Sensitivity Analysis for Key Parameter Estimation in a Groundwater-Dominated Basin

Transcription

1 Sensitivity Analysis for Key Parameter Estimation in a Groundwater-Dominated Basin Serdar Korkmaz and Emmanuel Ledoux Ecole des Mines de Paris, Centre de Géosciences Fontainebleau, France serdar.korkmaz@mines-paris.org, emmanuel.ledoux@mines-paristech.fr Abstract In this research, a distributed hydrogeological model named MODCOU (or coupled model) was applied to the Somme river basin in the north of France. The basin is prone to floods due to immense water storage in its large chalk aquifer. According to baseflow analysis, it was found that the groundwater contribution to the streamflow is about 90% which proves the strong groundwater domination in the hydrology of the basin. The model consists of surface, groundwater and unsaturated flow components. It computes the surface-groundwater interaction in every time step and the exfiltration of groundwater onto the surface. Input parameters are composed of meteorological data, superficial features and properties of aquifer including the unsaturated zone. Large number of parameters involved in the calibration of the model necessitates the usage of a sensitivity analysis. Sensitivity analysis is used to observe the impact of an input parameter on the output of model. It helps determine not only the most important calibration parameter but also the portions of the basin which are most sensitive to changes in input. The former decides the time to be spent on the calibration of each parameter and the latter facilitates future field data collection. These are essential to the current model as it will be integrated into two research projects in France; namely, REXHYSS and SIM. The project REXHYSS aims to estimate the impact of climate change on water resources of the Somme and the Seine river basins and to perform flood risk assessment studies. The project SIM is used for the real-time estimation of the soil moisture and to calculate the water and energy budgets for the entire France. Keywords: sensitivity analysis, the Somme, hydrological modeling, MODCOU Introduction In a general sense, sensitivity analysis is observing the effect of variation in the inputs of a mathematical model on the output of the model itself. The aim is to obtain information from the system with a minimum of physical or numerical experiments. Sensitivity analysis contributes to model development, model calibration, model validation, reliability and robustness analysis, decision-making under uncertainty, quality-assurance, and model reduction. Sensitivity analysis is widely used in hydrological modeling. Johnson (2007) used sensitivity analysis of MODFLOW-2000 (Harbaugh et al. 2000) in order to determine the most important input parameter and the optimum location of observation data for future model calibration. Similarly, Hill (1998) presented the use of sensitivity analyses as a guideline for evaluating potential new data. McCuen (2003) uses several simplified hydrologic models to demonstrate the potential of sensitivity in all phases of the modeling process and provides a comprehensive mathematical framework of sensitivity. McIntyre et al. (2005) applied an extensive regionalized sensitivity analysis to the Integrated Nitrogen in Catchments model (INCA) in application to the River Kennet. Sieber and Uhlenbrook (2005) introduced two different methods for sensitivity analyses of a complex process-oriented model named distributed tracer aided catchment model (TAC D ). Ho et al. (2005) used sensitivity analysis in the calibration of two different models in their application to different catchments to investigate the effects of urban change and climate change. In this research, sensitivity analysis is used to find out the key-parameter in the application of the hydrogeological model MODCOU (coupled model) in its application to the Somme river basin in the north of France. As the model is going to be used for a long time being integrated to other research projects, the main purpose of the analysis is to find the most important input parameters and to guide field data collection. BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

