Figure 1. Study area - upper Mississippi and lower Missouri River basins.
The study area encompasses the main stem of the Mississippi River above Cairo, Illinois, and the main stem of the Missouri River below Gavins Point Dam near Yankton, South Dakota. Also included are the many tributaries of these rivers such as the James, Des Moines, Illinois, and many other rivers and streams. This region of nearly 700,000 km2 was previously defined by the Scientific Assessment and Strategy Team (SAST) as the area most affected by the spring and summer floods of 1993 (SAST, 1994). States included in this study are Illinois, Indiana, Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, South Dakota, and Wisconsin (Figure 1). Exactly 180 Hydrologic Unit Code (HUC) sub-basins (8 digit) cover the study area.
Figure 1. Study area - upper Mississippi and lower Missouri River basins.
The goal of this project is twofold:
The water balance of a particular area represents a measure of the inputs to the hydrologic system and the outputs from that system over a specified period of time. In the case of this study, daily water balance maps were desired, therefore a decision was made to partition the study area into incremental drainage units based on the location of stream gage stations. These drainage units or gaging station zones provide the basis on which areal interpolation of precipitation measurements were made. The outlets of the 180 HUC boundaries rarely corresponded with a stream gage site, thus necessitating the subdivision of the study area into customized zones. The creation of the gaging station zones is shown in Figure 2. There are three possible zones: (1) no inflow; (2) one inflow; or (3) two or more inflows.
Figure 2. Gaging station zone configurations based on (a) no inflow, (b) one inflow, and (c) two or more inflows.
The equation for calculating the water balance of each gaging station zone is:
(Equation 1)
where S is the volume of water stored in each gaging station zone, t is the time index, and I and Q are inflow to the gaging station zone and outflow from the gaging station zone, respectively. The term on the right (I - Q) can be rewritten to account for the area of the gaging station zone:
(Equation 2)
where P is the rate of precipitation, E is the rate of evaporation, A is the area of the gaging station zone, Sum Qin is the sum of the inflows recorded at gages whose flows enter the zone and Qout is the outflow at the downstream end of the zone.
The change in storage (Delta S) can be found by combining equations (1) and (2) and integrating each term over a time interval of one day (Delta t):
(Equation 3)
In order to express Delta S in terms of average depth over the gaging station zone area, equation (3) can be rewritten as the following (Delta y = Delta S/A):
(Equation 4)
where Delta y is the change in storage depth per unit area of a gaging station zone. The values of Delta y can be computed on a daily basis (01/01/93 through 09/30/93) for each zone.
GIS and Water Resources
The raster GIS program GRID, a module available in the Arc/Info® software package, allows for several hydrologic modeling procedures including the determination of flow direction, flow downstream accumulation, and watershed delineation. One of the strengths of this cell-based modeling package is the availability of map algebra functions. With map algebra, the variables in a logical expression actually are map (raster grid) layers. Algebraic manipulation of these grids can be performed at the local or individual cell level, neighborhood level (cells surrounding the cell of interest), zonal level (entire cell groups change in value), or at a global level (entire grid changes in value) (Tomlin, 1990).
Prior to delineating the gaging station zones, several data sets were acquired from the GCIP Reference Data Set (GREDS) CD-ROM, produced by the U.S. Geological Survey. This CD-ROM is a collection of several geographic reference data sets of interest to the global change research community (Rea and Cederstrand, 1994). Arc/Info export files of 8-digit HUC boundaries and current streamflow gage sites were obtained from this CD-ROM, as was a 15" digital elevation model (DEM) of the region (500 meter resolution). RF1 river reach files in Arc/Info export format for the Upper Mississippi and Missouri Rivers were downloaded via the Internet from the USGS node of the National Geospatial Data Clearinghouse (http://h2O.er.usgs.gov/nsdi/wais/water/rf1.HTML).
