Measured And Simulated Latent And Sensible Heat ...

MEASURED AND SIMULATED LATENT AND SENSIBLE HEAT FLUXES AT TWO MARINE SITES IN THE BALTIC SEA ANNA RUTGERSSON1,2 , ANN-SOFI SMEDMAN1 and ANDERS OMSTEDT2,3 1 Department of Earth Sciences, Meteorology, Uppsala University, Uppsala, Sweden; 2 Swedish Meteorological and Hydrological Institute (SMHI), Norrköping, Sweden; 3 Department of Earth Sciences, Oceanography, Göteborg University, Göteborg, Sweden

(Received in final form 4 August 2000)

Abstract. In this study, turbulent heat flux data from two sites within the Baltic Sea are compared with estimates from two models. The main focus is on the latent heat flux. The measuring sites are located on small islands close to the islands of Bornholm and Gotland. Both sites have a wide wind direction sector with undisturbed over-water fetch. Mean parameters and direct fluxes were measured on masts during May to December 1998. The two models used in this study are the regional-scale atmospheric model HIRLAM and the ocean model PROBE-Baltic. It is shown that both models overestimate the sensible and latent heat fluxes. The overestimation can, to a large extent, be explained by errors in the air-water temperature and humidity differences. From comparing observed and modelled data, the estimated 8-month mean errors in temperature and humidity are up to 1 ◦ C and 1 g kg−1 , respectively. The mean errors in the sensible and latent heat fluxes for the same period are approximately 15 and 30 W m−2 , respectively. Bulk transfer coefficients used for calculating heat and humidity fluxes at the surface were shown to agree rather well with the measurements, at least for the unstable data. For stable stratification, the scatter in data is generally large, and it appears that the bulk formulation chosen overestimates turbulent heat fluxes. Keywords: Air-sea interaction, BALTEX, Baltic Sea measurements, Bulk transfer coefficients, Flux parameterisation, Turbulent heat fluxes.

1. Introduction Most of the water in the atmosphere has been evaporated from the oceans. Oceans cover about 75 percent of the earth’s surface, but knowledge about the exchange processes over the sea is still incomplete. The main reason for this is the sparseness of measurements. The importance of water exchange and heat balance over the sea was addressed in the BALTEX (Baltic Sea Experiment) research program (BALTEX, 1995). Probably the most uncertain component of the water balance is the net precipitation (precipitation minus evaporation), which has often been regarded as a residual term or has been neglected in water balance studies. In Omstedt and Rutgersson (2000), the net precipitation over the Baltic Sea differs by a factor of two when determined by different methods. In the present study, we will focus on evaporation (or latent heat flux) but also include results on the sensible heat flux, since the two heat fluxes are closely related. Latent and Boundary-Layer Meteorology 99: 53–84, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.

54

ANNA RUTGERSSON ET AL.

sensible heat fluxes are both important in the heat budgets of the atmosphere and ocean. Latent heat flux is one of the sources of humidity in the atmosphere, which affects both cloud and rain formation. The surface salinity and the depth of the mixed layer in the ocean are also influenced. Sensible heat flux is one of the parameters controlling the height of the mixed layer (Batchvarova and Gryning, 1991; Gryning and Batchvarova, 1996). Some previous studies have been performed of the turbulent heat fluxes over the Baltic Sea using models or voluntary ship measurements (Omstedt et al., 1997; Bumke et al., 1998; Isemer and Lindau, 1998). In a model study by Gustafsson et al. (1998) it was found that the regional forecast model HIRLAM gives latent heat fluxes that are too large. An earlier comparison of measured momentum and sensible heat fluxes and simulated fluxes using the HIRLAM model, also showed overestimation of the sensible heat fluxes in the model (Rutgersson, 2000). The present study is an extension of the investigation in Rutgersson (2000) but focusing on latent heat fluxes. The period is longer in the present study, one additional site (the Christiansø site) is added, and there is also a comparison with the PROBEBaltic ocean model. Most large-scale or regional-scale atmospheric models are verified against standard meteorological parameters (mostly over land), while ocean models are usually verified against sea surface temperatures. Very seldom have the surface fluxes over the sea been verified, except for limited periods. Before using the fluxes derived from models for budget estimations, it is thus important to compare the flux estimates to measurements. Consistent surface fluxes over the sea are also important in the context of developing coupled ocean-atmospheric systems. In this study, direct flux measurements of latent and sensible heat, as well as those calculated with bulk formulae, are compared with the fluxes given by one atmospheric model and one ocean model, at two different sites in the Baltic Sea. The use of two completely different kinds of models is motivated by two reasons, one of which is the purpose of developing a coupled atmosphere- ocean model system. The second reason is that both models are used for water and heat budget estimates over the Baltic Sea within the BALTEX project. When using an ocean model such as the PROBE-Baltic model, not only is sea-surface temperature (SST) calculated but also fluxes that are consistent with the SST calculations. Also, the ocean model can be used to close the water and energy cycles in the region (see Omstedt and Rutgersson, 2000). When direct flux measurements are not available, bulk formulation is generally used to obtain the fluxes. The transfer coefficients used in the bulk formulations are still under discussion, having a range of values in the literature. The validity of the transfer coefficients used in the present models will be investigated using data from one of the sites for an extended period.

TURBULENT HEAT FLUXES AT TWO SITES IN THE BALTIC SEA

55

2. Measurements Data have been used from two observation sites in the Baltic Sea area: Christiansø (A, Figure 1), north of Bornholm; and Östergarnsholm (B, Figure 2), 4 km east of Gotland. The period investigated is the first eight months of the PEP (Pilot Study of Evaporation and Precipitation over the Baltic Sea) period, from the beginning of May 1998 to the end of December 1998. 2.1. T HE C HRISTIANSØ

SITE

At site A, Christiansø, a 10-m high mast has been raised on a very small island near the main island of Christiansø. Turbulent fluctuations were measured with the eddy-correlation method, employing a Kaijo Denki DAT/TR-61B omnidirectional ultrasonic anemometer for wind and temperature fluctuations and an Ophir openpath instrument for humidity fluctuations. From these measurements, the virtual sensible and latent heat fluxes can be estimated; wind speed, wind direction, and temperature at the height of 10 m were also recorded. The various instruments were calibrated before the experiment. Synoptic data were taken at the Christiansø lighthouse some hundred metres from the site, and humidity, q, from the synoptic measurements at 2 m above surface. Sea surface temperature is measured once a day in the waters outside the island. Figure 2a shows a sketch of the site. For winds from the sectors 120–180◦ and 270–300◦ , there is an undisturbed over-water fetch for at least 100 km. In the sector 180–270◦ , the air has passed the island of Bornholm some 20 km away. To some extent, this can disturb the measurements; however, Bornholm is a small island and is not expected to have a large influence. The influence of surrounding areas and the limited water depth outside the island will be discussed further in Sections 2.3 and 6. 2.2. T HE Ö STERGARNSHOLM

SITE

Site B, Östergarnsholm, is a small, very flat island 4 km east of Gotland. A 30m tower has been erected at the south tip of the island; the base of the tower is situated about 1 m above mean sea level. Slow-response sensors for measurements of wind speed, wind direction, and temperature were placed at 8, 12.5, 15, 21, and 29 m above mean sea level, and humidity was measured at 8 and 10 m. The slow response instruments for temperature and wind were calibrated before the experiment and have an expected accuracy of ±0.02 ◦ C and ±0.05 m s−1 respectively (Högström, 1988). Turbulent fluctuations were measured with the eddy-correlation method, with SOLENT 101R2 (Gill Instruments, Lymington, UK) sonic anemometers at heights of 10, 16, and 26 m above mean sea level, giving momentum flux and virtual sensible heat flux. Directly measured latent heat fluxes were only available at Östergarnsholm for a very limited period, as described below. The sonic anemometers were calibrated individually in a wind tunnel prior to being

56


Figure 1. Map of the Baltic Sea showing the two measuring sites, Christiansø at A and Östergarnsholm at B, and the 13 sub-basins used in PROBE-Baltic model.

