Non-hydrostatic Model Research Articles

Non-hydrostatic model for internal wave generations and propagations using immersed boundary method

A non-hydrostatic model is developed to predict internal wave generations and propagations. The model employs a semi-implicit, fractional step algorithm to solve the governing equations based on the Cartesian grid system. Immersed boundary method is incorporated to deal with the complex geometry of uneven bottoms. The combination of the z-level vertical coordinate and the immersed boundary method enables the model to treat uneven bottoms and meanwhile to avoid numerical errors in the calculation of the baroclinic pressure force. To consider the effect of stratification, a variant of the Smagorinsky sub-grid scale model is employed to calculate the eddy viscosity and diffusivity. The capability of the model in resolving internal wave generation by tidal forcing over an idealized Gaussian-shaped topography is firstly validated by comparing the developed model with a terrain-following non-hydrostatic model. Then, two laboratory-scale test cases involving internal solitary wave propagations over variable topographies are considered. It can be found that the model captures the main characteristics of waveform evolution including internal hydraulic jump, wave breaking and waveform inversion. Thus, the proposed model provide an alternative to simulate internal wave generations and propagations.

Improved Circulation in the Northern Hemisphere by Adjusting Gravity Wave Drag Parameterizations in Seasonal Experiments With ICON‐NWP

AbstractThe stratosphere is one of the main potential sources for subseasonal to seasonal predictability in midlatitudes in winter. The ability of an atmospheric model to realistically simulate the stratospheric dynamics is essential in order to move forward in the field of seasonal predictions in midlatitudes. Earlier studies with the ICOsahedral Nonhydrostatic atmospheric model (ICON) point out that stratospheric westerlies in ICON are underestimated. This is the first extensive study on the evaluation of Northern Hemisphere stratospheric winter circulation with ICON in numerical weather prediction (NWP) mode. Seasonal experiments with the default setup are able to reproduce the basic climatology of the stratospheric polar vortex. However, westerlies are too weak and major stratospheric warmings too frequent in ICON. Both a reduction of the nonorographic, and a reduction of the orographic gravity wave and wake drag lead to a strengthening of the stratospheric vortex and a bias reduction, in particular in January. However, the effect of the nonorographic gravity wave drag scheme on the stratosphere is stronger. Stratosphere‐troposphere coupling is intensified and more realistic due to a reduced gravity wave drag. Furthermore, an adjustment of the subgrid‐scale orographic drag parameterization leads to a significant error reduction in the mean sea level pressure. As a result of these findings, we present our current suggested improved setup for seasonal experiments with ICON‐NWP.

Diversity of the Madden–Julian Oscillation: Initiation Region Modulated by the Interaction between the Intraseasonal and Interannual Variabilities

AbstractAs one of the aspects of the diversity of the Madden–Julian oscillation (MJO), the modulation of initiation regions of the boreal-winter MJO is studied in terms of the relationship between intraseasonal and interannual variabilities. MJOs are categorized as those initiating in the Indian Ocean (IO), Maritime Continent (MC), and western Pacific (WP), referred to herein as IO-MJOs, MC-MJOs, and WP-MJOs, respectively. The composite analyses for each MJO category using observational data reveal that the diversity of MJO initiation regions directly results from the modulation of areas where horizontal advective premoistening efficiently occurs via intraseasonal/synoptic-scale winds. This is supported by the difference in the zonal location of equatorial intraseasonal circulations established before MJO initiation, which is related to a spatial change in background convection and associated Walker circulations forced by interannual sea surface temperature (SST) variability. Compared to IO-MJOs (favored in the climatological background on average), MC-MJOs tend to be realized under the eastern-Pacific El Niño–like condition, as a result of eastward-shifted intraseasonal convection and circulation patterns induced by background suppressed convection in the eastern MC. WP-MJOs are frequently initiated under the central-Pacific El Niño–like and positive IO dipole–like conditions, in which the WP is selectively moistened with the aid of background enhanced (suppressed) convection over the WP (the southeastern IO and the central-to-eastern Pacific). This major tendency derived from sample-limited observations is verified by a set of 15-yr numerical experiments with a global nonhydrostatic MJO-permitting model under a perpetual boreal-winter condition where observation-based SSTs are prescribed.

