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National Environmental Research Institute Ministry of the Environment . Denmark

Model frameworks for the calculation of annual

runoff and nitrogen

emissions from Danish catchments

PhD thesis

Dirk-Ingmar Müller-Wohlfeil

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[Blank page]

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National Environmental Research Institute Ministry of the Environment.Denmark

Model frameworks for the calculation of annual runoff and nitrogen emissions

from Danish catchments

PhD thesis 2002

Dirk-Ingmar Müller-Wohlfeil

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Data sheet

Title: Model frameworks for the calculation of annual runoff and nitrogen emissions from Danish catchments

Subtitle: Ph D thesis

Author: Dirk-Ingmar Müller-Wohlfeil

Department: Department of Freshwater Ecology

University: University of Potsdam, Institute of Geography and Geoecology Publisher: National Environmental Research Institute 

Ministry of the Environment

URL: http://www.dmu.dk

Date of publication: November 2002 Editing complete: December 2001

Referee(s): Dr. Brian Kronvang, Prof. Dr. Axel Bronstert, Prof. Dr. H.R. Bork Financial support: The Danish Council for Research Policy

Please cite as: Müller-Wohlfeil, D.-I. 2002: Model frameworks for the calculation of annual runoff and nitrogen emissions from Danish catchments. National Environmental Research Institute, Silkeborg, Denmark. 115 pg.

Reproduction is permitted, provided the source is explicitly acknowledged.

Abstract: The main aspiration of project was to establish and test methods for the estimation of annual and monthly river discharge as well as N-leaching and riverine nitrogen loadings from Danish catchments to help solving tasks of the National Environmental Research Institute resulting from national and international obligations. The work performed was focused on three interrelated objectives. The first comprised the development of a modelling framework for computing annual and monthly runoff and nitrogen loadings from the whole Danish land mass by combining river discharge and nutrient load estimations and point source measurements from unmonitored areas with runoff and nutrient load measurements from monitored areas at the catchment level. The second encompassed suggestion of a procedure for assessing the long- term impacts of a potential future climatic change on runoff at catchment level, and a third specific goal included the establishment of modelling frames to simulate N-leaching at catchment scale. Most of the work performed revealed in particular water balance problems related to the available model input data and catchment properties, complicating proper simulations at the regional to national scale.

Keywords: Annual river discharge, monthly runoff, climatic change impacts, water balance problems, Danish catchments, nitrogen leaching, riverine nitrogen loading.

Layout: Dirk-Ingmar Müller-Wohlfeil & Hanne Kjellerup Hansen

ISBN: 87-7772-690-1

ISSN (print): 0905-815X

ISSN (electronic): 1600-0048

Paper quality: Cyclus print

Printed by: Schultz Grafisk

Environmentally certified (ISO 14001) and Quality certified (ISO 9002)

Number of pages: 115

Circulation: 100

Price: DKK 100,- (incl. 25% VAT, excl. freight)

Internet-version: The report is also available as a PDF-file from NERI’s homepage http://www.dmu.dk/1_viden/2_Publikationer/3_Ovrige

For sale at: Miljøbutikken or at: Miljøbutikken

Læderstræde 1-3 On-line bookstore:

1201 København K www.mim.dk/butik

Tlf. 33 95 40 00 butik@mim.dk

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Contents

Preface 5

Zusammenfassung 7 Summary 8

1. Objectives 9

2. Assignment of the simulation models employed 11

2.1 Categorisation of hydrological models 11 2.1.1 Stochastic models 12

2.1.2 Deterministic models 12

2.2 Water quality modelling related to nitrogen pollution from diffuse source 15

3. Important databases for hydrological and water quality modelling available at the national scale in Denmark 17

3.1 Climatic and runoff data 17

3.2 Information on subsurface conditions 19

3.2.1 Soils 19

3.2.2 Geological units 20

3.2.3 Maps on groundwater potentials and depths of ground water 20 3.2.4 Groundwater abstraction 21

3.3 Land use / land cover and relief 21 3.4 Agricultural statistics 21

4. Regional discharge patterns in Denmark 23 5. Patterns and trends in nitrogen losses 27

5.1 Nitrogen leaching 27

5.2 Riverine nitrogen loading 28

6. Introduction to the specific studies performed 29

6.1 Modelling annual and monthly runoff 29

6.1.1 Annual river discharge and riverine nitrogen loadings 29 6.1.2 Monthly runoff from Danish catchments 31

6.2 Analysing potential impacts of climatic change on the water balance at catchment scale 34

6.3 Assessment of nitrogen leaching 35

6.3.1 Derivation of a design for the calculation of long-term diffuse nitrogen pollution 35 6.3.2 Estimating the effects of different agricultural practises on nitrate leaching 38

7. Establishment of a harmonized tool for calculating river discharge and nitrogen loads from unmonitored areas in Denmark,

by D.-I. Müller-Wohlfeil, B. Kronvang, S.E. Larsen, N.B. Ovesen

and F. Wendland, Phys. Chem. Earth (B), Vol. 26, No. 7-8, 617-622 39

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8. Estimating annual river discharge and nitrogen loading to Danish coastal waters based on multiple regression,

by D.-I. Müller-Wohlfeil, B. Kronvang, S.E. Larsen, N.B. Ovesen International Journal of Environmental Studies, Section B

accepted for publication 47

9. Estimation of monthly river discharge from Danish catchments,

by D.-I. Müller-Wohlfeil, C.-Y. Xu and Hans Legard Iversen, Nordic Hydrology, Vol.34(4)03

accepted for publication 61

10. Response of a river catchment to climatic change: Application of expanded downscaling to northern Germany,

by D.-I. Müller-Wohlfeil, G. Bürger and W. Lahmer, Climatic Change, Vol. 47, 67-89 75

11. Model-based regional estimation of ground water nitrogen loads from diffuse sources,

by D-I. Müller-Wohlfeil, J.O. Jørgensen, C. Bjørklund, Å. Forsman, R. Kunkel and F. Wendland

IAHS publication no. 273, 201-205 91

12. The impact of land use changes on the future load of nitrogen to a Danish inlet -Quantification of leaching from the root zone,

by J. O. Jørgensen, D.-I. Müller-Wohlfeil, B. Kronvang, H.E. Andersen, L. Wiggers and J. Bidstrup

IAHS publication no. 273, 183-188 95

13. Evaluation of the study results 99

13.1 Water balance problems 99

13.2 Contemplation of the N-leaching and loading approaches 102

13.3 Status and needs of regional studies on climatic change on the catchment scale in Denmark 104

13.4 Concluding remarks 104

References 107

National Envrionmental Research Institute 115

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Preface

The work presented in this thesis was undertaken at the Danish National Environ- mental Research Institute (NERI) during a two-year period (October 1999 – October 2001) as a joint project between the Department of Lake and Estuarine Ecology and the Department of Streams and Riparian Areas. Many of the partial studies presented result from different national and international research projects, all with focus on diffuse nitrogen pollution.

