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TUBULENT FLUXES OF HEAT, MOISTURE AND MOMENTUM: PRACTICE OF PARAMETERIZATIONS Bulk formulae: Thus, we need to know either roughness length, or neutral.

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Presentation on theme: "TUBULENT FLUXES OF HEAT, MOISTURE AND MOMENTUM: PRACTICE OF PARAMETERIZATIONS Bulk formulae: Thus, we need to know either roughness length, or neutral."— Presentation transcript:

1 TUBULENT FLUXES OF HEAT, MOISTURE AND MOMENTUM: PRACTICE OF PARAMETERIZATIONS Bulk formulae: Thus, we need to know either roughness length, or neutral transfer coefficients to determine the fluxes!

2 V C dn C d (unstable) C d (stable) ~10 -3  To measure the flux (eddy correlation or inertial dissipation) under the neutral conditions and the mean variables simultaneously;  To derive experimental dependence of the neutral transfer coefficient on the wind speed;  To apply stability correction functions and to derive coefficients for different stability conditions. 1. Typical approach: parameterization from measurements

3 4. Smith and Banke (1975), Smith (1980), Smith (1988) – eddy correlation measurements with a thrust anemometer at a platform offshore US West coast. Stability correction: Bussinger et al. (1973), Dyer (1974), Paulson (1970). Parameterizations derived from field measurements: Kruegermeyer (1976) – 124 hours of profile measurements in the tropics. Hasse et al. (1978) – 1400 hours of profile measurements in the Tropical Atlantic (coefficients for neutral conditions) Garratt (1977) for the momentum flux + Garratt and Hyson (1975) for sensible and latent fluxes. About 790 eddy correlation measurements in different conditions from different platforms.

4 Smith 88 Large and Pond (1981, 1982) – same platform as Smith (1980, 1988), eddy correlation + inertial dissipation measurements. Additionally ship measurements in the Atlantic and Pacific were used. Scatter was slightly better for the neutral coefficients for heat and moisture dependent on C dn, than for the constant coefficients.

5 2. Modelling of surface atmospheric layer to determine exchange coefficients Liu, Katsaros and Bussinger (1979) (LKB) – surface renewal theory. Surface renewal theory was first introduced in chemical engineering and has been applied to air-sea interface by Liu and Bussinger (1975) and Liu et al. (1979). Main assumption: Whereas the atmospheric (and oceanic) surface boundary layer transports heat, mass and momentum to the interface by turbulent motions, at the surface itself there exists an interfacial layer of order 1 mm thick, in which molecular diffusion plays a significant role in the transport. Across this interfacial layer, small eddies of air transfer heat randomly and intermittently between the “bulk” turbulent fluid, of temperature T b, and the surface itself which therefore warms or cools by conduction from the eddies.

6 The temperature gradient and the surface heat flux are determined by the heat conduction equation: The solution for initial condition T(t=0) = T b = constant, and surface temperature T(z=0) = T s = constant: Liu and Businger (1975) introduced a function to describe the areal fraction of eddies which have been in contact with the surface for time t, and assume a characteristic time, t c, for which an eddy remains in contact with the surface before breaking away. For constant T s and a random distribution of contact duration the time-averaged temperature profile in the interfacial layer: - LKB flux-profile relationship Thermal diffusivity - heat flux and an average heat flux:

7 Values of the exchange coefficients for LKB, as functions of wind speed and stability

8 Variations of coefficients from different schemes  Differences in behaviour of the coeeficients with wind are in general larger than with stability, at least for moderate and strong winds  The largest uncertainty in stability is observed under small winds Typical variations: Cd, Ct, Ce ~ 0.5x103 Recommendations:  Do not hesitate to use simple paramterizations;  Try to rely more on parameterizations derived from field observations  Under the calm or low winds use LKB, if ……[LATER]!!!!!  Never say “The best parameterization is done by XXXX” – they are all very uncertaint  Smith (1988) is considered to be most reliable  More or less “officially recommended” are Smith (1988), Large and Pond (1981, 1982), LKB (among these very simple parameterizaions)

9 COARE-3.0 algorithm (Fairall et al. 2003) universal schemes: modelling, surface renewal theory “field-only” schemes ASTEX - White et al. (1995) CATCH - Eymard et al. (1998) FASTEX – Hare et al. (1995) LabSea: Bumke et al. (2002) Clayson et al. (1996) Zeng et al. (1998) Beljaars (1995) Bourassa et al. (1996)

10  Based on the TOGA-COARE results and 2777 covariance flux measurements at the ETL;  Tested using 4439 new values from field experiments between 1997 and 1999 including the wind speed regime beyond 10 m;  The average (mean and median) model results agreed with the measurements to within about 5% for moisture from 0 to 20 m. COARE-3.0 algorithm (Fairall et al. 2003)

11 Variations in turbulent fluxes due to different parameterizations North Atlantic

12 /helios/u2/gulev/handout: lapo3.for - Large and Pond (1981, 1982) –with German comments liu3.for – LKB (Liu, Katsaros and Bussinger 1979) potsmin1.for - Smith (1988) (all codes are for water vapor pressure, i.e. e z and not q) Compute the fluxes of sensible heat, latent heat and momentum for the following conditions: SST=10C, Ta=8C, ez=9mb, V=7m/s, Pa=1010mb SST=10C, Ta=12C, ez=11mb, V=7m/s, Pa=1010mb SST=10C, Ta=8C, ez=9mb, V=3m/s, Pa=1010mb SST=10C, Ta=8C, ez=9mb, V=12m/s, Pa=1010mb

