Atm S 547 Boundary Layer Meteorology

Transcription

1 Lecture 9. Nonlocal BL parameterizations for clear unstable boundary layers In tis lecture Nonlocal K-profile parameterization (e. g. WRF-YSU) for dry convective BLs EDMF parameterizations (e. g. ECMWF) Motivation: Countergradient eat transport in te DCBL Observations and LES of surface-eated dry convective BLs (e.g. dased line in Fig. 9.1) sow tat over muc of te upper alf of te boundary layer (0.4 < z/z i < 0.8), te θ gradient is very sligtly positive even toug te eat flux is also upward, opposite to te expectation from downgradient turbulent diffusion. Nonlocal scemes account for tis effect by adding a correction term to scalar fluxes in convective boundary layers. Fig. 9.1: Left: Dased line sows LES of DCBL θ profile. Rigt: Solid line sows corresponding eat flux profile. From Cuijpers and Holtslag (1998, JAS). Tis approac can be motivated by considering te budget equation for te flux of an advected scalar a in a surface-eated convective BL. Holtslag and Moeng (1991, JAS) started by taking a = θ (potential temperature) and examining te prognostic eat flux equation: w θ = w w w t z z + g θ θ 1 θ p ρ 0 z (9.1) 9.1

2 Using a 96 3 gridpoint LES of a dry convective boundary layer under a 4 K inversion, tey determined profiles of te four terms on te RHS (Fig. 9.2, left). Based on tese profiles and teoretical arguments, tey 1. Neglected storage (LHS) 2. Modeled te pressure-covariance term as: P = 1 θ p ρ 0 z = a g θ θ τ, a = 1 2. Fig. 9.2: Left: Terms in buoyancy flux budget for a DCBL, diagnosed from an LES. Rigt: Nondimensionalized vertical velocity variance profile, wic te scalar flux equation suggests is proportional to te eddy diffusivity profile. Here τ is a return-to-isotropy timescale for pressure forces to distort anisotropic turbulent eddies into isotropic turbulence, in te absence of oter effects, and will be specified later. Te assumption tat a = ½ is appropriate for convective boundary layers, but not stable BLs. 3. Modeled te turbulent transport term for DCBLs (based on Fig. 9.2 left) as T = w w θ = P + bw * 0, b = 2 z Putting tese assumptions togeter into Eqn. (9.1), we obtain so 0 = w w z + 2 w * 0 + (1 2a ) g θ θ 2 0 τ 9.2

3 w θ (z) = τ 2 w w z + τ w * Tat is, te eat flux as a downgradient component wit diffusivity 0, (9.2) K (z) = τ 2 w w (z) (9.3) and a second nonlocal term proportional to te surface eat flux. Te nonlocal term is tus seen to derive from te combined turbulent transport, pressure-covariance, and buoyancy contributions to te eat flux tendency. Tis derivation suggests tat te diffusivity sould scale wit te vertical velocity variance profile, wic is well-measured and easily simulated wit LES (Fig. 9.2, rigt): w w 2.8w 2 * Z(1 Z) 2, Z = z (9.4) Te timescale τ can be determined by noting tat at Z = 0.4, tere is no vertical θ gradient but te eat (buoyancy) flux is 0.5 times te surface value, so Tis gives te diffusivity profile = bτ 2 w * 0 τ = 0.5 w * K (z) 0.7w * z 1 z 2 (9.5) Nonlocal K-profile scemes Te above scale analysis applies only to a dry, nearly sear-free convective boundary layer. To andle seared boundary layers and acieve te appropriate log-layer scaling near te surface, BL parameterizations andle te nonlocal term somewat differently. In nonlocal K-profile metods, te turbulent flux of an advected scalar a is modelled using a K-profile wit a nonlocal correction γ a added for advected scalars in convective boundary layers w a = K a a z γ a, 0 < z < (9.6) Te nonlocal term on te rigt is interpreted as being due to boundary-layer filling convective eddies wic distribute te surface flux of a upward regardless of te local gradient of a. If te surface flux of a is positive, te nonlocal term produces a BL witin wic a decreases less wit eigt tan if pure first-order closure were used. Te nonlocal term is typically specified to be zero in stable boundary layers, and usually is applied only to scalars, not orizontal wind. Holtslag-Boville sceme An example is te Holtslag-Boville (1993, J. Clim.) sceme used in te CAM3 and CAM4 climate models. Te eddy diffusivity is specified using a K-profile based on te vertical velocity variance (9.4) of a CTBL, K a (z) = kw t z(1 - z/) 2, (9.7) 9.3

