Applications of GIS to Water Resources Engineering Francisco Olivera, Ph.D., P.E. Department of Civil Engineering Texas A&M University Rice University Department of Civil and Environmental Engineering Houston, Texas, April 4, 2002

Geographic Information Systems

The Problem zTo analyze hydrologic processes in a non- uniform landscape. zNon-uniformity of the terrain involves the topography, land use and soils, and consequently affects the hydrologic properties of the flow paths. Watershed divide Watershed point Flow path Watershed outlet Opportunity

The Solutions zLumped models: Easy to implement, but do not account for terrain variability. zSpatially-distributed models: Require sophisticated tools to implement, but account for terrain variability.

Overview zVertical processes: Soil Water Balance zHorizontal Processes: Flow Routing

Soil Water Balance Model Precipitation: P Evaporation: E Soil moisture: w Surplus: S Temperature: T Net Radiation: R n

Soil Water Balance Model Given: w fc : soil field capacity (mm) w pwp : soil permanent wilting point (mm) P : precipitation (mm) T : temperature (°C) R n : net radiation (W/m 2 ) Evaporation: Soil moisture and surplus: Calculated: w : actual soil moisture (mm) S : water surplus (mm) E : actual evaporation (mm) E p : potential evaporation (mm)

Global Data Precipitation and temperature data, at 0.5° resolution, by D. Legates and C. Willmott of the University of Delaware. Net radiation data, at 2.5° resolution, by the Earth Radiation Budget Experiment (ERBR). Soil water holding capacity, at a 0.5° resolution, by Dunne and Willmott. Precipitation (Jan.)Temperature (Jan.) Net Radiation (Jan.)Soil Water Holding Capacity

Monthly Surplus – Niger Basin February May August November Period between storms: 3 days.

Monthly Surplus – Niger Basin 10 days between storms 1 day between storms3 days between storms 30 days between storms Effect of disaggregation of monthly precipitation into multiple storms.

Global Monthly Surplus Animation prepared by Kwabena Asante

Overview zVertical processes: Soil Water Balance zHorizontal Processes: Flow Routing

Flow Routing Models zCell-to-cell zElement-to-element zSource to sink Source Flow-path Sink Cell Sub-Basin Junction Reach Sink

Cell-to-Cell zSets a mesh of cells on the terrain and establishes their connectivity. zCongo River basin subdivided into cells by a °  ° mesh. zWith this resolution, 69 cells were defined.

Cell-to-Cell zLow resolution river networks determined from high resolution hydrographic data. B C D 12 3 A 4

Cell-to-Cell

zRepresents each cell as a linear reservoir (outflow proportional to storage). One parameter per cell: residence time in the cell. zFlow is routed from cell-to-cell and hydrographs are calculated at each cell. K1K1 K2K2 K3K3 K4K4 K5K5 What if each cell is represented by a cascade of identical linear reservoirs instead of a single linear reservoir?

Element-to-Element zCongo River basin subdivided into sub-basins and reaches using CRWR-PrePro. zSub-basins and reaches delineated from digital elevation models (1 Km resolution). zStreams drain more than 50,000 Km 2. One sub-basins was defined for each stream segment.

Element-to-Element zHydrologic system schematic of the Congo River basin as displayed by HEC-HMS.

Element-to-Element zDetail of the schematic of the Congo River basin.

Element-to-Element zDefines hydrologic elements (basins, reaches, junctions, reservoirs, diversions, sources and sinks) and their topology. zElements are attributed with hydrologic parameters extracted from GIS spatial data. zFlow is routed from element-to- element and hydrographs are calculated at all elements. zDifferent flow routing options are available for each hydrologic element type. Sub-Basin Junction Reach Sink Sub-Basin CRWR-PrePro HEC-HMS

Source-to-Sink zDefines sources where surplus enters the surface water system, and sinks where surplus leaves the surface water system. zFlow is routed from the sources directly to the sinks, and hydrographs are calculated at the sinks only. zA response function is used to represent the motion of water from the sources to the sinks. Source Flow-path Sink Source Flow-path

Source-to-Sink zPure advection zAdvection, dispersion and losses Source - i Flow-path - i Sink  (t) U i (t) t t  (t) t U i (t) t

Source-to-Sink zAdvection (v): Transport with the average flow velocity. zDispersion (D): Transport with the actual water particle velocity. zLosses ( ): Decrease in quantity due to losses.

Source-to-Sink zDiffusion wave equation of a uniform segment of a flow-path: uwater flow (volume/time) cwave celerity, equal to the flow velocity v in linear systems Ddispersion coefficient first-order losses coefficient ttime variable xdistance variable

Source-to-Sink zSolution of the diffusion wave equation of a uniform segment of a flow-path, at x = L, for a unit impulse input  (t) at x = 0: vflow velocity Llength of the element Tresidence time in the element t u(t)

zIf X is a random variable that represents the time spent in the element, then u can be understood as the probability density function (pdf) of random variable X. zStatistics of the solution of the equation: Source-to-Sink Expected value (first moment): Variance (second moment):

Source-to-Sink zA non-uniform flow path is a sequence of uniform segments: 123 n-1 n  (t) UiUi t t U i (t)

Source-to-Sink zIf Y is a random variable that represents the time spent in the flow path, then U i can be understood as the pdf of random variable Y. zTherefore: u i response at the downstream end of flow element-i produced by an input at its upstream end U i response at the sink (i.e., downstream end of the flow path) produced by a unit impulse input at source-i (i.e., upstream end of the flow path) Random variable: pdf: Expected value: Variance:

Source-to-Sink zThe summations can be calculated automatically with the weighted flow length function in Arc/Info and ArcView.

Source-to-Sink zTo avoid computer-intensive convolution calculations, the flow path response function is taken as a two-parameter distribution, with known first and second moments. zThe flow path response function is taken as a first-passage-times distribution equal to:

Source-to-Sink zSinks are defined at the continental margin and at the pour points of the inland catchments. zUsing a 3°x3° mesh, 132 sinks were identified for the African continent (including inland catchments like Lake Chad).

Source-to-Sink zThe drainage area of each sink is delineated using raster- based GIS functions applied to a 1-Km DEM (GTOPO30). GTOPO30 has been developed by the EROS Data Center of the USGS, Sioux Falls, SD.

Source-to-Sink zLand boxes capture the geomorphology of the hydrologic system. zA 0.5°x0.5° mesh is used to subdivide the terrain into land boxes. zFor the Congo River basin, 1379 land boxes were identified.

Source-to-Sink zSurplus boxes are associated to a surplus time series. zSurplus data has been calculated using NCAR’s CCM3.2 GCM model over a ° x ° mesh. zFor the Congo River basin, 69 surplus boxes were identified.

Sources zSources are obtained by intersecting: ydrainage area of the sinks yland boxes ysurplus boxes zNumber of sources: yCongo River basin: 1,954 yAfrican continent: 19,170

Source-to-Sink Q sink =  Q i Q i = I i (t) * U i (t) zThe flow at a sink generated at source i Q i is calculated as the convolution of the input runoff/load by the flow path response function. zThe total flow at a sink Q sink is the sum of the contributing flows from all sources draining to it Q i.

Source-to-Sink Runoff Flow

Source-to-Sink Runoff Flow

Conclusions zAlthough GIS can be used to map results of spatially-distributed hydrologic models, it is only when the hydrologic topology of the flow elements is considered, that full advantage of GIS is taken.

Flooding t.u. Campus Animation prepared by Esteban Azagra

Flooding t.u. Campus Animation prepared by Esteban Azagra