Linear dynamics of Eady waves in the presence of horizontal shear

The problem of the instability of the flow of a stratified rotating fluid with constant vertical and horizontal shears is investigated within the framework of a quasi-geostrophic approximation. It is shown that the horizontal shear, when taken into account, leads to a qualitative change in the dynamics of Eady waves, i.e., wave solutions with zero potential vorticity. The main salient feature is related to the effect of the temporary exponential growth of the unstable waves, i.e., the growth effect in a finite time interval. This effect is manifested by an alternation of the stages of a smooth oscillating behavior (in time) with an exponential (explosive) growth of finite duration. A kinematic interpretation of the effect of the temporary exponential growth is suggested which is associated with the passage of a time-dependent wave disturbance vector across the domain of the exponential instability existing in the absence of horizontal shear. Along with the dynamics of individual Eady waves, the generation process of these waves—caused by an initial disturbance defined by one spatial Fourier harmonic—is also investigated. It is shown that this process is accompanied by the formation of nonmodal waves, with time-varying horizontal and vertical wavenumbers and nonzero potential vorticity. The interaction of the nonmodal wave with the background flow leads to an algebraic growth of the Eady wave at the initial cyclogenesis stage.     

A proposed adiabatic formulation of 3‐dimensional global atmospheric models based on potential vorticity

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.     

Moisture retrievals from simulated zenith delay "observations" and their impact on short‐range precipitation forecasts

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.     

A time‐split, forward‐backward numerical model for solving a nonhydrostatic and compressible system of equations

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.     

Dynamic parameters in models of atmospheric vortex structures

Vortex simulation and the computation of fields of dynamic parameters of vortex structures (velocity, rotor velocity, and helicity) are carried out with the use of exact hydrodynamic equations in a cylindrical coordinate system. Components of centripetal and Coriolis accelerations are taken into account in the initial equations. Internal and external solutions are defined. Internal solutions ignore the disturbances of the pressure field, but they are considered in external solutions. The simulation is carried out so that the effect of accounting for spatial coordinates on the structure of the above fields is pronounced. It is shown that the initial kinetic energy of rotating motion transforms into the kinetic energy of radial and vertical velocity components in models with centripetal acceleration. In models with Coriolis acceleration, the Rossby effect is clearly pronounced. The method of an “inverse problem” is used for finding external solutions, i.e., reconstruction of the pressure field at specified velocity components. Computations have shown that tangential components mainly contribute to the velocity and helicity vortex moduli at the initial stage.     

The impact of flow regimes on asymmetry of orographic drag at moderate and low Rossby numbers

The change of flow regimes from "flow over"(non‐blocked flow) to "flow around"(blocked flow) is generally identified by flow stagnation upstream of the mountain and increased deflection of flow around the edges of the mountain. Numerical calculations of simple flow past a smooth mountain ridge presented here reveal another fundamental property of this change of flow regimes. In the presence of the Coriolis force, the drag exerts a cyclonic couple on non‐blocked flows, but an anticyclonic couple on blocked flows. The delaying effect of the Coriolis force on the transition to the blocked flow regime is confirmed and the strength of the couple in blocked flows is also found to increase when the Rossby number U / fL decreases. A change in the flow regime from blocked to non‐blocked flow when the Rossby number decreases gives a new high‐drag regime at high non‐dimensional mountain height ( Nh / U ) and increases substantially the temporal fluctuations of the drag. The sensitivity of the couple to the Rossby number is confirmed in realistic simulations of blocked flow from PYREX. Data from Iceland defines two regimes: at low Rossby number and high Nh / U , the drag on the right hand side is favoured, while at high Rossby numbers and low Nh / U the drag on the left side is larger.     

