The Nucleus for European Modeling of the Ocean (NEMO) ocean model (https://www.nemo-ocean.eu/, last access: 24 March 2022) was used in bulk formula configuration to simulate the GOL region with two distinct simulations, both performed from 1 August 2012 to 31 July 2013. In bulk formula configuration, sea surface fluxes are computed from parameterized formulas using atmospheric and oceanic measurable variables as inputs, such as temperature and wind velocity. The following parameterized formulas are used to calculate the latent heat flux, QE, the sensible heat flux, QH, the longwave radiation heat flux, QLW, and the surface shear stress, τ: 1QE=ρ0ΛCE(qz-q0)|Δu|,2QH=ρ0cpCH(θz-SST)|Δu|,3QLW=QLW,a-ϵσSSTK4,4τ=ρ0CDΔu|Δu|. where z is the height above the sea surface the atmospheric variables are provided at, with the zero values (subscript “0”) representing the values at the sea surface. u is the horizontal wind vector, with Δu=uz-u0 as the difference between the wind velocity and sea surface current (assuming a no-slip condition at the ocean surface). q and θ are the specific humidity and potential temperature of air, respectively. Λ and cp are the latent heat of evaporation and the specific heat of water, respectively. ρ0 is the air density at the sea surface. SST is the sea surface temperature, with SSTK as the sea surface absolute temperature. ϵ is the sea surface emissivity, σ is the Stefan–Boltzmann constant, and QLW,a is the atmospheric longwave radiation. CE, CH, and CD are the coefficients of latent heat, sensible heat, and drag, respectively, and are defined in .

The net downward heat flux, Qnet, is described by the summation of the terms in the following equation : 5Qnet=QSW+QLW+QH+QE, where QSW is the downward shortwave radiation. Snowfall and precipitation are included in the simulation calculations but excluded here for brevity in the following sections, as the buoyancy loss due to the water flux at the surface is essentially negligible .

The NEMO model was run in the NEMOMED12 configuration using NEMO v3.6. The domain is shown in Fig. b; it covers the Mediterranean Sea and a buffer zone representing the exchanges with the Atlantic Ocean. This configuration features a horizontal resolution of 1/12∘ (roughly 7 km) and 75 vertical levels (with a variable vertical resolution from 1 m at the surface to 135 m at the bottom). The 3-D temperature and salinity fields are restored towards the ORAS4 global ocean reanalysis in the buffer zone. The conservation of volume in the buffer zone is achieved through strong damping of the sea surface height (SSH) towards the ORAS4 reanalysis. The Black Sea, runoff of 33 major rivers, and coastal runoff are represented by climatological data input from . A deeper explanation of the configuration and boundary conditions is given by in the following works: , , , , and . The initial conditions were provided by an ocean objective analysis by .

The atmospheric forcing used in the simulations were the outputs of RegIPSL, the regional climate model of IPSL , which used the coupling of the Weather Research and Forecasting Model (WRF) and the ORCHIDEE Land Surface Model . The run was a hindcast simulation (ERA-Interim downscaling) performed at 20 km resolution and spanning the period of 1979–2016 within the Med-CORDEX framework . The u and v components, specific humidity, potential temperature, shortwave and longwave downward radiation, precipitation, and snowfall were all used to force the ocean simulations.

For the “control” simulation, the forcings was used as is. For the “seasonal” simulation, the u and v wind components, specific humidity, and potential temperature were filtered (see Fig. ) over the entire domain shown in Fig. a. These variables were chosen as they are the primary variables that affect the surface flux calculations in the bulk formulae (Eqs. –). The variables relating to radiation and precipitation fluxes were left unchanged. The filtering removes the short-term anomaly-scale forcing from the forcing dataset (the phenomena with timescales of under a month), effectively removing the mistral's influence on the ocean response. This creates two separate forcing datasets, one with the anomaly-scale forcing included and one with just the seasonal-scale forcing (hence the designation of control and seasonal).

The filtering process was performed by a moving window average: 6χi=1i+N+1∑j=0i+Nxj, where χi is the averaged (filtered) value at index i of a time series of variable x with length n, where i=0→n. The window size is equal to 2N+1, which in this case is equal to 31 d. The ends have a reduced window size for averaging and thus show edge effects. The edge effects did not affect the forcing used for the NEMO simulations, as they were before and after the ocean simulation dates, as two full-year atmospheric-forcing datasets were used for the simulations.

