an early warning system for drought management using the palmer drought index

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATIONVOL. 33, NO.6 AMERICAN WATER RESOURCES ASSOCIATION DECEMBER 1997

AN EARLY WARNING SYSTEM FOR DROUGHT MANAGEMENTUSING THE PALMER DROUGHT INI)EX'

V. K Lohani and G. V Loganathan2

ABSTRACT: The Palmer Drought Severity Index (PDSI) is used ina non-homogeneous Markov chain model to characterize thestochastic behavior of drought. Based on this characterization anearly warning system in the form of a decision tree enumerating allpossible sequences of drought progression is proposed for droughtmanagement. Besides yielding probabilities of occurrence of differ-ent drought severity classes, the method associates a secondarymeasure in terms of likely cumulative precipitation deficit to pro-vide timely guidance in deciding drought mitigation actions. Theproposed method is particularly useful for water availability taskforces in various states for issuing drought warnings in advance.The applicability of the technique is illustrated for the Tidewaterclimatic division of Virginia.(KEY TERMS: drought management; Palmer drought severityindex; early warning system; drought contingency plans; wateravailability task force; Markov chain.)

INTRODUCTION

The common variables used to study droughtsinclude rainfall, temperature, evaporation, evapotran-spiration, soil moisture, streamfiow, reservoir levelsand storage, and ground water levels. A popularapproach has been to combine a subset of these vari-ables into an index which summarizes the status ofmoisture deficiency in a region using either numbersor letters. WMO(1975) gives an excellent review ofdrought indices based on rainfall, mean temperature,soil-water and crop parameters, evapotranspiration,and other climatic variables. A careful examination ofthese indices reveal that most of them present simpli-fied expressions of parameters to indicate various lev-els of moisture shortage. A better understanding ofdrought process can be had by analyzing droughtindices which more closely represent the physical

processes. Of all such indices, the Palmer DroughtSeverity Index (PDSI) (Palmer, 1965) comes close torepresenting the physical reality. This physical basisprobably explains why the index is still in widespreaduse more than 30 years after its development. In thefollowing, a brief description of its computationalscheme is given.

To begin with a long term monthly water balancefor the chosen region is carried out. In his original for-mulation Palmer used the Thornthwaite equation(Thornthwaite, 1948) for estimating the potentialevapotranspiration. The soil moisture is depleted atthe potential rate minus the precipitation as long asmoisture storage permits it; otherwise, entire avail-able moisture is used up. The soil moisture storage isdivided into two layers: the surface layer and theunderlying layer. The evapotran spiration requirementis first met by the surface layer. When its storage isused up, transfer from the underlying layer is initiat-ed. For soil moisture recovery, the surface layer stor-age must be full before transfer to the underlyinglayer can take place. Surface runoff is computed bysubtracting evapotranspiration and soil moisturestorage deficiency amounts. The aforementioned bal-ancing scheme is performed for a long period to obtainthe average evapotranspiration, soil moisturerecharge (refilling of moisture during large rainevents), runoff, and soil moisture loss. When rainfallis set to zero, the evapotranspiration losses are themaximum called the potential loss; potential rechargeis the maximum recharge possible for any given peri-od and is taken as the total soil moisture storageminus the available soil moisture storage; potentialrunoff is taken as total soil moisture storage minus

1Paper No. 96149 of the Journal of the American Water Resources Association (formerly Water Resources Bulletin). Discussions are openuntil August 1, 1998. (Recipient of the 1996 AWRA/UCOWR Student Paper Competition Award, Graduate Division.)

2Respectively, Assistant Professor, Engineering Fundamentals Department, and Associate Professor, Civil Engineering Department, Vir-ginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 1375 JAWRA

Lohani and Loganathan

the potential recharge; and the potential evapotran-spiration is obtained from the Thornthwaite equation.

The ratios of long term averages of evapotranspira-tion, recharge, runoff, and losses to the long termaverages of their respective potential values are com-puted. These ratios are used as multipliers for thepotential values and the resulting evapotranspiration,recharge, and runoff are added and soil moisture loss-es are subtracted to obtain that month's climaticallyappropriate for existing conditions (CAFEC) precipi-tation. The difference between the CAFEC precipita-tion and the actual rainfall is the precipitation deficitfor that month. This deficit is rescaled for comparisonamong regions and a moisture anomaly index, calledZ index, is computed which becomes part of thePalmer index. The Z index indicates the wetness ordryness of an individual month. The current cumula-tive deficit index is taken as the weighted sum of theprevious cumulative deficit index and the current Zindex. The current cumulative deficit index is thensubjected to a backtracking scheme to assess moisturedepletion or recovery phase with an associated changein the index value itself. Since its inception, somemodified versions of the PDSI have evolved. Forexample, Karl (1986) has described a modified version.known as the Palmer Hydrological Drought Index(PHDI) which is used for water supply monitoring.For operational purposes, a real time version of thePDSI was introduced in 1989 which is called modifiedPDSI (PDI) (Heddinghaus and Sabol, 1991).

