Initial data processing – missing pressure estimation

Figure 6.2 Schematic of alternative pressure estimation models. With a background flow in the direction shown, the pendulum method assumes a uniform inclination of the mooring to the vertical at angle θ, while the pmin method assumes that above a certain

pivot depth, the surface flotation is sufficiently strong that the mooring remains vertically aligned. The alternative positions with the pendulum model (black) or the pmin method (grey) are shown for Instrument 1. D’ is the vertical displacement of a given instrument from its minimum depth, assumed to occur when the mooring is upright. If D’ of one instrument is known, that of the remaining instruments can be estimated according to the preferred model.

To obtain a dynamic height time series from the Kiel-276 data set a pressure record is required for all measured temperature records. With one good pressure record for each mooring deployment we can estimate the vertical mooring structure through application of either the pendulum or pmin models (explained in Figure 6.2) and thus obtain

missing pressure records while incorporating the effects of mooring inclination in background flows. To evaluate alternative models we make use of deployments with

pressure sensors at multiple depths after initial screening for bad data which is rejected. Records are defined as bad if they drift by more than 10 dbar over the deployment duration or are unstable. This results in rejection of the 240 and 1120 m pressure records of deployment 276150, that at 697 m of deployment 276010 and at 500 m of 276160.

To explain the possible pressure models consider a mooring with two pressure records, from which we compute the deviation from the minimum depth of the upper and lower instruments, D₁! and D₂! respectively (in metres). The depth changes of either

instrument can then be estimated using both of the methods of Figure 6.2, and their relative performance evaluated. According to the pmin method

!

ˆ

D1 =D!2 and Dˆ2! = D1! (6.1)

while the pendulum model (following notation of Figure 6.2) states that

! ˆ D₁= D!₂ H1 H₂ and ! ˆ D₂ = D₁!H2 H₁ (6.2)

The standard error of the pmin method is equal for both instruments;

s_! = 1

n"1

(

)

2

(6.3) while for the pendulum method the standard error of the fit is dependent on whether we are extrapolating upwards or downwards, (with sε(up) the standard error of estimating the

upper instrument’s pressure from that of the lower instrument and vice-versa);

s_!(up) = 1 n"1 D2# H1 H₂ "D1# $ %& ' () 2 s_!(down) = 1 n"1 D1# H2 H₁ "D2# $ %& ' () 2 (6.4) the results of which are summarised in Figure 6.3 and Table 6.2.

In all cases except (ii) of Figure 6.3 the ratio of D1! toD2! is significantly greater than

1.0 at the 95% confidence level (Table 6.2). This means that the upper instrument experiences larger depth changes than the lower instrument due to currents overcoming mooring flotation. Thus the pendulum method is more appropriate than the pmin method. Slopes of the least squares regression of D1! toD2! are in good agreement with

the ratio of H1 to H2. Following equation (6.2), the pendulum method sets the y-

than ± 2 m. A non-zero offset may be due to inaccurate measurement of instrument separation before deployment rather than the pendulum method being inappropriate. 2 m is very small given a mooring cable over 5km long - which we attribute in large part to the careful data processing and nominal depth adjustments made by Siedler et al. (2005). The standard error of Dˆ' from the pendulum method is marginally smaller than, or equal to, that of the pmin model, supporting preference of the pendulum model. Both are smaller than 6 m for all deployments with multiple good pressure records. We note the validity of the pendulum model over a range of depth intervals from 270- 1000m in the case of 272190, and down to 1600m in 276180.

Figure 6.3 Correlation between upper and lower instrument D!, with regression lines overlaid. Data sets in each subplot correspond to those of Table 6.2 which also reports regression coefficients.

Following the above evaluation, we compute missing pressure records corresponding to each pressure record, and replace those deemed bad on the basis of drift, discontinuities or sticking, using the pendulum method applied to depth changes computed from the most stable pressure record of each deployment (Table 6.3). The estimated error in pressure is less than 6 m (dbar).

Table 6.2 Comparison of pendulum and pmin methods for mooring pressure model. For the selected deployments corresponding to the subplots of Figure 6.3, the instrument height ratio is based on a water depth of 5290m and the notation is from equation (6.2). For the N good data points of the two records, the linear regression of D1’ to D2’ coefficients, slope and y-intercept with 95% confidence intervals correspond to the green lines of Figure 6.3. The standard error is that resulting from using the pmin or pendulum model to estimate measured pressure records following equations (6.3) and (6.4). The upper error is that obtained using the lower record D’ to predict the upper with the pendulum model.

Deployment Reference

Instrument Pressures computed 264010 24 124, 376, 926 2966, 4707 276010 195 499, 995, 1095, 1591 276020 243 550, 1149, 1665, 3020 276030 194 428, 629, 1032, 1535 276040 243 475, 675, 1075, 1575, 2980, 5185 276050 327 560, 760, 1160, 1660, 3050, 5240 276060 327 562, 764, 1168, 1670, 3080, 5240 276100 367 800, 1100, 1200, 1700, 3050, 5185 276110 555 320, 755, 1055, 1155, 1655, 3045, 5190 276120 445 215, 645, 965, 1565, 3000 276130 270 1000, 1100, 3000, 5185 276150 470 240, 670, 970, 1120, 3030, 5275 276160 270 500, 1000, 1600, 3000, 5185 276170 270 500, 1000, 1600, 3000, 5185 276180 1000 270, 1600, 3000, 5185 276190 270 500, 1600, 3000

Table 6.3 Reference instruments and estimated records of Kiel-276 mooring deployments following the pendulum method. Records are replaced if bad.