An improved scheme for time-dependent boundary conditions in atmospheric general circulation models

 Atmospheric general circulation models (AGCMs) are often “coupled” with time varying observations of boundary conditions or some other aspect of the climate system. A typical example is the Atmospheric Model Intercomparison Project (AMIP) experimental protocol, which required the specification of sea surface temperature and sea-ice extent from observed monthly means. AGCMs ordinarily incorporate the prescribed conditions by evaluating an interpolating function at each time step. Typical schemes, such as that used in the second generation GCM (GCM2) of the Canadian Centre for Climate Modelling and Analysis (CCC), do not preserve monthly means and have a smoothing effect on the interpolated time series which tends to reduce the amplitude of annual cycle and interannual variability of sea surface temperature (SST). By solving a large set of linear equations, a simple linear time-interpolation scheme that preserves the observed monthly mean SST and hence its variability can be obtained. The new scheme improves upon that used previously in CCC GCM2 by eliminating the substantial loss of interannual variability (up to 20%) and the small attenuation of the annual cycle (less than 4% on average) incurred with the old scheme. The improved linear interpolation scheme is easily adapted to other quantities. Received: 4 August 1997 / Accepted: 26 November 1997     

Mixed-layer heat advection and entrainment during the sea breeze

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s^–1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.Symbols c entrainment parameter for sensible heat - c _p specific heat of air at constant pressure, 1010 J kg^–1 K^–1 - d ₁ the thickness of velocity shear at the mixed-layer top, m - Q _H surface sensible heat flux, W m^–2 - u _m mean mixed-layer wind speed, m s^–1 - u _* friction velocity at the surface, m s^–1 - w subsidence velocity, m s^–1 - W subsidence warming,^oC s^–1 - w _e entrainment velocity, m s^–1 - w _* convection velocity in the mixed layer, m s^–1 - x downwind horizontal distance from the water-land interface, m - y dummy variable forx, m - Z height above the surface, m - Z _i height of capping inversion, m - Z _m mixed-layer depth, i.e.,Z _i–Z_s, m - Z _s height of the surface layer, m - lapse rate of potential temperature aboveZ _i, K m^–1 - potential temperature step atZ _i, K - u _h velocity step change at the mixed-layer top - _m mean mixed-layer potential temperature, K     

Measurements of the upstream turbulent flow during wind tunnel simulations of agricultural field burning

Mean streamwise and vertical velocities as well as streamwise and vertical turbulence intensities were measured in a combustion wind tunnel used to collect pollutant emission data for agricultural field burning. Objectives were to compare the flow field upstream of a fire to that without a fire present and to compare the wind tunnel flow upstream of a fire to field conditions. Vertical centerline traverses with an anemometer were conducted for 32 separate wind tunnel operating configurations (wind speed, position in the tunnel, with or without fire, ceiling position, and floor condition) with one replication for each configuration (total of 64 traverses). Certain configurational changes in the wind tunnel had substantial effects on the flow field. Turbulence intensities and velocity profiles (as modeled by the log law-of-the-wall to determinez ₀ andu _* values) in the wind tunnel were comparable to those in the field as reported in the literature. Velocities and turbulence intensities were generally higher, however, with a fire present in the tunnel and all other conditions constant.     

An experimental appraisal of the terms in the heat and moisture flux equations for local advection

Terms in the heat and vapour flux equations, appropriate to the atmospheric surface layer with horizontal heterogeneity in one direction, have been evaluated empirically. The experimental site was a flooded rice field, which was bounded to windward by a semi-arid region. Local conditions over the rice were always stable, but the vertical fluxes of heat and water vapour were large. All terms in the flux equations were either measured directly, or, if sufficiently small, estimated, except the term containing fluctuating pressure, which was obtained by difference. The relative magnitudes of the major terms (production and pressure covariance) were similar to those reported previously for horizontally homogeneous flow with similar stabilities. Current parameterizations of the pressure covariance terms sometimes gave values which differed by factors of five or ten from the experimental results, and the interrelationships depended upon the stability.     

