On the Relationship Between Flood and Contributing Area

TLDR: In this article, a semi-distributed hydrological model (MESH-PDMROF) that can simulate contributing area and streamflow was employed to compare the contribution area and flood frequency distributions in a southern Manitoba, Canada catchment and test the hypothesis that the relationship between a catchment's floods and contributing area is a power function that influences the form of regional flood-area relationships.

Abstract: While it is well known that the vast majority of the time only a portion of any watershed contributes runoff to the outlet, this extent is rarely documented The power-law form of the streamflow and contributing area (Q-Ac) relationship has been known for a half century, but it is uncommon for it to be quantified or its controls evaluated In this study a semi-distributed hydrological model (MESH-PDMROF) that can simulate contributing area and streamflow was employed to compare contributing area and flood frequency distributions in a southern Manitoba, Canada catchment and test the hypothesis that the relationship between a catchment’s floods and contributing area is a power function that influences the form of regional flood-area relationships The model simulated streamflow reasonably well (Nash Sutcliffe values = 062) Modelled estimates of the area contributing to the mean annual flood were much lower (03) than those derived from independent topographic analysis (09) described in earlier literature, even after bias and error corrections Estimates of the coefficient and exponent of the Q-Ac power law function ranged from 008–014 and 09–112, respectively Lower exponent values of regional flood frequency curves suggest they are a construct of Q-Ac curves from individual basins The non-linear nature of this relationship implies any contributing area change will have a profound impact on flood magnitude The mean annual flood of the major river in this region, the Red, has increased 33 % since 1987 Applying the coefficient and exponent ranges above suggests this is associated with an expansion in contributing areas of 29–38 % There are implications for the attribution of causes and mitigation of nutrient transport from regional watersheds However, how physiography and land and water management could change Q-Ac power law exponents is poorly known and MESH-PDMROF does not provide explicit estimates of the spatial distribution of contributing area These are areas encouraged for future research

Figures

Table 3: The form of regional Q-A relationships for Red River tributaries, and the La Salle River.

Figure 5: Area – streamflow relationships for tributaries of the lower Red River. Values from the watersheds denoted by the black dots were used derive the Q2.33 – Ae relationship, while values from the watersheds represented by the grey dots were used to derive the Q100 – Ag

Figure 3: Flood frequency curves derived from the period 2002-2014 of observed (solid black line) and simulated (dashed black line) La Salle River annual maximum streamflow. The grey area denotes the probable range of contributing area fraction for each return period. The black dot represents the estimate of effective drainage area following methods by Agriculture Canada 5 (1983).

Table 1: Most influential MESH-PDMROF parameters on streamflow simulation.

Figure 1: The La Salle River Basin outlined in black. The white dot denotes the location of the Water Survey of Canada hydrometric gauge 05OG001. The grayed areas are those identified as non-contributing during the mean annual flood by Agriculture Canada (1983). 15

Figure 4: 2002-2014 time series of MESH-PDMROF simulated contributing area and observed streamflow.

Full text

1
On the Relationship Between Flood and Contributing Area
Spence Christopher
1
and Samson.Girma Mengistu
2
1
Environment and Climate Change Canada, Saskatoon, SK, CANADA
2
University of Alberta, Edmonton, AB, CANADA
5
Correspondence to: Christopher Spence (chris.spence@canada.ca)
Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2017-252, 2017
Manuscript under review for journal Hydrol. Earth Syst. Sci.
Discussion started: 29 May 2017
c
 Author(s) 2017. CC-BY 3.0 License.

2
Abstract: While it is well known that the vast majority of the time only a portion of any
watershed contributes runoff to the outlet, this extent is rarely documented. The power-law form
of the streamflow and contributing area (Q-A
c
) relationship has been known for a half century,
but it is uncommon for it to be quantified or its controls evaluated. In this study a semi-
distributed hydrological model (MESH-PDMROF) that can simulate contributing area and
5
streamflow was employed to compare contributing area and flood frequency distributions in a
southern Manitoba, Canada catchment and test the hypothesis that the relationship between a
catchment’s floods and contributing area is a power function that influences the form of regional
flood-area relationships. The model simulated streamflow reasonably well (Nash Sutcliffe
values = 0.62). Modelled estimates of the area contributing to the mean annual flood were much
10
lower (0.3) than those derived from independent topographic analysis (0.9) described in earlier
literature, even after bias and error corrections. Estimates of the coefficient and exponent of the
Q-A
c
power law function ranged from 0.08 – 0.14 and 0.9 - 1.12, respectively. Lower exponent
values of regional flood frequency curves suggest they are a construct of Q-A
c
curves from
individual basins. The non-linear nature of this relationship implies any contributing area change
15
will have a profound impact on flood magnitude. The mean annual flood of the major river in
this region, the Red, has increased 33% since 1987. Applying the coefficient and exponent
ranges above suggests this is associated with an expansion in contributing areas of 29 – 38%.
There are implications for the attribution of causes and mitigation of nutrient transport from
regional watersheds. However, how physiography and land and water management could
20
change Q-A
c
power law exponents is poorly known and MESH-PDMROF does not provide
explicit estimates of the spatial distribution of contributing area. These are areas encouraged for
future research.
Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2017-252, 2017
Manuscript under review for journal Hydrol. Earth Syst. Sci.
Discussion started: 29 May 2017
c
 Author(s) 2017. CC-BY 3.0 License.

