Gollnik, Tim

Gryanik, Vladimir M.

Lüpkes, Christof

English

Electronic Publication Information Center

Modelling the small-scale impact of leads on the polar atmospheric boundary layer using a new nonlocal turbulence closure

1.4 MODELLING THE SMALL-SCALE IMPACT OF LEADS ON THE POLARATMOSPHERIC BOUNDARY LAYER USING A NEWNONLOCAL TURBULENCE CLOSUREChristof Lu¨pkes1∗, Vladimir M. Gryanik1,2, and Tim Gollnik11Alfred-Wegener-Institute for Polar and Marine Research, Bremerhaven, Germany2A.M. Obukhov Institute for Atmospheric Physics, Moscow, Russia1. INTRODUCTIONThe polar sea ice cover is always smallerthan 100 %, since even during winter inhomo-geneous forcing by wind and ocean currents isgenerating leads which are either free of ice orcovered by thin new ice. From autumn to springthe large differences in the temperatures betweenthe surface of leads and the cold advected aircause strong atmospheric convection. Until nowits impact on the atmospheric boundary layer(ABL) is not fully understood. This is caused e.g.,by the difficulties in obtaining observations overthe leads. So, most of the available data (e.g.,Paulson and Smith, 1974; Andreas et al., 1979;Alam and Curry, 1997; Persson et al., 1997; An-dreas and Cash, 1999) were obtained from sta-tions downstream of leads and not in the cen-ter of the convective plumes. There are alsoonly few studies using high resolution models asthose by Glendening and Burk (1992), Zulauf andKrueger (2003), Weinbrecht and Raasch (2001)and most recently of Esau (2007). Such studiesrequire large computational costs which is due tohigh resolution required to resolve the processesover leads, whose widths range between meters(cracks) and sometimes a few kilometers.The goal of the present study was to investi-gate the physics of air ice interaction in the pres-ence of leads using different modeling strategiesas explained below. It is demonstrated that es-pecially during winter leads may have a strongimpact on the surface energy budget and near-surface air temperature. Furthermore, our studiesshow that the application of traditional turbulenceclosures in climate models may cause deficien-∗Corresponding author address: Christof Lu¨pkes,Alfred-Wegener-Institute for Polar and Marine Re-search, Postfach 120161, D-27515 Bremerhaven;e-mail: christof.luepkes@awi.deFigure 1: Convection over leads (schematic)cies in the turbulent fluxes of heat and momen-tum over a domain with leads. Our studies initi-ated in Lu¨pkes et al. (2008a,b) are carried outwith the nonhydrostatic atmospheric mesoscalemodel METRAS (Schlu¨nzen, 1990; Lu¨pkes andSchlu¨nzen, 1996) and are partly based on theanalysis of data obtained from the Large EddySimulation model PALM (Raasch and Schro¨ter,2001).2. MODELING STRATEGIESThe impact of convective processes over leadson the atmospheric boundary layer and its inter-action with sea ice can be investigated with differ-ent modeling strategies. The most complex oneis the use of Large Eddy Simulation (LES) withgrid sizes small enough to resolve individual ther-mals developing over the leads. We know fromsuch investigations (e.g. Weinbrecht and Raasch,2001) that these thermals generate an internalboundary layer, whose thickness δ is increasinguntil the capping inversion is reached and entrain-ment fluxes can develop. The warm air whichis transported downstream in a convective plumeis warming the ice surface in the environment ofleads, since over ice the near-surface heat fluxesare directed downward.There is a large discrepancy between the de-tailed modeling using LES and the modeling ofthe lead impact in a climate or weather forecastmodel which cannnot resolve the small scale pro-cesses over leads. In the best case such mod-els have a flux averaging scheme at the surfaceso that at least the lead and ice fraction can beprescribed and different fluxes occur over bothsurface types. Above the first grid level, how-ever, horizontal gradients in one grid box are zeroso that climate models implicitely apply instanta-neous horizontal mixing of all variables. This ap-proach is similar as if