LTC Modeling Examples

Abstract: This chapter explores several features of the IOBL by combining observations and modeling based on local turbulence closure as incorporated into a numerical model described in Chapter 7. The intent is to elucidate certain features of the response of the upper ocean to variations in forcing that require consideration of the time dependence of the physical conservation equations.

First, we show that an interesting series of upper ocean measurements at the SHEBA site near the time of maximum insolation, when there was a clearly discernible diurnal signal in both temperature and downward turbulent heat flux at two measurement levels, can be adequately simulated. However, the simulation makes sense only if solar radiation penetrating the compact ice cover is significantly greater than has been typically assumed in the past.

Next is a simulation of events observed in late summer at the SHEBA site, when there was energetic inertial motion of the ice and upper ocean. Inertial oscillation nearly always implies strong shear in the upper part of the pycnocline, and early models of mixed-layer evolution (e.g., Pollard et al. 1973; Niiler and Kraus 1977) related the rate of mixed-layer deepening ("entrainment velocity") to a Richardson number involving the inverse square of the velocity of a uniform slab of water (volume transport divided by mixed-layer depth). In the slab model of Pollard et al. (1973), for example, the velocity was inertial and any deepening was confined to the first half inertial period unless the inertial velocity increased. This was an unrealistic limitation and much effort was devoted to elaborating how entrainment would take place at the base of the mixed layer, while still retaining the simplicity of constant temperature, salinity, and velocity in the mixed layer (and the shear that this implied at the mixed-layer/pycnocline interface). Our initial measurements from the AIDJEX Pilot Experiment demonstrated convincingly that the IOBL was not "slablike" but exhibited definite and predictable shear in the IOBL. McPhee and Smith (1976, their Figs. 8.11 and 8.12) included an example during a storm where on the second day, the Ekman layer was confined to levels well above the obvious pycn-ocline established by stronger forcing on the first day. Nevertheless, it remains an article of faith among many oceanographers that inertially oscillating slabs are a primary mechanism by which mixed layers remain mixed. In Section 8.2 we look at this from the perspective of a model forced with different boundary conditions.

M. McPhee, Air-Ice-Ocean Interaction, 145-171. © Springer Science + Business Media B.V., 2008

Finally, in Section 8.3 we examine a time from the MaudNESS project near Maud Rise in the Atlantic sector of the Southern Ocean, when the cold upper layer was very close to the same density as the underlying Warm Deep Water, despite being less saline. Here we use the model to illustrate how nonlinearities in the equation of state, and possibly, differences in thermal and saline diffusion, come into play.

8.1 Diurnal Heating Near the Solstice, SHEBA

During the SHEBA drift, in June 1998, there was a period of about four days with relatively steady and moderate winds, during which ice drifted at just under 2% of the wind speed (Fig. 8.1a). This was reflected in moderate friction velocities in the upper part of the well mixed layer (Fig. 8.1b), more or less typical of average conditions for the entire project. What was notable about this period, however, was a clear, albeit small, diurnal signal in temperature of the well mixed layer, lagging solar zenith by a few hours (Fig. 8.2a). Apparently there was enough solar energy making its way through the ice cover to warm the well mixed layer during local afternoon, with some of the excess heat lost to the ice via upward heat flux at the interface when sun angle was low.

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Fig. 8.1 a Wind speed at 10 m and ice drift speed after removing inertial component, 16-20 June 1998, at the SHEBA station. Ice speed ordinate range is 2% of the wind speed range. Time is shown as days of 1998, where 167.0 is 0000UT on 16 June. b. Friction velocity (square root of kinematic Reynolds stress) measured at two distances from the ice/water interface (see also colorplate on p. 208)

SHEBA Turbulence Mast Temperatures

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Fig. 8.2 a Three-hour average turbulence mast temperatures. Shaded circles represent local solar zenith, at approximately UT + 23h. b Corresponding heat flux measurements: pcp (w'T') (see also colorplate on p. 208)

The general picture of diurnal heating and nocturnal cooling was supported by turbulent heat flux measurements at the TIC levels (Fig. 8.2b). Although not so clean as the temperature records, heat flux also showed a diurnally varying signal with maximum downward (negative) flux at or shortly after local noon, and upward heat flux at night (solar nadir). There was an upward overall trend in temperature over the four days, typical of SHEBA during the early summer. This was consistent with the increase in temperature elevation above freezing (AT = T — Tf (S)), shown in Fig. 8.3a, suggesting that the trend resulted from local heating rather than advection of the ice station into a different water type. Incoming shortwave radiation was strong during this period (Fig. 8.3a), reaching a maximum of about 600 W m—2 late on day 168, but with significant day-to-day variation.

