Seasonal predictability of baroclinic wave activity

Midlatitude baroclinic waves drive extratropical weather and climate variations, but their predictability beyond 2 weeks has been deemed low. Here we analyze a large ensemble of climate simulations forced by observed sea surface temperatures (SSTs) and demonstrate that seasonal variations of baroclinic wave activity (BWA) are potentially predictable. This potential seasonal predictability is denoted by robust BWA responses to SST forcings. To probe regional sources of the potential predictability, a regression analysis is applied to the SST-forced large ensemble simulations. By filtering out variability internal to the atmosphere and land, this analysis identifies both well-known and unfamiliar BWA responses to SST forcings across latitudes. Finally, we confirm the model-indicated predictability by showing that an operational seasonal prediction system can leverage some of the identified SST-BWA relationships to achieve skillful predictions of BWA. Our findings help to extend long-range predictions of the statistics of extratropical weather events and their impacts.

Laboratory experiments on the influence of stratification and a bottom sill on seiche damping

The damping of water surface standing waves (seiche modes) and the associated excitation of baroclinic internal waves are studied experimentally in a quasi-two-layer laboratory setting with a topographic obstacle at the bottom representing a seabed sill. We find that topography-induced baroclinic wave drag contributes markedly to seiche damping in such systems. Two major pathways of barotropic–baroclinic energy conversions were observed: the stronger one – involving short-wavelength internal modes of large amplitudes – may occur when the node of the surface seiche is situated above the close vicinity of the sill. The weaker, less significant other pathway is the excitation of long waves or internal seiches along the pycnocline that may resonate with the low-frequency components of the decaying surface forcing.

A semi-implicit pseudo-incompressible flow solver for diabatic dynamics: Baroclinic-wave life cycles

<p>This study introduces an efficient modeling framework for investigations of diabatic flows in the atmosphere. In particular, the spontaneous emission of inertia-gravity waves is addressed in idealized simulations of baroclinic-wave life cycles. Numerical simulations are perfomed using a finite-volume solver for the pseudo-incompressible equations on the f-plane with newly implemented semi-implicit time stepping scheme, adjusted to the staggered grid, which provides high stability and efficiency for long simulation runs with large domains. Furthermore, we have modified the entropy equation to include a heat source, allowing for a development of the vertically dependent reference atmosphere. Numerical experiments of several benchmarks are compared against an explicit third-order Runge-Kutta scheme as well as numerical models from the literature, verifying the accuracy and efficiency of the scheme. The proposed framework serves as a construction basis for an efficient simulation tool for the development and validation of a parameterization scheme for gravity-waves emitted from jets and fronts.</p>

Direct Numerical Simulation of an atmospheric-like differentially heated rotating annulus

<p>Using high-order discretization on a High-Performance Computing framework, direct numerical simulations of a differentially heated rotating annulus are performed. The geometry of the baroclinic wave tank is similar to the new atmospheric-like experiment designed at BTU Cottbus-Senftenberg (Rodda et al., 2020), which also consists of a differentially heated rotating annulus. The experimental observations reveal  spontaneous emissions of inertial-gravity waves in the baroclinic wave jet front in accordance with Hien et al. (2018). The different length scales of inertial-gravity instabilities and the baroclinic waves make direct numerical simulation challenging. This motivates the current design of a new higher-order/HPC solver devoted to stratified rotating flows (Abide et al., 2018). Specifically, some features of compact scheme discretizations are used to combine efficiently parallel computing and accuracy for reducing DNS wall times. The ability to reproduce experimentally measured flow regimes with non-axisymmetric regular steady waves to the vacillation regimes is also discussed.</p><p>S. Abide et al. (2018), Comput Fluids 174:300-310.<br>S. Hien et al. (2018), J Fluid Mech 838:5–41.<br>C. Rodda et al. (2020), Exp Fluids 61:2.</p>

Laboratory experiments on the influence of stratification and a bottom sill on seiche damping

The damping of water surface standing waves (seiche modes) and the associated excitation of baroclinic internal waves are studied experimentally in a quasi-two-layer laboratory setting with a topographic obstacle at the bottom, representing a seabed sill. We find that topography-induced baroclinic wave drag indeed contributes markedly to seiche damping in such systems. Two major pathways of barotropic-baroclinic energy conversions were observed: the stronger one – involving short-wavelength internal modes of large amplitudes – may occur when the node of the surface seiche is situated above the close vicinity of the sill. The weaker, less significant other pathway is the excitation of long waves, internal seiches along the pycnocline that may resonate with the low frequency components of the decaying surface forcing.

