Palmer Drought Severity Index (PDSI)
Palmer (1965) developed a soil moisture algorithm (a model), which uses precipitation, temperature data and local Available Water Content (AWC) of the soil. AWC is effectively a "model parameter", which has to be set at the start of calculations. Calculations result in an index (PDSI), which indicates standardized moisture conditions and allows comparisons to be made between locations and between months. Details of PDSI calculation may be found in Palmer (1965) and in many subsequent publications (e.g. Alley, 1984; Kim et al, 2002). A summary is also given in PDSI calculation procedure.
PDSI varies roughly between -6.0 and +6.0. More wet conditions are indicated by positive values of PDSI, more dry - by its negative values. Thresholds for classification of different wetness are arbitrary. PDSI values between -2 and +2 would normally indicate normal conditions, although the sub-range of -1 to -2 could also be treated as mild drought. PDSI in values in the range of -2 to -3 are indicative of moderate drought, -3 to -4 points to severe drought and values less than -4 would be associated with extreme drought. Following Alley (1984), it could be suggested that because the PDSI values are non-dimensional, the value of -4.0 in southern Afghanistan should have the same meaning in terms of the moisture departure from a climatic normal as a -4.0 in the eastern Rajastan, India, for example. It may be argued that the extremity of a drought should be defined in clear engineering terms - in terms of its return period rather than in terms of Palmer's arbitrary thresholds. At the same time, using such thresholds may be much more appealing (compared to return period) to non-technical agencies.
PDSI values are normally calculated on a monthly basis. Further interpretation of monthly PDSI allows drought duration to be taken into account as well. A drought sequence is interpreted as a sequence of three or more consecutive months with a PDSI value <= -2.0. A series of six or more months is a major drought event. The end of a drought sequence is taken as the last month where the PDSI is <= -2.0.
The PDSI is widely used in the USA in drought management, planning and monitoring (http://drought.unl.edu). PDSI was used in South Africa (e.g. du Pisani, 1990; Bruwer, 1990), but was found to be a poor indication of short-term (i.e. periods of several weeks) changes in moisture status affecting crops and farming operations. Kogan (1995) suggested that PDSI had little acceptance elsewhere except USA.
Some of the limitations of PDSI (e.g. sensitivity to AWC, arbitrary thresholds, no account of river flow, liquid precipitation only etc.) may be overcome by appropriate modifications of the calculation procedures. However, PDSI values may lag emerging droughts by several months. This limits its application in areas of frequent climatic extremes, like southwest Asia, where large areas are dominated by monsoon climate, for example. Also, the major problem associated with using PDSI is that its computation is complex and requires substantial input of meteorological data. Its application in Asia, where observational networks are scarce, is therefore limited in principle.
Bhalme-Mooley Drought Index (BMDI)
BMDI is defined for a K month period as
Where ik = c1 i k-1 +coPk io= 0
is the monthly index, and Pk is the standardized precipitation amount for month k.
Pk =(pk –mk)/dk
Here, pk is the monthly precipitation with the mean of mk and standard deviation of dk . The two coefficients - c1 and c0 - can be estimated by assigning a value BMDI = -4 to severe historical droughts and proportionally higher values to normal conditions: BMDI = 0 (Bhalme and Mooley, 1980). Monthly moisture conditions can then be defined as in the Table below (drought part of the BMDI is italicized). BMDI may be considered as a simplified version of the PDSI. Nearly comparable performances of the simpler BMDI and PDSI have been shown in Olapido (1985) for the Great Plains of North America and by Farago et al. (1989) for the Hungarian Great Plain.
