Modeling Dynamic Network Modeling Dynamic Network Systems with - PowerPoint PPT Presentation

Modeling Dynamic Network Modeling Dynamic Network Systems with State-Contingent Penalty Functions Penalty Functions Richard Howitt, Kristiana Hansen University of California Davis & Universite de Louvain University of California, Davis & Universite de Louvain CompSus09 Conference Cornell University Cornell University June 8-12, 2009

The Dynamic Network Problem The Dynamic Network Problem • Solved by restricted optimizing models • Two decision aspects – The Network problem- allocation over a spatial network within a year – The Carryover problem- allocation of states between years with stochastic supplies • Dimensionality restrictions usually prevent their simultaneous solution • Optimal spatial dynamic policy requires p p y p y q joint solution

Current Solution Approaches • Standard Approach to the Network problem – Solved by spatial Network Flow Program – Stochastic hydrology represented by historical St h ti h d l t d b hi t i l hydrologic sequences – Problem.. Spatial monthly allocation is nested within p y the annual stochastic state allocation problem • The annual dynamic allocation problem – Solved by stochastic dynamic programming So ed by s oc as c dy a c p og a g – Synthetic hydrology – Problem.. The curse of dimensionality prevents a realistic spatial specification and dynamic risk and realistic spatial specification and dynamic risk and preferences are hard to specify.

A State-Contingent approach • Managers operate with limited foresight. – They know the current stocks and states – They know the probability of future water year types. • State Contingent Calibration State Contingent Calibration. – Calibrated to reproduce observed behavior for a set of water year types. – Observed behavior reflects the effect of agency risk Observed behavior reflects the effect of agency risk and intertemporal preferences – Having reproduced past water management, we can now optimize under alternative scenarios now optimize under alternative scenarios. • Two sets of nonlinear ( quadratic) calibration functions. – Monthly for select spatial calibration nodes M thl f l t ti l lib ti d – Annual for storage carryover values

Modeling Approach • Characterize a small set of (3-5) years classified as a given water year type. • Use sets of observed or simulated flows and storage U t f b d i l t d fl d t with an objective function and calibration constraints for each year. • Solve each year and store the lagrangian values for nodal and carryover calibration constraints. • Obtain the calibration value functions by regressing on Obt i th lib ti l f ti b i the lagrange values for each set of years in each water y year type. Impose curvature properties on the estimates. yp p p p • Use the calibration values to simulate spatial dynamic decisions by solving recursively linked annual optimization problems one year Bellman solution optimization problems- one year Bellman solution.

Case Study- The Northern California Water network network • 124 nodes 211 arcs 124 nodes, 211 arcs • 13 reservoirs, 9 groundwater basins • 15 Urban demand points, 9 agricultural 15 U b d d i t 9 i lt l demand points. • 72 years simulated hydrology • Eight years used for calibration between g y 1960-1980- normal, dry and drought years. y

State Contingent Value Functions- Shasta 1200 1100 1000 900 800 700 $ per 10 Ac Ft Critical 600 Dry Normal 500 500 400 300 200 100 0 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250 4500 4750 5000

Sacramento Valley Water network Self-Calibrating Limited Foresight Netflow Model Schematic N, M, & S FORK YUBA Adapted from CALVIN Schematic (Draper et al 2003) RIVER, FRENCH DRY CREEK, DEER CREEK GREENHORN CREEK & BEAR DA67 AG RIVER ACCRETION CAMP FAR COSUMNES SR-NBB: New WEST TO WHEATLAND Bullards Bar GAGE RIVER CALAVERAS RIVER Reservoir and Englebright Lake MOKELUMNE RIVER Urban Areas in DA70 but N, M, and S SR-NHL New outside CVPM7 outside CVPM7 SR PR SR-PR Hogan Lake Hogan Lake SR CFW SR-CFW: FORKS Pardee FEATHER RIVER, Camp Far C37 DRY CREEK, West AMERICAN RIVER Reservoir / LOCAL WATER KELLY RIDGE Reservoir Camanche Reservoir GW-5 Depletion DA69 Yuba Urban Accretion: Urban Demand C43 American River Folsom to Fair C31 Oaks D37 D98 SR-8 Folsom C39 SR-6: Lake Losses Lake, Lake DA69 local Oroville, Natomas, Thermalito Fore- water Nimbus Dam GW-5 Aftebay UD 5 AD 5 C32 GW-8 Sacramento GW-7 Stockton C36 COTTONWOOD CREEK C80 C26 C307 PAYNES AND DA 14: BUTTE CREEK & GW-1 LITTLE CHICO CREEK SEVEN MILE ANTELOPE, CREEKS UD 8 MILL,DRY,DEER & Sac East C311 DA 58 LOCAL WATER D42 C34 AD 7 BIG CHICO CREEKS, Refuges AD 8 SUPPLY INC. COW CREEK Redding DA 10 LOCAL WATER & BATTLE CREEK LAKE SHASTA SUPPLY DA 15 DA70 local DA 10 DA 15 DA 70 water t D517 D517 DA 59 DA 59 INFLOW SR-4 Shasta D5 D73 C2 D74 C5 C87 D77 C1 C4 C69 D76b D66 D30 D31 D61 C301 D43 C67 C8 D503 Lake C42 DA55 local water C313 C306 C18 D511 D513 UD 4 D521 TRINITY RIVER, C3 AD 1 C6 AD 2 Glenn-Colusa Canal D515 C14 AD 6 DA 65 CLEAR CREEK, LEWISTON LAKE D522 INFLOW SR-3 Clair Engle THE DELTA Lake / Whiskeytown UD 2 DA65 local UD 6 C17 Lake GW-1 GW-4 water AD 4 D507 GW-6 D523 Trinity River Minimum C12 C13 Flows GW-2 C68 Tracy Pumping C305 C15 Plant GW- DA12 local Napa-Solano 9 D525 D550 C309 D59 water C314 Conties Sac West C11 C302 C303 REGION 1 Refuges DA 12 AD 9 C9 SR-LB Lake Southern CA CMWD SR-CL-IVR Berryessa Demand UD 3 Clear Lake/Indian Monticello Dam C86 Valley Reservoir Harvey Banks Contra Costa AD 3 AD 3 Pumping Plant Pumping Plant SR BBL SR-BBL UD 9 UD 9 P Pumping i Black Butte Plant Lake THOMES & C70 C310 Los Vaqueros GW-3 Pumping Plant D509 ELDER CREEKS D528 SR- REGION 2 LV DA 55 PUTAH STONY C71 CACHE CREEK CREEK Mallard Slough Walnut Creek CREEK Pumping Plant Pumping Plant Required and SR- EBMU Surplus Delta C201 Contra Costa Outflow EBMUD

