Understanding how water resources vary in response to climate at different temporal and spatial scales is crucial to inform long-term management. Climate change impacts and induced trends may indeed be substantially modulated by low-frequency (multi-year) variations, whose strength varies in time and space, with large consequences for risk forecasting systems. In this study, we present a spatial classification of precipitation, temperature, and discharge variability in France, based on a fuzzy clustering and wavelet spectra of 152 near-natural watersheds between 1958 and 2008. We also explore phase–phase and phase–amplitude causal interactions between timescales of each homogeneous region. A total of three significant timescales of variability are found in precipitation, temperature, and discharge, i.e., 1, 2–4, and 5–8 years. The magnitude of these timescales of variability is, however, not constant over the different regions. For instance, southern regions are markedly different from other regions, with much lower (5–8 years) variability and much larger (2–4 years) variability. Several temporal changes in precipitation, temperature, and discharge variability are identified during the 1980s and 1990s. Notably, in the southern regions of France, we note a decrease in annual temperature variability in the mid 1990s. Investigating cross-scale interactions, our study reveals causal and bi-directional relationships between higher- and lower-frequency variability, which may feature interactions within the coupled land–ocean–atmosphere systems. Interestingly, however, even though time frequency patterns (occurrence and timing of timescales of variability) were similar between regions, cross-scale interactions are far much complex, differ between regions, and are not systematically transferred from climate (precipitation and temperature) to hydrological variability (discharge). Phase–amplitude interactions are indeed absent in discharge variability, although significant phase–amplitude interactions are found in precipitation and temperature. This suggests that watershed characteristics cancel the negative feedback systems found in precipitation and temperature. This study allows for a multi-timescale representation of hydroclimate variability in France and provides unique insight into the complex nonlinear dynamics of this variability and its predictability.
Hydroclimate variability represents the spatiotemporal evolution of hydrological (e.g., discharge and groundwater level) and climate variables (e.g., precipitation and temperature) which are directly impacting hydrological variability. Studying how hydrological variables react to climate variability and change is a major challenge for society, in particular for water resource management and flood and drought mitigation planning
While different timescales have been identified in hydrological variability
In this study, we investigate the spatial homogeneity of hydroclimate variability in France across timescales. We aim at identifying homogeneous regions according to specific time frequency patterns. From the determination of homogeneous regions of hydroclimate variability, we will explore cross-scale interactions that may result from feedback processes between catchment properties and hydroclimate variability.
This study, therefore, has major implications for the comprehension of hydroclimate dynamics and their interactions with large-scale climate drivers and catchment properties. In addition, as recently suggested in
The work is divided into the following sections. Data and methods are introduced in Sect. 2. In Sect. 3, we establish homogeneous regions for precipitation, temperature, and discharge variability based on their time frequency patterns and then explore cross-scale interactions for each region of homogeneous variability in precipitation, temperature, and discharge. Finally, discussions of the main results and conclusions are provided in Sect. 4.
Location of stream gauges (gray dots), corresponding watersheds (pale red;
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The workflow of this study is repeated for precipitation, temperature, and discharge data sets.
The data consist of precipitation, temperature, and discharge time series located over 152 watersheds (Figs. 1, 2a and b). Discharge time series were extracted from French reference hydrometric network compiled by
The methodology described below (and summarized in the workflow in Fig. 2) is applied to precipitation, temperature, and discharge data sets.
For each of the 152 watersheds, continuous wavelet analysis is used to identify at which timescales and time locations the amplitude of variability (i.e., local variance) is the strongest (Fig. 2c;
Because the daughter wavelet translates and scales up, overlaps in time and frequency can occur, and wavelet coefficients can be overestimated, requiring statistical significance tests
For the reminder of this study, the terms intraseasonal, annual, and interannual refer to variations at
After each watershed wavelet spectrum is computed, we estimate the similarity between them, i.e., how similar the variability is, for given scales and time locations, among all wavelet spectra (Fig. 2d). Similarities between wavelet spectra are estimated from the entire wavelet spectrum, and not only on statistically significant signals, to guarantee more consistent comparison between spectra. Distances between two-dimensional data, such as wavelet spectra, are estimated using Euclidean distance between pairwise points (pED; i.e., computing
Fuzzy clustering has then been used to cluster the different watersheds based on their similarities (Fig. 2e). Fuzzy clustering is a soft clustering method
Fuzzy clustering performance is determined by the ability of the algorithms to recognize hybrid stations (i.e., stations incorporating multiple features from different patterns observed in other coherent regions), while allowing for a clear determination of the membership of stations with unique features
For each variable and each cluster, cross-scale interactions are explored (Fig. 2f). Cross-scale interactions refer to phase–phase and phase–amplitude couplings between timescales of a given time series
A system with directional cross-scale interactions.
