Overcoming set imbalance in data driven parameterization: A case study of gravity wave momentum transport

Machine learning for the parameterization of subgrid-scale processes in climate models has been widely researched and adopted in a few models. A key challenge in developing data-driven parameterization schemes is how to properly represent rare, but important events that occur in geoscience datasets. We investigate and develop strategies to reduce errors caused by insufficient sampling in the rare data regime, under constraints of no new data and no further expansion of model complexity. Resampling and importance weighting strategies are constructed with user defined parameters that systematically vary the sampling/weighting rates in a linear fashion and curb too much oversampling. Applying this new method to a case study of gravity wave momentum transport reveals that the resampling strategy can successfully improve errors in the rare regime at little to no loss in accuracy overall in the dataset. The success of the strategy, however, depends on the complexity of the model. More complex models can overfit the tails of the distribution when using non-optimal parameters of the resampling strategy.Comment: 26 pages, 10 figures, 2 table

Stratosphere–Troposphere Coupling in a Relatively Simple AGCM: The Importance of Stratospheric Variability

The impact of stratospheric variability on the dynamical coupling between the stratosphere and the troposphere is explored in a relatively simple atmospheric general circulation model. Variability of the model’s stratospheric polar vortex, or polar night jet, is induced by topographically forced stationary waves. A robust relationship is found between the strength of the stratospheric polar vortex and the latitude of the tropospheric jet, confirming and extending earlier results in the absence of stationary waves. In both the climatological mean and on intraseasonal time scales, a weaker vortex is associated with an equatorward shift in the tropospheric jet and vice versa. It is found that the mean structure and variability of the vortex in the model is very sensitive to the amplitude of the topography and that Northern Hemisphere–like variability, with a realistic frequency of stratospheric sudden warming events, occurs only for a relatively narrow range of topographic heights. When the model captures sudden warming events with fidelity, however, the exchange of information both upward and downward between the troposphere and stratosphere closely resembles that in observations. The influence of stratospheric variability on variability in the troposphere is demonstrated by comparing integrations with and without an active stratosphere. A realistic, time-dependent stratospheric circulation increases the persistence of the tropospheric annular modes, and the dynamical coupling is most apparent prior to and following stratospheric sudden warming events

Seasonal Variability of the Polar Stratospheric Vortex in an Idealized AGCM with Varying Tropospheric Wave Forcing

The seasonal variability of the polar stratospheric vortex is studied in a simplified AGCM driven by specified equilibrium temperature distributions. Seasonal variations in equilibrium temperature are imposed in the stratosphere only, enabling the study of stratosphere–troposphere coupling on seasonal time scales, without the complication of an internal tropospheric seasonal cycle. The model is forced with different shapes and amplitudes of simple bottom topography, resulting in a range of stratospheric climates. The effect of these different kinds of topography on the seasonal variability of the strength of the polar vortex, the average timing and variability in timing of the final breakup of the vortex (final warming events), the conditions of occurrence and frequency of midwinter warming events, and the impact of the stratospheric seasonal cycle on the troposphere are explored. The inclusion of wavenumber-1 and wavenumber-2 topographies results in very different stratospheric seasonal variability. Hemispheric differences in stratospheric seasonal variability are recovered in the model with appropriate choices of wave-2 topography. In the model experiment with a realistic Northern Hemisphere–like frequency of midwinter warming events, the distribution of the intervals between these events suggests that the model has no year-to-year memory. When forced with wave-1 topography, the gross features of seasonal variability are similar to those forced with wave-2 topography, but the dependence on forcing magnitude is weaker. Further, the frequency of major warming events has a nonmonotonic dependence on forcing magnitude and never reaches the frequency observed in the Northern Hemisphere.United States. National Aeronautics and Space Administration (Grant NNX13AF80G

Annular Mode Time Scales in the Intergovernmental Panel on Climate Change Fourth Assessment Report Models

The ability of climate models in the Intergovernmental Panel on Climate Change Fourth Assessment Report to capture the temporal structure of the annular modes is evaluated. The vertical structure and annual cycle of the variability is quantified by the e-folding time scale of the annular mode autocorrelation function. Models vaguely capture the qualitative features of the Northern and Southern Annular Modes: Northern Hemisphere time scales are shorter than those of the Southern Hemisphere and peak in boreal winter, while Southern Hemisphere time scales peak in austral spring and summer. Models, however, systematically overestimate the time scales, particularly in the Southern Hemisphere summer, where the multimodel ensemble average is twice that of reanalyses. Fluctuation-dissipation theory suggests that long time scales in models could be associated with increased sensitivity to anthropogenic forcing. Comparison of model pairs with similar forcings but different annular mode time scales provides a hint of a fluctuation-dissipation relationship