The moving window average was applied to each time point per day over a 31 d window (i.e. for 3-hourly data, the time series is split into eight separate series, one for each timestamp per day – 00:00, 03:00, 06:00, etc. – then averaged with a moving window before being recombined). This was done to retain the average intra-day variability yet smooth the intra-monthly patterns, as the diurnal cycle has been shown to retard destratification by temporarily reforming a stratified layer at the sea surface during slight daytime warming. This diurnal restratification has to be overcome first before additional destratification of the water column can continue during the next day and is shorter than the typical mistral event length of about 5.69 d (Table ).

An important note must be made about the filtering process. The mistral primarily acts in the higher-frequency range but at a lower frequency than the diurnal cycle, as mentioned above. However, it also features signal strength in the lower frequencies on the seasonal scale. This is due to the fact that the mistral becomes stronger, longer, and more frequent during the preconditioning phase than during the rest of the annual cycle . The moving window averaging we have applied to filter the mistral out of the atmospheric forcing primarily removes the higher-frequency portion of the mistral's presence. However, it also removes part of the lower-frequency portion as well that other filters, such as the Butterworth filter, struggle with, without removing more of the seasonal signal that is not influenced by the mistral than intended. This reveals a very interesting point about the structure of the mistral and the use of “seasonal” and “anomaly” timescales. Since the Mistral primarily acts in the higher frequencies, the anomaly timescale will refer to both the higher- and lower-frequency portions of the mistral that were filtered out but will be treated mainly as referring to the higher-frequency portion in the discussion. The “seasonal” timescale will then refer to the remaining lower-frequency signal and average diurnal cycle post-filtering.

The result of the filtering is shown in Fig. . Temperature and specific humidity were filtered as is, while the wind speed was component (u and v) filtered, preserving the general wind direction (Fig.  wind direction polar plot). Due to the slow movement of intermediate and dense water, which is on the order of about a year for newly formed WDMW to move into the southern Algerian Basin and on the order of decades for total circulation , we assume the processes outside the NW Mediterranean subdomain in Fig. b that are affected by the filtering have a negligible impact on the GOL processes on the preconditioning phase timescale.

Mistral events will be used for developing the simple model in Sect.  for their role in driving buoyancy loss at the ocean surface. Events were determined from the WRF/ORCHIDEE dataset in combination with the ERA-Interim Reanalysis dataset . Two main criteria were used to define a Mistral event:

northerly flow with a streamwise flow direction ±45∘ about the south cardinal direction above 2 m s-1 at two locations simultaneously, i.e., at Montélimar, France (45.5569∘ N, 4.7495∘ E), and in the GOL (42.6662∘ N, 4.4372∘ E),

The events during the preconditioning period, 30 August 2012 to 21 February 2013, were then manually checked and edited to remove single-day gaps to better represent the data according to a visual inspection of the atmospheric-forcing data. For k mistral events, each event's duration, Δtk, and period from the beginning of the event to the next event, Δτk, was determined and is provided in Table  for the entire ocean simulation period (for further analysis regarding the selection of these criteria; see ).

A useful metric to quantify the vertical stratification of a column of water is the stratification index (SI; ; sometimes called the “convection resistance”). It is derived from the non-penetrative growth of the mixed-layer depth (MLD; i.e., without entrainment; ), which has been shown to be an accurate approximation for open-ocean convection : 7∂z∂t=B(t)N2(z)z, where N2 is the Brunt–Väisälä frequency, z is the vertical coordinate along the water column, ∂z∂t is the growth of the mixed-layer depth, and B is the potential buoyancy loss the water column can endure before removing stratification (in m2 s-3). Separating by variable and integrating results in the equation for SI gives 8SI=∫0DN2zdz, where D is the depth of water column. If N2 is assumed to be constant throughout the water column, the integral simplifies to 9SI=D22N2. SI provides a zero-dimensional index to track stratification and can be easily related to the buoyancy loss experienced by the water column due to the atmosphere. Because of this, in this article SI will be used as the diagnostic to track the atmosphere's impact on the stratification of the GOL waters.

