Climate change affects natural streamflow regimes
globally. To assess alterations in streamflow regimes, typically temporal
variations in one or a few streamflow characteristics are taken into account.
This approach, however, cannot see simultaneous changes in multiple
streamflow characteristics, does not utilize all the available information
contained in a streamflow hydrograph, and cannot describe how and to what
extent streamflow regimes evolve from one to another. To address these gaps, we
conceptualize streamflow regimes as intersecting spectrums that are formed
by multiple streamflow characteristics. Accordingly, the changes in a
streamflow regime should be diagnosed through gradual, yet continuous
changes in an ensemble of streamflow characteristics. To incorporate these
key considerations, we propose a generic algorithm to first classify streams
into a finite set of intersecting fuzzy clusters. Accordingly, by analyzing
how the degrees of membership to each cluster change in a given stream, we
quantify shifts from one regime to another. We apply this approach to the
data, obtained from 105 natural Canadian streams, during the period of 1966
to 2010. We show that natural streamflow in Canada can be categorized into
six regime types, with clear hydrological and geographical distinctions.
Analyses of trends in membership values show that alterations in natural
streamflow regimes vary among different regions. Having said that, we show
that in more than 80 % of considered streams, there is a dominant regime
shift that can be attributed to simultaneous changes in streamflow
characteristics, some of which have remained previously unknown. Our study
not only introduces a new globally relevant algorithm for identifying
changing streamflow regimes but also provides a fresh look at streamflow
alterations in Canada, highlighting complex and multifaceted impacts of
climate change on streamflow regimes in cold regions.
Introduction
Natural characteristics of streamflow are critical to ecosystem livelihood
and human settlements around river systems (Poff et al., 2010; Nazemi and
Wheater, 2014; Hassanzadeh et al., 2017). Historically, humans have
considered the seasonality, variability, and magnitude of natural streamflow as
key factors for determining potentials for socio-economic developments
(Knouft and Ficklin, 2017). Streamflow characteristics are diverse and can
contain different information. While some streamflow characteristics
determine potentials for agriculture and energy production (Hamududu and
Killingtveit, 2012; Amir Jabbari and Nazemi, 2019; Nazemi et al., 2020),
some others act as proxies for the consequences of devastating disasters such as floods
or droughts (Arheimer and Lindström, 2015; Burn and Whitfield, 2016;
Zandmoghaddam et al., 2019).
A set of streamflow characteristics, collectively defining the overall flow
behaviour in a river reach, is called the streamflow regime (Poff et al.,
1997). Traditionally, streamflow regimes have been considered stationary in
time (Milly et al., 2008). However, the looming effects of climate change
along with human interventions through land and water management have raised
fundamental questions regarding the stationarity of streamflow regimes during the
current “Anthropocene” (Arnell and Gosling, 2013; Nazemi and Wheater, 2015a, b).
Even in undisturbed streams, recent literature is full of evidence
indicating major alterations induced by heightened climate variability and
change (Barnett et al., 2005; Stahl et al., 2010; Rood et al., 2016;
Hodgkins et al., 2017; Dierauer et al., 2018). As a result, assessing how
streamflow regimes are changing as a result of alterations in natural and
anthropogenic drivers is currently one of the imminent questions in the
field of hydrology.
Despite the extensive body of knowledge already gathered around assessing
the effects of climate change on altering streamflow regimes, there is
still room for methodological developments. Most importantly, among many
potential flow characteristics that can constitute and describe a streamflow
regime, often only a few are taken into account (Whitfield and Cannon, 2000;
Hall et al., 2014; Vormoor et al., 2015). This is a limitation because
climate change impacts are often manifested in the entire streamflow
hydrograph and not only around a unique set of streamflow characteristics
(Olden and Poff, 2003). This is particularly the case in cold regions as at
the watershed scale, multiple processes contribute to the streamflow
generation, each behaving differently in response to climate variability and
change (Whitfield and Pomeroy, 2016). As a result, alterations in streamflow
regimes are not only significant (e.g., Déry and Wood, 2005; MacDonald
et al., 2018; Islam et al., 2019; Champagne et al., 2020), but they are also
complex due to compound impacts of changes in temperature, shifts in forms
and magnitude of precipitation, and alterations in snow and ice
accumulation and melt (DeBeer et al., 2016; Hatami et al., 2018; Rottler et
al., 2020). At this stage of development, it is not yet possible to
systematically quantify streamflow regimes and their alterations to one
another using a large set of simultaneously changing streamflow
characteristics (Burn et al., 2016; Burn and Whitfield, 2018).
Here, we propose a new methodology to address this challenge. First, by
considering more streamflow characteristics, the distinctions between regime
types and their alterations become more fuzzy and relative. Accordingly, in
line with some recent suggestions in the literature (see, for example, Ternynck et
al., 2016; Burn and Whitfield, 2017; Knoben et al., 2018; Brunner et al.,
2018, 2019; Aksamit and Whitfield, 2019; Jehn et al., 2020), we
conceptualize streamflow regimes as continuous spectrums rather than
distinct states. This conceptualization requires a methodology that can
formally deal with subjectivity in the definition of streamflow regimes. For
this purpose, we use elements of fuzzy set theory (see Zadeh, 1965; Nazemi
et al., 2002) to provide a methodological basis to classify streamflow
regimes as intersecting clusters. We then measure the gradual departure from
one fuzzy cluster to others using significant monotonic trends in membership
degrees and use this information as an indicator for a regime shift in a
given stream. Accordingly, we highlight how such regime shifts are
attributed to changes in streamflow characteristics using a formal
dependence analysis.
We apply this algorithm in Canada, where the rate of warming is twice the
global average (Bush and Lemmen, 2019), and changes in streamflow
characteristics are significant in time and space (e.g., Buttle et al.,
2016; O'Neil et al., 2017; Dierauer et al., 2020). By considering more than
100 natural streams, we provide – for the first time – a homogeneous,
pan-Canadian view on recent alterations in natural streamflow regimes. The
remainder of this paper is as the following: sect. 2 describes our
three-step methodology related to (i) clustering regime types, (ii) detecting regime changes, and (iii) attributing regime changes to
alterations in streamflow characteristics. Section 3 introduces our case
study and the data. The results and discussions are presented in Sects. 4 and
5. Finally, Sect. 6 concludes our work and provides some further remarks.
MethodologyRationale and proposed algorithm
From both conceptual and computational perspectives, quantifying changes in
streamflow regimes is not a trivial task due to the relativity in the
definition of streamflow regime and how a change can be identified. On the
one hand, the flow regime at a given stream is defined by a large number of
streamflow characteristics, some of which have conflicting trends in time
and space. On the other hand, the flow regime is often identified based on
similarity/dissimilarity of characteristics in a set of benchmarking streams
with known regimes. Accordingly, regime shifts are not only defined based on
alterations in streamflow characteristics relative to the past but also
with respect to relative changes as regards other streams with known
regime types. This creates a complex mathematical problem due to the
“curse of dimensionality” (see, for example, Trunk, 1979), meaning that the complexity of the problem
increases exponentially by increasing the number of streams and/or
streamflow characteristics with which the streamflow regime is defined. To
solve this problem, the general tendency in the literature is to reduce the
dimensionality of the problem through the use of methodologies, such as
multidimensional scaling, empirical orthogonal functions, and principal
component analysis (e.g., Maurer et al., 2004; Johnston and Shmagin, 2008).
Despite methodological differences, all these approaches try to provide a
parsimonious representation of a hyperdimensional space by creating a much
simpler space that can preserve the sample variability in the original
domain (Guetter and Georgakakos, 1993). Although these methodologies are
able to substantially reduce the dimensionality and give valuable insights
into changes in hyperdimensional data sets, the results are hard to
interpret, particularly when attribution to some physical characteristics
are concerned (Matalas and Reiher, 1967; Overland and Preisendorfer, 1982;
Hannachi et al., 2009, and references therein). In the case of quantifying
changes in streamflow regimes, this limitation translates into an inability
to attribute the formation and transition in regime types directly to a set
of specific streamflow characteristics.
