Transport anomaly calculation and errors 1 The reference specific volume anomaly profile

Following equation (4.4) all transport anomalies are computed relative to a reference dynamic height profile. The reference specific volume anomaly profile (Figure 5.19) is computed separately for the three layers, 0-800m, 800-3000m and 3000-4700m as the mean on 20 dbar pressure surfaces from calibrated CTD casts selected as end stations.

Dynamic height anomaly profiles are referenced to 1000 dbar, consistent with the computation of geostrophic velocities of the transatlantic hydrographic sections (Section 3.2.4).

Figure 5.19 Specific volume anomaly reference profile constructed from CTD casts (i) with the standard deviation of specific volume anomaly between constituent casts (ii).

5.3.3.2 Appending CTD casts down the slope

Calculation of transport anomalies of the upper, intermediate and middle layers simply follows equation (4.4) with the end stations of Table 5.6 referenced to the dynamic height computed from the specific volume anomaly curve of Figure 5.19. The deep layer however is more complicated since stations deeper than 4700m (the maximum depth of the LNADW layer defined at this boundary) are frequently found more than 30 km from the 800m isobath, with significant transport inshore of this above the LNADW layer (e.g. Figure 5.11 insert). Eddies in the thermocline propagate westwards into the boundary on 70-100 day timescales (Lee et al., 1996), which combined with

meandering (Lee et al., 1996) or pulses in strength of the DWBC (Chave et al., 1997) make this a highly variable current regime. Referencing dynamic height to 1000 dbar means that temperature anomalies at mid depth are integrated into the deep layers. We argue that such anomalies 30km offshore resulting from any of the above variability mechanisms result in a deep dynamic height profile not representative of conditions at the boundary.

To compute the deep layer transport anomaly we therefore append, on pressure surfaces, two CTD casts crawling down the slope. The upper part of the profile is taken from the

middle layer end station and below its maximum depth we add the lower part of the CTD cast resolving 4700m, casts being separated in time by at most 1 day. To prevent temperature inversions due to isotherm slopes between the two appended stations, the 20 and 40 dbar properties below the lowest common pressure of the station pair are smoothed with a cubic spline interpolation over the property values 40 dbar above and 60 dbar below the lowest common pressure. This has a negligible effect on transport anomalies.

Figure 5.20 Comparison of transport anomalies resulting from appending CTD casts down the slope with those from a single offshore station. (i) Difference between transport anomaly per unit depth profiles computed using a single end station that resolved 4700m, and a station constructed by appending a middle and deep end station. All transport anomalies are referenced to 1000 dbar and the specific volume anomaly reference curve of Figure 5.19. The red line is the difference for 28th _February

1990, using stations at 26.55ºN, 76.75ºW, 11km offshore with depth 3061m and at 76.53ºW, 33km offshore with depth 4815m, locations plotted with topography in (ii). The individual transport anomaly per unit depth profiles for these stations are in (iii), solid line: appended cast, dashed line: single station.

CTD stations of 28th

February 1990 illustrate the error that could result if we did not follow the method of crawling down the slope. Both stations are along the 26.5ºN line, 11 and 32 km from the 800m isobath (Figure 5.20(ii)). The discrepancy between the transport anomaly per unit depth profiles from the appended and single CTD stations (Figure 5.20(iii)) is due in large part to a warm anomaly in the offshore profile between

1000 and 1307 dbar of approximately 0.4ºC, resulting in a difference between the deep layer transport anomalies of 3 Sv. We argue that carrying this warming signal in

dynamic height into the lower layer anomaly is unrealistic since the majority of shear in the profiles is found above 2000m - note the similarity in shape of the profiles below 1500m despite originating from different casts above 3060m (Figure 5.20(i)). The above cast pair is not an extreme case when compared with the difference between methods for all station pairs (Figure 5.20 (i)) which reaches -10 Sv in one case (appended minus single cast), with group mean and standard deviations of 0.4 Sv and 3.7 Sv respectively.

We believe that transport anomalies computed from CTD casts combined in this way, with that closest to the boundary deeper than 3000 m used to its full depth and the next offshore station to reach 4700m appended to its base, provide the best representation of boundary conditions, as required to resolve basin wide baroclinic flows.

