A comparison of five surface mixed layer models with a year of observations in the North Atlantic

Five upper ocean mixed layer models driven by ERA-Interim surface forcing are compared with a year of hy- drographic observations of the upper 1000 m, taken at the Porcupine Abyssal Plain observatory site using profiling gliders. All the models reproduce sea surface temperature (SST) fairly well, with annual mean warm biases of 0.11 ° C (PWP model), 0.24 ° C (GLS), 0.31 ° C (TKE), 0.91 ° C (KPP) and 0.36 ° C (OSMOSIS). The main exception is that the KPP model has summer SSTs which are higher than the observations by nearly 3 ° . Mixed layer salinity (MLS) is not reproduced well by the models and the biases are large enough to produce a non-trivial density bias in the Eastern North Atlantic Central Water which forms in this region in winter. All the models develop mixed layers which are too deep in winter, with average winter mixed layer depth (MLD) biases between 160 and 228 m. The high variability in winter MLD is reproduced more successfully by model estimates of the depth of active mixing and/or boundary layer depth than by model MLD based on water column properties. After the spring restratification event, biases in MLD are small and do not appear to be related to the preceding winter biases. There is a very clear relationship between MLD and local wind stress in all models and in the observations during spring and summer, with increased wind speeds leading to deepening mixed layers, but this relationship is not present during autumn and winter. We hypothesize that the deepening of the MLD in autumn is so strongly driven by the annual cycle in surface heat flux that the winds are less significant in the autumn. The surface heat flux drives a diurnal cycle in MLD and SST from March onwards, though this effect is much more significant in the models than in the observations. We are unable to identify one model as definitely better than the others. The only clear differences between the models are KPP’s inability to accurately reproduce summer SSTs, and the OSMOSIS model’s more accurate reproduction of MLS.


Introduction
1 Climate models are important tools for understanding the climate and 2 its response to various forcings (Flato et al., 2013). The surface mixed layer 3 forms the boundary between the ocean and atmosphere, and regulates ex-  interior. 50 We discuss the coherence between observations and model output, and 51 coherence with surface forcing. Note that we use potential temperature and 52 practical salinity throughout, and all densities are potential density anomalies 53 (σ θ ) relative to the surface and will be given without units.  where the mean flow is relatively weak and eddy kinetic energy is moderate.

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The variability in physical properties is likely to be representative of large 89 areas of the mid-latitude gyres.

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As part of the OSMOSIS field campaign, profiling ocean gliders (Seaglid- between CTD locations of a typical ship-based hydrographic survey, and for 100 the purposes of this paper, we treat the data as if they had all been ob-101 tained at the same location. There is an implicit linkage between spatial and 102 temporal variability in glider observations, and here we choose to treat it as 103 purely temporal variability.

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The depth of the surface mixed layer is calculated using a threshold value 105 of temperature or density from a near-surface value at 5 m depth (∆T = 0.2 • C 106 or ∆σ θ =0.03), whichever is the shallower (de Boyer Montegut et al., 2004).

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(MLD is calculated in the same manner for each model, see section 3.2.) 108 Thus, we aim to find the MLD even in cases where temperature and salinity 109 vary with depth in a density-compensating manner, as well as cases where 110 density varies with depth due to changes in salinity rather than temperature.

