**1. Introduction**

Effective water allocation and managemen<sup>t</sup> requires an understanding of the reliabilities at which various quantities of water can be provided under various conditions. Modeling and analysis strategies for quantifying capabilities for supplying water needs are explored in this paper based on the experience of the Texas water managemen<sup>t</sup> community in developing and applying a legislatively mandated water availability modeling system to support statewide planning and water allocation. The modeling system has been expanded and improved continually over the past twenty years to address evolving water managemen<sup>t</sup> strategies and issues. Current research, development, and implementation priorities include incorporation of legislatively mandated environmental flow standards in both the modeling system and actual water management. The Brazos River Basin represents the inaugural application of the latest version of the modeling system with expanded features added to incorporate environmental flow standards and serves as a case study to illustrate the concepts and issues discussed in this paper.

The river/reservoir system simulation and frequency/reliability analysis methods presented in this paper are implemented in a comprehensive, flexible modeling system developed at Texas A&M University (TAMU) called the Water Rights Analysis Package (WRAP) [1–6]. The public domain software package is generalized for application anywhere in the world and has been employed in various other countries and states but not to the same extent as its application in Texas. A water availability modeling (WAM) system maintained by the Texas Commission on Environmental Quality (TCEQ) consists of WRAP and input datasets for all of the river basins of Texas [7,8].

Generalized computer modeling systems have played increasingly important roles in various aspects of water resources planning and managemen<sup>t</sup> throughout the world over the past several decades [9,10]. The term "generalized" is used here to mean that the software is designed to be applied to real-world systems of various configurations at different locations by professional practitioners other than the original model developers. Generalized models should be thoroughly tested, clearly documented, and conveniently accessible. Wurbs [11], Lababie [12], Rani and Moreira [13], Lund et al. [14], and many others provide reviews of the massive literature on modeling multiple-purpose river/reservoir system operations. Most of the numerous river basin managemen<sup>t</sup> models reported in the literature are not generalized.

Wurbs [15,16] reviews the literature on modeling reservoir/river system managemen<sup>t</sup> and compares WRAP with other generalized modeling systems, focusing specifically on HEC-ResSim [17], RiverWare [18], and MODSIM [19]. RiverWare is marketed by the Center for Advanced Decision Support for Water and Environmental Systems (CADSWES) for a licensing fee. CADWES also provides consulting services to support application of RiverWare. HEC-ResSim, MODSIM, and WRAP software and documentation can be downloaded free-of-charge from their websites. HEC-ResSim, developed at the U.S. Army Corps of Engineers (USACE) Hydrologic Engineering Center (HEC), is applied nationwide to support operations of USACE multiple-purpose reservoir system operations, particularly flood control operations. MODSIM, developed at Colorado State University, is based on linear programming and has been applied to river/reservoir systems in many countries including systems operated by the U.S. Bureau of Reclamation in the United States. WRAP provides particular flexibility for modeling prior appropriation water rights permit systems and other institutional water allocation mechanisms. WRAP is designed for e fficient modeling and analysis of large complex river systems with many hundreds of reservoirs and water users [15,16].

Expanded capabilities for assessing water availability and supply reliability have been essential to recent improvements in water managemen<sup>t</sup> in Texas. Strategies and methods employed in Texas are applicable worldwide. Various issues that are still not fully resolved in Texas are also important in other regions of the world. The objective of this paper is to employ the Texas experience to outline water availability and allocation assessment practices proven to be e ffective and to highlight key complexities that have been successfully addressed along with needs for further advances. Computer-based modeling and analysis are integrated with water allocation and management.

### **2. Water Resources Planning, Allocation, and Management in Texas**

The geographic, climatic, hydrologic, and economic diversity that spans the state of Texas combined with high population growth and progressive water managemen<sup>t</sup> practices makes Texas an excellent laboratory for investigating water managemen<sup>t</sup> strategies and assessment tools that are generally applicable throughout the United States and the world. Motivated by continually intensifying demands on limited water resources, the state has implemented an array of strategies over the past twenty years that have greatly improved water managemen<sup>t</sup> [8,20,21]. Greatly expanded water availability modeling capabilities have provided essential decision support.

The 682,000 km<sup>2</sup> area of Texas (Figure 1) is comprised of 15 major river basins and eight coastal basins located between the major rivers. Mean annual precipitation increases from west to east across Texas from 20 to 145 cm. The population increased from 3,060,000 people in 1900 to 20,950,000 in 2000, to 25,390,000 in 2010 and 29,700,000 in 2020, and is projected by the Texas Water Development Board (TWDB) to increase to 46,360,000 by 2060 [20]. Declining groundwater supplies combined with population growth are resulting in intensified demands on surface water resources [8,20].