Figure 3 describes the necessary setting and characteristics of cross-scale interactions. A variable (
The balance between
Note that cross-scale interactions can occur from large-scale to small-scale processes and vice-versa. For instance, atmospheric circulation at seasonal timescales influences interannual and decadal timescales, which, in turn, influences seasonal variations
Following
The wavelet transform corresponding to each watershed's monthly time series have been computed, and all 152 watersheds' wavelet transforms have been checked for similarities using IEDC fuzzy clustering to identify and characterize homogeneous regions of hydroclimate variability over France. Once the homogeneous regions had been identified, an average time series for each region was computed. The global wavelet spectrum of this time series quantified the total variance expressed at each timescale, while its wavelet spectrum characterized how this variance is distributed in the time (location) and frequency (scale) domains. In addition, so as to focus on interannual timescales, we computed the wavelet spectrum of the time series filtered at the annual time step. Cross-scale interactions were then investigated for each homogeneous region.
Clustering of precipitation time frequency variability in France.
The following seven regions with homogeneous time frequency patterns are identified (Fig. 4a): northwestern (green), northeastern (blue), central north (red), central western (pink), central eastern (black), southwestern (yellow), and southeastern (dark green). Figure 4a shows that all watersheds converge toward singular clusters, meaning that all regions are highly coherent (i.e., pie charts in Fig. 4a show one dominant color).
In all regions, precipitation is varying at different timescales, ranging from intraseasonal to interannual scales (i.e., 2–8 years; Fig. 4b). Southwestern and southeastern regions are dominated by annual (1 year) variability, while their interannual variability (2–8 years) is low and the reverse for other regions. In addition, statistically significant areas in continuous wavelet spectra show that those timescales of variability are nonstationary (Fig. 4c), with temporal changes in terms of amplitude discriminating the different regions. For instance, southwestern regions are characterized by quasi-continuous significant annual variability until the late 1980s, while other watersheds show sparsely significant annual variability (Fig. 4c). Similarly, although there is significant interannual variability in all watersheds from the late 1980s, during this period, southwestern and southeastern regions do not show significant interannual variations (Fig. 4c). After removing the
Interannual precipitation time frequency variability in France.
In summary, different regions with coherent precipitation variability are identified and are characterized by three timescales of variability, i.e., intraseasonal, annual, and interannual. The amplitude of those timescales of variability, however, differs in time and over the French territory. Mediterranean regions (southwestern and southeastern) have comparatively weaker interannual variability as compared to annual timescales. The differences between regions are both dependent on the local expression of the climate forcing and watershed characteristics. Because those physical processes are interacting, studying cross-scale interactions in precipitation brings more insight on the dynamics behind the spectral characteristics of each region
Precipitation cross-scale interactions (95 % significance level). The driving timescale is on the horizontal axis and the driven on the vertical axis (i.e., the timescale where the
Figure 6 shows cross-scale interactions for each cluster of precipitation variability (see Fig. 4).
Northeastern, southeastern, north-central, northwestern, and central-eastern regions all show the phase of a 5–8-year variability driving the variability of smaller timescales (Fig. 6a; blue, dark green, red, green, and black; lower half of the graph). This cross-scale interaction is, however, more pronounced in the northeastern and southeastern regions (Fig. 6a). Similarly, eastern regions exclusively show 5–8 to 2–4-year interactions, while other regions show the self-interacting 5–8-year variability (Fig. 6a). The upper half of the graph, which refers to the higher frequency driving the lower-frequency variability, is populated by north-central, southeastern, northwestern, and northeastern regions (Fig. 6a; red, dark green, green and blue). The southeastern region shows cascade phase–phase interactions, (i.e., from 2–3 and 5–4 to 6–5 years; Fig. 6a, dark green). In addition, both southeastern and northwestern regions show mirror interactions with their lower-half counterparts, e.g., 5–6 to 4–5 years (Fig. 6a; dark green and green mirror patches about the diagonal). We also note that phase–phase interactions are very weak over the southwestern regions and absent in the central-western regions.
