Improved Simulation of the Polar Atmospheric Boundary Layer by Accounting for Aerodynamic Roughness in the Parameterization of Surface Scalar Exchange Over Sea Ice

A new, simple parameterization scheme for scalar (heat and moisture) exchange over sea ice and the marginal ice zone is tested in a numerical weather and climate prediction model. This new “Blended A87” scheme accounts for the influence of aerodynamic roughness on the relationship between momentum and scalar exchange over consolidated sea ice, in line with long‐standing theory and recent field observations, and in contrast to the crude schemes currently operational in most models. Using aircraft observations and Met Office Unified Model simulations of cold‐air outbreak (CAO) conditions over aerodynamically rough sea ice, we demonstrate striking improvements in model performance when the Blended A87 scheme replaces the model's operational treatment for surface scalar exchange, provided that the aerodynamic roughness over consolidated ice is appropriately prescribed. The mean biases in surface sensible heat flux, surface latent heat flux, near‐surface air temperature, and surface temperature reduce from 25 to 11 W m−2, 22 to 12 W m−2, 0.8 to 0.0 K, and 1.4 to 0.8 K, respectively. We demonstrate that such impacts on surface exchange over sea ice can have a marked impact on the evolution of the atmospheric boundary layer across hundreds of kilometres downwind of the sea ice during CAO conditions in the model. Our results highlight the importance of spatiotemporal variability in the topography of consolidated sea ice for both momentum and scalar exchange over sea ice; accounting for which remains a key challenge for modeling polar weather and climate.

where the subscript is the surface type, either ice (subscript ) or seawater (subscript ); is wind speed; − and − are the surface-air differences in potential temperature and specific humidity, respectively; is the air density; is the specific heat capacity of air; is the latent heat of vapourization; and , and are the exchange coefficients for momentum, heat, and moisture, respectively. For a given surface type, the surface exchange coefficients (adjusted for a neutral stratified surface layer) are related to the surface roughness lengths for momentum ( 0 ), heat ( 0 ) and moisture ( 0 ) using Monin-Obukhov similarity theory (Monin & Obukhov, 1954) as follows: where is the von Kármán constant (0.4); is the reference height at which the exchange coefficients are evaluated (here 10 m, as is standard).
The surface roughness lengths must be obtained empirically. However, obtaining the necessary in-situ measurements in the polar regions is challenging, and this has limited our capacity to constrain surface exchange schemes for sea ice. In recent years, substantial progress has been made with significant new data sets and analyses available (e.g., Elvidge et al., 2016Elvidge et al., , 2021Srivastava et al., 2022).
In recent years, a parameterization framework for momentum exchange over sea ice and the marginal ice zone (MIZ) has been established that accounts independently for skin drag associated with friction in the viscous sublayer and form drag associated with flow separation and pressure differentials generated by airflow over the vertical edges of ice floes in the MIZ (Arya, 1973(Arya, , 1975Birnbaum & Lüpkes, 2002;Garbrecht et al., 2002;Lüpkes et al., 2012;Lüpkes & Gryanik, 2015). Here, and over ice ( and ) are derived using Equations 1 and 4, then is given as a function of sea-ice concentration, , using the so-called mosaic or flux averaging approach (e.g., Claussen, 1990;Vihma, 1995) as follows: where is the momentum flux (or drag) over seawater (obtained from an ocean surface exchange scheme) and is the form drag from ice floe edges (obtained following, e.g., Lüpkes et al., 2012, andElvidge et al., 2016, in the case of the Met Office Unified Model, MetUM). Schemes using this framework have been constrained and evaluated using in-situ aircraft, tower and ship observations (e.g., Elvidge et al., 2016Elvidge et al., , 2021Lüpkes & Birnbaum, 2005;Srivastava et al., 2022) and implemented in a range of numerical models, including the MetUM (Renfrew, Elvidge, & Edwards, 2019), the European Centre for Medium-Range Weather Forecasts Integrated Forecast System (IFS) (Roberts et al., 2018), the Los Alamos Sea Ice Model (CICE) (Tsamados et al., 2014), and a regional coupled climate model (HIRHAM-NAOSIM 2.0) (Yu et al., 2020).
This new generation of momentum exchange parameterisation schemes for sea ice has brought significant improvements in numerical model performance. For instance, in the MetUM, benchmark testing has shown a 1%-2% improvement in mean-sea-level pressure and upper-troposphere winds in both the Southern and Northern Hemisphere 3 of 20 extra-tropics, as well as a 5% and 1%-2% improvement in mid-tropospheric geopotential height for the Southern and Northern Hemisphere extra-tropics, respectively (see Renfrew, Elvidge, & Edwards, 2019 for a thorough evaluation of the scheme's impact in the MetUM). Despite such radical progress, a major deficiency remains in the parameterization of momentum exchange over complete sea ice cover; that is, the representation of 0 over consolidated sea ice (i.e., 0 ). This important parameter is known to vary by several orders of magnitude in space and time due to variability in sea-ice topography related to characteristics such as sea-ice type, age and thickness; the presence of pressure ridging; and hydrological systems (e.g., Castellani et al., 2014;Elvidge et al., 2016;Overland, 1985;Petty et al., 2017;Srivastava et al., 2022). However, as yet there is no consensus on how to reliably represent this 0 variability in numerical models. Consequently, 0 is currently set as a fixed value in most models; for example, 5 × 10 −4 and 10 × 10 −4 m in the MetUM and IFS, respectively. Note that 0 appears in the derivation of both the momentum and scalar exchange coefficients (see Equations 4-6), so this deficiency affects the parameterization of both momentum and scalar fluxes over sea ice-the latter being the focus of this study.
