Abstract

Several advection experiments were conducted to test semi-Lagrangian schemes and Eulerian Warming-Kutler-Lomax (WKL) algorithms. The Eulerian WKL algorithms, as a special case of fourth-degree (order) Lagrange interpolation, exhibit unacceptable results in severe tests. Split semi-Lagrangian schemes using odd-order Lagrange interpolation are stable in the long-term deformation test, while the split even-order ones are unstable. This result suggests the superiority of odd-order Lagrange interpolation to even-order Lagrange interpolation used for semi-Lagrangian advection. Split cubic spline and cubic B spline are able to preserve a sharp-shaped box after long-term revolution with good accuracy comparable to these for fifth- and seventh-order Lagrange interpolations, but the spline interpolations exhibit strong numerical instability in the deformation test.

Abstract

A three-dimensional (3D) forward-in-time anelastic nonhydrostatic model in a terrain-following coordinate is developed to investigate mesoscale circulations over topography. The anelastic nonhydrostatic model utilizes the deep-continuity equation, rather than the vertical-momentum equation commonly adopted, to compute vertical velocity. Hence, the anelastic nonhydrostatic model is identical to the hydrostatic model, except that the former perturbation pressure must be solved from an elliptic equation to coincide with nondivergent wind. To enhance the efficiency of iterations for convergence, the elliptic pressure equation is transformed to an artificial parabolic form that allows semi-implicit time integration as adopted in most elastic nonhydrostatic models.

Numerical experiments using the anelastic model, the same anelastic model but employing the vertical momentum equation, and the compressible model were conducted for comparisons. The presented anelastic model is reasonably accurate as compared to linear analytical solution, and the three nonhydrostatic models show similar performances for 2D, less hydrostatic flow over a bell-shaped mountain. The anelastic approach was found to be reasonably efficient for nonlinear flow over terrain slopes somewhat less than 1, above which ill convergence for the pressure equation was observed. Simulations of 3D mountain-induced wake circulation with/without the boundary layer effects indicate that there is little difference between the downstream wake forms for the hydrostatic model and the anelastic nonhydrostatic model, a substantiation of the feasibility of the presented anelastic formulation.

Abstract

Quasi-conservative high-order semi-Lagrangian advection schemes are compared with several positive-definite Eulerian schemes in flux form, including Bott’s scheme. In this study, the conventional equipartition method is modified as a posterior iterative mass correction algorithm to restore conservation for semi-Lagrangian transport. The performance comparisons between semi-Lagrangian and Eulerian schemes are evidence that the fifth-order (seventh-order) Bott’s area-preserving algorithm without flux limitation is practically equivalent to the quintic (seventh-order) semi-Lagrangian scheme in the rotational flow, with the maximum directional Courant number smaller than 0.5. For positive-definite advection, Bott’s algorithm with the flux limitation obtains slightly better (worse) amplitude preservation in the rotational flow tests compared to semi-Lagrangian schemes of same order with (without) the mass correction algorithm. In the nonlinear deformational flow where the maximum directional Courant number is greater than 0.5, the former is slightly unstable and only the short-term results are acceptable, but the latter at the long-term remains stable, conservative, and reasonable.

Monotonic tests of semi-Lagrangian schemes were also conducted. It was found that quasi-monotone schemes based on a posterior monotonicity constraint are not influenced by the mass correction algorithm. Both monotonicity and mass conservation can be achieved simultaneously for semi-Lagrangian transport by the post adjustments. However, the monotonicity constraint itself cannot fully suppress the numerical dispersion in the strong nonlinear deformational flow where the mass correction procedure appears to be significantly important for strict mass conservation and a reduction in phase errors.

Abstract

A fourth-order Crowley-type advection scheme based on the multistep Warming-Kutler-Lomax (WKL) scheme is proposed in this study. This scheme utilizes a free parameter to minimize dispersion and dissipation and can be used to represent the advection of positive-definite scalars (such as moisture).

Linear Fourier component analyses indicate that the fourth-order Crowley-type scheme can reproduce the features of other modified Crowley-type schemes of third order, such as the scheme of Schlesinger and the quadratic upstream interpolation. Using the free parameter, the scheme may illustrate the limitation of the Crowley-type schemes for which diffusion is required for numerical stability of advective quantity. For these schemes, formulations that preserve amplitude are inevitably associated with smaller time steps. Adding the first cross-space term into these schemes could eliminate marginal instability or overshooting in linear advection.