Being attracted by the way NERI ensures an inter-linkage between national environ- mental monitoring and applied research, I applied for a position at the institute in 1996.

A basic guideline for the development of many of the procedures established at NERI is that they must contribute directly to the improvement of regional and national envi- ronmental monitoring, given the constraints of national and international legislation.

I am very grateful to the Danish Academy of Science and NERI for their financial support to my PhD project.

I am particularly grateful to Dr. Brian Kronvang, Jens Peder Jensen, Kurt Nielsen and many other colleagues at NERI in Silkeborg for valuable scientific discussions and for their personal and technical support during the research period.

I would like to thank Prof. Axel Bronstert for his cooperation, support and many helpful discussions during the last years.

Anne Mette Poulsen, Hanne Kjellerup Hansen and Anne-Dorthe Villumsen did a great job when helping me struggling with “Word” and checking the English.

Last but not least, I would like to thank my family for their support, tolerance and patience without which this work would not have been possible.

The first chapters of this thesis (Chapters 1-6) provide background information on the

framework behind and the partial studies performed, while the following chapters (7-

12) comprise papers that have resulted from the partial studies. These papers are finally

evaluated in the last chapter (Chapter 13).

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[Blank page]

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Zusammenfassung

Hauptziel der Promotionsarbeiten war die Ableitung und der Test von Methoden zur Abschätzung jährlicher und monatlicher Abflüsse, jährlicher Stickstofffrachten, sowie Stickstoffaus- waschungen aus Dänischen Flusseinzugsgebieten.

Die Arbeit beinhaltete drei Teilziele. Das erste dieser Teilzeile bestand in der Entwicklung und Anwendung eines Strukturkonzeptes zur Modellierung von Jahres- und Monatsabflüssen für die gesamte Dänische Landfläche durch Kombination geschätzter Abflüsse und Stoff- frachten sowie gemessener punktförmiger Einträge in Gebieten ohne kontinuierliche Messungen mit gemessenen Daten in beobachteten Einzugsgebieten. Das zweite Teilziel bestand in der Etablierung einer Methode zur Beurteilung langfristiger Auswirkungen von Klimaänderungen auf das Abflussverhalten von Einzugsgebieten. Ein dritter Abschnitt der Arbeiten galt der Unter- suchung von Stickstoffauswaschungen aus der ungesättigten Bodenzone.

Die prototypische Berechnung der Abflüsse und Stickstofffrachten in die Küstengewässer bein- haltete die Entwicklung von Regressionsmodellen zur Abschätzung der Beiträge aus un-beobachteten Gebieten. GIS-Datenbasen wurden erstellt zur i.) Gewinnung aller Informationen für die Erstellung des Regressionsmodells und eines mit monat- lichen Zeitschritten arbeitenden Wasserhaus- haltmodells (MWB), ii.) Berechnung der Jahres- abflüsse und Stofffrachten aus unbeobachteten und beobachteten Gebieten für das gesamte Land.

Eine entscheidende Restriktion für die Entwick- lung der verschiedenen Modelle besteht darin, dass bei Verwendung der klimatischen Daten des Dänischen Meteorologischen Institutes oftmals der beobachtete Abfluss geringer ist als die Differenz zwischen Niederschlag und Verdunstung auf Einzugsgebietsebene. Die Parametrisierung von MWB stützte sich daher ausnahmslos auf Einzugsgebiete (EZG), in denen der langfristige Abfluss größer ist als die Differenz zwischen Niederschlag und potentieller Verdunstung.

Deshalb würde die Anwendung von MWB, in Gebieten die nicht diese Bedingung erfüllen, zu einer Überschätzung der Abflüsse führen. MWB erfordert jedoch nicht nur eine Neuparame- trisierung in Abhängigkeit von zu korrigierenden Eingangsdaten, sondern auch die Einbindung neuer Komponenten, die es ermöglichen, Wasser- austausch zwischen benachbarten EZG sowie Wasserbewirtschaftung zu beschreiben.

Obgleich MWB sich in den meisten der für die Modellkalibrierung und -validierung untersuchten EZG als robuster Ansatz erwiesen hat, sind einige konzeptionelle Schwächen nachzuweisen, welche

die Entwicklung und den Test neuer Modell- komponenten erforderlich machen.

Wenn auch aufgrund der Größe der Wurzel des mittleren quadrierten Fehlers des gegenwärtigen Abfluss-Regressionsmodels noch keine opera- tionale Anwendung des Models auf nationaler Ebene möglich ist, besteht der Vorteil des Ansatzes darin, dass für die Modellableitung Abflussdaten nahezu aller verfügbarer EZG zwischen 10 und 300 km2 Größe verwendet wurde. Auch dieser Modelansatz erfordert jedoch Korrekturen, für den Fall, dass die Eingangsdaten korrigiert werden müssen. Darüber hinaus müssen einige Ersatz- variable langfristig erstattet werden.

Die Tatsache, dass für die Parametrisierung von MWB keine EZG verwendet werden konnten, welche keine geschlossenen Wasserbilanzen aufweisen hat zur Konsequenz, dass das Model in Gebieten mit Abflussdefiziten nicht eingesetzt werden kann. Gleichzeitig besteht jedoch ein Vorteil des Models darin, dass anders als beim Regressionsansatz einzelne Wasserhaushaltskom- ponenten explizit berechnet werden können.

Die Entwicklung des Ansatzes zur Untersuchung der Auswirkungen globaler Klimaänderungen auf den Wasserhaushalt von Flusseinzugsgebieten beinhaltet die Anwendung eines statistischen Downscaling-Verfahrens mit dessen Hilfe Eingangsdaten aus dem Gebiet der oberen Stör (1157 km2) für das hydrotopbasierte Model ARC/EGMO bezogen auf Zeitraum 1860-2100 bereit gestellt wurden. Ingesamt hat sich gezeigt, dass das vorgestellte Verfahren für die Durch- führung ähnlicher Studien in Dänemark geeignet ist.

Die im Rahmen des dritten Abschnittes der Teilarbeiten durchgeführte Entwicklung von Verfahren, welche die Berechnung von Stick- stoffausträgen aus der ungesättigten Bodenzone unterstützen, geschah unter besonderer Berück- sichtigung national verfügbarer Datenbasen zu Klima, Bodeneigenschaften und zur agrarkul- turellen Landnutzung. Insbesondere wurden Verfahren zur Ableitung von Eingangsdaten zweier Stoffaustragsmodelle sowie eines Modells zur Stickstoffreduktion im Grundwasser abgeleitet und in zwei Einzugsgebieten in Jütland zur Anwendung gebracht.

Im Rahmen sämtlicher durchgeführter Teilstudien stellte sich heraus, dass die Verlässlichkeit der Messdaten und anderer Gebietsgrundinformation von übergeordneter Bedeutung ist.