Phase–amplitude interactions are presented in Fig. 6b. The lower half of the graph, which refers to the lower frequency driving the higher-frequency variability, shows 5–8- to 2–4-year interactions for the western and north-central regions (Fig. 6b; pink, yellow, green, and red). The central-eastern regions are also showing the lower-frequency variability driving the higher-frequency variability but between 8- and 6-year variability (Fig. 6b). Notably, the northwestern region is the only one with cross-scale interactions driving the annual cycle (Fig. 6a; green). In the upper half of the graph, which refers to higher frequency driving lower-frequency variability, we only find north-central and northeastern regions showing 2–4- to 4- and 3–4- to 7–8-year phase–amplitude interactions (Fig. 6b; blue and red). Note that north-central, northeastern, and central-eastern regions show phase–amplitude and phase–phase interactions at very similar timescales (Fig. 6a and b; red, blue, and black), while timescales of phase–amplitude and phase–phase interactions do not match in central-western, northwestern, and southwestern regions (Fig. 6a and b; pink, green, and yellow). Regions to the east, thus, appear to have both phase–phase and phase–amplitude interactions at the same timescales, while western regions are more characterized by phase–amplitude interactions.
The precipitation cross-scale interactions can be of different forms, namely phase–phase, phase–amplitude, uni- or bi-directional, and from lower to higher timescales and vice versa. The presence of cross-scale interactions seems to be tied to specific spatial locations, suggesting different internal dynamics over the different regions of homogeneous precipitation variability. Interestingly, cross-scale interactions tend to converge toward specific timescales, notably 2–4 and 5–8 years, which were linked to ocean–atmosphere variability, such as the North Atlantic Oscillation, in previous hydroclimate studies over France
Clustering of temperature time frequency variability in France.
In temperature, the following nine regions with homogeneous time frequency patterns are identified (Fig. 7a): northwestern high (pink), northwestern low (black), northeastern (blue), central eastern (red), central western (green), southeastern high (yellow), southeastern low (brown), southwestern high (dark green), and southwestern low (purple). Fuzzy clustering shows that watersheds typically converge toward singular clusters, defining highly coherent regions (Fig. 7a). This is, however, not true for the central-western region, which is characterized by a mix of spectral characteristic defining other regions (see the red, green, black, yellow, and purple pie charts; Fig. 7a).
Using monthly data, temperature is primarily varying on an annual timescale, with very similar amplitudes for all regions (Fig. 7b and c). Since the dominant annual variability masks the other timescales, we use the annual time step to study interannual variability (Fig. 8a and b). Focusing on this interannual variability, significant temperature variations indeed emerge at 2–4- and 5–8-year timescales and show different timings and amplitudes over the different regions (Fig. 8a and b). All regions show 5–8-year variability, but, compared to northern regions, southern regions show significantly stronger variations on 2–4-year timescale (Fig. 8a). Similarly, while stronger 2–4-year variability occurs in the 1980s and 1990s in the southwestern low region, other regions show significant 2–4-year variability from the 2000s only (brown; Fig. 8b).
Interannual temperature time frequency variability in France.
Temperature cross-scale interactions (95 % significance level). The driving timescale is on the horizontal axis and the driven on the vertical axis (i.e., the timescale
Figure 9 shows cross-scale interactions for each cluster of temperature variability identified in Fig. 8a.
For temperature, phase–phase interactions are mostly concentrated in the upper half of the graph, which refers to higher frequency modulating lower frequency (Fig. 9a). Notably, a 2–6- to 6–8-year phase–phase interaction appears more pronounced over northern regions (Fig. 9a; blue, red, pink, and black). The central-western region shows similar phase–phase interactions, but at 1–3- to 4–6-year timescales (Fig. 9a; green). In the lower half of the graph, which refers to lower frequency modulating higher frequency, interactions are found at very similar timescales, but at slightly higher frequency, for all regions (e.g., 2–5- to 1–4-year variability; Fig. 9a). Temperature in the southwestern low region, however, show slightly different characteristics with phase–phase interactions between lower and higher frequency occurring between 7–8- and 3–4- and 7–8- to 3–4-year variability (Fig. 9a; purple).
