Frequency and Spatial Characteristics of Droughts in the Conchos River Basin, Mexico

Transcription

1 Internatonal Water Resources Assocaton Water Internatonal, Volume 27, Number 3, Pages , September 2002 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco Tae-Woong Km and Juan B. Valdés, The Unversty of Arzona, Tucson, Arzona, USA, and Javer Aparco, Mexcan Insttute of Water Technology (IMTA), Mexco Abstract: The temporal and spatal characterstcs of droughts are nvestgated to provde a framework for sustanable water resources management n a sem-ard regon. Usng the Palmer Drought Severty Index (PDSI) as an ndcator of drought severty, the characterstcs of droughts are examned n the Conchos Rver Basn n Mexco. Ths basn s mportant to both the Unted States and Mexco, because the Conchos Rver supples approxmately 80 percent of the flows of the Lower Bravo/Grande Rver above the bnatonal reservors of Amstad and Falcon. The temporal and spatal characterstcs of the PDSI are used to develop a drought ntensty - areal extent - frequency curve that can assess the severty of a regonal drought n the basn. The analyss of the PDSI suggests that the Conchos Rver Basn had a severe drought n the 990s, whch the basn has not experenced before. Based on ths analyss, the recent drought that occurred n the 990s has an assocated return perod of about 80 to 00 years over the basn. Keywords: Droughts, sem-ard regon, PDSI, frequency curve, return perod. Introducton Consderable research has been carred out n hydrology and water resources, but drought remans a serous concern n many regons of the world. Two major droughts, n terms of duraton and spatal extent, occurred n North Amerca n the 20 th century. Both the drought of the 930s, whch lasted up to seven years n the Great Plans, and the drought of the 950s, whch lasted fve years n the Southwestern Unted States, caused sgnfcant damages both n human lves and economc losses. These droughts also affected Mexco manly n the northern and central regons of the country (Tnajero, 986). In addton to these major droughts of the 20 th century, there have been several other droughts n recent decades n the North Amercan contnent. For example, the 987 to 989 drought lasted three years and covered 36 percent of the Unted States, causng severe losses n energy, water, ecosystems, and agrculture, estmated at US$39 bllon (NOAA Paleoclmatology Program, 2000). In Mexco, the droughts n the mddle of the 970s and the second half of the 990s produced extended damages to crops and cattle n the northwestern states. Droughts are generally assocated wth a sustaned perod of sgnfcantly lower sol mosture levels and water supply relatve to the normal levels that the local envronment and socety have stablzed. There s not, however, a unversal defnton of drought due to conflctng concepts of drought magntude and severty. Dracup et al. (980) have defned the type of drought n order to consder a set of decsons. Based on the nature of the water defct, they defned three types of droughts: meteorologc drought, hydrologc drought, and agrcultural drought. The meteorologc drought s defned as a lack of ranfall so low as to severely affect the flora and fauna of a regon. It leads to depleted water supples both for domestc purposes and for the operaton of power plants. The hydrologc drought s related to a perod durng whch streamflows are nadequate to supply establshed uses under a gven water resources management system. The agrcultural drought s usually descrbed n terms of crop falure from declne n sol mosture wthout any reference to streamflow (Dracup et al., 980). Nowadays, the socoeconomc drought assocated wth the supply and demand of economc goods wth elements of meteorologc, hydrologc, and agrcultural drought s used. The socoeconomc drought occurs when the demand for an economc good exceeds supply as a result of a weather-related shortfall n water supply (Natonal Drought Mtgaton Center, 2000). In general, precptaton data has been used for meteorologcal drought analyss, and streamflow data has been appled for hydrologc drought analyss (Dracup et al., 980; Henrques and Santos, 999; Shn and Salas, 2000). 420

2 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco 42 A large number of regonal drought analyses may be found n the lterature. Karl (983) showed that droughts have longer persstence n the nteror of the Unted States than n the coastal regons n the east and west. Clausen and Pearson (995) presented a method for nvestgatng the spatal and temporal varablty of droughts by a regonal frequency analyss of annual mnmum streamflows. Best regonal estmates of mean drought severty were found for lower truncaton levels, and the severtes and the duratons of the annual maxmum droughts at a ste were almost lnearly related. Shn and Salas (2000) proposed to analyze and quantfy the spatal and temporal patterns of meteorologcal droughts based on annual precptaton data. By usng a neural network algorthm, they determned the posteror probabltes of drought severty and assgned a Bayesan drought ndex for a ste, whch s useful for constructng drought severty maps that dsplay the spatal varablty of drought severty on a yearly bass. Recently, several studes analyzed the relatonshp between droughts and clmatc ndcators. Pechota and Dracup (996) nvestgated the hydroclmatc response n the Unted States to the extreme phases of the Southern Oscllaton. A strong relatonshp between El Nño and extreme drought years was found n the Pacfc Northwest and n the southern Unted States where dry condtons occur consstently durng La Nña events. Chew et al. (998) presented the relatonshp between ENSO and droughts n Australa and showed that dry condtons tend to be