# Is Catchment Classification Possible by Means of Multiple Model Structures? A Case Study Based on 99 Catchments in Germany

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## Abstract

**:**

^{2}to 1826 km

^{2}. We examined model performance in terms of streamflow predictions, based on various indices. Our results indicate that for some catchments many structures perform equally well, whereas for other catchments a single structure clearly outperforms the others. We could not identify clear relationships between relative model performance and catchment characteristics. This result led us to conclude that for the spatial scales considered, it is difficult to base the selection of a lumped conceptual model based on a priori assessment, and we recommend a posteriori selection based on model comparisons.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}to 1826 km

^{2}; 62 catchments are smaller than 200 km

^{2}and seven catchments are larger than 1000 km

^{2}. Several catchments are neighbored or nested. The catchments are situated in a comparatively small area with the maximum distance between two points of the study area being about 325 km. Geology is very variable. In the north of the study area, it consists of greywacke, quartzite, and sedimentary rock with tertiary and quaternary volcanism. In the south of the study area, it consists of sandstone, marl, and limestone. There is no considerable presence of karst.

#### 2.2. Data

#### 2.3. Methods

#### 2.3.1. Calibration

#### 2.3.2. Model Evaluation: Identification of Acceptable Models

_{SI}(Equation (1)). Because the sum of percentages as absolute values of biases can lead to misunderstandings, we set S

_{SI}as dimensionless:

_{SI}range between zero (perfect fit) and infinity (no fit).

_{obs}represents observed runoff, q

_{sim}represents simulated runoff, the overbar denotes the mean, and n is the length of the time series. The NSE is a common normalized measure to evaluate the performance of hydrologic models and compares the mean square error of the simulated runoff to the variance of the observed runoff (Equation (2)). It ranges from minus infinity to 1, where 1 indicates a perfect fit. For characterizing streamflow performance, it is typically considered that NSE is overly sensitive to large values [34] and that the NSE is not always expedient for model evaluation and comparison [23,35].

_{SI}is less than 70 and NSE is larger than 0.65. Models that do not fulfill these two criteria are no longer incorporated in the subsequent stages of the analysis.

_{SI}and NSE are selected based on experience. For the NSE, the selected threshold corresponds to adequate or very good reported performance ratings for NSE according to Moriasi et al. [36], whereas Oudin et al. [37] refer to a poorly modeled catchment when the NSE is less than 0.7. The threshold of 70 for S

_{SI}is based on visual inspections of suitable FDCs.

#### 2.3.3. Comparing Model Performances

- Multiple model structures simulate a catchment differently. The identification of a best performing model is possible. The model structure can be tentatively connected to the catchment behavior. If there are catchments with only one acceptable model, they belong to this group too.
- Multiple model structures simulate the catchment similarly. Model equifinality [12,18,43] makes it difficult to connect model structure and catchment structure or behavior. Catchments of this group are further divided into:
- catchments where all acceptable models simulate the runoff similarly; and
- catchments where at least 60% but not all acceptable models simulate runoff similarly.

Catchments without an acceptable model result constitute an additional group: - No model structure simulates the catchment acceptably. All structures fail to capture catchment behavior.

#### 2.3.4. Identification of Best Performing Models

_{SI}(Equation (1)) is the best performing model for this catchment. For catchments with only one acceptable model, this model is assigned as the best performing.

_{SI}is often possible, but not very reliable. For catchments with differences of S

_{SI}< 2.0 between models, we identify more than one best performing model.

#### 2.3.5. Correlation with Catchment Properties

## 3. Results

#### 3.1. Calibration

#### 3.2. Signature Indices

#### 3.3. Acceptable Models

#### 3.4. Comparing Model Performances

- I
- Multiple model structures simulate a catchment differently. The two example catchments (Figure 6I) show different patterns of signature indices.For 30 catchments of the study area (Table A1), multiple model structures produce different simulations, even though few models show related patterns of signature indices.Additionally, we include in this group the five catchments with only one acceptable model because of differentiated simulation results (Table A1).
- IIa
- IIb
- III

#### 3.5. Best Performing Models

_{SI}is possible but not reliable. Therefore, all models with only minor differences of performance to the lowest S

_{SI}(differences < 2.0) are regarded as best performing. Hence, we identify more than one best performing model for 18 catchments (Table A1). Most of these 18 catchments belong to categories IIa and IIb. Five catchments of category I show similar signature indices. Models with similar patterns of signature indices are not necessarily the best performing models of the catchment. For example, for catchment “Kocherstetten” (Figure 6IIb, on the right), the model based on structure M03 is the best performing model with an S

_{SI}of 24 while the S

_{SI}of other similar models are about 36.

