Lud's Wave Prediction FAQ
G'day all,
For those of you wanting to try your hand at surf
forecasting, and gain a greater insight into waves as an extra
benefit, all the info is out there in various meteorology and
oceanography books.
Could be something to do during those long flat spells).
Some of the books I've come across that have usefull chart's
and tables are:
Oceanography, second edition
Dietrich, Kalle, Krauss, Siedler.
Prentice Hall.
(Good chart which shows how far a swell has travelled, how long it has
travelled, and what the conditions were in the swell generating area,
ie wave size and wind strength, from the size and period of the swell
at your location!
Great for trying to correlate swell conditions today, with the weather
maps a number of day's back, ie identifying weather features which may
have generated the swell. *** GOOD)
Introduction to physical oceanography
Knauss
Prentice Hall
(Chart showing wave height vs windspeed in the generating area,
also fetch lenth and min. wind duration's required)
Estuary and Coastline Hydrodynamics
Engineering Societies monographs
Idden, Arthur T. ed.
McGraw Hill
(Wave generation and decay chart's, *** GOOD)
Physical Oceanography of coastal waters
K.F. Rowden
Ellis Horwood Ltd.
Halsted Press
(Wave generation chart for shallow coastal waters)
Proceedings of the International Synposium on Ocean Wave Measurement
and Analysis, Volumes 1 and 2
Published by the American Society of Civil Engineers
(All sorts of general papers on ocean waves etc)
After reading a great pile of these, (only the relavent stuff mind
you, the maths and other junk gets a bit heavy in some of them, but
they all seem to have snippet's of usefull information buried away
including all sort's of usefull chart's, tables etc.),
I was suprised by how relatively clearcut the whole thing of swell
prediction, and wave statistic's, sizes etc is, even though it's a
little to complicated to describe in one post.
There seem to be a couple of different methods used, and both give
slightly different answers, both methods seem to be a mixture of
theory, tempered/modified by actual wave statistic's.
(They also tell you how to measure the size of a wave), and,
it's not from the back), but these guy's are just oceanographer's,
so what would they know), sorry, just couldn't resist stirring the
frontside vs backside wave measurement argument again) )
Anyhow, here is a distillation of some of what I've gleaned, and
how I use it in my attempts at predicting surf.
With no background in meteorology, or oceangraphy, apart from a lot of
reading, and bobbing around on surfboard, off and on for quarter of a
century, I can't really vouch for the accuracy of what follow's,
so if you adopt a similar procedure, and after a three hour drive,
your favourite spot is flat, instead of the predicted double overhead,
I don't want to hear about it).
Simplified description of steps required to predict the surf are:
(For all the fine detail check the book's,
and references within, listed above).
1/ From a weather map that cover's your area of ocean,
locate an area on the ocean that is capable of producing
swell, ie any area of ocean, where there are winds of reasonable
strength, blowing for a reasonable duration and distance.
(ie, Isobars close together, for a reasonable distance, hundreds
of Km. minimum, but better if Km's are in the 000's.)
This could be anything from a cold front to a hurricane to a
prevailing wind etc., probably one particular weather pattern
will be the main swell producer in your area, and that will
probably vary throughout the year.
Obviously the swell/wind must be heading in your
direction, though you can make a rough allowance for swells
not heading directly towards you, say within 30 degrees.
(Reduce predicted swell size by cos * angle for this case)
To estimate the fetch length (Fetch is the distance the wind
is blowing over, at about the same strength and direction),
do a scale measurement off the weathermap, of the distance
where the isobars and wind are running roughly in your direction
(within, say, 30 degrees).
2/ From the wind strength, duration, and fetch length, one can
calculate, or use a chart/table to estimate the size of the
sea's at that point, and also the period of the waves, and
hence their speed, and therefore swell arrival time !.
The main problem is to get the windstrength.
For the wind direction, I make the assumption that it is
parallell to the isobar's, and the usual direction, clockwise
around the low's, anticlockwise around the highs for the
southern hemisphere, and vice versa up north.
