By Christine Dartiguenave
Graduate Research Assistant
Center for Research in Water Resources
J.J Pickle Research Campus Bldg.119
Austin, TX 78712
Email : firstname.lastname@example.org
As a graduate assistant, I am involved in a map-based modeling project
sponsored by the City of Austin. The goal of this research project is to build a model which can evaluate annual nonpoint source pollution loading in Austin creeks in function of different scenarios of land use:
The area of study does not correspond to a particular juridiction (county...) but to a hydrologic entity (drainage area).
The model will allow to evaluate the actual effectiveness of Best
Management Practices (BMP's) for the control of nonpoint source pollution.
It will also enable to determine the contribution of any jurisdiction (City, county...) to the pollution load, and then be a first tool towards decision-making processes for remediation decisions.
The annual pollution load is the product of the discharge by the concentration:
Load (mass/year) = Q(volume/year) * C(mass/volume)
The model uses a digital discretization, or grid representation, of a watershed for the approximation of average annual pollutant loading.
The procedure is the following:
The annual loading in any cell corresponds to the value of this cell in the weighted flow accumulation grid.
Digital Elevation Models (DEM's), which consist of a sampled array of elevations for ground positions at regularly spaced intervals, are used to build the flow direction grid and hence to delineate the watersheds.
A study has already be made for Austin with 90 m DEM's (Francisco Olivera, Spatial Hydrologic Databases of Austin). But some of the delineations are really not good at all. There is a 44% relative error between the areas observed on the field and delineated with the 90 m DEM's for Waller Creek, which is a small urban watershed (cf. following map).
Or it is very important to define as accurately as possible the drainage area corresponding to the gage stations as their data are used to build the model.
There was a need to improve the delineations realized with 90 m DEM's. 30 m DEM's (i.e. one elevation value for every 30m/30m square) are now available for the area of study. They give about 10 times more information than 90 m DEM's. The 30 m DEM's used are each composed of about 190,000 cells. Until now, I have received from the City 9 DEM's, which cover the east part of Austin, from the City. They correspond to about 1,700,000 cells. The following map shows in green the watersheds delineated with a 10,000 cells threshold with the 30 m DEM's available.
The 30 m DEM's improve greatly the delineation of Waller Creek watershed (in yellow on the previous map). The relative error between the observed and delineated areas drops to 0.5%.
A comparison between the delineation obtained with both types of DEM's shows the bigger accuracy of the 30 m DEM's, due to the smaller cell size.
However, there are two principal drawbacks to use 30 m DEM's:
The flow direction grid is based on the DEM's.
The DEM's have to be processed in order to be used in ArcInfo :
Arc: Describe austin1
Description of Grid /DATABASES/AUSTIN/CHRISTINE/AUSTIN1 Cell Size = 30.000 Data Type: Floating Point Number of Rows = 466 Number of Columns = 406 BOUNDARY STATISTICS Xmin = 608085.000 Minimum Value = 130.000 Xmax = 620265.000 Maximum Value = 332.000 Ymin = 3346845.000 Mean = 213.601 Ymax = 3360825.000 Standard Deviation = 40.454 COORDINATE SYSTEM DESCRIPTION Projection UTM Zone 14 Datum NAD27 Zunits METERS Units METERS Spheroid CLARKE1866 Parameters:
Arc: describe austin2
Description of Grid /DATABASES/AUSTIN/CHRISTINE/AUSTIN2 Cell Size = 30.000 Data Type: Floating Point Number of Rows = 466 Number of Columns = 405 BOUNDARY STATISTICS Xmin = 619965.000 Minimum Value = 555.000 Xmax = 632115.000 Maximum Value = 934.000 Ymin = 3360825.000 Mean = 779.027 Ymax = 3374805.000 Standard Deviation = 61.224 COORDINATE SYSTEM DESCRIPTION Projection UTM Zone 14 Datum NAD27 Zunits FEET Units METERS Spheroid CLARKE1866 Parameters:
The grids must have the same characteristics to be merged together. Or the elevation values of the grids are either in meters or in feet.
The value of the cell size after the projection is 100 ft.
The grid can then be displayed:
Grid: display 9999
Grid: mape aus_st
Grid: gridpaint aus_st value linear nowrap gray
Burn in process
It consists in digging the stream network in the grid to be sure the creeks are where there are supposed to be. A digitized stream network is used in the burn in procedure :
Flow direction computation
The sinks are filled in the burn in DEM to be sure that the water won't be trapped but will be able to flow across the landscape.
Grid: fill burn_dem aus_fil SINK ausfdr (ausfdr is the grid with the flow direction)
The water flows from one cell to its lowest neighbor along one of eight compass directions. Each cell is assigned a number corresponding to the direction of the cell with the steepest descent.
