Comparison of three Models of Avalanche Dynamics

Results and characteristics of three models for estimating avalanche flow speeds, flow heights, and run-out distances are compared: (1) Voellmy–Salm equation used with the traditional release, track, and run-out segmentation method; (2) Voellmy–Salm differential equation solved numerically along longitudinal profiles of avalanche paths, combined with modified assumptions for the flow in the run-out zone; (3) a granular-flow model introduced by Salm and Gubler. Within the limits of the accuracy of the field observations, all models are able to predict run-out distances correctly, at least for large avalanches, but the Voellmy–Salm type models significantly underestimate flow speeds. Modelling different flow regimes (sliding and partial fluidization) increases the range of avalanche sizes for which correct run-out modelling is possible without recalibration of model parameters.

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Avalanche Flow Dynamics with Material Locking

Annals of Glaciology ◽

10.1017/s0260305500009885 ◽

1985 ◽

Vol 6 ◽

pp. 5-8 ◽

Cited By ~ 4

Author(s):

Theodore E. Lang ◽

Tsutomu Nakamura ◽

Jimmle D. Dent ◽

Mario Martinelli

Keyword(s):

Flow Model ◽

Parameter Variation ◽

Uniform Flow ◽

Flow Dynamics ◽

Low Flow ◽

Snow Avalanches ◽

Total Drag ◽

Flow Equations ◽

Flow Speeds ◽

Avalanche Flow

Reported are results of incorporating recent snow avalanche processes into hydrodynamic uniform flow equations, used to model motion of snow avalanches. Actual modifications include the relating of dissipative coefficients of the flow model to slab release depth, the representation of the material as a locking fluid, and the mini-segmentation of the avalanche path at low flow speeds in order to numerically accomodate viscous transition and avalanche cessation of motion. The purpose in looking at different formulations of the uniform flow hydrodynamic flow equations is to reduce the variation in the drag coefficients when the theory is applied to different avalanche paths, as compared to what has been previous experience. The model that reduced parameter variation the most was one in which the total drag force decreased in an intermediate velocity range, a mechanism that has had recent experimental verification.

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Avalanche Flow Dynamics with Material Locking

Annals of Glaciology ◽

10.3189/1985aog6-1-5-8 ◽

1985 ◽

Vol 6 ◽

pp. 5-8 ◽

Cited By ~ 1

Author(s):

Theodore E. Lang ◽

Tsutomu Nakamura ◽

Jimmle D. Dent ◽

Mario Martinelli

Keyword(s):

Flow Model ◽

Parameter Variation ◽

Uniform Flow ◽

Flow Dynamics ◽

Low Flow ◽

Snow Avalanches ◽

Total Drag ◽

Flow Equations ◽

Flow Speeds ◽

Avalanche Flow

Reported are results of incorporating recent snow avalanche processes into hydrodynamic uniform flow equations, used to model motion of snow avalanches. Actual modifications include the relating of dissipative coefficients of the flow model to slab release depth, the representation of the material as a locking fluid, and the mini-segmentation of the avalanche path at low flow speeds in order to numerically accomodate viscous transition and avalanche cessation of motion. The purpose in looking at different formulations of the uniform flow hydrodynamic flow equations is to reduce the variation in the drag coefficients when the theory is applied to different avalanche paths, as compared to what has been previous experience. The model that reduced parameter variation the most was one in which the total drag force decreased in an intermediate velocity range, a mechanism that has had recent experimental verification.

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Algebraic Solution of the Horton-Izzard Turbulent Overland Flow Model of the Rising Hydrograph

Hydrology Research ◽

10.2166/nh.1977.0019 ◽

1977 ◽

Vol 8 (4) ◽

pp. 249-256 ◽

Cited By ~ 2

Author(s):

Mohammad Akram Gill

Keyword(s):

Differential Equation ◽

Turbulent Flow ◽

Flow Model ◽

Overland Flow ◽

Flow Equation ◽

Algebraic Solution ◽

Mixed Flow ◽

Overland Flow Model

In the differential equation of the overland turbulent flow which was first postulated by Horton, Eq.(6), the value of c equals 5/3. For this value of c, the flow equation could not be integrated algebraically. Horton solved the equation for c = 2 and believed that his solution was valid for mixed flow. The flow equation with c = 5/3 is solved algebraically herein. It is shown elsewhere (Gill 1976) that the flow equation can indeed be integrated for any rational value of c.

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A stochastic differential equation model of diurnal cortisol patterns

AJP Endocrinology and Metabolism ◽

10.1152/ajpendo.2001.280.3.e450 ◽

2001 ◽

Vol 280 (3) ◽

pp. E450-E461 ◽

Cited By ~ 41

Author(s):

Emery N. Brown ◽

Patricia M. Meehan ◽

Arthur P. Dempster

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Plasma Cortisol ◽

Equation Model ◽

Plasma Cortisol Level ◽

Model Parameters ◽

Kinetic Properties ◽

Simulation Studies ◽

Physiological Factors ◽

Diurnal Patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

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Prediction of snowmelt derived streamflow in a wetland dominated prairie basin

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-7-1103-2010 ◽

2010 ◽

Vol 7 (1) ◽

pp. 1103-1141 ◽

Cited By ~ 2

Author(s):

X. Fang ◽

J. W. Pomeroy ◽

C. J. Westbrook ◽

X. Guo ◽

A. G. Minke ◽

...

