual model of drought characterization across the climatic spectrum, primarly suited to subtropical and midlatitudinal regions. The model estimates expected values of drought duration, intensity, and recurrence interval as a function of the ratio of mean annual precipitation to annual global terrestrial precipitation.

Drought duration varies between 1 and 6 years across the climatic spectrum, and reaches a maximum toward the middle. Intensity varies directly with duration, and recurrence interval increases approximately in a geometric progression, from 2 years on the extreme dry side to about 100 years on the extreme wet side. Comparison of the conceptual model with drought data from several countries throughout the world shows that the model may be suitable as a framework for drought analysis and planning.

APPENDIX.  REFERENCES