To validate the model results, data from the HyMeX (https://mistrals.sedoo.fr/HyMeX/, last access: 24 March 2022) database were compared to the NEMO control simulation. Sea surface temperature (SST) data from Météo-France's Azur and Lion buoy were compared with the control simulation SST of the nearest grid point in NEMOMED12. Figure  shows the comparison. The Azur buoy data were missing SST measurements from 19 January to 10 July 2013, but where the data are available, NEMO corresponds well with the observations. The same is true for the Lion buoy data, which had measurements for the entire time covered by the simulations. This comes as no surprise, as the NEMOMED12 simulations' SST is restored to the observational dataset of . However, this also means that the calculated surface sensible heat fluxes should be fairly accurate, as both the sensible heat flux and latent heat flux calculations depend on the SST (Eqs. –).

Additionally, the control simulation density and potential temperature profiles were compared to conductivity–temperature–depth (CTD) measurements also procured from the HyMeX database. The CTD measurements were collected during the HyMeX Special Observation Period 2 mission. The CTD profiles collected at approximately the same time and location were averaged together to adjust for small variances and gaps in the data. The averaged profiles and their standard deviations are visualized in Figs.  and . The locations of the CTD profiles are shown in Fig. .

Like with the SST comparisons, the profiles from the nearest grid point in the control simulation domain were used for the CTD comparisons. The root-mean-square error (RMSE) and bias (calculated as the difference between the model values and the observation values) for each of the averaged CTD profiles and corresponding control simulation profiles was calculated and is presented in Table . Overall, the control simulation and CTD profiles are decently well correlated but not perfect, with low RMSE and bias for both density and potential temperature. The density profiles have an average RMSE that is lower than the average RMSE for the potential temperature profiles: 0.025 kg m-3 and 0.094 ∘C, respectively.

Argo float profiles from the HyMeX database were also compared to the control simulation, again with profiles from the nearest grid point being used. A total of 3118 potential temperature profiles within the box, bounded by the 40 to 44∘ N latitudes and the 2 to 8∘ longitudes, representing the GOL area were considered (see Fig. ). The average RMSE between the Argo profiles and control simulation profiles was 0.43 ∘C, with an average bias of 0.23 ∘C. These values are larger than the values of the comparison with the CTD profiles. However, considering the sheer volume of profiles and the fact that during stratified conditions the temperature can range over a few degrees from the surface to the lower layers, these results are not unexpected.

Temperature differences on the order of 10-2 ∘C are potentially all that is required to sustain an ocean convective cycle , and density differences for the same order of magnitude (10-2 kg m-3) are used to separate newly formed dense water during deep convection . This means our model results should be studied with a critical eye, as they may not be fully representative of the true ocean response, given the bias and RMSE values from comparing the simulation to CTD and Argo profiles. Additionally, meanders around 40 km in wavelength form due to baroclinic instability along the edge of the convection path . This could mean the deviations from observations are due to out-of-phase meanders around the convective patch region in the model relative to actuality. Regardless, we believe the simulations are accurate enough to provide interesting results for the transient and regional-scale response of the GOL, which covers the main interest of our study.

Figure shows the SI calculated over the GOL for both simulations: the top row is for the control simulation, and the bottom row is for the seasonal simulation. An important distinction between the two results is that deep convection is present in the control simulation but not in the seasonal simulation. This is more clearly seen in Fig. c (the closest NEMOMED12 grid point to 42∘ N, 5∘ E), as the control simulation MLD reaches the sea floor on 13 February 2013, while the seasonal MLD remains close to the sea surface. This confirms that atmospheric forcing with timescales less than a month, e.g., the mistral winds, provide a significant amount of buoyancy loss, as without them deep convection fails to occur. There is, however, still significant loss of stratification at the location of the GOL gyre in the seasonal simulation, which is visible in the bottom row of Fig.  for 13 February 2013. This spot of destratification is also present (but less so) in the preceding and proceeding plots of the same row.