2 The Somme River Basin The Somme river is located in the north of France. It takes its source near Saint-Quentin and flows into the English Channel at the Somme bay. The total length of the river is 245 km with a fairly constant and mild slope. The major tributaries of the Somme river are the Nièvre, Avre, Selle, Hallue and Ancre. The basin has an unconfined chalk aquifer with a thickness varying between 17 and 141 m. There is alluvium deposition in river valleys with thicknesses varying between 0 and 16 m. The only unconfined aquifer of the Somme is bounded by the Oise river in the east, by the Authie from the north to the English Channel, and by the Bresle from the southwest to the English Channel (Fig. 1). The other boundaries are impervious. The piezometry of the aquifer is observed by BRGM (Bureau de Recherches Géologiques et Minières) using 63 observation wells located all around the basin. Under normal circumstances, the piezometric level of the aquifer varies between 0 and 180 m and the mean level is 52 m. The Somme river basin has a complex formation in terms of water resources, such as rivers, marshes, ponds, trenches, ditches, channels, and diverse hydraulic works. There is a great contribution of groundwater to superficial waters (Deneux and Martin, 2001). The portion of wet valleys with respect to dry valleys is very small. Only the main valleys and the main tributaries are fed by permanent flow (Amraoui et al., 2002). The months with the largest precipitations are October December where December has the highest precipitation and May the lowest. Generally the basin climate is influenced by oceanic factors and the eastern region is also slightly affected by continental landscape; such that, on the western portion mean annual rainfall is more than 800 mm while on the eastern portion it is less than 750 mm. Annual potential evapotranspiration values are between 800 and 900 mm on great majority of the basin in the northwest southeast direction, on the other hand, values slightly below 800 mm are observed on smaller areas in the north and southwest. Figure 1. Delineation of the Somme river basin and the stream network with major tributaries; the circles indicate streamgage stations; total area of the basin is 8205 km². There are streamgage stations installed on the Somme and its tributaries measuring the mean daily discharge for a long time (Banque Hydro, 2007). The station at Abbeville started functioning as early as in The mean monthly discharge of 43 years according to the streamgage station on the Somme at Abbeville (catchment area 5560 km 2 ) is m 3 /s. Low discharges are observed between August and October with values around 25 and 30 m 3 /s, while high flowrates are generally observed between January and May with values around 40 m 3 /s. A damaging flood took place in the basin in spring 2001, after which the basin attracted the attention of researchers. Two main causes of the flood were the groundwater storage in the large chalk aquifer and the heavy rainfall that lasted for a long time. Hubert (2001) presented a detailed study on the flood of the Somme between March and May In this study, the coupled model, also known as MODCOU (Ledoux, 1980; Ledoux et al., 1984), is applied to the Somme river basin in the period between 1985 and 2003 including the flood of BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

3 Average RMSE MODCOU is a spatially distributed hydrogeological model used to simulate the surface runoff and groundwater flow in multilayered hydrological systems. The primary characteristic of the model is to decompose the water cycle into several stages. These stages are each represented by a model which can be considered to be independent and their outputs are separately controlled. Hence, it is possible to verify the validity of internal mechanisms while running the whole model. These models are namely, the surface model, the unsaturated-zone model, the groundwater model, and the coupled model, MODCOU, which gives its name to the whole structure. Further details on the model structure, the calibration and validation processes are presented by Korkmaz et al. (2009). Sensitivity Analysis After validation of the model, sensitivity analysis was made. The reasons are to find the most important parameters affecting the output of the model and the optimum location of observation data for future model calibration. Regarding the groundwater flow, transmissivity and specific yield; regarding surface-aquifer interaction, streambed conductance; and regarding the flood hydrograph, initial groundwater head distribution in the aquifer were subjected to sensitivity analysis. Initially, parameters controlling groundwater flow were examined. Sensitivity of the model to variations in transmissivity (T) and specific yield (S y ) was tested. Briefly, transmissivity controls the mean level of a piezometric head hydrograph while specific yield controls the seasonal fluctuation of it. In the sensitivity analysis, transmissivity and specific yield values of the whole domain were increased by 10, 25 and 50%. Therefore, the model was run 6 times in the period between 1985 and The effects of variations in transmisivity and specific yield on the average of the root mean squared errors (RMSE) at 50 piezometric head observation points are illustrated in Fig. 2 and those on the average groundwater level change are shown in Fig. 3. Average RMSE values were calculated by taking the average of 50 RMSE values corresponding to piezometric head fits obtained at the end of the calibration process. Similarly, average groundwater level changes were calculated by using the average of 50 simulated piezometric heads each of which is averaged over 18 years. As can be seen in these figures, the model is much more sensitive to transmissivity than specific yield. Average RMSE is linearly increasing for transmissivity while it remains almost constant for specific yield. On the other hand, the average groundwater level changes parabolically with increasing transmissivity, whereas it is slightly influenced by the specific yield. As a result, the most important parameter concerning the groundwater flow was found to be transmissivity. For future model calibration, field measurements concentrated on transmissivity can be performed T SY Change from calibrated values (%) Figure 2. Effect of transmissivity and specific yield change on the average of the root mean squared errors at 50 piezometric head observation points. BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

