Scales of motion captured in the Mumbai tide gauge
The surface of the sea
deforms continuously. Its level, measured relative to an arbitrary
datum, is called sea level, which changes with
time, and is the most obvious indicator of change in oceans. Changes
in sea level are greater in shallow waters in
the vicinity of a coast than in the open sea, and since a large
fraction of the human population resides in coastal areas, variations
in sea level have aroused interest for a long time. A reasonably
accurate prediction of sea level was necessary for safe navigation of
boats and ships in harbours. This need, and the relative ease of
measuring sea level compared to measuring, say, temperature or
currents, has led to it being one of the best-documented oceanic
variables. Hourly measurements of sea level are available at several
places over the globe, some of the records stretching back to the
nineteenth century. A tide gauge measures sea level relative to land;
an increase in sea level may either be due to an absolute rise in sea
level, or due to the sinking of land. The largest changes evident in
a typical sea-level record, like
that at Mumbai, are those due to astronomical tides. These regular,
periodic patterns are modified by the effects of weather; exchange of
energy between the atmosphere and the ocean occurs at all space and
time scales, from the generation of short-period wind waves to the
slow transfer of energy, over a century, from the tropics to the
poles by the global ocean circulation. The sea-level record also
includes the effect of secular changes forced by changes in the
volume of ice locked in major ice caps and glaciers. In the north
Indian Ocean, which we define as extending from about 5°S to the
Asian land mass in the north, the major signals in the coastal
tide-gauge records are the semi-diurnal and diurnal tides and the
seasonal cycle forced by the monsoon winds, the most significant
aspect of the weather of the region. Since these are the most
prominent signals, it is necessary to understand them before we begin
to study other frequencies evident in sea-level records: storm
surges, intra-seasonal oscillations, inter-annual and inter-decadal
changes, etc.
All these frequencies are
seen in the sea-level record at Mumbai.
The change in sea level due to tides is much greater than those
related to weather (top, or first, panel); the latter is obtained by
filtering the hourly sea-level record with a low-pass filter. Even
the surges due to storms (second panel) are almost an order of
magnitude smaller than the tide at
Mumbai. Tidal and non-tidal sea-level oscillations are usually
studied separately because of the vastly different ways in which they
are forced. In studying the large-scale or basin-scale circulation,
we ignore the tides, focusing instead on the seasonal cycle of sea
level at the Indian coast. Though this seasonal variation (third
panel) is much smaller than the tides, the related movement of the thermocline is
important. To obtain the seasonal cycle of sea level, it is necessary
to filter the tides and other high-frequency oscillations out of the
sea-level data. This de-tiding is most easily achieved by averaging
the hourly sea level over a month to obtain monthly sea level.
Monthly sea-level data are compiled by the Survey
of India from hourly measurements and are archived at the
Permanent Service for Mean Sea Level (PSMSL),
UK, along with a history of the datum with respect to which the sea
level was measured. A climatology is obtained from the monthly sea
level by averaging the data for a particular month, say January, over
all the years of the record. The climatological seasonal cycle is
then obtained by removing the annual mean from the climatology of
monthly sea level. As may be expected, there are differences between
the climatological seasonal cycle and the seasonal cycle for a given
year (fourth panel): the former (climatology) is what we expect and
is therefore the climate, while the latter is what we get, and
is therefore the weather.
The tide gauge at Mumbai shows variability over this entire range
of time scales, from the semi-diurnal and diurnal tide to
inter-decadal changes, with intra-seasonal, seasonal, and
inter-annual variations also prominent in the spectrum of
variability. Variability similar to that shown here for sea level
should be seen in all variables, but we do not have sufficient data
to document the variability for most of them.
. 
Illustration 1: Sea-level variability at Mumbai, hich has the only more-than-century-long sea-level record in the Indian Ocean. Hourly,
daily, monthly, and annual sea level (cm) are plotted as a functionof time to reveal the variability over a range of frequencies. (a)
Hourly sea level (red) and daily sea level (blue) during 16 May to 15 June, 1976. The residual signal (daily sea level) after removing
the tide is much smaller than the tidal oscillation. The de-tided signal is computed using a low-pass filter. (b) Daily sea level as
in (a), but with an increase in the scale ofthe ordinate. Note the storm surge of about 70 cm in the beginning of June. It is also seen
in (a) and perturbs the tidal cycle, which has a much larger range. (c) Daily sea level (blue) and monthly sea level (red) for 1976.
Monthly sea level is computed by averaging the hourly sea level, asmeasured by the gauge, over a month. (d) Monthly sea level for 1976
(red) as in (c), but with the ordinate changed again because the monthly average of sea level varies over a smaller range than does
daily sea level; superimposed on this monthly sea level for 1976 is the climatological monthly sea level (blue). The climatological
monthly sea level is the average over the length of the data record, which is more than a century at Mumbai, for each month. (e) The
annual sea level over the length of the data record (1878 to 1988 in this figure) (red), showing the inter-annual variability in sea
level at Mumbai. Filtering annual sea level with a 10-year boxcar filter (10-year running mean) (blue) reveals inter-decadal
variations. At Mumbai, these inter-decadal variations are as large as are the variations rfom year to year. (This discussion follows Shankar (2000).)
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