Barotropic Vorticity Model Research Articles

A mechanism for formation of the western North Pacific monsoon trough: nonlinear upscale cascade

Linear and nonlinear barotropic vorticity model frameworks are constructed to understand the formation of the monsoon trough in boreal summer over the western North Pacific. The governing equation is written with respect to specified zonal background flows, and a wave perturbation is prescribed in the eastern boundary. Whereas a uniform background mean flow leads no scale contraction, a confluent background zonal flow causes the contraction of zonal wavelength. Under linear dynamics, the wave contraction leads to the development of smaller scale vorticity perturbations. As a result, there is no upscale cascade. Under nonlinear dynamics, cyclonic (anticyclonic) wave disturbances shift northward (southward) away from the central latitude due to the vorticity segregation process. The merging of small-scale cyclonic and anticyclonic perturbations finally leads to the generation of a pair of large-scale cyclonic and anti-cyclonic vorticity gyres, straddling across the central latitude. The large-scale cyclonic circulation due to nonlinear upscale cascade can be further strengthened through a positive convection-circulation feedback.

The barotropic Rossby waves with topography on the earth’sδ-surface

AbstractThe Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’sδ-surface is investigated. First, applying scale analysis method, obtained the generalized quasi-geostrophic potential vorticity equation (QGPVE). Using The Wentzel–Kramers–Brillouin (WKB) theory, the evolution equation of Rossby waves is the variable-coefficient Korteweg–de Vries (KdV) equation for the barotropic atmospheric model. In order to study the Rossby waves structural change to exist in some basic flow and topography on theδ-surface approximation, the variable coefficient of KdV equation must be explicitly, Chebyshev polynomials is used to solve a Sturm-Liouville-type eigenvalue problem and the eigenvalue Rossby waves, these solutions show that the parameterδusually plays the stable part in Rossby waves and slow down the growing or decaying of Rossby waves with the parameterβ.

Multidecadal variations in ENSO-Indian summer monsoon relationship at sub-seasonal timescales

Customarily, the strength of the impact of El Nino-Southern Oscillation (ENSO) on Indian summer monsoon is evaluated with respect to the seasonal mean rainfall. As the rainfall occurring over the Indian subcontinent experiences strong variations intraseasonally, the impact of ENSO on these intraseasonal fluctuations is often more important for the agribusiness and economy when contrasted with the seasonal mean. The annual cycle of ISM rainfall peaks during July and August months. In this study, we investigate the impact of ENSO on ISM precipitation during July and August. We show that the relationship between ENSO and ISM rainfall during July and August has experienced significant changes at multidecadal timescales. While the impact of ENSO was significantly strong in August and significantly weak in July during 1948–1980, post-1980s August shows a weak ENSO-Monsoon relationship than that in July. We investigate these multidecadal changes in the ENSO-monsoon relationship using 68 years of observational records. ENSO produces strong (weak) upper tropospheric divergence over equatorial eastern Pacific Ocean in August (July) before 1980. A stronger divergence helps Rossby wave within the Pacific-Asian jet cools the upper tropospheric mid-latitude region by modulating the vorticity there. A colder mid-latitude temperature weakens the Indian summer monsoon. Thus, the impact of ENSO on the Indian summer monsoon was weaker (stronger) in July (August) before 1980 and vice versa after the 1980s. Further, we deploy a linear barotropic vorticity model to assess the association between upper tropospheric divergence over the Pacific Ocean region and vorticity (temperature) over the mid-latitude Asian region. A stronger forcing of divergence in the upper tropospheric Pacific region reinforces stronger positive vorticity in mid-latitude Asia resembling the findings above. Our study suggests that these multidecadal fluctuations in the sub-seasonal ENSO-monsoon relationship is linked to the physical changes in the state of the climate and could not be attributed to the stochastic processes. Such insight into the variability in ENSO-monsoon relationship at sub-seasonal timescales would help predictability and decision-making.

