Comparison of Calculated Runoff Flows through Dry Canyon using Empirical and GIS Methods
CEE 6440 Term Paper
Prepared by James Dixon
Introduction
Planning for and the management of water resources often requires that thorough analyses of stormwater runoff be performed. Stormwater analysis must be done accurately as well to prevent flooding and failures in structures. Without accurate information, large factors of safety have to be included to prevent the possibility of failure which can result in excessive costs. Many of the methods used to calculate this information were developed decades ago and are entirely empirical. When they were developed, modern technologies were not available to them. Since then, new technologies have been created and the capacity to develop something better been made available. One way to update these old methods is through the use of geographic information system (GIS) technologies.
Previous methods required few calculations with the use of rough averages and generic coefficients. ArcGIS has the ability to run these same calculations for thousands of cells so that averages are taken over very small areas instead of large acreages. This change can help improve the accuracies of the previous methods and, as a result, reduce unnecessary safety factors.
The empirical Rational Method and a model created with ArcGIS were used to determine the peak flows leaving Dry Canyon for a given storm event. The results of these methods demonstrate the need for new runoff calculation methods as well as the viability of an ArcGIS model to create those improvements. By improving on the empirical methods currently in use, more accurate flows could be predicted which would help reduce safety factors and, as a result, the size and cost of hydrologic structures.
Background and Problems with Empirical Estimations
The Rational Method has been in use for over 100 years and is possibly the most simple of runoff calculation methods. Because modern technologies to determine slopes, lengths, and other important variables were not available at the time, many important variables had to simply be accounted for in coefficients and rough estimated averages. While imperfect, these methods were extremely useful.
Although coefficients can be very good, empirical equations always come with limitations. These limitations may include things such as a maximum size for which an equation applies. The Rational Method in particular is recommended for use only on areas smaller than 200ac in size. If this limitation is exceeded, inaccuracies will begin to increase and the calculated flows can become useless. Each empirical method has its own limitations, but there has been no method developed which can work in any situation. Now that the technology is available, innovations could be made to the empirical methods for calculating runoff to provide much greater accuracy.
Data Collection
Several pieces of data were required in order to determine the amounts of runoff generated by a 1-hr 100-yr storm event in Dry Canyon. These data sources included rainfall, elevation, and land use classification data. To find this data, three different sources were used before manipulation of the data could begin.
The elevation data was taken from the Utah GIS Portal. Two meter digital elevation model (DEM) files were taken from this site to find the flow direction raster necessary for the calculation of peak flow. Because of the location of Dry Canyon, three different quadrants had to be downloaded. Rainfall data was taken from the NOAA atlases for the 1-hr 100-yr storm event. The interactive map was used to select the closest point to Dry Canyon containing frequency estimates. Land use was considered to be forest with poor cover and respective coefficients were then read from a table (ODOT, 2005).
Methods
To determine the effectiveness of the empirical methods, the Rational Method and ArcGIS were used to compute the peak flows exiting from Dry Canyon. The Rational Method was used as the empirical method because it is simple and uses very few variables. As a result, it was much easier to model the runoff using ArcGIS without adding the greater complexity of additional variables.
Rational Method
The Rational Method uses a single equation to determine the peak flow resulting from a given storm. Equation (1) shows the Rational Method:
Equation
(1)
In the Rational Method equation, Q represents the peak flow produced by a given storm, c is the runoff coefficient, i is the rainfall intensity for a given storm event, and A is the area of the basin over which the rain falls. In this equation, neither length of the basin nor the slope of the ground are accounted for. This can also be a problem because c values are given as rough averages over the entire area. In cases where these variables are more pronounced, inaccuracies may be produced.
Precipitation data was found to be 1.50in for the 1-hr 100-yr storm event (NOAA, 2006). Rainfall intensity data was gained by taking the precipitation data and dividing by the one-hour duration. The runoff coefficient was given a value of 0.2 for a forested area (ODST, 2005). Although not entirely empirical, the area was defined as the area of the Dry Canyon polygon developed in ArcMap.
It must be noted that the Rational Method is recommended for use with watersheds smaller than 200ac. Anything higher than this will result in increasing inaccuracies. Because Dry Canyon is so much larger, it was expected that inaccuracies would result although they could not be quanitified.
