Evaluation of factors affecting reservoir yield estimates

Journal of Hydrology, 112 (1990) 219-235

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Elsevier Science Publishers B.V., AmAterdam - - Printed in The Netherlands [1]

EVALUATION OF FACTORS AFFECTING RESERVOIR YIELD ESTIMATES

RALPH A. WURBS and CARLA E. BERGMAN

Civil Engineering Department, Texas A&M University, College Station, TX 77843(U.S.A.) Burns and McDonnell, Kansas City, MO 64141 (U.S.A.) (Received March 13, 1989; accepted after revision April 12, 1989)

ABSTRACT Wurbs, R.A. and Bergman, C.E., 1990. Evaluation of factors affectingreservoir yield estimates. J. Hydrol., 112: 219-235. Estimates of yield versus reliability relationships and firm yields are dependent upon approaches adopted for handling the complexities of modeling a river basin water management system. Factors affecting estimates of reservoir yield are evaluated ilere withi~ the general categories of basin hydrology, basinwide water management, and reservoir system simulation. Key aspects of reservoir yield analysis are identified and discussed from the perspective of an illustrative case study.

INTRODUCTION

Effective management of the surface water resource of a river basin r ~ u i r e s an understanding of the amount of water which can be provided under various conditions. Yield estimates are a key element in practically all studies and decisions involving water supply. Water supply planning and management involves complex institutional, legal, environmental, hydrologic, and physical systems. Streamflow, reservoir sedimentation, evaporation, water demands, and other variables pertinent to yielddeterminations are highly stochastic.Measured historicaldata are limited in extent and accuracy. The future is always uncertain. Water availability depends upon institutionalas well as hydrologic constraints. Mathematical models can only approximate the co~nplexities of reality. Consequently, reservoir yield studies necessarily involve uncertainties and approximations. Numerous papers have been published o11 the ~ubject of reservoir yield analysis. The focus of the literature is on development of mathematical modeling techniques. The present paper addresses the comple~ties of practical application of standard state-of-the-artanalysis methods. The paper provides an evaluation of key factors affectingreservoir system yield estimates.Although yield analysis models are discussed,the focus of the

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© 1990 Elsevier Science Publishers B.V.

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paper is on practical development of necessary input data and strategies for applying the models. Factors affecting reservoir system yield are discussed within the categories of basin hydrology, basinwide water management, and reservoir system simulation. These topics are addressed from the perspective of a particular illustrative case study. RESERVOIRYIELDANALYSISMETHODS

Modeling approaches Rippl presented his well-known mass diagram technique for determining reservoir firm yield over a century ago (Rippl, 1883). Since that time, a variety of mathematical models have been developed to evaluate the amount of water which can be supplied by a reservoir or multireservoir system. M c M a h o n and Mein (1986) provide a comprehensive treatment of a broad range of yield analysis methods. For purposes of the present brief summary overview, the numerous methods for analyzing reservoir yield are categorized as: (1) storage probability theory and related methods; (2) mathematical programming or optimization techniques; and (3) simulation of a stream/reservoir system for a specified hydrologic sequence. Storage probability theory and related methods have been addressed extensively in the research literature.M u c h of the work represents modifications or extensions of the basic Moran (1959) and Gould (1961) models. The objective of stochastic storage analysis methods is to determine the probability distribution of reservoir storage. In terms of practical usefulness, the most important methods in this group are described as probability matrix methods ( M c M a h o n and Mein, 1986). Other methods are of theoretical interest. K!emes (1981) provides an in-depth treatment of applied stochastic theory of reservoir storage. Wurbs et al. (1985) provide a state-of-the-artreview and annotated bibliography of systems analysis techniques applied to reservoir operation, which is directed toward optimization, simulation, and stochastic analysis methods. A majority of the over 700 references cited in the bibliography focus on optimization techniques. Optimization models are formulated in terms of determix.ing values for a ,,~et of decision variables which will maximize or minimize an objective function subject to constraints. Most of the applications of optimization techniques in reservoir system analysis involve linear programming, dynamic programming, or combining a simulation model with a search algorithm. As an example of the application of optimization techniques for yield analysis, linear programming can be used il~ a maturer described by Loucks et al. (1981) to compute firm yield. Simulation models are the most commonly used tool for analyzing reservoir system yield. The complexities of a river basin typically can be represented more realistically in a simulation model than in the other yield analysis approaches. Numerous generalized simulation models have been developed for

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analyzing reservoir yield. The HEC-3 and HEC-5 models (U.S. A r m y Corps of Engineers, 1981, 1982) were used in the case study discussed in this paper. The scope of studies described herein is limited to estimating firm yields and yield versus reliabilityrelationships using simulation models. The remainder of the paper addresses yield analysis from the perspective of simulation of a stream/reservoir system for a specified hydrologic sequence.