#### 3.6. Correlations with Catchment Properties

^{2}. However, there are no clear correlations between best performing models and catchment properties like runoff characteristics, climate, land use, or catchment size.

## 4. Discussion

^{2}. These catchments will be on average more homogeneous than larger catchments, and can therefore be well represented by a simple structure. Models based on these structures (M03 and M04, Figure 2) are best performing for about 20% of the catchments in this study.

## 5. Conclusions

- For about 15% of the catchments, no model had a suitable performance, which indicates model structural errors or data errors.
- For about 50% of the catchments, large parts of the models display a similar performance and thus demonstrate strong equifinality. About 35% of the catchments show no strong equifinality.
- Most of the catchments can be classified by a clear best performing model, which indicates that models may perform differently in different regions.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix

Catchment Name | State | Size (km^{2}) | Urban Area (%) | Forest Area (%) | River Length (km) | Mean Prec. (mm/year) | RC | AI | Best | Group |
---|---|---|---|---|---|---|---|---|---|---|

Abentheuer | RLP | 39 | 0 | 91 | 13 | 1139 | 0.59 | 2.05 | 4; 7 | I |

Abtsgmuend | BW | 246 | 5 | 36 | 46 | 968 | 0.51 | 1.61 | 7 | IIb |

Albisheim | RLP | 113 | 5 | 30 | 22 | 631 | 0.28 | 0.97 | 11 | I |

Altenahr | RLP | 748 | 2 | 55 | NaN | 780 | 0.35 | 1.19 | 7; 11 | IIa |

Altenbamberg | RLP | 318 | 4 | 31 | 51 | 662 | 0.30 | 1.03 | 11 | IIb |

Altensteig | BW | 135 | 2 | 76 | 24 | 1250 | 0.47 | 2.24 | 7 | I |

Argenschwang | RLP | 31 | 0 | 76 | 13 | 790 | 0.41 | 1.10 | 0 | I |

Bad Bodendorf | RLP | 864 | 3 | 54 | NaN | 773 | 0.33 | 1.17 | 12 | IIb |

Böhringsweiler | BW | 17 | 8 | 48 | 6 | 1040 | 0.56 | 1.45 | 0 | III |

Bad Rotenfels | BW | 466 | 5 | 85 | 64 | 1510 | 0.73 | 2.53 | 11 | IIa |

Denkendorf | BW | 128 | 29 | 14 | 26 | 744 | 0.48 | 1.12 | 7 | IIb |

Denn | RLP | 95 | 0 | 83 | 18 | 817 | 0.40 | 1.20 | 0 | III |

Doerzbach | BW | 1029 | 5 | 32 | 112 | 835 | 0.41 | 1.31 | 11; 7 | I |

Ebnet | BW | 257 | 3 | 61 | 26 | 1380 | 0.60 | 2.16 | 0 | III |

Elpershofen | BW | 816 | 6 | 32 | 84 | 830 | 0.45 | 1.32 | 3 | IIb |

Enzweiler | RLP | 22.9 | 6 | 62 | 11 | 899 | 0.32 | 1.36 | 7; 11 | IIa |

Erzgrube | BW | 34 | 2 | 83 | 10 | 1400 | 0.44 | 2.44 | 6 | IIa |

Eschelbronn | BW | 193 | 6 | 28 | 27 | 893 | 0.45 | 1.16 | 9; 12 | IIb |

Eschenau | RLP | 597 | 9 | 34 | 57 | 841 | 0.39 | 1.40 | 10; 11 | IIb |

Friedrichsthal | RLP | 681 | 6 | 41 | 91 | 908 | 0.42 | 1.38 | 12; 7 | I |

Gaildorf | BW | 733 | 6 | 51 | 76 | 945 | 0.49 | 1.53 | 3 | I |

Gaugrehweiler | RLP | 41 | 1 | 43 | 15 | 694 | 0.26 | 0.99 | 11 | I |