ArcGIS Method
While empirical methods can produce inaccuracies due to rough estimates and lost variables, ArcGIS has the ability to account for each of these things over very small areas. Rasters can be used to define these areas as cells and thousands of calculations may be run independent of surrounding cells. This allows for non-uniform precipitation values, slopes, distances, etc. so that more accurate flow values can be obtained.
To implement this idea of running calculations over smaller areas, a model that could account for those changes was planned. The initial idea behind this method was to create a raster with cell values that not only accounted for flow direction, but also accounted for the distance that each cell would have to “travel” before reaching the outlet. Slope values could be added to change the velocities across the cells as each cell would pass through them. This would account for the lengths and slopes lost in using the Rational Method. It was also hoped that GIS soil and land cover data could be found to input into ArcMap as a way to account for infiltration as well. It was hoped that the accuracies of peak flow calculations produced through these additions would improve over the empirical methods.
Due to the complexity of this method, a simplified version was instead used to find the peak runoff flows from the canyon. This simplified method also required finding a length of flow to the outlet for each cell. Using this knowledge, a count of cells with similar travel distances could be made. By assuming a uniform travel time from one cell to another, it could be assumed that cells with similar travel distances would arrive at the same time. Using the same 1-hr 100-yr storm event that was used in the Rational Method, the rainfall could be calculated over these cells and accumulated to find the volume of water associated with each set of cells with similar distances to travel. After the volumes and velocities had been found, a peak flow could be found from the set of cells with the largest volume of water arriving at the same time.
It should be noted that some of these simplifications required poor assumptions that decreased the accuracy of the method substantially. In order to provide a uniform travel time, distances were assumed to be the same from a cell to any other cell. This assumption does not account for the difference between flows travelling along a vertical or horizontal axis and flows travelling along the diagonal axes. Velocities were assumed to be constant for all calculations which does not account for those areas where the slope becomes steeper and velocities should be increasing. While not the only erroneous assumptions, these help show how the calculation of the peak flow may have been affected and also what would be required to correct those inaccuracies.
ArcGIS Manipulation and Calculations
Although the concept was simple, the implementation of calculating runoff through ArcGIS was much more difficult than was initially anticipated. Many steps were required and calculations soon became very complex. It was for this reason that the GIS model was simplified so greatly from the original concepts.
DEM manipulation
Three 2-meter DEM quadrants were initially taken from the Utah GIS Portal in order to determine the length of flow for each cell. Although it was relatively easy to add the DEM files to ArcMap, these files came as separate quadrants. To simplify later operations, these quadrants were merged into a single file and a “fill” was performed to eliminate any sinks that might exist within the surface layer (Figure 1).
Figure 1: (Left)DEM Quadrants before being merged, (Right) DEM after being merged
After creating a surface raster, a flow direction layer was created using the flow direction tool. This layer was a key step because so many of the later calculations required that it be accurate. This flow direction layer was then used to create a basins raster. After converting the basins into a polygon shapefile, the basins not included in Dry Canyon were deleted. The remaining basin polygons in Dry Canyon were then dissolved to form a single polygon of the entire canyon. This same polygon was used to clip the flow direction raster so that fewer calculations were needed in each step.
The newly clipped flow direction raster was used to create a flow length polygon with counts occurring “downstream” of each cell (Figure 2). Essentially, this tool counted the number of cells that each cell would have to “cross” before exiting through the outlet. Those cells farthest from the outlet contained the highest values while those closest held the lowest values. A count of each value was then needed to determine the maximum number of cells arriving at the outlet at any given time. However, the flow length raster using floating point values which could not be counted.
Figure 2: Flow Length Raster showing the number of cells that each cell must
"travel" through to reach the outlet in the northwest corner of the canyon
In order to get a count of the cell values, a reclassification was performed with a determined interval of 10 cells. This reclassification resulted in 739 “segments” being created where all the cells within those “segments” would arrive at the outlet at the same time. A count of these “segments” was then performed to create a frequency histogram for the canyon (Figure 3). This histogram was essentially a hydrograph for the outlet of the canyon. All remaining calculations were then performed in Excel.
Figure 3: (Left) Raster showing the counts of flow lengths, (Right) Histogram of the counts of flow lengths for each "segment"
Calculations using Excel
The most calculation heavy part of the GIS model was done in ArcGIS. However, several of the calculations were done using Excel so that inputs could easily be altered without having to repeat all subsequent calculations. These calculations were mostly simple calculations with values taken from the GIS model being used as inputs.
