AIRCRAFT MEASUREMENTS OF ROUGHNESS LENGTHS FOR SENSIBLE AND LATENT HEAT OVER BROKEN SEA ICE

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1 Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd 6th December 2002 International Association of Hydraulic Engineering and Research AIRCRAFT MEASUREMENTS OF ROUGHNESS LENGTHS FOR SENSIBLE AND LATENT HEAT OVER BROKEN SEA ICE David Schröder 1, Timo Vihma 2, Agathe Kerber 1, Burghard Brümmer 1 and Amélie Kirchgäßner 1 ABSTRACT Turbulent surface fluxes were measured at heights between 9 and 35 m by the German Falcon research aircraft over the marginal ice zone (MIZ) of the northern Baltic Sea and the Fram Strait. Applying the bulk formulas and the stability functions to the measurements, the roughness lengths for momentum z 0, sensible heat z T, and latent heat z q were calculated. As mean values over a wide range of sea ice conditions we obtain: z 0 = m, z T = m, and z q = m. An average ratio of z 0 /z T 10 4 was observed over the range of 10 6 m < z 0 < 10 2 m and differs from previously published results over compact sea ice (10 1 < z 0 /z T < 10 3 ). However, our z 0 /z T ratio approximately agrees with observations over heterogeneous land surfaces. Flux parameterizations based on commonly used roughness lengths ratios (z 0 = z T = z q ) overestimate the surface heat fluxes compared to our measurements by more than 100 %. INTRODUCTION Turbulent surface fluxes are an important link between the atmosphere and the underlying surface (ocean, ice, land). World-wide area-covering flux measurements do not exist, but these fluxes are nevertheless needed in all atmosphere-ocean-ice-land models. Direct flux measurements over heterogeneous surfaces are rare, particularly over broken sea ice. Results from such limited campaigns are nevertheless applied for general use. In this paper, we address the problem of turbulent flux parameterization over broken sea ice surfaces applying aircraft measurements. The turbulent surface fluxes of momentum τ, sensible heat H, and latent heat LE are generally parameterized by the bulk formulas: 1 Meteorological Institute, University of Hamburg, Germany 2 Finnish Institute of Marine Research, Helsinki, Finland τ = ρ C Dz V 2, (1) H = ρ c p C Hz (θ s θ z )V, (2) LE = ρ γ C Ez (q s q z )V, (3)

2 where ρ is the density, c p is the specific heat of air, γ is the latent heat of vaporization, V is the wind speed, θ s θ z and q s q z are the differences in potential temperature and specific humidity, respectively, between the surface s and a height z in the atmosphere. Applying the Monin-Obukhov similarity theory, the transfer coefficients for momentum C Dz, sensible heat C Hz, and latent heat C Ez, can be determined as functions of the roughness lengths for momentum z 0, sensible heat z T, and latent heat z q, and of the respective universal stability functions ψ M, ψ H, and ψ E (e.g. Holtslag and de Bruin (1988) and Högström (1988)): C Dz = κ 2 [ ln(z/z 0 ) ψ M (z/l) ] 2, (4) C Hz = κ 2 [ ln(z/z 0 ) ψ M (z/l) ] 1 [ ln(z/zt ) ψ H (z/l) ] 1, (5) C Ez = κ 2 [ ln(z/z 0 ) ψ M (z/l) ] 1 [ ln(z/zq ) ψ E (z/l) ] 1, (6) where κ is the von Karman constant and L is the Obukhov length. If the turbulent fluxes τ, H, and LE as well as the mean quantities V, θ s, θ z, q s, q z, and ρ are measured and if the stability functions are known, the roughness lengths z 0, z T, and z q, can be determined from Equations (4) to (6) with use of (1) to (3) as: z 0 = z [ exp ( (ρ κ 2 V 2 /τ ) 1/2 + ψm (z/l))] 1, (7) z T = z z q = z [ ( )] 1 ρ c p κ 2 (θ s θ z )V exp H [ ln (z/z 0 ) ψ M (z/l) ] + ψ H(z/L), (8) [ ( )] 1 ρ γ κ 2 (q s q z )V exp LE [ ln (z/z 0 ) ψ M (z/l) ] + ψ E(z/L). (9) Roughness lengths over heterogeneous surfaces are commonly referred to as effective roughness lengths. For simplicity we usually drop the word effective in this paper. AIRCRAFT OBSERVATION The experimental areas of BASIS 1998, ACSYS 1998, and FRAMZY 1999 are presented in Figure 1. A total of 17 missions were flown by the German Falcon research aircraft and took place under a wide range of synoptic situations. During all missions vertical profiles and horizontal legs were flown in the lowest 3 km. This study utilizes only the horizontal legs flown at low levels between 9 and 35 m to determine the surface fluxes along distances of 20 to 240 km. The aircraft-based turbulent fluxes of momentum τ, sensible heat H, and latent heat LE, were calculated according to their definitions as: τ = ρ (w u ) 2 + (w v ) 2 (10) H = ρ c p w Θ (11) LE = ρ γ w q, (12)

