Research Article Reservoir Sedimentation Based on ...reservoir sedimentation trend, and hence sediment density is subject to uncertainty. On the other hand, optimal design of reservoir

Research ArticleReservoir Sedimentation Based on Uncertainty Analysis

Farhad Imanshoar1 Afshin Jahangirzadeh2 Hossein Basser2 Shatirah Akib2

Babak Kamali2 Mohammad Reza M Tabatabaei3 and Masoud Kakouei4

1 Faculty of Civil Engineering University of Tabriz Tabriz Iran2Department of Civil Engineering Faculty of Engineering University of Malaya 50603 Kuala Lumpur Malaysia3 Faculty of Water and Environment Engineering Power and Water University of Technology Tehran Iran4Department of Computer Engineering Faculty of Engineering Payam Noor University Astaneh Ashrafieh Iran

Correspondence should be addressed to Afshin Jahangirzadeh afshinjkgmailcom

Received 16 September 2013 Revised 23 January 2014 Accepted 27 January 2014 Published 4 March 2014

Academic Editor Mohamed Fathy El-Amin

Copyright copy 2014 Farhad Imanshoar et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Reservoir sedimentation can result in loss of much needed reservoir storage capacity reducing the useful life of dams Thussufficient sediment storage capacity should be provided for the reservoir design stage to ensure that sediment accumulation will notimpair the functioning of the reservoir during the useful operational-economic life of the project However an important issue toconsider when estimating reservoir sedimentation and accumulation is the uncertainty involved in reservoir sedimentation In thispaper the basic factors influencing the density of sediments deposited in reservoirs are discussed and uncertainties in reservoirsedimentation have been determined using the Delta method Further Kenny Reservoir in the White River Basin in northwesternColorado was selected to determine the density of deposits in the reservoir and the coefficient of variation The results of thisinvestigation have indicated that by using the Delta method in the case of Kenny Reservoir the uncertainty regarding accumulatedsediment density expressed by the coefficient of variation for a period of 50 years of reservoir operation could be reduced toabout 10 Results of the Delta method suggest an applicable approach for dead storage planning via interfacing with uncertaintiesassociated with reservoir sedimentation

1 Introduction

Reservoir sedimentation is filling of the reservoir withsediment carried into the dam reservoir by streams [1]Understanding the reservoir sedimentation process is offundamental significance in hydrosystems engineering Sed-iment inflow and deposition can affect the function of damreservoirs Therefore it is of crucial importance to estimatethe sedimentation rate and the period of time before sedimentaccumulation could interfere with the useful functioning ofthe reservoir When designing a reservoir sufficient sedi-ment storage capacity should be taken into account so thatsediment accumulation will not impair the function of thereservoir during the useful operational-economic life of theproject [2]

Sedimentation process in a reservoir is quite complexbecause it is often influenced by several factors includinghydrological fluctuations in water and sediment inflow vari-ation in sediment particle size reservoir operation cycle and

physical controls such as size and shape of the reservoir [3 4]Other factors that may be important for some reservoirs arevegetation cover in upper reaches turbulence and densitycurrents erosion of deposited sediments and sluicing ofsediment through the dam

Once the volume of sediment inflow to a reservoirhas been determined effects of the sedimentation processover the life span and the daily operation of the reservoirmust be evaluated In the design of a reservoir the meanannual sediment inflow the efficacy of the reservoir intrapping sediment the ultimate density of the depositedsediment and the distribution of the sediment within thereservoir are among the most important factors that must beconsidered Additional storage volume equal to the volumeof the sediment expected to be deposited during the lifeof the reservoir is often included in the original design toprevent premature loss of storage capacity The United StatesBureau of Reclamation [2] suggests using a 100-year period of

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 367627 6 pageshttpdxdoiorg1011552014367627

2 Abstract and Applied Analysis

economic analysis and sediment accumulation in a reservoirLess than 100 years of sediment accumulation may also besuggested in cases where the economic analysis justifies lesserallocation However there is uncertainty associated with thefactors involved in reservoir sedimentation The sources ofuncertainty can be generally classified into two main groupsfirst group is natural factors (the natural factors are related tonatural happenings and conditions) which include meteoricfactors changes in watershed hydraulic characteristics andnatural disaster occurrences Second group is unnaturalfactors (the unnatural factors are caused by human-inducedactivities) which include land-use changes and managementstrategies [3 4]

On the whole natural variability and model relateduncertainties constantly have an effective role in accuracyof determining the amount of sediment deposition in thereservoir on a yearly basis the accumulated sediment volumein the reservoir over the number of years of reservoiroperation and the time it takes for the accumulation of acertain amount of sediment in the reservoir (eg a fractionof the death capacity or a fraction of the total capacity of thereservoir) [3 5 6] In this context the response of the systemto variable uncertain inputs can be statistically quantifiedthrough uncertainty analysis [7]

Salas and Shin [3] analyzed the uncertainty of manyfactors involved in reservoir sedimentation These factorscalled ldquostochastic inputsrdquo include those inputs associatedwith annual suspended and bed load sediment rating curvesthose associated with the type of incoming sediment thoseassociatedwith the trap efficacy of a reservoir and those asso-ciated with the variability of annual stream flow Intrinsicallythese inputs are of random phenomena [7 8] This type ofvariability is always associated with the factors involved inreservoir sedimentation and may not be controlled [3 9]

