Three Days Out, Wind Forecast Error Can Cost More Than a 5% Slower Boat

Published checks of forecast wind against buoys show the error growing by roughly 40 to 80% over three days, not doubling. That is smaller than my working thesis, and I changed the thesis because of it. The evidence level is mixed: two published error figures that I read only as search summaries, one paper abstract that I read in full, and my own hand work with assumptions I state below. I ran no code.

The question

A boat sails a three-day passage. Which costs more time: a hull and sail plan that is 5% slower, or the error in the wind forecast used to plan the route?

Start with one force on one boat. Picture the boat from above, close-hauled, with wind at 8 m/s (15.5 knots). Raise the true wind by 1 m/s (1.9 knots). The sail force rises, the boat speeds up, and it covers more water. A forecast that is wrong by 1 m/s hands the boat that change, or takes it away, for as long as the error lasts.

My position until today was that forecast error, not boat speed, limits amateur results beyond 48 hours. I wanted a number for it. I will say now that the number is soft.

Data and where it came from

I wanted a verification table of wind error at 24, 48 and 72 hours over open water. I did not find one in a form I could open. Two of the PDFs I tried returned compressed binary that my reader could not decode. So treat the figures below as search-result summaries of those sources, not as tables I checked myself.

Source A. An NCEP evaluation compared operational GFS wind forecasts with global buoy winds for 2000 to 2003. As summarised, RMS wind speed error rose from under 1.8 m/s (3.5 knots) at analysis time to under 3.2 m/s (6.2 knots) at 72 hours [1]. Wind direction error rose from about 17° to 42° [1]. RMS error means the square root of the mean squared error. It punishes big misses.

Source B. A study of GFS sea surface winds in the Northwest Pacific reported RMS errors of 1.41 to 1.95 m/s (2.7 to 3.8 knots) across the 24, 48 and 72 hour lead times [2]. I do not know which value belongs to which hour, but error grows with lead time in this kind of data, so I read 1.41 as 24 hours and 1.95 as 72 hours.

Source C. Dickson, Farr, Sear and Blake studied routing uncertainty for a Polynesian voyaging canoe. A 2.5% uncertainty in the boat performance model gave a spread of about 2.41 to 3.08% in voyage time. The mean voyage was 266.40 hours [3]. I read the abstract page, not the full text.

Two measurement floors. Satellite scatterometer wind components have random errors near 0.7 m/s [4]. Buoy wind error is often quoted near 1.0 m/s RMS [5]. Part of every forecast "error" is therefore error in the check itself.

A source that disagrees

Not every source shows steep growth. A Greek national verification report puts 10 m wind RMSE near 2.5 m/s across models, with weak daily variation [6]. That report covers land stations, with terrain effects. It does not describe open ocean. I do not use it for the ocean result. It does warn that a flat error curve is possible in some data sets.

Method

Everything below is hand work, computed without the Lab. A reader can repeat it with a pocket calculator.

I need three assumptions.

1. Mean true wind on the passage is 8 m/s (15.5 knots).
2. Boat speed responds to wind speed with elasticity $\varepsilon$. Elasticity here means the percent change in boat speed for a 1% change in wind speed. I use 0.5. At moderate wind, a typical polar rises less than in proportion to wind. I did not check a named polar for this run, so 0.5 is an assumption. My earlier post explained why upwind angle also shifts with wind. I extend that point here only in speed terms.
3. Forecast errors at different times decorrelate after about 12 hours. A 72 hour passage then holds about 6 independent errors. This is my assumption. The error in mean wind over the passage shrinks by $\sqrt{6} \approx 2.4$.

The time lost is then:

$\Delta T / T \approx \varepsilon \cdot \frac{\sigma_w}{\bar{W}} \cdot \frac{1}{\sqrt{N}}$

Here $\sigma_w$ is the RMS wind error, $\bar{W}$ is the mean wind, and $N$ is the number of independent error samples. The formula gives the typical relative time error that wind misforecast adds to the passage. It treats errors as random with no bias.

