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This paper presents efficient and practical implementations of sequential data assimilation methods for the Simplified Parameterizations, primitive‐Equation DYnamics (SPEEDY) Model, a well‐known numerical model, into the data assimilation community for climate prediction. In the SPEEDY model, the time evolution of dynamics is performed via the second‐order Leapfrog integration scheme; this time integrator relies on two steps: the position and the velocity. The computational implementation of SPEEDY blends the time integrator and the spatial discretization of dynamics to accelerate algebraic computations. Thus, there is no access to the right‐hand side function of the ordinary differential equations governing the time evolution of model dynamics. Consequently, the SPEEDY model is often treated as a black box wherein positions and velocities work as inputs and outputs. Since observations in operational data assimilation only match position states, we can exploit augmented vector states to propagate analysis innovations from positions to velocities. For this purpose, we formulate three variants of ensemble‐based filters and perform numerical experiments to assess their accuracies. We consider two scenarios for the experiments: an ideal case wherein positions and velocities can be observed and a more realistic one wherein measurements are only accessible for position states. Besides, we discuss the effects of the ensemble size on the accuracies of our formulations and, even more, the typical case in which velocities are not updated across assimilation steps. The results reveal that all filter formulations' accuracies remain the same in terms of Root‐Mean‐Square‐Error by neglecting observations from velocities (a realistic scenario) even for cases wherein the number of measurements decreases to 6% of model components. Furthermore, for all discussed filter implementations, the propagation of analysis increments from position to velocities improves up to 100% the performance of filter implementations wherein velocities are not updated, a typical operational scenario. [ABSTRACT FROM AUTHOR]

Quasi‐biennial oscillations (QBOs) in thirteen atmospheric general circulation models forced with both observed and annually repeating sea surface temperatures (SSTs) are evaluated. In most models the QBO period is close to, but shorter than, the observed period of 28 months. Amplitudes are within ±20% of the observed QBO amplitude at 10 hPa, but typically about half of that observed at lower altitudes (50 and 70 hPa). For almost all models, the oscillation's amplitude profile shows an overall upward shift compared to reanalysis and its meridional extent is too narrow. Asymmetry in the duration of eastward and westward phases is reasonably well captured, though not all models replicate the observed slowing of the descending westward shear. Westward phases are generally too weak, and most models have an eastward time mean wind bias throughout the depth of the QBO. The intercycle period variability is realistic and in some models is enhanced in the experiment with observed SSTs compared to the experiment with repeated annual cycle SSTs. Mean periods are also sensitive to this difference between SSTs, but only when parametrized non‐orographic gravity wave (NOGW) sources are coupled to tropospheric parameters and not prescribed with a fixed value. Overall, however, modelled QBOs are very similar whether or not the prescribed SSTs vary interannually. A portrait of the overall ensemble performance is provided by a normalized grading of QBO metrics. To simulate a QBO, all but one model used parametrized NOGWs, which provided the majority of the total wave forcing at altitudes above 70 hPa in most models. Hence the representation of NOGWs either explicitly or through parametrization is still a major uncertainty underlying QBO simulation in these present‐day experiments. [ABSTRACT FROM AUTHOR]

We compare the response of the Quasi‐Biennial Oscillation (QBO) to a warming climate in eleven atmosphere general circulation models that performed time‐slice simulations for present‐day, doubled, and quadrupled CO2 climates. No consistency was found among the models for the QBO period response, with the period decreasing by 8 months in some models and lengthening by up to 13 months in others in the doubled CO2 simulations. In the quadrupled CO2 simulations, a reduction in QBO period of 14 months was found in some models, whereas in several others the tropical oscillation no longer resembled the present‐day QBO, although it could still be identified in the deseasonalized zonal mean zonal wind timeseries. In contrast, all the models projected a decrease in the QBO amplitude in a warmer climate with the largest relative decrease near 60 hPa. In simulations with doubled and quadrupled CO2, the multi‐model mean QBO amplitudes decreased by 36 and 51%, respectively. Across the models the differences in the QBO period response were most strongly related to how the gravity wave momentum flux entering the stratosphere and tropical vertical residual velocity responded to the increases in CO2 amounts. Likewise it was found that the robust decrease in QBO amplitudes was correlated across the models to changes in vertical residual velocity, parametrized gravity wave momentum fluxes, and to some degree the resolved upward wave flux. We argue that uncertainty in the representation of the parameterized gravity waves is the most likely cause of the spread among the eleven models in the QBO's response to climate change. [ABSTRACT FROM AUTHOR]