Firm yield and reliability The stochastic nature of streamfiow and other pertinent variables must be reflected in methods for quantifying yield. The ~mount of water which can be supplied by a stream/reservoir system may be analyzed in a simulation study in terms of a firm or dependable yield, percent of time specified quantities of water are available, reliability of meeting various demand levels, risk of shortages, likelihood of various reservoir storage levels occurring, or a tabulation of the ~mount of water available during each period of a s~mulation based on specified conditions or assumptions. This paper focuses on yield versus reliability relationships and, in particular, firm yield. Firm yield is defined as the estimated m a x i m u m release or withdrawal rate which can be maintained continuously during a repetition of the hydrologic period-of-record. A number of definitions of reliability are cited in the literature.A COl~mon definitionis that reliabilityis the percentage of time that a specifieddemand level can be met. Precise textbook definitionsof firm yield and reliabilitycan be formulated for a simple river basin with a single reservoir and single water user. However, in actual practice, for a complex multiple reservoir, multiple user, river basin system, firm yield and yield versus reliabilityrelationships must be defined in terms of the basic assumptions and approaches used in handling various complicating factors. The traditional Rippl diagram and sequent peak algorithm approaches for estimating firm yield, which are amenable to manual computations, are outlined in standard hydrology textbooks. Firm yield is now usually computed using a reservoir system simulation model. For a given reservoir storage capacity and inflow sequence, the system is simulated with alternative trial demand levels,in an iterative search for the demand level which just empties the storage capacity. The iterative procedure for computing firm yield may be automated within the simulation model. Firm yield computational procedures are outlined by the Hydrologic Engineering Center (U.S. A r m y Corps of Engineers, 1975). Reliability estimates can be formulated on either a period or a volumetric basis. Period reliabilitycan be defined as the proportion of time that the system is able to meet demands. Volumetric reliabilityis the ratio of the volume of water supplied to the volume demanded. Various definitionsof reliabilityalso can be formulated for alternative time periods. For example, reliabilitymay be defined and computed as the percentage of months or days during a hydrologic period-of-record simulation for which a specified yield level is met without

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shortages. In this case, the firm yield would be the maximum yield level having a reliability of 100%. Alternatively, reliability estimates can be formulated in terms of the likelihood that demand can be met continuously during a long multiyear period. Computations would involve repeated simulations for a large number of synthetically generated equally-likely streamflow sequences of a specified length, such as 50 years. The reliability would be the number of sequences for which the demand is met divided by the total number of sequences. CASE STUDY

A yield study for a system of twelve reservoirs in the Brazos River Basin is documented by Wurbs et al. (1988) and Wurbs and Carriere (1988). Bergman (1987) presents a sensitivity analysis and evaluation of key factors affecting yield estimates for this system. The Brazos River Basin extends from eastern New Mexico southeasterly across Texas to the Gulf of Mexico. The basin has a drainage area of 118,000km 2, of which 111,000km 2 are in Texas and the remainder in New Mexico. Pertinent water amounts are tabulated in Table 1. The mean streamflow near the basin outlet over the period 1900-1984, after adjustments to remove the impacts of man's activities in the basin, is 221.7m as -1. The Brazos River and tributaries supply most of the surface water used in the Brazos River Basin and adjoining San Jacinto-Brazos Coastal Basin. Historical 1984 surface water use and 2010 water use projected in the Texas Water Plan (Texas Department of Water Resources, 1984) for the basins are presented in Table 1. The total of the permitted diversions which can be made under the prior appropriation water rights permit system is also shown. In general, surface water management can be categorized as being primarily influenced by either seasonal fluctuations in streamflow and/or water use or by TABLE 1 Basinwide water quantities Quantity

M e a n discharge (m ss- i)

1900-1984 mean naturalized streamflow Total 1984 surface water use: Brazos River Basin San Jacinto--Brazos Coastal Basin Total 2010 projected surface water use: Brazos River Basin San Jacinto-Brazos Coastal Basin 1984 water supply and hydropower releases from 12 U S A C E / B R A reservoirs Permitted water rights diversions associated with 12 U S A C E / B R A reservoirs Total permitted water rights diversions

221.7

22.1 12.1 67.5 25.3 23.2

53.6 110.3

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long-term t h r e a t of drought. In m a n y parts of the world, a reservoir will be filled during a distinct season of high rainfall or snowmelt and emptied during a dry season with high water demands. Thus, the reservoir level fluctuates greatly each year in a predictable cycle. This is not the case in Texas. Streamflow is highly variable, subject to extremes of floods and droughts. Although streamflow has seasonal variability, water management in Texas is greatly influenced by the long-term threat of multiyear drought. Although reservoir storage may be significantly depleted within several months, severe drought conditions are characterized as a series of several dry years rather t h a n the dry season of a single year. The drought of the 1950's is generally considered to be the most severe drought of record for much of Texas and the Southwest United States. This six-year drought began in 1951 and ended with widespread flooding in May 1957.

