We use the Regional Ocean Modeling System (ROMS), a primitive-equation, hydrostatic and free-surface ocean model that solves the Reynolds-averaged form of the Navier–Stokes equations. ROMS is a fully nonlinear, finite-difference model that uses terrain-following (sigma) vertical coordinates and horizontal orthogonal curvilinear coordinates on a staggered Arakawa C grid . The model domain (290×150) is rotated 52.14∘ clockwise to better resolve the NZNES and spans 332 km offshore at the widest point (near North Cape) (Fig. ). The domain has a horizontal resolution of approximately 2 km, which roughly captures coastline variability and still resolves the continental shelf and slope without large computational cost. The model has 30 vertical sigma layers, and model bathymetry was interpolated from the 250 m resolution bathymetric dataset built by the National Institute of Water and Atmospheric Research (NIWA – https://niwa.co.nz/our-science/oceans/bathymetry, last access: 27 June 2023). We use a vertical discretisation scheme that increases the resolution near the surface and bottom by applying stretching function type 4 and transformation equation option 2 . The vertical resolution is higher at the upper 200 m (4th–30th layer). On the slope (depth <1000 m), the vertical resolution is higher than 66 m, and in the open ocean the thickest level is 233 m (3838.6 m depth). The effect of bottom friction is parameterised using a constant drag coefficient of 3.0×10-3 , and the vertical mixing of tracers and momentum is done with K-ϵ , using the generic length scale (GLS) scheme . Baroclinic modes are resolved using a time step of 180 s, while the barotropic time step is 6 s.

Model surface forcing is from the Japanese atmospheric 55-year reanalysis for driving ocean models (JRA55-do; ). A previous study demonstrated that JRA55-do had the highest correlation with observed winds in comparison to other atmospheric forcing datasets in the southwest Pacific . Atmospheric forcing fields of wind speed, net shortwave radiation, downward longwave radiation, relative humidity, temperature, rain and pressure are provided every 3 h and are used to compute the surface fluxes of stress, heat and freshwater using the bulk flux parameterisation of . The model uses initial and boundary conditions of SSH, temperature, salinity and velocities from HYCOM–NCODA versions 91.1 and 91.2, which cover the period focus of this study. Annual average discharge from several rivers are included as lateral forcing in the model. The boundary forcing is applied daily using the condition for free surface, Shchepetkin condition for barotropic velocities and mixed radiation nudging for baroclinic velocities, temperature and salinity. A 5 d nudging coefficient is applied towards the lateral boundaries. The model aims to simulate continental shelf, slope and rise regions, including the offshore extent of the EAuC and its eddy variability. Tidal variability is not included in this study.

Remotely sensed observations of SSH and SST were used in all assimilative runs in this study. Optimally interpolated gridded maps of daily SSH with 1/4∘ of horizontal resolution created by AVISO were assimilated into the model. Daily SSH offsets (annual mean of ∼51 cm) were calculated prior to every assimilation cycle as the difference between the spatial average of observations and model daily averages for each assimilative experiment (1-year averages are shown in Fig. a as examples of this offset). These offsets were removed from AVISO observations before assimilation to ensure the comparisons were made on the same reference surface. Daily maps of SST (1/4∘) from AVHRR Pathfinder were used for assimilation into the model at a depth of 2 m. SSH and SST data were assimilated daily at 24:00 UTC in regions deeper than 200 m. Data points that are within 20 grid points of the boundaries were removed, and a total of 123 data points of SSH (or SST) were assimilated per day, with roughly an SSH/SST measurement every 12th grid point. We used an assimilation window of 7 d (see details in Sect. ), which gives a total of 861 SSH/SST data points per assimilation cycle (Table ).