Our weathermaps don't show the windstrength over the ocean,
so what I do is use a formula that gives an approximation of
the windspeed, based on the spacing of the isobars, ie air
pressure difference per km, and the latitude:
Geostrophic Wind = (delta P/ delta Km) / ( 2 * R * p * sin(L) )
where windspeed is in M/second, (Multiply by two to give Knots)
Delta P is the difference in airpressure, in mBars/10 , across the width
of the fetch, and Delta Km is the width of the fetch in Km.
-5
R is the earths rotation, 7.3 * 10 rads/sec
3
p is the air density, 1.3 kg/m
L is the latitude
All this simplifies down to :
Windspeed in knots = (( mb per km * 10000)/(19 * Sin Latitude)) * 2
To get the windspeed at sea level, this windspeed must be reduced
further, multiply it by 0.7
for example, fetch width=1000 km, air pressure on high pressure side
=1020 mb, on low pressure side =990mb, therefore mb per km =0.03,
latitude =45 degrees.
so windspeed in knots = ((.03*10000)/(19*sin(45)))*2
= 44.6 knots
multiply by .7 for sea level windspeed
= 31.26 knots
From the Table below, as long as the wind duration has been at least
24 hrs, and the fetch > 290 Nm, the mean wave height would be 4.5
metres at the end of the fetch.
The significant period is 12.4 seconds
Here are some typical figures for wave generation in "deep
water":
Wind Min. Min. Sig. Wave H1/10 Hmean
Speed Dur. Fetch Period Length Height Height
Knots Hrs. Nm Seconds Metres Metres Metres
11-16 5 24 3.9 47 1.12 .55
17-21 9 65 7.7 93 2.7 1.3
22-27 15 140 9.9 153 5.2 2.5
28-33 24 290 12.4 240 8.8 4.5
34-40 37 510 14.9 345 14.2 7.0
41-47 52 960 17.7 490 22.2 11.0
48-55 73 1510 20.8 675 32 15.8
56-63 101 2500 24 1060 45 22.2
H1/10 is the is the average height of the 10% of the highest
waves, and roughly correlates with the max size of a wave group (set)
that can be expected.
Hmean is the mean hight of all the waves.
The period and wavelength are those for the significant wave (H1/3)
which is the average height of the 1/3 highest waves, which is roughly
where the majority of wave energy is, and is approximately what an
observer would call the wave height of a particular swell.
Wave height is measured from TROUGH to CREST.
The calculation's, chart's etc. are different for swell's
generated by localised high intensity winds with short
fetches, ie hurricanes, intense low pressure systems,
vs long duration/fetches ie cold front's.
There are formulae for hurricane wave height's.
Swells generated in shallow water, (continental shelf ?) require
different chart's than swells generated in deep water.
3/ From the above figures you can now (more charts) ) obtain a
decay factor to indicate the final swell size as it approaches
your break.
Here are some typical figure's, but you really need the charts
to be more accurate, but these should serve as a rough guide.
Again, these figures are for "deep water".
Swell Decay Decay Swell Decay Decay
Height Dist. Factor Height Dist. Factor
Feet Nm Feet Nm
5 50 .73 10 50 .75
5 100 .6 10 100 .62
5 200 .47 10 200 .5
5 500 .35 10 500 .36
5 1000 .25 10 1000 .27
5 2000 .125 10 2000 .18
5 4000 .1 10 4000 .12
5 10000 .05 10 10000 .055
Swell Decay Decay Swell Decay Decay
Height Dist. Factor Height Dist. Factor
Feet Nm Feet Nm
20 50 .77 40 50 .78
20 100 .64 40 100 .65
20 200 .525 40 200 .54
20 500 .38 40 500 .41
20 1000 .285 40 1000 .305
20 2000 .165 40 2000 .2
20 4000 .14 40 4000 .15
20 10000 .07 40 10000 .08
Note the swell size and final wave size will not be the same,
as the swell moves into shallow water, it first decreases in
size, and then increases in size, by a factor of 1.5 to 2
before it break's, so to get the final wave size in the surf
zone, multiply the decayed wave size by 1.5 to 2.
The wave height is still from trough to crest.
An interesting point regarding the wave shape in shallow and
deep water, In deep water the swell shape is similar to a
sine wave, in that the crest elevation, and trough depression
are more or less symetricaly displaced with respect to the
mean water level.
