APPENDIX A1. VISUAL OBSERVATIONS OF WIND AND WAVES

Observations of Wind

Wind force is estimated from the appearance of the sea surface according to the interpretation of the Beaufort Scale of Wind Force given in [Table 1]. This interpretation, which has been in use since 1941, is based on the assumptions that the observation is made in the open ocean and that the wind has been blowing for long enough to generate the appropriate weather conditions. Consideration must therefore be given to the possibility of a time lag between the wind rising and the sea increasing; the appearance of the sea surface can also depend on the fetch of the wind, swell, tides, precipitation and air-sea temperature difference. Ranges of wind speed equivalent to each Beaufort force are shown in Table 1, and the observer, using his or her judgement to interpolate between the range limits, reports a wind speed to the nearest knot.

Beaufort Wind Force

Mean Wind Speed in knots

Limits of wind speed in knots

Descriptive term

Sea criterion

Probable Height of Waves in metres

Probable Maximum Height of Waves in metres

 

Measured at a height of 10m above sea level

       

0

00

Less than 1

Calm

Sea like a mirror.

-

 

1

02

1-3

Light air

Ripples with the appearance of scales are formed, but without foam crests.

0.1

0.1

2

05

4-6

Light breeze

Small wavelets, still short but more pronounced, crests have a glassy appearance and do not break.

0.2

0.3

3

09

7-10

Gentle breeze

Large wavelets. Crests begin to break. Foam of glassy appearance. Perhaps scattered white horses.

0.6

1.0

4

13

11-16

Moderate breeze

Small waves, becoming longer; fairly frequent white horses.

1.0

1.5

5

19

17-21

Fresh breeze

Moderate waves, taking a more pronounced long form; many white horses are formed. (Chance of some spray).

2.0

2.5

6

24

22-27

Strong breeze

Large waves begin to form; the white foam crests are more extensive everywhere. (Probably some spray).

3.0

4.0

7

30

28-33

Near gale

Sea heaps up and white foam from breaking waves begins to be blown in streaks along the direction of the wind.

4.0

5.5

8

37

34-40

Gale

Moderately high waves of greater length; edges of crests begin to break into spondrift. The foam is blown in well marked streaks along the direction of the wind.

5.5

7.5

9

44

41-47

Strong gale

High waves. Dense streaks of foam along the direction of the wind. Crests of waves begin to topple, tumble and roll over. Spray may affect visibility.

7.0

10.0

10

52

48-55

Storm

Very high waves with long overhanging crests. The resulting foam in great patches is blown in dense white streaks along the direction of the wind. On the whole the surface of the sea takes a white appearance. Tumbling of the sea becomes heavy and shock-like. Visibility affected.

9.0

12.5

11

60

56-63

Violent Strom

Exceptionally high waves. (Small and medium sized ships might be for a time lost to view behind the waves.) The sea is completely covered with long white patches of foam lying along the direction of the wind. Everywhere the edges of the wave crests are blown into froth. Visibility affected.

11.5

16.0

12

-

64 and over

Hurricane

The air is filled with foam and spray. Sea completely white with driving spray; visibility very seriously affected.

14 or over

-

Table 1 - A guide to show roughly what may be expected in the open sea.

If should be noted here that the NMIMET analysis uses the so-called 'Scientific Beaufort Scale' [3] widely considered to be quantitatively more reliable.

The reported wind direction is the direction from which the wind is blowing. It is reported in degrees from the North, to the nearest 10 degrees and is estimated by taking a compass reading (using the tops of waves, ripples, spray etc. as indicators of the wind direction).

At night, or in poor visibility, when it may not be possible for the observer to estimate the wind speed and direction from the appearance of the sea surface, other indications such as the feel of the wind upon the skin or the direction for which the exhaust is blowing can be used. Allowance must be then be made for the ship's course and speed.

As wind speed and direction are never constant, the values reported should be averages over a ten-minute period.

