Part 6 – Appendices
15 GR4J
Figure 40 shows the structure of the GR4J model. GR4J is a two-storage, four-parameter, daily-step conceptual RR model that has proven to give good results on a wide range of French catchments.
The four parameters have the following functions:
-X1: depth of the routing store -X2: depth of the production store -X3: leaks and gains (sub-surface exchanges with neighboring catchments and/or deep aquifer systems)
-X4: unitary hydrograph UH1 base time
For more details on GR4J, see Perrin et al. (2003).
Figure 40: Scheme of the four-parameter GR4J model
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Index
Acknowledgements ... 3
Résumé ... 4
Abstract ... 5
1 Introduction ... 7
Part 1 – Methods, databases and literature ... 11
2 Databases used in this thesis ... 13
2.1 Why should we use a large set of catchments? ... 14
2.2 How our dataset was made ... 14
2.3 How can we characterize a catchment? ... 15
2.4 Distribution of a few key descriptors and flow characteristics over our dataset ... 19
3 Methodological aspects ... 23
3.1 General principles of the comparative testing of alternative regionalization methods 24 3.1.1 Jack-knife approach to cross validation ... 24
3.1.2 There is no absolute truth in this world: we need benchmarks ... 24
3.1.3 Specificities of different models: how the regionalization exercise differs for a statistical and for a rainfall-runoff model ... 25
3.2 Catchment selection: differential approach for the donor and the receiver pool ... 26
3.3 Further methodological requirements to assess the robustness of a regionalization method27 3.3.1 Why this question makes sense? ... 27
3.3.2 Assessing the impact of the density of neighbors: metrological desert generation vs random network reduction ... 28
3.4 Synthesis of the methodological choices ... 32
4 Literature review on the regionalization of rainfall-runoff models ... 33
4.1 All agree more or less on a definition for an ungaged basin ... 34
4.2 For a hydrological fundamentalist, there is no special problem with ungaged basins…... 34
4.3 With ungauged basins, the solution lies in "putting more physically measurable" parameters in the model in order to reduce (suppress?) the dependency on calibration ... 35
4.4 With ungauged basins, the solution lies in finding a posteriori a relationship between calibrated parameters and relevant physiographic and climatic descriptors (or geographical coordinates) ... 36
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4.4.2 Relative relationships ... 37
4.5 With ungauged basins, the solution lies in finding one or more similar catchment(s) (in order to transfer parameters from them) ... 38
4.5.1 Methods focusing on spatial proximity... 38
4.5.2 Methods focusing on physical similarity ... 39
4.5.3 How to define similarity? ... 41
4.5.4 Concerning possible complementarities between spatial proximity and physical similarity ... 42
4.6 With ungauged basins, the solution lies in using a previously made statistical regionalization to guide us in the choice of model parameters ... 43
4.7 My opinion (before I started this work), how it evolved, and how the solutions I tried to implement relate to the literature ... 45
Part 2 – Studies relative to flow statistics and their regionalization ... 47
5 Linking flow statistics to physiographic descriptors ... 49
5.1 Brief review of the literature on the regionalization of flow statistics ... 50
5.2 Regression as a conceptual model of the relationship between physiographic properties, climate and streamflow ... 52
5.2.1 Nation-wide vs local formulations ... 52
5.2.2 Selecting relevant descriptors ... 53
5.3 Streamflow statistics considered and results ... 54
5.3.1 Streamflow statistics considered ... 54
5.3.2 List of physiographic descriptors ... 54
5.3.3 Results ... 55
5.3.4 Review of the dependence of the selected statistics on each descriptor ... 59
6 Using neighbour catchments residuals to improve the efficiency of flow statistics regionalization ... 63
6.1 Residual's spatial structure as a descriptor of overlooked or not observable properties... 64
6.1.1 IDW interpolation ... 64
6.1.2 Results ... 65
6.2 Constraints on the surface of donor catchments ... 67
6.3 Accounting for nested donor catchments ... 70
6.4 Excluding outliers from the donors' list ... 73 6.5 Final considerations on the results obtained for the regionalization of flow statistics
87
Part 3 – Regionalization of rainfall-runoff models – direct methods ... 89
7 Physiographic similarity regionalization ... 91
7.1 Introduction ... 92
7.1.1 Common points of the tested regionalization methods ... 92
7.2 Method based on Principal Component Analysis ... 93
7.2.1 Preliminary selection of explanatory variables ... 94
7.2.2 Principal Component Analysis as a tool to overcome the issue of correlated descriptors ... 95
7.2.3 Results ... 96
7.3 Backwards sorting method ... 99
7.3.1 Variable selection algorithm ... 99
7.3.2 Results ... 100
8 Joining spatial proximity and physiographic similarity... 103
8.1 Introduction ... 104
8.4 Comparison of the tested regionalization approaches ... 110
9 Sensitivity analysis of regionalization methods: how do they react to the lack of similar catchments? ... 113
9.1 Introduction ... 114
9.1.1 Results of the elimination neighboring donors ... 114
9.2 Sensitivity of regionalization methods to the lack of similar catchments ... 116
9.2.1 Results ... 116
9.3 Sensitivity of regionalization methods to thresholds of model efficiency ... 117
9.3.1 Results ... 117
Part 4 – Regionalization of rainfall-runoff models – the indirect path ... 121
10 Direct and indirect regionalization... 123
10.1 Introduction ... 124
10.1.1 Why could an indirect regionalization be advantageous? ... 124
10.2 Review of the relevant scientific literature ... 125 10.2.1 How does the work presented in this chapter relate to the existing literature?
125
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10.3 Issues of concern for implementing an indirect regionalization scheme ... 125
10.3.1 How does the first level of regionalization affect the second? ... 125
10.3.2 How to constrain the initial choice of possible parameter sets? ... 126
10.3.3 Can such a method be robust? ... 126
10.4 Method ... 127
10.4.1 General choices ... 127
10.4.2 Criterion used to further constrain the choice of parameter sets ... 129
10.4.3 Three benchmark comparisons. ... 129
10.5 Discussion of results ... 129
10.5.1 Number of parameter sets to be retained ... 130
10.5.2 Impact of statistics' regionalization quality on the following regionalization of RR model parameter sets ... 131
10.5.3 Could it be advantageous to constrain the choice of parameter sets with an additional criterion? ... 135
10.5.4 Robustness of the method: application of the metrological desert test ... 136
11 How the choice of an efficiency criterion impacts our vision of the 'best' regionalization method ... 139
11.1 What is the best regionalization method when we adopt an FDC-based performance criterion? ... 140
11.1.1 Performance criterion used for calibration ... 140
11.1.2 Regionalization results ... 140
11.2 Use of the Gupta et al. decomposition of NSE as diagnostic tool : where do lie the differences between C2M and the FDC-based criterion used in this chapter? ... 142
11.2.1 Detail of the NSE decomposition used ... 142
11.2.2 Difference in calibrated parameter sets ... 142
11.2.3 Difference in regionalized parameter sets ... 145
12 Conclusion ... 149
13 References ... 153
Part 6 – Appendices ... 157
14 Sensitivity to the elimination of similar donors: graphic results ... 157
15 GR4J... 193
Index ... 195
List of Figures ... 200
List of Tables ... 204