The parameterization of scalar exchanges over sea ice and the MIZ has received less attention than that of momentum exchange, and the representation of heat and moisture fluxes over sea ice in numerical models remains crude. In the MetUM-the numerical weather prediction (NWP) model used in this study-over sea ice 0 and 0 are proportional to 0 and given by Figure 1). Then and and the associated fluxes (SH and LH ) are derived using Equations 2, 3, 5 and 6. As with , SH and LH over sea ice and the MIZ are then derived using the mosaic approach: where SH and LH are the sensible and latent heat fluxes over seawater (again obtained from an ocean surface exchange scheme). Comparable treatments are found in other state-of-the-art numerical models including the IFS and CICE. Note the IFS employs a different, empirically-derived expression (following Andreas et al., 2010) to account for elevated surface roughness over the MIZ (see Section "3.2.4 Roughness lengths" in ECMWF, 2021). Note that, in contrast to momentum exchange, the effect of ice floe edges on scalar exchange is currently unaccounted for in operational NWP models. Lüpkes and Gryanik (2015) suggest a framework for incorporating this effect.
It is well established in the literature (e.g., Andreas, 1987) that surface scalar exchange over ice is dependent on aerodynamic roughness, expressed as the roughness Reynolds number over ice, * : where is kinematic viscosity; * is friction velocity over ice given by: where is a stability correction function (see e.g., Stull, 1988). A lack of sensitivity to * in the representation of surface scalar exchange has recently been highlighted as a major deficiency of existing surface exchange parameterization schemes for sea ice hereafter E21). E21 used in-situ aircraft observations and offline parameterization experiments to demonstrate for the first time that whilst these existing schemes canwith appropriate tuning of 0 -perform well for the MIZ in an aerodynamically smooth sea ice regime (defined and * , where 0 is the surface roughness length for scalar quantities (i.e., 0 for heat, or 0 for moisture) and * = 0 * is the roughness Reynolds number. The functional forms shown are from the surface exchange schemes used operationally in the MetUM and in the conceptual model of Andreas (1987). Gray background shading marks the transitional aerodynamic roughness regime, to the left of which ( * ≤ 0.135) is the smooth regime, and to the right of which ( * ≥ 2.5) is the rough regime. 4 of 20 by Roughness Reynolds Number, * < 0.135), they are inappropriate and perform poorly in an aerodynamically rough regime ( * ≥ 2.5). This is because in a rough regime, the introduction of pressure forces (form drag) across surface roughness elements extending above the viscous sublayer violates the assumption that momentum and heat transfer depend on the same turbulent eddies. Consequently, 0 and 0 cannot be proportional to 0 . Instead, 0 0 and 0 0 are inversely correlated to aerodynamic roughness in rough conditions.
A more sophisticated theoretical model for surface heat and moisture exchange over sea ice was developed by Andreas (1987). Based on surface-renewal theory, it provides 0 0 and 0 0 as non-linear functions of * (see Figure 1). This "A87 theoretical model" applies distinct, physically justified treatments for scalar exchange under smooth conditions (an advection-diffusion model) and rough conditions (a diffusion model). It has been shown to skillfully reproduce observed surface scalar fluxes over consolidated ice and snow surfaces, for example, over sea ice (Andreas, 1987;Andreas et al., 2010;E21) and over mountain glaciers (Fitzpatrick et al., 2019). However, it is only appropriate over consolidated ice and, consequently, not over the heterogenous ice-water mix of the MIZ.
To tackle the MIZ and other areas of unconsolidated sea ice, E21 proposed a new parameterization framework that blends the A87 scheme with the output of an ocean surface exchange scheme. Here, 0 0 and 0 0 are derived from * using polynomial approximations of the A87 theory (see equation (53) and Table I in Andreas, 1987). The scalar exchange coefficients and fluxes for consolidated sea ice area then derived using Equations 2, 3, 5 and 6, and fluxes across the MIZ are determined using the same mosaic approach as in the operational MetUM scheme (Equations 8 and 9). In offline tests, this Blended A87 scheme performed much better than the crude operational schemes in the MetUM and IFS for the aerodynamically rough conditions documented in observations obtained during the field campaign of the Iceland Greenland Seas Project (IGP) (E21).
