Estimating Runoff for Ungauged Watersheds Using Curve Number Method

Piero Cauptoa, Hadia Akbara, Tyler Leea a Department of Civil and Environmental Engineering, Utah State University, 4110 Old Main Hill, Logan, Utah,84321 ([email protected], [email protected], [email protected])

Abstract: This study presents a model for estimation of monthly streamflow volume in ungauged watersheds in South Eastern Utah, using ArcMap (10.5.1). The model uses physical and metrological parameters including watershed area, soil type, monthly precipitation, climate and land use classification. Monthly average precipitation was collected by the National Oceanic and Atmospheric Administration (NOAA) and interpolated using the Thiessen Polygon method. Curve number raster was created using landcover and soil data. Streamflow for the gaged basins was estimated using curve number and precipitation for May, June and July. The calculated flow was compared with the streamflow data from the gaged systems. The estimates were within 50% of the observed values for 9 out of 28 watersheds for at- least for two months out of three.

Keywords: Watershed; Stream Flow; Analysis; Geographic Information System (GIS); Ungauged Streams;

1 INTRODUCTION

1.1 Background

Streamflow data is one of the prime sources of information for a watershed. It can help identify the flow patterns, precipitation patterns or serve as an indicator of water availability for various analyses. This data can be used for planning and resource allocation. Though the United State Geologic Survey (USGS) has a very successful stream gauging network all across the US, the stream-gauging stations are relatively few given the size and number of streams. Utah alone has a gauge density of 1 gauge per 314 km2. This means that there are many areas in the state where there is no estimation of streamflow.

Stream flow estimation for un-gauged basin has been a challenge in hydrology. In the absence of gauged data, often records from nearby gauges are used to synthesize flow record for an un-gauged area/stream. However, this might not be applicable all the time if flow records are not available or there is not enough data for validation. Even if streamflow records are not available, climate data is readily available for the entire state. Additional data such as land cover and land use data, soil type and characteristics are also available that can be indicators of the streamflow patterns.

The purpose of our study is to create a model that predicts streamflow for an ungauged watershed based on data that is readily available or can be conveniently manipulated. The model we created is data dependent. Developing such models requires finding and acquiring data from various sources. The

analysis was also dependent on Geographical Information System (GIS) tools and the data required as input to those tools to predict streamflow.

1.2 Prediction of Runoff

Researchers have used some established methods to predict runoff of watersheds theoretically. Rainfall observations from gauged areas to predict flood probability in an assumed homogeneous river basin in Italy were used by (Boni et al, 2007). (Razavi & Coulibaly, 2016) used different regionalization models to estimate daily streamflow data by transferring hydrologic data from gauged to ungauged watersheds. Using the measured streamflow data by USGS, (Palanisamy, 2010) developed flow transferring characteristics of watersheds in Kentucky River Basin that helps predict streamflow at locations where streamflow is not recorded. A list of statistical methods for the prediction of runoff has been provided by (Blöschl et al, 2013). The application of these approaches depends on the data available and the scope of the study. The two “fundamental methods” can be statistical, or based. The statistical methods use relationships between runoff and the properties of the catchment, those correlations can be linear or non-linear. On the other hand, the based methods use a “combination of balance equations of mass, momentum and energy”. In this study, similar approach to the Index statistical method was used. (Blöschl et al., 2013) described that in this method the runoff will be predicted by the “usage of a scaled property of the catchment” to predict the total runoff of the studied basin. The scaled properties of the catchment used to analyze the watersheds were the Soil Conservation Service (SCS) Curve Number. SCS curve number method was chosen because of its simplicity and time constraints for the study.

1.3 SCS Curve Number method

Curve number (CN) is an empirical perimeter that is used to predict runoff depth from rainfall. Curve number is a function of soil type, land use and soil hydrologic condition. Since this method is very simple. it does not take into account the complex parameters such as spatial or temporal variability of infiltartion and other abstarctive losses. Rather it represents these losses in a constant (Ia) (Eq. 2). Using land use type and hydrologic soil class, runoff curve number is calculated which is a represntative number for the amount of runoff geenated in that area. The detials of specifics are mentioned in the USGS manual (NRCS, 1986). CN can range from 30-100, where 100 indicates maximum runoff/waterbodies. The curve number is related to soil moisture rentention(S) using (Eq. 1) 1000 � = – 10 (1) �� S is the used to calculate runoff for any potential rainfall event (P) (Eq. 2 )

(�−Ia)^2 � = (2) �−��+�

Where:

Q =runoff (in) P = rainfall (in) S = potential maximum soil moisture retention after runoff begins (in) Ia = initial abstraction (in)

Assumption, Ia=0.2S (NRCS, 1986)

2 METHODS

Methods developed in the analysis of ungauged watersheds in South Eastern Utah. The majority of the analysis took place using ArcGIS 10.5.1.

