Drought Criteria Richard J. Heggen Department of Civil Engineering University of New Mexico, USA rheggen@unm.edu Abstract Rainwater catchment is an anticipatory response to drought. Catchment design requires a prudent definition of target drought. Target drought might be a normal dry season, two rainless weeks, etc. Definition is by both duration and depth of precipitation. Target draught is often a balance drawn from past hydrologic history, consequences of rainwater catchment system failure, social implications and public acceptance. Most of the numerous drought indices are inappropriate as catchment performance targets. This paper briefly reviews drought definitions and suggests an analysis for identifying proper rainwater catchment design criteria. Analysis must anticipate the variety of meteorological futures that a catchment might experience. Stochastic analysis improves understanding of probable catchment behavior and the risks associated with alternative catchment designs. Drought Duration Depth Frequency analysis allows the time step for which a system is sized to be matched to the duration of drought. An example illustrates such assessment. Types of Drought Drought differs from aridity, a permanent feature of low rainfall. Drought is a deviation from the long-term balance between precipitation and evapotranspiration. Deviation can be an issue of magnitude, timing (e.g., delay in the start of the rainy season) or effectiveness of precipitation (e.g., number of rainfall events). Climatic factors such as high wind can aggravate drought impact. Meteorological Drought is defined on the basis of the degree and duration of dryness compared to some normal state. Some definitions identify periods by the number of days with precipitation less than some threshold. Other definitions relate deviations on monthly, seasonal, or annual time scales. Hydrological Drought is associated with the effects of precipitation shortfall on water supply. Frequency and severity are often defined on a river basin scale. Precipitation deficiency may result in a rapid depletion of soil moisture, but the impact of this deficiency on reservoir levels may not be noted for many months. Although climate is a primary contributor to hydrological drought, factors such as land use and the construction of dams also affect basin hydrology. Because hydrologic systems often interconnect regions, hydrological drought may extend beyond the borders of meteorological drought. Agricultural Drought links meteorological or hydrological drought to agricultural impact. Agricultural drought accounts for the variable susceptibility of crops from emergence to maturity. Deficient topsoil moisture at planting may hinder germination, leading to reduction of final yield. If topsoil moisture is sufficient for early growth requirements, however, deficiencies in subsoil
moisture at this early stage may not affect final yield if subsoil moisture is replenished during the growing season. Socioeconomic Drought associates the supply and demand of economic goods with elements of meteorological, hydrological, and agricultural drought. Socioeconomic drought depends on characteristics of supply and demand. The supply of such economic goods as water, forage and hydroelectric power depends on weather. Water supply is thus ample in some years but unable to meet human and environmental needs in others. Socioeconomic drought occurs when the demand for an economic good exceeds supply as a result of a weather-related shortfall in water supply. Indices of Drought Palmer Drought Severity Index (PDSI) is a meteorological estimate of soil moisture departure from normal conditions in response to abnormally dry or wet weather. PDSI uses precipitation and temperature data, as well as the local Available Water Content (AWC) of the soil. A basic water balance is determined, including evapotranspiration, soil recharge, runoff, and moisture loss from the surface layer. Human impacts are not considered. PDSI criteria determines when a drought or a wet spell begins and ends. An abnormally wet month in the middle of a long-term drought has little impact on PDSI. A series of months with near normal precipitation following a serious drought does not necessarily signal that the drought is over. PDSI calculates three intermediate parallel indices. If the probability that a drought is over is 100 percent, one index is used. If the probability that a wet spell is over is 100 percent, another index is used. If the probability is between 0 and 100 percent, the third index is employed. When conditions change from dry to normal or wet, the drought measured by PDSI ends without considering longer-term hydrologic impacts. PDSI is typically calculated on a monthly basis. Table 1 illustrates PDSI values. Table 1. PDSI Classification > 4.00 Extremely wet 3.00 to 3.99 Severely wet 2.00 to 2.99 Moderately wet 1.00 to 1.99 Mildly wet 0.50 to 0.99 Incipient wet spell 0.49 to -0.49 Near normal -0.50 to -0.99 Incipient dry spell -1.00 to -1.99 Mild drought -2.00 to -2.99 Moderate drought -3.00 to -3.99 Severe drought < -4.00 Extreme drought PDSI provides a standard for comparisons between locations and between months. A -4.0 in Brazil has the same meaning in terms of the moisture departure from a climatological normal as a -4.0 in California. Drawbacks include sensitivity to AWC of a soil type, conceptual simplification of soil horizons, exclusion of snow and frozen ground, non-consideration of the natural lag between