The PDSI or its modified versions have been usedin several ways in the field. Kibler et al., (1987) sug-gested the 25th, 10th, and 5th percentiles of PHDI fordrought watch, warning, and emergency, respectively,in Pennsylvania. Heddinghaus and Sabol (1991)reported that the principal uses of PDSI are in moni-toring hydrologic trends, crop forecasts, and assessingpotential fire severity. Johnson and Kohne (1993)used the PHDI for evaluating the susceptibility of 516reservoirs in the country and described the index use-ful for investigating droughts over large geographicareas. Jones et at. (1996) and Briffa et at. (1994) usedlong term PDSI data to describe the spatial and tem-poral details of relative moisture variability duringsummer (June-August) across Europe. Soule (1993)examined the spatial patterns of hydrologic droughtin the contiguous United States using the mean val-ues of the PDSI over the 90-year period 1900-1989.In Canada, a close correspondence was establishedbetween severity of drought characterized by PDSIand the frequency of dust storms (Wheaton, 1990). ANational Drought Atlas has been developed using thePalmer index (Wallis, 1993). In addition, PDSI hasbeen used by the Federal Government as one of theprincipal criteria for disaster designation to assessthe eligibility of those to receive federal drought relief

(Wilhite et al., 1986). There have been several criti-cisms of the Palmer index (Alley, 1984; Karl, 1986;Guttman, 1991), but the index remains the best foranalyzing drought processes.

Recent drought occurrences in the United Stateshave pointed out that almost every state in the Unionis vulnerable to water shortage. For example, during1996 while most states had normal rainfall amounts,seven southwestern states including Arizona, Col-orado, Utah, New Mexico, Oklahoma, Texas, andNevada experienced drought conditions (NDMC,1997). Among the most widespread droughts of therecent past, the 1988 drought is an important one.Some of its effects were: lower water levels in the BigMuskego lake in Wisconsin, which affected the waterquality, drought-related crop losses in the stateexceeded $900 million (Field, 1993; Holmstrom andEllefson, 1990); reduction in average corn yield (inbushels per acre) by more than 20 percent in 20 states(Agee, 1993); low ground water levels, streamflow.sand record low reservoir levels in Indiana (Fowler,1992); losses in agricultural productivity, increasedpublic costs, and the economic and environmenta'consequences of lowered water levels and waterscarcity in Great Lakes Basin (Crane et at., 1990); lowstreamfiows across Tennessee and critically low watersupplies in several communities in Middle Tennessee(Lowery and Connell, 1990); and notable stoppages ofbarge traffic on the )ower Mississippi River duringJune and July as a result of shallow areas producedby record low flows in the river, causing a 20 percentincome loss to the barge industry (Changnon, 1989).In view of the widespread droughts of the past twodecades various state governments have deviseddrought contingency plans (DCPs) and 27 states cur-rently have them in place (Wilhite and Rhodes, 1993).All DCPs use the PDSI in some form as a measure ofdrought severity, and typically supplement it withother indices. DCPs call for various task forces includ-ing a water availability task force which has theresponsibility to continuously monitor waterconditions and develop some kind of an early warningsystem. During a drought, the water availability taskforce concentrates on preparation of updates on cur-rent. drought conditions; however, formal mechanismsfor issuing early warnings are not well developed.This paper illustrates the use of the Palmer index indeveloping an early warning system for drought man-agement. The warning system methodology has beenapplied to the Tidewater climatic division (CD1) inVirginia (Figure 1). The method predicted the 1995drought three months in advance and predicted thatthere would be no drought in the region during 1996.It is also noted that these predictions were made sev-eral months in advance, and the drought progressionwas monitored in real time to assess the accuracy of

JAWRA 1376 JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION

An Early Warning System for Drought Management Using the Palmer Drought Index

DIVISIONS

TIDEWATER

EASTERN PIEDMONT

WESTERN PIEDMONT

the predictions. The methodology is presented in theensuing sections.

