Water balance Maxau - Rhine
branches
dr. ir. A.H. Weerts, ir. M.J.P. Mens
Report
September 2007
Executive Summary Water Balance Maxau-Rhine branches
(Phase 1-3)
The sole objective of the Project is to visualise the discrepancies in the water balance between the 14 key measurement stations between Maxau and Lobith using the hydrodynamic SOBEK model. The hydraulic model boundaries are either measured values (calibration set) or are operationally available measured values in combination with discharges calculated by the hydrological HBV model of the Rhine basin (HBV-mixed set) or they are all calculated by HBV model (HBV-only set). The sensitivity of the water balance to possible error sources as revealed has also been investigated. The detailed analysis and solution of the possible error sources is not an objective of this Project, such analyses will be taken up in subsequent studies.
The SOBEK-HBV models are used for (1) operational forecasting of water levels and discharges along the Rhine, (2) management and planning studies along the Rhine, and (3) climate change impact studies. In the past, the SOBEK models of various Rhine sections were calibrated separately. These section models were later on extended with models of the main tributaries, but were never recalibrated thereafter, nor has the coupled model downstream of Maxau been calibrated in its entirety. During calibration of the model Andernach-Lobith unacceptable differences were observed during flood periods which led to the addition of a ground water component on this reach. However, unacceptable differences are still observed in the operational forecasting system FEWS-NL mainly under low flow condition and under flood conditions with the tendency of simulating more water than being measured. To determine the main sources of error in the water balance to be able to resolve the problems mentioned above this study has been carried out.
The water balance analysis per section has shown that there are some sections, where the water balance is negative (this means at the downstream station more water is measured than could be expected from the input at the upstream station and the laterals) and others, where it is positive. In some cases errors in the water balance are totally compensated by the water balance of neighbouring sections, in other cases only partly.
Hysteresis in stage-discharge relationship is not taken into account in the measured rating curve used at the moment. This can be taken into account via a Jones correction. The maximum correction can be in the order of +/-7-10% of the discharge. The maximum water level gradient occurs mostly during intermediate floods (3000-5000 m3/s for the lower Rhine) when the water is in the main channel. Therefore, the maximum Jones correction is in the order of about 400-500 m3/s. Differences between the model and the measurements during the flood peaks of 1998 & 2003 can not be improved by a Jones correction, because these difference are caused by other factors than hysteresis. During the flood peaks other errors are dominant. The Jones correction, as expected, did not influence the water balance results. However, the Jones correction seems to improve the comparison of the model and measurements during intermediate floods. Therefore, it is recommended that hysteresis will be taken into account via the Jones correction.
Groundwater interaction was introduced during the calibration model Andernach-Lobith (Barneveld and Meijer, 1997) to obtain a better agreement between the SOBEK simulations and the measured water levels during flood periods. In the current configuration groundwater is a large net contributor to the discharge of the Rhine. This net contribution happens especially during low flow periods and is probably one of the causes of the overestimation of the discharge during low flows. The question remains how large the interaction between the Rhine and groundwater in reality is and if this should be taken into account in the SOBEK model. Therefore, it is recommended to study this exchange of water and to study the way the interaction is modelled along the whole river.
Another important issue affecting the water balance are the hydrofactors. These factors account for parts of the catchment which is downstream of the river gauge and may contribute to the lateral inflow of the Rhine. In this study differences between the lateral discharges from the calibration set and the HBV mixed set were found. Between Andernach and Lobith this is mainly caused by the fact that there are no data available for the several diffuse inflows (Zwischeneinzugsgebiete) in the calibration set. The difference between the sum of laterals of the calibration set and the HBV mixed set is similar for each section. However, the difference between individual lateral inflows of the two sets can be as large as 216%. The accumulated difference at Lobith between the calibration and HBV mixed set when running the model for Maxau-Lobith is about 2 Bm3/y (which is about 63 m3/s). This difference is already occurring even when the main tributaries are not considered in the comparison, because they are the same for the calibration set and HBV mixed set. Switching from the mixed HBV set to the HBV only set the effect on the over all the water balance is not very large. Critical evaluation of the hydrofactors is necessary as they have an effect on the water balance. Several issues related to the HBV model were detected and need improvement.
The SOBEK model is used in an operational forecasting system and it is also being used in several other management studies. It is therefore likely that the SOBEK and HBV model will be used in the future. It is strongly recommended to make a maintenance plan to regularly check all points raised above. This maintenance plan must contain a schedule when all items need checking and updating (regularly for instance every 5 years and occasionally after a major event). The items that need to be included are:
Evaluation & Updating of measured rating curves (key measurement stations & lateral inflows);
Evaluation & Updating of the input (rainfall data (gauges, radar, satellite, etc.), river gauges, evaporation data ) to the SOBEK and HBV models;
Updating the SOBEK model (river bathymetry, calibration, etc);
Contents
1 Introduction ...1–1 1.1 General ...1–1 1.2 Background and objectives...1–1 2 Overview ...2–1 2.1 Phase 1 ...2–1 2.2 Phase 2 ...2–1 2.2.1 Introduction...2–1 2.2.2 Water balance results ...2–3 2.2.3 Conclusions Phase 2 ...2–9 2.3 Phase 3 ... 2–10 3 Sensitivity Analysis ...3–1 3.1 Measured rating curves versus SOBEK rating curves ...3–1 3.2 Effect Hysteresis ...3–5 3.3 Effect of groundwater module ... 3–11 3.3.1 Overall ... 3–11 3.3.2 Flood periods... 3–17 3.3.3 Low flow period ... 3–19 3.3.4 Hysteresis effect versus effect of the SOBEK groundwater
4.2.6 HBV model ...4–4 4.2.7 Maintenance plan SOBEK and HBV model ...4–4 5 References ...5–1 Appendices
1
Introduction
1.1
General
On 25 July 2006, the Contract RI-4598/4500045718 was signed by Rijkswaterstaat RIZA and WL | Delft Hydraulics, which commissioned the latter to carry out the study “Waterbalans Maxau-Rijntakken”. The study concerns analyses of water balances between 14 main hydrometric stations of the Rhine from Maxau to Lobith for low, medium and high flows in the period July 1993 and July 2004. The Terms of Reference of the Project as specified in the RIZA document BIO/1994, dated 1 May 2006 and the proposal of WL | Delft Hydraulics of 22 May with reference ZWS-18383/Q4231/tk and its supplement with reference ZWS-18688/Q4231/lj, dated 2 June 2006 form an integral part of the above agreement.
The execution of the Project takes place in three phases:
Phase 1: Data collection and description of methods (see Mens et al., 2006);
Phase 2: Water balance analyses between the main hydrometric stations (see Weerts and Mens, 2007);
Phase 3: Sensitivity analysis of possible sources of errors in the water balance.
This document describes the activities carried out in Phase 3 of the Project. The Project background and the objectives of Phase 3 are described in the following paragraph. In Chapter 2, an overview of the results of Phase 1 and 2 are given, followed in Chapter 3 by a presentation of the results of the sensitivity analysis carried out. In Chapter 4 conclusions are drawn.
The first step of Phase 3, the fourth meeting of the Project, took place on June 8, 2007 at RIZA Arnhem and was attended by representatives of RIZA, BfG and WL | Delft Hydraulics. In this meeting the results of Phase 2 were reviewed, and actions agreed upon for the execution of Phase 3.
1.2
Background and objectives
For operational information on water levels and discharges of the Rhine use is made of coupled SOBEK-Rhine-section models downstream of Maxau (SOBEK-model FewsNL-Rijn version 2.05 as described in Memo WRR 2005-024, 2005) fed with lateral inflows derived from transformed stage observations and lateral inflows derived with the HBV-96 hydrological model of the Rhine basin. For forecasting all inflows are generated by the HBV-96 hydrological model.
