Large‐scale comparison of flow‐variability dampening by lakes and wetlands in the landscape

Considering the potential of wetlands to dampen temporal variability of water flow through the landscape, they are increasingly considered as possible nature‐based solutions to mitigate risks of flooding and drought. In this study, we investigate flow variability by means of a flow dampening factor and use observation data from 1984 to 2013 for 82 Swedish catchments to statistically and comparatively analyze the large‐scale effects on this factor of multiple wetlands and lakes in the landscape. The results show good correlation between large‐scale flow dampening and relative area of lakes and floodplain wetlands within a catchment. An increase in relative area up to around 15% for lakes and 0.5% for floodplain wetlands lowers the temporal standard deviation of runoff (R) to around 10%–15% of that for precipitation (P), compared with a common flow‐variability dampening of around 35% for catchments with lake‐wetland area close to zero. Further increase in these relative areas, or in those of wetland types other than floodplain wetlands, has little or no flow dampening effect. The results indicate that the large‐scale flow dampening effect of lakes and floodplain wetlands is mainly due to their water‐storage capacity and less due to their possible effects on the partitioning of P between R and evapotranspiration. Overall, the results emphasize the importance of accounting for the problem scale and relative water‐storage capacity of wetlands when considering their large‐scale efficiency as possible nature‐based solutions for large‐scale flow‐variability regulation in whole catchments.

activities (Mitsch & Gosselink, 2007). More recently, associated loss and degradation of ecosystem services have been recognized, leading to proposals to restore and construct wetlands as possible naturebased solutions for managing environmental changes and related ecosystem services in the landscape (Thorslund et al., 2017).
There are, however, potential pitfalls in judging the role that wetlands can play as nature-based solutions for large-scale management of ecosystem services in the landscape. One such pitfall can be to neglect how wetland ecosystems are defined and categorized. For example, wetlands are broadly defined in the Ramsar Convention (1971) and the Millennium Ecosystem Assessment (2005b) as encompassing all temporarily and permanently flooded areas of freshwater, including lakes, as well as brackish and salt-water bodies with a depth of up to 6 m. As the Millennium Ecosystem Assessment (2005b) notes, it would be erroneous to assume that all such types of watercovered landscape features have similarly significant beneficial roles; for example, for the landscape ecosystem service of flow regulation.
A global review of the role of wetlands on the terrestrial hydrological cycling concluded that wetlands may strongly affect this cycling but also warned against making generalized assumptions across various types of wetlands (Bullock & Acreman, 2003). For example, floodplain wetlands may reduce or delay flood magnitude, whereas upland, rainfed wetlands may decrease or increase it (Acreman & Holden, 2013;Bullock & Acreman, 2003). These findings highlight the need to study actual effects of different types of wetlands and lakes in and across different landscapes and parts of the world. Another potential pitfall is not considering the large-scale functions and services that may be provided by the whole spectrum of different lakes and wetlands and their spatial occurrence and distribution (Mitsch & Gosselink, 2000) over the large scales of whole catchments (Brauman et al., 2007;Thorslund et al., 2017).
One important aspect of the potential large-scale effects that lakes and wetlands may have on flow regulation is their influence on flow variability, that is, on dampening the magnitude of peaks and troughs in runoff through the landscape. In their global review of wetlands, Bullock and Acreman (2003) compiled a total of 439 published statements on the water quantity functions of wetlands; only 28 statements referred to flow variability. Of these, 12 conclude that upland wetlands increase flow variability, 10 conclude that floodplain wetlands decrease flow variability, and six conclude that there is no wetland effect on flow variability (Table 5e, Bullock & Acreman, 2003). However, nearly all of these statements refer to studies of only one or, at most, a few wetlands within only one or two catchments.
Only two of the statements were based on field studies of the combined effects of multiple wetlands on the variability of large-scale water flow (runoff). One of these studies concluded that multiple floodplain wetlands (along the Okavango and Sudd rivers) reduce large-scale flow variability (Sutcliffe & Parks, 1989), whereas the other concluded that multiple upland wetlands (peat bogs on steep slopes in the United Kingdom) increase it (Burt, 1995).
In more recent studies on the effect of wetlands on hydrological services related to flow regulation, Wang et al. (2010) have modeled the effects of wetland conservation and restoration, concluding that both measures reduce peak discharge but that the effect of conservation is greater. Yao et al. (2014) found an increase in peak flows due to loss of wetlands during the last half-century in a catchment, whereas Martinez-Martinez et al. (2014) instead found that wetland restoration generally reduces streamflow but has a negligible effect on daily peak flow rates and their frequency. Parry, Holden, and Chapman (2014) reviewed ecosystem services gained from peatland restoration and reported difficulties and knowledge gaps in determining if restoration affects peak flows. Larger scale studies have considered the role of geographically isolated wetlands as elements within greater hydrological and habitat networks (Cohen et al., 2016;Evenson, Golden, Lane, & D'Amico, 2015;Golden et al., 2016;Lane & D'Amico, 2010).
These studies and findings in the global review of wetland effects on the hydrological cycle by Bullock and Acreman (2003) converge with the recent meta-analysis by Thorslund et al. (2017) in highlighting the need for more large-scale studies of the function of whole wetlandscapes (defined as the landscape of an entire catchment with multiple wetlands within it).
Here, we contribute to addressing some large-scale knowledge gaps through a data-driven analysis of (a) how flow variability is affected by multiple lakes and wetlands, within and across multiple catchments; (b) possible seasonal differences in large-scale lake and wetland effects on flow variability; and (c) possible influence of longer term hydroclimatic change on the large-scale wetland effects on flow variability. Our analysis is carried out for lakes and each of the following types of wetlands: all wetlands (excluding lakes), floodplain wetlands, upland wetlands, open upland wetlands, and forested upland wetlands.
The analysis is statistical, using publicly available observation data from 1984 to 2013 for 82 Swedish catchments. In these long-term data series of relevant hydroclimatic variables, we specifically look for statistical signals of large-scale effects of lakes and wetlands in dampening the temporal variability of daily runoff, relative to that of the daily precipitation input, in and across the multiple investigated catchments. Figure 1 schematically illustrates the general conceptual basis for the quantification focus of this study on large-scale flow through whole hydrological catchments and how the temporal variability of this flow is influenced by the prevalence of wetlands and/or lakes within the catchment landscape. In general, the whole landscape and its various features, including wetlands and lakes, of any hydrological catchment, filters and dampens the temporal variability of incoming precipitation (P) to a considerably smaller temporal variability in the outgoing runoff (R). The main aim of this paper is to quantify and analyze the specific effects of wetland and lake prevalence within the catchment landscape on this flow dampening, with varying total wetland and lake areas relative to catchment area among different study catchments.