There were times during the period when heat flux at both levels approached zero (e.g., days 168.75 and 169.625 in Fig. 8.2b). Again reasoning that these times would provide an accurate "calibration bath," we calculated the difference in mean temperature between the TIC sensors, which was about 1.8 mK. Adjusting the lower thermometer by this amount for all the samples then provided an estimate of the temperature gradient between 4.2 and 8.2 m as a function of time. Comparison of the negative temperature gradient with the average heat flux from the two TICs shows the time series to be well correlated, despite the small magnitudes of both (e.g., a maximum absolute temperature difference between the two SBE thermometers of

Day of 1998

Day of 1998

Fig. 8.3 a Incoming shortwave radiation at the upper ice surface (data from the SHEBA Project Office installation, right caption) and departure of mast temperature from freezing (average of clusters 1 and 2 at 4.2 and 8.2 m, respectively). b Negative temperature gradient between clusters 1 and 2, after adjusting temperatures to agree at times near zero heat flux, along with turbulent heat flux averaged for both clusters (see also colorplate on p. 209)

Day of 1998

Fig. 8.3 a Incoming shortwave radiation at the upper ice surface (data from the SHEBA Project Office installation, right caption) and departure of mast temperature from freezing (average of clusters 1 and 2 at 4.2 and 8.2 m, respectively). b Negative temperature gradient between clusters 1 and 2, after adjusting temperatures to agree at times near zero heat flux, along with turbulent heat flux averaged for both clusters (see also colorplate on p. 209)

about 1 mK).1 To the degree that the different scale limits in Fig. 8.3b represent in the same way the variation in —dT/dz and pCp (WT'), their ratio provides a rough estimate of the mean eddy diffusivity throughout the period, namely about 2.5 x 10—3m2 s—1.

The period from day 167 to 171 (16-20 June 1998) was modeled as follows. Initially the temperature and salinity of the upper ocean were set to values measured by the SHEBA profiling CTD using a 3-h average centered at time 167.0. The upper boundary condition for momentum flux was specified (Section 7.2.2) from the time series of ice velocity after removing inertial motion. Surface roughness was assigned a value of 0.048 m from the "scaled up" analysis described later in Section 9.3.3. This is significantly rougher than the estimate for the immediate SHEBA Site 2 roughness (McPhee 2002), but was thought to be more appropriate for modeling thermal changes over the entire upper ocean. For the interface submodel, heat conduction in the ice was estimated from the temperature gradient in the lower 50 cm of ice at mass balance station "Pittsburgh," taken to be fairly representative of the entire floe. Over the four-day period, the average upward heat conduction in the ice based on this gradient was ~1.9W m—2.

1 For very small gradients, the adiabatic lapse rate in the well mixed layer is important; however, by calibrating the thermometers to a time of near zero heat flux, the difference between temperature and potential temperature has already been taken into account.

Solar radiation was introduced into the model water column by taking a fixed fraction (fsw) of the incoming surface solar radiation (Io) measured at the SHEBA Project Office site, and distributing it with an exponential attenuation in the upper ocean with an e-folding depth ¿sw = 4 m, to generate a source term

Parameters important in the interface submodel were assigned values: ah = 9.3 x 10~3, as = ah/35, and Sice = 6psu.

The main point of the modeling exercise was to gauge how much of the incoming radiation measured at the surface had penetrated the ice cover, in order to realistically account for both the diurnal variation and the secular trend in upper ocean temperature. The model results, run with three different values of fsw as shown in Fig. 8.4, indicate that about 8-10% of the short-wave radiation made its way through the multiyear ice floe. With these fractions, the model results indicate about the right amount of total heating over the four-day period (Fig. 8.4a), and show the same pattern of diurnal variation, although the model appears to somewhat underestimate the nocturnal cooling. Modeled friction velocity at 8 m is fairly accurate; mean values differ by less than 0.2mm s-1. At 4 m (not shown) average modeled u* exceeds measured by about 0.5mm s-1, perhaps not surprising because zo in the model is substantially larger than estimated for the smooth ice surrounding Site 2 (McPhee 2002).