This study focuses on identifying the basic factors influ-encing the density of sediments deposited in the reservoirsand determining uncertainties in reservoir sedimentationusing the Delta method A case study of Kenny Reservoirin the White River Basin in northwestern Colorado [3 9]was designated to determine the density of deposits in thereservoir and the coefficient of variation Thus the presentstudy is an attempt to ascertain the accuracy of determiningthe mean density of accumulated sediments after a certainperiod of time by calculating the coefficient of variation [9]

2 Factors Contributing toReservoir Sedimentation

21 Natural Factors Natural factors affecting reservoir sed-imentation are those intrinsic aspects of the worldrsquos waterhydrologic cycle and the rate of land surface change Thesefactors are meteoric factors (eg precipitation snow hailand wind) [3] watershed topography and geology vegetationcover natural disasters (eg floods and droughts) andthe hydraulic condition of the reservoir (eg the ratio ofreservoir capacity to inflowvolume the shape of the reservoirspecifications of bottom outlets the condition of reservoir

Table 1 Sediment classification according to size

Sediment type Size range (mm)Clay lt0004Silt 0004 to 0062Sand 0062 to 2

operation the trap efficiency of the reservoir flow turbulenceand physical properties of inflow) [11]

22 Unnatural (Human-Induced) Factors Overexploitationof forests destruction of grasslands and land-use changesinduced by human activities affect water resources andoften intensify soil erosion which consequently increasereservoir sedimentation rates in different ways Managementstrategies as a human-related factor can also directly affectthe sedimentation process in reservoir dams The maindeficiencies in this field could be the propensity to storewater from wet to dry seasons the tendency to producemore hydropower energy without considering sedimentaryaspects incorrect design of water works and shortcomingsof operation manuals [11 12]

3 Methods

31 Density of Deposited Sediments Basic factors influencingthe density of sediments deposited in a reservoir are (i) thereservoir operation and management (ii) the texture andsize of deposited sediment particles and (iii) the compactionor consolidation rate of deposited sediments [2 11] Amongthese the operational plan of the reservoir is probably themost significant factor [2 3 5] Sediments deposited in areservoir are subject to considerable drawdown with theresult that the sediments may be exposed for long periodsand therefore undergo greater consolidation On the otherhand reservoirs which operate under a fairly stable pool donot allow the deposits to dry out and consolidate as muchThe size of the incoming sediment particles has a significanteffect on density of deposits Sediment deposits composed ofsilt and sand have higher densities than those in which claypredominates [2] The classification of sediments accordingto size is proposed by the American Geophysical Union(Table 1)

Accumulation of new sediment deposits on top of pre-viously deposited sediments often changes the density ofearlier depositsThe consolidation process affects the averagedensity over the estimated life of the reservoir such asfor a 100-year period Therefore the influence of reservoiroperation is the most significant factor due to its effecton the amount of consolidation that can take place in theclay fraction of the deposited material when a reservoir issubject to considerable drawdown Strand and Pemberton[10] classified reservoir operations (Table 2)

Abovementioned reservoir types for operation were as-sessed by engineering judgment Selection of the properreservoir operation can usually be made through the oper-ation study prepared for the reservoir [10] This concept

Abstract and Applied Analysis 3

Table 2 Classification of reservoir operation [10]

No Reservoir operation1 Sediment always submerged or nearly submerged

2 Normally moderate to considerable reservoirdrawdown

3 Reservoir normally empty4 Riverbed sediments

depends on hydraulic conditions of the intake and sedimenttrap coefficient of the reservoir For example for reservoirtype 1 releasedwater of dam is clear or near to clear thereforethe sediments are always submerged or nearly submergedwhile for reservoir type 4 running river flow passes the damand in other words the released water is debris flow Theother two operations are judged in this manner

The size of sediment particles entering the reservoir alsoaffects the density as shown by the variation in initial massesOnce the reservoir operation number has been assessed thedensity of the sediment deposits can be estimated using (1)[2 10] Consider

1198820= 119882119862119875119862+119882119898119875119898+119882119878119875119878 (1)

where 1198820is unit weight (kgm3) 119875

119862 119875119898 and 119875

119878are the

percentages of clay silt and sand in the inflowing sedimentrespectively and 119882

119862 119882119898 and 119882

119878are coefficients of unit

weight of clay silt and sand respectively (Table 3) [2 10]Sediments accumulate in the reservoir in each of the 119879

years of operation and each yearrsquos deposit will have a differentcompaction time which is significantly dependent on thetype of reservoir operation and the size of the incomingsediment particles Thus density of sediments depositedduring 119879 years of reservoir operation can be estimated as anapproximation of the integral of (2) [5 13]

119882119879= 1198820+ 04343119870 [

119879

119879 minus 1

(ln119879) minus 1] 119879 gt 1 (2)

where119882119879is the average density after119879 years of operation119882

0

is the initial unit weight (density) derived from (1) and 119870 isconsolidation constant dependent on type of reservoir oper-ation and sediment size distribution (Table 4) In practice aweighted average of consolidation constants must be used fora mixture of sediment (3) [2 5 13]

119870119894= 119870119862119875119862+ 119870119898119875119898+ 119870119878119875119878 (3)