East = 1 South-East = 2 South = 4 South-West = 8 West = 16 North-West = 32 North = 64 North-East = 128
The watersheds can be delineated in function of the stream links or of the gage stations. Both delineations need to be made:
To delineate the watersheds, the stream network the computation is based on must first be built.
The stream network is based on the flow accumlation grid obtained from the flow direction grid.
Grid: ausfac = flowaccumulation (ausfdr)
The stream network delineation depends on the choice of the threshfold used for flow accumulation.
The streams are delineated by example for a 10,000 cells flow accumulation threshold.
Each cell has an area of 100*100 ft².
Grid: str10000 = con ( ausfac>10000 ,1 )
The grid can then be converted into a coverage.
Grid: stream10000 = streamline (str10000)
Each stream link of the stream network is separated:
Grid: link = streamlink ( str10000, ausdr)
The watersheds corresponding to these streamlinks are delineated using the watershed function.
Grid: shd = watershed (aus_fdr, link)
This grid is then converted into a coverage:
Grid: wshed = gridpoly (shd)
1 -98.0806 30.4208 2 -97.9078 30.3917 3 -97.7844 30.3719 4 -97.7861 30.3147 5 -97.9253 30.2961 ... end
The result is a point coverage of the stations in geographic coordinates.
It has to be projected to obtain a coverage in state plane projection, which is the projection used for a study at the scale of a city. The input and output parameters of the projection from geographic to state plane are written in a text file called sta_prj :
projection state plane
The coverage stations in geographic coordinates can now be converted into the coverage station in state plane coordinates:
Arc: project cover stations station sta_prj #
input [response'name and path of the input file']
build cover points
rename cover [response'name and path of the coverage']
The program can be runned in Arc by using the AML command :
It will prompt for the name and path of the input file and of the point coverage to create.
The stations should be located on the delineated creeks (the digitized coverage is not accurate enough). However, it is not always true and the errors have to be corrected. Arcview enables to check the location of the stations but it can not be used to do any modification. Only Arc Info enables to modify the data. The corrections can be made in ArcTools, which can be accessed from Arc or from Grid (in this case, a grid must first be displayed using display 9999). The coverages of the stations must first be converted into a grid (the grid str# of the stream network already exists):
Grid: station_gr = pointgrid (station)
Arcview is then used as a interface to display these grids
to check if the stations are located on the creeks.
If it is not true, then the grid must be
modified in order for the stations to be at the "right" place.
Once the grid with the stations is corrected, it is reconverted into a point coverage:
Grid: station_sta = gridpoint (station_gr)
The two following shows the stations coverages built by this procedure:
The point coverages of the stations must first be converted into grids which will be used in the watershed function.
If EII_st is
the coverage of the EII station then the procedure is:
Grid: EII_gr = pointgrid ( EII_st )
Grid: EIIwshed_gr = watershed (ausfdr, EII_gr)
Grid: EII_wshed = gridpoly (EIIwshed_gr)
Here is a comparison between for Waller Creek. On the left are the subwatersheds obtained from stream links for a threshold of 1,000 cells. On the right the green area represents the drainage area for the station at 38th. The purple and the green are the drainage area for the station at 23rd.
A comparison between the USGS data for the drainage area of the 38th and 23rd stations and the values given by the GIS delineation (square miles) shows that the difference is less than 5%.
Stations 38th 23rd USGS 2.31 4.13 30 m DEM 2.39 4.33 Error 3.5% 4.8%
Out of the 30 USGS stations in the area of study, 20 have a period of record including at least one complete year. The period of record is based on water-years, which start on October 1 and end on September 30. A water year is named by the year in which it ends. For example, water year 1980 starts in October 1979. The data for annual daily-mean discharge vary a lot from one year to another (e.g. from 1 to 7 cfs for Waller Creek at 23rd).
Can the prediction model be based on average values?
If we consider that pollutants concentrations are based only on the land use, then the pollution load for a given land use is directly proportionnal to the pollution load. In this case, using average values is not a good approach.
For the station at 23rd, the average annual daily-mean discharge is 3.5 cfs. For very wet years (discharge: 7cfs), the pollution loading is greatly under estimated (1/2 of the real load). On the other hand, for dry year (discharge: 1cfs), it is highly over estimated (3.5 times).
It is then much more realistic to use a probability distribution to predict the discharge.
The pollutant load is defined as the product of the concentration by the discharge:
LOAD = Q * C
LN(Q*C) = Ln(Q) + Ln(C)
The concentrations C are lognormally distributed (they are defined by a median and a coefficient
of variation (CV)). Hence LN(C) is normally distributed.