Temperature phase–amplitude interactions are mostly acting on the 3–4-year timescale for all regions (Fig. 9b). In particular, in temperature, more pronounced phase–amplitude interactions are found over the southwestern low region (Fig. 9b; purple), which is consistent with previous studies on phase–amplitude interactions in European temperature
As for precipitation, in temperature, phase–phase and phase–amplitude cross-scale interactions are region dependent and can be uni- or bi-lateral. However, in temperature, most phase–phase interactions occur from higher- to lower-frequency variability, while phase–amplitude interactions tend to occur from lower- to higher-frequency variability. Similarly, while timescales of variability that are involved for phase–phase and phase–amplitude interactions are very similar in precipitation, they differ largely in temperature (Fig. 9b). This suggests that, in temperature, the processes driving phase–phase and phase–amplitude cross-scale interactions are different. It also suggests that the processes driving cross-scale interactions are different in temperature and in precipitation.
Clustering of discharge time frequency variability in France.
The following six regions with homogeneous time frequency patterns are identified in discharge (Fig. 10a): northwestern (black), northeastern (blue), north central (red), central western (green), southeastern (yellow) and southwestern (pink). However, several watersheds, especially in the south, show memberships in multiple regions, suggesting lower spatial coherence in discharge than in precipitation and temperature. Lower spatial coherence, however, could mostly be explained by (i) mixing of solid and liquid precipitation in driving discharge variability in the Alps and (ii) the local heterogeneity of precipitation due to convective dynamics in the Pyrenees
Using monthly data, discharge is mainly varying on annual timescales, as determined through the global wavelet spectra (Fig. 10b). In addition, unlike other regions, southeastern watersheds show significant intraseasonal variability (Fig. 10b). Continuous wavelet spectra show that both annual and intraseasonal variability can be nonstationary, with temporal changes in terms of amplitude discriminating the different homogeneous regions of discharge variability (Fig. 10c). For instance, annual variability is only significant for specific periods in the southeastern watersheds, while other regions show quasi-continuous significant annual variability (Fig. 10c). Similarly, in the southeastern region, intraseasonal discharge variability sparsely appears significant from the 1980s, while they are absent in other regions (Fig. 10b).
Interannual discharge time frequency variability in France.
After removing the seasonality, and focusing on interannual variability, northeastern watersheds stand out as having continuous significant interannual variability throughout the time series, with 4–5- and 5–8-year variability before and after the 1990s, respectively (Fig. 11b). Southeastern and southwestern regions also stand out, as they show 2–4-year variability in the mid-1970s and 2000s (Fig. 11b; yellow and pink). In addition, southeastern regions do not show significant variability in discharge at timescales greater than 4 years (Fig. 11a and b).
Different coherent regions are thus identified for discharge variability. In addition, these homogeneous regions correspond well with regions identified in precipitation and temperature variability. As in precipitation and temperature, those regions seem strongly impacted constrained temperature, and southern regions, which may appear more complex in term of climate and its link to land surface processes, appear much less spatially coherent in discharge.
Discharge cross-scale interactions (95 % significance level). The driving timescale is on the horizontal axis and the driven on the vertical axis (i.e., the timescale
An important question concerning discharge cross-scale interactions is whether interactions found in either precipitation or temperature are also present in discharge. Phase–phase interactions that were found in precipitation are also identified in discharge, in particular over the northeastern, southeastern, and northwestern regions (blue, yellow, and black; Figs. 6a and 12a). Phase–phase interactions that were identified in temperature are much less evident (Figs. 9a and 12a). It should also be noted that many small patches, describing phase–phase interactions in precipitation and temperature, are systematically not transferred to discharge variability (Figs. 6a, 9a, 12a). Instead, discharge variability seems to exclusively preserve large patches of phase–phase interactions (Figs. 6a, 9a, 12a), suggesting that catchment properties are modulating the climatic signals (i.e., precipitation and temperature). Such filtering of climate signals is even more pronounced in certain regions, such as the north central, where phase–phase interactions are absent in discharge (Fig. 12a) but were identified in precipitation and temperature (Figs. 6a and 9a).
