Low flow modelling of the Meuse Recalibration of the existing HBV Meuse model
Document title Low flow Modelling of the River Meuse Recalibration of the existing HBV Meuse modelling Document number 2005.123X Status Final thesis Date October 2005
Author Martin Arends Under supervision of University Twente, Civil Engineering and Management, Section Water Engineering &management, Enschede, The Netherlands & Ministry of Transport, Public Works and Water Management, Directorate-general for Public Works and Water Management,Institute for Inland Water Management and Waste Water Treatment (RIZA), Arnhem, The Netherlands Committee of counsellors Dr. M.S. Krol (UT) Dr.ir. M.J. Booij (UT) Dr. M.J.M. de Wit (RIZA)
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Voorwoord Dit onderzoek is uitgevoerd als afsluitende doctoraalopdracht van de opleiding Civiele technologie en Management aan de Universiteit Twente. Het onderzoek is uitgevoerd bij het Rijksinstituut voor Integraal Zoetwaterbeheer en Afvalwaterbehandeling. Met veel plezier en trots kijk in terug op een voor mij geslaagde afstudeerperiode. Speciale dank gaat uit naar mijn begeleiders, Marcel de Wit, Maarten Krol en Martijn Booij. Mede dankzij hun goede adviezen, aanbevelingen en inzet is dit rapport tot stand gekomen.
Acknowledgements Rijkswaterstaat Direction Limburg provided the discharge data for Borgharen/Monsin. The discharge data for the Walloon stations has been provided by MET-Sethy. The meteorological 1968-1998 dataset is based on data from KMI and MeteoFrance and has been prepared by the Royal Meteorological Institute of the Netherlands (KNMI). Martijn Booij and Willem van Deursen calibrated the HBV model for the Meuse.
Page 3 of 104 Voorwoord
Low flow modelling of the Meuse Page 4 of 104
Samenvatting De Maas heeft een totale lengte van 875 kilometer en stroomt van zijn bron in Frankrijk naar de monding in Nederland. Het stroomgebied heeft een gematigd klimaat met een door neerslag en verdamping geregeerd afvoer patroon. De rivier levert water voor huishoudelijke, industriële, agrarische en scheepsvaart doeleinden. Vele verandering zijn in de rivierloop aangebracht om deze functies door het gehele jaar zo goed mogelijk te kunnen vervullen. Hoog- en laagwaters zijn natuurlijk voorkomende fenomenen die grote invloed kunnen hebben op deze functies. (Berger 1992) Dit onderzoek richt zich op laagwaters in het gedeelte van het stroomgebied bovenstrooms van Borgharen.
Het doel van dit onderzoek is het ontwikkelen van een nieuw HBV model dat beter instaat is om lage afvoeren te voorspellen zonder dat dit ten koste gaat van de voorspelling van normale en hoge afvoeren. Het gebruikte HBV model is ontwikkeld door het Zweedse Meteorologische en Hydrologische Instituut. De gebruikte schematisatie voor de Maas is ontwikkeld door Booij (2002) en aangepast door Van Deursen (2004). Deze schematisatie bevat geen sluizen, stuwen, reservoirs of andere menselijke ingrepen. Tijdens de calibratie uitgevoerd door Van Deursen is gebruik gemaakt van statistische criteria, de standaard R en de Nash-Sutcliffe coëfficiënt. Dit heeft geresulteerd in een goed werkend hydrologisch model voor normale en hoge afvoeren, Nash-Sutcliffe van 0.92. (Deursen, 2004) De kwaliteit van de laagwatervoorspellingen is echter een stuk lager.
Tijdens dit onderzoek is er een nieuwe set calibratie criteria opgesteld om de laagwater kwaliteit te meten. De uiteindelijke lijst bevat de volgende criteria • Totale afvoerdeficit tijdens de calibratie periode • Nash-Sutcliffe coëfficiënt voor lage afvoeren • Gesommeerde absolute fout in het afvoerdeficit Deze criteria zijn gebruikt tijdens de calibratie en validatie van het model.
De tijdens dit onderzoek gebruikte parameters beïnvloeden grondwaterprocessen en zijn niet gebruikt tijdens de Booij and Van Deursen calibraties. De volgende parameters zijn gebruikt; • k4, recessie coëfficient voor het langzame afvoer reservoir • perc, percolatie van het snelle naar het langzame afvoer reservoir
Omdat deze parameters invloed hebben op lange termijn processen moet tijdens de calibratie ook naar de lange termijn invloed van veranderingen in deze parameters worden gekeken. Daarom is er gebruik gemaakt van een “moving average” van de gemeten debieten over een periode variërend tussen de 41 en 9 dagen.
Calibratie heeft plaatsgevonden door voor verschillend k4 en perc waarden de uitkomsten van de verschillende criteria te bepalen. Vervolgens is de stapgrote verkleind tussen de parameter waarden waar de beste uitkomsten waren behaald. Dit is herhaald tot er een optimum gevonden was. Tijdens de eerste calibratie stappen bleken de invloeden van variaties van k4 en perc een grote onderlinge afhankelijkheid te vertonen. Het afvoerdeficit in combinatie met de absolute fout gemaakt in dit afvoerdeficit zijn de twee belangrijkste criteria geweest tijdens de calibratie. De Nash-Sutcliffe coëfficiënt voor lage afvoeren heeft gediend om de kwaliteit te controleren van de voorspellingen van de dagelijkse afvoeren tijdens perioden met een lage afvoer. De veranderingen in de k4 en perc waarden hebben de algehele model prestatie niet negatief beïnvloed, dezelfde Nash-Sutcliffe coefficient is behaald als voor het Van Deursen model.
Page 5 of 104 Samenvatting
De invloed van reservoirs op de laagwaterafvoeren is onderzocht door de situatie in de Vesdre te bestuderen. De Vesdre is het stroomgebied met relatief gezien de grote invloed van de aanwezige reservoirs. Door middel van een post processing van de modelresultaten is de invloed van de aanwezige reservoirs onderzocht. Dit onderzoek wees uit dat een model met reservoir beter resultaten kent dan een model zonder reservoir. De resultaten voor de Vesdre hadden waarschijnlijk beter kunnen zijn indien er informatie beschikbaar was geweest over de manier waarop de reservoirs beheerd worden. De verschillen tussen het model met en zonder reservoir zijn dermate klein dat gekozen is om met een model zonder reservoir verder te gaan. Dit omdat de transparantie van het geheel een stuk groter is zonder post-model processen. De verschillen die dit veroorzaakt in de resultaten voor Monsin zijn relatief klein.
De uiteindelijke calibratie en validatie resultaten tonen een behoorlijke verbetering van de laagwatervoorspelling wanneer gekeken wordt naar de lange termijn. De dagelijkse voorspellingen zijn, ook met de nieuwe afregeling onder de maat. Een van de verklaringen hiervoor is de aangebrachte kunstwerken in de Maas. Deze beïnvloeden de lage afvoeren in grote mate. De onttrekkingen tussen Borgharen en Monsin spelen hierin ook een grote rol.
Het uiteindelijke gesimuleerde afvoerdeficit voor Chooz is nagenoeg perfect wanneer wordt gekeken naar het deficit over de gehele validation periode. Wanneer gekeken wordt naar individuele jaren zijn er nog steeds afwijkingen. Voor Monsin zijn de resultaten minder goed, maar ze vertonen hetzelfde patroon als voor Chooz. De afwijkingen voor individuele jaren zijn echter groter, zowel relatief als absoluut. De afwijkingen lijken samen te hangen met voorafgaande natte jaren. De hoeveelheid data is echter te klein om hier bindende uitspraken over te doen.
Het uiteindelijke model kan gebruikt worden voor het voorspellen van afvoerdeficiten. De resultaten moeten echter wel kritisch bekeken worden alvorens ze worden toegepast. De voorspellingen van individuele afvoeren gedurende laag water perioden is iets beter geworden echt deze is onvoldoende om met enige nauwkeurigheid gebruikt te kunnen worden. De gevonden optimale parameter waarden vertonen een sterke relatie met de karakteristieken van de deelstroomgebieden. Gebieden met snelle en grote afvoerfluctuaties hebben andere parameter waarden dan gebieden met relatief kleine en langzame afvoerfluctuaties.
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Abstract The river Meuse has a length of 875 kilometres from its source in France to its mouth in The Netherlands. The basin of the river has a temporate climate with a rainfall-evaporation regime. It supplies water for domestic, industrial, agricultural and shipping uses. Many alternations have been made to fulfil these functions as best as possible throughout the year. Floods and low flows are natural phenomena, which can have a major impact on the functions the river fulfils. This research focuses specifically on low flows in the river part upstream of Borgharen.
The aim of this research is to develop a new HBV Meuse schematisation that better simulates low flows without influencing the simulation of high and normal flows. The HBV model used was developed by the Swedish Meteorological and Hydrological Institute. The schematisation used was developed by Booij (2003???) and modified by Van Deursen (2004). This schematisation does not include locks, weirs, reservoirs or other man made alternations. During the calibration, carried out by Van Deursen, statistical criteria where used, being the Standard R2 and Nash-Sutcliffe coefficient. This resulted in a proper working hydrological model that predicts normal and high discharge really well, Nash-Sutcliffe value of 0.92 during validation. The low flow predictions of the model are of a lesser quality.
During this research a new set of calibration criteria has been developed to evaluate the model performance during low flows. The final list of criteria used during calibration and validation consists of; • Discharge deficit • Nash-Sutcliffe coefficient for low flows • Accumulated absolute error in the discharge deficit
During this research parameters that influence groundwater processes have been used. Van Deursen did not use these parameters during his research. These parameters are; • k4, recession coefficient or slow runoff reservoir • perc, drainage from fast to slow runoff reservoir Because these parameters influence long-term processes the influence of changing should also be looked over a longer period. Therefore for some of the criteria a moving average has been used, varying between 41 and 9 days.
Calibration was carried out by calculating the scores of the three different criteria for different k4 and perc settings and reducing the step size between the different k4 and perc values in the area(s) with the highest scores. The discharge deficits for both thresholds in combination with the absolute error in these discharge deficits were the two most important criteria during calibration. The Nash-Sutcliffe coefficient for low flows has been used to make sure the performance of the individual daily discharges during low flow did not decrease during the calibrations. The changes of k4 and perc values have not influenced the normal and high flows; the same Nash-Sutcliffe coefficient was realized as in the Van Deursen model.
The influence of reservoirs on low flows has been researched by calibrating the Vesdre with different reservoir-operating regimes. A relatively simple post-model process was used for this and resulted in better results with a reservoir in place. However the result for the discharge deficit and absolute error in the discharge deficit were small. To keep the model transparent and as simple as possible the setting without the reservoir was used during the rest of the research. Results could probably have been better if more information about the reservoirs had been available.
The final calibration results show an improvement of the low flow on a long term. The daily discharge simulations of the model are still poor. The results for Chooz are better than the results for Monsin (and Borgharen). This can be explained by the man-made alternations and
Page 7 of 104 Abstract
abstractions. The bifurcations between Borgharen and Monsin influence the measured data by abstracting large quantities of water. During a large part of the research the correction for these abstractions is unreliable.
The simulated discharge deficits for Chooz are almost perfect when looking at the entire validation period, the individual years however still show deviations. The deviations for Monsin show the same pattern as the Chooz deviations, but are somewhat larger. The main deviations occur in 1989 and 1990 and seem to be related to the preceding wet years. The amount of data however is too small to be completely sure of this.
The final model can be used to predict discharge deficits for different thresholds. The model should not be used to predict individual daily discharge or even multiple daily discharges during periods of low flow, the errors made are relatively large. The final parameter settings are strongly related to the characteristics of the sub basins. Sub basins with a fast and relatively large discharge fluctuations have different parameter settings than sub basins with relative small and slow discharge fluctuations.
Low flow modelling of the Meuse Page 8 of 104
Table of contents Voorwoord ...... 3 Samenvatting...... 3 Abstract...... 3 Table of contents ...... 3 Chapter 1 Introduction ...... 3 Chapter 2 Description of the River Meuse ...... 3 2.1 Introduction ...... 3 2.2 River basin ...... 3 2.3 Description of the main tributaries upstream of Borgharen...... 3 2.4 Discharges and precipitation...... 3 2.5 Human interference ...... 3 Chapter 3 Current HBV Meuse model ...... 3 3.1 HBV model...... 3 3.2 Calibration parameters...... 3 3.3 Schematisation of Meuse basin ...... 3 3.4 Measured data ...... 3 3.5 Reservoirs...... 3 3.6 Current calibration criteria...... 3 3.7 Current results for Monsin for the Van Deursen criteria...... 3 Chapter 4 Calibration criteria ...... 3 4.1 Demands on new calibration criteria...... 3 4.2 Preliminary list of criteria...... 3 4.3 Critical threshold ...... 3 4.4 Results of preliminary list ...... 3 4.5 Discussion of potential criteria ...... 3 4.6 Final list of criteria ...... 3 4.7 Moving average ...... 3 Chapter 5 Calibration procedure...... 3 5.1 Calibration and Validation period en procedure...... 3 5.2 Calibration procedure...... 3 Chapter 6 Calibration and validation results ...... 3 6.1 Introduction ...... 3 6.2 Results first calibration steps Chooz...... 3 6.3 Calibration and validation results for Chooz ...... 3 6.4 Calibration and validation results for the Vesdre reservoirs...... 3 6.5 Calibration and validation results for the main tributaries ...... 3 6.6 Calibration and validation results for Monsin and Borgharen...... 3 6.7 Conclusions about calibration and validation entire model ...... 3 Chapter 7 Discussion and conclusions ...... 3 7.1 Discussion of errors and uncertainties...... 3 7.2 Discussion calibration procedure ...... 3 7.3 Conclusions ...... 3 7.4 Recommendations ...... 3 References ...... 3 List of figures ...... 3 List of tables...... 3 Appendix I...... 74 Appendix II...... 78 Appendix II...... 90
Page 9 of 104 Table of contents
Chapter 1 Introduction
During the summer of 2003 the Netherlands suffered a serious drought. The problems that arose during this drought brought the low water issues of the Netherlands under the attention of a broader audience. When looking at historical discharge data of the Meuse and Rhine, the situation of 2003 was not at all exceptional. The discharge can drop much lower and for a longer period as well, for example during the summer of 1976 (De Wit, 2004). When looking at the minimum discharge the summer of 2003 takes the 13th place of the last one hundred years. Despite this the situation was called critical, resulting in social turbulence. Analyses of historical discharge data do not reveal a trend towards more or less extreme low flow periods. Chances of a more severe drought occurring in the next couple of years are considerable. Therefore it is important to be better prepared for longer periods of low flows.
The Institute for Inland Water Management and Waste Water Treatment (RIZA) is currently working on a flood early warning system (using Delft-FEWS) for the Netherlands. The goal of this system is to predict water levels and discharges a couple of days in advance. The FEWS system combines hydrological and hydraulic models. For the Meuse the HBV Meuse model will be used to predict to amount of discharge. The current HBV Meuse model has been developed by Booij and been improved by Van Deursen. For the FEWS model to work properly the HBV model needs to make proper prediction for all discharges. The current HBV model has been calibrated using statistical criteria, standard R and Nash-Sutcliffe. Resulting in a proper working model for high and normal flows. However the model performance for low flows is relatively unknown. This research has been carried out to determine the low flow performance of the Model calibrated by Van Deursen and, if possible, improve the low flow performance of the model without influencing the high and normal flows.
Goal The goal of this research is to; improve the performance of the low flow output of the existing HBV Meuse model for the river part upstream of Borgharen without decreasing the overall model performance.
This goal has been split up in several research questions; these questions have been incorporated in the research plan. The three most important questions are;
1. Which parameters, not previously used during calibration, are most suitable for calibration of low flows?
2. Based on which criteria and period will the calibration take place?
3. Based on the calibration and validation results what can be said about the reliability and performance of the model during low flows?
Content The first part of this report, chapter two, describes the general characteristics of the river Meuse, and its tributaries, upstream of Borgharen. These general characteristics include a rough description of the riverbed, the mean gradient, mean (minimum) discharges and precipitation. The discharge pattern of the total chatchment is illustrated by for two specific years, 1976 and 1978, representing an extremely dry year and a normal year. Special attention is given to human interferences in the river; reservoirs, locks and weirs, abstractions and bifurcations.
The first research question is answered in Chapter three. The chapter begins with a general description of the HBV model, including the parameters that will be used during the calibration. Than the schematisation of the catchment(s) and the way the human alternations
Low flow modelling of the Meuse Page 10 of 104
have been incorporated in the Van Deursen model are presented. Special attention is given to the Vesdre reservoirs and the measured discharges. The last part of this chapter presents and explains the calibration criteria used by Van Deursen and gives the results for these criteria for the Van Deuresen model.
The criteria used by Van Deursen do not pay special attention to low flows. To calibrate the model for low flows a special list of potential criteria has been developed, this list is presented in chapter four. Chapter four also consists of the results for all these potential criteria, calculated for different k4 and perc settings. After the presentation of these results a final choice is made, resulting in three criteria that will be used during calibration. The calibration period and procedure are presented in chapter five.
The preliminary calibration results for Chooz are presented in first part of chapter six and show a strong correlation between the two parameters used during calibration. The rest of the chapter consists of the calibration results for; Chooz, Monsin, the Vesdre (reservoirs), the Lesse, the Ourthe and the Amblève. The final research question is answered in chapter seven. The uncertainties and limitations of the model and their origins are discussed. Final conclusions about possible improvements and recommendations about the use of the model are also made in this final chapter.
Page 11 of 104 Introduction
Chapter 2 Description of the River Meuse
2.1 Introduction The river Meuse is a rain fed river, which supplies water for domestic, industrial, agricultural and shipping uses. The river, and its riverbed, fulfils many ecological and recreational functions. Floods and low flows are natural phenomena, which can have a major impact on the functions the river fulfils. Many human settlements have been built in the favourable conditions of its floodplains. However the positions of these settlements cause troubles during floods. The benefits of the use of the floodplains of the river Meuse should be balanced with the risks associated with the use. A good understanding of the hydrology of the Meuse is needed to make up this balance. (Berger, 1992)
2.2 River basin The river Meuse, with a total length of 875 kilometres, flows form its source in Poulliy-en- Bassigny in France to its mouth the Holandsch Diep in The Netherlands. Its basin has a size of roughly 33.000 km2 divided over France, Luxemburg, Belgium, Germany and The Netherlands. This study focuses on the part upstream of Borgharen. The most important tributaries of this part of the river are; the Chiers, the Semois, the Viroin, the Lesse, the Sambre and the Ourthe and downstream of Borgharen the Roer, the Niers and the Dieze. The tributaries upstream of Borgharen will be closer looked at in the next paragraph. The basin has a temperate climate, with rivers that are dominated by a rainfall-evaporation regime, which generally produces high flows during winter and low fows during summer.
Generally the basin is divided into three hydrological zones; • The Upper reaches (Meuse Lorraine or Lotharingian Meuse), from the source at Poulliy- en-Bassigny to the mouth of the Chiers. Here the catchment is lengthy and narrow, the gradient is small and the major bed is wide. • The central reaches of the Meuse (Meuse Ardennaise or Ardennes Meuse) leading form the Chiers to the Dutch border near Eijsden. The main tributaries being the Viroin, Semois, Lesse, Sambre and Ourthe. • The lower reaches of the Meuse, corresponding with the Dutch part of the river. The lower reaches themselves may be split into the stretches from Eijsden to Maasbracht and from Maasbracht to the mouth. In the former part the slope is still relatively large, for this reason it is occasionally reckoned to be part of the Meuse Ardennaise. The stretch that forms the border between Belgium and The Netherlands is called the Grensmaas. Below Maasbracht the river is provided with weirs to make it navigable. The main tributaries are the Roer, Niers and Dieze. In the Roer reservoirs are found, providing a certain minimum discharge. From Boxmeer the river is a typical lowland stream, with summer dikes, flood plains and winter dikes. Figure 2-1 Meuse basin
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Figure 2-2 Gradient of the Meuse and its main tributaries, (Berger 1992)
Figure 2-2 shows the gradient of the river Meuse and its main tributaries. It clearly shwos the differences between the tributaries. Tributaries springing in the Ardennes/Eiffel Massif (Semois, Viroin, Lesse, Ourthe, Amblève, Vesdre, and the upper reaches of the Rur) have the largest gradients, up to 5 m km-1. The effects this has on the characteristics of the tributaries will be discussed in paragraph 2.3. The effects of changes in the floodplain will be discussed in this paragraph.
The floodplain of the river changes from South to North. In the Southern part of the basin the Meuse flows through a hilly landscape with wide floodplains. Here the Meuse is partly regulated by weirs and partly flanked by a lateral canal. Even during an average flood a wide floodplain gets inundated. These inundations cause a weakening of the flood. This explains why flooding events in the southern part of the Meuse basin often do not cause serious problems in the central and northern part of the Meuse basin.
In the central part of the Meuse basin, between Charleville-Mézières and Liège, the Ardennes Massif captures the Meuse. In this stretch the Meuse is completely regulated, the width of the floodplain varies between 200 and 2000 meters. Between Borgharen and Maasbracht there are no weirs and a lateral canal flanks the river. Further north the Meuse is regulated with weirs and becomes a typical lowland river with a small gradient. Downstream of Boxmeer the river is embanked. (Berger 1992)
2.3 Description of the main tributaries upstream of Borgharen The tributaries of the Meuse supply the greater part of its discharge. Ground water, precipitation and artificial extractions constitute the discharge to a smaller extent. The Meuse has a great number of tributaries, varying largely in size. The characteristics of the largest tributaries upstream of Borgharen are presented in Table 2-1. The ‘Outhe total’ catchment consists of the Vesdre, Amblève and Ourthe catchments.
Page 13 of 104 General description
Table 2-1 Main tributaries of the Meuse (Berger, 1992)
Tributary Size (km2) Gradient Mean discharge Mean annual (m3/s) Precipitation (mm) Chiers 2,222 1.0 * 10-3 27 859 Semois 1,358 1.5 * 10-3 27 1139 Viroin 593 2.0 * 10-3 6.9 940 Lesse 1314 5.0 * 10-3 16 954 Sambre 2863 0.7 * 10-3 28 825 Ourthe (total) 3,626 Vesdre 677 8.0 * 10-3 9.4 1104 Amblève 1.052 5.0 * 10-3 19 1104 Ourthe 1.597 3.7 * 10-3 23 968
2.3.1 Discharges and characteristics of the tributaries Table 2-2 shows the relation between the mean annual minimum discharge and the mean daily discharge. It also shows the impact the reservoirs have on the discharge. From this relation characteristics of the different tributaries can be derived. The Mehaigne and the Chooz have relative large MAM discharge compared to their MD discharge indicating a relatively high base flow and slow reaction to precipitation. The Ourthe, Lesse and the Vesdre have a much smaller relative MAM discharge; this is in accordance with the characteristics described by Berger (1992). Appendix I-1 contains a rough characterisation of discharge fluctuation of the different tributaries. (Uijlenhoet, 2001) The results are in accordance with Table 2-2.