installed on the tower; the calibration procedure was similar to that described in Grelle and Lindroth (1994). For two limited periods (in October 1998 and in October 1999), fluctuations of wind, heat, and humidity were recorded with a MIUU (Institute of Meteorology, Uppsala University) instrument at 10 m above mean sea level, giving turbulent fluxes of momentum, sensible and latent heat. This instrument is basically a three-


57

Figure 2. Sketches of the two sites, (a) showing Christiansø, mast and synoptic station, (b) showing Östergarnsholm, the site and wave rider buoy.

axial hot-film instrument mounted on a wind vane, with additional sensors for temperature and humidity (dry and wet bulb sensors). The instrument was tested both in a wind tunnel and in the field (Bergström and Högström, 1987; Högström, 1988, 1990). Profile data were recorded at 1 Hz and turbulence data at 20 Hz. During field measurements, the scatter due to inadequate statistical sampling mainly determines the accuracy of high-frequency measurements. According to Dyer et al. (1982), for sampling periods of about an hour, the statistical error in determining the heat flux, w 0 T 0 , is ±10%. Wave height and wave direction as well as water temperature were measured with a directional wave-rider buoy, owned and run by the Finnish Institute of Marine Research, moored 4 km south-southeast of the tower at a water depth of about 40 m. In the wind direction 70–220◦ , there is more than 150 km of openwater fetch, and only data from this sector have been used. The wave rider buoy was thus generally situated 4 km upwind of the measuring site. A sketch of the area is shown in Figure 2b. For the model comparisons, measurements of wind speed, wind direction, humidity, and the fluxes are taken at the 10-m level; for temperature, the 8-m level above mean sea level is used. SST accuracy based on the buoy data is about ±0.1 ◦ C. The instrumentation and measuring site are described in more detail in Smedman et al. (1999). 2.3. F OOTPRINT

ANALYSIS AND THE EFFECT OF LIMITED WATER DEPTH

The turbulent fluxes at some height on a tower originates from an upwind area at some distance from the tower – the flux footprint. It is assumed that the flux originates at the surface from a row of infinitely wide line sources oriented perpendicular to the mean wind direction. Assuming stationary, neutral conditions and a roughness length equal to z0 = 1.5 × 10−4 m, Smedman et al. (1999) found that for the 10-m level, 90% of the measured flux originated from beyond 250 m, 50%

58


originated from beyond 670 m, and 70% of the flux derives from areas between 250 and 1700 m. For higher levels, the corresponding percentages are from greater distances. The water depth in the footprint area is limited for both measuring sites. At Östergarnsholm the sea floor up to 500 m from the peninsula has an approximate slope of 1:30, varying somewhat in different directions; the slope is larger at Christiansø, where the depth reaches 30 m about 100 m from the island. The effect of the limited depth is investigated at Östergarnsholm. To quantify the influence of shallow water, the weighted mean phase speed over the footprint area is defined as in Smedman et al. (1999), Z ∞ hc0 i = F (x, z)c0 (x) dx, (1) 0

where c0 is the phase speed of the dominating wave and the weighting function is given by the flux footprint. The phase speed has been calculated using the dispersion relation g ω0 h c0 = , (2) tanh ω0 c0 where ω0 is the frequency of the dominating waves and h is the water depth. During light wind conditions it was found in Smedman et al. (1999) that, at the Östergarnsholm site, c0 varied between 92% and 99% of the deep-water value; according to Anctil and Donelan (1996), this would not create any significant shallow-water effects on the flux data. During gale conditions, c0 varied between 77% and 94% of the deep-water value over the footprint area. This is roughly the same as the range 79–91% for which Anctil and Donelan (1996) found no effects; thus, no significant shallow-water effects are expected at the Östergarnsholm site. At Christiansø the water depth is even greater than at Östergarnsholm, so no significant shoaling effects are expected at any of the sites. 2.4. C ORRECTION

OF HEAT FLUXES AND CALCULATION OF BULK FLUXES

The temperature signal from sonic anemometers is influenced by density changes due to water vapour, giving virtual air temperature and virtual sensible heat flux. The difference between the virtual and real sensible heat flux can be significant in marine conditions due to relatively high humidity levels (Kaimal and Gaynor, 1991). This is corrected based on Arya (1988), giving the second term on the right side in Equation (3), w 0 T 0 = w 0 Tv0 − 0.61 θz w 0 q 0 +

2uz u0 w 0 , C

(3)

where w 0 T 0 is the kinematic heat flux and w 0 Tv0 includes the humidity component. Mean wind speed and temperature at level z are uz and θz , respectively, and u0 w 0


59

is the kinematic flux of momentum. The constant C = 403 m2 s−2 K−1 is derived from the air temperature and the speed of sound. Including the virtual correction decreases the sensible heat flux by 13% using the data from Östergarnsholm and 15% for the Christiansø data for the studied period. There is also evidence of the need for a second correction due to cross-wind contamination (Schotanus et al., 1983; Kaimal and Gaynor, 1991). Cross-wind contamination is caused by signal deflection of the sound path in the instruments, created by the perpendicular wind component. The expression for this correction is, to some extent, a function of the geometry of the instrument. Since the correction imposed by the instruments used in this study is not clearly known, the correction from Kaimal and Gaynor (1991) is adapted for the instruments at both sites, giving the third term on the right side in Equation (3). The total effect of Equation (3) is a reduction in the sensible heat flux of about 10 W m−2 on the average, or between 5% and 30% of the data from Östergarnsholm and Christiansø. For situations with small heat fluxes and high wind speeds, the reduction can reach large relative values. 2.5. C ALCULATION

OF BULK FLUXES

Fluxes can be calculated from measured mean parameters using the bulk formulae, τ = ρCD u2z H = ρcp CH uz (θs − θz ) λE = ρλCE uz (qs − qz ),

(4)

where τ , H , and λE describe the vertical turbulent fluxes of momentum, sensible and latent heat; ρ is the air density, cp the specific heat capacity of air, and λ the latent heat of vaporisation. Humidity at level z is qz , and θs and qs are the potential temperature and humidity at the surface. CD , CH and CE are the transfer coefficients for momentum, sensible heat and latent heat. Using data from Östergarnsholm, turbulent heat fluxes are also calculated using bulk formulations. The neutral values of the transfer coefficients for heat and humidity are taken from DeCosmo et al. (1996), and the stability dependence using a simplified version of the scheme described in Launianinen (1995) (details are given in Appendix A). The calculated fluxes using bulk formulation are also sensitive to the values of the transfer coefficients. There is generally a large scatter in estimates of the heat transfer coefficient, due in part to measuring difficulties, but it is also an indication of the dependence on processes in the marine surface layer that are not completely understood, such as the influence of waves for limited fetch (Donelan, 1990). Different studies give different values, even though it appears that most studies fall around 1.1 × 10−3 for the neutral values of both CH and CE , as in DeCosmo et