STOCHASTIC BEHAVIOR OF PALMER INDEX

The monthly PDSI data (1895-1990), along withlong term precipitation data for the Tidewater climat-ic division (CD1), were used in computing the neededprobabilities for the early warning system. The divi-sional temperature and precipitation are among theneeded inputs to compute the PDSI values. Guttmanand Quale (1996) retrace the historical underpinningsof the climatic divisions in general and discuss thecomputational methodology to obtain climatic data forthe divisions. They point out that the climatic datafrom 1931 to the present are the unweighted arith-.metic means of monthly data from all representativestations (subjectively excluding stations not compati-ble with the division general climatology) within agiven division. The divisional averages prior to 1931periods were obtained as follows. Prior to 1931, thestatewide averages were taken to be arithmetic aver-age of the data from all reporting stations within each

state. Using an overlap period of 1931-1982, the divi-sional averages were related to the averages of thestates containing that division by linear regression.These linear regression equations were used to com-pute the divisional temperatures prior to 1931 fromthe USDA state averages (Ti. S. Dept. of Agriculture,1951). For precipitation, the same procedure was fol-lowed except that only those stations that reportedboth temperature and precipitation were included.That is, the averages of temperature and precipita-tion were calculated from the same set of stations(Karl et al., 1983; Karl and Knight, 1985). These cli-matic data are used in the water balance scheme tocreate the PDSI values.

Karl's (1986) seven class delineation of PDSI is pre-sented in Table 1. Let the random variable X repre-sent the drought (wet) class for month n. Forexample, X1 = Xjan = 5 represents the occurrence ofclass 5 in January. The underlying stochastic processis completely described by a Markov Chain if thetransition probabilities, denoted by pjf,fl+1, for mov-ing from class i in month n to class j in month (n+1)and the initial class vector, fO), describing the proba-bilities of the seven classes for the beginning month,are prescribed. Based on monthly Palmer index data


2

3

4 NORTHERN

5 CENTRAL MOUNTAIN

6 SOUTHWESTERN MOUNTAIN

LOCATION OF WELL # 58B13

0 STREAMGAGE STATION ONBLACKWATER RIVER AT LUNI

Figure 1. Study Area.


for 96 years (1895-1990), 12 monthly (non-homoge-neous) transition probability matrices describing theclass transfers from months January to February;February to March;.. ., and December to January areformulated for the selected climatic division in Vir-ginia. These matrices are assumed to be cyclic in thesense that there is no yearly variation; the transitionprobabilities depend only on the month and not on theyear. The transition probability

p,j(nn+l) = P [Xn+i = j I X = i], for i,j = 1,2,..

andn=1,2,...,12

.(n,n+1) = N .(n,n+1) / N()Fi,j 1,)

in which N,.(fln+l) = number of transitions from classi in month n to classj in month n+1;N(n) = number ofoccurrences of class i in month n. If N(n) is zero forsome i, we define p1(n,n+i) = 1/7 for all j = 1,2, . . .,7.

StochasticPDSI Value Weather Spell Class

4.00 or more Extremely Wet 1

3.00 to 3.99 Severely Wet 21.50 to 2.99 Mild to Moderate Wetness 3

-1.49 to 1.49 Near Normal 4-1.50 to -2.99 Mild to Moderate Drought 5-300 to -3.99 Severe Drought 6-4.00 or less Extreme Drought 7

Monthly Steady State Probabilities

The probability of occurrence of a particulardrought (wet) class will indicate proneness todroughtlwet conditions. Let f(k) be the class probabili-ty row vector which lists P[Xk = i] for i = 1, 2, . . ., 7for the seven classes after k transitions given by

fk) = [f(o)] [P1] [P2] ... [k]in which: fo) is initial state probability row vector andP1 = (7 x 7) monthly transition matrix associated withthe starting month, say January to February, i.e., P1

p(1,2) = p(Jan.,Feb.) Of course, the starting month canbe any one of the 12 months. Also, due to the cyclicnature of these matrices, the transition matrix for

months 14 to 15 denoted by p(l4,l5) is the same asp(2,3) = p(Feb.Mar.) , the February-March transitionmatrix. For the long term, that is as k —oc, we wouldlike to know whether ft") has steady class probabili-ties independent of f(°)• This will be true if the productof the transition matrices [em] through [Pki denotedby 4(m,k) called the composite matrix

(m,k) = [Pm] [1m+i] ... [Picil (4)

is a constant stochastic matrix with identical rows(Isaacson and Madsen, 1976) for large k. For such aconstant stochastic matrix, it follows from Equation(3) that fm(k) will be independent of f(0); furthermore,each class has a steady state probability value corre-sponding to that class' (column) constant probabilityof 4(m,k) However, because the beginning month, m,influences the value of 4(m,k) the steady class proba-bilities of fm0o) will depend on m. To interpret 'm ask —*oc, consider Equation (4) as follows. The constant(identical rows) stochastic matrix for January isdefined as the product of the sets of the consecutive12 monthly matrices with the beginning matrix beingthat of January which is

