Ocean Mixing with Lead-Dependent Subgrid Scale Brine Rejection Parameterization in a Climate Model

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1 J. Ocean Univ. China (Oceanic and Coastal Sea Research) DOI /s ISSN , (4): Ocean Mixing with Lead-Dependent Subgrid Scale Brine Rejection Parameterization in a Climate Model Meibing Jin 1), *, Jennifer Hutchings 1), Yusuke Kawaguchi 2), and Takashi Kikuchi 2) 1) International Arctic Research Center, University of Alaska Fairbanks, AK 99709, USA 2) Japan Agency for Marine-Earth Science and Technology, Yokosuka , Japan (Received July 9, 2012; revised August 24, 2012; accepted September 9, 2012) Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2012 Abstract Sea ice thickness is highly spatially variable and can cause uneven ocean heat and salt flux on subgrid scales in climate models. Previous studies have demonstrated improvements in ocean mixing simulation using parameterization schemes that distribute brine rejection directly in the upper ocean mixed layer. In this study, idealized ocean model experiments were conducted to examine modeled ocean mixing errors as a function of the lead fraction in a climate model grid. When the lead is resolved by the grid, the added salt at the sea surface will sink to the base of the mixed layer and then spread horizontally. When averaged at a climate-model grid size, this vertical distribution of added salt is lead-fraction dependent. When the lead is unresolved, the model errors were systematic leading to greater surface salinity and deeper mixed-layer depth (MLD). An empirical function was developed to revise the added-salt-related parameter n from being fixed to lead-fraction dependent. Application of this new scheme in a climate model showed significant improvement in modeled wintertime salinity and MLD as compared to series of CTD data sets in 1997/1998 and 2006/2007. The results showed the most evident improvement in modeled MLD in the Arctic Basin, similar to that using a fixed n=5, as recommended by the previous Arctic regional model study, in which the parameter n obtained is close to 5 due to the small lead fraction in the Arctic Basin in winter. Key words climate model; sea ice brine rejection; ocean mixing; parameterization 1 Introduction The polar sea ice extent has been an important indicator of global warming in recent decades. One of the difficulties affecting sea ice prediction in climate models has been that sea ice thickness is highly heterogeneous over a wide range of spatial scales, from several meters to hundreds of kilometers in the polar oceans. Convergence and divergence of sea ice in the polar oceans is manifest in ridged or rafted ice and leads. Current climate-model grids (ranging from 10 to 100 km) are unable to resolve sea ice features such as ridges and leads/polynyas with widths of 5 to 1000 m and lengths of 1 to 50 km (Morison et al., 1992). Multi-category approaches are used to represent the subgrid ice thickness distribution in sea ice models (Hibler, 1980; Bitz et al., 2001). The fluxes of brine rejection during ice formation and freshwater during ice melt exert strong impacts on the seasonal cycle of the upper ocean halocline. These fluxes differ greatly under different ice thicknesses, even with the same meteorological conditions (Maykut and Untersteiner, 1971). However, the standard ocean model in climate models uses a * Corresponding author. Tel: mjin@alaska.edu single-column ocean grid to communicate the average of fluxes through multi-category sea ice thickness. Although the ocean model can simulate the sinking process of icerejected salt, the spatial scale of the convention is much larger and weaker than the real ocean, in which convection occurs only under lead or thin ice, which represents a small fraction of the ocean grid cell. Several studies on parameterization of the subgridscale sinking of salt rejected during ice formation have significantly improved climate-model simulations of ocean convection, salinity profiles, etc., by uniform distribution of salt in the upper 160 m (Duffy and Calderia, 1997); uniform distribution of salt in the upper mixed layer defined by the depth with potential density 0.4 kg m -3 greater than the surface (Duffy et al., 1999); and exponential distribution of salt in the upper mixed layer, defined by the depth with density gradient greater than 0.02 kg m -4 (Nguyen et al., 2009). Duffy s model is global, and Nguyen s model is Arctic regional and optimized with CTD observations. Since the size mismatch between the lead and model grid is the key reason for the above parameterization, this study aims to address the impacts on the parameterization by the fraction of lead in a model grid. It is clear that when the lead fraction is close to 100% in a model grid, the parameterization becomes unnecessary. The lead frac-

