Geomorphological controls on streamflow response

Abstract:

1 Introduction

Conventionally, parameterization of hydrological models has been done by statistical analysis of how the catchment has been responding to meteorological inputs in the past. This requires historical data series for calibration and validation purposes, which might rarely represent the entire hydrological range that one wants to predict, implying that models often has to be extrapolated beyond the conditions for which they have been calibrated/validated. By basing the parameterization in physical catchment properties and process understanding (rather than statistical parameterisation) hydrological predictions are expected to become more reliable - during extreme conditions as well as during changing conditions such as climate change and landscape modifications, and/or when making predictions in ungauged basins.

Through comparative hydrology [Viglione et al., 2010], methods are sought to determining and understanding the hydrological similarity (e.g. between events and/or catchments), where the travel time distributions through the catchment can be used as a descriptor of the flow behaviour, [Rinaldo et al., 1991; McDonnell et al., 2010; Viglione et al., 2010]. The travel time distribution within stream channels is known to vary non-linearly with stage (discharge), depending on the combined effects of geomorphologic, hydrodynamic and kinematic dispersions. This non-linearity, implies that the stream network travel time decreases with increasing discharge - a factor that is important to account for in hydrological modelling, especially when making peak flow predictions where uncertainty is often high and large values can be at risk.

2 Objectives

The objective of this study revolves around the issue of deriving catchment-specific travel time distributions within the stream networks, i.e., the focus is solely put on the on the hydrodynamical mechanisms within the stream network (not e.g. the hillslope response). Through distributed routing in several stream networks in Sweden, the influence of, stage-dependency, flooded cross-sections and backwater effects are investigated. The primary focus is then put on how the derived stage-dependent travel time distributions can be linked to the geomorphological properties of the catchments. The primary focus is on the linkage between the derived stage-dependent travel time distributions and the geomorphological properties of the catchments. The purpose is to derive physically based catchment-specific streamflow response functions based in hydrodynamical theory using easily obtainable geomorphological properties (derived from DEMs, remote sensing etc.).

3 Methods

Through hydraulic analysis of several stream networks, we analyse how travel time distributions varies with discharge. For each of the studied stream networks, a 1D, steady-state, distributed routing model was set up to determine the velocities in each reach during different flow conditions [Åkesson and Wörman, 2012]. Although the model (based in the Manning friction formula) is built on the assumption of uniform conditions within sub-reaches, the model can on the stream network scale be considered to include effects of non-uniformity as supercritical conditions in sections of the stream network give rise to backwater effects that reduce the flow velocities in upstream reaches in the stream. By coupling the routing model to a particle tracking routine tracing water “particles” through the stream network, the average travel time within the stream network can be determined quantitatively for different flow conditions. The data requirements for the model are digitised stream network maps, topographical data (DEMs). The model is not calibrated in any way, but is run for different sets of parameters representing a span of possible friction coefficients and cross-sectional geometries. The model is then run for different discharges, assuming steady-state conditions during every model run to obtain an unambiguous relationship between stream network travel time and discharge. The routing model is implemented in several different stream networks (representing catchments of the spatial scale of a few hundred km²) in different geographic regions in Sweden displaying different geomorphological properties. With the objective being to find generalised methodologies to derive catchment-specific expressions for the streamflow response, the travel time distributions of the different studied catchments are normalised in different ways (for example by the average discharge, the average stream length, the average slopes, etc.) to be able to identify the key factors when determining the streamflow response.

4 Results and discussions

The results indicate (in analogy with e.g. the Manning equation) that the stream network travel time decreases non-linearly with stage (discharge). Also, it is shown to increase with extended degree of flooding and with increasing value of the friction coefficient. Previous studies have shown that using the inverse of the stage-dependent average travel time as a response coefficient for the streamflow subroutine of a lumped hydrological model (rather than a conventional, statistically derived and stage-independent response coefficient) improves the hydrological predictions, especially for peak flows [Åkesson and Wörman, 2012; Åkesson et al., 2014].

The results of the distributed routing also show that the geomorphological effects associated with backwater effects have a pronounced influence on the total stream network travel time, i.e., the very low velocities occurring in low gradient sub-reaches have a more dominant role on the total travel time compared to the differences due to variations in friction coefficients and cross-sectional geometries [Åkesson et al., 2014]. This suggests that knowledge of the geomorphological properties of the stream network (stream length, topography and topology) generally will be of relatively larger importance for determining stream network travel times than the exact knowledge of factors such as cross-sectional geometries and friction coefficients within individual reaches. These results are consistent with previous studies [e.g., Saco and Kumar, 2002], showing that the hydrodynamical dispersion have substantially smaller effect on the travel time distribution than the geomorphological and kinematic dispersion.

The kinematic dispersion is interrelated to the geomorphological dispersion as the location of low-velocity sub-reaches within a catchment influences the impact on the total travel time. Commonly in basins you will find steeper reaches in the headwaters and flatter reaches towards the catchment outlet [Saco and Kumar, 2002; Viglione et al., 2010], meaning that these low-gradient reaches can have a pronounced effect on the network-averaged travel time as all water in the catchment will travel through these downstream reaches. As the geomorphological properties often are available in the form of maps and/or DEMs of individual stream networks, it would be valuable to find explicit ways of incorporating this information into the streamflow response functions of lumped hydrological models.

5 Conclusions

The average travel time through a stream network has been shown to be a non-linear process, with higher flow velocities and, consequently, shorter travels times as the discharge increases. Although the stream reach hydraulic properties have an impact on the stream network travel time distributions, the streamflow response is primarily governed by the large-scale geomorphological properties in the landscape. Particularly, the spatial location of the low-gradient zones within the stream network has a large influence on the travel time. By coupling generic hydrodynamical relationships, reflecting the flow velocity as function of the discharge, with catchment-specific measures of the geomorphological properties, physically based streamflow response functions can be derived, facilitating hydrological predictions during extreme conditions as well as for catchment subjected to landscape and/or climate change.

Acknowledgements

This study was financially supported by Elforsk AB, as a part of the research activities of the Swedish Hydropower Centre (SVC). Thanks are also due to Göran Lindström and his colleagues at the Swedish Meteorological and Hydrological Institute for their co-operation.

References

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