Reducing systematic errors by empirically correcting model errors

A methodology for the correction of systematic errors in a simplified atmospheric general‐circulation model is proposed. First, a method for estimating initial tendency model errors is developed, based on a 4‐dimensional variational assimilation of a long‐analysed dataset of observations in a simple quasi‐geostrophic baroclinic model. Then, a time variable potential vorticity source term is added as a forcing to the same model, in order to parameterize subgrid‐scale processes and unrepresented physical phenomena. This forcing term consists in a (large‐scale) flow dependent parametrization of the initial tendency model error computed by the variational assimilation. The flow dependency is given by an analogues technique which relies on the analysis dataset. Such empirical driving causes a substantial improvement of the model climatology, reducing its systematic error and improving its high frequency variability. Low‐frequency variability is also more realistic and the model shows a better reproduction of Euro‐Atlantic weather regimes. A link between the large‐scale flow and the model error is found only in the Euro‐Atlantic sector, other mechanisms being probably the origin of model error in other areas of the globe.     

Formula for a baroclinic adjustment theory of climate

Recently, a theory relating baroclinic neutrality and midlatitudes tropopause height has been proposed. However, GCM results have shown that the dependence of the theory on external parameters is not consistent with that displayed by these numerical experiments. In the present paper we suggest an analytic formula for baroclinic adjustment to the neutrality of Eady waves through tropopause modification. This formula extends considerably the abovementioned theory by taking into account both a simple representation of the stratosphere and the topography. These modifications alter the tropopause condition for a baroclinically neutral state and its sensitivity to the external parameters. In particular, the topography introduces a dependence on the tropospheric vertical wind shear of the neutrality condition. This feature is not present in other models that assume a background state with a zero potential vorticity gradient in the troposphere. We show, furthermore, that the modified neutrality condition has sensitivities that may resemble those displayed by GCM simulations, with respect to the parameters defining the background flow.     

海洋模式中Boussinesq近似误差讨论

根据全球增暖的特点,设计了一个理想的数值试验方案,用Boussinesq POP海洋模式和改进的非Boussinesq POP海洋模式定量讨论了Bousiinesq近似在海洋模式计算中的误差。结果发现,在只有热力驱动的热力环流背景下,由热膨胀引起的海平面上升在水平方向上是基本均匀的,在所给的初始边界条件下,这种由Boussinesq近似引起的最大海平面误差可以达到59％,在Boussinesq POP模式中,热源中心处的海面高度要远小于由非Boussinesq模式计算的海面高度,而其周围有虚假的海面高度下降;在只有加热引起的热盐环流过程中,当模式作了Boussinesq假设以后,计算的经向和纬向垂直环流都会产生虚假的加强,虽然这种误差只是在1％左右;在Bousiinesq近似假定下,热量经向通量在赤道上垂直剖面的积分误差比质量经向通量在赤道上垂直剖面的积分误差大一个量级;非Boussinesq模式计算的气压梯度所做功的垂向分布在3000m以下是有波动的,而Boussinesq模式计算的气压梯度所做功的垂向分布在3000m以下基本上是均匀的,它的误差在10％以上。     

Lateral open boundary conditions for nested limited area models: A scale selective approach

This paper reviews current approaches to the lateral open boundary condition problem for nested regional primitive equation ocean numerical models and proposes a new approach that considers a scale decomposition of the nesting field variables for the barotropic lateral velocity boundary conditions. The Flather [Flather, R.A., 1976. A tidal model of the north-west European continental shelf. Memories de la Societe Royale des Sciences de Liege 6 (10):141–164] open lateral boundary condition is derived from mass conservation considerations and we use this approach to derive a generalized lateral open boundary condition for barotropic velocities. In addition we do a scale selective decomposition of the generalized Flather obtaining new and general lateral scale dependent boundary conditions. The performance of the new lateral boundary conditions have been evaluated in two kinds of experiments: (1) idealized and (2) realistic frameworks. In the idealized framework, as well as the realistic case, the results confirms that the scale selective open boundary conditions improves the solution almost everywhere but in particular in the shallow depth parts of the model domain. In the realistic case the assessment is more difficult and it is connected also to the capability of the nesting and nested model to reproduce the dynamics contained in the observations.     

