Development of Streamflow Drought Severity- and Magnitude-Duration-Frequency Curves Using the Threshold Level Method

Open Access Discussions ce, Gwangju, ered considerably ecting wide areas Sciences ffi ff ff Earth System Earth Hydrology and and Hydrology ect the streamflow drought sever- ff 3 14676 14675 , and K. S. Lee 2 , E.-S. Chung 1 This discussion paper is/has beenSciences under (HESS). review Please for refer the to journal the Hydrology corresponding and final Earth paper System in HESS if available. Ministry of Land, Infrastructure and Transport, Yeongsan Flood Control O Department of Civil Engineering, Seoul National University of ScienceDepartment and Technology, of Civil Engineering, Seoul National University, Seoul, Republic of Korea acteristics. Drought is a recurringand large regional numbers multi-dimensional of phenomenonintensity over people. a the Droughts last have fewhas decades dramatically significantly (ComEC, increased increased 2007). in due Industrial to addition, number sector the population and expansion; demand growth water for andparts water scarcities agricultural, of have energy, the occurred and worldmore almost in- (Mishra important every and but Singh, year is 2011). in complicated Thus, by many drought the lack risk of analysis a has precise become drought definition and char- four threshold methods could be derivedated at SDF any and frequency MDF and curves. durationresources These from systems the SDF for gener- and streamflow MDF drought curves and are water useful supply in management. designing water 1 Introduction intensity-duration-frequency curve). Severity was representedvolume as for the the total specific water drought deficit age duration, water and deficit. magnitude was The defined variableinstream as threshold flow the level requirement, daily method which aver- was canity introduced significantly and to a magnitude. set The the four target sired threshold yield levels for utilized water were use. fixed, Thefrom threshold monthly, the daily, levels other and for levels de- the and desiredmands represented yield were di more realistic considered. conditions The because streamflow real drought water severities de- and magnitudes from the This study developed a comprehensiveity method and to quantify magnitude streamflowwere drought developed: based the sever- on streamflow droughtthe a severity-duration-frequency (SDF) streamflow traditional curve drought frequency and magnitude-duration-frequency analysis. (MDF) Two curve types (e.g., of a curve rainfall Abstract Development of streamflow drought severity- and magnitude-duration-frequency curves using the threshold level method J. H. Sung Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/10/14675/2013/ 10, 14675–14704, 2013 doi:10.5194/hessd-10-14675-2013 © Author(s) 2013. CC Attribution 3.0 License. 1 Republic of Korea 2 Seoul, 139-743, Republic3 of Korea Received: 5 October 2013 – Accepted: 14Correspondence November to: 2013 E.-S. – Chung Published: ([email protected]) 3 December 2013 Published by Copernicus Publications on behalf of the European Geosciences Union. 5 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 14678 14677 values are typically larger than zero, the most cient magnitude over prolonged durations and ff ffi variations have been widely applied for drought analyses ff -moment ratio diagrams. Step 4 is to develop four SDF and MDF L ects general crops, causes temporary water scarcity for human/livestock consump- ecting everyday life. Dracup et al. (1980) defined drought as follows: (1) nature of Based on the reported drought definitions and threshold level approaches, this study However, drought is closely related to the deficiency of available water that negatively Drought implies a period of time when the supply of water cannot meet its typical ff ff dardized Precipitation Index) and PDSIknowledge (Palmer Drought of Severity probability Index): distributions (1) is no a required priori and (2) drought characteristics, such curves with four threshold levelscompare using all the SDFs selected and probability MDFs distribution. with Step the 5 four is2.2 threshold to levels. Streamflow drought severity and magnitude In temperate regions wherewidely the used runo method to estimate(Yevjevich, 1967; a hydrological Fleig drought et is al.,2012). the 2006; The threshold threshold Tallaksen level et approach level method al., has 2009; the Van following Loon advantages and over other Van SPI Lanen, (Stan- old levels for fixed,to monthly, daily, calculate and the monthly totalwater