Reservoir system The study focused on the system of twelve reservoirs listed in Table 2 and shown schematically in Fig. 1. The numerous other reservoirs in the basin were considered primarily from the perspective of their impacts on the twelve principal reservoirs. The twelve-reservoir system contains essentially all of the flood control and about 70% of the conservation storage capacity in the basin. The twelve reservoirs have conservation capacities totaling 3437 million m 3. A portion of the conservation capacity is inactive storage which provides head for hydroelectric power operations. Nine of the reservoirs are owned and operated by the U.S. Army Corps of TABLE 2 Reservoir system storage ca~,acity Reservoir

Drai!nage area (kin2)

Storage capacity (106ms) Conservation

Possum Kingdom Granbury Whitney Aquilla Waco Proctor Belton Stillhouse Georgetown Granger Somerville Limestone Total

61,000 66,500 70,4(~ 650 4,280 3,260 9,150 3,400 640 1,840 2,610 1,750

Flood control

Total

703 189 774 65 188 73 552 291 46 8! 198 278

0 0 1,693 115 708 388 794 487 116 220 429 0

703 189 2,467 180 896 462 1,346 778 161 301 626 278

3,437

4,950

8,387

224 ~ ProctorL ~

Poss~ K£ngdom Granbury

L • T~'httney

BeltonL

D

Aqutlla Waco S t : t l l h ~ Georget:om't Granger

<] Somerville Reservoir

Limestone

Fig.1.SchematicofUSACE/BRAreservoirsystem. Engineers (U,q ~CE), with the Brazos River Authority (BRA) having contracted for most of the water supply storage capacity. The other three reservoirs, which are Possum Kingdom, Granbury, and Limestone, are owned and operated by the BRA. The BRA sells water to a number of cities, industries, irrigators, and other water users. The nine USACE reservoirs contain flood control storage. All twelve reservoirs contain conservation capacity for municipal, industrial, and/or agricultural water supply. Several provide cooling water for steam electric power plants. Possum Kingdom and Whitney Reservoirs also have hydroelectric power plants. Most of the water released through the turbines is diverted at downstre~n locations for other beneficial uses. Recreation occurs at all the reservoirs. A majority of the municipal, industrial, and agricultural water use occurs in the lower basin and adjoining coastal basin. Diversions from the river occur at significant distances below the d-ms and can be met by releases from various combinations of several reservoirs.

Yield analysis approach The following generalized computer programs were used in the study: HEC-3 Reservoir $ys~em Analysis for Conservation; HEC-5 Simulation of Flood

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Control and Conservation Systems; Water Rights Analysis Program (TAMUWRAP); and Monthly Streamflow Simulation (MOSS-IV). Feldman (1981) describes the various generalized simulation models available from the Hydrologic Engineering Center (HEC) of the U.S. Army Corps of Engineers (USACE). HEC-3 simulates the operation of a reservoir system for conservation purposes such as water supply and hydroelectric power (USACE, 1981). HEC-5 (USACE, 1982) has most of the conservation capabilities of HEC-3 and greatly expanded flood control capabilities. HEC-5 is required for detailed flood control simulations. HEC-3 was the primary model adopted for the water supply oriented studies discussed here. Selected simulations were rerun with HEC-5 to ~heck the computations and to obtain output in a format which is a little more convenient for certain purposes. HEC-3 and HEC-5 have optional routines for computing firm yields and reliabilities for single reservoirs and multireservoir systems. MOSS-IV (Beard, 1973) is an impoved version of HEC-4, which synthesizes monthly streamflow data. MOSS-IV was used to fill in gaps in the streamflow records. TAMUWRAP (Walls and Wurbs, 1989) is a generalized model for simulating a water rights priority system. Input data includes: naturalized monthly streamflows covering the simulation period at each pertinent location; the diversion amount, storage capacity, priority date, type use, return flow factor, and location for each water right; the storage versus area relationship for each reservoir; and monthly reservoir evaporation rates. For each month of the simulation, TAMUWRAP performs water accounting computations for each water right in turn on a priority basis. Output includes diversions, diversion shortages, reservoir storage levels, streamflow depletions, and unappropriated flows. The streamflow depletion for a given water right in a given month represents the amount of water taken to meet the diversion requirement that month and to refill previously drawn-down reservoir storage capacity. Streamflow depletions plus unappropriated flows represent the amount of water available to a given water right after all senior water rights have been satisfied. Streamflow depletions and unappropriated flows computed with TAMUWRAP provide streamflow input data to HEC-3 for computing yields and reliabilities constrained by senior water rights. The simulation study included various types of analysis. This paper focuses on firm yield and, to a lesser extent, reliability analyses. Firm yields and yield versus reliability relationships were computed with HEC-3 and HEC-5 based on January 1900 through December 1984 monthly flows at nineteen locations in the basin. Firm yield is the m a x i m u m yield which can be prodded continuously throughout the 85-yr simulation period. Reliability is the vurnber of months a specifiedyield level can be met divided by 1020 months in the simulation period. Firm yield is the m a x i m u m yield with a r~liabilityof 100%. Yields are expressed on a mean annual basis, with monthly distribution factors incorporated in the models to reflect seasonal variations in water use. Numerous model runs were made to evaluate the sensitivity of firm yields

