Watershed topography plays an important role in determining the spatial
heterogeneity of ecological, geomorphological, and hydrological processes.
Few studies have quantified the role of topography in various flow variables.
In this study, 28 watersheds with snow-dominated hydrological regimes were
selected with daily flow records from 1989 to 1996. These watersheds are
located in the Southern Interior of British Columbia, Canada, and range in
size from 2.6 to 1780 km
Topography plays a critical role in geomorphological, biological, and hydrological processes (Moore et al., 1991; Quinn et al., 1995). Many topographic indices (TIs) have been derived to describe the spatial patterns of a landscape (Yokoyama et al., 2002), locate spatial patterns of species (Jenness, 2004), and simulate spatial soil moisture (Park et al., 2001). In hydrology, hydrological responses are forced by climatic inputs (e.g. precipitation) but are controlled by topography and other factors such as land use and land cover (Beven and Kirkby, 1979; Hewlett and Hibbert, 1967). In describing the role of topography in hydrology, numerous TIs have been developed and applied to help understand hydrological processes and to explain the variation between watersheds (Moore et al., 1991). Although the importance of topography in controlling various flow magnitudes has been widely recognized (Price, 2011), the quantitative relationship between specific TIs and various flow variables is not well understood.
TIs can be categorized into two groups, namely, primary and secondary (or
compounded) indices (Moore et al., 1988). Primary indices (e.g. slope,
elevation, and aspect) are normally directly calculated from a digital
elevation model (DEM), while secondary indices are the combination of
primary indices that are used to explain the role of topography in
geomorphological, biological, and hydrological processes. For instance, the
topographic wetness index (TWI) is defined as ln (
Studies of watershed topography on hydrological processes often include topics such as specific discharge (Karlsen et al., 2016), spatial baseflow distribution (Shope, 2016), transit time (McGuire et al., 2005; McGuire and McDonnell, 2006), and hydrological connectivity (Jencso and McGlynn, 2011). These studies were often based on a short period of data (< 5 years), limiting our ability to draw general conclusions on how topography affects hydrological processes. Moreover, hydrological responses are compounded by the spatially diverse effects of climate, vegetation, soil, and topography (Li et al., 2017; Wei et al., 2018; Zhang et al., 2017). For example, several hydrological models have been applied to test the effects of spatial distribution of a hydrological variable (e.g. specific discharge, soil moisture, or groundwater recharge) (Erickson et al., 2005; Gómez-Plaza et al., 2001; Li et al., 2014). However, the effects of topography alone on hydrology are not usually addressed in those studies. Finally, understanding how topography influences hydrology has significant implications for sustainable management of aquatic ecosystems (Zhang et al., 2016). Therefore, the major objectives of this study were (1) to examine the role of topography in various flow magnitudes in 28 selected watersheds with snow-dominated hydrological regimes in the Southern Interior of British Columbia, Canada; and (2) to identify the most important topographic indices that can be used to compare variations in flow magnitudes between watersheds under similar climatic conditions.
In this study, 28 watersheds were selected ranging in size from 2.6 to 1780 km
Annual mean temperature (
Based on availability and representation of TIs in literature, 22
topographic indices (TIs) were derived using a gridded DEM at a spatial
resolution of 25 m (Table 1). The DEM, geospatial streamflow networks, and lakes
and wetland coverage were obtained from GeoBC (Government of British
Columbia, available at
Locations and elevations of the 28 study watersheds, and their hydrometric stations (red star symbols).
Topographic indices and descriptions.
Note that bold TIs are selected by the factor analysis test.
Annual mean flow (
Because some initially selected TIs may be highly related, the first step was to introduce factor analysis (FA) to reduce the number of TIs while still retaining important topographic information. FA can be interpreted in a similar manner as principal component analysis. The major difference between the two approaches is that FA not only considers the total variance but also makes the distinction between common and unique variance (Lyon et al., 2012). As TIs were calculated in a region with similar topography, the average TIs at the watershed level are not varied dramatically between watersheds (McGuire and McDonnell, 2006; Price, 2011). Therefore, to ensure better differentiation, the standard deviations of TIs of a watershed were used for the FA test. It should be noted that the flow variables were not included in the FA test.