32 Analysis of Uncertainty of Reservoir SedimentationWhen designing hydrosystems it is essential to take uncer-tainty into consideration since many influences are func-tionally related to a number of uncertain variables Forinstance as already noted natural factors and unnaturalfactors result in a complex and uncertain procedure forreservoir sedimentation trend and hence sediment densityis subject to uncertainty On the other hand optimal designof reservoir geometry (dead storage and live storage) is afundamental goal for hydraulic engineers

Table 3 Initial unit weight of incoming sediments based onreservoir operation and type of sediments

Operationtype

Initial unit weight (kgm3)Clay-119882

119862Silt-119882

119898Sand-119882

119878

1 416 1120 15502 561 1140 15503 641 1150 15504 961 1170 1550

Table 4 119870 values for incoming sediments based on reservoiroperation and type of sediment [2]

Operationtype

119870 values for SI unitsClay-119870

119862Silt-119870

119898Sand-119870

119878

1 256 91 02 135 29 03 4 0 0 0

Severalmethods for uncertainty analysis have been devel-oped and applied in water resources engineering The mostwidely used methods are Monte Carlo Simulation (MCS)and first-order analysis (FOA) [3 5] The latter is based onlinearization of the functional relationship which relates adependent random variable and a set of independent randomvariables by Taylor series expansion The FOA method hasbeen applied to several water resource and environmentalengineering problems including uncertainty [5 6 14] Forexample Tehrani et al benefited from Latin Hypercube Sam-pling method to estimate accumulated reservoir sedimentvolume in Shahr-Chai Dam by FOA method and the sensi-tivity analysis showed that suspended sediment and bed loadfollowed by annual stream flow were the most importantfactors influencing the accumulated reservoir sedimentationvolume for both the total period and the wet and dry timeperiods and trap efficiency and percentage of sediments arethe next most important [5] Furthermore Hall used FOAmethod to extend a fuzzy set theory and possibility theoryfor coastal hydraulics [14]

In MCS method stochastic inputs are generated fromtheir probability distributions and are then entered intoempirical or analytical models of the underlying physicalprocess involved in generating stochastic outputs The gen-erated outputs are then analyzed statistically to quantify theuncertainty of the output [15 16] Salas and Shin [3] analyzedthe uncertainty of annual reservoir sedimentation volume(RSV) and accumulated reservoir sedimentation volume(ARSV) based on Monte Carlo Simulation (MCS) and LatinHypercube Sampling (LHS) The procedures were appliedto the case of Kenny Reservoir in the White River basin inColorado The results indicated that the variability of RSVmay be described by a Gamma-2 distribution for which thecoefficient of variation was of the order of 65 [3] This rateof variation for determining annual reservoir sedimentationvolume makes a serious challenge to design or manage thereservoir operation


Although the abovementioned studies developed me-thodical outcomes in hydrosystem analysis especially inalluvial hydraulics uncertainties in these researches thedensity of sediments which were deposited in the reservoirwas assumed constant The sediments which accumulatein the reservoir by passing the time will have a differentcompaction therefore their density will change dependingon variety of factors Consequently in this paper in order todevelop former studies it is aimed to focus on identifying thebasic factors which affect the density of sediments depositedin the reservoirs Also uncertainties in reservoir sedimentsdensity are determined using the Delta method

33 Analysis of Uncertainty (DeltaMethod) First-order anal-ysis of uncertainties which is also known as the Deltamethod is a rather straightforward and useful techniquefor the approximation of such uncertainties This methodis widely used in many fields of engineering due mainlyto its ease of application to a wide variety of problems[17ndash19] Mays stated that Delta method application is quitepopular in many fields of engineering and as a result hedeveloped a risk-based solution for storm sewersrsquo design[17] Imanshoar et al used Delta method to study trophicstate index (TSI) uncertainty and its variation for MiyunReservoir in China Their research showed that the aver-age TSI number and its variation for mentioned reservoiroscillated between Mesotrophic to Eutrophic category [18]Furthermore Resende et al appliedDeltamethod to estimatethe mapping from uncertainty in discrete choice modelparameters to uncertainty of profit outcomes and theyidentified the estimated 120572-profit as a closed form function ofdesign decision variables in computer science [19]

First-order analysis is often used to assess the uncertaintyin a deterministic model formulation involving parameterswhich are uncertain (ie not known with certainty) First-order analysis specifically enables us to determine the meanand variance of a random variable which is functionallyrelated to several other variables some of which are ran-dom Thus using first-order analysis the combined effect ofuncertainty in a model formulation and the use of uncertainparameters can be assessed [14 17] Consider a randomvariable 119910 that is a function of 119896 random variables (4)(multivariate case) [17]

119910 = 119866 (1199091 1199092 119909

119895) = 119866 (119909

119894) 119894 = 1 sim 119895 (4)

This function can be expressed as a deterministic equationsuch as the equation mentioned above a rational formula orManningrsquos equation or a complex model that must be solvedon a computerThe objective is to treat a deterministic modelthat has uncertain inputs in order to determine the effect ofthe uncertain parameters 119909

1 119909

119896on the model output 119910

Equation (4) can be expressed as 119910 = 119866(119909119894) where 119909 =

1199091 1199092 119909

119896 Using a Taylor series expansion of 119896 random

variables ignoring the second and higher order terms we canobtain [17]