| GENERAL CONCEPTUAL AND QUANTIFICATION BASIS
As a concrete, quantified example, Figure 1 illustrates this dampening of temporal variability in R relative to that in P with data from a typical catchment in the investigated Swedish region (Figure 2). This region, further described in Section 3, includes multiple hydrological catchments with data available to quantify the dampening of their flow variability from P to R and classify the catchments based on this quantification (different catchment colors, Figure 2).
In the illustrated catchment example in Figure 1, the standard deviation quantifying the temporal variability of daily R is σ R = 0.7 mm/day whereas that of the driving water flux input of daily P is σ P = 4.3 mm/day (including days with 0 mm P). We refer to the relation (σ R /σ P ) between the standard deviation of daily R to that of daily P in a catchment as the flow dampening factor, or just dampening factor, of that catchment. We use this factor to consistently and comparatively quantify and analyze the dampening of temporal flux variability from that in P to that in R and assess how it depends on the occurrence of wetlands and lakes in and across the multiple investigated catchments ( Figure 2).
For the catchment example illustrated in Figure 1, the flow dampening factor is (σ R /σ P ) = 0.7/4.3 = 0.16, that is, the characteristic temporal variability in daily R is 84% lower than that in P. Also, in the relative terms of coefficient of variation (CV; standard deviation normalized by the long-term average value), the CV of R is smaller than that of P; for the catchment example illustrated in Figure 1, CV R = 1 and CV P = 2. Assessment of relative flow-variability dampening by comparing the CV of R to that of P would imply dampening factor quantification as σ R =σ P ð Þ P=R À ) (=2/1 = 2 for the specific illustrated catchment case). In general, σ R =σ P ð Þ P=R À ) > (σ R /σ P ) because the partitioning of long-term average P between corresponding long-term average R and ET implies that R < P and thus P=R À ) > 1. This partitioning thus implies an additional dampening effect quantified by (σ R /σ P ) compared with that quantified by the CV relationship σ R =σ P ð Þ P=R À ).
Because this additional dampening effect is accounted for in (σ R /σ P ), so is also the influence of lakes and wetlands on P partitioning (van der Velde, Lyon, & Destouni, 2013) and through that on (σ R /σ P ). The P partitioning, and through that the dampening factor (σ R /σ P ), may also be further affected by hydrological seasonality (Verrot & Destouni, 2016), long-term changes in climate (van der Velde et al., 2014), and human land and water uses (Destouni, Jaramillo, & Prieto, 2013;. In this study, we want to capture all possible influences on flow-variability dampening due to lakes and wetlands and use therefore the standard deviation relation (σ R /σ P ) as our primary comparative flow dampening factor. WMDs, which we address in Section 6.
FIGURE 1 Schematic illustration of the conceptual basis and main investigation focus of this study. The terms P, R, and ET represent precipitation, runoff, and evapotranspiration, respectively

| STUDY AREA
The study area covers two Swedish WMDs, the North and the South Baltic Proper (Figure 2 is cold to freezing, with average levels of P and high levels of runoff ( Figure S4).

