Linear Programming for Flood Control on the Iowa and Des Moines Rivers1 David W. Watkins, Jr.2 Background The Great Midwest Flood of 1993 along the Upper Mississippi River and its tributaries caused an estimated 48 fatalities and $15-20 billion in economic damages, surpassing all floods in the United States up to that time (Natural Disaster Survey Report 1994). As a result of the flood, the Federal Emergency Management Agency declared 504 counties in nine states eligible for assistance, with the most severe damage occurring in Iowa, Illinois, and Missouri. The flood forced 74,000 people from their homes, disrupted commercial activity along the Mississippi and Missouri rivers and adjacent areas, and destroyed thousands of acres of crops. Many farms also lost facilities and equipment, and an estimated 72,000 private homes either were washed away or suffered major damage. Approximately 40,000 commercial structures were damaged. Virtually all forms of transportation on and across the Mississippi River were interrupted by the flood. Along the length of the Mississippi River that forms the western boundary of Illinois, more than 1,000 miles of roads were closed, and nine of the 25 non-railroad bridges were shut down (USACE, 1996). The Great Flood of 1993 was caused by a highly unusual series of thunderstorms repeatedly forming and moving over the same area, combined with above average precipitation and below average temperatures in the preceding months. Starting in November 1992, precipitation was above normal, and temperatures were below normal throughout much of the upper Midwest. Persistent rains and early snowmelt led to high spring runoff and very high soil moisture levels. Due to an eastward- flowing jetstream that extended from central Colorado northeastward across Kansas to northern Wisconsin, a weather-front convergence zone formed across the upper Midwest during the spring and summer of 1993. Moist, warm air from the Gulf of Mexico was drawn northward along this jetstream, where it collided with cooler air masses from central Canada. This combination of extreme conditions generated frequent occurrences of heavy precipitation over the upper Mississippi River basin, leading to the destructive floods. In January through July 1993, more than 20 inches of rain fell over most of the flood-affected area, with more than 40 inches of rainfall occurring in areas of northeast Kansas and east-central Iowa (USACE, 1996). In the aftermath of this disaster, some concern was voiced that the U.S. Army Corps of Engineers did not operate flood control reservoirs on Upper Mississippi tributaries in an optimal manner. Although there was no evidence of deviations from the reservoir regulation plans, a modeling study was commissioned to provide insight for 1 Based on Needham, J.T, D.W. Watkins, J.R. Lund, and S.K. Nanda (2000). “Linear Programming for Flood Control on the Iowa and Des Moines Rivers,” Journal of Water Resources Planning and Management, ASCE, 126(3): 118-127. 2 Professor, Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, MI 49931. E-mail: [email protected] 14 possible modifications to the operating plans (USACE, 1999). In particular, a deterministic optimization model was applied to a three-reservoir system on the Iowa and Des Moines Rivers to estimate the best possible operation of these reservoirs (with “perfect foresight”) and to determine whether or not tandem operating rules would provide appreciable benefits. Reservoir System The Iowa/Des Moines River Reservoir System consists of three reservoirs, one on the Iowa River main stem and two on the Des Moines River main stem, as shown in Figure 1. Authorized purposes for these reservoirs include flood control, low-flow augmentation, fish/wildlife, water supply, and recreation. The Rock Island District of the Army Corps is responsible for day-to-day decision making regarding reservoir operations. Operators follow guidelines described in the reservoir regulation manuals that have been prepared as part of the design of the system (USACE 1983, 1988, 1990). Saylorville C Iowa e Riv da Reservoir er r R iv er IOWA Coralville # DES MOINES CITY # Lake Reservoir Red Rock # LONE TREE # TRACY # WAPELLO # OTTUMWA De s M oin es KEOSAUQUA # R # BURLINGTON iv IOWA er MISSOURI ILLINOIS LA GRANGE # QUINCY # HANNIBAL# Figure 1. Map of Iowa/Des Moines River Reservoir System Total capacities and average inflows for the three reservoirs are shown in Table 1, and other pertinent characteristics of the Iowa and Des Moines Rivers are shown in Tables 2 and 3, respectively. Table 2 illustrates that Coralville Reservoir can regulate no more than 25% of the total average annual flow entering the Mississippi from the Iowa River. Because of this, one could expect that