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and reliabilities to various assumptions and conditions. The following evaluation of key factors affecting reservoir system yield estimates is based largely upon this study as well as past experience with other similar studies. The relative significance of various factors vary between river basins and types of yield studies. Consequently, the case study findings cited in the paper are not necessarily representative of other river basins in all respects. However, the case study does provide general insigiits on various aspects of yield studies. CONSIDERATIONS IN ESTIMATING RESERVOIR YIELD

Several key factors to be considered in reservoir yield studies are discussed below following the outline presented in Table 3.

Basin hydrology Stresmflow and reservoir evaporation rates are required to represent the basin hydrology in a model. Development of the basic hydrologic input data is clearly a key factor in reservoir yield studies. In the case study, complete homogeneous series of mean monthly streamflows covering the 1900-1984 simulation period were compiled for nineteen selected locations. In general, yield studies are typically based on mean monthly streamflows, but mean daily streamflows are sometimes used. Daily streamflows are used for many other types of simulation studies. For the case study, daily data offered no significant improvements in yield or reliability estimates. The stresmflow adjustments discussed below would have been tremendously more difficult using daily data. Development of a complete homogeneous set of streamflow data represents a large portion of the total effort of a yield study. Gaged monthly streamflows must be naturalized to remove nonhomogeneities caused by the activities of man in the basin. Missing data in the streamflow recor& at one location are filled in by a regression analysis with available streamflow data at other TABLE 3 Considerations in estimating reservoir yield Basin hydrology

Basinwide water management Reservoir system simulation

Streamflow da~a Evaporation data Channel losses Basin changes Other reservoirs and water users System operating policies Multiple purpose operations Seasonal distribution of water use l~servoir sedimentatio~l Definition of water supply sterage failure

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locations. Streamflows at the locations of gages must be transposed to other pertinent locations in the basin. Fortunately in the case study, gage records covering relatively long time periods were available at or near the d~m~ites and other locations of interest. The Texas Water Commission (TWC) had previously completed a detailed naturalization study to adjust streAmAow records for the period 1940-1976 for the effects of major reservoirs, numerous smaller reservoirs, withdrawals of water for beneficial use, and return flows. This work was extended in the present study to cover the remainder of the 1900-1984 simulation period. The same basic stresmflow records and net evaporation rate data used in the TWC naturalization study were also used in the present study; but the computations to extend the period covered were limited to adjustments for only 23 major reservoirs and selected diversions. Gaps in records were filled in using MOSSIV. Streamflows were transposed to nearby locations using drainage area ratios. The gaged and naturalized streRmflow data appear to be very similar in many respects. However, the naturalization most affects low flows and thus was found to significantly affect the yield estimates. Future, not past, conditions are of concern in water resources management. However, because future streamflows are unknown, reservoir yield studies are based on historical period-of-record hydrology. In the case study, a comparison of firm yields computed using two alternative simulation periods was developed by simply dividing the 85-yr simulation period into two periods, 1900-1939 and 1940-1984. Individual reservoir firm yields for twelve reservoirs computed based on the 1900-1939 period ranged from 100.0 to 140.0% and averaged 105.1% of the corresponding values based on the 1900-1984 period. The firm yields for the 1940-1984 period ranged from 100.0 to 109.2% and averaged 103.3% of the 1900-1984 values. The twelve-reservoir system firm yie|d was 100.0 and 101.4% of the 1900-1984 value for the 1900-1939 and 1940-1984 periods, respectively. Development of the field of stochastic or operational hydrology has focused largely upon problems of rp~ervoir planning and operation. Synthetic stresmflow generation is addressed extensively in the research literature., Loucks et al. (1981) provide a concise overview. Synthetic streamflow generation models, such as MOSS-IV, accept peried-of-record naturalized monthly stre~mflow as input. Monthly stre~n~ow sequences of any sgecified length are synthesized based on preserving the statistical parameters of the input data. The statistical parameters of the input streamflow data are preserved in the sense that the parameter values for an infinitely long sequence of generated streamflows would be the~ ~ n e as the values for the input data. Estimation of reservoir reliability usin~ synthetically generated streamflow sequences is based on the concept that preservation of statistical parameters results in a set of streemflow sequences which are equally likely to occur. The historical streamflow is one sequence representative of what could occur in the future. The synthetically generated stre~rn~ows represent alternative sequences which have the same likelihood of occurring in the ~ u r e . The

