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Observations and model calculations of aerodynamic drag on sea ice in the Fram Strait
Abstract
Wind and temperature profiles in the constant flux layer obtained by tethersonde were used to compute the total aerodynamic drag on an area of 60% pack ice in the Fram Strait (79°20′N, 1−3°W). The boundary layer appeared adiabatic to heights greater than 150 m, and there were only minor air/water temperature differences. Drag coefficients of 4.9 and 5.1 × 10 -3 referred to 10 m above ground level were found. Eddy correlation measurements in the local constant flux layers over ice floes were used to estimate the skin drag of an area of 100% ice cover. This was less than 40% of the total drag on the actual area. The corresponding drag coefficient was 1.4×10 -3 . A drag partition model is proposed for computing the total drag over an area of pack ice as a function of ice concentration, mean freeboard and length of the ice floes, and typical roughness lengths of ice and sea surfaces. The model predicts maximum form drag at 73% ice concentration for floes of the type observed in the Fram Strait. DOI: 10.1111/j.1600-0870.1988.tb00413.x
... Zusätzlic ist in der Abbildung 5.14 die von Hanssen-Bauer und Gjessing (1988) an die Messungen von Nägel (1943, 1946 angenähert Abschattungsformel (2.40) eingezeichnet (nachfolgend Nägeli-Formel) welche in einigen Modellrechnungen den Abschattungseffekt im Lee von Eisschollenkanten beschreibt (z.B. Hanssen-Bauer und Gjessing, 1988, Birnbaum, 1998. ...
... Um d a s Konzept auf diabatische Schichtung zu erweitern, wird die Gleichung (2.39) verwendet, die von anderen Autoren zur Berechnung des Formwiderstandes von Schollenkanten genutzt wurde (z.B. Hanssen-Bauer und Gjessing, 1988, Birnbaum, 1998 Lensu et al. (1996) erfaBt werden konnten. Die MeBwerte werden übe Klassen der atmosphärische Schichtung gemittelt (&/L = 0.025) und überdecke mit -0.59 < z/L < 0.14 labile bis schwach stabile Bedingungen (Tabelle 6.1). ...
... Such bulk drag models have been developed by, e.g., Arya (1975) to estimate the drag caused by pressure ridges on Arctic pack ice. This model was extended by Hanssen-Bauer and Gjessing (1988) for varying sea-ice concentrations. A more general drag model was proposed by Raupach (1992), which was extended by Andreas (1995) for sastrugi, by Smeets et al. (1999) for rough ice, and by Shao and Yang (2008) for surfaces with higher obstacle density, such as urban areas. ...
The aerodynamic roughness of heat, moisture, and momentum of a natural surface are important parameters in atmospheric models, as they co-determine the intensity of turbulent transfer between the atmosphere and the surface. Unfortunately this parameter is often poorly known, especially in remote areas where neither high-resolution elevation models nor eddy-covariance measurements are available. In this study we adapt a bulk drag partitioning model to estimate the aerodynamic roughness length (z0m) such that it can be applied to 1D (i.e. unidirectional) elevation profiles, typically measured by laser altimeters. We apply the model to a rough ice surface on the K-transect (west Greenland Ice Sheet) using UAV photogrammetry, and we evaluate the modelled roughness against in situ eddy-covariance observations. We then present a method to estimate the topography at 1 m horizontal resolution using the ICESat-2 satellite laser altimeter, and we demonstrate the high precision of the satellite elevation profiles against UAV photogrammetry. The currently available satellite profiles are used to map the aerodynamic roughness during different time periods along the K-transect, that is compared to an extensive dataset of in situ observations. We find a considerable spatio-temporal variability in z0m, ranging between 10−4 m for a smooth snow surface and 10−1 m for rough crevassed areas, which confirms the need to incorporate a variable aerodynamic roughness in atmospheric models over ice sheets.
... Momentum flux atmosphere-ice The ice and upper ocean circulation in the Arctic Ocean is mainly wind driven (Thorndike & Colony, 1982). The large scale aerodynamic drag on sea ice depends on wind speed, atmospheric vertical stability, ice concentration and surface roughness (Zubov, 1943, Smith et al., 1970, Overland, 1985, Guest and Davidson, 1987, Hanssen-Bauer & Gjessing, 1988. Models are developed for computing the aerodynamic drag on ice under different conditions (Sverdrup, 1918;Overland et al., 1983;Overland and Davidson, 1991;Overland and Guest,'1991;Walter and Overland 1991), but so far there have been few experiments to test these models. ...
... [5] The parametrization of the MIZ surface roughness has been discussed intensively during the last three decades, starting with studies by Overland [1985] and Guest and 1 Davidson [1987]. A general finding of Andreas et al. [1984], Hanssen-Bauer and Gjessing [1988], Stössel and Claussen [1993], Mai et al. [1996], Birnbaum and Lüpkes [2002], Lüpkes and Birnbaum [2005], and Lüpkes et al. [2012] was that atmospheric momentum fluxes are influenced not only by the skin drag of the open water surface and of the more or less plane ice floe surfaces but also by the form drag caused by the edges of floes, where often small ridges form due to floe collisions. So, the effective atmospheric drag over the MIZ was parametrized by accounting for both skin drag and form drag using schemes of different complexity. ...
