Abstract

Drought is a complex phenomenon that is difficult to accurately describe because its definition is both spatially variant and context dependent. Decision makers in local, state, and federal agencies commonly use operational drought definitions that are based on specific drought index thresholds to trigger water conservation measures and determine levels of drought assistance. Unfortunately, many state drought plans utilize operational drought definitions that are derived subjectively and therefore may not be appropriate for triggering drought responses. This paper presents an objective methodology for establishing operational drought definitions. The advantages of this methodology are demonstrated by calculating meteorological drought thresholds for the Palmer drought severity index, the standardized precipitation index, and percent of normal precipitation using both station and climate division data from Texas. Results indicate that using subjectively derived operational drought definitions may lead to over- or underestimating true drought severity. Therefore, it is more appropriate to use an objective location-specific method for defining operational drought thresholds.

1. Introduction

Drought is a complex phenomenon that is difficult to accurately describe because its definition is both spatially variant and context dependent. Therefore a uniform method for defining and monitoring drought conditions and quantifying the severity of drought does not exist. There are two main types of drought definitions: conceptual and operational. Conceptual definitions are formulated in general terms and they are used to help explain what a drought is. Operational definitions are very specific and they are used to identify the beginning, end, and degree of severity of a drought [see National Drought Mitigation Center (NDMC) site at http://www.drought.unl.edu]. Wilhite and Glantz (1985) identified more than 150 conceptual definitions of drought and classified these definitions into four categories: meteorological, agricultural, hydrological, and socioeconomic drought. The large number of conceptual drought definitions that exist illustrates the challenge of accurately describing drought and the lack of agreement in regard to drought definitions. Similar challenges exist when considering operational definitions of drought.

Developing appropriate operational drought definitions is extremely difficult since drought, unlike other natural hazards, has no definitive onset/end, is slow to evolve, and is regionally relative (Goodrich and Ellis 2006). However, the science behind defining and monitoring drought is at the center of the communication between stakeholders and policymakers. Failure to adequately define and monitor drought can have a significant negative impact, particularly if it fails to trigger a response (e.g., limiting water use) when one is sorely needed, or if it triggers a response when one is not required. There is very little discussion in the scientific literature regarding how drought indices should be used from an application standpoint to monitor drought and to trigger drought response (Goodrich and Ellis 2006). Because drought indices will be used by policymakers with little understanding of the mechanisms and flaws of each index, a certain level of standardization must be applied to limit the misleading or confusing message they may communicate to novice stakeholders.

Local, state, and federal agencies commonly use drought indices to monitor drought conditions and to communicate information about drought conditions to the private sector and public stakeholders. However, most drought indices were not specifically designed with this purpose in mind and they are commonly utilized in a variety of applications. For example, drought indices have been used in drought warning systems (Lohani and Loganathan 1997; Lohani et al. 1998), to calculate the probability of drought termination (Karl et al. 1987), to assess forest fire hazard and dust storm frequency (Cohen et al. 1992), to predict crop yield (Kumar and Panu 1997), to examine the spatial and temporal characteristics of drought, the severity of drought, and to make comparisons between different regions (Alley 1984, 1985; Dai et al. 1998; Kumar and Panu 1997; Nkemdirim and Weber 1999; Soule 1992). However, one of the most important uses of drought indices is for determining operational drought definitions, since these definitions are used to trigger water conservation measures and determine whether (and how much) drought assistance will be provided to affected regions (Wilhite et al. 1986).

More than 30 state drought plans were reviewed to identify the operational drought definitions that are currently being used within the United States. In most cases, states employ a single set of operational drought definitions for the entire state and these definitions have usually been developed using subjective criteria. The objective of this paper is to present a methodology for objectively determining operational drought definitions (or thresholds). The advantages of this methodology are illustrated by calculating meteorological drought thresholds for the Palmer drought severity index (PDSI), the standardized precipitation index (SPI), and percent of normal precipitation using data from six stations and 10 climate divisions in Texas.

