Mesoscale Predictability of Moist Baroclinic Waves: Variable and Scale-dependent Error Growth

This study seeks to quantify the predictability of different forecast variables at various scales through spectral analysis of the difference between perturbed and unperturbed cloud-permitting simulations of idealized moist baroclinic waves amplify- ing in a conditionally unstable atmosphere. The error growth of a forecast variable is found to be strongly associated with its reference-state （unperturbed） power spectrum and slope, which differ significantly from variable to variable. The shallower the reference state spectrum, the more spectral energy resides at smaller scales, and thus the less predictable the variable since the error grows faster at smaller scales before it saturates. In general, the variables with more small-scale components （such as vertical velocity） are less predictable, and vice versa （such as pressure）. In higher-resolution simulations in which more rigorous small-scale instabilities become better resolved, the error grows faster at smaller scales and spreads to larger scales more quickly before the error saturates at those small scales during the first few hours of the forecast. Based on the reference power spectrum, an index on the degree of lack （or loss） of predictability （LPI） is further defined to quantify the predictive time scale of each forecast variable. Future studies are needed to investigate the scale- and variable-dependent predictability under different background reference flows, including real case studies through ensemble experiments.

Two Modes and Their Seasonal and Interannual Variation of the Baroclinic Waves/Storm Tracks over the Wintertime North Pacific

In this study,a newly developed method,termed moving empirical orthogonal function analysis（MEOF）,is applied to the study of midlatitude baroclinic waves over the wintertime North Pacific from 1979 to 2009.It is shown that when the daily,high-pass filtered（2–10 days） meridional wind at 250 h Pa is chosen as the variable of the MEOF analysis,typical features of baroclinic waves/storm tracks over the wintertime North Pacific can be well described by this method.It is found that the first two leading modes of the MEOF analysis,MEOF1 and MEOF2,assume quite different patterns.MEOF1 takes the form of a single wave train running in the east–west direction along 40°N,while MEOF2 is a double wave train pattern running in the east–west direction along 50°N and 30°N,respectively.The shift composites of various anomalous fields based on MEOF1 and MEOF2 assume typical baroclinic wave features.MEOF1 represents a primary storm track pulsing with an intrinsic time scale of two days.It shows significant ＂midwinter suppression＂ and apparent interannual variability.It is stronger after the mid-1990 s than before the mid-1990 s.MEOF2 represents a double-branch storm track,also with an intrinsic time scale of approximately two days,running along 50°N and 30°N,respectively.It shows no apparent seasonal variation,but its interannual and decadal variation is quite clear.It oscillates with larger amplitude and longer periods after the mid-1990 s than before the mid-1990 s,and is heavily modulated by El Ni n°o–Southern Oscillation（ENSO）.

A Fluid Experiment of Large-Scale Topography Effect on Baroclinic Wave Flows

The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby number ROT = 0.1 and Taylor number Ta = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric circulation. The 'blocking' phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.

Effects of Surface Drag on Upper-Level Frontogenesis within a Developing Baroclinic Wave

This paper investigates the effects of surface drag on upper-level front with a three-dimensional nonhy- drostatic mesoscale numerical model （MM5）. To this end, a new and simple potential vorticity intrusion （PVI） index is proposed to quantitatively describe the extent and path that surface drag affects upper-level front. From a PV perspective, the formation of the upper-level front is illustrated as the tropopause folding happens from the stratosphere. The PVI index shows a good correlation with the minimum surface pres- sure, and tends to increase with the deepening of the surface cyclone and upper-level front. The surface drag acts to damp and delay the development of upper-level front, which could reduce the growth rate of the PVI index. However, the damping presents different effects in different development stages. It is the most significant during the rapid development stage of the surface cyclone. Compared with no surface drag cases, the tropopause is less inclined to intrude into the troposphere due to the surface drag. Positive feedback between the surface cyclone and upper-level front could accelerate the development of the frontal system.

EFFECTS OF BOUNDARY LAYER FRICTION AND TOPOGRAPHY ON THE INSTABILITY OF BAROCLINIC WAVES

In this paper,the simultaneous effects of boundary layer and topography on the instability of Eady wave are investigated by using a new parameterization of the vertical velocity at the top of PBL and the influences of the stratification of the PBL,roughness and the slope of terrain are shown.Furthermore,the effects of the boundary layer friction and topography on generalized Eady wave are also investigated.