desired water deficits yield deficit (or for volumes magnitude) water (or foris use. all severity), to drought Step durations, identify events 2 and the atand daily is best-fitted the MDF average four probability threshold using distribution levels. functions Step of 3 annual maximum SDF variable and one fixed threshold levelsyses. were This proposed methodology using was traditional applied frequency to anal- the Seomjin River basin in South2 Korea. Methodology 2.1 Procedure This study consists of five steps, as shown in Fig. 1. Step 1 is to determine the thresh- daily streamflows. developed a comprehensive conceptmagnitude to using quantify the a streamflowduration-frequency traditional drought (SDF) frequency and severity magnitude-duration-frequency and analysis. (MDF) Two curves streamflow with three drought severity- extended the steady threshold concept to the variable method, employing monthly and water availability”. Therefore, threshold levelity, approaches and to define magnitude the of duration,and a sever- annual drought event natural while runo(Yevjevich, considering 1967; the Sen, daily, 1980; monthly,Tallaksen, seasonal, Dracup 2003; Wu et et al.,jgevoort, al., 1980; 2012). 2007; These Kjeldsen Pandey approaches et et provideavailability an al., al., of analytical 2008a; interpretation 2000; river Tigkas of flow; Hisdal the et aold expected and al., drought level. 2012; occurs This when van levelto the Hui- is streamflow be falls frequently steady below taken the during as thresh- the a considered certain month, percentile season, flow and or is year. assumed Kjeldsen et al. (2000) Tsakiris, 2009; Wang et al., 2011; Tabari et al., 2013). a tion, and influences economicdefined renewable drought resources. as Tallaksen a and “sustained van and Lanen regionally (2004) extensive occurrence of below average data (e.g., month, season, orflows year); while (3) considering threshold the for distinguishing mean,(4) low median, regionalization flows mode, and/or from or standardization. high anyhave Based been other on proposed derived these over threshold; the definitions, and yearsof various to various indices identify, drought characterize, components, and quantify suchfactors. the as That attributes meteorological, is, hydrological, recent and studiesistics agricultural have using focused various indices on (Palmer, such 1965;and multi-faceted Rossi Wilhite, drought et 1999; character- al., Tsakiris 1992; McKee et et al., al., 1993; 2007; Byun Pandey et al., 2008a, b; 2010; Nalbantis and demand. Rainfall deficienciessubsequent of reductions su in streamflownomic intervene activities of with a the region,a normal leading to agricultural a and decrease eco- water in agriculture deficit production (e.g., and in precipitation, turn soil moisture, or streamflow); (2) basic time unit of 5 5 25 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (1) (2) , deficit i D and severity 1 , and the ratio c + i t -moment ratios, d L -moment ratio di- L and erent meanings, total ff i d for simplicity. This numbers are often used for perennial 1 + i 95 d Q for the fixed threshold considering or , as shown by the definition sketch to i i 70 T d Q 70 Q 10 % of , the mutually dependent drought events were c 14680 14679 = z c for several distributions are required. In the case z ) are plotted as a scatterplot and compared with 4 4 τ τ and between two droughts of duration 3 i τ t 3 days and -kurtosis ( , and time of occurrence, = i L -moment ratio diagram, the relationship between the parame- c S L t , c c z t -moment ratio curves of candidate distributions. − + ), and L 1 3 1 + τ -moment ratio diagram is a graph where the sample + i i L s d , respectively, are less than the predefined critical duration -moment ratios + 1 + L i + i i s . d s i i = s d = = and When plotting an A constant threshold from the FDC based on the entire record period is used in Fig. 3 To further describe the degree of hardship due to a drought event, the daily average If the “inter-event” time A sequence of drought events can be obtained using the streamflow and variable pool i -skewness ( -moment diagrams of various goodness-of-fit techniques were used to evaluate the pool i s ters and of a GEV distribution, the three-parameter GEV distribution described by Stedinger L the theoretical agrams have been suggestedcandidate distributions as for a a usefulused dataset to (Hosking graphical and assist tool Wallis, in forline 1997), the of discriminating Two best selection representations fit, amongst of whichdistribution. can statistical be