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1.
This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational ("adjoint") sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the "macroscopic climate sensitivity"(that is, the sensitivity of time‐averaged properties of the system to finite‐amplitude perturbations). This problem occurs even for time‐averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble‐adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter‐combinations to be explored further through direct finite‐amplitude perturbations.  相似文献   

2.
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3.
We compare the short‐ and medium‐range predictability of weather regimes of a quasi‐geostrophic model as defined by a hierarchical cluster algorithm and a Lyapunov‐based clustering method recently introduced in the literature. Both procedures lead to weather regimes displaying very different predictability properties on the short and medium range bases. While the former does not distinguish between stable and unstable weather regimes, the latter leads to clusters which do not display a good medium range predictability. We introduce a new clustering method taking advantages of the two previous techniques. Its application in the context of the quasi‐geostrophic model gives rise to regimes possessing at the same time a good medium range skill and well separated instability properties, indicating the possibility to build a systematic cartography of the short‐term predictability of weather fields in phase space.  相似文献   

4.
Simulations of Rossby–Haurwitz waves have been carried out using four different high‐resolution numerical shallow water models: a spectral model, two semi‐Langrangian models predicting wind components and potential vorticity respectively, and a finite‐volume model on a hexagonal–icosahedral grid. The simulations show that (i) unlike the nondivergent case, the shallow water Rossby–Haurwitz wave locally generates small‐scale features and so has a potential enstrophy cascade, and (ii) contrary to common belief, the zonal wavenumber 4 Rossby–Haurwitz wave is dynamically unstable and will eventually break down if initially perturbed. Implications of these results for the use of the Rossby–Haurwitz wave as a numerical model test case are discussed. The four models tested give very similar results, giving confidence in the accuracy and robustness of the results. The most noticeable difference between the models is that truncation errors in the hexagonal–icosahedral grid model excite the Rossby–Haurwitz wave instability, causing the wave to break down quickly, whereas for the other models in the configurations tested the instability is excited only by roundoff error at worst, and the Rossby–Haurwitz wave breaks down much more slowly or not at all.  相似文献   

5.
In this paper, we present a numerical procedure for solving a 2‐dimensional, compressible, and nonhydrostatic system of equations. A forward‐backward integration scheme is applied to treat high‐frequency and internal gravity waves explicitly. The numerical procedure is shown to be neutral in time as long as a Courant–Friedrichs–Lewy criterion is met. Compared to the leap‐frog‐scheme most models use, this method involves only two time steps, which requires less memory and is also free from unstable computational modes. Hence, a time‐filter is not needed. Advection and diffusion terms are calculated with a time step longer than sound‐wave related terms, so that extensive computer time can be saved. In addition, a new numerical procedure for the free‐slip bottom boundary condition is developed to avoid using inaccurate one‐sided finite difference of pressure in the surface horizontal momentum equation when the terrain effect is considered. We have demonstrated the accuracy and stability of this new model in both linear and nonlinear situations. In linear mountain wave simulations, the model results match the corresponding analytical solution very closely for all three cases presented in this paper. The analytical streamlines for uniform flow over a narrow mountain range were obtained through numerical integration of Queney's mathematical solution. It was found Queney's original diagram is not very accurate. The diagram had to be redrawn before it was used to verify our model results. For nonlinear tests, we simulated the famous 1972 Boulder windstorm and a bubble convection in an isentropic enviroment. Although there are no analytical solutions for the two nonlinear tests, the model results are shown to be very robust in terms of spatial resolution, lateral boundary conditions, and the use of the time-split scheme.  相似文献   