Gensingen | RLP | 196 | 5 | 20 | 45 | 560 | 0.15 | 0.82 | 10 | IIb |

Gerach | RLP | 63 | 4 | 54 | 20 | 850 | 0.38 | 1.33 | 11 | IIb |

Gondelsheim | BW | 127 | 8 | 34 | 22 | 800 | 0.20 | 1.06 | 12 | IIb |

Hausen | BW | 109 | 8 | 19 | 22 | 763 | 0.32 | 1.04 | 12 | IIb |

Heddesheim | RLP | 164 | 5 | 54 | 31 | 718 | 0.26 | 1.03 | 12 | IIb |

Heimbach | RLP | 318 | 6 | 43 | 29 | 1042 | 0.70 | 1.65 | 3 | I |

Hoefen | BW | 219 | 2 | 92 | 33 | 1330 | 0.61 | 2.04 | 3 | I |

Hopfau | BW | 201 | 5 | 41 | 30 | 1240 | 0.52 | 2.03 | 3; 4 | IIb |

Hüttlingen | BW | 107 | 13 | 50 | 23 | 956 | 0.80 | 1.44 | 0 | III |

Imsweiler | RLP | 171 | 6 | 37 | 24 | 688 | 0.30 | 1.09 | 9; 12 | IIb |

Iselshausen | BW | 147 | 5 | 44 | 24 | 992 | 0.36 | 1.55 | 4 | IIb |

Isenburg | RLP | 155 | 6 | 47 | 35 | 888 | 0.37 | 1.34 | 4 | I |

Jagstzell | BW | 329 | 6 | 41 | 41 | 850 | 0.43 | 1.32 | 7 | IIb |

Kallenfels | RLP | 251 | 4 | 40 | 42 | 773 | 0.35 | 1.20 | 4 | I |

KArnstein | RLP | 113 | 2 | 41 | 33 | 735 | 0.32 | 1.06 | 7 | IIb |

Kautenmuehle | RLP | 37 | 11 | 17 | 15 | 873 | 0.40 | 1.39 | 11 | IIa |

KEhrenstein | RLP | 66 | 1 | 34 | 21 | 910 | 0.44 | 1.31 | 12 | I |

Kellenbach | RLP | 362 | 2 | 35 | 49 | 721 | 0.33 | 1.11 | 11 | IIb |

KEngelport | RLP | 113 | 2 | 48 | NaN | 774 | 0.32 | 1.20 | 11 | I |

Kirmutscheid | RLP | 88 | 3 | 38 | 21 | 781 | 0.38 | 1.25 | 4 | IIa |

Kocherstetten | BW | 1289 | 6 | 44 | 120 | 911 | 0.47 | 1.47 | 3 | IIb |

Kreuzberg | RLP | 45 | 1 | 62 | NaN | 742 | 0.26 | 1.06 | 11 | IIa |

Kronweiler | RLP | 65 | 3 | 54 | 17 | 976 | 0.46 | 1.51 | 3 | I |

Lahr | BW | 130 | 6 | 68 | 26 | 1090 | 0.31 | 1.52 | 9; 11 | IIb |

Lautenhof | BW | 84 | 1 | 95 | 20 | 1490 | 0.60 | 2.55 | 7; 9 | IIa |

Lippach | BW | 10 | 1 | 39 | 7 | 835 | 0.42 | 1.31 | 0 | III |

Loellbach | RLP | 45 | 0 | 32 | 16 | 699 | 0.33 | 1.13 | 7 | IIb |

Martinstein | RLP | 1467 | 5 | 44 | 79 | 842 | 0.47 | 1.31 | 7 | I |

Miehlen | RLP | 102 | 2 | 38 | 17 | 724 | 0.42 | 1.03 | 11 | IIa |

Mittelrot | BW | 126 | 4 | 59 | 31 | 994 | 0.48 | 1.60 | 10 | IIb |

Monsheim | RLP | 198 | 5 | 21 | 30 | 625 | 0.24 | 0.91 | 11 | IIb |

Muesch | RLP | 353 | 2 | 39 | NaN | 759 | 0.33 | 1.27 | 9 | IIa |

Murr | BW | 505 | 8 | 44 | 48 | 918 | 0.51 | 1.37 | 12 | IIa |

Nanzdietschw. | RLP | 201 | 8 | 34 | 30 | 838 | 0.43 | 1.48 | 11 | I |

Nettegut | RLP | 368 | 10 | 31 | 65 | 697 | 0.31 | 0.98 | 11 | I |

Neuenstadt | BW | 142 | 5 | 38 | 33 | 859 | 0.40 | 1.28 | 7 | IIb |

Niederelbert | RLP | 16.4 | 6 | 59 | 8 | 930 | 0.42 | 1.35 | 4 | I |

Nierstein | RLP | 37 | 14 | 0 | 13 | 575 | 0.12 | 0.78 | 0 | III |

Oberingelheim | RLP | 365 | 8 | 1 | 62 | 542 | 0.11 | 0.79 | 0 | III |

Obermoschel | RLP | 61 | 1 | 15 | 20 | 653 | 0.25 | 0.97 | 0 | III |

Oberrot | BW | 62 | 5 | 57 | 19 | 1010 | 0.49 | 1.58 | 9; 12 | IIb |

