An Impact of Hydrostatic Extraction Scheme on BMRC’s Global Spectral Model

There are two important features in geophysical fluid dynamics. One is that the atmospheric and oceanic equa-tions of motion include the Coriolis force; another is that they describe a stratified fluid. The hydrostatic extraction scheme, or standard stratification approximation, posed by Zeng (1979), reflects the second aspect of geophysical flu-id dynamics. There exist two major advantages in this scheme; accurate computation of the pressure gradient force can be obtained over steep mountain slopes, and the accumulation error in vertical finite differencing can be reduced, especially near the tropopause.Chen et al (1987) introduced the hydrostatic extraction scheme into a global spectral model, which attained pre-liminary success at low resolution. Zhang and Sheng et al (1990) developed and improved the hydrostatic extraction scheme in a global spectral model, in which C0, the parameter that represents the stratification of the reference at-mosphere, changes not only with height, but also with latitude. The scheme has been incorporated BMRC’s global spectral model (IAPB). Four 5-day forecasts have been performed to test the IAPB with the hydrostatic extraction scheme. Objective verifications demonstrate a positive effect of the hydrostatic extration scheme on BMRC’s model, particularly at upper levels, over the tropics and the Antartic region.     

Instability in Lagrangian stochastic trajectory models,and a method for its cure

A number of authors have reported the problem of unrealistic velocities (“rogue trajectories”) when computing the paths of particles in a turbulent flow using modern Lagrangian stochastic (LS) models, and have resorted to ad hoc interventions. We suggest that this problem stems from two causes: (1) unstable modes that are intrinsic to the dynamical system constituted by the generalized Langevin equations, and whose actual triggering (expression) is conditional on the fields of the mean velocity and Reynolds stress tensor and is liable to occur in complex, disturbed flows (which, if computational, will also be imperfect and discontinuous); and, (2) the “stiffness” of the generalized Langevin equations, which implies that the simple stochastic generalization of the Euler scheme usually used to integrate these equations is not sufficient to keep round-off errors under control. These two causes are connected, with the first cause (dynamical instability) exacerbating the second (numerical instability); removing the first cause does not necessarily correct the second, and vice versa. To overcome this problem, we introduce a fractional-step integration scheme that splits the velocity increment into contributions that are linear (U _i ) and nonlinear (U _i U _j ) in the Lagrangian velocity fluctuation vector U, the nonlinear contribution being further split into its diagonal and off-diagonal parts. The linear contribution and the diagonal part of the nonlinear contribution to the solution are computed exactly (analytically) over a finite timestep Δt, allowing any dynamical instabilities in the system to be diagnosed and removed, and circumventing the numerical instability that can potentially result in integrating stiff equations using the commonly applied explicit Euler scheme. We contrast results using this and the primitive Euler integration scheme for computed trajectories in a drastically inhomogeneous urban canopy flow.     

Observational evidence for the Monin-Obukhov similarity under all stability conditions

Data collected in the surface layer in a northern suburban area of Nanjing from 15 November to 29 December 2007 were analyzed to examine the Monin-Obukhov similarity for describing the turbulent fluctu- ations of 3D winds under all stability conditions and to obtain the turbulence characteristics under different weather conditions. The results show that the dimensionless standard deviations of turbulent velocity com- ponents (σ u /u* , σ v /u* , σ w /u * ) and dimensionless turbulent kinetic energy (TKE) can be well described by "1/3" power law relationships under stable, neutral, and unstable conditions, with σ u /u * > σ v /u * > σ w /u* . Land use and land cover changes mainly impact dimensionless standard deviations of horizontal component fluctuations, but they have very little on those of the vertical component. The dimensionless standard devi- ations of wind components and dimensionless TKE are remarkably affected by different weather conditions; the deviations of horizontal wind component and dimensionless TKE present fog day > clear sky > overcast > cloudy; the trend of the vertical wind component is the reverse. The surface drag coefficient at a Nan- jing suburban measurement site during the observation period was obviously higher than at other reported plains and plateau areas, and was approximately one order larger in magnitude than the reported plains areas. Dimensionless standard deviation of temperature declined with increasing |z /L| with an approximate "-1/3" slope in unstable stratification and "-2/3" slope in stable stratification.     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ_*, z being height and Λ_* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ_* < 0.02), “weakly-stable” (0.02 < z/Λ_* < 0.6), “very-stable” (0.6 < z/Λ_* < 50), and “extremely-stable” (z/Λ_* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ_*)^3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.     