2 474 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): tion, therefore, should play a role in parameterization through lead-fraction-dependent parameters and should switch on/off in the parameterization. In Section 2, we first use idealized model experiments to illustrate the effects of lead fractions on simulated vertical salinity profiles and mixed layer depth (MLD), and further derive a lead-fraction-dependent parameter for the parameterization scheme. Section 3 discusses comparison between different parameterization schemes in the widely used Community Earth System Model (CESM) of the US National Center for Atmospheric Research (NCAR), which includes the Parallel Ocean Program (POP) and the Los Alamos sea ice model (CICE) as ocean and sea ice component modules. experiments (Table 1) are conducted with varying lead areas, and the lead percentage (or fraction) is evaluated in a 30 km by 30 km box in 1 km resolution model cases (A1 to A900, referred to as A case thereafter). The salt is added at one grid point (100%) in the 30 km horizontal resolution model case (B1). Since the total brine rejection rate is the same in each case, the larger the lead area, the smaller the rate per unit area. 2 Idealized Model Experiments of Lead Fraction Effects on Climate-Model Grid Average 2.1 Model Setting A series of numerical experiments were conducted using the 3-D Princeton Ocean Model (POM) (Mellor, 2004, no sea ice model), forced with the same total brine rejection rate, though different lead fractions within a climate model grid size (30 km 30 km is used in this section, but varying in the real climate model application). The POM is a 3-dimensional ocean model solving primitive equations of velocity (u, v, w in horizontal x, y, and vertical sigma directions), temperature (T), and salinity (S) fields with an embedded second-order turbulence closure submodel (Mellor and Yamada, 1974) used to provide vertical mixing coefficients. The model domain is configured with horizontal grid points and a uniform depth of 180 m, which is deep enough to have little bottom boundary effect on the simulation of the upper mixed layer. There are 60 uniform vertical layers, or 3 m/layer. The Coriolis parameter is set as constant s -1 in the whole domain. The open boundary condition is cyclic in both the x and y directions. Other model settings for all experiments are as follows: 1) Initial water temperature and salinity are horizontally uniform, using the Polar Ocean Profiler System (POPS) data from April 17, 2010 (or day 1, Fig.1a), at the North Pole Environmental Observatory (NPEO). In the upper Arctic Ocean, where temperature is near freezing under sea ice, density is mainly a function of salinity. The initial ocean condition is stable and stationary (zero velocity). The model runs for 40 d. 2) The model is forced with surface brine rejection (first vertical layer of the model) for the duration of the model run. The surface brine rejection is added in the middle of the model domain to reduce the impacts of boundary conditions. The rate of brine rejection is equivalent to freshwater freezing 50 m 3 s -1 in the lead (lead area is different in each case but the total salt added is the same). We use a 30 km horizontal grid to represent the typical climate model resolution in the Arctic. A series of model Fig.1 Initial salinity and temperature profiles in the idealized model settings. Table 1 List of idealized model experiments. The variables (i, j) denote the horizontal grid index, and ( i, j) denote the range of the lead around the center of the model domain. Horizontal resolution (km) 1 ( i, j) of the lead 1, 1 2, 1 3,1 2,2 5,1 6,1 7,1 8,1 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 15,15 20,20 30,30 Lead area (km 2 ) Lead percentage in a 30 km by 30 km box (%) Case name A1 A2 A3 A4 A5 A6 A7 A8 A9 A16 A25 A36 A49 A64 A81 A100 A225 A400 A , B1 2.2 Model Errors Analysis The rejected salt sinks down with less horizontal mixing in the surface, but with more at the base of the MLD, as shown in a section view of case A8 (Fig.2). In order to compare with coarse climate model results with the same rejection rate, we averaged S and T in 1 km grid cases in a 30 km by 30 km box (containing the lead) and then calcu-