Table 2-2 Characteristics of minimum discharges and reservoirs for different tributaries.(Uijlenhoet, 2001)
Catchment MDD MD MAMD RD MAMD/MDD (MAMD- (m3/s) (m3/s) (m3/s) (m3/s) [-] RD)/MDD [-] Lesse 17,4 0,6 2,1 0 12% 12% Chooz 147,0 10,2 26,0 0,2 18% 18% Mehaigne 2,5 0,4 0,8 0 31% 31% Ourthe total 51,1 2,8 8,4 2,4 16% 12% Vesdre 10,3 0,6 2,7 1,7 26% 10% Amblève 18,6 1,6 3,1 0,5 17% 14% Ourthe catchment 22,2 0,6 2,6 0 12% 12% Ourthe Occident 6,9 0,5 0,8 0 12% 12% Ourthe Orientale 5,3 0,3 0,6 0 12% 12% Borgharen 227,0 1,0 9,9 4,5 4% 2%
Note; MDD = Mean daily discharge MD = Minimum discharge MAMD = Mean annual minimum discharge RD = Reservoir discharge Ourthe total = Vesdre plus Amblève plus Ourthe catchment Ourhte occidental = Part of Ourthe catchment Ourhte Oriental = Part of Ourthe Catchment
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Table 2-2 clearly shows the influences of manmade structures and artificial abstractions on the size of the discharge during low flows. The reservoirs in the Ourthe catchment have on the mean annual minimum discharge is significant, more than 25 % of the MAM discharge comes from the reservoirs. The bifurcations between Monsin and Borgharen have a large influence on the low flows at Borgharen. When the abstractions from these bifurcations are ignored the discharge would be much higher and the ratios would be around 12 percent.
2.4 Discharges and precipitation The river Meuse has relatively high floods and low base flows, due to its character as a rain- fed river. Both the floods and the low flows may cause damage to shipping, agriculture, inhabitants, etcetera. The damage can be reduced significantly if it is known what discharges and water levels will occur. (Berger 1992) The average discharge of the Meuse at Borgharen is approximately 230 m3/s, 270 m3/s at Monsin. Between Monsin and Borgharen several canals abstract large quantities of water, causing a large difference between the “natural” discharge at Monsin and the discharge at Borgharen. Paragraph 2.5.3 looks at these abstractions in detail.
The design discharge at Borgharen has been estimated at 3800 m3/s with a change of occurrence of once every 1250 years. The mean annual minimum discharge at Borgharen is approximately 10 m3/s. (Uijlenhoet, 2001)
Hydrograph Monsin 1978 1200
1000
800
600
400
200 Mean daily discharge (m3/s)
0 1-1 29-1 26-2 26-3 23-4 21-5 18-6 16-7 13-8 10-9 8-10 5-11 3-12 31-12 Time (ddmm) Discharge critical boundary
Figure 2-3 Hydrograph of the discharge at Monsin of a average year (1978)
Figure 2-3 shows the discharge at Monsin in 1978, which was a reasonably average year. The total discharge was 7.76 106 m3 while the average annual discharge is approximately 8.3 106 m3. The number of days with a discharge lower than 60 m3/s was 44, average is approximately 33 (Uilenhoet, 2001). The discharge clearly shows a period with high flows and a period with low flows. It also shows that between different discharge peaks the discharge drops quite strongly, corresponding with the characteristics of a rain fed river. During the low flow period, starting at the end of July, the discharge fluctuates quit strongly on a daily bases. However when looking at a longer period the discharge remains relatively stable. The different reasons for these fluctuations will be closer looked at in paragraphs 2.4.4 and further.
Page 15 of 104 General description
2.4.1 Precipitation The average precipitation amounts to 800 to 900 mm per year. The Northern part of the basin with more than 1000 mm per year is slightly wetter than the Southern part with around 700 to 800 mm per year. The average discharge at the outlet (Hollands Diep) is approximately 350 m3/s, this corresponds with a precipitation surplus of almost 400 mm per year. (De Wit, 2002). The precipitation is evenly divided over the year.
Figure 2-4 shows the precipitation in 1978 in the Meuse basin. The precipitation is evenly distributed throughout the year. The evapotranspiration clearly has a large influence on the discharge.
Figure 2-4 Average precipitation in Meuse basin upstream of Borgharen, during an ‘average’ discharge and precipitation year (1978),
2.4.2 Floods A flood arises when in a short period of time, approximately ten days, the amount of precipitation in the catchment is high. During floods the discharge can increase to 15 to 20 time the mean discharge. The greatest known discharge ever measured at Borgharen was 3000 m3/s during the floods of 1926 and 1993. For precipitation to cause a flood there will have to be a minimum amount of 30-40 mm within a few days. The amount of precipitation needed dependents among other things on snowmelt, moisture content of the soil and geological components. As far as the Netherlands are concerned the discharge at Borgharen is normative. In the Netherlands the term “flood” is used if the discharge is exceeds the critical discharge of 1450 m3/s, which happens approximately once every two years. (Berger, 1992)
2.4.3 Low flows After a period of little if any precipitation the discharge of the Meuse is can drop below 50 m3/s at Monsin (North of Liège, before branching off of the Albertkanaal). In the Netherlands such a situation is formally called low flow. In case of low flows Monsin will generally be taken as the reference station instead of Borgharen because the discharge at the latter is no longer the undivided Meuse discharge. In the periods of low flows the Albertkanaal, the Zuid- Willemsvaart and the Julianakanaal extract a considerable percentage of water, so that at Borgharen the Meuse only receives a part of the Monsin discharge. The situation between
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Monsin and Borgharen will be closer looked at in paragraph 2.5.3 abstractions and bifurcations.
During the low flow period of 2003 the lowest measured discharge of the undivided Meuse (Monsin) was 40 m3/s. During the low flow period of 1976 this was around 20 m3/s. When only looking at minimum discharge records 2003 takes the 13th place of the last century. Also the number of days with a discharge smaller than 60 m3/s was not extreme. This is striking because not only the Dutch part of the catchment was suffering a drought but also the Belgian and French parts of the catchment. The explanation for this may lie in the preceding wet winter, resulting in relatively full groundwater reservoirs. The most extreme low flow periods of the last century, 1921 and 1976, had dry preceding winter periods, resulting in lower groundwater reservoirs. Generally one can say that a dry winter followed by a dry summer causes extreme low flow periods and a wet winter followed by a dry summer causes less extreme periods of low flow. (De Wit, 2004)
Hydrograph Monsin 1978 & 1976 1200
1000
800
600
400
200 Mean daily discharge (m3/s)
0 1-9 13-10 24-11 5-1 16-2 30-3 11-5 22-6 3-8 14-9 26-10 7-12 1976 1978 Time (ddmm)
Figure 2-5 Hydrograph of 1978 and 1976, an average and extremely dry year
Figure 2-5 shows the hydrographs of 1978 and 1976 and the preceding four months. The figure clearly shows the large differences in both the discharge pattern and amount between the two years. In 1976 the largest discharge peak is small, less than 700 m3/s, while in 1978 the largest peak is about 1100 m3/s. The difference in the total amount of discharge is striking 7,76 109 m3 in 1978 and only 2,35 109 m3 in 1976. In the Monsin catchment the amount of precipitation was 986 mm in 1978 and only 613 mm in 1976. The difference between the amounts of precipitation is much smaller than between the discharges. This can be explained by the evapotranspiration, only the precipitation surplus runs off. When the precipitation drops and the evapotranspiration stays roughly the same the total runoff will decreases with the same amount as the precipitation. A normal year has a surplus of almost 400 mm.
2.4.4 Discharge fluctuations Mosnin The measurements at Monsin show an irregular discharge pattern, Figure 2-6. Large differences between consecutive days exist while the weekly average discharge remains constant. For the calibration process it is important to get a good understanding of the causes of fluctuations and their sizes. When natural processes cause the fluctuations the
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model should be able to predict the same daily fluctuations. Figure 2-6 shows the fluctuations in the mean daily discharge of 1978 during a period of eight weeks. The precipitation used in this figure corresponds to the entire catchment. The discharge at Chooz is shows less fluctuations than the discharge at Monsin. This indicates that these fluctuations are caused by human interferences in the river. These human interferences can be; weirs and locks, reservoirs (power plants), bifurcations, abstractions and artificial discharges. The next paragraph deals with these human interferences.
Hydrograph 1978
150 14
125 12
100 10
8 75
6 50
Discharge (m3/s) 4 Precipitation (mm/day) 25 2
0 0 16/09 23/09 30/09 07/10 14/10 21/10 28/10 04/11 11/11
Time (dd-mm) Precipitation Chooz Monsin
Note; The precipitation used in this figure corresponds to the average of the entire Meuse basin. The average precipitation upstream of Chooz has roughly the same pattern
Figure 2-6 Hydrograph of 1978, showing fluctuations in daily discharges for Chooz and Monsin during a eight week period, starting September 16th 1978.
2.4.5 Precipitation during low flow During summer the discharge of the Meuse depends on the amount of precipitation, the evapotranspiration and the amount of water present in the groundwater system. After a period of little, if any precipitation, the soil gets dryer and the storage capacity will increase. When precipitation occurs the storage capacity will first be filled and only when this capacity is reached direct runoff will occur. (Bergström, 1998) However in reality direct runoff can occur without the storage capacity being reached. This can occur when the precipitation intensity is higher than the infiltration capacity or from impermeable surfaces. The real infiltration capacity is not a constant and depends on the amount of storage capacity that is being used.
During summer small rainfall events occur that have a high enough intensity to produce direct runoff. These small rainfall events cause fluctuations in the discharge. Another natural cause of the fluctuations is the time peaks need to reach Borgharen. Peaks from different tributaries do not take the same amount of time to reach Borgharen. This causes irregular discharge patterns.
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2.5 Human interference The river network of the Meuse has been affected by human activities ever since the first settlements. Agriculture, forestry and urbanisation have changed hydrological processes that relate to soil conditions and land cover, such as infiltration and evapotranspiration. However, the overall effect of these changes on the regime of the Meuse is not unequivocal and hard to quantify. Far more pronounced are the human impacts on the river network itself. Over large stretches the river has been regulated, deepened, and canalised. Weirs, locks, canals and reservoirs have been constructed all over the Meuse. All these river works have been motivated by the need to use the river as a reliable source for water supply, electricity production and navigation. Especially during low flows these river works have a strong impact on the discharge regime of the Meuse. (De Wit, 2002)
2.5.1 Weirs and locks The locks and weirs that are present in the river, and in its tributaries, have a large influence on the discharge, especially during low flows. Weirs have been constructed to maintain a minimum water depth during low flows. Construction of weirs does not change the total amount of discharge over a long period, for example a year. It only influences the discharge when the weir settings are changed. When the settings are changed the equilibrium depth changes, resulting in a shortage or surplus of water above the weir. In case of a shortage the discharge will temporarily drop and slowly increase again. These shortages or surplus will have short-term effects on the discharge. During periods of low flow the weirs will all be closed. The main effect of the weirs on the discharge then comes from the losses through the use of the locks. In parts where the river is navigational locks have been built to give ships the opportunity to pas the weirs. The lockage of ships causes losses of water. These losses differ from day to day; especially the difference between week and weekend days is significant, and cause fluctuations in the discharge.
2.5.2 Reservoirs and power plants Some of the tributaries contain one or more reservoirs, which of course influence the floods and low flows. The effects on the total amount of discharge during a year are small. Appendix I-2 contains a list of the important reservoirs in the upstream part of the Meuse basin. However this list contains only very rough information. No information is available about the actual operating regime of these reservoirs. During low flows these reservoirs may have a significant influence on the discharge.
Some of the reservoirs were built specially to supply power plants with water. These power plants often need a minimum amount of water to generate electricity. This causes irregularities in the discharges. Especially the power pant at Lixhe just upstream of Borgharen, this plant needs a minimum feed of 10-15 m3/s. During periods of low flows the discharge at Borgharen is strongly influenced by this plant. (Berger 1992)
2.5.3 Bifurcations between Monsin and Borgharen Another reason for the daily discharge fluctuations are the bifurcations between Monsin and Borgharen. These bifurcations have been built for navigation and water supply in Flander and the Southern part of the Netherlands. Figure 2-7 gives a schematic picture of the situation. The three most important canals are the Albertkanaal, the Julianakanaal and the Zuid-Willemsvaart. The Albertkanaal, finished in 1939, connects Liège with Antwerp and the Schelde. The Julianakanaal, finished in 1935, connects Maastricht and Maasbracht and the Zuid-Willemsvaart, built in the 19th century, connects Maastricht and ‘s Hertogenbosch. (Berger, 1992)
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Figure 2-7 Schematic picture of the canals between Monsin and Borgharen. (Berger,1992)
2.5.4 Meuse discharge treaty In 1995 Belgium and the Netherlands signed the Meuse discharge treaty (Maasafvoerverdrag), an agreement about the amount of water flowing through canals and the Grensmaas. Table 2-1 shows the discharge distribution regulated in this treaty. The basic principle of this agreement is the equal distribution of water between The Netherlands and Belgium, in such a way that the Grensmaas has a discharge of at least 10 m3/s. This agreement regulates all flows below 130 m3/s at Monsin. However even with this treaty it is difficult to predict the flow at Borgharen.
Table 2-3 Distribution of Meuse water during periods with low flow, regulated in the Meuse discharge treaty. (Raadgever 2004)
Undivided Meuse Underspend (avg Discharge Belgian use Dutch use discharge (m3/s) number of days per Grensmaas (m3/s) (m3/s) (m3/s) year) 130 > 100 60 35 35 100 92 50 25 25 60 33 10 25 25 30 2 10 10 10 20 0.2 6.7 6.7 6.7
During the largest part of this research period, 1968-1998, this treaty was not in place. The discharge through the individual canals is relatively unknown. This would not be a large problem if the discharges just before the first bifurcation and after the last were known. However the discharge at Monsin is unknown and is calculated using an estimation of the abstraction caused by the canals and the known discharge at Borgharen. This causes a large uncertainty in the input data of the model, especially during low flow situations. When the flow drops the distribution shifts, however the available information does not record this.
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Chapter 3 Current HBV Meuse model This chapter describes the current HBV model, which has been calibrated by Van Deursen, from this point on the current HBV model will be called Van Deursen model. The first paragraph gives a short description of the HBV model itself. The parameters used during calibration are described in paragraph two, the reason these parameters have been used is discussed as well. The third paragraph presents the schematisation used during the Van Deursen calibration. The measured data and its potential errors are presented in paragraph 4. The Vesdre reservoirs are studied in paragraph five to get a better understanding of the potential influence which reservoirs can have on discharges during low flows. The criteria used by Van Deursen are explained in paragraph six, the results for these criteria are presented in paragraph seven.
3.1 HBV model The HBV model used in this research is a conceptual hydrological model, developed by the Swedish Meteorological and Hydrological Institute (SMHI) in Norrköping, Sweden, by Bergström (1998). During this research the HBV96, version 4.4 was used. The HBV model simulates river discharge using precipitation, temperature and potential evapotranspiration as input and is semi-distributed, since differences can be made between areas with different altitudes and forested and non-forested areas. A basin can be divided into several sub basins.
The HBV model consists of 6 modules; • Precipitation routing; representing rainfall, snow accumulation and melt. • Soil moisture routine; determining overland and subsurface flow and actual evapotranspiration. • Fast runoff routine; representing storm flow • Base flow routine; representing base flow • Transformation routine; representing low flow delay and attenuation • Routing routine; flow through river reaches
Appendix II-1 and II-2 contain a detailed description of the parameters used by the HBV model and a description of the different modules of the HBV model.
3.2 Calibration parameters During his calibration Van Deursen did not use all HBV criteria, for most of them he used the default values. Appendix II-2 contains the complete list of HBV parameters, their meaning and a list of the parameters used by Van Deursen. During this research the following two parameters will be used;
K4 Recession coefficient for the slow runoff reservoir, the values must be between zero and one. When the value is one the entire slow discharge reservoir will be discharged in one day.
Perc Drainage from the fast runoff reservoir to the slow runoff reservoir. When enough water is present in the fast runoff reservoir an amount of water equal to perc will drain from the fast to the slow runoff reservoir.
These parameters have been not been previously used. These parameters have been chosen because of their influence on low flows. The influence on the normal and high flows will probably by small because these parameters have very limited influence on the fast runoff.
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3.3 Schematisation of Meuse basin The HBV Meuse model uses 15 sub catchments upstream of Borgharen. The schematisation is shown in Figure 3-1. This schematisation is the same as Van Deursen used during his research. This schematisation is slightly different from the schematisation used by Booij. The model does not include locks, weirs, reservoirs or other man made structures. For this research however the reservoirs are of special interest because of their ability to supply extra water during periods of low flow.
Legend;
1. Meuse source-St.Mihiel 2. Chiers 3. Meuse St. Mihiel-Stenay 4. Meuse Stenay-Chooz 5. Semois 6. Viroin 7. Meuse Chooz-Namur 8. Lesse 9. Sambre 10. Ourhte 11. Amblève 12. Vesdre 13. Mehaigne 14. Meuse namur-Borgharen 15. Jeker
Figure 3-1 Schematisation of the upstream parts of the river Meuse, used in the HBV model.
3.4 Measured data The measured data consists of daily average discharges, precipitation, temperature and potential evapotranspiration. However the data is not complete for all the sub basins. Appendix II-3 contains metadata about the measured discharges, precipitation, temperature and potential evapotranspiration.
3.4.1 Abstractions and bifurcations The river Meuse contains several large bifurcations between Monsin and Borgharen. These bifurcations abstract, and add, large amounts of water from the Meuse. These bifurcations and abstractions are not incorporated in the model, but the measured data is corrected for these abstractions. The same can and will be done if significant abstractions or artificial discharges exist.
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Comparing the discharge of Monsin and Borgharen will give information about the influence the bifurcations have on the fluctuations at Monsin. The discharge at Monsin however was not measured but calculated from the Borgharen discharge. For this calculation a correction factor was used. Until 1991 this factor is a contant for the entire year. The only exception is 1976, where a daily correction factor is available, presented in Figure 3-2.
Correctionfactor Borgharen - Monsin 1976
200
150 /s) 3 100
50
0 1-1 31-1 1-3 1-4 1-5 1-6 1-7 31-7 31-8 30-9 31-10 30-11 30-12 Correction factor (m -50
-100 Date (dd-mm)
Figure 3-2 Correction factor for the calculation of the Monsin discharge out of the Borgharen discharge, for the year 1976.
When the correction factor is constant the fluctuations seen at Borgharen will also be seen at Monsin. However when the correction factor is not constant the fluctuations for Monsin can be different from the ones at Borgharen. Figure 3-3 shows the discharge at Borgharen and Monsin in 1976. The Monsin discharge shows fewer fluctuations, especially from March until June. This supports the thesis that the fluctuations at Borgharen are, at least partly, caused by the bifurcations between Borgharen and Monsin.
Discharges of Borgharen and Monsin in 1976
700
600
500
400
300
Discharge (m3/s) 200
100
0 1-1 31-1 1-3 1-4 1-5 1-6 1-7 31-7 31-8 30-9 31-10 30-11 30-12
Date (dd-mm) Monsin Borgharen
Figure 3-3 Discharges of Borgharen and Monsin in 1976, measured data.
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3.4.2 Water balance between Chooz and Monsin The water balance check has been carried out to check the validity of the measurede data between Chooz and Monsin, especially during low flows. The difference between the measured discharge of Chooz and Monsin has been compared with the total discharge of the tributaries between Chooz and Monsin. Table 3-1 shows the size of the sub-basins between Chooz and Monsin and, if available, the average measured discharge. Only 45 percent of the contributing area consist of areas with a known discharge, this 45 percent contributes 58 percent of the discharge.
Table 3-1 Size of sub-basins between Chooz and Monsin.
Note; Areas do not have a measured discharge, total discharge is difference between Monsin and Chooz discharge, Ungauged data is difference between gauged and total.
Sub-basin Area size Average (1000 km2) Discharge (m3/s) Chooz Namur 11,4 - Lesse 13,1 17,3 Sambre (Flor./Salz.) 27,6 - Ourthe 16,0 22,0 Amblève 10,5 18,4 Vesdre 6,9 10,2 mehaigne 3,5 - Namur Monsin 15,5 -
Total 104,2 117,6 Gauged area 46,4 (45%) 67,8 (58%) Ungauged area 57,8 (55%) 49,8 (42%)
During floods the wave travel time between Monsin and Chooz is approximately 16 hours. During normal and low flows the velocity is smaller resulting in a longer travel time. For this research a travel time of 1 day has been used for the comparison between Chooz and Monsin and for the Lesse discharge. The other tributaries with a known discharge are all close to Monsin and do not need a correction. Comparing the discharges on daily bases does not consider the influence of fluctuations; therefore the comparison has been carried out using weekly totals.
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Table 3-2 shows the number of weeks that a specific range of differences occurs during the period 1968-1997. The largest part of the weeks is relatively close to the average. The table above shows the discharges for different stations. The difference between the average gauged data and the expected gauged discharge based on the difference for the entire period is presented in the last column. These differences are all between plus 15 and minus 18 m3/s.
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Table 3-2 Relative differences between gauged discharges and measured differences between Monsin and Chooz.
Note Discharge difference = gauged discharge divided by the measured difference between Monsin and Chooz
Discharge Number Avg Chooz – Avg gauged Avg 58% of Diff 58% and difference of weeks Monsin (m3/s) data (m3/s) Monsin Chooz Avg gauged data (m3/s) (m3/s) (m3/s) > 100 % 34 26 30 121 15 15 90% - 100% 23 47 45 162 28 17 80% - 90% 61 65 55 199 37 17 70% - 80% 180 91 67 241 53 14 60% - 70% 370 145 93 343 84 8 50% - 60% 450 125 67 239 73 -5 40% - 50% 307 100 46 200 58 -13 30% - 40% 128 70 25 128 40 -15 <30% 12 57 15 92 33 -18
3.4.3 Explanations The largest error occur during relative low flows, human interference is most of the errors occur during low flow, or even extreme low, flows one of the explanations can be the human interference. When locks and weirs are operated the water balance can be corrupted for a couple of days, influencing the weekly totals. Locks and weirs however do not explain a gap in the water balance between Chooz and Monsin for several consecutive weeks, for example in July 1974 the gauged discharge is higher than the difference between Chooz and Monsin during the entire month.
The discharges are measured using a relation between water level and discharge. This relation maybe incorrect when the discharge is low and weirs have a large influence on the water level. However these differences should then be structural. Meaning that the measured discharge is than always too large or too small. In this case however the discharges are both too small and too large.
The ‘measured’ discharge data at Monsin has not actually been measured at Monsin. The Monsin data has been constructed using the Borgharen discharge and correcting this discharge for the abstractions between Borgharen and Monsin. Until 1991 the correction factor is an average of the abstractions throughout the year(s), with exception of 1976. However these abstractions can be both smaller and larger influencing the difference between gauged discharges and the discharge difference between Monsin and Chooz. The data after 1991 do not show differences large than 86 %.