Keyword(s):

Soil Moisture ◽

Hydrological Model ◽

Snow Accumulation ◽

Model Parameters ◽

Field Observations ◽

Runoff Generation ◽

Stream Channels ◽

Physically Based ◽

Set Up ◽

Spot 5

Abstract. The eastern Canadian Prairies are dominated by cropland, pasture, woodland and wetland areas. The region is characterized by many poor and internal drainage systems and large amounts of surface water storage. Consequently, basins here have proven challenging to hydrological model predictions which assume good drainage to stream channels. The Cold Regions Hydrological Modelling platform (CRHM) is an assembly system that can be used to set up physically based, flexible, object oriented models. CRHM was used to create a prairie hydrological model for the externally drained Smith Creek Research Basin (~400 km2), east-central Saskatchewan. Physically based modules were sequentially linked in CRHM to simulate snow processes, frozen soils, variable contributing area and wetland storage and runoff generation. Five "representative basins" (RBs) were used and each was divided into seven hydrological response units (HRUs): fallow, stubble, grassland, river channel, open water, woodland, and wetland as derived from a supervised classification of SPOT 5 imagery. Two types of modelling approaches calibrated and uncalibrated, were set up for 2007/08 and 2008/09 simulation periods. For the calibrated modelling, only the surface depression capacity of upland area was calibrated in the 2007/08 simulation period by comparing simulated and observed hydrographs; while other model parameters and all parameters in the uncalibrated modelling were estimated from field observations of soils and vegetation cover, SPOT 5 imagery, and analysis of drainage network and wetland GIS datasets as well as topographic map based and LiDAR DEMs. All the parameters except for the initial soil properties and antecedent wetland storage were kept the same in the 2008/09 simulation period. The model performance in predicting snowpack, soil moisture and streamflow was evaluated and comparisons were made between the calibrated and uncalibrated modelling for both simulation periods. Calibrated and uncalibrated predictions of snow accumulation were very similar and compared fairly well with the distributed field observations for the 2007/08 period with slightly poorer results for the 2008/09 period. Soil moisture content at a point during the early spring was adequately simulated and very comparable between calibrated and uncalibrated results for both simulation periods. The calibrated modelling had somewhat better performance in simulating spring streamflow in both simulation periods, whereas the uncalibrated modelling was still able to capture the streamflow hydrographs with good accuracy. This suggests that prediction of prairie basins without calibration is possible if sufficient data on meteorology, basin landcover and physiography are available.

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Automated calibration of a two-dimensional overland flow model by estimating Manning's roughness coefficient using genetic algorithm

Journal of Hydroinformatics ◽

10.2166/hydro.2017.110 ◽

2017 ◽

Vol 20 (2) ◽

pp. 440-456

Author(s):

J. Drisya ◽

D. Sathish Kumar

Keyword(s):

Genetic Algorithm ◽

Flow Model ◽

Overland Flow ◽

Fitness Function ◽

Roughness Coefficient ◽

Model Parameters ◽

Automatic Data ◽

Automated Calibration ◽

Manning’S Roughness Coefficient ◽

Overland Flow Model

Abstract Calibration is an important phase in the hydrological modelling process. In this study, an automated calibration framework is developed for estimating Manning's roughness coefficient. The calibration process is formulated as an optimization problem and solved using a genetic algorithm (GA). A heuristic search procedure using GA is developed by including runoff simulation process and evaluating the fitness function by comparing the experimental results. The model is calibrated and validated using datasets of Watershed Experimentation System. A loosely coupled architecture is followed with an interface program to enable automatic data transfer between overland flow model and GA. Single objective GA optimization with minimizing percentage bias, root mean square error and maximizing Nash–Sutcliffe efficiency is integrated with the model scheme. Trade-offs are observed between the different objectives and no single set of the parameter is able to optimize all objectives simultaneously. Hence, multi-objective GA using pooled and balanced aggregated function statistic are used along with the model. The results indicate that the solutions on the Pareto-front are equally good with respect to one objective, but may not be suitable regarding other objectives. The present technique can be applied to calibrate the hydrological model parameters.