A cross shelf–slope mooring transect collected data from 6 May 2015 to 21 May 2016 (Fig. a, b). In situ observations of temperature and salinity and u and v components of velocity from three moorings (M3, M4 and M5) were assimilated into the model (Fig. b). MicroCAT CTDs were located near the surface and bottom at the three stations, and two extra CTDs were located around 200 m at M4 and M5 (green dots in Fig. b). A total of 26 temperature sensors were evenly distributed between the three stations, with higher density of instruments in the upper 200 m water column (black dots in Fig. b). Two long-range (LR) and two short-range (SR) ADCPs were located at M4 and M5 (grey rectangles in Fig. b). The water column was binned every 15 m (LR) or 4 m (SR) by the upward-looking ADCPs. Velocity (temperature and salinity) measurements were taken during a period of 2 min (1 min) every 10 min or less. The dataset is freely available and can be found in . All in situ observations were low-pass filtered at a period of 30 h to remove tidal signals and their interaction with other processes, as in . The observations were averaged at time bins of 6 h, centred at 03:00, 09:00, 15:00 and 21:00 UTC. Types of observations, their sources and the median number of observations per assimilation cycle are shown in Table .

Independent data from 30 Argo profiles were used for model–data-independent comparison. More details on model evaluation are described in Sect. .

Data assimilation is applied in a series of time windows using strong-constraint 4D-Var, i.e. neglecting model errors . Tests using 2, 3, 4 and 7 d as assimilation windows were conducted, and the OSEs with a 7 d window had the most realistic results in comparison to observations. Results from a 2 d window reanalysis were also analysed in the current study. In this work, 4D-Var is used to adjust the control variables including initial, boundary and atmospheric conditions. The ocean analysis is obtained via minimisation of model-to-data discrepancy or cost function (J) given by 1J(δz)=12δzTD-1δz+12(Gδz-d)TR-1(Gδz-d), where δz is the state vector constituted of increments (corrections) to the initial δx(t0), lateral δb(t) and surface δf(t) conditions. D and R are the background and observation error covariance matrixes, respectively. Superscripts T and -1 represent the transpose and inverse operations, respectively.

G≡HMf, where H is the linearised version of the observation function H that maps the model state to the observation time and locations. The operator Mf denotes the tangent linear operator of the model integration about the forecast (denoted by the subscript f) over the assimilation window. For the transpose, GT≡MfTHT, HT maps from observation to model space, and the MT operation integrates backward in time over the assimilation window.

Gδz-d represents the mismatch between the tangent linear model fields mapped to the observations (Gδz) and the observations d, which is called the innovation vector and is defined as the difference between observations and model background interpolated to observation location. SSH observations had a daily bias (or offset) between data and model reduced from the observations before the innovation values were computed.

The combination of control variables δza that minimises J is yielded iteratively in the subspace spanned by the linear combinations of the observed model variables. The method chosen in the present work is the physical-space statistical analysis system (4D-PSAS), and the algorithm that minimises the cost function is shown in Fig. 2 in . 4D-PSAS defines δza as 2δza=DGT(GDGT+R)-1d. δza can be equivalently written as δza=DGTwa, where wa is the subspace of the model state vector spanned by the observations (i.e. the dual space) and satisfies

3(GDGT+R)wa=d. The dual form has the advantage that the dimension of wa is equal to the number of observations, which is, in our case, several orders of magnitude smaller than the dimension of the full state vector. Thus, solving Eq. () may be less demanding than solving Eq. () . In addition, the number of observations d in Eq. () increases with the assimilation window; therefore, it is expected that runs with longer assimilation windows (7 d) rely more on observations rather than on background terms.

In practice, we find an acceptable reduction in the model-to-data discrepancy after 20 iterations (inner loops) when atmospheric and lateral forcings are adjusted every 12 h along with initial conditions at the beginning of the assimilation cycle. For further details of the method and its application, readers are referred to .

The diagonal background/prior error covariance matrix D cannot be completely calculated or stored; it is rather estimated via factorisation . D takes into consideration the background error standard deviations of initial, boundary, and forcing conditions; spatial decorrelation scales; and normalisation factors . The background error standard deviations were calculated from the average of 4 d variances computed from 2 years of the NoDA run ocean (initial conditions), boundary and forcing fields. Spatial decorrelation scales are implemented on D to limit the impacts of observations within certain ranges. Horizontal decorrelation length scales for SSH, velocities and active tracers (temperature and salinity) were 100, 50 and 100 km. Vertical decorrelation length scales for velocities and active tracers were 50 and 100 m. The normalisation factors are the costliest part of the covariance modelling, but they are computed only once for each combination of background error standard deviations and spatial decorrelation length scales. The normalisation factors were estimated via randomisation using 7500 iterations. Figure 3 in shows an example of convolution of a unit impulse function with the horizontal (vertical) decorrelation length scale set to 100 km (50 m). For more details on the computation of the background error covariance matrix D, see .