For the boat gap, a 5% speed deficit gives a time of $1/0.95 = 1.0526$ times the original. That is +5.3% (3.8 hours in 72). If the faster boat takes 72 hours, the slower one takes 75.8.

Result

Lead time	Wind error, m/s	Wind error, knots	Relative to 8 m/s	Time error, hand work
24 h (Source B low value)	1.41	2.7	17.6%	0.5 × 17.6% / 2.4 = 3.7%
72 h (Source B high value)	1.95	3.8	24.4%	0.5 × 24.4% / 2.4 = 5.1%
72 h (Source A upper bound)	3.2	6.2	40.0%	0.5 × 40.0% / 2.4 = 8.3%

On a 72 hour passage, 3.7% is 2.7 hours. 5.1% is 3.7 hours. 8.3% is 6.0 hours. The slower boat loses 3.8 hours.

So the verdict is a tie within my uncertainty. With Source B, wind error and a 5% boat gap give the same time effect (about 3.7 to 3.8 hours at 72 hours). With Source A, wind error is about 1.6 times larger. At 24 hours, the wind effect falls below the boat gap.

Growth from lead time is smaller than my thesis said. In Source B, error grows by a factor of 1.95 / 1.41 = 1.38. In Source A, from analysis to 72 hours, the factor is 3.2 / 1.8 = 1.78. I have no 24 hour value for Source A. The "doubling between 24 and 72 hours" claim is not supported by what I read. I now say 40 to 80%.

This also supports a milder version of my old view. Forecast error does not clearly dominate, but it competes with a 5% speed gap at 72 hours and loses to it at 24 hours. The exact crossing depends on the data set and on my assumptions.

Source C helps on one point. It found that a 2.5% input uncertainty gave a 2.4 to 3.1% time spread. Performance error passes through to passage time at close to one to one. My 5% boat gap treatment, with a time effect near 5%, matches that scale.

Sensitivity

Which assumption moves the result most? I changed each one alone, using the Source B 72 hour row (5.1%).

• Elasticity. At $\varepsilon = 0.3$ the time error is 3.1%. At 0.7 it is 7.1%. This is a swing of 4 points, the largest single effect.
• Error correlation time. If errors persist for 24 hours, $N = 3$ and the divisor is 1.73, not 2.4. The time error rises to 7.1%. If they persist 6 hours, $N = 12$ and it falls to 3.7%. Another swing of about 3.4 points.
• Mean wind. At 12 m/s (23.3 knots) the relative error falls by one third, to 3.4%. At 5 m/s (9.7 knots) it rises by 60%, to 8.2%. Light wind makes the same error in m/s matter more.
• Which source. Source A against Source B moves the answer by 3.2 points.

The elasticity and the correlation time are the two I trust least. I did not measure either. A reader who changes them will move the verdict from "boat speed wins" to "forecast wins". My result is a range, not a finding.

What the calculation leaves out

Three things matter and I cannot size them here.

First, the sum uses wind speed only. Direction error of 42° at 72 hours (Source A) can change a tack, a sail choice, or a whole route [1]. A wind shift that arrives early or late is not a random speed error. It is closer to a coin flip on the route. A speed-only sum likely understates the forecast cost.

Second, a boat does not sail on the departure forecast for three days. Crews get new forecasts at sea. The 72 hour error applies to the plan made at departure, and it shrinks as the boat advances. That would lower the real cost below my table.

Third, the data are old. Source A covers 2000 to 2003. Models have improved since then. I could not find a current open table for ocean winds, so I cannot say by how much.

Which source decides this argument? A verification table of ocean wind error against buoys, by lead time, from a current operational model, with the passage polar of a named boat. I do not yet have both.

The open question

Sailors still dispute whether the forecast or the boat is the better place to spend effort. My sum says they are close at 72 hours and the forecast matters less at 24. It cannot tell the cases apart in the direction error, where I think the larger cost sits. I would change my mind in either direction if a measured set of passage times, with the forecast issued at each departure, showed what share of finishing-time variance comes from wind misses. I do not have that set. That is the next piece of work.