120583119910asymp 119866 (119909) +

119895

sum

119894=1

(

120597119866

120597119909119894

)

119909

(119909119894minus 119909119894) (5)

where 120583119910refers to the mean value of 119910 under the variation of

119909119894and the derivation (120597119866120597119909

119894)119909are the sensitivity coefficients

that represent the rate of change of the function value 119866(119909119894)

at (119909119894minus 119909119894) Assuming that the 119896 random variables are

independent the variance of 119910 can be approximated as [17]

Ω2

119910=

119895

sum

119894=1

[(

120597119866

120597119909119894

)

2

119909119894

(

119909119894

120583119910

)

2

Ω2

119909119894] (6)

It is important to remember that all of the randomparametersare assumed to follow a uniform distribution so the meanand variance of each parameter can be calculated usingmean = (119886 + 119887)2 and variance = (119886 minus 119887)

212 in which 119886 and

119887 are the lower and upper bounds respectively (7) Consider

Ω =

120590

119883

=

radic3

3

(

119887 minus 119886

119887 + 119886

) (7)

331 Uncertainty Analysis for Density of Sediments DepositedNotwithstanding the advances made in understanding sev-eral factors involved in reservoir sedimentation predictingthe accumulation of sediment in a reservoir throughout theyears after construction of the dam is still a complex problemin hydraulic engineering As noted earlier the volume ofreservoir sedimentation depends among other factors onthe quantity of sediment inflow the percentage of sedimentinflow trapped by the reservoir and the specific weight ofthe deposited sediments considering the effect of compactionwith time The sediments entering a reservoir are generallya mixture of clay silt and sand The fraction of each typeof sediment namely 119875

119862 119875119898 and 119875

119878(for clay silt and sand

resp) vary from year to yearThus it would be impractical todetermine such variable fractions from field measurementsStandard statistical analysis can offer a certain distributionfunction for predicting fractions of each sediment typeFor instance it may be assumed that such fractions areuniformly distributed with lower and upper bounds that areobtained from the measurements Or the fractions of eachtype of sediments may be assumed to be independent In thisapproach the percentages of clay silt and sand will have to beadjusted so that they add up to 100 [3]

Therefore to determine the uncertainty associated withthe type of incoming sediment and their effect on depositedsedimentrsquos density (2) can be rewritten using (1) and (3) asfollows

119882119879= 119875119862119882119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119898119882119898+ 0434119870

119898[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119878119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1]

(8)


Using (5) and (6) the variation coefficient of deposited sedi-mentsrsquo density after119879 years of operation could be determinedas follows

Ω2

119882119879= (

120597119882119879

120597119875119862

)

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862+ (

120597119882119879

120597119875119898

)

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (

120597119882119879

120597119875119878

)

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(9)

whereΩ119882119879

is the coefficient of variation of sedimentsrsquo densityafter 119879 years of operation and Ω

119875119862 Ω119875119898 and Ω

119875119878are

the variation coefficient of clay silt and sand percentagerespectively Equation (9) can thus be rewritten as follows

Ω2

119882119879= (119882

119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862

+ (119882119898+0434119870

119898[

119879

119879 minus 1

(ln119879)minus1])

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(10)

4 Results and Discussion

41 Case Study (Kenny Reservoir) Uncertainty analysis ofdensity of sediments deposited in reservoir after 119879 years ofoperation as described earlierwas applied to theKennyReser-voir in the White River Basin in northwestern ColoradoTaylor Draw Dam was constructed in the early 1980rsquos andcreated the Kenny Reservoir with a capacity of about 17 times

106m3 which has been in operation since 1984 [3 20]The mean density of sediments deposited after 119879 = 50

years of operation and its coefficient of variation for KennyReservoir data was determined using the abovementionedmethod The range of percentages of each type of sediment(ie 119875

119862 119875119898 and 119875

119878for clay silt and sand resp) are inde-

pendent because of their physical differences It is importantto mention that Tobin and Hollowed evaluated statisticaldistributions of each type of sediment and found them closeto the uniform type and therefore they assumed them to beuniformly distributed [3 9] Also according to the reservoirhydraulic condition (permanent reservoir with long length)the sediments were always submerged Also the lower andupper bounds for each fraction were analyzed by Tobinand Hollowed using twenty samples of suspended sedimentwhich were collected [3 9] (Table 5)

It should be borne in mind that for each sample thepercentages of clay silt and sand should add up to 100(119875119862+ 119875119898+ 119875119878= 100) The mean percentages of sediment

accumulated (Table 5) can be summarized according to thetype and the coefficient of variation using (9)

Assuming the sediments are always submerged or nearlysubmerged in Kenny Reservoir (using Table 6 and (8)) the

Table 5 Clay silt and sand percentages range

Sediment type Lower bound Upper bound Distribution119875119862() 16 41 Uniform

119875119898() 39 63 Uniform

119875119878() 14 43 Uniform

Table 6 Statistical properties of stochastic inputs for uncertaintyanalysis

Sediment type Mean Standarddeviation

Coefficient ofvariation

119875119862() 285 7216884 0253224

119875119898() 51 6928197 0135847

119875119878() 285 837159 0293740

mean density of sediments after 119879 = 50 years of operationcan be obtained as follows