6.
The physical processes responsible for the formation in a large‐scale ice–ocean model of an offshore polynya near the Greenwich meridian in the Southern Ocean are analysed. In this area, the brine release during ice formation in autumn is sufficient to destabilise the water column and trigger convection. This incorporates relatively warm water into the surface layer which, in a first step, slows down ice formation. In a second step, it gives rise to ice melting until the total disappearance of the ice at the end of September. Two elements are crucial for the polynya opening. The first one is a strong ice‐transport divergence in fall induced by south‐easterly winds, which enhances the amount of local ice formation and thus of brine release. The second is an inflow of relatively warm water at depth originating from the Antarctic Circumpolar Current, that sustains the intense vertical heat flux in the ocean during convection. The simulated polynya occurs in a region where such features have been frequently observed. Nevertheless, the model polynya is too wide and persistent. In addition, it develops each year, contrary to observations. The use of a climatological forcing with no interannual variability is the major cause of these deficiencies, the simulated too low density in the deep Southern Ocean and the coarse resolution of the model playing also a role. A passive tracer released in the polynya area indicates that the water mass produced there contributes significantly to the renewal of deep water in the Weddell Gyre and that it is a major component of the Antarctic Bottom Water (AABW) inflow into the model Atlantic.  相似文献   

7.
Ensemble and reduced‐rank approaches to prediction and assimilation rely on low‐dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time‐independent systems are used to identify factors that cause the steady‐state analysis error covariance to admit a low‐dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix , a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady‐state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time‐dependent systems. If much of the steady‐state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady‐state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting non‐modal transient growth. Failure to observe growing modes leads to increased steady‐state analysis error variances. Leading eigenvectors of the steady‐state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest‐order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady‐state analysis error covariance matrix.  相似文献   

8.
Different climatic simulations have been obtained by using a 2‐Dim horizontal energy balance model (EBM), which has been constrained to satisfy several extremal principles on dissipation and convection. Moreover, 2 different versions of the model with fixed and variable cloud‐cover have been used. The assumption of an extremal type of behaviour for the climatic system can acquire additional support depending on the similarities found with measured data for past conditions as well as with usual projections for possible future scenarios.  相似文献   

9.
The wind dependence of sea‐ice motion was studied on the basis of ice velocity and wind observations, and weather model output. The study area was a transition zone between open water and the ice‐covered ocean in the northern Baltic Sea. In the centre of the basin the sea‐ice motion was highly wind‐dependent and the linear relationship between the wind and the drift velocities explained 80% of the drift's variance. On the contrary, the wind‐drift dependence was low near the coast. The wind‐drift coherence was significant over a broader frequency range in the central part of the basin than for the coastal drift. The ice motion was simulated by a numerical model forced with five types of wind stress and with two types of current data, and the outcome was compared with the observed buoy drift. The wind and the wind‐induced surface current were the main factors driving the ice in the basin's centre, while internal ice stresses were of importance in the shear zone near the fast ice edge. The best wind forcing was achieved by applying a method dependent on atmospheric stability and ice conditions. The average air–ice drag coefficient was 1.4×10−3 with the standard deviation of 0.2×10−3. The improvement brought about by using an accurate wind stress was comparable with that achieved by raising the model grid resolution from 18 km to 5 km.  相似文献   

10.
The physical mechanism by which seasonally varying atmospheric wind stress exerted on the sea surface is communicated to the solid earth as oceanic pressure torque (continental torque) and bottom frictional torque is investigated with a linear shallow‐water numerical model of barotropic oceans. The model has a realistic land–ocean distribution and is driven by a seasonally varying climatic wind stress. A novel way to decompose the wind stress into rotational and non‐rotational components is devised. The rotational component drives ocean circulations as classical theories of wind‐driven circulations demonstrate. The non‐rotational component does not produce ocean circulations within the framework of a barotropic shallow‐water model, but balances with the pressure gradient force due to surface displacement in the steady state. Based on this decomposition, it is shown that most of the continental torque which plays a major role in producing the seasonal variation of length of day (LOD) is caused by the non‐rotational component of the wind stress. Both continental torque due to the wind‐driven circulation produced by the rotational component of the wind stress and the bottom frictional torque are of minor importance.  相似文献   