3 where u, v, and w are the three wind components and w x is the eddy covariance, where x stands for potential temperature Θ, specific humidity q, or the horizontal wind components u and v. A prime (x ) denotes the deviation from the average (x). A linear trend was removed before applying the eddy correlation technique. Figure 1: Locations of the three field experiments BASIS, ACSYS, and FRAMZY and the approximate ice edge during March Brümmer et al. (2002) have shown that heat fluxes obtained from aircraft measurements (1) agree well with those obtained from ice surface stations and (2) react very sensitively to horizontal changes of the surface temperature. The reliability of the turbulent fluxes is further manifested by error calculations according to Kaimal and Finnigan (1994) and Lenschow et al. (1994). To determine a proper sampling length, calculations were performed varying the sampling length between 1 and 30 km. On the one hand the results show that relative errors decrease with increasing sampling length and on the other hand fluxes calculated for longer length intervals represent a kind of average of fluxes over shorter length intervals. As a compromise a sampling length of 8 km was chosen. The calculation of roughness lengths and neutral transfer coefficients (setting the universal functions ψ(z/l) = 0 and the reference height z = 10 m) requires accurate data. The accuracy increases with increasing magnitudes of V, Θ, q, H, and E. To be on the safe side we include only those measurement cases in our analyses where the magnitudes are at least three times larger than the measurement errors: V > 1.5 ms 1, Θ > 2.25 K, H > 6 Wm 2, and τ > Nm 2.

4 The transfer coefficients depend on the reference height z as shown in equations 4 to 6. Equations 1 to 9 are based on the assumption of a constant-flux layer, i.e. the fluxes are constant with height at least up to z. In a stably stratified boundary layer the assumption of a constant-flux layer is questionable. Our aircraft observations cover the whole stability range over broken sea ice, but to avoid problems, we restrict to unstable boundary layer cases only. In this way 32 independent cases with l = 8 km, ice concentration: 0.1 < n ice < 1, and heights z < 35 m were selected. Based on measurements of surface temperature, surface albedo, and on visual ice observations the 32 cases were divided into six ice categories: Grey young ice, mixture of grey and white ice and leads, rough multiyear ice, step changes between ice and water, loose ice fields and grease ice. ROUGHNESS LENGTHS AND NEUTRAL TRANSFER COEFFICIENTS The roughness lengths, the neutral transfer coefficients, the ice concentration, the surface albedo, the vertical potential temperature difference, and the wind speed are listed in Table 1 averaged for the two experimental areas and the six ice categories. The means of the roughness lengths are calculated as logarithmic means. The standard deviations are calculated as the root mean square errors of the 32 cases. For the Baltic Sea, the mean z 0 -value of m is close to the results of Launiainen et al. (2001) obtained for land-fast ice. The roughness lengths z T and z q amount to m and m being 3 to 4 orders of magnitude smaller than z 0. In the Fram Strait we obtain z 0 = m, z T = m, and z q = m. Averaging over all 32 cases, the mean roughness lengths are z 0 = m, z T = m, and z q = m. This corresponds to neutral transfer coefficients referred to 10 m of C DN10 = (1.9 ± 0.8) 10 3 m, C HN10 = (0.9 ± 0.3) 10 3 m, and C EN10 = (1.0 ± 0.2) 10 3 m. Studying the different ice categories, clear differences between the C DN10 -values are identifiable and to a certain extent explainable. The ice categories Grey young ice and Mixture of grey and white first-year ice and leads represent thin and smooth ice leading to a C DN10 of Over a step change between ice and open water and over loose ice fields the roughness is enlarged (C DN10 = and , respectively), and many thick and rough ice floes lead to the very large C DN10 of for the category Rough Multi-year Ice. The large C DN10 value of for the grease ice is surprising. Altogether, there is a wide range of momentum roughness lengths in the MIZ. In contrast to the momentum exchange, C HN10 and C EN10 are always around , except for the category of the rough ice (C HN10 = and C EN10 = ). The coefficient for heat exchange obviously depends less strongly on the ice characteristics than that for the momentum exchange, and they are clearly smaller in all six categories. IMPACT ON THE NEW ROUGHNESS LENGTH FOR HEAT ON THE PARAM- ETERIZED HEAT FLUX The mean roughness length for heat of our study, z T = m, is significantly lower than the values generally used in atmospheric and sea ice models. To demonstrate the consequences of this z T on the parameterized fluxes, we compared the observed fluxes to those based on three different assumptions for z T : (a) z T = z 0, (b) z T = f(z 0, Re) according to Andreas (1987), and (c) z T = m. In all three cases z 0 is set to our mean value of m and the universal functions of Högström (1988) are applied. The