The observational error covariance matrix R is assumed to be diagonal. The standard deviation used was the largest value between an assigned standard deviation and the observation error obtained from the AVISO and AVHRR products, with the assigned value being the highest most of the time. This strategy was applied to satellite observations, whereas in situ data used a given standard deviation only. According to values used in the literature (e.g. ), different standard deviations were tested, and the values that gave the best results were 0.04 m for SSH, 0.3 ∘C for satellite SST, 0.8 ∘C for subsurface temperature, 0.16 g kg-1 for subsurface salinity, and 0.15 m s-1 for water column u and v components of velocities. A large standard deviation was attributed to in situ temperature due to strong internal tides in the region and blow-down events that often happened at the three moorings. Depth of the thermistors was obtained assuming an inverted pendulum relationship between CTDs located near the surface and bottom , but a level of uncertainty remains in the depth of measurements. A summary of the observation standard deviation errors and the median number of observations per 7 d assimilation cycles is shown in Table .

Four data assimilation experiments and one free-running simulation (no data assimilation; NoDA) are part of the OSEs. The first data assimilation experiment incorporated SSH and SST and u and v components of velocity, mooring temperature and salinity (ASFUVTS). The other data assimilative experiments were similar but withheld subsurface temperature and salinity (NoTS), subsurface velocities (NoUV), and all mooring data (NoUVTS). Another experiment assimilating surface and all mooring data was also conducted using a 2 d assimilation window (ASFUVTS-2 d), which was designed to better match the observations. This experiment (ASFUVTS-2 d) differed from the other simulations in three aspects. It used 7 d variances to compute background error standard deviations and 200 km (m) as horizontal (vertical) decorrelation length scales of active tracers (temperature and salinity). The last difference is the 2 d assimilation window, which makes increments to the initial conditions more frequent. These modifications made ASFUVTS-2 d less comparable to the rest of the OSEs, but they were needed in order to achieve the best match between assimilated and independent observations – for results, see Sect.  and . Two other 7 d assimilation window experiments (ASFUVTS-2x and NoUVTS-2x) were run assimilating the same observations as in ASFUVTS and NoUVTS but with the background error covariance matrix used in ASFUVTS-2 d (doubled decorrelation length scales and 7 d variances). Those experiments showed that using doubled decorrelation length scales of tracers can lead to larger errors in temperature if subsurface data are not available. Those experiments were needed and are recommended during the development of an ocean operational forecast. Table  summarises the experiments' configurations.

The numerical simulations started on 1 May 2015 using an initial condition interpolated from HYCOM–NCODA, and they ran until 31 May 2016. The simulations started assimilating SSH and SST observations on 1 May and mooring data between 8 May 2015 and 21 May 2016. The simulations assimilated SSH and SST until 31 May 2016, and 57 (200) assimilation cycles were performed in the 7 d (2 d) reanalyses. The NoDA run was integrated until 31 December 2016. Model results were interpolated to the observations' spatial resolution for evaluation.