distributions plotted are on the the same sample graph to average facilitate and selecting the best-fit 2.4 Probability distribution function L best probability distribution function1990; for Chowdhury datasets et in1997). al., several The recent 1991; studies Vogel (Hosking, and Fennessey, 1993; Hosking and Wallis, the Korean hydrologic condition, namely, a monsoon climate. (top). The threshold can also bestudied fixed if using only seasonal the flowthresholds deficits data for from are summer the and relevant studied season winterapproaches. separately. seasons This Figure using variable study 3 monthlyreservoir. used presents and daily a two threshold fixed seasonal threshold based on the water demand to the The threshold choice is influenced byIn the general, study a objective and percentile region from andold. the available Relatively data. flow low duration curve thresholdsrivers (FDC) in (Kjeldsen can et the be al., range used 2000). This as of study the selected thresh- 2.3 Threshold selection water deficit magnitudefollows: of independent drought events is proposedm and defined as d This study assumed should be studied later in more detail. of minor drought events.et Because al. these (1997) droughts proposed arescribed that mutually using the some dependent, independent types Tallaksen sequence of of pooling, as drought described events below. musts be de- between the inter-event excess volume pooled to form a drought event as (Zelenhasic and Salvai, 1987; Tallaksen et al., 1997) sectors impacted by the drought. threshold level method. Each droughtvolume event (or is severity), characterized byin its Fig. duration, 2. With a prolonged dry period, the long drought spell is divided into a number as frequency, duration, and severity, are directly produced if the threshold is set by water deficit magnitude and dailytion. average water deficit magnitude, for a specific dura- Therefore, this study defined severity and magnitude as two di 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (in for (4a) 1 − α/κ ), building + 2 0, the GEV ξ 0,0, (3a) (3b) = ≤ 0.17. Hosking 6= = κ x = κ κ 1350 mmyr 3 τ < −∞ ≤ , 0 0, (4b) 6= = and 212.3 km, respectively. κ κ 2 0; and for the shape parameter’s GEV = 4 τ /k κ 1 ). Additionally, 69.2 % of the entire 2 ), forest land (3400.61 km ) 2 for ξ and 3 − τ is a shape parameter. For x ( ≤ ∞ κ κ α x . (5b) − ) 14682 14681 κ 1 − 2 (in the southeastern region) during the 1975–2012 − −∞ ≤ ξ − 1 − − α 0; x 6(1 /κ exp 1 · is a scale, and − + κ < ) 1 ) α κ − ) ξ ) is forest land. Major droughts occurred in the Southern Je- − κ ξ for /κ 2 3 − − exp 1 − α 2 − x 1600 mmyr − x ) ( − ξ ξ − > κ α ≤ ∞ (1 − − α 3, (5a) x − 10(1 x ), and other land uses (567.86 km x ( 1 − ≤ − 2 exp − κ ) ) is a location, α ) κ κ − − ξ κ − − − − α/κ 3 4 1 2 exp + − − − exp exp ξ 1 1 α α (1 = = 2(1 5(1 = = 0. Here, ) ) ) ) = = x x The land use consists of arable land (876.29 km The administrative districts where the basin is located cover three provinces, four 1000 mm of precipitation on average in 1977, 1988, 1994, and 2008. Among these x x ( ( ( ( 3 4 sites (67.12 km basin area (4,911.89 km olla Province from 1967 to< 1968 and from 1994years, to the 1995. annual The Seomjin precipitation Rivererage in basin of 1988 had 1385.5 was mm only fromthe 782.7 1967 mm “River to (56.5 %) Survey 2008, of representing Reportapproximately the a every (K-water, 10 annual serious yr. 1992)”, av- drought. According a to drought in Seomjin river basin occurs County, Gokseong County,Jangheung Gurye County in County, the Southern Hwasunern Jeolla Province; County, Gyungsang and Province). Boseong Handing Influx CountyJeolla County, rates in Province), the into and 44 South- % the (the basin NorthernProvince), by and Jeolla a Province), province total and are of 9 % 47 129 % 322 (Southern households (Southern Gyeongsang and 321 104 residents live in these areas. the north region) to observation period. In general,during approximately the 60 % wet of seasonsonality the (July in annual the through precipitation precipitation occurs September)(October causes in through periodic South March) shortages and Korea. of flood This water damage during extreme during the the sea- wet drycities, season. season and 11County countries in (Namwon the City, Northern Jinan County, Jeolla Imsil Province; Country, Suncheon and City, Gwangyang Sunchang City, Damyang The climate of South Koreacold is and characterized dry by under extreme themer seasonal dominant is variations. influence hot Winter of and is the humidsoon. Siberian with In air