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In idealized simulations of moist baroclinic instability on a sphere, the most unstable mode transitions from a periodic wave to an isolated vortex in sufficiently warm climates. The vortex mode is maintained through latent heating and shows the principal characteristics of a diabatic Rossby vortex (DRV) that has been found in a range of different simulations and observations of the current climate. Currently, there is no analytical theory for DRVs or understanding of the wave–vortex transition that has been found in warmer climates. Here, we introduce a minimal moist two-layer quasigeostrophic model with tilted boundaries capable of producing a DRV mode, and we derive growth rates and length scales for this DRV mode. In the limit of a convectively neutral stratification, the length scale of ascent of the DRV is the same as that of a periodic moist baroclinic wave, but the growth rate of the DRV is 54% faster. We explain the isolated structure of the DRV using a simple potential vorticity (PV) argument, and we create a phase diagram for when the most unstable solution is a periodic wave versus a DRV, with the DRV emerging when the moist static stability and meridional PV gradients are weak. Last, we compare the structure of the DRV mode with DRV storms found in reanalysis and with a DRV storm in a warm-climate simulation. Significance Statement: Past research has identified a special class of midlatitude storm, dubbed the diabatic Rossby vortex (DRV), which derives its energy from the release of latent heat associated with condensation of water vapor and as such goes beyond the traditional understanding of midlatitude storm formation. DRVs have been implicated in extreme and poorly predicted forms of cyclogenesis along the east coast of the United States and the west coast of Europe with significant damage to property and human life. The purpose of this study is to develop a mathematical theory for the intensification rate and length scale of DRVs to gain a deeper understanding of the dynamics of these storms in current and future climates. [ABSTRACT FROM AUTHOR]

Quasigeostrophic (QG) theory describes the dynamics of synoptic-scale flows in the troposphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by Ekman layer theory. The troposphere covers roughly the lowest 10 km of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative and turbulent heat fluxes which can be significant in about the lowest 3 km and in the middle latitudes. To address this deficiency, this paper extends the classical QG–Ekman layer model by introducing an intermediate dynamically and thermodynamically active layer, called the "diabatic layer" (DL) from here on. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time-independent background stratification. Instead, within the DL diabatic processes are allowed to affect the leading-order stratification. As a consequence, this layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasigeostrophic bulk flow. The result is the proposed extended quasigeostrophic three-layer QG–DL–Ekman model for midlatitude dynamics. [ABSTRACT FROM AUTHOR]

The near-tropopause energy spectrum closely follows a -5/3 power law at mesoscales. Most theories addressing the mesoscale spectrum assume unbalanced dynamics but ignore the tropopause (near which the bulk of the data were collected). Conversely, it has also been proposed that the mesoscale spectrum results from tropopause-induced alterations of geostrophic turbulence. This paper seeks to reconcile these a priori mutually exclusive theories by presenting simulations that permit both unbalanced motion and tropopauseinduced effects. The model integrates the nonhydrostatic Boussinesq equations in the presence of a rapidly varying background stratification profile (an idealized tropopause). Decaying turbulence simulations were performed over a wide range of Rossby numbers. In the limit of weak flow (U ≲ 1ms-1), the essential features of the Boussinesq simulations are well captured by a quasigeostrophic version of the model: secondary roll-ups of filaments and shallow spectral slopes are observed near the tropopause but not elsewhere. However, these tropopause-induced effects rapidly disappear with increasing flow strength. For flow strengths more typical of the tropopause (U~10ms-1), the spectrum develops a shallow, near-5/3 tail associated with fast-time-scale, unbalanced motion. In contrast to weak flows, this spectral shallowing is evident at any altitude and regardless of the presence of a tropopause. Diagnostics of the fast component of motion reveal significant inertia-gravity wave activity at large horizontal scales (where the balanced flow dominates). However, no evidence points to such activity in the shallow range. That is, the mesoscale of the model is dominated by unbalanced turbulence, not waves. Implications and limitations of these findings are discussed. [ABSTRACT FROM AUTHOR]

Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth's atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15% of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes. [ABSTRACT FROM AUTHOR]

A single-column modeling approach is proposed to study the interaction between convection and large-scale dynamics using the quasigeostrophic (QG) framework. This approach extends the notion of 'parameterization of large-scale dynamics,' previously applied in the tropics via the weak temperature gradient approximation and other comparable methods, to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating in an air column is resolved numerically by a single-column model or a cloud-resolving model. The large-scale vertical velocity, which controls vertical advection of temperature and moisture, is computed through the QG omega equation including the dry adiabatic terms and the diabatic heating term. The component due to diabatic heating can be thought of as geostrophic adjustment to that heating and couples the convection to the large-scale vertical motion. The approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases. The behavior of convection that is strongly coupled to large-scale dynamics is significantly different from that in the uncoupled case. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths on the order of the Rossby deformation radius. [ABSTRACT FROM AUTHOR]