The NoDA run and reanalyses were objectively validated using root mean square deviation (RMSD) given by 4RMSD=1nΣi=1n(xi-yi)2 and linear correlation (r) 5r=∑i=1n(xi-x¯)(yi-y¯)∑i=1n(xi-x¯)2∑i=1n(yi-y¯)2 between observed (x) and modelled (y) results, where i=1,2,…,n is the observation times or locations, and the averages - were applied in time or space. The daily offset between observed and modelled SSH was removed before performing the SSH RMSD calculation. SSH and SST RMSDs were computed using daily averaged model results (analysis) interpolated to observation locations inside the domain. Complex vector correlation was computed between simulated and observed 2D velocity vectors. Complex correlation converts a pair of 2D vector series into complex numbers and computes the correlation between their real parts and their relative angular displacement using their imaginary parts . Model bias is defined as the difference between simulated and observed quantities. Statistics computed between model and in situ observations used daily averaged data processed and studied in . A total of 30 Argo profiles were available inside the model domain (see Sect.  for details) during the reanalyses period, and these were used to provide independent temperature and salinity observations for model–data comparison. Argo data and model results were linearly interpolated from 0 to 2000 m depth using bins of 10 m. HYCOM–NCODA analyses, which assimilated SSH, SST and Argo profiles , were also compared against subsurface mooring and Argo data.

Documented periods with anti-cyclonic (A1 and A2) and cyclonic (C2) mesoscale eddies were used to compare the NoDA and ASFUVTS runs. ASFUVTS' SSH height fields showed good agreement with observed SSH structures, where the centre of modelled high and low SSH tended to match with the core of anti-cyclonic (A1 and A2) and cyclonic (C2) eddies, respectively (Fig. a, c, e). The NoDA run generated anti-cyclonic and cyclonic eddies close to the observed ones; however, the eddies' centres were displaced by tens of kilometres (Fig. b, d, f). This result can be attributed to SSH and velocity boundary conditions from HYCOM–NCODA, which provided accurate SSH at the border and forced the generation of eddies with the correct cyclonicity albeit displaced from the observed eddies. Smaller eddies were modelled in the two simulations due to their higher resolution (∼2 km) in comparison to the observations (∼25 km) (Fig. c, d). Mesoscale eddies that had their centre near the domain boundary were not well simulated by either experiment, such as the cyclonic eddy centred at 34∘ S and 174∘ E on 9 October 2015 and the anticyclonic eddy centred at 36∘ S and 178∘ E on 9 April 2016 (Fig. a, b, e, f). A statistical analysis of the representation of mesoscale eddies (SSH and SST fields) by the numerical experiments is shown in the rest of this section.

The RMSD was calculated in time and space against observations to objectively evaluate SSH and SST generated by the experiments. The RMSD is compared to the observations' standard deviation (SD), which shows regions or periods of larger mesoscale variability that might be harder to accurately simulate observed SSH and SST. All experiments had reduced SSH RMSD on the slope where observed SSH SD was smaller, and SSH RMSD tended to be higher in the open ocean (larger SSH SD) where mesoscale eddies are present (Fig. a, b, c, d). The most complete ocean analysis (ASFUVTS) had reduced SSH RMSD (mean =0.06 m) in comparison to the NoDA SSH RMSD (mean =0.08 m) for the majority of the domain (Fig. a, b). The NoUVTS run had similar average SSH RMSD (0.06 m) to the ASFUVTS run. However, ASFUVTS further reduced SSH RMSD upstream and downstream of the moorings (Fig. b, c). Experiments that assimilated in situ velocities (NoTS, ASFUVTS-2 d) also had a positive impact on SSH representation up- and downstream of the moorings (not shown). NoDA had large SSH RMSD, especially in areas of observed high SSH SD – north and east of the moorings and north of the East Cape (37∘ S, 178∘ E) (Fig. a, d). The dynamics in those regions were largely dominated by more than four mesoscale eddies that persisted for more than a month each .

The NoDA run had the highest average SST RMSD (0.72 ∘C) and showed the largest SST RMSD (>1.4 ∘C) near the model NW boundary, which was also seen in the assimilative runs (Fig. f, g, h). Assimilation of surface and subsurface fields (ASFUVTS run) reduced the maximum (∼1.0 ∘C) and average (0.45 ∘C) SST RMSD values in comparison to the NoDA run (Fig. f, h). Withholding subsurface temperature data (NoUVTS run), as well as NoUV and NoTS runs (not shown), had small impacts on the maximum (decrease of ∼0.2 ∘C) and mean (increase of 0.01 ∘C) SST RMSDs (Fig. f, g).