60


al. (1996). Some investigations are performed in coastal or shallow areas, which do change the drag coefficient (CD ), but the heat transfer coefficients are not expected to be as sensitive to limitations in water depth. The transfer coefficients are functions of surface-layer stability and can be parameterised in different ways, finite values as in Large and Pond (1982) or continuous functions as described in Launiainen (1995). Most investigations show relatively small variations with wind speed, but a slight effect for high winds cannot be ruled out (DeCosmo et al., 1996; Makin, 1998). For low winds, smooth surface effects and gustiness also appear to increase the transfer coefficients (Beljaars, 1994). Also in some investigations the state of the waves and roughness structure have been included (Liu et al., 1979; Fairall et al., 1996a). In some recent studies (Rogers et al., 1998; Oost et al., 2000), the fluxes and transfer coefficients show different behaviour in the stable situation, giving lower fluxes than earlier expected. The validity of the expressions used for the transfer coefficients for heat in this study is tested using available direct measurements at Östergarnsholm with undisturbed wind directions from the years 1995–1998, with the SOLENT anemometer for CH and with the MIUU instrument for CE . To avoid uncertain data and low-wind effects, we only used data with wind speeds greater than 2 m s−1 and an air-sea temperature difference larger than 1.5 ◦ C. In Figure 3a, the sensible heat transfer coefficient CH is shown as a function of stability. The scatter is large, but on the unstable side the averaged values agree relatively well with the formulation according to Appendix A, even though the measurements give slightly lower values. The difference between calculations and measurements is larger on the stable side. Mean values are CH −stab = (0.65 ± 0.2) × 10−3 and CH −unstab = (1.2 ± 0.4) × 10−3 . For the latent heat transfer coefficients, data are used from two days (October 30, 1998, and October 20, 1999) using the high quality MIUU instrument (see Figure 3b). The agreement with the formulation according to Appendix A is good. Figure 4a shows the sensible heat transfer coefficients reduced to the neutral values (see Appendix A); the mean value of the unstable data gives CH N−unstab = (1.0 ± 0.3) × 10−3 . The mean value of the stable data is significantly lower, CH N−stab = (0.77 ± 0.5) × 10−3 , which is close to that found by Large and Pond (1982). As a mean for all data, CH N = (1.0 ± 0.3) × 10−3 , and there is little variation with wind speed for CH N , at least for wind speeds from 4 to 13 m s−1 . At higher winds there are rather few data, but there is a possible increase in CH at both high and low winds for the unstable data. For the neutral latent heat transfer coefficient in Figure 4b, the averaged value is CEN = (1.2 ± 0.2) × 10−3 . The calculated transfer coefficients for sensible and latent heat during unstable conditions are in close agreement with earlier studies by Smith (1988, 1989). Figure 4a indicates that the correction generally made for stability is not accurate for the stable data, and that the fluxes during stable situations are lower than given by the usual bulk formulae.


61

Figure 3. Heat transfer coefficients using data from Östergarnsholm 1995–1998: (a) Dots represent the sensible heat flux, measured by the SOLENT sonic anemometer. The thick line is the values averaged over z/L intervals with ±1 standard deviation. (b) Stars represent the latent heat flux, measured by the MIUU instrument. The dashed line in (a) and (b) is according to Launiainen (1995) and DeCosmo et al. (1996) as described in Appendix A.

The sensible heat fluxes measured directly at Östergarnsholm, compared with sensible heat fluxes calculated according to Appendix A, can be seen in Figure 5a for the data used later in this study. The agreement is relatively good, even though the bulk formula possibly underestimates high fluxes. There is an average underestimation by the bulk formula of 1.0 W m−2 , with a correlation coefficient r0 = 0.88 and root-mean-square error rms = 15.0 W m−2 . Figure 5b shows the existing measurements during 1998 using the high-quality latent heat flux measurements compared to bulk calculations, also with relatively good agreement: r0 = 0.87, bias = 1.7 W m−2 , and rms = 17.2 W m−2 . The general agreement using bulk calculated fluxes and direct measurements is thus relatively good, supporting the use of bulk formulae with the described coefficients when estimating heat fluxes. The scatter in heat fluxes is similar to that found in other studies and can be explained by the uncertainties in the heat transfer coefficients.

62


Figure 4. Heat transfer coefficients using data from Östergarnsholm 1995–1998, when reduced to the neutral values. (a) Solid line is an average over z/L intervals for the unstable data; dashed line is an average over z/L intervals representing the stable data. (b) Stars represent the latent heat flux, measured by the MIUU instrument. The dashed-dotted line in (a) and (b) is according to DeCosmo et al. (1996).

3. Models Two models are used for the comparisons: one regional-scale atmospheric weather forecast model, HIRLAM, and one process-oriented ocean model, PROBE-Baltic. The models are briefly described below. It should be noted that data are only used when both measurements and models have undisturbed winds from the sea sector (120–300◦ for site A and 70–220◦ for site B). 3.1. HIRLAM The HIRLAM forecast model is a three-dimensional limited-area model covering the northern part of Europe, a detailed description of which can be found in Källén (1996). Here, only relevant details for this study are given. In the present study, data have been used from the HIRLAM version used operationally at the Swedish Meteorological and Hydrological Institute (SMHI). The


63

Figure 5. (a) Sensible heat flux and (b) latent heat flux calculated by the bulk formulation compared to the measured data (crosses). Solid line is the 1 : 1 relation. Data are from Östergarnsholm, May to December 1998.

64


horizontal resolution is 22 km, with 31 vertical levels and higher resolution closer to the surface. The lowest model level is situated at approximately 30 m above the surface. The vertical diffusion scheme is based on non-local first-order turbulent closure (Holtslag and Boville, 1993). The surface turbulent fluxes are determined from mean model parameters using a bulk formulation, Equation (4). The transfer coefficients are calculated according to Louis (1979) and Louis et al. (1982), as is shown in Appendix B. A constant-flux layer is assumed between the surface and the lowest model level. Parameters at low heights above the surface are calculated according to Monin–Obukhov similarity theory in a way consistent with the flux calculations in Appendix B. The transfer coefficients are also functions of the roughness length z0 , which is calculated using the Charnock formula, Equation (B5), with a relatively high value of the Charnock constant, α = 0.032. Surface roughness and, thus, transfer coefficients are the same for latent and sensible heat as for momentum, but use different stability functions. For sea-surface temperature and ice cover, the rather sparse measurements from the Baltic Sea are used in combination with satellite data giving SST maps that are updated every third day. For areas outside the Baltic Sea, analysed values are obtained from the European Centre for Medium Range Weather Forecasts (ECMWF). For each hour the operational HIRLAM forecast with a forecast period of 6 to 11 hours is used. For the vertical boundaries, data are obtained from the ECMWF global model. In the comparison with the HIRLAM model, we used the grid square completely covered by sea closest to each site. A similar procedure is also described in Rutgersson (2000). Surface-layer parameters such as wind speed, wind direction, temperature, and humidity are calculated at the same heights as the measurements are taken for most of the parameters (all but humidity at Christiansø): 8 m above mean sea level for temperature at Östergarnsholm, 10 m for wind speed, wind direction, and humidity there, and 10 m for all parameters at Christiansø. 3.2. PROBE-BALTIC The Baltic Sea model PROBE-Baltic (Omstedt and Nyberg, 1996) was applied using two different schemes for the parameterisation of sensible and latent heat fluxes. The model divides the Baltic Sea into 13 sub-basins based on bottom topography (Figure 1). The properties in each sub-basin are calculated with horizontally averaged, vertically resolved, time dependent, advective, diffusive conservation equations for temperature, salinity, momentum, turbulent kinetic energy and dissipation, as well as the conservation equations for volume and ice. Each sub-basin is coupled to surrounding sub-basins via horizontal flows, in which simplified strait flow models are applied. The model has been extensively verified, showing


65

Figure 6. Monthly averages of (a) sensible heat flux and (b) latent heat flux, for the old scheme (solid), and revised scheme (dashed) obtained with PROBE-Baltic.

good agreement between observed sea-surface temperatures and ice as well as the vertical structure of temperature and salinity (Omstedt and Axell, 1998). As meteorological input (wind speed and direction, temperature, humidity, precipitation, and cloudiness) to the model, the SMHI (1 × 1)◦ database is used (Omstedt et al., 1997). The database covers the Baltic Sea drainage basin with 1◦ grid squares and uses all available synoptic weather stations in the area, interpolated in space using optimum interpolation. River runoff is included as observed monthly means. The model calculates the horizontal mean properties of sea-surface temperature and ice concentration and thickness in each sub-basin. The turbulent fluxes are calculated from the bulk formulation, Equation (4). The neutral transfer