Finite-amplitude Rossby wave activity (FAWA) proposed by Nakamura and Zhu measures the waviness of quasigeostrophic potential vorticity (PV) contours and the associated modification of the zonal-mean zonal circulation, but it does not distinguish longitudinally localized weather anomalies, such as atmospheric blocking. In this article, FAWA is generalized to local wave activity (LWA) to diagnose eddy-mean flow interaction on the regional scale. LWA quantifies longitude-by-longitude contributions to FAWA following the meridional displacement of PV from the circle of equivalent latitude. The zonal average of LWA recovers FAWA. The budget of LWA is governed by the zonal advection of LWA and the radiation stress of Rossby waves. The utility of the diagnostic is tested with a barotropic vorticity equation on a sphere and meteorological reanalysis data. Compared with the previously derived Eulerian impulse-Casimir wave activity, LWA tends to be less filamentary and emphasizes large isolated vortices involving reversals of meridional gradient of potential vorticity. A pronounced Northern Hemisphere blocking episode in late October 2012 is well captured by a high-amplitude, near-stationary LWA. These analyses reveal that the nonacceleration relation holds approximately over regional scales: the growth of phase-averaged LWA and the deceleration of local zonal wind are highly correlated. However, marked departure from the exact nonacceleration relation is also observed during the analyzed blocking event, suggesting that the contributions from nonadiabatic processes to the blocking development are significant. [ABSTRACT FROM AUTHOR]

Based on a viewpoint that the North Atlantic Oscillation (NAO) is a nonlinear initial-value problem, the predictability of NAO event onset is studied through investigation of the relationship between the optimal precursor (OPR) to its onset and the optimally growing initial error (OGE) in onset prediction. The problem is explored by the method of conditional nonlinear optimal perturbation with a triangular T21, three-level, quasigeostrophic global spectral model. For the NAO onset, there are two types of OGEs. Numerical results show that, with the optimization time of 3 days, a type-1 OGE bears a great resemblance to OPR, and the similarity coefficient between them is 0.98 for both positive (NAO+) and negative NAO (NAO−). A type-2 OGE is also characterized by a similar pattern to OPR, but with an opposite sign. With the extension of the optimization time to 7 days, the similarity coefficient between OPR and type-1 (type 2) OGE gradually decreases to 0.82 (−0.81) for NAO− and 0.87 (−0.57) for NAO+. However, in the linear regime, such high similarity between OPR and OGE can only be found with an optimization time of 3 days. Further analysis reveals that a type-1 (type 2) OGE has a similar growth behavior to that of the corresponding OPR of the same-phase (opposite phase) NAO event, both of which develop into a dipole NAO anomaly pattern. This similarity between OPR and OGE suggests that the nonlinear process plays an important role in the NAO event, which simultaneously provides a theoretical foundation for its targeted observations. [ABSTRACT FROM AUTHOR]

The fluctuation-dissipation theorem (FDT) provides a means of calculating the response of a dynamical system to a small force by constructing a linear operator that depends only on data from the internal variability of the unperturbed system. Here the FDT is used to estimate the response of a two-layer quasigeostrophic model to two zonally symmetric torques, both barotropic, with the same sign of the forcing in the two layers, and baroclinic, with opposite sign forcing in the two layers. The supercriticality of the model is also varied to test how the FDT fares, as this parameter is varied. To perform the FDT calculations the data are decomposed onto empirical orthogonal functions (EOFs) and only those EOFs that are well resolved are retained in the FDT calculations. In the barotropic case good qualitative estimates are obtained for all values of the supercriticality, though the FDT consistently overestimates the response, perhaps because of significant non-Gaussian behavior present in the model. Nevertheless, this adds to the evidence that the annular-mode time scale plays an important role in determining the response of the midlatitudes to small perturbations. The baroclinic case is more challenging for the FDT. However, by constructing different bases with which to calculate the EOFs, it is shown that the issue in this case is that the baroclinic variability is poorly sampled, not that the FDT fails. The strategies developed in order to generate these estimates may be applicable to situations in which the FDT is applied to larger systems. [ABSTRACT FROM AUTHOR]