11.
This paper presents an analysis of the solutions for a steady state latent heat polynya generated by an applied wind stress acting over a semi‐enclosed channel using: (a) a dynamic–thermodynamic sea ice model, and (b) a steady state flux model. We examine what processes in the sea ice model are responsible for the maintenance of the polynya and how sensitive the results are to the choice of rheological parameters. We find that when the ice is driven onshore by an applied wind stress, a consolidated ice pack forms downwind of a zone of strong convergence in the ice velocities. The build‐up of internal stresses within the consolidated ice pack becomes a crucial factor in the formation of this zone and results in a distinct polynya edge. Furthermore, within the ice pack the across‐channel ice velocity varies with the across‐channel distance. It is demonstrated that provided this velocity is well represented, the steady state polynya flux model solutions are in close agreement with those of the sea ice model. Experiments with the sea ice model also show that the polynya shape and area are insensitive to (a) the sea ice rheology; (b) the imposition of either free‐ slip or no‐slip boundary conditions. These findings are used in the development of a simplified model of the consolidated ice pack dynamics, the output of which is then compared with the sea ice model results. Finally, we discuss the relevance of this study for the modelling of the North Water Polynya in northern Baffin Bay.  相似文献   

12.
A general perturbation–linearization scheme is proposed for the problem of data assimilation with an imperfect and nonlinear model, allowing for the application of the weak constraint representer method. The scheme is shown in discrete formalism for a generic model. An application example is given with computer‐generated data in the case of the Burgers equation. Discussion in reference to the assimilation example concerns: the rôle of the model error, seen as a forcing term in the dynamics; the rôle of representers as a posteriori error covariances; a comparison among different choices for a priori dynamic error variance and strong constraint assimilation. Weak and strong constraint methods are also compared in a forecasting experiment.  相似文献   

13.
A 2‐time‐level finite difference atmospheric general circulation model based on the semi‐Lagrangian advection of pseudo potential vorticity (which becomes potential vorticity in that part of the domain where the hybrid vertical coordinate becomes isentropic) has been formulated. At low levels, the hybrid vertical coordinate is terrain following. The problem of isentropic potential vorticity possibly becoming ill‐defined in the regions of planetary boundary layer is thus circumvented. The divergence equation is a companion to the (pseudo) potential vorticity equation and the model is thus called a PV‐D model. Many features of a previously developed shallow water PV‐D model are carried over: a modification of the PV equation needed to give computational stability of long Rossby waves; a semi‐Lagrangian semi‐implicit treatment of both the linear and the nonlinear terms; the use of an unstaggered grid in the horizontal; the use of a nonlinear multigrid technique to solve the nonlinear implicit equations. A linear numerical stability analysis of the model's gravity–inertia waves indicates that the potential temperature needs to be separated into horizontal mean and perturbation parts. This allows an implicit treatment of the vertical advection associated with the mean in the thermodynamic equation. Numerical experiments with developing baroclinic waves have been carried out and give realistic results.  相似文献   

14.
A low‐order climate model is studied which combines the Lorenz‐84 model for the atmosphere on a fast time scale and a box model for the ocean on a slow time scale. In this climate model, the ocean is forced strongly by the atmosphere. The feedback to the atmosphere is weak. The behaviour of the model is studied as a function of the feedback parameters. We find regions in parameter space with dominant atmospheric dynamics, i.e., a passive ocean, as well as regions with an active ocean, where the oceanic feedback is essential for the qualitative dynamics. The ocean is passive if the coupled system is fully chaotic. This is illustrated by comparing the Kaplan–Yorke dimension and the correlation dimension of the chaotic attractor to the values found in the uncoupled Lorenz‐84 model. The active ocean behaviour occurs at parameter values between fully chaotic and stable periodic motion. Here, intermittency is observed. By means of bifurcation analysis of periodic orbits, the intermittent behaviour, and the rôle played by the ocean model, is clarified. A comparison of power spectra in the active ocean regime and the passive ocean regime clearly shows an increase of energy in the low frequency modes of the atmospheric variables. The results are discussed in terms of itinerancy and quasi‐stationary states observed in realistic atmosphere and climate models.  相似文献   