**Figure 1.** Map of major rivers and largest cities in Texas.

Ground and surface water each currently provide about half of the total water supply in Texas, with a shift toward less groundwater. Groundwater is used throughout the state, though agricultural irrigation supplied from the Ogallala Aquifer in northwest Texas accounts for the largest portion of the groundwater use. Groundwater rights in Texas have been based on the common law rule allowing landowners to pump unlimited quantities of water from under their land [8,21,22]. Most land in Texas is privately owned. Increased regulation of groundwater is evolving over time primarily through the establishment of local groundwater conservation districts. The 102 diverse groundwater districts established to date cover all or part of 184 of the 254 counties of the state. These districts encourage water conservation, protect water quality, and to a limited but growing extent regulate pumping.

This paper focuses on water in streams and reservoirs. Surface water is owned by the state. A state agency, the TCEQ, regulates the diverse use of surface water by numerous users.

Allocation of stream flow in Texas evolved over several centuries of rule by Spain, Mexico, the Republic of Texas, and the State of Texas into an unmanageable assortment of diverse water rights based on various versions of the riparian and prior appropriation doctrines [22]. The waters of the Rio Grande are allocated between the U.S. and Mexico by a 1944 treaty. The economy of the Lower Rio Grande Valley is based on irrigated agriculture. A severe drought during 1950–1957 motivated massive lawsuits that resulted in judicial allocation of rights to use the Texas share of the Rio Grande. The Water Rights Adjudication Act of 1967 initiated a 25-year process of consolidating the numerous water rights for the remainder of Texas into a permit system. Texas participates with neighboring states shown in Figure 1 in interstate compacts for the following rivers and effective dates: Rio Grande—1939, Pecos—1948, Canadian—1952, Sabine—1954, and Red—1980. All of these surface water allocation schemes are reflected in the water rights system and simulated in the water availability model (WAM) system maintained by the Texas Commission on Environmental Quality (TCEQ).

Surface water rights are granted by a state license, or permit, which allows the holder to divert a specified amount of water annually at a specific location, for a specific purpose, and to store water in reservoirs of specified capacity. Any organization or person may submit an application to the TCEQ for a new water right or to change an existing water right at any time. The TCEQ will approve the permit application if unappropriated water is available, existing water rights are not impaired, efficient water conservation will be practiced, and proposed actions are consistent with regional water plans. A permit holder does not own surface water but only a right to use the water. However, water rights can be sold, leased, or transferred. Such transfers are encouraged but require TCEQ permit approval.

Water managemen<sup>t</sup> occurs within an institutional setting that includes laws enacted by the Texas Legislature that are implemented collaboratively by governmen<sup>t</sup> agencies, private industry, stakeholders, consulting engineering firms, university researchers, and the general public. Several legislatively mandated programs have motivated or necessitated advances in water availability modeling capabilities to support water planning, development, allocation, and management.

Omnibus water managemen<sup>t</sup> legislation enacted by the Texas Legislature as its 1997 Senate Bill 1 (SB1) authorized a statewide and regional water planning process and creation of the WAM system to support planning and water allocation [7]. The Texas Water Development Board (TWDB) has been conducting statewide planning since the 1950s. The 1997 SB1 created a structured planning strategy that emphasizes local and regional participation. Sixteen regional water plans developed by planning groups supported by the TWDB and consulting firms and a consolidated statewide plan developed by TWDB sta ff in collaboration with the water managemen<sup>t</sup> community are updated in a five-year planning cycle with a 50-year future planning horizon [20]. Reports documenting the 2002, 2007, 2012, and 2017 water plans are available at the TWDB website [23]. Work on the updated 2022 regional and statewide plans is progressing.

The 2001 Senate Bill 2 created the Texas Instream Flow Program to advance the science of environmental flows and associated managemen<sup>t</sup> strategies [24]. The 2007 Senate Bill 3 (SB3) created a process for establishing environmental flow standards (EFS) based on best currently available science and incorporating these standards in the WAM System [25]. Periodic updates to flow standards are anticipated with advances in instream flow science and managemen<sup>t</sup> strategies. Integration of SB3 environmental flow standards (EFS) in water managemen<sup>t</sup> and water availability modeling is a major focus of continuing e fforts to expand WRAP and the Texas WAM system.

The flow of rivers in Texas, like other regions throughout the world, is characterized by grea<sup>t</sup> variability that includes the extremes of intense floods and severe multiple-year droughts combined with seasonal and continuous fluctuations [26]. Large reservoir storage capacities are essential for managing flow variability and uncertainties regarding future water availability. Numerous water users share limited stream flow and reservoir storage that is used for a diversity of purposes. Multiple-purpose, multiple-reservoir system operations are fundamental to e ffective water management. Preserving the vitality of riverine ecosystems while supplying water, electrical energy, and other needs of growing populations and economies is a global challenge [27–30] as well as a legislatively mandated requirement in Texas [25].