(1,oc) = [Jan] ([Pr] [P21 Pill lIP12])

([P1J [P2] . . . [P11] [P12]) ... (5)

Because [Jan] is a constant stochastic matrix it fol-lows

row [Jan] f1(oc) (6)

Now consider

[Feb] = ([P211 lIP3] .Pii] [P2] [P111)

([P2] lIP3] . . . [P1J lIP12] {P111) ... (7)

and we obtain

[Feb] = lIP2] lIP3] . . . [P11] lIP12] lIJan] [P1j (8)

from which upon manipulation it follows

[Feb] = [Jan] [P1] (9)

(3) and therefore

row [Feb] = f2(°) = row lIJan] [P111

similarly we can show

row [Mar] = f3(") = row [Feb] [P2l


is computed as

(1)

(2)

TABLE 1. PDSI Values and Corresponding Stochastic Classes.

Source: Karl (1986).


row [Apr] = f4(") = row [Mar] [P31

row [Dee] = f12(oc) = row [Nov] [p11]

row [Jan] = f1(") = row [Dec] [P12]

In general we obtain, row [Month n+11 = row [Monthfl] [Pa]. Equation (10) provides a means to evaluatethe monthly drought/wet steady class probabilities. Itis a system of linear equations in terms of the month-ly steady class probabilities.

The monthly steady class probabilities for variousweather classes for the Tidewater region are given inTable 2. The table also provides the empirical esti-mates of these probabilities using 96 years of monthlyPDSI data. Specifically, the upper row represents ana-lytical result and the lower one is the empiricalresult. For example, the steady class probability ofoccurrence of class 3 in January using non-homoge-neous Markov chain model is .2200 which comparesvery well with'the empirical estimate of .2187. Thetable also contains Karl's (1986) empirical estimatesof the steady class probabilities computed for theentire USA across all months. Wallis (1993) reportsthat the probability of PDSI being in class 7 for themonth of July for CD1 is between 0.00 and 0.05; thepresent analysis yields 0.0208. Further, Guttman etal. (1992) observed probabilities of PDSI value beingin class 7 in January as ranging between .01- .05 inCD1, while our analysis yields a value of .0417. It isalso observed that long term probability of droughtclasses (class 5, 6, and 7) is close to 0.3 during Augustthrough October which agrees with the results of VanBavel and Lillard (1957). These results validate theuse of the non-homogeneous Markov chain techniquein evaluating the long term probabilities of droughtclasses using the Palmer index. These probabilitiesare used in developing an early warning system fordrought management as is subsequently discussed.

DROUGHT IN VIRGINIA ANDCONTINGENCY PLANS

Although the annual average precipitation in Vir-ginia is about 43 inches (109 cm) (SWCB, 1990), therehave been several occurrences of drought, the latestone in 1995. Analysis of historical patterns ofdroughts carried out by Van Bavel and Lillard (1957)and later updated by Vellidis et al. (1985) indicatesthat the probability of moisture deficiency from Junethrough September (part of growing season) is atleast 30 percent in the state. In a study conducted by

the State Water Control Board (SWCB, 1990) of Vir-ginia a drought is indicated when: (1) precipitation isless than 85 percent of the 30 year mean for at leastthree consecutive months; (2) PDSI is below -2.00 forat least three consecutive months; (3) streamfiow iswithin the lowest 25 percent of mean monthly flow for

(10) at least three consecutive months; and (4) groundwater level is within the lowest 25 percent of theaverage monthly level for three consecutive months.The study identified nine drought years in the stateduring the period 1957-87. It is clear that level of thethreshold plays a crucial role in the Virginia defini-tion of drought occurrence because of its "wait andsee" nature, with the waiting period being threemonths.

In view of widespread droughts in the country inrecent years, various state governments developedDrought Contingency Plans. In the operational modeof a DCP, three common features emerge. First, awater availability committee is established which con-tinuously monitors water conditions and prepares anoutlook for a month or season in advance. The prima-ry role of the committee is to coordinate the collectionand analysis of required data from various state andfederal agencies and deliver the products to decisionmakers on a timely basis. Second, a mechanism existsto assess potential impacts of water shortages on themost important economic sectors. Third, a committeeusually exists to consider current and potentialimpacts and recommend response actions to the gov-ernor. The ultimate purpose of drought plans is toreduce drought related impacts and improve efficien-cy in the allocation and use of resources. Wilhite andRhodes (1993) categorized the drought related mitiga-tion actions into nine primary areas, from monitoringand assessment programs to the development ofdrought contingency plans. Part of assessment pro-grams includes the development of criteria or triggersfor drought related actions and development of anearly warning system besides preparing updates ondrought conditions using various hydrometeorologicaldata. A review of DCPs indicates that, in most cases,the assessment programs mostly concentrate onpreparing drought updates using current data andformal mechanisms for issuing early warnings are notwell defined.

