Introduction
Hydrologists typically acquire process knowledge from detailed place
based studies and from representative experimental catchments, where
hydrometric and biophysical attributes can be intensively measured over
time. There are are large number of global catchment observation
networks, yet in many parts of the world they are in decline due to the
expense in establishing, operating and maintaining their infrastructure
(Laudon et al., 2017). Consequently, extrapolating process knowledge to
watersheds that are hydrologically similar, yet not necessarily
measured, has been a major focus of the hydrological community for the
past several decades with initiatives such as the Prediction in Ungauged
Basins (PUB) program (Sivapalan et al., 2003), whose goal was to predict
flow quantiles at ungauged or poorly gauged basins according to the
historical flow data collected at hydrologically similar basins.
Catchment classification has a long history as a means to generalize the
functional behaviour that exists within watersheds, quantify their
similarity, and to transfer information among them (Wagener et al.,
2007). While there is no universal hydrological classification, the
degree of similarity that exists is often defined from intrinsic and
response characteristics of watersheds such as: climate (e.g.
temperature, precipitation), watershed biophysical characteristics (e.g.
geological conditions, soil type, relief, and vegetation), and the flow
regime (e.g. annual hydrograph). Climate indices for classification
(e.g. K¨oppen, Thornthwaite) are widely applied at varying time scales
and have an extremely long history identifying the intrinsic
seasonality, thermal and moisture regimes of a region. Physiographic and
biophysical indices such as soils, topography and geology strongly
influence catchment behaviour (Buttle, 2006; Bormann, 2010), yet are not
always ideal in defining process controls on catchment behaviour across
scales and regions (Merz and Bloschl, 2005). Often, catchments with
similar climate and physical conditions are not hydrologically similar
(Oudin et al., 2010; Ali et al., 2012).
Evaluating catchment similarity based solely in terms of streamflow
characteristics is popular; particularly in aquatic ecology where
habitats are particularly sensitive to flow regimes (Poff et al., 1997).
However, as Sawicz et al. (2011) notes, ecological studies are not
typically aimed at understanding the behaviour of the catchment
including the causes of a particular regime. Over time, the flow regime
of a catchment is a descriptor of the seasonal behaviour of the
streamflow (Haines et al., 1988) and by its nature is an integrator of a
variety of hydrological processes produced by the interaction between
climate and catchment physical characteristics. After decades of
development, there are hundreds of indices available which
quantitatively characterize five major components of flow regime:
magnitude, timing, duration, frequency, and rate of change (Poff et al.,
1997). Flow statistics (e.g. mean, max, and quantiles, standard
deviation) at varying temporal scale are widely-used indices that reveal
first-order information regarding magnitude, distribution, and variation
of stream flow over a period of interest (Hall and Minns, 1999; Carey et
al., 2010; Ali et al., 2012; Toth, 2013). More sophisticated indices,
often explicitly reflecting specific hydrological processes, are
preferred in catchment classification with respect to hydrological
functions and system complexity (Sawicz et al., 2011). However, it
remains a challenge to design a combination of hydrological indices that
fully describe dominant hydrological characteristics of flow regimes,
maximize distinctiveness among different flow regimes, as well as avoid
information redundancy.
Classification based on flow statistics using clustering algorithms such
as C-means and artificial neural networks (ANN) (Hall and Minns, 1999),
hierarchical models (Snelder et al., 2005), and Bayesian clustering
algorithm (Kennard et al., 2010; Sawicz et al., 2014), have been
successfully applied for catchment classification and regionalization.
The premise is to identify groups (or regions) in a way that similarity
within a region is maximized whereas similarity between regions is
minimized. Self-organized mapping (SOM), an unsupervised ANN machine
learning technique has become increasingly appealing as it produces a
low dimensional (typically two) representation of higher dimensional
data that is simple to visualize. SOM preserves the topological
structure of data as it transforms information from high-dimension
feature space, and clusters information visually on maps where clustered
points are more similar that distal points. When hydrological indices
are transformed, catchments with homogeneous features are close on the
2-D map, and distance on the map can be used to visually infer
similarity (Di Prinzio et al., 2011; Ley et al., 2011; Razavi and
Coulibaly, 2013; Toth, 2013). Previously, SOM has been applied for
catchment grouping with a moderate (∼50) number of samples (Ley et al.,
2011; Toth, 2013), yet for extremely large data sets with thousands or
millions of samples, computational time increases with sample size,
challenging the utility of SOM application for very large data sets.
The objective of this research is to design and implement a novel method
to visualize and classify streamflow regimes for a large streamflow data
set focused on undisturbed rivers western North America. The
classification is based on annual daily hydrographs (ADHs) from 304
sites over multiple years, providing 17110 ADHs for classification. The
large nature of this data set renders traditional SOM impractical, and
we therefore utilize t-distribution Stochastic Neighbor Embedding
(t-SNE), an alternative machine learning algorithm proposed by van der
Maaten (2009), to map ADHs to 2D feature space to assess flow similarity
and compare this to traditional Principal Component Analyses.
Furthermore, we develop an encoder neural network that allows additional
data to be projected on to the t-SNE map; overcoming previous challenges
with the non-parametric t-SNE technique. While this methodology only
focuses on a limited region and does not attempt a universal
classification, we attempt to show the novelty, flexibility and
potential of this approach for future classification activities.