15.
The present case study evaluates the downward longwave radiation at the surface (DLR) in several high‐resolution (≈1°) general circulation models (GCMs) using surface observations from a semiarid continental site in New South Wales, Australia (Uardry, 34.39°S, 142.30°E). This site is located on a large grassland plain uniform in both its land use and landcover type, and is therefore particularly well suited for a comparison with GCM grid mean values. Monthly averages of newly constructed clear‐sky and all‐sky DLR climatologies and the resulting cloud‐radiative forcing are compared. It is shown that the GCMs exceed the observed DLR under cloud‐free conditions by 10–20 W m−2 at this semiarid site on an annual basis, with a strong seasonal dependence. The calculated clear‐sky fluxes are overestimated during the warmer summer season, with large absolute values of DLR, while the biases are reduced in the colder and dryer winter season with smaller fluxes. This gives direct support for recent evidence that the DLR model biases depend systematically on the thermal and humidity structure of the cloudless atmosphere. Fluxes from strongly emitting atmospheres tend to be overestimated, but may be underestimated from atmospheres with smaller emission. This points to common problems inherent in the simulation of the emission from the cloudless atmosphere in current longwave radiation codes.
The comparisons of the all‐sky climatologies at Uardry show that the clear‐sky biases are partly masked in the models with an insufficient cloud‐radiative forcing, thereby counterbalancing the excessive DLR of the cloud‐free atmosphere. On the other hand, when the cloudradiative forcing is improved, the biases in the cloud‐free atmosphere become fully apparent in the all‐sky fluxes.  相似文献   

16.
The feasibility of assimilating the GPS total zenith delay into atmospheric models is investigated within the framework of the "Observing System Simulation Experiment." The total zenith delay is made up of two terms: one is proportional to the pressure at the site of the GPS ground‐based receiver and the other to the overlying amount of water vapor. Using the MM5 mesoscale model and its adjoint, a set of 4‐dimensional variational (4DVAR) experiments is performed. Results from the assimilation of simulated precipitable water observations are used as the benchmark. The model domain covers Southern California. The observations are simulated with a 10 km horizontal resolution model that includes full physics, while a 20‐km resolution and a less comprehensive physics package are used in the 4DVAR experiments. Both, the 10‐km and 20‐km models employ the same set of 15 vertical levels. Moisture fields retrieved from the total zenith delay are found to compare very well with those retrieved from the precipitable water. Verified against the observations, the vertically integrated moisture is found to be very accurate. An overall improvement is also achieved in the vertical profiles of the moisture fields. The use of the so‐called background term and model initialization are shown to greatly reduce the negative impact that the sole assimilation of the total zenith delay can have on the pressure field and integrated water vapor. The adverse effect stems from the poor resolution of the topography needed to evaluate the model pressure at the GPS sites. The analysis increments of all model fields are found to be similar to the counterparts obtained from the assimilation of the precipitable water. The same is true for the short‐range precipitation forecasts initiated from the 4DVAR‐optimal initial conditions.  相似文献   