5.3.3.3 Transport errors

As reviewed in Section 5.3.1 end stations are selected so as to minimise the flow inshore of the station. We aimed to limit inshore flows to 1 Sv but the actual error is estimated to be larger due to variability; ± 2, ± 0.2, ± 2 and ± 3 Sv for the upper, intermediate, middle and deep layers respectively (Table 5.5). There remains an error due to accuracy of temperature, pressure and salinity observations used to compute dynamic height. These are estimated as in Section 5.2.3.2 with offsets of temperature, salinity and pressure of 0.02ºC, 0.005 and 3.5 dbar respectively (Table 5.7). For the deep layer there is an additional error due to flows below 4700m which are not resolved by end stations at this boundary since zonally integrated meridional transport profiles for the full section at 25ºN show LNADW transport down to approximately 5000m (Figure 3.11). Transport between 4700m and 5000m for the 1981, 1992, 1998 and 2004 sections is -1.3, -1.2, 0 and 0.8 Sv respectively (omitting the 1957 section due inferior resolution of bottom topography). These give a rms error of 1.0Sv for LNADW

transport due to excluding the component below 4700m. The combined errors from all sources are provided in Table 5.7.

There are two 2-3 day periods during which CTD stations were taken at different latitudes of the western boundary but still within our study region at distances offshore

suitable for use as end stations (Table 5.8). The variability in layer transport anomalies from these stations provides support for the estimated errors incurred through

application of the end station method (Table 5.7). For each group of stations, the transport range is within two times the expected error, consistent with the actual

transport anomaly lying within the bounds set by the mean of the group ± the calculated error. The only exception occurs for the deep layer, June 1990 when a transport range of 8.9 Sv is seen but this is only marginally larger than two times the expected error of 8.4Sv for this group.

Depth layer (m) ΔΤ = 0.002 ΔS = 0 Δp = 0 ΔΤ = 0 ΔS = -0.005 Δp = 0 ΔT = 0 ΔS = 0 Δp = 3.5 Obs. error Location error Total error 0-800 0.0 0.3 0.0 0.3 2.0 2.0 800-1100 0.0 0.1 0.0 0.1 0.2 0.2 1100-3000 0.1 1.2 0.1 1.3 2.0 2.4 3000-4700 0.2 2.8 0.2 2.8 3.0 4.2

Table 5.7 Estimated end station layer transport anomaly errors all in Sverdrups. Columns 2 to 4 are the root mean square errors resulting from addition of temperature, salinity or pressure offset to western boundary CTD casts, with the combined error, due to measurement errors and calibration of the CTD salinity (obs. error) in column 5. The location error of column 6 is that due to end station offshore position (Section 5.3.1) and the Total error (column 7) is the combination of Location and Observational errors, for the 3000-4700m layer this also includes the 1 Sv error due to flows between 4700 and 5000m.

Date Latitude Distance (km) Transport anomaly (Sv) Transport range (Sv) 28-Jun-90 24.26 2 -0.7 29-Jun-90 25.51 14 3.2 30-Jun-90 26.49 13 0.4 3.9 11-Aug-92 26.54 2 1.7 Upper layer 14-Aug-92 24.55 7 2.6 0.9 27-Jun-90 24.25 14 2.2 29-Jun-90 25.51 14 -2.3 4.5 11-Aug-92 26.50 14 -0.9 Middle layer 14-Aug-92 24.55 7 -1.6 0.7 27-Jun-90 24.25 14 5.7 29-Jun-90 25.49 19 -3.2 8.9 11-Aug-92 26.46 25 -2.9 Deep layer 14-Aug-92 24.61 24 -4.8 1.9

Table 5.8 Variability in end station layer transport anomalies for stations taken within 3 days, at different latitudes. Note that for the deep layer distance refers to the offshore, deeper station, of the appended pair.

In summary we accept that the variability seen at any one time is large within the layer transport anomalies (Table 5.8), but the estimated errors for this method appear to

account for this. The errors are dominated by the location component (with salinity calibration also important for LNADW) and are due predominantly to having to use CTD stations not immediately adjacent to the boundary. This is however necessary if we are to have enough historical end stations at the west to examine variability throughout the 25 years.

5.4

S

We have carefully selected CTD casts suitable for use as end stations at both boundaries of 26.5ºN in the Atlantic over the last 25 years. To minimise measurement errors, deep salinities are calibrated to a constant deep θ-S relationship at the east, while the

significant freshening trend observed at the west of LNADW (both DSOW and ISOW) at approximately 0.003 per decade on potential temperature surfaces is incorporated in the calibration procedure at the west. Transport anomalies (with errors estimates) are computed relative to the group mean for each of the upper, intermediate, middle and deep layers at each boundary although data coverage is notably better at the west; 29 or more stations for each layer, compared to 9 to 11 at the east.

CHAPTER 6: Methods and Data -