Three criteria were used in the FA procedure to exclude redundant TIs: the
Kaiser–Meyer–Olkin (KMO) test, Bartlett's test, and anti-image correlation. KMO
is a measure of sampling adequacy which tests whether partial correlations
among variables are small enough to ensure the validity of the FA test.
Bartlett's test of sphericity assesses the level of correlation between the
variables in the FA to determine if the combination of variables is suitable
for such analysis (Lyon et al., 2012). The diagonals of the anti-image
correlation matrix are a measure of sampling adequacy of specific TIs, which
ensures that TIs are adequate for the FA. If a TI makes the FA indefinite,
namely KMO < 0.7, Bartlett's test
The nonparametric Kendall's tau correlation examined the statistical
correlations between flow variables and the FA-selected TIs in the 28 study
watersheds. If a significant correlation is detected, it indicates high
topographic control on that flow variable. Multiple linear regression (MLR)
models were then built for each year between 1989 and 1996 for each flow
variable (see Sect. 5 in the Supplement for details). The purposes of the MLR
models were (1) to further exclude those TIs that were insignificantly
related to flow variables, and (2) to quantify the relative contributions of
the selected TIs to each flow variable in each year. In the MLR models, each
flow variable was treated as a dependent variable, while all FA-selected TIs
were regarded as independent variables. To exclude insignificant TIs to flow
variables, all the 11 selected TIs by the FA were initially included in the
MLR model. The ANOVA (analysis of variance) test was then adopted to identify the statistical
significance between TIs and each flow variable in each year. If one TI was
insignificant (
To quantify the role of each TI in regulating each flow variable, we defined
a contribution index (CI), which can be expressed as CI
A subset of 11 TIs was selected from the initial 22 calculated TIs using the
FA procedure. The KMO test (0.853), Bartlett's test (
Factor analysis of topographic indices (TIs) among 28 watersheds. The first and second factors explained 80.9 and 11.7 % of the total variance, respectively.
The nonparametric Kendall's tau test revealed significant correlations
between the TIs and each flow variable from 1989 to 1996 (Tables S2 to S8). The number of significant TIs in each year increased from 1 to 11 with
decreasing flow magnitudes. A larger number of the TIs were correlated to
low flow variables (
The regression models between flow variables and the selected TIs were all
significant (
Relative contributions of each topographic index (TI) to
In this study, our results show that a limited number of TIs are
significantly related to the
Five TIs including perimeter, LS, SA, openness, and TCI were identified as the major contributors to flow variables in this study. As far as we know, no studies have quantified topographic controls on various flow magnitudes. Nevertheless, the relationship between topography and the mean transit time (McGuire and McDonnell, 2006), temporal specific discharge (Karlsen et al., 2016), and hydrological connectivity (Jencso and McGlynn, 2011) have been investigated. There is no doubt that topography is one of the major contributors to hydrological variations (Price, 2011; Smakhtin, 2001). Although these studies pinpointed specific TIs and their interactions with hydrological responses, only a limited number of TIs were quantitatively assessed. In contrast, a total number of 22 TIs were calculated for 28 watersheds in this study. The much higher number of TIs that were initially included, along with the filtering methods applied, allowed us to select more suitable and significant TIs. Through this study design, we expect that the five selected TIs can effectively be used to support assessment or comparisons of low flows between watersheds in the study region. It should also be noted that we only selected the first five TIs that had substantially higher contributions than the other calculated TIs. The rest of the hydrological-related TIs showed only a minor ability to explain flow variations.
