12 TIDAL PREDICTIONS IN THE INDIAN & PACIFIC OCEANS
52 TIDAL LEVELS AND COMMON TIDAL TERMS
For the purpose of § 40-43, it is assumed that students, from their studies of Coastal Navigation, have some elementary notions of the causes of the tide, a working knowledge of tidal levels and the common tidal terms, and the ability to calculate heights of the tide for Standard and Secondary ports using the data in the Admiralty Tide Tables Volume 1: European Waters including the Mediterranean Sea.
Tide Tables give information by means of which the height of the tide at any time, or the time at which the height of the tide is any given amount, may be ascertained. Most maritime nations publish Tide Tables and the British Hydrographic Office publishes annually the Admiralty Tide Tables in three volumes which collectively cover the whole of the coastal regions of the world, Volume 1 of A.T.T. has been referred to above and most students will already be familiar with this volume and its use. Volume 2 of A.T.T. covers the Atlantic Ocean, Volume 3 the Indian Ocean and Volume 4 covers the Pacific Ocean and Adjacent Seas. The limits of these four volumes of the Admiralty Tide Tables are illustrated in fig. 52-1.
Ocean navigators, according to the extent of their voyaging will require either Volume 2/3 or Volume 4 of Admiralty Tide Tables, in addition to Volume 1. Because the tides in areas outside European and Mediterranean waters may be either semidiurnal, predominantly diurnal, or more usually a mixture of the two, the methods of tidal prediction using Volumes 2/3 and 4 of the Admiralty Tide Tables are different from those with which students will be familiar using Volume 1, particularly for finding the heights of the tide at times intermediate to those of high water and low water. At some times and in some places, the only satisfactory method of prediction is to use the harmonic tidal constants given in Volumes 2/3 and 4 of A.T.T. in conjunction with the Admiralty Method of Prediction, and this method is described later in this Chapter.
In order to understand the tides of non-European waters and the data given in Volumes 2/3 and 4 of A.T.T., it is necessary to go a little more deeply into tidal theory than was necessary to make tidal predictions from the comparatively simple data in Volume 1, and this tidal theory is explained in § 43. First, however, let us refresh students’ memories with some of the common tidal terms and tidal levels with which they are already familiar, before we introduce some of the new terms associated with more advanced methods of tidal predictions.
198. TIDAL LEVELS AND COMMON TIDAL TERMS
The tide is a phenomenon involving a periodic rising and falling of the sea surface due to a combination of so-called tidal forces which are Astronomical in origin. This rhythmic oscillation of sea level is associated with horizontal movements of water known as tidal streams, which should not be confused with currents which, as was shown in § 10, are horizontal movements of water due to non-periodic forces which are oceanographical in origin.
The period of the tide is the interval of time between successive high or low waters. The vertical distance between the levels of successive high and low water (or vice-versa) is known as the range of the tide. Both the period and the range of the tide at any place are variable. Where the tide is predominantly semi-diurnal the average period is about 12 hours. The range in the open oceans is usually less than 1 metre, but in some coastal regions ranges of up to 15 metres may be experienced.
The average level of the sea over a long period of time (preferably 18.6 years) or the average level which would exist in the absence of tides, is known as the mean sea level (M.S.L.) whereas the average level between successive high and low water levels is referred to as the mean tide level (M.T.L.) The average value of tidal levels, M.H.W.S., L.A.T., etc., vary from year to year in a cycle of approximately 18.6 years, and the tidal levels given in Admiralty Tide Tables are average values for the whole cycle. Fig. 52-2 illustrates the various tidal levels for a Highest Astronomical Tide H.A.T. semidiurnal tide, some of which are defined below: –
HIGHEST ASTRONOMICAL TIDE (H.A.T.) and LOWEST ASTRONOMICAL TIDE (L.A.T.) are the highest and lowest levels respectively which can be predicted to occur under average meteorological conditions and under any combination of Astronomical conditions. These levels will not be reached every year and H.A.T. and L.A.T. must not be regarded as the extreme levels which can be reached, as storm surges may cause considerably higher and lower levels to occur (see Storm Tides in § 10).
CHART DATUM is, in modern practice, established at or near L.A.T. The datum for tidal prediction must be the same as the datum soundings since the total depth of water is found by the addition of the charted depth to the height of the tide.
The levels at which datum have been established at Standard Ports, however, vary widely and the datum do not conform to any uniform level. These datum are being gradually adjusted as opportunity offers so as to approximate L.A.T.
MEAN HIGH WATER SPRINGS (M.H.W.S.) is the average height, throughout a year when the average maximum Dec. of the Moon is 23½°, of the heights of two successive high water during those periods of 24 hours (approximately once a fortnight when the range of the tide is greatest.
MEAN LOW WATER SPRINGS (M.L.W.S.) is the average height obtained by two successive low water during the same periods as for M.H.W.S.
MEAN HIGH WATER NEAPS (M.H.W.N.) is the average height, throughout a year when the average maximum Dec. of the Moon is 23½°, of the heights of two successive high water during those periods (approximately once a fortnight) when the range of the tide is least.
MEAN LOW WATER NEAPS (M.L.W.N.) is the average height obtained from the two successive low water during the same periods as for M.H.W.N.
HEIGHT OF TIDE is the vertical distance between the sea level at any instant of time and the plane of reference known as Chart Datum (C.D.) see above. The commonest tidal problem is that in which it is necessary to find the correction to apply to a sounding before comparing with the charted depth, and because chart depths are given below Chart Datum, the correction to the observed sounding is usually negative. For this reason, the term Reduction to Sounding has been applied to this common type of problem and is synonymous with the Height of Tide.
The graphical representation of observations of the changing level of the sea surface is known as a tidal curve. Students will be familiar with the tidal curves given for the majority of Standard Ports in Volume 1 of Admiralty Tide Tables. Observations by means of which tidal curves are obtained are made by means of a tide pole or tide gauge erected vertically from the sea bed in the place for which the tidal curve is required (fig. 52-3). Tidal curves for most European Standard Ports will be found to be rough cosine curves which have a period of about 12½ hours. A tide which yields this form of curve, in which there are two high and two low waters each day, is referred to as a semi diurnal tide. The tidal curves of certain places in the Gulf of Mexico and many Pacific areas have periods of about 24 hours, and these tides are known as diurnal tides. Some tides produce curves which are mixed, these having both semidiurnal and diurnal characteristics. Typical tidal curves of the three types are shown in fig. 52-4.
It will be seen from fig. 52-4, that in mixed tides there is a marked difference between the height of successive high (or low) water levels.
All tides are composed of both semi-diurnal and diurnal components, the latter introducing inequality in successive heights of high or low water and also in the times. When this diurnal inequality reaches a certain limit it becomes more informative to list the average heights of the higher and lower high and low waters rather than the average spring and neap values, and for many places in Volumes 2 and 3 of Admiralty Tide Tables these are the values which are quoted. This gives rise to some new tidal levels with which some students may not be so familiar:
HIGHER HIGH WATER (H.H.W.) is the higher of the two high water which occur in one tidal cycle of a mixed tide.
LOWER HIGH WATER (L.H.W.) is the lower of the two high water which occur in one tidal cycle of a mixed tide.
HIGHER LOW WATER (H.L.W.) is the higher of the two low water which occur in one tidal cycle of a mixed tide.
LOWER LOW WATER (L.L.W.) is the lower of the two low water which occur in one tidal cycle of a mixed tide.
MEAN LOWER HIGH WATER (M.L.H.W.) is the height of the mean of the lower of the two daily high water over a long period of time.
When only one high water occurs on some day’s ∆ is printed in the M.L.H.W. column of A.T.T. to indicate that the tide is usually diurnal.
MEAN HIGHER LOW WATER (M.H.L.W.) is the height of the mean of the higher of the two daily low water over a long period of time.
When only one low water occurs on some day’s ∆ is printed in the M.H.L.W. column of A.T.T. to indicate that the tide is usually diurnal.
MEAN LOWER LOW WATER (M.L.L.W.) is the height of the mean of the lower of the two daily low water over a long period of time.
When only one low water occurs on a day this is taken as the lower low water.
199. THE USE OF ADMIRALTY TIDE TABLES (A.T.T.) VOLUMES 2/3 & 4
General arrangement of Volumes 2/3 and 4 of Admiralty Tide Tables
Part 1 of these tables give daily predictions of the times and heights of high and low waters at a selected number of Standard Ports. The list of Standard Ports is given inside the front cover of each volume. The times of Standard Port predictions are given in the normal standard time kept by the port, but when using the tables it should be verified that this is the same as the time which is actually being kept. Changes in standard times are not always reported in sufficient time for inclusion in the latest edition of the tide tables. All predicted heights in Part 1 are given in METRES above Chart Datum, and Chart datum is understood to be the datum of soundings on the latest edition of the largest scale Admiralty Chart of the place.
Part 1a of Volumes 2/3 and 4 of A.T.T. give daily predictions of tidal streams at a limited number of places. When tidal streams are semidiurnal in character (as in N. European waters) they can be predicted by reference to a suitable Standard Port by tables printed on the published chart. However, in areas where the diurnal inequality of the tidal stream is large, this procedure is not possible. In certain important parts of these areas (e.g., the Sunda Strait, Surabaya Strait and Torres Strait in Volume 3 of A.T.T.) daily predictions of tidal streams are given in Part 1a of the tables.
These give the maximum rates and the times at which these occur, together with the times of slack water, i.e., when the direction of the stream turns. An extract from the 199X Tidal Stream Table for the Torres Strait is shown in fig. 52-5.
Part 11 of A.T.T. Volumes 2/3 and 4 gives data for prediction at a large number of secondary ports in the form of time and height differences referred to one of the Standard Ports in Part 1, together with harmonic constants which can be used for prediction by the Admiralty Method of Prediction on N.P. 159 (this method is described later in this chapter). Time differences for secondary ports, when applied to times of high water and low water at Standard Ports, will give times of high and low water at the secondary ports in the zone time tabulated for the secondary port. Any change in zone time at the Standard Port or any difference between zone times at Standard and secondary ports has no significance; the predicted values must be used unaltered. Only changes in zone time at the secondary port, where different from those tabulated, should be corrected for. It should be verified that the zone time tabulated for the secondary port is the same as that which is being kept.
For semi-diurnal ports, heights obtained by applying the height differences are those for the mean spring and neap levels. For the diurnal ports, heights obtained by applying the height differences are those for mean higher and lower high and low waters. The height difference in Part 11 is also given IN METRES and, when applied to heights at Standard Ports, will give heights referred to Chart Datum at the secondary port.
There are also a number of Supplementary Tables for use with the main tables, and these appear between the Introduction and Part 1 of each volume. Table 1 does not appear in Volumes 2/3 and 4 of A.T.T., only in Volume 1; Table 11 is a tidal curve for finding the height of the tide at times intermediate to the predicted times of high and low waters (see below); Table 111 is a multiplication table for use with Table 11,
Table 1V is a Conversion Table – meters to feet; Table V gives the Tidal Levels of all the Standard Ports in the volume; Table V1 does not appear in Volumes 2/3 and 4, only in Volume 1; Table V11 is a Table of Tidal Angles and Factors for use in the Admiralty Method of Prediction; and Table V111 is a Table of Astronomical Arguments (of no direct value to navigators).
200. FINDING THE HEIGHT OF TIDE AT STANDARD PORTS IN VOL. 2/3 AND 4 OF A.T.T.
Finding the times and heights of High Water (HW) and Low Water (LW) at a Standard Port in Volumes 2/3 and 4 of A.T.T., as in Volume 1, presents no problem because the times and heights of HW and LW are tabulated for every day in the year. Care should be taken, however, to ensure that the Zone Time used for the predicted times (given at the head of each page) is the same as the actual Zone Time being used, the predicted tide time being corrected if necessary.
In volumes 2/3 and 4 of A.T.T. the Standard Ports do not have individual Spring and Neap Curves and to find the height of the tide at times other than HW or LW one of two methods is employed, according to the type of tide involved. The first method is used when the tide is predominately semidiurnal in character and is based on the assumption that the rise and fall of the tide take the shape of a simple cosine curve. Examination of some of the actual tidal curves for semidiurnal tides given in A.T.T. Volume 1 will show that in practice the shape of the tidal curve may differ from a simple cosine curve, sometimes considerably, and this method must therefore be treated with some caution. The method uses a standard set of tidal curves at half-hourly intervals between durations of the rise and falls from 5 to 7 hours inclusive, these curves comprising Table II in each volume of A.T.T. Table II is shown in fig. 52-6.
The principle of the method using Table II is the same as that used for the tidal curves for European waters in Volume 1 of A.T.T., where the predicted range is multiplied by a factor, depending on the length of time before or after high water, the result being added to the height of low water to give the required height.
As can be seen from the diagram, the durations covered are from 5 to 7 hours inclusive; for intermediate durations interpolation should be employed, but no extrapolation should be attempted. At ports where the tidal curve is badly distorted, it will be found that the duration of the rise or fall of the tide will be outside the limits of the diagram, i.e., less than 5 hours or greater than 7 hours, and in such cases, this method cannot be used, and prediction can only be achieved by the Admiralty Method described later in this chapter. This latter should also be used when accuracy is important, even when the duration is within the limits of Table II.
To find the height of the tide at an intermediate time between HW and LW using Table II, the procedure is as follows: –
Turn to the Standard Port predictions for the day in question.
Determine the duration of rise or fall from the difference between the times of HW and LW.
Determine the interval from HW for the time required.
From the diagram (Table II), using the interval from HW and the duration of rise or fall, obtain the factor.
From the predicted heights of HW and LW, by subtraction, find the predicted range.
Multiply the predicted range by the factor.
Add the result to the predicted height of LW to obtain the predicted height at the time required.
Ex. No 01: Find the height of the tide at noon on 08th Nov at Singapore. (An extract from the tide table for Singapore is shown below)
201. FINDING TIMES & HEIGHTS OF HW & LW AT SECONDARY PORTS IN VOL. 2 / 3
When predicting times of HW and LW at a secondary port from Volumes 2 and 3 of A.T.T., the time differences from Part II of the tables are applied to the predicted times at the Standard Port to which the secondary port is referred. The Standard Port to be used is the next above the secondary port in question and for which data is printed in bold type between horizontal lines. Where the secondary port tide is mainly semidiurnal, i.e., the time differences are for M.H.W. and M.L.W. the time differences can be applied to both high waters and both low water without appreciable error, but where the diurnal component of the tide is large and the time differences are for H.H.W. and L.L.W., these differences may be used for the time of L.H.W. and H.L.W. but the resultant times at the secondary port should be treated with reserve as the probable error may be large.
As already stated, if the time differences are applied to the figures tabulated for the Standard Port the times of HW and LW so obtained for the secondary port will be in the Zone Time printed directly above the secondary port in Part II of the tables, irrespective of the Zone given for the Standard Port. The data used in obtaining the standard port figures should be the data for which the predictions are required, after allowing for the time differences to be applied, even if the secondary port and the Standard Port are on the opposite sides of the Date Line.
The heights of HW and LW are obtained by applying the height differences tabulated in Part II of the tables to the daily predictions for the same Standard Port which is used for the times. It must be noted, however, that the predictions for the Standard Ports include seasonal variations in mean sea level which may be different from the seasonal variations in mean sea level for the secondary port.
The first step in applying height differences must therefore be to SUBTRACT ALGEBRAICALLY the seasonal variation from the Standard Port from the predicted height obtained from Part 1. The next step is to apply the height difference corresponding to this corrected height at the Standard Port, interpolating or extrapolating as necessary. The final step is to ADD ALGEBRAICALLY the seasonal variation for the secondary port. A table giving the seasonal variations in mean level at both Standard and secondary ports is given at the foot of the right-hand pages of Part II. It is important to remember the algebraic rule of signs when applying the values for seasonal variation. For example, if the Standard Port height is 4.2m and the seasonal variation is – 0.2, then: –
Having obtained the corrected heights at the Standard Port, the height differences given for the secondary port would then be applied, giving an uncorrected height for the secondary port to which the seasonal variation for the secondary port should be added (algebraically), For example, if the uncorrected height at the secondary port is 2.1m. and the seasonal variation for the secondary port is + 0.2, then: –
Note in the example below, that the time differences for the secondary port were tabulated for M.H.W. and M.L.W., while the height differences were tabulated for M.H.H.W., M.H.L.W. and M.L.L.W.
Ex To find times/heights of high & low waters at Secondary Haven on 16th Jan using the following extracts:
Note: – Computation of H.W. is done from the two values of H.W. tabulated. Similarly, L.W. is computed from the two tabulated values of L.W.
In the next Example, the time differences for the secondary port are tabulated for H.H.W. and L.L.W. and the height differences for M.H.H.W. and M.L.L.W. only.
Ex To find the times and heights of high and low waters at Secondary Harbour on 10th February using the following extracts: –
Note: – Where only one H.W. and one L.W. value is tabulated in Part II, interpolation for either H.W. or L.W. must be made between these two values.
For some secondary ports no time differences are quoted in Part II of A.T.T., the letter ‘p’ being inserted instead. In these cases the only method of prediction is the Admiralty Method on Form N.P. 159. Similarly, to find the height of tide at a secondary port at times other than HW or LW a prediction for the day should be made using N.P. 159 and the Harmonic Constants given in Part II of A.T.T. The Admiralty Method of Tidal Prediction on Form N.P. 159 is explained in the next chapter, but in order to understand this, it is necessary to explain a little more about elementary tidal theory.