On the instability of a planetary boundary layer with Rossby-number similarity

The formation of longitudinal vortex rolls in the planetary boundary layer (PBL) is investigated by means of perturbation analysis. The method is the same as that used by previous authors who have investigated the instability of a laminar Ekman layer. To study the instability of the turbulent boundary layer of the atmosphere, vertical profiles are needed of the eddy viscosity and of the two components of the basic flow. These profiles have been obtained by a numerical PBL-model; they are universal for zz ₀. (However, the stability equations are not completely universal, i.e., independent of the external parameters). For each thermal stratification, expressed by the internal stratification parameter , one has a set of three consistent profiles.The numerical solution of the stability equations gives the critical values and the perturbation growth rates as functions of thermal stratification and of the surface Rossby number Ro₀. This is in contrast to the case of a laminar Ekman layer, where the instability depends on a Reynolds number only, which makes atmospheric applications difficult. The most unstable perturbations are found for Ro₀ = 1 × 10⁶ approximately, which is in the range of surface Rossby numbers observed in the atmosphere. However, considering vortex rolls oriented in the direction of the surface stress, the instability is found to be universal, i.e., independent of the external parameters combined in the surface Rossby number. With respect to thermal stratification, the results show that the instability of the perturbations increases with increasing static stability.     

A comparative study of the performance of various vertical discretization schemes

Summary Most finite-difference numerical weather prediction models employ vertical discretizations that are staggered, and are low-order (usually second-order) approximations for the important terms such as the derivation of the geopotential from the hydrostatic equation, and the calculation of the vertically integrated divergence. In a sigma-coordinate model the latter is used for computing both the surface pressure change and the vertical velocity. All of the above-mentioned variables can diminish the accuracy of the forecast if they are not calculated accurately, and can have an impact on related quantities such as precipitation.In this study various discretization schemes in the vertical are compared both in theory and in practice. Four different vertical grids are tested: one unstaggered and three staggered (including the widely-used Lorenz grid). The comparison is carried out by assessing the accuracy of the grids using vertical numerics that range from second-order up to sixth-order.The theoretical part of the study examines how faithfully each vertical grid reproduces the vertical modes of the governing equations linearized with a basic state atmosphere. The performance of the grids is evaluated for 2nd, 4th and 6th-order numerical schemes based on Lagrange polynomials, and for a 6th-ordercompact scheme.Our interpretation of the results of the theoretical study is as follows. The most important result is that the order of accuracy employed in the numerics seems to be more significant than the choice of vertical grid. There are differences between the grids at second-order, but these differences effectively vanish as the order of accuracy increases. The sixth-order schemes all produce very accurate results with the grids performing equally well, and with the compact scheme significantly outperforming the Lagrange scheme. A second major result is that for the number of levels typically used in current operational forecast models, second-order schemes (which are used almost universally) all appear to be relatively poor, for other than the lowest modes.The theoretical claims were confirmed in practice using a large number (100) of forecasts with the Australian Bureau of Meteorology Research Centre's operational model. By comparing test model forecasts using the four grids and the different orders of numerics with very high resolution control model forecasts, the results of the theoretical study seem to be corroborated.With 8 Figures     

An Improved Approach for Parameterizing Surface-Layer Turbulent Transfer Coefficients in Numerical Models

Based on classic iterative computation results, new equations to calculate the surface turbulent transfer coefficients are proposed, which allow for large ratios of the momentum and heat roughness lengths. Compared to the Launiainen scheme, our proposed scheme generates results closer to classical iterative computations. Under unstable stratification, the relative error in the Launiainen scheme increases linearly with increasing instability, even exceeding 15%, while the relative error of the present scheme is always less than 8.5%. Under stable stratification, the Launiainen scheme uses two equations, one for 0 < Ri _B ≤ 0.08 and another for 0.08 < Ri _B ≤ 0.2, and does not consider the condition that Ri _B > 0.2, while its relative errors in the region 0 < Ri _B ≤ 0.2 exceed 31 and 24% for momentum and heat transfer coefficients, respectively. In contrast, the present scheme uses only one equation for 0 < Ri _B ≤ 0.2 and another equation for Ri _B > 0.2, and the relative error of the present scheme is always less than 14%.     