Observations of waves

Before any estimates of wave height, period or direction are made the observer must first distinguish between the recognisable wind wave and swell wave systems. In general waves with the same directions as the local wind are classified as wind waves, but care must be taken to ensure that swell waves with the same direction as the local wind are not mistakenly identified as wind waves and vice versa. Swell waves have a more regular appearance than wind waves, travel in a well-defined direction, and usually have long, smooth crests. Bearing in mind the distinction between wind waves and swell waves, the observer should also differentiate between the separate wave systems on the basis of their appearance, direct, and period, as follows:

  1. Wave Direction. If the mean direction of all waves of more or less similar characteristics (in particular height and length) differs 30 degrees or more from the mean direction of waves of different appearance (in particular height and / or length), then the two sets of waves should be considered as belonging to separate wave systems.

  2. Appearance and period. When typical swell waves, characterised by their regular appearance and longcrestedness, arrive approximately from the direction of the wind (i.e. within 20 degrees), they should be considered as a separate wave system if their period is at least four seconds greater than the period of the larger waves of the locally generated system.

As long as the observer can distinguish between sea and swell waves, they should be reported separately. If there are two or more distinguishable sets of swell, then two swell wave groups should be reported. If the sea and swell both come from the same direction, they should only be reported as separate systems if the difference is well marked.

Wave heights or periods reported by the observer should be the average of about 15-20 separate estimates, and only the higher waves in groups of well-formed waves should be used. This is because height and period vary from wave to wave and because the height reported should be the 'significant wave height' i.e. the average height of the upper third of all waves belonging to a wave system.

The method used for the visual estimation of wave height depends upon the length of the waves relative to the length of the ship. If the length of the waves is short in comparison to the ships length, such that the vessel spans two or more waves crests, the height should be estimated from the appearance of the waves at or on the side of the ship, preferably when the pitching and rolling of the ship is least. This method cannot be used when the length of the waves exceeds the length of the ship. The observer should then take up a position on the vessel such that his or her eye is in line with an advancing wave crest and the horizon, when the ship is vertical in a wave trough. If the height of the observing position above sea level is known, then this will also be the wave height. Estimating wave height in these conditions is a difficult task, and the methods are described in more detail in [30]. Wind wave and swell wave heights are now reported directly in half metres. Prior to 1961 a variety of coarser or more complicated wave height reporting codes were used, although the method of observation was the same.

Wave period is also reported and can be estimated by timing the passage of a floating object from one wave crest to another. Wind wave and swell wave periods are both now reported directly in whole seconds. Prior to 1968 (for wind waves) and 1982 (for swell waves) a number of coarser reporting codes were used. However, it should be emphasised that Global Wave Statistics Online does not use the virtual estimates of period because these data have been found to be very unreliable.

Since 1956, when the old, slightly coarser code for reporting wave direction was replaced, wave direction has been reported in degrees from true North to the nearest 10 degrees. The direction, which should be that from which the waves are coming, is estimated by lining up directly along the wave crests adjusting the estimating direction by 90 degrees. Wind wave direction is not reported, as it is assumed to be the same as the reported wind direction.

The estimation of wave height, period and direction is difficult at night or in poor visibility, and they should not be reported if it is not possible to make good estimates.

APPENDIX A2: DATA RETRIEVAL FOR THE NMIMET ANALYSIS

A brief account of the data retrieval from the Marine Databank of the UK Meteorological Office illustrated by a sample array has been given  [NMIMET Analysis]. The purpose of this appendix is to explain some of the details of the retrieval procedure to help understanding of the precise meaning of the data.

For each area the data retrieved onto magnetic tape for use in the NMIMET analysis is in two parts. The first part is a set of three arrays listing the total frequencies of observations in each month of each year covered for the three data categories 'All Wind', '2-Group Wave/Wind' and 'All Wave/Wind'. The 'All Wind' data cover all occasions when winds were reported in the years 1854 to 1983. The '2-Group Wave/Wind' data cover all cases when the heights and of both sea and swell wave groups were reported in the period since 1949. The 'All Wave/Wind' cover all cases when both waves (in post 1949 code) and winds were reported. These arrays are included as diagnostic information and are not used in the NMIMET analysis.

The second part is a set of 45 arrays each in the format shown in [Figure 2]. These cover the 45 data categories ('Annual' + 4 seasons) x ('All Directions' + 8 Directional Sectors) and are used as input for the NMIMET analysis. Each array contains a joint frequency distribution of resultant wave height against Beaufort Wind Force from the 2-Group wave/wind data, accompanied by a separate set of normalized 'All Wind' frequencies.

