CHAPTER 6: Methods and Data Dynamic Height Moorings
6.2.5 Initial data processing – vertical interpolation
With temperature and pressure measured at discrete depths up to 730m apart in the vertical and the means to calculate salinity at these points, specific volume anomaly time series are available at a number of levels on the mooring. How to integrate these
vertically (interpolation between the measurement levels as well as extrapolation above the shallowest instrument) to give dynamic height time series from which we may compute transport anomalies is next addressed.
Figure 6.8 EOF’s of specific volume anomaly computed over 0-1300 dbar, after subtraction of the mean profile. In the expanded section between 100 dbar and 1300 dbar nominal instrument depths of 270, 500 and 1000m are overlaid joined by straight dashed lines, representing the profile produced by linear interpolation between the data points.
Examination of the vertical structure of specific volume anomaly changes as a function of pressure, relative to the mean, from the CTD casts of Section 6.2.4 (Figure 6.8), shows that while the first two EOF’s together account for more than 90% of the
variance and follow a similar structure below 300 dbar, linear interpolation (the simplest possible model) between measurement levels may not be suitable. The nominal
instrument depths plotted on Figure 6.8 of 270, 500 and 1000m represent a typical mooring configuration (Table 6.1) and show that most of the vertical structure would be captured by linear interpolation. The same cannot be said for low resolution cases such as deployment 267180 with no instruments between 270 and 1000m (Table 6.1). An alternative to linear interpolation is therefore sought, such as interpolation with a vertical temperature gradient (!T!p) climatology according the equation (6.5), where 1 and 2 identify two mooring instrument levels following Johns et al. (2005):
T(p)= wi T(pi)+ !T !p(T)dp pi p
"
# $ % & ' ( i=1 2)
or T(p)= wi T(pi)+ !T !p(p)dp pi p"
# $ % & ' ( i=1 2)
and wi =1* p* pi p2* p1 (6.5)The alternative forms of (6.5) account for whether the climatology is constructed as a function of pressure or temperature. Previous investigators (e.g. Zantopp and Leaman, 1984; Johns et al., 2005; Kanzow et al., 2006) constructed !T
!p climatologies in
temperature co-ordinates rather than pressure since Zantopp and Leaman (1984) found this better resolved the 18ºC water. Our interest in the upper water column and the idea that seasonal stratification may have a more robust vertical structure with respect to pressure rather than temperature, combined with the expected sensitivity of vertical interpolation employing a lookup procedure in temperature to small scale temperature irregularities, leads us to consider the relative merits of both climatology constructions. Accordingly we construct climatologies both as a function of pressure and temperature (Figure 6.9b) from the CTD casts between 31 and 33ºN, 21 and 23ºW deeper than 1300 dbar (total 52, plotted in Figure 6.9a) and compare the resulting errors in employment of equation (6.5).
Figure 6.9a Temperature profiles of the CTD casts used to compute the climatologies of Figure 6.9b.
Figure 6.9b Construction of a ∂T/∂p climatology, as a function of pressure (i) or temperature (ii). For vertical levels and smoothing employed refer to text. The mean (solid lines) with limits of ± 2 standard deviations (dashed or thin lines) are shown. Standard deviations of the climatologies are compared in (iii) with that constructed as a function of pressure plotted at the mean temperature for each pressure level (red solid line), while the black dashed line shows the standard deviation of the temperature co- ordinate reference curves.
6.2.5.1 The !T !p(p) climatology
Figure 6.10 The monthly reference ∂T/∂p climatology constructed as a function of pressure (i). Note the expanded vertical scale above 170 dbar, below which there is no temporal dependence. Construction details (see text) are illustrated in (ii). The + and o
are the monthly mean ∂T/∂p values at each depth, which are smoothed with a ± one
month running mean to give the coloured lines. Resulting monthly values are then smoothed in the vertical to give (i).
Construction of this climatology entails computation of ∆T for each 20 dbar level of the CTD casts. Points outside the mean ± two standard deviations are rejected and the mean
recomputed and smoothed once with a three point running mean. The resulting profile with variability shown by two times the standard deviation, smoothed as the mean is shown in Figure 6.9b(i). The upper water variability is likely to be seasonal so we also construct monthly mean profiles from the 57 CTD casts deeper than 300 dbar in the same way, although February is the mean of January and March since there are no CTD casts that month. The monthly profiles are temporally smoothed with a ± one month running mean (to reduce the impact of possible interannual variability on the
climatology from months where we have few CTD casts) into the seasonally varying
!T
!p(p) climatology of Figure 6.10(i). ∂T/∂p on 20 dbar levels are shown in Figure
6.10(ii) before and after temporal smoothing. The smoothed monthly resolution climatology is used for the upper 150 dbar of the ∂T/∂p reference, and below this the mean !T!p(p) of Figure 6.9b(i) is appended. Finally to ensure a smooth profile at the join between the upper variable section and deep constant parts, we apply a ± 20 dbar running mean to all months, resulting in the !T !p(p) climatology of Figure 6.10(i).