3.4.4 Conclusion validity discharge data Monsin The discharge data between Monsin and Chooz contains inconsistencies. The most reasonable explanations for these inconsistencies are the abstractions caused by the bifurcations between Monsin and Chooz and the influences that locks, weirs and other man- made structures have. Because the errors are within a range that can be caused by these man-made alternations all the available data for Monsin will be used. The results for Chooz and Monsin will be compared with the errors in the discharge in mind.
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3.5 Reservoirs The main goal of this research is to improve the performance of the Van Deursen HBV model for periods with relative low flows without influencing the high and normal flows. The Meuse catchment upstream of Borgharen contains several reservoirs. The available information about these reservoirs is limited to their size and an estimation of their discharge during periods of low flows.
Berger studied the influences of the reservoir operation on the discharge and discharge modelling. He focused on the error made by assuming the wrong reservoir operation, assuming a flood to be reduces while it is not, or vice versa. The error made by making such a wrong assumption can be large. For example if 50 % of the catchment is captured by a reservoir the modelled discharge can be of by a factor 3. (Berger 1992)
Berger proves that incorporating a reservoir into the HBV model can have a large influence on the performance of the model, especially when a wrong reservoir regime is used. Because the information about the reservoirs is very limited and because of the large influence they can have on normal and high discharges the existing reservoir will not be incorporated into the model. However the influence that reservoirs can have on low flows is important for the understanding of the models behaviour. The influence of the Vesdre reservoirs will be studied because these reservoirs have the largest discharges compared to the natural discharge during low flows.
3.5.1 Vesdre reservoirs The two Vesdre reservoirs have been built in 1876 and 1949 (heightened in 1971) and have a combined size of 51 106 m3 and have been build to supply waterworks and industries with water during periods of low flow. The two Vesdre reservoirs have a total contributing area of 160 km2, which is approximately 25 percent of the total catchment size of the Vesdre. The maximum peak flow reduction can therefore not be larger than 25 percent depending on the way the reservoir is operated. Most likely the discharge will not be blocked totally, so the reduction will be smaller than 25 percent. The reduction depends on the goal of the reservoir. During low flows the two reservoirs can provide a discharge of approximately 1.7 m3, compared to a mean annual minimum discharge of approximately 2.7 m3. During the most extreme days of the year these two reservoirs provide roughly sixty percent of the Vesdre discharge. (Berger 1992)
3.5.2 Model performance for individual months Under normal circumstances reservoirs are filled during the relative wet winter and spring and slowly release extra discharges during the dryer periods of the summer and autumn. This suggests that the modelled data should be slightly lower than the measured data during dry periods and slightly higher during wet periods.
Table 3-5 shows the average discharge during the different months of the year of the period 1968-1984. During the month July until December the model predicts too little discharge while predicting too much discharge during February until May. Depending on the control strategy of the reservoir this can indicate influence of the reservoir.
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Table 3.5 Average discharge during the year during the different months of the year.
Overall Jan Feb Mar Apr May Jun Jul Aug Sep Okt Nov Dec Meas avg 10,3 15,8 13,9 15,1 11,7 8,4 7,2 7,3 5,9 6,0 7,9 9,3 15,0 Model avg 10,5 16,3 15,7 16,8 13,3 9,4 7,5 7,0 5,7 5,5 6,8 8,2 14,0 Model/meas 102% 103% 113% 111%113% 112% 104% 96% 96% 92% 86% 88% 93%
Table 3-3 shows the Nash-Sutcliffe coefficient and the standard R coefficient for different months during the period of 1968-1984. Clearly the performance of the model is poorest in June, July and August. The standard R does show a correlation that is much higher than the Nash-Sutcliffe, this indicates that the model makes a structural error. This may well be explained by the presence of two reservoirs. Especially because of the larger influence the reservoirs can have on the low discharges than on the high discharges, up to 60 percent in comparison to a maximum of 25 percent.
Table 3-3 Nash Sutcliffe and standard R coefficients during different months of the year
All Jan Feb Mar Apr May Jun Jul Aug Sep Okt Nov Dec Nash-Sutcl. 0.79 0,80 0,77 0,75 0,82 0,65 0,22 0,45 0,46 0,67 0,73 0,76 0,82 Standard R 0.89 0,90 0,89 0,88 0,92 0,93 0,86 0,92 0,86 0,92 0,92 0,90 0,91
3.5.3 Conclusion Based on the above two tables the influence is not really clear. During the actual calibration of the Vesdre area two different reservoir-operating regimes will be compared and analyzed with a setting without a reservoir. This will be done with a simple post-model process, a spreadsheet program will be used to add an amount of discharge when the simulated discharge drops below a certain threshold, simulating the operation of a reservoir. This process will give an insight in the influence on the discharge of the Vesdre. This comparison will also be used to determine wetter or not other reservoirs should be looked at.
3.6 Current calibration criteria The criteria used by Van Deursen during his calibration process will also be used during this research. One of the preconditions of this research is that the performance during normal and high flows must not decrease. The Van Deursen criteria will be used to check this precondition. Van Deursen used the following four criteria;
• The water balance, accumulated runoff difference • Nash-Sutcliffe • Standard R • Visual comparison
The first three criteria, which are absolute values, can easily be calculated and compared with the value given in Van Deursen 2004. Visual comparison however is more difficult to duplicate. Therefore this criterion will not be use to check the precondition. The first three criteria will now be explained and the Nash Sutcliffe and standard R2 will be compared.
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3.6.1 Water balance This criterion gives the relative difference between the measured yearly discharge and the modelled yearly discharge. This criterion is the first to be looked at, when the amount of discharge is wrong the model will never describe reality in a proper way.
V −V 1 D = *100% 3-1 v V
Dv Relative difference between model and measurements [range - ∞ to 100%] V Measured average discharge [m3/s] V1 Modelled average discharge [m3/s]
This criterion can approach the perfect value of zero while at the same time the distribution of the discharge through the year can be completely wrong. When the average is used during the entire modelling period the water balance will be perfect. The criterion should only be used in combination with other criteria like the Nash-Sutcliffe coefficient and visual calibration.
Despite all this it is an important criterion; the water balance of the model should match with the measurements. The amount of precipitation and the sum of the discharge and evaporation should be the same, if not a correction should be made (Warmerdam). Good models have a value within a several percent of the measured value.
3.6.2 Nash-Sutcliffe coefficient The Nash Sutcliffe coefficient is a way to measure the overall performance of a model. It compares the measured values with the modelled and average values. The range of the Nash-Sutcliffe value ranges from -∞ to 1. When a model is worse than using the overall model values the NS value is less than zero. When it is better it is between zero and one, one being a perfect fit. Hydrologic model are considered to be good when the NS value is between 0.8 or higher.
n (Q − Q1 )2 2 ∑i=1 i i Rns =1− n 3-2 (Q − Q )2 ∑i=1 i a
R2 Nash-Sutcliffe coefficient [range -∞ to 1] n Number of days [-] 1 3 Qi Modeled discharge [m /s] 3 Qi Measured discharge [m /s] 3 Qa Average measured discharge [m /s]
3.6.3 Standard R The standard R is a normal and widely used correlation coefficient. It describes the relation between two datasets. Datasets that are perfectly correlated have a score of one. However a perfect correlation does not mean that the two datasets are identical. Structural difference will not interfere with the standard R value. These structural differences can be absolute as well as relative. Standard R given described by Poortema (2001);
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n [(Q −Q )*(Q1 −Q 1)] R = ∑i=1 i ai i ai n n 3-3 (Q − Q )2 (Q1 − Q1 )2 ∑i=1 i ai ∑i=1 i ai
R Standard R n Number of days [-] 1 3 Qi Modelled discharge [m /s] 1 3 Qai Average modelled discharge [m /s] 3 Qi Measured discharge [m /s] 3 Qai Average measured discharge [m /s]
3.6.4 Conclusion Van Deursen criteria The best way to look at calibration results is to look at both the Nash-Sutcliffe and the standard R. The standard R gives an inside in the correlation of the two datasets. When the correlation is high the two have the same behaviour, meaning that they increase and decrease at the same time with roughly the same amount. When only looking at the standard R however the absolute values of the two datasets do not have to be the same to create a perfect value. The Nash-Sutcliffe criterion demands that the datasets are identical before the perfect value of one is reached. Combining the two gives a good image of the direction that is needed to improve the model.
3.7 Current results for Monsin for the Van Deursen criteria In this paragraph the results of the Van Deursen model will be presented. The first part of this paragraph consists of the model results for the Van Deursen criteria; the second part consists of two hydrographs, which will pay special attention to an extreme dry year and a normal year. The current results will be presented for both Monsin and Chooz. During the rest of this research Monsin has been chosen instead of Borgharen because Monsin still has a “natural” discharge. In the schematisation used the difference between Monsin and Borgharen is the discharge of the Jeker and the abstractions caused by the bifurcations.
Chooz has been chosen because the discharge at Chooz is roughly half of the Monsin discharge and the character of the river upstream of Chooz differs from the character of the part downstream of Chooz. The number of man-made alternations upstream of Chooz is much smaller than the number upstream of Monsin. Therefore the discharge at Chooz is more natural and will give insight in the influence that man-made alternations have on the discharge at Monsin.
3.7.1 Water balance, Nash Sutcliffe and standard R
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Table 3-4 shows the Van Deursen model results for all three criteria used by Van Deursen during his calibration. The results for Chooz are marginally better results than the results for Monsin. An explanation for this may be the large number of manmade alternation between Chooz and Monsin, which have not been incorporated into the model. These manmade alternation cause unnatural discharge fluctuations which the model does not predict and therefore slightly decreases the Nash-Sutcliffe scores. Another reason may be the low flow errors that have been discovered in paragraph 3.4.2.
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Table 3-4 Van Deursen model results
Criterion Monsin Chooz Nash-Stucliffe 1968-1984 0.91 0.92 Nash-Stucliffe 1985-1998 0.93 0.94
Standard R 1968-1984 0.96 0.96 Standard R 1985-1998 0.97 0.97
Water balance 1968-1984 - 4,3 % + 4,9 % Water balance 1985-1998 - 1,1 % 0,0 %
3.7.2 Monsin hydrographs 1976 and 1978 The hydrographs of 1976 and 1978 give an indication of an extreme dry year and an average year. Figure 3-4 shows that the discharge peaks before the summer of 1976 are predicted very well. The model and measurements show very little deviation. During the dry period the modelled discharge keeps on going down, while the measured discharge shows a steady discharge with a even a slight increase. Clearly the relative difference between model and measurements is quite large. Also the model predicts much more discharge during the first peak after the dry period. These two errors seem to indicate that the (slow) groundwater and infiltration possesses have not been modelled properly.
Hydrograph 1976
700
600
500
400
300
200 Discharge (m3/s) 100
0 jan feb mrt apr mei jun jul aug sep okt nov dec
Time (dd-mm) Measured Model
Figure 3-4 Hydrograh Mosnin 1976
Figure 3-5 shows the hydrograph of Monsin in 1978, an average year. Again the model predicts the discharge peaks pretty well, but seems to make a relatively large error predicting the low summer discharges. Again the model predicts a decline of the discharge while the measurements show a steady discharge
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Hydrograph 1978
1400
1200
1000
800
600
400 Discharge (m3/s) 200
0 jan feb mrt apr mei jun jul aug sep okt nov dec
Time (dd-mm) Measured Model
Figure 3-5 Hydrograph Monsin 1978
3.7.3 Model results for individual months Table 3-5 shows the difference between the average measured and modelled discharges for individual months for Monsin and Chooz. The table shows that the model predicts too much discharge during relative dry months and too little during relative wet months. This is the case for Monsin and Chooz, suggesting a shortcoming of the model.
Table 3-5 Average discharge for specific months at Monsin and Chooz (from 1968 to 1998)
Monsin Chooz Month Measured Modelled Difference Measured Modelled Difference discharge discharge (%) discharge discharge (%) (m3/s) (m3/s) (m3/s) (m3/s) January 482 467 -3% 276 254 -8% February 483 476 -1% 291 261 -10% March 408 436 7% 228 225 -1% April 333 382 14% 186 200 7% May 213 259 21% 117 134 15% June 158 187 19% 86 97 12% July 135 152 12% 69 76 10% August 95 97 2% 48 46 -3% September 96 87 -9% 45 42 -7% October 158 149 -5% 80 78 -2% November 239 219 -8% 121 119 -2% December 408 379 -7% 224 205 -9%
3.7.4 Conclusions about Van Deursen model results Clearly the overall model performance is very well; however there are curtain discharge regions where the model performance is somewhat lower. The low discharges are not predicted very well. Therefore a closer examination will be carried out to establish the low flow performance of the model. This will be done with the same list of criteria used by Van
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Deursen. These criteria however will now be applied to individual months; this will give a good understanding of the model performance throughout the year.
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Chapter 4 Calibration criteria
4.1 Demands on new calibration criteria During the calibration it is important to have a clear and well-defined set of criteria. Roozenburg and Eekels (1998) described a clear method to make a program of demands for designing products. This method will be combined with logical sense used to come up with proper calibration criteria. Small adjustments to their method have been made to make it fit to this research.
A program of demands must be a proper result of the objectives of the research. This is the case when; • Every criterion is valid • All the criteria together cover the objectives • The program of demands must also be useable during the different phases of the research. Therefore the criteria must be; • Operational • None redundant • As small as possible
Valid With the help of criteria one tries to establish wetter or not the objective of the research has been reached. A criterion generally gives information about one aspect of the objective. A criterion is valid if it adequately describes the aspect it is referring to. Criteria should give the observer a correct impression about the degree of fulfilment of the objective and the value of the current design.
Complete A set of criteria is complete if all the major aspects of the objective are covered. Completeness is an important characteristic of a well-defined set of criteria. An incomplete set of criteria does not solve the entire problem.
Operational When comparing different alternatives it is important to be able to make a distinction between acceptable and non-acceptable solutions, and between good and better solutions. To be able to do this the criteria will have to be put in operation. Meaning they will have to be made as objective as possible. In a good set of objective criteria it must be clear;
• Which characteristics are assessed and how the score of an alternative will be measured. • How the outcome of the different criteria will be compared and an overall score of the alternative, base on all the criteria will be established. The criteria must be ranked.
Objective criteria can are useful to determine wetter or not a design is acceptable. To make a distinction between several acceptable criteria subjective criteria may have to be used. Another reason to use subjective criteria is that a list of objective criteria may be much longer than one subjective criterion.
None-redundant The set of criteria must be formulated in a way that a characteristic is only assessed once; otherwise a characteristic can have too much influence.
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Number of criteria Good decisions take all imaginable consequences of the decision into account. The number of criteria can easily grow to a list of dozens of different criteria. The complexity of a decision is strongly related to the number of criteria. Therefore the number of criteria must be kept as small as possible. None discriminating criteria should be taken out of the list of criteria.
Extra demands Furthermore the new set of criteria should: • Be only related to low flow situations or periods. • Look at the average discharge amount during periods of at least several days. • Occur for at least a 5-7 consecutive days during an average year,
The extra set of criteria should only look at low flow situations or periods because there are already enough criteria for the high and normal flow situations. Adding extra high flow criteria will not support the goal of this research, which is to improve the low flow situation, and does not support the necessary comparison of this simulation with the Van Deursen simulation.
Because of the lack of accurate distribution figures between Monsin and Borgharen and the influence of weirs, locks and reservoirs daily discharge figures are highly unreliable. The criteria used during calibration should look at longer periods, for example weeks or maybe even longer.
When a criterion is used that does not occur for at least 5-7 consecutive days during an average year the amount of times it will be examined will be small and the error made by using short periods will be large. The reliability of the criterion is therefore less than when more frequent limit is chosen.
4.2 Preliminary list of criteria In this paragraph a preliminary list of criteria will be presented. This list contains most of the possible criteria. The Van Deursen model will be used to compare the outcome of the entire list of preliminary criteria. During the comparison different perc and k4 settings will be used to determine the sensitivity of the criteria changes in the parameters. This will enable an objective comparison of the different criteria. It will also give a good insight in the possibly existing overlap of different criteria’s.
Preliminary set of criteria; • Discharge deficit per year, based on (two) different thresholds • Total discharge deficit during calibration period. • Sum of total daily absolute (yearly) errors made in discharge deficit, again based on two different thresholds. • Total number of (consecutive) days per year with a discharge lower than the two thresholds. • Standard R2 for low flow periods. • Nash Sutcliffe coefficient for low flow periods • Visual inspection of low flow events and fluctuations in daily discharges during low flow events.
4.2.1 Discharge deficit per year The discharge deficit is the total amount of water shortage compared to a certain threshold. For example, when the critical threshold is set to 60 m3/s and the occurring discharge is 40 m3/s the deficit is 20 m3/s. Figure 4-1 explains the way the discharge deficit is calculated. This criterion gives a very good inside in the low flows, especially because the deficit will be
Low flow modelling of the Meuse Page 36 of 104
looked at during a period of a year. From January till January, this can be done because the discharge in January never drops below 10 m3/s. The criterion immediately shows the characteristics of a particular dry year.