3 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): lated the density and MLD (Fig.3). In this study, MLD is all calculated using the same diagnostic method as used in the ocean model in NCAR s CESM. This method was introduced in turbulence k-profile parameterization (KPP, Large et al., 1994), which provides a smoothly varying MLD rather than a stair-wised one by a density gradient criterion (with changes in increment of one model layer thickness). The model salinity profiles on day 4 are largely different for A-cases with different lead fractions (Fig.3a), even though the total rejected brine (lead area times freezing rate) in the grid is the same. The smaller the lead fraction, the smaller the salinity increase at the surface and the greater at the base of MLD, thus, the more tilted the salinity profile. The MLD tends to be shoaling in small lead-fraction cases and deepening in the larger lead-fraction cases (Fig. 3b). The change in MLD is almost linear during the first 4 d, though it will gradually begin fluctuating afterward, as the added salt will eventually spread out of the averaging box from the base of MLD (Figure not shown). By contrast, the simulated salinity profiles and MLD in case B1 (Fig.4), which represents standard climate-model treatment of the rejected salt with a coarse 30 km grid, show a vertically uniform increase in salinity within the mixed layer and a gradual deepening of MLD over time. These characteristics are quite similar to case A900, with rejected salt added evenly in the 30 km by 30 km box (Figure not shown). If we consider the A-cases as a true solution, the coarse model has obvious errors in MLD and salinity profile in the mixed layer, especially when considering that the sea surface salinity (SSS) is too great and MLD is too deep. Since salinity profiles and MLD are different for different lead-fraction cases (Fig.3), the errors in the coarse model are lead-fraction dependent. Fig.3 Comparison of a) salinity profiles in day 4 and b) MLD time series from 1 km grid cases. The profile and MLD are averages of the 1 km model results in a 30 km by 30 km box centered by the lead. The lead fractions are 0.11%, 0.33%, 0.56%, 0.89%, 1.78%, 5.44%, 11.11% for cases A01, A03,, A100 in the legend. Fig.2 A cross-lead section view of the modeled salinity and velocity on day 4. The model grid is 1 km and the lead size is 1 km 8 km. The vertical velocity is multiplied by 100 in order to show directions. The salt flux in the lead can penetrate through the MLD (42.3 m in the initial profile), and the horizontal spread of the salt plume increases with depth until it reaches the neutral buoyancy near the bottom of the MLD. Fig.4 Time series of simulated salinity profiles and mixedlayer depth (MLD) in a 30 km grid model setting. 2.3 Lead-Fraction Dependent Parameterization To reduce ocean model errors caused by subgrid-scale brine rejection, parameterization has been introduced in

4 476 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): previous studies (Duffy et al., 1999; Nguyen et al., 2009). This method can be summarized in the following form of vertical distribution of added salinity in the upper mixed layer (Nguyen et al., 2009): in which (a, b, c) = ( , , ). The correlation coefficient between log(n c) and log(p) is 0.99, with significance test p-value (Fig.5b). The fitted curve displays increased n-values as the lead percentage decreases. In Eq. (2), the case of n = 5, recommended by Nguyen et al. (2009), corresponds to a very small lead percentage (0.054%). In Eq. (2), the parameter n turns negative when the lead fraction is greater than 25%, which corresponds to large opening and widely spread freezing in a grid cell; subgrid-scale parameterization is no longer needed under these conditions. In climate models, the lead fraction is known, but the shape of the lead is unknown. Fortunately, this relationship is consistent for different lead shapes, including squares and narrow but long strips (Table 1). n Az, if z D sz ( ) = 0, f z > Dsp sp. (1) Here z is depth, D sp is upper mixed layer or salt plume depth, n is an adjustable parameter and implies the distribution power of salt with depth, and A is determined by the total brine rejection, the distribution power n, and the mixed layer depth (Nguyen et al., 2009). The Duffy et al. (1999) method is equivalent to the case of n = 0 with D sp being the depth with density 0.4 kg m -3 greater than the surface density; Nguyen et al. (2009) otherwise found the model best fitted with various CTD data when