Precipitation Response Model
For Fourteenmile and Dry Thirteenmile Creeks
Rio Blanco County, Colorado
CEE 6440 : GIS in Water Resources
Collin Robinson
Term Paper
Fall 2004
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Contents
Introduction
Modeling Scheme
Parameter Derivation
Model Application
Conclusion
Credits
Introduction
Fourteenmile and Dry Thirteenmile Creeks are neighboring tributaries to Piceance Creek, which is located in Northwestern Colorado. They are intermittent streams which drain semi-arid semi-montane terrain, and overlie unconfined aquifers composed of oil shale bearing alluvium. They usually flow from spring snowmelt into early summer, and sporadically throughout the year in response to rainfall events. Neither creek is gauged, for which reason little hydrologic information is available for hydraulic structure design or water rights evaluation. This document sets forth the process and results of the author’s use of ArcGIS geographic information system (GIS) software with accompanying tools and extensions as a central component in the modeling of precipitation responses of the creeks under consideration as a means of estimating reasonable values for the otherwise unknown hydrologic quantity direct runoff. Direct runoff does not provide a complete hydrologic characterization; however, it is an important quantity and a good starting point. The following images show the site location, a schematic of the project objective, and a photograph taken onsite.
Site location and schematic of project objective.
The mouth of Fourteenmile Creek, from just upstream.
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Modeling Scheme
Two principal inputs drive the relatively simple modeling approach envisioned by the author, namely excess rainfall and watershed response. The particulars of dealing with those two inputs were considered in deciding just how to model direct runoff.
Excess rainfall can be calculated by a number of methods. One popular means based on soil properties such as hydraulic conductivity and initial degree of saturation is the Green-Ampt method. The Green-Ampt method is an at-a-point model requiring iterative numeric solution of an implicit equation for cumulative infiltration (Chow, 1988). Another popular approach is the Soil Conservation Service (SCS) method which is based on a general soil property parameter called the hydrologic soil group, a land use or land cover parameter, and an antecedent moisture class determined by the total rainfall during five days previous to the analysis. The SCS method allows for overall catchment characterization via area weighted average of the aforementioned properties as described by a composite curve number (CN), by which the method is sometimes referred to, and has an explicit solution (Chow, 1988). As initial degree of saturation data were not immediately available and the author was unaware of any other than overly generalized or less than cumbersome technique for applying the Green-Ampt method over the entire area being considered, the SCS method became the approach of choice.
Watershed response may also be estimated by a number of methods; however, since the catchments being considered are ungauged modeling must be limited to regional and synthetic hydrograph methods as there is no data for derivation of any actual impulse response. For reasons including the desire to maintain homogeneity in the modeling scheme the SCS synthetic unit hydrograph method was selected. This method requires as an input, the time of concentration for catchments of interest. The author has opted to use an empirical expression for time of concentration developed by Kirpich (Maidment, 1993).
Although not cutting edge, the resulting modeling scheme is highly utilitarian which suggests that reasonable output may be obtained without overstepping the scope of this project. Issues of concern remain; among them, the lack of gauge data (ungauged streams) for model calibration. In addressing this issue, it should be conceded that the absence of observed runoff values for calibration does indeed bring into question the validity of the model results, however it should also be noted that the lack of gauge data is one of the primary reasons the project location is of interest. Therefore, marginal credibility of results is acknowledged, but not allowed to stifle the project on the grounds that rough information is better than none.
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Parameter Derivation
The selected modeling scheme (SCS, curve number and synthetic unit hydrograph) requires the following inputs for estimation of stream discharge from direct runoff: length of main channel from divide to outlet, average channel slope, catchment area, spatial distribution of land cover types, spatial distribution of hydrologic soil groups, and incident precipitation hyetographs.
The first three parameters listed (length, slope, and area) are inputs for the synthetic unit hydrograph portion of the model. They are derived from digital elevation data, which, in this case, was obtained from by using terrain and or watershed processing extensions and or tool packs for ArcGIS. The author chose to use TauDEM, by Dr. David Tarboton, as it allows for convenient delineation of watersheds and streams from user-defined outlet points, and has a default stream delineation threshold which yielded drainage densities of substantial similarity to those observed on site. All calculations were done in NAD_1983 Albers Equal Area projected map units. The following image shows the site Digital Elevation Model (DEM), and associated TauDEM delineated streams and watersheds.
TauDEM delineated watersheds and streams.