Generation of inertia-gravity waves in idealized baroclinic-wave life cycles: Explicit vs. semi-implicit time stepping in a finite-volume solver for the pseudo-incompressible equations

<div> <div> <div> <p>Inertia–gravity waves (IGWs) emitted from jets and fronts are ubiquitous in the atmosphere and have a significant impact on atmospheric processes (Plougonven and Zhang, 2014). Since the mechanism responsible for the spontaneous emission of IGWs during the evolution of an initially balanced flow remain poorly understood, their representation in numerical weather prediction models is challenging (de la Cámara and Lott, 2015). Better understanding of this IGW source mechanism based on idealized numerical simulations is crucial to improve the accuracy of the forecasts. In this study, idealized baroclinic-wave life cycle experiments on the f-plane are performed to investigate spontaneous emission, using a finite-volume solver for the pseudo-incompressible equations (Rieper et al., 2013). In particular, the implementation of a semi-implicit time stepping scheme, along the lines of Smolarkiewicz and Margolin (1997) and Benaccio and Klein (2019), but adjusted to our staggered grid, permits longer simulation runs with much larger domains. A novelty is the implementation of a simple Newtonian heating function based on Held and Suarez (1994), which is used for forcing a baroclinically unstable temperature profile and allows the background state to vary in time (O’Neill and Klein, 2014). The results of the model with semi-implicit time stepping scheme will be documented and compared to an explicit Runge-Kutta scheme. The analysis may serve as a basis for the development and validation of a parameterization scheme for GWs emitted from jets and fronts.</p> <p>References:</p> <p>Benaccio, T., and R. Klein, 2019: A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics. Mon. Wea. Rev., 147, 4221-4240.<br>de la Cámara, A., and F. Lott, 2015: A parameterization of gravity waves emitted by fronts and jets. Geophys. Res. Lett., 42, 2071-2078.<br>Held, I.M., and M.J. Suarez, 1994: A Proposal for the Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models. Bull. Amer. Meteor. Soc., 75, 1825-1830.<br>O’Neill, W.P., and R. Klein, 2014: A moist pseudo-incompressible model. Atmos. Res., 142, 133-141. Plougonven R., and F. Zhang, 2014: Internal gravity waves from atmospheric jets and fronts. Rev. Geophys., 52, 33-76.<br>Rieper, F., Hickel, S., and U. Achatz, 2013: A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization. Mon. Wea. Rev., 141, 861-886. Smolarkiewicz, P.K., and L.G. Margolin, 1997: On forward-in-time differencing for fluids: an Eulerian/semi-Langrangian nonhydrostatic model for stratified flows. Atmosphere-Ocean, 35, 127- 152.</p> </div> </div> </div>

Locating sources of variability in the transition to Structural Vacillation in the baroclinic annulus