The NoDA run had larger spatial SSH RMSD in comparison to the ASFUVTS and NoUVTS runs for most of the year-long period of simulation (Fig. a). Assimilating subsurface velocity, temperature and salinity further reduced the average SSH RMSD by 14 %. The NoDA run average spatial SSH correlation was 0.51 and below 0.2 in some events (Fig. b). This shows the lack of skill in simulating the timing and location of the mesoscale eddies in the NoDA run. Assimilation of SSH and SST (NoUVTS) improved SSH correlation by 27 %, and the inclusion of subsurface data further increased the correlation (by 31 %), which was above 0.4 virtually during the entire year of simulation. The SSH represents the integral of subsurface density fields, which is a good proxy for representation of the whole ocean state, and the SSH was better represented when velocity, temperature and salinity observations were assimilated.

The NoDA run had spatial SST RMSD similar to the assimilative runs in the first two-thirds of the simulation period; however, it showed larger errors from February 2016 onwards and reached a maximum of 1.82 ∘C (Fig. c). The ASFUVTS run had smaller SST RMSD time mean (0.47 ∘C) in relation to the NoDA run (mean =0.68 ∘C). Withholding subsurface data (NoUVTS) had little impact on the SST RMSD (mean =0.46 ∘C). The NoDA run had small absolute SST difference to observations (<1.0 ∘C) during the first two-thirds of the time series, but a larger cold bias (<-1 ∘C) was developed in April 2016 (Fig. d). Assimilation of surface fields only (NoUVTS) had absolute SST bias below 0.5 ∘C throughout the year-long period of simulation. The inclusion of subsurface data (ASFUVTS) did not have a well-marked impact on model SST bias; most of the surface field correction was done by assimilation of SSH and SST more specifically.

Assimilation of subsurface data (ASFUVTS) improved SST in comparison to the experiment that withheld subsurface observations (NoUVTS). A larger positive impact was shown in SSH RMSD when subsurface data were assimilated. Assimilation of in situ velocity, especially, further reduced the SSH RMSD up- and downstream of the moorings. The main differences between experiments appeared in the subsurface field comparisons, which are shown in the next section.

The NoDA run had very little velocity complex correlation (<0.1) with observations at M4 and M5 (Fig. a, b). DA improved complex correlation between modelled and observed velocity vectors in all experiments at the two stations. These results can be related to assimilation of SSH, which corrects the geostrophic circulation that is responsible for the long-term (>30 d) upper-half water column current variability in the region . The most complete assimilative run (ASFUVTS) had better results in comparison to the NoDA run but not against other assimilative runs. Withholding temperature and salinity (NoTS and NoUVTS) improved upon ASFUVTS, and NoTS had the best overall results. ASFUVTS-2 d, on the other hand, had the best overall results. HYCOM–NCODA poorly represented velocity at M4 probably due to less accurate representation of the slope bathymetry (Fig. 11 in ). At M5, however, HYCOM–NCODA showed a velocity complex correlation coefficient similar to the 7 d assimilative runs. Velocity at M5 was more dominated by the mesoscale field and less controlled by topographic constraints when compared to M4 , which makes velocity easier to simulate even in lower-horizontal-resolution models.

The assimilative experiments had smaller temperature RMSD at the surface in comparison to the NoDA run at M4 and M5 (coloured markers at the surface in Fig. c, d). Assimilating subsurface temperature (ASFUVTS and NoUV) generated temperature RMSD smaller than the NoDA run RMSD in the upper 500 m at M4 and M5 (black and light blue lines in Fig. c, d). The lack of subsurface temperature for assimilation (NoTS and NoUVTS), however, led to larger RMSD (>1 ∘C) in the upper 200 m at M4 and M5 and below 500 m at M5 (pink and dark blue lines in Fig. c, d). The ASFUVTS-2 d run had improved temperature RMSD down to 1000 m at M5. HYCOM–NCODA showed improved temperature compared to the NoDA run (dashed and solid red lines in Fig. c, d). This is because HYCOM–NCODA assimilates temperature and salinity data from Argo floats.