A hierarchy of parametrizations of the neutral 10 m drag coefficients
over polar sea ice with different morphology regimes is derived on the
basis of a partitioning concept that splits the total surface drag into
contributions of skin drag and form drag. The new derivation, which
provides drag coefficients as a function of sea ice concentration and
characteristic length scales of roughness elements, needs fewer
assumptions than previous similar approaches. It is shown that form drag
variability can explain the variability of surface drag in the marginal
sea ice zone (MIZ) and in the summertime inner Arctic regions. In the
MIZ, form drag is generated by floe edges; in the inner Arctic, it is
generated by edges at melt ponds and leads due to the elevation of the
ice surface relative to the open water surface. It is shown that an
earlier fit of observed neutral drag coefficients is obtained as a
special case within the new concept when specific simplifications are
made which concern the floe and melt pond geometry. Due to the different
surface morphologies in the MIZ and summertime Arctic, different
functional dependencies of the drag coefficients on the sea ice
concentration result. These differences cause only minor differences
between the MIZ and summertime drag coefficients in average conditions,
but they might be locally important for atmospheric momentum transport
to sea ice. The new parametrization formulae can be used for present
conditions but also for future climate scenarios with changing sea ice
conditions.
The increasing movement and deformation of Arctic sea ice cover results in pronounced drag sheltering effects behind sea ice pressure ridges. This needs to be accounted for in the parameterization of the form drag of ridges, thereby posing a challenge to evaluate the ice–ocean dynamic feedback. Laboratory experiments were conducted in a water tank to explore the sheltering effect between adjacent ridges of various geometries. The form drag forces on the keel models were measured, and the particle image velocimetry (PIV) system was employed to capture the flow fields surrounding the models to explain the variations in the drag force. The key sheltering parameters were the ratio between keel spacing and keel depth L/H, flow velocity u, and keel slope angle α. The results showed that the drag force F1 on the upstream keel was close to the value of the single keel case, while the drag force F2 on the downstream keel was lower, for L/H ≤ 10 even opposite to the flow direction. Having changed from negative to positive, the sheltering coefficient Г = F1/F2 increased with increasing L/H. Г decreased remarkably with steepening α and was independent of u. To fully incorporate the effects of the L/H and α , we propose a new sheltering function fitted with the experimental results:Г =[1-1.56exp(sL/H)]*1.20α-0.08, s=0.001α-0.15. This function is compared with the previous sheltering functions and the actual ice conditions in the Arctic Ocean, pointing the way to obtain the final sheltering functions applicable to sea ice dynamics models.
The bottom topography of ridged sea ice differs greatly from that of other sea‐ice types. The form drag of ridge keels has an important influence on sea‐ice drift and deformation. In this study, both laboratory experiment (LabE) and fluid dynamics numerical simulation (FDS) have been carried out for a physical ridge model in a tank to better understand the quantitative characteristics of the form drag. The LabEs covered both laminar and turbulent conditions. The local form drag coefficient of a keel, Cdw, varied with the keel depth hw and the slope angle αw in the turbulent regime. After validated by the LabE measurements, the FDSs were employed to extend the parameterization from the finite water depth to deep water. The results gave Cdw = 0.68∙ln (αw/7.8°), R² = 0.998, 10° ≤ αw ≤ 90°, with Cdw ranging from 0.17 to 1.66, when the keel depth was much less than the water depth. For a large ridging intensity (keel depth/spacing ≥0.01), the variation of the local form drag coefficient and its contribution to total drag coefficient were sensitive to the keel slope angle. Assuming the log‐normal distribution for this angle, the average value of the local form drag coefficient was 0.75, recommended for sea‐ice dynamic models.
The aerodynamic roughness of heat, moisture and momentum of a natural surface is an important parameter in atmospheric models, as it co-determines the intensity of turbulent transfer between the atmosphere and the surface. Unfortunately this parameter is often poorly known, especially in remote areas where neither high-resolution elevation models nor eddy-covariance measurements are available. In this study we adapt a bulk drag partitioning model to estimate the aerodynamic roughness length (z0m) such that it can be applied to 1D (i.e. unidirectional) elevation profiles, typically measured by laser altimeters. We apply the model to a rough ice surface on the K-transect (western Greenland ice sheet) using UAV photogrammetry, and evaluate the modelled roughness against in situ eddy-covariance observations. We then present a method to estimate the topography at 1 m horizontal resolution using the ICESat-2 satellite laser altimeter, and demonstrate the high precision of the satellite elevation profiles against UAV photogrammetry. The currently available satellite profiles are used to map the aerodynamic roughness during different time periods along the K-transect, that is compared to an extensive dataset of in situ observations. We find a considerable spatiotemporal variability in z0m, ranging between 10−4 m for a smooth snow surface over 10−1 m for rough crevassed areas, which confirms the need to incorporate a variable aerodynamic roughness in atmospheric models over ice sheets.