frequent the mass, heavy Seomjin whereas rainfall River thesummer, associated basin, sum- and with the the the measured measured East precipitation Asian mean is mon- annual mainly concentrated precipitation in varies from The altitude range is rather large, spanning from approximately 0 to 1646 m (Fig. 4). bution function (CDF): f et al. (1993) has the following probability density function (PDF) and cumulative distri- τ f F F where κ > distribution reduces to theand classic Wallis Gumbel (1997) provided (EV1)The more distribution relationship detailed between with the information parameters regarding and distribution the can GEV be obtained distribution. as follows (Hosking and Wallis, 1997): τ 3 Study region The Seomjin River basin islength located of in the southwestern Seomjin Korea River (Fig. are 4). approximately The 4911.9 km area and total 5 5 25 15 20 10 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | for the fixed, monthly, erences, whereas the ff 1 − s 3 erent. That is, the drought identi- ff erences. To confirm the consistency ff during the winter were quite small. However, ff 14684 14683 cients among the four results were calculated ffi erent from the previous two results. The drought with the largest magnitude ff The duration and magnitude relationships were investigated using the remaining The analysis using the fixed threshold level indicated that 146 streamflow droughts The threshold levels for the desired yield during May were much larger than the levels of our approach, theand correlation are coe presentedand in daily Table threshold 4. levels. However, the Thethe durations, same total desired volumes, yield trend and threshold magnitudes wasfication level from were observed techniques completely based in di on thethe real fixed, drought precipitation and concept monthly, natural inproaches streamflows terms should did of be not included water reflect for supply specific and drought identification water and use. analysis. Therefore, two-way ap- three threshold methods, andima the values results of areresults. duration, The presented total durations in volume, from Fig. thetotal and four volumes 6. magnitude methods and The exhibited were magnitudes slight annual exhibited derived di large max- using di the above drought volume exhibited a trendbecame large similar when to the that durationpletely of was di the longer. duration, However, the becauseoccurred magnitude the trend volumes on was 23 com- had September short 1987. durations Three ofdecreased of with less the increasing than duration, top such sevenSimilar as five days. rainfall patterns largest intensity-duration-frequency Therefore, (IDF). were the droughtapproaches. observed severity magnitudes and in magnitude the results from the monthly and daily threshold and other physical variations, were reflected in this threshold. occurred from 1975 tonitudes 2012. are The listed in five1988–7 Table largest 3. October drought The 1989) durations, longest and volumes, drought and lasted it mag- for generated 102 the days (28 largest September total drought volume. The total of natural and artificial factors, such as climate variables, water use, land use change, and monthly threshold approachesThe were daily higher threshold displays than the those highest from number of the drought other events because thresholds. the impacts 4.2 Calculations of severity and magnitude The durations, total drought volumes, andwere magnitudes calculated of based all streamflow onsummarized drought the events values streamflow are drought listedyield concept threshold in approach and were threshold Table considerably higher 2. levels.because than those The the The from desired the maximum yields other were thresholds durationsuse. highest However, during from the May maximum the and streamflow June drought desired due severities to and agricultural magnitudes water of the daily much higher than during the other seasons. for the other thresholds becauseseason. the However, agricultural the water demand levelsother was for threshold the the levels. highest in desired this yield during May were smaller than the age threshold levels weredaily, 8.30, and 11.80, desired yields, 17.90, respectively. and Thebecause daily 13.81 m threshold of levels were the highly natural fluctuating the largest streamflow of variations the for fourfixed threshold the threshold levels level antecedent because was a 365 larger summersired than days period the yields. was and minimum This considered. levels were The phenomenon forboth the occurred the daily, water