Clustering CAMELS using hydrological signatures with high spatial predictability

The behavior of every catchment is unique. Still, we need ways to classify them as this helps to improve hydrological theories. 10 Usually catchments are classified along either their attributes classes (e.g. climate, topography) or their discharge characteristics, which is often captured in hydrological signatures. However, recent studies have shown that many hydrological signatures have a low predictability in space and therefore only dubious hydrological meaning. Therefore, this study uses hydrological signatures with the highest predictability in space to cluster 643 catchments from the continental United States (CAMELS (Catchment Attributes and MEteorology for Large-Sample Studies) dataset) into ten groups. We then evaluated 15 the connection between catchment attributes with the hydrological signatures with quadratic regression, both in the overall CAMELS dataset and the ten clusters. In the overall dataset, aridity had the strongest connection to the hydrological signatures, especially in the eastern United States. However, the clusters in the western United States showed a more heterogeneous pattern with a larger influence of forest fraction, the mean elevation or the snow fraction. From this, we conclude that catchment behavior can be mainly attributed to climate in regions with homogenous topography. In regions with a heterogeneous 20 topography, there is no clear pattern of the catchment behavior, as catchments show high spatial variability in their attributes. The classification of the CAMELS dataset with the hydrological signatures allows testing hydrological models in contrasting


Introduction
Every hydrological catchment is composed of a unique combination of topography and climate, which makes their discharge heterogeneous.This, in turn, makes it hard to generalize behavior beyond individual catchments (Beven, 2000).Catchment classification is used to find patterns and laws in the heterogeneity of landscapes and climatic inputs (Sivapalan, 2003).
Historically, this classification was often done by simply using geographic, administrative or physiographic considerations.
However, those regions proved to be not sufficiently homogenous (Burn, 1997).Therefore, it was proposed to use seasonality measures with physiographic and meteorological characteristics, but it was deemed difficult to obtain those information for a large number of catchments (Burn, 1997), even if only simple catchment attributes (e.g.aridity) are used (Wagener et al., 2007).Nonetheless, in the last decade datasets with hydrologic and geological data were made available, comprising information of hundreds of catchments around the world (Addor et al., 2017;Alvarez-Garreton et al., 2018;Newman et al., 2014;Schaake et al., 2006).This is a significant step forward as those large sample datasets can generate new insights, which are impossible to obtain when only a few catchments are considered (Gupta et al., 2014).Different attributes have been used to classify groups of catchments in those kind of datasets: flow duration curve (Coopersmith et al., 2012;Yaeger et al., 2012), catchment structure (McGlynn and Seibert, 2003), hydro-climatic regions (Potter et al., 2005), function response (Sivapalan, 2005) and more recently, a variety of hydrological signatures (Kuentz et al., 2017;Sawicz et al., 2011;Toth, 2013).Quite often, climate has been identified as the most important driving factor for different hydrological behaviour (Berghuijs et al., 2014;Kuentz et al., 2017;Sawicz et al., 2011).Still, it is also noted that this does not hold true for all regions and scales (Ali et al., 2012;Singh et al., 2014;Trancoso et al., 2017).In addition, a recent large study of Addor et al. (2018) has shown that many of the hydrological signatures often used for classification, are easily affected by data uncertainties and cannot be predicted using catchment attributes.Another recent study by Kuentz et al. (2017) used an extremely large datasets of 35,000 catchments in Europe and classified them using hydrological signatures.For their classification, they used hierarchical clustering and evaluated the result of the clustering by comparing variance between different numbers of clusters.They were able to find ten distinct classes of catchments.However, Kuentz et al. (2017) used some of the signatures identified to have a low spatial predictability by Addor et al. (2018).In addition, one third of their catchments was aggregated in one large class with no distinguishable attributes.Overall, we conclude that no large sample study exists that uses only hydrological signatures with a good spatial predictability.Therefore, we selected the best six hydrological signatures with spatial predictability to classify catchments of the CAMELS (Catchment Attributes and Meteorology for Large-Sample Studies) dataset (Addor et al., 2017).Those six hydrological signatures are evaluated together with the fifteen catchment attributes that were shown to have a large influence on hydrological signatures (Addor et al., 2018).The connection between the hydrological signatures and the catchment attributes is determined by using quadratic regression of the principal components (of the hydrological signatures) and the catchment attributes.This will help to explore, if a clustering with hydrological signatures that have a high predictability in space, provides hydrologically meaningful clusters, which can be used for further research.In addition, it will address the question, if the hydrological behavior is influenced from different catchment attributes, on the scale of the individual clusters and the whole dataset, respectively.