Oberstein | RLP | 557 | 6 | 50 | 55 | 995 | 0.60 | 1.56 | 0 | III |

Odenbach | RLP | 1087 | 9 | 35 | 78 | 784 | 0.38 | 1.30 | 9; 11 | I |

Odenbach Steinbruch | RLP | 85 | 2 | 16 | 25 | 723 | 0.38 | 1.10 | 4 | I |

Oppenweiler | BW | 181 | 4 | 66 | 23 | 1010 | 0.51 | 1.56 | 12 | I |

Papiermühle | RLP | 170 | 3 | 57 | NaN | 818 | 0.44 | 1.35 | 12 | I |

Pforzheim-E | BW | 1479 | 8 | 57 | 94 | 1020 | 0.41 | 1.61 | 6 | IIb |

Pforzheim-W | BW | 418 | 13 | 35 | 52 | 806 | 0.32 | 1.21 | 11 | I |

Planig | RLP | 171 | 4 | 20 | 44 | 588 | 0.23 | 0.87 | 7 | IIb |

Platten | RLP | 377 | 5 | 46 | NaN | 834 | 0.40 | 1.40 | 12 | I |

Rammelsbach | RLP | 78 | 7 | 17 | 18 | 901 | 0.49 | 1.42 | 3 | IIb |

Rheindiebach | RLP | 10 | 0 | 59 | 7 | 635 | 0.23 | 1.04 | 0 | III |

Schafhausen | BW | 238 | 16 | 33 | 23 | 802 | 0.36 | 1.21 | 0 | III |

Schenkenzell | BW | 76 | 4 | 65 | 19 | 1350 | 0.49 | 2.24 | 9; 11 | IIa |

Schulmuehle | RLP | 145 | 2 | 36 | 26 | 719 | 0.31 | 1.01 | 0 | III |

Schwabsberg | BW | 178 | 4 | 31 | 27 | 846 | 0.41 | 1.31 | 5 | I |

Schwaibach | BW | 954 | 3 | 72 | 69 | 1410 | 0.66 | 1.84 | 3 | IIa |

Schwarzenberg | BW | 179 | 4 | 87 | 30 | 1620 | 0.77 | 2.86 | 11 | IIa |

Seelbach | RLP | 193 | 6 | 36 | 41 | 994 | 0.51 | 1.53 | 3; 4 | I |

Seifen | RLP | 176 | 6 | 42 | 43 | 917 | 0.41 | 1.38 | 12 | IIb |

Sinspelt | RLP | 101 | 1 | 34 | NaN | 934 | 0.48 | 1.48 | 7 | IIb |

Stausee Ohmb. | RLP | 34 | 4 | 19 | 15 | 858 | 0.49 | 1.42 | 3 | IIb |

Steinbach | RLP | 46 | 0 | 47 | 11 | 750 | 0.45 | 1.13 | 11 | I |

Steinheim | BW | 76 | 8 | 38 | 18 | 831 | 0.39 | 1.30 | 9; 11 | IIa |

Talhausen | BW | 192 | 17 | 28 | 40 | 764 | 0.24 | 1.09 | 11 | I |

Talheim | BW | 73 | 8 | 32 | 19 | 816 | 0.32 | 1.20 | 0 | III |

Uffhofen | RLP | 85 | 3 | 45 | 22 | 612 | 0.20 | 0.88 | 11 | I |

Untergriesheim | BW | 1826 | 5 | 31 | 168 | 832 | 0.44 | 1.27 | 7 | I |

Vaihingen | BW | 1662 | 8 | 54 | 122 | 996 | 0.51 | 1.09 | 6; 7 | IIa |

Voerbach | BW | 44 | 4 | 57 | 10 | 1110 | 0.37 | 1.74 | 4; 7 | IIa |

Weinaehr | RLP | 215 | 13 | 41 | 38 | 887 | 0.40 | 1.34 | 12 | I |

Wernerseck | RLP | 242 | 5 | 39 | 56 | 734 | 0.33 | 1.07 | 12 | I |

Westerburg | RLP | 44 | 13 | 34 | 13 | 1049 | 0.47 | 1.80 | 4 | IIb |

Wiesloch_W | BW | 55 | 9 | 23 | 18 | 797 | 0.27 | 1.05 | 0 | III |

Wiesloch_L | BW | 114 | 10 | 22 | 21 | 808 | 0.31 | 1.03 | 11 | I |

Woellstein | BW | 468 | 7 | 43 | 51 | 943 | 0.53 | 1.52 | 3 | I |

Zollhaus | RLP | 243 | 4 | 53 | NaN | 734 | 0.34 | 1.05 | 7 | III |

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**Figure 1.**Catchments (black lines) of the study area in western Germany (red lines: federal states of Rhineland-Palatinate and Baden-Württemberg). Nested basins are sorted by size: smaller catchments are plotted on top of larger ones so that only headwater basins are displayed completely.

