Hurricane Predictability Analysis with Singular Vectors in the Multiresolution Global Shallow Water Model

2021 ◽  
Author(s):  
Xiaoxu Tian ◽  
Kayo Ide
Keyword(s):  
Shallow Water ◽  
Environmental Flows ◽  
Single Layer ◽  
Hurricane Sandy ◽  
Water Model ◽  
Time Interval ◽  
Variable Resolution ◽  
Singular Vectors ◽  
Predictability Analysis ◽  
Computational Resources

AbstractIn this study, the tangent linear and adjoint (TL/AD) models for the Model for Prediction Across Scales (MPAS) Shallow Water (SW) component are tested and demonstrated. Necessary verification check procedures of TL/AD are included to ensure that the models generate correct results. The TL/AD models are applied to calculate the singular vectors (SVs) with a 48-hour optimization time interval (OTI) under both the quasi-uniform resolution (UR) and smoothly variable resolution (VR) meshes in the cases of Hurricanes Sandy (2012) and Joaquin (2015). For the global domain, the VR mesh with 30210 grid cells uses slightly fewer computational resources than the UR mesh with 40962 cells. It is found that at the points before Hurricanes Sandy and Joaquin made sharp turns, the leading SV from the VR experiment show sensitivities in both areas surrounding the hurricane and those relatively far away, indicating the significant impacts from the environmental flows. The leading SVs from the UR experiments are sensitive to only areas near the storm. Forecasts by the nonlinear SWmodel demonstrate that in the VR experiment, Hurricane Sandy has a northwest turn similar to the case in the real world while the storm gradually disappeared in the UR experiment. In the case of Hurricane Joaquin, the nonlinear forecast with the VR mesh can generate a track similar to the Best Track, while the storm became falsely dissipated in the forecast with the UR mesh. These experiments demonstrate, in the context of SW dynamics with a single layer and no physics, the track forecasts in the cases of Hurricanes Sandy and Joaquin with the VR mesh are more realistic than the UR mesh. The SV analyses shed light on the key features that can have significant impacts on the forecast performances.

scholarly journals Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability

2013 ◽  
Vol 723 ◽  
pp. 40-68 ◽  
Author(s):  
Hanna Płotka ◽  
David G. Dritschel
Keyword(s):  
Shallow Water ◽  
Minimum Distance ◽  
Structural Changes ◽  
Single Layer ◽  
Relative Equilibria ◽  
Water Model ◽  
Equilibrium Configurations ◽  
Horizontal Size ◽  
Boundary Of Stability ◽  
Asymmetric Wave

AbstractWe examine the form, properties, stability and evolution of doubly-connected (two-vortex) relative equilibria in the single-layer $f$-plane quasi-geostrophic shallow-water model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio $\gamma = L/ {L}_{D} $ between the horizontal size of the vortices and the Rossby deformation length; the area ratio $\alpha $ of the smaller to the larger vortex; and the minimum distance $\delta $ between the two vortices. We vary $0\lt \gamma \leq 10$ and $0. 1\leq \alpha \leq 1. 0$, determining the boundary of stability $\delta = {\delta }_{c} (\gamma , \alpha )$. We also examine the nonlinear development of the instabilities and the transitions to other near-equilibrium configurations. Two modes of instability occur when $\delta \lt {\delta }_{c} $: a small-$\gamma $ asymmetric (wave 3) mode, which is absent for $\alpha \gtrsim 0. 6$; and a large-$\gamma $ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near ${\delta }_{c} $ may be classified as follows: (i) vacillations about equilibrium for $\gamma \gtrsim 2. 5$; (ii) partial straining out, associated with the small-$\gamma $ mode, where either one or both of the vortices get smaller for $\gamma \lesssim 2. 5$ and $\alpha \lesssim 0. 6$; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the large-$\gamma $ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.

scholarly journals Determination of the Boundaries of Flooded Zones Based on Hydrodynamic Modeling