On the dependence of climate sensitivity on convective parametrization

Two sensitivity experiments, in which CO₂ is doubled and sea-surface temperatures are enhanced, were carried out using a general circulation model to determine the influence of the convective parametrization on simulated climate change. In the first experiment, a non-penetrative layer-swapping convection scheme is used; in the second, a penetrative scheme is used. It is found that the penetrative scheme gives the greater upper tropospheric warming (over 4.5 K compared to 4 K) and the greater reduction in upper tropospheric cloud, consistent with recent CO₂ sensitivity studies. However, there is a 0.7 Wm^–2 greater increase in net downward radiation at the top of the atmosphere in the experiment with the non-penetrative scheme, implying a larger tropical warming which is inconsistent with recent CO₂ studies. Other possible explanations for discrepancies between recent studies of the equilibrium climate response to increasing CO₂ are considered and discussed. The changes in the atmospheric fluxes of heat and moisture from the tropical continents in the model with the penetrative scheme differ from those found using the non-penetrative scheme, and those in an equilibrium experiment using the penetrative scheme. Thus, changes in circulation may explain the apparent discrepancy in the current experiments, but prescribed sea-surface temperature experiments may not provide a reliable indication of a model's equilibrium climate sensitivity. Offprint requests to: JFB Mitchell     

Flow splitting at the bifurcation between two valleys: idealized simulations in comparison with Mesoscale Alpine Programme observations

Summary This paper investigates the characteristics of channelled airflow in the vicinity of a junction of three idealized valleys (one valley carrying the incoming flow and two tributaries carrying the outflow), using a two-dimensional single-layer shallow water model. Particular attention is given to the flow splitting occurring at the junction. Nondimensionalized, the model depends on the valley geometry, the Reynolds number, which is related to the eddy viscosity, and on the difference of the hydrostatic pressure imposed at the exit of the tributaries. At the spatial scale considered in this study, the Rossby number relating the inertial and Coriolis forces is always larger than 1, implying that the effect of earth rotation can be neglected to a first approximation. The analysis of the flow structure within the three valleys as well as the calculation of the split ratio (fraction of the air flow diverted into one of the two downstream valleys with respect to the total mass flux in the upstream valley) show that (i) the flow pattern depends strongly on the Reynolds number while the split ratio is comparatively insensitive; (ii) the valley geometry and the difference between the upstream and downstream hydrostatic pressures affect the flow pattern, the location of the split point and the split ratio; (iii) the relative contribution of flow deflection by the sidewalls and the blocking/splitting mechanism differs between the settings of a “Y-shape” valley and a “T-shape” valley. Quantitative comparison of the present results with numerical simulations of realistic cases and with observations collected in the region of the Rhine and Seez valleys (Switzerland) (“Y-shape” valley) and in the region of the Inn and Wipp valleys (Austria) (“T-shape” valley) during the Mesoscale Alpine Programme (MAP) field experiment shows good agreement provided that the normalized valley depth NΔH/U_u significantly exceeds 1, i.e., when “flow around” is expected. A structural disagreement between the idealized simulations and the observed wind field is found only when NΔH/U_u ≃ 1, that is, in the “flow over” regime. This shows that the dimensionless valley depth is indeed a good indicator for flow splitting, implying that the stratification is a key player in reality.     

The predictability of weather and climate

The last thirty years have seen the development of comprehensive numerical models of the large-scale circulation of the atmosphere, based on physical principles. Such models are quite skillful at describing the evolving weather up to a few days ahead, despite imperfect theory and inadequate observational data. Yet even a hypothetical perfect model, which exactly represented the dynamics of the real atmosphere, and which used data from the best conceivable observing system, could not produce an accurate forecast of indefinitely long range. Any forecast must eventually lose skill because of the intrinsic instability of the atmosphere itself.This limitation on the predictability of the detailed evolution of the atmosphere (weather) does not preclude the possibility of seasonal and longer-range forecasts of means and other statistical properties (climate). However, we are only beginning to learn what aspects of climate may be predictable, and what theoretical tools and observational data will be required to predict them.     