A Drought Monitoring Task Force (VDMTF) wasset up in Virginia in 1985 with the objective of moni-toring the development of drought conditions, and ofpreparing drought status reports in the case of a pro-gressing drought. The VDMTF is coordinated by theDepartment of Environmental Quality and is madeup of the representatives from the state and federalagencies including the Department of Agricultureand Consumer Services, State Climatology office,Department of Emergency Services, Department of



TABLE 2. Monthly Steady Class Probabilities, CD1, VA, Analytical and Empirical, PDSI Data.

ClassesMonth 1 2 3 4 5 6 7

Environmental quality, Department of Forestry,Department of Health, National Weather Service, andthe U.S. Geological Survey. The task force's reportsare crucial to plan for emergency actions duringa drought period. The VDMTF is activated onlywhen there are preconditions for drought such as

significant precipitation deficits, low streamfiows,high evaporative rates caused by prolonged high tem-peratures, widespread reports of water shortages, andrelated factors. The triggering factor for conveningthe task force is a combination of the Palmer droughtindex, moisture deficits, surface and ground water


JanuaryAnalyticalEmpirical

FebruaryAnalyticalEmpirical

MarchAnalyticalEmpirical

AprilAnalyticalEmpirical

MayAnalyticalEmpirical

JuneAnalyticalEmpirical

JulyAnalyticalEmpirical

AugustAnalyticalEmpirical

SeptemberAnalyticalEmpirical

OctoberAnalyticalEmpirical

NovemberAnalyticalEmpirical

DecemberAnalyticalEmpirical

12 Month Average

Karl (1986)

Empirical 12 Month Average

.0 104

.0104

.0104

.0 104

0.00.0

0.00.0

.0418

.04 17

.0104

.0104

0.00.0

.0 104

.0 104

.0 104

.0104

.0209

.0208

.0209

.0208

0.00.0

.0113

.05

.0113

.0521 .2200 .5198 .1146 .0417 .0417

.0521 .2187 .5208 .1146 .0417 .0417

.0314 .2299 .5411 .1249 .0312 .0312

.0313 .2292 .5417 .1250 .0313 .0313

.0627 .1775 .5414 .1666 .0208 .0312.0625 .1771 .5416 .1667 .0208 .0313

0.731 .1669 .5415 .1458 .0417 .0312.0729 .1667 .5417 .1458 .0417 .0313

.0313 .1669 .5424 .1354 .0521 .0104

.0313 .1667 .5426 .1354 .0508 .0104

.0417 .1668 .5625 .1458 .0625 .0104

.0417 .1667 .5625 .1458 .0625 .0104

.0626 .2085 .4584 .2083 .0416 .0208

.0625 .2083 .4583 .2083 .0416 .0208

.0730 .1980 • .4167 .2396 .0625 0.0

.0729 .1979 .4167 .2396 .0650 0.0

.0938 .1355 .4584 .2187 .0625 .0208.0938 .1354 .4583 .2188 .0625 .0208

.0625 .2084 .3959 .2604 .0312 .0208

.0625 .2083 .3958 .2604 .0313 .0208

.0521 .2605 .3959 .1979 .0417 .0312

.0521 .2604 .3958 .1979 .0417 .0313

.0730 .2084 .4688 .1667 .0521 .0312

.0729 .2083 .4688 .1667 .0508 .0325

.0591 .1956 .4886 .1771 .0451 .0234

.06 .17 .45 .17 .06 .04

.0590 .1953 .4887 .1771 .0451 .0234


levels, and related indices. No specific targets havebeen established for each of the triggering parame-ters, but in the past, the task force has convenedwhen the Palmer drought index has fallen below -3.00at the start of summer; when precipitation hasremained considerably below normal for severalweeks; or when there have been widespread reports ofwater shortages caused by wells or streams drying up(Erlinda Patron, Dept. of Environmental Quality,Commonwealth of Virginia, Personal Communication,1995).