Coralville Reservoir’s flood control effectiveness below the confluence of Cedar River and on the Mississippi River is limited. Conversely, as illustrated in Table 3, Saylorville and Red Rock 15 reservoirs regulate over half of the average flow entering the Mississippi River from the Des Moines River. Table 1. Capacities of and Average Inflows to the Three Reservoirs (m3 x 106) Inflows Capacity (acre-ft/year) Reservoir (acre-ft/year) Conservation Flood Control Total %a (1) (2) (3) (4) (5) (6) Coralville (Iowa River) 1,271,800 25,900* 435,300 461,200 18 Saylorville (D.M. 1,540,600 90,000 586,000 676,000 20 River) Red Rock (D.M. River) 3,568,000 265,500* 1,494,900 1,760,400 62 * Varies seasonally, value is minimum which corresponds to maximum flood storage a Percent of total federal project flood storage in Des Moines/ Iowa system Table 2. Iowa River Characteristics Drainage Area Mean Inflow Location (sq. mi.) (cfs) (1) (2) (3) Coralville Reservoir 3,115 1,760 Iowa River (Confluence w/Cedar R.) 4,770 2,360 Cedar River (Confluence w/Iowa R.) 7,870 4,230 Iowa River (Confluence w/Mississippi R.) 12,980 7,120 Mississippi River (Confluence w/Iowa R.) 89,000 49,000 Table 3. Des Moines River Characteristics Drainage Area Mean Inflow Location (sq. mi.) (cfs) (1) (2) (3) Saylorville Reservoir 5,823 2,200 Red Rock Reservoir 12,323 4,928 Des Moines R. (Confluence w/Mississippi R.) 14,540 8,210 Mississippi R. (Confluence w/Des Moines R.) 119,000 64,520 Under current operations, Coralville Reservoir is to be operated for flood control at Iowa City, Lone Tree and Wapello on the Iowa River; and Burlington, Iowa, on the Mississippi River (USACE 1990). Presumably, when operated in conjunction with the reservoirs on the Des Moines River, the flood peaks can be offset enough to cause a significant difference in the water levels on the Mississippi River during flooding. 16 Saylorville Reservoir and Lake Red Rock projects also are associated with the comprehensive flood control plan for the Upper Mississippi River Basin. According to the reservoir regulation manuals, Saylorville Reservoir is operated not only to reduce flood damage in the City of Des Moines, but it is also operated in tandem with Red Rock Reservoir to reduce flood damage at Ottumwa and Keosauqua on the Des Moines River and at Quincy, Illinois, on the Mississippi River (USACE 1983; USACE 1988). Flood control priorities for this system are summarized in Tables 4 and 5. Table 4. Coralville Release Priorities Priority Keep flow less than (cfs) At Location (1) (2) (3) 1 20,000 Iowa City- Iowa River 2 48,500 Wapello – Iowa River 3 265,000 Burlington – Miss. River 4 10,000 Iowa City – Iowa River 5 17,500 Lone Tree – Iowa River 6 30,000 Wapello – Iowa River 7 150,000 Burlington – Miss. River Table 5. Des Moines River Flood Control Priorities Priority Keep flow less than (cfs) at Location (1) (2) (3) 1 40,000 2nd Ave. - Des Moines River 2 107,000 Ottumwa - Des Moines River 3 335,000 Quincy - Mississippi River 4 19,400 2nd Ave. - Des Moines River 5 19,000 Ottumwa – Des Moines River 6 270,000 Quincy - Mississippi River 7 90,000 Keosauqua - Des Moines River 8 13,000 Tracy – Des Moines River 9 28,000 Keosauqua - Des Moines River Linear Programming Model A linear programming (LP) model was developed at the Hydrologic Engineering Center of the USACE to assist with Corps’ flood management studies (Figure 2). The model treats the flood-operation problem as one of finding a system-wide set of releases that minimize total system penalties for too much or too little release, 17 storage, and flow. Essentially embedded in the LP model constraints is a simulation model that computes storage and downstream flows based on reservoir releases. This model accommodates reservoir continuity and linear channel routing (e.g. Muskingum routing) and accounts for hydraulic limitations such as reservoir outlet capacities. The model constraint set includes continuity constraints for each reservoir and control point, along with constraints on reservoir release capacity, in each time period. The objective function includes penalties for too much or too little storage, release, or flow in each time period. Figure 2. Model Schematic of Iowa/Des Moines River Reservoir System The general form of the reservoir continuity constraints, for reservoir j, time period i, is 1 i Si, j Si1, j fi, j ct,k ft,k Ii, j t k ,1k t (1) where Si-1,j and Si,j = storage at the beginning and end of period i, respectively; fi,j = total release in period i; = set of all control points upstream of j from which flow is routed to j; ft,k = average flow at control point k in period t; ct,k = linear coefficient to route period t flow from control point k to control point j for period i; Ii,j = inflow to the reservoir.