A long time series of temporally high-resolution wind and potential temperature data from the 213-m tower at Cabauw in the Netherlands demonstrates the existence of two distinct regimes of the stably stratified nocturnal boundary layer at this location. Hidden Markov model (HMM) analysis is used to objectively characterize these regimes and classify individual observed states. The first regime is characterized by strongly stable stratification, large wind speed differences between 10 and 200 m, and relatively weak turbulence. The second is associated with near-neutral stratification, weaker wind speed differences between 10 and 200 m, and relatively strong turbulence. In this second regime, the state of the boundary layer is similar to that during the day. The occupation statistics of these regimes are shown to covary with the large-scale pressure gradient force and cloud cover such that the first regime predominates under clear skies with weak geostrophic wind speed and the second regime predominates under conditions of extensive cloud cover or large geostrophic wind speed. These regimes are not distinguished by standard measures of stability, such as the Obukhov length or the bulk Richardson number. Evidence is presented that the mechanism generating these distinct regimes is associated with a previously documented feedback resulting from the existence of an upper limit on the maximum downward heat flux that can be sustained for a given near-surface wind speed. [ABSTRACT FROM AUTHOR]

It is shown in this paper that there is no ambiguity in the final form of the governing equations of a quasigeostrophic (QG) model after partitioning the total flow into the geostrophic, balanced ageostrophic, and unbalanced ageostrophic components. The uniqueness of the QG model formulation ensures that the energetics of a QG model is the same as that derived from the QG potential vorticity equation. Particularly, the well-known but somewhat mysterious "missing term" in the energetics of Rossby waves, identified in the literature as the difference between the pressure work and the energy flux transported at the group velocity, can be easily recovered. The missing term is the pressure work on the convergence of the balanced ageostrophic flow, representing a "hidden" conversion between kinetic and potential energy of the geostrophic flow that excites the unbalanced flow. This energy conversion equals the convergence of a one-directional energy flux that always transports energy westward at the zonal phase speed of Rossby waves. The pressure work on the divergence of the unbalanced flow does the actual conversion between kinetic and potential energy of the geostrophic flow and the pressure work on the unbalanced flow causes energy propagation in other directions. Therefore, it is the pressure work on the unbalanced flow that causes Rossby waves to be dispersive, leading to the downstream development. The sum of the energy transported at the zonal phase speed of Rossby waves and the pressure work on the unbalanced flow exactly equals the energy transported at the group velocity of Rossby waves. [ABSTRACT FROM AUTHOR]

The eastward-propagating tropical low-frequency disturbances, such as the moist Kelvin waves or the Madden-Julian oscillation (MJO), are often observed to experience convective enhancement when meeting with the westward-propagating 2-day waves. A scale interaction (SI) model is built to understand the nature of the interaction between the 2-day waves and moist Kelvin waves or MJO. In this model, the convective complex of moist Kelvin waves modulates the strength and location of the 2-day waves, which feed back through the upscale eddy transfer. An ageostrophic model describing the 2-day waves is first solved, and the resultant westward-propagating, backward-tilted disturbances are consistent with the observed 2-day waves. An explicit representation of eddy momentum transfer (EMT), eddy heating transfer (EHT), and eddy moisture transfer (EQT) arising from the 2-day waves is then formulated. The SI model shows that the 2-day waves in front of moist Kelvin waves produce an EMT accelerating the low-frequency easterly in the lower troposphere, an EHT cooling down the middle troposphere, and an EQT moistening the middle troposphere. These three transfer terms have comparable magnitude. Although the negative EHT tends to damp the moist Kelvin waves, both the EMT and EQT provide instability sources for the moist Kelvin waves. The 2-day waves also slow down the moist Kelvin waves, mainly through the advective effects of the EMT. So the unstable moist Kelvin waves may exhibit convective enhancement when meeting with the 2-day waves. The theoretical results presented here point to the need to further observe the multiscale structures within the moist Kelvin waves and the MJO. [ABSTRACT FROM AUTHOR]

A diagnostic relationship between finite-amplitude wave activity and the associated adiabatic adjustments to the zonal-mean zonal wind and temperature is developed in the quasigeostrophic (QG) framework and is applied to a 23-yr segment (1979--2001) of the 40-yr ECMWF Re-Analysis (ERA-40) data. Wave activity is defined in terms of an instantaneous areal displacement of QG potential vorticity (PV) from zonal symmetry. Unlike previous forms, the tendency of wave activity equals exactly the negative of the eddy PV flux (Eliassen--Palm flux divergence) in the conservative limit, even at finite amplitude. This allows one to integrate the transformed Eulerian mean (TEM) theory in time and quantify the departure (adiabatic adjustment) of the zonal-mean state from an eddy-free reference state in terms of the observed wave activity. The structure of wave activity identifies synoptic eddies in the extratropics and planetary waves in the high latitudes of winter-to-spring stratosphere. In addition, a thin layer of high wave activity is found at the top of the lowermost stratosphere (∼∼17 km) in the summer extratropics. The reference state is constructed by ''zonalizing'' the PV contours conservatively (preserving area) on the isobaric surface and by inverting the resultant PV gradient for the mean flow. The adjustment associated with wave activity depends on the assumed surface boundary condition for the reference state. With a no-slip condition, the observed zonal-mean temperature is on average ∼∼33 (90) K higher than the reference state in the troposphere (stratosphere) of the Arctic winter, while the zonal-mean zonal wind is ∼∼30 m s−−1 slower in the upper stratosphere. Since the reference state filters out the advective eddy--mean flow interaction, it fluctuates less than the zonal-mean state, potentially improving the signal-to-noise ratio for climate diagnosis. [ABSTRACT FROM AUTHOR]