Data base
This work is based on a detailed analysis of catchment attributes and information contained in hydrological signatures.The CAMELS data set contains 671 catchment in the continental united states (Addor et al., 2017) with additional meta information such as slope and vegetation parameters.For our study, we used a selection of the available meta data (Table 1).We excluded all catchments that had missing data, which left us with 643 catchments.Those catchments come from a wide spectrum of characteristics like different climatic regions, elevations ranging from 10 to almost 3,600 m a.s.l. and catchment areas ranging from 4 to almost 26,000 km².To ensure an equal representation of the different catchment attributes classes (climate, topography, vegetation, soil, geology) we used three attributes per class.Climate: aridity, frequency of high precipitation events, fraction of precipitation falling as snow; Vegetation: forest fraction, green vegetation fraction maximum, LAI maximum; Topography: mean slope, mean elevation, catchment area; Soil: clay fraction, depth to bedrock, sand fraction; Geology: dominant geological class, subsurface porosity, subsurface permeability.Those catchment attributes were chosen due to their ability to improve the prediction of hydrological signatures (Addor et al., 2018) and because they are relatively easy to obtain, which will allow a transfer of this method to other groups of catchments world-wide.
Hydrological signatures cover different behaviors of catchments.However, many of the published signatures have large uncertainties (Westerberg and McMillan, 2015) and lack in predictive power (Addor et al., 2018).Therefore, we used the six hydrological signatures with the best predictability in space (Table 1) (Addor et al., 2018).Those signatures were calculated for all catchments.Due to this selection, no signatures that capture low flow behavior were used, as those signatures have a very low spatial predictability.

Data analysis
The workflow of the data analysis considers a data reduction approach with a principal component analysis and a subsequent clustering of the principal components.We only used principal components that account for at least 80% of the total variance of the hydrological signatures similar to Kuentz et al. (2017), which resulted in two principal components.We evaluated the connection between the principal components and the catchments attributes with the following procedure: 1) First we calculated quadratic regressions between the two principal components and the catchment attributes (with the principal component as the dependent variable).This resulted in one coefficient of determination for each pair of principal component and catchment attribute (e.g.PC 1 and aridity).
2) We then weighted the coefficient of determination by the explained variance of the principal components.This addresses the differences in the explained variance of the principal components (e.g., PC 1 explained 75% of the variance, PC 2 explained 19% of the variance).
3) The weighted coefficients of determination of the principal components were subsequently added, to obtain one coefficient of regression for every catchment attribute.
Quadratic regression was selected as interactions in natural hydrological systems are known to have unclear patterns and cannot be fitted with a straight line (Addor et al., 2017;Costanza et al., 1993).This was done first for the whole dataset and then for all clusters separately.
The principal components were clustered following agglomerative hierarchical clustering with ward linkage (Ward, 1963), similar to previous studies (Kuentz et al., 2017;Li et al., 2018;Yeung and Ruzzo, 2001).To make our results comparable to other published studies like Kuentz et al. (2017), we split the dataset into ten clusters.
For the principal component analysis and the clustering we used the Python package sklearn (0.19.1).The code is available at GitHub (Jehn, 2018).Validity was checked by a random selection of 50 and 75 % of all catchments.We found that the overall picture stayed the same (not shown).In all further analysis, we used all catchments to get a sample as large as possible to be able to make statements that are more general.