17.
Previous work on the classical problem of shocks in a 2‐layer density‐stratified fluid used either a parameterized momentum exchange or an assumed Bernoulli loss. We propose a new theory based on a set of viscous model equations. We define an idealized shock in two‐layer density stratified flow under a rigid lid as a jump or drop of the interface in which (1) the force balance remains nearly hydrostatic in the shock, (2) there is no exchange of momentum between the two layers except by pressure forces on the sloping interface, and (3) dissipative processes can be treated with a constant viscosity. We proceed in two steps. First, we derive a necessary condition for shock existence based on a requirement for wave steepening. Second, we formulate and solve a set of viscous model equations. Some results are the following: Shocks require strong layer asymmetry; one layer must be much faster and/or shallower than the other layer. The linearized equations describing the shock tails provide boundary conditions and a proof of shock uniqueness. It is possible to derive an analytical solution for weak shocks if the steepening condition is met. The weak shock solutions provide closed form expressions for the Bernoulli loss in each layer. Bernoulli losses are strongly concentrated in the expanding layer as the relative layer depth change is much larger in that layer. Bernoulli losses are independent of layer viscosity. A sudden cessation of shock existence is found for strong shocks when the possible end state migrates into the supercritical regime. Surprisingly, the new ideal shock theory compares well with a 2‐D, time‐dependent shallow water model (SWM) with a flux formulation, but with no viscous formulation. Both the Bernoulli drop and shock cessation condition agree quantitatively.  相似文献   

18.
Observations of multidecadal variability in sea surface temperature (SST), surface air temperature and winds over the Southern Hemisphere are presented and an ocean general circulation model applied towards investigating links between the SST variability and that of the overlying atmosphere. The results suggest that the dynamical effect of the wind stress anomalies is significant mainly in the neighbourhood of the western boundary currents and their outflows across the mid‐latitudes of each Southern Hemisphere basin (more so in the South Indian and South Atlantic than in the South Pacific Ocean) and in the equatorial upwelling zones. Over most of the subtropics to mid‐latitudes of the Southern Hemisphere oceans, changes in net surface heat flux (particularly in latent heat) appear to be more important for the SST variability than dynamical effects. Implications of these results for modelling and understanding low frequency climate variability in the Southern Hemisphere as well as possible links with mechanisms of decadal/interdecadal variability in the Northern Hemisphere are discussed.  相似文献   

19.
Baroclinic development is studied with 2 linear, quasi‐geostrophic models. One model is the Eady model, the other uses more realistic wind, density, Coriolis, and static stability. Initial‐value solutions are diagnosed using time series of potential enstrophy ( H ), total energy ( E ), the components of H and E , and the amplitude norm. Two vertical structures for the initial condition are used for both models. One initial condition is representative of a class of initial conditions studied previously having enhanced nonmodal growth (NG). The other initial condition approximates observed conditions prior to cyclogenesis. Results are shown for the most unstable normal mode wavelength of each model. The growth rates of the components of H and E evolve quite differently for different initial states and models tested. NG in H is shown to be sensitive to the contribution of the boundary potential vorticity (BPV) of the initial state; small adjustments in eddy structure at the boundary significantly alter BPV and H growth rates. The amount of NG is related to how far BPV present initially differs from the asymptotic normal mode. The effect upon NG of each approximation present in the Eady model (but not in the other model) are considered. Using realistic mean flow shear, static stability, or compressibility can significantly reduce NG but including linearly varying Coriolis parameter did not. Two conceptual models of NG are considered. Growth by increasingly favorable superposition remains relevant. Growth by "tilting into the vertical" is shown to be incorrect.  相似文献   

20.
3‐dimensional variational algorithms are widely used for atmospheric data assimilation at the present time, particularly on the synoptic and global scales. However, mesoscale and convective scale phenomena are considerably more chaotic and intermittent and it is clear that true 4‐dimensional data assimilation algorithms will be required to properly analyze these phenomena. In its most general form, the data assimilation problem can be posed as the minimization of a 4‐dimensional cost function with the forecast model as a weak constraint. This is a much more difficult problem than the widely discussed 4DVAR algorithm where the model is a strong constraint. Bennett and collaborators have considered a method of solution to the weak constraint problem, based on representer theory. However, their method is not suitable for the numerical weather prediction problem, because it does not cycle in time. In this paper, the representer method is modified to permit cycling in time, in a manner which is entirely internally consistent. The method was applied to a simple 1‐dimensional constituent transport problem where the signal was sampled (perfectly and imperfectly) with various sparse observation network configurations. The cycling representer algorithm discussed here successfully extracted the signal from the noisy, sparse observations  相似文献   

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