The climatology of transient wave activity flux defined by Plumb has been calculated for each calendar month, for high-frequency (HF) and low-frequency (LF) waves, using the NCAR-NCEP reanalyses for both hemispheres. Wave activity flux of both HF and LF waves shows upward propagation of waves from the lower troposphere into the upper troposphere, then into the lower stratosphere during the summer and at least up to the midstratosphere during other seasons. While the upward flux emanating from the lower troposphere is particularly large in the two storm tracks in the Northern Hemisphere (NH), it is large in most of the extratropics in the Southern Hemisphere (SH). The HF waves radiate equatorward most noticeably in the upper troposphere, whereas the LF waves do not show visible signs of equatorward radiation. The total horizontal flux is generally dominated by the advective flux that represents the eddy enstrophy advection by the mean flow and appears predominantly pseudoeastward. Divergence of the wave activity flux exhibits discernible large-scale characteristics at the lowest level in both hemispheres and in the upper troposphere in the NH. The divergence field indicates acceleration of the pseudoeastward mean flow near the surface in both hemispheres. In the NH, acceleration and deceleration, respectively, of the pseudoeastward mean flow in the storm tracks and downstream of the storm tracks in the upper troposphere are found. Seasonal variations in the wave flux are substantial in the NH but relatively minor in the SH. In the NH, the wave flux fields exhibit generally larger values during the cold months than during warm months. Also, the latitudes at which large wave flux values are seen are higher during warm months, as the jets and storm tracks shift northward from the winter to the summer. Anomalously large vertical flux of both HF and LF wave activity propagating up from the lower troposphere throughout the troposphere and stratosphere in the northern flank of the North Atlantic storm track is found to precede anomalous deceleration in the NH winter polar vortex, while anomalously small vertical flux in the same area precedes anomalous acceleration of the vortex. The accompanying horizontal flux anomalies tend to counteract the action of the anomalous vertical flux. These cases are found to be dissipation of strong anomalies in the polar vortex. The anomalous flux divergence does not prove the active role of the waves in the anomalous change in the polar vortex, however. No signs of the wave flux originating from specific areas preceding anomalous change in the polar vortex are found for the SH. [ABSTRACT FROM AUTHOR]

Nonlinear deterministic reduced models of large-scale atmospheric dynamics are constructed. The dynamical framework is a quasigeostrophic three-level spectral model with realistic mean state and variability as well as Pacific–North America (PNA) and North Atlantic Oscillation (NAO) patterns. The study addresses the problem of finding appropriate basis functions for efficiently capturing the dynamics and a comparison between different choices of basis functions; it focuses on highly truncated models, keeping only 10–15 modes. The reduced model is obtained by a projection of the equations of motion onto a truncated basis spanned by empirically determined modes. The total energy metric is used in the projection; the nonlinear terms of the low-order model then conserve total energy. Apart from retuning the coefficient of horizontal diffusion, no empirical terms are fitted in the dynamical equations of the low-order model in order to properly preserve the physics of the system. Using the methodology of principal interaction patterns (PIPs), a basis is derived that carefully compromises minimizing tendency error with maximizing explained variance in the resolved modes. A new PIP algorithm is introduced that is more compact and robust than earlier PIP algorithms; a top-down approach is adopted, removing modes from the system one by one. The mean state and standard deviation of the streamfunction as well as transient momentum fluxes are well reproduced by a PIP model with only 10 modes. Probability density functions are accurately modeled and autocorrelation functions are captured fairly well using 15 modes. Reduced models based on PIPs are substantially superior to reduced models based on empirical orthogonal functions (EOFs). The leading PIPs have a higher projection onto the PNA and NAO teleconnection patterns than the corresponding EOFs. Both with EOFs and PIPs, the interactions between the resolved modes are predominantly linear and the improvement of PIP models on EOF models stems entirely from better modeling these linear interactions although the full nonlinear tendencies are optimized. There is considerable influence of smaller-scale modes on the large-scale modes due to nonlinear coupling that is not well captured by either EOFs or PIPs. This nonlinear backscattering possibly plays a role in generating the low-frequency variability of the model. The results call for a nonlinear and/or stochastic closure scheme in which PIPs may be suitable basis functions. [ABSTRACT FROM AUTHOR]