The scales of dynamical processes in the Arctic atmosphere range from turbulence in the atmospheric boundary layer (ABL) via interactive mesoscale processes, such as orographic flows and Polar lows, to synoptic-scale cyclones, and further to hemispherical-scale circulations characterized by the Polar front jet stream and planetary waves. Specific boundary conditions for tropospheric dynamics in the Arctic include (a) sea ice and snow, which strongly affect the surface energy budget, (b) large transports of heat and moisture from lower-latitudes, and (c) the wintertime stratospheric Polar vortex, which has a large impact on tropospheric large-scale circulation and synoptic-scale cyclones. Knowledge on dynamics of the Arctic atmosphere is advancing but, compared to mid- and low-latitudes, still limited due to lack of process-level observations from the Arctic. The dynamics of the Arctic atmosphere poses a challenge for numerical weather prediction (NWP) and climate models, in particular in the case of ABL, orographic flows, Polar lows, and troposphere-stratosphere coupling. More research is also needed to better understand how the atmospheric dynamics affects and is affected by climate warming.
The Simulator for Arctic Marine Structures (SAMS) is used to model the performance of the icebreaker Oden in level ice. In particular, we use SAMS to perform a series of simulations of Oden transiting with constant headings and speeds in level ice. The simulations cover a wide range of ship velocities and ice thicknesses. The results are ice resistance curves, i.e., ice resistance as a function of the ship speed, for the different ice thicknesses. We then use the numerically simulated ice resistance curves together with the full-scale net-thrust curve of Oden from the literature to derive the relationship between the ice thickness and the maximum velocity of Oden, i.e., the h-v curve of Oden. We compare the simulated h-v curve of Oden with the full-scale h-v curve presented in the literature and show that the results are favorable. Moreover, we investigate the sensitivity of the simulation results to input parameters such as friction and form drag coefficients.
Die aerodynamische Rauhigkeit von Meereisoberflächen wurde bisher mit qualitativen Beschreibungen des Zustandes des Meereises in Beziehung gesetzt (z.B. Guest and Davidson, 1991). Quantitative Messungen der Meereisstruktur sind jedoch selten. Durch das verstärkte Interesse an globaler Klimamodellierung wird eine genaue Parameterisierung der Rauhigkeit einer Meereisoberfläche immer wichtiger. Konzeptionelle Modelle beschreiben den Gesamtwiderstand als Summe aus Formwiderstand und Oberflächenwiderstand. Zum Form-widerstand tragen Presseisrücken bei und, bei einer aufgebrochenen Eisfläche, die Schollenräder. Eisrücken und Schollenkanten können außerdem durch Abschattungseffekte eine Reduzierung des Oberflächenwiderstandes bewirken. Die Partitionierung des Widerstandes geht zurück auf Ayra (1975), der in seinem Modell die Beiträge von Rücken und Oberflächenwiderstand berücksichtigt. Hanssen-Bauer und Gjessing (1988) betrachten den Einfluß der Schollenräder und der Oberfläche. Mai (1995) kombinierte beide Modelle und benutzte gemessene Häufigkeitsverteilungen der Rauhigkeitselemente, um den Gesamtwiderstand zu bestimmen. Die Ergebnisse werden mit Resultaten aus Turbulenzmessungen verglichen. 0 0.01 0.02 0.03 0.04 F = hr e 0 1 2 3 4 1000 C dn10 1000 C d = 1.63 + 28.9 hr e Abbildung 1: Linkes Bild: Schema eines Meßfluges in 30m Höhe über einem Schollenfeld. In der Abbildung bedeuten hf die Schollenfreibordhöhe, hr die Eisrückenhöhe und lf die Schollenlänge. Rechtes Bild: Widerstandskoeffizient cdn10 (auf neutrale Schichtung und 10 m Höhe bezogen) als Funktion des Schollenformparameters F.
Ice thickness is one of the most important properties of sea ice. Ice thicknesses are very variable because they do not only depend on thermodynamic boundary conditions, but also on dynamic thickening due to sea ice motion and deformation, and regional redistribution of thick and thin ice. This chapter reviews characteristics of the local and global thickness distributions and their controlling processes. It compares the most common methods of submarine ULS, electromagnetic induction (EM) and airborne laser altimetry ice thickness measurements, reviews present knowledge of Arctic sea ice thickness change, and presents examples of thickness measurements showing the interplay of dynamic and thermodynamic processes affecting ice on local and regional scales.