Dd = (Q − Q1 )*T 4-1 n ∑Q1 3 Ddn Discharge deficit in year n [m ] 1 3 Qi Modelled discharge [m /s] 3 Qthres Threshold discharge [m /s] T Number of seconds per day Discharge deficit Figure 4-1 Calculation of the discharge deficit 4.2.2 Total discharge deficit The total discharge deficit is calculated as the sum of the yearly discharge deficits. His value gives a fast and simple view of the difference between model and measurements over the entire period of interest. 4.2.3 Total absolute error in the discharge deficit The total absolute error in the discharge deficit is calculated by summarizing the absolute difference between the model and the measurements whenever one of the two is below the critical threshold. The criterion gives information about the quality of the prediction. When the model predicts discharge deficits with a relatively similar to the measured discharge but the total absolute error is high error in the model compensate each other making the outcome unreliable. Ae = Q1 − Q *T 4-2 ∑Q1 Ae Absolute error [m3] 1 3 Qi Modelled discharge [m /s] 1 3 Qi Measured discharge [m /s] 3 Qthres Threshold discharge [m /s] T Number of seconds per day Page 37 of 104 Calibration criteria 4.2.4 Number of days with a discharge below critical boundaries The number of days with a discharge below the critical threshold also gives a lot of information about the seriousness of a low flow. It also gives a good image of the goodness of fit of the model. The average number of days below a boundary of 60 m3/s at Monsin is 37, for the 100 m3/s boundaries this is 102. The criterion occurs enough to be of significance. One of the disadvantages is the fact that the model has a lot of days just below the boundary while in the measurements these days are just above the boundary or vice versa. This criterion does not make a distinction between days that have a small error and days that have a large error. 4.2.5 Water balance of individual months The water balance of individual months gives a specific view about the amount of discharge during these months. It shows when the model and measurements have the large difference and can therefore be very useful to spot the areas that need attention. The criterion does not specifically look at periods of low flow. It works does not give as much information as the discharge deficit or the Nash-Sutcliffe coefficient for low flows. 4.2.6 Standard R2 for low flow periods Van Deursen used the standard R2 during his calibration for the entire period. This criterion can also be used for a smaller part of the calibration period. For example the standard R2 for the months with a small discharge can be calculated. This criterion gives a statistical analysis of the low flow periods. The complication is when to start and stop using it. Therefore it seems best to use it during certain months. [(Q −Q ) * (Q1 −Q 1)] ∑Q1 R Standard R n Number of days [-] 1 3 Qi Modelled discharge [m /s] 1 Qai Average modelled discharge during events when the modelled or the measured discharge is lower than the critical threshold. [m3/s] 3 Qi Measured discharge [m /s] Qai Average measured discharge during events when the modelled or the measured discharge is lower than the critical threshold. [m3/s] 4.2.7 Nash-Sutcliffe for low flow periods The Nash-Sutcliffe coefficient can also be calculated for periods with a discharge below a critical threshold. This gives an insight in the performance of the model during low flow periods. The average used in the calculation of this criterion is the average of the events of interest and not the average over the entire year or calibration period. Low flow modelling of the Meuse Page 38 of 104 (Q − Q1 )2 ∑Q1 R Nash-Sutcliffe coefficient [range -∞ to 1] n Number of days [-] 1 3 Qi Modelled discharge [m /s] 3 Qi Measured discharge [m /s] Qa Average measured discharge during events when the modelled or the measured discharge is lower than the critical threshold. [m3/s] 4.2.8 Visual inspection of low flow events and fluctuations during low flow events The low flows can of course also be inspected visually. The visual inspection gives more information on specific days and outcomes. It also generates inside in the timing and the possible cause of the errors made. The measurements of the flow at Borgharen show relatively large daily fluctuations in the mean daily discharge see Figure 2-6. A properly working hydrological model should predict fluctuations caused by natural causes. The Van Deursen model does not predict these fluctuations. The prediction of these fluctuations can be used to make a distinction between different calibration results. 4.3 Critical threshold Before this preliminary list of criteria can tested two critical boundaries will have to be defined. The most commonly used critical threshold for low flow at Monsin is 60 m3/s, below this discharge serious water demand problems arise. RWS Limburg uses a critical discharge of 100 m3/s, this is the first discharge where actions are taken to; sustain the discharge through the Grensmaas and restrict the water consumption of both the Netherlands and Belgium. During this research both thresholds will be used to analyze the calibration results. The discharge deficit, the sum of the absolute errors made during the calculation of the discharge deficit and the Nash-Sutcliffe coefficient for low flows will all be calculated using these two deficits. To be able to use these criteria for different measuring stations than Monsin the boundaries will have to be corrected. There are two ways to do this; The first way is to look at the relative difference between the average flow at Monsin and the tributary or flow of interest. The same relative difference will then be applied to the critical threshold of Monsin, resulting in a critical threshold for the tributary. The second way is to calculate the average number of days with a discharge below the critical threshold at Monsin. The tributary should then have a critical threshold resulting in roughly the same average number days with a discharge below this critical threshold. The critical boundaries of the following stations have been calculated using both methods; Chooz (Meuse), Membre (Semois), Gendron (Lesse), Tabreux (Ourthe), Martinrive (Amblève) and Chaudfontaine (Vesdre). The results are as shown in Table 4-1 and Table 4-2. Page 39 of 104 Calibration criteria Table 4-1 Critical threshold for different stations based on method 1, ratio of discharge Note; The measured data of the different flows have a different amount of significant numbers. All the stations but Chooz and Monsin measure to at least tenths of cubic meters. Therefore all the critical boundaries are in tenths except for Chooz and Monsin. Chooz Semois Lesse Ourthe Amblève Vesdre Monsin Threshold 1 33,3 5,4 3,9 5,0 4,2 2,3 60 Percentage of Monsin 56% 9,0% 6,5% 8,3% 6,9% 3,9% 100% # days below threshold 1 39 84 77 73 43 9 37 Threshold 2 55,6 9,0 6,5 8,3 6,9 3,9 100 Percentage of Monsin 56% 9,0% 6,5% 8,3% 6,9% 3,9% 100% # days below threshold 2 116 132 133 127 108 71 101 Table 4-2 Critical threshold for different stations based on method 2, average number of days with a discharge lower than the critical threshold Note; The measured data of the different flows have a different amount of significant numbers. All the stations but Chooz and Monsin measure to at least tenths of cubic meters. Therefore all the critical boundaries are in tenths except for Chooz and Monsin. Chooz Semois Lesse Ourthe Amblève Vesdre Monsin Threshold 1 33 3,0 2,4 3,3 4,0 3,2 60 Percentage of Monsin 55% 5,0% 4,0% 5,5% 6,7% 5,3% 100% # days below threshold 1 38 36 37 36 37 36 37 Threshold 2 50 6,5 5,0 6,5 6,5 4,5 100 Percentage of Monsin 50% 6,5% 5,0% 6,5% 6,5% 4,5% 100% # days below threshold 2 100 101 102 101 101 103 101 4.3.1 Choice of Method Table 4-1 and Table 4-2 clearly show the differences between the two methods, especially for the following tributaries; Semois, Lesse, Ourthe and Vesdre. These differences can be explained by the characteristics of these tributaries. The first method treats all the tributaries in the same way despite of their different characteristics. Clearly there are differences between the runoff schemes of the different tributaries. Based on the fact that the second method does pay attention to the differences between the different tributaries this method will be used. 4.4 Results of preliminary list The results for the preliminary list of criteria are presented in this paragraph. Not only the current scores are presented but also the scores with different k4 and perc settings. These extra settings give information about the sensitivity of the specific criterion to changes in the parameters of interest. When a criterion has a small sensitivity it’s value is smaller than when a criterion has a large sensitivity. The results will be presented for Monsin and will be in the same order as the preliminary list. For most figure only the results for the first threshold is presented. Low flow modelling of the Meuse Page 40 of 104 4.4.1 Discharge deficit per year, based on two different thresholds Figure 4-2 shows the difference between the modelled discharge deficit and the measured deficit. The model and measurements correspond reasonably well. Most of the years show a discharge deficit that is too large, indicating a structural error. The largest error is made in 1983 and 1976. Cumulative discharge deficit Monsin, threshold 1 1800 ) 3 1500 m 6 1200 900 600 300 Cumulative deficit (10 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Time (yy) Measured Modelled Difference Figure 4-2 Cumulative discharge deficit, based on yearly deficits, at Monsin, using a threshold of 60 m3/s. Cumulative discharge deficit threshold 1 (perc) 3000 ) 3 2500 m 6 2000 1500 1000 500 Cumulative deficit (10 deficit Cumulative 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Time (yy) Measured 0,6 Original 0,2 Figure 4-3 Cumulative discharge deficit at Monsin with different perc settings Figure 4-3 shows the sensitivity of the discharge deficit criterion to changes in the perc parameter. The deficit has a clear reaction to the changes; the difference between the settings is significant. The 0,6 setting increases the overall discharge deficit results in a Page 41 of 104 Calibration criteria hopeful manner. The individual years show little difference between model and measurements. Cumulative discharge deficit threshold 1 (k4) 2500 ) 3 m 6 2000 1500 1000 500 Cumulative deficit (10 deficit Cumulative 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Time (yy) Measured 0,015 Original 0,035 Figure 4-4 Cumulative discharge deficit at Monsin, based on yearly discharge deficits, with different k4 settings Figure 4-4 shows the sensitivity of the criterion to changes in the k4 parameter. When 0,015 is chosen instead of the current 0.23 the results improve strongly. The cumulative error is very small and the individual years do not show any large errors. The criterion shows a significant difference between the three different settings. 4.4.2 Total discharge deficit (106 m3) Table 4-3shows the differences between different parameter settings and the measured discharge deficit for two thresholds. Changing the parameters has a significant effect on the discharge deficit. Both thresholds show the same relations. Decreasing the k4 value improves the results for both threshold and vice versa. The same is true for the perc value. Table 4-3 Discharge deficit for entire period for different k4 values Discharge deficit (106 m3) K4 value Threshold 1 Threshold 2 (60 m3/s) (100 m3/s) 0,015 1027 5515 0,023 1600 6460 0,035 2169 7319 Measured 1027 5482 Low flow modelling of the Meuse Page 42 of 104 Table 4-4 Discharge deficit for entire period for different perc values Discharge deficit (106 m3) Threshold 1 Threshold 2 perc value (60 m3/s) (100 m3/s) 0,2 2743 8992 0,4 1600 6460 0,6 1230 5058 Measured 1027 5482 4.4.3 Absolute error in the discharge deficit The absolute error in the discharge deficit also shows a significant change when k4 or perc is changed. The two thresholds show the same reaction to the changing parameters. The absolute error in the discharge deficit shows the same reaction as the discharge deficit. Decreasing k4 improves the results, and increasing perc improves the results as well. Table 4-5 Absolute error in the discharge deficits Absolute error in the discharge deficit (106 m3) Threshold 1 Threshold 2 K4 value (60 m3/s) (100 m3/s) 0,015 1338 3515 0,023 1738 3740 0,035 2324 4195 Table 4-6 Absolute error in the discharge deficits Absolute error in the discharge deficit (106 m3) Threshold 1 Threshold 2 perc value (60 m3/s) (100 m3/s) 0,2 3350 5506 0,4 1738 3740 0,6 1600 3975 4.4.4 Average number of days with discharge below threshold The average number of days with a discharge below the threshold of 60 m3/s shows a significant difference for both k4 and perc. However changes in k4 do not result in significant changes in the number of days with a discharge below the threshold of 100 m3/s. this indicates that the k4 parameter mainly influences the extreme low discharges and not the discharges close to 100 m3/s. This characteristic can be interesting during calibration. Page 43 of 104 Calibration criteria Table 4-7 Average number of days with a discharge below thresholds. Yearly average number of days with a discharge below Threshold 1 Threshold 2 K4 value (60 m3/s) (100 m3/s) 0,015 42 112 0,023 54 112 0,035 61 113 Measured 44 104 Table 4-8 Average number of days with a discharge below thresholds. Yearly average number of days with a discharge below perc value Threshold 1 Threshold 2 (60 m3/s) (100 m3/s) 0,2 83 129 0,4 54 112 0,6 40 93 Measured 44 104 4.4.5 Nash Sutcliffe coefficient for low flow periods Figure 4-5 shows the Nash-Sutcliffe coefficient calculated over the entire research period with different discharge thresholds and different k4 and perc settings. When the threshold gets larger the Nash-Sutcliffe value increases. The differences between different settings are significant as long as the threshold is smaller than approximately 140 m3/s. When the discharge becomes larger the difference between different settings becomes smaller and smaller. Nash-Sutcliffe coefficient for low flows 1,0 0,5 0,0 0 40 80 120 160 200 240 280 320 360 -0,5 -1,0 Nash-Sutcliffe coefficient -1,5 3 Original k4 = 0.012 Threshold (m /s) k4 = 0.036 perc = 0.2 perc = 0.6 Figure 4-5 Nash-Sutcliffe coefficient for low flows using different k4 and perc settings Low flow modelling of the Meuse Page 44 of 104 4.4.6 Standard R coefficient for low flow periods Figure 4-6 shows the relation between different k4 and perc settings and the standard R for low flows. The graph shows that the differences between the different settings are relatively small, except one. Showing that a significant improvement in the low flow performance does show. Again the differences between different settings become smaller when the threshold is increased. The differences above 120 m3/s are negligible. Standard R coefficient for low flows 1,0 0,8 0,6 0,4 0,2 Standard R coefficient 0,0 0 40 80 120 160 200 240 280 320 360 3 Original k4= 0.015 Threshold (m /s) k4 = 0.035 perc = 0.6 perc = 0.2 Figure 4-6 Standard R for low flows using different k4 and perc values. 4.4.7 Visual inspection Figure 4-7 shows the differences between different perc values. The differences are significant for the part April till August. During September and October the different settings do not show a significant differences. The different settings all do not show fluctuations but smooth lines, modelling the fluctuations will not be accomplished by changing the prec value. Hydrograph 1976 100 90 80 70 60 50 40 30 Discharge (m3/s) 20 10 0 jan feb mrt apr mei jun jul aug sep okt nov dec Time (dd-mm) Measured Model 0,6 0,2 Figure 4-7 Hydrograph of 1976 with different perc settings. Page 45 of 104 Calibration criteria Figure 4-8 shows the different results for different k4 settings. The results show a significant difference. The difference starts to occur when the discharge drops below approximately 100 m3/s and ends with the first serious precipitation event during the last week of October. Again the model does not predict the daily fluctuations Hydrograph 1976 100 90 80 70 60 50 40 30 Discharge (m3/s) 20 10 0 jan feb mrt apr mei jun jul aug sep okt nov dec Measured Model Time (dd-mm) 0,015 0,035 Figure 4-8 Hydrograph of 1976 with different k4 settings. 4.5 Discussion of potential criteria In the paragraph the results of all the criteria are presented and compared. The advantages and disadvantage of the criteria will be mentioned. Yearly deficit during calibration period The yearly discharge deficit shows the yearly differences between the measured and modelled discharge deficits It shows large differences between different parameter settings. It gives a better insight in the situation than the total discharge deficit because it shows all the individual years. However the information about all the years makes selection of the best setting more difficult, improvement of one or more year can mean decreasing the result for other years. This criterion also looks at the sum over a period of a year, making it possible that the model compensates error within this period. Therefore this criterion should not be used without another criterion Total discharge deficit The total discharge deficit during calibration period gives the total deficit during the entire period of interest. It shows large differences between different settings, and also shows large improvements. This criterion shows the long term effects of changes in the k4 and perc settings for low flow periods. The simplicity of this criterion is one of its strong points, it immediately shows wetter the model results improve or not. The simplicity has a disadvantages, one of these is that it only looks at the sum of deficits, make it possible that this criterion shows a very good score while the model performance is worse. Compensation of errors is possible on a small scale, error in the same year, as on a larger scale, errors made in different years. Because of this the criterion should not be used without other criteria ensuring the overall model performance improvement. Low flow modelling of the Meuse Page 46 of 104 Absolute error in the discharge deficit The absolute error in the discharge deficit gives more insight in the “real” value of the discharge deficit. When the absolute error decreases the model performance is improved even when the difference between the modelled and measured discharge deficit is increased. The absolute error gives an indication of the size of the errors that have been made and compensated in the calculation of the discharge deficit. All differences are treated the same, a linear relation exists between differences and the criterion. Number of days with a discharge below threshold The number of days with a discharge below a threshold gives an insight in the way the discharge deficit is realized. When the number of days shows a large error the reliability of the discharge deficit is small. It is therefore an important indication of the model performance. This criterion shows large differences between different parameter settings. Compensation of errors is possible on a small scale, error in the same year, as on a larger scale, errors made in different years. The criterion is best used to check the value of other criteria like the discharge deficit. Standard R coefficient for low flows The standard R coefficient for low flows describes the correlation between the modelled and measured discharges during periods with discharges below certain thresholds. The correlation improves quit strongly when the threshold is increased. In other words the performance of the model gets better when the threshold is improved, indicating a better modelling result for discharges closer to the average. The results show that different parameter settings result in different outcomes for the Nash-Sutcliffe coefficient, proving that the criterion is sufficiently sensitive for parameter changes. One of the disadvantages of this criterion is that structural errors, relative and absolute, are ignored. Nash Sutcliffe for periods with low flows The Nash-Sutcliffe coefficient for periods with low flows shows bad results for discharges smaller than approximately 100 m3/s. In that region the Van Deursen model is worse than using average values. Above 400 m3/s the coefficient improves to above 0.75. The criterion is most sensitive to changes of k4 and perc up to a threshold of 120-130 m3/s. The criterion shows large differences between different parameter settings. It also shows in what region the model improves. The Nash-Sutcliffe coefficient is more sensitive to changes of the k4 and perc values than the standard R, also it does not ignore the effects of structural errors. The possibility of structural errors occurring because of the existence of reservoirs makes this an important characteristic. Visual inspection Parameter settings that show little visual difference can show a large difference when looking at them with different criteria. Further more it is very difficult to tell which setting is better and which setting is worse. Visual inspection is especially useful to compare the predicted fluctuations of the model and the fluctuations in the measured data. The different perc and k4 settings do not show a difference in the fluctuations. Visual inspection does not seem to have an added value during the calibration. 4.6 Final list of criteria The two most important characteristics of the low flow periods are; the amount of discharge during these periods and the reaction of the model to significant rainfall events during these periods. The results from the visual inspection in paragraph 4.4.7 showed that the changes Page 47 of 104 Calibration criteria of perc and k4 do not improve the performance of daily discharges during period of low flows. The model still does not respond (well) to rainfall during periods of low flow. The daily fluctuations measured at Monsin (and at Chooz) do not show in the modelled discharge. The focus of the calibration should therefore be the seasonal discharges and deficits and not on the daily discharges during low flows. The new model should predict the daily discharges at least as good as the Van Deursen model, meaning that the Nash-Sutcliffe for low flows must remain at least the same. When the list of demands for a program of demands is used on the preliminary list of criteria a proper list can be made. This final list contains a much smaller number of criteria and also does not contain criteria measuring the same characteristic. The final list consists of the following criteria; • Total discharge deficit using both thresholds • Total absolute error for both thresholds • Nash Sutcliffe for low flow periods The total discharge deficit gives information about the long-term discharge difference between the measurements and the model. It gives much more information than the number of days with a discharge below a certain threshold and the average monthly discharge. The number of days does not really add any information to the process; it basically comes back in the absolute error and the Nash-Sutcliffe coefficient. The same is the case for the average monthly discharge. If the mean average monthly discharge during the summer periods is wrong the Nash Sutcliffe coefficient, the absolute error and the discharge deficit will also measure this. The discharge deficit will be looked at using two different thresholds, this because of the fact that not only the extreme low flow are of interest but also the less extreme and more often occurring events are important for the model to work well. Using two thresholds also makes the criterion more reliable. All three criteria look at the differences between measured and modelled discharges on a daily bases. However in the Nash-Sutcliffe coefficient the larger differences have more influence on the score than the small differences. This is because of the square relation in the formula. The ‘absolute error in the discharge deficit’ criterion uses a linear relation and therefore finds a different optimum. For the long-term low flow influences of the changes the absolute error is therefore a better criterion. Although the prediction of daily discharge during low flows is not specifically looked at it is an important characteristic. The performance of the daily low flow predictions should not deteriorate. Therefore the Nash-Sutcliffe coefficient for low flows is used to measure and monitor the performance of these daily predictions. Moving average, technique to smooth daily discharge, discharge of a specific day is calculated by averaging the discharge over a specific period before and after this specific day. 4.7 Moving average Both k4 and perc are parameters influencing groundwater processes. These processes have a long-term influence on the discharge and are best compared looking at periods longer than one day. Therefore the calibration criteria should not look at daily influences but at periods much longer. One way of looking at these long-term processes is to use a criterion that itself looks at periods longer than a day. Another way is to use a moving average period on both measured and modelled data before comparing the two. The first criteria that was used during the calibration is the discharge deficit, this criterion looks at the discharge deficit over the entire calibration period and therefore already has a long-term view. The absolute error in the discharge deficit and the Nash-Sutcliffe coefficient Low flow modelling of the Meuse Page 48 of 104 for low flows however are looking at the difference between modelled and measured discharge of specific individual days. The use of a moving average period will increase the effectiveness of these criteria. Using a longer period will improve calibration results, because differences between modelled and measured get smaller when using a longer period. Which moving average period results in the largest sensitivity to changes in the parameters for each of the criteria? The sensitivity has been calculated separately for all three different criteria and two parameters, resulting in six different optimum periods. The sensitivity of a criterion score was measured by summarizing the differences between the scores calculated with different parameters settings and a fix moving average period. The moving average period with the largest sum of differences has the largest sensitivity for this specific criterion and parameter. The uses of the moving average period did not change the optimum setting found, only the value the criterion has at the different settings. For the moving average periods a step-size of 8 days has been used. For k4 the original setting of 0.4 has been used and 0.3 and 0.5. For perc the original (0.02307) was not used but 0.20 and 0.25. This resulted in the following moving average periods Table 4-9 Moving average period with highest sensitivity for changes in k4 parameter, overall values will be used during calibration. Nash-Sutcliffe coefficient Discharge deficit Error in DD perc value Q< 33 m3/s Q< 50 m3/s Q< 33 m3/s Q< 50 m3/s Q< 33 m3/s Q< 50 m3/s 0,3 41 17 1 17 9-17 25 0,4 (original) 33 17 1 1 9 25 0,5 25 9 1 1 9-17 9 Overall 41 17 1 1 9 25 Clearly the sensitivity changes somewhat with the changing of the perc value. Therefore the sensitivity scores of the different periods have been summarized and the period with the highest overall score has been presented in the row “Overall”. Table 4-10 Moving average period with highest sensitivity for changes in perc parameter, Overall values will be used during calibration. Note; original setting for k4 = 0,2307 Nash-Sutcliffe coefficient Discharge deficit Error in DD perc value Q< 33 m3/s Q< 50 m3/s Q< 33 m3/s Q< 50 m3/s Q< 33 m3/s Q< 50 m3/s 0,2 41 9 1 1 1 1 0,25 41 9 1 1 9 1 Overall 41 9 1 1 1 1 Table 4-9 and Table 4-10 show that the discharge deficit is most sensitive without the use of a moving average. This can be explained by the fact that the discharge deficit is a long-term criterion. The Nash-Sutcliffe coefficient and the error in the deficit do show a Page 49 of 104 Calibration criteria Table 4-11 Moving average periods used during calibration Criterion Moving average period (number of days) Discharge deficit 1 1 Discharge deficit 2 1 Error in discharge deficit 1 9 Error in discharge deficit 2 9 Nash-Sutcliffe coefficient 1 41 Nash-Sutcliffe coefficient 2 17 The calibration of k4 and perc will be done simultaneously. Therefore the same moving average period will have to be used for both parameters. Changing the moving average period does not change the calibration results, the same optimum parameter value will still be found. However the criteria value will be slightly different. Low flow modelling of the Meuse Page 50 of 104 Chapter 5 Calibration procedure 5.1 Calibration and Validation period en procedure The measured data period reaches from 1968 to 1998. During the simulations of Van Deursen the first 15 years, 1969-1984, was used for calibration of the model, the last 13 years, 1985-1998, where used for validation. The performance of the measured data gets better during the period. 