n = 5 and with D sp being the depth with a density gradient greater than 0.02 kg m -4 in the Arctic Ocean. In this study, we calculate D sp as the MLD following Large et al. (1997): the shallowest depth where the local, interpolated buoyancy gradient matches the maximum buoyancy gradient between the surface and any discrete depth within that water column. In this method, MLD is derived from vertical temperature and salinity profiles. For each A-case listed in Table 1, parameter n can be estimated (by a non-linear least squares fit method) using the vertical salinity profile, averaged between days four and six in the 30 km 30 km area. The method is as follows: 1) Calculate the salinity anomaly using the average vertical salinity profile minus the initial salinity profile. 2) Calculate coefficient A in Eq. (1) by letting the sum of the salinity anomaly ( S) in the mixed layer be equal to the vertical integration of the right side of Eq. (1) in the mixed layer: n + 1 A = Δ S. n 1 D + sp 3) Estimate n using the salinity anomaly profile within the mixed layer and Eq. (1). The lead fractions (p) and parameters n (>0) of all A cases are used to best fit a curve (Fig.5a), as described by the following equation: b n = a p + c, (2) Fig.5 Best fitted parameter n using 1km case with various lead in a 30 km 30 km box: a) fitted curve of n vs. lead fraction p in the box; b) linear correlation and student test p-value of log (n c) vs. log (p). 3 Application of Lead Fraction Dependent Parameterization in the CESM Ice-Ocean Model The CESM is a typical and widely used climate model and was chosen in this study to test the effectiveness of the lead fraction dependent parameterization, though the process study should be easily applicable to other climate models too. The model includes active sea ice and ocean modules (CICE and POP2). The coupled POP and CICE utilize the global GX1 ocean grid (with nominal 1-degree horizontal resolution and x, y, z dimensions at ), with a displaced North Pole in Greenland (see cesm.ucar.edu/models/). The horizontal grid in the Arctic is between 30 and 45 km. Vertical resolution is 10 m in the upper 150 m, and increases to a maximum of 250 m in deep oceans. The model forcing is by six-hourly NCEP reanalysis forcing from 1988 to The air-sea fluxes

5 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): of the data set are corrected according to Large and Yeager (2009) in the CESM for non-fully-coupled model runs without active air-sea feedbacks. Four experiments were conducted: 1) control run without parameterization; 2) case n0 (n = 0); 3) case n5 (n = 5); and 4) case nv (n varies according to Eq. (2)). The parameterization schemes are implemented in the ocean model, but the ice concentration and salt flux during ice formation are from the sea ice model. The modeled sea ice extent in the northern hemisphere (Fig.6; only the control run is shown, as the results are very close for all cases) reasonably reproduces seasonal and interannual variations compared with remote sensing data from the National Snow and Ice Data Center (NSIDC). The simulated sea ice thickness distribution at one grid point in the Canadian Basin was compared with submarine measurements (Fig.7) from the Scientific Ice Expeditions (SCICES), The highest percentage of thickness is distributed around 1 m for both the model and observation, though the model shows more thick ice but less thin ice. The modeled mean ice thickness in the grid is around 20% less than the observed for both the control and nv cases, with the thickness of the nv case only slightly greater than that of the control case. This indicates that the parameterization offers only slight feedback to the sea ice simulation. The reason here may be that the temperature in the upper mixed layer, under sea ice, is already at the freezing point, and the changes in ocean vertical heat flux caused by the parameterization are very small compared to the effects from atmospheric forcing. Fig.6 Comparison of the monthly modeled and NSIDC sea ice extent in the northern hemisphere. The ocean model solves the primitive equations using hydrostatic and Boussinesq approximations. The current version of POP2 includes many features through many years of continuous developments, summarized in Danabasoglu et al. (2012). In this study, we used the standard model parameter setting, except for background diffusivity, which is changed to north of 68 N, for this value is important for the correct modeling of the Arctic halocline, according to regional ice-ocean modeling