| Lakes and wetlands in the catchments
The wetland types used in this study are based on data on lake and wetland occurrence from Svenska Marktäckedata (SMD; eng. Swedish Land Cover Data), produced by Sweden's national mapping authority (Lantmäteriet, 2005). It is a primarily satellite-based (Landsat TM) geo-  In this study, we include both SMD lake classes, 'open-water' and 'vegetation-covered' as a single lake type. The SMD wetland classes included in this study are limnogenous marshes, bogs, and forest wetlands-salt marshes are not included. For this study, we consider the SMD limnogenous wetland class as floodplain wetlands and the SMD bog and forest wetland classes as upland wetlands. We adopt the term 'upland wetlands,' referring to upland, rain-fed wetlands (Acreman & Holden, 2013), which distinguishes these types of wetlands from predominantly surface-water fed floodplain wetlands. In this study, the SMD wetland classes are thus grouped into the following wetland types: all wetlands (excluding lakes), floodplain wetlands, upland wetlands, open upland wetlands, and forested upland wetlands.

| Assessing lake and wetland effects on flow dampening
For each catchment, we calculate the total area of all lakes and wetlands, as well as that of the different lake and wetland types. We further normalize this area by total catchment area to obtain relative lake area (A Lakes /A Catchment ) and relative wetland area (A Wetlands /A Catchment ). These relative lake or wetland-area measures are consistent with the area normalization of P and R data and allow direct comparison of catchments of different size (as do also the area-normalized P and R data).
For each catchment (i), the long-term average (mean) value (R i ), and standard deviation (σ R,i ) of daily R is calculated for each period, 1999-2013 and 1984-1998. For each period and catchment (i), we also extract the daily P data from the 4 × 4 km grid dataset and calculate corresponding mean (P i ) and standard deviation (

| Assessing seasonal differences in lake and wetland effects on flow dampening
For each catchment, a seasonal flow dampening factor is calculated, in addition to the whole-year factor, to capture possible seasonal differences in lake or wetland effects on flow dampening. Such differences may exist due to winter freezing, spring snowmelt, or peak evapo- where b Y i is the vector of the model predictions (for the seasonal dampening factor), Y i is the vector of observed values (of relative lake/wetland area), and n is the number of catchments, i.

| Assessing climate-period differences in lake and wetland effects on flow dampening
To address question (c), on the possible influence of longer term hydroclimatic change on the large-scale wetland effects on flow variability, we calculate for each catchment and climate-representative 1984-1998 and 1999-2013, the temporal standard deviation σ x , long-term average value x, and corresponding temporal coefficient of variation CV x ¼ σ x =x for daily P and R. Furthermore, we calculate and compare the dampening factor (σ R /σ P ) between the periods and its relation to relative lake or wetland area.
To characterize prevailing large-scale hydroclimatic conditions of P, R, and T, and quantify their differences between the two periods, we consider spatial average values of each variable over the whole North Baltic and South Baltic WMDs. Based on the nonoverlapping first-level catchments, seven in the North Baltic WMD and 26 in the South Baltic WMD (Figure 2), we calculate for each WMD the areaweighted spatial mean value of each variable x (T, P, and R) as where x i is average value in each catchment i and A i is catchment area.
An area-weighted spatial standard deviation among catchments of interannual variability (temporal standard deviation σ xi;annual ) in mean annual x over each period is also calculated as For P and R, corresponding seasonal (to the above annual) areaweighted statistics are also calculated for each WMD.

| Lake and wetland effects on flow dampening
Across all catchments of the North and the South Baltic WMD, there is considerable correlation between the dampening factor and relative lake area, with around 64% of the spatial variation of the flow dampening factor explainable by the variability of relative lake area in the catchments (Figure 3a). This is also discernible in Figure (Table 1); additionally, the degree of correlation is not much affected by the upland wetlands being open or forested.
The dampening factor correlation to respective area for lakes is only slightly less than that for lakes and floodplain wetlands taken together; the fitted regression equations for these lake or wetland types are also similar (Figure 3a and 3c), indicating that they may be viewed as a continuum of water reservoirs with similar physical function with regard to flow dampening in the landscape. Furthermore, the correlation conditions found are similar when considering the North or the South Baltic WMD separately, as illustrated for lakes and floodplain wetlands in Figure S2.
There is little correlation between the dampening factor and absolute catchment scale (Figure 3g). However, the results for catchment scale are more heteroscedastic (have unequal statistics across the range of investigated catchment scales) than for the other, relative lake or wetland area variables in Figure 3. Specifically, the range of dampening factor values is much greater for small catchments than for large catchments. There is no correlation between the relative area of lakes and floodplain wetlands or between catchment area and the