To investigate the time series ocean response in more detail, a spatially averaged time series of the SI for both simulations was analyzed at the grid point nearest to 42∘ N, 5∘ E. These coordinates were selected as it is the point with the most destratification in Fig.  and is the typical center of deep convection in the GOL . The spatial averaging involved horizontally averaging the immediately adjacent grid points such that nine grid points in total were averaged, centered around 42∘ N, 5∘ E. The stratification index from the control simulation is given as the sum of δSI+SIS, while the stratification index of the seasonal simulation is given as SIS. The difference between the two, δSI, should contain the change in stratification due to shorter timescale atmospheric events, such as the mistral, because of the filtering performed in Sect. . δSI+SIS, SIS, and δSI are all shown in Fig. .

Both the control and seasonal runs start off with an SI value of 1.57 m2 s-2 (beginning of Fig. a) and then diverge at the first major mistral event starting on 30 August 2012. After diverging, the two runs remain diverged until the end of the simulation run time, ending with a difference of about -0.22 m2 s-2, which is seen in δSI (shown in Fig. b). As noted earlier, the most striking difference between the control and seasonal runs is the occurrence of deep convection in the control run, occurring when δSI+SIS is equal to 0 (also signifying when the MLD reaches the sea floor), and the lack of deep convection in the seasonal run, as SIS only reaches a minimum of 0.43 m2 s-2. Additionally, if only the anomaly timescale atmospheric forcing is considered, and therefore δSI is the only stratification change from the initial 1.57 m2 s-2, the roughly -0.6 m2 s-2 of maximum destratification that the anomaly timescale provides is not enough to overcome the initial stratification. This means that both the intra-monthly and the inter-monthly variability of the buoyancy loss, reflected in δSI+SIS, are required for deep convection to occur.

Another significant result is the timing of the deep convection. Deep convection initially occurs on 13 February 2013, which is before SIS reaches its minimum on 21 February 2013 but after δSI reaches its minimum on 11 December 2012. After δSI reaches its minimum, it stays around -0.43 m2 s-2 until May 2013, where it starts to increase. This means that while the induced destratification from the anomaly-scale forcing would have been able to overcome ∼0.6 m2 s-2 of stratification to form deep convection in December, the seasonal stratification was only low enough in February for both δSI and SIS to have a combined destratification strong enough for the water column to mix. In other words, the seasonal atmospheric-forcing destratified the already preconditioned water column into deep convection along with a simultaneous mistral event. This means buoyancy loss due to the anomaly forcing may not necessarily be the only trigger for deep convection, at least for this year. This can be seen more clearly in the MLD, as the MLD grows over two mistral events preceding it reaching the seafloor.

To connect the mistral to the ocean's response, we make the assumption that the response is a superposition of the seasonal response and the anomaly response. This means the effects of the mistral can be categorized as anomalies affecting the short-term anomaly timescale and studied separately from the seasonal response. In terms of the Brunt–Väisälä frequency, this linear combination is represented by N2=δN2+NS2, where δ denotes the anomaly terms and “S” denotes the seasonal terms. To determine the mistral's effect, we derive a simple model to describe the SI of the water column in response to atmospheric forcing (for the full derivation, see Appendix ). We start with the energy equation for incompressible fluids , then multiply the equation by -g/T0 to express the energy equation in terms of buoyancy, assuming that the ocean's density varies negatively proportionally with temperature, ρ=-βT. We then perform partial differentiation with respect to z to obtain an equation describing the Brunt–Väisälä frequency, N2, in response to the atmospheric forcing, given by a forcing function, F(t). Separating by timescale, we arrive at the following partial differential equations: 10DδN2Dt=-δF(t),11DNS2Dt=-FS(t). F(t) is preceded by a minus sign for ease of derivation, as positive quantities of F(t) mean heat (and thus buoyancy) is removed from the water column.

To simplify the seasonal timescale, we assume NS2 is only a function of time, t: 12∂NS2∂t=-FS(t).

Assuming a homogeneous seasonal Brunt–Väisälä frequency over the depth of the water column gives us the relation for the seasonal stratification index, SIS, and seasonal atmospheric forcing: 13∂SIS∂t=-D22FS(t).

To simplify the analytical solution for the anomaly timescale, we describe the advection term, V⋅∇(δN2), as a restoring term, R=α(δN2), which relates the overall Brunt–Väisälä frequency to its seasonal component, NS2, using the linear assumption made before. This means the restoring coefficient, α, represents the advective operation. This results in the following differential equation: 14∂δN2∂t+α(δN2)=-δF(t).