It should be noted that the empirical constraint and validation of surface sea-ice exchange schemes has been predominantly based on observations from the Northern Hemisphere, reflecting the paucity of in-situ observations over sea ice from the Southern Hemisphere. Whilst the theoretical basis for these schemes would be expected to hold universally, it is plausible that the validity of certain assumptions made in their derivations, as well as the tuning of certain parameters, may differ between Arctic and Antarctic sea ice. This possibility is highlighted in Weiss et al. (2011)-one of the few publications documenting the surface roughness of Antarctic sea ice-who observed marked differences in sea-ice characteristics relative to the Arctic Ocean. On the other hand, the recent implementation in the MetUM of the Lüpkes et al. (2012) scheme for sea-ice surface momentum exchange was found to bring considerable benefits to model skill over the Southern Hemisphere (Renfrew, Elvidge, & Edwards, 2019), despite being constrained by Arctic observations (from Elvidge et al., 2016). Consequently, until further suitable observations over Antarctic sea ice are obtained, we have little choice but to use the same parameterization settings for each polar region.
In this paper, we use MetUM sensitivity experiments in tandem with aircraft observations obtained from two Arctic field campaigns, to establish.
• the impact of the Blended A87 scheme on the reproduction of surface heat and moisture fluxes over sea ice in an NWP model; • the sensitivity of Arctic boundary-layer conditions to changes in surface heat and moisture fluxes over sea ice in an NWP model; • the broader implications and current limitations of introducing aerodynamic-roughness dependence to surface scalar exchange over sea ice.

Atmospheric Modeling
The MetUM is a state-of-the-art atmospheric model solving the deep non-hydrostatic compressible equations for a fluid and incorporating parametrisations for physical processes including radiation, microphysics, orographic drag, boundary-layer turbulence and surface exchange. It is used by the Met Office for their operational weather forecasting and as a component in all their climate models (e.g., Walters et al., 2019). Here we employ regional simulations using the MetUM, with model physics based on the Regional Atmosphere and Land Science Configuration 1 for Mid-Latitudes (RAL1-M; Bush et al., 2020). The regional domain used here covers the northern Iceland Sea and southwest Greenland Sea (see Figure 2) and uses a horizontal grid spacing of 2.2 km and 70 vertical levels. This setup of the MetUM has previously proven reasonably accurate at simulating cases of coldair outbreaks and polar lows in this region (e.g., Abel Renfrew et al., 2021;Sergeev et al., 2017). Boundary conditions for the regional model simulations are provided by global operational MetUM simulations using a horizontal grid spacing of ∼10 km, with these simulations being initialized from Met Office analysis data.

Aircraft Observations Over Arctic Sea Ice
In-situ fluxes, 10-m neutral surface exchange coefficients and roughness lengths for momentum, heat, and moisture have been derived from aircraft observations along low-level flight legs (typically ∼40 m in altitude), using the eddy covariance technique and standard atmospheric surface-layer assumptions. For each flux observation we estimate the underlying sea-ice concentration based on albedo from surface shortwave radiation measurements following Elvidge et al. (2016). For further details on the acquisition, processing and quality control of these aircraft measurements, see E21.
Here we use observations in the vicinity of the MIZ to the north of Iceland and east of Greenland during seven flights undertaken between 28 February and 14 March 2018 as part of the IGP. These flights were all conducted during relatively weak cold-air outbreak (CAO) conditions-that is, broadly northerly winds bringing cold air from the high Arctic across the MIZ and over the ocean-with associated upward turbulent heat fluxes (see Figure 2). These IGP observations generally occupy the aerodynamically rough regime (the mean * is 257), with relatively strong winds over jagged, irregular sea ice (see E21). For further details on the IGP field campaign see Renfrew, Pickart, et al. (2019) and for an evaluation of MetUM forecasts using IGP buoy, ship, and aircraft observations see Renfrew et al. (2021).
In In total, 303 surface flux observations are available for this study, with 107 from the IGP and 196 from ACCA-CIA. However, quality control reduces this number to 99 + 168, 88 + 154, and 74 + 159 for IGP + ACCACIA, and for momentum, heat, and moisture exchange, respectively.

Experimental Design
In this study, a statistical analysis is conducted of the IGP aircraft observations shown in Figure 2 and the MetUM sensitivity experiments that reproduce them. All observations were obtained between 10 and 17 UTC, and corresponding simulations are initialized on each day of observations at 00 UTC and run for 24-hr. The period between 6 and 18 UTC on 14 March 2018 (spanning the observations within the blue box in Figure 2) is identified as Case A and is subject to further analysis of the model output on broader spatial scales, as are two additional periods just outside of the period of IGP aircraft observations, identified as Cases B and C. Case B is a strong, persistent CAO event spanning a period of 60 hr from 1 to 4 April 2018. Case C is a warm-air intrusion (WAI) event (relatively warm air sourced from the lower latitudes advected over sea ice) spanning a period of 108 hr from 17 to 22 February 2018. The simulations covering these cases were initialized at 00 UTC on the first day of each case and run continuously until the end of each case (so for 72 and 120 hr for cases B and C, respectively).