Convectively generated gravity waves (CGGWs) are important for numerical weather prediction due to their effect on the quasi‐biennial oscillation (QBO) in the stratosphere. Using global ECMWF IFS simulations at TCo7999 (or 1.25 km), TCo2559 (or 3.9 km) and TCo1279 (or 7.8 km) horizontal resolutions, sensitivity of resolved CGGWs to the horizontal resolution and to the explicit versus parametrized representation of deep convection is elucidated during the westerly shear phase of the QBO. Parametrized deep convection is found to inhibit CGGWs, resulting in a twofold reduction in CGGW forcing. When deep convection is explicitly resolved, the total CGGW forcing is almost unchanged across the horizontal resolutions. However, the contribution of long and mesoscale CGGWs (with horizontal wavelengths 100 km ≤λh<1,900 km) to the total CGGW forcing decreases and the contribution of smaller‐scale CGGWs (with λh<100 km) increases as the horizontal resolution increases. At the maximum CGGW forcing altitude, at TCo7999 resolution 43% of the total CGGW forcing is due to long and mesoscale waves, whereas at TCo2559 and TCo1279 resolutions their contribution is 70% and 90%, respectively. While CGGW forcing from long and mesoscale waves is similar at TCo7999 resolution with explicit deep convection and at TCo1279 resolution with parametrized deep convection, CGGW forcing from these waves is artificially enhanced at TCo1279 and TCo2559 resolutions with explicit deep convection. This is due to the explicit deep convection being too strong and having too much variance for 100 km ≤λh<1,900 km. Therefore, parametrizations of deep convection and CGGWs (to account for forcing from waves with λh<100 km) are required even at TCo2559 resolution. Additionally, resolved CGGW forcing at TCo7999 resolution is examined for the easterly shear phase of the QBO; similar to the westerly shear phase, the smaller‐scale waves contribute >55% to the total CGGW forcing at the maximum CGGW forcing altitude. [ABSTRACT FROM AUTHOR]

An ensemble of idealized experiments with the simplified general circulation model PUMA is used to analyze the response to reduced surface friction, that is a strengthening of the eddy‐driven jet, a weakening of the Eulerian mean overturning, and a suppression of baroclinic instability. The suppression of baroclinic instability is caused by an effect called the barotropic governor by which increased horizontal shear restricts the ability of baroclinic disturbances to convert available potential energy into kinetic energy. This governor effect ensures that the residual circulation and Eliassen–Palm flux (EP flux) divergence are largely invariant to the surface friction parameter despite the connection between surface friction, the Eulerian mean overturning, and the eddy‐momentum flux. The suppression of instability leads to an increase in persistence measured by the period of peak variance on synoptic time‐scales and a strengthened signal‐to‐noise ratio on seasonal time‐scales. These findings suggest that the signal‐to‐noise paradox seen in the context of seasonal prediction can be caused by excess mechanical damping in atmospheric prediction systems inhibiting the barotropic governor effect. [ABSTRACT FROM AUTHOR]