A HWRF-POM-TC coupled model forecast performance over North Indian Ocean: VSCS TITLI & VSCS LUBAN

The HWRF-POM-TC coupled model is run operationally at India Meteorological Department (IMD). This study is first attempt to assess the IMD's operational HWRF-POM-TC (Atmosphere-Ocean) coupled model forecast performance over North Indian Ocean (NIO). The two cyclonic storms one each in Arabian Sea and Bay of Bengal were examined. Among them, VSCS LUBAN formed over Arabian Sea (AS) and was followed by the formation of VSCS TITLI over Bay of Bengal (BoB). It constituted a rare case whereby two VSCS have formed in the north Indian Ocean (NIO) simultaneously.The HWRF-POM-TC modeling system, which was developed at National Centers for Environmental Prediction (NCEP) based on Non-hydrostatic Mesoscale Model (NMM) dynamic core, was customized for NIO conditions. For the two storms, VSCS LUBAN & VSCS TITLI, 28 and 15 consecutive 6-hourly HWRF model runs were performed. The HWRF-POM-TC coupled model showed great skill in forecasting of Track and Intensity for examined cyclones. The result shows that the model predicted the intensification and landfall of VSCS Luban & Titli in agreement with the best track data as made available by Cyclone Warning Division (CWD), India Meteorological Department which is also recognized as Regional Specialized Meteorological Center (RSMC) by WMO for NIO.

Multilayer-HySEA model validation for landslide-generated tsunamis – Part 1: Rigid slides

Abstract. This paper is devoted to benchmarking the Multilayer-HySEA model using laboratory experimental data for landslide-generated tsunamis. This article deals with rigid slides, and the second part, in a companion paper, addresses granular slides. The US National Tsunami Hazard and Mitigation Program (NTHMP) has proposed the experimental data used and established for the NTHMP Landslide Benchmark Workshop, held in January 2017 at Galveston (Texas). The first three benchmark problems proposed in this workshop deal with rigid slides. Rigid slides must be simulated as a moving bottom topography, and, therefore, they must be modeled as a prescribed boundary condition. These three benchmarks are used here to validate the Multilayer-HySEA model. This new HySEA model consists of an efficient hybrid finite-volume–finite-difference implementation on GPU architectures of a non-hydrostatic multilayer model. A brief description of model equations, dispersive properties, and the numerical scheme is included. The benchmarks are described and the numerical results compared against the lab-measured data for each of them. The specific aim is to validate this new code for tsunamis generated by rigid slides. Nevertheless, the overall objective of the current benchmarking effort is to produce a ready-to-use numerical tool for real-world landslide-generated tsunami hazard assessment. This tool has already been used to reproduce the Port Valdez, Alaska, 1964 and Stromboli, Italy, 2002 events.

A two-layer non-hydrostatic landslide model for tsunami generation on irregular bathymetry. 2. Numerical discretization and model validation

We describe a numerical treatment for a two-layer coupled model developed for the investigation of submarine landslides and resulting tsunami generation over irregular bathymetry. The landslide model is formulated in a Cartesian coordinate system oriented with the still water level in order to facilitate coupling between water and ground motions. Motions in the upper water layer are simulated using the 3D non-hydrostatic wave model NHWAVE. Governing equations for the lower-layer landslide are integrated over the slide thickness, and include options for choosing either Newtonian viscous or granular rheology closures. The lower layer equations retain the effects of non-hydrostatic pressure, allowing the model to simulate motions over arbitrary and locally steep bathymetry. The model equations are solved using a Runge–Kutta scheme for time integration and a Godunov-type finite volume scheme for spatial derivatives, with non-conservative terms formulated using a finite difference scheme. The resulting model is verified in comparison to two laboratory experiments involving granular slide motion, and compared to observations for a field event during the 1964 Alaska earthquake.

A three-dimensional non-hydrostatic model for tsunami waves generated by submarine landslides

A three-dimensional (3D) non-hydrostatic model for simulating nonlinear and dispersive waves is extended to compute submarine-landslide-generated waves. The model uses a projection method to solve the 3D Navier-Stokes equations on a 3D grid system built from a two-dimensional (2D) horizontal mesh by adding several horizontal layers in the vertical direction. The free surface is efficiently captured by the so-called free surface equation. The bottom movement is incorporated in the model by specifying the kinematic boundary condition at the impermeable bottom. The extension does not alter the property of the discretized Poisson equation for non-hydrostatic pressure correction terms. Thus, it can also be solved efficiently by the preconditioned conjugate gradient method. A wide range of tests including 2D and 3D landslide waves are simulated. Comparisons between numerical results and experimental data and/or other model results are presented. It is found that a good agreement has been obtained for a range of landslide waves using a very small number of horizontal layers (e.g. three or five layers) and the proposed model can be considered as an attractive alternative to simulating submarine-landslide-generated waves.