Temperature differences between models and observations at M4 showed small cold bias and relative warming at the beginning of the time series for all experiments (Fig. ). The small biases can be attributed to the initial and boundary conditions obtained from HYCOM–NCODA analysis, which shows a relative warming between July and August 2015 when Argo data were not available in the region (red shade and numbers in Fig. e). Larger differences between the OSEs started to appear in September 2015. The ASFUVTS and NoUV runs are colder than observed between September and November 2015 and March and May 2016 (<-1 ∘C – second-lightest blue shade in Fig. a, b). The NoUVTS and NoTS (not shown) runs are cooler in the upper 200 m water column from September 2015 onwards (Fig. c). Withholding subsurface temperature for assimilation (NoUVTS and NoTS) led to the continuous cooling of waters in the top 200 m until the end of the simulation. The NoDA run had a small temperature difference when compared to observations in September 2015, but these increased in October 2015 (Fig. d). The longest persistent cold bias in the NoDA run started in mid-March 2016, associated with the SST cold bias during the same period (Fig. d). Cooling of the upper water column in the NoTS and NoUVTS runs also occurred in the NoDA run. This effect might be intrinsic to the model configuration, and data assimilation of velocities and/or surface fields enhanced this bias. ASFUVTS-2 d had a marked negative temperature difference between August and September 2015 that was reduced in the rest of the year (Fig. e).

At M5, a mid-water-column warm bias (>1 ∘C) was simulated in the first half of the year-long period in all OSEs (second-lightest red shade in Fig. a, b, c, d). This also appeared in HYCOM–NCODA between June and September 2015 (Fig. e) probably due to the lack of Argo floats to the north of 35∘ S. ASFUVTS had the smallest differences to the observations out of all 7 d assimilation window experiments (Fig. a). In mid-August 2015, a near-surface cold bias (<-2 ∘C) was pronounced in all experiments but was further developed in the NoDA, NoTS and NoUVTS runs towards the end of the simulation period. This is associated with the lack of subsurface temperature and the near-surface cold bias in the NoDA run. The ASFUVTS (NoUV) run reduced the cold (warm) differences to values above -1 ∘C (below 2 ∘C) for most of the period of the simulation. It showed that the assimilation of subsurface temperature and salinity had a positive impact by reducing temperature biases at M4 and M5. ASFUVTS-2 d better matched the observations and had the smallest temperature differences at M5 (Fig. f). However, this assimilation configuration led to larger temperature differences when mooring temperature was not assimilated. Consequently, this configuration is not advisable in this region for an operational forecast system, as Argo floats can spend months without sampling the region.

Observed salinity time series from CTDs located near 200 m depth at M4 and M5 were compared to simulated salinity from three experiments and HYCOM–NCODA (Fig. ). All models' salinity tended to oscillate near the observed values, and average absolute biases were smaller than 0.1 g kg-1. The ASFUVTS run slightly degraded salinity results in comparison to the NoDA run; however, salinity RMSDs were smaller than the observation standard deviation (0.16 g kg-1). ASFUVTS-2 d and HYCOM–NCODA had larger peaks and troughs in salinity time series and the largest variances (0.02 g kg-1) at M5. This result can be attributed to the frequency of increments applied to the initial conditions – everyday in HYCOM–NCODA and every other day in ASFUVTS-2 d. Despite that, ASFUVTS-2 d had the best statistical performance amongst the simulations, which can also be attributed to the more frequent corrections to the initial conditions.

Salinity RMSD comparisons at three different depths at M4 and M5 are shown for all ROMS experiments and HYCOM–NCODA in Table . These experiments had salinity RMSDs oscillating around 0.16±0.04 g kg-1 in shallower depths (≤220 m) at M4 and M5 stations. An exception to this is ASFUVTS-2 d, which had the smallest salinity RMSD (<0.10 g kg-1) in the upper M4 and M5 depths. HYCOM–NCODA also had salinity RMSD around 0.16±0.04 g kg-1 in the upper and 200 m depth at both M4 and M5. Salinity RMSD was reduced near the bottom at M4 and M5 (<0.08 g kg-1) in all ROMS experiments as well as for HYCOM–NCODA. ASFUVTS-2 d, however, had the largest salinity RMSD near the bottom at M5. The bathymetry used in HYCOM–NCODA was shallower than near-bottom measurements at M5, and salinity RMSD was not calculated. These OSE's results suggest that future experiments should reduce salinity observation standard deviation (or error) below a certain depth. For instance, observed salinity error can be reduced to 0.06 g kg-1 below 1000 m as in , or an exponential decay can be applied from the surface (0.12 g kg-1) to 2000 m (0.02 g kg-1) . In the next section, model temperature and salinity are validated against Argo-independent observations.