Downward heat flux near maximum sun angle is modeled reasonably well at 8 m (Fig. 8.4c); however, the nocturnal upward (positive) heat flux is larger in the model than observed. At night the main heat sink in the system is basal melting, which in the model is consistent throughout the simulation period, so this might suggest that modeled basal heat flux is too large (i.e., ah is too large). This interpretation, however, is at odds with the relatively rapid observed nocturnal cooling (compared with the models) in Fig. 8.4a. A more likely explanation is that ice in the vicinity of the turbulence mast is smooth enough compared with the overall roughness of the floe (and model with zo = 4.8 cm) that the heat extraction from the water column is smaller than the average for the whole floe. Temperature of the well mixed layer would represent an integrated effect.

For the model run with fsw = 0.09, the mean basal heat flux was about 17 W m~2, which, when reduced by the small conductive flux in the ice, implied ice melt of around 2 cm over the four days. This produced an average buoyancy flux at the interface, {w'b')0 « 10~8W kg-1, which had little effect on turbulence near the surface, but produced a mean value for ^ of about 2.7 (Section 4.2.3). This is enough to reduce the dynamic boundary layer extent slightly (see Fig. 4.8).

When we first did these simulations, we were surprised that as much as 10% of the incoming solar radiation was making its way into the water. At the time, estimates from aerial photography put the fraction of ice area covered by open leads in the SHEBA region at about 2.5% (Perovich et al. 2002, their Fig. 8.6), providing effectively a lower limit on fsw. By mid June melt ponds had formed and were estimated to cover 15-20% of the surface (Perovich et al., op. cit.). Melt ponds

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Fig. 8.4 a Comparison of model well mixed layer temperature elevation above freezing in the upper 15 m of the water column with results from the SHEBA profiler. Dashed curve is for fsw = 0.09, envelope limits are shown. b Modeled (dashed curve, fsw = 0.09) and observed friction velocity at 8 m (error bars indicated ± one standard deviation of the 15-min realizations in each 3-h average). c Modeled and observed turbulent heat flux at 8 m typically reduce the surface albedo significantly and provide a potential conduit for short wave radiation entering the ocean. Still, discussions with G. Maykut (2000, personal communication) and others implied that, given the highly compact sea ice cover in the SHEBA region, it was unlikely that much more than 4% of the incoming radiation would be able to transit the ice pack, given commonly accepted values for shortwave broadband ice extinction coefficients (e.g., Grenfell and Maykut 1977). This was half or less than the amount of heating needed to produce the observed diurnal variation. The possibility of the ocean measurements being contaminated by the presence nearby of open water remained, but analysis of aerial photography indicated that any open water "upstream" of the ocean measurements was far enough away to have had little impact. The apparent discrepancy between the modeling example here and earlier estimates of light transmittance in ice appear to be resolved by recent work of Light et al. (2008). They report extinction coefficients for bare and ponded ice at SHEBA that are substantially smaller than previous estimates, and that 3-10 times as much solar radiation penetrates the ice cover than is predicted by current global circulation models.

8.2 Inertial Oscillations in Late Summer, SHEBA

By mid September at the SHEBA station in 1998, the ice cover was relatively compact, the well mixed layer had cooled to within few centikelvins of freezing but remained relatively shallow, as evidenced by strong inertial oscillations during much of the month (Fig. 8.5). Usually, the presence of strong inertial oscillation signals that the internal ice stress gradient is small enough that ice is in a "free-drift" state, i.e., wind driven. We chose a period during 14-22 September 1998, as a sort of "modeling laboratory" to look as different aspects of the upper ocean response (both modeled and observed) during a period of significant inertial oscillation. At 0900 on 14 September (257.375), the wind was still and ice drift speed near zero. Over the next five days, ice drift speed rose rather steadily to about 0.3m s_1, following wind closely at slightly over 2% of the wind magnitude (Fig. 8.5c). Late on day 262, wind dropped quickly, as did mean ice drift; however, a fairly strong train of inertial oscillations continued for several days.