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Summary

The main aspiration of this PhD-project was to establish and test methods for the estimation of annual and monthly river discharge as well as N- leaching and riverine nitrogen loadings from Danish catchments to help solving tasks resulting from NERI’s national and international obliga- tions. The work was focused on three different partial aims. The first was to develop a modelling framework for computing annual and monthly runoff and nitrogen loadings from the whole Danish land mass by combining river discharge and nutrient load estimations and point source measurements from unmonitored areas with runoff and nutrient load measurements from monitored areas at the catchment level. The second partial aim was to suggest a procedure for assessing the long-term impacts of a potential future climatic change on runoff at catchment level, and a third specific goal was to establish frames to simulate N-leaching at catchment scale.

The prototype procedure to calculate runoff and nitrogen loadings to the Danish coastal waters has comprised derivation of a regression model for calculating the contributions from ungauged catchments. GIS databases have been established to i.) procure all information required for the establishment of the runoff regression model and parameterisation of a monthly water balance model (MWB) used to calculate of monthly runoff, and ii.) to calculate annual runoff and nitrogen loadings from ungauged and gauged catchments for the whole country.

An important restriction hampering the develop- ment and test of the different models involved was the fact that in many catchments river discharge is smaller than the difference between precipitation and evapotranspiration when using the climatic data provided operationally by the Danish Meteorological institute (DMI). The parameterisa- tion of the monthly water balance model MWB was exclusively based on catchments where the long-term observed river discharge is larger than the difference between precipitation and potential evapotranspiration. Application of the MWB model in areas not fulfilling this requirement will lead to an overestimation in river discharge.

However, even if the input data remain un- changed, the model needs to be extended allowing for the description of water imports to and exports from the catchment to adjacent areas. Moreover, though MWB performed well in most of the calibration and test catchments, the parameterisa- tion studies revealed some conceptual weaknesses calling for development and test of new model components. Although, the root mean square error of the current multiple regression model for

annual river discharge is still too high for operational use of the scheme at the national scale, its main advantage is that the number of catch- ments, to be omitted for the model establishment, was limited. Hence, it represents to a large extent average properties based on almost all catchments larger than 10 km2 and smaller than 300 km2 for which input data are available. However, The regression equations derived will need to be modified if the input data to run the model have not been correct. Some of the surrogate explana- tory variables considered for the annual river discharge approach should be replaced in future.

The fact that the parameterisation of the MWB model required omission of all catchments not fulfilling the requirements of closed simple water balances means that the current model cannot be applied in areas where runoff could not be explained from simple water balance equations.

However, the main advantages of the conceptual water balance model, MWB, are, apart from the higher temporal resolution, its capability to calculate different components of the hydrological cycle not considered explicitly in the current regression model, such as fast-flow, slow-flow and actual evapotranspiration.

The second specific objective has involved the establishment of an approach to perform spatially distributed climatic change studies on the catchment scale, involving statistical downscaling of climate data used as input to the conceptual semi-distributed hydrological model ARC/EGMO.

The established approach was tested for the period 1860 to 2100 on the upper Stör catchment (1157 km2) located in northern Germany. The modelling approach seems to provide a good basis for similar future studies to be performed in Danish catch- ments.

Finally, methods were established supporting the calculation of N-leaching based particularly on nationally available data sets on climate, soil types and agricultural practices. Most importantly, techniques for deriving input data to the two leaching models used, as well as to a groundwater model applied as part of the first leaching study, were tested. Both methods were applied in catchments located in central and eastern Jutland, respectively, but may be used for larger areas as well, even at national scale.

However, it is generally important to keep in mind that any parameterisation is dependent on the reliability of the input data. Independent estima- tions of actual evapotranspiration, in particular, should be derived and tested as soon as the problems related to the calculation of potential evapotranspiration are solved.

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1. Objectives

During the past 20 years, export of excess nutrients from upstream watersheds to the sea, and with it over-enrichment of coastal and marine waters, has given rise to great concern and promoted the establishment of various research activities and monitoring programmes. One of them, which some of the studies presented in this thesis has been part of, is the “European Land-Ocean Interaction Studies” (ELOISE), a combination of coastal zone research projects aimed to investigate how the land-ocean interaction operates and how it is influenced by human activities, such as agriculture, under the fourth and fifth RTD Framework Programme of the European Commis- sion.

Also in Denmark, many of the monitoring and administrative activities undertaken and measures introduced by regional and national authorities to protect the aquatic environment have focused on anthropogenic nutrients loadings to freshwater and coastal water systems (Iversen et al., 1994;

Kronvang et al., 1996; Jeppesen et al., 1999).

In 1987, the ”Action Plan against Pollution with Nutrients of the Danish Aquatic Environment”, was established. It aimed to reduce the annual total nitrogen emission by 50 % and that of phosphorus by 80% within a 5-year-period (Danish EPA, 2000). However, the objectives could not be fulfilled in due course and the deadline had to be postponed to 2002. In 1991 the action plan was supplemented by the “Action plan for sustainable agriculture” initiated by the Ministry of Agricul- ture, which in 1996 became the Ministry of Agriculture Fisheries and Food. Also on a European scale, a 50 % reduction of nitrogen loading to the Baltic Sea and the North Sea from 1987 to 1995, as stipulated by the HELCOM (Helsinki Commission) and the OPSARCOM (Oslo-Paris Commission), proved to be unattain- able. In Denmark, following the action plan of 1987, which added to the monitoring programmes of the Danish counties, “the Aquatic Environment Nationwide Monitoring Programme” was established in 1989 to track the development of nutrient pollution and detect potential ecological effects of a possible reduction (Danish EPA, 1993).

As the third stage, the current programme, NOVA 2003, was commenced in 1998 and will be finished by 2003 (Danish EPA, 2000).

Nitrogen and phosphorous inputs to coastal areas have been reduced considerably during the last 15 years, the latter particularly due to effective wastewater treatment. Despite the fact that a decrease in nitrogen concentrations in water courses is now eventually significant for many of

the Danish catchments (NERI, 2001), the consider- able reduction of phosphorous inputs from sewage treatment plants and fish farms has caused that phosphorous is playing a more important role as limiting factor for primary production in Danish coastal waters (NERI, 1999) than nitrogen. For both phosphorous and nitrogen inputs agricultural activities are the most important sources for nutrient pollution to coastal areas in Denmark.

According to the Danish Environmental protection agency (Danish EPA, 2000) about 60-80 % of the nitrogen inputs to watercourses in Denmark derive from agricultural sources.

Being the responsible organisation for national monitoring program NERI has to ensure that necessary data and methods are available to solve tasks resulting from the national and international obligations, particularly with respect to the calculation of river discharge and nutrient loads at the national scale, now and in future.

Similarly, the regional authorities require simple methods to compare the different effects of various measures to reduce total nitrogen loadings in groundwater, rivers and coastal waters.