A total of 30 non-assimilated temperature and salinity profiles spread in time (Fig. ) and throughout the domain (Fig. e) were used for independent comparison. All experiments had small salinity differences when compared to the first five salinity profiles sampled by Argo floats, which can be attributed to HYCOM–NCODA's initial and boundary conditions (Fig. ). Larger salinity differences, however, appeared in the OSE's results in late August when simulated sea water was fresher in the upper 200 m depth and saltier underneath. Assimilation of surface and mooring data using a 7 d window did not generate any notable positive/negative impact in salinity in comparison to the NoDA run. ASFUVTS-2 d had the smallest differences between simulated and observed salinity (Fig. f), and its results were similar to HYCOM–NCODA (Fig. e), which assimilates Argo data. However, fresher sea water was simulated in mid-May 2016 when mooring salinity data collection had ended.

In this analysis, we included experiments using a 7 d assimilation window and doubled decorrelation length scales for tracers (NoUVTS-2x and ASFUVTS-2x) to show the impact of the larger decorrelation length scale on simulating temperature and salinity at Argo locations. All experiments' temperature RMSDs showed similar patterns to the results simulated at M4 and M5. When temperature was not assimilated (NoUVTS and NoTS), there was a higher temperature RMSD between 0 and 200 m in comparison to the NoDA run due to a colder bias (<-1 ∘C) that developed in these runs (Fig. a, b). Assimilation of subsurface temperature data (ASFUVTS, ASFUVTS-2 d and NoUV runs) resulted in smaller temperature RMSD in comparison to the NoDA run from the near surface down to 2000 m (Fig. a, b). HYCOM–NCODA reanalysis, which assimilates Argo, SSH and SST data, had the overall best temperature representation at the Argo locations. Assimilation of surface and mooring data using doubled decorrelation length scales (ASFUVTS-2x) slightly improved temperature representation near the surface and around 1000 m depth in comparison to ASFUVTS (Fig. a, b). However, when subsurface data were not assimilated (NoUVTS-2x), larger temperature RMSDs were generated between 200 and 1200 m depth in relation to the NoUVTS run.

Comparisons to Argo salinity measurements showed that all 7 d window experiments and the NoDA run had similar vertical structures in the salinity bias. Fresher salinity was modelled in the upper 200 m, and saltier waters were modelled below that, peaking at 600 m, in these experiments (Fig. c). ASFUVTS-2 d had the smallest salinity bias and RMSD in comparison to the 7 d window experiments (Fig. d). This suggests that more frequent corrections/increments to the initial conditions and doubled decorrelation length scales of tracers can improve salinity even with the small number of salinity observations. The ASFUVTS-2 d salinity results were close to HYCOM–NCODA reanalysis, which assimilated salinity data from Argo floats.

Applying doubled decorrelation length scales of tracers to the 7 d assimilation window experiments slightly reduced RMSD for temperature (3 %) and salinity (4 %) at the Argo locations when assimilating mooring temperature and salinity (ASFUVTS-2x) in comparison to using 100 km (100 m) as horizontal (vertical) length scale (Fig. ). However, when subsurface data were withheld (NoUVTS-2x), it increased the mean temperature (salinity) RMSD by 18 % (47 %). Larger RMSD occurred when withholding mooring temperature and salinity data using a 2 d assimilation window and double decorrelation length scales of tracers (NoUVTS-2 d – not shown).