Nonhydrostatic aspects of coastal upwelling meanders and filaments off eastern ocean boundaries

Coastal upwelling meanders and filaments are common features off eastern ocean boundaries. Their growth is reinvestigated herein using a nonhydrostatic three-dimensional model and a reduced-gravity model, with the objective of assessing contributions from two mechanisms that emerge in the nonhydrostatic regime. The first mechanism is caused by the vertical projection of the Coriolis force in the momentum equation. It is found that the vertical Coriolis force often acts as a restoring force against numerical damping off eastern ocean boundaries and thus enhances the growth of meanders and filaments. The second mechanism arises from unstable ocean stratification when the cold upwelled water intrudes seaward over the warm layer. The unstable stratification, albeit transient, further enhances the growth of meanders and filaments. It is concluded that although nonhydrostatic effects do not change our understanding of how meanders and filaments grow, the realism can be enhanced using a nonhydrostatic model insofar as meanders and filaments off eastern ocean boundaries are concerned.     

Significance of non‐rotational wind stress in the seasonal variation of continental torque

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.     

Downward longwave radiation in general circulation models: a case study at a semi‐arid continental site

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.     

A boundary-value problem for the parameterized mesoscale eddy transport

We present a physically and numerically motivated boundary-value problem for each vertical ocean column, whose solution yields a parameterized mesoscale eddy-induced transport streamfunction. The new streamfunction is a nonlocal function of the properties of the fluid column. It is constructed to have a low baroclinic mode vertical structure and to smoothly transition through regions of weak stratification such as boundary layers or mode waters. It requires no matching conditions or regularization in unstratified regions; it satisfies boundary conditions of zero transport at the ocean surface and bottom; and it provides a sink of available potential energy for each vertical seawater column, but not necessarily at each location within the column. Numerical implementation of the methodology requires the solution of a one-dimensional tridiagonal problem for each vertical column. To illustrate the approach, we present an analytical example based on the nonlinear Eady problem and two numerical simulations.     

地转及均匀背景流场对混合层深度SAR遥感反演的影响

以考虑了地转和均匀背景流场影响的两层流体界面内波频散关系模型为基础,得到新的利用SAR遥感图像计算混合层深度的方法。利用该方法对一幅南海北部SAR内波图像进行了实例研究,并且和时空同步的CTD资料进行了对比。结果表明,加入地转和均匀背景流场影响的模型更为合理,为更准确地反演混合层深度奠定了基础。     

Ideal shocks in 2‐layer flow Part I: Under a rigid lid

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.     

太湖夏季环流成因的数值研究

强潮河口盐水入侵对饮用水源地危害极大。基于平面二维水动力盐度模型, 对典型强潮河口—钱塘江的水动力及盐水入侵过程进行了数值模拟研究。结果表明枯水径流时盐度变化与潮位过程曲线类似, 潮差对盐度大小影响显著, 径流量的增加将逐渐减小其相似程度。当流量增加到一定程度后, 继续增加的一定径流量所产生的抑咸效果减弱, 水资源有效利用率降低, 此时允许水源地盐度超标并改从蓄淡避咸水库取水可有效节约水资源。盐度平面分布显示, 盐水入侵在强潮河口弯道处受涨潮流主流线影响明显, 靠近主流线一岸的盐度大于对岸, 单从盐水入侵角度考虑, 强潮河口弯道段的取水口应设置在远离涨潮流主流线一岸。钱塘江河口盐度数值模拟对于研究减轻盐水入侵对水源地危害的措施具有指导意义。     

Open boundary conditions for regional tidal simulations

The performance of regional tide model simulations is examined in relation to the choice of open boundary conditions. Three barotropic open boundary conditions, clamped elevation, clamped normal velocity, and Flather, give similar results when the prescribed values are exact; however, Flather is much less sensitive to errors in the prescribed values. Of particular concern, it was found that with a phase error between the two boundaries, both the clamped conditions resulted in magnitude errors in the unclamped variable (although the simulation remained stable).A modified flow relaxation scheme for the depth-varying prognostic variables is presented. This implementation allows the transmission of a range of vertical modes while retaining realistic topography at the boundary. It was found to be an excellent internal tide boundary condition in tests comparing simulations of different domain length encompassing a ridge and sloping bottom, and in a comparison to an analytical solution. Mass is conserved without any artificial volume constraint.     

Active and passive ocean regimes in a low‐order climate model

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.