A propriety of the normal distribution is that the sum of 2 normal distributions is a normal distribution, whose mean is the sum of the means and variance the sum of the variances. If the discharge was lognormal (LN(Q) normal), the natural logarithm of the pollution load would be the sum of 2 normal distributions, LN(Q) and LN(C). Or for a base period of 15 years (1980-1994), lognormal probability distributions fit quite well the observed discharge data which are highly variable (2 orders of magnitude).
The following equations can then be used to compute the pollution load.
The parameters defining the concentration and the discharge are the median (50% probability)
and the coefficient of variation. Or the equations use the mean and the variance.
For a lognormal distribution, the mean and the variance can be obtained from the median and the coefficient of variation by using the following relationships:
The discharge data are highly variable. Or they are directly related to the precipitation. A probability approach has equally to be used to determine the precipitation values which will serve as input to the model.
Precipitation data can be downloaded from the National Climatic Data Center (NCDC) web site (3 stations for Austin).
To get the discharge from precipitation values, some rainfall runoff relationships for every watersheds have to be established. These relationships will depend on the land uses (related to impervious cover).
From the precipitation and discharge data a runoff coefficient, defined as the ratio of the discharge to the precipitation, can be found. For an annual time scale, both contributions of base flow and direct runoff to the discharge are taken into account, so the base flow does not have to be substracted from the gauged streamflow. The following graph represent the variations of the runoff coefficient for the drainage area of the USGS station at 23rd in Waller Creek watershed.
The runoff coefficient is in a range from 0.21 to 0.46 over a 24 year period with an average value of 0.33. The discharge, and then the runoff coefficient are related to the precipitation and to land use.
The Estimated Mean Concentration values are associated with the land uses. The land use coverage will be given by the City of Austin. It will update the coverage of the Austin Spatial Database CDROM.
The categories used by the city of Austin are:
Current Impervious Code Land Use Categories Cover Percentage 100 Single Family 30%-40% -113 Mobile Home 30%-40% 200 Multi-Family 45%-80% 300 Commercial 60%-95% 400 Office 60%-95% 500 Industrial 60%-95% 600 Civic/Educational 30%-70% 700 Park 5%-15% 800 Transportation 85%-100% -870 Utilities 25%-75% 900 Vacant/Undeveloped 5%-15% -940 Water/Lake 100%These impervious cover estimates are based on the assumption that most streets and roads are included in the overall land use they support. The streets of a Single Family neighborhood are all included in the Single Family land use along with the homes and yards, and not broken out separately. The Transportation land use is reserved for only the largest of roadways, such as IH-35 and MoPac, or for other uses such as railroads, but not for average city streets. Impervious Cover in Urban vs. Non-Urban Watersheds For each land use category, the impervious cover is presented as a range. In most cases this range is due to the different development densities found in Austin. Single Family developments in the central city tend to be more dense, and have more impervious cover, than similar developments in more suburban areas. It is recommended that in Austinís more urbanized watersheds, land use categories be assigned impervious cover from the upper end of the range. Conversely, in Austinís non-urban watersheds values from the lower end of the range should be used.
Urban Impervious Non-Urban Impervious Land Use Category Cover Estimate Cover Estimate Single Family 40% 30% Mobile Home 40% 30% Multi-Family 80% 45% Commercial 95% 0% Office 95% 60% Industrial 95% 60% Civic/Educational 40% 40% Park 15% 5% Transportation 100% 85% Utilities 50% 50% Vacant/Undeveloped 15% 5% Water/Lake 100% 100%
The grid is the product of the EMC grid by the rainfall runoff grid.
Grid: load_grid = EMC_grid*Runoff_gr
NPS pollution assessment for any point is done by using the weighted flow accumulation function.
Grid: NPS_grid = flowaccumulation (ausfdr, load_grid)
To observe the results:
Grid: display 9999
Grid: mape NPS_grid
Grid: gridpaint NPS_grid value linear nowrap gray
Grid: linecolor 4
Grid: arcs creeks
Grid: polygons lakes
Grid: cellvalue *
The NPS pollution load for any cell is obtained by clicking with the mouse on this particular cell.
The grid can then be converted into a coverage.
Grid: NPSint_grid = int (NPS_grid)
Grid: NPS_cov = gridpoly (NPSint_grid)
The coverage can be displayed in Arcview by adding the theme NPS_cov. The repartition of the pollution load can be observed by choosing some concentration ranges in the legend editor.
GIS is a very efficient tool for the assessment of nonpoint source pollution load. However, as natural phenomena such as precipitation (rather unpredictable) are involved, and as there are not a lot of data available to build the model, NPS pollution load remains very difficult to evaluate accurately.
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