Adjustment time of the first baroclinic Rossby wave in the global oceans

According to the freely linear Rossby wave theory, global 1°×1°climatology of Rossby deformation radius and phase speed are studied under the fiat bottom fluid approximation. Geographical variations in the contours of the phase speed are very similar to those of the Rossby radius of formation, which are mainly affected by stratification, rotation, water depth, topography, etc. The basin-crossing time of the first baroclinic Rossby wave is obtained and analyzed in the global ocean basins. The results are useful to learn the importance of Rosaby wave and the adiabatic adjustment of large-scale ocean circulation.

Influence of Bottom Inclination on the Flow Structure in a Rotating Convective Layer

The formation of convective flows in a rotating cylindrical layer with an inclined bottom and free surface is studied.Convection is driven by localized cooling at the center of the upper free surface and by rim heating at the bottom near the sidewall.The horizontal temperature difference in a rotating layer leads to the formation of a convective flow with a complex structure.The mean meridional circulation,consisting of three cells,provides a strongly non-uniform differential rotation.As a result of the instability of the main cyclonic zonal flow,the train of baroclinic waves appears in the upper layer.The baroclinic waves provide most of the heat transfer in the middle radii and are responsible for strong temperature and velocity fluctuations.It is shown that the inclination of the bottom is a crucial factor for the structure of the convective cells and the dynamics of the baroclinic waves.The increase in the inclination angle leads to a significant increase in the energy of the waves.The obtained results may be important for heat and mass transfer in various geophysical and industrial systems,including transport of various additives and impurities in rotating crucibles,and crystallization processes.

Propagation of Envelope Solitons in Baroclinic Atmosphere

The propagation of finns amplitude baroclinic wave packets in the two-layer model is investigated by using the multiple-scale method.It is shown that the propagation of the wave packets can be described by the so-called unstable nonlinear Schrodinger equation which possesses envelope soliton solutions.The speeds of the solitons are independent of their amplitudes,while the width of the solitons is directly proportional to their speeds but inversely proportional to their amplitudes.

Surface and Upper-Level Features Associated with Wintertime Cold Surge Outbreaks in South Korea

The surface and upper-level features associated with a sharp drop ofwintertime daily temperature over South Korea is investigated in this study. This sharp drop indaily temperature is called a cold surge and is one of the most hazardous weather phenomena in EastAsian winters. An upper-level baroclinic wave of 60° wavelength propagating eastward at a phasespeed of 12° longitude per day across the continent of northern China from the west of Lake Baikaltoward the eastern coast of China causes the outbreak of cold air over South Korea. The coolingassociated with the upper-level baroclinic jvave is found at all altitudes under the geopotentialheight-fall center near the tropopause. The development in the ridge seems to derive the earlyevolution of the eastward-propagating sinusoidal wave, whereas the trough is connected directly withthe tropospheric temperature-drop. An enhancement of the wintertime East Asian jet stream after theoutbreak of a cold surge is a response to the steep temperature gradient associated with thedeveloping baroclinic wave.

The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology, the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction. To address this, it is important to invest in the development of global nonhydrostatic models. Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores, which can subsequently degrade the accuracy of the calculations. A new nonhydrostatic global spectral model, which utilizes the Eulerian spectral method, is developed here from NCAR Community Atmosphere Model 3.0 （CAM3.0）. Using Janjic＇s hydrostatic/nonhydrostatic method, a global nonhydrostatic spectral method for the primitive equations has been formulated and developed. In order to retain the integrity of the nonhydrostatic equations, the atmospheric curvature correction and eccentricity correction are considered. In this paper, the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out, which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration, as well as better simulation ability for short-term idealized integration. Then, a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes. The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind, temperature, and 500-hPa height.