4 Average water level change (%) Change from calibrated values (%) T SY Figure 3. Effect of transmissivity and specific yield change on the average groundwater level change obtained by using 50 piezometric head observation points. Another sensitivity analysis was performed to observe the effect streambed conductance (C riv ) on the flux exchange between the surface and the aquifer. Streambed conductance is a parameter controlling the stream-aquifer interaction as in the following relation: Q aq = min [C riv (H 0 -h), Q max, V/ t] (1) Streambed conductance term represents the product of hydraulic conductivity, K, of the sediment layer and cross-sectional area of flow (i.e. area of the cell) divided by the length of the flow path. However, these parameters are each difficult to estimate and it should be recognized that formulation of a single conductance term to account for three-dimensional flow processes is inherently an empirical exercise, and that adjustment during calibration is usually required (McDonald and Harbaugh 1988). In Eq. 1 streambed conductance is multiplied by the head difference between the river stage, H 0, and the groundwater head, h. In case of infiltration, this product is limited by two factors; the maximum infiltration rate, Q max, and the available volume of water, V, in the river cell for a given time step ( t). In case of exfiltration, the product is always negative (h>h 0 ) and as both Q max and V values are positive, there is no limit. In order to represent the inundations, exfiltration onto the non-river surfaces is made possible with the same relation; however, in the model the flow exfiltrating onto the surface is not permitted to re-infiltrate until reaching a river cell, therefore there is infiltration only on the river cells. Briefly, the infiltration is controlled by two parameters, namely, streambed conductance and maximum infiltration rate. However, during simulation the maximum infiltration rate was the parameter controlling the infiltration. In order to observe the role of streambed conductance, initially, the surface-aquifer flux exchange values were computed in a basin scale for each simulation year from 1/8/1985 to 31/7/2003. The annual values are shown in Fig. 4. When a spatial comparison is made among the simulation years, it is seen that exfiltration locations are approximately the same for all years, however, the intensities are different. The highest values are observed in the 16 th simulation year as follows; 0.24 m of river-based exfiltration, 0.11 m of surface-based exfiltration, and after deducting the river-based infiltration, a total exfiltration of 0.34 m occurs between 1/8/2000 and 31/7/2001 on an area of km 2. A total exfiltration value of 0.29 m is observed for the year 1995, however, the observed impact of the flood of 2001 was much greater. It should be noted that Fig. 4 represents only the simulated values and the actual value in 2001 might have been greater than 0.34 m, however, with today s technology it is almost impossible to measure the exfiltration flux on an area of 8205 km 2. Nevertheless, it is possible to measure how sensitive our model to input parameters creating such an exfiltration flux. BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