On the coupling of canopy flow to ambient flow for a variety of vegetation types and densities

A canopy flow coupling parameter is defined from earlier canopy flow research to describe the degree of coupling of air flow in vegetation to ambient flow of the surface boundary layer. This ratio concept employs an exponential wind-height relationship in the canopy referenced to the logarithmic wind-height relationship of the ambient air in close proximity to the vegetation interface. Qualitatively, the coupling ratio decreases as the index of canopy flow increases. Numerical criteria are derived to quantify the coupling upwind of the canopy, at the leading edge, through the transition zone, through the zone of established flow, at the trailing edge, and downwind from the canopy domain. It was found that coupling was relatively independent of element density for the more dense arrays, but increased rapidly as densities became more sparsely arrayed. A high degree of coupling existed both upwind and downwind of well-defined domains, while a degeneration of coupling is clearly evident through the zone of established flow. A seasonal contrast in coupling was also discerned. Gravity and slope flows contributed to a higher degree of coupling.     

On the formation of a stably stratified internal boundary-layer by advection of warm air over a cooler sea

As a warm well-mixed air mass flows off a land surface and over a cooler sea, the air is modified in a layer near the surface. Within this layer, humidity decreases while temperature increases with height and a stably stratified internal boundary layer is formed. The non-dimensional parameters governing the growth of the modified layer are derived by dimensional analysis; simple forms are found for the increase of layer height with fetch and for the shapes of humidity and temperature profiles.     

On the choice of relaxation coefficients for Davies' lateral boundary scheme for regional weather prediction models

Summary Relaxation coefficients for Davies' lateral boundary scheme for limited-area numerical weather prediction models are constructed in such a way that, under idealized conditions, the unwanted partial reflection of outgoing waves (leaving the limited area) at the boundary is minimized.With 2 Figures     

A comparison of high-order explicit and non-oscillatory finite difference advection schemes for climate and weather models

Summary The Euler equations govern the behavior of a fluid in motion. They have long been used as a test-bed for assessing the accuracy and efficiency of numerical schemes for solving them. This study focused on advection dominated flows so all other terms in the equations are omitted. The study examined only explicit schemes and does not address the many alternative approaches such as semi-Lagrangian and implicit formulations. The schemes examined here were applied to test cases of increasing complexity as it is well-known that a particular scheme may work very well on some test problems but fail on others. To avoid such problems, we began with the standard tests such as the advection of sine waves and various other one-dimensional shapes, then moved on to two-dimensional problems and finally tested cases that have many scales.Summarizing, the results from the range of test cases, it was found that the schemes that perform best are high-order upwind schemes, with diminishing returns above fifth- and sixth-order.Finally, the schemes were applied to cases where scalar advection requires that constraints such as positive-definiteness be satisfied. For these problems, the Flux Corrected Transport (FCT) and weighted essentially non-oscillatory (WENO) schemes were also applied. Similar conclusions were drawn, namely, that fifth- and sixth-order FCT and WENO schemes produced excellent simulations. However, these schemes were more computationally expensive than the standard high-order upwind and centred schemes.     

On gradient transport turbulence models for stably stratified shear flow

The gradient transport model for stably stratified horizontal shear flow in which eddy diffusivity and viscosity are assumed to depend on the gradient Richardson number, Ri, is augmented with terms representing a finite adjustment time of the exchange coefficients. Barenblatt et al. (J. Fluid Mech., 253: 341–358, 1993) showed that using such a model, initial value problems for the formation of a stepwise structure of the buoyancy distribution are well posed. The model proposed is analysed taking into account the interaction between buoyancy and velocity fields. A condition for the formation of steps is derived from a linear stability analysis. Numerical computations show that a realistic stepwise finestructure develops, provided linear instability is allowed on a finite interval of Ri only.     

On the validity of vertical dispersion coefficients derived from a Markov-chain scheme for use in gaussian diffusion models

This paper addresses the following question: how do the σ _z values derived from vertical concentration distributions computed by a Markov-chain diffusion model compare with the Σ values which must be used in a gaussian diffusion model to give the same ground level concentration distribution as the one computed by the sophisticated model?     