The first step in creating the gaging station zones was to edit the RF1 vector coverage to remove circular arcs and isolated lakes. Once a definite stream network was available, the vector coverage was converted to a raster grid, and then embedded into the 15" DEM, which had been corrected for spurious sinks or pits. This embedding procedure "raised" the elevation of the off-stream grid cells surrounding the network in the DEM relative to the stream grid cells. By embedding these stream cells, a more precise network was created on the DEM that exactly matched the original paths of the RF1 vector coverage. This stream "burn in" technique has been shown to be particularly effective in areas of low relief (Maidment, 1996). The resulting grid was then clipped with a polygon coverage of the study boundaries. A 50 km buffer had been applied to this boundary coverage to account for drainage outside of the study area.
The next steps involved the actual delineation of the stream network within their embedded channels on the DEM. In Arc/Info's version of this process, the flow direction is first determined by examining the neighborhood of eight grid cells that surround the cell of interest. The flow direction function identifies the lowest cell value in the neighborhood, and assigns a flow direction value to the corresponding cell in an output grid, thus creating an implicit stream network between cell centroids. Once this process was complete over the entire study area, a flow accumulation grid was made. The flow accumulation function in Arc/Info uses the flow direction grid to determine the number of "upstream" cells. A new value is assigned to the cells in an output grid showing the number of cells that contribute or flow to downstream cells. High values indicate confluences of streams, whereas values of zero indicate watershed boundaries (Maidment, 1995). A conditional statement was then set up in Arc/Info which isolated those cells that met a certain threshold of flow accumulation. Stream links were created, and the stream network was then in place.
After a suitable terrain model had been made, the next step was to precisely locate the USGS gage stations on the stream grid. The point coverage of station locations was converted to a grid, and then viewed as a background grid against the stream grid. Unfortunately, most of the gage cells did not lie directly on top of a stream cell, so the stream cell closest to a gage cell was given a unique value (the USGS-assigned station number) to differentiate it from adjacent non-gage stream cells. Initially, 460 gage cells were located on the stream grid, however, it was later determined that a number of these stations contained incomplete streamflow records. A total of 50 gages were removed which did not have complete records. This left 410 gages, which were unevenly distributed over the stream network. Some streams had many gages, whereas other stream segments contained one or less. The gage locations were viewed along with the HUC coverage to provide a better spatial representation of the gages with respect to watersheds. It was decided that those gages whose contributing drainage areas (an attribute in the Arc/Info point coverage of the gages) were less than 1,000 km2 would be removed from the collection. Also removed were gages that were concentrated in a particular watershed. Most HUCs contained between one and three gage stations, but several contained more than three. Unless the HUC was large in area, those extra gage stations exceeding three were also removed from the collection. Approximately 260 gage stations on the stream grid were retained, and these gage locations were for the most part uniformly distributed throughout the stream network.
The gaging station zones were then determined using the flow direction grid and the edited stream gage grid (Figure 3). The resulting grid contained approximately 260 sub-basins defined on the basis of the stream gage locations. Each gaging station zone was checked against its corresponding HUC to insure that the two sets of boundaries were mutually compatible.
Figure 3. Map of gaging station zones defined on the basis of the location of USGS streamflow gage stations.
GIS Database and Map Creation
Streamflow daily values for the 1993 water year were provided by the Water Resources Division of the USGS. After removing the 1992 values, and reformatting the data into comma-delimited ASCII text, the values were incorporated into the attribute table of the gage station point coverage. This point coverage reflected the edits made to the stream gage grid. Complete daily records for the gage stations were assigned to the point coverage for a total of nearly 71,000 daily values from January 1 to September 30, 1993 (273 days).
Precipitation values obtained from National Climatic Data Center Summary of the Day files were treated in a similar manner to the streamflow data. A total of 1,078 climate stations were mapped. This number includes stations within the study area, and those within a 50 km buffer of the study area. Stations in the buffer zone were included so that a more precise interpolation of the precipitation measurements could be achieved for the regions at the study area borders. Over 290,000 precipitation measurements were incorporated into the point attribute table of the stations coverage. Some of the climate stations had missing precipitation measures, so an Arc Macro Language (AML) program was written to eliminate those stations with missing data.