8.2.1 Wind Forced Model

The first LTC model exercise (SEP 14A) was initialized with the SHEBA profiler 3-h average T/S data in the upper 61 m of the water column, and driven by wind stress for the period 257.375-265, obtained by applying a drag coefficient, cío = 0.002, to the observed 10-m wind at the project office tower, and using the dynamic boundary condition for stress (Section 7.2.3). During this period shortly after the start of freeze-up, the temperature gradient in the lower part of the ice was slightly positive, indicating that even in relatively thin ice at the end of the melt season, the downward "freezing wave" had not yet reached the ice base. This was incorporated into the model as a downward interface heat flux averaging about -0.6Wm-2. Since there was not a lot of open water, for simplicity, we assumed that the long wave radiative loss from open water would roughly cancel incoming short wave gain. Undersurface roughness was set at 0.048 m as above.

Modeled versus observed surface velocity (Fig. 8.6) demonstrates reasonable simulation of both the mean and inertial components of ice velocity, including

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Fig. 8.5 a Northward ice drift velocity during September of the SHEBA project from satellite global positioning data. b Eastward component. The arrow indicates time shown in: c Wind speed and drift speed during the time from 257.375 (0900 UT on 14 September 1998) to 265.0. The scale for ice speed is 2% of the wind speed scale (see also Colorplate on p. 210)

the energetic oscillations associated with the rapid change in drift direction from NW to N (see Fig. 2.3). Reynolds stress measurements are compared with model estimates in Fig. 8.7. In general, they follow reasonably well, although on day 259 friction velocity 6 m from the boundary is inconsistent with both the 2-m measurements and the model. This may be due to "upstream" disturbance in the underice morphology from the particular drift direction on that day. Modeled and measured turbulent heat flux (Fig. 8.8) are also reasonably matched, although the model underestimates heat flux at 2 m on day 262. The overall assessment is that the relatively simple, first-order closure model driven only by wind and initial T/S conditions is successful at simulating the main features of both surface velocity (including inertial oscillation) and upper ocean turbulent fluxes.

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Fig. 8.7 Modeled (dashed) and observed (square symbols, ut = \(u'w') + i (u'w')|1/2) for model run Sep 14A, at 2 m a and 6 m b from the boundary. Error bars represent ± one standard deviation of the 15-min samples in each 3-h average

258 259 260 261 262 263 264 265 Day of 1998

Fig. 8.7 Modeled (dashed) and observed (square symbols, ut = \(u'w') + i (u'w')|1/2) for model run Sep 14A, at 2 m a and 6 m b from the boundary. Error bars represent ± one standard deviation of the 15-min samples in each 3-h average a

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Day of 1998

Fig. 8.8 As in Fig. 8.7, except turbulent heat flux, pcp (w'T')

Day of 1998

Fig. 8.8 As in Fig. 8.7, except turbulent heat flux, pcp (w'T')

It is not nearly as successful, however, at reproducing the mean evolution of the upper ocean structure. In the model, for example, the well mixed layer salinity (Fig. 8.9a) increases substantially in response to strong surface stress from 261-263 as more saline water is mixed upward from the pycnocline. Observed salinity decreases. In the model, ST also increases by upward mixing of warmer water, counter to the downward trend in the observations. In the absence of other information, it would appear then that the model has underestimated the amount of melting, since in a one-dimensional view, melting is the only source of fresh water, and more rapid melting would lower ST. But contour plots of salinity from the profiler and the model point up some other major differences. In the model, the impact of mixing is minor below about 40 m and salinity in the lower part of the model domain remains the same, while in the data there is an overall freshening trend (downward sloping isohalines) with an upwelling-like event during the time of maximum stress and a rapid deepening of the well mixed layer on day 262.

