Boundary Layer Parameterization Mesoscal Research Group …邊界層參數(shù)化中尺度的研究組…

1、boundary layer parameterization14 november 2012thematic outline of basic concepts what are the relevant physical processes that must be parameterized? how are these processes parameterized within a boundary layer parameterization? what is the difference between a local and a non-local closure for su

2、ch a parameterization?typical boundary layer structuresunrisesunsetsurface layerlaminarsublayeroverview boundary layer: layer over which the influence of the surface is directly transmitted to the free atmosphere. the boundary layer is a turbulent, mixed layer, characterized by small-scale turbulent

3、 eddies. turbulent eddies transport (or mix) heat, moisture, and momentum within the boundary layer.overview heat and moisture are mixed upward from the surface, where they are extracted via surface fluxes. momentum is typically mixed downward in an environment with wind speed increasing with height

4、. turbulent eddies also transmit the frictional stress exerted by the surface upon the atmosphere.turbulence there are two causes of turbulence buoyancy vertical shear of the horizontal wind buoyancy refers to the local instability created by daytime heating of the underlying land surface. dry conve

5、ctive plumes, both upward and downward, result from the release of this instability.turbulence the vertical extent of the daytime mixing defines the depth of the daytime boundary layer. at night, heating of the surface ends and the underlying surface cools. this creates a shallow stable, or inversio

6、n, layer near the ground. any turbulent energy within the nocturnal boundary layer must be extracted from the vertical wind shear. typically minimal unless the horizontal wind is strong.turbulence when vertical wind shear is small and there is no buoyancy, the flow is laminar, or nonturbulent. for l

7、arger vertical wind shear, the flow becomes mechanically turbulent. predominant during the nighttime hours. in the presence of buoyancy, the flow becomes convectively turbulent. dominant during the daytime hours.turbulence since the wind speed perpendicular to any rigid surface like the ground must

8、be zero, turbulence cannot exist at the surface. without turbulence, some other means of transporting water vapor and heat energy from the surface into the boundary layer must exist. this occurs in a shallow (thickness of millimeter or less) layer known as the laminar sublayer.turbulence in the lami

9、nar sublayer, heat, moisture, and frictional effects are communicated on a molecular level. molecular mixing reduces the magnitude of the vertical gradients of heat, moisture, and momentum. transport is down-gradient (from higher to lower values). molecular mixing is far less efficient than turbulen

10、t mixing, however.turbulence within the lowest 50 100 m of the boundary layer, turbulent transports vary little with height compared to their variability in the mixed layer above. the layer over which this is the case is known as the surface layer.overview of boundary layer structure laminar sublaye

11、r: interface between the ground and the surface layer. surface layer: interface between the laminar sublayer and boundary layer. boundary layer: interface between the surface layer and the free atmosphere.boundary layer parameterization a boundary layer parameterization must be able to accurately re

12、present boundary layer processes. a surface layer parameterization must be able to communicate information between the underlying surface and mixed layer in a model simulation. a land-surface parameterization encapsulates the impact of the surface, from the laminar sublayer to soil levels below grou

13、nd, upon the atmosphere.why boundary layer parameterization? turbulent eddies occur on spatiotemporal scales of centimeters to meters and seconds to minutes. true for both horizontal and vertical length scales. molecular mixing and transport processes occur on even smaller scales. local variability

14、in boundary layer processes remains somewhat unknown. e.g., roughness length and other surface contrastsboundary layer as a mixed layertimesalt flatvegetatedsandy sitevertical profile of potential temperature becomes progressively more uniform with time!boundary layer as a mixed layervertical profil

15、es of u, , and v are largely uniform (constant) with height in the mixed layer!daytime vs. nighttime turbulence(analogous to vertical motion) nocturnal turbulence, primarily associated with small-scale turbulent eddies, is of higher frequency but lower amplitude. daytime turbulence, associated with

16、both small- and large-scale turbulent eddies, reflects the superposition of the high and low frequency modes with overall greater amplitude.nocturnal boundary layer mixing in the nocturnal boundary layer can be intermittent or oscillatory in nature. vertical wind shear exceeds some critical value. m

17、ixing reduces the vertical shear to a subcritical value. above the nocturnal stable layer, residual turbulence remains from the daytime boundary layer. typically decays in depth and in intensity with time. cause of this decay: internal friction (not surface friction).typical boundary layer structure