5.1.1 Influence of calibration period on the overall performance of the model Van Deursen, Booij and Groot Zwaaftink used the same calibration and validation periods, calibrating from 1970 to 1984 and validating from 1985 to 1998. Velner used the second period for his calibration and the first for his validation. Table 5-1 (Aalders, 2004) shows the different Nash-Sutcliffe values for four different HBV studies. Table 5-1 Nash-Sutcliffe coefficients of the Ourthe catchment for different simulations and different calibration periods. Calibration Nash-Sutcliffe Validation Nash-Sutcliffe period Calibration period Validation Velner (2000) 1986-1996 0.92 1968-1986 0.87 Booij (2002) 1970-1984 0.80 1985-1996 0.86 Groot Zwaaftink (2003) 1970-1984 0.81 1985-1996 0.91 Van Deursen (2004) 1969-1984 0.87 1985-1998 0.93 All the simulations show a higher Nash-Sutcliffe value for the second period, indicating that the input data was better. The results of Van Deursen en Velner also seem to indicate that the performance of the model does not depend on the choice of the calibration period. Aalders studied the difference in the performance by looking at the performance difference of two separate models with different calibration periods. Aalders calibrated two separate models, one during the first period and one during the second period. The validation and calibration results show very little difference between the Nash-Sutcliffe values Table 5-2 Simulation of daily discharge with HBV model in terms of Nash-Sutcliffe value (Italic is calibration, bold is validation) (Aalders 2004) Nash-Sutcliffe Nash-Sutcliffe Nash-Sutcliffe 1970-1984 1985-1998 1970-1998 Run 1 0.88 0.93 0.91 Run 2 0.90 0.94 0.92 5.1.2 Choice of calibration period This clearly shows that the choice for a specific calibration period had little influence on the Nash-Sutcliffe value, and therefore the performance of their models. Furthermore using the same calibration periods as Van Deursen did, results in a better comparison of the high flow simulations. Therefore the same calibration and validation periods will be used during this research. Page 51 of 104 Calibration procedure 5.2 Calibration procedure The calibration process will start with the most upstream measuring station, calibrating the contributing catchments and work itself downstream. When downstream measuring stations are calibrated only the non-calibrated catchments will be changed (calibrated). The calibration of Monsin (and Borgharen) will look at the measured discharge at Monsin and not at the discharge difference between Monsin and Chooz. Figure 5-1 shows which sub basins will be calibrated separately and which catchments will be calibrated together. Sub basins with the same colour will be calibrated together. The dots represent the measuring stations. Figure 5-1 Calibration of sub basins During this calibration multi-week effect are most important. Therefore the most important criteria during this calibration are the total discharge deficit in combination with the absolute error in the discharge deficit. The absolute error in the discharge deficit is used to check the performance of the discharge deficit predictions. When the absolute error and the discharge deficit show the same optimum k4 and perc setting this setting will be chosen. The discharge deficits and absolute errors for both thresholds will be used to make sure the optimum is not depending on the threshold. The optimum settings found using the discharge deficit and the error in the discharge deficit will probably not be the optimum settings for the Nash-Sutcliffe coefficient for low flows. The Nash-Sutcliffe coefficient for low flows will serve to check that the performance of the daily discharge predictions does not deteriorate during this calibration. Calibration will start by calculating the outcome for all three criteria using different k4 and perc settings. During this first step the differences between different k4 and perc settings will be relatively large. This is done to make sure the whole range is covered. This first step serves to discover where the model performance is best. In this region the step size will be made smaller and smaller finally resulting in an optimum for k4 and perc. Low flow modelling of the Meuse Page 52 of 104 Chapter 6 Calibration and validation results 6.1 Introduction This chapter shows the results of the calibration and validation of the new model. Paragraph 6.2 presents the results of the first calibration steps for Chooz. These results show an interesting relation between the simulated discharge deficit and the two parameters that are being used during this calibration. The results of the Vesdre, using different reservoir regimes, are presented in paragraph 6.4. Paragraph 6.3 shows the final calibration and validation results for Chooz. Paragraph 6.5 shows the results for the three most important tributaries. In paragraph 6.6 the results for Monsin and Borgharen are presented and compared with the results for Chooz. General conclusions about the calibration and validation will be drawn in paragraph 37 The k4 and perc values used for the sub basins have been incorporated in Appendix III-12 6.2 Results first calibration steps Chooz In this first paragraph the results for Chooz are presented in detail. It shows the relation between different k4 and perc combinations and the three calibration criteria. First of all the results for the discharge deficits are presented in detail. 6.2.1 Discharge deficit The first step of the calibration is to calculate the discharge deficits for different combinations of k4 and perc values. This step serves to get a better image of the relation between parameter value and criteria scores. Table 6-1 and Table 6-2 below show the discharge deficit, calculated with a threshold of 33 m3/s and 50 m3/s, for the different parameter settings. Table 6-1 Relative difference between measured and modelled discharge deficit, accumulated over the calibration period, for Chooz using a threshold of 33 m3/s, with different k4 and perc parameter values. Note; shaded values are smaller than 5% k4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 6% -4% -13% -20% -26% -31% -35% -38% 0,011 15% 5% -3% -11% -17% -22% -26% -30% 0,012 25% 15% 6% -2% -8% -13% -18% -22% 0,013 34% 24% 15% 7% 1% -5% -10% -14% 0,014 43% 32% 24% 16% 9% 4% -1% -1% 0,015 51% 41% 32% 24% 18% 12% 7% 3% Table 6-1 shows the results for the relative difference between the modelled and the measured discharge deficit using a threshold of 33 m3/s and different k4 and perc values. The results show that different combinations of k4 and perc can have the same discharge deficit. The table shows a diagonal line with relative differences in discharge deficits all smaller than 5 %. When a smaller step size between the different parameter settings would have been used the relative differences could have been made even smaller. Resulting in a diagonal line with relative differences for the discharge deficit all approaching the perfect value of zero. For this threshold and criterion the k4 and perc are related in such a way that they can fully compensate for each other. Meaning that, within certain boundaries, a given Page 53 of 104 Calibration and validation results perc values combined with the right k4 will result in a perfect discharge deficit. This means that the discharge deficit with this threshold will not result in one optimum parameter setting. Table 6-2 Relative difference between measured and modelled discharge deficit, accumulated over the calibration period, for Chooz using a threshold of 50 m3/s, with different k4 and perc parameter values Note; shaded values are smaller than 5% k4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 17% 10% 2% -5% -11% -17% -22% -26% 0,011 20% 13% 6% -1% -7% -13% -17% -22% 0,012 23% 16% 9% 3% -3% -8% -13% -17% 0,013 26% 19% 12% 6% 0% -5% -9% -13% 0,014 29% 22% 15% 9% 4% -1% -5% -5% 0,015 31% 25% 18% 13% 7% 3% -2% -6% Table 6-2 also shows a diagonal line with relative differences smaller than 5%. When a smaller step size between the different k4 and perc values would have been used a line with relative differences approaching zero would have been found. The diagonal line found for this threshold shows a different angle than found in Table 6-2. Combining the two thresholds will result in an optimum parameter setting, found at the intersection of the two diagonal lines. Table 6-3 Sum of the relative differences between measured and modelled discharge deficits, accumulated over the calibration period, calculated with thresholds of 33 and 50 m3/s. Note; Absolute values of the individual differences have been used, shaded values are smaller then 5% k4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 23% 14% 15% 25% 37% 47% 56% 64% 0,011 36% 18% 9% 12% 24% 35% 44% 52% 0,012 48% 30% 15% 4% 11% 22% 31% 39% 0,013 60% 43% 27% 13% 1% 9% 19% 27% 0,014 72% 54% 39% 25% 13% 4% 6% 15% 0,015 83% 66% 50% 37% 25% 15% 9% 8% Table 6-3 shows the sum of relative differences in discharge deficits calculated with two thresholds. When the sum of the two criteria is used k4 and perc cannot compensate for each other fully, only one perfect discharge deficit exists. The table above shows the optimum value when perc = 0.50 and k4 = 0.013. Figure 6-1 also shows the relation between different k4 and perc settings and the sum of the relative differences of the discharge deficits. This 3-dimensional graph of the sum of the relative differences shows that different parameter combinations can have the same result. Low flow modelling of the Meuse Page 54 of 104 Sum of relative differences for discharge deficits 1 & 2 90% 80% Relative difference (%) 70% 60% 50% 40% 30% 20% 10% 0% 0,40 0,43 0,45 0,01 0,48 0,50 k4 0,011 0,53 ter 0,012 e pa 0,55 ram 0,013 a ram 0,58 rc p ete 0,014 Pe r 0,015 Figure 6-1 Sum of relative discharge deficit differences, calculated with thresholds of 33 and 50 m3/s. 6.2.2 Absolute error in the discharge deficit Table 6-4 shows the sum of the absolute error in the discharge deficit values for both thresholds. The individual tables for both thresholds have been incorporated in appendix III- 1. The absolute error in the discharge deficit has been calculated with a moving average period of 9 days. The sum of the errors shows that the optimum is not found at exactly the same parameter setting as the optimum discharge deficit. However the difference is small. The error found at the optimum discharge deficit setting is 1.31 * 109 compared to optimum for the error of 1.29 * 109 m3. The individual error results show optimum settings that deviated somewhat form the optimum of the sum, these differences are again small. Table 6-4 Sum of the absolute error in the discharge deficits (106 m3) made using both thresholds, accumulated during the calibration period, for Chooz. k4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 1592 1467 1369 1308 1301 1339 1401 1480 0,011 1639 1501 1396 1314 1285 1307 1357 1421 0,012 1690 1544 1431 1346 1292 1303 1340 1381 0,013 1754 1607 1483 1385 1313 1305 1322 1357 0,014 1816 1658 1532 1434 1355 1331 1327 1327 0,015 1884 1727 1587 1490 1412 1374 1354 1361 6.2.3 Nash-Sutcliffe coefficient for low flows The Nash-Sutcliffe coefficient for low flows has been calculated using the average of the discharge below the threshold of interest. This resulted in very poor Nash-Sutcliffe coefficients when compared to the value for the overall model. When using a small bantwith for the discharges of interest the Nash-Sutcliffe will always be smaller because of the relative Page 55 of 104 Calibration and validation results large difference between modelled and measured daily discharges compared to the differences between the measured discharge and the measured average discharge. Table 6-5 Average of Nash-Sutcliffe coefficients for both thresholds for Chooz Note; maximum score is 1 k4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 0,32 0,28 0,20 0,08 -0,06 -0,20 -0,36 -0,55 0,011 0,31 0,30 0,26 0,19 0,11 0,01 -0,09 -0,23 0,012 0,28 0,30 0,28 0,23 0,19 0,12 0,05 -0,03 0,013 0,24 0,27 0,27 0,25 0,22 0,18 0,13 0,07 0,014 0,18 0,23 0,25 0,24 0,23 0,20 0,18 0,18 0,015 0,13 0,18 0,21 0,22 0,23 0,20 0,19 0,17 Table 6-5 shows the results when the Nash-Sutcliffe coefficients for both thresholds are summarized. The individual results for both thresholds have been incorporated in appendix III-1, the optimum for these two thresholds is the same. The optimum found deviates from the optimum for the other two criteria quite a lot (0.22 compared to 0.32). The Nash-Sutcliffe coefficient still improved strongly in comparison to the original model (-0.36). Because the discharge deficit and the absolute error in the discharge deficit are the most important criteria during this research the optimum found with those criteria will be used. The Nash-Sutcliffe coefficient for low flows will be used to check the performance during low flows and to make sure this performance does not deteriorate. 6.3 Calibration and validation results for Chooz In this paragraph the final calibration and validation results of Chooz will be presented. For all the criteria the score of the old model and the new model will be compared. First of all the results for the van Deursen criteria will be presented for both the old and the new model during calibration and validation. This to ensure that the precondition that the overall model performance must remain the same is met. 6.3.1 Results Van Deursen criteria for Chooz The precondition that the overall model performance must remain the same is met, Table 6-6. The overall Nash-Sutcliffe coefficient, the water balance (average discharge) and the standard R do not change because of the changed k4 and perc values. Table 6-6 Results Van Deursen criteria at Chooz during calibration and validation for both the old and the new model. Average discharge (m3/s) Standard R Nash- Sutcliffe Period Van Deursen New Van Deursen New Van Deursen New Calibration 135 135 0,96 0,96 0,92 0,92 Validation 153 153 0,97 0,97 0,94 0,94 Low flow modelling of the Meuse Page 56 of 104 6.3.2 Results new calibration criteria for chooz Table 6-7 shows the measured, Van Deursen and new discharge deficits at chooz during calibration and validation using both thresholds. The results for both calibration and validation are very good. The difference between the measured and modelled discharge deficits is smaller than 3 percent. Table 6-7 Discharge deficits (106 m3) at Chooz for both thresholds and both models. Note; italic is calibration period, bold is validation period Threshold Measured Van Deursen New model (m3/s) (106 m3) (106 m3) (106 m3) 33 455 944 456 33 301 828 308 50 1991 2943 1994 50 1818 2765 1809 The question is whether or not other the model has the same quality for different thresholds. Table 6-8 shows the results for eight different thresholds. The model predicts the discharge deficits with these different thresholds almost as well. The validation period shows better results than the calibration period. This is in accordance with earlier results of Van Deursen and the overall Nash-Sutcliffe coefficient. Table 6-8 Differences in discharge deficits, for different thresholds during calibration and validation, between Van Deursen model and new model Calibration period Validation period Threshold Van Van (m3/s) Deursen New model Deursen New model 30 128% 5% 235% 1% 40 75% -1% 101% 4% 50 48% 0% 52% -1% 60 34% 2% 31% -2% 70 25% 4% 21% -2% 80 20% 4% 16% -1% 90 17% 5% 12% 0% 100 15% 5% 10% 1% Appendix III.2 shows the discharge deficits for individual years during both calibration and validation using both thresholds. The tables show the measured discharge, the modelled discharge and the difference between those two. When the modelled discharge is smaller than the measured discharge the difference is negative value. For most years the differences are relatively small. The error made during the extreme year 1976 is very small for both thresholds, only 2.4 % and 3.5 %. The model also predicts years without a discharge deficit in a proper way, for example in the years 1980 and 1981 both measurements and model do show a discharge deficit using a threshold of 33 m3/s. For the threshold of 50 m3/s the measured and modelled deficits are all smaller than 20 * 106 m3 with a maximum difference of only 3.6 106 m3. Page 57 of 104 Calibration and validation results During the calibration the discharge deficits and absolute errors in the discharge deficit have been minimized. The optimum found for the discharge deficit is different from the optimum found for the absolute error in the discharge deficit. This difference is small and the optimum found for the discharge deficit has been chosen. This has been done because the difference between the two k4 and perc settings was smaller for the absolute error than for the discharge deficits. The Nash Sutcliffe coefficient presented in Table 6-9 is not the optimum Nash-Sutcliffe value. However the value found is much better than the value for the original model. Compared to the original model the k4 and perc setting used does not deteriorate the simulation of daily discharges during low flow periods. Table 6-9 Absolute error in the discharge deficit and Nash-Sutcliffe low flow, for both thresholds. Note; italic is calibration period, bold is validation period Error in discharge deficit Nash-Sutcliffe low flow Threshold Van Deursen New model Van New model (m3/s) (106 m3) (106 m3) Deursen 33 794 313 -0,25 0,30 33 934 429 -1,46 -0,57 50 1598 999 -0.46 0.12 50 1676 1209 -1.51 -0.61 6.3.3 Conclusion calibration and validation of Chooz Clearly the model performance for low flow situations increases, for both long and short term predictions. The model predicts the total discharge deficit during the calibration and validation period very well. The individual years still show errors, but these errors are relatively small (< 3%). During the calibration period the relative differences are smaller for the larger of the two thresholds. The Nash-Sutcliffe coefficients in the table above do not show this increase in performance because of the moving averages used. The smaller of the two thresholds is calculated with a much larger moving average period (41 days compared to 17 days) and therefore shows better results. However earlier results have already shown that the performance of the model improves when the threshold is made larger. The short term predictions of the model have improved as well. The Nash-Sutcliffe coefficient for both thresholds shows this. However the performance of the model during low flows is still not very good. Appendix III-3 contains the hydrographs of 1976 and 1978 for chooz. During the relatively normal year of 1978 the prediction of the daily discharges is much better than during the extreme year of 1976. During the last part of the low flows the modelled discharge is much lower than the measured discharge. The hydrograph still shows the same type of error for the original and the new model. 6.4 Calibration and validation results for the Vesdre reservoirs The Vesdre reservoirs will be looked at with two different operating regimes. The first will be to add 1.5 m3/s when the discharge is lower than threshold 1 and add 1.0 m3/s when the discharge is between thresholds 1 and 2. The second will be to add 1,5 m3/s when the discharge is lower than threshold 2. These two operation regimes will be compared with the optimum found without a reservoir. Low flow modelling of the Meuse Page 58 of 104 Discharge deficits for Vesdre and Chooz using threshold 1 18 16 ) 3 14 m 6 12 10 8 6 4 Discahrge deficit (10 2 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 Period (yy) Vesdre Chooz Figure 6-2 Discharge deficits for the Vesdre and a corrected discharge deficit for Chooz during calibration and validation period using threshold 1. Before the start of the calibration the discharge deficits of the Vesdre and Chooz will be compared. The Chooz discharge deficits have been scaled down by dividing the individual years by the total discharge deficit of Chooz and multiplying it with the total discharge deficit of the Vesdre. Figure 6-2 shows that during the first period, 1968 to 1974, the Vesdre discharge deficit is much higher than the corrected Chooz discharge deficit. From 1975 and further the situation is the opposite, except for 1996. This suggests that the reservoir- operating regime changed after 1974. Therefore the calibration will use the period of 1975 to 1984, and validation will use the normal validation period. 6.4.1 Results Van Deursen criteria for the Vesdre The comparing the results’ using the Van Deursen criteria is not really fair. The post-model processes used only added water to low discharges but did not abstract water during high discharges. Therefore the water balance is no longer valid and the result for the Van Deursen criteria will not be presented. 6.4.2 Results new calibration criteria for the Vesdre The calibration of the two regimes has been done in the same way as the other calibrations, only the calibration period was shorter. The difference between measured and modelled discharge deficits and the error in the discharge deficit have been made as small as possible. The options will be compared for both calibration and validation period. Table 6-10 shows the discharge deficits for both thresholds during calibration and validation. The discharge deficits for all new models are very good during calibration, deviations of 1 * 106 m3 or less. The result for both calibration and validation are much better than the results of the original model. Reservoir regime 1 shows the best results, with deviations of 10 and 7 percent. The discharge deficits for individual years during the validation have been incorporated in appendix III-4. Page 59 of 104 Calibration and validation results Table 6-10 Discharge deficit for both thresholds for different reservoir regimes compared to the original model during calibration and validation period. Note; italic is calibration period, bold is validation period Threshold Measured Original Without Reservoir Reservoir (m3/s) (106 m3) model Reservoir regime 1 regime 2 (106 m3) (106 m3) (106 m3) (106 m3) 3,2 12 40 12 11 12 3,2 10 38 2 11 4 4,5 62 98 61 62 62 4,5 109 149 96 102 101 Table 6-11 show the results of the three new models and the original model. The new models are all much better than the original model during the calibration and validation periods. The difference between the new models is small and not univocal. For the smaller of the two thresholds the model without a reservoir shows the best results, for the larger of the two thresholds the model using reservoir regime 1 shows the best results. Table 6-11 Absolute errors in the discharge deficit for different reservoir regimes compared to the original model during calibration and validation period. Note; italic is calibration period, bold is validation period Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 regime 2 3,2 42 8 11 8 3,2 78 15 29 20 4,5 82 49 33 36 4,5 152 91 85 91 Table 6-12 shows the Nash-Sutcliffe coefficients for low flows. The table shows that the model with reservoir regime number one has the best results. During calibration the Nash- Sutcliffe coefficients for both reservoir regimes show a positive value. All new models show better results than the original model. Table 6-12 Nash-Sutcliffe values for different reservoir regimes compared to the original model during calibration and validation period. Note; italic is calibration period, bold is validation period Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 regime 2 3,2 -1,57 -0,81 0,65 0,27 3,2 -5,66 -0,71 -1,09 -1,02 4,5 -1,93 -0,88 0,44 0,08 4,5 -3,13 -3,93 -1,26 -2,15 Low flow modelling of the Meuse Page 60 of 104 6.4.3 Conclusion calibration and validation of Vesdre reservoirs The results for this reservoir research are very interesting. Appendix III-6 shows the calibration and validation results for the three new models calibrated using entire calibration period. The results clearly show that the models calibrated using only the second half of the calibration period have much better validation results. This combined with the difference between the discharge deficits measured for the Vesdre and at Chooz, Figure 6-2, proves the assumption that the reservoir regime changed after 1974. This also proves that reservoirs have a significant influence on the discharges during low flows. Appendix III-5 shows the results for the first part of the calibration period for the models calibration using the second half of the period. For the two models with a reservoir regime the results are presented with and without the influence of these reservoirs. The second reservoir regime without the reservoir gives the best results for all criteria except the absolute error in the discharge deficit. The difference however with the best outcome is very small. The other models, including the Van Deursen model, all show similar results. The fact that the regime 2 without the reservoir has the best results again proves the influence of the reservoirs in the Vesdre on the discharges during low flows. The results would probably have been best with one of the two reservoir still working. For this tributary the model with reservoir regime number one shows the best results during the second half of the calibration period and the validation. However the model without the reservoir will be used for the rest of this research because of the small difference and the transparency. When using the model with a reservoir the post-model process has to be used to obtain the correct results. This makes the model less user-friendly and transparent. During the calibration of the Monsin discharge the influences of this choice will be analyzed. The results in this paragraph show that the incorporation of a reservoir can improve the model performance. However the discharge deficit and the absolute error in the discharge deficit do not show a lot of difference between the new models with and without a reservoir. For other sub basins with smaller reservoirs the influence of these reservoirs will be much smaller and there is no need to put them through a post-model process. The current calibration process covers the influence of these reservoirs. 