During calibration of the model Andernach-Lobith unacceptable differences were observed during flood periods which led to the addition of a ground water component on this reach. However, unacceptable differences are still observed in the operational FEWS system mainly under low flow condition and under flood conditions with the tendency of simulating more water than being measured.
2
Overview
2.1
Phase 1
Phase 1 was the Inception phase of the Project Water balance Maxau-Rhine branches and was used for collecting all relevant data and to outline the analysis method used in Phase 2 (Mens et al., 2006). The collected data consist of
observed water levels and discharges of all the key measurements stations for the period 1/1/1989 – 31/12/2004;
measured or from measurements derived lateral inflows of all lateral inflows of the SOBEK model also for the period 1/1/1989 – 31/12/2004;
HBV-96 simulated lateral inflows of the SOBEK model for the period 11/1997 – 31/12/2004.
All the collected data was put into a HYMOS and MS Access database. At the end of Phase 1, an analysis method for investigating the water balance between the key measurement stations of the Rhine was proposed. A slightly changed version of the proposed analysis method (analysis has been done with SOBEK instead of HYMOS) has been used in Phase 2.
2.2
Phase 2
2.2.1 Introduction
The goal of the analysis in Phase 2 was to identify and detect errors in the input data of the SOBEK model that is also being used in FewsNL-Rijn. This means that in this Phase 2 report no solutions have been provided but only errors were detected. Possible sources of error are:
stage-discharge relationship at the upstream and downstream measurement point; calibration hydraulic roughness;
discharge model boundaries;
hysteresis effects in the stage-discharge relationship;
errors in the lateral inflows between measurement points in the main river; detention-effects;
interaction with groundwater (between Kaub and Lobith).
In FewsNL-Rijn, HBV calculated discharges (small tributaries and areas close to the main river) and discharges of the larger tributaries derived from water level measurements (using a stage-discharge relationship) provide input for the SOBEK models.
In Phase 2 water balance analyses have been carried out between 14 subsequent measurement points in the river Rhine leading to the 13 river sections as presented in Table 2.1 with special attention to low flow and flood periods.
1. SOBEK lateral inflows used during calibration, calibration set, (i.e. only measured data and data derived from measured data);
2. SOBEK lateral inflows used in the operational FewsNL-Rijn system during the update period, HBV mixed set, (i.e. data partly directly measured and partly resulting from HBV simulations).
These SOBEK simulations have been carried out for each section for the period 1/1/1993 – 31/12/2-2004 for the calibration set and 1/1/1997 – 31/12/2004 for the HBV mixed set. For the period 1989 until March 1996 no meaningful HBV simulations can be carried out with FewsNL because of a lack of synoptic data for this period.
In the water balance analyses the main focus has been on the period 1/11/1997 -31/10/2004. This choice is based on the fact that most of the analysis is done for German territory and it seems therefore logical to use German hydrological years. Note however, that the simulations for the floods of 1993 and 1995 using the calibration set have been carried out. For the upstream boundary of all the SOBEK models a discharge boundary, where the discharge series is derived from water levels using a single stage-discharge relation, is used. Besides these simulations, SOBEK simulations between Kaub and Lobith with groundwater model switched (section 5/6 – section 14) off have also been carried out with an observed discharge as upper boundary and calibration and HBV mixed set used for the laterals. Table 2.1 provides an overview of all the models used in Phase 2 of this study. The analyses of the water balance for interesting have been carried out for each section for the low flow period of 2003 and for the flood periods of 1993, 1995,1998, 1999 (only for the Upper Rhine), 2002 and 2003;
Table 2.1. Overview of SOBEK models used in this study. Note that all models have the same downstream model boundary conditions that consist of a water level at Werkendam, Krimpen a/d Lek and Ramspolbrug (all at the downstream end of the Rhine branches).
Model Upstream model
boundary
Calibration and HBV lateral
inflow set
with and without ground water
section 1 Maxau both with
section 2 Speyer both with
section 3 Worms both with
section 4 Mainz both with
section 5/6 Kaub both both
section 7 Andernach both both
section 8 Bonn both both
section 9 Köln both both
section 10 Düsseldorf both both
section 11 Ruhrort both both
section 12 Wesel both both
section 13 Rees both both
2.2.2 Water balance results
In Phase 2, a water balance was derived for each of the 14 sections between the key measurements stations of the Rhine for the period 1/11/1997-31/10/2004 and for several selected flood and low flow events. Besides the water balance results an overview and a comparison of the laterals of the calibration set and the HBV mixed set was also provided. The effect of the SOBEK groundwater module on the water balance was also investigated. The following table shows the available series that were compared. Each series has a unique series name (abbreviation) that is used in the tables and figures.
Table 2.2 Overview of available series with colour coding
Data Source Series name
Measured discharge Rhine as derived from discharge rating curve HYMOS QH Measured lateral discharge as derived from discharge rating curves,
including hydrological factor and factor for time lag
HYMOS QcalL
Lateral discharge derived with HBV, including hydrological factor and factor for time lag
HYMOS QhbvL
Table 2.3. Water balance error per section (I+SoL-O) (Bm3/y) based upon the measurements together with the cumulated water balance error (Bm3/y) based upon the measurements, the water balance error (%) per section relative to the downstream station based upon the measurements and the difference (%) between the SOBEK simulations (QcalQ and QhbvQ) and the measurement at the downstream station (QH, QH=100%) for the whole period 1/11/1997-31/10/2004. Note that I is inflow upstream, SoL is sum of lateral inflows, and O is outflow downstream.
Period 1/11/1997 - 31/10/2004 Section Water balance error per section (I+SoL-O) (Bm3/y) cumulated water balance error (I+SoL-O) (Bm3/y) Water balance error (I+SoL-O) per section relative to downstream station (%) Difference between QH and QcalQ per section relative to QH downstream station (%) Difference between QH and QhbvQ per section relative to QH downstream station (%) 1: Maxau – Speyer 0.64 0.64 1.51 1.50 1.65 2: Speyer - Worms -0.31 0.33 -0.65 -0.67 -0.02 3: Worms – Mainz 0.31 0.64 0.57 0.56 0.67 4: Mainz – Kaub -1.71 -1.07 -2.95 -2.96 -2.67 5/6: Kaub – Andernach 1.71 0.64 2.44 2.26 2.87 7: Andernach – Bonn -0.16 0.48 -0.23 -0.27 -0.03 8: Bonn – Köln -0.71 -0.23 -0.97 -0.64 -0.36 9: Köln – Düsseldorf 0.49 0.26 0.66 2.42 2.58 10: Düssel. – Ruhrort -2.01 -1.75 -2.57 -2.57 -2.46 11: Ruhrort – Wesel -0.77 -2.52 -0.97 -1.19 -1.02 12: Wesel – Rees 1.29 -1.23 1.61 1.88 2.07 13: Rees – Emmerich 0.95 -0.28 1.21 1.29 1.53 14: Emmerich – Lobith 1.46 1.18 1.89 1.95 2.13
From Table 2.3, it can be observed there are some sections with too much water and others with less water than measured. The negative water balance (column 1) at Worms (section 2) is completely compensated for at Mainz (section 3) and the same is valid for Kaub (section 4) and Andernach (section 5/6). For the other stations this compensation does not occur and for these stations also big differences in the water balance can be observed. Table 2.3 also shows the comparison of the water balance per section with the difference between the two SOBEK simulations with the measurement at the downstream station (QcalQ-QH and QhbvQ-QH in %). It is to be expected that the water balance based upon the measurements of the different sections are comparable with the differences found between the SOBEK simulations and QH. It can be observed in Table 2.3 that this is the case. The biggest positive difference (too much water) is found for section 9: Köln – Düsseldorf where the influence of the groundwater module present in the SOBEK models plays a big role (Weerts and Mens, 2007).
an effect of the groundwater module in the SOBEK models, is now also visible for section 10 and 11. However, for the low flow period of 2003 the effect of the groundwater module is again most notable for section 9. From Table 2.4 and on the basis of number of other flood periods (see Phase 2 report), it can be concluded that the indicative cumulated water balance error based upon the measurements at Lobith is in the order of 500 - 900 m3/s, which is substantial (5-9% of the discharge at Lobith).
