MOISTURE-TRANSFER COEFFICIENT FOR CLIMATE MODELS

(Research Note)

JINWU Air-Sea Interaction Laboratory, Graduate College of Marine Studies, University of Delaware,

Lewes, Delaware 19958, USA and Institute of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

(Received in final form 7 November 1995)

Abstract. Recent parameterizations of the moisture-transfer coefficient from measurements in the field and from tuning of the ECMWF model are reviewed. A formula for the neutral transfer coefficient varying continuously with the wind velocity is proposed for climate models.

1. Introduction

Recent interest in evaluating variations of the climate demands an accurate quan- tification of air-sea exchanges of momentum, heat and mass, which provide the forcing of both atmospheric and oceanic systems. Data on the moisture transfer reviewed by Friehe and Schmitt (1976) and reported by Large and Pond (1982) and Bradley et al. (199 1) appear to have the characteristics of aerodynamically smooth flows at low winds and rough flows at high winds; correspondingly, as the wind velocity increases, the neutral moisture-transfer coefficient decreases at low winds and increases at high winds (Wu, 1992b). With the inclusion of smooth-flow charac- teristics in the parameterization of the evaporation coefficient, Miller et al. (1992) showed an improved matching of the ECMWF (European Centre for Medium- Range Weather Forecasts) model with observations. For aerodynamically rough flows, the increase of the mass-transfer coefficient with wind velocity is consis- tent with results of an international experiment, specifically organized to examine such a dependency (DeCosmo, 1991). Taking together all these results, as well as requirements for the climate model, a continuous variation of the moisture-transfer coefficient with the wind velocity is suggested.

2. Summary of Recent Results

2.1. PROPOSED PARAMETERIZATION

In the atmospheric surface layer, the mass flux is represented by

c, = cWlG(Qo - Qz) (1)

Boundary-LayerMeteorology 77: 401-407,1996. @ 1996 Kluwer Academic Publishers. Printed in the Netherlands.

402 JINWU

where C, is the coefficient of vapour flux (C,, under neutral atmospheric condi- tions); q’ and ‘20’ are fluctuations of the moisture and vertical velocity, respectively; U and Q are the mean wind velocity and specific humidity, with the subscript z indicating the elevation of the measurements above the mean sea surface; the subscript o indicates the sea-surface value.

Moisture fluxes were measured by Large and Pond (1982) over intermediate wind velocities. The flux coefficient was found to have the smallest value at wind velocities of 6-7 m s-l, and increase from there towards both low and high winds (Wu, 1992b). More recently, moisture fluxes were measured by Bradley et al. (1991) under low winds. Their results followed the feature of aerodynamically smooth flows. Quantitatively, three formulae were proposed to represent these data (Wu, 1992b)

C,, = (0.55 $0.065Ui0) x 10-3, 1710 > 6.5 m s -1 (2)

C,, = (1.20-0.12InUio) x 10m3, 0.85 m s-l < 1710 < 6.5 m s -1 (3)

C,, = (1.12 - 0.60InUto) x 10p3, 0.1 m s-l < Ul0 < 0.85 m s-l (4)

in which Ulo expressed in m s-l is the wind velocity at 10 m above the mean sea surface. These expressions are shown as a dashed line in Figure 1.

2.2. THIS ECMWF MODEL

Miller et al. (1992) commented on the misrepresentation of mass flux in the ECMWF model, and went on to adopt the smooth-surface value suggested by Brutsaert (1982) for light winds. Coupling this with a constant thermal roughness length at high winds, they proposed

2, = 0.1 IV/U., t 0.018& (5)

zag = 0.62v/u, $ 1.3 x 1O-4

in which K is the von Karman universal constant, 2 = 10 m is the height for reference wind and moisture measurements, zoq is the roughness length of the moisture interfacial layer, U+ is the friction velocity, v is the kinematic viscosity of air, and g is the gravitational acceleration.

The moisture-transfer coefficient calculated from (5) is drawn as the dotted line in Figure 1. It deviates from the previous ECMWF model formulation, enhancing most significantly the evaporation at low winds, and reducing its trend of increasing with the wind velocity at high winds. With this new scheme, Miller et al. (1992) demonstrated that the ECMWF model was improved in all aspects of tropical

MOISTLJRE-TRANSFERCOEFFICIENTFORCLIMATEMODELS 403

3.0

2.5 - ‘?

0 c

u:: g 2.0 2

9 u 4 1.5 2, E & .g 2 1.0

7G b

z 0.5

0.0

-.- Decosmo and Katsaros [ 19911

......... Miller et al. [1992], corrected

--- Wu [1992b]

I I - Eq. (8)

. . . . . . . c/

.-.-

0 2 4 6 8 10 12 14

Wind Velocity, U,, (m s“)

Figure 1. A continuous variation of moisture-transfer coefficient with wind velocity.

simulations. Since winds in the tropical area are generally light, the ECMWF model is especially helpful in verifying the smooth-flow parameterization at low winds.