The Surface Exchange Parameterization Configurations
Four parameterization configurations are used for the surface exchange sensitivity experiments (Table 1,   6 of 20 (M IGP S IGP and M IGP S A87 ). Here "M" denotes the momentum exchange setting and "S" denotes the scalar exchange setting.
• M Op S Op uses operational settings for both momentum and scalar exchange, that is, 0 = 5 × 10 −4 m, (Lock et al., 2021). Note these are the same settings currently used operationally in all configurations (both global and regional) of the MetUM, including the RAL1-M configuration used for our simulations. The reason for tuning 0 to the observations in three of the four configurations is to minimize biases in momentum exchange and, consequently, highlight the impact of parameterization changes on scalar exchange. Recall this is necessary as SH and LH are dependent on 0 and -see Equations 2, 3, 5 and 6-and 0 and 0 are also functions of 0 . Note that the same IGP-derived value for 0 is used for the case B and C simulations as the sea ice will be morphologically similar during these periods (c.f. Ponsoni et al., 2019). Here, the parameterisations have been forced solely by the observations (i.e., run independently of the MetUM), where the exchange coefficients over seawater (ice concentration = 0) have been fixed to the median observed values, and used in the Blended A87 component of M IGP S A87 is set to the median observed value for each ice fraction bin.

For
, M IGP S Op and M IGP S A87 accurately reproduce the observed median values across all sea-ice concentrations due to the tuning of to the median observed value, whilst M Op S Op consistently underestimates these values, increasingly so at higher sea-ice concentrations. For and , M IGP S A87 reproduces the observed median values with reasonable accuracy, whilst M IGP S Op consistently overestimates them, increasingly so with increasing sea-ice concentration. This highlights the need to consider the impact on scalar exchange when tuning for momentum exchange. Note that even M IGP S A87 fails to reproduce the dip in and apparent in the observations for a sea-ice concentration of 1. However, the reliability of this specific bin of observations could be questioned, due to the low heat fluxes, as discussed in E21. Interestingly, M Op S Op is functionally similar to M IGP S A87 for and and appears to match the observations comparably well. However, as we will explain in Section 5, this is the result of compensating errors in momentum and scalar roughness lengths, and this serendipitous performance will not occur in all aerodynamic roughness regimes.

Validation of the Blended A87 Scheme in Simulations of a Persistent Arctic CAO Over Rough Sea Ice
In this section we evaluate the impact of the Blended A87 scheme on MetUM skill in reproducing the surface exchanges and rough surface-layer conditions during the persistent CAO documented in the IGP aircraft observations (all data points shown in Figure 2). The observations depict northwesterly to northeasterly winds of mean speed 7.4 m s −1 bringing cold, dry air with a mean temperature of 260.7 K (−12.5°C) and mean specific humidity of 1.2 g kg −1 over the generally warmer MIZ and ocean, with a mean surface temperature of 263.4 K (−9.8°C) resulting in convective conditions in the ABL (Figure 2; Table 2). SH and LH have mean values of 17 and 13 W m −2 , respectively (Table 2) Table 2). In the M Op S Op experiment, the wind speeds are generally overestimated, with a mean bias of 1.0 m s −1 resulting predominantly from overestimates at higher sea-ice concentrations and higher wind speeds (Figure 4a), and a greater RMSE of 2.71 m s −1 . These results closely reflect expectations; overestimates in M Op S Op wind speeds reflecting negative biases in surface drag that increase with increasing sea-ice concentration (Figure 3a).  Table 2). In the M IGP S Op experiment, the temperatures are generally overestimated, with a mean bias of 0.8 K resulting predominantly from overestimates at higher sea-ice concentrations and consequently lower temperatures (Figure 4e), as well as a greater RMSE of 1.23 K. Again, these results closely reflect expectations; overestimates in M IGP S Op air temperatures reflecting positive (upward) biases in surface heat exchange that increase with increasing sea-ice concentration (Figure 3b). These heat exchange biases are seen in the MetUM output, with a mean positive bias in SH of 25 W m −2 meaning too much heat transfer from the ocean into the cooler air. In the M IGP S A87 and M Op S Op experiments, these mean biases are smaller: 11 and 14 W m −2 , respectively ( Figure 5; Table 2).