Table 2.4. Water balance error per section (I+SoL-O) (m3/s) based upon the measurements together with an indicative estimate of the cumulative water balance error (m3/s) based upon the measurements, the water balance error (%) per section relative to the downstream station based upon the measurements and the difference (%) between the SOBEK simulations (QcalQ and QhbvQ) and the measurement at the downstream station (QH, QH=100%) for the flood period of January 2003. Note that I is inflow upstream, SoL is sum of lateral inflows, and O is outflow downstream.
Flood period January 2003
Table 2.5. Water balance error per section (I+SoL-O) (m3/s) based upon the measurements together with an indicative estimate of the cumulative water balance error (m3/s) based upon the measurements, the water balance error (%) per section relative to the downstream station based upon the measurements and the difference (%) between the SOBEK simulations (QcalQ and QhbvQ) and the measurement at the downstream station (QH, QH=100%) for the low flow period of September-October 2003. Note that I is inflow upstream, SoL is sum of lateral inflows, and O is outflow downstream.
Low flow period September-October 2003
Section Water balance error per section (I+SoL-O) (m3/s) Indicative estimate cumulated water balance error (I+SoL-O) (m3/s) Water balance error (I+SoL-O) per section relative to QH downstream station (%) Difference between QH and QcalQ per section relative to QH down stream station (%) Difference between QH and QhbvQ per section relative to QH down stream station (%) 1: Maxau - Speyer 0 0 0.01 1.17 1.73 2: Speyer - Worms 58 58 6.79 6.45 6.28 3: Worms - Mainz -8 50 -0.78 -1.44 -1.29 4: Mainz – Kaub 57 107 5.81 5.33 5.69 5/6: Kaub – Ander. 25 132 2.23 2.77 3.20 7: Ander. – Bonn -6 126 -0.53 1.03 1.21 8: Bonn – Köln 0 126 0.01 2.76 2.92 9: Köln – Düssel. -25 101 -2.02 7.11 6.98 10: Düssel. – Ruhrort -119 -18 -8.31 -6.70 -6.90 11: Ruhrort – Wesel 17 -1 1.19 2.00 2.38 12: Wesel – Rees -29 -30 -1.86 -0.54 -0.26 13: Rees – Emme. 107 77 7.73 8.47 8.89 14: Emme. – Lobith -33 44 -2.26 -1.95 -1.68
For all sections, it is clear that the two SOBEK simulations are very similar and deviate both more from the measured discharge than from each other. This is further illustrated by Figure 2.1 where the results of all 14 models (see Table 2.1) as a function of the river kilometres are shown. From Figure 2.1, it is clear that the two SOBEK simulations are very close together for each section. The clear bend visible in the Figure 2.1 from kilometre 837 (Rees) onwards is caused by the measured discharges used as upper boundary of the SOBEK models. The reason that the two SOBEK simulations are very close is also caused by the fact that in the calibration set and the HBV mixed set only the small laterals inflows differ and that the larger tributaries (Neckar, Main, Mosel, Lahn, Sieg, Ruhr, Lippe) are the same (derived from measured data).
From Table 2.6, it can also be observed that the groundwater starts playing a role in the section Köln – Düsseldorf and thereafter. The difference between the SOBEK simulations with the calibration set and HBV mixed set (4th column) deviates from the difference between the direct comparison of the calibration set and HBV mixed set (3th column). This deviation can only be caused by another source or sink of water in the model and in this case that is it is the groundwater module.
Section 9 is indeed the section with the strongest groundwater interaction as shown in Weerts and Mens (2007). Groundwater exchange plays a major role as shown in the cumulative effect of errors as shown in Figure 2.2. From this figure, it can be observed that the effect of the groundwater exchange is in the same order of the differences present in the laterals of the HBV and calibration set. It is also visible that section 9 between Köln (688 River km) and Düsseldorf (744 River km) is the most important section for the groundwater exchange. 300 400 500 600 700 800 900 40 45 50 55 60 65 70 75 80 85 River km D is cha rg e ( B m 3/y) Measured Calibration set HBV set
300 400 500 600 700 800 900 40 45 50 55 60 65 70 75 80 85 River km D is char ge ( B m 3/y) Measured Calibration set Calibration set without GW HBV set HBV set without GW
Figure 2.2. Overview of water balance results using model Maxau-Rhine branches (section 1) for each key measurement station along the Rhine.
Table 2.6. Overview of differences between the Sum of Laterals and the difference between the SOBEK simulations using the calibration set and HBV mixed set per section, together with the cumulative difference between the SOBEK simulations using both sets of laterals all for the period 1/11/1997 – 31/10/2004.
Measurement
station River Km SoL QcalL andDifferences
2.2.3 Conclusions Phase 2
The water balance analysis per section has shown that there are some sections, where the water balance is negative (this means at the downstream station more water is measured than could be expected from the input at the upstream station and the laterals) and others, where it is positive. In some cases errors in the water balance are totally compensated by the water balance of neighbouring sections, in other cases only partly.
The largest errors are probably present in the discharges of the main river, which are derived from the measured water levels and rating curves. Therefore the discharge given in the database are very dependent on the quality of these rating curves. Strong deviations exist between rating curves based on measurements and rating curves derived with the SOBEK model. This is partly caused by the fact that the rating curves do not include hysteresis effects. Besides the hysteresis effect, backwater effects of lateral inflows can influence the some of the rating curve as well. To investigate the rating curves of the key measurement stations the original data used for deriving the rating curves must be investigated. Furthermore, the calibration of the model versus the shifts and changes of the rating curves must be compared and investigated. Also the effect of the hysteresis which can conveniently be taken into account via a Jones correction should be investigated. Hysteresis will probably not affect the overall water balance but will have a significant effect on the fit to the measured discharges. This may be important for operational forecasting as the measured discharges may be used for state updating of the SOBEK model via Ensemble Kalman Filtering (see for instance Warmink, 2007).
There are differences between the lateral discharges from the calibration set and the HBV mixed set. Between Andernach and Lobith this is mainly caused by the fact that there are no data available for the several diffuse inflows (Zwischeneinzugsgebiete) in the calibration set. The difference between the sum of laterals of the calibration set and the HBV mixed set is similar for each section. However, the difference between individual lateral inflows of the two sets can be as large as 216%. The accumulated difference at Lobith between the calibration and HBV mixed set when running the model for Maxau-Lobith is about 2 Bm3/y (which is about 63 m3/s). This difference is already occurring even when the main tributaries are not considered in the comparison, because they are the same for the calibration set and HBV mixed set.
Currently, it is impossible to say which lateral from which set is good or bad. This is due to the fact that the SOBEK model deviates too much from the discharge derived from the rating curve and stage measurements. However, it is clear that strong deviations exist between the calibration and HBV mixed set. This difference should be further investigated to ensure that the SOBEK model is fed with the right lateral inflow when using the model for investigations concerning the Rhine basin or during operational forecasting of floods and droughts for the Rhine basin.