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validity of synthetic streamflow generation models in representing the likelihood of extreme low-flow conditions is an aspect of this yield analysis tool which has been subject to discussion. A reservoir reliabilitystudy using synthetically generated stre~mflow would be a logical extension of the case study but has not been conducted due to the time and effortrequired. Reservoir evaporation is computed in the model by multiplying the average water surface area during a month by an inputted net evaporation rate. The Texas Water Development Board (TWDB) maintains a computer fileof gross and net evaporation rates for each month since January 1940. The data cover the entire state of Texas on a one-degree quadrangle basis.The T W D B evaporation rates are based on a compilation of available pan evaporation data and monthly pan coefficients.Net evaporation is the difference between (a) gross evaporation and (b) precipitation lessrunoff (natural evapotranspiration loss). The T W D B monthly reservoir evaporation rates were used in the study. 1940-1984 averages for each of the twelve months were used for the period prior to 1940, for which data are unavailable. Higher than average evaporation normally accompanies drought conditions. However, the effects on firm yield estimates of using mean evaporation rates for the period prior to 1940 were somewhat minimized because the critical drawdown periods happened to generally be after 1940. Reservoir evaporation is an important consideration in surface water management in the Brazos River Basin. In the case study, net evaporation is in the range of 20-60% of the firm yield of the reservoirs. Yield estimates are fairly sensitive to assumptions regarding evaporation rates. For example, using gross evaporation instead of net evaporation decreases the firm yield estimates by 10-15%. Using twelve constant average monthly evaporation rates for all years, rather than actual monthly rates which vary between years, was found to increase firm yield by several percent. In the Brazos River Basin, diversion locations are often many miles below the dams from which water is released. Channel losses include seepage, evaporation, and unauthorized diversions. A simulation study is based on gaged stre~mflow data which reflecthistoricallosses upstream of the gage. However, special studies are required to determine changes in channel losses due to alternative reservoir operating policies. Changes in channel losses were neglected in the case study. Basinwide water management

Streamflow characteristics change with time as a result of man's activities in the basin. Land use changes, water use, river regulation by major reservoirs, capture of runoff by numerous small ponds, and changes in base flow from groundwater due to pumping may affect inflow to the reservoirs of interest. Climatic changes could also affect streamflows. As discussed previously, the objective of streamflow naturalization is to develop a set of input data representing historical conditions existing prior to man's activities changing the