66


coefficient for momentum is described in WAMDI (1988). In the original PROBEBaltic model, the bulk transfer coefficients for heat from Friehe and Schmitt (1976) were used. This scheme has been found to give evaporation that is too high, and in the present study the scheme is revised according to DeCosmo et al. (1996) and Launiainen (1995) as described in Appendix A. Comparisons between the new and the old scheme were performed for the eastern Gotland basin (see Figure 1). The main change with the new scheme is in the latent heat flux, but effects can also be seen in other parameters. The changes in SST for a two-year simulation with no ice, starting in the beginning of January 1997, show an average increase of 0.3 ◦ C, with maximum increase of up to 0.5 ◦ C occurring in late autumn. Monthly average values of sensible and latent heat fluxes are shown in Figure 6. The sensible heat flux is increased in autumn and winter with the new formulation, mainly due to the increased SST, but slightly decreased during early summer. The latent heat flux is decreased during all seasons except for two months at the beginning of summer. It is not always possible to foresee what influence changes in, for example, the heat flux formulation have on the fluxes, since the model also responds to changes in the SST, and therefore other parameters such as stability and longwave radiation are influenced. For the comparison of PROBE-Baltic with measurements, the Bornholm basin is used for Site A and the eastern Gotland basin for Site B. In the SMHI (1 × 1)◦ database, the geostrophic winds are reduced to a reference height of 10 m above the surface using a reduction algorithm based on observed winds at Östergarnsholm (L. Axell and A. Omstedt, personal communication). For temperature and humidity, the data represent a height of 2 m above the surface.

4. Comparison between Measurements and Models The two models, HIRLAM and PROBE-Baltic, are compared with measured data at the two sites for the 8-month period. Table I shows statistics for the comparison of the mean parameters between measurements, the HIRLAM model and also the forcing data for the PROBE-Baltic model. At Christiansø, mean parameters in both models behave in a similar way, in spite of the different origin of the data. The wind speed is higher in both models, and they are both colder and drier than the measurements. The sea-surface temperature agrees well, on average. At Östergarnsholm both temperature and humidity agree well with the measurements for the two models, but the SST is overestimated in the model compared to the measured data, especially in HIRLAM. For a more detailed comparison, the different SSTs are shown in Figure 7. The overall agreement is reasonably good, but the SSTs in HIRLAM show unrealistic variations on a short time scale, especially at the Christiansø site. This also results in a lower correlation coefficient (Table I). The excessive variations of SST in HIRLAM can be explained by the quality of the SST maps. The SST as


67

TABLE I Statistics for comparison of the mean parameters at Christiansø and Östergarnsholm. The correlation coefficient is r0 , bias is the averaged difference (modelled minus measured), rms is the root-mean-square error, and n the number of hourly values used for the statistics. U (m s−1 )

T (◦ C)

q (g kg−1 )

SST (◦ C)

Christiansø PROBEBaltic

r0 = 0.89 bias = 1.0 rms = 1.9 n = 2639

r0 = 0.94 bias = −1.2 rms = 2.2 n = 2026

r0 = 0.95 bias = −0.8 rms = 1.1 n = 344

r0 = 0.97 bias = 0.0 rms = 1.0 n = 142

Christiansø HIRLAM

r0 = 0.89 bias = 0.4 rms = 1.7 n = 2433

r0 = 0.91 bias = −0.9 rms = 2.3 n = 2174

r0 = 0.95 bias = −0.8 rms = 1.0 n = 322

r0 = 0.87 bias = 0.0 rms = 1.0 n = 120

Östergarnsholm PROBEBaltic

r0 = 0.82 bias = 0.1 rms = 1.7 n = 918

r0 = 0.97 bias = −0.0 rms = 1.2 n = 918

r0 = 0.97 bias = 0.2 rms = 0.7 n = 902

r0 = 0.97 bias = 0.4 rms = 1.0 n = 918

Östergarnsholm HIRLAM

r0 = 0.83 bias = −0.4 rms = 1.8 n = 1744

r0 = 0.97 bias = 0.1 rms = 1.3 n = 1166

r0 = 0.97 bias = 0.2 rms = 1.3 n = 1722

r0 = 0.90 bias = 1.2 rms = 2.0 n = 1270

analysed in the maps can, at a certain grid point, vary unrealistically between two consecutive three-day periods. This is not very satisfying and should be further developed since it will contribute to the scatter in the surface fluxes. There is also a systematic overestimation of the SST in HIRLAM at both sites during the autumn period. The comparisons of latent and sensible heat fluxes are shown in Table II and Figures 8 and 9. At Christiansø the directly measured heat fluxes are used. Both models overestimate the heat fluxes at Christiansø; the latent heat flux is overestimated by 25 to 30 W m−2 . In Figure 8a it can be seen that the overestimation is larger for the larger fluxes in HIRLAM and that the sensible heat flux in PROBEBaltic (Figure 8d) appears to underestimate large positive and negative values, even though there is a general overestimation. The scatter is larger for the latent heat flux than for the sensible heat flux in both model comparisons. At Östergarnsholm the bulk-calculated values are used for the latent heat flux, and both directly measured and bulk-calculated values are used for the sensible heat flux. PROBE-Baltic predicts the latent heat flux well (Figure 9c) and only

68


Figure 7. Sea-surface temperature from May to December 1998 from HIRLAM (dotted), PROBE-Baltic (dashed), and measurements (solid) for (a) Christiansø and (b) Östergarnsholm.

slightly overestimates the sensible heat flux (Figure 9d). HIRLAM overestimates both sensible (Figure 9a) and latent heat fluxes (Figure 9b) by about 20 W m−2 . From Figures 8 and 9 and also Table II it can be concluded that the models give different results for the two sites. HIRLAM overestimates both sensible and latent heat fluxes at the two sites. At Christiansø, the sensible heat fluxes agree much better, but the overestimation of the latent heat flux is larger compared to Östergarnsholm. PROBE-Baltic overestimates both sensible and latent heat fluxes at Christiansø, but both parameters agree very well at Östergarnsholm.

5. Causes of Differences 5.1. M EAN

PARAMETERS

The most obvious explanation for differences between measured and modelled heat fluxes is errors in the mean parameters used in the models. At Christiansø, both models are too dry and too cold in the lowest layer, which can explain the high values of the fluxes. The wind speed is also too high, which will result in an overestimation of the fluxes.


69

TABLE II Statistics for the heat flux comparison at Christiansø and Östergarnsholm. Statistical parameters are described in Table I. For Christiansø the directly measured fluxes are used; for Östergarnsholm the fluxes calculated with the bulk method are also included. H (W m−2 )

λE (W m−2 )

Christiansø PROBEBaltic Direct

r0 = 0.68 bias = 13.7 rms = 31.5 n = 2639

r0 = 0.47 bias = 25.9 rms = 45.6 n = 2639

Christiansø HIRLAM Direct

r0 = 0.77 bias = 4.9 rms = 24.3 n = 2433

r0 = 0.57 bias = 28.0 rms = 59.4 n = 2433

Östergarnsholm PROBEBaltic Direct

r0 = 0.66 bias = 8.0 rms = 22.3 n = 645

No data

Bulk-calculated

r0 = 0.79 bias = 6.3 rms = 19.4 n = 918

r0 = 0.86 bias = −0.1 rms = 27.2 n = 918

Östergarnsholm HIRLAM

r0 = 0.83 bias = 26.5 rms = 38.8 n = 728

No data

r0 = 0.89 bias = 19.1 rms = 31.7 n = 1101

r0 = 0.75 bias = 17.5 rms = 46.3 n = 1104

Direct Bulk-calculated

The humidity data for Christiansø are taken at the synoptic station from the Christiansø lighthouse, which implies a physical separation from the other data. At Östergarnsholm, both models have SSTs that are too high, resulting in excessive sensible heat fluxes, this being especially clear for HIRLAM. The latent heat fluxes agree better at Östergarnsholm than at Christiansø; this can partly be explained by

70


Figure 8. Latent and sensible heat fluxes in W m−2 for the period May 1998 to December 1998 from Christiansø. Pluses are the measured data compared to the models and the solid line the 1 : 1 relation. The comparison is (a) λE compared to HIRLAM, (b) H compared to HIRLAM, (c) λE compared to PROBE-Baltic, and (d) H compared to the PROBE-Baltic.