During the last decade, the replacement of static climatological forecast error covariance models with hybrid error covariance models that linearly combine localised ensemble covariances with static climatological error covariances has led to significant forecast improvements at several major forecasting centres. Here, a deeper understanding of why the hybrid's superficially ad hoc mix of ensemble‐based and climatological covariances yields such significant improvements is pursued. In practice, ensemble covariances are not equal to the true flow‐dependent forecast error covariance matrix. Here, the relationship between actual forecast error covariance and the corresponding ensemble covariance is empirically demonstrated. Using a simplified global circulation model and the local ensemble transform Kalman filter (LETKF), the covariance of the set of actual forecast errors corresponding to ensemble covariances close to a fixed target value is computed. By doing this for differing target values, an estimate of the actual forecast error covariance as a function of ensemble covariance is obtained. A demonstration that the hybrid is a much better approximation to this estimate than either the static climatological covariance or the localised ensemble covariance is given. The empirical estimate has two features that current hybrid error covariance models fail to represent: (i) The weight given to the static covariance matrix is an increasing function of the horizontal separation distance of the covarying model variables, and (ii) for small ensemble sizes and ensemble covariances near zero but negative, the actual forecast error covariance is a decreasing function of increasing ensemble covariance. While the first finding has been anticipated by other authors, the second finding has not been anticipated, as far as the authors are aware. Here, (ii) is hypothesised to be a consequence of spurious sample correlations and variances associated with reduced ensembles. Consistent with this hypothesis, the non‐monotonicity of this relationship is almost eliminated by quadrupling the ensemble size. [ABSTRACT FROM AUTHOR]

A coupled atmosphere–ocean data assimilation system, the Meteorological Research Institute-Coupled Data Assimilation System Version 1 (MRI-CDA1), was developed based on the coupled atmosphere–ocean general circulation model and separate atmosphere and ocean analysis routines operated by the JapanMeteorological Agency (JMA). To implement coupled atmosphere–ocean data assimilation, 6-hr data assimilation cycles with the coupled model in the outer loop are adopted in atmospheric data assimilation, whereas incremental analysis updates with 10-day data assimilation cycles are adopted in ocean data assimilation. A coupled data assimilation (reanalysis) experiment (CDA-Exp) is conducted using MRI-CDA1 along with an uncoupled reanalysis experiment (UCPL-Exp) in which the same atmospheric component of the coupled model is forced by prescribed sea surface temperature (SST) similarly to the JMA reanalysis, JRA-55. Climatological precipitation and variations in precipitation and sea surface air temperature (SAT) are better represented in CDA-Exp than in JRA-55, which is brought about by the modification of the atmosphere model physics of the coupledmodel to better represent climate states. In CDA-Exp, the SST adjustment to the atmosphere amplifies the lead/lag correlations between subseasonal variations of SST and precipitation. The atmosphere–ocean coupling generates SST variations associated with tropical instability waves, and the SAT field responds to SST variations. The SST–precipitation and SST–SAT relationships on the weather timescale are also recovered in CDA-Exp, although they are hardly seen in UCPL-Exp. The coupled model physics generates weather-timescale SST variations consistent with the atmospheric state, and the atmospheric parameters respond to the SST variations through the coupled model physics. This study suggests that the benefits of coupled data assimilation would be more evident if the ability of MRI-CDA1 to represent SST variations and its interaction with the atmosphere are improved. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Design, development and assessment of numerical algorithms based on Rossby–Ertel potential vorticity (PV) for the dynamical core of global models are of particular importance in atmospheric and oceanic modelling for improving representation of both balanced and unbalanced flows. The general circulation models are usually developed in various vertical coordinates and horizontal grids. The Diabatic Contour‐Advective Semi‐Lagrangian (DCASL) algorithm based on contour representation of an approximate form of PV is further developed by (a) inclusion of a form of arbitrary Lagrangian–Eulerian method for the hybrid σ–θ vertical coordinate, and (b) extension to the σ–p vertical coordinate with both Charney–Phillips (CP) and Lorenz (L) grids. Using a baroclinic instability test case, the working of DCASL in the newly developed σ–θ is compared with two other forms of DCASL in σ–p developed with CP and L grids. These comparisons show that the initialisation problem present in σ–θ vertical coordinate is removed and the solutions become close to the numerically convergent solutions of four other dynamical cores, within the range of their uncertainties, when the σ–p vertical coordinate is used. Results also show the usefulness of DCASL in σ–p, even though the prognostic variable representing vortical flow is less materially conservative than that of the σ–θ. [ABSTRACT FROM AUTHOR]