precipitation and runoff, the estimate of potential evapotranspiration, and its inappropriateness over large topographic variations. Modified Palmer Drought Severity Index (PMDI) differs from the PDSI during transition periods between dry and wet spells. PMDI weights the wet and dry index terms by probability. PMDI and PDSI are the same during an established drought or wet spell, but differ during transition periods. Palmer Hydrological Drought Index (PHDI) is a near-real time hydrological index of soil moisture based on moisture inflow (precipitation), outflow, and storage, without regard to the long-term trend. PHDI numeric values correspond to the meanings of PDSI. Palmer Z Index (ZNDX) measures moisture anomaly. The Z statistic indicates departure from normal monthly PDSI. ZNDX responds to a month of above-normal precipitation, even during periods of drought. Table 2 compares PHDI and ZNDX values. Table 2. PHDI and ZNDX Classification Cumulative Frequency Percent PHDI ZNDX > 96 > 4.00 > 3.50 Extremely wet 90 to 95 3.00 to 3.99 2.50 to 3.49 Severely wet 73 to 89 1.50 to 2.99 1.00 to 2.49 Mildly to moderately wet 28 to 72-1.49 to 1.49-1.24 to 0.99 Near normal 11 to 27-1.50 to -2.99-1.25 to -1.99 Mild to moderate drought 5 to 10-3.00 to -3.99-2.00 to -2.74 Severe drought < 4 < -4.00 < -2.75 Extreme drought Surface Water Supply Index (SWSI) is computed with snowpack, precipitation, and reservoir storage inputs in the winter. During the summer, streamflow replaces snowpack as a component. Monthly data are summed for precipitation, reservoir, snowpack and streamflow stations. Long-term frequency analysis yields the normalized nonexceedence probability for each component. Component are weighted depending on contribution to surface water and summed. SWSI is centered at zero and has a range between -4.2 and +4.2. SWSI is simple to calculate and gives a representative regional indication of surface water supplies. Adding or dropping stations requires new frequency determinations. Changes in water management, such as flow diversions or new reservoirs, require redeveloped weights. Thus, it is difficult to maintain a homogeneous record. Extreme events beyond the historical time series also cause problems. Standardized Precipitation Index (SPI) is the number of standard deviations that the observed precipitation deviates from the long term mean, assuming normal distribution. SPI can be compared across regions with markedly different climates. Since precipitation is not normally distributed, an appropriate transformation is required. Crop Moisture Index (CMI) is a meteorological monitor of week-to-week crop conditions. CMI was developed from procedures within the PDSI. Whereas PDSI monitors longterm meteorological wet and dry spells, CMI evaluates short-term moisture conditions. CMI is based on the mean temperature and total precipitation for each week as well as CMI of the previous week. CMI s rapid response to changing conditions may provide misleading
information about the long-term. CMI typically begins and ends each growing season near zero, preventing CMI use in droughts extending over several years. Percent of Normal Precipitation (PNP) is one of the simplest measurements of rainfall for a location. PNP can be calculated for a variety of time scales but can be used for a single region or a single season. PNP comparison implies that the mean and median are the same. PNP is easily misunderstood and may give different indications depending on location and season. Deciles divide precipitation occurrences over a long term into ten percent groupings. The first decile is the rainfall amount not exceeded by the lowest 10 percent of the precipitation occurrences. The fifth decile is the median. The decile method is simple to calculate, and requires less data and fewer assumptions than the PDSI. National Rainfall Index (NRI) compares precipitation abnormalities on a continental scale. NRI is calculated for a country by taking a national annual precipitation average weighted according to long-term averages of all stations. Because NRI is weighted by annual rainfall, stations in wetter areas have a greater influence. NRI is independent of absolute amounts of localized rainfall. A frequency distribution of NRI allows historical comparisons not possible with PNP. If the record is not complete for an individual station, NRI can be calculated without that station. Dependable Rains (DR) are rainfall occurring in four of every five years. The relationship of the DR to the mean may reflect characteristics of annual precipitation across a continent. Near the Sahara, DR is approximately 40-50 percent of the annual mean, while in the 700-800 mm precipitation zone DR is about 80 percent of the mean. Keetch-Byram Drought Index (KBDI) is a soil/duff index based on a soil capacity of 20 mm of water. KBDI factors are maximum daily temperature, daily precipitation, antecedent precipitation, and annual precipitation. As noted in Table 3, KBDI is used for wildfire management. Table 3. KBDI Classification 0 to 200 Soil moisture and large class fuel moistures are high and do not contribute to fire intensity. Typical of spring dormant season. 