FIGURE 3
The flow-dampening factor for 1999-2013 plotted against (a) the relative area of lakes to catchment area, (b-f) the relative area of different wetland categories to catchment area, and (g) to the catchment area, for the 82 catchments in the North and South Baltic Water Management Districts relative area of lakes or floodplain wetlands ( Figure S3); thus, there is no colinearity effect between any combination of these variables on flow variability.
Variables related to, for example, topography and land-cover types other than wetlands and lakes investigated here, may also have large-scale effects on the flow dampening factor (van der Velde et al., 2013) and more generally on flow variability (Botter, Basso, Rodriguez-Iturbe, & Rinaldo, 2013). However, the primary purpose of this study is to specifically compare and contrast the large-scale flow dampening effects of the main water-covered features, lakes and wetlands, in and across multiple catchment landscapes. As described in Section 3, the topographic, land-cover, and soil-type characteristics are, overall, consistent across the investigated catchments. We therefore expect the main differences in the flow dampening factor to reflect quantified differences in wetland and lake occurrence, to the degree that these different

| Seasonal differences in lake and wetland effects on flow dampening
Regarding seasonal conditions in the recent period 1999-2013, the dampening factor correlation with relative lake and floodplainwetland area (taken together) is greater in spring (explaining 64% of the variation among catchments) and winter (62%) than in autumn (42%) and summer (33%; Figure 4). These seasonal results are consistent with lakes and floodplain wetlands contributing most (least) to flow dampening in the seasons with the greatest (smallest) differences in relative P and R variability (CV value), which are spring and winter (autumn and summer; Figure S4, right panels). Spring and winter also have the smallest, whereas summer and autumn have the largest relative differences between average seasonal P and R ( Figure S4, left panels); that is, the relative P-water partitioning to ET is smallest (greatest) in spring and winter (summer and autumn). Furthermore, with regard to fitted functional relationships, the dampening-factor decrease with increasing relative lake or wetland area is greatest for spring, followed by winter, autumn, and summer ( Figure 4). This magnitude order is opposite to that of average seasonal P-water input, which is smallest for spring, followed by winter, autumn, and summer ( Figure S4, left panels). which have a much greater relative area than floodplain wetlands, and for the summer and autumn seasons, which have the greatest water partitioning to ET (and thus smallest to R) relative to the total seasonal P input of water. Neither of these effect signals are found in this study; instead, a lower correlation between flow dampening factor and relative lake or wetland area is observed in summer and autumn than in spring and winter or the whole year ( Figure 4).
Finally, the fitted whole-year regression function for the dampening-factor relationship with relative lake or wetland area

| Climate-period differences in lake and wetland effects on flow dampening
Over the 33 non-overlapping (first level) catchments in the North and South Baltic WMDs (Figure 2), the area-weighted long-term mean P and R values have increased slightly (by~5% for P and~8%-9% for R in each WMD) from 1984-1998to 1999). Much of the increase in P has occurred in summer whereas much of the increase in R has occurred in winter ( Figure S4). In both the North and South Baltic WMDs, the temporal CV is around 2 for daily P and around 1 for daily R, essentially remaining close to these levels between the periods ( Figure 5). Corresponding seasonal results are shown in Figure S4. Similarly, the area-weighted mean annual precipitation and runoff (mm/year) are shown in the charts in the middle. The temporal coefficient of variation (temporal standard deviation divided by the corresponding temporal mean) for daily precipitation and daily runoff is shown in the charts on the right. For the area-weighted mean values, the error bars show the spatial standard deviation among catchments. These statistics were calculated using non-overlapping catchments (all first-level catchments, Figure 2) For the lake or wetland effects on the dampening factor, the total relative area of lakes and floodplain wetlands can explain up to 64% of the dampening factor variability among catchments in 1999-2013 and 62% in 1984-1998 ( Figure 6). Thus, there is only a slight change in flow dampening factor behavior between the periods. This is consistent with relatively small P and R changes, even though there has been considerable warming (T increase), between the periods.

| CONCLUSIONS
This large-scale, multi-catchment study complements previous research, which has mostly focused on single or a few wetlands within one or two comparative catchments. The present results contribute to