3
1 Introduction
The concept that the dynamics of runoff contributing area control streamflow yield and flood
magnitude has existed for at least half a century. Betson (1964) was among the first to suggest
the idea that only a portion of a catchment supplies water to the outlet when he introduced the
partial area concept which describes the spatial manifestation of Hortonian overland flow. After
5
saturation overland flow was identified (Hewlett and Hibbert, 1963), the perception of possible
contributing area controls and dynamics expanded as it became recognized that subsurface
conditions could also control expansion and contraction of these areas (Hewlett and Hibbert,
1967; Dunne and Black, 1970). If ‘contributing area’ can be defined as that area that provides
water to a catchment outlet over a defined period, for instance a rainfall-runoff event and a
10
water-year, it has become evident from the literature (Beven and Wood, 1983; Devito et al.,
2005; Tetzlaff et al., 2007) that how this area manifests is not only a function of predominant
hydrological processes, as noted above, but also heteorogeneity in landscape topography,
topology and typology.
15
Static physiographic characteristics control where contributing area is likely to occur, but it is
variable atmospheric and soil climate conditions that control the temporal variability of
contributing area. The state of contributing area is a function of the magnitude of water
available, the distribution of water storage, and rates of loss along runoff pathways. Some of the
original investigations of the relationship between contributing area and runoff response were
20
based upon the idea that the fraction of the basin that was an effective contributing area during a
storm was simply the ratio of storm runoff to effective precipitation (Dickinson and Whiteley,
1970) and this approach has been applied to evaluate relationships between contributing area and
Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2017-252, 2017
Manuscript under review for journal Hydrol. Earth Syst. Sci.
Discussion started: 29 May 2017
c
 Author(s) 2017. CC-BY 3.0 License.

4
antecedent conditions (Gburek, 1990). Dry regions or periods typically experience conditions
where there is no area contributing to flow, essentially resulting in the disappearance of the
stream. The distribution and application of water to the catchment during such conditions can
have a profound impact on the extent of contributing areas and the duration they remain, and in
turn, how catchment streamflow responds (Jencso et al., 2009; Spence et al., 2010). It would be
5
wrong to suggest contributing area dynamics are arguably more predictable in wetter conditions
because saturated portions of the landscape have more persistence and runoff pathways are
engaged with the stream along a smooth continuum (Dunne, 1978). Evidence suggests there
remain significant non-linearities in the relationship between contributing area and runoff
response (Dickinson and Whiteley, 1970; James and Roulet, 2007; Ali and Roy, 2010).
10
This issue of importance to hydrology is significant for biogeochemistry. The influence of
contributing area behaviour is implicitly understood to be very important for solute fluxes. The
concepts of ‘hot moments’ and ‘hot spots’ (McClain et al., 2003; Bernhardt et al., 2017) capture
this idea that there are locations and periods that provide disproportionate sources of chemical
15
loads to streams and lakes. To explain and solve many of today’s problems associated with
contaminants and excess nutrients in the aquatic ecosystem and human water supply, it is not
only necessary to identify the extent and location of contributing areas of solutes, but also the
frequency and duration with which these areas are engaged. The contributing area frequency
distribution dictates the characteristics of the periods during which constituents remain to be
20
processed on the landscape, as well as their rate of flushing (Creed et al., 1996), which is
important for controlling chemical concentrations, and in turn, loads.
Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2017-252, 2017
Manuscript under review for journal Hydrol. Earth Syst. Sci.
Discussion started: 29 May 2017
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 Author(s) 2017. CC-BY 3.0 License.

5
Unfortunately, beyond the methods discussed above that assume the runoff ratio is a substitute
for contributing area fraction, there are few examples of contributing area measurement
techniques that will enable analysis of how contributing area dynamics are controlled by climate
or landscape traits. There are common topographic index methods to estimate contributing area
(Beven and Wood, 1983), but these assume saturation overland flow and the variable source area
5
concepts are applicable. Mapping would be very useful for model validation, but is uncommon,
generally applying either remote sensing (Phillips et al., 2011) or field observations (Spence et
al., 2010). Other methodologies include the use of soil moisture indices (James and Roulet,
2007), aquatic chemistry (Ali et al., 2010), or those that map stream networks (Godsey and
Kirchner, 2014) from which contributing area can be deduced. Few of these studies have
10
developed time series robust enough to elaborate on the frequency distribution of contributing
areas. Jencso et al. (2009), Smith et al., (2013) and Reaney et al. (2013) are excellent examples
of how numerical models have been applied to fill this gap. By explicitly accounting for
hydrological connections, these models have been used to identify the frequency, duration or
extent of contributing areas in actual and synthetic watersheds. These studies were able to
15
describe some key aspects of how contributing area traits are related to flood magnitude, but did
not determine if the fundamental contributing area – streamflow relationship follows a power
law function of the form first hypothesized by Gray (1961):
    

(1)
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Before Jencso et al., (2009), the water resource community had not traditionally conceptualized
contributing area as having traits similar to floods, such as frequency, duration and extent.
Perhaps the closest useful example is from Canada. Contributing areas expected to produce the
Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2017-252, 2017
Manuscript under review for journal Hydrol. Earth Syst. Sci.
Discussion started: 29 May 2017
c
 Author(s) 2017. CC-BY 3.0 License.