Sea ice is sensitively dependent on the fluxes of energy, mass and momentum between the ocean and the atmosphere, making it worth investigating the modification of these fluxes by the respective boundary layers. Complementary to earlier investigations with a coupled sea-ice–oceanic mixed-layer model for the Southern Ocean, the atmospheric forcing in the present investigation is changed from monthly, observational data to daily, essentially modelled values computed by an operational numerical weather-prediction model. Applying these computations directly as atmospheric surface forcing to the sea-ice–oceanic mixed-layer model yields (in first order) encouraging results, indicating the general reliability of these data. As a supplement to the oceanic mixed-layer model, the fluxes derived from the atmospheric forcing are modified in a first step to include the stability dependency of the atmospheric surface-layer. Compared to the application of usual adjustment practices, this leads to improved results, especially with respect to the ice velocities in divergent ice fields. In the next step, the atmospheric forcing level is raised to the geostrophic level thus incorporating the entire atmospheric boundary layer. While the forcing fields become less dependent on the prescribed boundary conditions of the weather-prediction model, the simulations appear to be reasonable only when the near-surface wind forcing is applied, the overall roughness length is increased and the large-scale stability is reduced. This leads to important implications for coupled atmosphere–sea-ice–ocean models. DOI: 10.1034/j.1600-0870.1992.t01-3-00004.x
A parameterization of subgridscale surface fluxes over the marginal sea ice zone which has beenused earlier in several studies is modified and applied to a nonhydrostatic mesoscale model.The new scheme accounts for the form drag of ice floes and is combined with a so-called fluxaveraging method for the determination of surface fluxes over inhomogeneous terrain. Individualfluxes over ice and water are calculated as a function of the blending height. It is shown bycomparison with observations that the drag coefficients calculated with the new parameterizationagree well with data. The original scheme strongly overestimates the form drag effect.An improvement is mainly obtained by an inclusion of stratification and by use of a moreadequate coefficient of resistance for individual ice floes. The mesoscale model is applied to officeflows over the polar marginal sea ice zone. The model results show that under certainmeteorological conditions the form drag can have a strong influence on the near-surface windvelocity and on the turbulent fluxes of momentum. Four case studies are carried out. Themaximum influence of form drag occurs in the case with strong unstable stratification and withwind oblique to the ice edge. Under these conditions the wind stress on sea ice is modified byat least 100% for ice concentrations less than 50% if form drag is taken into account. DOI: 10.1034/j.1600-0870.2002.00243.x
The concept of drag partitioning to parameterise the surface roughness of sea ice is validatedusing topography data of regions with high sea ice concentrations. The parameterised drag iscompared to measurements obtained by aircraft and ship. The form drag can well be expressedas a function of mean ridge heights and spacings averaged over flight legs of 12 km, if animproved approximation for the coefficient of resistance of a single ridge is used. We find agood agreement between the parameterised and observed drag coefficients. The highest sea iceroughness was encountered close to coastal regions and the lowest in the central Arctic. DOI: 10.1034/j.1600-0870.2002.01253.x
This chapter summarises mesoscale modelling studies, which were carried out during the ACSYS decade until 2005. They were aiming at the parameterisation and improved understanding of processes in the Arctic boundary layer over the open ocean and marginal sea ice zones and over the Greenland ice sheet. It is shown that progress has been achieved with the parameterization of fluxes in strong convective situations such as cold-air outbreaks and convection over leads. A first step was made towards the parameterization of the lead-induced turbulence for high-resolution, but non-eddy resolving models. Progress has also been made with the parameterization of the near-surface atmospheric fluxes of energy and momentum modified by sea ice pressure ridges and by ice floe edges. Other studies brought new insight into the complex processes influencing sea ice transport and atmospheric stability over sea ice. Improved understanding was obtained on the cloud effects on the snow/ice surface temperature and further on the near-surface turbulent fluxes. Finally, open questions are addressed, which remained after the ACSYS decade for future programmes having been started in the years after 2005.
The problem of computing of the momentum and energy fluxes from the atmosphere to the ocean is one of the complex problems of air-sea exchange. The investigation concerns the problem of modeling and computing of the momentum and turbu-lent energy fluxes near the atmosphere — ocean surface, covered by ice floes. The mean drag of such surface depends on the length scale of the ice floes and its concentrations. Horizontal inhomogeneity creates the fluctuations of the buoyancy and surface stress. As a result the additional fluxes of momen-tum and turbulent energy from the air to the sea surface (and from the surface into the ocean) are pre-sented. We investigate two separate problems with two simplified models: 1). The turbulent — advective model for analyses of effect of surface roughness inhomonogeneity; 2). The turbulent — convective model for study of buoyancy influence on the energy fluxes near the surface. As a result the problem of using of the averaged fields of wind velocity and surface roughness for estimation of mean values of energy fluxes is decided.
Over the polar oceans, near-surface atmospheric transport of momentum is strongly influenced by sea-ice surface topography. The latter is analyzed on the basis of laser altimeter data obtained during airborne campaigns between 1995 and 2011 over more than 10000 km of flight distance in different regions of the Arctic Ocean. Spectra of height and spacing between topographic features averaged over 10 km flight sections show that typical values are 0.45 m for the mean height and about 20 m for the mean spacing. Nevertheless the variability is high and the spatial variability is stronger than the temporal one. The total topography spectrum is divided into a range with small obstacles (between 0.2 m and 0.8 m height) and large obstacles (≥0.8 m). Results show that large pressure ridges represent the dominant topographic feature only along the coast of Greenland. In the Central Arctic the concentration of large ridges decreased over the years, accompanied by an increase of small obstacles concentration and this might be related to decreasing multi-year ice. The application of a topography dependent parameterization of neutral atmospheric drag coefficients reflects the large variability in the sea ice topography and reveals characteristic differences between the regions. Based on the analysis of the two spectral ranges we find that the consideration of only large pressure ridges is not enough to characterize the roughness degree of an ice field, and the values of drag coefficients are in most regions strongly influenced by small obstacles.