Currently, the authors are constructing a daily precipitation grid with 4 km cell resolution which will be interpolated from the gaged precipitation data using the inverse distance weighting method. A cross-validation check will be performed on a randomly selected group of stations (20% of the total) to determine the validity of this method of interpolation. The best interpolation method will subsequently be used to create all 273 grids of daily precipitation values. The Arc/Info GRID function "zonalaverage" will be used to get an average value of precipitation depth, as well as potential evapotranspira-tion (PET), over the gaging station zones. PET monthly values were compiled from the National Weather Service (file "cde93.dat"). Since values of PET vary slowly from month to month and the study area was saturated during the 1993 floods, it was felt that evaporation was most likely constant (i.e., one PET value per month) over the month in each gaging station zone.
The resulting grids will show unique gaging station zones with average precipitation and evaporation depth values in each zone. Net streamflow grids will be created that showed daily values averaged over each gaging station zone. These grids will be created by subtracting Qout from the sum of Qin, and dividing the answer by the area of the gaging station zone. The final map series will involve a combination of all of the preceding maps. Daily storage change (Delta y) grids will be produced using the map algebra functions in Arc/Info GRID and equation (4). Essentially, the equation will change from
(Equation 4) to
(Equation 5)
where S Grid is a grid of daily storage depth change, P Grid is a daily precipitation grid, E Grid is a daily evaporation grid, and NS Grid is a daily net streamflow grid. Maps of cumulative storage depth were obtained by summing the grids. The resultant 273 grids will show water storage depth of each gaging station zone in the study area on a daily basis.
Visualization
The final products of this study consist of maps that represent the water storage depth which occurred on each sub-basin or gaging station zone, as a result of the heavy precipitation events between 01/01/93 and 09/20/93. Each day's maps represent a snapshot of how much precipitation occurred in the study area, and how it affected the land surface. Although the GIS can perform all of the tasks necessary to determine water storage, a final step remains in order to fully understand the temporal aspects of the flooding events. This step usually goes by the umbrella term "visualization", which can describe a whole host of software packages, coloring and animation procedures, and output types.
GIS software packages have provided the spatial sciences with an excellent set of tools for performing hydrologic analyses. The main problem with the technology today is its relative inability to handle temporal information. This paper has described a method of incorporating temporal data into the attribute files of GIS coverages, but the final product, as described up to this point, remains a series of static portrayals of a dynamic event. To overcome this problem, various visualization methodologies are being investigated as an additional component to the GIS hydrologic modeling process. Buttenfield and Mackannes (1991) describe GIS-related visualization as the interface of three processes: (1) computer analysis (data collection, organization, modeling, and representation); (2) human cognition (perception, pattern identification, and mental imaging); and (3) graphic design principles (construction of visual displays). MacEachren (1994) further describes the concept of "geographic visualization" as stressing map use that can be conceptualized as a three-dimensional space. Both descriptions of visualization imply that maps and associated images can now be constructed that incorporate 3-D and 4-D perspectives. This ideally suits geographic visualization techniques as an end product to temporal representation using a GIS.
Currently, the authors are investigating several methods of geographic visualization. Most involve some form of geographic animation as a way of representing the temporal aspects of the flood. Initially, the 273 maps of water storage depth will be color-coded based on the depth of water storage in each gaging station zone. Blue is the most likely color, and will range in shades from light or pale (no water saturation of the land surface) to dark or bright (saturated land surface). These choropleth maps will be chronologically arranged from 01/01/93 to 09/30/93, and then put into an animation software package. Viewing these maps in sequence will provide the user with a dynamic display of water leaving gaging station zones and saturating downstream zones.
Another means of visualizing flow through the basin would be through the use of the stream network. The representation of the network in the GIS does not really account for its changing form and velocity during the flood months of 1993. A series of 273 numbers representing streamflow velocity is assigned to the cells representing stream gage locations along the rasterized network (500 m. resolution), but the actual channel dimensions remain the same throughout the time period. Visualization procedures can be used in conjunction with the streamflow values to produce a dynamic representation of streamflow velocity through the basins. The flow velocity can be represented by some type of hydrologically significant symbol which speeds up or slows down depending upon the streamflow value at the gage location. This iconic representation of streamflow will increase in size as flow becomes faster downstream. Combining the symbology of flow velocity with the choropleth map described above is also feasible.
