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Table of contents
General introduction
1 Context
2 Scientific questions of this thesis
3 Structure of the thesis
Part I A brief review of concentration-discharge (C-Q) relationships
1 Introduction
2 Non-univocal concentration-discharge (C-Q) relationship (hysteresis)
3 Concentration-discharge (C-Q) relationship models
3.1 One-component models
3.1.1 Power-law model
3.1.2 Hyperbolic model
3.2 N-component models
3.2.1 Mixing models
4 Hydrograph separation methods
4.1 Non tracers-based method
4.1.1 Recession curves analysis methods
4.1.2 Filtering methods
4.2 Tracers-based methods
4.2.1 Isotopic tracers
4.2.2 Geochemical tracers
5 Quantification of the end-members
5.1 Eigenvector analysis
5.1.1 Principal Component Analysis (PCA)
5.1.2 Factor analysis (FA) or positive matrix factorization (PMF)
5.2 Classification analysis
5.2.1 Cluster analysis (CA)
5.2.2 Discriminant analysis (DA)
5.3 Mixed analysis
5.3.1 End member mixing analysis (
5.3.2 MIX method
6 Study site – The Oracle-Orgeval observatory
6.1 Characteristics of Oracle-Orgeval observatory
6.1.1 Location and brief history
6.1.2 Topography and Climate
6.1.3 Geology and hydrogeology
6.1.4 Pedolog
6.1.5 Land use and hydro-agricultural infrastructures
6.2 Hydrological measurements of Oracle-Orgeval observatory
6.3 Chemical measurements of Oracle-Orgeval observatory
6.3.1 Long-term monitoring
6.3.2 River Lab. and high-frequency measurements
6.3.3 Typology of high-frequency measurements of ions concentrations during flow events
6.4 Hydrological and chemical behavior of the catchment
7 References
Part II Revisiting the concentration-discharge (C-Q) relationships
Chapter 1: Revisiting the one-component models – power law model
Technical Note: A two-sided affine power scaling relationship to represent the concentration–discharge relationship
1 Introduction
2 Tested dataset
3 Mathematical formulations
3.1 Classic one-sided power scaling relationship (power law)
3.2 Limits of the power law
3.3 A two-sided affine power scaling relationship as a progressive alternative to the power law
4 Numerical identification of the parameters for the 2S-APS relationship
5 Results
5.1 Results in calibration mode
5.2 Results in validation mode
6 Conclusion
7 Appendix 1 – Description of the River Lab
8 Appendix 2 – Graphical representation of the numerical identification of parameters
9 References
Chapter 2: Revisiting the n-component models – mixing model Hydrograph separation issue using high-frequency chemical measurements
1 Introduction
1.1 Hydrograph separation: an age-old issue
1.2 A variety of solutions proposed for hydrograph separation
1.3 Joining the strengths of hydrological and chemical approaches for hydrograph separation
1.4 Using high-frequency chemical measurements to revisit the hydrograph separation issue
2 Methodology
2.1 Study site and data set
2.2 Hydrograph separation methods
2.2.1 Lyne – Hollick method (LH)
2.2.2 Eckhardt method (ECK)
2.2.3 Hydrological recession time constant of the catchment
2.2.4 MB method
2.3 Comparison of the two RDF methods through an hydrological and a chemical calibration
2.3.1 The hydrological recession time constant (τ) from hydrological MRC approach
2.3.2 Sensibility of the RDF methods to the hydrological recession time constant of the catchment (τ)
2.3.3 The hydrological recession time constant of the catchment (τ) from MB approach
2.4 Comparison between the components 𝑪𝒃𝒋 and 𝑪𝒒𝒋 obtained from the optimal hydrograph separation and the field chemical dataset.
3 Results and Discussion
3.1 Hydrological approach to calculate the hydrological recession time constant of the catchment (τ)
3.2 Baseflow exploration from RDF methods with hydrological recession time constant (τ) values
3.3 MB approach to find the optimal hydrological recession time constant
3.4 Comparison between the components 𝑪𝒃𝒋 and 𝑪𝒒𝒋 obtained from the optimal hydrograph separation and the field chemical dataset.
4 Conclusions
5 References
Chapter 3: Combining the one- and n-component models Combining concentration-discharge relationships with mixing models
1 Introduction
2 Procedure for combining mixing models and C-Q relationships
2.1 Case 1: chemostatic components ( bb = bq = 0)
2.2 Case 2: single 2S-APS relationship (ab =aq = a and bb = bq = b)
2.3 Case 3: General case (a and b are different)
3 Application of the combining model
3.1 Study site and datasets
3.2 Methodology
4 Results and discussion
4.1 Identification of the parameters and overall performance of the models
4.2 Performances for selected storm events
5 Conclusions
6 References
Chapter 4: Identification and quantication of the end-members
Identification of potential end members and their apportionment from downstream high – frequency chemical data
1 Introduction
1.1 Formulation of the problem and main resolution techniques
1.2 Identification and contribution of end members methods
1.2.1 Tracer mass balance methods (TMB)
1.2.2 Multivariate statistical methods (MS)
1.2.3 Principal Component Analysis (PCA) and End member mixing analysis (EMMA) .
1.2.4 Positive Matrix Factorization method (PMF)
1.2.5 MIX method
1.3 Scope of this paper
2 Material and method
2.1 Study site
2.2 Data set processing
2.3 Methodology
2.3.1 Optimization function
2.3.2 Sensitivity analysis of end members
3 Results and discussion
3.1 Relation between the criterion VR and A/B ratio
3.2 Average monthly concentrations of the potential end-members and their respective apportionment
3.3 Sensitivity analysis of end members
3.4 Potential end-members to identify observed evolution in a synthetic manner .
3.5 Potential end-members versus pre-identified possible end-members
4 Conclusions
5 Appendix
5.1 Cluster analysis for evolution of end-members using a variable VR (0.02<VR<0.10)
6 References
Part III Conclusions and Perspectives
1 Conclusions
1.1 Main achievements of the thesis
1.1.1 The affine power scaling relationship
1.1.2 Calibration of the Hydrograph separation
1.1.3 Combining of affine relationship and mixing model
1.1.4 Identification and quantification of potential end-members
1.2 The develop of a parsimonious model
2 Perspectives