2020 ◽  
pp. 12-22
Author(s):  
Tatyana Dyakonova ◽  
Vladislava Krivko ◽  
Ekaterina Agafonnikova ◽  
Anna Klikunova ◽  
Evgeniy Sokolovskiy ◽  
...  
Keyword(s):  
Shallow Water ◽  
Spatial Data ◽  
Single Layer ◽  
Hydrodynamic Modeling ◽  
Water Levels ◽  
Water Model ◽  
Inundation Maps ◽  
Cadastral Maps ◽  
The Republic ◽  
State Registration

The paper discusses the problem of determining the boundaries of flooding zones, flooding of territories. The paper describes technique for constructing cadastral maps of flooded zones for various values of the estimated availability of water levels, which is based on hydrodynamic and geoinformation modeling. For creating digital elevation models (DEM) of the conformation, we use spatial data obtained from a large number of sources. We applied the described technique to construct cadastral maps for a number of settlements in the Volgograd region of the Russian Federation. As a result, we get a set of xml-files prepared for registration with the Federal Agency for State Registration, Cadastre and Cartography. For the Republic of Belarus, the problem of flooding the territories is also urgent. The floodplain areas of the Pripyat River are most prone to flooding. We built a DEM for the area in the vicinity of Petrikov city and carried out hydrodynamic modeling. As a result, the inundation maps were obtained. The method proposed in this work is based on a mathematical model of shallow water in a single-layer approximation. This model is successfully applied in simulation of flooding for territories by flood waters. Solving the problem of determining the boundaries of flooding zones requires a transition to a two-layer shallow water model that takes into account the interaction of surface and ground waters.

scholarly journals Simply-connected vortex-patch shallow-water quasi-equilibria

2014 ◽  
Vol 743 ◽  
pp. 481-502 ◽  
Author(s):  
H. Płotka ◽  
D. G. Dritschel
Keyword(s):  
Shallow Water ◽  
Single Layer ◽  
Water Model ◽  
Shallow Water Model ◽  
Geophysical Fluid Dynamics ◽  
Vortex Patch ◽  
Horizontal Size ◽  
The Stability ◽  
Simply Connected ◽  
Boundary Of Stability

AbstractWe examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer $f$-plane shallow-water model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasi-equilibria. Namely, these are the ratio $\gamma = L/L_D$ between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio $\lambda $ between the minor to major axes of the vortex; and a potential vorticity (PV)-based Rossby number $\mathit{Ro}= q^{\prime }/f$, the ratio of the PV anomaly $q^{\prime }$ within the vortex to the Coriolis frequency $f$. By defining an appropriate steadiness parameter, we find that the quasi-equilibria remain steady for long times, enabling us to determine the boundary of stability $\lambda _c=\lambda _c(\gamma ,\mathit{Ro})$, for $0.25 \leq \gamma \leq 6$ and $\delimiter "026A30C \mathit{Ro}\delimiter "026A30C \leq 1$. By calling two states which share $\gamma ,\delimiter "026A30C \mathit{Ro}\delimiter "026A30C $ and $\lambda $ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic ($\mathit{Ro}> 0$) and anticyclonic ($\mathit{Ro}<0$) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for large-$\gamma $, large-$\mathit{Ro}$ states, (b) filamentation for small-$\gamma $ states and (c) vortex splitting, asymmetric for intermediate-$\gamma $ and symmetric for large-$\gamma $ states.