Hitherto, national annual reporting of runoff and nutrient loads has been based on a combination of measurements from monitored areas and different estimations for unmonitored areas. Runoff estimations are based on daily measurements at approximately 100 reference gauging stations located within 67 precipitation areas (Land Development Service, 1990). An area/runoff ratio established for each station within the reference runoff area is used to estimate river discharge in downstream areas based on measurements performed upstream of the reference river system, while national approximations of nutrient loads for unmonitored areas are provided independently on a regional scale by the 14 Danish counties for each of the 49 coastal areas used as reference units in Denmark for regional and national assessments.

As of yet a model based on homogeneous assessment of runoff and nutrient loads to the sea has not been developed for the country in total, which covers an area of approximately 43,000 km2. Currently, annual estimations of runoff and nutrient loads from unmonitored areas entail measurements from monitored areas for the corresponding year, which is problematic with respect to the investigation of future scenarios.

Any initiation of measures to reduce environ- mental impacts on aquatic and coastal ecosystems also needs to account for potential future changes in environmental conditions. Among the most recognised changes society faces up to are those

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related to climatic conditions. This was the main reason why the Danish government in 1998 decided to establish the Danish Climate Centre.

Although many Danish hydrologists and scientists from neighbouring scientific fields are involved in climate and climate impact research, the number of studies focusing on hydrological regimes at the catchment scale is relatively limited (Henriksen, 1998; Sælthun et al., 1998; Parry, 2000).

Another important question related to the assessment of future developments is, how long will it take from the implementation of measures to reduce nitrogen inputs until a significant change in the regional fluxes of nitrogen can be detected ?

Answering this question requires investigations about nitrogen retention in catchments.

Simple methods are needed for administrative purposes at the national and regional scale to estimate long-term effects on groundwater and surface water of nitrogen inputs associated with agricultural activities.

The main objective of this PhD-project is to establish and test methods for the estimation of annual and monthly river discharge as well as N- leaching and riverine nitrogen loadings from Danish catchments (Fig. 1.1). These methods are vital to help solving main tasks resulting from the regional and national monitoring of the aquatic environment as well as from international obligations.

Most importantly, new methods are required to estimate runoff and nutrient loads at the regional and national scale. The first specific objective of the thesis is therefore to elaborate a modelling frame for computing annual and monthly runoff and nitrogen loadings from the whole Danish land mass by combining river discharge and nutrient load estimations and point source measurements from unmonitored areas with runoff and nutrient load measurements from monitored areas at the catchment level.

A second specific objective of the thesis is to suggest a procedure for assessing the long-term impacts of a potential future climatic change on runoff at catchment level. The establishment of such a procedure will help regional water management authorities to take into account the effects of potential climatic change when establishing measures to protect the aquatic environment and reduce nutrient inputs from different sources (Ferrier et al., 1995, Mimikou et al., 2000).

The third specific objective of the thesis is to establish frames to simulate N-leaching at catchment scale.

This objective involves two aspects: 1) the formation and test of a method allowing long-term assessment of the impacts of diffuse nitrogen pollution on leaching, which is a prerequisite for the estimation of long-term-denitrification in groundwater, and 2) the elaboration of a scheme allowing estimation of the impact of changes in agricultural practises on N-leaching at the catchment scale relative to the eutrophication of coastal waters. Both aspects have involved the application of simple empirical methods and the combination of different detailed agricultural databases available at the regional and national scale.

Figure 1.1 Overview about the different issues and linkages covered in the thesis (reference to chapter numbers is given in parenthesis)

Regional to national

scale

Riverine nitrogen loadings (7/8)

Annual river dicharge (7/8)

Monthly river discharge (9) Current conditions

Current conditi-

Local to regional scale

Current conditions

Changed conditions

Long-term- aspects (11)

Nitrogen leaching

Variation in agricultural practises and land

use (12)

Climatic change impacts on the water balance (10)

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2. Assignment of the simulation models employed

2.1 Categorisation of hydrological models

Several simulation models have been applied within the framework of this thesis. To facilitate a better understanding of the different approaches, this section gives a brief overview of different model types with special focus on the models applied. It is important to keep in mind that most of the existing classifications reflect the scientist’s specific conception and scientific background, and the existing terminology is not at all unique and well defined.

In recent decades several articles have given an overview of the conceptual differences and similarities of hydrological models (Clarke, 1973;

Todini, 1988; Becker and Serban, 1990; O’Connel, 1991; DeVries and Hromadka, 1992; Wheather et al., 1993; Singh, 1995; Edijatno et al., 1999; Rodda and Rodda, 1999). Most of the existing review publications are specific since they cover single areas of interest, such as approaches linked to GIS (Wilson, 1996), monthly water balance models (Alley, 1984; Xu and Singh, 1998), water quality models (Thorsen et al., 1996) or models applicable at larger scales (Hagen and Kleeberg, 1993;

Sivapalan and Blöschl, 1995; Bronstert et al., 1998).

Beven (2000) focuses on the selection of different models, their advantages and disadvantages, and most importantly limitations and uncertainty related to modelling. Hitherto, the most extensive publication comprising a collection of well-known and adapted deterministic simulation models used in catchment hydrology, irrespective of scale and thematic focus, was issued in 1995 (Singh, 1995).

The question of which model to select will be determined by the objective of the study, the modeller’s perception of the importance of the individual processes involved and various frame conditions such as the accessibility of data to

calibrate, run and test the respective model as well as the time available for the study.

One main structural difference between hydrologi- cal models is related to the way cause and effect processes are described as well as to the physical and mathematical concepts applied for this purpose (Fig. 2.1).

Other important criteria to distinguish between models are:

• Spatial distribution

Lumped models are not subdivided horizontally, i.e.

single catchments are treated as one unit. If only vertical processes such as infiltration, evapotran- spiration and percolation are of importance, one- dimensional models can be used to provide output at the patch or point scale, also without considering a horizontal extension, while distributed models require input and provide output in a horizontally or geographically subdivided way. Most of the models applied in this thesis belong to the category of spatially lumped or patch scale approaches. Fully distributed models require geographically explicit input information and allow also simulation of lateral flows between the elementary units used to represent the catchment or area of interest. Semi-distributed approaches, which are based on a pre-classification of the catchment sub-areas, have been considered as an alternative scheme for spatial discretisation of a number of conceptual models (e.g. TOPMODEL (Beven and Kirkby, 1979), ARC/EGMO ((Becker and Pfützner, 1987; Pfützner et al., 1997), applied in Chapter 10 of this thesis), HBV (Bergström, 1995), SWIM (Krysanova et al., 1998a)). Both, fully- distributed and semi-distributed approaches are based on the assumption that the elementary area or units used for subdivision are homogenous with respect to system inputs, outputs and biogeo- chemical properties. The main idea of a semi- distributed approach is that the elementary units

Figure 2.1 Causality-based classification of hydrological models.