The sensitivity in surface temperature matches that for air temperature, with a mean positive bias that is largest in the M IGP S Op experiment at 1.4 K, and smaller in the M IGP S A87 and M Op S Op experiments at 0.8 and 0.9 K, respectively. This difference is due to the warm bias in air temperatures in M IGP S Op translating to a warm bias in surface temperatures via a corresponding bias in surface heat exchange over the ice portion of model grid cells. Note that the surface temperature of seawater is prescribed in these atmosphere-only simulations (and, in reality, varies little on these timescales). In contrast to wind speed and temperature, model performance for atmospheric humidity does not match expectations. There are significant (negative) mean biases for specific humidity in all the Note. Results are shown for wind speed ( ), air and surface temperatures ( Air , Sfc ), specific humidity ( ), surface sensible and latent heat fluxes (SH , LH ), and LH sub-sampled for when the model bias in is < 0.1 g kg −1 ( low−q−bias ). Note that positive surface heat flux values indicate upward fluxes. For each variable, the lowest bias and RMSE are underlined.  Figure 3c). This is due to a compensating error related to widespread negative biases in humidity inherited from the global model simulations. This humidity bias is also apparent from IGP observations obtained far from the MIZ (over the northeastern Iceland Sea; not shown) and has previously been reported by Renfrew et al. (2021). Despite this bias, the model performance for LH is otherwise as expected, with a mean positive bias in all experiments that is greatest in the M IGP S Op experiment. This larger positive LH bias in the M IGP S Op experiment is the compensating error that leads, via upward moisture transfer, to the smaller negative humidity bias in this experiment. Note that a subsample of the data for which the model bias in specific humidity is small (<0.1 g kg −1 ) exhibits smaller biases in LH in all model experiments, including a very small mean bias (1 W m −2 ) in the M IGP S A87 experiment. Table 2 also summarizes the performance of the M IGP S IGP model experiment (recall this uses fixed observed values for 0 and 0 ). Comparing its performance with that of M IGP S A87 reveals the importance of wind speed sensitivity in the Blended A87 scheme, noting that if in Equation 11 is fixed to the median value from all the observations, then the values of 0 / 0 and 0 / 0 derived using the A87 theoretical model are very close to the median observed value of 3.9 × 10 −4 that is used in the M IGP S IGP experiment. The biases and RMSE for this experiment are very similar to those of the M IGP S A87 experiment, implying that the variability in wind speed in our IGP observations is relatively unimportant to the heat and moisture fluxes derived from the Blended A87 scheme.
The impact of the Blended A87 scheme on key meteorological properties is significant, relative to the errors in reanalysis products over open water in this region reported in previous studies. For example, using meteorological buoy observations from the central Iceland Sea over a 2-year period, Harden et al. (2015) report mean biases (RMSE) in ECMWF's ERA-Interim product for wind speed, air temperature, and sensible heat flux of 0.12 (1.60) m s −1 , 0.43 (0.82) K, and −8.3 (15.8) W m 2 , respectively. Using buoy observations from the northwest Iceland Sea over a 78-day period that coincides with the IGP field campaign, Renfrew et al. (2021) report mean biases (RMSE) in ECMWF's newer ERA-5 product for wind speed, air temperature, sensible heat flux, and latent heat flux of 0.61 (1.62) m s −1 , 0.05 (1.11) K, −1.7 (18.7) W m 2 , and 6.9 (15.7) W m 2 , respectively. These reported mean biases are consistently smaller in magnitude than the improvements in MetUM bias for equivalent variables shown in Table 2 for the replacement of the M Op S Op scheme (for wind speed) or the M IGP S Op scheme (for all other variables) with the M IGP S A87 scheme, whilst the RMSEs are of the same magnitude. A caveat here is that fluxesand consequently model errors in fluxes and bulk fields-are typically smaller over open water than over the MIZ.

Sensitivity of the Arctic Atmospheric Boundary Layer to Surface Scalar Exchange Over Rough Sea Ice
In this section we focus on the three case studies described in Section 2.3-Cases A, B and C-to explore the impact of the Blended A87 scheme on the Arctic ABL in different meteorological regimes. Figure 6 shows 10 of 20 instantaneous mean sea level pressure and boundary-layer wind vectors from the M IGP S A87 experiments at times that are broadly representative of conditions at the "peak" (in terms of wind strength) of each case study. During "peak" conditions in Case A, a weak, zonally-oriented high-pressure ridge weakening eastward is associated with relatively weak northwesterly winds bringing cold air across the MIZ in the north of the model domain and weak northeasterly winds in the south of the domain. During "peak" conditions in Case B, a low-pressure system in the eastern Iceland Sea and broadly northwest-to-southeast pressure gradients are associated with strong northerly-to-northeasterly winds bringing cold air across the entire model domain. During "peak" conditions in Case C, a pressure gradient from the eastern Iceland Sea to the Denmark Strait drives southerly winds bringing relatively warm air from lower latitudes across the MIZ. Of the two CAO cases (A and B), Case B is simpler to analyze due to the relative homogeneity of the wind field-broadly northerly winds-across the entire model domain. For Case C, the sensitivity of conditions to surface exchange parameterization is relatively small in most diagnostics. Consequently, we now focus on Case B, although we return to Cases A and C later. Figure 7 shows the differences between the M IGP S A87 experiment and the two control experiments in key diagnostics over consolidated/pack ice (light gray), the MIZ (dark gray) and open water (black) within the target region (defined as the region enclosed by the red dashed line in Figure 6), time-averaged over the 60-hr duration of Case B. As with the results of Section 3, these differences broadly align with expectations. Figures 8-10 provide spatial context to the results illustrated in Figure 7, showing map plots and roughly-meridional-oriented cross sections of key diagnostics at the time of "peak" Case B conditions. The most notable differences between the M IGP S A87 and M Op S Op experiments are in the winds (Figure 7a). Mean wind speed in the target region is ∼0.7 m s −1 weaker over pack ice and the MIZ in the M IGP S A87 experiment, reflecting enhanced surface drag over these surfaces (c.f. Figure 3a). The mean difference over the open ocean is smaller (∼0.25 m s −1 lower in the M IGP S A87 experiment), however Figure 8 shows significant instantaneous wind speed differences elsewhere over the ocean, both within and above the ABL. This includes a relative weakening of a low-level wind jet that emerges from the Peninsula south of the Scoresby Sund Fjord and extends southwards; and a relative strengthening of the northerly winds over the Iceland Sea to the east of the transect line in Figure 8.