In the absence of mixing from below, the only source of salt in the model domain is freezing (positive) or melting of ice. The integrated change in salt over the 60 m domain of run Sep 14A is

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equivalent to about 2 cm of ice melt. A similar calculation for As in the upper 60 m from the starting and ending SHEBA salinity profiles shows a change in salt content of about — 36kg m—2, requiring enough melting (1.7m) to completely eliminate the ice pack! Another model simulation (run Sep14B) was made in which a small constant advective source term was specified across the entire model domain at each time step:

where As(obs) is the observed total change in salt content in the upper 60 m over the ^8 days, making the modeled As match the observed value. The model results for stress are not much different from run Sep 14A; modeled heat flux is somewhat less. Results for ST in the well mixed layer (Fig. 8.11) show about the same overall decrease as in the data. The simulation is not meant to be very realistic, given the temporal changes evident in Fig. 8.10a, but rather to show that the observed decrease in ST probably resulted from advection instead than local vertical processes. In effect, the advective decrease in salinity as the station drifted north more than offset the upward vertical mixing of both salt and heat from the pycnocline.

An important point to be made from this exercise is that in general it is quite difficult to evaluate the performance of upper ocean models by testing their ability to simulate short-term changes in mean properties of the upper ocean. Often

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258 259 260 261 262 263 264 265 Day of 1998 Model Upper Ocean Salinity

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Fig. 8.10 Contour plots of salinity in the upper ocean from SHEBA profiler a and wind-driven model Sep 14A b (see also Colorplate on p. 211)

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Fig. 8.11 Comparison of modeled and observed dT for model Sep 14B with a small negative salinity source term as an approximation to advective flux

Day of 1998

Fig. 8.11 Comparison of modeled and observed dT for model Sep 14B with a small negative salinity source term as an approximation to advective flux relatively small horizontal gradients encountered as the ice drifts will swamp the signal from local vertical exchanges. On the other hand, vertical fluxes are often relatively immune to horizontal property gradients except in front-like conditions, hence in general provide a superior assessment of the particular mixing scheme used in the model.

8.2.2 Models Forced by Surface Velocity

A third model simulation of the same period (run Sep 14C) is identical to run Sep 14A except that the dynamic stress interface boundary condition was replaced by the surface velocity boundary condition as in Section 7.2.2. The same value (0.048 m) was used for zo. Apart from minor details the two simulations are similar for exchanges at the interface (Fig. 8.12) as well as the rest of the IOBL. The mean modeled values for friction velocity over the simulation period differ by about 10% (if Cio is increased to 0.0025 they match). During winter there are often periods when the ice clearly responds to wind forcing, but is also influenced by internal stress gradients. In this case, provided the geostrophic (sea-surface tilt) velocity is small compared to ice velocity, forcing the IOBL with ice velocity clearly is a better strategy than forcing by wind (unless ice stress is known).

Especially during winter, a common consequence of internal ice forcing is that inertial oscillation is severely damped even if the ice appears to be moving freely in response to the wind (McPhee 1981). An obvious question then arises: would the modeled response of the upper ocean be much different if inertial oscillation is absent? We performed a fourth simulation (run Sep 14D) of the September 14-22 period which was identical to run Sep 14C except that surface velocity was specified

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Model Sep14D: Northward Ice Velocity

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Fig. 8.13 Velocity (dashed) used to force the model run Sep 14D, compared with the actual ice velocity. a Northward component; b southward component

Day of 1998

Fig. 8.13 Velocity (dashed) used to force the model run Sep 14D, compared with the actual ice velocity. a Northward component; b southward component as the ice velocity after removing inertial components (i.e., forced by the Vo term in [2.22]). Surface velocity used to force the model is shown as the dashed curves in Fig. 8.13. Differences in results from the models forced by the complete surface velocity (run Sep 14C) and by surface velocity with inertial components removed are summarized at two levels in Figs. 8.14 and 8.15. The ML/Pycnocline level is defined as the deepest z (flux) grid point in the well mixed layer, i.e., where

It varies with time, but because of the strong initial stratification, remains relatively shallow, averaging about 15.4 m for each run.