The solution for the seasonal timescale is relatively straightforward. As already shown, Eq. () relates the seasonal stratification, SIS, to the seasonal atmospheric forcing, FS(t). We have the following definition of FS(t) from Appendix : 15FS(t)=∂∂zqa,SgρcpT0=gρcpT0∂qa,S∂z, where cp is the specific heat capacity of water, taken as 4184 J kg-1 K-1; g is gravity; ρ is the density of water, taken as 1000 kg m-3; and T0 is the reference temperature, taken as the average seasonal sea surface temperature of 292.4 K. This means SIS can be related to the seasonal volumetric atmospheric heat transfer, qa,S. Setting qa,S=-Qnet,S/D, where Qnet,S is the seasonal net downward heat flux at the ocean surface from Eq. (), we can calculate ∂SIS∂t from Qnet,S. If we integrate both sides of Eq. () using z, after plugging in Eq. () and the relationship for Qnet,S, as SIS is constant with respect to (w.r.t.) z, Eq. () becomes 16∂SIS∂t=g2ρcpT0Qnet,S, where g2ρcpT0≈10-9 m4 J s-2, which means the derivative of SIS w.r.t. time, t, multiplied by 109 is on the same order of magnitude as Qnet (with the subscript S now dropped for convenience, as the rest of the subsection discusses seasonal heat fluxes), which is what we see in Fig. a for the 2013 winter, with ∂SIS∂t×109 following the curve of Qnet. This relationship means when Qnet crosses zero with a negative derivative, SIS experiences a maximum and vice versa for a minimum. Additionally, the longer Qnet remains negative, the more seasonal destratification is incurred by the ocean. The seasonal variation of Qnet is primarily driven by the solar radiation, QSW, which is evident in Fig. b. Consequently, the maximum and minimum values for SIS occur around 21 September and 21 March, the fall and spring equinoxes. The asymmetry in Qnet is mostly caused by the slightly seasonally varying latent heat flux, QE, followed by the sensible heat flux, QH, both of which also decrease the net heat flux by roughly 100 to 200 W m-2, depending on the time of the year. QLW remains roughly constant during the year, decreasing Qnet by roughly -100 W m-2. These results are corroborated by the results of multiple model reanalysis for the region as well .

Equation () and Fig.  convey that the seasonal stratification is primarily driven by shortwave downward radiation. The other terms, the longwave, latent heat, and sensible heat fluxes shift the net heat flux negative enough for the ocean to have a destratification–restratification cycle. If the net heat flux was always positive, stratification would continue until the limit of the simple model applicability. This is an important finding because if future years feature less latent and sensible heat exchange due to warming or more humid winters, there will be less seasonal destratification, requiring more destratification from the anomaly timescale to cause deep convection. Consecutive years of decreasing latent and sensible heat fluxes could form a water column that is too stratified to allow deep convection to occur.

To solve for the anomaly timescale, described by Eq. (), we assume δF(t) can be represented by a pulse function shown in Fig. . This pulse function assumes the primary forcing at the anomaly timescale is represented by the mistral events. Each Mistral event, k, has a duration, Δtk, and a period between the start of the current and following event, Δτk. δFk is the strength of the forcing for each event. Inserting this into Eq. () allows us to solve it in a piecewise manner. As with the seasonal timescale, we assume the water column has a homogeneous Brunt–Väisälä frequency, allowing us to make use of Eq. (). The restoring coefficient then only represents the horizontal advection, as the vertical component becomes zero with our assumption of a homogeneous N2. The last assumption is that the restoring coefficient remains constant for each section of the forcing function: 17δSIk(t)=δSIk-1(tk)+δFkαd1-eαd(t-tk)⋅e-αd(t-tk)[tk,tk+Δtk)δSIk-1(tk)+δFkαd1-eαdΔtk⋅e(αa-αd)Δtk-αa(t-tk)[tk+Δtk,tk+Δτk), where αd and αa are the restoring coefficients during ([tk,tk+Δtk)) and after ([tk+Δtk,tk+Δτk)) a mistral event, respectively.