a 1D model were used. Theeffect of leads as obtained in a climate model canbe investigated therefore using a 1D model, whichis done in the next section.Due to the large discrepancy between LESand the treatment in non-eddy resolving modelsan intermediate method has been developed byLu¨pkes et al. (2008b), which uses a model withgrid sizes small enough to resolve the plume re-gion (Figure 1), but not the individual thermalslike LES. So, such a model which will be calleda microscale model needs its own turbulenceparametrization, since strong horizontal gradientsare present which cannot be treated by traditionaltubulence parametrizations. Its advantage com-pared with LES is that it needs much less cpu-time, its disadvantage is that up to now only sim-ple lead geometries are possible. The develop-ment of the turbulence parametrization for sucha model contributes to a deeper understandingof the convective processes over leads, sincethe driving parameters and reasons for the smallscale ABL structure have to be identified to obtainfinally a physically well-grounded parametriza-tion.3. RESULTSIn the following we discuss results which wereobtained with the modeling strategies obtainedabove. This includes also the description of theturbulence parametrization developed for the mi-croscale model which is based on results of theLarge Eddy Simulation model PALM (Raasch andSchro¨der, 2001).0.96 0.98 1.00sea ice concentration225230235240245250           10 m  pot. temp. (°C)|vg|=12ms-1|vg|=8ms-1|vg|=5ms-1|vg|=2ms-1Figure 2: 10 m-potential temperature as afunction of prescribed sea ice concentration andgeostrophic wind after 2 days of simulationobatained with a 1D version of the coupled air-ice/snow model METRAS.3.1 1D-ModelingAs concerns the impact of leads on the polar cli-mate, one of the most important questions is, ifleads have an impact on the ABL temperature.We show here a result, discussed by Lu¨pkes at al.(2008a), who used a 1D-version of the mesoscalemodel METRAS (15 layers below 300 m) whichwas coupled with a high resolution snow/sea icemodel (1 cm grid size). The model was initi-ated with a temperature profile being typical for alate winter situation with a cloud topped boundarylayer. A sea ice and lead fraction was prescribedas well as the geostrophic wind and clear-sky dur-ing polar night was assumed during the simula-tion time. So, the atmospheric temperature andwind evolution was considered under the impactof radiative cooling and convective heating overthe lead fraction as well as cooling over the seaice fraction. After about two days of simulation aquasi-stationary temperature profile developed.An example of results is shown in Figure 2with the 10-m temperature as a function of theprescribed sea ice concentration. According tothis figure leads can have a strong impact on theABL temperature, since only one percent change0 2 4 6distance (km) 0100200300height (m) 250.08250.08 250.12250.12250.16250.16250.16250.16250.20250.20250.20250.24250.28250.60250.840100200300height (m) 40404080 80-15-5-5-5-5-5000000 00000 000000Figure 3: Fluxes of sensible heat (W m−2) (top)and potential temperature (K) (bottom) as a func-tion of distance to a lead of 1 km width. Result ofthe LES model PALM discussed in Lu¨pkes et al.(2008b).of the sea ice fraction can result in up to 4 Kchange of the 10m-temperature. Although onecan expect that clouds would have a damping ef-fect this result shows that the lead impact shouldbe considered in more detail in the future due toits large potential to affect the ABL and surfaceenergy budget. Previous investigations could notfind a similar effect (e.g. Ebert and Curry, 1993),since the atmospheric conditions were prescribedfrom observations already containing the lead im-pact so that the atmosphere ice system could notfreely develop.3.2 3D-LES and 2D-microscale modelingThe above results motivate a more detailed in-vestigation of processes over leads. We considerin the following cases with a flow orthogonal toa small scale lead. Figure 3 shows a result ob-tained with the LES model PALM which was