5 Change in Flux Exchange (%) flux exchange (m/year) Year (+) exfiltration total river exf. surface exf. river inf (-) infiltration Figure 4. Flux exchange between the surface and the aquifer in the period 1/8/ /7/2003. During simulations, a streambed conductance value of C riv = 0.1 m 2 /s was used. Similarly, in the sensitivity analysis the value of streambed conductance was increased by 10, 25 and 50%. The result is depicted in Fig. 5. To obtain this figure, the flux exchange values corresponding to the period 1/1/ /12/2001 were used. The reason is that the year 2001 is recognized as the period of heavy rainfall and the flood. The most sensitive output parameter to the change in streambed conductance was found to be the infiltration in river cells. The exfiltration in surface cells is slightly affected by the value of streambed conductance whereas exfiltration in river cells is almost not affected. The reason is that the infiltration is limited by the maximum infiltration rate, Q max, and the values falling below this limit increased with increasing streambed conductance; however, exfiltration is only limited by the volume of water in the aquifer cell which was already exfiltrating due to head difference before the change in streambed conductance. In addition to these, the values of average RMSE of piezometric heads and average groundwater level remains nearly unchanged for variations in streambed conductance. When the overall effect of infiltration in river cells is considered as shown in Fig. 4, it can be concluded that streambed conductance does not have a significant effect on the flow river inf. river exf. surface exf Increment in Streambed Conductance (%) Figure 5. The effect of streambed conductance on surface-aquifer flux exchange. Further analysis was made to find out reasons causing the flood in spring There was a question arising; if the initial groundwater level was lower would there still be flood? In order to answer this question, an analysis was made to assess the impact of initial groundwater level on the flood of Two test runs were performed in the period 1/8/ /7/2001 using the groundwater head distributions of 1/8/1998 and 1/8/1999 as initial conditions. The discharge hydrographs of the observation, calibration and the two tests are illustrated in Fig. 6. The minimum, maximum and average discharges at the Abbeville streamgage station (5560 km 2 ) for observation, calibration and BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

6 the two tests are presented in Table 1. As a result, the run with the values of 1/8/1998 yielded a slightly lower flood peak; however, similar consequences would probably occur for there was not a significant reduction in the maximum discharges. As can be observed in Fig. 6, the difference between the calibrated and the tested discharges closes rapidly and towards the end of the simulation period this difference becomes negligible. Figure 6. The discharge hydrograph at Abbeville (5560 km 2 ) for observation, calibration and test simulations. Table 1. The discharges at Abbeville streamgage station (5560 km 2 ) concerning the observation, calibration and test simulations with initial piezometric levels of 1/8/1999 and 1/8/1998. discharge Q min (m 3 /s) Q max (m 3 /s) Q avg (m 3 /s) observation calibration test (1999) test (1998) It can be concluded that the flood in year 2001 does not depend only on the level of groundwater table. The volume of water contained in the unsaturated zone and the intensity of rainfall should also be considered to be the causes of the flood. Conclusions Sensitivity analyses were performed in order to find out the most important input parameters affecting the output of the hydrogeological model MODCOU in its application to the groundwater-dominated Somme river basin in the north of France. The basin with its large chalk aquifer has become the center of attention of researchers after the flood of spring 2001 (Amraoui et al., 2002; Hubert, 2001; Deneux and Martin, 2001; Korkmaz et al., 2009). After the calibration and validation of the model (Korkmaz et al., 2009), the parameters regarding the groundwater flow and surface-aquifer interaction as well as their effect on the flood were analyzed. Initially, sensitivity of the model to variations in transmissivity and specific yield were tested in the period between 1/8/1985 and 31/7/2003. These parameters were increased everywhere inside the basin by an amount of 10, 25 and 50% respectively. While making a comparison between transmissivity and specific yield, their effects on the average RMSE of 50 piezometric head fits and average groundwater level of the aquifer are considered. It was observed that transmissivity had a much stronger effect. The next analysis was performed to observe the effect of streambed conductance on the streamaquifer flux exchange. As there is no known precise technique to determine streambed conductance, it is usually considered as a calibration parameter. Its effect on the river- and surface-based exfiltration and river-based infiltration were examined. Initially, the surface-aquifer flux exchange values were computed in a basin scale for each simulation year from 1/8/1985 to 31/7/2003. For all of the simulation years, the largest value was river-based exfiltration and the smallest was river-based BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