Here, we aim at addressing this problem through a new methodology that does
not rely on dimension reduction; rather, it tries to embrace the inherent
high dimensionality of the problem. Below we suggest an integrated approach
to (1) classify natural streamflow regimes into a set of interpolating
regime types, (2) diagnose the gradual evolution in regime types and their
shifts in time, and (3) attribute changes in streamflow regimes to
alterations in streamflow characteristics. Figure 1 shows the proposed
procedure. We use MATLAB® programming platform for the
implementation of this procedure.
The workflow of the proposed three-step algorithm for
classifying streamflow regime, diagnosing shift in streamflow regime, and
attributing the regime shift to the changes in streamflow characteristics.
Our approach is built upon two fundamental considerations. First, we
acknowledge that streamflow regimes are constituted by several streamflow
characteristics, and therefore changes in streamflow regimes are manifested
through changes in a large ensemble of streamflow characteristics. Second,
we recognize that there are soft as opposed to hard distinctions between
streamflow regimes, and regime shifts occur gradually rather than abruptly.
We select a large set of streamflow characteristics – or features – to
collectively characterize the streamflow regime. We then use the fuzzy
c-means algorithm (FCM) to classify streams into a set of overlapping regime
types during a common initial data period. We accordingly quantify changes
in degrees of association to each regime type during the entire data period
using a moving trend analysis. By monitoring the co-occurrence of divergent
trends in membership values, the transitions of regime types to one another
can be identified. Finally, we monitor the co-evolution of regime shifts
with the alterations in streamflow characteristics through a formal
dependency analysis.
Feature selection
Indicators of hydrologic alterations (IHAs; Richter et al., 1996) are
commonly applied as features to characterize changes in natural streamflow regimes
(e.g., Wang et al., 2018). Different sets of IHAs can be considered to
constitute streamflow regimes. Here we consider 15 IHAs, including annual
mean flow, monthly mean flows, and timings of the annual low and high
flows that together can represent the shape of the annual hydrograph. At
each stream, we use the mean (first moment) and variance (second moment) of
these 15 indicators during a multi-year timeframe to come up with 30
features that together can capture the shape of the expected annual
hydrograph and the variability around it. Table 1 shows the name and
notation of the features used, where xj=1:15 and yj=1:15 denote
the mean and the variance of the 15 considered IHAs.
The thirty streamflow features used for clustering natural
streamflow regime in Canada.
Clustering is the process of arranging data into a finite set of classes so
that members in the same class have similar characteristics. Various
statistical methodologies are used for clustering in hydrology (see Tarasova
et al., 2019; Brunner et al., 2020), often to non-overlapping (i.e., hard)
classes (Olden et al., 2012). Recent theoretical developments have
alternatively considered a set of overlapping (i.e., soft) classes, in
particular in the form of fuzzy clusters (e.g., Knoben et al., 2018; Wolfe
et al., 2019). The association to each fuzzy cluster can be quantified using
a degree of membership (see Bezdek, 1981; Sikorska et al., 2015). The
process of clustering streamflow regime using FCM can be summarized as the
following: assume that streamflow data from N hydrometric gauges during a
common timeframe w with the length of l years are available. For each
stream, the first and second moments of n IHAs (here n=15), i.e., X=xijY=yij;i∈1,…,N, j∈1,…,n, can be extracted during the initial
timeframe w. Before going forward, extracted features are normalized to avoid
scale mismatches:
1ax‾i,j=xi,j-min{xi=1:N,j}max{xi=1:N,j}-min{xi=1:N,j}∀j∈1,…,n,1by‾i,j=yi,j-min{yi=1:N,j}max{yi=1:N,j}-min{yi=1:N,j}∀j∈1,…,n,
where X‾=x‾ij and Y‾=y‾ij are the matrices of normalized streamflow features (NSFs). FCM
partitions the N streams into C fuzzy clusters such that the sum of
distances for all streams i∈1,…,N between
NSFs and cluster centroids is minimized. This is often formulated through an
iterative optimization procedure aiming at finding the cluster centroid by
minimizing the generalized least-squared error function as the objective of
optimization (Bezdek, 1981).
JU,V|X‾,Y‾=∑c=1C⋅∑i=1Nui,c2⋅d2[x‾i,j=1:ny‾i,j=1:n],vc,m=1:2n
This objective function is subject to the following two constraints:
2b∑c=1Cui,c=1∀i∈1,…,N,2c0<∑i=1Nui,c<N∀c∈1,…,C,
where V=vc=1:C,m=1:2n=x∗‾c,j=1:n,y∗‾c,j=1:n=[x∗‾c,1…x∗‾c,ny∗‾c,1…y∗‾c,n]∈R2n is the matrix of cluster centroids (i.e., regime types);
the matrix of U=ui,c;i∈1,…,Nc∈1,…,C
is the matrix of memberships; and d2[x‾i,j=1:n,y‾i,j=1:n],vc,m=1:2n is the
matrix of squared Euclidian distances between NSFs of stream i and
a cluster's centroid c. The fuzzy membership matrix can be accordingly
calculated as follows:
ui,c=1d2[x‾i,j=1:ny‾i,j=1:n],vc,m=1:2n∑c=1C1d2[x‾i,j=1:ny‾i,j=1:n],vc,m=1:2n;i∈1,…,N,c∈1,…,C.
The number of clusters C (here regime types) can be chosen as a priori or
empirically using validity indices (Srinivas et al., 2008). Here, we
implement three validity indices of the Xie–Beni index (VXB; Xie and Beni,
1991), partition index (VSC; Bensaid et al., 1996), and separation
index (VS; Fukuyama and Sugeno, 1989). These indices are based on two
criteria, namely compactness and separation. The compactness characterizes
how close members to each cluster are, whereas the separation measures how
distinct two clusters are. A good clustering result should have both small
intra-cluster compactness and large inter-cluster separation. The Xie–Beni
validity index is the ratio of compactness to the separation, quantified by
the average of the fuzzy variation in NSFs from a cluster's centroid to the
minimum squared distance between cluster centroids. Note that ∑i=1Nui,c2d2x‾i,j=1:n,y‾i,j=1:n,vc,m=1:2n is the compactness of fuzzy cluster
c, and separation of fuzzy clusters is quantified by the minimum squared
Euclidean distance between cluster centroids.
VXB=∑c=1C∑i=1Nui,c2d2x‾i,j=1:n,y‾i,j=1:n,vc,m=1:2nN×minc,l≠cd2vl,m=1:2n,vc,m=1:2n
Partition index is quantified by the sum of individual fuzzy cluster variations (i.e.,
the compactness of fuzzy clusters) to the sum of the distances from cluster
centroids (i.e., the separation of fuzzy clusters). This ratio is further
normalized by fuzzy cardinality weight γc, defined by γc=∑i=1Nui,c, to avoid the bias made by cluster
sizes.
VSC=∑c=1C∑i=1Nui,c2d2x‾i,j=1:n,y‾i,j=1:n,vc,m=1:2nγc×∑l=1cd2vl,m=1:2n,vc,m=1:2n
The separation index, also known as Fukuyama and Sugeno index, is defined
based on the difference between the compactness and the separation of fuzzy
clusters:
VS=∑c=1C∑i=1Nui,c2.d2[x‾i,j=1:n,y‾i,j=1:n],vc,m=1:2n-∑c=1C∑i=1Nui,c2.d2[vc,m=1:2n,v‾,
in which v‾=∑c=1Cvi/c. We identify the optimal
number of clusters using the elbow method (see Satopaa et al., 2011; Kuentz
et al., 2017), which involves finding the maximum number of clusters, beyond
which slopes of improvement in validity indices flatten significantly, and
adding a new cluster does not justify the increased complexity.