Potential vorticity redistribution by localised transient forcing in the shallow-water model

2018 ◽  
Vol 852 ◽  
pp. 199-225 ◽  
Author(s):  
Michael C. Haigh ◽  
Pavel S. Berloff
Keyword(s):  
Shallow Water ◽  
Ocean Circulation ◽  
Potential Vorticity ◽  
Single Layer ◽  
Current Theory ◽  
Water Model ◽  
Eddy Flux ◽  
Shallow Water Model ◽  
Background Flow ◽  
Uniform Background

This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of $\unicode[STIX]{x1D6FD}$-plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.

scholarly journals Multilayer shallow-water model with stratification and shear

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 351
Author(s):  
F. J. Beron-Vera
Keyword(s):  
Shallow Water ◽  
Baroclinic Instability ◽  
Single Layer ◽  
Vertical Shear ◽  
Water Model ◽  
Type Model ◽  
Inhomogeneous Layer ◽  
Good Representation ◽  
Water Type ◽  
Dissipation Energy

The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and startificaion in horizontal space and time. This is achieved by writing the layer velocity and buoyancy fields as linear functions of depth, with coefficients that depend arbitrarily on horizontal position and time. The model is a generalization of Ripa's (1995) single-layer model to an arbitrary number of layers. Unlike models with homogeneous layers the present model is able to represent thermodynamics processes driven by heat and freshwater fluxes through the surface or mixing processes resulting from fluid exchanges across contiguous layers. By contrast with inhomogeneous-layer models with depth-independent velocity and buoyancy, the model derived here can sustain explicitly at low frequency a current in thermal wind balance (between the vertical vertical shear and the horizontal density gradient) within each layer. In the absence of external forcing and dissipation, energy, volume, mass, and buoyancy variance constrain the dynamics; conservation of total zonal momentum requires in addition the usual zonal symmetry of the topography and horizontal domain.  The inviscid, unforced model admits a formulation suggestive of a generalized Hamiltonian structure, which enables the classical connection between symmetries and conservation laws via Noether's theorem.  A steady solution to a system involving one Ripa-like layer and otherwise homogeneous layers can be proved formally (or Arnold) stable using the above invariants. A model configuration with only one layer has been shown previously to provide: a very good representation of the exact vertical normal modes up to the first internal mode; an exact representation of long-perturbation (free boundary) baroclinic instability; and a very reasonable representation of short-perturbation (classical Eady) baroclinic instability. Here it is shown that substantially more accurate overall results with respect to single-layer calculations can be achieved by considering a stack of only a few layers. A similar behavior is found in ageostrophic (classical Stone) baroclinic instability by describing accurately the dependence of the solutions on the Richardson number with only two layers.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Evaluate of head loss, sediment value and copper removal in sand media (rapid sand filter)

2014 ◽  
Vol 3 (2) ◽  
pp. 276-286 ◽  
Author(s):  
Daneshi Navab ◽  
Banejad Hossein ◽  
Pirtag Hamedany Reza ◽  
Daneshi Vahab ◽  
Farokhi Maedeh
Keyword(s):  
Water Resources ◽  
Copper Concentration ◽  
Technology Development ◽  
Wastewater Treatment Plants ◽  
Single Layer ◽  
Head Loss ◽  
Copper Removal ◽  
Time Interval ◽  
Water And Wastewater Treatment ◽  
Sand Filter

Along with the technology development and increasing consumption of water resources, we are experiencing low qualities in the mentioned resources. Copper brings about serious environment al pollution, threatening human health and ecosystem. This metal found variously in water resources and industrial activities. Therefore, it needs to treat the water resources from these excessive amounts. Different methods have used for this reason but the most used method during recent years has been the absorption by economic absorbers such as sand. Rapid sand filters usually used in water and wastewater treatment plants for water clarification. In this research, a single layer gravity rapid sand filter has used to reduce different concentrations of copper. sediment value and head loss arising in filter media is simulated by using combination of Carman-Kozeny, Rose and Gregory models in different discharges of rapid sand filter. Results have shown that with increasing in discharge and decreasing in input copper concentration, arriving time to given head loss, is increasing. In addition, results demonstrated that with increasing in copper concentration in influent, removal efficiency is decreasing somewhat. Results of this research can applied in an appropriate design of rapid sand filter to copper removal, a prediction of rapid sand filter ability to copper removal and an estimation of arising head loss during filter work thus evaluating of time interval backwash. DOI: http://dx.doi.org/10.3126/ije.v3i2.10641 International Journal of the Environment Vol.3(2) 2014: 276-286