But as the waves move into shallow water, ie
surf zone, the crest's actually increase in height, and the
wave troughs flatten out, so that what you have in effect, is
an area of relatively flat water, between the crests,
with a series of solitary, much more peaky crest's
comprising the set waves.
The majority of the height increase as the waves move into
shallow water, comes from the crest elevation above the mean water
level, eg, for a 20 ft wave, (trough to crest), 17 to 18 feet
would be crest elevation above the mean water level, and 2 to
3 feet would be the trough below the mean water level.
The height increase comes about, because the waves bunch up,
ie the wave speed and wavelength decrease, but the period
remains the same when the waves enter the shallower water,
that same wave energy is now contained in a shorter distance,
and hence the height increases.
Swell direction and local geography, bottom topography etc. will
also alter the final wave size, and also if you get any of the
swell at all (swell windows).
Wave refraction must also be taken into consideration,
but it gets too complex, it's easier to incorporate a local
"fudge factor" to allow for these differences.
4/ Swell Travel time.
From the period of the wave you can determine the swell travel
time, from fetch to your location.
Note that the speed of a wave group (set)
is half the speed of individual waves (for deep water)
ie the swell itself progresses at half the wave speed.
You can see this by watching a set of waves in deep water from
a high vantage point, if you watch the first wave of a group,
you will see it dissapear !, only to pop up at the back of the
set, this keeps repeating until waves get to shallow water.
It's sort of like taking two steps forward, and one step
back.
The group speed (in Km/hr.) = 2.8 times the period (seconds)
So to predict the travel time of the swell, multiply the wave
period from the above chart by 2.8, which will give you the
group speed in km/hr, divide that by how far away the fetch is from
your location (Km) and you have an approximate travel time for the
swell. (For deep water conditions only)
For shallow water the wave group speed, and the wave speed are
the same, see books for formulae.
4/Period Increase, as the waves move out of the generating area and
start to decay (swell), the period also increases.
Here are some typical values, again original chart is required for
accurate figures.
Wave Decay Period
Period Dist. Increase
(sec) Nm factor
10 100 1.14
10 500 1.23
10 1000 1.33
10 2000 1.38
10 5000 1.45
10 10000 1.49
12 100 1.15
12 500 1.29
12 1000 1.36
12 2000 1.42
12 5000 1.5
12 10000 1.54
14 100 1.15
14 500 1.31
14 1000 1.4
14 2000 1.45
14 5000 1.54
14 10000 1.57
*** Note, the definition of "shallow" or "deep" water in wave terms,
is defined as the water depth relative to the wavelength of the swell,
if the depth is greater than 0.5 times the wavelength its deep water
as far as the wave is concerned, and the wave does not feel the
bottom, and if the depth is less than 1/20 the wavelength, its shallow
water.
Inbetween these two values it's intermediate, a different set of
formulae apply in each of the 3 case's for wave speed etc etc.
The period (time between waves) is important because in conjunction
with the size of the waves, it can tell you how from far away the swell
originated, how long the swell has travelled for, and what the swell
size, (more accurately the Sea size, as swell is defined as waves that
have moved out of the generating area) and wind strength were at the
swell's origin !, pretty amazing I think.
(From a chart in oceanography book listed above, too difficult to
tabulate)
To measure the period, it's best to average out the duration of a set,
ie number of waves in the set, less one, divided by the time taken to
pass some reference point, could be a rock, end of pier, or even the
beach itself.
It doesnt matter what reference point you use to time the passing of
the waves, as the period remains constant, regardless of water depth,
though the wave speed and wavelength do vary.
There will be some variation in the period from set to set, but
drastic differences could indicate two different swell trains.
The weather maps ideally need to cover a reasonable section of the
ocean, otherwise swell's can arrive from outside that area, which
obviously can't be predicted, but it's nice to be suprised by a decent
groundswell coming from many thousand's of miles away anyhow).
That's it!), Iv'e run out of patience, RSI has set in to my two
typing finger's , I'm going for a surf, there's a few more things to
say but that will have to wait......
some-one else will have to proof read this,
predicting head high, 15 sec period and offshore winds)........
Cheer's, keep surfing, (or predicting if it's flat)