Effect of sea ice morphology during Arctic ... - Wiley Online Library

GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 446–451, doi:10.1002/grl.50081, 2013

Effect of sea ice morphology during Arctic summer on atmospheric drag coefficients used in climate models C. Lüpkes,1 V. M. Gryanik,1,2 A. Rösel,3 G. Birnbaum,1 and L. Kaleschke3 Received 24 October 2012; revised 7 December 2012; accepted 11 December 2012; published 31 January 2013.

[1] Realistic modeling of polar sea ice dynamics and atmospheric processes over sea ice needs a detailed representation of the near-surface atmospheric fluxes of momentum. In this study, parametrizations of neutral drag coefficients mostly used in different general circulation models are compared with a recently developed parametrization including the impact of sea ice morphology. The new parametrization, using the sea ice and melt pond fraction as governing parameters, accounts for the effect of form drag caused by edges at leads, melt ponds, and floes. Based on remote sensing data of ice and melt pond fraction, it is shown that during Arctic summer the traditionally used drag coefficients differ from the new ones by a factor 0.5–1.2. The geographic distribution of drag coefficients obtained from both parametrizations is very different. Differences are due to a nonlinear and non-monotonic dependence of drag coefficients on sea ice concentration in the new parametrization. Citation: Lüpkes, C., V. M. Gryanik, A. Rösel, G. Birnbaum, and L. Kaleschke (2013), Effect of sea ice morphology during Arctic summer on atmospheric drag coefficients used in climate models, Geophys. Res. Lett., 40, 446–451, doi:10.1002/grl.50081.

1. Introduction [2] Results from polar climate models depend strongly on the quality of the parametrization of subgridscale physical processes, such as processes related to clouds, radiation, and turbulence [e.g., Tjernström et al., 2005; Shonk et al., 2012; Saha et al., 2006]. Important processes with respect to air–ice–ocean interaction are the near-surface transport of energy and momentum, which are influenced by the meteorological and oceanographic forcing and by the sea ice characteristics. A detailed parametrization of these transports is especially important with respect to realistic modeling of the currently observed changes of Arctic sea ice area and thickness. [3] In the present study, we concentrate on the momentum exchange between the Arctic atmosphere and the sea ice covered ocean during summer. Our goal is to investigate differences between parametrizations of the neutral drag coefficients as being used in state-of-the-art general circulation models (GCM). They will be compared with drag coefficients Cd following from a recently developed new

parametrization by Lüpkes et al. [2012] (LU12) that extended an idea of Andreas et al. [2010] to treat drag coefficients in melt pond covered regions in a similar way as in the marginal sea ice zones. [4] LU12 derived a hierarchy of Cd parametrizations on the basis of physical arguments and analyses of data sets for summer sea ice and for the polar marginal sea ice zones obtained during several campaigns in different regions and seasons. In contrast to parametrizations of drag coefficients that are traditionally used in most GCMs, the new parametrizations allow accounting for changes in the sea ice morphology, for example, during melting of sea ice. They were developed, especially, for the use in regional and global climate models (grid sizes of order 20–100 km) for regions with fractional sea ice cover as in the marginal sea ice zones during all seasons and in the whole Arctic during summer. Then, the sea ice concentration A is the governing parameter for the surface drag and further parameters like ice freeboard and sizes of leads and melt ponds can be expressed as functions of A (see Section 2). [5] Assuming that the parametrizations can be applied to a wide range of Arctic conditions, we present here for the first time a geographical distribution of Cd for the whole Arctic that is based on observed data. For this purpose, we use a data set of sea ice concentration and melt pond cover derived by Rösel et al. [2012] based on remote sensing data (see Section 3). We consider two 8 day periods in 2004 and 2007, in each year one at the end of June and another one at the end of August. The sea ice extent was extremely small in August 2007 while the largest August value of the last 9 years occurred in 2004 according to sea ice index data [Fetterer et al., 2009] shown by NSIDC (nsidc.org/data/ seaice_index). Finally (see Section 4), we compare the drag coefficients resulting from the new parametrization with traditional drag coefficients as used in different GCMs, for example, in the atmospheric models ECHAM5 [Röckner et al., 2003] and CAM5 [Neale et al., 2010] with its sea ice model CSIM as a part of the Community Climate System Model (CCSM), and in the ocean model MITgcm [Marshall et al., 1997; Losch et al., 2010]).