Relation of the principal components and the hydrological signatures
The rivers considered in this study show a wide range in hydrological signatures.This can be seen in the clusters of principal components of the hydrological signatures (Figure 1).However, most of the rivers are opposite of the loading vectors (the

Impacts of catchment attributes on discharge characteristics in the whole dataset 120
After the clustering, we examined the weighted coefficient of determination of the catchment attributes for the whole dataset.
This analysis shows not only differences in their score between the single attributes, but also between the different classes of With the exception of the mean slope, the first seven catchment attributes are all related to climate and vegetation.The last seven attributes on the other hand are all related to soil and geology, except the catchment area.They also show much lower scores of the weighted coefficient of determination.This indicates that soil and geology are less important for the chosen hydrological signatures.Similar patterns were also found by (Yaeger et al., 2012).They stated climate as the most important driver for the hydrology.However, they also unraveled that low flows are mainly controlled by soil and geology.The minor importance of soil and geology in our study might therefore be biased by the choice of hydrological signatures, which excluded low flow signatures due to the low predictability in space.(Table 1).Nevertheless, our study probably captures a more general trend as we used a larger dataset and hydrological signatures which have a better predictability in space (Addor et al., 2018).
Addor et al. ( 2018) also explored the influence of different catchment attributes in the CAMELS dataset on discharge characteristics.They found that climate has the largest influence on discharge characteristics, well in agreement with Coopersmith et al. (2012).The latter also used a large group of catchments in the continental United States from the MOPEX dataset.They conclude that the seasonality of the climate is the most important driver of discharge characteristics.However, Coopersmith et al. (2012) only analyzed the flow duration curve, which has a mediocre predictability in space and it is therefore more unclear what it really depicts (Addor et al., 2018).Overall, this study here is in line with other literature in the field.
Using the weighted coefficient of determination reliably detects climatic forcing as the most important for the discharge characteristics for a large group of catchments.This can probably be extrapolated to most catchments in the continental US without human influence, as the CAMELS dataset contains large samples of undisturbed catchments (Addor et al., 2017).In the next step, we will test whether these relations also hold for the clusters of the catchments.145

Exploration of the catchment clusters
While the catchment attributes in the CAMELS and other datasets, as a whole, show often a pattern that resembles climatic zones (Addor et al., 2018;Coopersmith et al., 2012;Yaeger et al., 2012), the picture is less clear for the catchment clusters.
This is directly observable in the spatial distribution of the clusters (Figure 3).If climate were the main driver, the clusters would be located along a climatic gradient.However, this is only true for the eastern half of the United States (for a climatic map of the United states see (Beck et al., 2018).In this part of the United States, the low relief allows large regions with a uniform climate, that only changes of larger scales.This implies that climate is a good indicator for the discharge characteristics as long as the topography is homogenous.This would also explain why studies like Sawicz et al. (2011) or Berghuijs et al. (2014) were able to find strong connections between climate and their catchment clusters, as most of their catchments were located in the eastern half of the United states.This region has only few, but very distinct changes in topography such as the Apalachian Mountains and therefore climate has the largest influence.The same effect can be seen in the distribution of the clusters of this study (Figure 3).While the catchments in the eastern half of the United States form large spatial patterns of similar behaviour, the catchments in the west are patchier.
This would also explain why spatial proximity seems to be important in some studies that look into explanations of catchment behaviour (Andréassian et al., 2012;Sawicz et al., 2011), but not in others (Trancoso et al., 2017).Therefore clustering by climate or spatial proximity might only work in regions without abrupt changes in the topography.In addition, this is also linked to the problem that it is easier to find the most important drivers for the behaviour in some regions then in others (Singh et al., 2014) and that often catchments show a surprisingly simple behaviour across many different climate and landscape properties (Troch et al., 2013).The regions where it is easy to find the most important drivers show a homogenous topography, while catchments that are hard to understand with current hydrological knowledge, are controlled by a very complex interaction of factors like land use, soil or vegetation.This complex interaction is overwritten in regions with strong climatic influence.
The descriptions of the catchment clusters are summarized in Table 2.A detailed description of the clusters can be found in the appendix, together with figures showing the distribution of hydrological signatures (Figure A1) and catchment attributes (Figure A2).A list of all catchment with index, position and cluster is given in the supplementary material.