Detection of change in streamflow regimes
Clustering natural streams into c regime types takes place during a baseline
timeframe (i.e., the first initial years with the length of l years), in
which the optimal number of clusters, cluster centroids, and initial
membership degrees to each regime type are identified. For each stream, the
timeframe can be moved year-by-year, and the membership values can be
recalculated for the new window using Eq. (3). Figure 2 exemplifies this
process in a hypothetical case. This results in C time series of membership
degrees at each stream, showing how the association to each regime type
evolves in time – see Jaramillo and Nazemi (2018). In order to quantify the
gradual change in membership degrees, the Mann–Kendall trend test with the
Sen's slope is applied (Mann, 1945; Sen, 1968; Kendall, 1975). As the sum of
memberships in each timeframe is 1 (see Eq. 2b), a positive trend in
memberships to one cluster should coincide with a negative trend in the
membership of at least one other cluster. At each stream, this transition
can be identified by significant negative dependencies between membership
degrees.
A schematic view to the procedure of identifying the
evolution in membership values using a moving window: (a) a decadal
timeframe slides over the streamflow time series year-by-year, and (b) membership degrees are recalculated at each decadal timeframe to
systematically determine the changes in association to each regime type
determined in the beginning of the data period.
Given the pair of clusters p and q in the stream i, the rate of shift
from p to q can be quantified using Eq. (7), where ui,pw and ui,qw are membership degrees to clusters
p and q in stream i during the timeframe w, w∈1,…,r, r is the number of moving timeframes needed
to cover the whole data period year-by-year, E(ui,p) and E(ui,q) are the
expected memberships, and Si,(p,q) is the slope of the best-fitted
line.
Si,p,q=∑w=1mui,qw-Eui,qui,pw-Eui,p∑w=1mui,qw-Eui,q2
The procedure of attributing changes in membership
degrees to changes in streamflow characteristics. The left column shows the
co-evolution of membership degrees and normalized streamflow features (i.e.,
NSF1 and NSF2). The right column measures the correspondence
between changes in membership degrees and normalized streamflow features
through percentage of described variance quantified using R2. Red
and blue dots show the positive and negative dependencies, respectively.
Attribution of change in streamflow regime to alterations in streamflow
characteristics
Here, the existence of significant dependence between membership values and
streamflow features is taken as the basis for attribution. Accordingly, we
use Kendall's tau (Genest and Favre, 2007; Nazemi and Elshorbagy, 2012) to
detect the co-occurrence between changes in memberships and changes in NSFs.
Figure 3 shows the procedure of attribution. Left panels show the changes in
membership degrees of two hypothetical clusters (purple lines), along with
the corresponding changes in two NSFs (grey lines). Right panels show the
scatter plots of membership degrees vs. the NSFs. We identify the significance
and the direction of dependence using Kendall's tau coefficient. To
measure the linear association between changes in streamflow features
xi,j and membership values ui,c, the coefficient of
determination (R2; see Legates and McCabe, 1999) is used. R2
varies between [0, 1] and determines how much of the variability in the
degrees of membership can be described by the variability in a given
streamflow characteristic. The greater the R2 is, the stronger the
association between changes in degrees of membership and the streamflow
characteristics is. The coefficient of determination can be calculated as follows:
R2ui,c,xi,j=∑w=1rui,c-Eui,cxi,j-Exi,j2∑w=1rui,c-Eui,c2∑w=1rxi,j-Exi,j2∀i∈1,…,N.
By the simultaneous use of Kendall's tau and R2, we try to facilitate
quantitative communication of the impact of changes in a specific streamflow
characteristic on the transition from one regime type to another. By using
Kendall's tau, we identify the sign and significance of dependencies
between changes in membership degrees and streamflow characteristics using a
non-parametric approach that can handle nonlinearity in the form of
association. Using R2, we quantify how much of the variability in the
membership degrees can be described by the variability in the changes in
streamflow characteristics. This is to provide a comprehendible measure of
association between the two quantities. As R2 is a linear-based measure,
we repeat the experiment by replacing the R2 with squared Kendall's tau
and discuss the uncertainty in our attribution. The key advantage of our
proposed algorithm is in providing a workflow in which the detection of a
change in streamflow regime is directly attributed to changes in streamflow
characteristics. Figure 4 shows this integration using a hypothetical
example. Figure 4a demonstrates a multifaceted change in the shape of
the annual hydrograph in a given stream during two separate periods, shown
with grey and pink envelopes. The black and red lines are expected annual
hydrographs for each envelope (i.e., the mean of annual streamflow
hydrographs over the timeframe). Any shift between flow
regimes is described by at least a pair of membership time series with
opposite trends. The strength of the link is measured using R2. Figure 4b shows the rates of shifts and the attribution to changes in
streamflow characteristics. The thickness of links is proportional to rates
of shift and/or R2 values.
An example for transitions between regime types along
with attribution of change to streamflow characteristics. Panel (a) shows annual hydrographs in two separate periods using grey and pink
envelopes. Panel (b) shows the dominant shift in the flow
regime by maximum rate of shift and attributes this shift to changes in
significantly dependent streamflow characteristics. The dominant shift is
visualized by the thickest grey envelope. The strength of the association
between regime shift and significantly dependent streamflow characteristics
are measured and communicated by R2.
Case study and data
With a total drainage area equivalent to 6 % of the global land area,
Canadian rivers support important socio-economic activities such as
agriculture and hydropower production. River systems in Canada can be
divided into four major ocean-drained basins, namely Pacific, Atlantic,
Arctic, and Hudson Bay that can be further divided into a number of
sub-basins (Pearse et al., 1985; Natural Resources Canada, 2007). The
Pacific basin, the smallest among all, spreads along the west coast from the US
border to Yukon and drains around 1 million km2. The main
sub-basins in the Pacific include Fraser, Yukon, Columbia, and the Seaboard.
In the east coast, the Atlantic basin drains a total area of 1.6 million km2 and includes important water bodies such as the Great
Lakes. The basin includes three sub-basins, namely the St. Lawrence River,
Seaboard, and the Saint John-St. Croix. Towards the north, the Arctic basin
drains over 3.5 million km2 of northern lands and includes
some of Canada's largest lakes other than the Great Lakes such as the Slave,
Athabasca, and Great Bear lakes. The Mackenzie, Peace–Athabasca, and
Seaboard are the main sub-basins in the Arctic basin. With an area of 3.8 million km2, Hudson Bay is the largest drainage basin in
Canada, covering five provinces from Alberta in the west to Québec in
the east. The basin includes four major sub-basins, namely Western and
Northern Hudson Bay, Nelson, Northern Ontario, and Northern Québec.
Nelson, Saskatchewan, and Churchill rivers are the major river systems in
Hudson Bay.
Natural streamflow regimes in Canada have undergone drastic changes in
recent years which are expected to increase under future climate change
conditions (Woo et al., 2008). Observed and projected changes in streamflow
regimes are not only between different regions (Kang et al., 2016; Islam et
al., 2019), but they also occur within the same ecological and/or hydrological
regions (Whitfield, 2001; Whitfield et al., 2020). For instance, there are significant
differences among forms of change in streamflow regimes between the
northern and southern Pacific (Kang et al., 2016; Brahney et al., 2017).
Similarly, glacier-fed rivers in northern Canada show increases in summer
runoff (Fleming and Clarke, 2003), whereas other rivers show a tendency
toward decreasing summer runoff (Fleming and Clarke, 2003; Janowicz, 2008,
2011). To diagnose simultaneous changes in natural streamflow regimes across
Canada, we use the data from the Reference Hydrometric Basin Network (RHBN;
Water Survey of Canada, 2017, http://www.wsc.ec.gc.ca/, last access: August 2020). RHBN includes 782
Canadian hydrometric stations that measure streamflow at unregulated
tributaries and are particularly suitable to address climate change impacts
on natural streamflow regimes (Brimley et al., 1999; Harvey et al., 1999).
In the period of 1903 to 2015, we search for the largest subset of
hydrologically unconnected stations with the longest continuous daily record
during a common period and less than a month worth of missing data in a
typical year. This results in selecting 105 streamflow stations during the
water years of 1966 to 2010 (1 October 1965 to 30 September 2010).