Abrupt Circulation Responses to Tropical Upper-Tropospheric Warming in a Relatively Simple Stratosphere-Resolving AGCM

The circulation response of the atmosphere to climate change–like thermal forcing is explored with a relatively simple, stratosphere-resolving general circulation model. The model is forced with highly idealized physics, but integrates the primitive equations at resolution comparable to comprehensive climate models. An imposed forcing mimics the warming induced by greenhouse gasses in the low-latitude upper troposphere. The forcing amplitude is progressively increased over a range comparable in magnitude to the warming projected by Intergovernmental Panel on Climate Change coupled climate model scenarios. For weak to moderate warming, the circulation response is remarkably similar to that found in comprehensive models: the Hadley cell widens and weakens, the tropospheric midlatitude jets shift poleward, and the Brewer–Dobson circulation (BDC) increases. However, when the warming of the tropical upper troposphere exceeds a critical threshold, ~5 K, an abrupt change of the atmospheric circulation is observed. In the troposphere the extratropical eddy-driven jet jumps poleward nearly 10°. In the stratosphere the polar vortex intensifies and the BDC weakens as the intraseasonal coupling between the troposphere and the stratosphere shuts down. The key result of this study is that an abrupt climate transition can be effected by changes in atmospheric dynamics alone, without need for the strong nonlinearities typically associated with physical parameterizations. It is verified that the abrupt climate shift reported here is not an artifact of the model’s resolution or numerics

Testing the Annular Mode Autocorrelation Time Scale in Simple Atmospheric General Circulation Models

A new diagnostic for measuring the ability of atmospheric models to reproduce realistic low-frequency variability is introduced in the context of Held and Suarez’s 1994 proposal for comparing the dynamics of different general circulation models. A simple procedure to compute τ, the e-folding time scale of the annular mode autocorrelation function, is presented. This quantity concisely quantifies the strength of low-frequency variability in a model and is easy to compute in practice. The sensitivity of τ to model numerics is then studied for two dry primitive equation models driven with the Held–Suarez forcings: one pseudospectral and the other finite volume. For both models, τ is found to be unrealistically large when the horizontal resolutions are low, such as those that are often used in studies in which long integrations are needed to analyze model variability on low frequencies. More surprising is that it is found that, for the pseudospectral model, τ is particularly sensitive to vertical resolution, especially with a triangular truncation at wavenumber 42 (a very common resolution choice). At sufficiently high resolution, the annular mode autocorrelation time scale τ in both models appears to converge around values of 20–25 days, suggesting the existence of an intrinsic time scale at which the extratropical jet vacillates in the Held and Suarez system. The importance of τ for computing the correct response of a model to climate change is explicitly demonstrated by perturbing the pseudospectral model with simple torques. The amplitude of the model’s response to external forcing increases as τ increases, as suggested by the fluctuation–dissipation theorem

The Relationship between Age of Air and the Diabatic Circulation of the Stratosphere

The strength of the Brewer–Dobson circulation is difficult to estimate using observations. Trends in the age of stratospheric air, deduced from observations of transient tracers, have been used to identify trends in the circulation, but there are ambiguities in the relationship between age and the strength of the circulation. This paper presents a steady-state theory and a time-dependent extension to relate age of air directly to the diabatic circulation of the stratosphere. In steady state, it is the difference between the age of upwelling and downwelling air through an isentrope and not the absolute value of age that is a measure of the strength of the diabatic circulation through that isentrope. For the time-varying case, expressions for other terms that contribute to the age budget are derived. An idealized atmospheric general circulation model with and without a seasonal cycle is used to test the time-dependent theory and to find that these additional terms are small upon annual averaging. The steady-state theory holds as well for annual averages of a seasonally varying model as for a perpetual-solstice model. These results are a step toward using data to quantify the strength of the diabatic circulation.National Science Foundation (U.S.) (AGS-1547733

Numerical impacts on tracer transport: A proposed intercomparison test of Atmospheric General Circulation Models