2. Parametrizations of the Neutral Drag Coefficients Over Polar Sea Ice

1

Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany. 2 A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia. 3 Institute of Oceanography, University of Hamburg, Germany. Corresponding author: C. Lüpkes, Alfred Wegener Institute for Polar and Marine Research, Postfach 120161, D-27515, Bremerhaven, Germany. ([email protected]) ©2013. American Geophysical Union. All Rights Reserved. 0094-8276/13/10.1002/grl.50081

[6] In state-of-the-art GCMs the effective neutral 10 m drag coefficients Cdn10 over a mixture of ice and open water are calculated by averaging the contributions over open water and sea ice weighted by their respective concentrations. This results in a linear, monotonic dependence of Cdn10 on the sea ice concentration while it has been shown by many studies (most recently by [Andreas et al., 2010; LU12]) that the effect of form drag caused by floe edges and melt pond edges can generate a nonlinear, non-

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monotonic dependence. The physical reason for this nonlinearity is that form drag is proportional to the reciprocal of the floe and melt pond sizes, which are in general a nonlinear function of the sea ice concentration. Another reason is the sheltering of the flow when the distance between edges is very small, which reduces then the form drag significantly. [7] We use the LU12 parametrization including form drag and apply a version (their equation 50) which can be most easily used in GCMs. This parametrization, which we call AWI parametrization in the following, reads Cdn10 ¼ ð1 AÞ Cd;w þ A Cd;i þ Ce Am ð1 AÞnþ1=ð10bÞ ; he Ce ¼ 60 103 Dmax

(1)

where A is the sea ice concentration. The first two terms represent the skin drag over open water and over 100 % sea ice with the drag coefficients Cd,w and Cd,i Form drag caused by melt pond and lead edges is parametrized by the third term. Dmax is the maximum width of melt ponds and leads. During summer, leads consist mainly of melt ponds melted already through the floes. The positive powers m and v quantify the rate of change of the sea ice freeboard (elevation of ice surface relative to the water surface in melt ponds and leads) as a function of A. Both parameters have been considered as tuning parameters with the most representative values m = v = 1. In this case, the length scale he resulting from the freeboard parametrization by LU12 is 4hp,max, where hp,max is the sea ice freeboard for A = 0.5. The nondimensional ß describes the effectivity of the flow sheltering by pond edges and is set to1. [8] In Equation (1), A is the concentration of ice at the surface, which means that 1-A represents the open water fraction related to ponds on ice floes, to ponds which melted already through the ice, and to leads. This is different from the sea surface related ice fraction ASSI in GCMs where the pond fraction Ap is not treated as open water. We rewrite Equation (1) using ASSI = A + Ap so that Cdn10 ¼ 1 ASSI þ Ap Cd;w þ ASSI Ap Cd;i 1:1 þCe ASSI Ap 1 ASSI þ Ap :

(2)