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals Development of a Practical Model for Predicting Soil Salinity in a Salt Marsh in the Arakawa River Estuary

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2054
Author(s):  
Naoki Kuroda ◽  
Katsuhide Yokoyama ◽  
Tadaharu Ishikawa
Keyword(s):  
Salt Marsh ◽  
Hydraulic Conductivity ◽  
Shallow Water ◽  
Soil Salinity ◽  
River Estuary ◽  
Flow Simulation ◽  
Design Tool ◽  
Water Model ◽  
Shallow Water Model ◽  
Practical Model

Our group has studied the spatiotemporal variation of soil and water salinity in an artificial salt marsh along the Arakawa River estuary and developed a practical model for predicting soil salinity. The salinity of the salt marsh and the water level of a nearby channel were measured once a month for 13 consecutive months. The vertical profile of the soil salinity in the salt marsh was measured once monthly over the same period. A numerical flow simulation adopting the shallow water model faithfully reproduced the salinity variation in the salt marsh. Further, we developed a soil salinity model to estimate the soil salinity in a salt marsh in Arakawa River. The vertical distribution of the soil salinity in the salt marsh was uniform and changed at almost the same time. The hydraulic conductivity of the soil, moreover, was high. The uniform distribution of salinity and high hydraulic conductivity could be explained by the vertical and horizontal transport of salinity through channels burrowed in the soil by organisms. By combining the shallow water model and the soil salinity model, the soil salinity of the salt marsh was well reproduced. The above results suggest that a stable brackish ecotone can be created in an artificial salt marsh using our numerical model as a design tool.

scholarly journals Learning Case Study of a Shallow-Water Model to Assess an Early-Warning System for Fast Alpine Muddy-Debris-Flow

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 750
Author(s):  
Antonio Pasculli ◽  
Jacopo Cinosi ◽  
Laura Turconi ◽  
Nicola Sciarra
Keyword(s):  
Debris Flow ◽  
Shallow Water ◽  
Early Warning ◽  
Debris Flows ◽  
Early Warning System ◽  
Warning System ◽  
Extreme Weather Events ◽  
Water Model ◽  
Computational Time ◽  
Processing Unit

The current climate change could lead to an intensification of extreme weather events, such as sudden floods and fast flowing debris flows. Accordingly, the availability of an early-warning device system, based on hydrological data and on both accurate and very fast running mathematical-numerical models, would be not only desirable, but also necessary in areas of particular hazard. To this purpose, the 2D Riemann–Godunov shallow-water approach, solved in parallel on a Graphical-Processing-Unit (GPU) (able to drastically reduce calculation time) and implemented with the RiverFlow2D code (version 2017), was selected as a possible tool to be applied within the Alpine contexts. Moreover, it was also necessary to identify a prototype of an actual rainfall monitoring network and an actual debris-flow event, beside the acquisition of an accurate numerical description of the topography. The Marderello’s basin (Alps, Turin, Italy), described by a 5 × 5 m Digital Terrain Model (DTM), equipped with five rain-gauges and one hydrometer and the muddy debris flow event that was monitored on 22 July 2016, were identified as a typical test case, well representative of mountain contexts and the phenomena under study. Several parametric analyses, also including selected infiltration modelling, were carried out in order to individuate the best numerical values fitting the measured data. Different rheological options, such as Coulomb-Turbulent-Yield and others, were tested. Moreover, some useful general suggestions, regarding the improvement of the adopted mathematical modelling, were acquired. The rapidity of the computational time due to the application of the GPU and the comparison between experimental data and numerical results, regarding both the arrival time and the height of the debris wave, clearly show that the selected approaches and methodology can be considered suitable and accurate tools to be included in an early-warning system, based at least on simple acoustic and/or light alarms that can allow rapid evacuation, for fast flowing debris flows.

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