A top-down model to generate ensembles of runoff from a large number of hillslopes

Furey, Peter R.; Gupta, Vijay; Troutman, Brent M.

doi:10.5194/npg-20-683-2013

Cited by 6 publications

(7 citation statements)

References 44 publications

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“…Together they produce the runoff variability across spatiotemporal scales. It would be interesting to investigate how the interactions of the spatial variation and the temporal persistence of these contributing factors lead to the behavior of runoff spatiotemporal variation, as in, for examples, Lin () and Furey and his colleagues (Furey et al, ; Furey & Gupta, ).…”

Section: Discussionmentioning

confidence: 99%

“…However, characterization of small‐scale spatial variation of event runoff yield and its temporal dynamics is limited in existing studies. One approach to work around this problem is to use statistical distributions of runoff coefficient in distributed models (e.g., Furey et al, ; Gottschalk & Weingartner, ; Merz et al, ; Viglione et al, ). Such parameterization of spatial runoff variability will benefit from empirical evidence obtained by analyzing observational data.…”

Section: Introductionmentioning

confidence: 99%

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Spatial Variability and Temporal Persistence of Event Runoff Coefficients for Cropland Hillslopes

Chen

Krajewski

Helmers

et al. 2019

Water Resources Research

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Using data collected from collocated hillslopes in central Iowa, the United States, the authors (1) explored the spatial variability of runoff coefficient at the event scale by examining the relationships between the standard deviation and coefficient of variation of runoff coefficient and the mean and (2) analyzed the temporal persistence of spatial pattern of runoff coefficient using Spearman rank and Pearson correlation coefficient. This study considered 12 cropland hillslopes with 0-20% native prairie vegetation coverage distributed at different hillslope locations. Seventy runoff events over the period 2008-2011 were investigated, of which 51 occurred during crop active growing season, when the hydrologic responses of crops and prairie vegetation are similar. For these events, the spatial coefficient of variation had a median value of 0.80, which indicate high variation of event-scale runoff coefficients across neighboring hillslopes. This spatial variation largely cannot be consistently explained by the individual hillslope structural properties investigated. The standard deviation and mean of runoff coefficient showed a convex upward relationship across the range of runoff coefficients, with the maximum standard deviation value at the mean runoff coefficient of about 0.48. The coefficient of variation exponentially decreased with increasing runoff coefficient. For 71% of the cases, the results of both correlation analyses were statistically significant (p ≤ 0.05), which indicate stable spatial pattern of runoff coefficient across events. This temporal persistence could be disrupted under extremely dry and wet conditions. The spatial variation-mean empirical relation and the temporal persistence of spatial pattern provide insight for parameterizing spatial variability of runoff coefficient in distributed hydrologic models.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial Variability and Temporal Persistence of Event Runoff Coefficients for Cropland Hillslopes

Chen

Krajewski

Helmers

et al. 2019

Water Resources Research

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“…Three different methods as outlined in Eqs. (1), (5), and (15) from a large number of hillslopes (Furey et al, 2013). We do not discuss this issue here any further.…”

Section: Applications Of the Horton Laws For Diagnosing A Rainfalmentioning

confidence: 96%

“…Furey et al (2013) addressed this long-standing problem and hypothesized, based on basin-and point-scale observations taken from the 21 km 2 Goodwin Creek Experimental Watershed (GCEW) in Mississippi, USA, that total hillslope water loss for a rainfall-runoff event is inversely related to a function of a lognormal random variable. They used a "topdown approach" to develop a new runoff generation model in order to test their physical-statistical hypothesis and to provide a method for generating ensembles of runoff from a large number of hillslopes.…”

Section: Self-similarity and Horton Laws: A Brief Reviewmentioning

confidence: 99%

Classical and generalized Horton laws for peak flows in rainfall-runoff events

Gupta

Ayalew

Mantilla

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km(2) before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.

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“…Given space-time rainfall intensity field for any rainfallrunoff event, the theory attempts to predict stream flow hydrographs at all the "junctions" (where two or three channels meet) in a channel network. The theory requires a model to transform rainfall to runoff in space and time in a basin (Furey et al, 2013), and space-time river flow dynamics in a network (Mantilla, 2007). Modeling of flow dynamics requires a theory of H-G in a channel network, because practically no such data sets exist.…”

Section: K Gupta and O J Mesa: Horton Laws For Hydraulic-geometmentioning

confidence: 99%

Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks

Gupta

Sánchez

2014

Nonlin. Processes Geophys.

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Abstract. An analytical theory is developed that obtains Horton laws for six hydraulic-geometric (H-G) variables (stream discharge Q, width W , depth D, velocity U , slope S, and friction n ) in self-similar Tokunaga networks in the limit of a large network order. The theory uses several disjoint theoretical concepts like Horton laws of stream numbers and areas as asymptotic relations in Tokunaga networks, dimensional analysis, the Buckingham Pi theorem, asymptotic self-similarity of the first kind, or SS-1, and asymptotic self-similarity of the second kind, or SS-2. A self-contained review of these concepts, with examples, is given as "methods". The H-G data sets in channel networks from three published studies and one unpublished study are summarized to test theoretical predictions. The theory builds on six independent dimensionless river-basin numbers. A mass conservation equation in terms of Horton bifurcation and discharge ratios in Tokunaga networks is derived. Assuming that the H-G variables are homogeneous and self-similar functions of stream discharge, it is shown that the functions are of a power law form. SS-1 is applied to predict the Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynolds number are predicted and tested against three field data sets. One basin shows deviations from theoretical predictions. Tentatively assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H-G exponents are derived. Our predictions of the exponents are the same as those previously predicted for the optimal channel network (OCN) model. In direct contrast to our work, the OCN model does not consider Horton laws for the H-G variables, and uses optimality assumptions. The predicted exponents deviate substantially from the values obtained from three field studies, which suggests that H-G in networks does not obey SS-1. It fails because slope, a dimensionless river-basin number, goes to 0 as network order increases, but, it cannot be eliminated from the asymptotic limit. Therefore, a generalization of SS-1, based on SS-2, is considered. It introduces two anomalous scaling exponents as free parameters, which enables us to show the existence of Horton laws for channel depth, velocity, slope and Manning friction. These two exponents are not predicted here. Instead, we used the observed exponents of depth and slope to predict the Manning friction exponent and to test it against field exponents from three studies. The same basin mentioned above shows some deviation from the theoretical prediction. A physical reason for this deviation is given, which identifies an important topic for research. Finally, we briefly sketch how the two anomalous scaling exponents could be estimated from the transport of suspended sediment load and the bed load. Statistical variability in the Horton laws for the H-G variables is also discussed. Both are important open problems for future research.

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A top-down model to generate ensembles of runoff from a large number of hillslopes

Cited by 6 publications

References 44 publications

Spatial Variability and Temporal Persistence of Event Runoff Coefficients for Cropland Hillslopes

Spatial Variability and Temporal Persistence of Event Runoff Coefficients for Cropland Hillslopes

Classical and generalized Horton laws for peak flows in rainfall-runoff events

Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks

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