[9] The best fit to Cdn10 observations from various campaigns described in Andreas et al. [2010] is obtained with Cd,i = 1.4 10 3 and Ce = 2.23 10 3 (see Figure 1a, curve AWI). This value of Ce is obtained with Dmax = 33 m and he = 1.2 m. Curves AWI + and AWI show results with Ce leading to a variation of the maximum of Cdn10 by +25% (AWI+) and by 10% (AWI). The number 25% corresponds to roughly one half of the upper observed limit and 10 % to the lower limit of observations. Thus both values are realistic and could arise e.g., from variable freeboard of ponds when they are surrounded by ridges or sastrugi. [10] The GCMs CAM5, ECHAM5, and MITgcm, which we consider here, use parametrizations of Cdn10 which neither account for form drag (Ce = 0) nor for the effect of Ap (Ap = 0). The difference between these currently used GCM parametrizations consists only in their values of Cd, w and Cd,i. There are, however, case studies with other GCMs accounting for form drag by floe edges such as the study by Stössel et al. [2008]. [11] In the models CAM5 (respectively CSIM), and MITgcm Cd,w is prescribed by the same parametrization of

Figure 1. (a) Cdn10 as a function of sea ice concentration for U10 5 ms1. The red curves represent equation 1 with d = 1.1, Cd,i = 1.4 10 3, and different values of Ce, thick solid (AWI): Ce = 2.23 10-3 (optimum value), upper dashed curve (AWI+): Ce =4.2 10-3, lower dashed curve (AWI): Ce = 1.35 10-3; light green: Cd,i =1.6 10-3 , Ce = 0 (P1); dark green: Cd,i =1.89 10-3, Ce = 0 (P2); blue: Cdn10 =1.1 10-3, Ce = 0 (P3). (b) Cdn10 over open water used in both CAM5 and MITgcm (blue) and results of the parametrization used in ECHAM5 (dark green).

Large and Yeager [2009]. This is based on multiple data sets spanning a wide range of wind speeds. It is described by the equation Cd;w ¼ a1 =U10 þ a2 þ a3 U10 3

(3)

with the empirical constants a1 = 2.70 10 ms , a2 = 1.42 10 4, a3 = 7.64 10 5 sm-1 and where U10 is the 10 m wind speed, with the lower limit u10 = 0.5 ms-1. [12] ECHAM5 uses a Charnock-type formulation for the local roughness length z0,w over open water (z0;w ¼ ac u2 =g) with a lower limit z0,w = 1.5 10 5 m. u* is the friction velocity, g the gravitational acceleration and ac the Charnock constant). Using a logarithmic wind profile, one obtains 2

-1

32

6 7 k 7 Cd;w ¼ 6 4 5 ln ga C 10 U 2 c d;w 10

(4)

where k = 0.4 is v. Karman’s constant. This equation can be solved for Cd,w by iteration, or Cd,w = 0.89 10 3 at the lowest limit of z0,w.

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[13] Figure 1b shows Cd,w obtained with equations (3) and (4) as a function of U10. In (4), we use ac = 0.018 as currently prescribed in ECHAM5. [14] Here, we aim to study only those differences between the results from parametrizations which are caused by the choice of Cd,i and by the neglect or inclusion of form drag. Thus we calculate drag coefficients for a wind speed of 5 ms1 which occur frequently during Arctic summer according to observations at several Arctic drifting stations (see Figure 2f of Vihma et al. [2008]). In this case, we obtain from Figure 1b Cd,w 1.1 10 3 for both parametrizations (3) and (4). [15] Curves P1, P2, and P3 in Figure 1a represent the results of GCM parametrizations using Equation (2) with Ap = 0 and Ce = 0 as well as the above mentioned Cd,w = 1.1 10 3 and three different values of Cd,i, namely Cd,i = 1.6 10 3 (P1), Cd,i = 1.89 10 3 (P2), and Cd,i = 1.1 10 3 (P3). P1 refers to the default value of Cd,i in the CAM5 (and CCSM) documentation [Neale et al., 2010] and P2 to the Cd,i value recommended in the ECHAM5 documentation. It is furthermore close to the value 2.0 10-3 which is the Cd,i baseline value of MITgcm. Although the value used for P3 is clearly below the range of observations, we include it in the comparison because it is suggested by Nguyen et al. [2011] based on MITgcm runs adjusting model results to various observations such as sea ice thickness and area. Note that the assumptions for P3 result in Cdn10 values which are independent on the sea ice concentration. This independence holds even when the wind is changing between about 3 and 10 ms1. Cd,w varies only slowly in this range of wind speed when we consider its parametrization given by Equation (3) (see Figure 1b).