Between the M IGP S A87 and M IGP S Op experiments, the differences in wind speed are generally small, but there are significant differences in the other key diagnostics (Figure 7b). Mean air temperature and humidity within the target region are lower in the M IGP S A87 experiment over all three surface types, but most so over the MIZ, with differences of ∼1.2 K and ∼0.1 g kg −1 , respectively. These differences in air temperature and humidity correspond with differences in mean sensible and latent heat fluxes, which are lower in the M IGP S A87 experiment by 31 and 13 W m −2 , respectively, over the MIZ, owing to smaller surface scalar exchange coefficients (c.f. Figure 3). Figure 9 shows potential temperature maps and cross sections illustrating the typical ABL structure seen during a CAO (e.g., Renfrew & Moore, 1999). The surface exchange experiments clearly show significant differences in 11 of 20 the structure of the inversion-capped ABL as it evolves and deepens downwind of the MIZ. Significant differences in potential temperature (of at least 0.5 K; Figure 9b) and specific humidity (not shown) persist in the ABL for hundreds of kilometers downwind of the MIZ. Due to weaker upward sensible heat fluxes (Figures 10a and 10c), the ABL warms at a slower rate over the pack ice and MIZ in the M IGP S A87 experiment, than the M IGP S Op experiment, so at the sea-ice edge the near-surface air temperature is up to 2 K cooler and is cooler for hundreds of km downwind (Figure 9b). This makes the air-sea temperature gradient in the M IGP S A87 experiment larger, resulting in 12 of 20 larger upward SH fluxes over the ocean; as a consequence, the ABL temperature increases at a faster rate between the sea-ice edge and ∼300 km downwind along the transect and the ABL is 100-300 m deeper (Figure 9). Mean surface temperature over sea ice in the target region is significantly lower in the M IGP S A87 experiment than in the M IGP S Op experiment: ∼0.7 K lower over pack ice, and ∼0.6 K lower over the MIZ (Figure 7). Figure 10d shows that in some regions this deficit can reach 1.5 K, broadly coinciding with the largest time-averaged air-temperature deficits (note shown).
Note that although we lack in-situ observations with which to validate model performance for this case, the impact of the new scheme here is consistent with the beneficial impact it had for the broadly similar conditions observed during IGP (presented in Section 3), including during Case A.  Figure 7, but for Cases A and C, respectively. The case-mean sensitivities shown in Figure 11 for the CAO conditions of Case A are qualitatively and quantitatively similar to those for the CAO conditions of Case B. This reflects the fact that although Case B was stronger (in terms of wind strength) at its "peak" (see Figure 6), it was more intermittent over its duration than Case A. For the WAI event of Case C, qualitatively similar differences are apparent between the M IGP S A87 and M Op S Op experiments, with significantly weaker mean wind speeds in the former, by 0.5-0.6 m s −1 over pack ice and the MIZ. However, the differences between the M IGP S A87 and M IGP S Op are far smaller. During Case C, warm on-ice advection results in statically stable conditions over the sea ice, which suppresses turbulence and leads to relatively weak heat fluxes directed downwards into the ice. The weakened fluxes lead to only modest differences in air temperature, humidity and surface heat fluxes between the WAI model sensitivity experiments (Figure 12). There is a more significant difference in surface temperature over pack ice-albeit a reduced one relative to cases A and B-again with the lower mean value in the M IGP S A87 experiment, by ∼0.4 K over pack ice. This is a result of reduced downward surface heat transfer over ice in the M IGP S A87 experiment (c.f. Figure 3). However, it should be noted that the mean surface sensible heat flux over pack ice is not, as might be expected, greater in the M IGP S A87 experiment. This appears to

Wider Implications
In Sections 3 and 4 it has been shown that introducing aerodynamic-roughness dependence to surface scalar exchange over sea ice in aerodynamically rough conditions results in significant changes in simulations of the Arctic ABL over and downwind of sea ice, and that doing so is vital if 0 is allowed to vary regionally in a physically realistic way. These findings match our expectations based on an analysis of the surface exchange coefficients derived using simplified ("offline") forms of the parameterization schemes. However, our simulations have been limited to rough conditions. In this section we extend our analysis of the "offline" parameterisations to explore the behavior of sea-ice surface exchange parameterization configurations across the full range of plausible aerodynamic roughness conditions.  Figure 13 shows the surface exchange coefficients over sea ice as functions of * for both IGP and ACCACIA aircraft observations, and for the M Op S Op , M IGP S Op and M IGP S A87 parameterization schemes. The observations are binned by * , and include all those where the observed sea-ice fraction is >0.5. We use this threshold to obtain a larger set of observations, and so a more robust analysis, with the justification that similar mean values are found for higher sea-ice fraction thresholds.