The influence of a single pressure ridge of 4.5 m height on the structure of the atmospheric surface layer is studied. The field of the mean wind velocity is governed by typical features of a Bernoulli effect with a speedup over the crest and a shadowing effect downwind of the ridge. It is found that the turbulence generated by the ridge compensates for the deformation of the flow field by mixing momentum downward. Both mean and turbulent fields are restored to their upwind values at a distance of ~ 300 m downwind of the ridge, which is equivalent to an aspect ratio of ~0.015. The level of maximum turbulence generated by the ridge is characterized by a linear relationship. A formulation for the determination of the form drag of a single ridge is proposed and generalized toward an ensemble of ridges. We estimate that the form drag contributes
The advection of sea ice and associated freshwater/salt fluxes in the Weddell Sea in 1986 and 1987 are investigated with a large-scale dynamic-thermodynamic sea ice model. The model is validated and optimized by comparison of simulated sea ice trajectories with observed drift paths of six buoys deployed on the Weddell Sea ice. The skill of the model is quantified by an error function that measures the deviations of simulated trajectories from observed 30-day sea ice drift. A large number of sensitivity studies show how simulated sea ice transports and associated freshwater/salt fluxes respond to variations in physical parameterizations. The model reproduces the observed ice drift well, provided ice dynamics parameters are set to appropriate values. Optimized values for the drag coefficients and for the ice strength parameter are determined by applying the error function to various sensitivity studies with different parameters. The optimized model yields a mean northward sea ice volume export out of the southern Weddell Sea of 1693 km3 in 1986 and 2339 km3 in 1987. This shows the important role of sea ice transport for the freshwater budget of the Weddell Sea and gives an indication of its high interannual variability.
The parameterization of heat and momentum fluxes over a heterogeneous surface consisting of sea ice and large areas of open ocean (polynyas) has been studied. Various theories required to calculate grid-averaged fluxes are discussed, and a two-dimensional mesoscale boundary layer model has been applied to simulate the flow and heat exchange processes inside a single grid element of a hypothetical atmospheric general circulation model. The theories are compared with model results. Considering the surface fluxes of sensible and latent heat, a mosaic method, based on the use of estimates for local surface temperature, air temperature, specific humidity, and wind speed over the ice-covered and ice-free parts of the grid square, performed well in the comparison. Parameterizing the net longwave radiation, an estimate for the subgrid distribution of cloudiness was useful. Parameterization of surface momentum flux seemed to be most reasonable on the basis of the surface pressure field and a geostrophic drag coefficient depending on the air-surface temperature difference.
A laser profiler mounted on a helicopter was used to measure the surface topography of sea ice in the Weddell Sea. The measurements were carried out during the cruise Antarkus X/4 of R/V Polarstern as part of the Winter Weddell Gyre Study 1992 (WWGS'92). The total length of the measured surface profiles amounts to 793 km. The observed mean ridge heights and mean ridge spacings are fairly well correlated. Therefore the ridging intensity R(sub 3), which is the ratio of ridge height and spacing, was used as a quantitative classifier in order to arrange the laser data into different groups. At a cutoff height of 0.8 m the average ridge height and spacing are 1.16 m and range (0.02 less than R(sub 1) less than 0.04), and 1.3 m and 26 m at the uppermost range (R(sub 1) less than 0.04), respectively. The best fits to the observed ridge height distributions are achieved by negative exponentials, at lower ridging intensities as a function of ridge height, at the regime of highest ridging intensity as a function of the ridge height squared. The distributions of ridge spacing are well described by a lognormal distribution function. A simple model is used to estimate the average thickness h(* sub d) and the areal fraction of ridged ice from the laser data. The values of h(* sub d) range from 3.1 m with an areal coverage of 5% at the lowermost range of R(sub 1) to 3.7 m with an areal coverage of 31% at the uppermost range. If the ridged ice is distributed as a uniform layer over a unit area, the corresponding effective thickness values are 0.14 m and 1.16 m, respectively. Mean ridge heights and spacings are determined for different cutoff heights in order to enable comparisons to other measurements. The effect of ridges on the surface stress over the ice is estimated using the drag partition theory, which is applicable to the regime of lowest ridging intensity.
The sensitivity of Southern Ocean sea ice to the strength of the atmospheric momentum forcing is investigated in the framework of a global ocean general circulation model. In contrast to the usual approach of having the momentum flux just depend on the wind speed and a constant drag coefficient, the newly introduced momentum flux driving sea ice considers the local stratification and roughness over ice in one case, and the flux-aggregated stratification and roughness using the blending-height concept in the other case. While both cases thus allow for an interactive feedback, only the latter case accounts for the subgrid-scale heterogeneity of the sea-ice pack. In particular, the sea-ice feedback is in the former case only provided by the simulated ice thickness, affecting the surface temperature and local stratification, while in the latter case it is also determined by the ice concentration. Both parameterizations yield predominantly statically stable, but dynamically unstable conditions at any instant over the wintertime sea-ice pack. In the winter mean, statically and dynamically unstable conditions prevail over coastal polynyas, and lead to a positive feedback with increased momentum flux. The larger momentum flux enhances the along and offshore ice drift, leading to corresponding changes in the winter-mean ice-thickness distribution, a reduction in coastal ice concentration, and an increase of heat loss due to sensible heat flux. In the case where surface heterogeneity is accounted for, the impact of the lower coastal ice concentration leads to a larger momentum flux than in the homogeneous case. The long-term deep-ocean properties are only affected when in the heterogeneous case the form drag is raised by increasing the ice freeboard and decreasing the maximum ice concentration. Only the combination of both yields a significant increase of Antarctic Bottom Water formation, as reflected by a long-term cooling and freshening of the global deep-ocean properties.