3. Sea Ice Data [16] Because the AWI drag parametrization points to the impact of melt ponds, we use a sea ice data set which contains both sea ice concentration and melt pond fraction. Such data have been derived by Rösel et al. [2012] on the basis of data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and in-situ observations. Starting with the year 2000, Arctic wide data (8 day averages) are available at the Integrated Climate Data Center (ICDC), CliSAP/KlimaCampus, University of Hamburg, Germany (http://icdc.zmaw.de.). [17] We use here data of two 8 day periods in 2004 and 2007 (end of June and end of August) which are typical for the situation between end of May and end of August also in other years (not shown here). According to Figures 2a and 2b (bottom lines), in both periods, melt ponds cover a large part of the sea ice with a typical value of roughly 15–30% (related to the whole grid area surface consisting of ice and water) for Ap so that the values ASSI –Ap differ strongly from those for ASSI which form the basis for the drag calculation in traditional schemes. [18] We can estimate roughly the error in Cdn10 resulting from errors in the knowledge of the melt pond fraction. With Ap around 20% for ASSI = 80%, a 30 % error in Ap would result in ASSI = 80% 6%. This means that Cdn10 would show a variation smaller than 5% if the AWI curve is considered in Figure 1a.

4. Results [19] Figure 2 shows ice data and values of Cdn10 resulting from the different parametrizations for the mentioned periods in 2004 and 2007. We recall here that the present versions of the GCMs do not include the melt pond effect on the roughness so that the panels with current GCM parametrizations are obtained as in Figure 1a using Equation (2) with Ce = 0 and Ap = 0. Results of the AWI parametrization (labels AWI, AWI+, and AWI) are shown for the same three different values of the tuning coefficient Ce as in Figure 1a. [20] Considering Cdn10 values in Figure 2, the first important result is that the range of variability over the sea ice covered region is similar in both periods 2004 and 2007 although the sea ice covered region is much smaller in 2007. This is due to an invariance of variability in the range of sea ice concentrations in both years. [21] Differences between the results from different parametrizations become clear by considering Figures 2 and 3 together. The latter shows Cdn10 used in GCMs (P1, P2, P3) divided by the values resulting from the AWI parametrization with different values of constants as in Figures 1 and 2. According to Figures 2 and 3, the second important result is that there are large differences between Cdn10 values when different parametrizations are used. The P3 parametrization strongly underestimates Cdn10. Values amount to only 60% to 75% of those resulting from the AWI parametrization. As already clear from Figure 1a, no dependence on the sea ice concentration is present in the P3 results. Compared with the AWI result, differences to the P1 parametrization are especially pronounced where melt pond cover is largest. Best agreement is obtained with AWI, however differences depend on the region and values amount in some regions to only 65% of AWI + values and to 80% if the most recommended constants (AWI) are used. [22] In 2004, differences between the AWI parametrization and P1 and P2 results are especially large in the Canadian and East Siberian Arctic. South from 80 N, in 2004, the levels of Cd values obtained by the P2 and AWI parametrizations are similar while the latter produces smaller values (up to 20%) north of 80 N. Differences are, however, larger when AWI + or AWI is considered as reference, with values up to 30% (factor 1.3) in the Canadian Arctic for the comparison with AWI+. The differences between parametrizations shown here for a wind speed V of 5 ms1 are representative for V between 4 and 22 ms1 (see Figure 1b). We found that the dependences of Cd,w on wind (Equations 3 and 4) in this range modifies the maximum drag coefficient by 10% only. [23] The third important finding is that, especially, in 2004, the distribution of values obtained by the P1 and P2 parametrizations differs qualitatively strongly from those obtained with the AWI parametrization. AWI, AWI+, and AWI deliver minimum values north of 80 N while values are larger south of 80 N. This is in contrast to the results of the P1 and P2 parametrization. We consider this finding as especially important because it points to a principal physical change of air–ice interaction when the AWI parametrization would be used in GCMs. [24] A hint on the size of the possible impact is given in a study of Zhang and Rothrock [2003] with a global ocean and sea ice model. Reducing Cd,i to the value of Cd,w as in