2. Methods

a. Data

Three indicators of meteorological drought (percent normal, PDSI, and SPI) were evaluated at six Historical Climate Network (HCN) stations and the 10 climate divisions located in Texas (Fig. 1; Table 1). All of the stations have long (∼100 yr of data) and relatively complete precipitation records (<5% missing daily data). Most of the HCN stations began reporting data in the late 1890s and are continuing through the present. Missing data were replaced by applying the inverse weighting of the square difference method to neighboring HCN stations (McRoberts 2008). Daily temperature and precipitation data were aggregated to monthly values and these monthly data were used to calculate percent normal, PDSI, and SPI for the entire period of record for each station. Monthly climate division data (1895–2001) were obtained from the National Climatic Data Center (www.ncdc.noaa.gov). Data from each climate division represent an unweighted average of all representative stations within that division (Guttman and Quayle 1996). From 1895 to 1930, a regression technique was used to calculate the divisional averages based on available U.S. Department of Agriculture (USDA) statewide averages (Guttman and Quayle 1996). Thus, the pre-1930 climate division data should be treated with caution since the data cannot fully account for intrastate climatic variability. The climate division data are serially complete from 1895 to the present; however, only data from 1895 to 2001 were used to facilitate comparison with the HCN stations.

Fig. 1.

Mean annual precipitation (mm) and location of Texas climate divisions and six HCN stations.

Fig. 1.

Mean annual precipitation (mm) and location of Texas climate divisions and six HCN stations.

Table 1.

Location, record length, and percentage of missing data for the six HCN stations used in this study.

Location, record length, and percentage of missing data for the six HCN stations used in this study.
Location, record length, and percentage of missing data for the six HCN stations used in this study.

1) Percent normal

Percent normal is a simple method for comparing observed precipitation with normal precipitation for a particular location and time period. Observed precipitation is divided by normal (or mean) precipitation (usually based on 30 yr of data) and the result is expressed as a percentage. It can be calculated for any time scale of interest (e.g., day, week, month, season, year). For this study, monthly precipitation data were used to calculate percent normal.

2) PDSI

The PDSI and the Z index were both developed by Palmer (1965) and have been widely used in the scientific literature (Alley 1984; Karl et al. 1987). The PDSI and Z index are derived using a soil moisture/water balance algorithm that requires a time series of daily air temperature and precipitation data and information on the available water content (AWC) of the soil. Soil moisture storage is handled by dividing the soil into two layers. The top layer has a field capacity of 25 mm, moisture is not transferred to the second layer until the top layer is saturated, and runoff does not occur until both soil layers are saturated. Potential evapotranspiration (PE) is calculated using the Thornthwaite (1948) method and water is extracted from the soil by evapotranspiration when PE > P (where P is the precipitation for the month). Evapotranspiration loss from the surface layer of the soil (Ls) is always assumed to take place at the potential rate. It is also assumed that the evapotranspiration loss from the underlying layer of the soil (Lu) depends on the initial moisture conditions in this layer, PE, and the combined available water content in both layers.

The Z index is a measure of the monthly moisture anomaly and it reflects the departure of moisture conditions in a particular month from normal (or climatically appropriate) moisture conditions (Heim 2002). The first step in calculating the monthly moisture status (Z index) is to determine the expected evapotranspiration, runoff, soil moisture loss, and recharge rates based on at least a 30-yr time series. A water balance equation is subsequently applied to derive the expected or normal precipitation. The monthly departure from normal moisture (e.g., Z index) is determined by comparing the expected precipitation to the actual precipitation.

While both the Z index and the PDSI are derived using the same data, their monthly values are quite different. The Z index is not affected by moisture conditions in the previous month, so Z-index values can vary dramatically from month to month. On the other hand, the PDSI varies more slowly because antecedent conditions account for two-thirds of its value. Although the PDSI was designed to measure meteorological drought, it may be more appropriate as a measure of hydrological drought (Akinremi et al. 1996; Strommen and Motha 1987) and, according to Karl (1986), the Z index may be a better measure of meteorological or agricultural drought. It should be noted that although both the Z index and PDSI are strongly weighted by both precipitation and temperature anomalies (Hu and Willson 2000), most other meteorological indices [e.g., SPI, effective drought index (EDI), percent normal, and deciles] are calculated using only precipitation. Alley (1984), Karl (1986), and Guttman (1998) have completed detailed evaluations of the limitations of the PDSI and Z index. Their work, along with the work of other researchers, has been summarized by Heim (2002).