Sea ice drift in the Weddell Sea was studied on the basis of data from seven buoys deployed on ice floes in January-February 1996. Six of the buoys formed an array with initial mutual distances of 50 km, which by October 1996 were stretched to ~400 km in an east-west direction. The differential kinematical parameters i.e., divergence, shearing rate, and vorticity, were estimated from the buoy array positions by applying a time-dependent method. The large-scale drift of the array was divergent until August 1996, but after the array came under the influence of the Antarctic Circumpolar Current the deformation was mainly shearing. Meteorological data from European Center for Medium-Range Weather Forecasts analyses and Special Sensor Microwave Imager derived ice concentrations were interpolated at the buoy sites. The drift velocity was highly wind-dependent; it was also wind-dependent in winter when the momentum balance was mainly between the internal ice stress and the air drag. The drift divergence and shearing rate were related to the wind forcing, while the array vorticity correlated better with the air pressure itself. We estimated the air-ice drag coefficient to be 1.8×10-3 at a height of 10 m over the ice and the geostrophic drag coefficient to be 6.1×10-4. The stability effects on the coefficients were mostly felt in conditions of light winds. The average ice-water drag coefficient based on 5 day periods was 2.1×10-3. The ice transport through a transect crossing the Weddell Sea was computed on the basis of the geostrophic winds, observed wind-drift dependence, SSM/I-derived ice concentrations, and the literature on ice draft statistics. The resulting annual mean net export in 1996 was 1600 km3 yr-1.
A brief description of a nine-level grid-point global atmospheric general circulation model is presented with the emphasis A brief description of a nine-level grid-point global atmospheric general circulation model is presented with the emphasis
on the physics parameterizations. This model was developed by the modeling group from Institute of Atmospheric Physics as on the physics parameterizations. This model was developed by the modeling group from Institute of Atmospheric Physics as
one task of the CO2-Climate cooperation project between Chinese Academy of Sciences and United States Department of Energy. The task was initiated one task of the CO2-Climate cooperation project between Chinese Academy of Sciences and United States Department of Energy. The task was initiated
by Qing-Cun Zeng (IAP) and Robert D. Cess (SUNY). The operational design, computer coding and climate simulation tuning of by Qing-Cun Zeng (IAP) and Robert D. Cess (SUNY). The operational design, computer coding and climate simulation tuning of
the model were mainly carried out by Xue-Hong Zhang (for dynamics) and the author (for physics) in SUNY at Stony Brook. The the model were mainly carried out by Xue-Hong Zhang (for dynamics) and the author (for physics) in SUNY at Stony Brook. The
final version was frozen in September 1990. Preliminary diagnoses showed that the model reproduces principal features of the final version was frozen in September 1990. Preliminary diagnoses showed that the model reproduces principal features of the
observed climatology. observed climatology.
A large-scale sea-ice - oceanic mixed-layer model for the Southern Ocean is forced with daily atmospheric fields from operational numerical weather prediction analyses. The strength of the atmospheric forcing is modified considering atmospheric surface-layer physics, which is itself directly dependent on the instantaneous sea-ice condition provided by the sea-ice model. In earlier applications, the atmospheric drag on sea ice was computed from the local momentum transfer over ice. In the present study, this is replaced by a large-scale momentum flux, which is characterized by a large-scale stability function and a large-scale roughness length. The large-scale roughness length depends on the local skin drags and on the form drag, where the latter is given as a function of the ice-plus-snow freeboard and the ice concentration, both provided by the sea-ice model. The thermodynamic part of the calculation is given by the local fluxes, which depend on the local stability of the atmospheric surface layer. This, physically more reasonable, description of the largescale dynamic forcing generally leads to an increase of the momentum transfer via an increase of the roughness length and a decrease of the stability in the atmospheric surface layer. Finally, this yields improved model results, especially in terms of a more dynamic pattern of the ice-thickness distribution.
The aerodynamic drag of Arctic sea ice is calculated using surface data, measured by an airborne laser altimeter and a digital camera in the marginal ice zone of Fram Strait. The influence of the surface morphology on the momentum transfer under neutral thermal stratification in the atmospheric boundary layer is derived with the aid of model concepts, based on the partitioning of the surface drag into a form drag and a skin drag. The drag partitioning concept pays attention to the probability density functions of the geometric surface parameters. We found for the marginal ice zone that the form drag, caused by floe edges, can amount to 140% of the skin drag, while the effect of pressure ridges never exceeded 40%. Due to the narrow spacing of obstacles, the skin drag is significantly reduced by shadowing effects on the leeward side of floe edges. For practical purposes, the fractional sea-ice coverage can be used to parameterize the drag coefficientCdn, related to the 10 m-wind. Cdnincreases from 1.2 · 10-3 over open water to 2.8 · 10-3 for 55% ice coverage and decreases to 1.5 · 10-3 for 100% ice coverage.