QUASI-RESONANCE OF BAROCLINIC ATMOSPHERIC WAVES AND EXTRATROPICAL LOW-FREQUENCY OSCILLATION

In operating the quasi-geostrophic two-layer model,the quasi-resonance occurs possibly in two cases:(1)pure barotropic waves;(2) two baroclinic and one barotropic waves.For case (2),we find the analytical solution of triad amplitude of quasi-resonance and approximate expression for the period of wave energy variation.Both the approxi- mate expression and numerical calculation indicate that this period tends to approach the period (2πε)/(△ω) of the quasi-resonance frequency mismatch △ω itself for the baroclinic atmosphere than for the barotropic atmosphere.Phys- ically,there is a feedback mechanism between the wave phase and amplitude,and the slowly varying phase difference be- tween the barotropic wave and the baroclinic wave causes the conversion of kinetic energy and available potential energy,which gives rise to the wave-related low-frequency oscillation alternatively strengthening and weakening with the oscillation period identical to the above approximate formula.For △ω～(0.1-0.02) 0(ωj),the averaged energy peri- od is 12-43 days and when △ω=0,i t is 366 days.Therefore,the occurrence of frequency mismatch △ω is probably a new important mechanism for the formation of extratropical low -frequency oscillation in baroclinic atmosphere as well.

The Impact of Global Warming on the Pacific Decadal Oscillation and the Possible Mechanism

The response of the Pacific Decadal Oscillation （PDO） to global warming according to the Fast Ocean Atmosphere Model （FOAM） and global warming comparison experiments of 11 IPCC AR4 models is investigated. The results show that North Pacific ocean decadal variability, its dominant mode （i.e., PDO）, and atmospheric decadal variability, have become weaker under global warming, but with PDO shifting to a higher frequency. The SST decadal variability reduction maximum is shown to be in the subpolar North Pacific Ocean and western North Pacific （PDO center）. The atmospheric decadal variability reduction maximum is over the PDO center. It was also found that oceanic baroclinic Rossby waves play a key role in PDO dynamics, especially those in the subpolar ocean. As the frequency of ocean buoyancy increases under a warmer climate, oceanic baroclinic Rossby waves become faster, and the increase in their speed ratio in the high latitudes is much larger than in the low latitudes. The faster baroclinic Rossby waves can cause the PDO to shift to a higher frequency, and North Pacific decadal variability and PDO to become weaker.

Dynamic Mechanism of Interannual Sea Surface Height Variability in the North Pacific Subtropical Gyre

In this study, the dynamic mechanisms of interannual sea surface height （SSH） variability are investigated based on the first-mode baroclinic Rossby wave model, with a focus on the effects of different levels of wind stress curl （WSC）. Maximum covariance analysis （MCA） of WSC and SSH anomalies displays a mode with significant WSC anomalies located primarily in the mid-latitude eastern North Pacific and central tropical Pacific with corresponding SSH anomalies located to the west. This leading mode can be attributed to Ekman pumping induced by local wind stress and the westward-propagating Rossby wave driven by large- scale wind stress. It is further found that in the middle latitudes, the SSH anomalies are largely determined by WSC variations associated with the North Pacific Gyre Oscillation （NPGO）, rather than the Pacific Decadal Oscillation （PDO）. The sensitivity of the predictive skill of the linear first-mode baroclinic model to different wind products is also examined.

Circulation in the South China Sea is in a state of forced oscillation:Results from a simple reduced gravity model with a closed boundary

The South China Sea(SCS)is a narrow semi-enclosed basin,ranging from 4°–6°N to 21°–22°N meridionally.It is forced by a strong annual cycle of monsoon-related wind stress.The Coriolis parameter f increases at least three times from the southern basin to the northern basin.As a result,the basin-cross time for the first baroclinic Rossby wave in the southern part of the basin is about 10-times faster than that in the northern part,which plays the most vitally important role in setting the circulation.At the northernmost edge of SCS,the first baroclinic Rossby wave takes slightly less than 1 year to move across the basin,however,it takes only 1–2 months in the southernmost part.Therefore,circulation properties for a station in the model ocean are not solely determined by the forcing at that time instance only;instead,they depend on the information over the past months.The combination of a strong annual cycle of wind forcing and large difference of basin-cross time for the first baroclinic Rossby wave leads to a strong seasonal cycle of the circulation in the SCS,hence,the circulation is dominated by the forced oscillations,rather than the quasi-steady state discussed in many textbooks.The circulation in the SCS is explored in detail by using a simple reduced gravity model forced by seasonally varying zonal wind stress.In particular,for a given time snap the western boundary current in the SCS cannot play the role of balancing mass transport across each latitude nor balancing mechanical energy and vorticity in the whole basin.In a departure from the steady wind-driven circulation discussed in many existing textbooks,the circulation in the SCS is characterized by the imbalance of mechanical energy and vorticity for the whole basin at any part of the seasonal cycle.In particular,the western boundary current in the SCS cannot balance the mass,mechanical energy,and vorticity in the seasonal cycle of the basin.Consequently,the circulation near the western boundary cannot be interpreted in terms of the wind stress and thermohaline forcing at the same time.Instead,circulation properties near the western boundary should be interpreted in terms of the contributions due to the delayed wind stress and the eastern boundary layer thickness.In fact,there is a clear annual cycle of net imbalance of mechanical energy and vorticity source/sink.Results from such a simple model may have important implications for our understanding of the complicated phenomena in the SCS,either from in-situ observations or numerical simulations.