2.3. ADDITIONAL MEASUREMENTS

An intensive program, ‘HEXOS - Humidity Exchange over the Sea’, was carried out at moderate and high winds (Katsaros et ul., 1987). Results of water vapour fluxes were parameterized by DeCosmo and Katsaros (199 1) as

Cl0 = (0.68 $ 0.075UlO) x 1o-3 (6)

c,, = [0.18 + 0.75( 103clop] x 1o-3 (7)

404 JINWIJ

in which Cta is the wind-stress coefficient. The moisture-transfer coefficient is then confirmed to increase with the wind velocity, but the rate of increase is smaller than that of Cto increasing with Utu.

3. A Continuous Variation of C,, with 1710

3.1. PHYSICAL BASES

A model for air-sea exchanges of water vapour at light winds was proposed by Liu et al. (1979), stressing molecular constraints on the inter-facial transfer. The surface layer has been shown to depart from this state at the wind velocity of about 3 m s-l, and becomes fully rough around 7 m s -t (Kondo, 1975; Wu, 1981). Consequently, Liu et al.3 model is not applicable at moderate and high winds.

For aerodynamically rough flows, coefficients of heat and mass transfer were reasoned by Wu (1992a,b) to increase with the wind velocity on the following bases:

(a) The transfer coefficient over the solid rough surface, with fixed roughness ele- ments, was shown to increase with the roughness Reynolds number U,Z,/V (Owen and Thompson, 1963). Over the sea surface, not only the friction veloc- ity increases with wind velocity, waves constituting roughness elements also grow with the wind. Therefore, the increase of transfer coefficients with wind velocity should be even more intensified over the air-sea interface.

(b) As for the data, systematic variations with wind velocity were actually detected by Wu (1992a,b) in heat- and mass-transfer coefficients compiled by Friehe and Schmitt (1976) and reported by Smith (1980). These trends are even more clear with the extensive sets of data provided by Large and Pond (1982), Bradley et al. (1991) and DeCosmo and Katsaros (1991).

3.2. QUANTITATIVE RESULTS

Results of Bradley et al. (199 1) parameterized in (3) and (4) are compared in Fig- ure 1 with those from the ECMWF model (Miller et al., 1992) parameterized in (5). Both groups (dashed and dotted lines) follow well the characteristics of aero- dynamically smooth flows; the transfer coefficient decreases as the wind velocity increases from zero. The transfer coefficient in Miller et aZ.‘s proposal, however, starts to increase with the wind velocity at about Utc = 2.6 m s-l, in contrast to 6.5 m s-l proposed earlier by Wu (1992b).

At moderate and high winds, data of Large and Pond (1982) parameterized in (2) and those by DeCosmo and Katsaros (1991) in (6) and (7) have the same overall trend, but differ quantitatively. At the lower bound of applicability for (2) of Uto = 6.5 m s-t, the transfer coefficients in the two groups actually have about the same value: C,, = 0.973 x 1O-3 from the former and 0.990 x 10m3 for the latter.

MOISTURE-TRANSFERCOEFFICIENTFORCLIMATEMODELS 405

Consequently, their difference lies mainly in the rates of increase with the wind velocity. The rate of dC,,/dUtc = 0.065 m-l s shown in (2), being the same as that of the wind-stress coefficient (Wu, 1980), is probably too large. On the other hand, the results of DeCosmo and Katsaros might be somewhat suppressed by the shallow water depth. The transfer coefficient is, therefore, suggested to increase with the wind at about the average of the two rates. The transfer coefficient suggested by Miller et al. (1992) is seen in Figure 1 to have a much greater value. This is caused by their adoption of .zoq = 1.3 x 1O-4 m, not the constant transfer coefficient of Smith (1989) as stated by them. In any event, the emphasis of Miller et al.‘s work is concentrated on low winds; it is quite justifiable to associate our parameterization at moderate and high winds with only in-situ measurements.

3.3. PROPOSED FUNCTION

Measurements of Large and Pond (1982) and Bradley et al. (1991) were shown earlier (Wu, 1992b) to have a minimum value near Uro = 6.5 m s-l and increase toward both low and high winds. These trends are largely supported by results of the climate model (Miller et al., 1992), and consistent with measurements of a specially designed experiment (DeCosmo and Katsaros, 1991). Although providing the closest representation of data reported by Large and Pond and by Bradley et al., the three-segment formula shown in (2), (3) and (4) is not suitable for application in general circulation models. The division of segments introduces singularities around wind velocities at which various segments are divided. Furthermore, the rate of increase at high winds needs to be adjusted downward according to the results of HEXOS. Functionally, the transfer coefficient was shown to vary inversely with the natural logarithm of wind velocity for the smooth-flow regime (Wu, 1988), and linearly with the wind velocity for the rough-flow regime (Smith, 1980; Wu, 1992b). A smooth function consisting of all these features is proposed,

C,, = (1.20 $O.O88Utu - 0.421n 1710) x 10e3 (8)

in which 1710 is again in m s- I. Trends at low and high winds of this expression drawn in Figure 1, were justified in previous sections. The minimum value near the wind velocity of about 5 m s-l is also consistent with recent observations (Bradley et al., 1993).