3) Standardized precipitation index

The SPI provides a simple and versatile method for quantifying moisture supply (McKee et al. 1993, 1995). The SPI is based on statistical probability and was designed to be a spatially invariant indicator of drought. To calculate the SPI one only needs precipitation data. The SPI can be calculated for any time period of interest. It is commonly calculated using 1-, 3-, 6-, 9-, 12-, and 24-month intervals. These time scales are appropriate for monitoring different types of drought (e.g., meteorological, agricultural, and hydrological). The SPI is spatially invariant (Guttman 1998; Heim 2002; Wu et al. 2007) so values of the SPI can readily be compared across time and space. Although the SPI can be calculated in all climatic regions (Heim 2002), it is important to note that arid regions, those that experience many months with zero precipitation, may be problematic for the SPI depending on which probability density function (PDF) is used to normalize precipitation (Wu et al. 2007). The SPI is easy to understand and interpret since its value is only based on precipitation and since it is reported in standard deviations away from the mean.

The SPI is influenced by the normalization procedure (e.g., PDF) that is used. Although the NDMC, Western Regional Climate Center (WRCC), and Greenleaf Project (greenleaf.unl.edu; previously known as the National Agricultural Decision Support System), all use the two-parameter gamma PDF to calculate SPI, this is not necessarily the best normalization procedure. Guttman (1999) analyzed six different PDFs (including the two-parameter gamma; the two-parameter gamma for which the parameters are estimated by the maximum likelihood method; the three-parameter Pearson type III; the three-parameter generalized extreme value; the four-parameter kappa; and the five-parameter Wakeby) and determined that the Pearson type III was the most appropriate PDF and the two-parameter gamma was ranked as the second best PDF for calculating SPI. Guttman (1999) concluded that because Pearson type III has three parameters it is more flexible in fitting precipitation data than the gamma PDF. Figure 2 compares 1-month SPI values calculated for Luling, Texas (415429), using the three-parameter Pearson type III and the two-parameter gamma PDFs. The results indicate that generally there is strong agreement between both methods (R2 = 0.987). The scatter of points is closely clustered around the perfect prediction line for SPI values between −1.5 and 2.0; however, outside of this range there is more scatter. Not surprisingly, the differences between the two PDFs are most apparent in the tails of the distribution. The relationship between the 1-month SPI values calculated using the three-parameter Pearson type III and the two-parameter gamma is similar at the other five HCN stations (results not shown) and the coefficient of determination at the six HCN stations ranges from 0.979 to 0.992.

Fig. 2.

SPI (1 month) calculated using Pearson type III (x axis) and two-parameter gamma (y axis) PDFs based on monthly precipitation data from Luling (n = 1224 months). Black line is the perfect prediction (1:1) line. Red line is the least squares line of best fit (equation shown on graph).

Fig. 2.

SPI (1 month) calculated using Pearson type III (x axis) and two-parameter gamma (y axis) PDFs based on monthly precipitation data from Luling (n = 1224 months). Black line is the perfect prediction (1:1) line. Red line is the least squares line of best fit (equation shown on graph).

When only the driest SPI values (<−1.5 using Pearson type III) are considered, the agreement between the two methods of calculating 1-month SPI values is much weaker for Luling (R2 = 0.543). Table 2 provides a comparison of the driest SPI values calculated using Pearson type III and two-parameter gamma PDFs based on monthly precipitation data for the six HCN stations. The coefficient of determination at the six HCN stations ranges from 0.339 to 0.620, the mean absolute deviation (MAD) ranges from 0.18 to 0.29, and the maximum deviation ranges from 0.69 to 1.45. These results indicate that SPI values are quite sensitive to the PDF that is used, particularly in the left tail of the distribution. In this study the Pearson type III PDF will be used to calculate the SPI and therefore the drought thresholds that are calculated in this study should not be generalized to SPI calculated with other PDFs.

Table 2.

Comparison of SPI values <−1.5 (based on Pearson type III) calculated using Pearson type III and two-parameter gamma PDFs based on monthly precipitation data from six HCN stations in TX.