2.1 Study Area

We chose to develop the model for area in Southeastern Utah as this area is very inadequately gaged for stream measurement (Fig. 1). The major river flowing through the area is Colorado River.

Figure 1. Location of USGS stream gauges in Utah.

2.2 Data

The data for the study was acquired from a number of sources. The elevation raster was downloaded from the 3D Elevation Program at USGS. Precipitation data was acquired from NOAA. Soil characteristics data was downloaded from State Soil Geographic Data (STATSGO). 2011 Land Cover and Land use raster data were acquired from Multi-Resolution Land Characteristics Consortium (MRLC).

2.3 Delineation of watersheds

The following steps were followed to delineate watersheds in the study area. A Digital Elevation Model (DEM) raster for the entire study area was created using the Mosaic To New Raster tool in ArcMap. The DEM layer was then used to create flow direction using the Flow Direction tool. Following the flow direction raster generation the Flow accumulation, Set Null and Stream to Feature tools were used to generate the stream network of the study areas (Horsburgh, 2018). The watersheds were delineated using the stream gages as the downstream points using Watershed tool in ArcMap. The workflow of the model is shown in

(Appendix A, Figure 1). Prior to delineation, the stream gages’ location were compared to National Hydrography Dataset (NHD) stream network and Topographic base map in ArcMap. The locations of gages were slightly adjusted to match approximate location and on actual stream network. The stream gages that were present downstream of the reservoir were eliminated from the analysis as the streamflow may be regulated at those stream gages.

2.4 Curve Number Analysis

Curve number is an empirical perimeter that is used to predict runoff from rainfall. HEC-GeoHMS toolbar was used to create a composite curve number that represents runoff potential base on soil properties and landuse (Merwade, 2012). The tool requires DEM, land use, soil hydrologic groups and table for curve number lookup

2.4.1. Data Preparation and generating composite curve number raster Since the tool uses soil hydrologic groups, we needed to extract that from STATSGO database. Complete procedure on how to do that is given in Appendix B. Curve numbers for certain land use classes for corresponding hydrologic soil group are derived as shown in (Appendix A ,Table A1) (NRCS, 1986). Each hydrologic soil group was given a curve number from 30 to 100 based on runoff on surface, 100 being the highest. Having a value of 100 means that all precipitation will contribute as runoff. Each soil class was converted to a percentage of soil present for each map unit in soil layer, this is used later, to find out percentage of soil present in each watershed. Land use raster was converted to polygon to be merged with the land use data. The land use and soil features were merged together using Union tool. The resultant layer had all the characteristics of the land use and soil data. The polygons that did not have characteristics of either layers were deleted from the attributes table as they were marginal polygons. These data were used in the Generate CN Grid tool in Hec GeoHMS tool to create a composite curve number grid raster for the entire area.

2.5 Precipitation Analysis Precipitation data was collected from 57 National Oceanic and Atmospheric Administration (NOAA) stations in southern Utah. Each of these stations was evaluated to determine the average precipitation received in each month for year 2011. Once the data was obtained, the next task was associating it with vector data. The Join tool in ArcMap 10.5.1 was used to combine the table of average monthly values with the vector data's attribute table. Once the data was obtained the precipitation data for each month was interpolated and extrapolated using the Create Thiessen Polygon Tool. The resulting vector data was then converted to 12 precipitation rasters for each month. An important step to guarantee concurrency was setting the snap raster so all raster's have the same extent, cell size and origin.

2.6 Weighted Raster The final process was the development of a weighted raster which was used to analyze each watershed's monthly average precipitation depth from the Thiessen Polygon analysis. Using the Polygon to Raster tool and the appropriate environments, the Thiessen polygons were converted and clipped to a similar format as the Curve numbers. (Figure B6:B8, Appendix B). Furthermore, the Raster Calculator tool was used to calculate the runoff depth using the Equation (2) Obtained from (Hawkins et al, 1985) Q and P the total runoff and precipitation total depth in (inches) and S the curve number. As a final step, a Zonal Statistics tool was used to sum the entire runoff depth of all cells that a watershed was comprised of.