Linear and nonlinear advection tests show that the performance of the proposed scheme is comparable to the fourth-order leapfrog scheme (which requires more computer memory) and the cubic upstream spline (which requires more computer time). This two-time-level advection scheme can thus be used in a numerical model to save computer resources.

Abstract

Cold air advection over the Gulf Stream off the Carolinas and the Appalachian Mountains is studied using idealized two-dimensional cases for the Genesis of Atlantic Lows Experiment (GALE) lop 2 conditions. An anelastic hydrostatic mesoscale model is used. Turbulent transfer in the planetary boundary layer, diurnal heating, cloud dynamics, atmospheric longwave and shortwave radiation and subgrid cumulus parameterization are included in the model.

Model results show that the geometry of the oceanic and coastal rainbands depends on the direction of the ambient flow (onshore or offshore). For onshore flows, the rainbands remain in the vicinity of the oceanic baroclinic zone. The rainbands become, transient and migrate downwind of the Gulf Stream front for offshore flows. Depths of the marine boundary layer (MBL) and the cloud (or rain) bands depend more on the ambient flow speed than its direction. The rainbands develop primarily in response to the strong low level convergence.

As expected, southward winds are produced at the eastern side of the Appalachian Mountains for onshore conditions. A significant amount of the turning, however, results from the baroclinic zone over the ocean. Upstream influence of the mountain intensifies the updrafts'in the MBL and moves the oceanic rainbands further offshore. The effects of the atmospheric longwave and shortwave radiation, subgrid cloud heating and diurnal ground heating are of secondary importance in influencing the structure of the MBL as compared to the surface turbulent beat fluxes. Diurnal effects can change the coastal inland flow regime considerably, resulting in a local breeze and the formation of another cloud (or rain) band.

Abstract

A three-dimensional mesoscale planetary boundary layer (PBL) numerical model is used to investigate mesoscale circulations over the Carolina coastal and Gulf Stream baroclinic zones. Idealized ambient onshore and offshore flows are investigated, which represent the synoptic conditions during the Intensive Observation Period-2 (IOP-2) of the 1986 Genesis of Atlantic Lows Experiment (GALE). For the easterly onshore flow, a confluence zone appears west of the Gulf Stream in response to the effect of the oceanic baroclinicity. The confluence zone is nearly parallel to the coastline and the SST isotherms, with northeasterly (southwesterly) flow to the west (east). A shallow coastal front forms below 2 km as the cyclonic shear of the ageostrophic flow becomes strong. Quasi-stationary rainbands are produced by cumulus convection along the coastal front. The northern part of the front and the rainbands later encroach inland as the cold air intensity over ground weakens due to onshore warm air advection. The modeled coastal circulation is in agreement with the observations, suggesting that differential boundary-layer modification may be the main mechanism for the formation of the coastal front. The existence of an onshore ambient flow appears to be a necessary condition for the presence of the Coastal front. For the northerly offshore ambient flow, the rainband therefore appears along the eastern edge of the Gulf Stream, which then moves slowly downstream in response to the generated atmospheric baroclinicity. For both flows, the development of the rainbands is sensitive to variations in eddy Prandtl number, and their growth rate can be explained in terms of conditional symmetric instability.

Abstract

Typhoon Nesat (2017) headed west-northwestward toward Taiwan but took a relatively larger northward deflection about 300 km away and then a leftward deflection after landfall at northern Taiwan. A global model MPAS, employing a multiresolution of 60–15–3 km mesh, is used to investigate the underlying mechanisms of the track changes. The global model simulations are capable of resolving the detailed topographical effects of the Central Mountain Range (CMR) in Taiwan, giving reasonable 5 day tracks in agreement with the observations for Typhoons Soudelor (2015) and Megi (2016), and comparing better with the observed deflection of Nesat (2017) than the regional model simulation of WRF. Sensitivity experiments indicate that flattening the CMR only partially reduces the track deflection of Nesat, while the elimination of the initial cyclone over the South China Sea disables the possible Fujiwhara effect and leads to a southward-biased track with much weaker northward deflection. The northward deflection of Nesat is mainly in response to the wavenumber-1 (WN-1) horizontal PV advection as the southerly flow east of the typhoon center is enhanced by convergence with the outer cyclonic typhoon flow and the large-scale southwesterlies. Upward motions and PV in the troposphere thus are much stronger to the east of the center than to the west, resulting in westward translation induced by negative WN-1 vertical PV advection but eastward translation induced by positive WN-1 vertical differential latent heating to the east. Near landfall, with stronger upward motions produced over the northern CMR, vertical differential latent heating averaged in 3–8-km height becomes negative and thus retards the westward translation.