Deterministic models

Process- description-

based Conceptual

Stochastic models

Empirical

Regression models Artificial

intelligence (Artific.neur al network Fuzzy logic)

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can be classified according to their hydrological response (hydrological response unit concept (HRU) of Leavesley and Stannard (1990)). The response units, which need not be located near to each other within the (sub-)catchment are typically classified on the basis of information on catchment properties such as soil conditions, topography and climate. Remaining differences in hydrological properties between elementary units belonging to one class can be accounted for by the use of statistical distribution functions. Many of the lumped and semi-distributed models have been extended towards a distributed description of processes at a certain level. Recently, two different versions of the semi-distributed model HBV were developed and applied to various catchments of the Elbe drainage basin (Krysanova et al., 1998b).

Spatial distribution was implied through linkage of output from various subcatchments and channel routing. While the original version of ARC/EGMO (Becker and Pfützner, 1987; Pfützner et al., 1997) was based on the concept of HRU, called hydro- topes, the development of new model features focused on the introduction of features that explicitly enable modelling of lateral flows within the specific catchment (Pfützner et al. 1997).

• Temporal continuity and resolution

Models can be event-based or continuous and operate with fixed time intervals (such as minutes, hours, days, months or years) or time intervals that are related to the dynamics and variability of the processes they are representing. The models applied in the paper are continuous approaches, except SoilN-light (Forsman and Grimvall, 2001), the latter focuses on long-term conditions without any dynamics.

• Purpose

Models can also be classified according to the processes they cover and the systems they describe (e.g. river discharge, slopes, catchments, ground- water vs. surface water, various aspects of water quality) as well as whether they should be applied to increase the process knowledge or provide fast and simple results for practical applications.

The following overview is structured according to the causality-based classification

2.1.1 Stochastic models

Stochastic models take into account some forms of probabilistic uncertainty and randomness related to uncertainty of input data, the description of boundary conditions and the model parameter values (Beven, 2000). Stochastical methods have mainly been applied i.) to account for uncertainty related to initial conditions and the parameters of

deterministic models (Bodo and Unny, 1987;

Sarino and Serrano, 1990; Hromodika II and Whitley, 1994; Lee et al., 2001; Willems, 2001), ii.) to estimate model parameters (Dagan and Rubin, 1988; Kuczera, 1997) or iii.) to perform time series modelling. The latter is based on algorithms representing the probability distribution of a stochastic variable, river discharge by way of example (Salas and Smith, 1981; Van Geer and Zuur, 1997; Tingsanchali, 2000; Toth et al., 2000).

Approaches such as “autoregressive moving- average (ARMA) models” used for streamflow predictions comprise an autoregressive (AR) and moving average part (MA). Autoregression implies that the current observation can be estimated as a linear function of previous observations and a random deviation. The combination of the autoregressive part with the moving average term leads to (2.1):

where the

φ

’s are the autoregressive parameters and the θ’s are the moving average parameters to be estimated, the X’s are the original time series and the a’s the series of unknown random errors that are assumed to be normally distributed.

Different variations, extensions and modifications of the basic model type exist.

2.1.2 Deterministic Models

Basically, a model can be called fully deterministic if all the variables are considered to be free from random variation. For a given set of input and parameter values the model output is unique (Beven, 2000).

2.1.2.1 Empirical models

Empirical models are basically derived from an analysis of data and appropriate fitting procedures rather than theoretical principles (Reckhow and Chapra, 1983). As indicated in fig. 2.1 empirical models may comprise many stochastic elements.

Neural networks

Neural networks and fuzzy logic are methods belonging to the group of artificial, computational intelligence or soft computing and are assumed to be particularly attractive to handle noisy data in cases where the physical structure driving the hydrological process is not fully understood (Openshaw and Openshaw, 1997). Artificial neural networks (ANN) are “collections of adaptive non- linear processing elements” that are interconnected and organised in layers to detect patterns and establish knowledge based on training data sets (Anmala et al., 2000). This knowledge will be remembered if similar conditions occur and then

q t t

t p t t

t X X a a a

X1 1+...+φ1 + −θ1 1−...−θ1 (2.1)

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used to predict consequences (Lam and Swayne, 1996). ANN are particularly useful in cases where prediction is more important than explanation and where an extensive amount of training data exist.

Most of the applications within hydrological sciences are related to simple rainfall-runoff schemes and river discharge (Karunanithi et al., 1994; Smith and Eli, 1995; Minns and Hall, 1996;

Abrahart and Kneale, 1997; See et al., 1997, Abrahart and See, 2000), particularly for flooding estimations (Toth et al., 2001). Many authors regard ANN as a feasible alternative to stochastic time series modelling approaches (Raman and Sunilkumar, 1995; Teegavarapu, 1998; Tingsan- chali and Gautam, 2000).

Fuzzy rules

Any data analysis is confronted with uncertainty and lack of preciseness resulting from limited observation accuracy, deficiency of data and the pre-classification of landscape properties (Mole- naar and Janssen, 1991; Droesen and Geelen, 1993).

The basic idea of fuzzy logic is to launch a way to account for uncertainty in a non-probabilistic framework (Bárdossy and Duckstein, 1995).

Imprecise information is formulated mathemati- cally with the use of fuzzy sets, which are sets whose boundaries are not sharp, implying that objects belonging to one set can be a member of manifold sets, with a different degree of member- ship in each set (Havringa et al., 1999). Curve fitting methods can be used to determine the best fitting functions. A fuzzy rule, which is often described verbally, consists of a number of premises in the form of fuzzy sets with on the one hand, membership functions and, on the other, a consequence, which is usually also a fuzzy set (Bárdossy, 1996). The number of publications comprising Fuzzy-rule based modelling has increased considerably during the last 10 years.

Fuzzy rules have hitherto mainly been applied i) to derive simple models directly based on measured data (Droesen and Geelen, 1993; Bárdossy and Duckstein, 1995), ii) to mimic the response of conceptual models (Haberlandt et al., 2001), iii) to substitute routines used within conceptual models (Hundecha et al., 2001), iv) as an alternative to the numerical solution of water flow equations (Bárdossy and Disse, 1993; Bronstert, 1994;

Bárdossy, 1996; Schulz and Huwe, 1997) or v) in combination with other models (See and Abrahart, 2001). Similar to the neural network approach, fuzzy logic is particularly useful for the analysis of non-linear data (Haberlandt, 2000).

Regression models

Multiple linear regression, which is the type of method used in this thesis to estimate both annual runoff and nitrogen loading (chapter 7 and 8 of this

thesis), the hydrograph-separation in chapter 11 as well as the N-leaching described in chapters 11 and 12, is based on the assumption that the hydrologi- cal target or response variable Yi, is linearly correlated with a number of explanatory variables (2.2):

i mi m li

l

i X X E

Y =α+β ⋅ +K+β ⋅ +

where α is the intercept, α, β1,…,βm are model parameters, Xli,…Xmi are explanatory variables and Ei is the random error. The parameters α and βi are typically estimated from the least-squares method, which is a technique that minimises the sum of squares of the differences between the actual response values and the values predicted by the model.