assocated wth El Nño. Acosta (988) found a remarkable relatonshp between El Nño occurrences and storage scarcty n dams n northern Mexco. Lu et al. (997) utlzed a Kalman flter to forecast droughts n the Gulf regon of Texas. In ths study, we ntally consdered the drought as a meteorologcal phenomenon characterzed by a prolonged and abnormal mosture defcency as defned by Palmer (965), who developed the Palmer Drought Severty Index (PDSI) to measure the departure of the mosture supply takng nto account the precptaton defct at certan locatons. It has been wdely used to detect the meteorologcal drought and s well documented (Karl, 983; Pechota and Dracup, 996; Cook et al., 999; Kothavala, 999). The pont estmates of the PDSI may then be regonalzed usng geostatstcs technques lke krgng. In spatal analyss, krgng has been wdely appled n a varety of felds such as mnng engneerng, hydrology, and sol scence. A practcal methodology for developng a drought ntensty - areal extent - frequency curve s proposed n ths paper. Ths method would allow decson makers to characterze a regonal drought and to provde useful nformaton for water supply and management plans n a sem-ard basn. The methodology s appled to the Conchos Rver Basn n Mexco. Overvew of the Conchos Rver Basn The Conchos Rver Basn les wthn 26 N-30 N and 04 W-08 W and has an area of 7,964km 2 at ts mouth to the Bravo/Grande Rver near Ojnaga, Mexco. The Conchos Rver orgnates n the ard/sem-ard Tarahumara range n the Mexcan state of Chhuahua. Before reachng the Bravo/Grande Rver at Ojnaga, Mexco, the rver flows almost 560 km through Lake La Boqulla, whch was formed by La Boqulla dam, and receves flow from three major trbutares (e.g., Flordo, San Pedro, and Chuvíscar rvers) as shown n Fgure. Topographcally, Fgure. Stem dagram of the Conchos Rver (935 to 998).

3 422 T-W Km, J.B. Valdés, and J. Aparco the Conchos Rver can be dvded nto three man zones: a relatvely small mountanous regon n the Chhuahuan Serra wth massve plateaus, whch have a mean alttude of 2,500 m and an annual precptaton of around,000mm; a transton zone formed by seres of valleys surrounded by mountanous zones, wth an annual precptaton of about 450 mm; and the Chhuahuan desert at an alttude of about,200 m and an annual precptaton of nearly 300 mm. Mean annual precptaton n the whole basn s about 390 mm, although t s not evenly dstrbuted n tme or space. The waters of the Conchos Rver are used prmarly for rrgaton of nearly 80,000 ha n three major rrgaton dstrcts and for use n hydroelectrc power plants located at La Boqulla and other mnor dams. Surface water rrgaton s fed by water stored n La Boqulla, Francsco I. Madero and Lus L. León dams, among others. Addtonally, about 70,000 ha are rrgated by groundwater. Important Mexcan ctes such as Chhuahua, Hdalgo del Parral, and Delcas are n the basn and growng rapdly due to ncreasng ndustralzaton. The Conchos Rver s also the most mportant trbutary of the Bravo/Grande Rver. The flow of the Conchos Rver supples approxmately 70 to 80 percent of the flow of the Bravo/Grande Rver above the manstream bnatonal reservors of Amstad and Falcon. A bnatonal treaty between the Unted States and Mexco sgned n 944 specfes the mnmum flows to be delvered by Mexco at the confluence of the Conchos Rver wth the Bravo/Grande Rver. Detals of ths treaty may be found n Houston Advanced Research Center (2000) and Texas Center for Polcy Studes (200). Ths treaty allows the flows to be below the mnmum (n a fve-year average) under condtons of extraordnary drought. However, ths concept s not explctly defned n the treaty (Texas Center for Polcy Studes, 200). The sustanablty of the expandng water uses for agrculture and urban purposes, as well as the water rghts for ths regon, are the man ssues between the Unted States and Mexco. The flows of the Conchos Rver to the Bravo/Grande Rver, shown n Fgure 2, have declned substantally snce 994 due to an extended drought n Mexco (Texas Center for Polcy Studes, 200). Lverman et al. (200) ponted out that northern Mexco and the southwest Unted States experenced the worst droughts on record n the 950s, whch suggests that the enhanced mpact of a large-scale forcng mechansm over the clmate of subtropcal North Amerca. The basn was also under extreme drought condtons from the md 940s to early 960s, and wetter condtons began n the late 970s and ended at the begnnng of the 990s. Falure of the summer rans has a dramatc mpact over the basn. Dry sol and hgh surface temperatures ncrease the evapotranspraton, whch affects grassland and agrculture. The drought n the Conchos Rver Basn, wth respect to lower than normal ranfalls, resulted n rrgaton cutbacks and severe agrcultural losses on both sdes Annual Flow (cms) Annual Flow Mean of Annual Flow Year Fgure 2. Annual flows of the Conchos Rver at Ojnaga, Mexco, 955 to of the border. Despte the enormous water management challenge n the Conchos Rver Basn and the deep nterdependence between the avalablty of water n the Lower Bravo/Grande Rver and flows from the Conchos Rver, there has been lttle nvestgaton and publc dscusson of water use and trends n the Conchos Rver Basn (Texas Center for Polcy Studes, 200; Lverman et al., 200). The 990s ranfall was sgnfcantly below normal. For example, as shown n Fgure 3, n 998 not only the magntude of precptaton was affected but also the tmng. Less than 3 percent of the mean annual precptaton n the regon fell n the wnter-half year (November to May), and more than 85 percent of the ranfall occured durng the summer (May to October). The drought durng the 990s drove many small farmers off the land and pro- Fgure 3a. The spatal dstrbuton of precptaton n 998 n the Conchos Rver Basn (Velasco, 2000).