2.3
Phase 3
In Phase 3, the sensitivity of possible error sources as revealed in Phase 2 have been investigated. As mentioned in Chapter 6 of the Phase 2 report not all sources could be investigated in Phase 3, because they fall outside of the scope of this study. The points below have been carried out in the analysis of Phase 3:
As mentioned in the paragraph above, the largest errors are probably present in the discharges of the main river, which are derived from the measured water levels and rating curves. The quality of the rating curves have therefore a large impact on the water balance of each section. To get an idea of possible problems with the rating curves and the effect on the water balance two investigations have been carried out:
into the difference between the rating curves derived with the SOBEK model and the rating curve used for stage transformation for all key measurement stations as was done for Worms already in Phase 2;
into the effect of hysteresis on the water balance and on the comparison of the derived and simulated discharge for a selected section and one or two flood periods.
Next to the measured discharge of the key measurement stations and the groundwater module, the contribution of the lateral inflows is the most important factor of the water balance. For taking into account runoff from areas where no data (measured of simulated) are available, factors are introduced for correction. But how good the “hydro factors” are and how they influence the water balance is not known. Therefore investigation has been carried out:
into the laterals of one section (for instance Speyer-Worms) that contribute most to the difference between the laterals of the HBV mixed set and the calibration set (effect of the hydro factors during a flood period and low flow period);
into the effect of the hydro factors on the water balance purely based upon the measurements.
In Phase 2, the water balance is investigated for the sets of laterals as used in calibration (calibration-set) and as used in FEWS (HBV mixed set), when measured data for the laterals are available. In this latter case for the larger tributaries measured data are used, for the smaller tributaries data simulated by HBV are used. This HBV mixed set represents the way things are done in FewsNL. In other cases, when SOBEK is used for investigations concerning the River Rhine basin, only HBV simulations (HBV full set) are used as input into the SOBEK models. Therefore, it is important to know what the effects are on the water balance, when for the big tributaries HBV-results are used. Therefore, investigations have been carried out
into the lateral inflows of the large tributaries calibrations set versus the HBV-96 results as already has been done in Phase 2 for the smaller tributaries. The influence on the water balance is estimated;
In Phase 2, it was shown that the groundwater module has a remarkable effect on the results of the overall water balance. Therefore, further investigation has been carried out:
3
Sensitivity Analysis
3.1
Measured rating curves versus SOBEK rating curves
All measured rating curves are compared with the simulated rating curves. Figure 3.1 -Figure 3.4 show examples of this comparison for Maxau, Worms, Wesel and Lobith. The figures for the other stations are plotted in Appendix A. As can be observed from Figure 3.1 - Figure 3.4 big differences are presented between the measured rating curves and the rating curves of the SOBEK model. As an illustration, it can be observed in Figure 3.4 that when the water level at Lobith is 16 meter the derived 'measured' discharge is 10100. At that same water level the model simulates a discharge of 10650-10800 m3/s (rising limp) and 10400 m3/s (falling limp). In other words, the measured rating curve does not lie within the simulated rating curve. Another good example is Worms, where the simulated rating curves from 4000 m3/s on shows a bend, which can not be found in the measured curves at all. The stations with the largest differences between the measured rating curve and the rating curve of the SOBEK model are Maxau, Worms, Kaub, Andernach, Bonn, Ruhrort, Rees, Emmerich and Lobith.
There are several issues that have an effect on this comparison:
the measured rating curve contains errors (due to extrapolation, measurement errors); the measured rating curve doesn't take into account hysteresis;
the SOBEK model contains model errors (such as errors in river bathymetry, hydraulic roughness, groundwater and lateral inflow).
The measured rating curve at several locations has been changed frequently. These changes in rating curves reflect the morphodynamics of the channel geometry. The changing channel geometry is not taken into account in the SOBEK model. This means that the bathymetry of the SOBEK model might not be representative for the present situation. Figure 3.5 shows the comparison of the simulation with the SOBEK model of section 1: Maxau-Rhine branches (see Table 2.1) at Lobith with the measurements of the water level and the discharge. The results for the key measurement stations are given in Figure B.1 - Figure B.13. From Figure 3.5a, it can be observed that the simulations of the water level at Lobith with SOBEK:
tend to be to higher than the measured water levels at water stages between 12 – 17 meter NAP.
For all key measurements stations the SOBEK simulations of the water level tend to be higher than the measured water level at higher water stages.
As was concluded in Phase 2, it is necessary to investigate the rating curves of the key measurement stations using the original data used for deriving the rating curves. However from Figure 3.4 is also clear that improvements in bathymetry and calibration (roughness, groundwater) of the model are also necessary. An improved model and improved measured rating curves will improve the agreement between the model and the measurement and yield an improved water balance for the whole Rhine. For forecasting purposes the measured rating curves and the SOBEK model should be updated frequently.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 100 101 102 103 104 105 106
107 Simulated rating curve for Maxau
Discharge (m3/s) Wat er l ev el (m ) Simulated Measured
0 1000 2000 3000 4000 5000 6000 84 85 86 87 88 89 90 91
92 Simulated rating curve for Worms
Discharge (m3/s) Wat er l ev el (m ) Simulated Measured
Figure 3.2. Measured rating curve (blue line) versus rating curve (grey lines) of the SOBEK model for Worms. 0 2000 4000 6000 8000 10000 12000 12 14 16 18 20 22 24
Simulated rating curve for Wesel
0 2000 4000 6000 8000 10000 12000 6 8 10 12 14 16
18 Simulated rating curve for Lobith
Discharge (m3/s) Wat er l ev el (m ) Simulated Measured
Figure 3.4. Measured rating curve (blue line) versus rating curve (grey lines) of the SOBEK model for Lobith.
3.2
Effect Hysteresis
Hysteresis will probably not affect the overall water balance but will have a significant effect on the comparison of the simulated discharges with the measured discharges as may be clear from the above paragraph. Hysteresis can conveniently be taken into account via a Jones correction. This may be important for operational forecasting as the measured discharges may be used for state updating of the SOBEK model via Ensemble Kalman Filtering (see for instance Warmink, 2007).
The effect of the hysteresis on the water balance of one flood for section 12 Wesel-Rees has been investigated. Also the effect of Jones correction on the comparison of the simulated and measured discharge has been investigated. The Jones formula (see Appendix Ogink and Stolker, 2004) is given by
1
(1
)
rch
Q Q
Sc t
with Q = actual discharge (m3/S)Qrc = discharge according to rating curve (m3/s) S = energy slope (-) at constant discharge c = celerity flood wave (m/s)
h = water level (m) t = time (s)
The hysteresis effect is maximal when the water level gradient ( h/ t) is at its maximum (rising limp) or minimum (falling limp). Ogink and Stolker (2004) show that the parameters of the Jones correction change with water level. At Lobith, the celerity c varies between 1.2-1.8 m/s and also changes with rising and falling of the flood wave. The energy slope (at constant discharge) varies with water level between 0.55*10-4 at 9.5 m and 1.25*10-4 at 16.5 m. Based on their analyses, Ogink and Stolker (2004) were able to derive a relationship for 1/Sc for Lobith as a function of the water depth:
0.976 1
74910H
Sc
with:
H is the water depth (m).
Table 3.1. Parameters Jones formula Wesel and Rees together with an indication of the maximal effect for rising and falling limp
Location S x 10-4 (-) c (m/s) max ( h/ t) x10-4 (m/s) max ( h/ t) x10-4 (m/s) Q/Qrc Q/Qrc
Rising Falling Rising Falling
Wesel 1.4 1.40 0.36 -0.17 1.09 0.95
Rees 1.0 1.15 0.36 -0.19 1.11 0.93
Figure 3.6/Table 3.2 and Figure 3.7/Table 3.3 show the effect of the Jones correction of two major flood peaks (1998 & 2003) on the water balance. The effect on the water balance is indeed negligible. However, there is a shift in the measured discharge during the rising limb of the flood peak in the order of 200-300 m3/s and -200 m3/s for the falling limb.