A velocity of 1.0m/s and a travel distance of 5.0m from one cell to another were assumed to be constant over the entire canyon. Knowing this, the number of “segments” that could be traversed by a single cell could be calculated to determine the amount of rainfall that would affect each cell. Essentially, each cell was found to be able to travel through nearly 150 cells, or ten “segments”, during a one-hour period. Using the previous velocity, it was found that each cell would spend about 50 seconds within each “segment” before moving into the next “segment”. During this time, 50 seconds of rainfall would fall on this cell. Although the rainfall would remain constant over the entire canyon, the area over which it fell would change depending on the “segment” being passed. Rainfall would continue to accumulate over a length of 15 “segments” before rainfall would cease and the flow would simply travel to the outlet.
Because the amount of rainfall was uniform, the easiest way to determine the amount of water that would accumulate over the one-hour period was to simply find the area of the largest, consecutive, fifteen “segments” in the canyon. These “segments” were those that fell in the range of values from about 460 to about 490 on the histogram. The number of cells counted from these “segments” were summed and multiplied by the area of a single cell to determine the area of canyon that would receive rain.
The volume of water that arrived at the outlet was then divided by the length of 150 cells to determine an average cross-sectional area for the volume of water. This area was then multiplied by the assumed velocity to calculate the peak flow from the canyon.
Results
A peak flow of 682.4cfs resulted when using the Rational Method. This value was a little high, but could not be verified because no gaging station is used to monitor flows from Dry Canyon. Using ArcGIS, a flow of 520.1cfs was calculated. This value appears to lie substantially below the value found using the Rational Method but, again, could not be verified without a gaging station. Table 1 shows the peak flow values for each method. A difference of 24% resulted between the flows of the two methods.
|
Table 1: Peak Flow
Results using the Rational Method and the
ArcGIS Model |
|
|
|
cfs |
|
Rational Method |
682.4 |
|
ArcGIS Model |
520.1 |
Discussion
Even though no actual gage data was available to determine the accuracies of the two methods, it can be assumed that each of the two methods contained some inaccuracies. The area of Dry Canyon was over ten times the recommended size for use with the Rational Method. Also, the calculations run in ArcGIS were very simplified and contained several inaccurate assumptions. Together, these may explain the large difference between the resulting values.
It is important to note that many of the assumptions used in the calculations were erroneous and may have caused this discrepancy in the results of these two methods. However, these assumptions were used in order to simplify the complex model that would have otherwise resulted from the use of additional variables. Fortunately, because the consequences of these assumptions were understood, future work can more easily correct these issues.
The calculated peak flows also show two important concepts. The first is that the Rational Method appears to show a much more conservative value than that provided by GIS methods while the second shows that an accurate GIS model is viable.
The initial idea that empirical methods provide a more conservative estimate of peak flows is corroborated by the fact that the flows resulting from GIS were smaller. This point is significant because it indicates the importance of developing a more cost effective method for predicting runoff flows. Smaller estimated flows would mean that smaller structures could be required and that costs would decrease as a result.
While a difference of over 24% existed between the two calculated flows, the flows developed by the ArcGIS model were close enough to show that a fairly accurate model could be created. This would require that many of the simplifications used in this model be changed to include several variables that were previously disregarded such as the slope, infiltration, and true distance between cells. Further modifications could also be made to this model by including soil data and land cover datasets. This data would allow for differences in each cell and their accurate calculation. Currently, these pieces of data are only used in rough estimates over an entire area. As these datasets become more readily available, they could easily be integrated into an ArcGIS model.
Conclusions
The GIS model retained many inaccuracies because of its simplicity. However, in spite of the many variables that were not accounted for, the model was still able to get within 25% of the value calculated by the Rational Method. By modifying the model to include additional variables such as slope, true length, and infiltration, accuracies could be greatly improved although the complexity of the model would also greatly increase.
While the comparison of the results of the Rational Method and the model created in ArcGIS showed a significant difference in peak flow values, the validity and importance of a GIS runoff model was clearly demonstrated. By using GIS models, the accuracy of flow calculations could be greatly increased and smaller safety factors could be used. This could lead to smaller structures and smaller costs which is considered a benefit for most projects.