120583119908119879

=

285

100

416 + 04343 times 256 [

50

50 minus 1

(ln 50) minus 1]

+

51

100

1120 + 04343 times 91 [

50

50 minus 1

(ln 50) minus 1]

+

285

100

1500 + 0 = 106542 kgm3

(11)

Then using Table 4 (reservoir type 1) and (10) coefficient ofvariation of sedimentsrsquo density after 119879 = 50 years of Kennyreservoir operation can be assessed as follows

Ω2

119882119879= 00098 997888rarr Ω

119882119879= 0099 (12)

Hence the accuracy in determining the mean density ofsediments after 119879 = 50 years of operation in this reservoiris plusmn99 Further the standard deviation of this parametercan be determined as follows

120590119882119879

= 120583119882119879

Ω119882119879

(13)

Thus

120590119882119879

= 106542 times 0099 = 10548 kgmminus3 (14)

where 120590119882119879

refers to the standard deviation of variable 119910 (inthis case 119910 = 119882

119879)

Results of this case study indicate that the mean densityof sediments deposited after 50 years of operation in KennyReservoir is 106542 plusmn 10548 (mean plusmn SD) kgm3 (14)Therefore the accuracy of calculating the mean density ofsediments deposited after the 50th year of operation and theneeded volume for dead storage design is 99 (sim10)

5 Conclusion

Due to the wide range of uncertain parameters involved inthe design procedure predicting the deposition and accu-mulation of sediments in a reservoir is a complex problem


one that has attracted the attention of hydraulic engineersand scientists for many decades In this paper the problemof analyzing and quantifying the uncertainty of mean densityof sediments deposited in a reservoir and its compactionthrough the years of reservoir operation has been addressed

Since in previous studies the density of sediments whichwere deposited in the reservoirwere assumed constant in thispaper the former studies were developed by identifying thebasic factors which affect the density of sediments depositedin the reservoirs Also uncertainties in reservoir sedimentsdensity are determined using the Delta method

For this purpose the uncertainty of the input factors(stochastic inputs) was analyzed first Then using the Deltamethod the uncertainty associated with the type of incomingsediments and their effect on density of sediments and itscoefficient of variation were determined

Results of this research indicate that the mean densityof sediments deposited after 50 years of operation in KennyReservoir is 106542 plusmn 10548 (mean plusmn SD) kgm3 Thereforethe accuracy of calculating the mean density of sedimentsdeposited after the 50th year of operation and the neededvolume for dead storage design is 10 This user-friendlymethod can be applied to engineering practices to optimizedead storage planning via interfacing with uncertaintiesassociated with reservoir sedimentation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Financial support by the high impact research grants of theUniversity of Malaya (UMC6251HIR116 account num-ber J-16002-00-7383000-000000) and (UMC6251HIR61 account number H-16001-00-D000061) is gratefully ac-knowledged Also authors would like to thank the partlysupport of IPPP grant number PV058-2012A

References

[1] F Imanshoar Y Hassanzadeh M T Aalami and A Danandeh-mehr ldquoUncertainty analysis for determining density of depositsin damsrsquo reservoirsrdquo Journal of Water and Soil Science vol 23pp 27ndash38 2013 (Persian)

[2] United States Bureau of Reclamation (USBR) Design of SmallDams United States Bureau of Reclamation (USBR) DenverColo USA 3rd edition 1987

[3] J D Salas and H Shin ldquoUncertainty analysis of reservoir sedi-mentationrdquo Journal of Hydraulic Engineering vol 125 no 4 pp339ndash350 1999

[4] S W Fleming A Marsh Lavenue A H Aly and A AdamsldquoPractical applications of spectral analysis of hydrologic timeseriesrdquo Hydrological Processes vol 16 no 2 pp 565ndash574 2002

[5] M V Tehrani J M V Samani and M Montaseri ldquoUncertaintyanalysis of reservoir sedimentation using Latin Hypercubesampling andHarrrsquosmethod Shahar Chai Dam in Iranrdquo Journalof Hydrology New Zealand vol 47 no 1 pp 25ndash42 2008

[6] Y K Tung and B C YenHydrosystems Engineering UncertaintyAnalysis McGraw-Hill New York NY USA 2005

[7] S Franceschini andCW Tsai ldquoAssessment of uncertainty sour-ces in water quality modeling in the Niagara RiverrdquoAdvances inWater Resources vol 33 no 4 pp 493ndash503 2010

[8] O O Osidele W Zeng and M B Beck ldquoCoping with uncer-tainty a case study in sediment transport and nutrient loadanalysisrdquo Journal ofWater Resources Planning andManagementvol 129 no 4 pp 345ndash355 2003

[9] R L Tobin and C P Hollowed ldquoWater quality and sedimenttransport Characteristics in Kenney reservoir White riverbasinrdquo Northwestern Colorado Report US Geological SurveyDenver Colo USA 1990

[10] R I Strand and E L Pemberton ldquoReservoir sedimentationrdquoTechnical Guideline for Bureau of Reclamation US Depart-ment of Interior Bureau of Reclamation Denver Colo USA1982

[11] G L Morris and J Fan Reservoir Sedimentation HandbookDesign andManagement of Dams Reservoirs andWatersheds forSustainable Use McGraw-Hill New York NY USA 1997

