Hydrological Modeling Report

HYDRO EUROPE 2011 Hydrological Modeling Report Team 6 18.02.2011 Team members: Manuel GOMEZ (supervisor), Liza ASHTON, Thibault DESPLANQUES, Jens Harold DRASER, Panagiota GKAVAKOU, Kyung Tae LEE, Maxime NARDINI, Jieun PARK, Jiyoung PARK, Gabor SZABO & Anastassi STEFANOVA

Table of Contents Table of Contents... 1 List of Figures... 2 List of Tables... 4 1. Introduction... 5 2. Rainfall distribution... 6 3. Comparison of rainfall distribution methods... 8 3.1 Lumped or quasi distributed method... 8 3.1.1. Thiessen Polygon Method... 8 3.2 Distributed Method (Best Linears Unbiaised Estimators)... 9 3.2.1. Inverse Distance Weights... 9 3.2.2. Spline... 9 3.2.3. Kriging... 10 3.3 Conclusion... 14 4. Land Use Analysis... 15 4.1 Lag Time & Time of Concentration... 16 5 Hydrological modeling with HEC-HMS... 21 5.1 Why a model?... 21 5.2 Model Construction Steps... 21 5.3 Transform Method... 23 5.4 Routing Method... 24 5.5 Loss Method... 24 5.6 Baseflow Method... 25 5.7 HEC HMS limitations:... 26 6 Results... 26 6.1 Final Parameters... 26 6.2 Final Hydrograph... 27 6.3 Validation... 28 7 Comparison between Quasi-Distributed and Lumped Model... 29 8 Hydrological Modelling with MikeSHE... 31 8.1 Purpose of the model... 31 8.2 Model Construction Steps... 32 8.3 Validation / Results... 35 1

8.4 Remarks / Problems... 36 9 Hydraulic Modelling input Hydrograph... 37 References... 38 List of Figures Figure 1 : Thiessen polygons method, apply to the case of study.... 7 Figure 2 : Comparison of Thiessen method efficiency, depending of sampling density.... 8 Figure 3 : Comparison between Thiessen and BLUE s method.... 9 Figure 4 : Rainfall distribution with Spline method. Figure 5 : Rainfall distribution with IDW method.... 10 Figure 6 : Rainfall distribution with Kriging method.... 11 Figure 7 : Rainfall distribution with IDW and Kriging method, made in ArcGIS.... 11 Figure 8 : ArcGIS print screen of zonal statistic, of IDW rainfall distribution in all the subbasins.... 12 Figure 9 : Graph representing the rainfall distribution with Kriging and Thiessen method.... 13 Figure 10 : Influence of the rainfall distribution method on the flood peak... 14 Figure 11 : Land use repartition, from ArcGIS.... 15 Figure 12 : Flood hydrograph for the case 1.... 18 Figure 13 : Flood hydrograph for the case 6.... 18 Figure 14 : Influence of time of concentration methods.... 19 Figure 15 : Graph showing the comparison of Socose and SCS lag time.... 20 Figure 16: Typical representation of watershed runoff.... 21 Figure 17: Models used in modeling the Var Runoff at the napoleon bridge.... 21 Figure 18: Var Basin Model.... 22 Figure 19: Meteorologic Model.... 22 Figure 20: Gage weights input screen.... 22 Figure 21: Time-Series Data.... 22 Figure 22: Estimated hydrograph at Napoleon Bridge.... 23 Figure 23: Input precipitations... 23 Figure 24: Final Hydrograph at Napoleon Bridge.... 27 Figure 25: Final Hydrograph.... 27 Figure 26: Daily discharges at the napoleon bridge in 1994... 28 Figure 27: Daily discharges at Napoleon Bridge in January 1994... 28 Figure 28: Comparison between computed and observed hydrograph in January 1994 28 Figure 29: Comparison of quasi-distributed and fully lumped model hydrograph.... 29 Figure 30:Typical presentation of the processes in MikeSHE... 31 Figure 31: Methods used in MikeSHE model... 31 Figure 32: Model Domain and Grid (up)... 31 Figure 33: Topography of 300m (left) and 75m grid (right)... 31 Figure 34: Thiessen polygons and sample precipitation rate time series... 33 2

Figure 35: River network and domain... 34 Figure 36: Landuse and assigned Strickler coefficients... 35 Figure 37: Output Hydrograph obtained by MikeSHE models... 36 Figure 38: Output Hydrographs obtained from all Hydrological models.... 37 3

List of Tables Table 1: Rain gauge location in Lambert II extend.... 6 Table 2: Thiessen weights for each rain gauge depending on their location.... 7 Table 3: Rainfall distribution for each sub-basin depending on the Thiessen weights.... 8 Table 4: Comparison between Kriging, IDW and Thiessen polygons method.... 12 Table 5: Comparison between kriging and Thiessen rainfall distribution, with hourly rainfall.... 13 Table 6: Repartition of land use in percentage, for each sub-basin.... 15 Table 7: Impervious percentage depending on the land use.... 16 Table 8: Impervious percentage of all the sub-basins.... 16 Table 9: Slope and maximum flow length for each sub-basin.... 16 Table 10: Results of different time of concentration methods... 16 Table 11: Sensitivity analysis for 6 different cases of CN values.... 17 Table 12: Comparison of the influence of time of concentration methods... 18 Table 13: Influence of the lag time on the hydrograph... 19 Table 14: Curve Number for each sub catchments.... 25 Table 15: Monthly average flows for each subcatchments.... 25 Table 16: Final calibration parameters.... 26 Table 17: Sensitivity Analysis Application on the Initial Abstraction parameter... 26 Table 18: New parameters based on mean values.... 29 Table 19: Comparison of peak outflow, time of peak flow and volume between quasi-distributed and fully lumped model... 30 4