Although drainage basins are often used as the spatial unit in which
alteration in streamflow regimes is investigated, there are substantial
differences within a drainage basin in terms of climate, topography,
vegetation, geology, and land use. This results into multiple forms of
hydrological responses within one drainage basin. In contrast to drainage
basins, terrestrial ecozones are identified based on similarity in climate
and land characteristics, and therefore, they can be more representative of
different hydrological responses (Whitfield, 2001). In brief, an ecozone is a
patch of land with distinct climatic, ecologic, and aquatic characteristics
(see Wiken, 1986; Marshall et al., 1999; Wong et al., 2017). Canada includes
15 ecozones. Starting from the north, the Arctic Cordillera (EZ1), covering
2 % of Canada's landmass, contains the only major mountainous region in
Canada other than the Rockies. The Northern Arctic (EZ2) is equivalent to
14 % of Canada's landmass and covers Arctic islands (Coops et al., 2008).
The Southern Arctic (EZ3) includes the northern mainland, covering 8 % of
Canada. The Taiga Plains (EZ4) extends mainly on the western side of the
Northwest Territories, covers 6 % of Canada's landmass, and includes a
large number of wetlands. Taiga Shield (EZ5), with a large number of lakes,
covers 13 % of Canada's landmass in the south of the southern Arctic
(Marshall et al., 1999). The Boreal Shield (EZ6) is Canada's largest ecozone
covering 18 % of the country's landmass, extending from northern
Saskatchewan toward the south into Ontario and Québec and then
northward toward eastern Newfoundland (Rowe and Sheard, 1981). The Atlantic
Maritime (EZ7) includes the Appalachian mountain region, covering 2 % of
Canada and extending from the mouth of the St. Lawrence River and Bay of Fundy
to coastlines of New Brunswick, Nova Scotia, and Prince Edward Island. The
Mixedwood Plains (EZ8) is the most southerly ecozone, covering 2 % of
Canada, but includes the country's most populated regions in Ontario and
Québec. The Boreal Plains (EZ9) covers 7 % of Canada's landmass in
western Canada, from British Columbia to the southeastern corner of Manitoba
in the south of the Boreal Shield (Ireson et al., 2015). The Prairies (EZ10)
extend from south-central Alberta to southeastern Manitoba, covering 5 %
of Canada's landmass and the majority of Canada's agricultural lands (Nazemi
et al., 2017). The Taiga Cordillera (EZ11) includes 3 % of Canada with the
least amount of Canada's forest and lies along the northern portion of the
Rocky Mountains (Power and Gillis, 2006). The Boreal Cordillera (EZ12)
covers 5 % of Canada from northern British Columbia to the southern Yukon,
with mountainous uplands and forested lowlands. The Pacific Maritime (EZ13)
mainly includes the coastal mountains of British Columbia and lands adjacent
to the Pacific coast, having the warmest and wettest climate in the country,
in an area around 2 % of Canada (Wiken, 1986). The Montane Cordillera
(EZ14), with the most diverse climate in Canada, includes 5 % of Canada in
mountainous areas of southern British Columbia and southwestern Alberta and
provides headwater flow to some important river systems such as Fraser,
Saskatchewan, and Athabasca (Marshall et al., 1999). Finally, Hudson Plains
(EZ15) includes 4 % of Canada in the southern part of Hudson Bay with a
large number of wetlands. Table 2 summarizes the selected stations within
each ecozone.
List of Canadian ecozones with at least one RHBN station
in this study, along with their abbreviations and the number of RHBN
stations considered within each ecozone.
AbbreviationEcozonesNo. of stationsAbbreviationEcozonesNo. of stationsEZ2Northern Arctic1EZ8Mixedwood Plains5EZ3Southern Arctic1EZ9Boreal Plains6EZ4Taiga Plains1EZ10Prairies2EZ5Taiga Shield4EZ12Boreal Cordillera7EZ6Boreal Shield25EZ13Pacific Maritime9EZ7Atlantic Maritime25EZ14Montane Cordillera19
Tables S1 to S4 in the Supplement introduce these stations across the four
drainage basins in Canada. Figure 5 shows the distribution of the selected
stations across the 15 ecozones. As is clear, the density of selected
stations varies greatly among ecozones. The highest numbers of stations are
within Atlantic Maritime, Boreal Shield, and Montane Cordillera, while
the southern and northern Arctic, as well as Taiga Plains, include only one; and
there is no station in the Arctic Cordillera, Taiga Cordillera, and Hudson
Plains. At the basin/sub-basin scale, the selected stations cover all 14
main Canadian sub-basins – see Table S5 and Fig. S1 in the Supplement.
The distribution of the selected 105 RHBN streamflow
stations within the Canadian ecozones.
Results
We apply the framework proposed in Sect. 2 to the selected RHBN streams. At
each stream, we first convert the daily discharge data into runoff depth in
millimetres per week and calculate the thirty streamflow features introduced
in Table 1. We then consider a multi-year timeframe for clustering and
assigning initial membership values. The length of this timeframe should be
chosen in a way that (1) provides a notion for streamflow regime and (2) provides enough timeframes to assess evolution in membership values. As the
aim is to address temporal changes in the streamflow regime, the baseline
timeframe is considered at the beginning of the streamflow time series.
Here, we present our result based on considering decadal timeframes and the
period of 1966 to 1975 as the baseline. We address and discuss the sensitivity
of our results to these assumptions in Sect. 5.
Identifying natural streamflow regimes in Canada
We attempt to find the optimal number of clusters empirically from the pool
of c={2,3,…,10}, using the three validity
indices introduced in Sect. 2.3. Figure S2 in the Supplement shows the
result of this investigation, indicating the optimal number of clusters
as c=6, in which decreasing slopes of the three validity indices flatten.
To provide a sense of these streamflow regimes and their changes in time, we
visualize the shapes of annual streamflow hydrographs in the archetype
streams during the baseline and the last decadal timeframe (i.e., 1966 to
1975 vs. 2001 to 2010) in Fig. S3 in the Supplement. Archetype streams are
those streams that have the highest association with the identified regime
types and can represent the characteristics of a given regime better than
other members of the cluster. Table 3 introduces these six regimes along
with their notation and archetype streams. We name clusters based on two key
characteristics, i.e., the form of hydrologic response (i.e., fast vs.
slow response) and the timing of the annual peak flow (i.e.,
cold-season, freshet, and warm-season peaks). The form of hydrologic response
can be proxied by variability in the annual streamflow hydrograph. The
greater the variability in the annual streamflow hydrograph is, the faster
the hydrologic response is.
Six identified regime clusters along with their labelled
regime type and archetype stream.
ClusterRegime typeArchetype (representative) streamC1Slow-response/warm-season peakKazan River above Kazan Falls (HYDAT ID: 06LC001)C2Fast-response/warm-season peakClearwater River near Clearwater Station (HYDAT ID: 08LA001)C3Slow-response/freshet peakMatawin River at Saint-Michel-des-Saints (HYDAT ID: 02NF003)C4Fast-response/freshet peakGander River at Big Chute (HYDAT ID: 02YQ001)C5Slow-response/cold-season peakBeaver Bank River near Kinsac (HYDAT ID: 01DG003)C6Fast-response/cold-season peakSproat River near Alberni (HYDAT ID: 08HB008)
Figure 6 shows a synoptic look at the distribution of streams belonging to
each flow regime during the initial baseline timeframe. In each panel, the
red star represents the archetype stream, and streams with membership values
of 0.1 and larger are shown with circles. The larger the size of a circle
is, the greater the degree of membership to each cluster is. As Fig. 5
shows, the six clusters are geographically identifiable and resemble some of
the already-known regime types across the country (see Whitfield, 2001;
Bawden et al., 2015; Burn and Whitfield, 2016; Bush and Lemmen, 2019).