It may be seen that the watershed delineated for Dry Thirteenmile corresponds to an outlet point other than the confluence with Piceance Creek. The false outlet point is at a location of interest to the author. It may also be seen that the base map contains additional data for reference. This data was obtained from: and Total length was calculated for each main channel by manually selecting all main channel reaches, exporting selected data to Excel, and summing the lengths, after which an ArcMap measuring tool derived length from the upstream end of the main channel to the divide was added. Average channel slope was calculated for each as the difference between the elevation at the outlet and the elevation at the location along the divide directly upslope from the upstream end of the channel, divided by the total length. Catchment area for each was read from the attribute table of the TauDEM delineated streams, as the downstream contributing area corresponding to the stream segment directly adjacent to the designated outlet point.
In addition to the DEM, a land cover raster was also obtained from as seen in the image below.
Land cover raster, trimmed by delineated watersheds.
The portion overlying the Dry Thirteenmile watershed is slightly shaded for visual separation.
Soil data were obtained from (STATSGO) for the whole state of Colorado. They were added to an ArcMap data frame as polygons for processing. Next, the comp and layer tables were joined to the polygon shapefile by map unit ID (MUID), allowing symbolization by surface texture, hydrologic soil group, or any number of other characteristics. In the following image soil polygons are symbolized by surface texture.
Soil polygons.
The polygons were then clipped and codified using ‘if’ statements in the Field Calculator as shown in the two images below, after which they were converted to rasters in order to yield hydrologic soil group values for the areas of interest. The area overlaying Dry Thirteenmile has been shaded for visual separation.
Hydrologic soil groups.
Codifying hydrologic soil groups.
The rasters thus obtained were added to the land cover rasters to yield codified curve number rasters (seen in the next image) representative of the spatial distribution of infiltration capacity.
Codified curve number raster.
The raster attribute tables were then exported to Excel to be decodified according to curve number values given in the Dewberry Companies’ Land Development Handbook (2002) and combined into composite curve numbers, as seen in the following table.
Curve number for Fourteenmile Creek.
A similar calculation was performed for Dry Thirteenmile, and although there is variation in soil and cover between the two drainages, it just so happens that due to differing ratios and associations they have the same curve number when rounded to the first digit.
Incident precipitation data were obtained from (TD3505 - Surface Data, Hourly Global) and (Precipitation Frequency Maps). With a little tidying up they were converted into the following hyetographs.
Hourly data from the Meeker gauge was obtained, because relative to the project site it is the closest gauge for which there is data available. The next closest gauges are not actually very close at all, and they lie in areas which differ substantially from the project site with respect to climatic characteristics. It was, therefore, not deemed wise to derive site specific precipitation values by interpolation, so the author opted to assume that the site received the same precipitation as the town of Meeker on the dates shown (a fairly reasonable assumption in general, and especially so since here corroborated by weather report radar images for those dates) in order to provide a scenario for modeling. In addition, design storm data (100-year 6-hour precipitation selected for this project) were read from a contour map which showed the majority of the project site to lie in a zone of approximately uniform precipitation equal to 20 tenths of an inch. The first scenario to be considered was the storm observed during the morning of September 20, 2004. All hourly data prior to that is for use in determining antecedent moisture class. The data for that event were adjusted to fit 15-minute increments, which seemed reasonable since the actual measurement durations ranged from 8 to 240 minutes with the majority being about 25 minutes. The first hyetograph shown is a little misleading, as it doesn’t appropriately depict duration. That is amended in the second, which was derived from the first via calculations which assume the rainfall rate to be constant over the measurement duration. The same assumption was used in converting the value read from the precipitation frequency map into the third hyetograph shown. In both scenarios it is assumed that all precipitation falls uniformly over the entirety of the catchments of interest, which is not likely to be entirely accurate, but probably isn’t a terrible assumption either, as the catchments are fairly small.
Thus all parameters necessary for modeling were derived. Parameter values not given above will be presented as given (blue) values in tables in the following section.
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Model Application
Once parameters have been derived, the first step in modeling the direct runoff is computation of excess rainfall. The SCS method compensates for antecedent moisture condition by categorizing the total precipitation for five days previous to the event into three classes, I for very little precipitation, II for average, and III for much. The following equations are provided for curve number adjustment.
The potential maximum retention, S in the same units as precipitation, is then calculated with the following equation.
Initial abstraction (infiltration) and continuing abstraction are then calculated according to these formulas.
HereIa is initial abstraction in the same units as precipitation, Fa is continuing abstraction in the same units, and P is cumulative precipitation. With these equations, the composite curve number already derived, and the incident rainfall hyetograph already obtained, the excess rainfall hyetograph for the September 20th, 2004 event may be calculated as shown in the following table and set of plots.