Further assuming δFk=δF, Δtk=Δt, and Δτk=Δτ for all k, which results in a periodic pulse function with constant amplitude and period, we can simplify Eq. () using the sum of a finite geometric series. At the beginning of the preconditioning period, destratification has not yet begun, and therefore the initial δSI is zero, resulting in the following equation set: 18δSIk(t)=D22δFαd[1-eαdΔt1-e[(αa-αd)Δt-αaΔτ]k1-e[(αa-αd)Δt-αaΔτ]-1+1-eαd(t-tk)]e-αd(t-tk)[tk,tk+Δtk)D22δFαd[1-eαdΔt1-e[(αa-αd)Δt-αaΔτ]k1-e[(αa-αd)Δt-αaΔτ]-1+1-eαdΔtk]e(αa-αd)Δtk-αa(t-tk)[tk+Δtk,tk+Δτk), This final equation set allows us to describe the integrated effect of consecutive mistrals and to easily pick apart the effects of the mistral's different attributes, including the frequency of the events.

To determine the value of the restoring coefficients, a normalized function was derived for each section of a mistral event (derivation shown in Appendix  for during an event and Appendix  for after an event). The resulting normalized functions were fitted against the NEMO δSI results in Fig.  for the denoted ideal events in Table  (denoted as “d” for the dates with ideal destratification taking place during the event and “a” for the dates with ideal restratification taking place after the event) and given the average event values of Δt‾=5.69 d and Δτ‾=10.88 d. The result of the fitting is shown in Fig. , with αd having a fitted value of 0.235 d-1 and αa having a fitted value of 0.021 d-1. If we recall the meaning of αd and αa from the derivation of the simple model in Sect. , this means the advective term in Eq. () has a larger role in the destratification phase of the mistral event than in the restratification phase, as it is an order of magnitude larger. This result suggests horizontal mixing occurs between events, as a smaller value for the restoration coefficient during the restratification phase means the existence of weaker horizontal gradients than during the preceding destratification phase.

The strength of each Mistral event, δFk, was found in a similar way by solving for δFk after noting that the initial value of δSIk(tk) is equal to δSIk-1(tk) (derivation found in Appendix ). Following this, the values of δSI from the NEMO results in Fig.  were plugged in to determine the values of δFk (see Table  in Appendix A for the resulting values).

A complete and average mistral destratification and restratification event according to Eq. () is given in Fig. c, which took the average mistral values from Tables  and and the restoring coefficients from Appendix . During the event, marked in green, the mistral causes destratification. After the event, marked in blue, the ocean column restratifies until another event occurs (denoted by the dashed line). This is the same behavior we see in Fig. .

If we put together Eq. () with the duration and period information from Table  and mistral strength information from Table , we can create a time series of δSI to compare the integrated response of the simple model to the NEMO model results. This comparison is presented in Fig. . The simple model results resemble the NEMO simulation results quite well, which is expected as the fitted values for the restoring coefficients and the values for the Mistral event strengths are extracted from the NEMO model results. However, this means that a series of variable pulse like mistral events can recreate the patterns that we see in the NEMO results for δSI with decent accuracy. This essentially confirms that the mistral events are the primary driving component of the heat loss at the anomaly timescale that leads to destratification.

As we are comparing separate years together, the time series simulation results were spatially averaged over a larger area for the additional years: from 42 to 42.5∘ N and 4.25 to 5∘ E. Figures  and show the SI time series for the 1994 and 2005 winters, respectively. The increased spatial averaging reduces the extent at which the SI destratifies due to surrounding stratified water being averaged in, which makes the 2005 winter appear as though it is too stratified to deeply convect (0.22 m2 s-2), even though it is more destratified than the 1994 winter (0.36 m2 s-2). The MLD, however, clarifies that the 2005 winter experiences deep convection in the simulation results and the 1994 winter does not (not shown), which is consistent with other findings .

Similar to the 2013 winter simulation set, the seasonal run for the 2005 winter does not experience deep convection, again demonstrating the necessity to include forcing on both timescales for deep convection to occur. The 1994 winter reveals something just as interesting: the δSI is more negative for the 1994 winter, at -0.55 m2 s-2, than for the 2013 winter at the time of minimum control SI (with deep convection in the latter but not the former), at -0.43 m2 s-2. This means even a larger anomaly-driven destratification is not able to overcome the residual stratification in a non-convecting year, despite the fact that both the 1994 and 2005 winters each featured a lower maximum control SI than the 2013 winter: 1.83 m2 s-2 for the 2013 winter and 1.73 and 1.79 m2 s-2 for the 1994 and 2005 winters, respectively. This emphasizes the importance of the destratification caused by the seasonal forcing.