Role of advection and penetrative convection in affecting the mixing-height variations over an idealized metropolitan area

This study deals with the variability of mixing height during daylight hours in the summer months for weak wind regimes. A two-dimensional model was employed using simulated input variables which are quite representative of conditions found over the midwestern United States in late summer and early fall. With the aid of this model and various analytical techniques, the dependence of the urban mixing height on such factors as horizontal advection, downward heat flux across the stable mixing-layer interface, lapse rate in the stable layer, etc., was delineated and compared with actual mixing height variations observed in St. Louis, Missouri during selected days for August, 1972.The experiment indicated the following: (1) A spatially symmetric surface heating profile over a city is accompanied by a similarly symmetric mixing-height profile in the absence of vertical wind shear; (2) When the same heating assumption is invoked and vertically variable wind profiles are introduced, the model-generated mixing-height contours become increasingly asymmetric with vertical wind shear; (3) The modelled mixing heights are more sensitive to temperature fluctuations than to those of wind over the range of speeds studied (wind speeds 4ms^–1); (4) Present operational methods of predicting the time of erosion of an inversion (based upon forecast surface temperature ranges and adiabatic diagram considerations) underestimate breakup time by a factor which is proportional to the amount of available downward heat flux from the stable layer into the mixed layer below.     

Design storm studies for the Upper Krishna river catchment upstream of the Almatti dam site

Summary The Almatti dam is the major engineering feature in the development of water resources in the Upper Krishna river forming a storage reservoir of 6425 million m³ at spillway crest level. In this paper, the design storm rainfalls for different return periods and also the Probable Maximum Precipitation (PMP) for the catchment above Almatti dam have been estimated to review the adequacy of the flood spillway design for the dam. The design storm rainfalls of various return periods have been computed from a statistical analysis of point and areal time series of annual maximum rainfall. In evaluating the PMP, the maximum observed rainfall obtained by Depth Duration method were maximized as the orography of the Western Ghats plays profound influence over the catchment. It was found that (area 35925 km²) the highest areal rainfalls over the catchment were 14.0 cm, 21.5 cm and 24.6 cm in 1, 2 and 3-day durations, respectively. These are scaled up by a factor of 1.23 to obtain the PMP rainfalls. The areal PMP estimates for the upper Krishna River (UKR) catchment above Almatti dam have been found to be 18.0 cm, 27.0 cm and 31.0 cm, respectively.With 6 Figures     

Determining the optimal soil temperature scheme for atmospheric modelling applications

The treatment of the land surface can have a significant impact on the performance of atmospheric models, influencing the surface energy balance and near surface atmospheric variables. In numerical weather prediction models it is especially important to reproduce the observed diurnal cycle in screen-level temperature, which requires an accurate representation of the surface temperature, and therefore an accurate and computationally efficient representation of soil heat storage and transfer. We present a technique for analysing the accuracy of numerical soil temperature schemes, and a methodology for choosing the optimal layer thicknesses for schemes with a given number of layers. Furthermore, the analysis suggests that first generation land surface schemes, which typically used a layer-average surface temperature, may be more accurate in this respect than the latest land surface schemes, which tend to use a skin surface temperature boundary condition.The British Crowns right to retain a non-exclusive royalty-free license in and to any copyright is acknowledged.     

Interactions between thermal advection in frontal zones and the urban heat island of Wrocław, Poland

Summary This paper deals with variability in the air temperature field of an urban area during thermal advection, associated with frontal zones, and its interaction with an urban heat island (UHI). Thermal changes experienced in Wrocław, Poland form the basis of this case study analysis. The discussion also contributes to questions concerning the definition of the UHI and ways to select UHI episodes from existing data sets. It is shown that changes in temperature generated during periods of advection are of short duration, only a few hours at most, but thermal contrasts between various parts of a city at such times are sometimes large, reaching an intensity of 5–6 K, even as large as 9 K. Thus, their intensity is comparable with that of the UHI occurring on cloudless and windless nights. The thermal influence of advection is often greater than that due to urban factors; it is only on occasions with less dynamic advection, that a concentric temperature field is formed due to the modified physical properties of the city. In the majority of cases, the thermal field is non-concentric and this is linked with the location of a frontal zone at any given time. The thermal effects of advection recorded in a data set might easily be viewed as episodes of UHI existence, especially if analysis is conducted based on the data derived from just two stations – one urban the other rural. On occasions when such ‘quasi-UHI’ occur the role of the location of the rural, reference station is also evaluated. Precise definition of the urban heat island can be of significance when conducting comparative studies of the UHI in cities located in different geographical zones and when making an urban climate synthesis.     