4. Concluding Remarks

The moisture-transfer coefficient has been largely considered to have a constant value (Smith, 1989); it failed to recognize either the featured trend of aerodynami- cally smooth flows at low winds, or the increase of transfer coefficient with the wind velocity at moderate and high winds. In other cases, either only one of these trends

was adopted, or discrete formulae were suggested instead of a continuous func- tion. An attempt is made here to rectify these deficiencies, and to take into account recent comprehensive data as well as model results. The formula proposed contains a continuous variation of the transfer coefficient with wind velocity, approaching the logarithmic and linear variations with wind velocity featured respectively at low and high winds.

Acknowledgement

I am very grateful to the sponsorship of my work provided by the Ocean Sci- ence Educator Award, Office of Naval Research and the Division of Engineering, National Science Council.

References

Bradley, E. F., Coppin, P A. and Godfrey, J. S.: 1991, ‘Measurements of Sensible and Latent Heat Fluxes in the Western Equatorial Pacific Ocean’, J. Geophys. Rex 96,3375-3389.

Bradley, E. F., Godfrey, J. S., Coppin, P. A. and Butt, J. A.: 1993, ‘Observations of Net Heat Flux into the Surface Mixed Layer of the Western Equatorial Pacific Ocean’, J. Geophys. Res. 98, 22521-22532.

Brutsaert, W. A.: 1982, Evaporation into the Atmosphere, Reidel, 299 pp. DeCosmo, J.: 1991, ‘Air-Sea Exchange of Momentum, Heat and Water Vapor over Whitecap Sea

States’, Ph.D. Thesis, University of Washington, Seattle, Washington. DeCosmo, J. and Katsaros, K. B.: ‘Air-Sea Exchange of Sensible Heat and Water Vapor over

Breaking Waves’, Preprint Fifth American Meteorological Society Conference on Meteorology and Oceanography of the Coastal Zone, Miami, Florida, pp. 172-176.

Friehe, C. A. and Schmitt, K. F.: 1976, ‘Parameterization of Air-Sea Interface Fluxes of Sensible Heat and Moisture by the Bulk Aerodynamic Formulas’, J. Phys. Oceanogr. 6,801-809.

Katsaros, K. B., Smith, S. D. and Oost, W. A.: 1987, ‘HEXOS - Humidity Exchange over the Sea - A Program for Water-Vapor and Droplet Fluxes from Sea to Air at Moderate to High Wind Speeds’, Bull. Am. Meteorol. Sot. 68,466476.

Kondo, J.: 1975, ‘Air-Sea Bulk Transfer Coefficients in Diabatic Condition’, Boundary-LayerMete- oral. 9,91-l 12.

Large, W. G. and Pond, S.: 1982, ‘Sensible and Latent Heat Flux Measurements over the Ocean’, J. Phys. Oceanogr. 12,464-482.

Liu, W. T., Katsaros, K. B. and Businger, J. S.: 1979, ‘Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor Including the Molecular Constraints at the Interface’, J. Atmos. Sci. 36, 1722-1735.

Miller, M. J., Beljaars, A. C. M. and Palmer, T. N.: 1992, ‘The Sensitivity of the ECMWF Model to the Parameterization of Evaporation from the Tropical Oceans’, J. Climate 5,4 18-434.

Owen, P R. and Thompson, W. R.: 1963, ‘Heat Transfer Across Rough Surface’, J. Fluid Mech. 15, 321-334.

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.: 1989, ‘Water Vapor Flux at the Sea Surface’, Boundary-Layerkfeteorol. 47,277-293. Wu, Jin: 1980, ‘Wind-Stress Coefficients over Sea Surface Near Neutral Conditions - A Revisit’, J.

Phys. Oceanogr. 10,727-740. Wu, Jin: 1981, ‘On Critical Roughness Reynolds Numbers of the Atmospheric Surface Layer’, J.

Geophys. Res. 86,6661-6665.

MOISTURE-TRANSFER COEFFICIENT FOR CLIMATE MODELS 407

Wu, Jin: 1988, ‘Wind-Stress Coefficients at Light Winds’, J. Atmos. Oceanic Tech. 5,885888. Wu, Jin: 1992a, ‘Variation of the Heat Transfer Coefficient with Environmental Parameters’, J. Phys.

Oceanogr. 22,293-300. Wu, Jin: 1992b, ‘On Moisture Flux Across the Sea Surface’, Boundary-LayerMeteorol. 60,361-374.