compensating effects of a surface that is too warm and slightly overstated humidity in the two models, which cause lower evaporation. The bias for the mean parameters seems to be within what can be expected from regional-scale models. We then need to consider what accuracy is needed to obtain correct fluxes. To evaluate the sensitivity in the calculations of the fluxes to errors in mean parameters, the bulk scheme in Appendix A is used together with the mean parameters from PROBE-Baltic at Christiansø for the 8-month period. Table III displays the averaged fluxes from these tests. Increasing the air temperature by 1 ◦ C decreases H substantially, and changing the specific humidity by 1 g kg−1 has a large effect on the latent heat flux. A shift in mean wind speed of 1 m s−1 is not nearly as important for the resulting fluxes. Sea-surface temperature is an important parameter for both the latent and the sensible heat fluxes, and we can thus conclude that with changes on the order of 1 ◦ C in air-sea temperature difference and 1 g kg−1 in humidity, the observed and calculated sensible and latent heat fluxes, based on the bulk formulation, are within 1 W m−2 and 5 W m−2 from the directly measured, respectively. This implies that given correct mean parameters, the sensible and


71

Figure 9. Latent and sensible heat fluxes in W m−2 for the period May 1998 to December 1998 from Östergarnsholm. Pluses are the measured data compared to the models and the solid line the 1 : 1 relation. The comparison is (a) λE compared to HIRLAM, (b) H compared to HIRLAM, (c) λE compared to PROBE-Baltic, and (d) H compared to the PROBE-Baltic.

latent heat fluxes can possibly be calculated with the same accuracy as the observed data, when averaged for an extended period. 5.2. PARAMETERISATION

SCHEME

When we have an error in air or water temperature of the order of 1 ◦ C, the result does not appear to be very sensitive to the values of the coefficients in the parameterisation scheme. But a 10% uncertainty in the heat transfer coefficients results in 10 W m−2 uncertainty in the heat fluxes, and a scheme with erroneous parameterisation can give substantial systematic errors. The scheme used in HIRLAM can be questioned during high wind-speed situations, since the roughness lengths are assumed to be the same for heat and humidity as for momentum. This will give a large wind-speed dependence in the heat transfer coefficients (CE and CH ), which is not supported by measurements (see discussion in Section 2.5; Donelan, 1990; DeCosmo et al., 1996). This can be seen in Figure 10, where the data from Christiansø are divided into measured wind speed ranges. The overestimation of

72


TABLE III Sensitivity of calculated fluxes to changes in mean parameters at Christiansø. Fluxes are calculated using a bulk formulation with an increase in air temperature of 1 ◦ C (T + 1), an increase in humidity of 1 g kg−1 (q + 1), a decrease in wind speed of 1 m s−1 (U − 1), and a decrease in sea-surface temperature of 1 ◦ C (SST − 1). Averaged fluxes in W m−2 . Measured

H = 1.7 λE = 21.3

Bulk calculated Reference T + 1

q+1

U −1

SST − 1

H = 13.6 λE = 47.2

H = 13.6 λE = 16.1

H = 12.5 λE = 42.0

H = 1.1 λE = 30.1

H = 1.1 λE = 46.0

Figure 10. Latent heat flux divided into wind speed ranges. Data are from Christiansø for the period May 1998 to December 1998. The top of each bar shows the number of data used for the interval.

the fluxes is more pronounced for the higher wind speeds in HIRLAM. PROBEBaltic overestimates the latent heat fluxes for all wind speeds because the surface layer used as input to the model is too dry. A new scheme for HIRLAM, with different roughness lengths for momentum and heat and different constants in the Charnock equation, Equation (B5) for coastal areas and for open sea, is described in Woetmann-Nielsen (1998) (see also Appendix C). The new scheme, HIR55−new, was tested with data from one month (October 1998), using HIRLAM with a coarser grid than the previous HIRLAM data, 55 km × 55 km, and also different lower boundary conditions. Table IV


73

TABLE IV Statistics for original scheme and new scheme using HIRLAM. Verification is performed using 12 synoptic stations at islands or along the coast in the Baltic Sea. HIR55 is the original HIRLAM formulation and HIR55−NEW the new, with improved formulation of the roughness lengths for momentum, heat, and humidity according to Woetmann-Nielsen (1998). HIR55

HIR55−NEW

2-m temperature (◦ C)

bias rms

−0.21 1.25

−0.32 1.27

2-m humidity (g kg−1 )

bias rms

1.97 2.50

1.65 2.24

Cloud cover Precipitation (mm)

bias rms bias rms

−0.31 2.44 0.31 0.65

−0.16 2.36 0.32 0.65

10-m wind speed (m s−1 )

bias rms

−1.45 2.68

−0.58 2.37

Sea-level pressure (hPa)

bias rms

−0.58 0.91

−0.53 1.00

shows verification using 12 synoptic coastal stations within the Baltic Sea. The old scheme, H I R55, is included for comparison. There is an improvement in some of the mean parameters, such as humidity at two metres and wind speed at 10 metres, but also in the cloudiness. The latent heat fluxes are shown in Figure 11 for the two sites. The heat fluxes are significantly reduced using the new scheme, and are in better agreement with the measured data. More careful investigations are needed before drawing any further conclusions about the parameterisation in HIRLAM, but the comparison shows that changes in parameterisation can improve both fluxes and mean meteorological parameters. Table V lists averaged evaporation using different versions of the two models and bulk calculated fluxes for 16 days in October. The difference between different schemes used in the same model are on the order of 10%, which is less than the difference seen when testing different parameterisation schemes using ship data. In Bumke et al. (1998), the annual mean evaporation for one year from ship data over the entire Baltic Sea varied from 458 mm to 617 mm due to the formulation of the turbulent heat fluxes. Differences due to parameterisation schemes are, however,

74


Figure 11. (a) Directly measured latent heat flux at Christiansø and (b) bulk calculated latent heat flux at Östergarnsholm for October 1998 using reference (solid) and new (dashed) formulation in HIRLAM. Crosses are the measured values. HIRLAM data are the 6-hour forecasts for every sixth hour.


75

TABLE V Averaged latent heat flux, calculated for 16 days in October 1998 using different methods. Two parameterisation schemes of 55-km resolution HIRLAM are tested (HIR55 and HIR55−NEW). HIRLAM with 22-km resolution and different lower boundary conditions is also included (HIRLAM22 ). Two parameterisation schemes in PROBE-Baltic are also tested (old scheme and new scheme according to Section 3.2); finally, fluxes are calculated using bulk formulation and mean parameters measured at Östergarnsholm. λE (W m−2 ) HIRLAM HIR55 HIR55−NEW

156 137

PROBE-Baltic Old scheme New scheme

120 109

HIRLAM22

147

Bulk

105

expected to be smaller in models, since the models can adjust themselves somewhat to the new scheme. PROBE-Baltic comes close to the data using the new parameterisation of bulk formulation, but HIRLAM still gives excessive evaporation for this site and period. 5.3. M EASUREMENT

QUALITY

When comparing measurements and models, the question about the quality of measurements naturally arises. This problem can be divided into two parts: (i) measuring errors and (ii) representativity of measurements. The quality of the measurements is discussed in Sections 2.1, 2.2, and 2.3, giving a statistical uncertainty in the determination of the sensible heat flux of ±10% and probably a slightly larger uncertainty for the latent heat flux due to greater measuring difficulties. There is no indication of systematic errors in the measured heat fluxes even if the result can be biased on certain occasions, such as during extreme wind conditions (Grelle and Lindroth, 1996) or rain. For extended unattended periods, other problems can occur, such as birds or rime disturbing the measurements. This can contribute to the data scatter. At Östergarnsholm the validity of the bulk-calculated fluxes is also an issue. The figures show relatively good agreement during unstable stratification, but the stability correction applied