Spatial patterns and trends of daily rainfall regime in Peninsular Malaysia during the southwest and northeast monsoons: 1975–2004

Model precipitation can be produced implicitly through convective parameterization schemes or explicitly through cloud microphysics schemes. These two precipitation production schemes control the spatial and temporal distribution of precipitation and consequently can yield distinct vertical profiles of heating and moistening in the atmosphere. The partition between implicit and explicit precipitation can be different as the model changes resolutions. Within the range of mesoscale resolutions (about 20 km) and cumulus scale, hybrid solutions are suggested, in which cumulus convection parameterization is acting together with the explicit form of representation. In this work, it is proposed that, as resolution increases, the convective scheme should convert less condensed water into precipitation. Part of the condensed water is made available to the cloud microphysics scheme and another part evaporates. At grid sizes smaller than 3 km, the convective scheme is still active in removing convective instability, but precipitation is produced by cloud microphysics. The Eta model version using KF cumulus parameterization was applied in this study. To evaluate the quantitative precipitation forecast, the Eta model with the KF scheme was used to simulate precipitation associated with the South Atlantic Convergence Zone (SACZ) and Cold Front (CF) events. Integrations with increasing horizontal resolutions were carried out for up to 5 days for the SACZ cases and up to 2 days for the CF cases. The precipitation partition showed that most of precipitation was generated by the implicit scheme. As the grid size decreased, the implicit precipitation increased and the explicit decreased. However, as model horizontal resolution increases, it is expected that precipitation be represented more explicitly. In the KF scheme, the fraction of liquid water or ice, generated by the scheme, which is converted into rain or snow is controlled by a parameter S ₁. An additional parameter was introduced into KF scheme and the parameter acts to evaporate a fraction of liquid water or ice left in the model grid by S ₁ and return moisture to the resolved scale. An F parameter was introduced to combine the effects of S ₁ and S ₂ parameters. The F parameter gives a measure of the conversion of cloud liquid water or ice to convective precipitation. A function dependent on the horizontal resolution was introduced into the KF scheme to influence the implicit and explicit precipitation partition. The explicit precipitation increased with model resolution. This function reduced the positive precipitation bias at all thresholds and for the studied weather systems. With increased horizontal resolution, the maximum precipitation area was better positioned and the total precipitation became closer to observations. Skill scores for all events at different forecast ranges showed precipitation forecast improvement with the inclusion of the function F.     

Spectral Short-circuiting and Wake Production within the Canopy Trunk Space of an Alpine Hardwood Forest

Using synchronous multi-level high frequency velocity measurements, the turbulence spectra within the trunk space of an alpine hardwood forest were analysed. The spectral short-circuiting of the energy cascade for each velocity component was well reproduced by a simplified spectral model that retained return-to-isotropy and component-wise work done by turbulence against the drag and wake production. However, the use of an anisotropic drag coefficient was necessary to reproduce these measured component-wise spectra. The degree of anisotropy in the vertical drag was shown to vary with the element Reynolds number. The wake production frequency in the measured spectra was shown to be consistent with the vortex shedding frequency at constant Strouhal number given by f _vs = 0.21ū/d, where d can be related to the stem diameter at breast height (dbh) and ū is the local mean velocity. The energetic scales, determined from the inflection point instability at the canopy–atmosphere interface, appear to persist into the trunk space when , where C _du is the longitudinal drag coefficient, a _cr is the crown-layer leaf area density, h _c is the canopy height, and β is the dimensionless momentum absorption at the canopy top.     

The impact of new land surface physics on the GCM simulation of climate and climate sensitivity

 Recent improvements to the Hadley Centre climate model include the introduction of a new land surface scheme called “MOSES” (Met Office Surface Exchange Scheme). MOSES is built on the previous scheme, but incorporates in addition an interactive plant photosynthesis and conductance module, and a new soil thermodynamics scheme which simulates the freezing and melting of soil water, and takes account of the dependence of soil thermal characteristics on the frozen and unfrozen components. The impact of these new features is demonstrated by comparing 1×CO₂ and 2×CO₂ climate simulations carried out using the old (UKMO) and new (MOSES) land surface schemes. MOSES is found to improve the simulation of current climate. Soil water freezing tends to warm the high-latitude land in the northern Hemisphere during autumn and winter, whilst the increased soil water availability in MOSES alleviates a spurious summer drying in the mid-latitudes. The interactive canopy conductance responds directly to CO₂, supressing transpiration as the concentration increases and producing a significant enhancement of the warming due to the radiative effects of CO₂ alone. Received: 16 March 1998 / Accepted: 4 August 1998     