18、sunrisesunsetsurface layerlaminarsublayer the depth of mixed layer can be or the 1 km shown above and is proportional to the heating of the underlying surface. influences upon surface heating include meteorological conditions, seasonality, continentality, and land-surface structure.surface and inver

19、sion layersinversion layer structure potential temperature increases with height, creating a stable thermodynamic situation. horizontal wind speed increases with height. impact of surface friction becomes negligible dashed line, fig. 4.12b: theoretical wind speed w/o friction moisture decreases with

20、 height. entrainment within the inversion mixes in drier air from above the boundary layer.surface layer structure potential temperature decreases with height due to strong sensible heating of the underlying surface. superadiabatic lapse rate; unstable. horizontal wind speed increases with height. w

21、ind profile is a log-wind profile (more shortly). moisture decreases with height. surface latent heat flux keeps surface moisture content relatively high.surface layer structure boundary layer structure is strongly impacted by the characteristics of the underlying land-surface. this is particularly

22、manifest via the roughness of that surface, or the roughness length (z0). smooth surfaces have relatively small roughness lengths. rougher surfaces have larger roughness lengths. typical length scales: o(mm) to o(cm) or larger.surface layer structure the roughness length impacts the vertical structu

23、re of the horizontal wind within the surface layer. this subsequently impacts the near-surface turbulent fluxes of heat, moisture, and momentum. for a well-mixed boundary layer, it can be shown: 0*lnzzkuzuu(z) = speed of the mean horizontal wind at a height z above the groundu* = friction velocity (

24、not a function of height)k = von karman constant (typically 0.35 0.4)surface layer structure the friction velocity represents the drag of the atmosphere against the surface (the frictional stress). the roughness length is the height at which the mean wind speed goes to zero in neutral conditions. as

25、 u* and k are both constant with height, the mean horizontal wind speed increases logarithmically with increasing height.surface layer structurenote that if the assumption of neutrally stable does not hold, qualitatively similar results are obtained (dashed lines).boundary layer non-uniformity bound

26、ary layer structure is not always as uniform as the foregoing discussion may make it seem. potential causes of non-uniformity. non-uniform spatial and size distributions of aerosols can impact radiative transfer within the boundary layer. horizontal contrasts in land-surface properties, drastic or s

27、ubtle, can lead to internal boundary development,boundary layer non-uniformity examples of internal boundary development. boundary layer air moving from a drier, warmer, smoother surface to a moister, cooler, rougher one. downstream advection of a mixed layer that forms due to heating over elevated

28、terrain. downstream advection over a cooler body of water of a mixed layer that formed over hot, dry land surfaces. the drier, warmer boundary layer will lift over the moister, cooler one, forming an internal boundary.boundary layer non-uniformityschematic of an elevated mixed layer over the great p

29、lains.boundary layer parameterization how do we parameterize all of these processes and structures within a numerical model? we start by examining the primitive equations to demonstrate the terms that must be parameterized. well do this explicitly only for the momentum equations, but note that the s

30、ame is also done for other equations. subsequently, we discuss different mathematical constructs for the parameterization of these terms.boundary layer parameterization momentum equations, in tensor notationijijijijixpufgxuutu133i, j = (1, 2, 3), with j independent of iui u1 = u, u2 = v, u3 = wxi x1

31、 = x, x2 = y, x3 = zij is 1 when i = j but zero otherwiseijk = 1 if i, j, k are in ascending order-1 if i, j, k are in descending order0 if any of i, j, k are equal to one anotherboundary layer parameterization separate dependent variables into mean (resolved) and perturbation (turbulent) components

32、 expand and make the assumption that n, with n being the total number of pbl grid pointsnon-local closure we define a variable cab, or the fraction of air at point a that has been transported from point b over t. the exchange between a and each b is given by cab has dimensions n x n, since all b can

33、 also be an a, and is a function of the turbulence. thus, it is the same for all possible parameterization problem requires appropriately defining cab nbbabattctt1non-local closure approach 2: blackadar method (fig 4.15c) vertical exchange takes place between each pbl grid point and the lowest grid

34、point. presumes that both small and large eddies alike have their roots within the surface layer. intensity of the daytime vertical exchange is determined from the surface heat flux and the thermal structure of the entire mixed layer.non-local closure example turbulent transfer term: m represents the fraction of mass in a grid box in the column exchanged with the surface grid box over t. parameterization problem requires appropriately defining m. this is similar to the transilient turbu