### **3. Water Rights Analysis Package (WRAP) and Water Availability Modeling (WAM) System**

The monthly version of the WRAP modeling system is routinely applied in Texas with simulation input datasets from the WAM system maintained by the TCEQ. The generalized WRAP combined with a simulation input dataset for a particular river basin is called a water availability model (WAM). Model users modify the TexasWAM system datasets to reflect water use requirements, proposed projects, and managemen<sup>t</sup> strategies of interest. For applications outside of Texas, model users develop their own input datasets for river/reservoir systems of interest. Input datasets range from small and simple to extremely large and complex. The monthly WRAP has been routinely applied for many years while continually being expanded and improved. Integration of SB3 EFS into the WAMs and comprehensive water managemen<sup>t</sup> has motivated development of daily modeling capabilities that are now transitioning from research and development to implementation.

### *3.1. Evolution of the WRAP Modeling System*

Software, manuals, datasets for examples in the manuals, and other information are available free-of-charge at the TAMU WRAP website [31], which links with the TCEQ WAM website.

The manuals [1–6] are published as technical reports by the Texas Water Resources Institute (TWRI) of the Texas A&M University (TAMU) System. Other WRAP-related technical reports are also available at the TWRI website [32]. The reference manual [1] includes a Bibliography of WRAP-Related Publications that lists 18 M.S. theses and ten Ph.D. dissertations by TAMU graduate students and many reports and journal and conference papers.

The predecessor toWRAP, called TAMUWRAP, was developed in a project funded by a federal/state cooperative research program administered by the U.S. Department of Interior and TWRI with the Brazos River Authority (BRA) serving as a nonfederal sponsor [1,33]. The modeling system has been continually improved and expanded since its implementation in the TCEQ WAM System [7]. The TCEQ has sponsored WRAP research and development at TAMU continuously during 1997–2003 and 2005–2021, concurrently with other WRAP-related research projects funded by other agencies. Development of methods incorporated in WRAP and research studies at TAMU using WRAP to explore various water managemen<sup>t</sup> issues have been funded by the TCEQ, TWDB, TWRI, BRA, Texas Advanced Technology Program, U.S. Army Corps of Engineers, U.S. Department of Energy, National Institute for Environmental Global Change, and other agencies [1].

The components of WRAP routinely applied with Texas WAM datasets are based on a monthly computational time step. The May 2019 WRAP software and manuals accessible at the WRAP website expand the monthly modeling system to also include daily modeling capabilities with monthly-to-daily naturalized flow disaggregation, flow routing, forecasting, flood control reservoir operations, and instream flow standards with subsistence, base, and high-pulse flow components.

A driving motivation for the daily modeling system is the 2007 Senate Bill 3 (SB3) requirement that environmental flow standards (EFS) be established and incorporated in the TCEQ WAM system [25]. As of late 2020, SB3 EFS have been incorporated in developmental daily versions of the Brazos, Trinity, and Neches WAMs to compute daily instream flow targets that are summed to monthly targets for incorporation in the WRAP input dataset for the monthly models [34–36]. These daily WAM datasets and detailed technical reports are available at the TAMU WRAP website [31].

### *3.2. Texas Water Availability Modeling (WAM) System*

The WAM System was created pursuant to the 1997 SB1 by the TCEQ, TWDB, other partner agencies, and contractors consisting of consulting engineering firms and university researchers [7]. Authorized use and current use scenario versions of 20 WRAP simulation input datasets covering all Texas river basins, an array of other information, and a link to the TAMU WRAP website are accessible at the TCEQ WAM website [37].

The TCEQ is the lead agency in maintaining the WAM System along with administrating the water rights permit system and interstate river basin compacts. Water right permit applicants, or their consultants, are required by the TCEQ to apply the WAMs to assess water supply reliabilities of proposed actions and the impacts on the reliabilities of all other water users. TCEQ sta ff apply the modeling system in evaluating permit applications. The TCEQ usually has over 200 water right permit applications under review at any time. Many are proposed modifications to existing permits.

The TWDB and 16 regional planning groups apply the WAMs in the regional and statewide planning process established by the 1997 SB1. River authorities and other entities apply the WAMs in operational planning studies and other endeavors. The modeling system has also been applied in U.S. Army Corps of Engineers (USACE) regulatory activities, environmental flow studies, project feasibility studies, university research studies, and other water managemen<sup>t</sup> endeavors.