6.5 Calibration and validation results for the main tributaries The main tributaries of the Meuse are the Vesdre, Lesse, Ourthe, Amblève and the Sambre. The Sambre does not have a measured discharge; the results for the Vesdre have all ready been presented in paragraph 6.4 and will therefore not be presented in this paragraph. This paragraph contains the results of the Lesse, the Ourthe and the Amblève. 6.5.1 Results Van Deursen criteria for the main tributaries Table 6-13 shows that all preconditions are met. The results for the Van Deursen criteria have not deteriorated. The differences are so small that the table below does not show them. Page 61 of 104 Calibration and validation results Table 6-13 Results Van Deursen criteria for the Lesse, Ourthe and Amblève during calibration and validation Average discharge (m3/s) Standard R Nash- Sutcliffe Van New Van New Van New Deursen Deursen Deursen Calibration Lesse 16,9 16,9 0,82 0,82 0,89 0,89 Validation Lesse 19,0 19,0 0,85 0,85 0,91 0,91 Calibration Ourthe 21,1 21,2 0,86 0,86 0,86 0,86 Validation Ourhte 23,2 23,2 0,90 0,90 0,93 0,93 Calibration Amblève 18,1 18,0 0,93 0,93 0,85 0,85 Validation Amblève 19,2 19,2 0,95 0,95 0,91 0,91 6.5.2 Results new calibration criteria for main tributaries Table 6-14 shows the discharge deficits for the three main tributaries during calibration and validation using both thresholds. It shows very good results for both thresholds during calibration. However the results during the validation periods are less univocal. The results for the Ourthe and Amblève are better both thresholds. The results for the Lesse are not, the smaller of the two thresholds shows a result equal to the Van Deursen model, the larger of the two thresholds shows a result worse than the Van Deursen Model. Table 6-14 Discharge deficit (106 m3) results for main tributaries during calibration and validation. Lesse Ourthe Amblève Period Meas Van New Meas Van New Meas Van New Deursen Deursen Deursen Cali thres 1 36 49 35 63 114 62 39 82 39 Vali thres 1 23 29 17 58 87 33 43 69 19 Cali thres 2 267 301 260 329 442 329 269 315 268 Vali thres 2 293 266 226 360 431 312 278 325 267 Table 6-15 and Table 6-16 show the results for the absolute error in the discharge deficit and the Nash-Sutcliffe coefficient for both thresholds during calibration and validation. The results during the calibration period show better results for all tributaries when looking at the absolute error and Nash-Sutcliffe coefficient, except the Nash-Sutcliffe coefficients for the Lesse. During the validation only the Amblève shows better results for both absolute error and Nash-Sutcliffe coefficient. The Ourthe shows similar absolute errors and Nash-Sutcliffe coefficients that are worse. The Lesse only has results that are worse than the Van Deursen model. Table 6-15 Absolute error in the discharge deficit (106 m3) for the Lesse, Ourthe and Amblève for both thresholds. Lesse Ourthe Amblève Period Van Deursen New Van Deursen New Van Deursen New Calibration thres 1 36 36 84 55 83 52 Validation thres 1 41 41 103 90 85 51 Calibration thres 2 166 160 254 222 173 159 Validation thres 2 151 165 239 251 189 189 Low flow modelling of the Meuse Page 62 of 104 Table 6-16 Nash-Sutcliffe coefficients for low flows during calibration and validation for the Lesse, Ourthe and Amblève, using both thresholds Lesse Ourthe Amblève Period Van Deursen New Van Deursen New Van Deursen New Calibration thres 1 -0,14 -0,22 -0,13 0,16 -2,17 -1,49 Validation thres 1 -0,89 -1,77 -0,64 -1,16 -0,85 -0,21 Calibration thres 2 -0,42 -0,54 -0,19 0,02 -1,91 -1,38 Validation thres 2 -1,29 -2,58 -0,62 -1,18 -0,76 -0,44 6.5.3 Conclusion calibration and validation of main tributaries The validation of the three main tributaries showed that not all the results for the new model are better than the Van Deursen model. Only the results for the Amblève are univocal and show an improvement for all criteria during calibration and validation, the new setting will be used during the rest of this research. The results for the Ourthe are not univocal but the two most important criteria have a better score for the new model than for the Van Deursen model and therefore the new model is chosen. For the Lesse the Van Deursen model works much better during validation and the results for the calibration do not show large differences, therefore the old settings will be used during the rest of this research. 6.6 Calibration and validation results for Monsin and Borgharen In the schematisation used during this research the only difference between the discharge at Monsin and Borgharen is the addition of the Jeker and the abstractions of the canals between Monsin and Borgharen. The Jeker has a measured discharge deficit during the entire calibration period of less than 1 *106 m3, so the difference between Borgharen and Monsin is small. The difference between comparing Monsin and comparing Borgharen is that for Monsin the measured data of Borgharen is corrected to represent the discharge at Monsin. When Borgharen is compared the modelled data is corrected to represent the measured Borgharen discharge. The critical thresholds used during this research are all based on the natural discharge. When the Borgharen discharge is compared the threshold will have to been corrected according to the same correction list as the discharge. This will result in a changing threshold. Comparing the Monsin discharge can be done with a constant threshold, making this comparison easier and more transparent. Therefore the Monsin discharge will be used for validation. 6.6.1 Results Van Deursen criteria for Monsin Table 2-1 shows the results for the Van Deursen model and the new model. Both models have the same outcome for the Van Deursen criteria. The changes in the k4 and perc parameters have not changed the overall model performance. Table 6-17 Results for Van Deursen criteria at Monsin during calibration and validation for both the old and the new model. Average discharge (m3/s) Standard R Nash- Sutcliffe Van Deursen New Van Deursen New Van Deursen New Calibration 258 258 0,96 0,96 0,91 0,91 Validation 288 288 0,97 0,97 0,93 0,93 Page 63 of 104 Calibration and validation results 6.6.2 Results new calibration criteria for Monsin Table 6-18 shows the discharge deficits at Monsin for both calibration and validation period. The modelled discharge deficits are very well during calibration, deviations of less than one percent. However during validation the discharge deficits show deviations of approximately 120% and 40%. These results however are much better than the original model. Appendix III-7 shows the discharge deficit for individual years for both thresholds during calibration and validation. Table 6-18 Discharge deficits (106 m3) at Monsin for both thresholds and both models. Note; italic is calibration period, bold is validation period Threshold Measured Van Deursen New model (m3/s) (106 m3) (106 m3) (106 m3) 60 1021 1443 1013 60 370 1299 805 100 5209 5776 5227 100 3700 5723 5126 Table 6-19 shows the absolute error made in the discharge deficit and the Nash-sutcliffe coefficient for low flows. The Absolute error made in the discharge deficit is much smaller; especially for threshold one the difference is large, minus 50%. The Nash-Sutcliffe coefficient also shows large improvements, especially during the validation period. Table 6-19 Error in discharge deficit and Nash-Sutcliffe for low flows at Monsin for both thresholds and models. Note; italic is calibration period, bold is validation period Error in discharge deficit (106 m3) Nash-Sutcliffe low flow Threshold (m3/s) Van Deursen New model Van Deursen New model 60 783 453 -0,04 0,36 60 1391 667 -3,47 -1,84 100 2740 2500 -0,33 0,11 100 3321 2888 -2,90 -1,66 6.6.3 Conclusion calibration and validation of Monsin The post-model process for the Vesdre has not been incorporated in the results presented in this paragraph. The k4 and perc values used for the Vesdre come from a calibration without reservoirs and calibration during the entire calibration period. Appendix III-9 contains the results for Monsin when the post-model process for the Vesdre reservoir is carried out. The differences are small; however the results with the reservoir are slightly better. During the validation the modelled discharge deficit is almost always higher than the measured deficit. This is especially true for 1989 and 1990. This can be explained by the discharge of the preceding 5 to 10 years. During these preceding years the winter discharge were all, but one, larger than average, Appendix III-10. During the summers the discharge did not drop below 60 m3/s and showed relatively small discharge deficit using the threshold of 100 m3/s, Appendix III-8. Because of this relatively wet period the system probably contained more groundwater than normal. This excess of water lowered the discharge deficit during ‘89 and ‘90. The same can be said for ’95 and 96, the winters preceding these years Low flow modelling of the Meuse Page 64 of 104 were also very wet, resulting in an overestimation of the discharge deficit. The opposite is true for ’74 and ‘92 which both had relatively dry preceding winters. Because of this the model underestimated the discharge deficit during these years. Despite the overestimation during the validation period the model results have improved. Especially for the smaller of the two thresholds the model is performing much better. The difference between Chooz and Monsin are probably caused by the man-mate alternations and the errors in the discharge data, shown in paragraph 3.4.2, during the calibration period of Monsin. In retrospective the periods that contain obvious discharge errors during the calibration period could have been left out. However this would have made the calibration questionable as well, which periods should be left out and why. The current results show that the prediction of the discharge deficit increases strongly. 6.7 Conclusions about calibration and validation entire model The overall model performance of the model was not influenced by the changes of k4 and perc, all three van Deurse criteria remain the same. The model performance for individual discharges during low flows still shows the same daily errors, however the errors have become smaller. The main goal of this research was to improve the long term prediction of discharge during periods of low flow, this was established. The calibration results for the entire model show discharge deficits that have a maximum deviation of 1 percent. The validation of the different sub basins shows large differences. Some of the sub basins show discharge deficits that are similar to the measured data. The best results were established for Chooz and the Vesdre catchment including a reservoir. The worst results were established for the Lesse were the Van Deursen model showed better results than the new model. The results for Monsin have improved but still show large differences between measured and modelled discharge deficits. This may well be explained by errors in the measured data during the calibration period. The spatial distribution of the perc and k4 values shows resemblance to the characteristics of the catchments as mentioned in De wit et all (De Wit, 2001). Catchments with relatively low and slow discharge fluctuations have a relatively large perc value and a small k4 value. While the catchments with relatively large and fast discharge fluctuations have a small perc value and a large k4 value. Table 6-20 Characteristics of sub basins and their k4 and perc settings Characteristics Distribution perc and k4 Mehaigne Relatively low and slow discharge fluctuations Mehaigne Meuse upstr Chooz ↑ Vesdre Vesdre Amleve Ambleve Meuse upst chooz Ourthe Ourthe Lesse ↓ Lesse semois Relatively large and fast discharge fluctuations Semois Page 65 of 104 Calibration and validation results Chapter 7 Discussion and conclusions 7.1 Discussion of errors and uncertainties Reliability of discharge data during low flows The hydrological modelling of low flows is much harder than the modelling of normal and high flows. The main raison for this is the larger relative impact that small (structural) errors in the measured discharge data can have. Small structural differences of only a couple of cubic metres per second will cause a relatively large relative error. The measured discharge data itself are less reliable during low flows. Water flowing through the gravel and soil on the riverbed for example is hard to measure but can make a large difference. Another cause for errors are the unknown influences and discharges/abstractions of the weirs, locks, abstractions and power stations present in the Meuse and its tributaries. These man made alternations have a much larger influence on low flows than on normal and high flows. The Meuse and its tributaries contain a large number of weirs. These weirs have been not only been built to maintain shipping possibilities during low flows but also to prevent the water from flowing downstream. The operating regime of these weirs is unknown, making predictions of daily discharges during low flows almost impossible. Abstractions and bifurcations between Monsin and Borgharen The reliability of the data also suffers from the abstractions between Monsin and Borgharen. The discharge was only measured at Borgharen, therefore the discharge at Monsin had to be composed of the discharge at Borgharen and an estimation of the size of the abstractions. For the larger part of this research the correction for these abstractions is constant throughout the year, with exception of 1976 and from 1991 and further. For the entire research period the discharge difference between Chooz and Monsin has been compared with the discharge of the tributaries between the two. During the seventies a couple of periods, consisting of several consecutive weeks each, have been found were the measured discharge of the tributaries was larger than the measure difference between Chooz and Monsin. The only explanation for this phenomenon is errors occurring in the measured discharge data. The discharge data also shows periods during which the discharge of the tributaries is much lower, less than 30 percent, than the measured difference between Chooz and Monsin, these periods also have had a large influence on the calibration. Because errors occur on both sides and because of the limited amount of available data, all measurements have been used during calibration and validation. A pre-processing step could have improved the reliability of the data, however the boundaries are highly disputable and eliminating data can have a dramatic effect on the outcome. Schematisation The schematisation used during this research fits reasonably well with the measured data. However the sub basins upstream of Chooz could have been made into one sub basin. The available data is very limited. The schematisation does not include man made alternations. These man-made alternations can have a significant effect on low flows. However no information is available about the operation of these alternations like weirs, locks and reservoirs. Therefore the absence is acceptable. Despite the lack of information on the operating regimes the influences of the reservoir in the Vesdre has been research. This research showed that reservoirs can improve the low flow performance of the model. When looking at the discharge deficits or the absolute error in the discharge deficits the difference with a schematisation without a model is not very large. Therefore it is not necessary for improvement of the low flow prediction based on these criteria to incorporate reservoirs in other tributaries. For the Vesdre the optimum setting without a reservoir is used because of Low flow modelling of the Meuse Page 66 of 104 the greater transparency. The difference for Monsin between the setting with and without a reservoir is small. 7.2 Discussion calibration procedure Model parameters The parameters used during this research were chosen for three different reasons, firstly because of their influence on low flows, secondly because of their very limited influence on normal and high flows and thirdly the parameters chosen were not used by earlier calibrations. The parameters used did not change the reaction of the model to precipitation. However the parameters did change the amount of discharge during periods with relatively low flows. The use of other parameters may have resulted in better results during low flows, because of a better reaction to precipitation, but was outside the boundaries of this research. The performance during normal and high discharges would have been influenced by these other parameters. Calibration criteria During this research a number of parameters has been compared and finally a list of three criteria has been used during calibration. These three criteria have not all been used in the same way. The Nash-Sutcliffe coefficient for low flow has only been used to check the model performance for daily discharge predictions and has not been used to select the best parameter setting. The other two criteria have been selected because they specifically look at seasonal discharges and errors. This was done because of the large daily discharge fluctuations most likely cause by unnatural causes, which makes proper prediction of daily discharges virtually impossible. Using different criteria may have resulted in different parameter settings and therefore a different model performance. However the other criteria measured roughly the same characteristics and performance, the difference in the settings found by these criteria will probably have been small. Calibration procedure During the calibration the measured and modelled discharge have been compared for different sub basins. This comparison was carried out using the entire discharge at the measuring station and not the difference between two measuring stations. For example the total discharge at Monsin was used and not the difference between Monsin and Chooz. This resulted in the best performance for the overall model, but does not necessarily result in the best performance for individual sub basins. The errors made in the total discharge deficit for Chooz are very small for both calibration and validation period the performance for Monsin is, when looking at the total discharge deficit, therefore not influenced by the errors made at Chooz. 7.3 Conclusions Daily discharge predictions during periods of low flow. The Van Deursen model does not simulate the daily discharges during low flows properly. During periods with low flow the model predicted too much discharge during the first part of this period and too little during the last part of the period. Also the model did not show significant responses to small precipitation events occurring during low flow. The new model still does not show a significant response. However the prediction of the daily discharge did improve, the Nash-Sutcliffe coefficient for low flows improved form almost -3 to -1,7 Page 67 of 104 Discussion & conclusions (threshold2). The explanation for the differences between modelled and measured daily discharges during low flows is partly the simplicity of the model and partly the quality of the measured data. Average monthly discharges The average discharge during individual months shows significant relative differences between the model and the measurements. These differences show the same pattern for Chooz and Monsin, making errors in the measured data an unlikely cause, see Appendix III- 10 The model overestimates the discharge form march until September and underestimates the discharges during the other months. The Van Deursen models show the same pattern as the new model, which proves that it cannot be solved by changing k4 or perc values. The modelled data shows less variation than the measurements. Seasonal prediction during low flows The new model simulates the discharge deficits for Chooz and Monsin much better than the Van Deursen model. Also the absolute error made in the discharge deficit is much smaller. For Chooz the total discharge deficit over the entire validation period show a deviation of only 3 percent. Individual years still show large errors but these errors are also smaller than with the Van Deursen model. The result for Monsin shows a similar pattern, the same years show similar errors. For instance the relatively dry year of 1989 shows a modelled discharge deficit for Chooz and Monsin that is much too high. The relatively wet preceding years are the explanation for this overestimation of the discharge deficit. The HBV model does not simulate these influences in a proper way. The deficits for Monsin show larger error this is caused by the errors caused by the bifurcations between Monsin and Borgharen and also by other human interferences, which cause the river to flow less natural. HBV model during low flows The improvement of the model was accomplished without influencing the performance during normal and high discharges. The current HBV model, schematisation and available data are not suitable for predicting daily discharge during periods of low flows. The multi-week discharges during periods of low flow have improved but still show large errors for Monsin. The multi week discharges for Chooz are much better. The reasons for the differences between Chooz and Monsin are the uncertainties in the Monsin discharge data and the human interferences between Monsin and Chooz. Before a final conclusion about the ability of the HBV model to simulate low flows can be drawn the influence of other parameters on low flows will have to be looked at. Also the influence of preceding wet or dry years on the discharge during low flows will have to be researched. Calibration procedure The calibration procedure used resulted in an increased model performance during low flows. The criteria used showed significant differences between different settings and resulted in one optimum setting. The parameters used during this research resulted in better results for seasonal discharges during periods of low flows. However they did not result in a model that responds different to precipitation during low flows. The model still does not show a significant response while the measurements do. The optimum parameter setting found during this research show a strong correlation to the characteristics of the sub basins found by Uijlenhoet (2001). This existing relation confirms Low flow modelling of the Meuse Page 68 of 104 7.4 Recommendations Extra measured data During this research the limited available data influenced the calibration in a negative way. to be able to come up with a better model the following data is usefull; • Measured data at Monsin or detailed information about the abstractions caused by the bifurcations between Monsin and Borgharen and information about the fluctuations caused by the power plant at Lixhe. This information would give a much better insight in the daily fluctuations at Monsin. It would also give information about the validity of the measured data between Monsin and Chooz. • Measured discharge data of the Sambre, one of the largest tributaries of the Meuse. The Sambre is influenced by several reservoirs, build for navigational and domestic purposes, and a large drinking water abstraction; both influences are relatively unknown but can play a significant role on the low flow performance of the model at Monsin. • Information about the operating regime of the reservoirs present in Meuse and its tributaries. The additional discharge of the reservoirs during periods of low flow can have a significant influence on the discharge at Monsin. Because the operating regime of these reservoirs is unknown they have not been incorporated into the model. • Detailed information about the operating regime of the weirs and locks present in the Meuse and its tributaries. Information about the operating of weirs will give a better understanding of the flow during and preceding periods of low flows. Information about the use of locks and the losses caused by the use of these locks will give a better understanding in of the low flows. Capabilities HBV To get a better insight in the capabilities of the HBV model to simulate low flows a more detailed research for the Chooz area should be carried out. This research should focus on all the criteria used by Van Deursen and during this research and give an answer to the question whether or not a proper response to precipitation during low flows is possible with the HBV model. This research should also look at the influence that preceding wet, or dry, years (winters) can have on the summer discharges. The research should look at Chooz because the influence of human interference on the discharge is smallest at Chooz. The results of this research will be a better insight in the capabilities of the HBV model simulated low flows. Page 69 of 104 Discussion & conclusions References Aalders, P, Rainfall Generator for the Meuse basin, Case study Ourthe basin, Arnhem; RIZA, 2004 Berger, H.E.J., Flow Forecasting for the River Meuse, afvoervoorspelling voor de Maas, Delft; University of Delft, 1992 Bergström, S, The HBV story in Sweden, Norrköping (Sweden); Swedish Meteorological and Hydrological Institute, 1998 Booij, M.J., Appropriate modelling of climate change impacts on river flooding, Enschede; University Twente, 2002 Deursen, W van, Afregelen HBV model Maasstroomgebied, Rotterdam; Carthago Consultancy, 2004 Groot Zwaaftink, M.E., Hydrological Modelling of the Ourhte, A compariosn of Rainfall-Runoff Models, Riza, 2003 Poortema, K, Statistek I voor CiT, Enschede; University Twente, 2001 Raadgever, T, Schademodelering laagwater Maas, Een onderzoek naar de omvang en de opbouw van de schade ten gevolge van lage Maasafvoeren in de huidige situatie en in een aantal scenario’s voor autonome ontwikkelingen en beheer, Maastricht; Royal Haskoning, 2004 Roozenburg, N.F.M., Productontwerpen, structuur en methoden, 2e druk, Utrecht; uitgeverij Lemma B.V., 1998 Tu, M, ‘Extreme floods in the Meuse river over the past century: aggravated by land-use changes?’, Physics and Chemistry of the EARTH, 30 (2005) 267-276 Uijlenhoet, R, Statistical analysis of Daily Discharge Data of the River Meuse and its Tributaries (1968-1998): Assesment of Drought Sensitivity, Wageningen; University of Wageningen, 2001 Velner, R.G.J., Neerslag-afvoer modellering van het stroomgebied van de Ourthe met het HBV model, Een studie ten behoeve van verlenging van de inzichttijd van hoogwatervoorspellingen op de Maas, RIZA, 2000 Wit, M.J.M. de, Effect of Climate Change on the Hydrology of the River Meuse, Wageningen; Wageningen University, 2001 Wit, M. de, A hydrological description of the Meuse basin, In: Proceedings fo the First international Scientific Symposium on the River Meuse, Maastricht November 2002, Liège (Belgium); 2002. Low flow modelling of the Meuse Page 70 of 104 List of figures Figure 2-1 Meuse basin...... 