That there is little difference in u*o between the models is not surprising (Fig. 8.14a) — we seldom see much inertial component in velocity measured near the ice (in a reference frame drifting with the ice), because the ice and upper ocean oscillate in phase, and mean shear is not much affected. Near the base of the well mixed layer, it is not obvious that inertial shear would be so unimportant, but according to the model comparisons (Fig. 8.14b), the impact remains relatively small. Similar results hold for the turbulent heat flux. There is some reduction in mean heat flux when inertial oscillation is removed: about 6% near the base of the well mixed layer, and 4% at the interface. Nevertheless, it appears that even with

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8.2.3 Short-Term Velocity Prediction

Development of the complex demodulation technique for analyzing sea-ice drift described in Section 2.5 (see also McPhee 1988) was spurred by a practical task of predicting where ice floes tracked by radar in the vicinity of exploratory oil drilling platforms in the Beaufort Sea might drift over the next few days. Inertial oscillations were a prominent feature in the radar tracked trajectories of nearby floes, with rapidly changing directions and speeds, so that depending on where the tracking picked up in the inertial loop, the floe might be headed directly toward the platform at high speed, then a short time later going in a quite different direction. Extrapolating future drift from a short history of observed drift thus required consideration of the inertial motion.

The problem of starting a model at a particular time for short term predictions is related to the fact that a simple harmonic oscillator (e.g., equation (2.22)), when forced from rest impulsively will oscillate continuously about a steady state that it never reaches. In reality, of course, the ice/IOBL system is not frictionless, yet it is clear from records like Fig. 8.5 that oscillations can persist for several days. In the SHEBA examples of Sections 8.2.1 and 8.2.2, the model was started from a time when wind and ice drift velocity were nearly zero, so impulsive initial forcing was not much of an issue. But suppose we wished to predict ice motion starting early on day 263, when the wind is high but forecast to diminish, and inertial motion is large. To highlight the problem, we drive the ice/IOBL system with the observed wind, initialized with T/S structure as observed at time 263.125, and started from rest (all velocities zero). Results for drift velocity (Fig. 8.16) show that although inertial oscillations are generated in the model, they are substantially out of phase with the observations and would be of little use in actually estimating where the floe would be in a short time.

To address this problem the IOBL model was initialized by (i) solving a steady version of the model (described in detail in Chapter 9), and then (ii) adding to the steady solution for velocities in the mixed layer, the inertial component of velocity from the complex demodulation record synthesized from the GPS positions (this assumes that the ice and IOBL are oscillating in phase). In this case (Fig. 8.17), the first few inertial cycles are much closer to the observations.

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263.2 263.4 263.6 263.8 264 264.2 264.4 264.6 264.8 265 Day of 1998

Fig. 8.16 Simulated surface velocity compared with observed for a model forced by observed wind and started from rest at a time of high wind stress and large inertial motion. The model quickly adjusts to the stress forcing, but generates its own inertial oscillations out of phase with the observations

Model Sep20B: Northward Ice Velocity

Model Sep20B: Northward Ice Velocity

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263.2 263.4 263.6 263.8 264 264.2 264.4 264.6 264.8 265 Eastward Ice Velocity

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263.2 263.4 263.6 263.8 264 264.2 264.4 264.6 264.8 265 Day of 1998

Fig. 8.17 Results from a model identical to that of Fig. 8.15 except that the initial velocity structure is specified by solving a "steady" version of the IOBL model given the wind stress at time 263.125, and adding the inertial component of velocity from satellite navigation analysis to the well mixed layer velocities

8.3 Marginal Static Stability, MaudNESS

The last example of applying the one-dimensional LTC model arises from another practical requirement encountered in planning for the MaudNESS experiment near Maud Rise in the Weddell sector of the Southern Ocean. The basic plan for MaudNESS was to perform a fast, relatively shallow CTD survey across the seamount, concentrating on the margins, and use a combination of special weather forecasts and ice concentration analyses to estimate the most likely regions for thermobaric instability and deep-reaching convection based on CTD stations made at different times and places. To this end a forecast model was needed that was simple enough to update several candidate profiles with every new (daily) weather forecast, with the goal of enhancing operational planning by identifying areas where mixing would occur in the least stable density environment. Overall, our objective was to measure turbulent exchange in a low stability environment to understand what conditions might remove the thin ice cover completely over a substantial area.