<p>The baroclinic rotating annulus is a classic experiment to investigate the transition from regular waves to complex flows.  A well documented transition via Amplitude Vacillation leads to low-dimensional chaos through a sequence of canonical bifurcations.  However, the transition to geostrophic turbulence is usually through a regime of 'Structural Vacillation' (SV) which retains the overall spatial structure of regular waves but includes small-scale variability.  Even though the SV vacillation occurs with a clear time scale, the dynamics of SV cannot usually be described by low-dimensional dynamics.  For example, attractor dimension estimations tend to fail: they may not show any scaling region or converge to an unrealistic values.  Explanations of the origin of SV have variously invoked higher radial modes of the fundamental baroclinic waves, local secondary instabilities in the baroclinic waves caused by high thermal gradients (gravity waves) or velocity shear (barotropic instability), or instabilities within the side-wall (Stewartson) boundary layers.</p><p>The aim of this paper is to identify where within the fluid different signals of variability are located at different stages in the transition from a steady wave to pronounced SV.   To this end, a set of experiments in a water-filled rotating annulus with a free surface (inner radius 45 mm, outer radius 120 mm, fluid depth 140 mm) was carried out covering a temperature difference between the heated outer wall and the cooler inner wall of between 6 and 9.5 K, and a range of rotation rates from 0.84 to 2.29 rad/s (<em>Ta</em>= 4.75 x 10<sup>7</sup> - 3.53 x 10<sup>8</sup> and <em>Θ</em> = 0.0617 - 0.629).   The flow was observed through an infrared camera capturing the temperatures of the free surface.  Images of the flow were recorded for a period of 15 minutes at a sampling rate of 1 Hz at the lower rotation rates and 2 Hz at the higher rotation rates.</p><p>The initial processing of the time series of temperature images involved normalisation of the temperatures followed by rotation of the images to a coordinate system co-rotating with the main baroclinic wave mode. The resulting images were separated into the time-mean wave field and the fluctuation field, resulting in a set of normalised temperature fluctuations at fixed points relative to the main baroclinic wave.   Each of the time series was then used to calculate the power spectrum at that location.  The low-frequency part of the spectra (up until half the tank rotation frequency) was used in a k-means cluster analysis to identify clusters of similar spectral shape and, from this, create a map of which spectral shape was found at which location in the flow field.</p><p>The results show isolated locations of a high frequency peak near the inner boundary at the onset of visible fluctuations.  Further into the regime of clear structural vacillations, areas of pronounced variability at lower frequencies become visible at the lee shoulder of the cold jets in the fluid interior, followed by activity where the end of the cold jet interacts with the hot jet emanating from the outer boundary layer.</p>

Normal Mode Spectra of Idealized Baroclinic Waves

Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra (GE and AE, respectively) are compared to the rotational and divergent kinetic energy (RKE and DKE, respectively), which are often employed as proxies for vortex and wave energy. In our idealized f-plane framework, the horizontal modes are Fourier, and the vertical modes are found by solving an appropriate eigenvalue problem. For low vertical mode number n, both the GE and AE spectra are steep; however, for higher n, while both spectra are shallow, the AE is shallower than the GE and the spectra cross. The AE spectra are peaked at the Rossby deformation wavenumber knR, which increases with n. Analysis of the horizontal mode equations suggests that, for large wavenumbers k≫knR, the GE is approximated by the RKE, while the AE is approximated by the sum of the DKE and potential energy. These approximations are supported by the simulations. The vertically averaged RKE and DKE spectra are compared to the sum of the GE and AE spectra over all vertical modes; the spectral slopes of the GE and AE are close to those of the RKE and DKE, supporting the use of the Helmholtz decomposition to estimate vortices and waves in the midlatitudes. However, the AE is consistently larger than the DKE because of the contribution from the potential energy. Care must be taken when diagnosing the mesoscale transition from the intersection of the vortex and wave spectra; GE and AE will intersect at a different scale than RKE and DKE, despite their similar slopes.

Analysis of Large-Scale Dynamics and Gravity Waves under Shedding of Inactive Flow Components

The Ertel’s potential vorticity (EPV) budget equation does not see the contribution of an inactive EPV flux component ∇θ × ∇B because it drops out when taking the divergence. A part of the actual EPV flux can always be interpreted as such an inactive component and is thus likewise shed from the EPV budget equation. The deviation from this inactive EPV flux is called the active EPV flux and the associated wind is called the active wind. The horizontal active wind is comparable to the ageostrophic wind. The vertical active wind component is similar to the isentropic displacement vertical wind. In contrast to the actual wind, the vertical active wind does not vanish at the surface, because the inactive wind blows along isentropes, which may intersect the ground. Transformed governing equations are derived as functions of the active wind components. The terms on the right of the transformed equations can be scrutinized with respect to their effects on the evolution of the atmospheric state. An idealized baroclinic wave in a dry atmosphere is discussed with focus on the fronts and the generation or depletion of kinetic energy. Since the vertical inactive wind does not necessarily vanish at the surface, the arising vertical active wind is responsible for the cooling (raising of isentropes) and the warming (sinking of isentropes) in the different regions of a cyclone. The new method allows for a unique separation of gravity waves and vortical modes. This facilitates the analysis of gravity wave generation and propagation from jets and fronts.