during monthly, demand and the and de- the natural winter thresholds runo in levels for Korea, the and daily, monthly, as and desired a yields result, during the summer were 4.1 Determination of the threshold levels This study used four thresholdare levels, as presented described in in Fig. Fig. 5, 3. and The the calculated thresholds specific values are listed in Table 1. The annual aver- 4 Results 5 5 25 15 20 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | - L -moment -moment L L depending -skewness, 3 L m 8 to 10 2 -moment ratios, L erent because the four threshold erently. ff ff -moment ratio diagrams have been suggested 14686 14685 L erences. In contrast, in the MDF curve, the variations exhibited the opposite -moment ratio diagrams were derived for the four threshold approaches and ff L -moment diagrams of various goodness-of-fit techniques were used to evaluate -kurtosis are plotted as a scatterplot and compared with the theoretical L L Four threshold level approaches were used to quantify streamflow drought severity The total and average daily water deficits increased with increasing frequencies. In The average daily water deficit, respectively, fordiagram the specific method, durations. Using the the GEV was selected for the best-fit probability distribution. As level approaches defined the streamflow drought di 5 Conclusions This study developed adroughts using novel frequency analyses. concept SDF todeveloped and to MDF describe quantify curves a for the specific streamflow volume characteristics droughtThis according were study of to used a streamflow severity specific and duration magnitude, and frequency. which represented the total water deficit and a slightly smaller waterited deficit. a In contrast, very the dynamicon water its and supply duration. wide-ranging demand In deficit the thresholdsmall case volume; exhib- water of from deficit, MDF, the 10 whereas fixedwater the threshold deficit. level daily approach However, threshold exhibited these level a values very had were the quite highest di maximum daily addition, the severity andMDF magnitude curves decreased can as bement the very strategies duration useful with increased. respect for to SDF developing specific appropriate and streamflow water drought severities resources and manage- and magnitudes. magnitude. Table 5quency compares and duration. all In of thethe the case largest of severities water SDF, monthly and deficit and magnitudes volumes daily of for threshold all levels each produced durations. fre- The fixed threshold level exhibited with increasing duration. In theconsiderably, whereas SDF the curve, the severity from severitysmall from the the desired di fixed yield threshold threshold varied exhibitedtrend. relatively The magnitudes fromthe the magnitudes desired from yield the fixed threshold threshold varied exhibited considerably, relatively whereas small variations. increased with increasing duration, whereas the average daily water deficit decreased deficit volume and (severity)-duration-frequencyerage and water (2) deficit streamflow and (magnitude)-duration-frequency. drought The daily total av- water deficit volume dots denote the durations, total volumesvolumes, (severities), respectively. magnitudes, and maximum deficit 4.4 Development of the SDF andSDF MDF and curves MDF curvestions, were as developed shown using the inand derived Figs. 100 yr-frequency probability 8 magnitudes distribution were and func- SDF calculated 9, and at respectively. MDF 10, For described 20, two these 30, types and plots, of 40 two, day relationships: durations. (1) five, streamflow 10, drought 20, total water 50, are displayed in Fig.(PT3), Generalized Normal 7. (GNO), Of and Generalizedappeared the Extreme Value consistent (GEV) distribution distributions with models theirhalf tested, datasets, of only and the the ofselected observations Pearson as those a Type approached three representative 3 distribution. the distributions, In Fig. fewer GEV 7, than the line. red, blue, Thus, black, and the grey colored GEV distribution was ratio curves of candidate distributions. to be aa useful dataset (Hosking graphical and toolstatistical Wallis, 1997). distributions for Two are discriminating representations the usedted amongst sample to on average candidate assist the and in same distributions line selecting an graph of for to SDI best facilitate MDF fit, the curve, which selectionbased can the on of be the proper the statistical plot- probability best-fit results, distribution. distribution as To described function develop in