Summary and conclusion
This study explored the influence of catchment attributes on the discharge characteristics in the CAMELS dataset.We found that over the whole dataset climate (especially aridity) is the most important factor for the discharge characteristics.This changes when we look at clusters that are derived from specific hydrological signatures.While some clusters still have aridity as the most important factor, it can be the elevation, vegetation and amount of snow for others.We link this to the location of the catchments.The catchments that are most influenced by climate are mainly located in the eastern continental United States, where we find large regions without abrupt changes in the topography.Those catchments that are influenced mostly by other factors than aridity, show a patchier spatial pattern and are located in the western continental United States, where the topography changes on small scales.From this, we conclude that climate is the most important factor for the discharge characteristics in regions with homogenous topography.For regions with a heterogeneous topography, on the other hand, this leads to catchments that can be quite different on a very small scale, as differences in elevation and slopes create abrupt changes in most catchment attributes (e.g.soil or vegetation).This also hints why those kind of catchments are difficult to simulate (Semenova and Beven, 2015).They probably have many features with a roughly equal influence on their behavior and those features alter and influence each other.This complex interaction can also lead to catchments that are quite different in their attributes, but show very similar discharge characteristics.An example for this is Cluster 4 that contains catchments from the Northwestern Forested Mountains and Florida.Two very different regions, but still the catchments show a similar behavior.
This indicates that a catchment classification based only on catchment attributes is predestined to fail in regions were the main driver is not climate.
We acknowledge that the results are somewhat dependent on the amount and size of the clusters, the catchment attributes considered and the hydrological signatures used.Still, we think that the CAMELS dataset offers an excellent overview of different kinds of catchments in contrasting climatic and topographic regions.In addition, the hydrological signatures used have been identified as the ones with clear hydrological meaning.
For further research, we think the clusters identified here can be used to explore the usefulness of the CAMELS dataset in studies dealing with parameter transferability of hydrological models, either between different types of catchment clusters or how different kinds of models perform in the same cluster.In addition, the groups of indistinct catchments should get more attention in modelling and fieldwork, as those catchments are probably also difficult to understand, because it is not clear what is causing them to behave the way they do.As long as there are catchments that cannot even be clustered by our current understanding, we as the hydrological community, still have gaps in our knowledge.
vectors are shown as arrows in the figure).This shows that most rivers have relatively low values for all hydrological Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-129Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 April 2019 c Author(s) 2019.CC BY 4.0 License.signatures and only some, more extreme rivers, have higher values for specific hydrological signatures.Most typical for the behavior of the river are the hydrological signatures mean annual discharge and Q95 (high flows), as they have a strong correlation with the first principal component.For the second principal component, the mean half-flow date (an indicator for seasonality) has the highest correlation.Therefore, the first principal component can be seen as a measure of overall discharge 115 and amount of high flows, while the second principal component can be seen as a measure of seasonality.

Figure 1 :
Figure 1: Biplot of the principal components (PC).Colours indicate the cluster of the catchment.

Figure 2 :
Figure 2: Importance of catchment attributes evaluated by quadratic regression for all considered catchments.Attributes are colored according to their catchment attribute class.

Figure 3 :
Figure 3: Locations of the clustered CAMELS catchments in the continental US.

Figure 4 :
Figure 4: Importance of the catchment attributes evaluated by the quadratic regression.For the catchment clusters.
Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2019-129Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 2 April 2019 c Author(s) 2019.CC BY 4.0 License.Table 2: Properties of the catchment clusters.Typical signatures/attributes refers to the signature/attribute of the cluster with the lower coefficient of variation scaled by the mean coefficient of variation of the whole dataset.Dominating attribute refers to the catchment attribute that has the highest weighted coefficient of determination.

Figure A1 :
Figure A1: Swarm plot of the hydrological signatures sorted by catchment clusters.