The term 'resultant wave height' is here defined as:

when both the wind wave and the swell wave directions fall within the same 45 directional sector, which has been found to be so in the majority of cases. Otherwise, the resultant wave height was taken to be the height of the higher wave component. The assignment of the 45 direction class for the resultant wave was determined by the direction of the wave group with the greater height.

For both the wave/wind scatter table and the normalized wind frequencies, it was necessary to make an estimate of the number of 'calms' to be apportioned to each 45 sector as follows:

  1. Wind Wave Scatter Tables. The total number of observed calms (i.e. observations with wind speed, wind direction, wave height and wave direction all zero) was multiplied by the ratio of the number of observations in the appropriate direction to the total number of wind/wave observations for all directions (calms excluded). This figure was then taken to he the number of calms to be apportioned to the direction sector.

  2. Normalised Wave Frequencies. The estimated number of calms in each direction sector for each month in each year was obtained by multiplying the observed number of calms in the month by the ratio of the number of wind observations in the direction sector to the total number of wind observations for all directions in the month (calms excluded). The wind frequency totals are referred to as 'normalised' because an attempt was made to ensure that individual months with relatively high observation counts did not cause bias in the overall frequency distributions. Whenever there were more than 30 wind observations (over all directions) in any month of any given year, the wind frequencies for each Beaufort Force and direction sector in the month were multiplied by 30 and divided by the number of wind observations from all directions in the month. The resulting frequency distribution was then added to the other monthly wind frequencies in the usual manner to produce normalized seasonal and 'whole year' wind frequency totals. The normalization limit of 30 observations as decided upon empirically during the development of the NMIMET technique

All visually-estimated wind reports (dating from 1854 onwards) were used in compiling the database, but wave observations were only included if they were made after January 1949, if they passed the Marine Databank quality-control checks on wind wave height against wind speed and if the heights and of both sea and swell waves were reported. Observations made before 1949 were excluded from the analysis, as the wave height reporting codes used were too coarse to be compatible with the post-1949 coding of wave height in half-metre units.

APPENDIX A3: THE NMIMET ANALYSIS

Detailed accounts of the development and validation of the NMIMET program may be found in [24]-[27]. This appendix provides a brief summary to aid understanding of the data in the Global Wave Statistics Online database and the basis of the reliability enhancement achieved

It is convenient to explain the NMIMET analysis as applied here in three stages. The first concerns the derivation of coefficients for a parametric model relating wave height and wind speed statistics. The second concerns use of this model to derive wave height statistics of enhanced reliability from input of all the available wind data. The third concerns generation of the joint probability distributions of wave heights and periods. In the case of the third stage, the procedure used for Global Wave Statistics Online and the current NMIMET output is slightly different from that used for generating the original form of the NMIMET output. To avoid possible misunderstanding both procedures will be explained.

Before explaining these stages in detail, it may be helpful to define the relationships involved symbolically Thus, the required joint probability distributions of wave height H and wave period T may be written as P (H, T), and may be derived by use of the following relationships:

Where:

= The marginal probability distribution of wave height

= The marginal probability of wind speed W for the class r.

= The conditional probability of wave height given the wind speed.

= An analytical model of with parameters H2, n, a, b, c and d to be determined.

= The conditional probability of wave period given the height H

 

An analytical model of with parameters to be determined.

(a) The Relation of Wave Heights and Wind Speeds

Parameters for fH.

The function relating wave heights and wind speeds is modelled (Figure 3) in terms of formulae for the mean value and standard deviation of the wave heights of the wave heights in each wind speed class, expressed as functions of the wind speed thus:

where:




H2, n, a, b, d and d are modelling parameters to be determined.

In general when using the NMIMET program there are two possible modes of analysis involving different procedures for determining the modelling parameters. The first known as the 'Smoothing Mode', is suitable for use when there are adequate samples of joint wave and wind data available for the area concerned. In this case, the parameters are determined by best fitting of the data. The second, known as the 'Predictive Mode' can be used when there are no adequate joint wave and wind data and, in this case, the parameters are chosen on the basis of experience.

For purposes of the data in the Global Wave Statistics Online worldwide database, only 'Smoothing Mode' analysis has been used and the parameters have been derived by best fitting of joint wave and wind data sets data sets from the Marine Databank. These were supplied in the form of bivariate frequency distributions of observed wave heights and wind speeds for each data category (seasonal and directional class) of each area corresponding to an individual record in the database. In compiling these data sets, it should be noted that only cases in which two wave groups (corresponding to observations of both sea and swell) have been reported were included.