During the drought of 1995, the VDMTF issued tworeports up to September 1995. Typically, these reportsincluded an update on the current drought conditionsbased on an evaluation of current conditions of pre-cipitation, stream flow, ground water, and the PalmerDrought Index on a continual basis. The reports alsoincluded a brief description of the impacts of droughton forestry and crop and soil sectors. In a decisionmaking context, it is desirable that in addition to theinformation on current drought conditions, thereshould also be an anticipative mechanism to forecast(say, 2-3 months ahead of time) the worsening orrecovering trend of a drought. Towards this end, thepaper suggests an early warning system for droughtmanagement.

EARLY WARNING SYSTEM FORDROUGHT MANAGEMENT

The early warning system in the form of a decisiontree analysis is suggested for making operationaldecisions. The decision tree enables a decision makerto decompose a large complex decision problem intoseveral smaller problems (Winston, 1991). In this par-ticular application, the decision tree shows all possi-ble drought state occurrences in terms of the PDSI.Several secondary drought parameters can be associ-ated with this decision tree to assess the progres-sion of a drought. In this study, the cumulativeprecipitation at each month is used as such a

secondary parameter in addition to the PDSI. Howwell the PDSI can represent the shortages in stream-flow and ground water is also explored. The StateWater Control Board (SWCB, 1990) has been using anindex stream gaging station (located on Blackwaterriver at Luni) and official observation well # 58B13(located in Suffolk county) for getting streamfiow andground water data, respectively, within the CD1region (Figure 1). The PDSI data of the region hasbeen correlated with the streamfiow and groundwater level data obtained from SWCB( 1990) (Table 3).The correlation values are around 0.6. This correla-tion seems to support the use of PDSI as a surrogatefor low streamfiow and ground water levels. Addition-al details are given in Lohani (1995). In the ensuingsections, the development of various components ofthe decision tree are described.

Identification of Starting Month For Droughts

To establish the most critical beginning month for adrought, the PDSI data of the region from 1895-1990are analyzed. A drought event is considered to haveoccurred when the PDSI value falls in class 5. For theentire period of record, such events were counted andthe results are given in Table 4. It is seen that 19 per-cent of the total historical drought events began inthe month of July and 55 percent of drought eventsbegan in the months of June through September. Thesteady state probabilities indicate August throughOctober as the months having the highest probabilityof droughts. This can a'so be explained due to higherevapotranspiration losses during preceding hotsummer months. Therefore, for the purposes ofdrought monitoring and of making early warning pre-dictions, it was decided to choose May as the droughttrigger month. In other words, for declaring the pos-sibility of a drought year in advance, it is suggestedthat precipitation and PDSI conditions be monitoreduntil the end of May every year. To set a deterministiccriterion for triggering drought warning at the end ofMay, a detailed analysis of past precipitation and

TABLE 3. Correlation Between PDSI and Streamfiow and Ground Water Data, Tidewater Region, Virginia.

Mon J-J F-F MM A-A MM J-J J-J A-A S-S 0-0 N-N D-D

CCp8 .72 .45 .74 .84 .73 .45 .50 .58 .64 Go .75 .61

CCPG .78 .72 .83 .87 .84 .90 .62 .79 .64 .59 .65 .60

CCp = Correlation coefficient between PDSI and streamfiow data.CCPG = Correlation coefficient between PDSI and ground water data.J-J = January PDSI and January streamfiow (ground water data).

JOURNAL OF THE AMERICAN WATER RESOURCES AssociATioN 1381 JAWRA


PDSI data was carried out. A brief description is asfollows.

Precipitation Deficit / Surplus Analysis

Table 5 lists the drought years along with the pre-cipitation amount as identified by the SWCB (1990)during 1957-87 in CD1. On the average, about 7 inch-es (17.8 cm) of precipitation shortfall during a calen-dar year led to a drought year. To capture the patternof cumulative rainfall deficit over months duringdrought years, precipitation data were analyzed fordeficit on a monthly basis. Based on long term aver-age monthly rainfall values, deficitlsurplus in rainfallfor each month was computed and accumulated fromJanuary through May for each drought year. Mostdrought years experienced consecutive deficit monthsfrom January through May. For the sake of contrast,deficitJsurplus characteristics of those years whichreceived above normal precipitation and were notclassified as drought years in SWCB (1990) were alsostudied. All non-drought years had a surplus accumu-lation of rainfall until the trigger month of May.