BMDI > 4 Extremely wet
4> BMDI > 3 Very wet
3> BMDI > 2 Moderately wet
2> BMDI > 1 Slightly wet
1> BMDI > -1 Near normal
-1> BMDI > - 2 Mild drought
-2> BMDI > - 3 Moderate drought
-3> BMDI > - 4 Severe drought
Crop Moisture Index (CMI) and other indices of soil moisture condition
The Crop Moisture Index (CMI), also developed by Palmer (1968), is a complement to the PDSI. It measures the degree to which crop moisture requirements are met, is more responsive to short-term changes in moisture conditions and is not intended to assess long-term droughts. CMI is normally calculated with a weekly time step, is based on the mean temperature, total precipitation for each week and the CMI value from the previous week. Each growing season, CMI typically begins and ends near zero. It is, in principle, possible to use a combination of PDSI and CMI for drought monitoring, where PDSI would serve as a long-term drought monitoring tool, whereas the CMI may indicate the progression of seasonal water shortages during a crop growing stage.
A number of other indices, which focus on soil water availability for crops, have been developed. As a rule, these methods calculate soil moisture balance with a 1, 5, 7 or 10-day time steps and then compute some integral measure (an index) which indicates the degree to which the crop water requirement have been met. These group of indices includes FAO water satisfaction index (Frere and Popov, 1979), Agro-hydropotential (Petrasovits, 1990), Index of Moisture Adequacy (IMA - Rao et al., 1981; Sastri, 1993), Moisture Availability Index (MAI -Heddinghaus, 1991). Tate et al (2002) lists some other similar indices. These indices are normally developed for the purpose of agro-meteorological crop monitoring and yield prediction.
Agro-Hydro Potential (AHP)
The AHP is the actual evapotraspiration of the crop (ETactual) divided by the optimal evapotranspiration of the same (EToptimal). According to Petrasovits (1984), this index shows to what degree an for how long a certain land can satisfy the water demand of a given plant. It is therefore good for the expression of the occurrence of drought and of the different levels of the water scarcity. More detailed explanations of the index can be found in Palfai et al. (1995). By definition, AHP varies between 0 and 1. The Table below explains the categorization of AHP.
|
AHP range |
Explanation |
|
1.0 - 0.8 |
the water scarcity of the plant stand is only theoretical, because the water supply to the plants is continuous and not limited |
|
0.8-0.5 |
the water demand satisfying ability of the area is still continuous, but it is getting increasingly restricted |
|
0.5-0.3 |
the water scarcity is becoming high, the water supply to the plants is periodical and restricting, there-fore water-stress develops |
|
< 0.3 |
strong water- stress occurs, causing considerable - biomass- and yield deficiency, and - when this stage lasts long - also the death of the plant. |
For the expression of drought severity, the number of days with water-stress can be determined. These are days when the AHP below 0.5 (which means that the water supply of the plants is only less than half of the water requirement). The larger the number of water-stress days is, the stronger the drought severity of the plant stand or the cultivated area is.
Standardized Precipitation Index (SPI)
SPI was developed in Colorado by McKee et al (1993), is based on the probability distribution of precipitation and requires less input data and calculation efforts then PDSI. A long-term precipitation record at the desired station is fitted to a probability distribution, which is then transformed into a normal distribution so that the mean SPI is zero (Edwards and McKee, 1997). SPI may be computed with different time steps (e.g. 1 month, 3 months,...48 months) and is reported to be able to identify emerging droughts sooner than Palmer Index. The use of different time scales under the umbrella of the same index allows the effects of a precipitation deficit on different water resources components (groundwater, reservoir storage, soil moisture, streamflow) to be assessed. A summary of calculations is given in SPI calculation procedure.(download from Colorado Climate Center web site).
Positive SPI values indicate greater than median precipitation and negative values indicate less than median precipitation. Similarly to the PDSI, SPI may be used for monitoring both dry and wet conditions. The “drought” part of the SPI range is arbitrary split into “near normal” conditions (0.99 < SPI <-0.99), moderately dry (-1.0 < SPI < -1.49), severely dry (-1.5 < SPI <-1.99) and extremely dry (SPI < -2.0). A drought event starts when SPI value reaches -1.0 and ends when SPI becomes positive again. The positive sum of the SPI for all the months within a drought event is referred to as “drought magnitude”.
