CONDITIONAL RELIABILITY MODELING OF SHORT-TERM RIVER BASIN MANAGEMENT ASCE Texas Section Spring Meeting 2003 By: A.Andrés Salazar, Ph.D. Freese and Nichols, Inc. and Ralph A. Wurbs, P.E., Ph.D. Texas A&M University
TEXAS WATER AVAILABITY MODEL Senate bill 1 (1997) directed TCEQ (before TNRCC) to develop water availability models. Objectives of WAM Provide data analysis necessary for water management. Determine how much water is available for water rights. Facilitate planning efforts. 2
TEXAS WAM PROJECT ( continued) Databases User Interfaces WAM G.I.S. WRAP model (TAMU) Graphic programs 3
TEXAS WAM PROJECT ( continued) Applications: AVAILABILITY OF WATER BY RIVER BASIN 6 basins were completed in December 1999 16 basins completed in January 2002 Rio Grande expected by January 2003 WATER RIGHTS PERMITS APPLICATION PLANNING Part of the statewide water plan by TWDB will use WAM data. 4
WRAP MODEL : Basic concepts and input data CP-1 CP-2 Q NAT Evaporation Evaporation Q NAT Water right (1985) CP-3 CP-4 Water right (1976) Q NAT Q NAT Channel losses CP-5 Q NAT Water right (1970) Gaged Control Points Ungaged Control Points 5
WRAP MODEL : Results Q REG ; Q UNA Evaporation Evaporation Q REG ; Q UNA Water right diversion EOP Storage Water right diversion Q REG ; Q UNA Q REG ; Q UNA Channel losses Water right diversion Q REG ; Q UNA Gaged Control Points Ungaged Control Points 6
WRAP MODEL: Limitations It is not appropriate for evaluating reliabilities for water rights in the near future, which are highly dependent on known current conditions of reservoir storage. 7
WRAP MODEL: Limitations 400 Storage (x 1000 ac-ft) 300 200 100 0 Jan-34 Jan-37 Jan-40 Jan-43 Jan-46 Jan-49 Jan-52 Jan-55 Jan-58 Jan-61 Year Jan-64 Jan-67 Jan-70 Jan-73 Jan-76 Jan-79 Jan-82 Jan-85 Jan-88 Periods without shortage = 657 out of 672 (97.8%) What is the probability of satisfying demand when reservoir falls below 100,000 ac-ft? 8
CONDITIONAL RELIABILITY Statistical analysis of small sequences. INITIAL CONDITION Simulation 1 Q1 (Jan 1939) Q2 (Feb 1939) Q3 (Mar 1939) Qm (Dec 1939) Simulation 2 Q1 (Jan 1940) Q2 (Feb 1940) Q3 (Mar 1940) Qm (Dec 1940)...... Simulation n Q1 (Jan 2002) Q2 (Feb 2002) Q3 (Mar 2002) Qm (Dec 2002) Output 1 Output 2 Output n 9
WRAP CONDITIONAL RELIABILITY WRAP-CRM is based on the combination of: 1- Conditional Frequency Duration Curves (Measures the probability of flows) 2- Level of water supply achieved with the flow 10
EXAMPLE OF CFDC Nat. flow (ac-ft/month) 180000 Initial Storage 150000 ρ (1)= 0.2748 Low 120000 Medium 90000 High Total 60000 30000 0 0% 20% 40% 60% 80% 100% Percentage of months the flow is equaled or exceeded 11
NAT. FLOW-DIVERSION RELATIONSHIP Several short term simulations 100% Storage as % of the conservation pool 80% 60% 40% 20% S=1 - exp[-(q/59.8) 2.369 ] 0% Q (Mm 3 ) = 0 40 80 120 160 200 P = (1.00) (.38) (.24) (.16) (.10) (.08) (.0)` 12
RELATING PROB. OF EXCEEDENCE WITH DIVERSION 180000 150000 Naturalized flow (ac-ft/month) 120000 90000 60000 30000 0 0.0 0.2 0.4 0.6 0.8 1.0 Probability the flow is equaled or exceeded 100% Diversion amount (ac-ft/month) 100% 80% 60% 40% 20% Diversion amount 80% 60% 40% 20% 0% 0 0.2 0.4 0.6 0.8 1 Probability the diversion will be equaled or exceeded 0% 0 30000 60000 90000 120000 150000 180000 Nat. Flow (ac-ft) 13
AUTOCORRELATED VS. INDEPENDENT Probability of storage using equally likely assumption Storage (% of capacity) 100% 80% 60% 40% 20% 0% S=12,000 0.0 0.2 0.4 0.6 0.8 1.0 Probability the storage is equaled or exceeded Storage (% of capacity) 100% 80% 60% 40% 20% 0% S=120,000 0.0 0.2 0.4 0.6 0.8 1.0 Probability the storage is equaled or exceeded Independent Autocorrelated 14
AUTOCORRELATED VS. INDEPENDENT SERIES ( continued) Probability of storage using WRAP-CRM S=12,000 S=120,000 100% 100% Storage (% of capacity) 80% 60% 40% 20% Storage (% of capacity) 80% 60% 40% 20% 0% 0.0 0.2 0.4 0.6 0.8 1.0 Probability the storage is equaled or exceeded 0% 0.0 0.2 0.4 0.6 0.8 1.0 Probability the storage is equaled or exceeded Independent Autocorrelated 15
EXAMPLE: Proctor Reservoir CDFC after 6 months 1000 100 Nat. Flow (ac-feet) 10 1 high 0.1 med-high low 0.01 0% 20% 40% 60% 80% 100% % of months the flow is equaled or exceeded 16
EXAMPLE: Proctor Reservoir Probability distribution of storage after 6 months 1.0 Initial Storage = 0 Prob. of equaling or exceeding the storage WRAP-CRM 0.8 Eq.likely 0.6 0.4 0.2 0.0 0% 20% 40% 60% 80% 100% Storage at the end of six months 17
PRACTICAL APPLICATION: City of Corpus Christi Atascosa San Chacon River Miguel Creek CHOKE CANYON RESERVOIR Frio River Nueces River Lagarto Creek LAKE CORPUS CHRISTI CALLALEM DAM Nueces Bay Corpus Christi Bay 18
DROUGHT CONTINGENCY PLANS Releases as function of storage Monthly release (thousands ac-ft) 30.0 25.0 20.0 15.0 10.0 5.0 S90 values 2% 5% 10% 15% 20% 25% 30% 35% 40% 45% 100% 80% 60% 40% 20% Percentage of total releases 0.0 0% 0% 10% 20% 30% 40% 50% Initial Storage 19
RESERVOIR RESILIENCE The ability to recover from low storage 100% Canyon Lake S10 Percentage of storage 80% 60% 40% 20% Exp. S50 0% 1 3 6 12 18 24 36 Month S90 20
CONCLUSIONS The CRM overrides the assumption of having sequences equally likely. It is able to incorporate serial flow properties by using a simple and yet significant parameter such as the storage. 21
CONCLUSIONS The application exercises showed that the CRM can be used in a variety of planning activities. It is able to assess management policies in regard to the level of risk. Formulation/Evaluation Drought Contingency Plans Defining releases as a function of storage Resilience Filling up nature of reservoirs Test of operational rules. 22
ACKNOWLEDGMENTS Sponsors: Texas Commission of Environmental Quality (TCEQ). Texas Water Resources Institute (TWRI). U.S. Army Corps of Engineers, Fort Worth District. 23