3 RESULTS

3.1 Watersheds

The resulting watersheds from the model developed for the watershed delineation are shown in (Figure B1, Appendix B). The watersheds share few qualities aside from their general location in southern Utah. Each watershed has independent slopes, land use designations, evapotranspiration and other factors not included in this analysis. Another important result from the model used to produce the watersheds is the identification of sub basins. Since stream-gauges might be located at different points in the same watersheds, instead of creating one large watersheds the model created smaller sub basins were created using every stream-gauge as the drainage point. As shown in (Figure B1), watershed number 27 is shown as a medium watershed. However, in real life watershed number 27 will also include watershed 20,12, 17, and 14. For the final analysis it was important that this relationship was treated accordingly

3.2 Precipitation Raster

The precipitation raster developed using the Thiessen polygon method can be seen in (Fig. 2). As a result of the Thiessen polygon method, each polygon has the weather station at its center. Each cell has then been assigned a value based on its location relative to precipitation stations. The values of each cell were used in combination with the curve number raster to produce the final combination raster. Beyond this point the remainder of the analysis was performed separately for each month.

Figure 3: Precipitation using the thiesen polygon method for the months used in the model.

3.3 Curve Number Raster

The curve number raster used for the final analysis can be seen in (Fig. 3). Each individual watershed is visible with the associated observation point. No watershed has one consistent curve number but rather a collection of curve numbers. It is important to note that results shown in Figure 3 followed expected trends the areas that should have the highest runoff should be bare parcels with exposed rock. Land type that should have the lowest runoff would include crops and forested areas.

Figure 3: Curve number values for each cell compared against their location in each watershed.

The large assumption made in the use of the curve number raster is the application of curve number value to individual cells. It is common engineering practice to assign one curve number value to a watershed to model runoff. While, the use of curve number values to individual cells is possible it does not follow the trend of assigning one value to a watershed.

3.4 Combination Raster for Runoff

The next step was to combine the precipitation raster and the curve number raster. The combination was completed using the Raster Calculator and Eq. 1 and Eq. 2. to determine runoff. The model up to this point was constructed so that runoff for any precipitation event could be calculated. In our study the months of May June and July were used. The final combination map for May is shown in Figure 4, the remaining maps for other months are presented in Appendix B (Figure B3:B4).

Figure 4: Runoff calculations or the combination raster for May 2011

The precipitation value for each area controls the majority of the outputs. While the curve number is a significant controller the determining value for runoff ultimately is the precipitation received. While little explanation has been provided for soil moisture values the curve number analysis used in this model assumes normal moisture conditions however a more detailed analysis of soil moisture outside of this mode can be seen in (Appendix B, Figure B1). The initial soil moisture will have significant effects on the resulting runoff and curve number. The next step was to sum the total runoff for each watershed. The summation will provide us with in per 30 m cell size. The second to last step to obtain stream runoff values was to convert the in per cell to cubic feet per watershed. Finally, to obtain the final volume for each stream-gage the contributing watersheds runoff volume was added to the outfall.

3.5 Correlation Testing / Validation

Results were not conclusive for simple relation using curve number as described in the methods section. While results were inconclusive, a developing trend was visible for some of the watersheds. Runoff for some watersheds was within 50% of the observed flow for some months and not for other. A discernable pattern couldn’t be identified. The percentage error for the observed and calculated runoff for the watersheds for the selected months is shown in Figure 5. 7

Figure 5: Percentage Error between observed and calculated runoff

Watersheds final precipitation results were filtered, those watersheds that had an error less or equal to 50 percent for each month were selected to do a correlation analysis. (Figure 6) shows curve fitting for the selected watersheds. The linear trend lines show different trends for the three analyzed months.

Figure 6: Correlation Factors and Curve Fitting of May, June and July Precipitation Results.