1000 2000 3000 4000 5000 5000 6000 0 0 OCT NOV DEC JAN FEB 1960 MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB 1961 MAR APR MAY JUN JUL AUG SEP OCT NOV Shasta Storage (KAF)-1960-1965 DEC JAN FEB 1962 MAR APR In-sample calibration MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB 1963 MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB 1964 MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB 1965 MAR APR MAY JUN JUL AUG SEP Model base

Shasta Storage 1980-1993 ( Out of Sample) 6000 5000 4000 4000 LFN LFN Actual K A F 3000 2000 1000 0 1 9 80 1 9 81 1 9 82 1 9 83 1 9 84 1 9 85 1 9 86 1 9 87 1 9 88 1 9 89 1 9 90 1 9 91 1 9 92 1 9 93 Normal Dry y Normal Normal Normal Dry y Normal Dry y Critical Dry y Critical Critical Critical Normal

T i it St Trinity Storage 1980- 1993 1980 1993 (out of sample) 3000 3000 2500 2000 LFN K A F 1500 Actual Actual 1000 500 500 0 1 9 8 0 1 9 8 1 1 9 8 2 1 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 Normal Normal Dry Dry Normal Normal Normal Normal Normal Normal Dry Dry Normal Normal Dry Dry Critical Critical Dry Dry Critical Critical Critical Critical Critical Critical Normal Normal

O Oroville Storage 1980-1993 ill St 1980 1993 (Out of Sample) 4500 500 4000 3500 3000 LFN 2500 K A F Actual ctua 2000 1500 1000 500 0 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Normal o a Dry y Normal o a Normal o a Normal o a Dry y Normal o a Dry y Critical C t ca Dry y Critical C t ca Critical C t ca Critical C t ca Normal o a

Computation times Computation times • Calibration and Estimation time- 3 year types- 8 years in total– years in total Desktop Time 14.6 minutes • Simulation time desktop – 5.4 minutes/year average– 14 (1980-93) years 1.25 hours . average 14 (1980 93) years 1 25 hours S l ti Solution times are comparable or faster than static ti bl f t th t ti linear programming network program solutions.

Spatial Dynamic Conclusions • The contingent calibrated functions are able to model spatial dynamic problems using recursive optimization. ti i ti • The model reservoir and groundwater The model reser oir and gro nd ater management responds well to different year types, particularly drought years. yp , p y g y • Solution times make recursive optimization p models a practical tool for dynamic network problems .

Salinity Projections 2004- 2030 Sa ty oject o s 00 030 • Sources--- Shoups & Hopmans 2005, Shoups(2004), Orlob(1991), San Joaquin Valley Drainage report(1990) “Rainbow Report”. S J i V ll D i (1990) “R i b R ” • Average annual net salt increase 499,000 tons • Change in salt affected area Shoups (2004) Change in salt affected area- Shoups (2004) 0.5% / year- Increase of 240,000 acres (13%) by 2030 • Salinity levels and areas- DWR SJ Valley Drainage Monitoring Program 2001- Plate 1. g • 5 salt levels in shallow saline water. Current salt affected area 1.85 million acres • Deep aquifer salinity accumulation Shoups & Hopmans 2005 50% percolation– net average aquifer salinity change 2004- 2030— 264mg/L – 343 mg/L.