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Back-calculation of the 2017 Piz Cengalo-Bondo landslide cascade with r.avaflow

10.5194/nhess-2019-204 ◽

2019 ◽

Cited By ~ 2

Author(s):

Martin Mergili ◽

Michel Jaboyedoff ◽

José Pullarello ◽

Shiva P. Pudasaini

Keyword(s):

Debris Flow ◽

Flow Model ◽

Rock Avalanche ◽

Simulation Software ◽

Process Models ◽

Rock Fall ◽

Model Parameters ◽

Rock Slide ◽

Glacier Ice ◽

Initial Rock

Abstract. In the morning of 23 August 2017, around 3 million m3 of granitoid rock broke off from the east face of Piz Cengalo, SE Switzerland. The initial rock slide-rock fall entrained 0.6 million m3 of a glacier and continued as a rock(-ice) avalanche, before evolving into a channelized debris flow that reached the village of Bondo at a distance of 6.5 km after a couple of minutes. Subsequent debris flow surges followed in the next hours and days. The event resulted in eight fatalities along its path and severely damaged Bondo. The most likely candidates for the water causing the transformation of the rock avalanche into a long-runout debris flow are the entrained glacier ice and water originating from the debris beneath the rock avalanche. In the present work we try to reconstruct conceptually and numerically the cascade from the initial rock slide-rock fall to the first debris flow surge and thereby consider two scenarios in terms of qualitative conceptual process models: (i) entrainment of most of the glacier ice by the frontal part of the initial rock slide-rock fall and/or injection of water from the basal sediments due to sudden rise in pore pressure, leading to a frontal debris flow, with the rear part largely remaining dry and depositing mid-valley; and (ii) most of the entrained glacier ice remaining beneath/behind the frontal rock avalanche, and developing into an avalanching flow of ice and water, part of which overtops and partially entrains the rock avalanche deposit, resulting in a debris flow. Both scenarios can be numerically reproduced with the two-phase mass flow model implemented with the simulation software r.avaflow, based on plausible assumptions of the model parameters. However, these simulation results do not allow to conclude on which of the two scenarios is the more likely one. Future work will be directed towards the application of a three-phase flow model (rock, ice, fluid) including phase transitions, in order to better represent the melting of glacier ice, and a more appropriate consideration of deposition of debris flow material along the channel.

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The 2017 Rigopiano Avalanche—Dynamics Inferred from Field Observations

Geosciences ◽

10.3390/geosciences10110466 ◽

2020 ◽

Vol 10 (11) ◽

pp. 466

Author(s):

Dieter Issler

Keyword(s):

Snow Cover ◽

Central Italy ◽

Snow Avalanche ◽

Field Observations ◽

Flow Front ◽

Moderate Amount ◽

Vulnerability Curve ◽

Abruzzo Region ◽

Avalanche Dynamics ◽

Different Parts

Data on the disastrous snow avalanche that occurred on 18 January 2017 at the spa hotel Rigopiano, municipality of Farindola in the Abruzzo region of central Italy, are analyzed in different ways. The main results are the following. (i) The 2017 Rigopiano avalanche went beyond the run-out point predicted by the topographic-statistical α-β model with standard Norwegian calibration, while avalanches in neighboring paths appear to have run no farther than the β-point of their respective paths during the same period. (ii) The curvature and super-elevation of the trimline between 1500 and 1300 m a.s.l. indicate that the velocity of the front was around 40 m s−1. In contrast, the tail velocity of the avalanche can hardly have exceeded 25 m s−1 in the same segment. (iii) The deposits observed along all of the lower track and in the run-out zone suggest that the avalanche eroded essentially the entire snow cover, but fully entrained only a moderate amount of snow (and debris). The entrainment appears to have had a considerable decelerating effect on the flow front. (iv) Estimates of the degree to which different parts of the building were damaged is combined with information about the location of the persons in the building and their fates. This allows to refine a preliminary vulnerability curve for persons in buildings obtained from the 2015 Longyearbyen avalanche, Svalbard.

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Analysis of parameter uncertainty of a flow and quality stormwater model

Water Science & Technology ◽

10.2166/wst.2009.434 ◽

2009 ◽

Vol 60 (3) ◽

pp. 717-725 ◽

Cited By ~ 18

Author(s):

C. B. S. Dotto ◽

A. Deletic ◽

T. D. Fletcher

Keyword(s):

Water Quality ◽

Bayesian Methods ◽

Flow Model ◽

Model Parameters ◽

Rainfall Runoff ◽

Sources Of Uncertainty ◽

Music Model ◽

Rainfall Runoff Model ◽

Water Quality Models ◽

Runoff Model

Uncertainty is intrinsic to all monitoring programs and all models. It cannot realistically be eliminated, but it is necessary to understand the sources of uncertainty, and their consequences on models and decisions. The aim of this paper is to evaluate uncertainty in a flow and water quality stormwater model, due to the model parameters and the availability of data for calibration and validation of the flow model. The MUSIC model, widely used in Australian stormwater practice, has been investigated. Frequentist and Bayesian methods were used for calibration and sensitivity analysis, respectively. It was found that out of 13 calibration parameters of the rainfall/runoff model, only two matter (the model results were not sensitive to the other 11). This suggests that the model can be simplified without losing its accuracy. The evaluation of the water quality models proved to be much more difficult. For the specific catchment and model tested, we argue that for rainfall/runoff, 6 months of data for calibration and 6 months of data for validation are required to produce reliable predictions. Further work is needed to make similar recommendations for modelling water quality.

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