Can Machines Learn to Predict Weather? Using Deep Learning to Predict Gridded 500‐hPa Geopotential Height From Historical Weather Data

AbstractWe develop elementary weather prediction models using deep convolutional neural networks (CNNs) trained on past weather data to forecast one or two fundamental meteorological fields on a Northern Hemisphere grid with no explicit knowledge about physical processes. At forecast lead times up to 3 days, CNNs trained to predict only 500‐hPa geopotential height easily outperform persistence, climatology, and the dynamics‐based barotropic vorticity model, but do not beat an operational full‐physics weather prediction model. These CNNs are capable of forecasting significant changes in the intensity of weather systems, which is notable because this is beyond the capability of the fundamental dynamical equation that relies solely on 500‐hPa data, the barotropic vorticity equation. Modest improvements to the CNN forecasts can be made by adding 700‐ to 300‐hPa thickness to the input data. Our best performing CNN does a good job of capturing the climatology and annual variability of 500‐hPa heights and is capable of forecasting realistic atmospheric states at lead times of 14 days. Although our simple models do not perform better than an operational weather model, machine learning warrants further exploration as a weather forecasting tool; in particular, the potential efficiency of CNNs might make them attractive for ensemble forecasting.

Barotropic Instability across the Moat and Inner Eyewall Dissipation: A Numerical Study of Hurricane Wilma (2005)

Abstract Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls become elliptical prior to their dissipation. These elliptical features indicate that the barotropic instability (BI) across the moat (aka, type-2 BI) may play a role in the process. To investigate the mechanism for dissipation, a WRF simulation of Hurricane Wilma (2005) is performed. The results reveal an elliptical elongation of the inner eyewall and a change in the structure of the radial flow from wavenumber (WN) 1 to WN 2 at the lower levels. A linear stability analysis as well as idealized nonlinear experiments using a nondivergent barotropic vorticity model initialized with the vorticity fields before the change in the dominant wavenumber of the radial flow are presented with the results supporting the presence of a type-2 BI at the lower levels. The accompanying WN-2 radial flow is also found to dilute the vorticity within the inner eyewall and the eye. However, this dilution is not seen at higher levels as the type-2 BI becomes weak and short lived at the middle levels and reaches its weakest strength at the upper levels. This phenomenon is traced to the fact that a higher growth rate comes with a narrower moat for type-2 BI. As the outward slope of the outer eyewall is larger than that of the inner eyewall, the moat width increases with height so that the growth rate decreases with height. The results presented here thus highlight the potential role played by the barotropic instability across the moat in inner eyewall dissipation.

Review article: Comparison of local particle filters and new implementations

Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential importance sampling, suited for nonlinear and non-Gaussian filtering problems. Unless the number of ensemble members scales exponentially with the problem size, particle filter (PF) algorithms experience weight degeneracy. This phenomenon is a manifestation of the curse of dimensionality that prevents the use of PF methods for high-dimensional data assimilation. The use of local analyses to counteract the curse of dimensionality was suggested early in the development of PF algorithms. However, implementing localisation in the PF is a challenge, because there is no simple and yet consistent way of gluing together locally updated particles across domains. In this article, we review the ideas related to localisation and the PF in the geosciences. We introduce a generic and theoretical classification of local particle filter (LPF) algorithms, with an emphasis on the advantages and drawbacks of each category. Alongside the classification, we suggest practical solutions to the difficulties of local particle filtering, which lead to new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz 40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms, even for a mildly nonlinear system.

Localization and the iterative ensemble Kalman smoother

The iterative ensemble Kalman smoother (IEnKS) is a data assimilation method meant for tracking the state of nonlinear geophysical models efficiently. It combines an ensemble of model states to estimate the errors similarly to the ensemble square‐root Kalman filter, with a four‐dimensional variational analysis performed within the ensemble space. As such, it belongs to the class of four‐dimensional ensemble variational methods. It could require the use of localization of the analysis when the state‐space dimension is high. However, its localization needs to be defined across time and to be as consistent as possible with the dynamical flow within the data assimilation window where the four‐dimensional variational analysis is performed. We show that a Liouville equation governs the time evolution of the localization operator, which is linked to the evolution of the error correlations. It is argued that the time evolution of the localization operator depends strongly on the forecast dynamics. Using either covariance localization or domain localization, we propose and test several localization strategies meant to address the issue: (i) a static and uniform localization, (ii) propagation through the window of a restricted set of dominant modes of the error covariance matrix and (iii) the approximate propagation of the localization operator using covariant local domains that are moved in accordance with the dynamical flow. These schemes are illustrated with the one‐dimensional Lorenz 40 variable model and with a two‐dimensional barotropic vorticity model. In both cases, local analysis based on the covariant local domains leads to a systematic improvement of the data assimilation performance.