Variability in temperature increments to the initial conditions at M4 revealed oscillation between positive and negative increments through time in all experiments (Fig. ). The 7 d window experiments that assimilated subsurface temperature and salinity (ASFUVTS and NoUV) had positive increments extending from the surface down to 500 m (darker red shade in Fig. a, b). In contrast, experiments that did not assimilate temperature and salinity (NoTS and NoUVTS) had strong positive increments bounded to near the surface (Fig. c, d). ASFUVTS-2 d did not have large positive increments near the surface, but increments tended to vary from positive to negative values between assimilation cycles (Fig. e).

Near-surface average temperature increments had a distinct difference between experiments that did and did not assimilate subsurface temperature at M4 and M5 (Fig. a, b). Assimilation of in situ temperature (ASFUVTS and NoUV) generated larger average positive increments (>0.04 ∘C) around 100 m depth in comparison to the simulations that withheld subsurface temperature (NoTS and NoUVTS). The latter experiments had near-surface mean negative temperature increments that increased towards 0 ∘C below 200 m. ASFUVTS-2 d had smaller average and standard deviation increments near the surface in comparison to the 7-day experiments (Fig. a, b).

Surface mean heat flux analysis fields varied according to the presence/absence of subsurface temperature for assimilation (Fig. ). Simulations that withheld subsurface temperature (NoUVTS and NoTS) had large positive heat flux near the moorings and in the majority of the domain (Fig. a, b). The positive heat flux in the NoTS and NoUVTS runs was related to the near-surface negative temperature increments at M4 and M5 (dark blue and pink lines in Fig. ). The combined positive heat flux and negative temperature increments corrected the surface cold bias present in the NoDA run but not the cooling trend around 200 m. Experiments that assimilated subsurface temperature (ASFUVTS, NoUV and ASFUVTS-2 d) had negative average heat flux (or near-zero heat flux – ASFUVTS-2 d) near the moorings that extended north and south with varying size between experiments (Fig. c, d, e). This negative heat flux increment balances the positive temperature increment at M4 and M5, which aims at correcting both surface and upper thermocline (∼200 m) cold biases. The large variability in heat flux analysis fields between experiments (Fig. ) might be related to the 4 d variances used to compute the background error covariance. The 4 d variances used here include daily cycle and cloud coverage variabilities, which generated large heat flux uncertainty and increments.

The ASFUVTS-2 d run had smaller negative heat flux analysis near the moorings. This happened due to the smaller average negative increments (M4) and positive increments (M5) added to the initial condition of temperature at these stations (dashed black line Fig. ). The NoDA run average net heat flux was mostly positive north of 35∘ S and was negative southwards (Fig. f). On average, the atmosphere has a warming effect on the ocean north of 35∘ S and a cooling effect south of 35∘ S. This is observed in JRA55-do (Fig. 48 in ), in which the NZNES is located near the average zero net heat flux contour line in the atmospheric forcing dataset.

Annual average wind stress is mainly from the northwest in the 7 d window runs and from the west in the ASFUVTS-2 d and NoDA runs (vectors in Fig. ). Wind stress curl showed some spatial variability between the assimilative runs (red and green shade in Fig. ). Experiments that did not assimilate subsurface temperature and salinity (NoUVTS and NoUV) had average negative wind stress curl at the moorings' location (Fig. a, b). Conversely, assimilation of subsurface temperature and salinity (NoUV and ASFUVTS) generated average positive wind stress curl on top of M5 (M3–M5 in ASFUVTS) (Fig. c, d). Positive wind stress curl generates convergence and downwelling of warmer water masses that might be acting to prevent the cold bias in the numerical model. These changes in wind stress curl can also explain why assimilation of subsurface temperature and salinity (ASFUVTS and NoUV) slightly degraded the representation of velocity at M4 and M5 compared to withholding subsurface temperature and salinity (NoTS and NoUVTS). The ASFUVTS-2 d run had smaller wind stress curl magnitude compared to the other simulations. Its wind stress curl field resembles the NoDA wind field forced with JRA55-do, especially in the regions of negative wind stress curl near the coast around 37.5∘ S and observed by using the Cross-Calibrated Multi-Platform wind vector analysis (CCMP).