Table 6 gives a range of the accumulated averagedeficitisurplus rainfall through May for both droughtand non-drought years. In deriving these ranges, theextreme values on both the lower and upper endswere discarded in view of the very small sample sizein those classes, since the interest was more to obtaingeneral deficitisurplus pattern. During drought years,the cumulative deficit in precipitation from Januarythrough May has been in the range of 0.08 to 5.75inches (0.20 to 14.60 cm) [average about 2.91 inch(7.39 cm)]. Further, in 6 out of 8 drought yearsthe PDSI based weather class (see Table 1) observed

during May was class 5 or higher. In the case of thenon-drought years the cumulative, January throughMay, precipitation surplus was in the range of 4.47 to7.28 inches (11.35 to 18.49 cm)(average about 5.88inch(14.94 cm)). Further, the PDSI based weatherclasses during all non-drought years were class 3 orlower during May. Based on this analysis, a determin-istic guideline to trigger drought warning can be for-mulated as follows. If the cumulative deficit inprecipitation from January through May in any yearis of the order of 0.08 to 5.75 inches [0.20 to 14.60 cm)(average about 2.91 inch (7.39 cm)II and weather classin May is 5 or higher, there is a high probability of adrought extending in the region through the remain-ing months of the year, and the option of issuing adrought warning should be seriously considered.

TABLE 6. Range of Cumulative Deficit/Surplus (inch)Through May, CD1, Virginia.

Drought Years Non-Drought Years

-0.08 to -5.75 (average -2.91) 4.47 to 7.28 (average 5.88)

1 inch = 2.54 cm.

Decision Tree Analysis

The month of May is considered as the triggermonth for droughts in CD1 whenever the PDSI valuesfall in classes 5 or higher with a cumulative deficit inprecipitation of about 2.91 inches(7.39 cm). Consider-ing the end of most agricultural seasons and the onset

TABLE 4. Percentage of Drought Events Starting Various Months, Tidewater Area, Virginia, Data Period 1895-1990.

Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

% 0 6 11 4 4 8 19 17 11 8 6 6

Drought Event = Weather state entering class 5.

TABLE 5. Drought Years and Associated Annual Rainfall (inch), Tidewater Area, Virginia, 1957-1987.

Year 1965 1966 1968 1976 1980 1981 1985 1986

Rainfall 29.26 38.10 35.65 38.96 35.73 42.71 45.20 34.59

D/S -14.61 -5.77 -8.22 -4.91 -8.14 -1.16 1.33 -9.28

D/S = Deficit/Surplus (minus sign indicates deficit); long term average annual rainfall = 43.87 inch; 1 inch = 2.54 cm.


An Early Warning System for Dmught Management Using the Palmer Drought Index

of winter, the month of September is chosen to definea critical period for the issuance of drought warnings.The decision tree displays the pathway to reach thecurrent state of drought class along with all possibleways of leaving that class with the associated proba-bilities. A complete description of weather class tran-sitions from May through September along with theassociated probabilities is shown in Figure 2 for thestarting class of 5 in May. Similar decision trees canbe developed for starting classes of 6 and 7 in May.As shown, class 5 in May will transit to either class 5with 0.8 probability or to class 6 with 0.2 probabilityin June. Then, if in class 5 in June, it will transit toclass 5 in July with a probability of 0.67. Likewise,the transition probability of weather for all monthsand classes can be included in the decision tree.

May —,.

June -÷

July -+

Aug. -

While the PDSI is a holistic index for interactingmoisture related mechanisms, in a decision makingcontext it is useful to display other measures ofdeficits as well. Therefore, a secondary drought mea-sure, the likely precipitation deficit, is also used inthe decision tree. It is seen in Figure 2 that to go fromclass 5 in May to class 5 in June, there will be adeficit of 0.47 inch (1.19 cm) in June from the normalrainfall. To compute this amount, all weather eventsof transition from class 5 in May to class 5 in June forthe period of study are considered. For each event, theobserved deficit in precipitation from normal in Junemonth was computed and then an average deficit of0.47 inch (1.19 cm) was derived. Using the decisiontree the total deficit / surplus for, each possible path ofweather transition from May to September and its

Sept.

-.47" - deficit of .47 - Weather Class 4 () - 80% probability

Figure 2. Decision Tree of Possible Weather Scenarios, May Class 5.