Comparison of SPI values <−1.5 (based on Pearson type III) calculated using Pearson type III and two-parameter gamma PDFs based on monthly precipitation data from six HCN stations in TX.
Comparison of SPI values <−1.5 (based on Pearson type III) calculated using Pearson type III and two-parameter gamma PDFs based on monthly precipitation data from six HCN stations in TX.

b. Objective method for determining operational drought definitions

Goodrich and Ellis (2006) proposed an objective methodology for developing operational drought definitions for any drought index. They recommend fitting a parametric statistical distribution model, also referred to as a PDF, to the drought index data and then using preselected percentiles to determine the drought thresholds. Goodrich and Ellis (2006) used the five categories from the drought monitor (Svoboda et al. 2002) to classify drought (Table 3). This percentile-based methodology was also employed by Steinemann (2003). Our approach for objectively determining operational drought definitions differs from Steinemann (2003) and Goodrich and Ellis (2006) because they simply used the empirical distribution to determine drought thresholds while we have fit each drought index using the normal, gamma, lognormal, and exponential PDFs and then evaluated the goodness of fit using the Kolmogorov–Smirnov (KS) Lilliefors test. The PDF with the lowest KS value was then employed to determine the operational drought thresholds for each drought index. Our methodology is described in more detail below.

Table 3.

USDM drought definitions (Svoboda et al. 2002).

USDM drought definitions (Svoboda et al. 2002).
USDM drought definitions (Svoboda et al. 2002).

Fitting a PDF to the drought index data provides a method for estimating the relative frequency (rarity) of a given drought event based on the observed data (Husak et al. 2007). Precipitation is not normally distributed since it has a fixed lower boundary (e.g., zero) that produces a distribution that is positively skewed. There are a variety of distributions that have been recommended for fitting precipitation (drought) data, including gamma, lognormal, Pearson type III, and Box–Cox (Guttman 1999; Husak et al. 2007; Legates 1991; Wu et al. 2007). The gamma distribution is frequently used to represent precipitation because it can represent a variety of distribution shapes using only two parameters, the shape and the scale (Husak et al. 2007). One of the advantages of using the gamma distribution to represent precipitation is that it is bounded on the left by zero. This is important since negative precipitation is impossible. The gamma distribution is also positively skewed, so this matches precipitation. Finally, it is a very flexible distribution that can represent a variety of distribution shapes ranging from exponential decay (when shape ∼ 1) to nearly normal forms (when shape ∼ 20) (Husak et al. 2007).

Once a distribution is selected and the parameters are estimated, the ability of the distribution to approximate precipitation (drought) can be tested by comparing the fitted distribution (e.g., gamma) with the empirical distribution using the KS goodness-of-fit test. When the values being tested are the same as the values that were used to determine the distribution parameters, the test is known as the KS Lilliefors test (Husak et al. 2007). This test compares the cumulative distribution functions of the theoretical distribution (e.g., gamma) with the observed values and returns the maximum difference between the two cumulative distributions. If the maximum difference is large, then it means that the theoretical distribution is not adequately representing the observed precipitation (drought) at this location. The acceptable value for the KS statistic varies depending on the sample size and the rejection level chosen. In this study each drought index was fit using the normal, gamma, lognormal, and exponential distributions, and the PDF with the lowest KS value was then employed to determine the operational drought thresholds for each drought index.

3. Results

a. Existing operational drought definitions

Because there is no federal policy to address local water deficiencies (drought) within the United States, many individual states have developed their own methods for monitoring and responding to drought. There are currently 39 states that have some type of drought plan and 2 additional states (California and Florida) have delegated drought planning activities to local authorities (Fig. 3). According to the NDMC, there were only 9 states that lacked a drought plan as of October 2006 (Alabama, Alaska, Arkansas, Louisiana, Michigan, Mississippi, Tennessee, Vermont, and Wisconsin). The 33 state drought plans that were available in a digital format (http://www.drought.unl.edu/plan/stateplans.htm) were reviewed to identify which drought indices are most commonly used for monitoring drought and to determine the operational drought definitions (thresholds) that are used for triggering drought response measures.

Fig. 3.

Status of state drought planning activities as of October 2006 (http://www.drought.unl.edu/mitigate/status.htm).

Fig. 3.

Status of state drought planning activities as of October 2006 (http://www.drought.unl.edu/mitigate/status.htm).

The most commonly used drought indices are shown in Fig. 4. It is clear that most states are primarily interested in monitoring meteorological and hydrological/water supply drought since the most commonly used drought monitoring indices are reservoir levels, PDSI, precipitation, and streamflow. There appears to be fairly good agreement in regard to what data are most important for drought monitoring since these indices were specifically mentioned in the majority of the state drought plans that were reviewed. Some state drought plans also utilized indicators of agricultural drought such as soil moisture levels, crop moisture index (CMI), and a variety of vegetation/crop indicators.