For the M Op S Op scheme, the surface exchange coefficients do not vary with * as all roughness lengths are fixed. For the M IGP S Op scheme, sensitivity to * is present only through variability in 0 (c.f. Equation (10) Figure 13a). Moreover, given that variability in * is dominated by that in 0 (see Figure 5e in E21), the relationship between and * shown in Figure 13a is dominated by self-correlation. Note this is not the case for the relationships between the scalar exchange coefficients and * shown in Figures 13b and 13c (as established in E21; their Appendix A).
For most of the rough regime ( * > ∼10), Figure 13 corroborates the parameterization performance results discussed above. The M Op S Op scheme is shown to underestimate surface drag (Figure 13a), and to relatively accurately reproduce surface scalar exchange (Figures 13b and 13c). The latter is, as previously mentioned, a result of compensating errors; 0 is too small and so, according to Equation 5 and 6, 0 and 0 must be too large. The M IGP S Op scheme corrects the surface drag but considerably overestimates the surface scalar exchange in the rough regime. The M IGP S A87 scheme not only corrects the surface drag but also reproduces both surface scalar exchange coefficients to a relatively accurate degree; biases in and being less than half the respective observed median values for each * bin (with the exception of one bin-that of 10 4 < * < 10 5 -for , though note there is only one observational data point in this bin).
For smooth and transitional conditions ( * < 2.5), 0 and 0 are, in observations (e.g., Andreas, 1987Andreas, , 2010E21) and in theory (Andreas, 1987), roughly proportional to 0 , and so setting 0 0 and 0 0 to constants is appropriate (see Figure 2). Consequently, as illustrated in Figure 13, the M IGP S Op and M IGP S A87 schemes perform well for both surface drag and scalar exchange for smooth and transitional conditions. The M Op S Op scheme on the other hand overestimates both surface drag and scalar exchange, due to the overestimated 0 , 0 and 0 . Note there is a convergence in all three parameterization schemes, and in the observations, at * ∼6 in Figure 13. Here, the values assigned operationally in the MetUM for 0 , 0 0 and 0 0 are all appropriate, likely reflecting previous intentional tuning of these parameters to this moderate * value. Recall the results shown in Figure 13 pertain only to conditions over consolidated sea ice; however, Figure 3 demonstrates that, for the most part, the performance of the surface exchange schemes over consolidated sea ice qualitatively reflects their performance over lower sea-ice concentrations. Therefore, the parameterization implications discussed in this section can be considered qualitatively representative of surface exchange over any ocean model grid cell containing sea ice. Figure 13 and the analysis presented in this section encapsulates that the surface exchange scheme currently operational in the MetUM is only appropriate for both momentum and scalar exchange across a narrow range of aerodynamic roughness conditions. Optimizing this scheme for surface momentum exchange whilst keeping its handling of scalar exchange the same (with 0 and 0 changing linearly with changes in 0 ) widens this range to include the lower aerodynamic roughnesses (the smooth and transitional regimes) but is hugely detrimental to the reproduction of scalar exchange at the higher aerodynamic roughnesses (the rough regime). This is because whilst in the smooth regime a change in 0 changes both momentum and scalar exchange through skin friction; in the rough regime a change in 0 changes surface-layer pressure gradients, which directly affects momentum exchange through form drag but not, in theory, the scalar exchanges. As illustrated here, a parameterization that accounts for the aerodynamic roughness, such as the Blended A87 scheme, is necessary for accurate reproduction of both momentum and scalar exchange across the full range of roughnesses.

Discussion and Conclusions
Turbulence in the atmospheric boundary layer (ABL) provides a pathway through which physical and chemical constituents are exchanged between the atmosphere and the frozen oceans of the polar regions. This air-sea-ice "communication" is a vital component of the polar and global climate systems and is chiefly governed by the concentration and properties of sea ice. Recent advances in our understanding of the drag exerted by sea ice on the atmosphere, via both skin drag from surface friction and form drag from ice floe edges, have led to improved representation of surface momentum exchange over sea ice in numerical weather and climate models. However, the treatment of surface scalar (notably heat and percentiles (whiskers). The number of data points in each bin is shown at the median value. Gray background shading marks the transitional aerodynamic roughness regime, to the left of which ( * ≤ 0.135) is the smooth regime, and to the right of which ( * ≥ 2.5) is the rough regime. For each panel, the total number of data points plotted (N) is given. moisture) exchange over sea ice in such models has remained crude. In this study, we have tested a new parameterization for this scalar exchange in a state-of-the-art NWP model (the MetUM); the Blended A87 scheme, which accounts for the important influence of aerodynamic roughness (i.e., the roughness Reynolds number, * ) on the relationship between scalar and momentum exchange over consolidated sea ice, in line with long-standing theory and recent field observations.