[12] V Jothiprakash and V Garg ldquoRe-look to conventional tech-niques for trapping efficiency estimation of a reservoirrdquo Inter-national Journal of Sediment Research vol 23 no 1 pp 76ndash842008

[13] C R Miller Determination of the Unit Weight of Sediment forUse in Sediment Volume Computations US Department ofInterior Bureau of Reclamation Denver Colo USA 1953

[14] J W Hall ldquoHandling uncertainty in the hydroinformatic pro-cessrdquo Journal of Hydroinformatics vol 5 pp 215ndash232 2003

[15] J D Salas Analysis and Modelling of Hydrologic Time SeriesMcGraw-Hill New York NY USA 1993

[16] J M V Samani M Tehrani andMMontaseri ldquoThe evaluationof three methods of uncertainty (MCS LHS and Harr) in damreservoir sedimentationrdquo Journal of Engineering and AppliedSciences vol 2 pp 1074ndash1084 2007

[17] L W Mays Water Resources Engineering John Wiley amp SonsNew York NY USA 2nd edition 2005

[18] F Imanshoar YHassanzadeh andMRMTabatabai ldquoAnalysisof trophic state uncertainty and its Variation Miyun ReservoirBeijing Chinardquo in Proceedings of the 1st International Con-ference on Dams amp Hydropower (ICDHP rsquo12) Tehran IranFebruary 2012

[19] C B Resende C G Heckmann and J J Michalek ldquoRobustdesign for profit maximization under uncertainty of consumerchoice model parameters using Delta methodrdquo in Proceedingsof the ASME 2011 International Design Engineering TechnicalConferences amp Computers and Information in Engineering Con-ference Washington DC USA 2011

[20] H L Chen Stochastic characteristics of environmental and hy-drologic time series [dissertation] Purdue University StillwaterOkla USA 1999

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Stochastic AnalysisInternational Journal of


economic analysis and sediment accumulation in a reservoirLess than 100 years of sediment accumulation may also besuggested in cases where the economic analysis justifies lesserallocation However there is uncertainty associated with thefactors involved in reservoir sedimentation The sources ofuncertainty can be generally classified into two main groupsfirst group is natural factors (the natural factors are related tonatural happenings and conditions) which include meteoricfactors changes in watershed hydraulic characteristics andnatural disaster occurrences Second group is unnaturalfactors (the unnatural factors are caused by human-inducedactivities) which include land-use changes and managementstrategies [3 4]

On the whole natural variability and model relateduncertainties constantly have an effective role in accuracyof determining the amount of sediment deposition in thereservoir on a yearly basis the accumulated sediment volumein the reservoir over the number of years of reservoiroperation and the time it takes for the accumulation of acertain amount of sediment in the reservoir (eg a fractionof the death capacity or a fraction of the total capacity of thereservoir) [3 5 6] In this context the response of the systemto variable uncertain inputs can be statistically quantifiedthrough uncertainty analysis [7]

Salas and Shin [3] analyzed the uncertainty of manyfactors involved in reservoir sedimentation These factorscalled ldquostochastic inputsrdquo include those inputs associatedwith annual suspended and bed load sediment rating curvesthose associated with the type of incoming sediment thoseassociatedwith the trap efficacy of a reservoir and those asso-ciated with the variability of annual stream flow Intrinsicallythese inputs are of random phenomena [7 8] This type ofvariability is always associated with the factors involved inreservoir sedimentation and may not be controlled [3 9]

This study focuses on identifying the basic factors influ-encing the density of sediments deposited in the reservoirsand determining uncertainties in reservoir sedimentationusing the Delta method A case study of Kenny Reservoirin the White River Basin in northwestern Colorado [3 9]was designated to determine the density of deposits in thereservoir and the coefficient of variation Thus the presentstudy is an attempt to ascertain the accuracy of determiningthe mean density of accumulated sediments after a certainperiod of time by calculating the coefficient of variation [9]

2 Factors Contributing toReservoir Sedimentation

21 Natural Factors Natural factors affecting reservoir sed-imentation are those intrinsic aspects of the worldrsquos waterhydrologic cycle and the rate of land surface change Thesefactors are meteoric factors (eg precipitation snow hailand wind) [3] watershed topography and geology vegetationcover natural disasters (eg floods and droughts) andthe hydraulic condition of the reservoir (eg the ratio ofreservoir capacity to inflowvolume the shape of the reservoirspecifications of bottom outlets the condition of reservoir

Table 1 Sediment classification according to size

Sediment type Size range (mm)Clay lt0004Silt 0004 to 0062Sand 0062 to 2

operation the trap efficiency of the reservoir flow turbulenceand physical properties of inflow) [11]

22 Unnatural (Human-Induced) Factors Overexploitationof forests destruction of grasslands and land-use changesinduced by human activities affect water resources andoften intensify soil erosion which consequently increasereservoir sedimentation rates in different ways Managementstrategies as a human-related factor can also directly affectthe sedimentation process in reservoir dams The maindeficiencies in this field could be the propensity to storewater from wet to dry seasons the tendency to producemore hydropower energy without considering sedimentaryaspects incorrect design of water works and shortcomingsof operation manuals [11 12]