From Figure 6.10 we see that the !T!p(p) climatology captures the expected annual stratification cycle of the upper water column. Waters are vertically well mixed from January through April when we see the onset of summer stratification of the upper 100 dbar, with vertical gradients strongest between 30 and 70 dbar. Stratification peaks towards early autumn and the peak is later deeper in the water column (in July, August, September and October at 10, 30, 50 and 70 dbar respectively) consistent with surface wind mixing eroding stratification downwards. With weakened incoming solar radiation in autumn, rapid vertical homogenisation results through to December (Figure 6.10).
6.2.5.2 The !T !p(T) climatology
The !T
!p(T)reference curve of Figure 6.9b(ii) is obtained by computing temperature
changes in 20 dbar levels at the mean temperature of the two levels, points are grouped in 0.2ºC intervals and smoothed vertically with a three point running mean after
rejection of points outside the mean ± two standard deviations. Preliminary bi-monthly mean profiles showed no difference between those of December/January,
February/March or April/May. Therefore to construct the climatology of Figure 6.11 we work with a winter mean profile of December to May inclusive and bi-monthly means for the rest of the year. These curves are smoothed twice vertically with a 5 point (1ºC) running mean before appending to the lower ∂T/∂p profile below 17.3ºC. A final smoothing is done with a 1ºC running mean over data points up to 0.4ºC away from 17.3ºC to produce the seasonally dependent reference curves plotted in Figure 6.11.
Figure 6.11 The monthly reference ∂T/∂p climatology constructed as a function of temperature, with limits of ± one standard deviation.
6.2.5.3 Climatology comparison
The errors associated with vertical interpolation using both climatologies (Figure 6.12) are assessed by subsampling the reference CTD stations at nominal depths sampled by Kiel-276 and recomputing temperatures at 20-dbar resolution according to equation (6.5). Between each instrument pair we interpolate downwards from the upper
measurement level in 20 dbar increments keeping the bottom temperature and pressure fixed, best illustrated with the following example. With mooring observations at 270 and 1010 dbar, we first compute temperature at 290 dbar from equation (6.5) with the 270 and 1010 dbar observations as instruments 1 and 2, then temperature at 310 dbar is computed by re-application of equation (6.5) with instrument 1 as the previously estimated 270 dbar observation, and instrument 2 still as 1010 dbar. This process is continued downwards in 20 dbar increments until we reach 990 dbar. Above the depth
of the upper instrument (l in equation 6.6), we must rely on extrapolation upwards using the value of temperature computed a cycle before (20 dbar below), and so on to the surface: Tl!20 =Tl + "T "p T=T l #p with Δp = -20 dbar. (6.6)
The ∂T/∂p climatology constructed as a function of pressure performs better in the upper 100 m (where seasonal effects are important) than that constructed on temperature surfaces, with mean errors of -0.5ºC and -1.9ºC respectively (Figure 6.12). This is consistent with our reasons for investigating the use of the former, and we are reassured that the estimated error range of -2 to 0.5ºC at the surface (mean ± one standard
deviation) is still notably smaller than the 7ºC range observed in the 10 dbar constituent CTD temperatures (Figure 6.9a). Below this depth, there is little difference in the errors of the alternative climatologies, although that of temperature performs marginally better around 800 m (Figure 6.12). The actual errors are dependent on mooring resolution with effectively no error at each instrument location and maximum errors roughly halfway between instruments.
Figure 6.12 Error in CTD temperature after subsampling temperature and pressure at a typical mooring vertical resolution (270, 490, 990 and 1590 dbar) and recomputing the 20 dbar resolution temperature profile using equation (6.5) with the ∂T/∂p
climatology as a function of temperature (black) or pressure (red). The error is the mean of the 44 CTD casts which have depths greater than 1590 dbar (heavy line) with
We adopt the !T
!p(p) climatology (Figure 6.10) for vertical interpolation of the Kiel-
276 mooring data set given the smaller estimated error over the upper 100m (Figure 6.12) and negligible differences in performance with the !T!p(T)below this. A formal
assessment of the errors associated with the vertical interpolation is presented in Section 6.2.7.