7 infiltration. In sensitivity analysis, the simulations were performed in the period 1/1/ /12/2001 and streambed conductance values were increased by 10, 25 and 50%. Contrary to initial simulations, river-based infiltration turned out to be the most sensitive parameter to changes in streambed conductance, because the infiltration is limited by the maximum infiltration rate and the values falling below this limit increased with increasing streambed conductance; however, exfiltration is only limited by the volume of water in the aquifer cell which was already exfiltrating due to head difference before the change in streambed conductance. On the other hand, there was no change in the average RMSE values of piezometric heads and average groundwater level. As the overall effect of river-based infiltration is very small, streambed conductance does not have a significant effect on the flow. In the final sensitivity analysis, the effect of initial groundwater head distribution on the flood of 2001 was investigated. Therefore, the groundwater head distributions of previous years corresponding to the same season were taken for the initial condition of the simulation year It was observed that the discharges rise rapidly to higher stages due to heavy rainfall and storage in the unsaturated zone. As a result, the initial groundwater level is not considered as a major cause of the flood. In conclusion, by altering the input parameters of the model one at a time, it is easy to determine the key parameter affecting the flow. In this application, transmissivity has by far become the key parameter and it is suggested to be calibrated for a longer time than others. Further sensitivity analyses can be performed to determine the most sensitive portions of the aquifer to changes in transmissivity which will give an idea for future field data collection. References Amraoui, N., Golaz, C., Mardhel, V., Négrel, Ph., Petit, V., Pinault, J.L. and Pointet, T., 2002: Simulation par modèle des hautes eaux de la Somme. BRGM/RP FR report, 184 p. Banque Hydro, 2007: Banque nationale de données pour l hydrométrie et l hydrologie. Ministry of Ecology and Sustainable Development, France. Available at: last accessed: Jan 8, Deneux, M., and P. Martin, 2001: Rapport de la commission d enquête sur les crues de la Somme, Sénat, 34, 606 pp. Harbaugh, A.W., E.R. Banta, M.C. Hill, and M.G. McDonald., 2000: MODFLOW-2000, the U.S. Geological Survey modular ground-water model User guide to modularization concepts and the ground-water flow process. USGS Open-File Report Reston, Virginia: USGS. Hill, M.C., 1998: Methods and guidelines for effective model calibration. USGS Water-Resources Investigations Report Reston, Virginia: USGS. Ho, C. M., Cropp, R. A. and Braddock, R. D., 2005: On the Sensitivity Analysis of Two Hydrologic Models. In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2005, pp Hubert, P., 2001: La crue et les inondations de la vallée de la Somme de mars à mai 2001, report, Cons. Gén. de la Somme, Amiens, France. Johnson, R. H., 2007: Ground Water Flow Modeling with Sensitivity Analyses to Guide Field Data Collection in a Mountain Watershed. Ground Water Monitoring & Remediation, 27 (1), Korkmaz, S., Ledoux E. and Önder, H., 2009: Application of the Coupled Model to the Somme River Basin. Journal of Hydrology, 366, Ledoux, E., 1980: Modélisation intégrée des écoulements de surface et des écoulements souterrains sur un bassin hydrologique. PhD Thesis, ENSMP-UPMC, France. BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May

8 Ledoux, E., Girard, G. and Villeneuve, J. P., 1984: Proposition d un modèle couplé pour la simulation conjointe des écoulements de surface et des écoulements souterrains sur un basin hydrologique. La Houille Blanche, 1/2, McCuen R.H., 2003: The role of sensitivity analysis in hydrologic modeling, Journal of Hydrology, 18(1), McDonald, M. G., and Harbaugh, A. W., 1988: A Modular Three-Dimensional Finite Difference Ground-Water Flow Model. U.S. Geological Survey Open-File Report, McIntyre, N., Jackson, B., Wade, A.J., Butterfield D. and Wheater, H.S., 2005: Sensitivity analysis of a catchment-scale nitrogen model, Journal of Hydrology, 315 (1-4), Sieber, A. and Uhlenbrook, S., 2005: Sensitivity analyses of a distributed catchment model to verify the model structure, Journal of Hydrology, 310 (1-4), BALWOIS 2010 Ohrid, Republic of Macedonia 25, 29 May