The 15 major river basins and eight coastal basins of Texas are modeled as 20 WAMs, with three WAMs containing two adjoining basins. Activities of numerous water managemen<sup>t</sup> entities operating over 3400 dams/reservoirs and other constructed facilities in accordance with treaties between the U.S. and Mexico, five interstate compacts, two water right permit systems with 6200 active permits, federal water supply contracts, and other institutional arrangements are simulated.

Authorized and current use scenario datasets are available at the TCEQ WAM website for each of the 20 WAMs. The authorized use scenario is based on the premise that all water right permit holders use the full amounts to which they are legally entitled, subject to water availability. Many permits include projected future water needs. The current use scenario represents actual recent water use. The TWDB has developed WAM datasets representing projections of future water needs.

The modeling system contributes greatly to water managemen<sup>t</sup> and continues to be expanded to address various issues. Modeling support for establishing SB3 EFS is currently a priority research, development, and implementation focus, along with improving capabilities for water managemen<sup>t</sup> during drought and more e fficiently updating simulation input datasets.

### **4. Modeling and Analysis Methodologies**

WRAP simulates capabilities of river/reservoir systems in meeting specified water management, regulation, and use requirements for given sequences of naturalized stream flows and reservoir net evaporation less precipitation rates. A specified scenario of water managemen<sup>t</sup> is combined with natural historical hydrology. Since the future is unknown, historical hydrology is used to statistically capture the hydrologic characteristics of a river basin. The water managemen<sup>t</sup> and use scenario might be actual current water use, projected future conditions, the premise that all permit holders use their full authorized amounts, or some other scenario of interest. Simulation results are organized in optional formats including tabulations and plots of entire time sequences, summary tables, water budgets, frequency relationships, and various types of reliability indices. Water managemen<sup>t</sup> capabilities are expressed in terms of the likelihood (reliability) of meeting water supply targets or portions thereof and stream flow and reservoir storage frequency relationships.

The WRAP modeling system includes executable computer programs that perform the functions outlined as follows.

	- • Program HYD described by the Hydrology Manual [4] develops and updates SIM input files of monthly naturalized stream flows and reservoir net evaporation-precipitation rates.
	- • Program DAY documented by the Daily Manual [5] is used to calibrate routing parameters and otherwise compile daily hydrology input data for SIMD.
	- • The Hydrologic Engineering Center (HEC) Data Storage System Visual Utility Engine (DSS-Vue) [38] is used to compile, analyze, and manage times series datasets.
	- • Program SIM performs monthly simulations as described by the Reference, Users, and Fundamentals Manuals [1–3].
	- • Program SIMD performs daily simulations as described in the Reference, Users, and Daily Manuals [1,2,5].
	- • Program SALT performs a salinity simulation by combining the results of a SIM simulation with a salinity input file [6,39].
	- • Program TABLES reads SIM, SIMD, and SALT simulation input and results, performs frequency and reliability analyses, and creates a variety of tables to organize, summarize, analyze, and display simulation results [1–3].

• HEC-DSSVue [38] reads HYD, SIM, SIMD, TABLES, and SALT DSS input and output files containing time series of hydrology input or simulation results, prepares plots, and performs mathematical and statistical analyses and other data managemen<sup>t</sup> functions.

The well-established but still evolving WRAP simulation model SIM performs water accounting computations using a monthly time step. SIMD is a recently developed expanded version of SIM that performs the simulation computations using a daily time step. The daily SIMD maintains all capabilities of the monthly SIM while incorporating additional features for monthly-to-daily disaggregation of stream flows and water use targets, flow routing, forecasting, flood control reservoir operations, and tracking high-pulse flows defined by environmental flow standards.

The USACE Hydrologic Engineering Center (HEC) Data Storage System (DSS) has been fully integrated in WRAP for managing time series data. The latest versions of the WRAP programs create, read, and store data in DSS files. The DSS interface HEC-DSSVue [38] is an integral component of WRAP. The HEC of the USACE developed and maintains several generalized modeling systems that are extensively used by governmen<sup>t</sup> agencies, engineering firms, and universities throughout the United States and abroad. HEC-DSS and its HEC-DSSVue interface are shared by HEC models and have also been incorporated in other non-HEC modeling systems, including WRAP.