1. Introduction The hydrological modeling analysis consists in building the flood hydrograph located at the Napoleon Bridge. In that optic, it s necessary to conduct a rainfall distribution analysis all over the Var catchment. The choice of the method depends primarily on the information available on the raingauge. In that sense, according to the number of raingauges covering the Var catchment (6 in total), we can affirm that this number should not allow interpolation methods application. To confirm this statement, we ll compare the Thiessen polygons method with other interpolation methods like Best Linear Estimators Unbiaised (SPLINE, Inverse Distance Weight and Kriging). Once the precipitations are spatially distributed, it is important to focus on the land use in order to better understand the occupation of soils in terms of percentage of imperviousness, slope and longest flow path. The loss parameters which are the time to peak and the time of concentration are inferred from this analysis for each sub-basin. A sensitivity analysis is then conducted using the Excel spreadsheet of Mr. Laborde which allows us to rebuild a flood effect by the method of unit hydrograph. This approach will permit to understand the influence of the rainfall runoff method and parameters of the loss method (CN). The relevance of time of concentration methods are next evaluated (Passini, Ventura and Nasch) by comparing the simulation results with estimated hydrograph. to compare the lag time. Finally we will see the stages of construction of the flood hydrograph in HEC-HMS and MIKE SHE. In the first place, HEC-HMS software will help us to build a quasi-distributed numerical model in order to predict runoff volumes, peak flows, and timing of flows by simulating the behaviors of the watersheds. After validating the model, a fully lumped model will be build with the purpose of comparing it with the quasi-distributed one. In the second place, another hydrograph will be also compute with MIKE SHE software in order to evaluate the interest of distributed model. 5

2. Rainfall distribution We choose to use the Thiessen polygons to make the rainfall distribution of the 5 sub catchments. We built our polygons using the software ArcGIS. At first we define our sub-basins in ArcGIS by merging different sub-basins according to drainage points. We then collected the rain gauges locations on website of METEO-FRANCE ( http://climatheque.meteo.fr ). METEO-France is the French meteorological agency, a public administrative institution in charge of forecasting and the study of meteorological phenomena. The website allows us to access to different data about the instruments of hydrological measurements. We were therefore able to reap the Lambert II extended coordinates for each rain gauge. We have 6 rain gauges in the Var catchement: Lambert II extend Rain gauge X Y Z Carros 992400 1877100 78 Levens 992100 1883800 691 St Martin 994400 1909300 1064 Vésubie Guillaumes 961500 1910200 780 Roquesteron 975500 1886100 405 Puget Theniers 965800 1894500 441 Table 1: Rain gauge location in Lambert II extend. The Thiessen method permit to converts input rain gauges points to an output feature class of Thiessen proximal polygons. These polygons have the unique property that each polygon contains only one input point, and any location within a polygon is closer to its associated point than to the point of any other polygon. 6

Figure 1 : Thiessen polygons method, apply to the case of study. So we could put the geo-referenced rain gauges on the basins that had the same projection systems. Thanks to ArcGIS we select the intersect area between the sub-catchments and the Thiessen Polygons. That permits to compute the Thiessen Weights: Up Var Low Var Tinée Vésubie Esteron Guillaumes 53.08 0.00 47.56 0.00 0.00 Puget 37.36 0.00 0.13 0.00 38.84 Roquesteron 6.70 0.00 0.27 0.00 45.65 Levens 2.39 36.79 5.48 21.33 7.53 Carros 0.00 63.21 0.00 0.00 7.98 St Martin Vesubie 0.48 0.00 46.55 78.67 0.00 Table 2: Thiessen weights for each rain gauge depending on their location. Once we have these coefficients, we can assign them to the rain gauges rainfall data and determine the sub basins rainfall. Below we can observe the rainfall for each sub-basin: Date Time Up Var Low Var Tinée Vésubie Esteron 3/11/1994 12 00 0.000 0.000 0.000 0.000 0.000 3/11/1994 13 00 0.265 0.000 0.238 0.000 0.000 3/11/1994 14 00 0.033 0.000 0.233 0.393 0.228 3/11/1994 15 00 0.651 0.184 0.265 0.107 0.426 3/11/1994 16 00 0.904 0.000 0.476 0.000 0.388 3/11/1994 17 00 0.796 0.000 0.713 0.000 0.000 3/11/1994 18 00 0.000 0.000 0.000 0.000 0.000 3/11/1994 19 00 0.519 0.000 0.471 0.393 0.651 3/11/1994 20 00 0.543 1.000 0.293 0.213 0.806 3/11/1994 21 00 0.272 4.896 0.397 1.033 2.074 3/11/1994 22 00 2.763 2.316 2.695 2.787 3.341 7

3/11/1994 23 00 3.645 0.368 4.062 2.967 1.275....... 5/11/1994 12 00 7.217 8.472 7.419 8.640 9.093 5/11/1994 13 00 11.389 16.482 11.217 9.754 13.049 5/11/1994 14 00 6.722 11.415 13.904 20.967 7.904 5/11/1994 15 00 4.052 5.368 5.035 5.213 2.929 5/11/1994 16 00 0.622 0.368 2.393 3.360 0.532 5/11/1994 17 00 1.704 1.632 4.255 6.507 3.751 5/11/1994 18 00 2.663 1.816 2.673 2.287 1.928 5/11/1994 19 00 1.469 0.000 2.115 1.967 0.617 5/11/1994 20 00 4.389 2.000 2.002 1.213 3.942 5/11/1994 21 00 0.643 0.000 1.034 0.944 0.117 5/11/1994 22 00 0.159 0.000 0.143 0.000 0.000 5/11/1994 23 00 0.234 0.000 0.469 0.551 0.078 5/11/1994 24 00 0.193 0.000 0.143 0.000 0.228 6/11/1994 01 00 0.159 0.000 0.143 0.000 0.000 Total (mm) : 143.254 104.035 150.652 152.933 148.054 Table 3: Rainfall distribution for each sub-basin depending on the Thiessen weights. 3. Comparison of rainfall distribution methods We then took the time to compare the pattern of rainfall distribution in different ways. Here we will try to compare Thiessen polygon method with Best Linears Unbiaised Estimators (Spline, Inverse Distance Weights and Kriging). 3.1 Lumped or quasi distributed method 3.1.1. Thiessen Polygon Method Thiessen proposed a method to evaluate spatial averages over a domain from anecdotal. One way underlying the "method of Thiessen" is an interpolation technique based on the "law " of the nearest neighbor. Clearly, the main advantage of this method is its simplicity. There is no objective information on the representativeness of interpolations. As illustrated in the diagrams below where the problem is presented in one dimension, if the density of sampling points is very strong, representativeness may be about right (left picture below), in other cases Instead the results can be very disappointing (right picture below). Figure 2 : Comparison of Thiessen method efficiency, depending of sampling density. 8