4 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco 423 Fgure 3b. The cumulatve precptaton n 998 n the Conchos Rver Basn (Velasco, 2000). duced a 30 percent reducton n the cattle nventory (Comsón Naconal del Agua, 997). In addton, n the fve-year cycle of the treaty endng on October 2, 997, due to severe reducton of the Conchos Rver nflow to the Bravo/Grande Rver n the 990s (Fgure 2), Mexco owed the Unted States about,240 Mm 3 (.024 mllon ac-ft) wth respect to water delvery under the 944 U.S./ Mexco Treaty on the use of the Bravo/Grande Rver (Texas Center for Polcy Studes, 200). The Palmer Drought Severty Index (PDSI) Palmer (965) proposed the Palmer Drought Severty Index (PDSI) based on a balance between mosture supply and demand. The ndex uses a monthly tme seres of precptaton (P) and temperature (T) to produce a sngle numercal value that represents the severty of wetness or ardty for a partcular month. In dry spells, a PDSI of 0.5 to 0 s consdered near normal,. 0 to 0. 5 ncpent drought, 2. 0 to. 0 mld drought, 3. 0 to 2.0 moderate drought, 4. 0 to 3. 0 severe drought, and 4. 0 or less extreme drought. The followng procedure to calculate the PDSI s orgnally descrbed n the report by Palmer (965) and related papers (Karl, 983; 986; Alley, 984; 985). The computaton of the PDSI begns wth a clmatc water balance usng hstorc records of monthly precptaton and temperature. Sol mosture storage s consdered by dvdng the sol nto two layers. The upper layer, called surface sol layer, s assumed to contan one nch of avalable mosture at feld capacty, whch Palmer orgnally used and the Natonal Clmatc Data Center (NCDC, recommends. The underlyng layer has an avalable capacty that depends on the sol characterstcs of the ste beng consdered. Palmer used an avalable water capacty (AWC) of nne nches for central Iowa and fve nches for western Kansas. The AWC vares sol to sol and can be taken as a value, whch s more or less representatve of the area n general. Mosture cannot be removed from the underlyng layer untl all of the avalable mosture has been removed from the surface layer. Runoff (RO) s assumed to occur f both layers reach ther combned mosture capacty (AWC). Four potental values are computed for clmate coeffcents. Potental evapotranspraton (PE) was computed n our study usng the Hargreaves method, whch s commonly used because of ts broad emprcsm (Shuttleworth, 992). The Hargreaves equaton has shown to provde more reasonable estmates of evapotranspraton, because t contans an explct lnk to solar radaton through the water equvalent of extraterrestral radaton, and the dfference between maxmum and mnmum temperature (Jensen et al., 990; Shuttleworth, 992) nstead of the Thornthwate method orgnally used by Palmer. Potental recharge (PR) s the amount of mosture requred to brng the sol to feld capacty. Potental loss (PL) s the amount of mosture that could be lost from the sol to evapotranspraton provded precptaton durng the perod was zero. Potental runoff (PRO) s the dfference between the potental precptaton and the potental recharge. The clmate coeffcents are computed as a proporton between averages of actual versus potental values for each of 2 months at each locaton. These clmate coeffcents are used to compute the amount of precptaton requred for the Clmatcally Approprate For Exstng Condtons (CAFEC). The dfference, d, between the actual ( P ) and CAFEC precptatons ( Pˆ ) s an ndcator of water defcency for each month. d = P Pˆ = P ( α PE + βpr + PRO + δpl ) () where α = ET PE, β = R PR, = RO PRO, and δ = L PL for 2 months. The value of d s regarded as a mosture departure from normal because the CAFEC precptaton s an adjusted normal precptaton. A Palmer Mosture Anomaly Index (PMAI), Z, s defned as Z = Kd (2) where K s a weghtng factor. The value of K s determned from the clmate record before the actual model calculaton. After consderable experments, Palmer suggested emprcal relatonshps for K such that K 7.6 = 2 D K = ' K where D s the average of the absolute values of d, and ' K s dependent on the average water supply and demand, gven by ' (3)