On the inner-layer scale height of boundary-layer flow over low hills

Jackson and Hunt's (1975) equation for the depth of the inner layer of flows over low hills does not depend on any closure assumption as contrarily supposed in literature. This equation contains a constant which can arbitrarily be specified. It is suggested that this inner-layer constant should be determined from experimental data. A preliminary check with some data from the Askervein experiment suggests that Jackson and Hunt's equation fits these data almost as well as Jensen's equation provided that fitted inner-layer constants are used.     

On the inner-layer scale height of boundary-layer flow over low hills

The scaling properties of the depth of the inner-layer of flow over low hills are studied by means of numerical solution of the equations. Two closure schemes are applied: the mixing-length model and the E- formulation. It is shown that the scale relation for the inner-layer depth lies between two formulations proposed in literature. It is also shown that the scale relation depends on the closure scheme.Presently at the European Centre for Medium-Range Weather Forecasts, Shinficld Park, Reading, Berkshire RG2 9AX, England.     

On deep mean flow generation mechanisms and the abyssal circulation of numerical model gyres

Mesoscale resolution ocean general circulation model (EGCM) experiments have been carried out under a variety of different model physical assumptions, and the different model systems often produce very different deep mean flow fields. The flat bottom, rectangular basin experiments exhibit two distinct types of deep mean flow, which are here called “corotating” and “counterrotating”. Counterrotating deep flow, in which two adjacent deep gyres, with circulation of opposite senses, underlie the upper ocean eastward jet and its recirculation, has been found only in models with adiabetic two-layer model physics. None of the more complex model systems exhibit counterrotating deep flows; this type of flow is apparently restricted to a particular range of forcing/dissipation parameter space and/or particular model physical assumptions.Since the deep flow in these EGCM systems is generally weak, geostrophic dynamics provides the basic deep flow interior balance and the mean vertical velocity field, through the lower layer vorticity equation, largely determines the deep interior flow. The dynamical constraints on the mean vertical velocity field introduced by different model physical equations are reviewed and the adiabatic quasi-geostrophic (QG) two-layer model system is shown to be strongly constrained in several respects. In particular, the idea that eddy and mean heat flux divergence (or “layer thickness flux divergence”) drive the mean vertical velocity does not generalize to more complicated dynamical systems in which there is the possibility of altering the mean vertical density profile and/or in which the horizontal flow can be divergent. As a consequence of the constraints, there can be no basin net vorticity input to the lower layer via vortex stretching in the QG system.Because of the adiabatic QG constraints and the particular parametric regime in which the published adiabatic QG EGCM experiments exist, a very plausible explanation can be found for the existence of the deep cyclonic circulation of the model subtropical gyre. It is this cyclonic circulation that causes these deep flows to differ so dramatically from those of the more physically complex model systems. Because all the published adiabatic QG experiments that have non-trivial deep flows exhibit the counterrotating behavior, and because available ocean data do not support the existence of such a gyre in the North Atlantic, it seems important to thoroughly understand the reasons for the existence or absence of the deep cyclonic circulations. If they are an invitable feature of adiabatic QG systems, these models may need to be treated with caution as tools for understanding the mean ocean circulation.     

A numerical simulation scheme for the albedo of city street canyons

A numerical scheme is described for the calculation of effective albedo values of long city street canyons. The method is based on a generalization of the radiation model for inclined surfaces recently presented by Brühl and Zdunkowski (1983). Calculated albedo values are compared with Aida's (1982) experimentally determined results. It is found that experiment and theory are in reasonable and in some cases in excellent agreement. Additional results obtained by varying the geometry of the street canyon as well as the surface reflectivities are shown to demonstrate the versatility of the calculation scheme.