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basin. However, yields are typically computed for some present or future condition. In the case study, the impacts of the numerous reservoirs and water users in the basin were reflected in the yield models, but other types of basin changes were considered to have l-legligible effects on yields and were not modeled. A river basin is a complex system. Various approaches can be adopted to represent the hydrologic and institutional interactions between the reservoirs, for which yields are being analyzed, and other reservoirs and water users in the basin. For example, the impacts of historical or projected future water use by other users may be simulated. In the case study, basinwide water management was represented by the water rights system. Firm yields and yield versus reliability relationships for the twelve reservoirs were computed assuming all other water rights holders utilize the full amount of water to which they are legally entitled, with return flows estimated based on return flow factors developed from historical records. Thus, the yields are constrained by senior water rights. Texas has a prior appropriation permit system with priorities based on appropriation dates. About 1040 individual citizens, private companies, cities, and public agencies hold permits to use the waters of the Brazos River and tributaries. The water rights include diversions totalling 84.9m3s -1 and storage capacities totalling 5634 million m3 in 598 reservoirs. Of the total permitted annual diversion amount, 51, 29, 19, and 1.0%, respectively, is for municipal, industrial, irrigation, and mining uses. Priority water rights for releases or withdrawals from the twelve USACE/BRA reservoirs listed in Table 2 are 29.5 m 3s -1 or 35% of the basin total. The BRA also has an excess flows permit which allows diversion of an additional 2 5 . 4 m 3 $ -1 a s long as no other water rights are adversely impacted. The excess flows permit has no priority. About 19% of the total water rights diversions with assigned priorities have locations upstream of one or more of the twelve USACE/BRA reservoirs. The remaining 46% of the permitted diversions are below the reservoir system. The water rights associated with the twelve reservoirs have different priority dates, and some reservoirs have several rights with different priorities.Each of the reservoirs are constrained by numerous other rights with senior priorities. Inflows must be passed through a reservoirto meet senior rights at downstream locations. Although two hydroelectric power plants are operated in the basin, no water rights exist specifically for hydropower. Hydroelectric power is generated by unappropriated flows and water supply releases. TAMUWRAP was used in combination with HEC-3 to compute firm yields and yield versus reliabilityrelationships constrained by senior water rights. The output of a T A M U W R A P simulation includes streamflow depletions associated with a water right and unappropriated strearnflows at a location. The streamflow depletion for a given water right in a given month includes filling of previously drawn-down storage capacity as well as meeting the diversion requirement for that month. Streamflow depletions plus unappropriated flows represent the water available to a given water right considering

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all other water rights in the basin. These adjusted streamflows were provided as streemflow input data to HEC-3 to analyze yield constrained by senior water rights. An alternative set of firm yields was computed without considering water rights. The term "hydrologic firm yield" is adopted herein for these yields. Hydrologic firm yields were computed following a traditional approach in which reservoir inflows consist of unregulated local flows plus spills from upstream reservoirs. For reservoirs in tandem, the firm yield for the downstream reservoir was computed with upstream reservoirs included in a model with diversions at the upstream reservoirs set equal to their previously computed firm yield. Thirteen reservoirs were incorporated in the model including the twelve USACE/BRA reservoirs shown in Fig. 1 and Hubbard Creek Reservoir which is located upstream of Possum Kingdom Reservoir. Hubbard Creek Reservoir was included in the modeling due to its relatively large storage capacity. The numerous other smaller reservoirs and water users in the basin are not included in the hydrologic firm yields. This general approach of reflecting the impacts of a few selected major reservoirs or large water users has been commonly applied in yield studies in Texas and elsewhere. Yields for a system of ten reservoirs computed using alternative approaches are tabulated in Table 4. The ten reservoirs include all those listed in Table 2 except Waco and Whitney. The storage in Waco Reservoir is essentially totally committed to the City of Waco. The conservation storage capacity in Whitney Reservoir is divided between hydroelectric power and water supply by contractual agreements, with a majority of the storage capacity being allocated to hydropower. The other ten reservoirs, which are included in Table 4, are largely system reservoirs. Water demands at downstream locations can be met by releases from s e v e ~ ~ : ~ ,-~,~.~ ,.~ ~ . ~ z~ervoirs. System firm yields were

TABLE 4 Yields for ten reservoirs Type of yield

Yield (roSs-z)

Sum of individual reservoir hydrologic firm yields System hydrologic firm yield excluding downstream unregulated flows including downstream unregulated flows Sum of individual reservoir firm yields constrained by senior water rights System firm yield constrained by senior water rights excluding downstream unregulated flows including downstream unregulated flows 95% reliability system yield constrained by senior water rights excluding downstream unregulated flows including downstream unregulated flows