5 424 T-W Km, J.B. Valdés, and J. Aparco K PE + R + RO D P L + ' =.5 log where PE s the potental evapotranspraton, R s the recharge, RO s the runoff, P s the precptaton, and L s the loss. Havng establshed the value of K, the PDSI s gven by PDSI + = PDSI where the PDSI of the ntal month n a dry or wet spell s equal to Z. 3 Although the PDSI s consdered as a meteorologcal drought ndex, the procedures mentoned above contan the concepts of hydrologcal drought. The term hydrologc drought ndex s used as t pertans to systematc accountng of the terms assocated wth mosture nflow, outflow, and change of storage (Karl, 986). Accordng to Alley (984), the PDSI has postve characterstcs useful for drought montorng. For example, t provdes a measurement of the abnormalty of weather for a regon and an opportunty to place current condtons n hstorcal perspectve. In addton, the PDSI s a standardzed value avalable to compare and assess regonal drought (Natonal Drought Mtgaton Center, 2000). It has also been appled as an ndex to forecast droughts n the Gulf regon of Texas by Lu et al. (997) usng clmatc precursors. Temporal Characterstcs of Droughts n the Conchos Rver Basn The PDSI was used to provde an ndcator of drought severty n ths study. There are some lmtatons to consder when usng the PDSI. The PDSI s senstve to the AWC of a sol type, and only two sol layers for sol mosture storage s a smplfcaton so that these assumptons may not be accurate for a locaton. Due to the lack of sol type nformaton n the basn, t was assumed that the surface sol layer water capacty s one nch and the underlyng sol layer water capacty s sx nches. These values, whch were adopted from the NCDC, are values of the AWC used n the Texas Clmatologc Regon 5, located n the mmedate vcnty of the Conchos Rver Basn. Another lmtaton s that the PDSI may be naccurate n wnter when snow occurs or n regons where the ground s frozen, because all precptaton s treated as ran (Alley, 984; Karl and Knght, 985). However, n ths case, because the basn les n a semard regon, the annual precptaton falls durng the warm season, so that a large part 3 Z (4) (5) of the nterannual varatons are strongly assocated wth the summer precptaton varablty. The precptaton and temperature data n the Conchos Rver Basn were provded by the Mexcan Insttute of Water Technology (IMTA, Each staton has a dfferent data perod (Table ) and s rregularly dstrbuted n the Conchos Rver Basn (Fgure 4). The regonal representatve of PDSI was calculated usng the areal mean of precptaton and temperature to reconstruct across the basn (Fgure 5a). The basn has experenced droughts n terms of severty and duraton n the late of the 930s, at the begnnng of the 950s, and n the 990s. Durng the perod of 934 to 998, the basn also had 234 months of moderate drought (PDSI < -2.0), 27 months of severe drought (PDSI < -3.0), and 76 months of extreme drought (PDSI < -4.0). Severe droughts contnued n the 990s wth respect to severty and duraton. The drought n the 990s resulted n the lack of avalable water n northern Mexco, whch brought several problems to the socety and n the lack of avalable water n the Lower Bravo/Grande Rver (Texas Center for Polcy Studes, 200). The Standardzed Precptaton Index (SPI) s another ndcator of drought severty wdely used. The SPI was desgned to facltate the detecton and montorng of droughts by McKee et al. (993), and t s easer to calculate than the PDSI. The SPI s manly based on the probablty of precptaton for a gven tme perod. A key feature of the SPI s the flexblty to measure drought at dfferent tme scales. Values range from 2.00 and above (extremely wet) to 2.00 and less (extremely dry) wth near normal condtons rangng from 0.99 to A drought s defned whenever the SPI reaches a value of.00 and contnues untl the SPI becomes postve agan. Fgure 5b shows the SPI n the Conchos Rver Basn. Velasco (2000) also ndcated a sgnfcant drought durng the 990s from the analyss of SPI for the Conchos Rver Basn. In ths study, the PDSI was manly used for regonal drought analyss because t takes nto account the mosture stored n the upper sol layers and therefore consders, even f n a rela- Table. Precptaton and Temperature Statons n the Conchos Rver Basn Staton # Staton Name Perod Chhuahua Balleza Camargo Cudad Jmenez Ojnaga Cudad Delcas Hdalgo Del Parral La Boqulla Las Burras Meoqu Ojo Calente Vlla De Aldama