Abstract

The global model FV3GFS is used to simulate Typhoon Lekima (2019), which exhibited track deflection when approaching west-northwestward toward Taiwan. The model successfully simulates the observed northward deflection and the track deflection is produced by topographically induced wavenumber-1 flow with a pair of vorticity gyres around the typhoon center. The gyres tend to rotate counterclockwise about the typhoon center and thus induce an earlier northward and then westward movement. Azimuthal-mean kinetic energy budget of the typhoon indicates that the effect of Taiwan terrain modifies the correlation between the recirculating flow and pressure gradient force east of Taiwan, leading to a slight weakening of the typhoon during the later track deflection. The northward cyclonic deflection in general will be induced for a cyclone to move toward the central to northern terrain such as Lekima. The curvature of the northward cyclonic deflection, however, is large (small) for a northwestbound (nearly westbound) vortex depending on the track-topography-impinging angle. The curvature difference can be explained with the concept of recirculating flow, which is the flow splitting due to topography and rejoins the vortex to produce the wavenumber-1 asymmetry. The cyclonic track curvature of the northwestbound Lekima is larger than that of the westbound Maria (2018) in the FV3GFS simulations. This adds robustness to the conclusion that minor to moderate terrain-related track deflections can be well simulated by the FV3GFS global model near Taiwan.

Abstract

In this study, the impact of global positioning system (GPS) radio occultation (RO) data on the prediction of the genesis of 10 tropical cyclones over the western North Pacific Ocean is assessed. With the use of a nonlocal excess phase observation operator in cycling data assimilation, the probability of detection for tropical cyclogenesis is increased from 30% to 70% for the cases considered, all of which developed into typhoons. However, the probability of detection is only increased to 40% when a local observation operator is used, indicating that the observation operator can significantly influence the performance of RO data assimilation in capturing tropical cyclogenesis. A nonlocal excess phase operator, which considers the atmospheric horizontal gradients by integrating the refractivity along a ray path, gives superior performance over the local observation operator. Additional sensitivity experiments on 3 of the 10 typhoon cases show that the RO data in the vicinity of the incipient cyclones (within 500 km of the cyclone center) are most critical to successful cyclogenesis prediction. This reflects the fact that having good RO observations at the right time and place is critical for RO to have beneficial impacts on tropical cyclogenesis. Further analyses for Typhoon Nuri (2008) show that assimilation of RO data using the nonlocal operator leads to moistening of the lower and middle troposphere, organized convection, robust grid-scale vertical motions, and the development of midlevel relative vorticity, all of which are favorable for tropical cyclogenesis.

Abstract

The Model for Prediction Across Scales (MPAS) with variable resolution (60–15–1 km) is used to investigate the track deflection of Typhoon Chanthu (2021) near Taiwan. Chanthu exhibited a rightward track deflection as it approached southeast Taiwan and underwent a leftward deflection when moving northward offshore of northeast Taiwan. Numerical experiments are conducted to identify the physical processes for the track deflection. The rightward deflection of the northbound typhoon is induced by the recirculating flow resulting from the effect of Taiwan’s topography. A wavenumber-1 potential vorticity (PV) budget analysis indicates that horizontal PV advection dominates the earlier rightward deflection, while the later leftward deflection is mainly in response to stronger asymmetric cloud heating at low levels at the offshore quadrant of the typhoon. A pair of cyclonic and anticyclonic gyres in the wavenumber-1 flow difference is induced by Taiwan’s topography. These rotate counterclockwise to drive the track deflection, most often in westbound typhoons. Idealized WRF simulations are also conducted to explore the track deflection under different northbound conditions. The simulations confirm the track deflection mechanism with similar PV dynamics to the MPAS simulations for Chanthu and illustrate the variabilities of the track deflection for different steering conditions and vortex origins. The rightward deflection of northbound typhoons is essentially determined by a reduced ratio of R/L_E , where R is the vortex size and L_E is the effective length of the mountain range.