studies by Zhang and Steele (2007) and Nguyen et al. (2009). In this implementation, we assumed, for comparison, all brine rejection is from lead as in Nguyen et al. (2009). We will work on differentiating brine rejection from different ice categories in future studies. MLD from the turbulence k-profile parameterization (KPP, Large et al., 1994) was used as D sp in Eq. (1). The cases n0, n5 and nv are only different by the parameter n in Eq. (1), but the resulting differences are comprehensive, including differences for vertical profiles of salinity, temperature and MLD. Fig.7 Comparison of modeled thickness distribution with submarine ice draft measurements (SCICEX97 data). The date, latitude/longitude ranges and mean ice thickness in the grid are shown in the legend. Model results were compared with two year-long vertical profiles of CTD data from 1) the Surface Heat Budget of the Arctic data (SHEBA, October 1997 to September 1998, track in Fig.8a); and 2) an ice-tethered profiler (ITP, operated by Woods Hole Oceanographic Institution, October 2006 to December 2007, track in Fig.8c). Both CTD instruments moved passively with sea ice. The observed temperature and salinity were averaged daily in 10-m vertical layers in the upper 150 m, and MLD was calculated using the same method as in POP2. The modeled T, S, and MLD were extracted from the same location and time of the CTD data. The observed MLD showed weak seasonal variation with SHEBA data (Fig.8b) but strong seasonal variation with ITP data (Fig.8d), maybe due to their different locations. All cases showed wellmodeled shallow MLD in the summer (July to September) due to ice melting, and gradually deepening MLD in early winter from October to November due to strong ice formation. There were large differences in MLD among cases during late winter, from December to May (Figs.8b and d): 1) the observed MLD stopped deepening and fluctuated around 20 m in SHEBA and between 20 and 40 m in ITP; 2) the MLD in the control case continued deepening and reached a maximum of 80 m in both Figs.8b and d; and 3) all cases with parameterization showed improvements (less MLD deepening), and cases n5 and nv were very similar and most improved (closest to observation), in agreement with the n5 case in Nguyen et al. (2009). The similar results of cases nv and n5 indicated that the

6 478 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): lead fractions in the Basin area were far less than 1% and the resulting n was close to or larger than 5, for model improvements were more sensitive for small n than for larger n (e.g., n > 5). The root mean square errors (RMSE) of the modeled T and S (Table 2) showed improvements for all cases with parameterization over the control case, although the improvements were more significant for salinity, which is the focus of the parameterization. The improvements of modeled temperature were probably in effects of the subgrid scale mixing correction; but since the temperature in the upper mixing layer was at the same freezing point, the improvements were small and limited to the base of MLD. The improvements in case n0 were generally smaller than those in cases n5 and nv. The salinity improvements in ITP for cases n5 and nv were almost twice that in SHEBA, indicating that the improvements may vary largely in time and location. The salinity improvements were uneven in different vertical layers. The mean (over the entire CTD time series) salinity (Figs.9a and 9b) showed that the salinity for case nv was most improved in the upper mixed layer. The model errors in case nv were well reduced to match SHEBA data in the upper 30 m and m, but only slightly reduced between 40 and 130 m (Fig.9a). The upper mixed layer salinity in case nv was also most improved in the ITP data comparison (Fig.9b), but the remaining errors were still high (2 psu). These errors may be caused by errors in many related processes, including errors in atmospheric forcing, the heavy ice melt in 2007, the strength of Beaufort Gyre to trap freshwater in the upper mixed layer in the Canadian Basin, etc. Model errors cannot be corrected by the employed parameterization alone. The March mean MLDs of the n0 and nv cases (the results of case n5 are very similar to case nv and thus not shown) in 2007 were compared with that of the Polar Science Center (PHC; Steele et al., 2001) 3.0 dataset (Fig. 10). Significant differences were shown over the entire Arctic Basin areas, with large over-estimation in the con- Fig.8 (a) SHEBA track; and (b) comparison of MLD from model cases and ITP data along the track. The * indicates the position on the first day of each month. c), d) are similar to a), b) but for ITP data. Table 2 Root mean square errors (RMSE) of modeled T and S in the upper 150 m along the tracks of the SHEBA and ITP (the numbers in the table are in the form of SHEBA/ITP). Relative improvement (%) over control case = (RMSE Control RMSE Case )/RMSE Control 100. SHEBA ( )/ITP ( ) Control Case n0 Case n5 Case nv RMSE of T ( ) 0.462/ / / /0.495 RMSE of S 0.930/ / / /1.285 Relative improvement of T (%) 6.9/ / /15.8 Relative improvement of S (%) 3.6/ / /21.9