Among the five selected TIs, the perimeter, a primary TI, is commonly used in scientific studies to describe the characteristics of watershed topography. Our study further proves that it has a large influence on low flow variables. However, four secondary TIs (LS, SA, openness, and TCI) are mainly used in geomorphology to characterize ruggedness or roughness of landscapes and to identify topographic functioning of ecosystems. For examples, TCI has been used to map soil organic matter concentration (Zeng et al., 2016). Park et al. (2001) revealed that TCI is a better TI to predict soil depth than TWI, plan curvature, and profile curvature (see definitions in Table 1). LS is one of the key inputs to the Universal Soil Loss Equation being used to quantify soil erosion hazards (Desmet and Govers, 1996). SA was used to estimate animal species and habitat (Jenness, 2004) and map the spatial patterns of a floodplain (Scown et al., 2015). Openness was initially adopted to identify the boundary of different geological units and can be used to identify surface convexities and concavities, which is better than the commonly used profile and plan curvature (Yokoyama et al., 2002). In this study, the five selected TIs were initially filtered by the FA test, indicating that each selected TI has uniqueness in describing watershed topographic characteristics and outperformed the other tested TIs in describing variation in flow variables in our study region. Therefore, we expect that the five selected TIs can be applied to support hydrological analysis and modelling.
To our surprise, some commonly used TIs in hydrology, such as slope, median elevation, upslope contribution area, and wetland areas are not included in the FA list as the topographic information contained in those primary TIs also exists in some secondary TIs. Secondary TIs have the advantage of describing the hydrology-related landscapes in fuller detail. For example, slope is directly included in calculations of the TWI (secondary) and DDG (secondary). UCA (primary TI) is included in TWI and TCI (secondary). It is also worth mentioning that some secondary TIs played critical roles in determining the spatial heterogeneity of ecological and geomorphological processes, but their roles in hydrological processes in our study region were not demonstrated. These TIs were, therefore, not selected in this study. For example, the TWI has long been used as a key input variable for TOPMODEL and is an indicator of soil moisture (Beven, 1995). Our study identified that TWI and wetland area were not significantly related to flow variables, indicating that these factors played a limited role in the selected flow variables in our region. This may be because the watersheds in this area need to overcome a soil moisture storage threshold prior to releasing water (Karlsen et al., 2016). In summary, our selected five TIs significantly represent low flow characteristics of the watersheds in the Southern Interior of British Columbia, Canada, which is characterized by a snow-dominated hydrological regime.
In our study, FA was first introduced to exclude reductant TIs. The MLR
models were further employed to exclude the insignificant TIs to various
flow magnitudes. There is a concern whether the TIs excluded by FA were
significantly related to flow magnitudes but not included in the MLR
models. To address this concern, we re-ran a subset of analyses by
conducting the MLR models for
There are several uncertainties in our study. Firstly, hydrological
responses are the resultant effects of climate, soil, vegetation,
topography, and geology (Price, 2011; Smakhtin, 2001). In this study, the
LAI, which represented the variations of vegetation cover in different watersheds, was
included in our analysis in order to minimize the effects of different
levels of vegetation coverage in the study watersheds. However, it was
excluded by the FA test, confirming that the differences in vegetation cover
and their effects were minor; therefore our selected watersheds are comparable
in terms of forest coverage. In addition, the climate could be a confounding
factor affecting our comparisons. In this study, annual flow variables were
standardized by the annual precipitation to minimize the effects of climate
on flow variables. In this way, the effects of climate variability were
considered to some extent, but not in full detail. For examples, in extreme
dry or wet years (e.g. 1994 and 1996 are the driest and wettest years in
our study period, respectively) (Figs. S2–S5), hardly any of the TIs were
significantly correlated to
This study concludes that topography plays a significant role in low flows, while its role in high flows is limited. A total number of five topographic indices, including perimeter, LS (slope length factor), SA (surface area), openness, and TCI (topographic characteristic index), were identified with significant contributions to low flow variables. It is recommended that these five above-mentioned TIs can be used to assess the magnitude of low flows in a study region which is characterized by a snow-dominated hydrological regime with watershed sizes up to several thousand square kilometres. Our research methodology can be applied to other regions for investigating how topography controls flow magnitudes.
Topographic indices of study watersheds are freely available upon request by sending an email to the corresponding author.
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
We thank Environment Canada and GeoBC for their data on streamflow and DEM. The authors would also like to thank the editor (Thom Bogaard) and two reviewers (Petra Hulsman and Niclas Hjerdt) for their constructive comments on the earlier version of the paper. The research funding for supporting this project was provided by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2015-06032), the National Natural Science Foundation of China (numbers 41771415 and 31770759), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (number: 164320H116). Edited by: Thom Bogaard Reviewed by: Niclas Hjerdt and Petra Hulsman