3 Figure 2-2 Gradient of the Meuse and its main tributaries, (Berger 1992) ...... 3 Figure 2-3 Hydrograph of the discharge at Monsin of a average year (1978)...... 3 Figure 2-4 Average precipitation in Meuse basin upstream of Borgharen, during an ‘average’ discharge and precipitation year (1978), ...... 3 Figure 2-5 Hydrograph of 1978 and 1976, an average and extremely dry year...... 3 Figure 2-6 Hydrograph of 1978, showing fluctuations in daily discharges for Chooz and Monsin during a eight week period, starting September 16th 1978...... 3 Figure 2-7 Schematic picture of the canals between Monsin and Borgharen. (Berger,1992)...... 3 Figure 3-1 Schematisation of the upstream parts of the river Meuse, used in the HBV model...... 3 Figure 3-2 Correction factor for the calculation of the Monsin discharge out of the Borgharen discharge, for the year 1976...... 3 Figure 3-3 Discharges of Borgharen and Monsin in 1976, measured data...... 3 Figure 3-4 Hydrograh Mosnin 1976...... 3 Figure 3-5 Hydrograph Monsin 1978...... 3 Figure 4-1 Calculation of the discharge deficit ...... 3 Figure 4-2 Cumulative discharge deficit, based on yearly deficits, at Monsin, using a threshold of 60 m3/s...... 3 Figure 4-3 Cumulative discharge deficit at Monsin with different perc settings...... 3 Figure 4-4 Cumulative discharge deficit at Monsin, based on yearly discharge deficits, with different k4 settings ...... 3 Figure 4-5 Nash-Sutcliffe coefficient for low flows using different k4 and perc settings...... 3 Figure 4-6 Standard R for low flows using different k4 and perc values...... 3 Figure 4-7 Hydrograph of 1976 with different perc settings...... 3 Figure 4-8 Hydrograph of 1976 with different k4 settings...... 3 Figure 5-1 Calibration of sub basins...... 3 Figure 6-1 Sum of relative discharge deficit differences, calculated with thresholds of 33 and 50 m3/s...... 3 Figure 6-2 Discharge deficits for the Vesdre and a corrected discharge deficit for Chooz during calibration and validation period using threshold 1...... 3 Low flow modelling of the Meuse Page 71 of 104 List of tables List of tables Table 2-1 Main tributaries of the Meuse (Berger, 1992)...... 3 Table 2-2 Characteristics of minimum discharges and reservoirs for different tributaries.(Uijlenhoet, 2001) ...... 3 Table 2-3 Distribution of Meuse water during periods with low flow, regulated in the Meuse discharge treaty. (Raadgever 2004)...... 3 Table 3-1 Size of sub-basins between Chooz and Monsin...... 3 Table 3-2 Relative differences between gauged discharges and measured differences between Monsin and Chooz...... 3 Table 3-3 Nash Sutcliffe and standard R coefficients during different months of the year ...... 3 Table 3-4 Van Deursen model results...... 3 Table 3-5 Average discharge for specific months at Monsin and Chooz (from 1968 to 1998) ...... 3 Table 4-1 Critical threshold for different stations based on method 1, ratio of discharge...... 3 Table 4-2 Critical threshold for different stations based on method 2, average number of days with a discharge lower than the critical threshold ...... 3 Table 4-3 Discharge deficit for entire period for different k4 values ...... 3 Table 4-4 Discharge deficit for entire period for different perc values...... 3 Table 4-5 Absolute error in the discharge deficits ...... 3 Table 4-6 Absolute error in the discharge deficits ...... 3 Table 4-7 Average number of days with a discharge below thresholds...... 3 Table 4-8 Average number of days with a discharge below thresholds...... 3 Table 4-9 Moving average period with highest sensitivity for changes in k4 parameter, overall values will be used during calibration...... 3 Table 4-10 Moving average period with highest sensitivity for changes in perc parameter, Overall values will be used during calibration...... 3 Table 4-11 Moving average periods used during calibration...... 3 Table 5-1 Nash-Sutcliffe coefficients of the Ourthe catchment for different simulations and different calibration periods...... 3 Table 5-2 Simulation of daily discharge with HBV model in terms of Nash-Sutcliffe value (Italic is calibration, bold is validation) (Aalders 2004)...... 3 Table 6-1 Relative difference between measured and modelled discharge deficit, accumulated over the calibration period, for Chooz using a threshold of 33 m3/s, with different k4 and perc parameter values...... 3 Table 6-2 Relative difference between measured and modelled discharge deficit, accumulated over the calibration period, for Chooz using a threshold of 50 m3/s, with different k4 and perc parameter values ...... 3 Table 6-3 Sum of the relative differences between measured and modelled discharge deficits, accumulated over the calibration period, calculated with thresholds of 33 and 50 m3/s...... 3 Table 6-4 Sum of the absolute error in the discharge deficits (106 m3) made using both thresholds, accumulated during the calibration period, for Chooz...... 3 Table 6-5 Average of Nash-Sutcliffe coefficients for both thresholds for Chooz ...... 3 Table 6-6 Results Van Deursen criteria at Chooz during calibration and validation for both the old and the new model...... 3 Table 6-7 Discharge deficits (106 m3) at Chooz for both thresholds and both models...... 3 Table 6-8 Differences in discharge deficits, for different thresholds during calibration and validation, between Van Deursen model and new model ...... 3 Table 6-9 Absolute error in the discharge deficit and Nash-Sutcliffe low flow, for both thresholds...... 3 Table 6-10 Discharge deficit for both thresholds for different reservoir regimes compared to the original model during calibration and validation period...... 3 Low flow modelling of the Meuse Page 72 of 104 Table 6-11 Absolute errors in the discharge deficit for different reservoir regimes compared to the original model during calibration and validation period...... 3 Table 6-12 Nash-Sutcliffe values for different reservoir regimes compared to the original model during calibration and validation period...... 3 Table 6-13 Results Van Deursen criteria for the Lesse, Ourthe and Amblève during calibration and validation ...... 3 Table 6-14 Discharge deficit (106 m3) results for main tributaries during calibration and validation...... 3 Table 6-15 Absolute error in the discharge deficit (106 m3) for the Lesse, Ourthe and Amblève for both thresholds...... 3 Table 6-16 Nash-Sutcliffe coefficients for low flows during calibration and validation for the Lesse, Ourthe and Amblève, using both thresholds ...... 3 Table 6-17 Results for Van Deursen criteria at Monsin during calibration and validation for both the old and the new model...... 3 Table 6-18 Discharge deficits (106 m3) at Monsin for both thresholds and both models...... 3 Table 6-19 Error in discharge deficit and Nash-Sutcliffe for low flows at Monsin for both thresholds and models...... 3 Table 6-20 Characteristics of sub basins and their k4 and perc settings...... 3 Low flow modelling of the Meuse Page 73 of 104 List of tables Appendix I Meuse basin and main tributaries I.1 Description of the main tributaries of the Meuse upstream of Borgharen The tributaries of the Meuse supply the greater part of its discharge. Ground water, precipitation and artificial extractions constitute the discharge to a smaller extent. The Meuse has a great number of tributaries, varying greatly in size. The most important tributaries will now be discussed from South to North. Special interest will go to their contributions to low flows. The Chiers The Chiers is one of the largest tributaries of the Meuse, it springs near Differdange (Luxemburg) at approximately NAP + 339 m. The mouth is near Rémily-Aillicourt at approximately NAP + 149 m and its length is 144 km, making the average gradient 1 10-3. The contributing area amounts to 2,222 km2 of which 89 percent lies upstream of the measuring station of Carignan. The main tributaries of the Chiers are the Ton, the Crusnes, the Othain and the Loison. The catchment can be split up into different parts with different characteristics. The valley in the downstream part of the Chiers is very permeable; the southern part of the catchment contains many impermeable soils and loamy soils, in the north and east much sandstone and limestone is found. During floods the northern part of the catchment supplies a somewhat greater share, the reason being the smaller permeability. During the dry summer of 1976 the Chiers still had a minimum discharge of over 4 m3/s, doubling the discharge at Sedan, which is normal. The draining of the iron mines influences the low flow, it is expected that this discharge will decrease with approximately 0.3 m3/s during low flows. The Semois The Semois springs near Arlon (France) at NAP + 411 m, flowing west to its mouth near Monthermé (Belgium) at approximately NAP + 138 m. With a length of 167 km the catchment is lengthy, the mean gradient is 1.5 10-3. The size of the catchment is 1,358 km2, of which 40 percent is covered with forests. The main tributaries, the Rulles and the Vierre, flow out into the river in the upstream part. The tributaries spring at a higher level than the Semois itself. The upstream part of the catchment lies in a relatively even area being part of the Belgian Lorraine, with different permeability. Downstream of the mouth of the Vierre the nature of the river changes, the gradient goes from 1.1 10-3 to 1.7 10-3. The river flows through the Ardennes Massif with rocks of a Palaeozoic origin. In the Vierre tributary a small reservoir, 1.3 106 m3, was build in 1970, the water is mainly used for generation of electricity, the capacity is too small to cause a significant increase in the low flows in the Meuse. Measurements by the IRM (Institute Royal Métérologigue de Belgique) showed that at the end of 1976 the Vierre no longer carried water. The Viroin The Viroin is a medium-sized catchment of the Meuse with a size of 593 km2, of which 93 percent lies above the measuring station. The water is supplied ia the Eau Blanche and the Eau Noire, below the confluence of the two rivers is called Viroin. Rocroi (France) is taken as the source and the mouth lies near Vireux (France), the largest part of the catchment lies in Belgium. The southern part of the catchment forms part of the Rocroi Massif, with hard and Page 75 of 105 Appendix II impermeable Cambrian rock. The Northern section and the central part contain rock and limestone. The source lies at NAP + 359 m, the mouth at NAP + 106 m. the highest point of the catchment is at NAP + 388 m. The river is only 57 km long and has a mean gradient of 2 10-3. The Eau Noire contains a reservoir, 2.2 106 m3, to provide the surroundings with drinking water and industrial water. According to the Ministère des Travaux Publics the capacity is sufficient for supplying 8600 m3 /day (0.1 m3/s) during two dry years. The Lesse The Lesse may be considered a typical Ardennes River. It springs at NAP + 403 m near Libramont (France, near Belgium border) an the mouth lies just beneath the weir of Anseremme at NAP + 89 m. The catchment has a size of 1314 km2. The main tributaries are the Gembes, Lomme, Wimbe and the Ywenne. The river has a length of 83 km and a mean gradient of 5 10-3. The highest point of the catchment is at NAP + 585 m. The northeastern part of the catchment has some underground flowing parts. Near its source the gradient of the Lesse is great and towards the mouth it decreases more and more. The mean gradient amounts to approximately 5 10-5. Most of the tributaries have he same kind of course as the Lesse, regarding their length and gradient, resulting in great peak discharge in case of an occurring flood. According to the IRM the low flow discharges may sink to very low values. The Sambre The source of the Sambre lies in Garmouzet (France) at NAP + 210 m, its mouth in Namur (Belgium), at NAP + 77 m. The length of the Sambre is approximately 184 km, resulting in a mean gradient of 7 10 –4. The main tributaries are; the Helpe Majeure, the Solre, the Thurne and Eau d’Heure. The first four tributaries flow out into the upper course of the Sambre, the last into the central course. The catchment has a total size of 2,863 km2, 80 of which lies above Charleroi. The discharge of the Sambre is hardly natural owing to the presence of many weirs and lock. The discharge is further influences by artificial withdrawals and discharges. The Sambre is a special tributary compared to others in being the only tributary that admits shipping over a greater length. Mainly below Charleroi shipping is intensive. As a result locks need much water, more than can be supplied in a natural way during periods of low flow. Therefore several reservoirs have been constructed. The largest of these reservoirs does not have sufficient natural feeding. During nighttime pumps pump the water up into the reservoir. The same water is released during daytime, generating energy in the process. Upstream of this largest reservoir three dams, small reservoirs, have been built to keep the water level as constant as possible. This entire system of reservoirs creates large fluctuations in the daily discharges and makes predicting (low) discharges much more difficult The Ourthe The Ourthe is the largest of all the tributaries with a catchment size of 3,626 km2 and a length of 72 km. It is a typical Ardennes river and therefore has great discharges that rise fast. Through its nature and geographic position, near the Dutch boarder, it is the most important Meuse tributary for flood forecasts. In the upper course the Ourthe consist of two branches; the Ourthe Occidentale and the Ourthe Orientale, uniting near Nisramont. Near Comblain-au- Pont the Amblève joins the Ourthe and near Angleur the Ourthe also receive the Vesdre. Those two tributaries are so important that special attention will be paid to them for two reasons, one their discharges can be larger then those of many other Meuse tributaries, two because their mouths are very close to the mouth of the Ourthe. Also the measuring station Low flow modeling of the Meuse Page 76 of 105 in the Ourthe does not always produce reliable values of the discharges as a result of the changing positions of the weir elements of the Grosses Battes Weir. The Vesdre The Vesdre springs at NAP + 626 m east of Eupen (Belgium), its mouth in the Ourthe is near Chênée (a suburb of Liège) and Angleur at NAP + 62 m. The main tributaries are the Hoegne and the Gileppe. The river has a length of 72 km and a mean gradient of 8 10-3. For the main part the catchment lies on rocks, carrying small amounts of water. The combination of the rocks and the large gradient caused a shortage of water during summer. Two large reservoirs, capacity of 25 106 m3 each, have been constructed to solve this problem; both reservoirs can maintain a discharge of 75,000 m3/day (0.87 m3/s), guaranteeing a minimum discharge of 1.7 m3/s. Another consequence of the reservoirs is that they are blocking great discharges, the total size of the catchment areas amount to 24 percent of the total Vesdre catchment, which is also the part with the most precipitation. Berger researched the influence of the reservoirs on the discharge and came to the conclusion that the discharge is rather constant. A low flow model for the Meuse will have to contain a constant component in the discharge, although it only concerns some percent of the Maastricht-St.-Pieter discharge. The Amblève The influence of the Amblève on the discharge of the Ourthe is considerable; the size of the Amblève catchment is 1,052 km2, which is nearly 30 % of the total catchment of the Ourthe. The Amblève springs at NAP + 584 m near ravage, its mouth is near Comblain-au-Pont at NAP + 108 m. The river has a length of approximately 88 km, with exception of the upper course the gradient is 5 10-3. The Cascade of Coo, below the mouth of the Salm, forms a curiosity, the river drops as much as 12 m over a length of 70 m. The Amblève has a number of tributaries showing great similarities from a hydrologic point of view. These tributaries, The Lienne, Salm, Eua Rouge, Warche and Recht, all flow out into the central course of the Amblève, spring between 450 m and 650 m, are approximately 20 km long and for the greater part their catchments have rock of Caledonian origin as their basis. This causes the river to react rapidly to precipitation and to have very low lows during dry seasons. The Sambre contains several reservoirs of which the reservoir near Butgenbach is the most one form a hydrologic point of view. The water level may vary strongly, in the spring months April and May the reservoir is completely filled (11 106 m3), in October and Novermber the reservoir is minimally filled (3 106 m3). During the summer half year the discharge is artificially increased with an average of 0.5 m3/s, and decrease with the same amount during winter. Ourthe upstream from Tabreux The Ourthe consists of two branches, the Ourthe Occidentale and the Ourthe Orientale. Both spring at approximately NAP + 500 m. The confluence is in the Nisramont reservoir, which has a size of 3 106 m3. The main purpose of the reservoir is generating electricity; the influence on the discharge at Borgharen is small. The catchment has a size of 1,597 km2 and mainly consists of Palaeozoic rock. The river has a length of approximately 90 km and a mean gradient of 3.7 10-3. The characteristics of the river, impermeable grounds, great gradient, steep slopes in the landscape, cause the river to be an important tributary during floods. During periods of low flow the discharge is very small. Page 77 of 105 Appendix II I.2 Abstractions and artificial discharges upstream of Borgharen Abstraction Discharge Reason Sub-basin (m3/s) (m3/s) Power station 0.5 Chooz - Monsin Drinking water 3 Sambre Canals Monsin - Borgharen • Albertkanaal 21 - 24 Monsin - Borgharen • Zuid-Willemsvaart 14 - 16 Monsin - Borgharen • Julianakanaal 15 - 16 Monsin - Borgharen • Monsin, Cheral 3.5 - 4 Monsin - Borgharen • Lanaye Locks 8 Monsin - Borgharen Total 38 - 44 Reservoirs • Barrage de la Vierre 0.1 Semois • Etang de Virelles 0.1 Viroin • Cerfontaine unknown Sambre • Eupen 0.87 Vesdre • Gileppe 0.87 Vesdre • Butgenbach 0.5 Amblève • Nadrin 0.1 Ourthe Notes; • The Sambre has an unknown discharge, no data is available. The complex of reservoirs build to maintain a minimum flow of 5 m3/s is operated with pumps. The abstraction of the drinking water and the influence of the reservoir will probably compensate each other during low flows. • The reservoirs in the Vesdre will be researched in detail to get a better understanding of the impact and influences the reservoirs can have. Low flow modeling of the Meuse Page 78 of 105 Appendix II Description BHV model II.1 HBV model description (Groot Zwaaftink, 2003) Evapotranspiration Precipitation Snowfall Rainfall Precipitation Refreezing routine Snow Free water Snowmelt Infiltration Soil moisture Soil moisture routine Capillary Seepage Direct transport runoff Fast runoff Fast runoff reservoir Fast runoff routine Percolatio Baseflow Baseflow reservoir Baseflow routine MAXBAS Transformation routine River flow of catchments upstream of the catchment Routing River reservoir routine River flow below the catchment Figure II-1 Schematisation of the HBV model with six routines Page 79 of 105 Appendix II Figure II-2 Structure of the HBV model (source: SMHI, 1999) Low flow modeling of the Meuse Page 80 of 105 Precipitation routine Precipitation can occur as rainfall or snowfall. Snowfall occurs if the air temperature T [oC] is below a defined temperature TT [oC] and rainfall occurs if T >TT (Figure II-2). Snowfall is added to the dry snow reservoir (within the snow pack) and rainfall is added to the free water reservoir, which represents the liquid water content of the snow pack. Interactions between these two components take place through snowmelt and refreezing. snow melt = CFMAX ⋅ (T − TT ) (III-1) refreezing melt water = CFR ⋅CFMAX ⋅ (TT − T) (III-2) CFMAX = melting factor [mm/(d x oC)] CFR = refreezing factor [-] The free water reservoir content is at most equal to a specified fraction (0-1) of the water equivalent of the dry snow content. If this fraction is exceeded through rainfall or snowmelt, the water becomes available for the soil moisture routine. Soil moisture routine The amount of soil moisture in the catchment is computed with a soil moisture reservoir, representing the unsaturated zone (Figure II-2). The volume of soil moisture in this reservoir is symbolised by SM (soil moisture content). The maximum storage of the reservoir, the maximum soil water content of the reservoir, is represented by FC. The inflow of this reservoir is the precipitation and snowmelt, symbolised by P. The inflow is divided into direct discharge (DR, [mm/d]), indirect discharge or seepage (R, [mm/d]) and evapotranspiration (EA, [mm/d]). If the maximum soil moisture storage in the reservoir is exceeded ((SM+P)>FC), direct discharge occurs. DR = max{}()SM + P − FC ,0 SM = FC ⇒ DR = P (III-3) The volume of infiltrating water into the soil moisture reservoir (IN, [mm/d]) is: IN = P - DR (III-4) A part of this infiltrating water will contribute to the soil moisture content SM , the other part will run through the soil layer as indirect discharge R . The indirect discharge (R, [mm/d]) through the soil layer is determined by the amount of infiltrated water (IN) and the soil moisture content (SM, [mm]), through a power relationship with parameter β . β SM R = IN ⋅ (III-5) FC From this relation follows that the indirect discharge is increasing with increasing soil moisture content. For a smaller value of β , the increase is stronger. In equation III-5 it is also assumed that as long as there is no infiltration, there is no indirect runoff. This is consistent with the behaviour of the unsaturated zone of a soil. The amount of water that does not run off is added to the soil moisture. The third outflow of this routine is the actual evapotranspiration (EA, [mm/d]), computed with the potential evapotranspiration (EP, [mm/d]). Page 81 of 105 Appendix II SM EA = ⋅ EP SM < LP (III-6) LP ⋅ FC EA = EP SM ≥ LP (III-7) where LP (limit for potential evapotranspiration) is a fraction between 0 and 1. The actual evapotranspiration is thus equal to the potential evapotranspiration if the actual soil moisture is above a specified threshold (LP). The general effect of the soil routine is a small contribution to the runoff from rain or snow melt if the soil is dry, and a great contribution during wet conditions. The actual evapotranspiration decreases as the soil dries out. Fast runoff routine The outflow of the soil moisture routine, DR + R , is available for the fast and base flow routine. The runoff delay is simulated through the use of two reservoirs. One reservoir represents fast runoff (overland flow and interflow) and the other represents baseflow. The direct (DR) and indirect discharge (R) percolate into the baseflow reservoir, until the baseflow reservoir gets saturated and a specific threshold (PERC, [mm/d]) is exceeded, the redundant water flows into the fast runoff reservoir. The fast runoff out of this (fast) reservoir Q0 into the river network is defined as follows (1+α ) Q0 = K ⋅UZ (III-8) where UZ is the storage in the fast runoff reservoir [mm], α a measure for the nonlinearity of the reservoir [-] and K a recession coefficient [d-1]. The recession coefficient K is determined by using α and two additional parameters hq and khq , representing respectively a high flow rate [mm/d] and a recession coefficient [d-1] at a corresponding reservoir volume [mm]. Parameter hq is determined by: hq = khq ⋅UZ hq (III-9) The parameter hq is a peak flow, and khq the corresponding recession coefficient. The high flow rate hq can be directly derived from observed average flow rate mq and average annual maximum flow rate mhq (both in mm/d) hq = mq ⋅ mhq (III-10) The combination of equation III-8, III-9 and III-10 with chosen α and khq finally gives recession coefficient K Another process in this routine is the capillary upward transport into the soil moisture reservoir. The capillary flow [mm/d] depends on the amount of water stored in the soil moisture zone. The parameter CFLUX [mm/d], a maximum value of capillary flow, determines a limitation for the capillary flow. The capillary flow depends on the soil moisture deficit, the difference between FC (maximum storage of the soil moisture reservoir, [mm]) and SM (storage in the soil moisture reservoir, [mm]). If the difference is positive, a fraction of CFLUX will flow capillary upward. Low flow modeling of the Meuse Page 82 of 105 capillaryflux = CFLUX ⋅ (FC − SM ) / FC (III-11) It should be noticed that the actual evapotranspiration and the capillary flux are both a function of the maximum storage of the soil moisture reservoir. Baseflow routine The baseflow Q1 [mm/d] out of the baseflow reservoir is the second part of the response function. The reservoir represents the groundwater storage of the catchment contributing to -1 the baseflow. The recession coefficient K4 [d ] is the only calibration parameter of this linear reservoir. The baseflow is represented by the following equation: Q1 = K4 ⋅ LZ (III-12) in which LZ is the water level in the reservoir [mm]. Transformation routine The total discharge Q = Q0 + Q1 can be further transformed to get a proper shape of the hydrograph by using a transformation function. The transformation function is a simple filter technique with a triangular distribution of the weights, which is controlled by the parameter MAXBAS , see Figure II-3. A value of 1 distributes the runoff of a certain day over the same day. A higher value of MAXBAS will distribute the runoff of one day over a larger period of time. This procedure results to a delay in the subbasin discharge. Figure II-3 The transformation function (SMHI, 1999) Page 83 of 105 Appendix II II.2 Desciption of het parameters in het HBV model (Groot Zwaaftink, 2003) Model recstep [-] Number of internal computation step in the response routine during one time step of the model. Default value is 999 if hbv96 is on and 0 if hbv96 is off. Precipitation pcorr [-] General precipitation correction factor. Default value = 1.0 whether hbv96 is on or off. This correction can be used to correct systematic error in precipitation data. pcalt [1/100m] Elevation correction factor for precipitation. Default value is 0.1 if hbv96 is on and 0 if hbv96 is off. To correct precipitation data for elevation, the precipitation is multiplied with 1+h*pcalt, with h being the elevation difference between the elevation and the elevation of the measuring station. tcalt [0C/100 m] Temperature lapse. Default value is 0.6 if hbv96 is on and 0 if hbv96 is off. Temperature