Correlation coefficient 1,0 Gandin Krigeage 0,9 0,8 0,7 0,6 0,5 0,4 Spline Ariytmétic mean Of 5neighbour Thiessen 0,3 0% y 50% 100% Pourcentage reconstructed rainfall periode Figure 3 : Comparison between Thiessen and BLUE s method. Thiessen polygons assign a weight to the gauges and then distributes in a homogeneous distribution on the sub-basins. However, we can consider this traditional method of interpolation as quasi Distributed. Indeed we allocate different weights to rain gauges and we do not consider an equal distribution of rainfall across our main basin. Full lumped model would consider a uniform distribution on all the Var basin. By going a little deeper, we can say that lumped model for each sub catchment basins would consider that with no rain sub-basins would not undergo rainfall. 3.2 Distributed Method (Best Linears Unbiaised Estimators) We have chosen here to compare three methods to give us a distribution of rainfall much more accurate and with a better distribution. We will detail three methods of interpolation's BLUE (Best Linear Estimators Unbiaised). We will begin with the Spline method (minimum curvature), then we will focus on the method of inverse distance weight (IDW) and we will then finish with the Kriging method. 3.2.1. Inverse Distance Weights This is a deterministic interpolation techniques that create surfaces from measured points, based on either the extent of similarit. The inverse distance weight technique provides an interpolation using a linearly we combination of the rain gauge locations. To predict a value for any unmeasured location, IDW will use the measured values surrounding the prediction location. Those measured values closest to the prediction location will have more influence on the predicted value than those farther away. Thus, IDW assumes that each measured point has a local influence that diminishes with distance. 3.2.2. Spline The basic form of the minimum curvature Spline interpolation imposes the following two conditions on the interpolant: The surface must pass exactly through the data points. The surface must have minimum curvature. 9

The basic minimum curvature technique is also referred to as thin plate interpolation. It ensures a smooth (continuous and differentiable) surface, together with continuous firstderivative surfaces. Rapid changes in gradient or slope (the first derivative) can occur in the vicinity of the data points; hence, this model is not suitable for estimating second derivative (curvature). 3.2.3. Kriging This is a geostatistical interpolation techniques using the statistical properties of the measured points. Geostatistical techniques quantify the spatial autocorrelation among measured points and account for the spatial configuration of the sample points around the prediction location. Kriging generates an estimated surface from the points introduced (rain stations). Kriging is a spatial interpolation method, sometimes considered the most accurate a statistical point of view, which allows a linear estimate based on the expectation and also on the variance of the spatial data. As such, kriging is based on the calculation, interpretation and modeling of the variogram, which is a measure of the variance depending on the distance between data. This interpolation method differs from other methods (inverse distance, Thiessen polygons) because it has two advantages. First, kriging is best linear unbiased: the means are identical and the minimum variance. We built the three rainfall distribution in SURFER 8 software: Figure 4 : Rainfall distribution with Spline method. Figure 5 : Rainfall distribution with IDW method. 10

Figure 6 : Rainfall distribution with Kriging method. We have built spherical variogram method (scale = 375, length = 15100) and we also wanted to reflect uncertainty measures by imposing a Nugget effect (N = 10). But we met problems when we had to build our variograms. Indeed it is difficult to establish a regression with so few data, (whether in a linear exponential or spherical for the variograms components). Finally we decide to use ArcGIS software that allows us, to self calibrate the correlation and so variogram could be more accurate. So we rebuilt our distribution of rainfall in ArcGIS. But we rejected the Spline method. This method does not give us smooth. This method gives us a massive distribution of rainfall spread over Tinée while the sub basins do not have a rain gauge. Figure 7 : Rainfall distribution with IDW and Kriging method, made in ArcGIS. We use in ArcGIS the interpolation to raster from spatial analysis. We the use IDW and Kriging methods with a spherical variogram for Krigging and we choose a inverse distance squared weighted interpolation. We then apply a zonal statistic to know the rainfall distribution in all the sub-basins. 11

Figure 8 : ArcGIS print screen of zonal statistic, of IDW rainfall distribution in all the sub-basins. We initially wanted to compare the sums of hourly rainfall (from 03.11.1994, 12:00 to 11/06/1994 1:00 am) on each sub-basins. Comparisons of the Thiessen polygon results with IDW method and Kriging method could then be carried out, which are shown in Table 2 below: Comparison: Kriging (Spherical) vs. IDW vs. Thiessen Polygons Kriging IDW (Power = 2) Thiessen Polygons Catchments mean (mm) Vesubie 147.855 147.714 152.933 Esteron 146.381 145.752 148.054 Lower Var 117.058 110.642 104.035 Tinee 144.175 146.725 150.652 Upper Var 142.486 143.812 143.254 VAR 697.955 694.645 698.928 Table 4: Comparison between Kriging, IDW and Thiessen polygons method. Then the hourly rainfall for the method of Thiessen polygons and krigging were compared. See below the summary table giving rainfall in mm for each sub-basin: Thiessen Kriging Thiessen Kriging Thiessen Kriging Thiessen Kriging Thiessen Kriging Date Time Up Var Low Var Tinée Vésubie Esteron 3/11/94 12 00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3/11/94 13 00 0.265 0.225 0.000 0.015 0.238 0.195 0.000 0.019 0.000 0.011 3/11/94 14 00 0.033 0.146 0.000 0.076 0.233 0.200 0.393 0.254 0.228 0.230 3/11/94 15 00 0.651 0.396 0.184 0.275 0.265 0.329 0.107 0.286 0.426 0.316 3/11/94 16 00 0.904 0.763 0.000 0.025 0.476 0.401 0.000 0.055 0.388 0.317 3/11/94 17 00 0.796 0.675 0.000 0.046 0.713 0.585 0.000 0.056 0.000 0.034 3/11/94 18 00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3/11/94 19 00 0.519 0.417 0.000 0.416 0.471 0.417 0.393 0.417 0.651 0.417 3/11/94 20 00 0.543 0.519 1.000 0.925 0.293 0.416 0.213 0.307 0.806 0.779 12