6 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco Ro Conchos Basn 5 Lattude (Degree) Ro San Pedro Ro Conchos Lus L. Leon Dam 2 Ro Chuvscar Francsco I. Madero Dam La Boqulla Dam 4 7 Ro Flordo Longtude (Degree) Fgure 4. Locaton of precptaton and temperature statons n the Conchos Rver Basn (Adapted from Houston Advanced Research Center, 2000). tvely elementary fashon, the drought persstence. However, a more profound research on the matter of persstence wll be made n future researches. Regonal Drought Analyss Although the estmaton of drought severty at a pont or as a regonal representatve generally gves useful nformaton for water management, t may be nterestng to assess the drought for the entre basn. Ths regonal drought analyss s useful for declarng the drought condton or determnng the drought ntensty durng a partcular year (Shn and Salas, 2000). One of most useful methods to assess drought n a regon s the drought severty area frequency curve, whch was proposed by Henrques and Santos (999). They obtaned the area of nfluence of each staton usng the Thessen method and constructed the severty area frequency curves usng the drought severty from the synthetc precptaton seres. The Thessen method, however, does not consder the stochastc characterstcs of the data. In ths study, the regonal drought s analyzed based on a drought ntensty areal extent frequency curve developed usng a geostatstc technque to estmate regonal varables (Matheron, 963) for each return perod. Geostatstcs s a collecton of generalzed lnear regresson technques, whch s used to estmate the areal extent of the droughts n the Conchos Rver Basn. Ths spatal dsplay wll provde valuable nformaton for the preparaton of drought preparedness plans for the basn. Detals of the krgng technque are provded n the Appendx of ths paper. In order to make a regonal varable for descrbng a phenomenon spatally dstrbuted over a regon, drought ntensty was ntroduced at each staton. Drought ntensty can be calculated by multplyng the annual sum of PDSI n dry spells by the probablty of drought occurrence for each year. The probablty of drought occurrence s determned by dvdng the number of months that have a PDSI lower than.0 by 2 months. In ths way, each drought event can be allotted evenly for the partcular year, and we can examne the drought for the year avodng the ntermttence. The drought ntensty areal extent frequency curve provdes useful nformaton that contan drought ntensty and area subjected to drought for a gven drought return perod. A summary of the procedure for the drought ntensty areal extent frequency curve proposed n ths study follows: For every year, evaluate drought ntensty at each staton. Estmate the spatal dstrbuton of the drought ntensty usng a krgng estmator. Obtan the drought ntensty assocated wth the areal extent percent usng the dstrbuton map produced n the prevous step. Perform the frequency analyss for each drought areal extent to assocate drought ntensty wth return perods. Construct the drought ntensty areal extent fre-

7 426 T-W Km, J.B. Valdés, and J. Aparco quency curve for the regon by consderng the adequate probablty dstrbuton. In drought studes, the frequency analyss s a tradtonal and practcal method. Usng the annual values n the frequency analyss, only the magntude of a drought s of nterest. In our study, the drought ntensty has defntely negatve values. To be appled before fttng to an avalable dstrbuton, the drought ntensty should be converted to postve values n order to represent the extreme condton and to analyze the assocated rsks of the droughts usng the exceedance probablty. The Kolmogorov- Smrnov (K-S) test and the Ch-Square (χ 2 ) tests, whch are standard tests for probablty dstrbutons, were used. As shown n Table 2, most of the dstrbutons passed the test. The Extreme Value Type I (EV I) dstrbuton was selected n ths study. Ths dstrbuton s a specal case of the Generalzed Extreme Value (GEV) dstrbuton wth two parameters. It has been conventonal to use the EV I dstrbuton to represent precptaton extremes, and also has been used for drought analyss, e.g., Henrques and Santos (999). The tme seres of PDSI (Fgure 5a) and SPI (Fgure 5b) suggest that the Conchos Rver Basn has experenced severe droughts n the last 60 years. It also shows that the Conchos Rver Basn had an extreme drought n the 990s based on the PDSI (Fgure 5a). Usng the drought ntensty areal extent frequency curve we proposed, we examned the drought n the basn based on the ntensty of the return perod. For examnng the drought n the 990s, the spatal dstrbuton of droughts that occurred n the 990s was estmated by a krgng estmator usng the drought ntensty, as shown n Fgure 6. The krgng estmated the areal extent subjected to drought usng 2 stes (Table and Fgure 4). The drought