SPI to date is finding more applications in southwest Asia than other drought indices due to its limited input data requirements, flexibility and simplicity of calculations.
Effective Drought Index (EDI)
Unlike many other drought indices, the EDI in its original form (Byun and Wilhite, 1999) is calculated with a daily time step. EDI is a function of precipitation needed for a return to normal conditions (PRN). PRN is precipitation, which is necessary for the recovery from the accumulated deficit since the beginning of drought. PRN, in turn, effectively stems from daily effective precipitation (EP) and its deviation from the mean for each day. Details are summarized in EDI calculation procedure.
Similarly to SPI, EDI values are standardized, which allows drought severity at two or more locations to be compared with each other regardless of climatic differences between them. EDI varies in the range from -2 to 2. Similarly to PDSI and SPI, it has thresholds indicating the range of wetness - from extremely dry to extremely wet conditions. The "drought range" of EDI indicates extremely dry conditions at EDI < - 2,severe drought at -1.5 < EDI < 1.99 and moderate drought at -1 < EDI < -1.49. Near normal conditions are indicated by - 0.99 < EDI < 0.99.
EDI as the measure of drought has been suggested recently and has not yet received much attention in the context of southwest Asia. It is, in principle, applicable for drought monitoring over large regions. Moghaddasi et al (2003) used EDI for regional drought assessment in one of the provinces of Iran. The major problem associated with EDI is that it is based on daily precipitation data. These data, although they naturally exist, are much less readily available from government agencies in the region at present. At the same time the EDI may similarly be calculated using monthly step data. It is logical and appealing to test EDI performance (compared to other drought indices) if monthly precipitation data are used as input.
Surface Water Supply Index (SWSI)
This index was developed in Colorado (Shafer and Dezman, 1982) and is adopted by several American states (Oregon, Montana, Idaho, and Utah), where snow forms a large component of water balance. SWSI integrates reservoir storage, streamflow and two precipitation types (snow and rain) at high elevations into a single index number. SWSI is expressed as
where a, b, c, and d = weights for snow, rain, streamflow and reservoir storage respectively.( a + b + c + d = 1) and Pi = the probability (%) of non-exceedence for each of these four water balance components. Calculations are performed with a monthly time step. In winter months, SWSI is computed using snowpack, precipitation and reservoir storage. In summer - streamflow, precipitation and reservoir storage data are used. For each month, the values of each component measured at all stations (or reservoirs) across the region/basis are summed. Each sum is normalized and its non-exceedence probability is determined. Weights are assigned to each water balance component depending on its typical contribution to surface water within a basin. Subtracting 50 and dividing by 12 are the normalization procedures designed to make SWSI values to have a similar range as PDSI (-4.2 to +4.2).
SWSI is relatively easy to calculate and it gives a representative measure of water availability across a river basin or selected region/province. It is however unlikely that it could be successfully used for large regions with significant spatial hydrological variability: the weights may differ substantially from one part of the region to another (e.g. Doesken et al., 1991). If the measurements at any station are discontinued, observations on one or more components are interrupted and new frequency distributions need to be calculated. Similarly, new dams or diversions in the basin/region will require modification of weights for each water balance component. It is therefore difficult to maintain a homogeneous time series of SWSI (Heddinghaus and Sabol, 1991). In addition, extreme events may cause a problem: if they have not been recorded previously, a frequency distribution of a relevant component needs to be revisited. This may be a serious limitation for the use of SWSI over the entire region of Southwest Asia, which hosts a variety of climates - from the monsoon-dominated areas to arid zones with limited lengths of historical hydrometeorological time series.
More information on SWSI may be found in Doesken et al. (1983, 1991). These reports are available on-line at http://ccc.atmos.colostate.edu/pdfs/climo_rpt_91-3.pdf or http://ccc.atmos.colostate.edu/pdfs/climo_rpt_83-3.pdf.