4 were k = 0.4 is te von Karman constant, but using a scaling velocity tat is also applied for stable and neutral boundary layers: w t 3 = Pr{u * 3 + c 1 w * 3 }, c 1 = 0.6, Pr = 1 (neutral)- 0.6 (pure convective) (9.8) Te nonlocal term is modelled to be proportional to te surface buoyancy flux: ( ) 0 γ a = A w * w 2 t, A = 7.2 (9.9) Since te nonlocal flux is proportional to w *, it is only active in unstable boundary layers were te convective velocity w * > 0. In stable or neutral BLs, te parameterization reduces to a K- profile sceme. Te nonlocal flux is largest near at z/ = 0.3, were it carries over alf of te overall eat flux. YSU sceme Te YSU sceme popular in te WRF (Hong et al MWR) is structurally similar to te Holtslag-Boville sceme. In addition to te two terms in HB, te YSU sceme also includes a flux explicitly representing te effects of entrainment at te boundary layer top : e(z) = z w a () = w e Δa 3 w a () Te entrainment rate is picked rougly following te Moeng and Sullivan closure: w e Δb = w'b'() = 0.15w t 3 Tis approac regulates te entrainment at te top of te boundary layer better tan HB and seems to give better overall results tan oter WRF PBL parameterizations over land sites (e. g. Hu et al JAMC). EDMF scemes Anoter nonlocal approac for convective boundary layers, EDMF (Eddy Diffusion-Mass Flux) parameterization (Siebesma et al JAS), is used in te ECMWF weater forecasting model (Koeler et al QJRMS). In a dry-convective boundary layer, te vertical velocity as a positively-skewed pdf, implying tat updrafts tend to be narrower and more intense tan downdrafts, ence presumably more vertically organized. Siebesma et al. separated out vertical fluxes associated wit tese strongest updrafts, covering a orizontal area fraction A ~ of te orizontal area Tey treated tese fluxes using a mass-flux term in wic te scalar flux is represented using te mean updraft velocity w u (z) and mean scalar value a u (z) in tese updrafts and compensating uniform downward motion across te remaining fraction 1 - A of te domain: MF = Aw u a) + (1 A)w d (a d a) = Aw u a) + (1 A) Aw u A a) Aw u a) if A << 1. (1 A) (1 A) 9.4

5 Te term M = Aw u is called te updraft mass flux (strictly speaking it is te upward volume flux of a in te organized updrafts per unit orizontal area). Tis approac was taken from cumulus parameterization, were it is attractive because te cloudy updrafts are typically muc more intense tan te subsidence around tem. An attraction of EDMF is tat it can consistently represent strong updrafts as tey go troug te top of a subcloud convective layer and into te bases of overlying cumulus clouds. Tus it can unify boundary-layer and cumulus parameterization in one matematical framework. Oter eddies are assumed to be lesss vertically organized and are treated using eddy diffusion. Tus, te overall turbulent transport is assumed to ave te form: w a = K(z) da dz + M(z) a u (z) a(z) { } (9.10) Te form of K(z) is similar to te HB form (9.2). Te mass flux and te value of a u are calculated from a differential equation describing turbulent mixing into te organized updrafts, again using ideas transferred from cumulus parameterization: da u dz = ε(z)(a a u) (1 2µ) d 2 w u dz 2 = B bεw 2 u, were µ = 0.15 accounts for pressure forces, b = 0.5. B is te updraft buoyancy, and based on LES, te lateral entrainment rate into te updraft is ε(z) = z + 1 z and is determined as te eigt at wic w u goes to zero. Initial updraft scalar excesses near te surface are proportional to te corresponding surface flux divided by a diagnosed vertical velocity variance at te lowest grid level. Like ADHOC scemes, EDMF scemes can unify dry, stratocumulus and cumulus convection into one parameterization (Neggers et al. 2009, JAS; Park 2014a,b, JAS), but tere are still callenges wit accurately simulating transitions between tese BL types. Watc out for In all te above scemes, te underlying ideas are important to appreciate, but te details and numerical implementation on a discrete grid (often relegated to appendices of papers or Fortran coding details) are also critical to teir success. In particular, te diagnosis of a PBL eigt between grid levels can strongly affect a K-profile parameterization, especially for convection under a strong temperature inversion (e. g. Vogelezang and Holtslag, 1999, BLM). 9.5