More importantly, there is no phase–amplitude interaction in discharge (Fig. 12b). This points out that watershed properties modulate the interacting processes in precipitation and temperature. Because our data set is mostly composed of low groundwater support, those modulations are unlikely to result from the water table, especially as phase–phase interactions are inherited from precipitation. In addition, further analysis at the Paris Austerlitz gauging station, which includes very large groundwater support, reveals the same absence of phase–amplitude interaction in discharge (not shown;
Cross-scale interactions are only of phase–phase nature in discharge. All phase–phase interactions in discharge seem to be primarily related to precipitation, even though the strong correlations between rainfall and temperature makes it difficult to detect. However, differences between regions of homogeneous discharge variability are very similar to those detected in precipitation. Further work is, however, needed to understand why phase–amplitude cross-interactions are absent in discharge variability. Catchment properties appear to involve positive rather than negative feedback, thus resulting in a loss in phase–amplitude interactions.
As recommended by
Our study reveals different coherent regions of precipitation, temperature and discharge variability. Yet, some watersheds are characterized by a mix of spectral characteristics from surrounding regions or regions with the same topographic characteristics. Those coherent regions are homogeneously distributed over France in precipitation and discharge but show larger discrepancies in term of spatial extension in temperature. According to previous clustering of hydroclimate variability over France, northern regions are more homogeneous than what was found here
The timescales identified in this study have been shown to be important in climate processes, such as the North Atlantic Oscillation or the Gulf Stream front
Feedback mechanisms can occur between any physical processes of the hydroclimate system, and identifying or attributing the nature of these processes is an intractable issue using observational data. Nevertheless, we can use the mandatory conditions for cross-scale interactions to discuss the processes that are potentially at play (Fig. 3). In precipitation, cross-scale interactions involve lower-frequency timescales driving higher-frequency timescales. North Atlantic climate variability encompasses various processes, such as North Atlantic Oscillation or sea surface temperature anomalies, that drive climate variability
Interannual temperature variability is tied to both the soil state and atmospheric circulation, but that relation is location dependent. Large-scale patterns, such as the North Atlantic Oscillation, are shown to be source of both interannual precipitation and temperature variability, especially during wintertime, including for southwestern France
Regarding cross-scale interactions in discharge variability, the absence of phase–amplitude was particularly interesting. As our discharge data set is mostly composed of low groundwater support, the absence of phase–amplitude interactions is unlikely to result from the water table, especially as phase–phase interactions are inherited from precipitation. To test this hypothesis, we computed cross-scale interactions on the gauging station at Paris Austerlitz, which was not included in our original data set, as it shows large groundwater support and anthropogenic influence. Results at Paris Austerlitz are consistent with other regions and do not show any phase–amplitude interactions (not shown). As it has been shown that spatial heterogeneity (in the variable dynamics) favors cross-scale interactions, one possible explanation is that converging of runoff into the main drain cancels that spatial heterogeneity and, thus, phase–amplitude variability
In this study, we interpreted cross-scale interactions based on the mandatory structure for such interactions to arise, identified interacting timescales, and compared cross-scale interactions in both precipitation, temperature, and discharge. Dedicated studies are needed to explore, in depth, the drivers of those interactions, as feedback mechanisms are complex, and likely different for each variable, even though phase–phase interactions in discharge clearly show the signature of those identified in precipitation.
Those findings allow for a better identification of climate-deterministic processes controlling hydroclimate variability, notably using cross-scale analysis, which could help in identifying more robust climate drivers. For instance, it is important to discriminate pure climate influence from climate–land processes interactions. This has large implications for seamless hydrological predictions based on climate information, as only some parts of the climate signals are transferred to discharge systems. Thus, causal cross-scale relationships could be used to inform and improve existing seasonal to multi-year seamless forecasting for hydrological variability, including extremes (e.g., flood and drought). Preliminary work in this direction was recently proposed by
The code used for this study is available at
The Safran precipitation and temperature data set can be obtained from
The figures presented in this article are available in a colorblind-friendly palette in the Supplement. The supplement related to this article is available online at:
MFos, NM, and BD conceptualized the study. MFos took responsibility for the methodology, software, formal analysis, investigation, original draft preparation, and visualization. MFos, BD, NM, and MFou validated the study. JPV collected the resources, and MFos and JPV curated the data. MFos, BD, NM, and JPV reviewed and edited the paper.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors would like to thank Nikola Jajcay, for his support with the adaptation of the Conditional Mutual Information algorithm (pyclits) to our context. The authors would also like to thank the Centre Régional Informatique et d'Applications Numériques de Normandie (CRIANN), for providing the HPC environment needed for all computations. This research work is part of a contribution to the EURO-Friend group 2.
This paper was edited by Miriam Coenders-Gerrits and reviewed by two anonymous referees.