### *4.1. SIM and SIMD Simulation Models*

The spatial configuration of a river system is defined in the simulation model by a set of control points, with the next downstream control point being specified for each control point. All reservoirs, water supply diversions, return flows from surface and groundwater supply sources, hydroelectric power plants, instream flow requirements, and other system components are assigned control point locations. Essentially, any configuration of stream tributaries and conveyance systems may be modeled. The 20 WAMs contain over 12,000 control points of which about 500 are primary. The term "primary" control point refers to a site, usually a stream flow gauge, at which naturalized stream flows are stored in the WAM input datasets. Naturalized flows at primary control points are developed by adjusting observed flows to remove the e ffects of human water development and use. Naturalized flows at all other control points are computed in the simulation based on the naturalized flows at the primary control points and watershed parameters contained in the WAM datasets.

Regulated and unappropriated flows are computed in the simulation for all control points. Regulated flows represent the stream flows hypothetically occurring when historical naturalized flow sequences are repeated with the water use scenario reflected in the WAM. Unappropriated flows are the stream flows still remaining after all water rights in the WAM are allocated their appropriate shares to supply their storage and use targets. Unappropriated flows may be less than regulated flows due to instream flow requirements and appropriations by senior water rights at downstream sites.

The term "water right" is used in WRAP to refer to a set of water use requirements and associated constructed facilities and operating rules designed to supply the water use requirements. Many water right permits are modeled simply as WRAP water rights. However, a complicated actual water right permit may be simulated with multiple "model water rights". Water use requirements and facilities that are not associated with water right permits are also modeled as "model water rights". Flexibility is provided for simulating complicated water supply, hydropower, and instream flow target-setting criteria and reservoir system operating rules.

Texas, like most states in the western half of the United States, has a water rights system based on the prior appropriation doctrine [21,22]. Priorities are based on dates specified in the 6200 permits reflecting when the right was initially established. Most of the water rights in the WAMs reflect this priority system. However, the generalized WRAP simulation model includes flexible capabilities that include various options for assigning priorities. Subordination agreements that circumvent water right priorities are modeled. One WRAP option assigns priorities in upstream-to-downstream sequencing, modeling the riparian doctrine common in the eastern half of the U.S.

The monthly SIM and daily SIMD simulation computations are performed in a water rights priority sequence that is embedded within a computational time step loop. SIM/SIMD execution begins with reading and organizing input data. Water rights are sorted into priority order based on priority numbers and/or other user-defined options. Naturalized flows provided as input at primary control points are distributed to all other sites within the simulation based on watershed parameters. For each sequential month or day, water accounting computations are performed as each set of water use requirements (water right) is considered in priority order. Water allocation and managemen<sup>t</sup> are modeled by accounting procedures within the water rights priority loop.

SIM or SIMD simulation results include time series of any of the computed variables. SIM generates only monthly quantities, while SIMD produces daily quantities and monthly summations of the daily quantities. The model-user selects the control points, water rights, and reservoirs for which simulation results are recorded. The simulation results time series variables include: naturalized, regulated, and unappropriated flows, stream flow depletions, and return flows for each selected control point; channel losses and channel loss credits for each selected control point representing the reach below the control point; storage volume, surface elevation, net evaporation, inflows, releases, diversions, and hydroelectric energy at each reservoir; diversion targets and shortages, return flows, available stream flows, stream flow depletions, and storage for each selected water supply right; hydropower targets, firm energy produced, secondary energy produced, energy shortages, and storage for each hydroelectric right, and flow target and shortage for each instream flow right.

The simulation model can be executed in either conventional long-term analysis or short-term conditional reliability modeling (CRM) modes. In the long-term simulation mode normally employed, a specified water management/use scenario is combined with naturalized flows and net reservoir evaporation rates covering the entire hydrologic period-of-analysis in a single simulation. The results are used to generate water supply reliability and stream flow and reservoir storage metrics without reference to present storage contents. In the short-term CRM mode, the hydrologic input is divided into multiple sequences. The simulation is automatically repeated with each hydrologic sequence starting with the same specified initial storage condition. Tables of frequency and reliability metrics from the simulation results are computed with program TABLES. For example, in a CRM analysis, the estimated probabilities of reservoir storage contents reaching various levels any specified number of months in the future conditioned upon specified initial storage levels can be computed [1,2,40].

The simulation model also has options that involve automated repetitions of the complete long-term simulation. A dual simulation option is useful in modeling multiple rights with di fferent priorities associated with the same reservoir system. Another option sets reservoir storage contents at the beginning of a second simulation equal to the storage at the end of an initial simulation.

The TCEQWAM Systemis appropriately and effectively constructed based on amonthly computational time step, which is generally optimal for most WAM applications. However, daily computations are needed to model reservoir operations during floods and to incorporate SB3 environmental flow standards (EFS), particularly high-flow pulse components, in the WAMs. The primary di fferences between daily SIMD and monthly SIM simulation models are as follows.