76


is not the correct one during stable stratification. The uncertainty of the transfer coefficients is nevertheless smaller than the average bias between measurements and models. At Östergarnsholm the sea-surface temperature measured at the buoy about 4 km upwind is used for flux calculations, compared with measured fluxes on the mast. The water close to the shoreline is, of course, relatively shallow, but the depth increases quickly to about 30 to 50 m, which is the depth of the buoy. In Section 2.3 the effect of limited water depth was analysed, but no significant effect was found at the 10-m measuring level at Östergarnsholm. Effects of upwelling between the footprint area and the buoy can probably be neglected (see below), so for onshore winds it is realistic to assume that the buoy water temperature represents the fluxes at the mast. As for the representativity problem, the assumption is that a point measurement (at Östergarnsholm or Christiansø) represents a grid square or a basin average in a model. The measurements are not just representing one point, but are a footprint of the conditions upwind the the measuring site (Section 2.3). Hourly averages of measurements are used, so that small-scale fluctuations are smoothed out, and only data with onshore winds are included. For the 22 km × 22 km resolution in HIRLAM, the grid square representation of a measuring site is not an unrealistic assumption. For the PROBE-Baltic this is perhaps more questionable, since the PROBE-Baltic basins are several thousand square kilometres in area. Close to a coastline or an island, there is always the problem with coastal effects such as upwelling. In the eastern Gotland basin, upwelling is not so frequent and does not reach very far out from the coastline, so the surface temperature seems to be relatively homogeneous (Gidhagen, 1984). This could be a greater problem in the Bornholm basin, where upwelling eddies are frequently observed (Gidhagen, 1984). Since both measuring sites are near the middle of each basin, the conditions are assumed to be rather homogeneous in space. However, the problem with representativity can explain some of the scatter and differences between the model and the measurements, especially in the Bornholm basin.

6. Discussion Measurements from two sites in the Baltic Sea and simulations with two models show interesting aspects of the accuracy of models and flux calculations. The latent heat flux at Christiansø is overestimated by HIRLAM and PROBE-Baltic compared to measurements, but at Östergarnsholm the agreement is better (there is still an overestimation by HIRLAM). This can partly be explained by the mean parameters in the two models. At Christiansø HIRLAM produces a surface layer that is too cold and too dry, which leads to an increase in the latent heat flux. The same trend is found in the meteorological forcing field for the PROBE-Baltic


77

model. At Östergarnsholm the high SSTs in the models are compensated by a slightly more humid surface layer. The mean parameters are of critical importance for the resulting fluxes, and the accuracy in SST, low-level air temperature, and humidity needs to be very high. In Fairall et al. (1996a) it was shown that the accuracy needs to be ±0.2 ◦ C for temperature and ±0.2 g kg−1 for humidity to give fluxes within ±10%. This accuracy is almost one order better than has been achieved using the HIRLAM and the PROBE-Baltic models. The surroundings of the two sites can also explain some of the differences. At site A, the island of Bornholm can influence the measurements, but the models are probably even more influenced by Bornholm and other nearby land areas surrounding the Arkona and Bornholm basins, due to the larger scales in the models and the SMHI (1 × 1)◦ database. The overly dry surface layer in the Christiansø comparison indicates too much land influence. In the bay northwest of site A (Hanöbukten), upwelling is frequent (Gidhagen, 1984), whereas site B is less disturbed by coastlines and heterogeneities in SSTs. In the calculation of bulk heat fluxes, the resulting fluxes are very dependent on the sea-surface temperature. The buoy temperature measurements are taken at a certain depth, so there is a possible difference between the temperature at the air-sea interface (skin surface temperature) and the temperature actually measured (bucket temperature). From the tropical ocean measuring experiment TOGA-COARE, Fairall et al. (1996b) estimated these effects and found a cool skin effect varying between 0.3 ◦ C at night and 0.18 ◦ C as average local noon value. The peak afternoon warming due to warm layer effects could approach 4 ◦ C in light wind conditions. Applying the equations from Fairall et al. (1996b) to the data from Östergarnsholm for May to December 1998 gives a very small warm-layer effect. A maximum of 0.12 ◦ C occurs on some specific occasions, mainly near midday with stable stratification and low winds during spring. Also, the cooling was smaller than in Fairall et al. (1996b). From the Östergarnsholm data, the average cooling was 0.15◦ C with a maximum of 0.5 ◦ C. Including the skin surface temperature, therefore, had a small effect on the latent heat fluxes when calculated with the bulk formulation and a slightly larger one for the sensible heat flux. The average reduction in H and λE was 9% and 3% respectively. Skin effects are thus probably of minor importance compared to other errors. The scatter in the heat fluxes is considerably larger than for the mean parameters. This is due to a combination of parameters with large scatter and also due to the fact that the scatter in the estimates of transfer coefficients is large. This indicates that we do not describe all processes influencing the direct measurements, neither by bulk formulation nor by the models; for example, wave effects are not included in the models. In particular, swell is expected to influence the turbulent structure over sea (Smedman et al., 1999; Drennan et al., 1999), and there are also indications that differences in wave and wind directions change the magnitude of the transfer coefficients (Donelan et al., 1997). The effects of these phenomena are still not very well known.

78


When making improvements in a model, like HIRLAM, which is extensively used and tuned to give right values of temperature and wind speed, it is possible that improving the parameterisation of surface fluxes gives lower agreement for other parameters. This is explained by compensating errors in the model and is often present (Beljaars, 1995; Rutgersson, 1998). But for the investigated onemonth period, the improved surface parameterisation actually also improves other parameters (Table IV).

7. Summary and Conclusions The sensible and latent heat fluxes from two sites in the Baltic Sea for an 8-month period during 1998 have been investigated, including the bulk formulation and stability dependence. The modelling of these fluxes was then analysed using two models, one atmospheric (HIRLAM) and one oceanic (PROBE-Baltic). Our conclusions can be summarised as follows: − The observed heat transfer coefficients (CH and CE ) at Östergarnsholm follow those given by DeCosmo et al. (1996) and Launiainen (1955) relatively well during unstable conditions, even though there was substantial scatter. For stable conditions, the observed coefficients were lower than most previously published results, and lower than those generally used in models. − Both models tend to overestimate turbulent heat fluxes. At one of the measurement sites, this can be explained by a possible error in the air-sea temperature difference of 1 ◦ C and in the air humidity of 1 g kg−1 . This corresponds to a mean error in the sensible and latent heat fluxes of about 15 and 30 W m−2 , respectively. An accuracy of some tenths of a ◦ C and some tenths of 1 g kg−1 is needed for flux estimates within ±10%, which is also the estimated error in the measured data. The accuracy in present atmosphere and ocean models applied to the Baltic Sea, however, is far from this level. − The lack of agreement between models and measurements indicates that there is a need for further development of models and grided meteorological data sets before drawing far reaching conclusions concerning heat and water budgets. Also the study illustrates the need for direct flux measurements and improved understanding of the marine atmospheric boundary layer, particularly during stable conditions. Since the behaviour of the models differs between the two sites, it is difficult to generalise the results to the entire Baltic Sea. Land and coastline influence large areas of the Baltic Sea, and models with higher resolution are probably needed to give information of the fluxes in such areas. The investigated models have the potential for reliable heat flux calculations if the mean parameters in the models are correct and if parameterisation schemes are used without systematic errors.


79

Acknowledgements This work was performed within the framework of the EU-funded project PEP in BALTEX (contract no. ENV4-CT97-0484). Sven-Erik Gryning is gratefully acknowledged for the measurements from Christiansø. The synoptic data at Christiansø are from the Danish Meteorological Institute (DMI). We thank Hans Bergström and others at Uppsala University for the help with the data at Östergarnsholm. Stefan Gollvik and Ulf Högström have contributed valuable comments on the manuscript. We would also like to express thanks for constructive comments by two anonymous reviewers.