dis-cussed in Lu¨pkes at al. (2008b). Results are pre-sented as averages parallel to the lead orienta-0 2 4 6distance from lead edge (km) 0100200300height (m) 250.08250.12 250.12250.12250.16 250.16250.16250.16250.20250.20250.20 250.20250.24 250.24250.28 250.28250.40 250.48250.76 250.92251.44250.120100200300height (m)4040 80 -5-5-500Figure 4: Same as Figure 3, but results were ob-tained with the microscale model METRAS usingthe new closure.tion and orthogonal to the surface wind direction.An inclined plume indicating an internal boundarylayer can be clearly identified by considering thefluxes of sensible heat. Comparing the upwardflux field for this typical winter time flow with thefield of potential temperature, it becomes clearthat outside a core region of the convective plume(see Lu¨pkes et al., 2008b) fluxes can be consid-ered as of nonlocal nature. They are related tothermals, whose size is in the order of the internalboundary layer height, rather than to small scaleeddies. This feature formed the basic idea for thedevelopment of a closure for the microscale re-solving the convective plume.The most simple possibility accounting fornonlocal heat fluxes is to add a countergradienttransport term in the equation for the heat flux sothatw′Θ′ = −Kh(∂Θ∂z− Γ)(1)where Kh is the eddy diffusivity for heat and Γis the countergradient term. Both Kh and Γ de-pend in homogeneous conditions on the surfacebuoyancy flux B and on the mixed layer heightzi. The latter form the convective velocity scalew? = (Bzi)1/3. Lu¨pkes at al. (2008b) transferredthis concept to the nonhomogeneous case withthe convection over leads. Now, Kh and Γ de-pend on the internal boundary layer height δ andon the surface bouyancy flux over the lead Blead.A new vertical velocity scale is given then bywl(y) = c (Blead δ)1/3 exp[−(y/D)] . (2)The exponential decay function with decay lengthscale D is assumed, since turbulence is decayingwith increasing distance y on the downstrean sideof the lead. δ can be derived asδ(y) = zi [1− exp(−y/D)]3/2 (3)with the assumption that the change of δ withdistance is proportional to wl/U , where U is thecharacteristic horizontal wind speed upstream ofthe lead and is influencing the plume inclination.It can be shown that D follows asD =32a(U3Blead)1/3z2/3i . (4)The factor U3/Blead arises in D which is similarto the Monin Obukhov length, while U occurs hereinstead of u?. It should be stressed that the abovescale does not depend on the lead width, sincewe considered up to now only small leads. In amore general formulation D depends also on thelead width L, but the principal structure of D re-mains unchanged.Figure 4 shows results obtained with theabove closure using the model METRAS with mi-croscale resolution (horizontal grid size of 200 m).Although there are certain differences betweenthe LES results of Figure 3 and the METRAS re-sult in Figure 4 the general structure with the po-tential temperature increasing with height in mostof the shown region is reproduced. Such a struc-ture could only be obtained with a new nonlocalclosure based on equations (1)-(4). Any attemptswith a local traditional or nonmodified nonlocalclosure failed to reproduce this detailed structure.Thus the simulations give at least a hint that thenew scaling captures the basic physics of the in-volved processes.With the new model it becomes possible toperform a large number of simulations over pop-ulations of leads and comparing high resolutionruns with results of models using much larger gridsizes. Such a first test has been carried out. Themicroscale model with 200 m grid size was ap-plied to the flow over an ensemble of leads ina domain of 120 km width. The same domainwidth with the same domain averaged sea iceconcentration was then presecribed, but a ver-sion of METRAS was used with 35 km horizontalgrid size which is similar to the resolution of a re-gional climate model. The domain averaged fluxprofiles differed strongly from each other. Com-pared to the microscale version the climate ver-sion underestimated the fluxes of sensible heatby roughly 50 %, while momentum fluxes wereoverestimated by 40 % near the surface. The lat-ter effect is caused by a strong deceleration ofthe flow over the ice regions in the microscale so-lution.4. CONCLUSIONSOur results showed that leads may have a strongimpact on the near-surface temperature. Thisforms a challenge for climate modeling for tworeasons. The first is that the present day coupledair-ice-ocean (climate) models cannot reproducethe sea ice concentration with the required accu-racy which is according to the present study in theorder of 1 %. The second reason is that accordingto the present results even the geometry of theopen water areas is important. The assumptionof leads generates a different kind of heteroge-neous convection than the assumption of a con-tinuous open water fraction.It was shown that the convective processesover leads are of nonlocal nature. A new scal-ing generalizing Deardorff scaling to nonhomo-geneous conditions works well in a microscalemodel using grid sizes allowing to resolve con-vective plumes over leads.ACKNOWLEDGEMENTSWe thank S. Raasch, M. Gryschka and B. Withafor providing results of the LES model PALM. Thiswork was supported by the EU project DAMO-CLES which was financed in the 6th Frame-work Programme for Research and Development(grant 18509) and by DFG (grant LU 818/1-1/2).5. REFERENCESAndreas, E.L., and B. Murphy, 1986: Bulk trans-fer coefficients for heat and momentum overleads and polynyas, J. Phys. Oceanogr., 16,1875-1883.Andreas, E. L., Paulson, C. A., Williams, R. M.,Lindsay, R. W., and J.A. Businger, 1979:The turbulent heat flux from Arctic leads,Boundary-Layer Meteorol., 17, 57-91.Andreas, E.L., and B.A. Cash, 1999: Convec-tive heat transfer over wintertime leads andpolynyas, J. Geophys. Res., 104 (C11),25,721-25,734.Ebert, E.E., and J.A. Curry, 1993: An intermedi-ate one-dimensional thermodynamic sea icemodel for investigating ice-atmosphere inter-actios, J. Geophys. Res., 98(C6), 10,085-10,109.Esau, I.N., 2007: Amplification of turbulent ex-change over wide arctic leads: Large-eddysimulation study, J. Geophys. Res., 112,D08109, doi:10.1029/2006JD007225.Glendening, J.W., and S.D. Burk, 1992: Turbu-lent transport from an Arctic lead: A largeeddy simulation, Boundary-Layer Meteorol.,59, 315-339.Paulson, C.A., and J.D. Smith, 1974: The AIDJEXLead experiment, AIDJEX Bull., 23, 1-8.Persson, P. O. G., Ruffieux, D., and C.W. Fairall,1997: Recalculations of pack ice and leadsurface energy budgets during the ArcticLeads Experiment (LEADEX) 1992, J. Geo-phys. Res., 102, 25085-25089.Lu¨pkes, C., Vihma, T., Birnbaum, G., Wacker, U.,2008a: Influence of leads in sea ice on thetemperature of the atmospheric boundarylayer during polar night, Geophys. Res. Lett.,35, L03805, doi:10.1029/2007GL032461.Lu¨pkes, C., Gryanik, V.M., Witha, B., Gryschka,M., Raasch, S., Gollnik, T., 2008b: Modelingconvection over arctic leads with LES and anon-eddy-resolving microscale model, Jour-nal of Geophysical Research, 113, C09028.,doi:10.1029/2007JC004099Lu¨pkes C., Schlu¨nzen K.H., 1996: Modelling theArctic convective boundary layer with differ-ent turbulence parameterizations. Boundary-Layer Meteorol., 79, 107-130Raasch, S., and M. Schro¨ter, 2001: A large-eddy simulation model performing on mas-sively parallel computers, Meteorol. Z., 10,363–372.Schlu¨nzen, K.H., 1990: Numerical studies on theinland penetration of sea breeze fronts at acoastline with tidally flooded mudflats. Beitr.Phys. Atmosph., 63, 243-256Weinbrecht, S. and S. Raasch, 2001: High-resolution simulations of the turbulent flow inthe vicinity of an Arctic lead, J. Geophys. Res.,106 (C11), 27,035-27,046.Zulauf, M.A., and S.K. Krueger, S.K., 2003: Two-dimensional numerical simulations of Arcticleads: Plume pen-etration height, J. Geophys. Res., 108(C2),8050, doi:10.1029/200JC000495

Modelling the small-scale impact of leads on the polar atmospheric boundary layer using a new nonlocal turbulence closure

Abstract

Similar works

Full text

Available Versions

Electronic Publication Information Center

Electronic Publication Information Center