Fig. 4.

Indices most commonly used for monitoring drought in state drought plans (based on 33 state drought plans).

Fig. 4.

Indices most commonly used for monitoring drought in state drought plans (based on 33 state drought plans).

There is less information in the state drought plans about the particular operational drought definitions that are being used to trigger drought response. Specific operational drought definitions were listed in only 13 of the 33 state drought plans that were reviewed. This number decreases further when considering a specific drought index such as the PDSI or SPI. Drought definitions based on the PDSI are reported in Table 4. It should be noted that the drought categories listed in Table 4 may not correspond to the drought categories that are used in all of the state drought plans. Most states (24 out of 33) use between three and five categories for classifying drought severity. This table was compiled by first matching the drought definitions (thresholds) used for the most extreme drought category. Then the second most severe drought thresholds were compared, followed by the third, and so on. This provides a means to compare the drought thresholds across states even though some of the states use a different number of categories and different category labels. The strong agreement between the state drought thresholds and those employed by the U.S. Drought Monitor (USDM) suggests that this is an appropriate approach (Tables 4, 5).

Table 4.

Drought definitions based on the PDSI as defined by the USDM and described in selected state drought plans.

Drought definitions based on the PDSI as defined by the USDM and described in selected state drought plans.
Drought definitions based on the PDSI as defined by the USDM and described in selected state drought plans.
Table 5.

Drought definitions based on the SPI as defined by the USDM and as described in selected state drought plans.

Drought definitions based on the SPI as defined by the USDM and as described in selected state drought plans.
Drought definitions based on the SPI as defined by the USDM and as described in selected state drought plans.

The strong agreement between states in regard to the operational drought definitions that they use is somewhat surprising given that these states are located in very different climatic regions (Table 4 includes states from the northeastern, central, southern, and Gulf Coast regions). If the PDSI were a spatially invariant indicator of drought, this would not be a serious problem. However, since the PDSI is known to be a spatially variant indicator of drought and since the probability of getting a particular PDSI value is a function of the climate, this means that it is impossible for these drought definitions to be appropriate for all (or perhaps any) of the states listed (Alley 1984; Guttman 1998; Guttman et al. 1992; Heim 2002).

According to Palmer’s classification, extreme drought is associated with a PDSI < −4.0. This threshold is being used by the majority of states listed in Table 4. Thus it appears that these definitions have been taken, almost without modification, from the thresholds defined by Palmer (1965). Palmer’s thresholds were subjectively developed using data from Iowa and Kansas and therefore they are not necessarily well correlated with drought impacts and should not be applied in other climate regions (Alley 1984). The use of Palmer’s subjective drought thresholds in state drought plans could lead to drought responses being triggered more (or less) frequently than intended.

Drought definitions based on the SPI are reported in Table 5. Although there are only four states listed in Table 5, it is apparent that there are similarities in the drought thresholds that are used. The operational drought definitions that are being used are similar to those proposed by McKee et al. (1993). Although the SPI is a standardized drought index that is more spatially invariant (consistent) than the PDSI, using a single set of operational drought definitions can still create problems for some climates. For example, arid regions that experience many months with zero precipitation may have difficultly standardizing the SPI depending on which PDF is used to normalize precipitation (Wu et al. 2007). SPI is also influenced by the length of the precipitation record and by the PDF that is being used to standardize the precipitation. Therefore, even though SPI thresholds are based on event probability and therefore have some scientific (and practical) merit, they also should be selected with care to make sure that they are appropriate for classifying drought in the region of interest.

It appears that none of the state drought plans that published their drought thresholds utilized an objective methodology for selecting these operational drought definitions. Instead it seems that, at least for the PDSI and SPI, most states either adopted the drought thresholds described in the literature or used other subjective means to establish them.