A comparison of upper ocean conditions during late summer at SHEBA in the western Arctic (79.9 °N, 161.6 °W) with late winter at MaudNESS in the Weddell (65.5°S, 001.1 °E) illustrates a striking contrast in static stability of the water column (Fig. 8.18). In the former (used to initialize the model run described in Section 8.2 above), potential density (Fig. 8.18c) increases by nearly 3.5kg m—3 in the upper 150 m, while for the latter (MaudNESS Station 91), the increase is two orders of magnitude less, about 0.03 kg m—3, and is barely perceptible when drawn at the same scale. Thus by comparison the Weddell profile is near to being statically neutral; nevertheless, there is a steep thermocline (Fig. 8.17a) starting at around 100 m with far more heat content close to the surface than in the Arctic. A much less obvious halocline (again when drawn at the scale appropriate for the Arctic) contributes to a slightly stable pycnocline (in potential density, less stable for in situ density) that separates the upper cold layer from the underlying Weddell Deep Water. Because of the low stability, it is relatively easy to mix heat upward from the large WDW reservoir, whenever there is vigorous stirring at the surface (which is common in the Weddell in winter). But this is the source of the thermal barrier (Martinson 1990) that melts ice when basal heat flux exceeds conduction through the ice cover, forming a shallower halocline that severely inhibits deeper convection. As the profiles indicate, the system is very delicately balanced. Note that below about 120 m in the MaudNESS profile, temperature and salinity are very uniform, indicating some active mixing activity.

In the operational mode, the model strategy was to use the weather forecast and ice concentration data provided daily via satellite communications from the Arctic Mesoscale Prediction System (AMPS) MM-5 regional model (Powers et al. 2003) to project ahead five days from the current time, keeping backward track at a particular location from the time at which an initial upper ocean structure was measured. This was done by accepting the "nowcasts" that initialized each daily weather forecast as valid analyses. Comparison of the nowcasts with ship observations were generally favorable, although the MM5 temperatures often appeared to be biased high by a few degrees. In this way, we could construct for a given location in the operation

8.3 Marginal Static Stability, MaudNESS Temperature

Salinity

-100

-150

8.3 Marginal Static Stability, MaudNESS Temperature

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-100

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Salinity

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30 32 34

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-100

-150

Fig. 8.18 Comparison temperature a, salinity b, and Go c profiles in the upper 150 m from SHEBA in the western Arctic on 14 September 1998 (dashed) and from MaudNESS in the Weddell Sector, Antarctica, 19 August 2005 (solid)

area a continuous record of wind, temperature, ice concentration, and other pertinent fields. In this section, we use such a time series to model the subsequent upper ocean conditions starting from observations about noon UT on 19 August 2005 at Maud-NESS Phase 1 station 91, and extending 20 days. Station 91 was chosen because it exhibited the lowest "thermobaric barrier" index (McPhee 2000) of the MaudNESS phase 1 survey. The 1-d ocean forecast model accounts for open water as stipulated in the supplied ice concentration data (averaged in a 90 km square centered on the station site) by assuming that when ice is absent, the surface loses 200 W m-2, and that, provided this exceeds heat flux from ocean, it forms ice that migrates away from the region (but leaves salt). The treatment is crude, but proved not very important since according to the imagery analysis, ice concentrations remained high during the modeling period. Heat loss through the ice was estimated by assuming a one-layer ice model with heat flux proportional to the air-ocean temperature difference divided by the ice thickness. Thermal conductivity in the ice was assumed to be 2W m-1 K-1. Surface momentum flux was estimated from MM5 surface wind with a 10-m drag coefficient 0.0015. The time series synthesized from the MM5 nowcasts at the Station 91 site is summarized in Fig. 8.19. Throughout the period, winds were moderate (by Southern Ocean standards) with an average temperature around -14 °C.

MM5 Wind, Site Maud 91

7 10

232 234 236 238 240 242 244 246 248 250

Fig. 8.19 Environmental parameters extracted from the MM5 model output: a 10-m wind speed; b 2-m air temperature; and c ice concentration

MM5 Wind, Site Maud 91

232 234 236 238 240 242 244 246 248 250

Air Temperature

b

232 234 236 238 240 242 244 246 248 250

Ice Fraction

232 234 236 238 240 242 244 246 248 250

Ice Fraction

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c

Y

232 234 236 238 240 242 244 246 248 250

Day of 2005

232 234 236 238 240 242 244 246 248 250

Day of 2005

236 238 240 242 244

246 248 250

232 234

236 238 240 242 244

246 248 250

232 234 236 238 240 242 244 246 248 250 Day of 2005

Fig. 8.20 a PD Model interface friction velocity (dashed) and departure of mixed layer temperature from freezing (shaded); b ice draft (shaded) and interface buoyancy flux (dashed) for an IOBL model where all density gradients are based on potential density. (see also colorplate on p. 211)