ntensty means tme average of drought severty n dry spells and represents the drought severty classfed by Palmer, whch s ndcated by a gray scale between 0 and -6. Krgng exhbted a good approach PDSI Jan-34 Jan-42 Jan-50 Jan-58 Jan-66 Jan-74 Jan-82 Jan-90 Jan-98 Tme Fgure 5a. The Palmer Drought Severty Index (PDSI) n the Conchos Rver Basn. SPI Jan-34 Jan-42 Jan-50 Jan-58 Jan-66 Jan-74 Jan-82 Jan-90 Jan-98 Tme Fgure 5b. The Standard Precptaton Index (SPI) n the Conchos Rver Basn. n estmatng the dstrbuton of drought ntensty, even though data statons are rregularly dstrbuted. Because krgng consders an mplct covarance structure wthn the data, t s able to produce unbased estmates. In fact, when we use a determnstc method n estmatng regonal varables, t s troublesome to deal wth the sparse and rregularly dstrbuted data ponts. Fnally, n Fgure 7, the hstorcal droughts are compared wth the drought ntensty areal extent frequency curve, whch was constructed usng data before 990. Under ths analyss, the droughts that occurred n 994, 996, and 998 have an assocated return perod of 0 to 30 years. Especally the drought that occurred n 995 s the most severe drought ever experenced n the basn. As shown n Fgure 5a, the basn has never experenced droughts lke that before 990. Data after 990 was not used to construct the drought ntensty areal extent frequency curve, whch has a hgher return perod of more than 80 years. The 990s drought ntensty has a return perod of approxmately 00 years wth an ncrease n areal extent. In addton to the hgh return perod, t s a very extreme drought of the basn snce more than 70 percent of the basn was below 4 (Extreme drought condton). The 990s droughts caused explodng water demands and subsequent mpacts n the basn and n northern Mexco. A survey of some of these severe mpacts affectng several bnatonal rvers may be found n Lverman et al. (200). Concludng Remarks Ths study was focused on analyzng temporal and spatal extents of droughts n the Conchos Rver Basn usng the PDSI as an ndcator of drought severty. The PDSI s one of the drought ndces that have been more wdely used for a varety of applcatons. It provdes decson makers wth a measurement of the abnormalty of recent weather for a regon and an opportunty to place

8 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco 427 Table 2. The Results of Goodness Ft Test for Canddate Dstrbutons for Areal Extent 50 Percent Dstrbuton Remark Remark # of Remark Remark S.L. K-S % 5% χ 2 D.F. % 5% % 5% Normal 0. OK OK OK OK Log-Normal 0.0 OK OK OK OK Gamma 0.2 OK OK OK OK Pearson Type OK OK OK OK Log-Pearson Type OK OK OK OK Extreme Type I 0.09 OK OK OK OK Generalzed Extreme 0.0 OK OK OK OK Wakeby 0.09 OK OK OK OK 5.. Sgnfcant Level (S.L.) of K-S Test % = 0.27 and 5% = 0.23 Fgure 6. Areal dstrbuton of drought ntensty for hstorcal droughts that occurred n the 990s for the Conchos Rver Basn.

9 428 T-W Km, J.B. Valdés, and J. Aparco Drought Intensty (PDSI) Area Extent (%) 0 Yr 20 Yr 30 Yr 50 Yr 80 Yr 00 Yr Fgure 7. Drought ntensty - areal extent - frequency curve for the Conchos Rver Basn wth the hstorcal droughts that occurred n the 990s. current condtons n hstorcal perspectve. In addton, t provdes spatal and temporal representatons of hstorcal droughts. The man objectve of ths study s to develop methodologes to analyze and quantfy regonal droughts n sem-ard regons. The proposed drought analyss approaches were appled to the Conchos Rver Basn, whch s one of the most mportant rver basns of the Unted States/Mexco border regon. The basn has experenced droughts n terms of severty and duratons n the 930s, 950s, and 990s. In partcular, the persstent droughts n the 990s serously affected urban water supply and agrcultural rrgaton, as well as reducton of nflows nto the Bravo/Grande Rver. A regonal frequency analyss was presented as a method for nvestgatng the spatal and temporal varablty of droughts based on the drought ntensty usng the PDSI. The spatal drought dstrbutons were examned usng a krgng estmator. The drought ntensty areal extent frequency curve constructed n ths study contans drought severty and drought area wth respect to drought return perod so as to descrbe and characterze the spatal and recurrence patterns of droughts. It s shown that the drought that occurred n the 990s s assocated wth a return perod of 80 to 00 years wth a large areal extent. The droughts n the Conchos Rver Basn and the related