5 Number n ice A i V Θ z 0 z T z q C DN10 C HN10 C EN10 of cases [ms 1 ] [K] [m] [m] [m] Baltic Sea ±0.5 ±0.2 ±0.2 Fram Strait ±1.0 ±0.3 ±0.3 Total (MIZ) ±0.8 ±0.3 ±0.2 Grey young ice ±0.3 ±0.1 ±0.2 Mixture of grey and ±0.5 ±0.2 ±0.3 white ice and leads Rough multi-year ice Step change betw. ice ±0.4 ±0.2 ±0.2 and water Loose ice fields ±0.2 ±0.2 ±0.2 Grease ice Total (2 km) ±1.0 ±0.4 ±0.4 Total (20 km) ±0.8 ±0.2 ±0.2 Open water (A w ) ±0.6 ±0.2 ±0.2 Table 1: Effective roughness lengths z 0, z T, and z q and neutral transfer coefficient C DN10, C HN10, and C EN10 determined from aircraft flights during BASIS 1998, ACSYS 1998 and FRAMZY The results hold for 8 km length intervals on principle and unstable stratification. The mean values of ice concentration n ice, ice surface albedo A i, wind speed V, and vertical potential temperature difference Θ are shown. results are given in Figure 2. In case a (Figure 2a) the mean parameterized H of 90 Wm 2 is 49 Wm 2 larger than the mean observed one. H is overestimated in all cases and the root-mean-square error (RMSE) amounts to 62 Wm 2. Case a is included here because z T = z 0 is usually assumed in climate models (e.g., the ECMWF model (DKRZ, 1994) and HIRLAM (Källen, 1996). In case b (Figure 2b), the discrepancies between measured and parameterized H are reduced, but H is still overestimated ( H = 32 Wm 2, RMSE = 41 Wm 2 ). In case c (Figure 2c), the agreement is much better ( H = 3 Wm 2, RMSE = 15 Wm 2 ), but cannot be interpreted as a verification of our new roughness lengths and transfer coefficients because the same data set was used in deriving them. It is, however, noteworthy that simply applying a new constant z T (that is not equal to z 0 ) reduces the RMSE-value by a factor of 3 to 4 in a data set that includes observations over various types of sea ice cover. Our z T -modification leads to a relative reduction of H by a factor of more than two (on the average) and to an absolute reduction of up to 150 Wm 2 in individual cases in comparison to case a and up to 100 Wm 2 in comparison to b, thereby demonstrating the large sensitivity. Changes of such an order of magnitude have an important impact on the surface energy balance. It should be noted that we do not critisise the validity of Andreas (1987) over a compact ice cover it was recently verified in Andreas (2002) but show that the situation is different over a heterogeneous ice cover.