13 /helios/u2/gulev/handout/ (for the same parameter values) flux_test.f – program to compute instantaneous values of urbulent fluxes, using Liu et al. (1979), Large and pond (1981, 1982) and Simth (1988) schemes. Compilation: f77 –o flux_test flux_test.f lapo3.for liu3.for potsmin1.for Results: flux.res

14 References Blanc, T.V., 1985: Variation of bulk-derived surface flux, stability and roughness results due to the use of different transfer coefficient schemes. J. Phys. Oceanogr., 15, 650-669. Blackadar, A., 1998: Turbulence and diffusion in th eatmosphere. Springer-Verlag, 186 pp. Blanc, T.V., 1987: Accuracy of bulk-method determined flux, stability, and sea surface roughness. J. Geophys. Res., 92, 3867-3876. Bumke, K., U.Karger, and K.Uhlig, 2002: Measurements of turbulent fluxes of momentum and sensible heat over the Labrador Sea. J.Phys. Oceanogr, 32, 401-410. da Silva, A.M., C.C. Young, and S.Levitus, 1994: Atlas of surface marine data. NOAA Atlas NESDIS 6, Volume 1-6, US Dept. Commerce, NODC, NOAA/NESDIS, Washington DC. Dyer, A.J., 1974: A review of flux-profile relationships, Bound.-Layer Meteor., 7, 363-372. Eymard, L., G. Caniaux, H.Dupuis, L.Prieur, H.Giordani, R.Troadec, P.Bessemoulin, G. Lachaud, G.Bouhours, D.Bourras, C.Guerin, P.LeBrogne, A.Brisson, and A. Marsouin, 1999: Surface fluxes in the North Atlantic current during CATCH/FASTEX. Quart. J. Roy. Meteor. Soc., 125, 3563-3599. Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmosphere Coupled-Ocean Atmosphere Response Experiment. J. Geophys. Res., 101, 3747-3764. Geernaert, G., and W.J.Plant, 1990: Surface waves and fluxes. Kluwer AP, 2 volumes. Golitsyn, G.S., and A.A.Grachov, 1986: Free convection of multi-component media and parameterization of air-sea interaction at light winds. Ocean-Air Interactions, 1, 57-78. Grachov, A.A., and G. Panin, 1984: Sensible and latent heat flux parameterization over water surface under natural conditions. Izv. Acad. Sci. USSR. Atmos. Oceanic. Phys. 20, 364-371. Hasse, L., 1971: The sea surface temperature deviation and the heat flow at the sea-air interface. Bound.-Layer Meteor., 1, 368-379. Hasse, L., and S.D. Smith, 1997: Local sea surface wind, wind stress, and sensible and latent heat fluxes. J.Climate, 10, 2711-2724. Isemer, H.-J., and L. Hasse, 1987: The Bunker Climate Atlas of the North Atlantic Ocean. Vol. 2, Air- Sea Interactions, Springer-Verlag, 252 pp.

15 References-continue Josey, S., E.C.Kent, and P.K.Taylor, 1999: New insights into the ocean heat budget closure problem from analysis of the SOC air-sea flux climatology. J. Climate, 12, 2856-2880. The LabSea Group, 1998: The Labrador Sea Deep convection Experiment. Bull Amer. Met. Soc., 79, 2033-2058. Large, W.G., and S.Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Oceanogr., 11, 324-336. Large, W.G., and S.Pond, 1982: Sensible and latent heat fluxes over the ocean. J.Phys.Oceanogr., 12, 463-482. Liu, W.T., K.Katsaros, and J.Businger, 1979: Bulk parameterization of air-sea exchanges of heat and water vapor including molecular constraints at the interface. J.Atmos.Sci., 36, 1722-1735. Oberhuber, J.M., 1988: An Atlas based on the COADS data set: the budgets of heat, buoyancy and turbulent kinetic energy at the surface of the global ocean. MPI fuer Meteorologie report, No. 15, 19pp. [Available from Max-Plank-Institute fuer Meteorologie, Bundesstrasse 55, Hamburg, Germany]. Paulson, C.A., 1970: Representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J. Appl. Meteor., 9, 857-861. Renfrew, J., G.W.K. Moore, P.S. Guest and K. Bumke, 2002: A comparison of surface-layer, surface heat flux and surface momentum flux observations over the Labrador Sea with ECMWF analyses and NCEP reanalyses. J. Phys. Oceanogr., 32, 383-400 Smith, S.D., 1980: Wind stress and heat flux over the ocean in gale force winds. J. Phys. Oceanogr., 10, 709-726. Smith, S.D., 1988: Coefficients for sea surface wind stress, heat flux and wind profiles as a function of wind speed and temperature. J.Geophys. Res., 93, 15467-15474. Stull., R., An introduction to boundary layer meteorology. Kluwer AP, 667 pp. Yelland, M.J., B.I.Moat, P.K.Taylor, R.W.Pascal, J.Hutchings, and V.C.Cornell, 1998: Wind stress measurements from the open ocean corrected for air flow disturbance by the ship. J. Phys. Oceanogr., 28, 1511-1526. Zeng, X., M. Zhao, and R. Dickinson, 1998: Intercomparison of bulk aerodynamic algorithms for the computation of sea surface fluxes using TOGA COARE and TAO data. J.Climate, 11, 2628-2644.

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