The “slow-response/warm-season peak” regime, i.e., cluster C1, includes
streams with strong seasonality, high discharge in summer, and smaller
variability in annual streamflow hydrograph compared to cluster C2, i.e.,
the “fast-response/warm-season peak” regime. Cluster C1 is characterized by a
gradual rise after spring snowmelt, prolonged peak discharge throughout
summer, gradual recession during fall, and low runoff in winter (Déry et
al., 2009). Streams belonging to C1 spread mostly in northwestern Canada and
are either glacial-fed or lake-dominated streams, in which the hydrologic
responses are delayed due to the slow rate of glacial retreats and/or storage
effects of large in-stream lakes. The Kazan River releasing into Baker
Lake in Nunavut is the archetype stream for this regime type. C2 is very
similar to C1, however with greater variability in annual streamflow
hydrographs. The streams belonging to this stream type are mainly concentrated in
western Canada, particularly in the Montane Cordillera (46 % of streams), and
include streams that are fed mainly through snow and glacial melts (Eaton
and Moore, 2010; Moore et al., 2012; Schnorbus et al., 2014). There are,
however, streams belonging to C2 that are located in the Boreal Shield (23 %
of streams), where the streamflow generation is governed by other processes
such as fill-and-spill in which segments of a basin have to be filled above
their capacity before spillage (Spence and Phillips, 2015). The Clearwater
River near Clearwater in southern Alberta is the representative stream for
this regime type.
The distribution of the identified regime types across
Canadian ecozones during the baseline l timeframe of 1966 to 1975. Each
stream is represented by a circle with a radius proportional to a membership
degree quantifying the association to a given regime type. Only RHBN
stations with degrees of membership of 0.1 or larger are shown in each
panel. The red stars are the archetype stations related to each regime type.
The cluster C3, i.e., the “slow-response/freshet peak” regime, includes
streams in which the annual streamflow volume is mainly contributed by a
short high-flow period during spring snowmelt, sharp recession in summer,
yet relatively smaller variations in the shape of hydrograph compared to the
cluster C4, i.e., “fast-response/freshet peak” regime. Nearly 45 % of the
streams with this regime type are located in Atlantic Maritime. The rest are
distributed in the Boreal Shield (28 %), Mixedwood Plains (15 %), and
Montane Cordillera (12 %). The Matawin River originating from lake
Matawin in Québec is the archetype for the C3 regime. The streams
belonging to C4 are also dominated by spring snowmelt but showing more
variation in the shape of annual hydrographs compared to the C3 regime.
Streams belonging to the C4 regime often have two distinct peaks, one in
spring induced by snowmelt and one in fall due to high precipitation, and
from that sense, they largely resemble nival–pluvial streams (Hock et al.,
2005). Almost all streams belonging to the C4 regime are located in eastern
Canada (50 % in Atlantic Maritime, 26 % in the Boreal Shield, 16 % in
Mixedwood Plains). Gander River at Partridgeberry Hill in Newfoundland is
the archetype for this regime.
The cluster C5, i.e., “slow-response/cold-season peak” regime, comprises
streams with weak seasonality and slightly more discharge in fall and
winter. The annual flow for streams belonging to this regime is more
influenced by rainfall around late fall, followed by a slight increase in
discharge due to snowmelt; therefore, they resemble a hybrid
pluvial–nival regime (Kang et al., 2016). The concentration of streams
belonging to this regime is again in eastern Canada (48 % in Atlantic
Maritime; 33 % in the Boreal Shield), with a few streams being in the Pacific
Maritime. Beaver Bank River in Nova Scotia is the representative stream for
this regime type. Finally, the cluster C6, i.e., “fast-response/cold season
peak regime, is similar to the C5 regime and exhibits a weak seasonality
but with a greater variation in shapes of annual hydrographs. The runoff in
streams belonging to this regime is dominated by heavy precipitation,
especially during winter, and lower runoff during summer, resembling the
pluvial regime (Wade et al., 2001; Whitfield, 2001). Streams belonging to
this regime are only concentrated in the Pacific. The Sproat River near
Alberni is the archetype stream of the C6 cluster.
Detection of changing streamflow regimes
To understand temporal shifts in streamflow regimes throughout selected RHBN
streams, we calculate the decadal membership values as shown in Fig. 2. We
accordingly apply the Mann–Kendall trend test with the Sen's Slope on the
time series of decadal memberships. The detailed results including the
membership time series for all streams and corresponding trend analyses are
shown in Figs. S4 and S5 in the Supplement over major drainage
basins/sub-basins and the terrestrial ecozones in Canada,
respectively. Figure 7 summarizes our findings over the 15 Canadian
ecozones. The colour (blue vs. red) and the size (large vs. small) of triangles
show decreasing vs. increasing trends, as well as significant vs. insignificant
trends at p value ≤0.05. Although inconsistent patterns of change are
observed in the Boreal and Montane cordilleras, particularly between the southern
and northern regions, there are clear downward trends in the member of
regime C1 in the Taiga Shield and Boreal Shield. Upward trends are observed in
membership values of C2 in the Boreal Cordillera and Taiga Shield, while
downward trends are seen in the member of C2 in southern and eastern parts
of the Montane Cordillera and Boreal Shield. The C3 regime shows intensification
in the Montane Cordillera and Boreal Shield. It also intensifies in southern
parts of Atlantic Maritime but weakens in northern regions. The pattern of
change in C4 is very similar to C3 but with fewer significant downward
trends in northern parts of Atlantic Maritime. Considering the C5 regime,
streams mainly show decreasing trends in the Appalachian region including
the eastern Boreal Shield and southern parts of Atlantic Maritime. Mixed
patterns of change in membership degree are observed in the Pacific Maritime
for both C5 and C6 regimes.
Trends in decadal memberships, quantifying the change in
association of the 105 selected RHBN streams to the six regime types during
1966 to 2010.
The nature of regime shifts at each stream can be investigated by
quantifying the rate of relative shift between opposing significant trends.
Figure S6 in the Supplement summarizes the results. Overall, the dominant
modes of transition at the ecozone scale are from C1 to C2 in the northern
ecozones (EZ5 and EZ12), from C2 to C1 and from C2 to C3 in the western
ecozones (EZ9 and EZ14), from C2 to C3 at the two stations located in the
Prairies, from C1 to C3 in the eastern ecozones (EZ6, EZ8, and EZ15), and
from C5 to C4 in the Appalachian region (EZ7 and eastern part of EZ6). The
variability between the regime shifts inside each ecozone can be described
by elevation. To better synthesize our findings in Canada and highlight
dominant regime shifts and their geographic extent across the country, Fig. 8 shows Sankey diagrams demonstrating the initial regime types in the
considered streams. Streams are grouped by the ecozones on the left side of
each panel and transform to one particular target regime type (right side
of each panel). The six natural regime types are distinguished by colour
codes, and stations within each ecozone are sorted from the lowest to the
highest elevation from top to the bottom. The width of each arrow is
proportional to the rates of shift, calculated using Eq. (7). The highest rate
of a shift in each stream and/or ecozone can be considered as the dominant
regime shift.
Sankey diagrams showing transitions in Canadian natural
streamflow regimes described across ecozones from 1966 to 2010. Each panel
presents the transformation from five potential regime types to one particular
target regime. Streams in the left side are grouped according to ecozones
and are sorted from the lowest to highest elevations from the top to the
bottom. Colours show the six regime types. The widths of arrows are
proportional to the rate of shift.
Some important findings can be made from Fig. 8. While regime shifts are
varied, there are some dominant regime shifts that are frequently observed
across different ecozones. For example, frequent shifts are observed from C2
to C1, as well as C1 to C2, that are quite strong across the Montane Cordillera
and Taiga Shield, respectively. Second, it is possible that the streamflow
regime in a given ecozone shifts from one regime to two or more regime
types. For instance, streamflow in Atlantic Maritime shifts from C5 to C3
and C4. Also, it is possible to have opposing regime shifts in a given
ecozone. As an example, the flow regime varies from C5 to C6 and vice versa
across Pacific Maritime. Such variabilities in regime shift can be partially
explained by latitude. More generally, it is possible to shift from two or
more regime types into one or more regime types across a particular ecozone.
For example, streams with C1 and C5 regimes are shifting to C3 and C4 across the
Boreal Shield. Such variabilities within an ecozone can be described in many
cases by elevation. In the Boreal Shield, for example, elevation controls the
constitution of the initial streamflow regime from C5 in lowlands to C1 in
highlands. Finally, the most frequent regime shifts are not necessarily the
strongest ones. For instance, the streamflow regime shifts across six ecozones
toward C3 and C4, but the rates of the shift are not strong when compared
with the shift between C6 to C5 that happens in limited streams in Pacific
Maritime, but quite strong.