The Nonhydrostatic ICosahedral Atmospheric Model for CMIP6 HighResMIP simulations (NICAM16-S): experimental design, model description, and impacts of model updates

Abstract. The Nonhydrostatic ICosahedral Atmospheric Model (NICAM), a global model with an icosahedral grid system, has been under development for nearly two decades. This paper describes NICAM16-S, the latest stable version of NICAM (NICAM.16), modified for the Coupled Model Intercomparison Project Phase 6, High Resolution Model Intercomparison Project (HighResMIP). Major updates of NICAM.12, a previous version used for climate simulations, included updates of the cloud microphysics scheme and land surface model, introduction of natural and anthropogenic aerosols and a subgrid-scale orographic gravity wave drag scheme, and improvement of the coupling between the cloud microphysics and the radiation schemes. External forcings were updated to follow the protocol of the HighResMIP. A series of short-term sensitivity experiments were performed to determine and understand the impacts of these various model updates on the simulated mean states. The NICAM16-S simulations demonstrated improvements in the ice water content, high cloud amount, surface air temperature over the Arctic region, location and strength of zonal mean subtropical jet, and shortwave radiation over Africa and South Asia. Some long-standing biases, such as the double intertropical convergence zone and smaller low cloud amount, still exist or are even worse in some cases, suggesting further necessity for understanding their mechanisms, upgrading schemes and parameter settings, and enhancing horizontal and vertical resolutions.

A Large-Eddy Simulation Study on the Diurnally Evolving Nonlinear Trapped Lee Waves over a Two-Dimensional Steep Mountain

AbstractThe diurnally evolving trapped lee wave over a small-scale two-dimensional steep mountain is investigated in large-eddy simulations based on a fully compressible and nonhydrostatic model [Icosahedral Nonhydrostatic (ICON)] with triangular grids of 50-m-edge length. An idealized atmospheric profile derived from a realistic case is designed to account for influences from the stagnant layer near the surface, the stability of the atmospheric boundary layer (ABL) and the upper-level jet. First, simulations were done to bridge from the linear regime to the nonlinear regime by increasing the mountain height, which showed that larger-amplitude lee waves with longer wavelength can be produced in the nonlinear regime than in the linear regime. Second, the effects of the stagnant layer near the surface and the ABL stability were explored, which showed that the stagnant layer or the stable ABL can play a similar wave-absorbing role in the nonlinear regime as in linear theories or simulations. Third, the role of the upper-level jet was explored, indicating that a stronger (weaker) upper-level jet can help to produce longer (shorter) lee waves. The stable ABL with a stagnant layer can more (less) efficiently absorb the longer (shorter) lee waves due to the stronger (weaker) jet, so that the wave response is more sensitive to the wave-absorption layer when an upper-level jet is present. Finally, the momentum budget was analyzed to explore the interaction between the upper and lower levels of the troposphere, which showed that the momentum flux due to the upward-propagating waves and trapped waves varies with the upper-level jet strength and low-level stagnancy and ABL stability.

Gravel Barrier Beach Morphodynamic Response to Extreme Conditions

Gravel beaches and barriers form a valuable natural protection for many shorelines. The paper presents a numerical modelling study of gravel barrier beach response to storm wave conditions. The XBeach non-hydrostatic model was set up in 1D mode to investigate barrier volume change and overwash under a wide range of unimodal and bimodal storm conditions and barrier cross sections. The numerical model was validated against conditions at Hurst Castle Spit, UK. The validated model is used to simulate the response of a range of gravel barrier cross sections under a wide selection of statistically significant storm wave and water level scenarios thus simulating an ensemble of barrier volume change and overwash. This ensemble of results was used to develop a simple parametric model for estimating barrier volume change during a given storm and water level condition under unimodal storm conditions. Numerical simulations of barrier response to bimodal storm conditions, which are a common occurrence in many parts of the UK were also investigated. It was found that barrier volume change and overwash from bimodal storms will be higher than that from unimodal storms if the swell percentage in the bimodal spectrum is greater than 40%. The model is demonstrated as providing a useful tool for estimating barrier volume change, a commonly used measure used in gravel barrier beach management.

