On the Relative Role of Hillslope and Network Geometry in Hydrologic Response

Mesa, Oscar J.; Mifflin, Edward R.

doi:10.1007/978-94-009-4678-1_1

Cited by 133 publications

(133 citation statements)

References 18 publications

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“…This method of expressing flow in terms of the width function is given in a number of publications in the context of GIUH (see for example Mesa and Mifflin, 1986;Marani et al, 1991;Rinaldo and Rodríguez-Iturbe, 1996 and Rodríguez-Iturbe and Rinaldo, 1997, Eq. 7.112).…”

Section: On Flowsmentioning

confidence: 99%

Scaling of peak flows with constant flow velocity in random self-similar networks

Mantilla

Gupta

Troutman

2011

Nonlin. Processes Geophys.

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Abstract.A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters p i and p e , respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β (E) and φ (E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β (E) and φ (E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ (E) and φ with respect Correspondence to: R. Mantilla (ricardo-mantilla@uiowa.edu) to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

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Section: On Flowsmentioning

confidence: 99%

Scaling of peak flows with constant flow velocity in random self-similar networks

Mantilla

Gupta

Troutman

2011

Nonlin. Processes Geophys.

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“…On the other hand, we will address the value for catchment similarity studies. Following intentions by Mesa and Mifflin (1986), who suggested the width function as an indicator of catchment similarity, it might be worthwhile to investigate how results of the distance-factor function can be used to characterize similarity.…”

Section: Discussionmentioning

confidence: 99%

“…Throughout the development and ongoing research of the geomorphologic instantaneous unit hydrograph (Rodríguez-Iturbe and Valdés, 1979;Gupta et al, 1980), the width function as introduced by Kirkby (1976) and the subsequently developed area function or weight function (Mesa and Mifflin, 1986;Snell and Sivapalan, 1994;Robinson et al, 1995) were applied to describe the distribution of runoff-producing area with respect to flow distance from the outlet (Mesa and Mifflin, 1986). In particular, the weight function provided the probability distribution for a uniform areal precipitation intensity for the choice of flow path (Snell and Sivapalan, 1994).…”

Section: Distance-factor Functionmentioning

confidence: 99%

“…In this study we will present a method to address these patterns by combining the width function (Kirkby, 1976;Mesa and Mifflin, 1986) with soil properties like pore volume and topographic characteristics like surface slope. Unlike traditional methods for spatial pattern evaluation (like point-bypoint or optimal logical alignment methods; Grayson and Blöschl, 2001) we retain the allocation of catchment properties.…”

Section: Introductionmentioning

confidence: 99%

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A method to employ the spatial organization of catchments into semi-distributed rainfall–runoff models

Oppel

Schumann

2017

Hydrol. Earth Syst. Sci.

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Abstract.A distributed or semi-distributed deterministic hydrological model should consider the hydrologically most relevant catchment characteristics. These are heterogeneously distributed within a watershed but often interrelated and subject to a certain spatial organization which results in archetypes of combined characteristics. In order to reproduce the natural rainfall-runoff response the reduction of variance of catchment properties as well as the incorporation of the spatial organization of the catchment are desirable. In this study the width-function approach is utilized as a basic characteristic to analyse the succession of catchment characteristics. By applying this technique we were able to assess the context of catchment properties like soil or topology along the streamflow length and the network geomorphology, giving indications of the spatial organization of a catchment. Moreover, this information and this technique have been implemented in an algorithm for automated sub-basin ascertainment, which included the definition of zones within the newly defined sub-basins. The objective was to provide subbasins that were less heterogeneous than common separation schemes. The algorithm was applied to two parameters characterizing the topology and soil of four mid-European watersheds. Resulting partitions indicated a wide range of applicability for the method and the algorithm. Additionally, the intersection of derived zones for different catchment characteristics could give insights into sub-basin similarities. Finally, a HBV 96 case study demonstrated the potential benefits of modelling with the new subdivision technique.

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“…By including the normalized area function, we can account for geomorphic dispersion (i.e., the attenuation of the flood peak due to the fact that rainfall that falls on the landscape will take different paths to the outlet and hence reach the outlet at different times) in our analyses. The normalized area function, A(x) (unitless), is defined as the portion of basin area, A L (x) (m 2 ), that contributes flow to the main-stem channel within a given range of distances (x) from the outlet, normalized by the total basin area, A T (m 2 ; Mesa and Mifflin, 1986;Moussa, 2008). The normalized area function is assumed to be triangular in shape, with a maximum value at the midpoint of the main-stem channel from the outlet.…”

Section: Flood Discharge Calculationsmentioning

confidence: 99%

Constraining frequency–magnitude–area relationships for rainfall and flood discharges using radar-derived precipitation estimates: example applications in the Upper and Lower Colorado River basins, USA

Orem

Pelletier

2016

Hydrol. Earth Syst. Sci.

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Abstract. Flood-envelope curves (FECs) are useful for constraining the upper limit of possible flood discharges within drainage basins in a particular hydroclimatic region. Their usefulness, however, is limited by their lack of a well-defined recurrence interval. In this study we use radar-derived precipitation estimates to develop an alternative to the FEC method, i.e., the frequency-magnitude-area-curve (FMAC) method that incorporates recurrence intervals. The FMAC method is demonstrated in two well-studied US drainage basins, i.e., the Upper and Lower Colorado River basins (UCRB and LCRB, respectively), using Stage III Next-GenerationRadar (NEXRAD) gridded products and the diffusion-wave flow-routing algorithm. The FMAC method can be applied worldwide using any radar-derived precipitation estimates. In the FMAC method, idealized basins of similar contributing area are grouped together for frequencymagnitude analysis of precipitation intensity. These data are then routed through the idealized drainage basins of different contributing areas, using contributing-area-specific estimates for channel slope and channel width. Our results show that FMACs of precipitation discharge are power-law functions of contributing area with an average exponent of 0.82 ± 0.06 for recurrence intervals from 10 to 500 years. We compare our FMACs to published FECs and find that for wet antecedent-moisture conditions, the 500-year FMAC of flood discharge in the UCRB is on par with the US FEC for contributing areas of ∼ 10 2 to 10 3 km 2 . FMACs of flood discharge for the LCRB exceed the published FEC for the LCRB for contributing areas in the range of ∼ 10 3 to 10 4 km 2 . The FMAC method retains the power of the FEC method for constraining flood hazards in basins that are ungauged or have short flood records, yet it has the added advantage that it includes recurrence-interval information necessary for estimating event probabilities.

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On the Relative Role of Hillslope and Network Geometry in Hydrologic Response

Cited by 133 publications

References 18 publications

Scaling of peak flows with constant flow velocity in random self-similar networks

Scaling of peak flows with constant flow velocity in random self-similar networks

A method to employ the spatial organization of catchments into semi-distributed rainfall–runoff models

Constraining frequency–magnitude–area relationships for rainfall and flood discharges using radar-derived precipitation estimates: example applications in the Upper and Lower Colorado River basins, USA

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