We have tested the impact of the new Blended A87 scheme in the MetUM using in-situ aircraft-derived surface-layer turbulence observations and MetUM simulations of a persistent cold-air outbreak (CAO) characterized by cool, northerly winds over the Iceland and Greenland Seas. The observations were obtained as part of the field campaign of the Iceland-Greenland Seas Project (IGP).
In the sea ice surface exchange scheme currently operational in the MetUM, the exchange coefficients for both momentum and the scalars are functions of sea-ice concentration only (i.e., 0 , 0 0 and 0 0 are fixed). This crude treatment of surface exchange over consolidated sea ice is unphysical outside of a narrow range of * values. In aerodynamically rough conditions, momentum exchange is generally underestimated, as revealed by a positive mean wind speed bias of ∼1 m s −1 (against aircraft observations) in operational MetUM simulations; however, owing to compensating errors in the roughness lengths for momentum and the scalars, the scalar exchange is reproduced with reasonable accuracy. In aerodynamically smooth conditions, we demonstrate that overestimates in both surface momentum and scalar exchange are to be expected, although we have not explored this in the context of full MetUM simulations here.
To isolate model sensitivities to the scalar component of the surface exchange scheme, and in anticipation of future advances in the treatment of surface roughness due to sea-ice topography, we have run additional MetUM simulations in which momentum exchange over consolidated sea ice is optimized by prescribing 0 from the IGP observations. We show that replacing the operational treatment for scalar exchange with the Blended A87 scheme yields substantial improvements in model skill; reducing mean biases in surface sensible heat flux, surface latent heat flux, air temperature and surface temperature from 25 to 11 W m −2 , 22 to 12 W m −2 , 0.8 to 0.0 K, and 1.4 to 0.8 K, respectively. This impact is large relative to reported biases in reanalysis products in this region. We have demonstrated that these improvements are predominantly the result of the new scheme's sensitivity to 0 , via * , and that its sensitivity to wind speed is of secondary importance.
To evaluate the broader impact of the Blended A87 scheme on ABL conditions in a model, we have explored, independently of our observational data, the sensitivity of the MetUM to surface exchange parameterization for three case studies that exemplify distinct meteorological conditions across the Iceland and Greenland Seas. In simulations of a strong, long-lived CAO case that occurred a few weeks after the IGP field campaign, replacing the operational scalar exchange treatment with the Blended A87 scheme causes a reduction in the time-averaged total surface turbulent heat flux over the MIZ (consolidated ice) of 44 (16) W m −2 -20% (50%) of the mean values of 215 (33) W m −2 in the operational simulation-and corresponding reductions in low-level air temperature and surface temperature of 1.2 (0.3) K and 0.6 (0.7) K, respectively. Furthermore, significant changes in the properties and structure of the ABL are apparent for hundreds of kilometers downwind of the MIZ. In simulations of a long-lived warm air intrusion, the impact of the new scheme is generally much smaller, owing to the suppression of ABL turbulence under conditions of elevated static stability.
There may be scope for extending the Blended A87 scheme to incorporate the effect of turbulence generated over ice floe edges, for example, using the framework suggested by Lüpkes and Gryanik (2015). However, further work is required using observations to verify the physical basis for this.
The results of this study demonstrate that introducing aerodynamic-roughness dependence to the parameterization of surface scalar exchange over sea ice through the implementation of the Blended A87 scheme has the potential for considerable improvements in the prediction of polar weather and climate, and consequently of surface temperature and sea ice. This is particularly the case under aerodynamically rough conditions, which have recently been found to characterize a large proportion of sea ice in the Arctic Ocean (albeit based on ship measurements that are limited to the MIZ) (Srivastava et al., 2022). However, to fully harness these benefits in global model simulations, it is necessary to represent spatiotemporal variability in the topography of consolidated sea ice on aerodynamic roughness. This remains a major challenge for the modeling of surface fluxes over sea ice. Presently, we lack understanding of the factors that govern this variability across the Polar Oceans, and there is a paucity of observations to constrain it, especially in the Southern Ocean where marked differences ELVIDGE ET AL.

10.1029/2022MS003305
19 of 20 in sea-ice characteristics relative to the Arctic Ocean may require accounting for in parameterization schemes (Weiss et al., 2011). Finally, whilst there is the potential to use satellite observations and/or sea ice models to derive sea ice surface roughness lengths for assimilation into weather and climate models, there is as yet no substantiated method for doing so.

Data Availability Statement
This study uses aircraft-based observations from the ACCACIA and IGP field campaigns. These observations are available at CEDA via British Antarctic Survey (2014) for the ACCACIA data set, and via Renfrew (2019) for the IGP data set. The study also comprises of model simulations in the Met Office Unified Model (MetUM). For reproducibility, Section 2.1 describes in detail the baseline MetUM configuration used for these simulations, whilst Section 2.4 describes in detail the sea ice surface exchange parameterisation settings used in each individual simulation. The simulations were carried out on the MONSooN supercomputer. MONSooN is a collaborative facility supplied under the Joint Weather and Climate Research Programme, a strategic partnership between the Met Office and NERC.