5/11/94 19 00 1.469 1.487 0.000 0.199 2.115 1.862 1.967 1.782 0.617 0.682 5/11/94 20 00 4.389 2.892 2.000 2.687 2.002 2.832 1.213 2.756 3.942 2.810 5/11/94 21 00 0.643 0.663 0.000 0.080 1.034 0.892 0.944 0.856 0.117 0.168 5/11/94 22 00 0.159 0.135 0.000 0.009 0.143 0.117 0.000 0.011 0.000 0.007 5/11/94 23 00 0.234 0.272 0.000 0.050 0.469 0.389 0.551 0.477 0.078 0.113 5/11/94 24 00 0.193 0.133 0.000 0.131 0.143 0.133 0.000 0.133 0.228 0.135 6/11/94 01 00 0.159 0.135 0.000 0.009 0.143 0.117 0.000 0.011 0.000 0.007 Total (mm) : 143.254 148.145 104.035 120.582 150.652 149.592 152.933 142.339 148.054 142.593 Table 5: Comparison between kriging and Thiessen rainfall distribution, with hourly rainfall. We can now compare the rainfall on each sub-basin by editing graphics. We note the similarity of rain on the various sub-basins. See below the rain by the two methods considered in the basin Up Var: Figure 9 : Graph representing the rainfall distribution with Kriging and Thiessen method. In order to confirm our observations, we compare the peaks of flood generated by these different methods. For this, we used our model calibrated for HEC-HMS. We have not changed any other settings, on the purpose to only observe the influence of the rainfall distribution method. 13

Figure 10 : Influence of the rainfall distribution method on the flood peak. 3.3 Conclusion The choice of interpolation method depends primarily on the information available. One can distinguish between Climate methods (where there are several observations of the field, or using purely spatial (this is our case). In our case the number of rain gauges is too small for the numerical values to be reliable. Indeed we note that there are not enough points to be able to assimilate the information for the variogram. Consequently whe the variogram was set up to perform a method of Best Linear Estimators Unbiaised (IDW, spline, Krigging) the gridding was not accurate and we will lose here all the interest of the correlation. It would be very interesting to have more data and to make a correlation between rainfall and the distance to the sea and altitude. It would require us to apply the exponential law for the distance to the sea and make a log normal regression to the altitude. This work could be done with SURFER software. By observing the three different methods we can notice that the results are almost similar. The impact of the distribution of rainfall over the flood peak is negligible. We can therefore conclude that in our case study the rainfall distribution method should be Thiessen polygons. This method is faster to implement and gives us more extreme rainfall, which may be interesting to take into account to model the event having the greatest impact. 14

4. Land Use Analysis We further discussed the land use. The land use will allow us to know the distribution of soil occupation characteristics. We therefore use the text file "land use" in ArcGIS. We then grouped the different land uses in 5 parts: Artificial surfaces, Agricultural Areas, Forest and semi natural areas, Wetlands, Water Bodies. Figure 11 : Land use repartition, from ArcGIS. Knowing the areas of all sub-basins and the occupied areas for each land use we have established a table: Esteron Low Var Up Var Tinée Vésubie Areas (km²) 451 152 1090 748 394 Artificial surfaces (%) 0.400 10.400 0.220 0.240 0.600 Agricultures areas (%) 7.600 22.000 3.330 0.780 3.300 Forest & Semi natural areas (%) 91.980 65.400 96.300 98.930 96.080 Wetlands (%) 0.020 0.000 0.150 0.000 0.000 Water bodies (%) 0 2.200 0.000 0.050 0.020 Table 6: Repartition of land use in percentage, for each sub-basin. The table allowed us to identify our coefficients for the loss, SCS Curve Number, method. This table was also used to determine the coefficient of soil permeability. Here we have assigned a coefficient of impermeability to each land use (Source: U.S. Soil Conservation Service): 15

% Impervious = f (land use) Artificial surfaces 0.78 Agricultures areas 0.05 Forest & Semi natural areas 0.05 Wetlands 1 Water bodies 1 Table 7: Impervious percentage depending on the land use. Knowing what percentage of each land use for each sub basins, we have determined the permeability coefficients for each of our five sub-basins. % imperviousness Esteron 5.2227 Low Var 5.457 Up Var 5.2227 Tinée 2.6134 Vésubie 276.95 Table 8: Impervious percentage of all the sub-basins. To calculate the parameters of our loss and transform methods we need to determine in ArcGIS the slopes and the maximum flow length for each sub-basin. These parameters will allow us to calculate our time of concentration and rise times by different methods. 4.1 Lag Time & Time of Concentration The rise time depends on the concentration time of our basins. Time of concentration on a watershed is defined as the maximum required to a drop of water to traverse the path between hydrological points of the basin to the outfall. Area (km²) Slope (m/m) Maximum flow length (km) Esteron 451 0.0194 52 Low Var 152 0.0062 33 Up Var 1090 0.021 80 Tinée 748 0.0262 62 Vésubie 394 0.0358 40 Table 9: Slope and maximum flow length for each sub-basin. We after choose different methods for the time of concentration, and also for the lag time. Tc (hr) Kirpich Ventura Passini Nasch Esteron 6.31 19.36 22.19 22.19 Low Var 6.90 19.89 23.48 19.00 Up Var 8.53 28.93 33.05 28.58 Tinée 6.44 21.46 23.97 24.69 Vésubie 4.07 13.32 14.31 19.44 Table 10: Results of different time of concentration methods. 16

We immediately dismiss the formula Kirpich. Indeed, this method is only applicable for basins with areas less than 0.8km ². The equation below concern Lag Time methods: Triangular Unit Hydrograph: We can also use the Nash lag time: We then conduct a sensitivity analysis using the Excel file of Mr. Laborde. This file allows us to rebuild a flood effect by the method of unit hydrograph.we decide to use the SCS Curve number, loss merhod. This will therefore enable us to understand the influence of the Curve Number on our flood peak but also understand the influence of our time of concentration and our lag time. We will then detail the flood hydrograph build the SCS CN method with a time of concentration corresponding to Ventura formula, and a lag time corresponding to the method of SCS (triangular hydrologic units),. Once we assess the CN we change our time of concentration by comparing with Ventura and Nasch Passini. Finally we use the lag time of the Nasch formula. Once all our parameters are clearly understood and defined by the senility analysis we will implement them in HEC HMS. Using the excel sheet we were able to simulate for each sub-basin, six cases, allowing us to understand the influence of CN on our hydrographs. Below we can see the results of different scenarios without changing the curve number. SCS Curve Number Difference with observed hydrograph Up Var Low Var Tinée Vesubie Esteron Time (hours) Discharge (%) Volume (%) Case 1 65 80 65 65 70 4 28.46 28.62 Case 2 65 80 65 70 70 4 26.09 25.80 Case 3 65 80 70 70 70 4 21.71 20.50 Case 4 70 80 70 70 70 4 16.40 13.08 Case 5 75 80 75 75 75 3 4.38-4.21 Case 6 75 80 75 70 75 3 6.55 1.62 Table 11: Sensitivity analysis for 6 different cases of CN values. 17