If the Jones correction is applied to moderate discharge peaks the Jones correction it seems to improve the comparison of the measured discharge and the simulated discharge as show in Figure 3.8. For these moderate flood peaks the difference between the measured rating curve and the simulated rating curve is not as large as is the case for the higher flood peaks. Thus, apparently differences at higher flood peaks are caused by factors other than hysteresis.
Note that for the calculations in this report dh/dt was calculated using a backward difference scheme. This is probably also the reason why the discharge series is very noisy. A better way of calculating dh/dt is (Slats et al., 1986) to use a central difference scheme
( ) ( )
2
dh h t t h t t
dt t
and for the first element to use a forward difference scheme
( ) ( )
dh h t t h t
dt t
and for the last element to use a backward difference scheme
( ) ( )
dh h t h t t
03/11/98 03/11/98 04/11/98 05/11/98 9000 9200 9400 9600 9800 10000
10200 Discharge at Rees - adjusted upper boundary
Dis charge ( m 3/ s) Qcal hysteresis Qcal QH QH hysteresis
Table 3.2. Overview water balance section 12: Wesel-Rees for the flood period of 1998 (in Bm3=109m3) based on measurements (QH) and two SOBEK simulations (QcalQ, laterals from calibration set) and (QhbvQ, laterals from HBV mixed set). indicates the difference between results obtained using the calibration set and the HBV mixed set (HBV-cal). QcalL and QhbvL (in Mm3=106 m3) are the laterals from the calibration set and the HBV mixed set, respectively.
Section 12: Wesel – Rees
Flood period: 03/11/1998 02:00 – 05/11/1998 11:00 Water balance from derived discharges
without hysteresis Wesel & Rees with hysteresis Wesel & Rees
Average volume (Bm3) Average volume(Bm3) Wesel 2.00 1.99 Rees 1.99 1.99 Sum of Laterals 0.08 0.08 I+SoL-O1 0.08 0.08
Water balance from SOBEK calculations
without hysteresis Wesel with hysteresis Wesel
Average volume (Bm3) Average volume(Bm3) QcalQ QhbvQ QcalQ QhbvQ Wesel 2.00 - - 1.99 - -Rees 2.07 - - 2.07 - -Sum of Laterals 0.08 - - 0.08 - -I+SoL-O1 0.01 - - 0.00 - -Overview laterals Average volume (Mm3) Average volume (Mm3) QcalL QhbvL QcalL QhbvL Schermbeck 76.47 76.47 0 76.47 76.47 0 LowRhine3b 0 6.06 6.06 0 6.06 6.06 Sum of Laterals 76.47 82.52 6.06 76.47 82.52 6.06
05/01/03 06/01/03 06/01/03 07/01/03 9000 9200 9400 9600 9800 10000 10200 10400 10600
10800 Discharge at Rees - adjusted upper boundary
Dis charge ( m 3/ s) Qcal hysteresis Qcal QH QH hysteresis
Table 3.3. Overview water balance section 12: Wesel-Rees for the flood period of 1998 (in Bm3=109m3) based on measurements (QH) and two SOBEK simulations (QcalQ, laterals from calibration set) and (QhbvQ, laterals from HBV mixed set). indicates the difference between results obtained using the calibration set and the HBV mixed set (HBV-cal). QcalL and QhbvL (in Mm3=106 m3) are the laterals from the calibration set and the HBV mixed set, respectively.
Section 12: Wesel – Rees
Flood period: 05/01/2003 05:00 – 07/01/2003 20:00 Water balance from derived discharges
without hysteresis Wesel & Rees with hysteresis Wesel & Rees
Average volume (Bm3) Average volume(Bm3) Wesel 2.28 2.28 Rees 2.23 2.23 Sum of Laterals 0.09 0.09 I+SoL-O1 0.14 0.13
Water balance from SOBEK calculations
without hysteresis Wesel with hysteresis Wesel
Average volume (Bm3) Average volume(Bm3) QcalQ QhbvQ QcalQ QhbvQ Wesel 2.28 - - 2.28 - -Rees 2.36 - - 2.36 - -Sum of Laterals 0.09 - - 0.09 - -I+SoL-O1 0.01 - - 0.00 - -Overview laterals Average volume (Mm3) Average volume (Mm3) QcalL QhbvL QcalL QhbvL Schermbeck 86.47 - - 86.47 - -LowRhine3b 0 - - 0 - -Sum of Laterals 86.47 - - 86.47 -
25/12/95 28/12/95 01/01/96 04/01/96 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400
Discharge at Rees - adjusted upper boundary
Dis ch ar ge (m 3/ s) Qcal hysteresis Qcal QH QH hysteresis
Figure 3.8 Measured discharge at Rees without Jones correction (black solid line) and with Jones correction (black dashed line) versus simulated discharge at Rees without (blue solid line) and with (blue dashed line) Jones correction upper boundary.
3.3
Effect of groundwater module
3.3.1 Overall
In Phase 2, it was concluded that in the current SOBEK model groundwater is a large net contributor to the discharge of the Rhine. To further investigate this issue first an overview of the effect of the groundwater module on the SOBEK simulation is given followed by an analysis of the effect of the groundwater module on the water balance of two flood periods and one low flow period. SOBEK simulations with the section 1 model Maxau-Lobith with the groundwater model switched off have been carried out with an observed discharge as upper boundary and calibration and HBV set used for the laterals. Table 3.1 of the phase 2 report (Weerts and Mens, 2007) provides an overview of all the models with and without modelled groundwater interaction.
Kaub-main river increases as well. For the section Bonn-Köln (Figure 3.10), the behaviour is different (difference is mainly negative) and the groundwater is a net contributor of water to the river (see also Weerts and Mens (2007)). This effect is even stronger in the next section Köln-Düsseldorf (see also Weerts and Mens (2007)). The results for the sections downstream of Düsseldorf are too much influenced by the section Köln-Düsseldorf to indicate a specific contribution or loss of those sections. However, it can be observed that the groundwater module lowers the discharge at Lobith during a flood and increases the discharge at intermediate and low flows.
Figure 3.12. Difference in simulated discharge of the SOBEK model without and with the groundwater (blue line, left y-axis) together with the measured discharge (black line, right y-axis). The red line (left y-axis) denotes zero difference.
Figure 3.13 shows the difference in the simulated water levels between the SOBEK model without and with the groundwater module on the simulated water levels at Lobith. With the groundwater module the simulated water level during dry periods is 0.20-0.40 cm higher than without groundwater module. With the groundwater module the simulated water level during a flood is maximal 0.20 cm lower than without groundwater module. This is further illustrated by Figure 3.14 and Figure 3.15 that show a close up of the simulations with and without groundwater module of a flood event (November 1998) and low flow event (September-October 2003). A more general picture is given by Figure 3.16 where the correlation between the difference in discharge between the SOBEK simulations with and without groundwater model and the measured discharge at Lobith and the correlation between the difference in water level between the SOBEK simulations with and without groundwater model at Lobith are given.
Figure 3.15. SOBEK simulated water level without (blue line) and with the groundwater module (magenta line) together with the measured water level for the low flow event of September-October 2003.
3.3.2 Flood periods
The effect of the groundwater module on the simulated flood peaks and on the water balance during those flood peaks is shown in Figure 3.17/Table 3.4 and Figure 3.18/Table 3.5. The calculations have been done with the model for section 9: Köln-Düsseldorf (see Table 2.1). This section was chosen because it showed the largest influence on the water balance over the period 1/11/1997-31/10/2004 (see Weerts and Mens, 2007).