3 Methods

31 Density of Deposited Sediments Basic factors influencingthe density of sediments deposited in a reservoir are (i) thereservoir operation and management (ii) the texture andsize of deposited sediment particles and (iii) the compactionor consolidation rate of deposited sediments [2 11] Amongthese the operational plan of the reservoir is probably themost significant factor [2 3 5] Sediments deposited in areservoir are subject to considerable drawdown with theresult that the sediments may be exposed for long periodsand therefore undergo greater consolidation On the otherhand reservoirs which operate under a fairly stable pool donot allow the deposits to dry out and consolidate as muchThe size of the incoming sediment particles has a significanteffect on density of deposits Sediment deposits composed ofsilt and sand have higher densities than those in which claypredominates [2] The classification of sediments accordingto size is proposed by the American Geophysical Union(Table 1)

Accumulation of new sediment deposits on top of pre-viously deposited sediments often changes the density ofearlier depositsThe consolidation process affects the averagedensity over the estimated life of the reservoir such asfor a 100-year period Therefore the influence of reservoiroperation is the most significant factor due to its effecton the amount of consolidation that can take place in theclay fraction of the deposited material when a reservoir issubject to considerable drawdown Strand and Pemberton[10] classified reservoir operations (Table 2)

Abovementioned reservoir types for operation were as-sessed by engineering judgment Selection of the properreservoir operation can usually be made through the oper-ation study prepared for the reservoir [10] This concept








1198820= 119882119862119875119862+119882119898119875119898+119882119878119875119878 (1)


119862 119875119898 and 119875

119878are the


119862 119882119898 and 119882




119882119879= 1198820+ 04343119870 [

119879

119879 minus 1

(ln119879) minus 1] 119879 gt 1 (2)


0


119870119894= 119870119862119875119862+ 119870119898119875119898+ 119870119878119875119878 (3)



Operationtype


119862Silt-119882

119898Sand-119882

119878

1 416 1120 15502 561 1140 15503 641 1150 15504 961 1170 1550


Operationtype


119862Silt-119870

119898Sand-119870

119878

1 256 91 02 135 29 03 4 0 0 0







119910 = 119866 (1199091 1199092 119909

119895) = 119866 (119909

119894) 119894 = 1 sim 119895 (4)


1 119909



1199091 1199092 119909



120583119910asymp 119866 (119909) +

119895

sum

119894=1

(

120597119866

120597119909119894

)

119909

(119909119894minus 119909119894) (5)







Ω2

119910=

119895

sum

119894=1

[(

120597119866

120597119909119894

)

2

119909119894

(

119909119894

120583119910

)

2

Ω2

119909119894] (6)




Ω =

120590

119883

=

radic3

3

(

119887 minus 119886

119887 + 119886

) (7)


119862 119875119898 and 119875




119882119879= 119875119862119882119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119898119882119898+ 0434119870

119898[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119878119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1]

(8)



Ω2

119882119879= (

120597119882119879

120597119875119862

)

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862+ (

120597119882119879

120597119875119898

)

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (

120597119882119879

120597119875119878

)

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(9)

whereΩ119882119879


119875119862 Ω119875119898 and Ω

119875119878are


Ω2

119882119879= (119882

119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862

+ (119882119898+0434119870

119898[

119879

119879 minus 1

(ln119879)minus1])

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(10)





119862 119875119898 and 119875








119875119898() 39 63 Uniform

119875119878() 14 43 Uniform




119875119862() 285 7216884 0253224

119875119898() 51 6928197 0135847

119875119878() 285 837159 0293740


120583119908119879

=

285

100

416 + 04343 times 256 [

50

50 minus 1

(ln 50) minus 1]

+

51

100

1120 + 04343 times 91 [

50

50 minus 1

(ln 50) minus 1]

+

285

100

1500 + 0 = 106542 kgm3

(11)


Ω2

119882119879= 00098 997888rarr Ω

119882119879= 0099 (12)


120590119882119879

= 120583119882119879

Ω119882119879

(13)

Thus

120590119882119879

= 106542 times 0099 = 10548 kgmminus3 (14)

where 120590119882119879


119879)


5 Conclusion









Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1198820= 119882119862119875119862+119882119898119875119898+119882119878119875119878 (1)


119862 119875119898 and 119875

119878are the


119862 119882119898 and 119882




119882119879= 1198820+ 04343119870 [

119879

119879 minus 1

(ln119879) minus 1] 119879 gt 1 (2)


0


119870119894= 119870119862119875119862+ 119870119898119875119898+ 119870119878119875119878 (3)



Operationtype


119862Silt-119882

119898Sand-119882

119878

1 416 1120 15502 561 1140 15503 641 1150 15504 961 1170 1550


Operationtype


119862Silt-119870

119898Sand-119870

119878

1 256 91 02 135 29 03 4 0 0 0







119910 = 119866 (1199091 1199092 119909

119895) = 119866 (119909

119894) 119894 = 1 sim 119895 (4)


1 119909



1199091 1199092 119909



120583119910asymp 119866 (119909) +

119895

sum

119894=1

(

120597119866

120597119909119894

)

119909

(119909119894minus 119909119894) (5)







Ω2

119910=

119895

sum

119894=1

[(

120597119866

120597119909119894

)

2

119909119894

(

119909119894

120583119910

)

2

Ω2

119909119894] (6)




Ω =

120590

119883

=

radic3

3

(

119887 minus 119886

119887 + 119886

) (7)