Parametrizations of sea surface turbulent fluxes used in general circulation models (GCMs) assume horizontal homogeneity of atmospheric properties at the grid‐cell scale. The present study assesses the contribution of the meso‐scale (i.e., subgrid) to the grid‐scale surface fluxes, for GCM resolution ranging from 20 to 200 km, and thus quantifies the associated GCM surface flux error. A coarse‐graining method allows for an a priori analysis of the subgrid information. It is based on an atmospheric reference dataset produced by the convection‐permitting operational model AROME. The meso‐scale relative contribution to GCM‐scale fluxes exceeding 10% is shown to have large regional patterns, with large values (up to 90%) and high frequency of occurrence (up to 76% of the time). These meso‐scale motions are not necessarily due to convective activity but also occur frequently under dynamical perturbation conditions. Contributions to surface fluxes, at both the GCM scale and the meso‐scale, are disentangled through a Reynolds decomposition. It is found that temperature and humidity meso‐scale heterogeneities do not contribute much to the GCM‐scale fluxes. The subgrid dynamical processes are the main meso‐scale contribution and consist of two parts. The first one represents the wind magnitude and wind direction heterogeneities and corresponds to the so‐called gustiness approach. It is clarified that the contribution of the gustiness wind in the transfer coefficients cannot be neglected. The second part is the contribution of the wind speed subgrid variance, which contributes up to 10% of the GCM‐scale momentum flux. [ABSTRACT FROM AUTHOR]

The climate and circulation of a terrestrial planet are governed by, among other things, the distance to its host star, its size, rotation rate, obliquity, atmospheric composition and gravity. Here we explore the effects of the last of these, the Newtonian gravitational acceleration, on its atmosphere and climate. We first demonstrate that, if the atmosphere obeys the hydrostatic primitive equations, which are a very good approximation for most terrestrial atmospheres, and if the radiative forcing is unaltered, changes in gravity have no effect at all on the circulation except for a vertical rescaling. That is to say, the effects of gravity may be completely scaled away and the circulation is unaltered. However, if the atmosphere contains a dilute condensible that is radiatively active, such as water or methane, then an increase in gravity will generally lead to a cooling of the planet because the total path length of the condensible will be reduced as gravity increases, leading to a reduction in the greenhouse effect. Furthermore, the specific humidity will decrease, leading to changes in the moist adiabatic lapse rate, in the Equator‐to‐Pole heat transport, and in the surface energy balance because of changes in the sensible and latent fluxes. These effects are all demonstrated both by theoretical arguments and by numerical simulations with moist and dry general circulation models. [ABSTRACT FROM AUTHOR]

The sensitivity of an operational numerical weather prediction model to the parametrized microphysical properties of ice hydrometeors is examined. The effects of varying ice-particle size distribution, fall speed, mass and depositional capacitance are considered in kilometre-scale simulations of midlatitude cloud systems and 20 year global climate integrations. It is shown that the observed sensitivity can be obtained from steady-state arguments, whereby the vertical moisture flux is balanced by the hydrometeor sedimentation flux and supersaturation production is in equilibrium with depositional growth. The high-resolution simulations are compared with in situ measurements from the Constrain field campaign (Prestwick, UK). [ABSTRACT FROM AUTHOR]

Tropical precipitation is caused by many processes that occur over a wide range of temporal and spatial scales. Such processes vary from local, diurnal convection driven by a destabilisation of the boundary layer to planetary-scale systems that result in rainfall over many days. It is therefore important to assess whether general circulation models (GCMs) can represent these processes given that such models are routinely used to project future rainfall in the low latitudes. In this study, we evaluate the rainfall and circulation characteristics of ten GCMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5) over northern Australia. This work shows that the diurnal cycle of the low-level (925 hPa) flow around the heat low is represented well by the models but the timing of precipitation is not (triggered too early). There is also evidence that mid-level synoptic systems that are responsible for initiating rain in the observations are also present in all of the models. Nevertheless, the biases in the modelled seasonal mean precipitation seem to be linked to the strength of both the meridional flow into northern Australia and the vertical mass flux. Furthermore, there is also evidence that the representation of convection in these models is likely contributing to both the precipitation and circulation errors over northern Australia. [ABSTRACT FROM AUTHOR]

