Statistics

ADCP/MODAS comparison

The comparison between in-situ velocity measurements by ship-mounted ADCP (see figure below) and estimates from the MODAS field indicates a reasonable agreement between the two estimates. For each ADCP data point (estimated at 30 min intervals if the ship was underway) the corresponding MODAS velocity was derived from the daily MODAS SSH field according to the well known equations:

with g = 9.81 ms^-2 being the gravitational constant, f the Coriolis parameter and h the MODAS steric sea surface height. The MODAS field was prepared at a resolution of 1/8°, which corresponds to 14 km in the meridional and 11 km (at 40°S) in the zonal direction

fig_5.gif (8026 bytes)

ADCP velocity (u- and v-component, speed and direction between 25 to 75m depth) as dots versus concurrent surface velocities estimates from MODAS (solid lines).

The resulting correlation coefficients range between 0.5 and 0.75 (see Table below), with the zonal component slightly better correlated than the meridional component. The MODAS field, due to the objective analysis process involved in its generation, is clearly smoother than the ADCP data. The amplitude (or maximum velocities) observed in the MODAS data are nevertheless quite comparable (with the exception of data points 20-30) which suggests that the covariance scales used in MODAS are sufficiently short to allow most mesoscale features to exhibit their full strength.

Table of correlation coefficients between ADCP (25-75m bin) and MODAS velocities . The correlation coefficients for the ARC region are calculated using data points 40-180:

Correlation coefficients	u	v	speed	direction
R _overall	0.74	0.61	0.50	0.57
R _ARC	0.76	0.77	0.57	0.64

RAFOS/MODAS comparison

The selection of float data considered to be located within the ARC was compared against surface velocities calculated from MODAS SSH. For each ARC float data point the co-located, simultaneous surface velocity was calculated according to the procedure in described the section "ADCP/MODAS comparison." A linear dependence is clearly visible for the zonal and meridional velocity components as well as for direction. Correlation coefficients are satisfyingly high (0.70 and 0.79, see Table below) for the total ensemble of 15 floats (1520 degrees of freedom). To study possible trends in the correlation with increasing depths, the floats were subsequently grouped according to their temperature. Three temperature classes (3°-6°C, 6°-8°C and 8°-10°C) were chosen. Alternatively, the floats were sorted according to type; a) shallow isopycnal floats ballasted for s_q = 26.8, b) isobaric floats which cover an intermediate depth but overlap with the depth ranges of both the shallow isopycnal as well as the last group c) deep isopycnal floats ballasted for s_q = 26.8. Lastly, a group of data with pressures between 900 and 1100m was formed. The resulting correlation coefficients (see table below) show no significant difference in correlation between float and MODAS data between the zonal and meridional components or the direction. The speed however shows a general decrease with depths. For example the correlation coefficient between float and MODAS speeds decreases from 0.72 for the shallow isopycnal group to 0.18 for the 900-1100m group. Most probably this is due to an barotropic velocity component unaccounted for in the MODAS field.

Table of correlation coefficients between ARC RAFOS float velocities and corresponding MODAS velocities:

Correlation coefficients	zonal	meridional	speed	direction
R_{isopycnal floats (shallow)}	0.82	0.82	0.72	0.74
R_{isobaric floats}	0.64	0.81	0.37	0.86
R_{isopycnal floats (deep)}	0.67	0.73	0.07	0.79
8°- 10°C	0.81	0.82	0.59	0.78
6°- 8°C	0.59	0.78	0.24	0.88
3°- 6°C	0.71	0.76	0.37	0.81
900 – 1100m	0.56	0.80	0.18	0.81
R_{all floats}	0.70	0.79	0.42	0.81

With increasing depth this barotropic component becomes more dominant over the isopycnal velocity component, which presumably is more closely correlated with the MODAS field. To test this hypothesis, the correlation between zonal and meridional velocity components as well as speed were fitted with a linear fit which coefficients are given in the following Table.

Table of linear fit parameters ( y = ax +b) between ARC RAFOS float velocities and corresponding MODAS velocities:

data selection	zonal comp.		meridional comp.		deg. of freedom	num. of floats
	a	b [cm/s]	a	b [cm/s]
isopycnal floats (shallow)	0.48	7.9	0.29	-1.1	469	4
isobaric	0.36	7.5	0.23	-0.9	712	9
isopycnal floats (deep)	0.24	8.6	0.16	0.6	335	2
8°- 10°C	0.47	8.3	0.27	-1.9	593	7
6°- 8°C	0.35	11.5	0.23	0.3	258	7
3°- 6°C	0.30	5.6	0.19	-0.2	665	7
900 – 1100m	0.19	11.2	0.22	0.3	402	9
all	0.36	7.8	0.23	-0.6	1520	15

Throughout the table, the zonal float velocity is offset by order 10 cm s^-1 with respect to the MODAS velocities. This offset is also reflected in the correlation of float versus MODAS directions. The figure below (lower right panel) shows that float velocities exceed the bisect for angles between 0° and 90°T, while they fall below for angles between 90° and 180°T. This is explicable by the 10 cm s^-1 offset in the zonal velocity, which results in a stronger eastward flow than depicted by MODAS. The effect the offset has on the angle obviously depends on the baroclinic (MODAS) velocity, and is smaller for higher speeds. A set of curves depicting speeds between 20 and 120 cms^-1 clearly explain the deviation of the correlation curve from the bisect.

The fit zonal and meridional data suggests that about 25 to 30% of the surface velocity is present at mid-depth, or in terms of kinetic energy, 6 to 9%. Again, a decrease is observed with depth. The difference in correlation between direction and speed probably indicates that the structure of the MODAS field appears realistic, while is amplitude misses some of the energy present in the float data.

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Comparison of velocities from RAFOS floats measured between 600 and 1200m and surface velocities from MODAS SSH: a) the zonal component, b) the meridional component, c) speed and d) direction. Note that one of the conditions for the selection of ARC RAFOS data was speed greater 10 cms^-1, which is reflected in the cut-off velocity visible in panel (c). Panel d) shows a set of curves (thick black lines) modeling the angular correlation for velocities between 20 and 120 cm s^-1. The bisect is indicated by a thin black line.