7 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): Fig.9 Vertical salinity profiles of all cases. a) SHEBA; b) ITP. Fig.10 March mean MLD of a) PHC3.0 climatology; b) Case control; c) Case n0; d) Case nv of trol case. The model cases did not show differences in permanently open oceans, as expected. The errors in MLD were most reduced in the nv case, indicating that the lead-fraction dependent parameterization is effective to improve ocean mixing processes in climate models. 4 Summary Ocean mixing under sea ice is a critical process for the Arctic Ocean. It influences the seasonal cycle of the halo-

8 480 Jin et al. / J. Ocean Univ. China (Oceanic and Coastal Sea Research) (4): cline, the freshwater budget, ocean-sea ice-air exchange of heat and salt, and sea ice area and extent. Using a series of idealized, high-resolution, lead-resolving model experiments, this study first analyzed the characteristics of the vertical distribution of rejected brine and MLD and their comparison to low-resolution model results (with resolution equivalent to that of the current climate models). When the lead is unresolved, both the vertical salinity profile and MLD show systematic errors resulting in a saltier sea surface and deeper MLD, and this can cause severe model drift in long-term climate model runs. The errors related to added salinity by brine rejection were found to be lead-fraction dependent according to the model experiments. An empirical lead-fraction dependent parameterization of subgrid-scale mixing by brine rejection was developed to derive a parameter n as a function of lead fraction in a model grid. Empirical function showed significant correlations between the parameter n and lead fraction, consistent over different shapes of lead. The lead-fraction dependent parameterization also clarified that the parameterization is necessary only when lead fraction is small, and this was shown in the large model improvements in the Arctic Basin vs. the small changes in seas with seasonal ice cover (Fig.10). The parameterization is unnecessary where lead fraction is large (>25%), e.g., the simulation of salinity change in large polynya (Hu et al., 2011). Model experiments in CESM with lead-fraction dependent parameterization showed significant correction of model errors in simulating MLD and vertical salinity profile over the control run and case n0. The close results revealed that the average parameter n was close to 5 in the Arctic Basin, due to the very small lead fraction. The remote sensing ice concentrations in winter (not shown) are very close or equal to 100% in the Arctic Basin, but the accuracy of the satellite instruments is not sufficient enough to detect very small lead fractions. Limited in situ measurements using up-looking sonars from submarines and moorings in the Canadian Basin showed that lead fraction is normally less than 0.1%. Direct observations of ocean mixing under lead brine rejection are needed in the future to study model errors related to ocean mixing caused by brine rejection. Acknowledgements This work was funded by the University of Alaska Fairbanks, the International Arctic Research Center under NSF Climate Process Team (CPT) projects ARC and ARC This research was also funded through grants to the International Arctic Research Center, University of Alaska Fairbanks, from the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), as part of JAMSTEC and IARC Collaboration Studies (JICS). Thanks Mrs. Dapeng Qu and Kaiguo Fan for their works at the early stage of the project. References Bitz, C. M., Holland, M. M., Weaver, A. J., and Eby, M., Simulating the ice-thickness distribution in a coupled climate model. Journal of Geophysical Research, 106 (C2): , DOI: /1999JC Danabasoglu, G., Bates, S., Briegleb, B. P., Jayne, S. R., Jochum, M., Large, W. G., Peacock, S., and Yeager, S. G., The CCSM4 ocean component. 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