Scatter plots (X-Y-dotty-plots) can help to detect whether the relationship between the explanatory variables and the response variable is linear. If this is not so, both or either the response variable or any of the explanatory variables may be trans- formed. Several conditions should be checked to test whether the model assumptions are fulfilled with respect to the random errors: i) the effects of the explanatory variables have to be additive and the expected random errors effects have zero mean ( =0

Ei

ε ) ii) the variance of the errors is constant (var Ei2), iii) Ei should follow a normal distribution, and iv) Ei should be independent in time and space, i.e. the errors are uncorrelated across observations.

The need for transformation of variables may also result from violation of one of the above assump- tions. Transformation of variables leads to so- called intrinsically linear model types that are non- linear in the variables. The definition of the precise form of the normal distribution is based on first and second statistical moments of the residual samples, which are the mean and standard deviation. By definition, 68% of all observations must fall within a range of ±1 standard deviation from the mean, while 95% of the samples are located within a range of ±2 standard deviation.

Several tests exist to test the residuals for normal- ity (SAS, 2000).

Users of regression models have to be aware of the possibility that a near-linear relationship between some of the explanatory variables might exist, resulting in high standard errors of the regression coefficients and non-significant p-values. Remov- ing one of the correlating variables from the regression will then cause a change of the parameter values of the correlated explanatory variable. Different analyses can be performed to detect this phenomenon called multi-collinearity.

Regression equations for runoff estimations have been used for decades (Linsley et al., 1949; Wright,

(2.2)

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1978 (c.f. chapter 8 of this thesis); Hirsch, 1982; Jones, 1984; Kaczmarek, 1993; Yates, 1997; Kletti and Stefan, 1997).

One example, which has been included in comparison studies (Chiew et al., 1993; Perrin et al., 2001), is the model of Tsykin (1985), where current runoff is explained by current rainfall and rainfall during previous time steps, both specified as days and months. Previous precipitation periods serve as substitute for antecedent soil-moisture indices.

Antecedent Precipitation Index (API) approaches use an index number based on previous rainfall amounts, the length of time since the rainfall and other rainfall and catchment statistics to relate rainfall to runoff. The empirical relationships employed to assess e.g. storm flow are often represented by coaxial graphs (Maniak, 1997).

More recently, multiple regression approaches have been used to explain annual water-quality dynamics for large regions such as the contermi- nous United States (Smith et al., 1997) or areas covering up to 2.9 million km2 of the midwest of the United States (Mizgalewicz and Maidment, 1996; Battaglin and Goolsby, 1997).

An important reason for deriving a multiple regression approach to annual discharge has been that such a simple method is directly adapted to and driven by the data currently available on the national scale, which helps to identify essential variables that can explain runoff patterns, even if some of the variables may act as a surrogate for phenomena that need further investigation and improvement of basic data sets.

Initial water balance calculations revealed that in many catchments, measured or observed river discharge is lower than the difference between precipitation and potential evapotranspiration, which is impossible if only natural processes within the area covered by the topographic catchment boundary are to be considered.

Approaches requiring closed water balances could not be considered for this first part of this study, since the modelling frame should enable calcula- tions of river discharge for the whole country including catchments with “shortage” in river discharge relative to net-precipitation. Moreover, the ultimate goal of the very first part of the thesis was to estimate annual nitrogen loads to the Danish coastal waters. Previously, a regression model for riverine nutrient transport has been derived from observations sampled from various parts of Denmark (Larsen, 1996). It was therefore and due to the tight time frame of this project decided to extend the existing nutrient loading model, which until now has been based on measured discharge, by a conceptually similar model for river discharge.

Of course, one significant disadvantage related to the establishment of regression models is the need for a large number of observations covering various hydrological conditions and situations and that processes causing the hydrological response are not formalised.

2.1.2.2 Conceptual models

Conceptual models are designed to reproduce the general structures and processes of the hydrologi- cal cycle based on simplified equations (Duan et al., 1992). The equations applied are physically sound, yet do not aim to provide a precise process description (Seibert, 1999). This class of models occupies an intermediate position between empirical and stochastic models on the one hand, and process-description-based models on the other. Hydrological processes, such as water flow, are typically computed by linear and non-linear interlinked storages representing components of the hydrological system (Clarke, 1973). Although soil moisture dynamics are accounted for, spatially and physically detailed features, like infiltration and groundwater levels, are typically not simulated explicitly. Some well-known examples of conceptual models are the Stanford Watershed Model (Crawford and Linsley, 1963), the TANK model (Sugawara, 1995), the SSARR model (Schermerhorn and Kuehl, 1968), the TOPMODEL (Beven and Kirkby, 1979), the IHACRES model (Jakeman et al., 1990; Littlewood et al., 1997), the VIC model (Wood et al., 1992), the XINANJIANG model (Zhao et al., 1980), the HBV model (Bergström, 1995) and the MODHYDROLOG model (Chiew and McMahon, 1994).

The monthly water balance model MWB-3 (Xu et al., 1996), which was used to simulate monthly runoff is less complex than ARC/EGMO (Becker and Pfützner, 1987; Pfützner et al., 1997), being applied in the climate impact study. While MWB-3 is a lumped approach requiring only three parameters to be specified or automatically calibrated, ARC/EGMO belongs to the category of semi-distributed models operating with time steps ranging from hours to years.

MWB-3 used as the monthly water balance model partly deviates from a scheme comprising several interlinked storages. The two runoff components considered, called “slow-flow” and “fast-flow”, are related to one common storage, although one might consider these components as representing discharge from groundwater aquifers and surface near runoff.

The advantage of MWB when compared to ARC/EGMO is its simplicity and the small number of parameters necessary for calibration, which favours MWB with respect to parameterisa-

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tion for ungauged catchments. In contrast, ARC/EGMO considers many more hydrological processes and components of the hydrological cycle in detail and provides spatially distributed output, which is regarded as an advantage when investigating single catchments.

2.1.2.3 Process-description based models

The main concept of process-description-based models (according to the classification scheme used by Beven (2000)) or physically-based models (according to Bathurst et al., 1995; Calver and Wood, 1995) is that equations derived from basic physical laws are used to describe the hydrological processes, examples being the differential equations of the highly non-linear Richards equation for unsaturated and saturated subsurface flow or the Saint-Venant equation for the simula- tion of stream flow. Apart from some special cases with simple initial and boundary conditions, approximate numerical techniques are required, implying spatial and temporal discretisation. The domain of interest, such as the catchment, needs therefore to be discretized into a network of elementary units varying in shape according on the solution scheme applied. There are many different solution methods, such as finite differ- ences, integrated finite differences, finite elements, finite-volumes and boundary elements. The equations are solved for each node point, either on the edges or at the centre of the elements. Within each of the single units, homogeneity has to be assumed. Many of these models require several input parameters to be specified in detail, and this information is often not available at the regional or national scale. Some of the most prominent representatives of this kind of models are SHE (Abbott et al., 1986) and IHDM (Beven et al., 1987).