In some data categories the samples of such joint wave and wind observations were not adequate, and in these cases the corresponding database wave records have been inhibited. It would have been possible in most of them to use a 'Predictive Mode' analysis, but it was felt that the extent of subjective judgement needed for choosing the parameters would he unacceptable for the present purpose.

For the purpose of the NMIMET data service, the alternative 'Predictive Mode' of analysis, in which the modelling parameters are chosen on the basis of other experience for similar sites, is sometimes used. In this case wave height statistics can be derived from input of wind observations and the analysis can thus be applied when wave observations are either inadequate or nonexistent, provided that suitable experience for choosing the modelling parameters is available. A powerful method, which can be used when joint wave/wind observations are too few to determine reliable values of all the six parameters, is a combination of the smoothing and predictive modes. In such cases, as many as possible of the six parameters, normally two or four, are derived from the local wave/wind data and the remainder are given 'predictive' values. This so-called 'Hybrid' model is then applied to the wind data to derive the wave height statistics.

(b) The Enhanced Wave Height Distributions P(H)

When the parameters of the function fit used for modelling have been determined as above, the enhanced wave height distributions P(H) can be derived by use of the formula:

The wind speed distribution used as input for this stage of the analysis is supplied from the Marine Databank, and is compiled from all the available wind observations for each data category of each area corresponding to an individual record in the database. In compiling these 'All Wind' data sets a normalizing procedure was applied to minimize bias due to variations of reporting rate in individual months of individual years. Details of the procedures used are described in Appendix A2 on data retrieval methods.

Since winds have been reported more frequently over a much longer period (since 1854) than wave heights (reported in non-coarse code only since 1949) the samples of 'All Wind' data are correspondingly much larger. In considering the significance of this difference in sample sizes it is important to appreciate the nature of the roles of the respective data inputs. The role of the joint wave and wind data sets is to determine modelling parameters. For this purpose, it is important for the relations between wave heights and wind speeds, rather than the long-term climate properties to be correctly modelled. Experience has shown that relatively small samples of data are adequate for establishing the required parameter values, and that more reliable results are obtained by using only the so-called '2 group' wave observations (which include estimates of both sea and swell heights) and associated wind speeds and not applying any normalization.

The role of the 'All Wind' data sets, on the other hand, is to provide input which realistically describes the long-term climate. For this purpose the large sample sizes and long time spans of the wind observations are a major advantage but it is important to apply normalization procedures.

(c) The Joint Distributions of Wave Heights and Periods: P(H,T).

When data for the enhanced wave height distributions P(H) have been derived as above, the required joint probability distributions of heights and periods P(H,T) can be computed in terms of the function used to model which may be defined, for the case of Global Wave Statistics Online output, as follows.

P (H) is the enhanced height distribution as derived in (b) above.

where:

= Standard deviation of h
  = Mean value of h = Ln H
= Standard deviation of t
= Mean value of t = Ln T
= Correlation coefficient

In determining the above parameters needed for computing fT, the values of and , which depend only on the statistics of wave heights, are calculated directly from the enhanced probability distributions P(H).

The remaining parameters, , and depend on the wave period statistics, but values can be determined by use of empirical formulae derived by regression analysis of over 20 sets of measured height and period statistics. In deriving these formulae it was found that data from areas with long fetches, exposed to high levels of swell, yielded slightly different coefficients from those from more sheltered areas.

In specifying the formulae used here, a distinction is thus made between exposed and sheltered areas, by reference to the parameter H2 of the function fH described above. H2 is the mean value of height Hr in the absence of wind, and is thus a measure of the level of exposure to swell. The relevant formulae are.

where A and B are functions of H2

where:

= The mean value of H determined by analysis of P (H).

In the case of the original NMIMET output [25] and [26], as mentioned earlier, a slightly different method was used for generating P(H,T), which lead to a fully analytical model of the distribution, completely determined by 6 parameters. This was achieved by using a parametric model of the enhanced wave height distribution P(H) as input to the above equation for P(H,T). In all other respects the procedure used was identical to that now used for NMIMET and used for Global Wave Statistics Online as described above.