Disturbed micrometeorological flows example local advection

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1 Disturbed micrometeorological flows example local advection Horizontal gradients of mean properties ( u, T, u ' w ', w ' T ' etc.) in the atmospheric surface layer may be generated by inhomogeneity in the surface boundary conditions** inhomogeneity in surface properties and fluxes e.g. Δ Q H0, Δ Q E0, Δ z 0,... due to varying soil moisture, surface elevation/cover, by purely aerodynamic disturbances (windbreaks, hills, buildings, ) by a combination of these types of influences Note: the flow need not be disturbed at the boundary in order to be inhomogeneous (Philip*, 1959, The Theory of Local Advection, J. Meteorol. Vol. 16) Our subject material so far has addressed flows that are horizontallyhomogeneous. We now progress to consider examples of disturbed flows, with emphasis on their modelling which, to the extent that it is accurate, is indicative of our ability to generalize from specific instances of disturbed flows Q* QH0 Q E0 eas572_localadvection.odp JDW vers. 20 Nov * J.R. Philip was chief of CSIRO s Pye Lab (Canberra), and provided ingenious analytical solutions to the mass conservation equation applied to soil moisture and soil solute flows solutions vitally useful in the pre-computer era Q G **The surface energy budget

2 The Paradigm of the Internal Boundary Layer z Horiz. unif at x<0 MOST applies known inflow profiles h b (x) Blending region new equilibrium layer, MOST applies x Paradigm: h b x σ w u (z) = σ w u(αh b (x )) Neutral case h b z 0 [ ln h b z 0 1 ] + 1= A x z 0 Weakness: this approach neglects disturbance to pressure and considers the disturbance propogates like a passive tracer gas 1 ρ R 2 p= u i x j u j u ' i x i x j u j ' x i g T R T z Useful reading: Garratt pp (Sec. 4.5 up to eq. 4.30) This Poisson eqn easily derivable from the Reynolds eqns. Solution for mean pressure at point P responds to r.h.s. over all positions r, weighted as P r -2. This implies a disturbance has upstream influence

3 An early expt. & test of Philip s analytical theory of local advection wind blows off tarmac onto short grass infinite Bowen ratio Q H0 /Q E0 in the approach flow Height [cm] Mean temperature Height QJRMS Vol. 89, 1963 Interpretive paradigm = eddy diffusion; steady state; divergences of sensible and latent heat flux vectors vanish; imposed (unvarying) power law profiles of wind and diffusivity Absolute humidity ρ v

Incoming terrestrial (longwave) radiation Outgoing terrestrial (longwave) radiation Later authors** refined the treatment of the lower boundary condition; useful to reframe in terms of equivalent

4 Incoming terrestrial (longwave) radiation Outgoing terrestrial (longwave) radiation Later authors** refined the treatment of the lower boundary condition; useful to reframe in terms of equivalent temperature and saturation deficit (ρc p T eq is total thermodyn. energy). T eq =T + e γ γ the psychrometric constant temperature if all latent heat converted to sensible D=e sat (T ) e e is vapour pressure Q H +Q E = ρ R c p K T eq **Raupach (1991; Vegetatio, Vol. 91) preceded by McNaughton z LHS constrained at gnd by sfc energy balance

5 Observed variation of the profile of the (advecting) mean wind speed implies one should account for conservation of momentum as well as heat and latent heat Rider, Philip & Bradley had treated net radiation less soil heat flux as invariant with x, implying Q H0 + Q E0 =const. = ρ R c p [ K T eq z ]0

6 Local advection experiment (La Crau Valley, France; N.J. Bink, Ph.D. thesis, Wageningen Agric. Univ.) z U 0 (z) hot dry cool, humid dry plain x=0 moist field x z z inversion T 0 (z) T(x,z)

7 Rao-Wyngaard-Coté 2 nd -order closure model of local advection: 17 equations in 17 unknowns (symmetry along y-axis, ie. 2d implementation): U W P T Q u v w u w u T u Q w T w Q '2 '2 '2,,,,,,,, ' ', ' ', ' ', ' ', ' ', '2 '2 T, q, q ' T ', ε Very similar to other 2 nd -order closures, e.g. Launder,Reece & Rodi U-mtm: hor.flx. 2 ( ) ( ) 1 P UU + σ u + UW + u ' w' = x z ρ x hor.flx. vrt.flx. 0 pressure disturbance (not allowed for in original RWC treatment) σ u 2 : adv. diff. '2 '2 '2 '2 u '2 '2 u '2 U U 2 c11 '2 2 U u atτ u + W u atτ w = 2u 2 u ' w' ε u k x x z z x z 3 τ 3 shear prod. redistrib. '2 '2 u u + atτ u ' w' + atτ u ' w' x z z x effective diffusivity (here a t is a closure constant) τ = 2 k ϵ a turbulence time scale The closure constants are not free they are constrained by forcing the model to reduce to an exact model of the ideal NSL

8 Computational domain and boundary-conditions for application** of Rao-Wyngaard-Cote 2 nd -order closure model to La Crau experiment: z= 80 m, flow undisturbed x = -20 m x=120 m u *1 MOST profiles (Q*- Q G ) 1 (Q*- Q G ) 2 z 01 r c1 x = 0 z 02 r c2 (canopy resistance for evaporation) **