sgnfcant decrease n the flows of the Conchos Rver reachng the Bravo/Grande Rver have created strong controversy n both the Unted States and Mexco. Characterzaton of the droughts n the Conchos Rver Basn wll be useful not only for the development of a drought preparedness plan n the basn but also for the provsons of the nternatonal treaty that regulates the flows of the Bravo/Grande Rver trbutares between the Unted States and Mexco. The next step n our research wll be to evaluate the forecastng potental usng clmatc precursors to predct drought ndces lke Lu et al. (997; 998). Prelmnary analyses performed by the authors ndcate small correlatons between ENSO and the summer precptaton n the Conchos Rver Basn. Lverman et al. (200) also analyzed possble teleconnectons n the basn. Also, an analyss ncludng persstence wll be done n a future work. Acknowledgments Ths study s based upon work supported by SAHRA (Sustanablty of Sem-Ard Hydrology and Rparan Areas) at the Unversty of Arzona under the STC Program of the Natonal Scence Foundaton, Agreement No. EAR The authors are grateful to Drs. Kevn Lansey, Tereza Cavazos and Mohammad Karamouz of the Unversty of Arzona for ther valuable comments and suggestons n our research. The authors are also grateful to Dr. Carolne Lafleur for provdng the krgng estmaton code ( About the Authors Tae-Woong Km s a PhD student n the Department of Cvl Engneerng and Engneerng Mechancs and a research assstant at the NSF Scence and Technology Center for Sustanablty of Sem- Ard Hydrology and Rparan Areas (SAHRA) at the Unversty of Arzona, PO Box 20072, Tucson, Arzona , USA. Emal: taek@emal.arzona.edu. Hs research s focused on hydrologc forecastng and stochastc hydroclmatology n water resources systems. Dr. Juan B. Valdés s Professor and Head of the Cvl Engneerng and Engneerng Mechancs and a Co-Investgator at the NSF Scence and Technology Center SAHRA at the Unversty of Arzona, MS 20072, Tucson Arzona , USA. Emal: jvaldes@ u.arzona.edu and s a professor n the Department of Hydrology and Water Resources. Dr. Valdes has held academc and admnstratve postons at Smon Bolvar Unversty where he was head of the graduate program n hydrology and water resources (Caracas, Venezuela), and at Texas A&M Unversty where he was head of the Envronmental, Ocean, and Water Resources Dvson, Cvl Engneerng, and Assocate Drector of the Clmate System Research Program. He s a fellow of the Amercan Socety of Cvl Engneers and the Amercan Geophyscal Unon. Hs research nterests focus on stochastc and determnstc hydrology, flood and drought forecastng, the analyss, synthess, and samplng of hydrologc processes, mathemat-

10 Frequency and Spatal Characterstcs of Droughts n the Conchos Rver Basn, Mexco 429 cal models of natural resources systems, the modelng of space-tme precptaton, envronmental rsk assessment, and the stochastc modelng of envronmental processes. Dr. Javer Aparco s head of the Hydrologc Technology Dvson at the Mexcan Insttute of Water Technology, Paseo Cuauhnáhuac 8532, Jutepec 62550, Mor., Méxco snce 994. Emal: aparco@tlaloc. mta.mx. He has been a professor at the Natonal Unversty of Mexco for 22 years and serves as assocate edtor of the journal, Ingenería Hdráulca en Méxco (Hydraulc Engneerng n Mexco). He s a member of the Mexcan Academy of Engneerng, the Mexcan Hydraulcs Assocaton, and the Amercan Socety of Cvl Engneers. He has publshed more than 90 papers and reports on hydrology, water resources, computatonal hydraulcs and rver mechancs. He receved the Javer Barros Serra award for the best book on cvl engneerng, Fundamentals of Surface Hydrology, by the Mexcan Cvl Engneers College. Hs recent research nterests are drought characterzaton and forecast, numercal methods for unsaturated flow smulaton and hydrologc modelng. Dscussons open untl March, References Acosta, G.A El Nño: sus efectos sobre el norte de Méxco (El Nño: Its Effects on Northern Méxco). Ingenería Hdráulca en Méxco 3, No. : Alley, W.M The Palmer Drought Severty Index; Lmtatons and Assumptons. Clmate Appl. Meteor. 