correction for elevation. An increase of the elevation with 100 m results in a decrease of the temperature with tcalt degrees. rfcf [-] Rain fall correction factor. Default value = 1.0 whether hbv96 is on or off. In case of a systematic rainfall error the rainfall can be correct by multiplying wit this factor. sfcf [-] Snow fall correction factor. Default value = 1.0 whether hbv96 is on or off. This factor corrects the amount of snowfall; values lower then one decrease the amount of snow, values larger then one increase the amount of snowfall fosfcf [-] Forest snow fall correction factor. Default value = 1.0 whether hbv96 is on or off. Influences the amount of snowfall in forest areas. tt [0Celcius] Threshold temperature. Default value = 0 whether hbv96 is on or off. Middle of the snowfall interval, at this temperature half of the precipitation consists of snow. Ad the edges of the interval all the precipitation consist of rain (highest value) or snow (lowest value). This relation is linear. tti [0Celcius] Total length of a temperature interval. Default value is 2.0 if hbv96 is on and 0 if hbv96 is off. Total lenth of the snow fall interval around the middle tt. Sclass [-] Number of snow classes. Default value is 3 if hbv96 is on and 0 if hbv96 is off. Every zone is divided into several sub zones with the same size. The values for sdfistfo and sfdistfi will be varied over the sub zones sfdistfo [-] Distribution of snow fall in forest zones if the parameter sclass is used. Default value is 0.2 if hbv96 is on and 0 if hbv96 is off. Distribution of snowfall in forested areas (if sclass is being used).A value of zero will give the same accumulation of snow for all the snow classes. While a value between zero and one means that snowfall will Low flow modeling of the Meuse Page 84 of 105 be multiplied with a factor, which increases linear, from 1-sfdistfo to 1+sfdistfo. . sfdistfi [-] Distribution of snow fall in field zones if the parameter sclass is used. Default value is 0.5 if hbv96 is on and 0 if hbv96 is off. Distribution of snowfall in areas without forest (if sclass is being used). A value of zero will give the same accumulation of snow for all the snow classes. While a value between zero and one means that snowfall will be multiplied with a factor, which increases linear, from 1- sfdistfi to 1+sfdistfi. dttm [0Celsius] Factor to be added to tt to give the threshold temperature for snow melt. It is often zero. Default value = 0 whether hbv96 is on or off. cfmax Snow melting factor. [mm/0Celsius•day] Default value is 3.5 if hbv96 is on and 0 if hbv96 is off. Describes the rate at which accumulated snow will melt per degree of temperature rise above tt+dttm 0C. focfmax [-] Factor that will be multiplied by cfmax for zones of type forest. Default value is 0.6 if hbv96 is on and 1.0 if hbv96 is off. Is used to decrease the rate of snow melt in forested areas. whc [mm/mm] Water holding capacity of snow. Default value is 0.1 if hbv96 is on and 0 if hbv96 is off. The amount, in millimetres, of water present in a millimetre of snow. cfr [-] Refreezing factor in the snow routine. Default value is 0.05 if hbv96 is on and 0 if hbv96 is off. Gives the fraction of water that will freeze after being released from the melting snow at a temperature between tt+dttm and 0 0C. Soil moisture FC [mm] Maximum soil moisture storage. Default value is 200 if hbv96 is on and 0 if hbv96 is off. Maximum amount of water that can be stored in the unsaturated zone, value range from 100 to 350. beta [-] Exponent in formula for drainage from soil. Default value is 2.0 if hbv96 is on and 0 if hbv96 is off. Exponent that describes the discharge from the unsaturated zone to the fast runoff reservoir. Values between 1 and 4. lp [-] Limit for potential evaporation. Default value is 0.9 if hbv96 is on and 0 if hbv96 is off. Limit for pontential evaporation, described as a fraction of FC (1,0 or less). When the saturated zone reaches the value of FC * lp the evaporations reaches the maximum value. The relation between soil moisture and evaporations is linenair when the soil moisture value is between 0 and FC * lp cevpfo [-] Correction factor for potential evaporation in forest zones. Default value is 1.15 if hbv96 is on and 1.0 if hbv96 is off. cflux [mm/day] Maximum capillary flow from upper response box to soil moisture zone. Default value is 1.0 if hbv96 is on and 0 if hbv96 is off. Page 85 of 105 Appendix II Fast runoff reservoir alfa [-] Parameter in the outflow equation for the upper response box. Default value is 1.0 if hbv96 is on and 0 if hbv96 is off. Alfa is a measure for the nonlinearity. When Alfa is equal to 0 the discharge of the fast runoff reservoir is a linear function of the amount of stored water, an increasing value increases the nonlinearity of the relation between the amount of water stored and the size of the discharge. hq [mm/day] Discharge when the recession coefficient for the upper response box equals khq. Default value is 3.0 if hbv96 is on and 0 if hbv96 is off. The value of the recession coefficient is supposed to be equal to this value. This parameter is the discharge from the fast runoff reservoir divided by the size of the catchment and calculated in mm/day. When alfa, hq and khq are known the discharge of the fast runoff reservoir can be calculated with the formula; hq = khq * UZhq khq [day-1] Recession coefficient for the upper response box when water discharge equals hq. Default value is 0.17 if hbv96 is on and 0 if hbv96 is off. Slow runoff reservoir perc [mm/day] Percolation from upper to lower response box. Default value = 0 whether hbv96 is on or off. Percolation of the fast runoff reservoir to the slow runoff reservoir. When enough water is present in the fast runoff reservoir an amount of water equal to perc will be discharge to the slow runoff reservoir. -1 k4 [day ] Recession coefficient for lower response box. Default value = 0 whether hbv96 is on or off. Recession coefficient for the slow runoff reservoir. The value of this parameter must be larger then 0 and smaller or equal to 1. When the value is one the entire content of the slow runoff reservoir will be discharge during the day. Transformation function maxbas [days] Number of days in transformation routine. Default value = 0 whether hbv96 is on or off. Number of days in the transformation function to get a transformed discharge pattern. The program automatically takes care that the maxbas is not smaller then the chosen time step of the model. Low flow modeling of the Meuse Page 86 of 105 II.3 Measured data The measured data consists of corrected precipitation, temperature and the potential evapotranspiration series for all the 15 sub catchments and is collected by the Dutch meteorological institute (KNMI). All the series are daily averages for the entire sub catchment and have been corrected for elevation. Precipitation The precipitation series for all the 15 sub catchments are complete. For all the catchments the daily total precipitation is available. These daily totals have already been corrected for relative height of the area. For three of the sub catchments additional adaptations have been made to improve the reliability of the outcome; The Sambre catchment is partly located in Belgium (two thirds) and partly in Franche (one third). For both parts precipitation series are available. Based on these series a precipitation set for the Sambre catchment has been constructed based on the size of the two parts. The precipitation figures from the Dutch bureau of meteorology contain negative daily total precipitation figures for two sub catchments (Chooz-Namur and Namur-Borgharen). These negative precipitation figures do not have a clear physical meaning and are set to zero. Evapotranspiration Belgian catchments The evapotranspiration figures of the Belgian catchments consist of potential evapotranspiration figures that have already been corrected for relative height of the area. Four of the sub catchments contain hiatus, which are filled up using a simple linear approximation. The Meuse catchment of Chooz-Namur does not consist of any figure after the first of January 1989. This hiatus is filled up using the Viroin catchment for which there is a complete set of evapotranspiration figures after January 1989. The assumption has been made that the areas will have similar evapotranspiration. This is confirmed by average annual totals during the period of 1968 to 1986. This period is a reliable indicator because during this period the evapotranspiration figures for all the catchment are complete. During this period the Chooz-Namur area has a average yearly total evapotranspiration of 528 mm compared to 530 in the Vroin region. From this difference a transformation factor of 0.997 has been derived, which will be used to calculate the Chooz-Namur set by multiplying the Virioin set with this factor. The Amblève and Vesdre catchments both have a hiatus from the first of January 1987 until the thirty-first of 19990. The catchment of the Ourthe shows many similarities with the Amblève and Vesdre catchments and will therefore be used to fill up the hiatus. The transformation factors for are again derived for the 1968 to 1986 period and are 1,107 (Amblève) and 1,136 (Vesdre). The Meuse catchment Namur-Borgharen shows the same hiatus, starting January the first 1987 and lasting until December thirty-first 1990. The average evapotranspiration from 1968- 1986 shows a strikingly low evapotranspiration figure of only 511 mm. The Sambre catchment shows a similar evapotranspiration figure of 527 mm, corresponding with a transformation factor of 0.969. Page 87 of 105 Appendix II French catchments The French catchments show evapotranspiration figures that are systematically higher then the Belgian stations. Most likely the French figures are open water transpiration. To correct these figures the average Belgian evapotranspiration have been applied to Meuse Source- st.Mihiel, Chier St.Mihiel-Stenay and Meuse Stenay-Chooz. This is a rough simplification of reality but this will not have a major influence on end result of this research. Temperature For eleven different measuring stations average day temperatures are available. These stations are Aachen (B), Beek (B), Chimay (B), Dourbes (B), Ernage (B), Forges (B), Lacuisine (B), Langres (F), Reims (F) and St. Hubert (F). For every catchment the average temperature of the four topographically closest stations has been taken. The longitude of the measuring stations is an important factor in the distance, because of the temperature differences in the longitudinal direction. Because of the elevation differences between the measuring stations and the average elevation of the catchment of interest corrections have to be made. An increase of the elevation with 100 meters causes the temperature to drop 0.6 °C. The result of the averaging and correcting is a set of average daily temperature of the catchment. Hiatus present in individual stations get negligibly small. Table II-1 Catchments and their assigned measuring station Catchment Station 1 Maas Source-St.Mihiel Langres Loxeville Reims Lacuisine 2 Chiers Loxeville Reims Lacuisine St.Hubert 3 Maas St.Mihiel-Stenay Loxeville Reims Lacuisine Forges 4 Maas Stenay-Chooz Lacuisine Forges St.Hubert Dourbes 5 Semois Lacuisine Forges St.Hubert Dourbes 6 Viroin St.Hubert Forges Chimay Dourbes 7 Maas Chooz-Namur Forges Chimay Dourbes Ernage 8 Lesse Lacuisine Forges St.Hubert Dourbes 9 Sambre Forges Chimay Dourbes Ernage 10 Ourthe Lacuisine Dourbes Forges St.Hubert 11 Amblève Lacuisine St.Hubert Ernage Aachen 12 Vesdre Dourbes Beek Ernage Aachen 13 Mehaigne Aachen Dourbes Ernage Beek 14 Maas Namur-Borgharen Aachen Dourbes Ernage Beek 15 Jeker Aachen Dourbes Ernage Beek Discharge Average daily discharge figures will be used during calibration and validation. The HBV catchments correspond to areas upstream of discharge measuring stations. The following discharge figures are available. Low flow modeling of the Meuse Page 88 of 105 Catchment Measuringstation Period Source 1 Maas Source-St.Mihiel St. Mihiel 1968-1996 DIREN 2 Chiers Carignan - 3 Maas St.Mihiel-Stenay Stenay 1980-1996 DIREN 4 Maas Stenay-Chooz Chooz 1968-1997 DIREN 5 Semois Membre 1968-1982 MET (Friend database) 6 Viroin Treigne - 7 Maas Chooz-Namur - - 8 Lesse Gendron 1968-1998 MET 9 Sambre Floriffoux/Salz. - 10 Ourthe Tabreux 1968-1998 MET 11 Amblève Martinrive 1968-1998 MET 12 Vesdre Chaudfontaine 1968-1998 MET 13 Mehaigne Moha 1968-1996 MET 14 Maas Namur-Borgharen Borgharen 1968-1998 RWS (also derived Monsin series available) 15 Jeker Maastricht 1980-1993 Roer en Overmaas Note - = missing data (2, 6, 7, 9) Figure II-4 Catchments and their measuring stations and period. Within the series there are some hiatus, especially in the DIREN data there are several hiatus. With exception of the Borgharen series no metadata is available. Therefore the quality of the data is questionable Page 89 of 105 Appendix II II.4 Comparison discharges of Monsin and the feeding (measured) tributaries The table below gives the difference between the discharge at Monsin and Chooz. The discharges have been summarized over a period of a week and been compared with the discharge of the measured tributaries. The periods in the table are periods during which the total of the feeding tributaries is larger then the measured difference between Chooz and Monsin. Table II-2 Comparison of the discharges difference between Chooz and Monsin and the gauged tributaries Note; Monsin week discharge and Tributaries week discharge are weekly totals in million cubic metres. The date given in the first column is the last day of the week. Date Monsin week Tributaries week Ratio Monsin (dd-mm-yy) discharge (106 m3/s) discharge (106 m3/s) modelled 06-10-69 24,2 27,0 1,12 25-06-73 44,4 47,1 1,06 02-07-73 35,8 39,4 1,10 09-07-73 33,5 33,6 1,00 06-08-73 32,6 33,5 1,03 17-06-74 34,2 35,9 1,05 24-06-74 33,8 35,1 1,04 01-07-74 35,1 35,8 1,02 15-07-74 37,9 39,6 1,04 22-07-74 41,2 44,1 1,07 05-08-74 33,4 33,4 1,00 26-08-74 26,1 29,2 1,12 02-09-74 23,9 25,0 1,04 05-07-76 13,6 14,1 1,04 12-07-76 12,2 13,4 1,10 10-10-77 34,6 38,5 1,11 17-10-77 30,8 35,1 1,14 31-10-77 30,2 31,6 1,04 06-10-80 46,5 47,5 1,02 06-01-86 142,1 145,1 1,02 13-11-95 29,9 37,2 1,24 Low flow modeling of the Meuse Page 90 of 105 Appendix III Calibration and validation results III.1 Nash-Sutcliffe and absolute error results for Chooz Table III-1 Nash-Sutcliffe coefficients for Chooz using a threshold 33 m3/s. K4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 0,41 0,35 0,28 0,20 0,09 -0,05 -0,22 -0,44 0,011 0,40 0,39 0,34 0,29 0,22 0,14 0,02 -0,13 0,012 0,37 0,38 0,36 0,32 0,29 0,23 0,17 0,09 0,013 0,33 0,36 0,37 0,34 0,30 0,28 0,24 0,20 0,014 0,28 0,32 0,33 0,35 0,33 0,30 0,28 0,28 0,015 0,23 0,27 0,30 0,31 0,33 0,29 0,28 0,27 Table III-2 Nash-Sutcliffe coefficients for Chooz using a threshold 50 m3/s. K4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 0,23 0,20 0,12 -0,04 -0,20 -0,34 -0,50 -0,66 0,011 0,21 0,21 0,18 0,09 -0,01 -0,13 -0,20 -0,32 0,012 0,18 0,20 0,19 0,14 0,08 0,00 -0,07 -0,14 0,013 0,13 0,17 0,18 0,16 0,13 0,08 0,01 -0,07 0,014 0,08 0,13 0,16 0,14 0,14 0,11 0,08 0,08 0,015 0,02 0,08 0,12 0,13 0,12 0,10 0,09 0,07 Table III-3 Absolute error (106 m3) made in discharge deficit during calibration, using a threshold of 33 m3/s. K4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 355 323 305 287 295 311 328 345 0,011 383 344 321 298 294 300 310 325 0,012 414 370 342 317 302 301 308 316 0,013 447 401 368 340 313 305 303 309 0,014 487 430 393 364 335 319 312 312 0,015 522 464 421 390 363 341 329 322 Table III-4 Absolute error (106 m3) made in discharge deficit during calibration, using a threshold of 50 m3/s. K4 \ perc 0,40 0,43 0,45 0,48 0,50 0,53 0,55 0,58 0,010 1237 1144 1065 1020 1006 1028 1072 1135 0,011 1256 1157 1074 1015 991 1007 1048 1096 0,012 1276 1174 1089 1030 990 1001 1032 1064 0,013 1308 1206 1115 1045 1000 1000 1019 1047 0,014 1330 1228 1139 1070 1020 1012 1016 1016 0,015 1362 1262 1165 1099 1049 1033 1025 1039 Page 91 of 105 Appendix III III.2 Discharge deficits at Chooz for individual years Discharge deficit threshold 1, Chooz 240 200 ) 3 m 6 160 120 80 40 Discharge deficit (10 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 -40 Time (yy) Measured New model Difference Figure III-1 Discharge deficit (106 m3) per year at Chooz during calibration with a threshold of 30 m3/s Discharge deficit threshold 1, Chooz 120 100 ) 3 m 80 6 60 40 20 0 85 86 87 88 89 90 91 92 93 94 95 96 97 Discharge deficit (10 -20 -40 Time (yy) Measured New model Difference Figure III-2 Discharge deficit (106 m3) per year at Chooz during validation with a threshold of 33 m3/s Low flow modeling of the Meuse Page 92 of 105 Discharge deficit threshold 2, Chooz 600 500 ) 3 m 6 400 300 200 100 Discharge deficit (10 0 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 -100 Time (yy) Measured New model Difference Figure III-3 Discharge deficit (106 m3) per year at Chooz during calibration with a threshold of 50 m3/s Discharge deficit threshold 2, Chooz 350 300 ) 3 250 m 6 200 150 100 50 0 85 86 87 88 89 90 91 92 93 94 95 96 97 Discharge deficit (10 -50 -100 Time (yy) Measured New model Difference Figure III-4 Discharge deficit (106 m3) per year at Chooz during validation with a threshold of 50 m3/s Page 93 of 105 Appendix III III.3 Hydrograph 1976 and 1978 for Chooz Hydrograph 1976 for Chooz 350 300 250 /s) 3 200 150 Discharge (m 100 50 0 01/01 31/01 01/03 01/04 01/05 01/06 01/07 31/07 31/08 30/09 31/10 30/11 30/12 Date (dd/mm) Measured New Van Deursen Figure III-5 Hydrograph 1976 for Chooz Hydrograph 1978 for Chooz 800 700 600 /s) 3 500 400 300 Discharge (m 200 100 0 01/01 31/01 02/03 02/04 02/05 02/06 02/07 01/08 01/09 01/10 01/11 01/12 31/12 Date (dd/mm) Measured New Van Deursen Figure III-6 Hydrograph 1978 for Chooz Low flow modeling of the Meuse Page 94 of 105 III.4 Discharge deficits for the Vesdre, based on individual years for thresholds 1 & 2, during calibration and validation Discharge deficits Vesdre during validation using threshold 1 12 ) 3 10 m 6 8 6 4 Discahrge deficit (10 2 0 85 86 87 88 89 90 91 92 93 94 95 96 97 Period (yy) Measurements Van Deursen New model New reservoir 1 New reservoir 2 Figure III-7 Discharge deficit for individual years for the Vesdre during calibration, using threshold 1 and three different new models. Discharge deficits Vesdre during validation using threshold 2 30 ) 3 25 m 6 20 15 10 5 Discahrge deficit (10 0 85 86 87 88 89 90 91 92 93 94 95 96 97 Period (yy) Measurements Van Deursen New model New reservoir 1 New reservoir 2 Figure III-8 Discharge deficit for individual years for the Vesdre during calibration, using threshold 2 and three different new models. Page 95 of 105 Appendix III III.5 Results for the new Vesdre models, calibrated using the second half of the calibration period, during first half of calibration period Table III-5 Discharge deficit for both thresholds for different reservoir regimes compared to the original model during calibration and validation period. Threshold Measured Original Without Reservoir Reservoir (m3/s) (106 m3) model Reservoir regime 1 (106 m3) regime 2 (106 m3) (106 m3) (106 m3) Without With Without With reservoir reservoir reservoir reservoir 3,2 35 17 1 107 5 55 4 4,5 124 55 46 231 48 172 42 Table III-6 Absolute errors in the discharge deficit for different reservoir regimes compared to the original model during calibration and validation period. Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 (106 m3) regime 2 (106 m3) Without With Without With reservoir reservoir reservoir reservoir 3,2 52 52 55 51 55 50 4,5 136 136 105 97 97 94 Table III-7 Nash-Sutcliffe values for different reservoir regimes compared to the original model during calibration and validation period. Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 (106 m3) regime 2 (106 m3) Without With Without With reservoir reservoir reservoir reservoir 3,2 -2.95 -2,95 -8,24 -3.24 -0.30 -4.65 4,5 -5.57 -5,57 -6,69 -3.34 -0.32 -4.76 Low flow modeling of the Meuse Page 96 of 105 III.6 Calibration and validation results for Vesdre model calibrated using entire calibration period (1968 to 1984) Table III-8 Discharge deficit for both thresholds for different reservoir regimes compared to the original model during calibration and validation period. Threshold Measured Original Without Reservoir Reservoir (m3/s) (106 m3) model Reservoir regime 1 regime 2 (106 m3) (106 m3) (106 m3) (106 m3) 3,2 47 57 47 47 47 3,2 10 38 33 43 42 4,5 186 153 186 185 187 4,5 109 149 187 183 185 Note; calibration period is Italic, calibration period is bold Table III-9 Absolute errors in the discharge deficit for different reservoir regimes compared to the original model during calibration and validation period. Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 regime 2 3,2 95 72 70 66 3,2 78 63 90 87 4,5 217 169 147 152 4,5 152 155 149 164 Note; calibration period is Italic, calibration period is bold Table III-10 Nash-Sutcliffe values for different reservoir regimes compared to the original model during calibration and validation period. Threshold Original Without Reservoir Reservoir (m3/s) model reservoir regime 1 regime 2 3,2 3.2 -1.19 -0.65 -0.04 3,2 3.2 -5.66 -4.39 -3.78 4,5 4.5 -2.40 -0.86 -0.26 4,5 4.5 -3.13 -2.65 -2.63 Note; calibration period is Italic, calibration period is bold Page 97 of 105 Appendix III III.7 Discharge deficits for individual years at Monsin during calibration and validation. Discharge deficit threshold 1, Monsin 480 440 400 ) 3 360 m 320 6 280 240 200 160 120 80 40 0 Discharge deficit (10 -40 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 -80 -120 Time (yy) Measured New model Difference Figure III-9 Discharge deficit (106 m3) per year at Monsin during calibration with a threshold of 60 m3/s Discharge deficit threshold 1, Monsin 200 ) 3 150 m 6 100 50 0 Discharge deficit (10 85 86 87 88 89 90 91 92 93 94 95 96 97 -50 Time (yy) Measured New model Difference Figure III-10 Discharge deficit (106 m3) per year at Monsin during validation with a threshold of 60 m3/s Low flow modeling of the Meuse Page 98 of 105 Discharge deficit threshold 2, Monsin 1300 1200 1100 ) 1000 3 900 m 6 800 700 600 500 400 300 200 100 0 -100 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Discharge deficit (10 -200 -300 -400 Time (yy) Measured New model Difference Figure III-11 Discharge deficit (106 m3) per year at Monsin during calibration with a threshold of 100 m3/s Discharge deficit threshold 2, Monsin 800 700 ) 3 600 m 6 500 400 300 200 100 0 Discharge deficit (10 85 86 87 88 89 90 91 92 93 94 95 96 97 -100 -200 Time (yy) Measured New model Difference Figure III-12 Discharge deficit (106 m3) per year at Monsin during validation with a threshold of 100 m3/s Page 99 of 105 Appendix III III.8 Hydrographs for Monsin 1976 and 1978 Hydrograph of 1976 for Monsin 800 700 600 500 400 300 Discharge (m3/s) 200 100 0 01/01 15/02 01/04 16/05 01/07 15/08 30/09 14/11 30/12 Time (dd/mm) RWS original new Figure III-13 Hydrograph of 1976 for Monsin Hydrograph of 1978 for Monsin 1400 1200 1000 800 600 Discharge (m3/s) 400 200 0 01/01 15/02 02/04 17/05 02/07 16/08 01/10 15/11 31/12 Time (dd/mm) RWS original new Figure III-14 Hydrograph of 1978 for Monsin Low flow modeling of the Meuse Page 100 of 105 III.9 Differences in calibration and validation results for Monsin between Vesdre with and without reservoir Discharge deficit (106 m3) Absolute error Nash-Sutcliffe (106 m3) coefficient Threshold Measured With Without With Without With Without (m3/s) reservoir reservoir reservoir reservoir reservoir reservoir 60 1021 1015 1013 898 906 0,38 0,35 60 370 766 805 1220 1267 -2,00 -2,01 100 5209 5290 5227 2485 2495 0,13 0,09 100 3700 5045 5126 2852 2898 -1,79 -1,82 Note; calibration is Italic, validation is bold. Page 101 of 105 Appendix III III.10 Discharge during winters for individual years at Monsin and Chooz. Table III-11 Discharge during winter months for individual years at Monsin and Chooz Note; discharge calculated over the months December till April Monsin Chooz Discharge Percentage Discharge Percentage Year (106 m3) of average (106 m3) of average 1968 4951 90% 2860 92% 1969 4299 78% 2485 80% 1970 7026 128% 4059 130% 1971 3111 57% 1712 55% 1972 2555 47% 1438 46% 1973 2821 51% 1451 47% 1974 4341 79% 2317 74% 1975 6520 119% 3426 110% 1976 2483 45% 1354 43% 1977 4582 84% 3037 97% 1978 5314 97% 3390 109% 1979 6172 113% 3769 121% 1980 6157 112% 3814 122% 1981 6766 124% 4005 128% 1982 6930 127% 4116 132% 1983 7657 140% 4563 146% 1984 6481 118% 3802 122% 1985 4840 88% 2617 84% 1986 5601 102% 3092 99% 1987 6079 111% 3242 104% 1988 8535 156% 4611 148% 1989 6357 116% 2979 95% 1990 4901 89% 2663 85% 1991 4917 90% 2813 90% 1992 4077 74% 1994 64% 1993 4875 89% 2599 83% 1994 9385 171% 5502 176% 1995 9686 177% 5718 183% 1996 2627 48% 1566 50% 1997 4283 78% 2588 83% Average 5478 3119 . Low flow modeling of the Meuse Page 102 of 105 Relative discharge during winter months 200% 180% 160% 140% 120% 100% 80% 60% 40% Relative winter discharge (%) 20% 0% 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 Time (yy) Figure III-15 Relative discharge during winter for Monsin. Page 103 of 105 Appendix III III.11 Difference between measured and modelled average monthly discharges for Chooz and Monsin Table III-12 Discharge difference between measured and modelled average monthly discharges for Chooz and Monsin for Van Deursen model and new model. Van Deursen model New model Month Monsin Chooz Monsin Chooz January -3% -8% -4% -10% February -1% -10% -2% -12% March 7% -1% 6% -3% April 14% 7% 13% 6% May 21% 15% 20% 15% June 19% 12% 18% 14% July 12% 10% 13% 17% August 2% -3% 7% 11% September -9% -7% -3% 7% October -5% -2% -2% 3% November -8% -2% -7% -2% December -7% -9% -7% -11% Low flow modeling of the Meuse Page 104 of 105 III.12 Final parameters settings for all sub basins Table III-13 Final parameter settings for all sub basins 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 fc 293 321 318 160 300 384 365 260 365 260 210 270 266 180 273 lp 0.39 0.36 0.35 0.95 0.45 0.28 0.31 0.50 0.28 0.53 0.68 0.68 0.41 0.66 0.40 beta 1.39 1.48 1.73 1.2 1.62 1.92 1.58 1.6 1.42 1.80 1.90 1.80 2.07 1.79743 1.97 khq 0.079 0.082 0.079 0.076 0.086 0.089 0.078 0.095 0.08 0.099 0.10 0.145 0.078 0.12 0.078 alfa 0.73 0.61 0.68 3.5 0.62 0.80 0.57 1.10 0.27 1.10 1.0 1.10 0.24 0.70 0.15 hq 2.54 1.69 2.54 4.3 3.66 3.23 3.02 2.56 3.27 4.30 3.50 2.56 3.40 2.56 k4 0.013 0.013 0.013 0.013 0.0205 0.013 0.026 0.0195 0.026 0.015 0.0105 0.010 0.004 0.026 0.015 perc 0.50 0.50 0.50 0.5 0.37 0.50 0.22 0.42 0.22 0.44 0.53 0.69 0.425 0.22 0.40 maxbas 1.2 2.5 2.0 2.2 1.40 1.10 1.10 pcorr 1.01 0.94 cflux 2.0 1.3 1.37990 pcalt 0.0 tcalt 0.0 cevpl 1.1 cfmax 3.6 4.0 Table III-14 Default parameter settings for all parametes not mentioned in talbe III-13 Parameter Value Parameter Value Parameter Value Parameter Value maxbas 1.00000 Rfcf 0.99714 Focfmax 0.60000 ecorr 1.00000 sfcf 1.01758 Tti 1.00000 cfr 0.05000 sfdistfi 0.50000 fosfcf 0.80000 Pcorr 1.00000 whc 0.10000 sclass 1.00000 cfmax 3.75653 Pcalt 0.10000 cevpl 1.00000 sfdistfo 0.20000 tt -1.41934 Tcalt 0.60000 recstep 999.000 cevpfo 1.15000 dttm 0.54391 Focfmax 0.60000 critstep 1.00000 ecalt 0.10000 Page 105 of 105 Appendix III