The authors are also experimenting with various means of stream channel visualization. As previously mentioned, the streams reside in the GIS as a 500 meter wide grid network. Of course, the streams vary in size in the Upper Mississippi and Missouri River basins from creeks a few meters wide, to the Mississippi River at Cairo, Illinois, which is nearly 1 km wide during normal flow conditions. Vector representation of the stream network would allow some flexibility in the appearance of the channels, and this method is currently being investigated with the GIS software package ArcView®. Satellite and radar imagery will also be incorporated into a visualization package to provide a more realistic view of the flooding events. By using imagery draped over a DEM of the study area, three-dimensional viewpoints can be achieved which provide even greater flexibility in terms of visualization and human cognition of the floods.
Summary and Conclusions
In this study, geographic information system software has been utilized as a first step to visualizing the water balance that was in place during the 1993 Midwest floods. A series of 273 maps are being produced that combine streamflow, precipitation, and evaporation measurements. This series of maps, while informative and meaningful to the group of people who understand GIS, needs to be made available to the public in a different form. The second step will be the development of a dynamic representation of this temporal data through the use of geographic visualization procedures. The final product of this research will be useful to many different people who study such natural hazards as flooding. Methodologies developed in this study can be used to investigate future floods, and will hopefully provide the end users with several different views of the 1993 Midwest flood which will enable them to make wise decisions regarding floodplain management and land use practices.
Acknowledgments
This research is being supported by a grant from the U.S. Geological Survey to Drs. Maidment and Ridd. Thanks are also due to Dr. William Kirby, of the USGS Water Resources Division in Reston, VA, for supplying the authors with necessary data sets, Dr. Barbara Buttenfield for providing some ideas about geographic visualization, and the University of Utah Department of Geography DIGIT Lab for computer support.
References
Buttenfield, B.P. and W.A. Mackaness, 1991. Visualization, in Maguire, D., M. Goodchild, and D.W. Rhind, eds., Geographical Information Systems: Principles and Practice. Longman, London, p. 427-443.
MacEachren, A.M., 1994. Visualization in Modern Cartography: Setting the Agenda, in MacEachren, A.M., and D.R. Fraser-Taylor, eds., Visualization in Modern Cartography. Pergamon, Oxford, p. 1-12.
Maidment, D.R., 1995. GIS & Hydrology: A Workshop of the 15th Annual ESRI User Conference. Environmental Systems Research Institute, 63 p.
______________ 1996. GIS and Hydrologic Modeling - An Assessment of Progress: Paper Presented at the Third International Conference on GIS and Environmental Modeling, Santa Fe, New Mexico. National Center for Geographic Information and Analysis, Santa Barbara, California, 1 CD-ROM.
Rea, A., and J.R. Cederstrand. 1994. GCIP Reference Data Set (GREDS): U.S. Geological Survey Open-File Report 94-388. USGS, Reston, Virginia, 1 CD-ROM.
SAST, 1994. Science for Floodplain Management into the 21st Century, Preliminary Report of the Scientific Assessment and Strategy Team Report of the Interagency Floodplain Management Review Committee to the Administration Floodplain Management Task Force. Washington, D.C., 272 p.
Tomlin, C.D., 1990. Geographic Information Systems and Cartographic Modeling. Prentice Hall, Englewood Cliffs, New Jersey, 249 p.
2.
Pawel J. Mizgalewicz
University of Texas
Center for Research in Water Resources
10100 Burnet Rd., Bldg. 119
Austin, TX 78758
Email: pawel@crwr.utexas.edu
3.
David R. Maidment, Ph.D.
University of Texas
Department of Civil Engineering
Austin TX 78712
-and-
Center for Research in Water Resources
10100 Burnet Rd., Bldg. 119
Austin, TX 78758
Email: maidment@crwr.utexas.edu
4.
Merrill K. Ridd, Ph.D.
University of Utah
Department of Geography
270 Orson Spencer Hall
Salt Lake City, UT 84112
Email: mridd@geog.utah.edu
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