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Figure 2. Cdn10 103 resulting from different parametrizations P1, P2, and P3 used in GCMs and from parametrizations AWI, AWI+, and AWI (see Section 2) using ASSI, and Ap given here in percent of the grid area. These concentrations are derived from MODIS (see section 3) averaged over Julian days 177-184 in 2004 (a) and days 241-248 in 2007 (b). 449


Figure 3. Cdn10 from different GCMs divided by the parametrizations AWI, AWI+, and AWI, respectively (see Section 2), for Julian days 177–184 in 2004 (a) and days 241–248 in 2007 (b).

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wind forcing from reanalyses or melt pond fraction predicted from GCMs will be the topic of a future study. It will be relevant, especially, with respect to the currently observed drastic changes of Arctic sea ice.

parametrization P3 reduced the spatial correlation coefficient between simulated and observed ice thickness from 0.75 to 0.4. Thus we expect that form drag can have a distinct impact on Arctic sea ice, especially south of 80 N. This is supported to some extent by Stössel et al. [2008], who found that the inclusion of sea ice form drag in a global ocean and sea ice model can have a noticeable effect on long-term ocean properties in regions with low sea ice concentration as in the polynya regions along the Antarctic shelf.

[29] Acknowledgments. We thank Edgar L Andreas, Martin Losch, and Jörg Hartmann for helpful comments and discussions, as well as two anonymous reviewers for constructive comments. This work was conducted as a subproject of MiKlip, a project funded by the German Federal Ministry of Education and Research (FKZ: 01LP1126A).

5. Concluding Remarks

References

[25] In the range of the studied conditions, differences between the results of the traditional sea ice roughness parametrizations mostly used in GCMs are obviously large. Furthermore, they differ strongly from drag coefficients obtained with a recently developed parametrization by Lüpkes et al. [2012] (AWI parametrization, see Equations 1 or 2) which is based on observations from several campaigns. Differences concern both absolute values and their geographic distribution. Traditionally used drag coefficients attain always maximum values at the largest sea ice concentrations A, which occur mostly north of 80 N. In contrast to the mostly used parametrizations in GCMs, the AWI parametrization produces the maximum of drag coefficients for A 50% and thus further south in the periphery of the sea ice covered regions. [26] For a wide geographic region with low and moderate sea ice concentration, momentum exchange between atmosphere and sea ice would be underestimated by GCMs using drag parametrizations without form drag. Vice versa, in regions with large A, momentum exchange would be overestimated by widely used parametrizations. Note, however, that in all parametrizations considered here, the impact of ridges and sastrugi in regions with large sea ice concentration is accounted for only in the constant drag coefficient Cd,i. An explicit treatment in a further improved scheme would perhaps lead to increased values for large sea ice concentration but would not reduce the differences to the presently used parametrizations in large parts of the Arctic with moderate sea ice concentration. Furthermore, the ridge impact is unclear; recent results of Andreas [2011] suggest a minor importance of the impact of large ridges. [27] We have shown that the coefficient Ce in the AWI parametrization, describing the effect of sea ice morphology, has a large impact. Here, Ce has been prescribed based on observations. Ce is related to the ice freeboard at melt pond edges as well as to the maximum pond lengths. Thus, it could be determined in future studies prognostically if GCMs are used with sea ice models predicting these parameters. [28] Finally, a detailed analysis of the interannual variability of summertime drag coefficients using, for example,

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