International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 3
Number 2
June 2009
143
1 INTRODUCTION
1.1 The 1-2-3 Rule
The 1-2-3 rule consists in extending the forecast
storm field of the cyclone with an approximated val-
ue of the forecast error based on 10 years of the rel-
evant forecast time interval. The rule is recommend-
ed for the North Atlantic waters, but it can be easily
adopted for other sea areas. The mean error of a giv-
en forecast is added to the largest forecast radius of
the stormy area. Consistently, 100 Nm distance is
added as the forecast error to the longest radius of
the stormy area for 24 hour forecast for all quad-
rants. Similarly, 200 Nm is added for 48 hour fore-
cast and 300 Nm for 72 hour forecast. The method
does not take into consideration effects of sudden
change in the intensification of the cyclone system,
which consequently extends the stormy zone of
winds ≥34 knots. Besides, it does not account for the
cyclone changes into extra-tropical stages, which al-
so result in sudden changes of storm force winds.
Additionally, it is recommended in the method de-
scription to further extend the dangerous area with-
out specifying any values, particularly when fore-
casts are highly unreliable, captain and crews’
experience is limited, the vessel’s seaworthiness is
restricted or there are other limiting factors defined
by the captain. Therefore, the method does not pre-
cisely determine the area to avoid. If we combine the
principle of avoiding the storm area where wind
W≥34 knots with the extended zone where risk is
high, we obtain a danger area to avoid by applying
the 1-2-3 rule (Fig.1) [1].
Figure 1. The 1-2-3 Rule [1].
1.2 Calculations
Evolutionary algorithms were used in calculations of
the time-minimum route which passes by the are af-
fected tropical cyclones [4].
The randomly chosen initial population of routes
consisted of 50 individuals. The routes were pro-
cesses by two operators: crossover and mutation.
The number of generations amounted to 700.
As time passed by, the area threatened by tropical
cyclone determined by the 1-2-3 rule increased and
was treated as prohibited to navigation, which means
no computing route point could appear within this
field.
2 ROUTE CALCULATIONS
There were two tropical cyclones in the examined
period over the North Atlantic, Gordon and Helene.
The vessel began a voyage from Gibraltar to New
Application of the 1-2-3 Rule for Calculations
of a Vessel’s Route Using Evolutionary
Algorithms
B. Wisniewski, P. Medyna & J. Chomski
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: An example is shown of the 1-2-3 rule application for calculations to determine a route avoid-
ing tropical cyclones. The dynamic programming used is based on regularly received weather reports contain-
ing present and forecast data on tropical cyclones. The results were compared with the post factum calculated
route which utilized only weather analyses concerning the relevant moments of the voyage and with routes
calculated using the cyclone fuzzy domain as an area dangerous to navigation. The calculations were made in
the evolutionary algorithms environment.
144
York. Starting at 0300UTC on 15 September 2006
from position 36N/007W, the vessel headed for po-
sition 40N/073W.
Figure 2 presents the situation of the voyage be-
ginning where the 1-2-3 rule was applied. The route
is almost loxodromic one. It can be seen that only
waves, having nothing to do with tropical cyclones,
affect the way it runs (long distance to the cyclones,
forecasts up to 72 hours are considered as prescribed
by the 1-2-3 rule).
Figure 2. Vessel’s position and calculated route on 15 Septem-
ber, 0300UTC – start of the voyage.
On 17 September at 0300UTC the vessel ap-
proached the danger area affected by tropical cy-
clone Gordon and avoided the storm field going
south of it. Cyclone Helene then was not dangerous
for the vessel (Fig. 3.).
Figure 3. Vessel’s position, calculated route and cyclone-
threatened areas to avoid – 17 September, 0300UTC.
From 1500UTC 19 September the proximity of
the cyclone significantly affected the calculation re-
sults and the danger area to avoid determined with
the 1-2-3 method (Fig.4.).
Figure 4. 19 September, 1500UTC – initial population
Cyclone Gordon was out of the vessel’s way at
that time. The initial population of routes avoiding
Helen, as shown in Figure 4, indicates there are two
possible groups of routes to avoid the cyclone:
northern and southern ones.
Calculations of the best track (time-minimum
route) recommend avoiding the cyclone to the north
(Fig.5.). The calculated route has only one point ad-
jacent to the forecast circle of danger area (T+72
h
)
defined by the 1-2-3 method. This, however, was not
in compliance with other navigational principles;
one of them says: never cross the track.
Figure 5. Vessel’s position, calculated route and cyclone-
threatened areas to avoid – 19 September, 1500UTC
Six hours later (19 Sept at 1200UTC) calculations
dramatically changed the previous decision concern-
ing which route to choose to avoid the cyclone. Now
the vessel’s track went to the south of the cyclone
(Fig.6.).
145
Figure 6. Vessel’s position, calculated route and cyclone-
threatened areas to avoid – 19 September, 2100UTC.
This results from such factors as noticeable accel-
eration of cyclone Helene’s speed of movement ac-
cording to the latest short-term forecasts and from
the range of forecasts considered in the 1-2-3 meth-
od.