Flow rates that vary continuously over time in the real world are modeled as volumes occurring during discrete time intervals. Variability is reduced with a larger flow rate averaging time interval. Maximum flood peaks are lowered and minimum flows during low flow periods increase. Monthly flows are less variable than daily flows. Reliabilities of rights with large reservoir storage capacities are less sensitive to time step. Di fferences are more pronounced for rights with minimal or no storage.

Outflow equals inflow with no attenuation in a monthly SIM simulation whenever a reservoir conservation (water supply and hydropower) pool is full. SIMD simulates flood control operations of any number of reservoirs based on allowable flows at any number of downstream control points. High-flow pulses are also tracked in daily modeling of environmental flow standards.

SIMD disaggregates monthly naturalized flows based on patterns defined by inputted daily flow hydrographs while maintaining the original monthly volumes. Water supply diversions, return flows, reservoir releases, and storage refilling result in changes in stream flows at downstream locations. Flow changes propagate through the stream system in the same month in SIM. Routing in SIMD refers to the downstream propagation of these changes to stream flow. A lag and attenuation routing method is employed in SIMD. A reverse routing algorithm is also applied to replicate the e ffects of routing in the procedure for forecasting flow availability.

Flow forecasting makes daily computations in SIMD much more complicated than a monthly simulation. Senior water users may be adversely a ffected by actions of upstream junior users occurring one or more days earlier. Likewise, flood control reservoir operations are based on making no releases that contribute to flows exceeding maximum non-damaging flow limits at downstream gauges that may be located several days of flow travel time below the dam. For each day of the SIMD simulation, the final simulation is preceded by a forecast simulation covering a future forecast period that generates stream flow availability information for that current day.

### *4.2. Water Availability and Supply Reliability Metrics*

The programs TABLES and HEC-DSSVue are used to organize SIM or SIMD simulation results in various user-specified formats, including time series plots or tabulations of selected variables, water budgets, statistical summaries, and various types of frequency relationships and reliability indices.

Options employing either relative counts or probability distribution functions are employed in TABLES and HEC-DSSVue to develop frequency relationships. Relative frequency is expressed by Equation (1) or Equation (2), where *m* is the rank and *N* is the sample size. The sample size *N* is the number of days, months, or years in the period-of-analysis and the rank *m* is the number of periods during the simulation that a particular flow, storage, or other quantity is equaled or exceeded.

$$\text{Exceedance Frequency} = \frac{m}{N} \text{ (100\%)}\tag{1}$$

$$\text{Exercise }\text{Frequency} = \frac{m}{N+1} \begin{pmatrix} 100\% \end{pmatrix} \tag{2}$$

Frequency analyses can be performed with WRAP for any time series variable, including any of the numerous simulation input and simulation results variables, variables derived therefrom, or other variables. Equation (1) is commonly applied with stream flow and reservoir storage quantities. With a 1940–2017 period-of-analysis, *N* is 936 for monthly or 28,490 for daily series of flow or storage quantities and 78 for annual series of July (or any specific month) flow or storage volume. Frequency formula, options Equations (1) and (2) are usually applied for the typically large values of *N* in WRAP analyses. The log-normal or log-Pearson type III probability distribution options are often applied with annual series generated in a daily SIMD simulation study, such as the minimum or maximum daily stream flow or reservoir storage volume in each year or the minimum or maximum 7-day, 30-day, or any other period stream flow in each year.

The terms "target", "demand", "need", and "requirement" are used interchangeably and may refer to either water supply for municipal, industrial, agricultural, or other types of water use or hydroelectric energy generation. Volume and period reliabilities provide concise metrics for measuring capabilities for meeting water supply diversion and hydroelectric energy generation requirements. Volume reliability ( *RV*) is the ratio of volume of water supplied or energy produced (*v*) to the target (*V*), converted to a percentage, Equation (3). Period reliability is the percentage of the total number of periods of the simulation during which the specified target is either fully supplied or at least a specified percentage of the target is supplied. Period reliability ( *RP*) is computed by TABLES from the results of a SIM or SIMD simulation, such as Equation (4), where n denotes the number of periods

(days, months, years) during the simulation for which a specified percentage of the demand target is met, and *N* is the total number of periods considered.

$$R\_V = \frac{v}{V} \text{ (100\%)}\tag{3}$$

$$R\_P = \frac{n}{N} \left( 100\% \right) \tag{4}$$

*RP* is an expression of the percentage of time that the full demand target or a specified percentage of the demand target can be supplied. Equivalently, *RP* represents the likelihood or probability of the target being met in any randomly selected month or year. Reliabilities may be tabulated with the WRAP program TABLES for all or selected individual water rights, the aggregation of all rights associated with individual control points or reservoirs, or user-selected groups of water rights.