The groundwater module lowers the amount of water during a flood peak with approximate 0.4% of the measured discharge QH, which is about 36-50 m3/s. Assuming this is the average effect of the groundwater module per section, the groundwater module accounts for a maximum lowering of the discharge of about 320-450 m3/s at Lobith. From Figure 3.12 and Figure 3.16 it can be observed that this is a good estimate of the total effect of the groundwater module during a flood period.
withGroundwater without Groundwater
02/11 03/11 03/11 04/11 04/11 8200 8400 8600 8800 9000 9200
Measured and simulated discharge Duesseldorf 1998
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 02/110 03/11 03/11 04/11 04/11 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 1998
date Vol um e ( m 3) QhbvQ-QH QcalQ-QH 02/11 03/11 03/11 04/11 04/11 8200 8400 8600 8800 9000 9200
Measured and simulated discharge Duesseldorf 1998
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 02/110 03/11 03/11 04/11 04/11 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 1998
date Vol um e ( m 3) QhbvQ-QH QcalQ-QH
Table 3.4. Overview water balance section 9: Köln-Düsseldorf (in Bm3/y=109m3/y)based on discharges derived from rating curves (QH) and two SOBEK simulations QcalQ (using the laterals , QcalL, from calibration set) and QhbvQ ( using the laterals, QhbvL, from HBV mixed set) with and without the groundwater.
Section 9: Köln – Düsseldorf
Flood period: 02/11/1998 12:00 – 04/11/1998 14:00 Water balance from SOBEK simulations with groundwater
Average volume
(Bm3/y) Average volume relative to QH Düsseldrof (%)
QcalQ QhbvQ QcalQ QhbvQ
Köln 1.60 1.60 0.00 100.30 100.30 0.00
Düsseldorf 1.62 1.62 0.00 101.68 101.98 0.29
Sum of Laterals 0.02 0.03 0.01 1.45 1.97 0.52
I+SoL-O1 0.00 0.00 0.00 0.07 0.29 0.22
Water balance from SOBEK calculations without groundwater Average volume
(Bm3/y) Average volume relative to QH Düsseldorf (%)
QcalQ QhbvQ QcalQ QhbvQ
Köln 1.60 1.60 0.00 100.30 100.30 0.00
Düsseldorf 1.62 1.63 0.01 102.06 102.62 0.56
Sum of Laterals 0.02 0.03 0.01 1.45 1.97 0.52
I+SoL-O1 0.00 -0.01 0.00 -0.31 -0.35 -0.05
1I =inflow upstream, O=outflow downstream, SoL=Sum of Laterals.
withGroundwater without Groundwater
04/01 05/01 05/01 06/01 06/01 07/01 8200 8400 8600 8800 9000 9200 9400
Measured and simulated discharge Duesseldorf 2003
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 04/01 05/01 05/01 06/01 06/01 07/01 0 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 2003
date Vol um e ( m 3) QhbvQ-QH QcalQ-QH 04/01 05/01 05/01 06/01 06/01 07/01 8000 8500 9000 9500
Measured and simulated discharge Duesseldorf 2003
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 04/01 05/01 05/01 06/01 06/01 07/01 0 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 2003
date Vol um e ( m 3) QhbvQ-QH QcalQ-QH
Table 3.5. Overview water balance section 9: Köln-Düsseldorf (in Bm3/y=109m3/y)based on discharges derived from rating curves (QH) and two SOBEK simulations QcalQ (using the laterals , QcalL, from calibration set) and QhbvQ ( using the laterals, QhbvL, from HBV mixed set) with and without the groundwater.
Section 9: Köln – Düsseldorf
Flood period: 04/01/2003 09:00 – 07/01/2003 06:00 Water balance from SOBEK simulations with groundwater
Average volume
(Bm3/y) Average volume relative to QH Düsseldrof (%)
QcalQ QhbvQ QcalQ QhbvQ
Köln 2.24 2.24 0.00 100.16 100.16 0.00
Düsseldorf 2.26 2.27 0.01 101.15 101.49 0.34
Sum of Laterals 0.03 0.03 0.01 1.17 1.52 0.36
I+SoL-O1 0.00 0.00 0.00 0.17 0.19 0.02
Water balance from SOBEK calculations without groundwater Average volume
(Bm3/y) Average volume relative to QH Düsseldorf (%)
QcalQ QhbvQ QcalQ QhbvQ
Köln 2.24 2.24 0.00 100.16 100.16 0.00
Düsseldorf 2.27 2.28 0.01 101.57 101.97 0.40
Sum of Laterals 0.03 0.03 0.01 1.17 1.52 0.36
I+SoL-O1 -0.01 -0.01 0.00 -0.25 -0.29 -0.04
1I =inflow upstream, O=outflow downstream, SoL=Sum of Laterals.
3.3.3 Low flow period
withGroundwater without Groundwater 24/09 26/09 28/09 30/09 02/10 04/10 650 700 750 800 850
900 Measured and simulated discharge Duesseldorf 2003
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 24/09-2 26/09 28/09 30/09 02/10 04/10 -1 0 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 2003
date V ol um e (m 3) QhbvQ-QH QcalQ-QH 24/09 26/09 28/09 30/09 02/10 04/10 650 700 750 800
850 Measured and simulated discharge Duesseldorf 2003
date QhbvQ (simulated) QcalQ(simulated) QH (measured) 24/09-2 26/09 28/09 30/09 02/10 04/10 -1 0 1 2 3 4 5x 10
7 Accumulated difference Duesseldorf 2003
date V ol u m e (m 3) QhbvQ-QH QcalQ-QH
Figure 3.19. (a left) Measured discharge (black line, QH) versus SOBEK with the groundwater module simulated discharge using the calibration set (magenta line, QcalQ) and the HBV mixed set (cyan line, QhbvQ) at Düsseldorf, (b left) accumulated difference at Düsseldorf for both the calibration set and the HBV mixed set, (a right) Measured discharge (black line, QH) versus SOBEK without groundwater module simulated discharge using the calibration set (magenta line, QcalQ) and the HBV mixed set (cyan line, QhbvQ) at Düsseldorf, (b right) accumulated difference at Düsseldorf for both the calibration set and the HBV mixed set.
Table 3.6. Overview water balance section 9: Köln-Düsseldorf (in Bm3/y=109m3/y)based on discharges derived from rating curves (QH) and two SOBEK simulations QcalQ (using the laterals , QcalL, from calibration set) and QhbvQ ( using the laterals, QhbvL, from HBV mixed set) with and without the groundwater.
Section 9: Köln – Düsseldorf Flood period: 24/09/2003 – 04/10/2003
Water balance from SOBEK simulations with groundwater Average volume
(Bm3/y) Average volume relative to QH Düsseldrof (%)
QcalQ QhbvQ QcalQ QhbvQ
Köln 0.59 0.59 0 95.16 95.16 0.00
Düsseldorf 0.66 0.66 0.00 107.11 106.98 -0.13
Sum of Laterals 0.02 0.02 0.00 2.82 3.29 0.47
I+SoL-O1 -0.06 -0.05 0.00 -9.13 -8.54 0.59
Water balance from SOBEK calculations without groundwater Average volume
(Bm3/y)
Average volume relative to QH Düsseldorf (%) QcalQ QhbvQ QcalQ QhbvQ Köln 0.59 0.59 0 95.16 95.16 0.00 Düsseldorf 0.60 0.60 0.00 97.47 97.94 0.46 Sum of Laterals 0.02 0.02 0.00 2.82 3.29 0.47 I+SoL-O1 0.00 0.00 0.00 0.50 0.51 0.01
3.3.4 Hysteresis effect versus effect of the SOBEK groundwater module
It was shown that the effect of the Jones correction and the groundwater module on the discharge is of the same order (+/- 300-500 m3/s, see Table 3.1 and Figure 3.12). For completeness, Figure 3.20 shows the effect of hysteresis versus the effect of the groundwater module at Lobith for the flood peak of 1995. The simulations were done using the model for section 1: Maxau-Rhine branches (see Table 2.1). Note that in Figure 3.20 the large difference between the measurement and the models are mainly caused by the large difference between measured rating curve and the rating curve of the SOBEK model.In the rising limb, the Jones correction has a large effect on the measured discharge. This correction gradually becomes less, because the rate of change of the water level decreases. In the falling limb the sign of the rate of change is negative and discharge is affected negatively. Overall the Jones correction has no effect on the water balance. In contrast, the higher the water level (and therefore discharge) the more water is lost to the groundwater, when the water level drops the loss of water stops and both simulations are almost the same. During low flow periods water flows from the groundwater to the river. In other words, the groundwater module affects the water balance for low flow periods and flood periods.