AN EXPERIMENTAL STUDY ON THREE DIMENSIONAL STRUCTURE OF BAROCLINIC WAVY JET STREAM IN A ROTATING ANNULUS SUBJECT TO RADIAL TEMPERATURE GRADIENT

Three dimensional structure of baroclinic wavy jet was experimentally studied in rotating annulus subject to a negative radial temperature gradient. General features of wavy surface jet in the system were obtained. Based on the precise measurements of velocity distribution of the jet with LDV and the three dimensional temperature field in the convective system, three dimensional thermodynamic structures of jet were gained, and by using a correlation of three dimensional disturbed temperature, the unstable mechanism of disturbed temperature of baroclinic fluid in a rotating system was further discussed.

AN EXPERIMENTAL STUDY ON EFFECTS OF THE BETA TOPOGRAPHY ON SURFACE FLOWS IN A ROTATING ANNULUS SUBJECT TO RADIAL TEMPERATURE GRADIENT

Beta effects on surface flows in a rotating annulus with a radial temperature gradient and a sloping bottom were studied experimentally. An azimuthal jet was produced by the action of the Coriolis force in the convective region between the two side walls of the annulus. Propagating velocity and patterns of the baroclinic wave on the surface were obrained by using a frequency-meter and a streak photograph respectively. It is shown that there exists the nonlinear interaction between the baroelinic and beta effects. The beta effect exerts little influence on the stratification flows and constrains the baroclinic instability, and it prompts the instability of the weak stratification flows and results in the surface pattern of waves with higher frequency. It is also indicated that the beta effect can reduce the propagating speed of the surface waves in the jet, and increase the thermal Rossby number for those same surface patterns under a given Taylor number.

Comparison of Different Order Adams-Bashforth Methods in an Atmospheric General Circulation Model

The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams- Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR （National Center for Atmospheric Research） CAM 3.1 （Community Atmosphere Model 3.1） and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2At wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams- Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation.

Adjoint Sensitivity Study on Idealized Explosive Cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.

The Dynamical and Climate Tests of an Atmospheric General Circulation Model Using the Second-Order Adams-Bashforth Method

The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations.The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splitting instability.A new semi-implicit atmospheric general circulation spectral model is developed on the basis of NCAR（National Center for Atmospheric Research）CAM3.0（Community Atmosphere Model 3.0）.In this new model,the second-order Adams-Bashforth method is used as an alternative to the leapfrog scheme,and a Crank-Nicholson scheme is incorporated for the treatment of fast gravity modes.In this paper,the new model is tested by the Held-Suarez test and an idealized baroclinic wave test.Results of the Held-Suarez test show that the second-order Adams-Bashforth model has similar climate states to those of many other global models and it converges with resolutions.Based on the idealized baroclinic wave test,the capability of different time differencing methods for keeping the initial steady-state are compared. This convinces a better ability of the second-order Adams-Bashforth method in maintaining the stability of the initial state.Furthermore,after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation,the second-order Adams-Bashforth method has an excellent property of convergence,and can represent the process of the baroclinic wave development much better than the original scheme in CAM3.0.A long-term integration of the new model during the period of 1980–1999 is also carried out and compared with that of CAM3.0.It is found that due to the reduction of simulation errors of prognostic variables,the second-order Adams-Bashforth method also has a better simulation ability for the diagnostic variables,such as precipitation.