Further in the course of the voyage, in tests per-
formed every six hours, the vessel consistently
avoided cyclone Helene sailing south of it, and from
1500UTC 22 September the vessel headed directly
for her destination (Fig.7.).
Figure 7. Vessel’s position, calculated route and cyclone-
threatened areas to avoid, 22 September 1500UTC.
Finally, the tested route took 254
h
12’ to cover.
Figure 8 shows the route together with the locations
of Helene and Gordon at the start of the voyage and
their further routes, worked out from real analyses.
Figure 8. Final route based on 6-hour tests and the positions of
cyclones Gordon and Helene at voyage start and their further
movements.
3 THE RESULTS DISCUSSION
The test results concerning a vessel route from Gi-
braltar to New York, using the 1-2-3 method and ac-
tual analysis and forecast data real received onboard
the vessel every six hours from 15 to 25 September
2006 will be compared to earlier results published in
[5, 6]. Those studies took into account analyses that
appeared after the cyclone had occurred as well as
operational T+48h forecasts and available forecasts
for periods up to 120 hours. The calculations using
48h and 120h forecasts regarded cyclone’s danger
area as a fuzzy domain according to the methodolo-
gy found in [2, 3]. The overall results are given in
Table 1 and Figures 9 and 10.
Table 1. Duration times and distances of a vessel’s route for
various methods of calculation.
___________________________________________________
route 1-2-3 rule 120h forecast 48h forecast, analysis
calculation fuzzy domain fuzzy domain (post fatum)
type
___________________________________________________
time 254h 12’ 260h 12’ 231h 48’ 214h
distance 3128.4Nm 3616.6Nm 3260.8Nm 3071.8Nm
___________________________________________________
Figure 9 compares two resultant routes, calculated
using:
− the 1-2-3 method (route D),
− forecasts up to 120h received in uptodate reports
and description of the danger area with a fuzzy
domain, as presented in authors’ previous publi-
cation [5].
Both routes differ to some extent. The route ob-
tained from the 1-2-3 method is shorter in terms of
time by six hours and considerably shorter in terms
of distance.
146
Figure 9. Route calculated using T+120h (C) forecasts and 1-2-
3 rule (D).
Knowing the results of other tests, considering
only up to 48h forecasts and using analyses made af-
ter the cyclone operation, we notice significant dif-
ferences in the character of routes. The considered
voyage assumed the same vessel speed and account-
ed for the actual weather conditions and the same
departure and arrival points, etc.
Figure 10. A – post factum route, B – 48h forecasts and cy-
clone’s fuzzy domain, C –120h forecasts and cyclone’s fuzzy
domain, D –1-2-3 method.
The application of the 1-2-3 method yields results
comparable to those obtained from the method using
long-term T+120h forecasts.
The danger area generated by this method, a cir-
cle increasing in time up to 72 hours until the mo-
ment the vessel comes relatively close to the cy-
clone, does not show substantial differences as
compared to other methods.
4 CONCLUSIONS
The conclusion reached in previous publications has
been confirmed. As the time horizon of forecast in-
creases, its reliability decreases and regardless of the
method used, the area of potential danger due to
tropical cyclone dramatically extends in time. For
the 1-2-3 method, after 72 hours this area is a circle
with a 600 Nm diameter plus the forecast cyclone
diameter. This hinders effective determination of
routes that would not abruptly change the actual
courses of vessels underway.
It seems reasonable to grade the value of unrelia-
bility of tropical cyclone area of storm depending on
the time to reach it (distance, vessel’s speed charac-
teristics, weather conditions outside the cyclone ar-
ea).
The 1-2-3 method should not add the values of
100, 200 and 300Nm to the longest radius of the four
quadrants of cyclone storm field. At least, it should
make a difference between its two semi-circles.
LITERATURE
[1] Carr M., Burkley G., Chesneau L., 1999, Hurricane Avoid-
ance Using the “34-Knot Wind Radius” and “1 2 3” Rules,
Mariners Weather Log, August 1999
[2] Wiśniewski B., Medyna P., 2004, Prognozowany zasięg po-
la sztormowego cyklonu jako domena rozmyta cyklonu.,
Zeszyt Naukowy AM Szczecin Nr 2 (74), Konferencja
Explo-Ship, str. 419-430
[3] Łebkowski A., Śmierzchalski R., Tomera M., Tobiasz M.,
Dziedzicki K., 2005, Modelowanie domen oraz obszarów
pogodowych w procesie wyznaczania trasy przejścia statku,
VI Międzynarodowe Sympozjum Nawigacyjne, Gdynia
[4] Wiśniewski B., Medyna P., Chomski J., 2006, Zastosowa-
nie algorytmów ewolucyjnych do wyboru trasy statku na
oceanie z uwzględnieniem omijania stref sztormowych cy-
klonów tropikalnych, Inżynieria Morska i Geotechnika
nr4/2006, str. 257-262
[5] Wiśniewski B., Medyna P., Chomski J., 2008, Comparison
of ship routes avoiding tropical cyclones, TST’08, ZN
Politechniki Śląskiej
[6] Chomski J., Wiśniewski B., Medyna P., 2008, Analysis of
ship routes avoiding tropical cyclones., Wyd. AMW, Gdy-
nia