3.4
Effect hydro factors
3.4.1 Overall water balance
The sum of laterals (SoL) used to calculate the water balance based upon the measurement as shown in Table 2.3 are calculated by making use of hydro factors. The hydro factors are (1) used to correct for basin area that is ungauged and lies between the measurement station and the outflow location to the river model. For example Rheinzabern which covers only a small area of the lateral UpRhine1 is multiplied with 11.02 to account for the basin area that is ungauged. Using such factors might be wrong because the characteristics of the gauged area might be different from the ungauged area. Therefore the effect of the hydro factors has been investigated by putting all hydro factors to unity.
Table 3.7 shows the water balance error per section and cumulated on the basis of measurements with and without hydro factors. When the hydro factors are not used the total water balance error based upon the measurements decreases by a factor of 3.7. Note that for the section 5/6: Kaub - Andernach the SoL increases (due to the hydro factors smaller than 1) and gives rise to an increase of the water balance error.
It is clear that putting all hydro factors to unity is rather extreme. However, this gives an idea about the total effect of the hydro factors. An other option that may be worth investigating in the future is the effect of putting the hydro factors of the point lateral inflows to unity and keeping the hydro factors of the diffuse inflows as they are or leaving these areas away at all (hydro factors = 0).
Table 3.7. Water balance error per section (I+SoL-O) (Bm3/y) together with the cumulated water balance error (Bm3/y) based upon the measurements for the whole period 1/11/1997-31/10/2004 both with and without the use of hydro factors. Note that I is inflow upstream, SoL is sum of lateral inflows, and O is outflow downstream.
1/11/1997 – 31/10/2004 Period
with hydro factors without hydro factors
3.4.2 Laterals section Speyer-Worms
Table 3.8 shows the effect of removing the hydro factors of the calibration set on the sum of laterals for section 2: Speyer-Worms. In other words, all laterals have been put to unity. From this table, it can be observed that the effect of removing the hydro factors for this section is small for both the complete overview period and the flood period of 1998. Therefore, the effect on the water balance will also be very small for this section.
Removing the hydro factors or adjusting them will only shift the complete curve up or down. In Appendix C of the Phase 2 report (Weerts and Mens, 2007), it is shown that the dynamics of the calibration set and HBV mixed set do not match very well. Adjusting the hydro factors will not improve the dynamics of the calibration or HBV mixed set. Another way of improving the comparison of the HBV simulations and calibration set is to adjust pcorr values in the HBV model on the basis of the water balance result of this study. By adjusting the pcorr value the water balance of the HBV simulation can be affected including the dynamics of the HBV simulation.
Table 3.8. Overview effect hydro factors on the Sum of Laterals of the calibration set (QcalL) of Section 2: Speyer – Worms for the overview period 1/11/1997-31/10/2007 and a flood period of 1998.
Period 1/11/1997-31/10/2007 21/03/2002 22:00 – 23/03/2002 21:00 Lateral hydro factor with hydro factors (Bm3/s) without hydro factors (Bm3/s) with hydro factors (Mm3/s) without hydro factors (Mm3/s) Ubstadt 2.48 0.09 0.04 3.13 1.26 Meckesheim 2.1 0.14 0.07 4.32 2.06 NE1 Itter 1.66 0.07 0.04 2.61 1.57 NE1 (ZWEI) 1.18 0.05 0.04 1.85 1.57 NE1 (ZWEII) 1.13 0.05 0.04 1.77 1.57 NE1 (ZWEIII) 0.07 0.00 0.04 0.11 1.57 NE1(ZWEIV) 0.69 0.03 0.04 1.08 1.57 NE1 (ZWEV) 0.65 0.03 0.04 1.02 1.57 Wiesloch 2.03 0.05 0.03 1.34 0.66 Monsheim 4.24 0.13 0.03 3.52 0.83 Rockenau 1 4.93 4.93 253.85 253.85 Sum of Laterals -5.56 5.33 274.61 268.08
3.5
Calibration set vs. HBV simulations larger tributaries
enough rain gauges and therefore the interpolated rainfall is too low. This results in a negative relative volume difference. At Grolsheim, Königstrasse and Kalkofen the opposite is the case. Apparently, too much rainfall is produced here that results in a positive relative volume difference. The large error for Grolsheim is caused by errors in the rainfall data that have not been removed (validation).
The simulation at Neubrück (Erft) is influenced by an initial value of the lower zone (2250 mm) that is much too high. This problem was already discovered by Renner (2007). The result of this very high initial value of the lower zone is shown in Figure 3.21.
Errors during peaks can be as large as 1250 m3/s for Cochem. This is probably also caused by a lack of rain data in the upper Mosel area. The maximum error for Rockenau is also very large.
Table 3.10 shows the effect of switch from the HBV mixed set to a set based solely on HBV simulations (HBV only set). From this table, it can be observed that by a switch from the mixed HBV set to a HBV only set the effect on the water balance will not be very large. In some section there is a larger impact (due to the Main, Nahe and Sieg). But difference in the different section balance each other out in downstream direction.
Table 3.9. Overview statistical information regarding the large tributaries of the Rhine. The Nash-Sutcliffe Efficiency (NSE) is given together with the relative volume difference (QhbvL-QcalL)/QcalL, the maximal and mean absolute difference of QhbvL-QcalL.
Jan970 Dec97 Dec98 Dec99 Dec00 Dec01 Dec02 Dec03 Dec04 50 100 150 200 NeubrueckQcal m3 /s Qcal Qhbv
Jan970 Dec97 Dec98 Dec99 Dec00 Dec01 Dec02 Dec03 Dec04 2 4 6x 10 9 V ol um e ( m 3) cumsum(Qhbv-Qcal)
Figure 3.21. (a) Calibration set lateral versus HBV set lateral for Neubrück, (b) accumulated difference between simulation and measurement.
Table 3.10. Overview of differences between the Sum of Laterals from the calibration set and HBV mixed set and the calibration set and the HBV only set all for the period 1/11/1997 – 31/10/2004.
Measurement station River Km Differences
SoL QcalL and SoL QhbvL (HBV mixed set)
(Bm3/y)
Differences SoL QcalL and SoL from a HBV only set
4
Conclusions & Recommendations
4.1
Conclusions
4.1.1 Model and rating curves
Large differences are visible when the rating curve of the model is compared with the measured rating curve. These errors are caused by extrapolation of the measured rating curve and by not taking into account hysteresis in the measured rating curve. The measured rating curves have a very large effect on the calculated water balance.
The current SOBEK model represents only one situation of the river geometry. This and other errors (bathymetry/calibration/lateral inflow) are visible when the model results are compared with the measurements. As a result of the errors in the model and errors in the measured rating curve, there are large differences present when comparing the measured discharge to the model simulations.
