Model Configuration

a. ADCP Ekman Models

Models were run for viscosities of 0.0025, 0.005, 0.01, 0.0425, 0.1, 0.2 and 0.447m2_s-1_{. To simplify}

the model we assumed that latitude, and therefore the Coriolis parameter, could be treated as a constant. This is a reasonable assumption as our data covers a relatively narrow latitude range from 41ο_{S to 48}ο_{S. The infinite-depth Ekman models were approximated by using a boundary layer depth}

of 1000 m with a free slip bottom boundary condition to approximate the effect of an infinite BLD. Finite depth LEMs were configured with a BLD of either 105m or 336m (in line with the fits to the ADCP and EM-APEX data discussed in Chapter 4) and a no slip boundary condition. All linear Ekman models applied to the shipboard ADCP observations were run on vertical grids with dz of 0.5m. Stokes drift was computed (as in Chapter 3) from reanalysis wave period and significant wave heights interpolated onto the ship track before the resulting surface stresses for the modified LEMs were computed as described above. Geostrophic shear was computed from the shipboard ADCP observations using the method outlined in Chapter 3 assuming a reference depth of 200m. Time steps were computed from Equation 5.3. Output was saved to disk for later analysis every 1600 seconds.

To characterise the time varying performance of the model we compared the statistical distribution of modelled currents with the nominal 23.5m ADCP observations. However, the ADCP observations actually represent the currents observed in a ‘bin’ surrounding the nominal depth. The width of this depth bin varied with the mode in which the ADCP was running and whether RV James Cook’s keel was raised or lowered. As a result the 23.5m ADCP observations include contribution from currents between 10m and 30m depth. Hence, it is not appropriate to compare the model time series at 23.5m depth to the observations and we must instead construct a representative time series. We considered two time series; one created by taking the mean velocity over the 10-30m interval at each time step and the other taking the maximum current by amplitude over the 10-30m depth. We found the time series constructed using the maximum current by amplitude produced a

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probability density function closer to the PDF produced using the ADCP data; hence, we proceeded with this modelled time series for the subsequent analysis.

Autocorrelation as a function of time lag for each model configuration at a particular viscosity was computed via a bootstrap method; the velocity time-series was split into a number of overlapping segments and the correlation by component as a function of time lag was calculated for each segment. Mean autocorrelation as a function of time-lag and the corresponding 95%

confidence intervals were then computed from the bootstrap estimates.

b. EM-APEX Ekman Models

Ekman models for the floats were run with the same viscosities and BLD configurations as the models applied to the ADCP data. As float current time-series were two to three times longer than the duration of the shipboard time-series, applying the same time-steps used in the ADCP model runs was likely to result in excessive run times. Hence, following Equation 5.3, we opted to use a lower resolution vertical grid with dz of 1m.

We considered model performance over all floats rather than on a float by float basis to maximize the number of datapoints available to ensure our analysis of time-varying performance was robust. Time series of simulated and observed velocities were generated in a similar manner to the shipboard case before the output from all floats was aggregated into a single dataset. We then applied the two sample KS test and computed the probability density functions and generated QQ plots. Autocorrelation as a function of time-lag was computed using a similar bootstrap method as applied to the ADCP model runs, only differing in that we took the mean and 95% confidence intervals over all floats. Similarly, the time-mean current profiles were generated by averaging over all floats.

c. PWP Models

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The PWP models were implemented on a 1m vertical grid with a maximum depth of 1000m and run with 600 s time steps. Wind-forcing, as above, was derived from the CERSAT blended ERA-

Scatterometer dataset (described in Chapter 3) and interpolated onto each float trajectory. To simplify the model we assumed that latitude, and by extension the coriolis parameter, could be treated as constant, as we did for the linear Ekman models.

Six hour resolution solar short wave incoming radiation, the outgoing long-wave radiation and precipitation were sourced from the NCEP/NCAR reanalysis product and interpolated onto the time and locations of all EM-APEX profiles. While NCEP/NCAR provides lower spatial resolution compared to the ECMWF ERA reanalysis products, all ERA products offer the relevant data at 12hr temporal resolution, limiting the alibility of the model to capture the diurnal cycle in stratification. As diurnal changes in stratification have been proposed (Price et al., 1987) as a major influence on the structure of the Ekman spiral, we judged the improvement in temporal resolution from using NCEP to outweigh the loss of spatial resolution. Meridional SST gradients were obtained from a 24hr-0.25° resolution blended SST dataset derived from Advanced Very High Resolution Radiometer (AVHRR) and Advanced Microwave Scanning Radiometer (AMSR) satellite systems (Reynolds et al., 2007).