should Sect. be 2.4. determined The the best probability distributionmoment function ratio for diagram datasets is inand a several recent graph studies. in The which the sample 4.3 Identification of the probability distribution function 5 5 25 15 20 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | - L 10.5194/hess-10-535- erently. SDF and MDF curves can erent because the four threshold ff ff 14688 14687 This study was supported by the funding from the Basic Science Re- -moments: analysis and estimation of distributions using linear combina- L , 2006. This study can be applied to various hydrologic analyses and water resources man- analysis, Water Resour. Manag., 6, 249–277, 1992. 2008b. meteorological and physiographic factorsResour. for Manag., assessment 24, of 4199–4217, 2010. vulnerability to drought, Water Weather Bureau, Washington DC, 1965. analysis of Betwa river system (India), Water Resour. Manag., 22,flow 1127–1141, drought 2008a. severity using ephemeral streamflow data, Int. J. Ecol. Econ. Stat., 11, 77–89, Manag., 23, 881–897, 2009. partial duration modeling of45, hydrological 285–298, droughts 2000. in Zimbabwean rivers, Hydrolog. Sci.to J., time scales, Proc.17–22 January, 8th 1993. Conf. Appl. Climatol., American Meteor. Soc., Boston, 179–184, Moments, Cambridge Univ. 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Climate, 12, 747–756, 1999. level approaches defined the streamflowbe drought very di useful for developing appropriaterespect water to resources specific management streamflow strategies drought with magnitudes. agement systems, such as desiredmethod yield will and be dam extended safe yield.SDI to In magnitudes conduct addition, at regional our ungagged frequency SDI sites. analyses, MDF which can estimate flow drought total wateraverage deficit daily volume-duration-frequency water and deficit-duration-frequency. The (2) totalwith streamflow water deficit drought increasing volume duration, increased whereascreasing duration. the The average total daily andfrequencies. average water However, daily deficit these water deficits decreased values increased with were with in- increasing quite di a result, SDF and MDF curves were derived to evaluate two relationships: (1) stream- Rossi, G., Benedini, M., Tsakins, G., and Giakoumakis, S.: On regional drought estimation and Pandey, R. 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ASCE, 106, 99–115, 5 5 30 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Number of drought event ) 1 − day 3 Maximum Magnitude (m ] 1 − s 3 14692 14691 ) 3 Maximum Severity (m Threshold level [m Fixed Monthly Daily Desired yield Maximum duration JanFeb 8.300Mar 8.300 3.800Apr 5.562 8.300May 3.918 10.100 8.300 7.291 8.300Jun 10.017 9.947 5.420 7.632Jul 8.300 4.392 12.784 2.281 Aug 9.590 8.300 4.238 9.906Sep 8.300 38.006Oct 19.975 8.300 28.784 9.245 57.472Nov 39.243 15.877 8.300 50.423 34.843 Dec 8.300 3.590 38.645 29.717 8.300 3.330 15.021 4.200 4.150 3.699 4.039 4.295 3.992 3.760 Summary of four threshold approaches. Monthly averaged of four threshold levels. FixedMonthlyDailyDesired yield 102 69 278 49 148 052 571 291 486 115 860 728 297 2 160 000 2 21 885 031 935 654 611 836 708 24 146 789 244 394 256 533 Threshold level method Table 2. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | year month day 14694 14693 Fixed Monthly Daily Desired yield Fixed Monthly Daily Desired yield Fixed Monthly Daily Desired yield FixedMonthlyDailyDesired yield 1 0.684 0.139 1 0.418 0.696 0.961 0.360 1 1 Duration FixedMonthlyDailyDesired yield 1 0.870 0.075Total volume 1 0.200 0.888 0.975 0.237 1 1 Magnitude FixedMonthlyDailyDesired yield 1 0.686 0.107 1 0.272 0.666 0.760 0.380 1 1 561465253 21 3 4 19 44 755 200 6 356 571 2 131 200 8 405 486 39 793 2 371 118 1990 857 Oct 2 2 101 2012 094 371 388 Jun 1989 1989 10 Aug Oct 21 7 10 81351377 6881 5635 497 10748 654 46 400 86 930 742 1 583 38 152 966 400 68 1 552 1995 334 795 56 233 82 524 342 Nov 1984 46 1 31 794 2008 Jan 007 107 654 4 400 Oct 86 930 742 1 1977 583 152 13 Oct 82 524 1 342 552 27 1995 62 334 862 171 Nov 1 794 3 1984 007 2 027 812 Jan 4 1977 1987 Oct 13 Sep 3 26 Top five largest drought events to duration, total drought volume and magnitude from Correlations between four threshold approach. Magnitude 49 1 2 160 000 2 160 000 1987 Nov 23 Category Drought orderDuration Duration Severity 50 Magnitude Start Severity 102 50 148 052 571 1 451 495 102 1988 Sep 148 28 052 571 1 451 495 1988 Sep 28 Table 4. Table 3. fixed threshold approach. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