2.2 Water quality modelling related to nitrogen pollution from diffuse sources

As for the hydrological models, a large number of approaches have been developed during the last 30 years to simulate transport and fate of nitrogen related to agricultural land use, and the number of model categories is as least as large as for the hydrological models, ranging from stochastic approaches (Worall and Burt, 1999) and empirical models comprising the use export coefficients (Beaulac and Reckhow, 1982; Johnes, 1996) or regression equations (Sparrow (Smith et al., 1997)) for nitrogen loadings to comprehensive conceptual catchment models (such as SWAT (Arnold et al., 1994) or SWIM (Krysanova et al., 1998a)) and process-description-based leaching models, such

as LEACHM (Wagenet and Hutson, 1989), SOILN (Johnson et al., 1987) and DAISY (Hansen et al., 1990). Leaching models are restrained to one- dimensional processes occurring in the root zone in contrast to catchment models providing at least information about the riverine nutrient loadings.

Comprehensive overviews about different model types for N-leaching and loadings are provided by e.g. Donigian and Huber (1991), de Willigen (1991), DeVries and Hromadka (1992), Singh (1995), Thorsen et al. (1996) and NRC (2000).

The main focus in model development during the past 30 years has been on approaches to be applied in detailed patch or field-scale studies (CREAMS (Knisel, 1980), EPIC (Williams et al., 1984), GLEAMS (Leonard et al., 1987), OPUS (Smith, 1992)) in which data availability presumably presents no significant problem. The single fields are typically assumed to be homogeneous with respect to input and bio-geochemical properties, and lateral flows are often not established. There are only a few examples of complex models developed and applied to catchments larger than 1000 km2 (SWAT (Arnold et al., 1994)), MATSALU (Krysanova et al., 1989), SWIM (Krysanova et al., 1998a)). These large-scale approaches follow the concept of semi-distributed models.

The ways in which the components of the hydrological cycle are treated vary with scale and model complexity. The empirical annual nitrogen loading model applied in this thesis in combina- tion with the annual runoff model and the model of Simmelsgaard et al. (2000) use external models for water movement, while comprehensive models like SWIM may explicitly include both snow melt, evapotranspiration, surface runoff percolation, subsurface lateral flows and river routing. SoilN- light (Forsman and Grimvall, 2001), which was used for the first leaching study in this thesis was derived from the SOILN-model that uses a process-oriented external model for water flow.

Schemes used to describe vertical water movement in leaching models may be based on the Richard’s equation (DAISY, LEACHM) and may even include the possibility of simulating preferential flow paths (RZWM (DeCoursey et al., 1989)). More often routing from storages is described by linear or non-linear functions (CREAMS, EPIC, SWIM, CANDY (Franko et al., 1995)). Solute transport is typically defined as a simple product of nutrient concentrations and water flows (SWIM, ANIMO (Berghuijs et al., 1985), SOILN), more seldom convection and dispersion processes are taken into account (DAISY, STOMOD (Reiche, 1994)).

Various schemes are established in the different models to account for the complexity of processes that explain the differences between input of nitrogen originating from inorganic and organic

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fertilizers, organic material, wet and dry deposi- tion and irrigation on the one hand, and removal via crop yield, water drainage, denitrification and ammonia volatilisation on the other. Haag and Kaupenjohann (2001) provide a comprehensive overview of important nitrogen transport and retention mechanisms occurring at various scales.

According to Rijtema et al., (1991), it is necessary to consider nitrogen mineralization and immobilisa- tion related to processes in the carbon cycle on the one hand, and denitrification in relation to (partial) anaerobios and decomposing organic materials on the other. In many process-oriented models, mineralization is often described as a first order process, but the number of organic pools included may differ widely (Thorsen et al., 1996). There is also significant variation with respect to N-uptake by crop vegetation. In some cases crop modules have been included (DAISY, SWIM), while in other instances crop uptake may be predefined (SOILN), and crop cover may be calculated from empirical functions (LEACHM).

Models based on regression equations usually do not consider specific chemical processes. Estimated nitrogen inputs to the catchments and catchment properties are in stead related to leaching rates and/or riverine nitrogen loads. Differences in vegetation cover considered in N-leaching models are often accounted for by the use of different coefficients that are specific for each crop type class.

In Denmark, there are basically two different model type classes that have been considered, either separately or in combination, for the simulation of N-leaching and riverine nitrogen loads; one mainly represented by the process- oriented numerical model DAISY (Hansen et al., 1990), used also in combination with the process-

oriented hydrological model MIKE SHE (c.f. SHE;

Abbott et al., 1986), the other comprising a number of regression models both for N-leaching (e.g.

Simmelsgaard, 1991; Andersen et al., 1999;

Simmelsgaard et al., 2000) and riverine loading (Larsen, 1996; Skop and Sørensen, 1997).

SoilN-light (Forsman and Grimvall, 2001), which is the model used for the first leaching study described in this thesis (Chapter 11), was estab- lished as a tool for a simple reproduction of the response of a complex numerical model, via the identification of the most important variables and the establishment of regression equations for estimating long-term N-leaching. This philosophy is to a certain extent similar to the approach of Børgesen et al. (2001) who derived a regression model for N-leaching based on the outputs of a selected number of simulation runs performed with the DAISY model.

The basic incentive for the establishment of the empirical leaching model “N-LES” applied in the second leaching study (Chapter 12 of this thesis) was the need to provide estimates for larger regions (Simmelsgaard et al., 2000), where the detailed data required to run numerical models that typically involve a large amount of input information and status variables to be identified are typically not available. Reduction of the number of variables also has the advantage that an empirical leaching model is easier to comprehend and to elucidate than comprehensive process-oriented approaches.

N-LES has been developed based on data from field measurements and drainage water studies performed at the Danish Institute of Agricultural Sciences (DIAS) and at NERI. Approximately 600 annual observations of N-leaching have been included in the investigations.

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3. Important databases for hydrological and water quality modelling available at the national scale in Denmark

As in many other countries, only few agreements have been made on the establishment of homoge- neous databases and assessment procedures to be applied at the national and regional scale, both for administrative and research purposes, since the organisations involved in hydrological research and the generation of digital hydrological databases have followed their own necessities and guidelines. To overcome some of the difficulties resulting from the lack of co-ordination, the Ministry of Environment and Energy launched in 1995 a project on the establishment of a national

“area information system (AIS)”. The main goal of the project was to: i) collect and adjust existing digital geographical databases, and ii) obtain new digital data sets from various digital and non- digital sources to support environmental research and administration at the regional and the national scale. The system was finally set up in 2000 and comprises about 40 digital maps of, among others, land use, watercourses, gauging stations, catch- ment boundaries, lakes, near-surface geology and land cover/land use (Nielsen et al., 2000).