b. Objective operational drought definitions for Texas

1) Percent normal

Percent normal data for six HCN stations and 10 Texas climate divisions were fit using the normal, gamma, lognormal, and exponential distributions. The KS Lilliefors test was applied to evaluate how well these distributions fit the percent normal data (Table 6). The gamma distribution provided the best fit for all of the climate divisions and for the majority of HCN stations and therefore the gamma PDF was used to calculate objective operational drought definitions for the five drought classes employed by the USDM (ranging from abnormally dry to exceptional drought) (Table 7). These drought thresholds vary significantly over the state. This is not surprising given that Texas is a large state that has a strong east–west precipitation gradient. Climate divisions (and stations) located in drier locations had lower thresholds than stations in wetter locations. For example, based on the objective drought thresholds, moderate drought (D1) is associated with 7.60% of normal precipitation in west Texas (climate division 5) and 17.88% of normal precipitation in northeastern Texas (climate division 4), extreme drought (D3) is associated with 2.36% of normal precipitation in west Texas (climate division 5) and 10.84% of normal precipitation in northeastern Texas (climate division 4), and exceptional drought (D4) is associated with 1.06% of normal precipitation in west Texas (climate division 5) and 7.88% of normal precipitation in northeastern Texas (climate division 4). These large spatial differences in drought thresholds typically exceed the differences between drought categories. For example, 10% of normal precipitation would be categorized as abnormally dry (D0) in west Texas and severe drought (D2) in northeastern Texas. Of course these thresholds are only appropriate for dealing with 1-month precipitation and they would change if a different accumulating time period (e.g., 3 months, 12 months) was used.

Table 6.

KS statistic for percent normal after being fit using gamma, normal, lognormal, and exponential PDFs.

KS statistic for percent normal after being fit using gamma, normal, lognormal, and exponential PDFs.
KS statistic for percent normal after being fit using gamma, normal, lognormal, and exponential PDFs.
Table 7.

USDM drought thresholds for percent normal calculated using the gamma distribution.

USDM drought thresholds for percent normal calculated using the gamma distribution.
USDM drought thresholds for percent normal calculated using the gamma distribution.

It is interesting to note that while the drought thresholds for the six HCN stations also increase from west to east, they differ significantly from the climate division thresholds. Generally the drought thresholds for the HCN stations are ∼1%–2% lower than the severe (D2), extreme (D3), and exceptional (D4) drought thresholds for the climate divisions and they are about 2% higher for the abnormally dry (D0) thresholds. These differences arise because stations measure precipitation at a point, while the climate divisions use a mean areal estimate of precipitation. The drought thresholds at the stations are lower because of the spatial heterogeneity of precipitation. This means that there is a greater likelihood that precipitation at a point will be lower (or higher) than it is for precipitation for a whole climate division. The differences between the station and climate division thresholds may not be large, but they correspond to a one-category difference in drought classification. For example, the severe drought (D2) and extreme drought (D3) thresholds for Crosbyton, Texas (412121), are 3.04% and 1.44% while the severe drought (D2) and extreme drought (D3) thresholds for climate division 1 are 5.76% and 3.48%. Therefore if observed precipitation was 3% of normal it would be classified as severe drought if the station-based drought thresholds were used and extreme drought if the climate division–based thresholds were used.

There are also significant differences from station to station, even when they are located in the same climate division. For example, Llano (415272) and Boerne (410902), Texas, are both located in climate division 6, but the difference between their drought thresholds varies from 2.48% (D0) to 0.52% (D4). These differences are primarily due to the fact that Boerne is in a slightly wetter location than Llano, but differences in record length and missing data can also have an influence.

Overall there is a significant variation in the percent normal drought thresholds across Texas as well as between stations and climate divisions. These differences suggest that using a single drought threshold for the state is inappropriate and that drought thresholds for percent normal should be calculated separately for each spatial scale of interest (e.g., stations, counties, and climate divisions).