Identifying forms of transformation in streamflow regimes
The procedure presented in Sect. 2.5 attributes regime shifts to changes in
streamflow characteristics using dependence analysis. Figure 9 summarizes
the results of attribution for the 105 RHBN stations. Streams are shown in
rows, grouped in each ecozone, and ordered from low to high elevations from
the top to the bottom. For each stream, there are three groups of cells,
with 15, 15, and 2 cells from left to right. The first two
groups of cells are related to the values of mean (i.e., x1 to
x15) and variance (i.e., y1 to y15) of the 15 considered
IHAs. In these two groups of cells, shades of blue and red
show negative and positive dependencies between a given pair of streamflow
characteristic and membership degree, respectively. Note that we only
identify those streamflow characteristics that have significant dependencies
with variations in membership degrees based on Kendall's tau (p value ≤0.05) Colour saturations show the values for the coefficient of
determination, quantifying the fraction of variability in membership degrees
that are described by the variability in streamflow characteristics. The
last two cells are related to the dominant regime shift in each stream from
one initial regime (left hand cell) to an altered regime (right hand cell).
The colour scheme, defining the regime types, is shown in the legend. The
analyses over basin and sub-basin scales are presented in Figs. S7 and S8 in
the Supplement.
The most important observation is the fact that in more than 80 % the
considered natural streams, there are some identifiable regime shifts that
are significantly dependent on the changes in the streamflow
characteristics. Some dominant regime shifts are frequent within an ecozone,
while some are less frequent and may depend on latitude and/or elevation. In
the only considered stream in the Northern Arctic Ecozone, the shift from the C2 to
the C1 regime is attributed to the earlier and more variable timing of the
annual low flow, as well as the increasing June flow. An opposing shift is observed
in Taiga Shield, i.e., from C1 to C2, which can be attributed to the earlier
and more variable timing of annual high flow, as well as the increasing seasonal
flow in fall. The regime shift from C5 to C4 in the lowlands of the Boreal
Shield is attributed to the decreasing mean of and variance in annual flow
particularly in August. In the highland of this ecozone, however, the
dominant regime shift is from C1 to C3 and can be attributed to the
decreasing monthly flow in August and September, as well as more variability in the
timing of the annual low flow. In Atlantic Maritime, particularly across
lowlands, decreasing mean of and variation in the flow in August along with
decreasing monthly flow in June and July, as well as decreasing mean annual and
seasonal flow in the fall, lead to a shift from C5 to C4.
Dominant regime shifts across 105 RHBN streams in Canada
attributed to the first and second moments of the 15 IHAs considered. Shades
of red and blue show the positive and negative dependencies between changes
in streamflow features and degrees of membership. Colour saturations are
proportional to the values of the coefficient of determination. The dominant
regime shift at each stream is identified by the colour scheme described in
the legend. Streams are grouped in ecozones and ordered from low (top) to
high (bottom) elevations.
In Mixedwood Plains, the shift from C1 to C3 is attributed mainly to the earlier
and more variable timing of annual low flow. In the lowlands of Boreal
Plains, the increasing variation in April's flow and decreasing annual and
summer flows contribute to the shift from C2 to C1. Streams in the highlands
of Boreal Plains, however, shift from C1 to C2 due to the increasing annual
and summer flows, along with the later and more variable timing of low flows. In the
Prairies, in the two considered streams, the shift from C2 to C3 is
attributed to the delayed and more variable timing of low flows and decreasing
summer flows. In the Boreal Cordillera, more variable annual flow and increasing
mean of and variation in May flow correspond to the shift from C1 to C2.
Opposing shifts from C2 to C1, however, are mainly attributed to the
increasing monthly flows in February, March, April, and May. The most
pronounced shift in Pacific Maritime is from C5 to C6, which mainly
corresponds to increasing mean of and variation in October flow, as well as increasing
annual flows. The most pronounced shift in the Montane Cordillera is from C2 to
C1 for the streams in the northern part, attributed to decreasing mean of and
variability in July flow and increasing monthly flow in April and May.
Streams in southern parts, however, shift from C2 to C3, attributed mainly
to increasing monthly flow in February, March, and April, more variability
in the timing of the low flow, and decreasing September flow.
Discussion
The application of the proposed methodology in Canada identifies six
distinct natural regimes across the country, address their change in time
and space, attribute dominant regime shifts to changes in a range of
streamflow characteristics at each stream, and accordingly upscale the
findings from individual streams to ecozones. Having said that, still there
are some unanswered questions. First, it is still unclear how robust our
proposed algorithm is particularly in light of the assumptions made with
respect to the length of the timeframes and/or selecting the baseline
period. Second, it is obvious that our selected streams are only a sample of
available RHBN stations across Canada, and it is still unclear how our
findings can be extended to out-of-sample streams. Finally, there is a large
body of literature reporting shifts in streamflow regimes across different
regions in Canada due to changes in temperature patterns, magnitude and form
of precipitation, and snowmelt and snow accumulation, as well as glacier retreat
and permafrost degradation. Accordingly, it is crucial to frame and position
our findings with respect to earlier studies. These three tasks are pursued
in this section.
Addressing uncertainty
The results presented in Sect. 4 are based on decadal timeframes
and the selection of the first decadal timeframe as the baseline period. Here we
relax these two assumptions and monitor alterations in our findings. First,
we repeat the clustering algorithm over all possible decadal timeframes
throughout the study period and recalculate the cluster centers. This
experiment addresses the sensitivity of our clustering algorithms to the
choice of baseline period. Second, we repeat the approach implemented in
Sect. 4 again with 15- and 20-year timeframes and address how
cluster centers, as well as our specific findings, would be altered by increasing
the length of timeframe. We do not consider timeframes less than decadal
length due to the insufficiency of numbers of data points for trend
analysis. We also do not consider timeframes larger than 20 years to allow there to be at
least two fully independent timeframes during the study period with a gap of a few years. Figure 10 summarizes our findings in terms of the sensitivity of
our clustering results with respect to the two assumptions made. Panel (a)
shows the cluster centers when different decadal baselines are considered.
Coloured dots show the centers of clusters related to all possible decadal
timeframes except the period of 1966 to 1975. The centers of clusters are
scaled into two dimensions using multidimensional scaling (MDS; Cox and
Cox, 2008), in which the distance between the dots represents the
approximate dissimilarity of centers of clusters. Dimensions 1 and 2
delineate the space in which the original data are mapped. Black crosses
show the centers of the first decadal timeframe mapped using MDS. Colours
identify regime types. The result clearly shows that despite changing the
baseline timeframe, the distinctions between cluster centers are maintained,
and the position of centers does not substantially change by changing the
baseline period. Panel (b) shows the results of our sensitivity analysis
with respect to changing the length of timeframe. Again, there are not
notable changes in the cluster centers. These two findings highlight the
robustness of our clustering analysis.
The sensitivity of the cluster centers to (a) the choice
of decadal timeframe for clustering and (b) the length of the timeframe
used for analysis. In panel (a) dots show the two-dimensional scaling of the
cluster centers in which distances between dots represent dissimilarities
between cluster centers. Black crosses show the centers identified by
choosing the first decadal timeframe. Panel (b) shows the two-dimensional
scaling of the cluster centers considering 10-, 15-, and 20-year timeframes.
We also look at possible differences in the direction of trends in
membership degrees, dominant regime shifts, and the attribution to
streamflow features at the basin scale if the length of timeframes are
changed. Figure 11 (left column) intercompares the results obtained by 10-,
15-, and 20-year timeframes in terms of percentages of similarities in the
direction of trends during 1966 to 2010 at each basin. In brief, there is
at least 80 % agreement between the results obtained in the Pacific and
the Arctic basins. There are more discrepancies in the direction of trends
in the Atlantic and Hudson Bay basins. This is particularly the case for the
C1 regime in Hudson Bay and for the C3 and C4 regimes in the Atlantic,
for which the results are less consistent among different timeframes; yet,
in the worst-case scenario (i.e., the C4 regime in Atlantic), there is still
more than 60 % agreement between the results of trend analysis obtained by
10-, 15-, and 20-year timeframes.