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In 67% of the record the MLD is set by the density threshold, 19% by the 112 temperature threshold, and in 13% of the record the two thresholds give the 113 same MLD. There is no clear seasonal pattern in which threshold sets the 114 MLD. We chose 5 m as the reference depth because above that there are too 115 5 many gaps in the observational data due to the removal of salinity spikes 116 during quality control. Spiking in the near-surface is unfortunately common 117 in glider observations due to surface manoeuvres altering the flow of water 118 past the sensors, cooling or warming while at the surface and air bubbles and 119 particulates in/on sensors when leaving the surface. Note that this means 120 that MLDs shallower than 5 m cannot be identified. 121 Figure 2: Definition of seasons as used in this paper. a) MLD calculated from the observations (gray), and running mean MLD (blue) calculated at each observation time over a 5-day window (i.e., with a window extending from 2.5 days before that observation time to 2.5 days after that observation time). Black horizontal lines are at 25 and 100 m. b) standard deviation of the observed MLD, calculated over a 5-day window as for the running mean MLD. This will be referred to as the running standard deviation of MLD. Black horizontal lines are at 10 and 35 m. Black vertical dotted lines on both panels show the dates which divide the year into seasons, as labeled on b).
We divide the year into four seasons based on the behaviour of the ob-122 served MLD. The start of winter is deemed to be the day when the running 123 6 mean MLD, calculated over a 5 day window, is deeper than 100 m and the 124 running standard deviation of MLD (calculated over the same 5 day window) 125 is greater than 35 m (figure 2), and these criteria are fulfilled for a period 126 of at least 5 days. In other words, winter is the period when the MLD is 127 consistently deeper than 100m but is also quite variable due to the lack of 128 a strong pycnocline within the upper water column (see below). The start 129 of spring is deemed to be the day when the running mean MLD is shallower 130 than 100 m and remains so for a period of at least a week, consistent with 131 previous definitions used in this area (Lampitt et al., 2010b). Summer is 132 deemed to be the period when the running mean MLD is shallower than 25 133 m, and the running standard deviation of MLD is less than 10 m, i.e., the 134 MLD is consistently shallow and shows low variability due to the presence of 135 a strong pycnocline. Using these definitions, autumn is the period from the       All models use Jerlov water type 1B, which is considered to be an appro-  2D wave spectra m 2 s radians −1 Surface Stokes drift components * m s −1 * Obtained from 2D wave spectra + Surface stress calculated using drag coefficient and wind components  has no impact on the vertical mixing scheme itself, but for the PWP, KPP 257 and OSMOSIS models these are length scales that have actual numerical 258 Figure 4: Profiles used to initialize the models: a) potential temperature, b) practical salinity, c) potential density.
impacts. All MLDs and IMLDs will be shown as positive downwards.
where U is a horizontal velocity component, w is the vertical velocity com- where c k and c H k are dimensionless coefficients or stability functions, l k is a Yamada, 1982), 'k − ' (Rodi, 1987) and 'k − ω' (Wilcox, 1988 where h bl is the boundary depth, w b ent is the buoyancy flux associated where u * is the surface friction velocity and u s0 is the surface Stokes drift.

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For stable conditions the equation for the depth of the boundary layer is where w b L is the buoyancy flux averaged over the depth of the boundary The layer average buoyancy flux, w b L , is estimated by assuming that the 407 sum of the turbulent and radiative heating rates is constant over the depth 408 of the boundary layer (Kim, 1976), which gives where α E is the thermal expansion coefficient of sea water, I is the solar  to be a true feature with a certain percent confidence.
where P k is the mean power spectrum, k = 0, 1 ... N/2 is the frequency        obviously not present in a 1D model.

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It is worth noting, however, that local differences in MLS in this region 564 are unlikely to have a large influence on large scale climate modelling because 565 MLS does not directly affect the atmosphere in the same way that SST does.

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Biases in MLS over a wide area and long time scales might be important 567 since these would affect water mass formation and circulation, but that is 568 beyond the scope of this paper. in winter would lead to the formation of a higher density water mass than 574 that found in the real ocean, which could have implications for the wider 575 circulation. 576 We estimate equivalent density biases by calculating density for the ob-    TKE KPP OSMOSIS  MLD  21  23  22  22  23  23  IMLD  21  17  19 17 19     The surface heat flux also drives a diurnal cycle in MLD and SST from 789 March onwards, though this effect is much clearer in the models than in the 790 observations. We believe this is because the models and reanalysis forcing 791 data do not include a number of processes which complicate the observed 792 SST and MLD, so the diurnal cycle is less apparent in the observations. 793 We are not able to say that one model is 'better' than the others, they  It is noticeable that all models had low biases in MLD in spring and sum-805 36 mer despite the MLS and MLD biases in the preceding winter. This suggests 806 that initializing these models using a relatively low resolution profile (e.g.,

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from an Argo float) in late winter when stratification is low may give a quite 808 reasonable spring stratification, which could be useful in regions where higher 809 resolution profiles capable of resolving a steep pycnocline are not available.

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The variability in winter time MLD, which may be of significance for nutri-811 ent fluxes and winter bloom dynamics, is reproduced much better by model 812 IMLDs than model MLDs.

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Given the lack of differences between them, any of these models would 814 give similar results when used for modelling in seasonal areas similar to the 815 OSMOSIS site, i.e., at mid latitudes away from topography.