119862 119875119898 and 119875




119882119879= 119875119862119882119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119898119882119898+ 0434119870

119898[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119878119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1]

(8)



Ω2

119882119879= (

120597119882119879

120597119875119862

)

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862+ (

120597119882119879

120597119875119898

)

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (

120597119882119879

120597119875119878

)

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(9)

whereΩ119882119879


119875119862 Ω119875119898 and Ω

119875119878are


Ω2

119882119879= (119882

119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862

+ (119882119898+0434119870

119898[

119879

119879 minus 1

(ln119879)minus1])

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(10)





119862 119875119898 and 119875








119875119898() 39 63 Uniform

119875119878() 14 43 Uniform




119875119862() 285 7216884 0253224

119875119898() 51 6928197 0135847

119875119878() 285 837159 0293740


120583119908119879

=

285

100

416 + 04343 times 256 [

50

50 minus 1

(ln 50) minus 1]

+

51

100

1120 + 04343 times 91 [

50

50 minus 1

(ln 50) minus 1]

+

285

100

1500 + 0 = 106542 kgm3

(11)


Ω2

119882119879= 00098 997888rarr Ω

119882119879= 0099 (12)


120590119882119879

= 120583119882119879

Ω119882119879

(13)

Thus

120590119882119879

= 106542 times 0099 = 10548 kgmminus3 (14)

where 120590119882119879


119879)


5 Conclusion









Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119910 = 119866 (1199091 1199092 119909

119895) = 119866 (119909

119894) 119894 = 1 sim 119895 (4)


1 119909



1199091 1199092 119909



120583119910asymp 119866 (119909) +

119895

sum

119894=1

(

120597119866

120597119909119894

)

119909

(119909119894minus 119909119894) (5)







Ω2

119910=

119895

sum

119894=1

[(

120597119866

120597119909119894

)

2

119909119894

(

119909119894

120583119910

)

2

Ω2

119909119894] (6)




Ω =

120590

119883

=

radic3

3

(

119887 minus 119886

119887 + 119886

) (7)


119862 119875119898 and 119875




119882119879= 119875119862119882119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119898119882119898+ 0434119870

119898[

119879

119879 minus 1

(ln119879) minus 1]

+ 119875119878119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1]

(8)



Ω2

119882119879= (

120597119882119879

120597119875119862

)

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862+ (

120597119882119879

120597119875119898

)

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (

120597119882119879

120597119875119878

)

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(9)

whereΩ119882119879


119875119862 Ω119875119898 and Ω

119875119878are


Ω2

119882119879= (119882

119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862

+ (119882119898+0434119870

119898[

119879

119879 minus 1

(ln119879)minus1])

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(10)





119862 119875119898 and 119875








119875119898() 39 63 Uniform

119875119878() 14 43 Uniform




119875119862() 285 7216884 0253224

119875119898() 51 6928197 0135847

119875119878() 285 837159 0293740


120583119908119879

=

285

100

416 + 04343 times 256 [

50

50 minus 1

(ln 50) minus 1]

+

51

100

1120 + 04343 times 91 [

50

50 minus 1

(ln 50) minus 1]

+

285

100

1500 + 0 = 106542 kgm3

(11)


Ω2

119882119879= 00098 997888rarr Ω

119882119879= 0099 (12)


120590119882119879

= 120583119882119879

Ω119882119879

(13)

Thus

120590119882119879

= 106542 times 0099 = 10548 kgmminus3 (14)

where 120590119882119879


119879)


5 Conclusion









Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Ω2

119882119879= (

120597119882119879

120597119875119862

)

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862+ (

120597119882119879

120597119875119898

)

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (

120597119882119879

120597119875119878

)

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(9)

whereΩ119882119879


119875119862 Ω119875119898 and Ω

119875119878are


Ω2

119882119879= (119882

119862+ 0434119870

119862[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119862

120597120583119882119879

)

2

Ω2

119875119862

+ (119882119898+0434119870

119898[

119879

119879 minus 1

(ln119879)minus1])

2

(

120597119875119898

120597120583119882119879

)

2

Ω2

119875119878

+ (119882119878+ 0434119870

119878[

119879

119879 minus 1

(ln119879) minus 1])

2

(

120597119875119878

120597120583119882119879

)

2

Ω2

119875119878

(10)





119862 119875119898 and 119875








119875119898() 39 63 Uniform

119875119878() 14 43 Uniform




119875119862() 285 7216884 0253224

119875119898() 51 6928197 0135847

119875119878() 285 837159 0293740


120583119908119879

=

285

100

416 + 04343 times 256 [

50

50 minus 1

(ln 50) minus 1]

+

51

100

1120 + 04343 times 91 [

50

50 minus 1

(ln 50) minus 1]

+

285

100

1500 + 0 = 106542 kgm3

(11)


Ω2

119882119879= 00098 997888rarr Ω

119882119879= 0099 (12)


120590119882119879

= 120583119882119879

Ω119882119879

(13)

Thus

120590119882119879

= 106542 times 0099 = 10548 kgmminus3 (14)

where 120590119882119879


119879)


5 Conclusion









Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Reservoir Sedimentation Based on ...reservoir sedimentation trend, and hence sediment density is subject to uncertainty. On the other hand, optimal design of reservoir