A modification of SWSI is known as Reclamation Drought Index (DI), used in Oklahoma, USA, as part of their drought management plan (as a trigger for drought relief funds). It is calculated similarly to SWSI, but also includes a temperature-based demand component. The RDI range and thresholds are similar to those of PDSI and SWSI. Normal to mild drought occurs when RDI values are 0 to - 1.5, moderate drought - of RDI is within - 1.5 to - 4.0. If RDI is less than -4.0 the drought is severe. The similarity between RDI and SWSI implies that RDI also has similar limitations, although RDI may be adapted to any region as it takes into account both climate and water supply factors. There is no indication to date that SWSI or RDI have been used for drought monitoring anywhere within the region of Southwest and South Asia.
Deciles
In this approach suggested by Gibbs and Maher (1967) monthly precipitation totals from a long-term record are first ranked from highest to lowest to construct a cumulative frequency distribution. The distribution is then split into ten parts (tenths of distribution or deciles). The first decile is the precipitation value not exceeded by the lowest 10% of all precipitation values in a record, the second is between lowest 10 and 20% etc. Any precipitation value (e.g. from current or past month) can be compared with and interpreted in terms of these deciles. A reasonably long precipitation record (30-50 years) is required for this approach. This is not a shortcoming of a method, but rather a requirement of a statistical analysis. Decile Indices (DI) are grouped into five classes, two deciles per class. If precipitation falls into the lowest 20% (deciles 1 and 2), it is classified as "much below normal". Deciles 3 and 4 (20 to 40%) indicate "below normal" precipitation, deciles 5 and 6 (40 to 60%) give "near normal" precipitation, 7 and 8 (60 to 80%) - "above normal" and deciles 9 and 10 (80 to 100%) are "much above normal". DI is relatively simple to calculate, requires only precipitation data and fewer assumptions than more comprehensive indices (like PDSI or SWSI).
Deciles are widely used in Australia (Coughlan, 1987; Smith et al., 1993) to trigger drought relief programs. The method has been tested in Southwest Asia (Moghaddasi et al, 2003; PMD, IMD) and may be appropriate for the condition of this region if a set of representative meteo stations with long and good quality records is identified.
Percent of normal and other rainfall deficiency indices
These indices are simple by definition, easy to calculate and are easily understood by general audience. "Normal" may be and usually is set to a long-term mean precipitation value. It may be calculated for a day, a month, a season or a year and is considered to be 100%. The same percent of normal may have different specific impacts at different locations and therefore it is a bit of a simplistic measure of precipitation deficit. Also, what is normal, may be perceived differently in different regions.
There are multiple definitions of a drought based on the percent or a proportion of normal. Bates (1935) suggested to define droughts in USA when annual precipitation is 75% of normal or monthly precipitation is 60% of normal. Hoyt (1936) used less than 85% of normal threshold for any time step. Banerji and Chabra (1964) considered severe drought conditions in the State of Andhra Pradesh, India to be coincident with seasonal rainfall deficit of more than 50% (which means rainfall of less than 50% of normal). Ramdas (1950), also in India, considered a drought to arrive when actual rainfall for a week is half of normal or less. Another definition from India suggests that annual rainfall < 75% of the average may be regarded as a drought (Clarke, 1991). If so defined, about 13% of Indian territory is in a drought every three 3 years on average. Droughts in South Africa are defined as periods with less than 70% of normal precipitation. This becomes a disaster or severe drought when two consecutive seasons experience 70% of normal rainfall or less (Bruwer, 1990). There are many other similar indices and associated drought definitions. They are normally region-specific and explicitly set locally appropriate rainfall limits and duration of rainless periods for the definition of droughts of different extremity.