A shortage volume in a particular month is the water supply diversion target less the simulated actual diversion as constrained by water availability. Program TABLES creates an optional vulnerability and resiliency table that includes the maximum monthly shortage, average sum of consecutive shortages, maximum number of consecutive shortages, and other shortage indices.

For new water right permits or amendments to existing permits, TCEQ criteria require that an agricultural irrigation right supply at least 75% of the proposed diversion target and at least 75% of the time computed on both a monthly and annual basis. Reliabilities of 100% are required for approval of new municipal water right permits. Existing reliabilities of senior rights are protected. Many older water rights do not meet the reliability criteria imposed on applicants for new or amended permits.

### **5. Brazos River Basin and Brazos Water Availability Model (WAM)**

The monthly SIM or daily SIMD simulation model combined with an input dataset for the Brazos River Basin (Figures 1 and 2) and adjoining San Jacinto-Brazos Coastal Basin is called a Brazos WAM. Monthly Brazos WAM authorized and current use datasets are available at the TCEQ WAM website along with monthly datasets for all Texas river basins. A daily Brazos WAM authorized use scenario dataset available at the TAMU WRAP website reflects recently expanded modeling capabilities. A detailed technical report [34] documenting development of the daily Brazos WAM and investigation of various modeling issues is available at both the WRAP and TWRI websites. Daily Trinity and Neches WAM datasets and reports [35,36] can also be downloaded from the WRAP website [31]. Conversion of other monthly WAMs to daily are planned over the next several years.

### *5.1. Brazos River Basin and Adjoining Brazos-San Jacinto Coastal Basin*

The Brazos River Basin encompasses an area of 119,000 square kilometers (km2), with 111,000 km<sup>2</sup> in Texas and 8000 km<sup>2</sup> in New Mexico. The TCEQ WAM System combines the Brazos River Basin and adjoining San Jacinto-Brazos Coastal Basin in the same dataset. This coastal basin located south of the City of Houston between the Brazos and San Jacinto River Basins has a watershed area of 3000 km2. Much of the water use from diversions from the Brazos River regulated by reservoirs shown in Figure 2 occur in the coastal plain south of Houston. Mean annual precipitation varies from 48 cm in the upper Brazos River Basin which lies in the high plains to 115 cm in the lower basin in the coastal region. The San Jacinto-Brazos Coastal Basin has a mean annual precipitation of 118 cm.

Mean daily observed flow rates at the U.S. Geological Survey (USGS) gauges near the cities of Waco and Richmond during January 1900 through July 2020 and October 1922 through July 2020 respectively, are plotted as Figures 3 and 4. The daily mean flows plotted in these figures reflect large long-term means but tremendous temporal variability in daily, monthly, and annual flows. The many water quantity and quality parameters included in the National Water Information System (NWIS) maintained by the U.S. Geological Survey (USGS) includes daily stream flows at 28,288 gauges, which include 1044 gauges in Texas [41]. Observed flows at 72 USGS gauges including the flows of Figures 3 and 4 were used in the compilation of naturalized stream flow data for the Brazos WAM.

**Figure 2.** Sixteen largest reservoirs and nineteen gauge sites with SB3 EFS in the Brazos River Basin [27].

**Figure 3.** January 1900 through July 2020 daily flow of Brazos River at Waco gauge.

**Figure 4.** October 1922 through July 2020 daily flow of Brazos River at Richmond gauge.

*5.2. Water Management in the Brazos River Basin and Adjoining Coastal Basin*

The Brazos River Basin contains 673 reservoirs and the coastal basin has seven reservoirs cited in water right permits, of which 43 have conservation storage capacities of 6.17 million cubic meters or greater. The 16 reservoirs listed in Table 1 and included on the map of Figure 2 are the only reservoirs in the Brazos River Basin that have a combined conservation and flood control storage capacity of greater than 100 million cubic meters. There are no reservoirs this large in the coastal basin. These 16 reservoirs contain 80% of the total conservation storage capacity of the 680 reservoirs in the Brazos WAM and supply about 40% of the total annual permitted diversion volume.

The U.S. Army Corps of Engineers (USACE) owns and operates nine multiple-purpose reservoirs (Table 1) that contain all gated flood control storage capacity in the Brazos River Basin. Nonfederal sponsors control the storage capacity allocated to water supply and reimburse all costs allocated to water supply [42].