Precipitation Characteristics and Future Changes Over the Southern Slope of Tibetan Plateau Simulated by a High‐Resolution Global Nonhydrostatic Model

AbstractCurrent climate model resolution cannot accurately describe the complex topography over the Tibetan Plateau, which limits our understanding of past and future precipitation over this region. This study investigates the daily precipitation characteristics and its future changes over the Tibetan Plateau, especially for the southern slope of Tibetan Plateau (SSTP), by 14‐km Nonhydrostatic ICosahedral Atmospheric Model (NICAM) with explicitly calculated convection for historical and future 30‐years period. By comparing with the satellite Global Precipitation Measurement (GPM), NICAM well reproduces the historical precipitation spatial pattern, seasonal cycle, and the extreme precipitation belt over SSTP, but overestimates precipitation amount by ∼35%. It is found that heavy precipitation probability decreases as elevation becomes higher while the light precipitation generally shows the opposite. For the precipitation changes during June to September from 1979–2008 to 2075–2104, NICAM predicts that mean precipitation will decrease over low‐level SSTP but increase over high‐level SSTP. Nonprecipitation and heavy precipitation probability will increase while light precipitation probability will decrease in the future over SSTP. The extreme precipitation probability and intensity will increase ∼50%/°C and ∼8%/°C over SSTP, and this increase is more obvious as elevation becomes higher. The robust increase of extreme precipitation along the SSTP topography is unique and has not been identified by the climate model simulations before. The strong meridional gradient of specific humidity over SSTP is found to be further enhanced under global warming, and this gradient enhancement is suggested to be responsible for the increase in the extreme precipitation over SSTP.

Resolving nonhydrostatic effects in oceanic lee waves

With increased computing power, the horizontal grid-spacing of regional ocean models is decreasing to the point where they can directly simulate lee waves. Although oceanic lee waves can be inherently nonhydrostatic, such as in the abyssal ocean or in the Gulf Stream, regional ocean models are frequently run in hydrostatic mode to avoid the computational expense of solving the nonhydrostatic pressure. However, the effects of the nonhydrostatic pressure and the numerical error on the accuracy of the simulated lee waves is not immediately obvious. To quantify these effects, this paper presents hydrostatic and nonhydrostatic simulations of an idealized lee wave over both linear and nonlinear height and varying length bathymetry utilizing a range of horizontal grid-spacings. We present an analysis of the numerical error arising from the discrete linear, stratified Euler equations to identify the numerically induced physics in lee wave simulations. As expected for the second-order accurate model, the numerical error in the lee wave drag decreases quadratically with respect to horizontal grid refinement, although the error arises from two primary sources. The first is related to discretization of the kinematic bottom boundary condition, which acts to decrease the lee wave drag. The second is related to discretization of the nonhydrostatic pressure, which acts to increase the drag. Together, the results offer a regional ocean modeler several cautionary notes for calculating and interpreting properties of simulated lee waves, namely, that a hydrostatic model can produce the correct form drag due simply to numerical error, and attempting to employ a nonhydrostatic model to correct for this error can require prohibitively fine grid resolution.

New High-Resolution Modeling of the 2018 Palu Tsunami, Based on Supershear Earthquake Mechanisms and Mapped Coastal Landslides, Supports a Dual Source

The Mw 7.5 earthquake that struck Central Sulawesi, Indonesia, on September 28, 2018, was rapidly followed by coastal landslides and destructive tsunami waves within Palu Bay. Here, we present new tsunami modeling that supports a dual source mechanism from the supershear strike-slip earthquake and coastal landslides. Up until now the tsunami mechanism: earthquake, coastal landslides, or a combination of both, has remained controversial, because published research has been inconclusive; with some studies explaining most observations from the earthquake and others the landslides. Major challenges are the numerous different earthquake source models used in tsunami modeling, and that landslide mechanisms have been hypothetical. Here, we simulate tsunami generation using three published earthquake models, alone and in combination with seven coastal landslides identified in earlier work and confirmed by field and bathymetric evidence which, from video evidence, produced significant waves. To generate and propagate the tsunamis, we use a combination of two wave models, the 3D non-hydrostatic model NHWAVE and the 2D Boussinesq model FUNWAVE-TVD. Both models are nonlinear and address the physics of wave frequency dispersion critical in modeling tsunamis from landslides, which here, in NHWAVE are modeled as granular material. Our combined, earthquake and coastal landslide, simulations recreate all observed tsunami runups, except those in the southeast of Palu Bay where they were most elevated (10.5 m), as well as observations made in video recordings and at the Pantoloan Port tide gauge located within Palu Bay. With regard to the timing of tsunami impact on the coast, results from the dual landslide/earthquake sources, particularly those using the supershear earthquake models are in good agreement with reconstructed time series at most locations. Our new work shows that an additional tsunami mechanism is also necessary to explain the elevated tsunami observations in the southeast of Palu Bay. Using partial information from bathymetric surveys in this area we show that an additional, submarine landslide here, when simulated with the other coastal slides, and the supershear earthquake mechanism better explains the observations. This supports the need for future marine geology work in this area.