Dominant regime shifts are also performed with 15- and 20-year timeframes
and are intercompared with corresponding results obtained by decadal
timeframes. Our analysis shows that results obtained by 15- and 20-year
timeframes are in agreement with the results obtained using decadal
timeframes. Even for the case with the largest discrepancy (i.e., C4 regime
in the Atlantic), there is 86 % agreement in terms of the direction of
shift in streamflow regimes, obtained by 10- and 20-year timeframes. In
terms of attribution of regime shifts to changes in streamflow
characteristics, again the results obtained by different lengths are in
large agreement in at least 80 % of streams.
Finally to investigate the sensitivity of attribution to the choice of
measure, we substitute R2 with squared Kendall's tau and repeat the
experiment. The result of this experiment is summarized in Fig. S9 in the
Supplement. Comparing Fig. S9 with Fig. 9 shows that in general the
selected streamflow characteristics are similar with no remarkable changes
in the degrees of attribution that influence our general findings. The most
sensitive ecozones to the choice of measure of association are EZ5 and
EZ14, demonstrating the greater values of association measured by the
squared Kendall's tau. This is due to the higher degree of nonlinearity between
regime shifts and alterations in streamflow characteristics in these
ecozones.
Similarities (in percentage) between the results
obtained by 10-, 15-, and 20-year timeframes related to trends in membership
values, direction of shift in streamflow regimes, and attribution to
streamflow characteristics in the four major Canadian basins.
Validation in out-of-sample streams
One important question remaining unanswered is how the six regime types
identified can be extended into out-of-sample streams. Here we investigate
this in the Prairies ecozone, a region with importance for global food
security. Natural streams in the Prairies have been relatively overlooked in the
literature (Whitfield et al., 2020) because often the streams do not have
continuous streamflow records partially due to the fact that many streams
are seasonal. In addition, the majority of annual streamflow volume is
contributed from mountainous headwaters outside of the Prairies, and the fact is that at many basins a large proportion of the land does not normally
contribute to the streamflow (Spence et al., 2010; Shook et al., 2015;
Mekonnen et al., 2015). In addition, only two stations in the Prairies meet our
data criteria in Sect. 3. Here, we reduce the length of data and investigate
for new streams that satisfy our data criteria during 1976 to 2010. This has
resulted in the selection of nine new stations – see Fig. 12 for the location
of these stations (P1 to P9). The detailed information about these stations
are provided in Table S6 in the Supplement. Here we investigate how these
new stations fit into previously identified regime types, check the trends in
the membership degrees, and identify dominant regime shifts in these
streams. We compare our findings for the nine new stations with the two
previously selected stations in the Prairie region, namely, Waterton River
near Waterton Park (S69; 05AD003) and Belly River near Mountain View (S70;
05AD005) during the common period of 1976 to 2010 for which the nine new
stations are selected. The right panel shows the analysis of trends in
anomalies of decadal memberships, in which stations are ordered from the
east to west from the top to the bottom. The analysis of trends in
membership degrees shows mainly decreasing trends for C1 and C2 regimes and
increasing trends for C5 and C6 regimes. Regarding C3 and C4 regimes, mainly
upward trends are observed in the east, whereas downward trends are
observed in the west. These findings are in line with our results in S69 and
S70. The two columns at the right side of right panel are related to the
dominant regime shift in each stream. The legend identifies the six
identified regime types. Although the regime shifts are vibrant, the
dominant regime shift observed is from C2 to C5, which is the same in S69
and S70 during the period of 1976 to 2010.
Summary of findings and positioning against earlier studies
Although to the best of our knowledge our work is the first study in which
a systematic algorithm is used to provide a temporally homogeneous view on
recent changes in pan-Canadian streamflow regime, the literature of Canadian
hydrology is rich in terms of documenting changes in streamflow
characteristics across the country. Thanks to the pioneering work of so many
hydrologists before us, including the late iconic northern hydrologist,
Richard Janowicz, to whom this paper is dedicated. Here we attempt to
position our results with respect to earlier studies. Table 4 summarizes our
findings in terms of dominant regime shifts and associated changes in
streamflow characteristics at the sub-basin scale.
Positioning our findings with respect to earlier studies
across major Canadian basins and sub-basins.
BasinSub-basin (stream location)Dominant regime shiftsEarlier findings on changes in streamflow characteristics (reconfirmed in this study)New findings on changes in streamflow characteristics (discovered exclusively in this study)PacificYukonC3 to C1Earlier timing of low and high flows; greater variability in timing of high flows (Burn, 2008; Brabets and Walvoord, 2009; St. Jacques and Sauchyn, 2009)Increasing flow in September; increasing flow variability in April and MaySeaboard (north)C1 to C2Increasing winter flows (Déry et al., 2009)Increasing monthly flow in May; earlier timing of low flow; increasing variability in March, May, and annual flowsSeaboard (south)C1 to C3Decreasing annual and monthly flows from April to June; decreasing flow in fall (Déry et al., 2009; Pike et al., 2010)Delayed and more variable timing of annual low flow; increasing variability in February's monthly flowFraser (north)Case 1: C1 to C2 Case 2: C2 to C1No earlier study in this region foundCase 1: increasing mean of and variance in annual and summer flows; increasing monthly flows in May and June; increasing variation in timing of low flow and the quantity of spring flows. Case 2: decreasing mean of and variance in annual flow; decreasing monthly flows in July and October; earlier timing of high flow; decreasing variability in monthly flows in May, August, and SeptemberFraser (south)C2 to C5Decreasing summer flows (Stahl and Moore, 2006); Increasing variability in monthly flows in November and April (Déry et al., 2012; Thorne and Woo, 2011)Earlier timing of high flows; increasing mean monthly flows in November and AprilColumbia (north)C2 to C1Decreasing annual and summer flows (Stahl and Moore, 2006; Fleming and Weber, 2012; Forbes et al., 2019)Decreasing variability in annual flow and monthly flows of August and SeptemberColumbia (south)C1 to C3Increasing flow in April and decreasing flow in September (Whitfield and Cannon, 2000; Whitfield, 2001); earlier timing of high flow (Burn and Whitfield, 2016; Burn et al., 2016)Delayed timing and greater variability in the annual low flow; increasing mean of and variance in November's flowAtlanticSeaboard (north)C5 to C3Increasing spring flows, corresponding to increased snow precipitation (Thistle and Caissie, 2013)Increasing monthly flow in April; decreasing monthly flow in June; delayed and less variable timing of low flows; less variation in annual timing of high flows; decreasing mean of and variation in monthly flow in AugustSeaboard (south)Case 1: C5 to C4 Case 2: C3 to C5Case 1: decline in the annual flow (Whitfield and Cannon, 2000; Yue et al., 2003; Thistle and Caissie, 2013) Case 2: decline in winter flows probably due to positive Atlantic Multidecadal Oscillation (Whitfield and Cannon, 2000; Assani et al., 2012)Case 1: decreasing monthly flow in May, June, and August; increasing monthly flow in March; decreasing variability in February's monthly flow. Case 2: decreasing monthly flow in May and June; later timing of low flowsSt. Lawrence (north)C3 to C1Smaller variations in timing of low flow (Thistle and Caissie, 2013)Decreasing annual flow, as well as seasonal flows, in summer and winter; decreasing monthly flows in June; less variation in monthly flows of February, May, and JuneSt. Lawrence (south)C1 to C3No earlier study in this region foundIncreasing mean of and variation in monthly May flows; decreasing mean of and variation in September flows; decreasing flow in October; increasing flow in February; increasing variance in timing of low flows; increasing variability in January's monthly flowsSaint John-St. CroixC5 to C4Decreasing monthly flow in May (Kingston et al., 2011)Decreasing annual flow; deceasing monthly flows in February and June; decreasing mean of and variability in monthly flows in October and August
Continued.