200 to 400 Typical of late spring, early growing season. Lower litter and duff layers are drying and beginning to contribute to fire intensity. 400 to 600 Typical of late summer, early fall. Lower litter and duff layers burn actively. 600 to 800 More severe drought with increased wildfire occurrence. Live fuels expected to burn actively at these levels. Drought Duration Depth Frequency (DDDF) analysis is akin to the Precipitation Duration Depth Frequency (PDDF) analysis common in hydrology. DDDF shows the historic relationship of average precipitation, duration and probability at the bottom end of the distribution. DDDF is obtained by stepping through m consecutive days of precipitation record, counting the number of n-day series in which precipitation equals or exceeds a given proportion of the long-term average. A string of m days yields m-n comparisons. The results plots as a cumulative distribution. Fig. 1 illustrates DDDF drought definition for Albuquerque, NM, USA. The record is 47 years and n varies from 2 to 90 days
Figure 1. Drought Duration Depth Frequencies, Albuquerque, NM Fig. 1 indicates 100a 30 percent chance of all of the following: Average less than 20 percent of mean daily precipitation in 20 consecutive days. Average less than 30 percent of mean daily precipitation in 26 consecutive days. Average less 80 than 40 percent of mean daily precipitation in 36 consecutive days. Average less than 50 percent of mean daily precipitation in 68 consecutive days. Percent of Mean Daily Precipitation Rainwater Catchment 60 Drought Criteria Nonexceedence Probability A rainwater catchment system (RWCS) is designed to harvest some percent 0.60 of mean daily precipitation. 40 The percentage is less than 100 if some rainfall spills from the cistern 0.50 on occasion. RWCS failure is when the target water supply cannot be supplied. (It should be 0.40 emphasized that failure by this definition is usually successfully withstood in a socioeconomic sense. 0.30 A RWCS is 20 often a component in a larger water resource system managed as a conjunctive 0.20 unit. Consumers anticipate having to ration and/or seek other water sources during drought conditions.) DDDF 0criterion allows RWCS design to balance risks at a socially acceptable level over both short and long terms for whatever percent of mean daily precipitation is targeted. In Fig. 1, receiving less than 0 40 percent 10 20 of mean 30 daily 40 precipitation 50 60 occurs 70 in 80 approximately 90 25 percent of all two-month periods. As droughts Consecutative are generally considered Days to be events significantly rarer than 1:4 odds, 60 days with 40 percent average precipitation is probably not perceived to be a drought. A socially reliable RWCS should be built large enough for this scenario. On the other hand, three months with only ten percent average rainfall has an extrapolated probability of something less than 0.10. The designer may not need to size the RWCS for this target, as users would not likely not expect full RWCS target supply in 9 out of 10 three-month periods. While the numeric 0.70
targets, both in terms of catchment yield and drought duration, will vary with applications, the concept of trying to target a prudent expectation is universal. The 47 years of record provides this case study some accuracy in anticipating the duration of extreme dry periods. Were only 10 years available, one would be less certain about the low 10 percent. For most RWCS, such certainty is not a critical issue. No RWCS design guarantees 100 percent reliability. Users learn that their cisterns may go dry, say, a third of the time if they do not ration or secure an alternative water source for the short term. With a realistic expectation of drought, consumption adjusts. DDDF drought criteria help identify when such adjustment is statistically warranted. Conclusions Criteria for drought serve many purposes. As RWCS design generally deals with meteorological abnormalities and human consumption, there is little cause to confuse the goals with agricultural or complex water balance criteria. DDDF requires only a record of historic rainfall and can address system behavior for duration and risk appropriate to RWCS needs. DDDF analysis anticipates how often a RWCS will fail to sustain a given rate of consumption. References Extensive information is electronically published on all referenced drought indices except the DDDF. www.epri.com/mecca/droughts.html enso.unl.edu/ndmc/enigma/def2.html nris.state.mt.us/wis/indices.html www.ncdc.noaa.gov/onlineprod/drought/readme.html For DDDF background, Heggen, R.J., 1993, Critical Events for Rain Water Catchments, Journal of International Rainwater Systems, 1:1, JIRCSA, 46-48