A note of interest for the 2005 and 2013 winters is the occurrence of the δSI minimum. In the 2013 winter, the minimum occurs significantly before deep convection (in December). For the 2005 winter, the minimum occurs roughly about the time of deep convection (around the beginning of March; seen more clearly in the MLD and not shown here), and also during a mistral event, much like the 2013 winter. However, unlike the 2013 winter, the seasonal destratification is less active at the time of deep convection, whereas the anomaly destratification drops almost -0.62 m2 s-2, most of it occurring during a larger mistral event, to start deep convection. This suggests that the mistral event occurring during this time triggers the deep-convection event. While deep convection does not occur in the 1994 winter, the δSI minimum is also at about the same time as the minimum in the control SI, with a small mistral event occurring at that date and with seasonal destratification remaining roughly constant. This suggests that if this year had further seasonal destratification or less initial destratification, the mistral may have been the main trigger for deep convection, along with the larger mistral event preceding it.

A note of interest for all three winters is the location of the seasonal SI minimum and the time of deep convection (or minimum of control SI for 1994). For the 2013 winter, the minimum is at roughly the time of deep convection but is almost a month later in the 2005 winter. And for the 1994 winter, the minimum occurs before the Control minimum. This begs the question of whether the location of the Seasonal SI minimum relative to the Control SI minimum is important, and, if this is the case, how important it is in terms of deep convection occurring or not occurring.

The seasonal sea surface fluxes for both years resemble the fluxes of the 2013 winter (see Fig. ). The solar radiation component drives the main shape of the SI time series, with the major component contributing to the asymmetry being the latent heat flux, followed by the sensible heat flux. However, in the 2005 winter, the latent heat flux has a larger heat loss value than the 1994 winter, reaching over 300 W m-2 vs. under 200 W m-2 in the latter, driving the net heat flux to be more negative and causing more destratification according to the simple model, resulting in deep convection encompassing a few days on either side of the beginning of March.

The simple model for the seasonal SI is fairly accurate for the 1994 winter, similar to the 2013 winter, but not quite as accurate for the 2005 winter (see Fig. ). For the 2005 winter, the simple model deviates during the deepest part of the winter. This could be due to more advective behavior captured by the destratification with the larger spatial averaging, which is neglected in the seasonal component of the simple model.

The simple model for the anomaly scale was calculated for both the 1994 and 2005 winters, following the same steps as in Sect. . The value of the restoration coefficients, αd and αa, were carried over from the 2013 winter analysis, with the mistral dates determined through the same process outlined in Sect.  and manually adjusted to fit the visual data (again with the same method described in Sect. ). The mistral strengths of the events during the preconditioning phase were determined through the same process as in Sect. . The mistral dates and strengths are presented in Appendix . The results are shown in Figs.  and , and the simple model follows the NEMO simulation results quite closely, only deviating majorly at extreme peaks and troughs, despite utilizing the restoration coefficients from the 2013 winter. This reinforces the importance of the mistral as a dominating factor for destratification on the anomaly timescale.

The different components of the mistral (strength, δF, duration, Δt, and period, Δτ) are separated in the same manner as for the 2013 winter to determine the main factor of the mistral leading to destratification according to these additional years. For the 1994 winter, the contributions due to strength, duration, and period are equal to -8.71×10-2, -6.39×10-2, and 5.83×10-2 m2 s-2 (recall that a larger period means less frequent Mistral events), respectively. For the 2005 winter, the contribution due to strength, duration, and period are equal to -1.51×10-1, -5.23×10-2, and 4.89×10-2 m2 s-2, respectively. The 2005 winter results have the same order of magnitude as the 2013 winter results, with all three winters having the same order of importance for the mistral attributes: first strength, then duration, and finally the length of the period. Only for the 1994 winter was the strength term found to not be as dominant as in the other years, with the term having the same order of magnitude as the other terms. However, as the order of importance was still the same for all 3 years, this aids the conclusion that the strength term of the mistral is generally its most important factor driving destratification.