Numerical study of a regularized barotropic vorticity model of geophysical flow

We study a Crank–Nicolson in time, finite element in space, numerical scheme for a Bardina regularization of the barotropic vorticity (BV) model. We derive the regularized model from the simplified Bardina model in primitive variables, present a numerical algorithm for it, and prove the algorithm is unconditionally stable with respect to the timestep size and optimally convergent in both space and time. Numerical experiments are provided that verify the theoretical convergence rates, and also that test the model/scheme on a benchmark double-gyre wind forcing experiment. For the latter test, we find the proposed model/scheme gives a good coarse mesh approximation to the highly resolved direct numerical simulation of the BV model, and compares favorably to related regularization model results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1492–1514, 2015

Preemptive Forecasts Using an Ensemble Kalman Filter

Abstract An ensemble Kalman filter (EnKF) estimates the error statistics of a model forecast using an ensemble of model forecasts. One use of an EnKF is data assimilation, resulting in the creation of an increment to the first-guess field at the observation time. Another use of an EnKF is to propagate error statistics of a model forecast forward in time, such as is done for optimizing the location of adaptive observations. Combining these two uses of an ensemble Kalman filter, a “preemptive forecast” can be generated. In a preemptive forecast, the increment to the first-guess field is, using ensembles, propagated to some future time and added to the future control forecast, resulting in a new forecast. This new forecast requires no more time to produce than the time needed to run a data assimilation scheme, as no model integration is necessary. In an observing system simulation experiment (OSSE), a barotropic vorticity model was run to produce a 300-day “nature run.” The same model, run with a different vorticity forcing scheme, served as the forecast model. The model produced 24- and 48-h forecasts for each of the 300 days. The model was initialized every 24 h by assimilating observations of the nature run using a hybrid ensemble Kalman filter–three-dimensional variational data assimilation (3DVAR) scheme. In addition to the control forecast, a 64-member forecast ensemble was generated for each of the 300 days. Every 24 h, given a set of observations, the 64-member ensemble, and the control run, an EnKF was used to create 24-h preemptive forecasts. The preemptive forecasts were more accurate than the unmodified, original 48-h forecasts, though not quite as accurate as the 24-h forecast obtained from a new model integration initialized by assimilating the same observations as were used in the preemptive forecasts. The accuracy of the preemptive forecasts improved significantly when 1) the ensemble-based error statistics used by the EnKF were localized using a Schur product and 2) a model error term was included in the background error covariance matrices.

Energy extremals and nonlinear stability in a variational theory of a coupled barotropic flow - Rotating solid sphere system

A new variational principle—extremizing the fixed frame kinetic energy under constant relative enstrophy—for a coupled barotropic flow—rotating solid sphere system is introduced with the following consequences. In particular, angular momentum is transferred between the fluid and the solid sphere through a modeled torque mechanism. The fluid’s angular momentum is therefore not fixed but only bounded by the relative enstrophy, as is required of any model that supports super-rotation. The main results are: At any rate of spin Ω and relative enstrophy, the unique global energy maximizer for fixed relative enstrophy corresponds to solid-body super-rotation; the counter-rotating solid-body flow state is a constrained energy minimum provided the relative enstrophy is small enough, otherwise, it is a saddle point. For all energy below a threshold value which depends on the relative enstrophy and solid spin Ω, the constrained energy extremals consist of only minimizers and saddles in the form of counter-rotating states. Only when the energy exceeds this threshold value can pro-rotating states arise as global maximizers. Unlike the standard barotropic vorticity model which conserves angular momentum of the fluid, the counter-rotating state is rigorously shown to be nonlinearly stable only when it is a local constrained minima. The global constrained maximizer corresponding to super-rotation is always nonlinearly stable.

On the Separation of a Barotropic Western Boundary Current from a Cape

AbstractThe problem of western boundary current separation is investigated using a barotropic vorticity model. Specifically, a boundary current flowing poleward along a boundary containing a cape is considered. The meridional gradient of the Coriolis parameter (the β effect), the strength of dissipation, and the geometry of the cape are varied. It is found that 1) all instances of flow separation are coincident with the presence of a flow deceleration, 2) an increase in the strength of the β effect is able to suppress flow separation, and 3) increasing coastline curvature can overcome the suppressive β effect and induce separation. These results are supported by integrated vorticity budgets, which attribute the acceleration of the boundary current to the β effect and changes in flow curvature. The transition to unsteady final model states is found to have no effect upon the qualitative nature of these conclusions.

Numerical Analysis of Stochastic Schemes in Geophysics

We present and study the stability, convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic implicit leapfrog scheme which has been developed for the approximation of the so-called barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and discussed.

Analysis of stochastic numerical schemes for the evolution equations of geophysics

We present and study the stability and convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic “implicit leapfrog” scheme which has been developed for the approximation of the so-called barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and discussed.