27.7

1

41.7 57.7 21.4 25.4 33.1 38.1 48.6

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computed for the ten reservoirs releasing for a c o m m o n downstream diversion located near the coast where actual water use is cor~centrated. Firm yields constrained by senior water rights and hydrologic firm yields are compared in Table 4. As discussed above, different approaches for modeling the impacts of other reservoirs and water users in the basin are reflected in the hydrologic firm yields versus yields constrained by senior water rights. The hydrologic firm yields reflectthe impacts of three other large reservoirs on the yields of the ten reservoirs. The firm yields constrained by senior water rights reflect the impacts of 588 other reservoirs on the yields of the ten selected reservoirs. The sum of the individual reservoir hydrologic firm yields for the ten selected reservoirs is 27.7m3s -I. The corresponding sum of individual reservoir firm yields constrained by senior water rights is 21.4m 3s- I or 77% of the hydrologic firm yields. Yields tabulated in Table 4 are discussed further below in conjunction with system operation. Reservoir system simulation Modeling reservoir characteristics and operating policies is another aspect of yield studies. Yield, either firm yield or yield associated with a specified reliability, is a hypothetical potential, rather than actual historical or projected future, water use. Yield computations necessarily involve simplified representations of actual reservoir operating procedures. However, the accuracy of yield estimates is dependent on the manner in which actual operating procedures are represented in the computer model. Reservoir yield has traditionally,in Texas and elsewhere, been quantified in terms of individual reservoir firm yield.The total yield supplied by a river basin or reservoir system is typically viewed as the summation of individual firm yields for the reservoirs included in the basin or reservoir system. However, system firm yield was found to be an important consideration in quantifying water availability in the Brazos River Basin. The case study focused on two aspects of system operations: (1) coordinated operation of multiple reservoirs, and (2) coordinated operation of reservoir releases with unregulated flows entering the river downstream of the dams. System yields were simulated based on a diversion requirement at a downstream location being met by a combination of releases from several upstream reservoirs and unregulated flows entering the river below the dams. Multireservoir system operation involves coordinated releases from two or more reservoirs to supply c o m m o n diversions at downstream locations. Multireservoir system operation is beneficial because the criticaldrawdown periods for the individually operated reservoirs do not perfectly coincide. Operated individually, one reservoir may be completely empty and unable to supply its users while significant storage remains in th~ other reservoirs. At other times, the other reservoirs may empty. System operation balances storage depletions. Utilization of unregulated flows entering the river below the most downstream dams was found to be another key aspect of system operation. The

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naturalized streamflow data at all locations in the basin have months of zero discharge. Thus, unregulated flows have zero firm yield. However, unregulated flows in the lower basin are of significant magnitude most of the time. When combined with reservoir releases during low-flow periods, the unregulated flows greatly increase the overall stream/reservoir system firm yield. As indicated by Table 4, individual reservoir firm yields constrained by senior water rights total 21.4 m s s -1 for the ten reservoirs. The corresponding ten-reservoir system firm yields are 25.4 and 33.1 m 3s -1, respectively, excluding and including downstream unregulated flows, or 118 and 154% of the sum of the individual reservoir firm yields. The system firm yields are based on the ten reservoirs releasing for a common diversion location near the basin outlet. System hydrologic firm yields were computed for the ten reservoirs releasing for the common downstream diversion, with the other three nonsystem reservoirs included in HEC-3 with local diversions equal to their individual reservoir firm yields. The resulting ten-reservoir system firm yields, excluding and including downstream local flows, are 41.7 and 57.7 m3s -~, respectively, or 151 and 208% of the sum of the corresponding individual reservoir firm yields. Thus, Table 4 demonstrates that for the case study reservoir system, a detailed consideration of the impacts of other water users based on senior water rights significantly decreases firm yields, and system operations significantly increase firm yields. Firm yield, by definition, has a reliability of 100%. Greater yields have lesser reliabilities. However, yield levels significantly larger than firm yield result in shortages a relatively small percent of the time. For example, a yield of 38.1roSs -~, which is 150% of the system firm yield, has a reliability of 95%. In the case study, release decisions in the model were based on balancing the percentage of storage depletion in each of the reservoirs. This operational plan probably results in near-maximum system firm yields for this system. However, a more selective release approach might be beneficial for this system and other reservoir systems. The objective might be to release from the reservoir with the highest probability of spills and/or highest evaporation potential. The individual reservoir yield computations are based on a single diversion at each reservoir. The system firm yield computations are based on multiple reservoirs releasing for a single diversion at a downstream location. Return flows were not considered. In actuality, diversions are made at a number of locations in the stream/reservoir system. Return flows associated with diversions at upstream locations contribute to stre~mflow available at downstream locations. Also, local inflows available at the downstream diversion location adopted for the system firm yield estimates actually are not accessible at the various actual upstream diversion locations. Since diversion locations are significant travel times below the dams, uncertainties in real-time prediction of downstream local inflows result in excess reservoir releases. However, the cited system firm yields were estimated assuming perfect forecasting, which tends to increase firm yields. HEC-3 has an option for incorporating a contingency factor in releases to reflect imperfect