Appendix A: Formulation of Heat Transfer Coefficients Neutral values of the sensible and latent heat transfer coefficients from DeCosmo et al. (1996) are used, viz. 103 CH N = 1.1,

(A1)

103 CEN = 1.1.

The roughness lengths for momentum (z0 ), heat (zH ), and humidity (zE ) can be written in terms of the neutral values of the transfer coefficients,

z0 = exp

z √κ CDN

zH = exp

zE = exp

,

z

, √ κ CDN CH N

(A2)

z

, √ κ CDN CEN

where z is the height, κ is von Karman’s constant, and CD the drag coefficient with neutral value CDN . The stability dependence of heat transfer coefficients is assumed to follow Launiainen (1995). As stability parameters the Obukhov length L and the bulk Richardson number Ri are used. L=−

u3∗ T0

κgw 0 Tv0 z g (θz − θs ) Ri = , T0 u2z

(A3)

where u∗ is the friction velocity, T0 is the mean temperature of the layer, g acceleration of gravity. Mean parameters at the measuring height are uz and θz and at the

80


surface θs ; w 0 T 0 is the kinematic sensible heat flux. The relation between Ri and z/L and the non-dimensional gradients for temperature and wind φh and φm are expressed as follows. For unstable conditions (z/L ≤ 0),   2 z ln z0 z   − 0.55 Ri, = z L ln zH

φm = (1 − 16z/L)−1/4 ,

φm−1 + 1 9m = 2 ln 2

+ ln(

π φm−2 + 1 ) − 2arctan φm−1 + , 2 2

(A4)

φh = (1 − 16z/L)−1/2 , ! φh−1 + 1 9h = 2 ln . 2 For stable conditions, a form is used that can extend to stronger stability (z/L ≥ 0), z z/L = 1.89 ln + 44.2 Ri2 z0 z0 z − 1.5 ln − 1.37 Ri, + 1.18 ln z0 zH φm = φh = 1 + a1 z/L + (1 + c1 − d1 z/L)z/Lb1 exp(−d1 z/L), (A5) 9m ≈ 9h = −b1 c1 /d1 − a1 z/L − b1 (z/L − c1 /d1 ) exp(−d1 z/L), where a1 = 0.7, b1 = 0.75, c1 = 5, d1 = 0.35, and 9m and 9h are the integrated forms of the non-dimensional gradients. Also, κ2 , CH = ln zz0 − 9m ln zzT − 9h (A6) κ2 . CE = ln zz0 − 9m ln zzq − 9h Using the measured data, neutral transfer coefficients are calculated according to Geernaert (1999), h i 1/2 −1/2 CH N = CH 1 − 9m CDN k −1 − 9H CH N CDN k −1 + 9m 9H CH N k −2 , (A7) h i 1/2 −1 −1/2 −1 −2 CEN = CE 1 − 9m CDN k − 9H CEN CDN k + 9m 9H CEN k .


81

Appendix B: Calculation of Transfer Coefficients in HIRLAM The transfer coefficients in the adopted version of HIRLAM are calculated according to, z fγ = CDN fγ Ri, , (B1) z0 where γ = D, H or E for momentum, sensible and latent heat respectively. The neutral transfer coefficients are given by CDN

z −2 = κ ln z0 2

(B2)

and fγ is a stability function. In unstable stratification fγ has the form fγ = 1 −

aγ Ri √

1 + bγ CDN Ri · z/z0

(B3)

in which aD = 10, aH = aE = 15 and bγ = 75. In the stable case fγ has the form fγ =

1

d , 1 + cγ Ri 1 + eγ Ri

(B4)

where cγ = 10, dD = −0.5, dH = dE = 0.5, eD = 5, and dH = dE = 1. Surface roughness length, and, thus, the neutral transfer coefficients, are the same for latent and sensible heat as for momentum and are given by the Charnock formula over sea according to z0 = αu2∗ /g,

(B5)

where α is a constant with the value 0.032 used in the present version of HIRLAM, u∗ the friction velocity, and g is the acceleration of gravity. Appendix C: Calculation of Transfer Coefficients in the Revised Version of HIRLAM The transfer coefficients in the revised version of HIRLAM are calculted according to Woetmann-Nielsen (1998). The revised version considers different roughness lengths for momentum, heat, and humidity and modifies the free convection behaviour. Equation (C1) is replaced by fγ = 1 −

aγ Ri p . 1 + bγ Cγ N Ri · z/dγ

(C1)

82


The revised neutral transfer coefficient becomes !−1 ln zzγ0 Cγ N = CMN 1 + , ln zz0

(C2)

where dγ is a free convection length scale. The roughness lengths are specified as 2 −1 z0 = (1 − f (u)) 0.11νu−1 ∗ + f (u) αu∗ g ,

ln

z0 = mH Re∗1/4 − 2, zH

ln

z0 z0 = ln − mE Re∗1/4 , zE zE

(C3)

where ν is the molecular kinematic viscosity for air, Re∗ the roughness Reynolds number and f (u) a wind speed function determining the transition from smooth to rough sea. The coefficient α has the value 0.032 in coastal waters and 0.014 over the open ocean.

References Anctil, P. and Donelan, M. A.: 1996, ‘Air-Water Momentum Flux Observations over Shoaling Waves’, J. Phys. Oceanogr. 26, 1344–1353. Arya, S. P.: 1988, Introduction to Micrometeorology, Academic Press, New York, 303 pp. BALTEX: 1995, ‘Baltic Sea Experiment BALTEX. Initial Implementation Plan’, International BALTEX Secretariat 2, GKSS Research Center, Geesthacht, Germany, 84 pp. Batchvarova, E. and Gryning, S. E.: 1991, ‘Applied Model for the Growth of the Daytime Mixed Layer’, Boundary-Layer Meteorol. 56, 261–274. Beljaars, A. C. M.: 1994, ‘The Parameterization of Surface Fluxes in Large Scale Models under Free Convection’, Quart. J. Roy. Meteorol. Soc. 121, 255–270. Beljaars, A. C. M.: 1995, ‘The Impact of Some Aspects of the Boundary Layer Scheme in the ECMWF Model’, in Parameterization of Sub-Grid Scale Physical Processes, pp. 125–161, ECMWF, Shinfleld Park, Reading RG2 9AX, U.K., 423 pp. Bergström, H. and Högström, U.: 1987, ‘Calibration of a Three-Axial Fiber-Film System for Meteorological Turbulence Measurements’, Dantec Information 5, 16–20. Bumke, K., Karger, U., Rasse, L., and Niekamp, K.: 1998, ‘Evaporation over the Baltic Sea as an Example of a Semi-Enclosed Sea’, Contr. Atmos. Phys. 71, 249–261. DeCosmo, J., Katsaros, K. B., Smith, S. D., Anderson, R. J., Gost, W. A., Bunike, K., and Chadwick, H.: 1996, ‘Air-Sea Exchange of Water Vapor and Sensible Heat: The HEXOS Results’, J. Geophys. Res. 101, 12001–12016. Donelan, M. A.: 1990, ‘Air–Sea Interaction’, in B. LeMehaute and D. Hanes (eds.), The Sea: Ocean Engineering Science, Vol. 9, John Wiley, New York, pp. 239–292. Donelan, M. A., Drennan, W. M., and Katsaros, K. B.: 1997, ‘The Air-Sea Momentum Flux in Conditions of Mixed Wind Sea and Swell’, J. Phys. Oceanog. 27, 2087–2099. Drennan, M. W., Kahma, K. K., and Donelan, M. A.: 1999, ‘On Momentum and Velocity Spectra over Waves’, Boundary-Layer Meteorol. 92, 489–515.