2) PDSI

PDSI data for six HCN stations and 10 Texas climate divisions were fit using the normal, gamma, lognormal, and exponential distributions. The KS Lilliefors test was applied to evaluate how well these distributions fit the PDSI data (Table 8). Since the normal distribution fits the PDSI data best at all six stations and the majority of climate divisions, the normal PDF was used to determine the objective operational drought thresholds for the five USDM drought classes (Table 9). It is evident that the drought thresholds are not consistent across Texas. The station-based drought thresholds for abnormally dry conditions (D0) varied from −1.30 to −1.70, the thresholds for moderate drought (D1) varied from −1.90 to −2.50, the thresholds for severe drought (D2) varied from −2.90 to −3.50, the thresholds for extreme drought (D3) varied from −3.70 to −4.30, and the thresholds for exceptional drought (D4) varied from −4.50 to −5.10. The climate division–based drought thresholds for abnormally dry conditions (D0) varied from −1.09 to −1.49, the thresholds for moderate drought (D1) varied from −1.75 to −2.22, the thresholds for severe drought (D2) varied from −2.73 to −3.27, the thresholds for extreme drought (D3) varied from −3.40 to −4.16, and the thresholds for exceptional drought (D4) varied from −3.99 to −5.08. Unlike for percent normal, these spatial variations in drought thresholds are not solely controlled by aridity. There is some tendency for the PDSI drought thresholds to be lower in drier climates and higher in wetter climates, but this only holds for the D0 and D1 thresholds. The lowest D3 and D4 thresholds are found in climate division 7 in south-central Texas and the highest D3 and D4 thresholds are found in climate division 10 in the lower Rio Grande River valley. This suggests that factors other than mean precipitation can influence the spatial pattern of drought thresholds.

Table 8.

KS statistic for PDSI after being fit using gamma, normal, lognormal, and exponential PDFs.

KS statistic for PDSI after being fit using gamma, normal, lognormal, and exponential PDFs.
KS statistic for PDSI after being fit using gamma, normal, lognormal, and exponential PDFs.
Table 9.

USDM drought thresholds for PDSI calculated using the normal distribution.

USDM drought thresholds for PDSI calculated using the normal distribution.
USDM drought thresholds for PDSI calculated using the normal distribution.

It is evident that the station-based drought thresholds tend to be higher (less extreme) than climate division–based drought thresholds. For example, the extreme drought threshold (D3) for climate division 6 is −4.03 while the extreme drought thresholds for Llano (415272) and Boerne (410902) are −3.90 and −3.70, respectively. The reasons for these systematic differences between the climate division– and station-based PDSI drought thresholds are not clear, but they could be related to the method used to estimate climate division data prior to 1930.

The drought thresholds for the stations and the climate divisions differ significantly from those proposed by Palmer (1965). The threshold for moderate drought according to Palmer’s scheme (and therefore the threshold used in most state drought plans) is −2.0. Five of the six HCN stations and 7 of the 10 climate divisions have moderate drought (D1) thresholds that are less than −2.0. This suggests that if Palmer’s definition of moderate drought were utilized in Texas, moderate droughts would be overreported. The drought thresholds also differ significantly from those recommended by the USDM. In particular, the threshold for exceptional drought (D4) based on the climate division thresholds is higher than the USDM thresholds in 9 of the 10 climate divisions and the mean absolute deviation is 0.41. This underscores the fact that the PDSI is not a spatially invariant method for measuring drought conditions and therefore using a single drought threshold for the state is inappropriate.

3) Standardized precipitation index

SPI data for six HCN stations and 10 Texas climate divisions were fit using the normal, gamma, lognormal, and exponential distributions. The KS Lilliefors test was applied to evaluate how well these distributions fit the SPI data (Table 10). The normal distribution fits the SPI data extremely well for all stations and climate divisions. This is not surprising given that the SPI is normalized when it is calculated. The fitted normal distribution was used to determine the drought thresholds for the five USDM drought classes (Table 11). It is evident that there are minor variations in SPI drought thresholds across Texas, but there is very little difference between the climate division and station-based drought thresholds. The drought thresholds for abnormally dry conditions (D0) varied from −0.45 to −0.53, the thresholds for moderate drought (D1) varied from −0.75 to −0.84, the thresholds for severe drought (D2) varied from −1.15 to −1.28, the thresholds for extreme drought (D3) varied from −1.50 to −1.64, and the thresholds for exceptional drought (D4) varied from −1.85 to −2.03. The spread amongst the station/climate division drought thresholds increases slightly with drought severity because the lowest SPI values are influenced by a small number of climate-specific extreme events. Therefore the variations in the SPI drought thresholds are controlled by variations in precipitation. The drier stations and climate divisions tend to have less extreme thresholds and the wetter ones tend to have more extreme thresholds. Climate divisions 1 and 5 are the driest climate divisions in Texas and they always have less extreme drought thresholds than the wet climate divisions (e.g., climate division 4). For example, the threshold for exceptional drought (D4) is −1.95 in climate divisions 1 and 5 and it is −2.01 in climate division 4.

Table 10.