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forecasts of downstream local flows. This option was not applied in the case study. As indicated in Table 2, the reservoir system has a large amount of flood control storage capacity. The flood control capacity was found to have essentially no effect on firm yield estimates. If water from previous flooding remained in a flood control pool in the first month of the critical drawdown period, the firm yield could be increased by flood control operations. However, this situation does not occur in the Brazos River Basin data set. Hydroelectric power is generated at two of the reservoir projects. Releases through the hydroelectric plant at Possum Kingdom were assumed to be incidental to water supply and did not affect the yield analysis. Whitney Reservoir was operated in the simulation to meet power demands specified in the hydroelectric power contract. Thus, the system firm yields for water supply cited above reflect the impacts of hydropower operations at Whitney Reservoir. Water demands, as well as water availability, are highly seasonal. Monthly distribution factors determined from historical water use patterns were incorporated in the yield analysis. Water use rates during the summer months are several times higher than during winter months. However, variations in monthly distribution factors were found to have relatively little impact on firm yield estimates. For example, the system firm yield is increased by less than 2% by assuming a constant diversion throughout the year rather than using the monthly water use distribution factors. By definition, yield represents a constant annual diversion or release rate. Year-to-year variations in water use are not reflected in the simulation. However, in actuality, water demands may vary significantly from year to year with variations in precipitation and other conditions. Yield analyses are performed for a specified condition of reservoir sedimentation. Sedimentation is reflected in a simulation model by the reservoir water surface elevation versus storage and area relationships. Sediment volume estimates were developed by the construction agencies during project design based on data provided by the Texas Water Development Board (1959). The distribution of sediment volume within the reservoir pool was computed using methods presented by Borland and Miller (1958). Prediction of reservoir sedimentation is extremely approximate. Since sediment transport fluctuates widely from very little during dry weather to large amounts during major flood events, predicting the sediment accumulation expected during a short period of a few years is even more difficult than predicting long-term averages. The total conservation storage capacity in the twelve reservoirs for estimated year 2010 sediment conditions is 91% of the storage capacity for 1984 sediment conditions. The sum of the 2010 individual reservoir firm yields is 94.5% of the sum of the 1984 firm yields. At individual reservoirs, the 1984 to 2010 predicted reduction in storage capacity varied from 1.8 to 33%. The 1984 to 2010 reduction in firm yield varied from 1.6 to 33% for the twelve individual reservoiors. Reservoir storage capacity versus yield relationships are highly nonlinear. Decreases in storage capacity result in decreases in yield. However, the

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percentage decrease in yield is generally much less than the corresponding percentage decrease in storage capacity. In the case study, firm yield was considered to be the diversion or release rate which just emptied the conservation storage. Reservoir releases continued uninterrupted in the model until the conservation capacity was totally depleted. However, in actuality, storage depletions can be expected to significantly affect water supply capabilities before the reservoir storage capacity is completely empty. In an actual drought, as storage depletions increase the risk of future severe shortages, water managers will likely impose restrictions on water use. Such restrictions would represent a shortage or inability to meet full demands before the conservation storage capacity is totally depleted. Development of an unacceptably high risk of severe shortage in the unknown future is actually a water supply storage failure, which occurs prior to emptying the reservoir capacity. Low reservoir storage levels can also cause water quality problems which severely restrict the use of the remaining water. If a water supply storage failure is defined more stringently than totally depleted conservation storage capacity, the yield versus reliability relationships and firm yields developed in the case study could be significantly affected. SUMMARYAND CONCLUSIONS Estimates of yield versus reliability relationships and firm yield are fundamental to water supply planning and management. Simulation models are commonly used for reservoir yield studies. Numerous generalized computer progrems are readily available for such studies, including the HEC-3, HEC-5, MOSS-IV, and TAMUWRAP models applied in the case study. The paper presents an evaluation of key practical aspects of analyzing reservoir system yield from the perspective of an illustrative case study. The various factors affecting reservoir yield estimates can be classified as involving: (1) compilation and development of basic data representing'basin hydrology; (2) simulation of the physical characteristics and operating policies of the reservoir system; and (3) modeling the impacts of basinwide water management and use and other related activities on the reservoir system of concern. A number of factors are addressed by the paper. The stochastic nature of streamflow and evaporation, changes in a river basin over time, loss of reservoir storage capacity due to sedimentation, reservoir system operating policies, and interactions between multiple water users are particularly important fundamental aspects of a water supply and use system which must be considered in yield studies. An entire river basin should be viewed as an integrated system in analyzing the ~mount of water which can be provided under various conditions. ACKNOWLEDGMENTS The research on which this paper is based was financed in part by the Department of the Interior, U.S. Geological Survey, through the Texas Water

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Resources Institute. The Brazos River Authority provided nonfederal matching funds. Contents of this publication do not necessarily reflect the views or policies of the United States Department of Interior or the Brazos River Authority, nor does mention of trade names or commercial products constitute their endorsement by the United States Government or the Brazos River

Authority. REFERENCES

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