4.1.2 Hysteresis
Hysteresis is not taken into account in the measured rating curve. This can be taken into account via a Jones correction. The maximum correction can be in the order of +/-7-10% of the discharge. The maximum water level gradient occurs mostly during intermediate floods (3000-5000 m3/s for the lower Rhine) when the water is in the main channel. Therefore, the maximum Jones correction is in the order of about 400-500 m3/s. Differences between the model and the measurements during the flood peaks of 1998 & 2003 can not be improved by a Jones correction. The Jones correction, as expected, did not influence the water balance results. However, the Jones correction seems to improve the comparison of the model and measurements during an intermediate flood.
4.1.3 Groundwater module
4.1.4 Hydro factors
When the hydro factors are not used (all put to 1) the water balance error based upon the measurements over the period 1/11/1997-31/10/2004 decreases by a factor of 3.7. The effect of the hydro factors on the sum of laterals for Section 2: Speyer-Worms is relatively small. This is the case for the period 1/11/1997-31/10/2004 and also during a flood period (2002). Changing the hydro factors will not improve the comparison of the calibration set with the HBV set because the dynamics of the simulated discharge curve (HBV set) is not affected. The effect of putting the hydro factors to unity for section 2 has a small effect on the water balance of this section.
4.1.5 HBV simulations large tributaries
The HBV simulations Grolsheim (Nahe), Kalkofen (Lahn), Menden (Sieg), Opladen (Wupper), and especially Neubrück (Erft) are not very good. The simulation for Neubrück (Erft) is affected by a very high initial value of the Lower Zone (2250 mm). The HBV simulations of the other tributaries are either affected by too much or not enough rainfall (possible due to interpolation/rain gauge density). The maximum difference between model and measurements are also very high (>1000m3/s) for Cochem (Mosel) and Rockenau (Neckar) probably also due to problems with the interpolated rainfall (interpolation/rain gauge density).
The effect of using the simulations of the large tributaries instead of the measured values on the water balance will overall be relatively small. This is due the fact that difference in the different sections balance each other out in downstream direction. However, for some sections this effect might be considerable due to large differences in lateral inflow in these sections (section 3 (due to the Main), 4 (due to the Nahe) and 8 (due to the Sieg)).
4.2
Recommendations
4.2.1 Measured Rating Curves
The measured rating curves have a very large impact on the calculated water balance. Large errors are probably present in the rating curves of the key measurement stations. The calibration of the SOBEK models largely depends on these rating curves. And the rating curves are also used during operational forecasting (e.f for updating procedures such as error correction and Ensemble Kalman Filtering). Therefore, it is recommended to check all rating curves of the key measurement stations along the Rhine and also the rating curves of the lateral inflow. Such a study must take into account all knowledge available
about the (changing) river geometry;
about the changes of the rating curves in the past; about the discharge measurements at different stages; backwater effects;
4.2.2 Jones Correction
Applying the Jones correction for calibration purposes and during operational forecasting for improving the model input (upper model boundary) and visual comparison of the model results with the (Jones corrected) measured discharge is also recommended. The Jones correction can easily be taken into account using the formulas in Chapter 3.2. The water depth dependent energy slope and wave celerity can be determined using the approach of Ogink and Stolker (2004).
4.2.3 River Groundwater Interaction
Groundwater interaction was introduced during the calibration model Andernach-Lobith (Barneveld and Meijer, 1997) to obtain a better agreement between the SOBEK simulations and the measured water levels during flood periods. The currently used SOBEK groundwater module shows also significant influence on the water balance during low flow periods leading to a lowering of the simulated water level of 0.2 -0.4 m. The question remains how large the interaction between the Rhine and groundwater is. Therefore, it is recommended to further study this exchange of water and to study the way the interaction is modelled. Section 9 showed the most groundwater interaction and may therefore be the most interesting section to conduct such an investigation.
Section 12, 13, and 14 may also be interesting to look at. Here the overall water volume decreases in downstream direction, indicating that there might be a loss of water from the river to the groundwater and then flowing paralleling the direction of the river or from the Niederrhein to the IJssel.
River groundwater interaction is not only occurring in the Lower Rhine. It is also a phenomenon that takes place near the mouth of the Neckar. So it may be worthwhile, given the point above, to look at the whole river and to see where this river groundwater interaction might be important.
4.2.4 Hydro factors
Another important issue affecting the water balance are the hydro factors. Critical evaluation of the hydro factors is necessary as they have an effect on the water balance. Several options can be explored such as
setting all hydro factors diffuse inflows to zero; setting all hydro factors point inflows to 1; combination of the above;
etc;
4.2.5 SOBEK model
As was shown the SOBEK simulations of the water level deviated from the measured water levels. It is also clear that several measured rating curves have been changed in the past indicating changes in the river bathymetry. Updating the river bathymetry of the model for the present situation (for instance for operational forecasting) is necessary. This will lead to several models valid for different periods.
4.2.6 HBV model
Several issues related to the HBV model were detected and need improvement:
Sub basin Neckar5 stays relatively wet leading to too much discharge of the Itter and the ZWE1-5 (Eberbach);
Erft has a very large lower zone, the initial value of the lower zone in the operational system is too high leading to too much discharge at Neubrück;
Problems exist with the interpolated rainfall in the operational system. This rainfall deviates too much from the rainfall used for calibrating the model leading to large differences between the HBV simulations and the calibration set.
4.2.7 Maintenance plan SOBEK and HBV model
The SOBEK model is used in an operational forecasting system and it is also being used in several other management studies. It is therefore likely that the SOBEK and HBV model will be used in the future. It is recommended to make a maintenance plan to regularly check all points raised above. This maintenance plan must contain a schedule when the all items need checking and updating (regularly for instance every 5 years and occasionally after a major event). The items that need to be included are:
Evaluation of measured rating curves (key measurement stations & lateral inflows); Evaluation of the input to the SOBEK and HBV models;
Updating the SOBEK model (river bathymetry, calibration, etc);
5
References
Barneveld, H.J. and Meijer, D.G., 1997. SOBEK-model Andernach-Lobith, Model construction, calibration
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Kroekenstoel, D.F., 2003. Calibratie interne grondwatermodule SOBEK-model Andernach-Lobith, RIZA
Memo WSR 2003-027 (in Dutch).
Lammersen, R., 2006. Waterbalans FEWS Rijn 2.05, RIZA Memo WRR 2006-018 (in Dutch).
Mens, M.J.P., A.H. Weerts and H.J.M. Ogink, 2006. Water balance Maxau – Rhine branches. Phase 1: Data
collection and description of methods. WL | Delft Hydraulics report, Q4231, commissioned by RIZA-RWS.
Ogink, H.J.M. and C. Stolker, 2004. Verbetering Qf-relaties. WL | Delft Hydraulics report, Q3847,
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Renner, M., 2007. Low flow prediction at the Rhine. Quality of simulation and forecasts using the hydrological
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Slats, G.N., N. Booij and H.R. Vermeulen, 1986. Voorspellingsmodel voor hoogwater op de Rijn. TH Delft,
WW440, commissioned by RWS (in Dutch).
van der Veen, R., 2004. SOBEK-Rijn versie 2004.1 en 2004.2, RIZA Memo ADV 2004-003(A) (in Dutch). van der Veen, R., 2005. Bouw SOBEK-model FEWS Rijn 2.03 and 2.04, RIZA Memo WRR 2005-024 (in
Dutch).
Warmink, J., 2007. Data assimilation in FewsNL-Rhine, WL | Delft Hydraulics report, Q4141.
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(in Ducth), WL | Delft Hydraulics report, Q3558, commissioned by RIZA-RWS.
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