Drought indices derived from flow data
Most of the indices described above are derived from the meteorological observations (precipitation (primarily) and temperature). These data are normally readily available throughout the world (compared to other data types) which partially explains the variety of such indices and the general popularity of this approach. Droughts may also and should, wherever possible, be assessed and monitored using other types of data (e.g. river flow).
In river hydrology, droughts are often referred to as periods of low flow. International glossary of hydrology (WMO, 1974) defines low flow as a flow of water in a stream during prolonged dry weather.
This definition does not make a clear distinction between low flows and droughts. Low flows are a seasonal phenomenon, and an integral component of a flow regime of any river. Drought, on the other hand, is a natural event, which results from less than normal precipitation for an extended period of time and affects more than just river flow. Drought is therefore a more general phenomenon, and may be characterized by more factors than just low flows. Droughts include low-flow periods, but a continuous seasonal low-flow event does not necessarily constitute a drought, although many researchers refer to a continuous low flow period in one year as an "annual drought" (e.g. Selenhasic and Salvai, 1987; Clausen and Pearson, 1995; Tallaksen et al, 1997).
The review of low-flow analyses and indices may be found in Smakhtin (2001) and is not repeated here. Some of these analyses focus on the frequency of flow minima or on how fast the flow in a river recedes in the absence of rain. Others, like flow duration curves, are somewhat similar to the already mentioned deciles. As a rule, these analyses do not allow the start and end of dry periods to be determined directly. In the drought context, the most relevant type of hydrological analyses is, perhaps the analysis of continuous periods during relevant type of hydrological analyses is, perhaps the analysis of continuous periods during which a flow in a river stays below some pre-defined threshold(s) (often referred to as reference discharge or truncation level). These periods are known as "spells", or "runs" (Yevjevich, 1967; IH, 1980; Dracup et al. , 1980; Zelenhasic and Salvai, 1987; Bonacci, 1993).
The spell or run analysis may be performed on data with any temporal resolution from daily (Zelenhasic and Salvai, 1987) to annual (Sen, 1980). A number of consecutive time intervals where the selected flow variable (a discharge or flow volume) has lower values than a reference flow level indicate the duration of a drought event. For each such event, the sum of deviations of a flow variable from the reference level represents the cumulative flow deficit amount (drought severity). This deficit divided by the duration is the measure of drought intensity. After all drought events in the available flow time series are identified and their characteristics are calculated, a frequency analysis is performed on them. This analysis allows the return periods of these drought characteristics to be estimated. The procedure may be repeated for different reference discharges.
From the water resources management perspective, it is important to define the reference flow levels and indicators of drought severity (what drought duration and/or flow deficit constitutes mild or severe drought). While these indicators would normally differ from region to region, some existing definitions of water shortages may serve as a starting point (Dracup, 1980).
-
A deep shortage - when annual runoff is lower than the mean, by at least one standard deviation.
-
A continuous shortage - when annual volumes are lower than the mean, during at least 4 consecutive years.
-
An extended shortage - when a deep or continuous shortage extends over the entire region under consideration.
The same threefold definition approach may be modified and extended to the attempts to define drought using data with temporal resolution smaller than 1 year.
Apart from the river flow, reservoir storage is also a useful indicator of water shortages, due to data availability often on a daily or weekly basis. At the same time, these data are strongly influenced by the reservoir operation rules. Also, drought may be defined in terms of the differences between water supply and water demand time series. The supply time series may be represented by a river flow and the demand time series - by the demand of a particular user (e.g. irrigation) or by the total demand of all users. When demand exceeds supply, the water shortages occur, which represent the start of a drought. Tate et al (2000) provide examples on supply-demand issues related to reservoir operations, while Smakhtin (2001) lists multiple other references on the topics of low-flow spell and storage-yield analyses.