The representation of rainfall, and in particular its diurnal cycle, is generally poor in general circulation models (GCMs). Nonetheless, studies make use of GCMs in future climate projections in regions where precipitation has a strong diurnal cycle. In this study we evaluate whether one GCM (ACCESS1.3) can represent the rainfall in such a region (Australia) where the diurnal cycle of rainfall is produced as a result of both the destabilisation of the boundary layer (convection) and a larger-scale reorganisation of the low-level flow, the latter of which may be resolved by a GCM. In northern and eastern Australia, where the diurnal cycle of rainfall is controlled by convective processes, the GCM produces rain 3 to 6 h too early in the day. Nevertheless, the model represents the continental-scale reorganisation of the low-level circulation that results from the diurnal cycle of surface heating and cooling. A nocturnal low-level jet forms over the western half of the continent with strong convergence at the jet exit, which initiates rain overnight in the continental northwest, in agreement with previous work. The model also captures the change in the air-flow direction, from a southeasterly to a northeasterly, responsible for bringing the necessary moisture for precipitation to occur. Thus, while the model may have a tendency to initiate convection too early, it is able to represent the larger-scale nocturnal reorganisation of the flow and the associated rainfall. [ABSTRACT FROM AUTHOR]

A third-order global shallow-water model was developed on an icosahedral-hexagonal grid with the application of the multi-moment constrained finite-volume (MCV) method. Using the hexagonal grid, the sphere is divided into quasi-uniform elements and free of polar problems. The MCV model defines seven degrees of freedom (DOFs) as the prognostic variables which are the point values at the six vertices and the centre for each hexagonal element to construct a third-order scheme. The time evolution equations to update the DOFs are derived through the constraint conditions on different moments, i.e. the point value and the volume-integrated average (VIA) moments. Rigorous conservation is guaranteed by the constraint on the VIA through a flux form. The MCV formulation is very simple and easy to implement. We evaluated the model with benchmark tests, and the competitive results reveal the proposed model to be an accurate and practical framework for developing general circulation models. [ABSTRACT FROM AUTHOR]

An investigation of how stationary Rossby wave (SRW) propagation can change in response to the A2 climate change scenario is made using six coupled ocean-atmosphere general-circulation models (OAGCM). The simulation results for the present-day climate (1960-1990) are compared with the NCEP/NCAR and ECMWF ERA-40 re-analyses. The zonal wind, the SRW kinetic energy (KE) pattern along the waveguide and the stationary wave-number are used to analyse the changes in the SRW propagation for the winter season of each hemisphere. The main result shows that in future climate (2069-2099) the SRW propagation for longer distances is unfavourable for the main waveguides in the Northern Hemisphere (NH) and Southern Hemisphere (SH), which is confirmed through the SRW KE decrease. A poleward shift of the subtropical jet stream in future climate is also shown by five models in the SH and by three in the NH. [ABSTRACT FROM AUTHOR]

Numerical models of the atmosphere should fulfil fundamental physical laws. The second law of thermodynamics is associated with positive local entropy production and dissipation of available energy. In order to guarantee this positivity in numerical simulations, subgrid-scale turbulent fluxes of heat, water vapour and momentum are required to depend on numerically resolved gradients in a unique way. The task of parametrization remains to deliver phenomenological coefficients. Inspecting commonly used parametrizations for subgrid fluxes, we find that some of them obey the second law of thermodynamics and some do not. The conforming approaches are Smagorinsky momentum diffusion, phase changes and sedimentation fluxes for hydrometeors. Conventional turbulent heat-flux parametrizations do not conform with the second law. A new water-vapour flux formulation is derived from the requirement of locally positive entropy production. The conventional and new water-vapour fluxes are compared using high-resolution radiosonde data. Conventional water-vapour fluxes are wrong by up to 10% and exhibit a negative bias. Two numerical tests (the Boulder windstorm test case and a convective boundary-layer experiment) are performed with the Icosahedral Nonhydrostatic model at the Institute for Atmospheric Physics (ICON-IAP). The experiments compare conventional and entropy-consistent heat-flux parametrizations. Both test cases indicate that negative thermal dissipation can occur for the conventional heat flux. Obviously, the additional energy made available by this negative dissipation to the resolved turbulence is later on dissipated by friction, so that the total dissipation is again comparable, at least for the boundary-layer experiment. [ABSTRACT FROM AUTHOR]