A Weakly Non-hydrostatic Shallow Model for Dry Granular Flows

A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope.

A two-layer non-hydrostatic landslide model for tsunami generation on irregular bathymetry. 1. Theoretical basis

We describe a two-layer, coupled model for landslide motion over irregular bathymetry and resulting water column motion and tsunami generation. The three-dimensional non-hydrostatic wave model NHWAVE (Ma et al., 2012) is applied as the upper-layer model to simulate landslide-generated tsunami waves. Here, we focus on the derivation of governing equations for the lower-layer model, where the landslide is described as either a viscous mud flow or a saturated granular debris flow. The governing equations are depth-integrated in a Cartesian coordinate system referenced to the still water surface. Vertical acceleration of the slide is taken into account by including non-hydrostatic pressure effects within the slide. The model is validated in comparison to analytic results of Mangeney et al. (2000) and the slope-oriented numerical approach of Ma et al. (2015). The numerical approach and further examples are described in the companion paper Zhang et al. (2021).

A three-dimensional non-hydrostatic mathematical model with mixed triangle and quadrilateral grids

The three-dimensional numerical models based on the hydrostatic pressure hypothesis can’t accurately and effectively simulate the cases of estuaries or natural rivers with the presence of short wave flow, stratified gravity flow, sudden change of local topography or flow near underwater buildings. Therefore it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. Based on the mixed grids of triangle and quadrilateral, a three-dimensional non hydrostatic mathematical model is presented. The control equations are discretized by the semi-implicit fractional step method. The pressure is divided into the hydrostatic pressure and non-hydrostatic pressure terms. At each step, the water level is calculated by solving the sparse equations, and then the non-hydrostatic pressure is obtained by the pressure Poisson equation. Three typical examples were adopted to simulate strong three-dimensional flow. As a result, the results show that the model can accurately and effectively simulate strong three-dimensional flow with a few layers.

Dispersive Model for Undular Hydraulic Jump Behind a Weir

In this paper, we investigate a suitable weir design which yields in an undular jump phenomenon using both hydrostatic and non-hydrostatic models. We solved the hydrostatic model using numerical and analytical methods. After that, we validated the output from both methods using the experimental data. In order to simulate the undular jump better, modification towards the hydrostatic model is needed. Hence, for the non-hydrostatic model, we consider the existence of hydrodynamic pressure and solved the model numerically. The outcome of this paper can be beneficial for hydraulic structures design and the management of water resources.

Prediction Skill of the Boreal Summer Intra-Seasonal Oscillation in Global Non-hydrostatic Atmospheric Model Simulations with Explicit Cloud Microphysics

Prediction Skill of the Boreal Summer Intra-Seasonal Oscillation in Global Non-hydrostatic Atmospheric Model Simulations with Explicit Cloud Microphysics

Numerical Prediction of Local Meteorological Processes above a City with a Supercomputer

This paper presents a parallel algorithm for numerical solution of equations for the non-hydrostatic mesoscale meteorological model TSUNM3. To justify the choice of the Message Passing Interface technology, computational experiments were performed to compare the effectiveness of the following parallelizing technologies: MPI, OpenMP, OpenACC, and CUDA. 2D decomposition of the gridded domain for the TSUNM3 model has been carried out with MPI technology. It allows for a numerical forecast for the next day in 17 minutes of CPU time on 144 cores of the TSU Cyberia computing cluster.

全球非静力学大気モデルにおける粒径解像エアロゾル微物理モジュール: モデルの記述と検証

全球非静力学大気モデルにおける粒径解像エアロゾル微物理モジュール: モデルの記述と検証