Remotely and Regionally Forced Pre‐Monsoon Signals Over Northern India and Neighbourhood

AbstractA detailed diagnostic examination of the National Centre for Environmental PredictiodNational Centre for Atmospheric Research Reanalysis data supplemented by a theoretical study is undertaken with the goal of investigating the dynamics of pre‐monsoon stationary wave anomalies occurring over northern India and adjoining region prior to weak Indian summer monsoons. It is seen from the analysis that the rotational wind anomalies preceding weak monsoon years are primarily forced by tropical divergent wind anomalies located over the tropical central‐eastern Pacific ocean, south Indian ocean and locally over north‐west India. the divergent wind anomalies over the central‐eastern Pacific ocean can be linked to anomalous changes in the tropical Pacific sea surface temperature arising due to El Nioñ/Southern Oscillation (ENSO). the upper level divergent wind forcing overlying the south Indian ocean seems to be locally connected to the warm sea surface temperature anomalies over that region.Results of simple experiments using a forced divergent barotropic vorticity model establish that the maintenance of rotational wind anomalies over north India prior to weak monsoons is attributable to the existence of anomalous divergent wind forcing over the aforementioned regions in the tropics. A normal mode experiment shows that the climatological basic flow alone is not sufficient to support these pre‐monsoon vorticity perturbations. Furthermore, calculation of vorticity generation terms suggests that the divergent wind advection and Rossby source terms make significant contributions to the production of rotational anomalies over north India during the pre‐monsoon months. Based on the above results, it is conjectured that energy injection into the subtropics via Rossby wave dispersion could be a foremost dynamical mechanism which efficiently sustains rotational wind perturbations over north India and neighbourhood. an assessment of the relative importance of the ENSO and non‐ENS0 divergent forcings, shows that the latter tend to exert a larger influence on the pre‐monsoon signals over north‐west India.The implications of using the pre‐monsoon signals for long range forecasting of Indian summer monsoon activity are determined by two factors viz., (i) the robustness and intensity of the pre‐monsoon signals and (ii) the persistence of the signals during the following months. the first factor in turn depends on the manner in which the different forcing anomalies co‐ordinate. the amplitude of the pre‐monsoon signals can be large (small) depending on whether the ENSO and non‐ENSO boundary forcings act in a mutually co‐operative (competitive) manner. the second factor, which is related to the maintenance of anomalous quasi‐stationary patterns during the following months, depends crucially on how the different boundary forcings evolve during the summer monsoon season.

Barotropic Instability of Midlatitude Zonal Jets on Mars, Earth and Venus

We have used a linearized nondivergent barotropic vorticity model on a sphere to intercompare the fastest growing, barotropically unstable wave modes computed for zonal jets at high latitudes in the middle atmospheres of Venus, Earth, and Mars. Such zonal jets have been observed in the wintertime stratosphere on Earth and have been inferred from remotely sensed temperatures in the Venus middle atmosphere and in the wintertime Martian atmosphere. The comparison was done by extending the results of Hartmann for his simple analytic profile of a latitudinally varying terrestrial zonal wind to zonal wind profiles characterized by the larger Rossby numbers (Ro) appropriate to Mars and Venus. As Hartmann's results suggested, the fastest growing barotropic waves continue to grow more quickly as Ro increases. Eventually, the fastest growing mode shifts from a zonal wavenumber k = 1 to a k = 2 mode, both located on the poleward flank of the high-latitude jet. However, for somewhat higher Rossby numbers, the k = 2 mode on the equatorward side of the zonal jet becomes the fastest growing planetary-scale barotropic mode, and this transition is marked by a discontinuous shift to longer wave periods. The Venus high-latitude zonal jet appears remarkably close to this transition Ro. For each of the three planets, satellite-borne instruments have detected wave patterns in the thermal radiance field in the vicinity of the high-latitude zonal jets. As reported earlier for the terrestrial wintertime stratosphere by Hartmann and for Venus by Elson, these observed waves have characteristics similar to those computed for the fastest growing barotropic modes. For Mars, we find that such modes would have zonal wavenumbers 1 or 2, with e-folding times of 2-3 days and periods of 0.75–2.5 days; the longer period (k = 2) equatorward mode would dominate for the faster and narrower zonal jets. A poleward mode with k = 1 and a period of 1.2 days is the barotropic mode most likely to be consistent with the Mariner-9 IRIS observations of thermal waves above the 1 mb (˜20 km) level in the Martian atmosphere.