BasinSub-basin (stream location)Dominant regime shiftsEarlier findings on changes in streamflow characteristics (reconfirmed in this study)New findings on changes in streamflow characteristics (discovered exclusively in this study)ArcticSeaboardC1 to C2Earlier and more variable timing of high flows; increasing winter flows (Burn, 2008; Déry et al., 2016); earlier timing of high flows (Yang et al., 2015)Increasing mean of and variability in seasonal flow in fall; heightened variability in monthly flow in JuneLower MackenzieC1 to C2Increasing annual and winter flows (Smith et al., 2007; Walvoord and Striegl, 2007; St. Jacques and Sauchyn, 2009; Rood et al., 2016)Increasing annual and seasonal flows during fall; increasing monthly flow in June; heightening variability in the timing of high flowsPeace–AthabascaC2 to C1Decreasing monthly flow in July (Yang et al., 2015)Earlier and less variable timing of low flowsHudson BayWestern and Northern Hudson BayC1 to C3Increasing winter flows; decreasing summer flows; increasing variability in winter flows (Déry et al., 2011, 2018)Delayed and more variable timing of low flows; increasing variability in February's monthly flowNorthern Québec and OntarioC1 to C2Increasing annual and winter flows; increasing variability in timing of high flows (Déry et al., 2011)Increasing annual and seasonal fall and summer flows; decreasing and less variable monthly flows in May; decreasing monthly flow in JuneNelsonC1 to C3Decreasing summer and fall flows (Rood et al. 2008); decreasing summer flows; increasing variability in fall and spring flows (Déry et al., 2011)Decreasing monthly flow in May and June; increasing variability in timing of low and high flows; increasing annual flow and seasonal flows in summer and winter
Validation of the proposed algorithm in nine
out-of-sample streams during 1976 to 2010 in the Canadian Prairies. The
colour bars in the left map show the degrees of membership to each cluster.
The right panel shows the trends in the degree of membership in the six
clusters at the 11 stations considered. Positive and negative trends are
shown with red and blue colours, respectively. Sharp colours show significant
cases. The out-of-sample stations S1 to S9 are sorted from east to west from
the top to the bottom.
Table 4 makes a clear distinction between the earlier findings and those
exclusively found in our study. Even though earlier studies have different
data periods and may include streams that are not within the RHBN streams,
our study reconfirms previous findings and also discovers new changes in
streamflow characteristics that have remained previously overlooked. Our
study clearly shows that changes in variability in monthly, seasonal, and
annual flows can be important drivers of shifts in streamflow regimes across
the majority of sub-basins in Canada. This is another line of evidence for
the complex and multifaceted nature of change in streamflow regimes and the
need for a simultaneous look at alterations in both expected values and
variability in streamflow characteristics to diagnose changes in natural
streamflow regimes.
Concluding remarks and outlook
This study presents an attempt toward providing a globally relevant
algorithm for identifying changing streamflow regimes. The proposed approach
is based on two fundamental considerations. First, a streamflow regime is
collectively formed by a large number of streamflow characteristics. Second,
streamflow types are rather in the form of spectrums, not clear-cut states;
if regime shifts are caused by climate change, the transition from one
regime type to another should be gradual rather than abrupt. To accommodate
these two considerations, we suggest representing streamflow regime types as
intersecting fuzzy sets in such a way that the belongingness of each stream to
each regime type can be quantified by a membership function. Accordingly,
monitoring the trends in membership values in time and space can provide a
basis to identify the regime shift from one type to another. We consider the
existence of a significant trend in membership values as evidence for the
regime shift. In addition, analyzing the covariance of membership values
with streamflow characteristics can provide a basis to attribute regime
shifts to alterations in certain streamflow characteristics in time and/or
space. A significant dependence between a given regime shift and
simultaneous alterations in streamflow characteristics highlights
attribution, which can be communicated by R2.
To apply this algorithm, we consider 45 years of daily data from 105 RHBN
streamflow gauges across Canada to provide a comprehensive and temporally
homogeneous look at forms and extents of change in natural streamflow regime
in Canada, from coast to coast to coast. Our results show that streamflow regimes
in Canada can be categorized into six distinct regime types with clear
physical and geographical interpretations. Analyses of trends in membership
values show that alterations in natural streamflow regimes are vibrant and
can be different across different regions. Overall, in more than 80 % of
the considered streams there is a dominant regime shift that can be
attributed to changes in streamflow characteristics. At the ecozone scale,
the dominant regime shifts are from C1 to C2 in the northern ecozones (EZ5
and EZ12), from C2 to C1 and from C2 to C3 in the western ecozones (EZ9 and
EZ14), from C2 to C3 at the two stations located in the Prairies, from C1 to
C3 in the eastern ecozones (EZ6, EZ8, and EZ15), and from C5 to C4 in the
Appalachian region (EZ7 and eastern part of EZ6). The variability between
the regime shifts inside each ecozone can be described by elevation and/or
latitude. At the basin scale, dominant modes of transition are from C3 to C1
in the northern Pacific and from C1 to C3 in the southern Pacific, between
the C4 and C5 regimes, as well as C3 and C5, in the Atlantic, between
C1 and C2 in the Arctic, and between the C1 and C3, as well as C2 and C3,
regimes in Hudson Bay. The details of change in streamflow regime, however,
are subject to a spatial variability within each drainage basin. In the Atlantic
and Pacific regions, there are clear divides between dominant regime shifts
in northern and southern regions. For instance, In the Pacific, the
association to C1 is increasing in Yukon and northern parts of the Columbia and
Fraser sub-basins, but it is significantly decreasing in the southern
regions. This can be due to different manifestations of climate change,
which are more apparent as temperature increases in the north and growing
ratios of rain over precipitation in the south, shifting the streamflow more
toward rain-dominated regimes (Fleming and Clarke, 2003). This reconfirms
the important role of latitude in driving the streamflow response to climate
change.
The proposed framework provides an opportunity to identify the changing
streamflow regimes and attributes such changes to a large set of streamflow
characteristics. This approach, however, does not explore the attribution of
the shifts in streamflow regimes to the changes in temperature pattern, form
and magnitude of precipitation, snowmelt, glacial retreat, and permafrost
degradation. These can be potential areas for future research. We hope our
study triggers more attention to the multifaceted nature of change in streamflow
regimes in Canada and the rest of the world during the current Anthropocene.
Data availability
The analysis is based on data provided by the Reference Hydrometric Basins
Network (RHBN) of Environment Canada. The data set can be accessed through the
streamflow records of HYDAT, complied by the Water Survey of Canada (2020), https://collaboration.cmc.ec.gc.ca/cmc/hydrometrics/www/, last access: August 2021).
Video supplement
The evolution of regime types in archetype natural streams in Canada; data provided by Water Survey of Canada (Zaerpour, 2021): 10.4211/hs.da68a6ec2e2946b48075ac1ba4bb21cd.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-25-5193-2021-supplement.
Author contributions
MZ, AN, and SH designed the methodology. MZ and SH developed the
computational procedure. MZ executed the literature review and the numerical
work. MZ and AN analyzed the results and developed manuscript outline and
flow. MZ and SH developed the figures. MZ wrote the first draft. AN, SH, and
JS commented on and revised the paper. AN and MZ finalized the manuscript. AN
supervised the work and acquired the funding.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Elmira Hassanzadeh of Polytechnique Montréal provided valuable inputs on earlier versions of this paper. The paper has also benefited tremendously from thorough, constructive, and selfless comments from the editor, Kerstin Stahl, and two anonymous reviewers. We can clearly see the positive impacts of these comments on our final product.
This study is conducted with love and sweat, and it is dedicated to the memory of Richard Janowicz, the iconic Yukon-based hydrologist who made fundamental discoveries on recent changes in natural streamflow regimes in the Great White North: northern hydrology owes you, Rick.
Financial support
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (grant no. RGPIN/5470-2016) and Concordia University (grant nos. V01182 and VC0025).
Review statement
This paper was edited by Kerstin Stahl and reviewed by two anonymous referees.
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