4 CONCLUSION AND RECOMMENDATIONS This analysis shows that there is a practical solution for the prediction of final runoff flows correlating hydrological features of a representative population of watersheds. It can be concluded that curve number is not best suited for large and non-homogenous areas. There can be a few reasons for such variability in results. Streamflow is governed by a multitude of inputs that can't be sufficiently modeled with the limited scope of this project. Most of the watersheds had variety of land cover classes that would have variable runoff at a small scale (Figure B2, Appendix B). Our model estimated runoff by aggregating the values of runoff for a large area that might have introduced the variability. Similarly, most of the watershed had combination of slopes and not a very homogenous slope overall. Additionally, June and July might have high ET in the area, since our model does not account for it hence we expect the difference in result. The model estimates runoff based on monthly total precipitation and does not account for possible intense summer storm that could generate large runoff in one rainfall event. Further study can be undertaken on smaller area, watershed with more homogenous land cover and slopes and for individual precipitation events. Moreover, this study can be done for same months for different years to see if same equation governs the runoff pattern as developed in this study.

ACKNOWLEDGEMENT We would like to acknowledge Caleb Buahin in helping us throughout our study.

REFERENCES Boni, G., Ferraris, L., Giannoni, F., Roth, G., & Rudari, R. (2007). Flood probability analysis for un-gauged watersheds by means of a simple distributed hydrologic model. Advances in Water Resources, 30(10), 2135–2144. https://doi.org/10.1016/j.advwatres.2006.08.009 Blöschl, G., Sivapalan, M., Wagener, T., Viglione, A., & Savenije, H. (2013). A synthesis framework for runoff prediction in ungauged basins. Pub, 11–28. https://doi.org/10.1017/CBO9781139235761.005 Hawkins, R. H., Hjelmfelt, A. T., & Zevenbergen, A. W. (1985). Runoff Probability, Storm Depth, and Curve Numbers. Journal of Irrigation and Drainage Engineering, 111(4), 330–340. https://doi.org/10.1061/(ASCE)0733-9437(1985)111:4(330) Horsburgh, J. (2018). Asignment 7. Logan: Utah State University. Merwade, V. (2012). Creating SCS Curve Number Grid using HEC-GeoHMS Preparing land use data for CN Grid, 101–114. NRCS. (1986). Urban Hydrology for Small Watersheds TR-55. USDA Natural Resource Conservation Service Conservation Engeneering Division Technical Release 55, 164. https://doi.org/Technical Release 55 Palanisamy, B. (2010). Streamflow Prediction Using Gis for the Kentucky River Basin. Razavi, T., & Coulibaly, P. (2016). Improving streamflow estimation in ungauged basins using a multi- modelling approach. Hydrological Sciences Journal, 61(15), 2668–2679. https://doi.org/10.1080/02626667.2016.1154558 Rhynsburger, D. (1972). Analytic Delineation of Thiessen Polygons.

Appendix A Supplementary Data for Methods Section In the following appendix section, supplementary data for the methods section is presented.

Figure A1. Workflow to delineate watersheds in ArcMap.

Table A1. Composite Curve Number for Land Cover Classes and Corresponding Soil Hydrologic class.

Land Cover Class and Hydrologic Soil Group Code

Code Land Cover Class A B C D 11 Open Water 100 100 100 100 21 Developed, Open Space 49 69 79 84 22 Developed, Low Intensity 77 86 91 94 23 Developed, Medium Intensity 88 92 95 96 24 Developed, High Intensity 98 98 98 98 31 Barren Land 77 86 91 94 41 Deciduous Forest 30 41 61 71 42 Evergreen Forest 30 41 61 71 43 Mixed Forest 30 41 61 71 52 Shrub/Scrub 49 68 79 84 71 Herbaceuous 51 62 74 85 81 Hay/Pasture 39 61 74 80 82 Cultivated Crops 61 70 77 80 90 Woody Wetlands 100 100 100 100 95 Emergent Herbaceous 100 100 100 100 Wetlands

APPENDIX B Supplementary Data for Results Section

In the following appendix, results that were not presented in report are shown.

Figure B1: Watershed delineation for the model area. Each watershed has been assigned a numerical value for organizational purposes.

Figure B2: Soil moisture retention for each cell compared against their locations in each watershed.

Figure B3: Runoff calculations or the combination raster for June 2011

Figure B4: Runoff calculations or the combination raster for July 2011

Figure B5: Land cover classes in each watershed

Figure B6: Watershed's Total Runoff May 2011

Figure B7: Watershed's Total Runoff June 2011

Figure B8: Watershed's Total Runoff July 2011