The analysis of river flow data for any purpose, including drought management is however often hampered by the lack of such data, shorter records available (compared to rainfall, for example), artificial influences (e.g. catchment land-use change, effluents, abstraction), etc. In addition, in the context of Southwest Asia, flow data are often of poor quality and are not easily available from relevant authorities, at least at present. Drought indices and definitions based solely on flow or reservoir storage are normally designed for reservoir operation and are seldom (if at all) used as triggers for drought relief, or for drought monitoring over vast territories. As has been shown above, some general indices of water availability (e.g. SWSI) explicitly include reservoir storage and river flow time series available in a region into calculations.
DROUGHT-RELATED INIDICES DERIVED FROM REMOTE SENSING DATA
Several indices, which could be used, amongst the others, for drought monitoring, have been developed over the past few decades using remote sensing data. They are calculated from the reflectance in different bands and may be obtained for each pixel (the size of a pixel depends upon the resolution of a sensor). These indices have a few advantages over conventional climate-data related indices described above, as they "cover" large areas and may show how drought is progressing over the area. While this is particularly important in data scarce regions, such indices may not be sensitive actual meteorological conditions on the ground and are not the direct measures of drought conditions. They have to be "calibrated" against available ground climate data. Some of these indices may have lagged vegetation response to drought.
Normalized difference vegetation index (NDVI).
NDVI is calculated as
Where 
is the reflectance in the near infra-red & red bands respectively.NDVI ranges form -1 to 1. (Jordan, 1969; Deering, 1978;Tucker,1979).
Drought severity may be evaluated as the difference between the NDVI for the current month (e.g. January 2003) and a long-term mean NDVI for this month (e.g. a 20-year long mean NDVI for January).
Where NDVIi is the current NDVI for month i and NDVImean,m is the long-term mean NDVI for a calendar month m (m = 1,2,..12). Positive departure (difference) from the mean NDVI indicates that the vegetation condition is better than normal in this month (wetter month than usual). Negative departure from the mean NDVI points to months, which are dryer than usual.The more negative the departure the drier is the month.
Enhanced vegetation index (EVI)
The enhanced vegetation index (EVI) was developed by Huete et al. (2002) for use with MODIS data. Unlike NDVI, it takes the advantage of multiple bands. The EVI is calculated as:
The coefficients adopted in the EVI algorithm are, L=1, C1 = 6, C2 = 7.5, and G (gain factor) = 2.5. EVI is more sensitive in high biomass regions and ensures the improved monitoring through a reduction in atmosphere influences (Huete, 2002). At the same time, it is computationally intensive and is not widely used at present. EVI may be used in Drought Severity formula above.
Vegetation condition index (VCI)
This index was first suggested by Kogan (1995, 1997). It shows, effectively, how close is the current month's NDVI to the minimum NDVI calculated from the long-term record of RS images.
Where, 
and 
are calculated from the long-term record (e.g., 20 years) for that month (or week), and j is the index of the current month (week). The condition (health) of vegetation presented by VCI is reported in percent and may serve as an approximate measure of how dry the current month is. In the case of extremely dry month, the vegetation condition is poor and the VCI is close or equal to zero. The VCI of 50% reflects a fair vegetation condition. At optimal condition of vegetation the VCI is close to 100%. At this condition, NDVI for the current time step (month, week) is equal to NDVImax.
Temperature condition index (TCI)
The TCI was also suggested by Kogan (1995, 1997) and is calculated similarly to VCI. However, in contrast to the VCI, the TCI includes the deviation of the current month's (week's) value from the recorded maximum:
Where BT is the brightness temperature (e.g. AVHRR band 4. Under the atmospheric conditions, objects emit heat in this thermal band). The max and min values of BT are calculated from the long-term (e.g. 20 years) record of RS images for each calendar week or month j. The low TCI value (close to 0%) indicates the very high temperature in that month or week. Consistently low TCI values over several consecutive time intervals point to drought occurrence.
References to the cited liturature may be found under frequently cited sources.
Descriptions of more drought indices are added to this page occasionally. Please contact us with description of drought indices not yet included in this page.