The most important institutions involved in water quality investigations in Denmark are:

• The National Environmental Research Institute (NERI), which is the principal institution in charge of the monitoring and the protection of the environmental status of surface waters at the national scale

• The National Geological Survey of Denmark and Greenland (GEUS), likewise part of the Ministry of Environment and Energy. GEUS is responsible for monitoring the groundwater resources at the national scale

• The National Environmental Protection Agency, Danish EPA, (Miljøstyrelsen (MST)) and the Danish Forest and Nature Agency (Skov og Naturstyrelsen (SNS)), which define frame conditions and main targets for envi- ronmental administration and research in Denmark

• The Danish Institute of Agricultural Sciences DIAS (Danmarks Jordbrugsforskning, DJF), which belongs to the Ministry of Agriculture, Fisheries and Food

• The Danish Meteorological Institute (Dan- marks Meteorologiske Institut (DMI))

• The environmental departments of the Danish counties

3.1 Climatic and runoff data

In principle, climatic data are available from the Danish Meteorological Institute (DMI) as point

information associated with single climatic gauging stations. The temporal resolution and the number of stations per area vary according to the employed climatic variables and measurement methods.

For studies at the regional and national scale, information on precipitation from 1981 onwards are also available as grid cell data with a spatial resolution of 10 x 10 km2 mesh size, while records from previous periods are only accessible with a mesh size of 40 x 40 km2.

There are several problems related to the meas- urement, processing and spatial interpolation of precipitation data. When using conventional gauging units, the most serious potential error is related to wind-field deformation around the gauge. It is elevated 1.5 m above–ground, which causes aerodynamic blockage and may lead to an underestimation of 3-15 % for rain and up to 100 % or more for snow (Sevruk, 1993). Another important source of error is related to evaporative and wetting losses, the latter being caused by adhesive moistening of the inner surface of the gauge. The estimated error caused by wetting is assumed to be approximately 5% (Vejen et al., 1998) and is usually greater than the loss by splashing and evaporation of water accumulated in the gauge (Sevruk, 1993).

The empirical model suggested by DMI for correction of point measurements of precipitation is based on the results of a North-European project. Investigations performed for 212 Danish gauging stations during the period 1989-1997 revealed that the total uncertainty related to daily point measurements and subsequent correction does not exceed ± 8 % (Vejen et al., 1999).

To derive two-dimensional precipitation fields from a total number of the approximately 500 stations available for Denmark, DMI applied an inverse distance interpolation method (IDW), using a linearly weighted combination of a set of sample points (gauge stations), where the weight is a function of inverse distance ((distancea)-1) with a being the power parameter. The value of the power parameter chosen by DMI is 2. Up to 4 stations are considered for each grid cell of 5 x 5 km2. The area around the centre point of each 5 x 5 km2 grid cell is divided into 4 quadrant sectors, and the nearest neighbour within each of the sectors is taken to interpolate the 5 x 5 km2 grid cell values, which are then averaged to 10 x 10 km2 values to avoid a potential overrepresentation of single stations. An important restriction of this method is related to the fact that the influence of

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any input point on the interpolated value is isotropic, which means that significant differences in landscapes such as ridges are not maintained and accounted for as part of the interpolation (Philip and Watson, 1982). All stations fulfilling the above-stated requirements are included in the calculations, irrespective of their relative topo- graphic location. Based on randomly selected three-month periods with daily data, I found that the mean difference between the centre of each grid cell and the first 6 stations considered for interpolation of the grid cell value varied, on average, between 11.4 and 16.6 km.

Due to the shortcomings of the IDW-methods, other geostatistical techniques, such as kriging, are often preferred (Tabios and Salas, 1985; Phillips et al., 1992) and provide better results in case of low sampling density (Dirks et al., 1998; Borga and Vizzaccaro, 1997). Additionally, such methods supply information on the prediction error.

Extended versions of kriging, such as cokriging (Hevesi et al., 1992) and external drift kriging (Raspa et al., 1997), provide an opportunity to add information on secondary attributes if the number of sampled observations for the main attribute is limited.

Another challenge is related to the use of the correction factors suggested for each of the 10 x 10 km2 grid cells. Originally, these factors were established to correct for errors at the scale of single gauging stations. Currently, two alternative versions of correction factors exist. The first version provides monthly correction values that are similar for all grid cells and years, which means that for all the 609 grid cells covering all terrestrial areas of Denmark as a whole, the same correction values are to be applied for all years. For the second data set, the values are regionally specific and vary between years. The latter

“distributed” correction factor-set has not been completed yet and can therefore not be used operationally for all parts of the country.

For both correction data sets, users may choose between three different categories, depending on the topographic location and the exposition to wind fields of the respective stations. Since most of the 500 stations used are categorised as “interme- diate” and the users normally do not know which stations have been considered for each of the single grid cells, DMI suggests the use of the intermedi- ate correction factor for each single grid cell.

When comparing the values expressed as a national and annual average, the precipitation values that have been corrected in a distributed way, are approximately 24 % larger than the uncorrected ones, while the “global” correction leads to an increase of approximately 20 % (table 3.3). Differences in the results between the two

applications are not only related to the fact that the first correction data sets are spatially lumped with no differences between the years, but also the circumstance that the first set is based on data from the normal climatic period 1961-1990.

Table 3.1 Monthly factors suggested by DMI to be used for the “global” correction of precipitation.

Month Factor

January 1.41

February 1.42

March 1.35

April 1.24

May 1.13

June 1.11

July 1.10

August 1.10

September 1.11

October 1.14

November 1.23

December 1.17

Table 3.2 Range and distribution of monthly precipita- tion correction factors, based on 609 grid cells during all months of the period 1989-1997, suggested by DMI to be used for “distributed” correction of precipitation for intermediate conditions.

Month Average Min. Max. Stddev.

January 1.54 1.12 3.15 0.41

February 1.59 1.17 3.57 0.49

March 1.48 1.18 2.53 0.31

April 1.33 1.16 2.48 0.16

May 1.18 1.08 1.53 0.08

June 1.24 1.08 3.58 0.33

July 1.16 1.07 1.60 0.09

August 1.13 1.05 1.46 0.07

September 1.15 1.08 1.31 0.05

October 1.15 1.08 1.28 0.04

November 1.31 1.13 2.09 0.18

December 1.43 1.15 3.18 0.35

Table 3.1 shows the “global” correction values suggested by DMI, while table 3.2 comprises statistics of the “distributed” correction factor during the period 1989-1997. Both tables are related to gauging stations with intermediate shelter conditions.

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