The focus of this paper is on the representation of Antarctic coastal polynyas in global ice-ocean general circulation models (OGCMs), in particular their local, regional, and high-frequency behavior. This is verified with the aid of daily ice concentration derived from satellite passive microwave data using the NASATeam 2 (NT2) and the bootstrap (BS) algorithms. Large systematic regional and temporal discrepancies arise, some of which are related to the type of convection parameterization used in the model. An attempt is made to improve the fresh-water flux associated with melting and freezing in Antarctic coastal polynyas by ingesting (assimilating) satellite ice concentration where it comes to determining the thermodynamics of the open-water fraction of a model grid cell. Since the NT2 coastal open-water fraction (polynyas) tends to be less extensive than the simulated one in the decisive season and region, assimilating NT2 coastal ice concentration yields overall reduced net freezing rates, smaller formation rates of Antarctic Bottom Water, and a stronger southward flow of North Atlantic Deep Water across 30 S. Enhanced net freezing rates occur regionally when NT2 coastal ice concentration is assimilated, concomitant with a more realistic ice thickness distribution and accumulation of High-Salinity Shelf Water. Assimilating BS rather than NT2 coastal ice concentration, the differences to the non-assimilated simulation are generally smaller and of opposite sign. This suggests that the model reproduces coastal ice concentration in closer agreement with the BS data than with the NT2 data, while more realistic features emerge when NT2 data are assimilated.
This paper estimates the air/sea drag coefficient for first-year ice from recent aircraft measurements and reconciles the range of observed drag coefficients (103CD = 1.2–3.7 referenced to 10 m) for all sea ice types, based on ice roughness and seasonal meteorology. For the purpose of sea ice modeling, it is necessary to define an effective drag coefficient which relates regional stress to regional wind, because sea ice is heterogeneous on scales less than 20 km. Regional stress is influenced by the distribution of surface roughness, the buoyancy flux from quasi-periodic leads, and external atmospheric conditions, principally the inversion height. 103CD is 1.3–1.5 for smooth ice but is much greater for nonflat surfaces. For wind speeds greater than 5 m/s and air temperatures below freezing, the effective 103CD is 2.5–3.0 for nearly continuous pack ice, such as first-year ice in seasonal ice zones and central Arctic basin. The range of values of 103CD is 3.0–3.7 for unstable boundary layers typical of off-ice winds in the marginal ice zone (MIZ) or even greater if the ice has been broken by a recent storm. CD values at the lower end of these ranges are associated with low inversion heights. These coefficients are confirmed by 103CD of 2.9, 2.5, and 3.1 for first-year sea ice calculated from gust probe data collected by the NOAA P-3 aircraft, interior to the inner MIZ in the Bering Sea during the Marginal Ice Zone Experiment (MIZEX-West) in February 1983, and 103CD of 2.6 for the Arctic calculated from Arctic Ice Dynamics Joint Experiment (AIDJEX) aircraft data for February 1976. The effective drag coefficient with the presence of even a small concentration of sea ice is greater than the oceanic value as shown by a 103CD of 2.2 calculated from NOAA P-3 gust probe data over a 40-km track of 0.4 ice concentration in the outer MIZ of the Greenland Sea in June 1984 during MIZEX-84. The relation of surface wind and stress to the geostrophic wind for shallow inversion heights, typical of high latitudes, is reviewed with a turbulent closure atmospheric boundary layer model. The winter Arctic is typified by low inversions (
For a free-drift case a method is developed for simultaneously
determining air (Ca) and water (Cw) drag
coefficients by solving the vertically integrated stress balance
equation for sea ice. The method allows the algebraic determination of
Ca and Cw from measurements of relative wind and
relative current at single reference levels, from estimates of the
densities of all three fluids and ice thickness, and from estimates of
the accelerations caused by the nonsurface stress terms derived from
position measurements. The method treats the ice as a natural drag plate
and therefore includes contributions from both skin and form drag. One
shortcoming of the technique is that if the relative wind and current
are colinear, then only the ratio of Ca and Cw can
be determined. Another is that the accelerations caused by other forces
need to be independently determined. An experiment was conducted on a
single floe in the eastern Bering Sea over the continental shelf during
March 1981. The site was about 80 km from the ice edge and was occupied
for approximately 3 days following the passage of a storm which had
broken the pack into 10-20 m diameter floes. Both profile and slab
inversion estimates of drag were made from the current meter and
anemometer measurements at the site: Ca at 3 m was
4.55×10-3 by the profile method, compared to
3.63-4.39×10-3 for slab, depending on assumptions;
Cw at 1.1 m by profile was 24.2×10-3,
compared to 18.3-22.0×10-3 for slab. The two methods
gave results which were not statistically separable and which were among
the highest drags observed for sea ice. The instantaneous stress balance
on the floe included contributions from material acceleration, Coriolis
force, the two surface stresses, and sea-surface tilt relative to mean
current and tide.
Wind velocity and temperature fluctuations have been recorded over a
large, flat, snow covered ice floe in the Gulf of St. Lawrence using
sonic anemometer-thermometers. Reynolds stresses and heat fluxes have
been computed digitally by the eddy correlation method. The average drag
coefficient, C10 = 0.0014, is the same as that of the sea
surface and about half that of moderately rough ice. Spectra and
cospectra of velocity and temperature fluctuations are expressed in
dimensionless forms, and coherence cospectra of the fluctuations at
various lateral separations are examined.