23: Alley, W.M The Palmer Drought Severty Index as a Measure of Hydrologc Drought. Water Resour. Bulletn 2, No.: Chew, F.H.S., T.C. Pechota, J.A. Dracup, and T.A. McMahon El Nno/Southern Oscllaton and Australan Ranfall, Streamflow and Drought: Lnks and Potental for Forecastng. J. Hydrology 204: Comsón Naconal del Agua. Centro de Investgacones sobre la Sequía Plan Hdráulco Gran Vsón del Estado de Chhuahua Cook, E.R., D.M. Meko, D.W. Stahle, and M.K. Cleveland Drought Reconstructons for the Contnental Unted States. J. Clmate 2: Dracup, J.A., K.S. Lee, and E.G. Paulson Jr On the Defnton of Droughts. Water Res. Res. 6, No. 2: Henrques, A.G., and M.J.J. Santos Regonal Drought Dstrbuton Model. Phys. Chem. Earth (B) 24, No. -2: Houston Advanced Research Center Water and Sustanable Development n the Bnatonal Lower Ro Grande/Río Bravo Basn. Houston, Texas, USA. Jensen, M.E., R.D. Burman, and R.G. Allen Evapotranspraton and Irrgaton Water Requrements. ASCE Manual 70. Karl, T.R Some Spatal Characterstcs of Drought Duraton n the Unted States. J. Clmate and Appled Meteorology 22: Karl, T.R The Senstvty of the Palmer Drought Severty Index and Palmer s Z Index to Ther Calbraton Coeffcents Includng Potental Evapotranspraton. J. Clm. Appl. Met. 25: Karl, T.R. and R.W. Knght Atlas of Monthly Palmer Hydrologcal Drought Indces (93-983) for the Contguous Unted States. Ashevlle, North Carolna, USA: Natonal Clmatc Data Center. Kothavala, Z The Duraton and Severty of Drought Over Eastern Australa Smulated by a Coupled Ocean-atmosphere GCM wth a Transent Increase n CO2. Envronmental Modelng & Software 4: Lu, Z., J.B, Valdés, and D. Entekhab Merged Forecasts of Drought Index Anomales Along the Gulf Coast n the US Usng Multple Precursors. Expermental Long-Lead Forecast Bulletn, Natonal Weather Servce NCEP-CPC 6, No. 2: 9. Lu, Z., J.B. Valdés, and D. Entekhab Mergng and Error Analyss of Fegonal Hydrometeorologc Anomaly Forecasts Condtoned on Clmate Precursors. Water Res. Res. 34, No. 8: Lverman, D., T. Cavazos, M.C. Lemos, E. Trgoso, and M. Hart Clmate Assessment for the US-Mexco Border and Northern Mexco. Post presentaton for the frst annual meetng of SAHRA. The Unversty of Arzona. Matheron, G Prncples of Geostatstcs. Econom. Geol. 58: McKee, T.B., N.J. Doesken, and J. Klest The Relatonshp of Drought Frequency and Duraton to Tme Scales. Preprnts, 8th Conference on Appled Clmatology, 7-22 January, Anahem, Calforna, USA: Natonal Drought Mtgaton Center Drought Scence: Understandng and Defnng Drought. ndmc/engma/def2.htm. NOAA Paleoclmatology Program North Amercan Drought: A Paleo Perspectve. paleo/drought/. Palmer, W.C Meteorologcal Drought. Research Paper No. 45. Washngton, D.C., USA: U.S. Weather Bureau. Pechota, T.C. and J.A. Dracup Drought and regonal hydrologc Varaton n the Unted States Assocaton wth the El Nno-Southern Oscllaton. Water Res. Res. 32, No. 5: Shn, H.S. and J.D. Salas Regonal Drought Analyss Based on Neural Networks. J. Hydrologc Engneerng 5, No. 2: Shuttleworth, W.J Evaporaton. In Handbook of Hydrology. D.R. Madment, ed. New York, New York, USA: McGraw Hll:

11 430 T-W Km, J.B. Valdés, and J. Aparco Texas Center for Polcy Studes The Ro Conchos: A Prelmnary Overvew. Austn, Texas, USA. Tnajero, G.J Análss de la sequía en Méxco en el perodo (Analyss of droughts n Méxco n the perod ). Las varacones clmátcas, la sequía y la desertfcacón, Secretaría de Agrcultura y Recursos Hdráulcos (Secretary of Agrculture and Water Resources), Méxco. Velasco, V. I Metodología para formular lneamentos de estratega y planes de accón para afrontar sequías (Methodology to formulate strategy gudelnes and acton plans to face drought). Internal report, Mexcan Insttute of Water Technology, Mexco. Appendx: Bref Descrpton of Krgng Technque The krgng estmator z * (x 0 ) n Equaton 6 s a best lnear unbased estmator (BLUE) because the weghts l are chosen to satsfy the condtons of unbasedness and mnmum varance (Borga and Vzaccaro, 997; Olea, 999). * N z ( x ) = λ z( x ) (6) 0 = A krgng system of n+ lnear equatons wth n+ unknowns,.e., λ,, λ n, m s N λ + µ = j= N j j 0, =,, N (7) λ j = (8) j= where µ s a Lagrange multpler arsng from the unbasedness condton (Borga and Vzaccaro, 997), and s the semvarogram functon, whch represents the spatal correlaton structure of the regonalzed varables. Let z(x) s the observed value at pont x. The expermental semvarogram can be estmated by N( h ) 2 ( h ) = [ z( x ) z( x + h )] (9) 2N( h ) = where N(h) s the number of pars of observatons separated by a dstance, h. Usng matrx, the krgng system can be expressed n more compact form. AX=b (0) where X s the vector of the unknowns, b s the rghthand-sde n Equaton 7, and A s the coeffcent matrx. X=[ λ λ λ µ ] 2 L () N A= 2 M N 2 22 M 2N L L L L L N N 2 M NN 0 (2) b=[ L ] (3) 0 20 N0