The transport of trace gases by the atmospheric circulation plays an important role in the climate system and its response to external forcing. Transport presents a challenge for Atmospheric General Circulation Models (AGCMs), as errors in both the resolved circulation and the numerical representation of transport processes can bias their abundance. In this study, two tests are proposed to assess transport by the dynamical core of an AGCM. To separate transport from chemistry, the tests focus on the age‐of‐air, an estimate of the mean transport time by the circulation. The tests assess the coupled stratosphere–troposphere system, focusing on transport by the overturning circulation and isentropic mixing in the stratosphere, or Brewer–Dobson Circulation, where transport time‐scales on the order of months to years provide a challenging test of model numerics. Four dynamical cores employing different numerical schemes (finite‐volume, pseudo‐spectral, and spectral‐element) and discretizations (cubed sphere versus latitude–longitude) are compared across a range of resolutions. The subtle momentum balance of the tropical stratosphere is sensitive to model numerics, and the first intercomparison reveals stark differences in tropical stratospheric winds, particularly at high vertical resolution: some cores develop westerly jets and others easterly jets. This leads to substantial spread in transport, biasing the age‐of‐air by up to 25% relative to its climatological mean, making it difficult to assess the impact of the numerical representation of transport processes. This uncertainty is removed by constraining the tropical winds in the second intercomparison test, in a manner akin to specifying the Quasi‐Biennial Oscillation in an AGCM. The dynamical cores exhibit qualitative agreement on the structure of atmospheric transport in the second test, with evidence of convergence as the horizontal and vertical resolution is increased in a given model. Significant quantitative differences remain, however, particularly between models employing spectral versus finite‐volume numerics, even in state‐of‐the‐art cores

Understanding Hadley Cell Expansion versus Contraction: Insights from Simplified Models and Implications for Recent Observations

This study seeks a deeper understanding of the causes of Hadley Cell (HC) expansion, as projected under global warming, and HC contraction, as observed under El Niño. Using an idealized general circulation model, the authors show that a thermal forcing applied to a narrow region around the equator produces “El Niño–like” HC contraction, while a forcing with wider meridional extent produces “global warming–like” HC expansion. These circulation responses are sensitive primarily to the thermal forcing’s meridional structure and are less sensitive to its vertical structure. If the thermal forcing is confined to the midlatitudes, the amount of HC expansion is more than three times that of a forcing of comparable amplitude that is spread over the tropics. This finding may be relevant to recently observed trends of rapid tropical widening. The shift of the HC edge is explained using a very simple model in which the transformed Eulerian mean (TEM) circulation acts to diffuse heat meridionally. In this context, the HC edge is defined as the downward maximum of residual vertical velocity in the upper troposphere ϖmax *; this corresponds well with the conventional Eulerian definition of the HC edge. In response to a positive thermal forcing, there is anomalous diabatic cooling, and hence anomalous TEM descent, on the poleward flank of the thermal forcing. This causes the HC edge (ϖmax *) to shift toward the descending anomaly, so that a narrow forcing causes HC contraction and a wide forcing causes HC expansion

The Circulation Response to Volcanic Eruptions: The Key Roles of Stratospheric Warming and Eddy Interactions

Proxy data and observations suggest that large tropical volcanic eruptions induce a poleward shift of the North Atlantic jet stream in boreal winter. However, there is far from universal agreement in models on this effect and its mechanism, and the possibilities of a corresponding jet shift in the Southern Hemisphere or the summer season have received little attention. Using a hierarchy of simplified atmospheric models, this study examines the impact of stratospheric aerosol on the extratropical circulation over the annual cycle. In particular, the models allow the separation of the dominant shortwave (surface cooling) and longwave (stratospheric warming) impacts of volcanic aerosol. It is found that stratospheric warming shifts the jet poleward in both summer and winter hemispheres. The experiments cannot definitively rule out the role of surface cooling, but provide no evidence that it shifts the jet poleward. Further study with simplified models demonstrates that the response to stratospheric warming is remarkably generic and does not depend critically on the boundary conditions (e.g., the planetary wave forcing) or the atmospheric physics (e.g., the treatment of radiative transfer and moist processes). It does, however, fundamentally involve both zonal-mean and eddy circulation feedbacks. The timescales, seasonality, and structure of the response provide further insight into the mechanism, as well as its connection to modes of intrinsic natural variability. These findings have implications for the interpretation of comprehensive model studies and for post-volcanic predictio