83

Dyer, A. J., Garratt, R. J., Francey, R. J., McIlroy, I. C., Bacon, N. E., Hyson, P., Bradley, E. F., Denmead, O. T., Tsvang, L. R., Volkov, Y. A., Koprov, B. M., Elagina, L. G., Sanashi, K., Monji, N., Hanafusa, T., Tsukamoto, O., Frensen, P., Hicks, B. B., Wesley, M., Miyake, M., and Shaw, W.: 1982, ‘An International Turbulence Comparison Experiment (ITCE 1976)’, Boundary-Layer Meteorol. 24, 181–209. Fairall, C. W., Bradley, E. F., Rogers, D. P., Edson, J. B., and Young, G. S.: 1996a, ‘Bulk Parameterization of Air-Sea Fluxes for Tropical Ocean-Global Atmosphere Coupled-Ocean Atmosphere Response Experiment’, J. Geophys. Res. 101, 3747–3764. Fairall, C. W., Bradley, E. F., Godfrey, J. S., Wick, G. A., Edson, J. B., and Young, G. S.: 1996b, ‘Cool-Skin and Warm-Layer Effects on Sea Surface Temperature’, J. Geophys. Res. 101, 1295– 1308. Friehe, C. A. and Schmitt, K. F.: 1976, ‘Parameterization of Air-Sea Interface Fluxes of Sensible Heat and Moisture by the Bulk Aerodynamic Formula’, J. Phys. Oceanog. 6, 801–809. Geernaert, G. L.: 1999, ‘Theory of Air-Sea Momentum, Heat and Gas Fluxes’, in G. L. Geernaert and P. W. J. (eds.), Air-Sea Exchange: Physics, Chemistry and Dynamics, Kluwer Academic Publishers, Dordrecht, 578 pp. Gidhagen, L.: 1984, Coastal Upwelling in the Baltic – A Presentation of Satellite and In Situ Measurements of Sea Surface Temperatures Indicating Coastal Upwelling, RHO 37, SMHI, SE-601 76 Norrköping, Sweden, 34 pp. Grelle, A. and Lindroth, A.: 1994, ‘Flow Distortion by a Solent Sonic Anemometer: Wind Tunnel Calibration and its Assessment for Flux Measurements over Forest and Field’, J. Atmos. Oceanic Technol. 11, 1529–1542. Grelle, A. and Lindroth, A.: 1996, ‘Eddy-Correlation System for Long-Term Monitoring of Fluxes of Heat Water and CO2 ’, Global Change Biol. 2, 297–307. Gryning, S. E. and Batchvarova, E.: 1996, ‘A Model for the Height of the Internal Boundary Layer over an Irregular Coastline’, Boundary-Layer Meteorol. 78, 405–413. Gustafsson, N., Nyberg, L., and Omstedt, A.: 1998, ‘Coupling High Resolution Atmosphere and Ocean Models for the Baltic Sea’, Mon. Wea. Rev. 126, 2822–2846. Högström, U.: 1988, ‘Non-Dimensional Wind and Temperature Profiles in the Atmospheric Surface Layer: A Re-Evaluation’, Boundary-Layer Meteorol. 42, 55–78. Högström, U.: 1990, ‘Analysis of Turbulence Structure in the Surface Layer with a Modified Similarity Formulation for Near Neutral Conditions’, J. Atmos. Sci. 47, 1949–1972. Holtslag, A. A. and Boville, B. A.: 1993, ‘Local versus Nonlocal Boundary-Layer Diffusion in a Global Climate Model’, J. Climate 10, 1825–1842. Isemer, H. and Lindau, R.: 1998, ‘Climatological Estimates of Precipitation and Evaporation over the Baltic Proper Based on COADS’, in Conference Preceedings of the Second Study Conference on BALTEX, International BALTEX Secretariat Publication, pp. 80–81. Källén, E.: 1996, Hirlam Documentation Manual. System 2.5, SMHI, SE-601 76 Norrköping, Sweden, 180 pp. Kalmal, J. C. and Gaynor, J. E.: 1991, ‘Another Look at Sonic Anemometry’, Boundary-Layer Meteorol. 56, 40l–4l0. Large, W. G. and Pond, S.: 1982, ‘Sensible and Latent Heat Flux Measurements over the Ocean’, J. Phys. Ocean. 12, 464–482. Launialnen, J.: 1995, ‘Derivation of the Relationship between the Obukhov Stability Parameter and the Bulk Richardson Number for Flux Profiles’, Boundary-Layer Meteorol. 76, 165–179. Liu, W. T., Katsaros, K. B., and Businger, J. A.: 1979, ‘Bulk Parameterization of Air-Sea Exchange of Heat and Water Vapour Including the Molecular Constraints at the Interface’, J. Atmos. Sci. 36, 1722–1735. Louis, J. F.: 1979, ‘A Parametric Model of Vertical Eddy Fluxes in the Atmosphere’, Boundary-Layer Meteorol. 17, 187–202.

84


Louis, J. P., Tiedke, M., and Geleyn, J. F.: 1982, ‘A Short History of the PBL Parameterization at ECMWF’, in Proceedings of the ECMWF Workshop on Boundary-Layer Parameterization, ECMWF, Shinfield Park, Reading RG2 9AX, U.K., pp. 59–79. Makin, V. K.: 1998, ‘Air-Sea Exchange of Heat in the Presence of Wind Waves and Spray’, J. Geophys. Res. 103, 1137–1152. Omstedt, A. and Axell, L. B.: 1998, ‘Modeling the Seasonal, Interannual, and Long-Term Variations of Salinity and Temperature in the Baltic Proper’, Tellus 50A, 637–652. Omstedt, A. and Nyberg, L.: 1996, ‘Response of Baltic Sea Ice to Seasonal, Interannual Forcing and Climate Change’, Tellus 48A, 644–662. Omstedt, A. and Rutgersson, A.: 2000, ‘Closing the Water and Heat Cycles of the Baltic Sea’, Meteorol. Z. 9, 57–64. Omstedt, A., Meuller, L., and Nyberg, L.: 1997, ‘Interannual, Seasonal and Regional Variations of Precipitation and Evaporation over the Baltic Sea’, Ambio 26, 484–492. Oost, W. A., Jacobs, C. M. J., and van Oort, C.: 2000, ‘Stability Effects on Heat and Moisture Fluxes at Sea’, Boundary-Layer Meteorol. 95, 271–302. Rogers, D. P, Dorman, C. E., Edwards, K., Brooks, I. M., Melville, M. W., Burk, S. D., Thompson, W. T., Holt, T., Ström, L., Tjerström, M., Grisogono, B., Bane, J. M., Nuss, W. A., Morley, B. M., and Schanot, A. J.: 1998, ‘Highlights of the Coastal Waves Experiment 1996’, Bull. Amer. Meteorol. Soc. 79, 1307–1326. Rutgersson, A.: 1998, ‘The Effect on Surface Fluxes over Sea Using Different Surface Parameterizations’, Hirlam Newsletter, Vol. 32, SMHI, SE-601 76 Norrköping, Sweden, pp. 32–38. Rutgersson, A.: 2000, ‘A Comparison between Measured and Modeled Sensible Heat and Momentum Fluxes Using a High Resolution Limited Area Model (HIRLAM)’, Meteorol. Z. 9, 29–37. Schotanus, P. F. T., Nieuwstadt, M., and de Bruin, H. A. R.: 1983, ‘Temperature Measurement with a Sonic Anemometer and its Application to Heat and Moisture Fluxes’, Boundary-Layer Meteorol. 26, 81–93. Smedman, A., Högström, U. Bergström, H., Rutgersson, A., Kahma, K., and Pettersson, H.: 1999, ‘A Case-Study of Air-Sea Interaction during Swell Conditions’, J. Geophys. Res. 104, 25,833– 25,851. Smith, S. D.: 1988, ‘Coefficients for Sea Surface Wind Stress’, J. Geophys. Res. 3, 15,467–15,472. Smith, S. D.: 1989, ‘Water Vapor Flux at the Sea Surface’, Boundary-Layer Meteorol. 47, 277–293. WAMDI: 1988, ‘The WAM Model. A Third Generation Ocean Wave Prediction Model’, J. Phys. Oceanog. 18, 1775–1810. Woetmann Nie1sen, N.: 1998, ‘Inclusion of Free Convection and a Smooth Sea Surface in the Parameterization of Surface Fluxes over Sea’, Hirlam Newsletter, Vol. 32, SMHI, SE-601 76 Norrköping, Sweden, pp. 44–51.