La Crau run 42 specification of controlling boundary conditions Vincent Van Gogh: Harvest at La Crau Surface treated as a big leaf and coupled to model atmosphere s lowest plane of gridpoints (at )

9 La Crau run 42 specification of controlling boundary conditions Vincent Van Gogh: Harvest at La Crau Surface treated as a big leaf and coupled to model atmosphere s lowest plane of gridpoints (at ) using the Penman- Monteith evapotranspiration eqn ϵ sa Q E0 λ E 0 = ϵ sa +r v /r h [Q * Q G ]+ ρ λ D a /r h ϵ sa +r v /r h Canopy resistance r c is the excess resistance for vapour loss, such that λ the latent heat of vapourization; ε sa ratio of the slope of the sat n vapour pressure curve to the psychrometric constant; D a the saturation deficit at the surface, varying with x

10 Aside on bulk transfer resistances e.g. let r h be the transfer resistance for heat between levels z=z 0 to z=h, defined by If the flux is height-independent it is easy to prove that We can use MOST (entailing the assumption of height-independent flux) to calibrate the resistance: r h

11 Observations at La Crau Valley (France) versus numerical solution of conservation equations using RWC 2 nd -order closure modification of the mean temperature profile z [m] 10 x [m] = Upwind x = 80 m x=126 m x = 183 m x = 265 m Τ

An application of the RWC local advection model Inference of gas emissions (NH 3, CH 4 ) from agricultural lagoons familiar techniques are predicated on a horizontally-uniform flow and existence of a

12 An application of the RWC local advection model Inference of gas emissions (NH 3, CH 4 ) from agricultural lagoons familiar techniques are predicated on a horizontally-uniform flow and existence of a constant flux layer over the source. Generate a synthetic lagoon flow and test several micromet methods Preparation entailed comparing RWC with the La Crau local advection expt. adding a passive scalar and comparing with Project Prairie Grass and adding a windbreak momentum sink to test model s treatment of windbreak flow (covered in detail elsewhere). The RWC model performed very well in all tests U U 2, T 2, C 2 U 1, T 1, C 1

13 Mean wind reduction behind a long porous fence (h /z 0 =600, k r =2) mounted perpendicular to neutrallystratified flow Mulhearn & Bradley field observations versus solution of (augmented) RWC conservation equations: U/U 04 U/U More details on this in later class z/h = x/h Tracer concentration field from a ground level area source at x>0, in horizontally-uniform and neutral flow lines from RWC, symbols from the wellmixed Lagrangian stochastic model for this flow (known to agree with Prairie Grass): 1000 x / z0 = gas plume z / z 0 z/z x= u* C / kv Q

14 Proved model is competent to generate disturbed field of wind, temperature, humidity, tracer gas (and their fluxes) now generate synthetic lagoon flow z =80 m z 01 = z 02 = 0.01 m Δx=1m, Δz=0.2m unstable, neutral or stable approach flow L MO,1 =fixed unstable, neutral or stable IBL T 01 (const) T 02 (const) x [m] 100

15 z [m] Stable approach flow encounters a warm lagoon, T lag =T up + 5 (case F) distance over lagoon [m] Q? z [m] Τ [oc] U [m s-1]

16 Performance of flux-estimators Q? L a g o o n U p w i n d D o w n w i n d z 0 ( m ) T up ( C ) L ( m ) ( x = 5 0 m ) z 0 ( m ) T ( C ) lag L ( m ) F l u x - G r a d i e n t I H F B L S z 1 = z 2 = 0. 4 z 1 = 0. 4 z 2 = z 1 = 0. 4 z 2 = 1. 4 u p d o w n A B C D E F G H I J

17 Conclusions RWC local advection model does plausible job of calculating disturbed microclimate, as judged by its comparison with observed development of (T,Q) in flow from dry to moist land tracer dispersion (indirectly verified against Prairie Grass) reduction in mean wind speed behind a fence When flux estimators are applied to synthetic data at x = 50m over the lagoon, Integrated Horizontal Flux method (i.e. mass balance) excellent, 10% or better (model-independent, but practicality depends on geometric simplicity); backwards LS (model-based, source-receptor method) also very good (20%) despite neglect of flow disturbance; flux-gradient method (which assumes existence of a constant flux layer that does not prevail in distrubed flow except in the growing equilib. layer) very poor in some cases Broader conclusion relative to eas572 this and other examples will illustrate the prevalent way of thinking relative to flow disturbances; and show we have some skill in the mathematical representation of disturbed micromet flows. The basic limitation is the closure problem (RANS models far from perfect); as yet LES impractical for routine application to disturbed flows Q?

18 Disturbed micrometeorological flows

EVAPORATION GEOG 405. Tom Giambelluca

EVAPORATION GEOG 405. Tom Giambelluca EVAPORATION GEOG 405 Tom Giambelluca 1 Evaporation The change of phase of water from liquid to gas; the net vertical transport of water vapor from the surface to the atmosphere. 2 Definitions Evaporation: