would have to come "out of the pape

would have to come "out of the paper" at speed Vv
8.4 The geostrophic equation
The Coriolis force is sometimes called the "geostrophic" ( = earth turned)
force and the equation
2Ù sin ö Vx = g tan i (8.6)
is one version of the geostrophic equation, which expresses a balance between
the pressure force and the Coriolis force.
CURRENTS WITHOUT FRICTION 69
In principle, this geostrophic equation should permit us to determine the
speed Vx by measuring the slope i of the isobaric surface. In practice we cannot
do this because we cannot determine p directly with the necessary accuracy.
Instead we have to determine p from the hydrostatic equation p = — $pgdz
after having determined the distribution of density p with depth. Even with this
method we cannot determine the angle i absolutely. The reason is that we make
our measurements from a ship on the surface of the sea and we do not know if
the sea surface is level or not (disregarding waves). In fact, if there are currents in
the surface waters the sea surface will not be level because the geostrophic
equation applies there (neglecting wind effects which we shall add in Chapter
9), and motion gives rise to a Coriolis force which requires the water surface to
be sloping so that the horizontal component of the pressure gradient can act to
balance the Coriolis force. All that we can do is determine the difference
between ix at level z1 and i2 at level z2 as described shortly. This difference will
give us the velocity at level zx relative to that at level z2, and a finite difference
estimate of the velocity shear (d V/dz).
The slopes are small, e.g. 2Ù sin ö ~ 10 "4 at 45° latitude and for Vx
= 1 ms"1, tan i ^ 10~5, i.e. the surface rises by 1 m in 100 km, a distance
typical of the width of a strong current such as the Gulf Stream.
A technique for determining the absolute slope of the sea surface which is
receiving much attention is to use radar or laser altimetry from satellites.
Cheney and Marsh (1981a) demonstrated the estimation from Seasat satellite
radar altimeter observations of the change of sea surface elevation across the
Gulf Stream of 140 ± 35 cm or a slope of (1.2 ± 0.3) x 10"5 for three months in
1978. Substantially improved techniques with smaller standard deviations are
anticipated in the future. A review of techniques for satellite altimetry of the sea
surface was given by Cheney and Marsh (1981b).
The geostrophic equation applies equally to the atmosphere but the
meteorologist is more fortunate than the oceanographer. He can measure air
pressure directly at a number of places on the ground or at known levels in the
atmosphere and then determine the horizontal pressure-gradient term
(a (dp/dn) sin i) directly and so calculate the geostrophic wind speed. In
addition, because the speeds of currents in the ocean are small compared with
wind speeds in the atmosphere, the meteorologists can ignore the water slopes
and use "mean" sea level as a reference level.
8.41 Why worry about the geostrophic equation!
The reason why the oceanographer concerns himself about using the
geostrophic equation to determine currents is because direct measurement of
ocean currents in sufficient quantity to be useful is technically difficult and
expensive.
In shallow water a ship can anchor and hang a current meter over the side to
70 INTRODUCTORY DYNAMICAL OCEANOGRAPHY
measure the current, or can hang several meters to measure at several depths
simultaneously. However, this procedure only gives information about the
currents at the one point where the ship is anchored. Also, a ship usually does
not remain stationary when anchored but moves about (i.e. it surges and
swings) relative to the anchor. Part of this motion will be added to the water
motion measured by the current meter and constitutes a source of error for
which it is difficult to correct. In the deep ocean, it is much more difficult to
anchor and the ship motion error may be much larger than the real water
motion.
A more practical method is to use recording current meters which are hung
in a "string" from a moored buoy (see Descriptive Physical Oceanography,
Pickard and Emery (1982) for a description of instruments and techniques or
Dobson, Hasse and Davis (1980) for more details). A number of such buoys
moored in a pattern in the ocean will provide information about the threedimensional
distribution of currents as a function of time. However, because of
the expense, the difficulties of working at sea and the complicated nature of the
currents when examined in detail, it is not possible to obtain observations over
as much of the ocean as we would like.
Why should we need to measure the currents over a period of time? Why is
not one measurement at each place sufficient? Simply because real ocean
currents are not steady. They fluctuate in speed and direction and the only way
to determine the mean and the variation with time is to make frequent
measurements for a sufficient period of time (probably several months at least).
The geostrophic method for calculating the current requires information on
the distribution of density in the ocean; it is easier to obtain this information
(from measurements of temperature and salinity) than it is to measure currents
directly. The method suffers from several disadvantages, but when used
intelligently and in parallel with other information it can be very helpful. In
fact, most of our knowledge of ocean circulation below the surface has been
obtained in this way. The geostrophic method is also useful in strong currents
(e.g. the Gulf Stream as we shall show in Section 8.10) in which it is difficult to
moor recording current meters.
We should add that currents in the surface layer can be deduced from the
navigation records of ships, and most of our surface-layer information has
been acquired from this source. The method of using navigation records is to
assume that the difference between the intended path, based on the speed and
direction of the ship relative to the water, and the one actually followed
(determined by astronomical, satellite, etc., navigation) is due to the water
currents. Obviously such data are "noisy", that is any one observation may have
a large error, but by averaging over many years using all the observations in a
particular area (e.g. 5° latitude by 5° longitude) one can obtain the "climatological"
or long-term average motion. There are undoubtedly significant
variations of the actual motions from these averages; variations of several times
CURRENTS WITHOUT FRICTION 71
the mean seem common according to our limited direct current observation
data. There are probably cases of smaller-scale features of the flow than are
resolved by such means. For example, the pattern of flow in the equatorial
Pacific deduced from observations has become more and more complicated as
more detailed observations have been made. (Because of effects of surface wave
currents, many current meters do not work well near the surface, so obtaining
better observations of surface currents remains a problem. See also Baker,
1981. Surface drifters tracked by satellite are beginning to give direct

Hasil (Bahasa Indonesia) 1:

would have to come "out of the paper" at speed Vv8.4 The geostrophic equationThe Coriolis force is sometimes called the "geostrophic" ( = earth turned)force and the equation2Ù sin ö Vx = g tan i (8.6)is one version of the geostrophic equation, which expresses a balance betweenthe pressure force and the Coriolis force.CURRENTS WITHOUT FRICTION 69In principle, this geostrophic equation should permit us to determine thespeed Vx by measuring the slope i of the isobaric surface. In practice we cannotdo this because we cannot determine p directly with the necessary accuracy.Instead we have to determine p from the hydrostatic equation p = — $pgdzafter having determined the distribution of density p with depth. Even with thismethod we cannot determine the angle i absolutely. The reason is that we makeour measurements from a ship on the surface of the sea and we do not know ifthe sea surface is level or not (disregarding waves). In fact, if there are currents inthe surface waters the sea surface will not be level because the geostrophicequation applies there (neglecting wind effects which we shall add in Chapter9), and motion gives rise to a Coriolis force which requires the water surface tobe sloping so that the horizontal component of the pressure gradient can act tobalance the Coriolis force. All that we can do is determine the differencebetween ix at level z1 and i2 at level z2 as described shortly. This difference willgive us the velocity at level zx relative to that at level z2, and a finite differenceestimate of the velocity shear (d V/dz).The slopes are small, e.g. 2Ù sin ö ~ 10 "4 at 45° latitude and for Vx= 1 ms"1, tan i ^ 10~5, i.e. the surface rises by 1 m in 100 km, a distancetypical of the width of a strong current such as the Gulf Stream.A technique for determining the absolute slope of the sea surface which isreceiving much attention is to use radar or laser altimetry from satellites.Cheney and Marsh (1981a) demonstrated the estimation from Seasat satelliteradar altimeter observations of the change of sea surface elevation across theGulf Stream of 140 ± 35 cm or a slope of (1.2 ± 0.3) x 10"5 for three months in1978. Substantially improved techniques with smaller standard deviations areanticipated in the future. A review of techniques for satellite altimetry of the seasurface was given by Cheney and Marsh (1981b).The geostrophic equation applies equally to the atmosphere but themeteorologist is more fortunate than the oceanographer. He can measure airpressure directly at a number of places on the ground or at known levels in theatmosphere and then determine the horizontal pressure-gradient term(a (dp/dn) sin i) directly and so calculate the geostrophic wind speed. Inaddition, because the speeds of currents in the ocean are small compared withwind speeds in the atmosphere, the meteorologists can ignore the water slopesdan menggunakan "berarti" permukaan laut sebagai tingkat referensi.8.41 mengapa khawatir tentang persamaan geostrophic!Alasan mengapa Kelautan menyangkut sendiri tentang menggunakanpersamaan geostrophic untuk menentukan arus adalah karena langsung pengukuranarus laut dalam jumlah yang memadai untuk menjadi berguna sulit secara teknis danmahal.Di perairan dangkal kapal dapat jangkar dan menggantung meter arus ke sisi untuk70 OSEANOGRAFI DINAMIK PENGANTARmengukur arus, atau dapat bertahan beberapa meter untuk mengukur pada beberapa kedalamansecara bersamaan. Namun, prosedur ini hanya memberikan informasi tentangarus pada satu titik mana kapal berlabuh. Juga, sebuah kapal biasanya tidaktidak tinggal diam ketika berlabuh tapi bergerak tentang (yaitu lonjakan danayunan) relatif terhadap jangkar. Bagian dari gerakan ini akan ditambahkan ke dalam airgerak diukur oleh meteran saat ini dan merupakan sumber kesalahanyang sulit untuk memperbaiki. Di laut dalam, itu jauh lebih sulit untukjangkar dan kapal gerak kesalahan mungkin jauh lebih besar daripada air nyatagerak.Sebuah metode yang lebih praktis adalah dengan menggunakan rekaman sekarang meter yang digantungdalam "string" dari sebuah pelampung ditambatkan (Lihat deskriptif tsunami,Pickard dan Emery (1982) untuk keterangan tentang alat dan teknik atauDobson, Hasse dan Davis (1980) untuk detail lebih lanjut). Sejumlah pelampung tersebutditambatkan di pola di laut akan memberikan informasi tentang threedimensionaldistribusi arus sebagai fungsi dari waktu. Namun, karena daribiaya, kesulitan bekerja di laut dan sifat rumitarus apabila diteliti secara rinci, hal ini tidak mungkin untuk memperoleh pengamatan atassebanyak laut seperti kami ingin.Mengapa harus kita perlu mengukur arus selama jangka waktu? Mengapa adalahtidak satu pengukuran di setiap tempat yang cukup? Hanya karena laut nyataarus tidak stabil. Mereka berfluktuasi dalam kecepatan dan arah dan satu-satunya carauntuk menentukan mean dan variasi dengan waktu adalah membuat seringpengukuran untuk jangka waktu yang cukup (mungkin beberapa bulan setidaknya).Metode yang geostrophic untuk menghitung saat ini membutuhkan informasi padadistribusi kepadatan di laut; lebih mudah untuk mendapatkan informasi ini(dari pengukuran suhu dan salinitas) daripada untuk mengukur aruslangsung. Metode menderita dari beberapa kekurangan, tetapi ketika digunakancerdas dan secara paralel dengan informasi lainnya dapat sangat membantu. DalamBahkan, sebagian besar pengetahuan kita tentang sirkulasi laut di bawah permukaan telahDiperoleh dengan cara ini. Metode geostrophic ini juga berguna dalam arus kuat(misalnya Teluk Stream sebagai kita akan tunjukkan di bagian 8,10) di mana itu sulit untukMoor rekaman sekarang meter.Kita harus menambahkan bahwa arus di lapisan permukaan boleh disimpulkan dariCatatan navigasi kapal, dan sebagian besar informasi lapisan permukaan kami telahbeen acquired from this source. The method of using navigation records is toassume that the difference between the intended path, based on the speed anddirection of the ship relative to the water, and the one actually followed(determined by astronomical, satellite, etc., navigation) is due to the watercurrents. Obviously such data are "noisy", that is any one observation may havea large error, but by averaging over many years using all the observations in aparticular area (e.g. 5° latitude by 5° longitude) one can obtain the "climatological"or long-term average motion. There are undoubtedly significantvariations of the actual motions from these averages; variations of several timesCURRENTS WITHOUT FRICTION 71the mean seem common according to our limited direct current observationdata. There are probably cases of smaller-scale features of the flow than areresolved by such means. For example, the pattern of flow in the equatorialPacific deduced from observations has become more and more complicated asmore detailed observations have been made. (Because of effects of surface wavecurrents, many current meters do not work well near the surface, so obtainingbetter observations of surface currents remains a problem. See also Baker,1981. Surface drifters tracked by satellite are beginning to give direct