KS statistic for 1-month SPI after being fit using normal, gamma, lognormal, and exponential PDFs.

KS statistic for 1-month SPI after being fit using normal, gamma, lognormal, and exponential PDFs.
KS statistic for 1-month SPI after being fit using normal, gamma, lognormal, and exponential PDFs.
Table 11.

USDM drought thresholds for 1-month SPI calculated using the normal distribution.

USDM drought thresholds for 1-month SPI calculated using the normal distribution.
USDM drought thresholds for 1-month SPI calculated using the normal distribution.

Although the SPI drought thresholds are more consistent within Texas than the PDSI or percent normal, the drought thresholds differ significantly from those of McKee et al. (1993) as well as those that have been defined in state drought plans. For example, according to McKee et al. (1993), the threshold for moderate drought (D1) is −1.0, while the moderate drought (D1) thresholds in Texas varied from −0.75 to −0.84. Similarly, for severe drought (D2) and extreme drought (D3) the SPI thresholds in Texas vary between −1.15 and −1.28 and between −1.50 and −1.64, respectively. These thresholds are much higher (less severe) than those defined by McKee et al. (1993) for severe (−1.5) and extreme drought (−2.0). This means that if the thresholds proposed by McKee et al. (1993) were used to determine the operational drought definitions for Texas, the severity of drought conditions would be underestimated and drought responses would not be triggered early enough.

It is evident that even though the SPI is a standardized index (and one that is normally distributed), drought thresholds do vary across Texas. However, even more problematic are the differences between the objective drought thresholds defined in this paper and those being used in state drought plans. This suggests that even for a standardized drought index such as the SPI it is necessary to develop objective drought thresholds using local data.

4. Conclusions

The purpose of this paper was to identify the most appropriate method for determining operational drought definitions (thresholds). A review of state drought plans revealed that many states have adopted drought thresholds listed in the scientific literature without considering whether they are appropriate for the climate of the state or whether the drought indices that they are using are spatially invariant. This paper demonstrated how operational drought definitions can be developed for any drought index by fitting an appropriate distribution function and then using the fitted distribution to define drought thresholds (ranging from abnormally dry to exceptional drought) based on the percentiles used by the USDM. Using this objective approach for determining drought definitions ensures that droughts are accurately and correctly identified at the local level. Objectively defined drought thresholds for percent normal and PDSI varied significantly across Texas and the objectively defined thresholds differed significantly from those reported in state drought plans. The climate division– and station-based drought thresholds for percent normal and PDSI were also inconsistent with each other. Although the objectively defined drought thresholds for SPI were more consistent across Texas than the drought thresholds for PDSI and percent normal, they differed significantly from those described in the literature and in state drought plans. Therefore, using a single set of subjectively defined drought thresholds is inappropriate because it can lead to a mischaracterization of drought conditions (e.g., over- or underestimating drought severity) and incorrect triggering of drought responses. Using a single set of subjectively defined drought thresholds is particularly problematic in a large and climatically diverse state such as Texas.

It is more appropriate to use an objective, location-specific method for defining drought thresholds. Applying this method involves the following steps:

  1. utilize a relatively long record to calculate the drought index of interest (e.g., SPI);

  2. apply an appropriate PDF to the drought index data; since some drought indices are not normally distributed it may not be appropriate to use a Gaussian (normal) distribution for all indices; and

  3. utilize the PDF to determine appropriate drought thresholds based on the percentiles used by the USDM.

This methodology should be applied to all drought indices, including those that are supposed to be spatially invariant (e.g., SPI). Ideally these definitions should be determined at the local (e.g., county) level by fitting a PDF to all of the available stations that have a long record and then interpolating the parameters of the PDF to determine what the thresholds should be in data-sparse regions. However, this methodology can also be applied to climate division data as demonstrated in this paper. Using an objective approach for determining drought definitions ensures that variations in climate and spatial resolution (e.g., station versus climate division) are correctly accounted for so that drought severity is accurately classified.

Acknowledgments

This research was partially supported by Contract 2005483028 from the Texas Water Development Board. The author thanks Anna Nordfelt for her assistance in reviewing the state drought plans and Lei Meng for writing the code to fit the PDFs.

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Footnotes

Corresponding author address: Steven M. Quiring, Department of Geography, Texas A&M University, College Station, TX 77843-3147. Email: squiring@tamu.edu