6 a) z T =z 0 b) z T =f(z 0,Re) H [Wm 2 ] (parameterized) BIAS = 49 Wm RMSE = 62 Wm H [Wm 2 ] (measured) H [Wm 2 ] (parameterized) c) z T =10 8 m BIAS = 32 Wm RMSE = 41 Wm H [Wm 2 ] (measured) 200 H [Wm 2 ] (parameterized) BIAS = 3 Wm RMSE = 15 Wm H [Wm 2 ] (measured) Figure 2: Measured versus parameterized sensible heat flux H based on 8 km samples and the universal functions of Högström (1988): z 0 is set to our mean value of m and z T is set (a) equal to z 0, (b) according to Andreas (1987), and (c) to our mean value of 10 8 m. CONCLUDING REMARKS Our results obtained in the MIZ of the northern Baltic Sea and the Fram Strait show that the mean effective roughness lengths for sensible and latent heat are four to three orders of magnitude smaller than those for momentum. The ratios of the roughness lengths and transfer coefficients differ from previously published results for compact sea ice (Andreas, 1987; Launiainen et al., 2001). We are not aware of previous observations of roughness lengths for heat over the MIZ. The ratio z 0 /z T 10 4 is, however, in agreement with observational results of Beljaars and Holtslag (1991) and Mahrt and Ek (1993) obtained for heterogeneous land surfaces. This appears to be reasonable, because from the point of view of the surface temperature distribution, a mixture of sea ice and leads resembles more a heterogeneous land surface than a compact ice cover. The question arises why z T and z q are so much smaller than z 0 over heterogeneous surfaces. A possible physical explanation given by Beljaars and Holtslag (1991) is that the heat transfer is dominated by the prevalent surface cover, whereas the momentum transfer is dominated by the largest obstacles. Transferred to a broken sea ice cover, z T is rela-

7 tively small due to larger areas of flat ice, whereas z 0 is increased by the ice ridges and floe edges. Further, the form drag caused by ridges and floe edges does not directly affect heat exchange and C HN10, which depends both on z 0 and z T. Hence, to compensate the effect of increased z 0 in C HN10, z T must be decreased. Therefore, z T over a broken sea ice is lower than that over uniform sea ice. The same holds for z q. In the presence of ice ridges (larger z 0 ), z T decreases also according to Andreas (1987), but in our case the decrease is larger. This may be related to the fact that we study a heterogeneous surface, over which the validity of Monin-Obukhov similarity theory is not guaranteed. It is, however, in lieu of any better theory, applied in weather prediction and climate models over various kinds of heterogeneous surfaces. This is relevant because also over heterogeneous surfaces the turbulent fluxes (τ, H and LE) depend on the surface-air differences of the mean quantities (V, Θ and q). The quantitative dependence and the structure of turbulence may, however, be different from that over a homogeneous surface. Accordingly, experimentally based parameter values are needed to describe the flux-profile relationships over heterogeneous surfaces, and it is reasonable that these parameter values may differ from those found for homogeneous surfaces. A comparison between the measured and parameterized fluxes using different roughness lengths shows that (1) the commonly used parameterizations (z T = z 0 ) strongly overestimate the surface heat fluxes over a broken sea ice cover, and (2) realistic heat fluxes can be parameterized if significantly smaller values for z T and z q than for z 0 are used. REFERENCES Andreas, E.L. Parameterizing scalar transfer over snow and ice: a review. Journal of Hydrometeorology 3: (2002). Andreas, E.L., Paulson, C.A., Williams, R.M., Lindsay, R.W. and Businger, J.A. The turbulent heat flux from Arctic leads. Boundary Layer Meteorology 17: (1979). Beljaars, A.C.M. and Holtslag, A.A.M. Flux parameterization over land surfaces for atmospheric models. Journal of Applied Meteorology 30: (1991). Brümmer, B., Schröder, D., Launiainen, J., Vihma, T., Smedman, A.S. and Magnusson, M. Temporal and spatial variability of surface fluxes over the ice edge zone in the northern Baltic Sea. Journal of Geophysical Research 107(C8): 3096, doi: /2001jc (2002). DKRZ. The ECHAM 3 Atmospheric General Circulation Model. Technical Report 6, Deutsches Klimarechenzentrum, Modellbetreuungsgruppe, Hamburg, Germany (1994). Högström, U. Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Boundary Layer Meteorology 42: (1988). Holtslag, A.A.M. and De Bruin, H.A.R. Applied modeling of the nighttime surface energy balance over land. J. Appl. Met. 27: (1988). Källen, E. (Ed.) HIRLAM Documentation Manual 2.5. SMHI, Stockholm, Sweden (1996). Kaimal, J.C. and Finnigan, J.J. Atmospheric Boundary Layer Flows. Oxford University Press, Oxford (1994), p. Launiainen, J., Cheng, B., Uotila, J. and Vihma, T. Turbulent surface fluxes and air-ice coupling in BALTEX-BASIS. Annals of Glaciology 33: (2001). Lenschow, D. H., Mann, J. and Kristensen, L. How long is long enough when measuring

8 fluxes and other turbulence statistics? J. Atmos. and Oceanic Technol. 11: (1994). Mahrt, L. and Ek, M. Spatial variability of turbulent fluxes and roughness lengths in HAPEX-MOBILHY. Boundary Layer Meteorology 65: (1993).

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