The excess rainfall hyetograph for the 100-year 6-hour event may be calculated similarly as shown in the next table and set of plots.
Thus excess rainfall computation was completed according to the SCS method as described by Chow (1988). The next step is derivation of unit hydrographs for each catchment and incremental precipitation measurement duration. Chow also gives equations for the SCS synthetic unit hydrograph as follow.
Here qp is the unit hydrograph peak value in cfs for a pe equal to 1.0 inch, C is a unit conversion multiplier whose value is 484 (given as 483.4 by Chow), A is catchment area in square miles, Tp is the time to hydrograph peak in hours, D is the input duration in hours, Tc is the time of concentration (time for droplet landing furthest away to reach outlet) in hours, and Tb is the output duration in hours. Some minor liberties were taken with the nomenclature. Given a catchment area and impulse duration, only the time of concentration remains to be described in order to yield a solution. As noted earlier, this modeling effort will use Kirpich’s empirical formula for time of concentration given by Maidment (1993) as shown below.
Tc is used here rather than Kirpich’s tc in an effort to standardize nomenclature. Tc is time of concentration in minutes, L is total length of main channel from divide to outlet in feet, and S is average channel slope.
With these equations and the previously mentioned GIS derived values of watershed property parameters synthetic unit hydrographs can be calculated as shown by the following tables and plots.
The final step in application of the modeling scheme is calculation of precipitation responses in the form of direct runoff hydrographs for each catchment and storm scenario. This is done by convolution of excess precipitation and unit hydrograph time-series values. A minor difficulty arises in determining which excess precipitation hyetographs to use – those corresponding to antecedent moisture class I, II, or III. Arguments for each are: (1) due to the extreme drought and or well drained nature of the surface soil types in the catchment being considered, dry conditions will prevail regardless of recent precipitation, so the AMC I hyetographs should be used; (2) due to the drought and the well drained nature of the catchments, recent precipitation is not likely to have saturated the soil, so AMC II hyetographs should be used; and (3) Chow (1988) gives 2.1 inches as the growing season threshold for class III, and since September is generally considered a part of the growing season, and the five day antecedent precipitation for the event on the 20th is 2.6 inches AMC III hyetographs should be used. The author selected what he deemed to be the appropriate AMC according to the following considerations: (a) none of the AMC I hyetographs show any excess precipitation, and the model output would be pretty boring with zero values for excess precipitation, so rule out AMC I; (b) for the scenarios being modeled a simple calculation of any qpmultiplied by the corresponding maximum excess precipitation hyetograph value for AMC III results in an unfathomably high flow rate, so rule out AMC III, leaving AMC II as the only reasonable alternative. Thus the AMC II hyetographs were convoluted to yield the direct runoff hydrographs shown in the following tables and plots, which constitute the end result of modeling for this term project.
It should be noted that the 100-year 6-hour event scenario is assumed to happen at the same time, or take the place of the September 20th event in that the calculations shown above assume the same antecedent moisture condition. It should also be noted that the direct runoff hydrographs shown as output have been calculated to show catchment response from the time of ponding on, as opposed to beginning at time of first precipitation.
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Conclusion
This direct runoff modeling exercise has been very educational with regard to the use of GIS for terrain analysis and spatial data processing as well as general hydrologic modeling topics such as time scale issues. It has also provided a good opportunity to become better acquainted with the project site. In addition, the simple modeling scheme used did in fact yield rational results. For these reasons the project should be considered a success. This does not mean, however, that the modeling results are satisfactorily accurate. Based on first and second hand knowledge of the site, the predicted flow rates are deemed artificially high, albeit within an order of magnitude of the probable values. This is likely because the empirical methods used in modeling were not specifically developed for the site or for substantially similar regions. With no gauge to calibrate the model there isn’t any readily apparent means of improving its accuracy. Such is the case for many ungauged streams. Still, the modeling results are better than nothing which is all that was previously available.
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Credits
Applied Hydrology. Chow, V.T. et al. Copyright 1988, McGraw-Hill
Handbook of Hydrology. Maidment, D.R. et al. Copyright 1993, McGraw-Hill
Land Development Handbook. Dewberry Companies. Copyright 2002, McGraw-Hill
TauDEM ArcGIS Extension. Tarboton, D.G. Copyright2004, Utah State University
online data sources as enumerated in text
personal communication with:
Dr. David Tarboton
Mr. Stewart Edwards
Mr. Jacob Young
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