Figure 12 : Flood hydrograph for the case 1. Figure 13 : Flood hydrograph for the case 6. We chose to keep the parameters of case study 6. Indeed, this scenario is one that allows us to get as close as the volume observed. It should be noted that we are aware that the observed flood hydrograph is interpolated. During the flood of 1994 measuring devices was destroyed above 600 m 3 /s. So we will try to get closer to the curve on the peak time, which is the only parameter known with certainty. We will then in HMS HEC try to get closer to the volume and flood peak. Subsequently we will modify the time of concentration using different methods (Ventura, Passini, Nasch). Difference with the observed hydrograph Ventura Passini Nasch Time (hours) Discharge (%) Time (hours) Discharge (%) Time (hours) Discharge (%) Cas 6 3 6.55 4 13.40 5 9.92 Table 12: Comparison of the influence of time of concentration methods. 18

Figure 14 : Influence of time of concentration methods. By comparing the concentration time, we note that this setting has no effect on volumes. However we note that the peak discharge and peak time varies. The formula for time of concentration of Ventura seems most appropriate here. Indeed it remains close to the curve observed at the peak time and at the maximum rate as well. Knowing our CN and therefore our method for determining the concentration time, they we have to understand the influence of lag time. To do this we will compare two methods. The first method is the rise time of the SCS triangular unit hydrograph, the latter being the method of SOCOSE. Difference between the observed hydrograph Time Discharge (%) (hours) Socose 1 0.223274193 SCS Triangular UH 4 6.550094434 Table 13: Influence of the lag time on the hydrograph. 19

Figure 15 : Graph showing the comparison of Socose and SCS lag time. We note that SOCOSE method allows us to obtain a flood peak very similar to the observed one, either in time or flow. To conclude this sensitivity analysis allowed us, to understand the various parameters involved in the construction of the hydrograph. We will use later in HEC-HMS, the CN determined, the concentration time of Ventura and SOCOSE Lag Time. By inputting these parameters at the beginning of our set up we will make a more accurate calibration and it will save time. We'll also be able to apply different methods in HEC-HMS that either loss or transform. The software will also allow us to integrate the routing settings and more. 20

5 Hydrological modeling with HEC-HMS Built by the US Army Corps of Engineers, HEC-HMS is a numerical model which can help to predict runoff volumes, peak flows, and timing of flows by simulating the behaviors of the watersheds, channels, and reservoirs. 5.1 Why a model? We propose in our project to use HEC-HMS in order to compute the runoff volume drained to the sea all over the Var catchment. This software use a simple view of the hydrologic process as illustrated in the figure 16 took from the technical reference manual. Each components of the runoff process are integrated in the software as models: Runoff-volume models that compute effective precipitations; Direct-runoff Models corresponding to water that moves over or beneath the soil; Baseflow Models that calculate the subsoil water volume drained into the channel; Routing Models that take into account storage and energy flux through the stream channels. The following illustration gives the final methods used in the project: Figure 16: Typical representation of watershed runoff. Rainfall distribution: THIESSEN Loss model : SCS Curve Number Direct runoff: Clark Unit Hydrograph Observed Hydrograph Channel flow routing : Muskingum Figure 17: Models used in modeling the Var Runoff at the napoleon bridge. 5.2 Model Construction Steps The model has been built following the steps below: 21

Enter basin, time-series and meteorological model data; Enter parameters values for loss, transform, baseflow and routing model; Enter control specifications; Run the model. The few following screenshots illustrate the precedent steps: Figure 18: Var Basin Model. Figure 19: Meteorologic Model. The Thiessen method involves choosing first for each subcatment the raingauges concerned and next to input depth weights (%) for each of them. Figure 20: Gage weights input screen. Precipitation gages correspond to the hourly rainfalls from November 3rd 1994 12h to November 6 th 1994 at midnight. We also added the napoleon bridge estimated hydrograph. Figure 21: Time-Series Data. 22

Figure 23: Input precipitations. Figure 22: Estimated hydrograph at Napoleon Bridge. 5.3 Transform Method The transform parameters that have to be assumed in Clark Transform method are time of concentration (Tc) and the storage coefficient (R). Respectively, these 2 parameters represent two critical processes in the transformation of excess precipitation to runoff: Translation or movement of the excess precipitation from the watershed origin throughout the drainage to the outlet. Attenuation or reduction of the discharge peak as the excess is stored throughout the watershed [3]. The Ventura method has been chosen determing the time of concentration Tc regarding the peak shape with the Jean Pierre Laborde spreadsheet. The basin storage coefficient R, is an index of the temporary storage of excess precipitation in the watershed as it drains to the outlet point. Clark (1945) indicated that R can be computed as a flow at the inflection point on the falling limb of the hydrograph divided by the time derivative of flow (slope at that point). After several tests, this method of computation don t give relevant results. We can just assume that the storage coefficient varies from 0.1 to 0.9, depending upon the characteristics of the area of study. An average value of 0.05hours is for sandy geographies while a 0.95hours is for impervious areas. In our case, according to the land use analysis, the Var watershed is mostly made up of forest and semi natural areas, and overall charactherized by karst. Hence, the initial value is assumed to be 0.3. Besides, because of the lack of information relative to the volume of water drained by karst aquifers, the representation for this coefficient is not relevant and it could have an impact on the model. 23