关于大气层結对于近地面层中湍流交換的影响問題

本文第一部分运用相似理論和因次分析对层結大气近地面层中湍流交換的問題作了分析,获得了与作者过去根据湍流能量平衡方程所得到的結果一致.第二部分根据新近国外发表的直接測量资料确定了普遍函数中的經驗系数D的大小;还确立了强迫对流向自由对流状态的过渡,与Priestley所指出的不同,它具有极平緩的性貭,計算結果与观測事实符合.在稳定情况下則沒有类似过渡发生.第三部分根据因次分析构成了特征尺度L_(R_i),并建立了以L_(R_i)为特征尺度的湍流交換的模式.討論結果表明,采用这一模式比前一模式合理一些,而且实用上更为方便。     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS*

In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations.     

Evaluation of a land-surface scheme at Cabauw

Summary We study the response of the land-surface to prescribed atmospheric forcing for 31 May 1978 at Cabauw, Netherlands, using the land-surface scheme from the Coupled Atmospheric boundary layer-Plant-Soil (CAPS) model. Results from model runs show realistic daytime surface fluxes are produced using a canopy conductance formulation derived from Cabauw data (for 1987, a different year), and un-tuned parameterizations of root density (near-uniform with depth) and soil heat flux (reduced thermal conductivity through vegetation). Sensitivity of model-calculated surface heat fluxes to initial values of soil moisture is also examined. Results of this study provide the land-surface base state for a coupled land–atmosphere modeling study.     

Short term variability of atmospheric turbidity and optical turbulence in a desert environment

Summary Variability of atmospheric turbidity calculated from direct beam solar radiation measurements and the transverse coherence length,r ₀, derived from differential image motion of stellar sources show pronounced fluctuations on the order of a few minutes under convectively unstable conditions in a desert environment. The quiescent periods, neutral events, when local near surface adiabatic conditions occur show substantial reductions in the fluctuations of the same quantities. Image motion results for nighttime (stable) conditions display slowing varying patterns with reduced short term (few minutes) variations.The measurements were taken using a suite of instrumentation probing the same volume of atmosphere. The instrumentation used includes a pyrheliometer, Atmospheric Turbulence Measurement and Observation System (ATMOS), a sodar, a scintillometer, and tower- mounted sensors. A time-height display of sodar data calibrated for the refractive index structure parameter,C _n ² , coupled with scintillometer measurements show the diurnal evolution of the boundary layer responding to the local heating-cooling cycle and drainage flows from the surrounding mountains. Several atmospheric features are seen and discussed in these results as they affect the nature of the patterns of turbidity andr ₀. Of particular interests are the development of convection, changes in the capping inversion, thermal plume structures, neutral events, and wave-turbulence interactions. Sinusoidal oscillations, identified as internal gravity waves, are seen in the nighttime laminated structures.With 10 Figures     

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, and , between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient C _d, the geostrophic wind coefficient C _f, and the angles , and , of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S ₁ and S ₂ as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.Formerly Visiting Research Associate, Applied Physics Branch, Earth Observations Division, NASA-Manned Spacecraft Center, Houston, Texas.     

Improving the CoLM in Taklimakan Desert hinterland with accurate key parameters and an appropriate parameterization scheme

Improving and validating land surface models based on integrated observations in deserts is one of the challenges in land modeling. Particularly, key parameters and parameterization schemes in desert regions need to be evaluated in-situ to improve the models. In this study, we calibrated the land-surface key parameters and evaluated several formulations or schemes for thermal roughness length (z 0h ) in the common land model (CoLM). Our parameter calibration and scheme evaluation were based on the observed data during a torrid summer (29 July to 11 September 2009) over the Taklimakan Desert hinterland. First, the importance of the key parameters in the experiment was evaluated based on their physics principles and the significance of these key parameters were further validated using sensitivity test. Second, difference schemes (or physics-based formulas) of z 0h were adopted to simulate the variations of energy-related variables (e.g., sensible heat flux and surface skin temperature) and the simulated variations were then compared with the observed data. Third, the z 0h scheme that performed best (i.e., Y07) was then selected to replace the defaulted one (i.e., Z98); the revised scheme and the superiority of Y07 over Z98 was further demonstrated by comparing the simulated results with the observed data. Admittedly, the revised model did a relatively poor job of simulating the diurnal variations of surface soil heat flux, and nighttime soil temperature was also underestimated, calling for further improvement of the model for desert regions.