USACE flood control operations occur whenever lake levels rise above the top of the conservation pool and are based on non-damaging flow limits at downstream gauges. No releases are made that contribute to flows exceeding 708 cubic meters per second (m<sup>3</sup>/s) at the Waco gauge, 1700 m<sup>3</sup>/s at the Richmond gauge, or other specified non-damaging flow limits at other gauges. The effects of flood control operations of Whitney and Waco Reservoirs, with initial impoundment in 1951 and 1965 (Table 1), on flows at the gauge on the Brazos River near Waco are pronounced in Figure 3 because the gauge is located a short distance below the dams. The gauge on the Brazos River near Richmond is located significant distances downstream of all nine of the USACE flood control reservoirs. The effects of the dams are not as clearly evident in the flows at the Richmond gauge in Figure 4.

Water right permits authorize the use of stream flow to fill reservoir storage and supply water needs subject to specified conditions. Water right priorities reflecting the dates that stream flow was first appropriated or permit applications submitted range from 29 June 1914 to near the present for the Brazos River Basin and adjoining coastal basin. Over 1000 entities that include a river authority, water districts, cities, private companies, farmers, and other appropriators hold 1220 water right permits that authorize annual diversions totaling 3.05 billion m<sup>3</sup>/year in the Brazos Basin and coastal basin for municipal (47.6%), industrial (30.1%), agricultural irrigation (18.0%), and other (4.3%) uses.


**Table 1.** Largest reservoirs in the Brazos River Basin.

The Brazos River Authority (BRA) has contracted for the conservation storage capacity in the nine federal reservoirs, owns three other existing reservoirs, and holds a water right permit for a proposed reservoir that is not ye<sup>t</sup> constructed. The BRA also owns and operates regional water and wastewater treatment and water conveyance facilities. The BRA sells water under contract to cities, industries, and farmers subject to authorizations defined in the multiple water right permits held by the BRA. The City of Waco has multiple water right permits for Lake Waco, though the BRA is the nonfederal sponsor for the water supply storage in the federal reservoir. The BRA holds water right permits for the 11 other reservoirs of the 12-reservoir USACE/BRA system.

Hydroelectric energy is generated at Whitney Reservoir. Essentially all releases through the hydropower turbines are diverted downstream for municipal, industrial, or agricultural use. The conservation pool includes storage for head for hydropower as well as water supply. The electricity is marketed through a U.S. Department of Energy agency to a local electric power cooperative.

Environmental flow standards (EFS) have been established at the 19 USGS gauge sites on the Brazos River and its tributaries shown in Figure 2 following the process established pursuant to Senate Bill 3 (SB3) enacted by the Texas Legislature in 2007 [25,43]. An officially constituted expert science team [44] developed recommended EFS considering only environmental needs that were then refined by a stakeholder committee [45] based on consideration of all water needs. The science team and stakeholder committee submitted their recommendations to the TCEQ for final public and agency review, approval, and publication in the Texas Water Code [43]. The SB3 EFS include subsistence, base, and in-bank and overbank high-pulse flow components that vary seasonally and with hydrologic

conditions. The procedures, reports, and other relevant information regarding establishment of SB3 EFS for the Brazos and other river basins are accessible at the TCEQ WAM website. The SB3 process for establishing EFS includes periodic review and improvement of the EFS.

### *5.3. Water Availability Model (WAM) for the Brazos River Basin and Adjoining Coastal Basin*

The Brazos WAM simulates operation of 680 reservoirs and other facilities in accordance with 1220 water right permits. The authorized use scenario simulation with results presented in Section 5.4 is based on the premise that all water right holders appropriate the full amounts allowed in their water rights permits. Current use and other water use scenarios can also be simulated. The hydrologic period-of-analysis is January 1940 through December 2017. The 1940–2017 monthly naturalized flows at 77 control points provided in the simulation input dataset are disaggregated to daily and distributed to over 3000 other sites during the simulation.

SB3 EFS are incorporated the daily SIMD. Daily instream flow targets computed in a SIMD simulation in accordance with the EFS specifications are summed to monthly quantities within SIMD and recorded in a DSS file. The monthly targets are incorporated in the monthly SIM input dataset.

SB3 EFS are inserted in the WAM datasets with a priority based on the date that the designated science team and stakeholder committee submit recommendations to the TCEQ. The Brazos SB3 EFS were adopted in 2014 with a priority date of 1 March 2012. Existing senior water right permit holders are not a ffected. However, the SB3 EFS significantly reduce WAM simulated unappropriated flows available for future water right permit applicants.

The monthly SIM or daily SIMD simulation is based on the premise that water use requirements are supplied subject to water availability during each of the 936 months or 28,490 days of the 1940–2017 hydrologic period-of-analysis. The 1940–2017 naturalized flows provided as simulation input represent the stream flows that would have occurred naturally without human water resources development and use. Frequency and reliability metrics are computed from simulation results.