232 234 236 238 240 242 244 246 248 250 Day of 2005

Fig. 8.20 a PD Model interface friction velocity (dashed) and departure of mixed layer temperature from freezing (shaded); b ice draft (shaded) and interface buoyancy flux (dashed) for an IOBL model where all density gradients are based on potential density. (see also colorplate on p. 211)

In the modeling examples described below, the intent is not to faithfully predict the evolution of upper ocean structure at station 91 for the entire 20-day period (which is unknown), but rather to explore ramifications of mixing in a low static stability environment. To that end, the model was run first with all of the buoyancy flux dependent parameters calculated from gradients in potential density, and with no mixing (beyond molecular) below the IOBL extent, which was determined by dynamic conditions at the surface along with modeled changes in the temperature and salinity profiles. This model is designated PD (indicating that gradients depend on potential density) and its results are summarized in Fig. 8.20. Parameters that govern basal heat flux (friction velocity and elevation of mixed layer temperature above freezing) show that in the second part of the period, higher AT is somewhat compensated by lower u*o and lower air temperature, so that until the very end of the period, ice continues to grow as its upward heat conduction (plus small loss in open water) exceeds heat flux from the ocean. Total ice growth of about 12 cm supplies a small but nearly continuous negative buoyancy flux (dashed curve in Fig. 8.20b, mean value —2 x 10—8W kg-3). In the PD model, this contributes to turbulence in the IOBL and a slow deepening of the thermocline (Fig. 8.21). For the most part, the dynamic IOBL depth (white dashed curve in Fig. 8.21, defined here as the depth below which u* < 0.5 x 10—3m s—1) follows the thermocline closely. As upper layer salinity increases from the downward salt flux, the pycnocline weakens, until on about day 243, it erodes enough of the thermocline to cause a noticeable temperature spike

Model PD Temperature

Model PD Temperature

240 245

Day of 2005

Fig. 8.21 Contours of PD model temperature for the upper 200 m of the water column. The white dashed curve is the dynamic boundary layer depth, below which friction velocity is less than 0.5mm s—1

240 245

Day of 2005

Fig. 8.21 Contours of PD model temperature for the upper 200 m of the water column. The white dashed curve is the dynamic boundary layer depth, below which friction velocity is less than 0.5mm s—1

near the base of the upper layer, and a rapid increase in mixed layer temperature by about 0.1 K (Fig. 8.20a). Note that because of the large temperature contrast, minor deepening of the well mixed layer has large impact on its temperature, thus strongly reinforcing the "thermal barrier" effect.

During the 20-day PD model run, the density contrast between the upper and lower layers continues to decrease. In Fig. 8.22, the density jump across the ther-mocline is shown from two perspectives, one in which it is simply the difference in potential density (dashed), and the second when it is calculated at pressure corresponding to the depth of the thermocline (solid). The shaded areas are ther-mobarically unstable, i.e., water just above the thermocline, if displaced slightly downward, would be heavier than its surroundings. Any subsequent mixture of upper- and lower-layer water would be denser than either type by itself by virtue of the curvature of isopyncnals in T/S space (Fig. 2.11). To address this in the context of the one-dimensional LTC model, we formulated a simple algorithm as follows.

In the first-order-closure model, buoyancy flux is calculated as the eddy diffusiv-ity times the gradient in buoyancy frequency squared, N2 = (—g/p)pz, where in the model grid scheme (Fig. 7.1)

Azzi-i

232 234 236 238 240 242 244 246 248 250

Day of 2005

Fig. 8.22 Difference between density in the upper 5 m of the pycnocline and the well mixed-layer density, determined from potential density and density, where the latter refers to density calculated at pressure corresponding to the mixed layer/thermocline interface

232 234 236 238 240 242 244 246 248 250

Day of 2005

Fig. 8.22 Difference between density in the upper 5 m of the pycnocline and the well mixed-layer density, determined from potential density and density, where the latter refers to density calculated at pressure corresponding to the mixed layer/thermocline interface

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