During a traverse of the Antarctic marginal ice zone (MIZ) near the
Greenwich Meridian in October 1981, we launched a series of radiosondes
along a 150-km track starting at the ice edge. Since the wind was from
the north, off the ocean, these radiosonde profiles showed profound
modification of the atmospheric boundary layer (ABL) as the increasing
surface roughness decelerated the flow. The primary manifestation of
this modification was a lifting of the inversion layer with increasing
distance from the ice edge by the induced vertical velocity. But there
was also a cooling of the stably stratified mixed layer below the
inversion and a consequent flux of sensible heat to the surface that
averaged over 200 W/m2. The magnitude of this flux suggests
that atmospheric heat transport plays a significant role in the
destruction of ice in the Antarctic MIZ. Using the rising of the
inversion and ABL similarity theory, we estimated the change in the
neutral stability drag coefficient, CD, across the MIZ.
CD increased from its open ocean value,
1.2×10-3, at the ice edge to 4.0×10-3
at 80-90% ice concentration. We present an equation for this dependence
of drag on ice concentration that should be useful for modeling the
surface stress in marginal ice zones.
Turbulent flux measurements were made at four levels (42, 90, 195, and
340 m) by the NOAA P-3 aircraft over first-year sea ice in the northern
Bering Sea during February 1982. Three profiles of momentum flux and
mean wind were used to calculate an air-ice drag coefficient
CD of 3.0 ± .6 × 10-3 referenced to a
10-m anemometer height. The boundary layer was slightly unstable
(zi/L = -1.2, where zi, was the inversion height
of 660 m and L the Monin-Obukhov length). The mean wind speed at the
42-m height was 17 m/s, and the air temperature was -20°C. From
turbulent heat flux measurements the value of the bulk heat transfer
coefficient CH was 0.73 ± 1.6 × 10-3,
giving a CH/CD of 0.24. The Bowen ratio was
greater than 2.8. Comparison of the present turbulent flux and variance
profiles with those collected over the ocean shows agreement, which
increases confidence in the calculations. The geostrophic drag
coefficient |u*|/|G|, where u* is the friction
velocity and G is the geostrophic wind, was 0.047. The turning angle of
the surface wind (measured by an anemometer at a height of 3 m on the
ice) was 32°, and the ratio of surface wind speed to the geostrophic
wind speed was 0.76.
A simple drag partition theory is developed for the classical problem of boundary layer flows over regular arrays of two- or three-dimensional roughness elements. The theoretical expression for the ratio of the form drag on these elements to the total drag is shown to be in good agreement with wind tunnel observations. It is used for determining the contribution of form drag on pressure ridges to the total wind stress on the arctic pack ice. The theory also leads to an expression for the large-scale roughness parameter as a function of mean ridge height, ridging intensity, small-scale or local roughness parameter, and an average form drag coefficient. It is required for determing the average wind stress over large areas of the Arctic on a routine basis, using the so-called geostrophic drag method, as envisaged in the Aidjex program.
Various methods of measuring air stress on the arctic ice surface are discussed; however, none of them could possibly take into account the form drag due to pressure ridges. An expression is derived for the form drag per unit area in terms of certain key parameters of ridge statistics and a suitable drag coefficient. By using the available field and laboratory measurements of these parameters an estimate is made of the ratio of the form drag to the frictional stress. It depends on the geographical location in the Arctic, the season of the year, and the meteorological conditions in the atmospheric surface layer. It is found, contrary to the common assumption, that the form drag on pressure ridges may be much larger than the frictional stress on the ice surface, especially under stably stratified conditions.
The influence of the roughness length on calculated fluxes of momentum and matter in the boundary layer is discussed. From observations of the velocity profiles of wind and water current, the roughness length of arctic sea ice is found to vary greatly around an average of 0.02 cm for the upper and 2 cm for the lower surface.
Measurements of the momentum flux were made by the Reynolds flux and dissipation methods on a deep water stable tower operated by the Bedford Institute of Oceanography . A modified Gill propeller-vane anemometer was used to measure the velocity. Drag coefficients from 196 Reynolds flux measurements agree well with those previously reported. Based on 192 runs, a comparison of the dissipation and Reynolds flux results shows excellent agreement on average, for wind speeds from 4 to 20 m sSUB-SUB1. The much more extensive dissipation data set (1086 h from the tower and 505 h from the weathership PAPA, CCGS Quadra) was used to investigate the dependence of the drag coefficient on wind speed, fetch and stability. Some time series of the momentum flux and drag coefficient are shown to demonstrate additional sources of variation in the drag coefficient. (from authors' abstract)
The partition of the total shearing stress, [tau], between that contribution attributable to the roughness elements projecting from a wind tunnel wall, , and the shearing stress at the intervening wall surface, [tau]g, is expressed as: , where F is the total wall area of which F' is not covered by roughness elements.
The mechanics of viscous fluids
- L Prandd
Further investigation of the wind conditions in areas with shelterbelts
- W Nägeli