For this reason, we decide to compare this method with another lumped model, the SCS Unit Hydrograph which depends only on the time to peak (SOCOSE Lag Time). This transform method revealed relevant results (see final calibration 6.2) conforting our final decision to use it for our hydrological modeling project. 5.4 Routing Method The Muskingum routing method uses a simple conservation of mass approach to route flow through the stream reach. By the continuity equation: time. Where I is inflow, O is the outflow rate, S is storage and t the Storage is modeled in the reach as the sum of prism storage (volume defined by a steady-flow water surface profile) and wedge storage (additional volume due to flood wave) multiplied by the travel time through the reach, K. This lead to the equation of the storage S t : Where the required parameters are K, the travel time of the flood wave through routing reach and X, a dimensionless weight ranging from 0 to 0.5. In order to apply a rational Muskingum model, we must also take into account the computational time step Δt respecting the ratio 0 < Δt / K < 2. Computing with an hourly time step, we can affirm that the travel time can t go below 0.5. Regarding the X parameter, experience has shown that for steeper streams, it will be closer to 0.5 whereas for channels with mild slopes and over-bank flow, it will decrease gradually to 0. Hence, the dimensionless weight X will be close to 0,5 in the upper part of the Var watershed and around 0 for the Lower Var reach. 5.5 Loss Method The Soil Conservation Service Curve Number model estimates precipitation excess as a function of cumulative precipitation, soil cover, land use and antecedent moisture by using equation: Where: P e = accumulated precipitation access at time t; P = accumulated rainfall depth at time t; S = potential maximum retention; I a = initial loss = 0,2*S (from SCS) The maximum retention, S is related with watershed characteristics through SCS Curve Number (CN) as: 24

CN for a specific watershed can be estimated using tables published in the Technical Reference Manual of HEC-HMS, appendix A. The soil type estimated range to moderate to high runoff corresponding to soil group C. For the case of the Var catchment which consists of several soil types and land uses, a composite CN was calculated as: in which CN composite is the CN used for runoff volume computations; i = an index of watersheds subdivisions of uniform land use and soil type; CN i = the CN for subdivision I, and A i = the drainage area of subdivision i. Esteron Low Var Var Up Var Tinée Vésubie CN Artificial Surfaces (km²) 1,80 15,81 2,40 1,80 2,36 90 Agricultures areas (km²) 34,28 33,44 36,30 5,83 13,00 82 Forest & Semi natural areas (km²) 414,83 99,41 1049,67 740,00 378,56 77 Wetlands (km²) 0,09 0,00 1,64 0,00 0,00 100 Water Bodies (km²) 0,00 3,34 0,00 0,37 0,08 100 Sum Areas (km²) 451,00 152,00 1090,00 748,00 394,00 CN composite computed 77 80 77 77 77 Table 14: Curve Number for each sub catchments. Looking to the table 14, the CN composite will be most represented by forest and semi natural areas corresponding to CN = 77. Coupling these results with the intermediate calibration using the spreadsheet and the observed hydrograph, we finally chose the values shown in the final parameters table 16. 5.6 Baseflow Method Like the direct runoffs of precipitation, the baseflow is also a component of the streamflow hydrograph. Baseflow is the sustained or fair weather runoff of prior precipitation that was stored temporarily in the watershed, plus the delayed subsurface runoff from the current storm. Three alternative methods are proposed in the model: Constant, Monthly-Varying Baseflow; Exponential Recession Model; Linear-reservoir volume accounting model. We chose in our model the simplest one, constant monthly, because of the lack of data required for the other methods. However, it is important to notice that this baseflow method is intended normally to continuous simulation. Hence, it could be interesting to implement the linear-reservoir baseflow, which is more appropriate to model the recession after a storm event. We used constant daily flows over 36 years (1974 to 2000) available in the excel sheet var-discharge and compute the monthly average discharges for each subcatchments based on area weighting. The table below presents the final discharges: January February March April May June July August September October November December Area Monthly average flows 48,06 38,71 43,56 60,41 73,87 57,46 33,75 24,96 32,67 64,40 61,30 44,80 Upper Var 18,48 14,88 16,75 23,23 28,40 22,09 12,98 9,60 12,56 24,76 23,57 17,22 1090,00 Vesubie 6,68 5,38 6,05 8,40 10,27 7,99 4,69 3,47 4,54 8,95 8,52 6,23 394,00 Tinee 12,68 10,21 11,49 15,94 19,49 15,16 8,91 6,59 8,62 16,99 16,17 11,82 748,00 Esteron 7,64 6,16 6,93 9,61 11,75 9,14 5,37 3,97 5,20 10,24 9,75 7,13 451,00 Lower Var 2,58 2,08 2,34 3,24 3,96 3,08 1,81 1,34 1,75 3,45 3,29 2,40 152,00 Table 15: Monthly average flows for each subcatchments. 25

5.7 HEC HMS limitations: The use of this software must be done keeping in mind the limitations. Indeed, the fluctuations of the tide, dams, bridges, and the existence of lateral flow phenomena can create backwaters that reduce and shift over time the peak flood. In that sense, we are aware that being based on an approximation of uniform flow, patterns of kinematic wave and Muskingum cannot model their effects on the flow. In our case of study, the flood overflowing the bed of the river, the wave will flood the surrounding plains. In some cases, these plains will thus constitute storage basins. The model used must take into account the possible passage of the flow of the riverbed floodplain. Often in these cases, we calculate the hydraulic properties of the riverbed and surrounding plains separately, and then combine them with a composite formula. We are conscious that this cannot be achieved by models Kinematic wave or Muskingum, because the respective parameters they use are constant and cannot take into account a change of hydraulic properties of flow. 6 Results 6.1 Final Parameters The table below presents the final parameters implemented in HEC-HMS after calibration. Hydrologic Elements Upper Var Tinee Vesubie Esteron Lower Var Reach1 Reach2 Reach3 Runoff volume Parameters Direct Runoff Parameters Channel Flow Parameters SCS Curve Number Clark Unit Hydrograph SCS Unit Hydrograph SCS CN Percent Initial Muskingum K Muskingum Storage Impervious Abstraction Tc (hr) Lag Time (min) (hr) X Coeff. (hr) (%) (mm) 77 5,3 15,17 28,934 0,500 578,678 - - 75 5,22 16,93 21,459 0,400 429,174 - - 70 5,46 21,77 13,323 0,400 266,465 - - 75 5,31 16,93 19,364 0,400 387,276 - - 80 14,6 12,70 19,885 0,800 397,704 - - - - - - - 0,9 0,4 - - - - - 0,7 0,2 - - - - - 1,2 0,1 Table 16: Final calibration parameters. In order to better understanding the influence of each parameter on the final hydrograph, a sensitivity analysis has been done. The main purpose consists in computing the percentage difference between computing values with initial values in terms of peak discharge, time of peak and volume of water reaching the outlet of the Var basin. The table below gives the example for the initial abstraction influence: No. of Run Input Parameters Percent of change 1 initial value 2 5% 3 10% 4 30% 5 60% Initial Abstaction, Ia (mm) 6-5% 7-10% 8-30% 9-60% Calculated Values Percentage Difference Between Calculated Value to the initial Value Peak Discharge (m3/s) Time of Peak mm/dd/yr Volume (MM) Peak Discharge (%) Time of Peak (hr) Volume (%) 3215,7 11/05/1994, 16:00 51,49 - - - 3187,1 11/05/1994, 16:00 50,67-0,89 0-1,59 3157,7 11/05/1994, 16:00 49,85-1,80-0,33-3,19 3034,6 11/05/1994, 16:00 46,62-5,63-0,33-9,46 2831,3 11/05/1994, 17:00 41,93-11,95-0,33-18,57 3243,8 11/05/1994, 16:00 52,32 0,87 0 1,61 3271,3 11/05/1994, 16:00 53,15 1,73 0 3,22 3376,2 11/05/1994, 16:00 56,52 4,99 0 9,77 3519 11/05/1994, 16:00 61,7 9,43 0,17 19,83 Table 17: Sensitivity Analysis Application on the Initial Abstraction parameter 26