13 14696 14695 2 yr 5 yr 10 yr 20 yr 50 yr 100 yr

20304020 4.130 2.840 8.3 1.3 5.620 10.3 2.6 111.430 6.8 39.7 235.4 11.940 3.1 323.4 29.8 81.6 7.7 13.4 412.4 60.0 3.420 101.5 411.430 73.0 534.9 8.5 14.3 116.3 385.0 803.040 3.6 632.4 1389.1 341.2 604.8 130.7 81.9 848.5 2469.7 370.1 8.9 138.8 518.1 5422.8 3.8 89.8 1200.5 36.7 9940.2 713.6 1925.6 32.7 53.2 93.9 2777.2 26.5 1077.8 51.2 86.9 1466.2 39.8 78.0 167.2 52.7 126.0 463.8 69.6 253.3 1061.3 100.5 442.3 132.9 Values of magnitude-duration-frequency at Seomjin River basin.

Fig. 1. Procedure of this study this of 1. Procedure Fig. Procedure of this study.

Monthly 10Daily 221.2 10Desired Yield 370.1 10 518.1 713.6 1077.8 412.7 1466.2 867.9 38.9 1591.7 2994.8 57.0 7058.8 115.8 13 618.7 323.9 1551.7 5299.5 MethodFixed Duration [day] Return period [yr] 10 9.8 19.9 27.8 36.4 49.5 60.8 398 399 400 Fig. 1. Table 5. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

404

, 2008) 15

rganization O

14 levels: Fixed (top); monthly varying (middle); daily varying varying (middle); daily varying monthly (top); Fixed levels: 14698 14697

drought events events drought

threshold

eteorological eteorological M general orld orld

Fig. 3. Examples of 3. Examples Fig. (W (bottom)

407 408 405 406

Fig. 2. A definition sketch of of sketch definition A 2. Fig. A deﬁnition sketch of general drought events. Examples of threshold levels: ﬁxed (top); monthly varying (middle); daily varying (bottom)

300

200

Day

17 16 14700 14699

100 Fixed Fixed Water requirement Supply Monthly inflow Monthly Daily Daily 0 0 early averaged threshold levels and monthly inflow and monthly levels threshold averaged early

20 60 40

. Location of the selected river basin, including elevation and river and elevation including basin, river selected the of . Location 120 4 Threshold levels [cms] levels Threshold Y 5

Fig. Fig.

Fig. Fig. Yearly averaged threshold levels and monthly inﬂow. Location of the selected river basin, including elevation and river.

1.2e+9 1.0e+9 8.0e+8 6.0e+8 4.0e+8 2.0e+8 0.0

Drought volume [m volume Drought ] 3 Year (b) Total water deficit volume (drought severity) severity) (drought volume deficit water Total (b) 14702 14701 1980 1990 2000 2010 Fixed Monthly Daily requirement supply Water

1.8e+8 1.6e+8 1.4e+8 1.2e+8 1.0e+8 8.0e+7 6.0e+7 4.0e+7 2.0e+7 0.0

]

Year [m magnitude Drought 3 (c) Daily average water deficit (drought magnitude) deficit (drought water average (c) Daily 1980 1990 2000 2010 0

350 300 250 200 150 100 Drought duration [yr] duration Drought -moment diagrams for probability distribution identiﬁcation. (a) Drought duration (a) Drought L Time series of annual maxima values of duration, severity and magnitude. Fig. 7. Fig. 6. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | y l h t n Mo

) b ( 14704 14703 MDF curves of four threshold level approaches in Seomjin river basin. SDF curves of four threshold approaches in Seomjin river basin. Fig. 9. Fig. 8.