**Figure 2.**Model structures, adapted from Fenicia et al. [17]. D: partition between fast and slow reservoir; E

_{f}(Ce): actual evaporation; E

_{u}(Ce): unsaturated evaporation; I = interception; K: storage coefficient; P: precipitation; Q: discharge; S: storage; Su

_{max}: storage; β: power function; f = fast; r = riparian; s = slow; t = total; u = unsaturated.

**Figure 3.**Meaning and position of the four signature indices derived from the FDC [23]. (Copyright permission from IWA Publishing: Ley, R.; Hellebrand, H.; Casper, M.C.; Fenicia, F. Comparing classical performance measures with signature indices derived from flow duration curves to asses model structures as tools for catchment classification. Hydrol. Res.

**2016**, 47, 1–14.)

**Figure 4.**Box and whisker plots of the four signature indices of all models and 12 model structures. The boxplots show the interquartile ranges as boxes and the median by a black line in the middle of the box; the whiskers show the minimum and the maximum up to the 1.5 interquartile range and outliers outside the 1.5 interquartile range.

**Figure 5.**Numbers of acceptable models per catchment (

**a**) and number of catchments where model structures M01 to M12 produce acceptable models (

**b**).

**Figure 6.**Different sensitivities of simulated runoff to model structures for single catchments. The signature indices of a catchment are displayed and connected by a line creating a performance pattern for this model. Model structures are indicated by colors and named in the legend with the number of the model structure. (

**I**) displays examples of catchments with differentiated patterns of signature indices; (

**II**) performance pattern of catchments with all (

**a**) or most (

**b**) acceptable models with similar patterns of signature indices; and (

**III**) catchments without an acceptable model. (

**I**,

**II**) show only acceptable models for these catchments; (

**III**) shows all models of a catchment.

**Figure 7.**Spatial distribution of catchments with similar or different patterns of signature indices (

**a**). Borders of large catchments with several upstream catchments are marked with a bold line. Please note, nested catchments are sorted by size: only the headwater catchments are displayed completely. (

**b**–

**e**) display catchment properties of catchments in categories I to III.

**Figure 8.**Spatial distribution of catchments with equal best performing models. Catchments with two best performing models are striped in the color of both model structures. Please note that nested catchments are sorted by size: only the headwater catchments are displayed completely. Borders of large catchments with several upstream catchments are marked with a bold line.

**Figure 9.**Catchment characteristics of catchments sorted by the best performing model structures M01 to M12 and catchments without an acceptable model (“Model structure” 0): (

**a**) mean annual precipitation; (

**b**) mean runoff coefficient; (

**c**) percentage of forested area; and (

**d**) catchment size.

**Table 1.**Parameter ranges of the 12 model structures. All parameters, except D and M, are converted to a logarithmic value for calibration.

Parameter | Minimum | Maximum |
---|---|---|

Ce (-) | 0.01 | 30 |

D (-) | 0 | 1 |

Imax (mm) | 0.000001 | 20 |

Kf (1/d) | 0.0000001 | 1 |

Kr (1/d) | 0.00001 | 1 |

Ks (1/d) | 0.0000001 | 1 |

M (-) | 0 | 0.3 |

Rmax (mm/day) | 0.001 | 30 |

Sumax (mm) | 0.1 | 0.000001 |

Tf (d) | 1 | 500 |

β (-) | 0.001 | 50 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ley, R.; Hellebrand, H.; Casper, M.C.; Fenicia, F.
Is Catchment Classification Possible by Means of Multiple Model Structures? A Case Study Based on 99 Catchments in Germany. *Hydrology* **2016**, *3*, 22.
https://doi.org/10.3390/hydrology3020022

**AMA Style**

Ley R, Hellebrand H, Casper MC, Fenicia F.
Is Catchment Classification Possible by Means of Multiple Model Structures? A Case Study Based on 99 Catchments in Germany. *Hydrology*. 2016; 3(2):22.
https://doi.org/10.3390/hydrology3020022

**Chicago/Turabian Style**

Ley, Rita, Hugo Hellebrand, Markus C. Casper, and Fabrizio Fenicia.
2016. "Is Catchment Classification Possible by Means of Multiple Model Structures? A Case Study Based on 99 Catchments in Germany" *Hydrology* 3, no. 2: 22.
https://doi.org/10.3390/hydrology3020022