6.2 Final Hydrograph 4000 Final Calibration 3500 3000 Observed hydrograph (cm/s) Clark Unit Hydrograph (cm/s) SCS Unit Hydrograph (cm/s) 2500 2000 1500 1000 Peak Discharge 05/11/1994 18:00; 3680 cm/s 05/11/1994 23:00; 3126 cm/s 05/11/1994 21:00; 3586 cm/s Figure 24: Final Hydrograph at Napoleon Bridge. 500 0 The hydrograph built with the "SCS Unit Hydrograph" method will be finally the final one used for river modeling because of its better representation of reality. The main argument depends more on the required parameter than on the hydrograph shape as the observed one was estimated after 600cm/s. The final hydrograph, located at the junction 3, is presented below: Figure 25: Final Hydrograph. 27

6.3 Validation Model validation is the process of determining if a proposed model accurately represents a physical process and provides predictive capability [5]. In other words, the calibrated model built for the Var river project must be able to reproduce field observations from an independent data set. In that optic, a new model has been built using daily precipitation datas and observed hydrograph at the napoleon bridge from January 1 st to January 31 st 1994. The choice of January month is mostly explained by the fact that it constitutes the second most important peak flow in 1994. Concerning the other parameters values, they remain exactly the same. The table and graph below describe in detail the event [6] : Figure 26: Daily discharges at the napoleon bridge in 1994 Figure 27: Daily discharges at Napoleon Bridge in January 1994 The first observation that can be done concerns the 1994 flood in the figure 26 that doesn t represent the estimate peak flow as it stops at 1450cm/s. The figure below presents the final result after computation: 2000 1800 1600 1400 1200 1000 800 Model Hydrograph (cm/s) Observed flow (cm/s) 600 400 200 0 0 5 10 15 20 25 30 Figure 28: Comparison between computed and observed hydrograph in January 1994 28

It appears clearly that the model built for the 1994 flood event doesn t match with this event. Indeed, it s difficult to have a relevant comparison knowing that we built the model of November 1994 based on extreme discharges and hourly whereas the observed flow corresponds to mean daily values. However, knowing that the maximum discharge for January 1994 was on 7 and reach 884cm/s, we can affirm that the trend of the curve is right and hence that the model should give relevant results for an episode closed to November 1994 one. In that sens, it could be interesting to validate the model on another event but based this time on extreme values. 7 Comparison between Quasi-Distributed and Lumped Model In this final part, we propose to compare the results of the final model (quasi-distributed) with a fully lumped model based on mean values for each subcatchment and parameter. The average values are presented in the table 17: Hydrologic Elements Upper Var Tinee Vesubie Esteron Lower Var Fully Lumped Model Reach1 Reach2 Reach3 Fully Lumped Model Runoff volume Parameters Direct Runoff Parameters Channel Flow SCS Curve Number Clark Unit Hydrograph Unit Hydrog SCS CN Percent Initial Muskingum Muskingum Storage Lag Time Impervious Abstraction Tc (hr) K (hr) X Coeff. (hr) (min) (%) (mm) 77 5,3 15,17 28,934 0,500 578,678 - - 75 5,22 16,93 21,459 0,400 429,174 - - 70 5,46 21,77 13,323 0,400 266,465 - - 75 5,31 16,93 19,364 0,400 387,276 - - 80 14,6 12,70 19,885 0,800 397,704 - - 75,40 7,18 16,70 20,59 0,50 411,86 - - - - - 0,9 0,4 - - - - - 0,7 0,2 - - - - - 1,2 0,1 - - - - - 0,9 0,3 Table 18: New parameters based on mean values. Regarding precipitation, mean hourly values have been computed gathering all the raingauge giving at the end only one rainfall event for the entire basin. After running the model, the results are the following: 4000 3500 3000 2500 2000 1500 1000 Observed hydrograph (cm/s) SCS Unit Hydrograph (cm/s) SCS fully Lumped (cm/s) 500 0 Figure 29: Comparison of quasi-distributed and fully lumped model hydrograph. 29

SCS Unit Hydrograph (cm/s) SCS fully Lumped (cm/s) Observed hydrograph (cm/s) Total Residual SCS U H Total Residual SCS fully Lumped Peak Outflow (cm/s) 3585,8 3411,4 3680 94,20 268,60 Time of peak flow (h) 5/11/94 21:00 5/11/94 21:00 5/11/94 18:00 3h 3h Volume (mm) 94,43 67,61 91,56-2,87 23,95 Table 19: Comparison of peak outflow, time of peak flow and volume between quasi-distributed and fully lumped model. Finally, the results show differences between the two models but not alarming. Indeed, the gap in peak outflow is 268.6 cms below the estimated hydrograph peak against 94.2 cms for the quasi-distributed model. The volume decreases consequently to 24mm whereas the time of peak flow stands quite similar. To conclude, this study shows that using mean value give also relevant results. However, the choice depends more on the level of understanding of both hydraulics and hydrological processes, and also numerical modeling of physical processes by the user than the project purpose in itself. Indeed, even if we have switched for mean values, a detailed analysis of each parameter is essential in order to catch up with the reality. So for example, we cannot affirm after this study that a fully lumped model will not be adapted to modeling a retention basin as the volume is far from the reality. In our case, in view of the fact that the Var catchment brings complex processes, it is advisable to use a quasi-distributed model. Concerning the question of distributed model, it will be conducted in the next part related to Mike She. 30