3.26' -0.1" -1.89" .96" -1.57 -3.15" 3.26" -.O1 -1.89" .96' -1.57' -3.15" 2.5 .97"


associated probability level can be worked out. Forexample, the event when May = 5; June = 5; July = 5;August = 5; and September = 6 (we refer to this eventas 55556) will have an occurrence probability of

P [June =5; July = 5; Aug. = 5; Sep. = 6 I May 5]

= p55May Jun p55Jun Jul p55Jul Aug p56Aug Sep

= .8 .67 .72 .3 = .1158 (11)

Figure 2 shows that the event 55556 involves a totaldeficit of 4.53 inch (11.51 cm) from June throughSeptember [0.47 inch (1.19 cm) June; 0.35 inch (0.89cm) July; 0.56 inch (1.42 cm) August; and 3.15 inch(8.0 cm) September] and has a probability of 11.58percent. Likewise probability of all possible eventsand associated deficits/surplus are computed andgiven in Table 7. It may, however, be noted that theprecipitation deficits shown on Figure 2 provide addi-tional detail and are not the CAFEC (ClimaticallyAppropriate For Existing Conditions) deficits used tocompute the Z and PDSI values (Palmer, 1965). FromTable 7 there is a 60.38 percent probability that therewill be a cumulative deficit from June throughSeptember when the drought state is 5 in May. Also,when a particular branch is followed in the decisiontree, the deficits at each node should be added to theMay cumulative deficit [i.e., about 2.91 inch (7.39 cm)]to obtain the total deficit at that node (for thatmonth). For example, traversing along the branch5-6-6 starting in May in Figure 2 yields a total deficitof(-2.91+(-2.07) +0.26) = -4.72 inches (-12.0 cm) by theend of July. Considering a typical drought year isdeclared when the rainfall shortage is around 7 inch-es (17.78 cm), about 5 inches (12.70 cm) shortage atthe end of July requires serious consideration for issu-ing drought warning.

It is seen that the information given in Figure 2provides a decision making body like the VDMTF anin depth analysis of all possible scenarios should con-ditions for an impending drought develop. The tech-nique proposed herein is flexible and can be used withany other starting month! class and region. The val-ues of deficit or surplus amount in the decision treehave scope for further modification using a longerperiod of record and should be periodically updatedwith the arrival of new data.

Application of Decision Thee Analysis to Years1995 and 1996

An analysis of the cumulative monthly deficit dur-ing 1995 shows that until May 1995 there was acumulative shortfall of 2.37 inches (6.02 cm). Further,

the PDSI based weather class during May 1995 was5. Therefore, as per the deterministic criterion devel-oped in the precipitation deficit/surplus analysis,there was a high probability of drought in the regionin the following months which could have beendeclared in May 1995. In reality, drought did occur inthe region during 1995 and an emergency to thiseffect was declared in September 1995. Precisely, dur-ing 1995 the event 55565 (see Table 7) took place.Our analysis would have tempted the decision makersto declare drought possibility in May 1995, about 3months ahead. An analysis of precipitation deficitduring 1996 indicated that there was a surplus of theorder of 3.41 inches (8.66 cm) until May 1996. ThePDSI value during May 1996 was in class 4. There-fore, as per our analysis, there would not be a droughtin 1996 in CD1, Virginia, and 1996 turned out to be anormal year. (In reality, this assessment was made byMay 1996 and the prediction was monitored duringthe year which proved to be a success.)

Deficit/SurplusEvents Probability (inch)

55443 .0169 5.8455444 .1537 2.4855445 .0169 0.6955454 .0230 1.9555455 .0306 -0.5855456 .0230 -2.1655543 .0067 3.8555544 .0615 0.5855545 .0067 -1.3055554 .1158 -0.4255555 .1544 -2.9555556 .1158 -4.53

55564 .0375 0.8155565 .0375 -0.72 .

56656 .0300 -2.0956655 .0400 -0.5156654 .0300 2.0256664 .0500 0.7956665 .0500 -0.74

SUMMARY

In this paper, a decision tree framework has beenput forward for use in issuing drought warnings. Thekey advantage-is the enumeration of all possible

TABLE 7. Weather Transition Events from May ThroughSeptember Deficits/Surplus and Associated Probabilities.

Minus sign indicates deficit, 1 inch = 2.54 cm.



sequences of occurrences. With such a procedure, adecision maker can observe how the progression ofdrought has taken place up to a certain stage indicat-ed by a particular month. For any such stage, one isprovided with all possible future scenarios with theirassociated probabilities. Along with the probabilitiesof future PDSI based weather classes, a secondarymeasure in terms of cumulative precipitation short-age has also been provided with each drought state(node) for a particular month (stage) of the decisiontree, which should provide an intuitive feel in decid-ing the future courses of action. Based on results ofpresent analysis, the realized drought situation inCD1 region in Virginia during 1995 could have beenwarned as early as May 1995.

ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers andthe Editor for their constructive comments. The writers would alsolike to thank Dr. Thomas Karl of NCDC, Asheville, North Carolina,for providing valuable information.

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an early warning system for drought management using the palmer drought index

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