8 Hydrological Modelling with MikeSHE MikeSHE is a complete software package by DHI, used as a modelling tool for a wide range of water resources and environmental problems related to surface water and groundwater and can be applied on scales ranging from local infiltration studies to regional watershed studies. It is a dynamic, and simulates all the major processes of the hydrological cycle. 8.1 Purpose of the model After computing the runoff volume of the flood event in the Var catchment with HEC-HMS, we chose to model and compare the output hydrograph with a fully distributed model that could be provided by MikeSHE. This software uses a more or less, according to the needs of the model, complex view of the hydrological processes, as illustrated in figure 30. Flow Model: computes the runoff by simulating all the processes involving water movement: Overland flow Channel flow Evapotranspiration Unsaturated Flow Saturated Flow Water Balance Calculation: computes the storage depths, changes and model errors for individual model components. Figure 30:Typical presentation of the processes in MikeSHE Overland Flow: Finite Difference Rivers and lakes (OC) Flow Model Rainfall distribution: THIESSEN Observed Hydrograph Figure 31: Methods used in MikeSHE model For our project we created a flow model using the Overland flow (Finite Difference method) and the Channel flow (Rivers and Lakes). The choice of these water movements was based on the assumption that after the 3 day event that proceeded the flood event, there is only saturated soil and there were no data provided that could indicate the opposite or assist in the calculation of saturated or unsaturated flow. Moreover, in this way we consider the full effect of rainfall to the flood event and model an extreme event as such of 1994. Especially for the overland flow, the finite difference was preferred over the Subcatchment Based since our interest was focused on the entire basin and particularly the lower Var. 31

An overview of the model and methods are illustrated in figure 31. 8.2 Model Construction Steps The model was built following the steps below and in this report is presented with the final parameters used: Fill simulation specifications; Choose water movement; Input grid, topography, precipitation rate, landuse; Input river network from Mike11 Determine the overland flow parameters and HD parameters; Run the model. 8.2.1 Simulation specification The simulation parameters are illustrated in the table below. Simulation Period 04/11/1994 00:00 06/11/1994 00:00 Time Step Control Initial time step 0.01 hours (6 minutes) Max allowed OL time step 0.1 hours Max precipitation depth per time step 0.5 mm Max infiltration amount per time step 1 mm Input precipitation rate requiring its own 0.5 mm time step OL Computational Control Parameters Maximum number of iterations 20 Maximum head change per iteration 0.00005 m Threshold gradient for applying lowgradient flow reduction 0.000001 Manning equation (using OL flow (checked) manning numbers) HD Parameters Upstream boundary condition 0 Initial conditions water depth 0.5m discharge 10m 3 /s Bed resistance 30 (uniform for the whole river) Table 19: Simulation specification 8.2.2 Model Domain and Grid, Topography Both of the files used were derived in GIS from the ascii file (topography) and the hydro-analysis using ArcHydro Tools (domain). All files were re-projected in the same coordinate system (France III) and then were input to the model. The topography was converted to dfs file, in order to ensure speed of the model. 32

Figure 32: Model Domain and Grid (up).. Figure 33: Topography of 300m (left) and 75m grid (right). 8.2.3 Climate For the Climate, the station based precipitation rate was used to ensure the spatial distribution in the basin, according to Thiessen polygons. The shape file with the polygons that was created in ArcGIS was imported and the time series of the six rain gages were edited in MikeSHE. The software calculates the Thiessen polygons without further interaction of the user. Figure 35: Thiessen polygons and sample precipitation rate time series 33

The net rainfall fraction was considered uniform and equal to 0.9, considering a very small part of losses since there was no infiltration parameter set. In fact, the sensitivity analysis provided a very small difference in the result using 0% or 10% infiltration, but with the 10% to reach the observed hydrograph better. 8.2.4 Rivers and Lakes The Mike11 files of the network and cross sections were used as input. The projection had to be changed to the system our data was projected in. A simulation file was created in Mike11, with the network, cross sections and the coupling with MikeSHE shifted to the right location. Upstream boundary condition (inflow) was considered 0.0001to avoid numerical errors, since the river is considered to be fed only by the rainfall. Figure 35: 36: River network and domain. 8.2.5 Overland flow In the overland flow, no separated flow areas were used, as the only spatial distributed information we had was the Strickler coefficient through the landuse information. For the Strickler coefficient, the 34

values were obtained from the mean values of empirical tables for the manning coefficient and adjusted to the 4 types that occur in Var basin. Figure 37: Landuse and assigned Strickler coefficients For the Detention Storage and Initial Water Depth uniform values were used, of zero and 0.5m (as mentioned earlier), respectively. It has to be mentioned, that for the river bed, we used the maximum Strickler coefficient that can be used in the software (30 M). We would like to be able to use different coefficients for different parts of the river, using at least the only option given to divide the river in 3 parts, but during calibration, the results were not good. Therefore we used the uniform option of 30M, to approximate the mean value throughout the river. 8.2.6 Storing of results The desired results can be viewed in MikeSHE or MikeView (especially for the hydrograph). In order to indicate the outlet, points located near the mouth were put with an interval of 300m and 75m for the respective grids. 8.3 Validation / Results The sensitivity analysis, using logical ranges of the variables, did not provide much diversity. The best used variables were mentioned above. The validation of the 75m model originally would be done with the 300m one, but for reason explained in the Problem section, the 300m model was validated with the 300m model obtained by the data on HydroEurope archive (referred to as MikeSHE Tutorial). The main difference between the two MikeSHE models is the use of distributed Strickler according to the landuse, instead of uniform (Tutorial) and the initial conditions that were other than zero in our model. The simulation of flood event of 1994, compared to the observed hydrograph at Napoleon III Bridge and the Tutorial is illustrated in the following figure. 35