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1 INTRODUCTION
In 2024 Port of Santos (Brazil) had a throughput of
179.8 million tons and 5.4 million TEUs, 29.0% of the
Brazilian trade flow (or US$ 174.43 billion) and
received the traffic of 5,557 vessels in its fairway [1],
including New-Panamax (LOA = 366 m, B = 51.0 m).
According to [2] it is the first in container handling in
Latin America (see Fig. 1). It is the most significant in
the Southern Hemisphere for all types of cargo and
holds strategic importance for Brazil.
In this era of climate change, the awareness of more
frequent and severe extreme events impacting port
operations motivated by this quantitative analysis of
historical trends. Previous studies are not known in
this concern. The port's environmental downtime rate
is increased by the probability of total traffic
suspension when waves exceed 3.0 m, the limit of
significant height on the fairway established by the
Maritime Authority's Pilotage Regulations.
This paper presents the main results of the
hindcasting of extreme wave heights in Santos Bay
since 1940. Utilizing wave measurements obtained
from an oceanographic buoy, extreme wave events
were identified with the objective of calibrating the
series in an oceanographic model. The series, covering
1940 to 2023, received this adjustment. The correlation
between offshore and nearshore wave heights was
determined using a coastal buoy managed by Santos
Pilots. Nearshore records from other periods were
employed to validate this correlation, with the aim of
making it more realistic.
Hindcasting of Extreme Wave Events in the Fairway
of Port of Santos (Brazil) over the Last Eighty Years
P. Alfredini
1
, E. Arasaki
1
& H.L. Puia
2
1
University of São Paulo, São Paulo, Brazil
2
Zenith Litoral Hidrografia Ltda and Santos Pilots, Santos, Brazil
ABSTRACT: Port of Santos is responsible for 29.0% Brazil’s trade flow. A concern arisen due to climate changes
has been the increase in the frequency and severity of extreme wave events on the fairway. The limit established
by the Maritime Authority's Pilotage Regulations for the total suspension of traffic on the fairway regarding
waves is when significant heights greater than 3.0 m occur. A summary of the hindcasting of extreme wave events
in Santos Bay since 1940 has been presented. The findings of the statistical assessment since that time identified
an increase of more than 6 times in environmental downtime due to extreme wave events and the analysis of
extreme wave height values for return periods of 50, 75 and 100 years revealed increases of 3.8% to 9.9%,
depending on the statistical distribution used and the return period considered.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 1
March 2025
DOI: 10.12716/1001.19.01.32
270
Figure 1. Santos Bay and its 8 km of fairway. The Port is
located inside the Estuary of Santos. The fairway is
maintained by permanent dredging at level -15.0 m (Chart
Datum) and is 8 km long, facing SSW, from where the swell
responsible for most extreme wave events comes.
2 SOURCES OF DATA OF SIGNIFICANT WAVE
HEIGHT OF THE EXTREME EVENTS
Hourly offshore wave heights were taken from Santos
Buoy, which uses directional measurements with
accelerometers and angular sensors ([3]). The Brazilian
Navy Hydrography Centre's National Buoy Program -
PNBOIA maintained the meteoceanographic
anchoring buoy from May 2011 to November 2018. Fig.
2 shows the coordinates of the buoy positioned in deep
waters at a depth of approximately 200 meters.
Hourly wave height data from the deep-sea
oceanographic model were extracted at the grid point
nearer to the Santos buoy from the oceanographic
hindcasting global model ERA5 model (provided by
the European Centre for Medium-Range Weather
Forecasts - ECMWF [4]), from 1940 to 2023 (see the
location in Fig. 2).
Hourly wave height data in the nearshore region
were collected using an Acoustic Doppler Current
Profiler (ADCP) positioned at level – 11,0 m (Chart
Datum), near Santos Port Fairway in Santos Bay (refer
to Fig. 2), maintained since 2015 by Santos Pilots [5].
The period evaluated was from April 2015 to July 2023.
Two other series of nearshore wave records were
used to validate the correlation between offshore and
nearshore wave heights: the campaign from February
1982 to September 1984 [6], with a waverider (of one
accelerometer) record every 3 hours at the location
marked as UNA in Fig. 2, at level – 16,0 m (Chart
Datum); the campaign from October 1972 to November
1973 [7], with an ultrasonic wave gauge record two
times of day located in the central region of Santos Bay,
between 24° 00’ 00” S, 46° 21’ 18” W (level – 10,0 m,
Chart Datum) and 24° 02’ 40” S, 46° 21’ 32” W (level –
14,0, Chart Datum, nearby the fairway mouth).
Figure 2. Coordinates of the locations employed in the
extreme wave events height assessment. The assessment of
the offshore wave climate (deep water from the waves) used
data from the PNBOIA Santos Buoy, located at the edge of
the Continental Shelf (approximately 200 m deep), and from
the nearest grid point of the oceanographic hindcasting
global ERA5 model (approximately 1,000 m deep). For the
assessment of nearshore waves, the most extensive wave
series were those from the ADCP located near the fairway to
the Port of Santos (11 m deep) and from the UNA WAVE
RIDER, which operated in 16 m deep at a location
approximately 68 nautical miles SW of the fairway.
3 METHODS
3.1 Statistical analysis of the significant wave height
of the extreme events offshore
According to [8], the theory of statistics requires that
individual data points employed in statistical analysis
are statistically independents, and to produce
independent data points we need to think of extreme
events, rather than individual hourly storms (or with
another sampling time) wave heights. The most
employed method to separate wave heights in extreme
events is called Peak Over Threshold (POT) analysis. It
involves choosing a wave height threshold arbitrarily.
The only data points used in the POT statistics are the
peaks (maximum wave heights) occurring during each
extreme event. Thus, when threshold selection is
appropriate, the values of extreme events will be very
representative.
Extensive studies have been conducted on the wave
climate in Santos Bay and offshore. A 4.0 m wave
height threshold was used to apply the POT to ERA5
and PNBOIA offshore data. This value matches the
highest significant wave heights recorded in Santos
Bay near the fairway (nearshore), therefore it
represents a known rare limit for extreme wave events
nearshore, obviously making it a practical threshold to
adopt. Therefore, the independence of wave peaks was
ensured by empirical observations along time.
271
With this procedure, it was possible to identify 89
significant wave heights pairs of extreme events,
obtained from ERA5 and PNBOIA, in which at least
one height of the pair exceeded 4.0 m, during the
period from May 2011 to November 2018.
3.2 Adjustment of the ERA5 significant wave height data
to PNBOIA
Adjusting ERA5 significant wave height data to match
PNBOIA records at Santos Buoy yielded an adjusted
coefficient based on the 89 extreme wave events. This
adjustment was made using a linear regression based
on a scatter plot. This coefficient was considered valid
for the entire ERA5 model series (from 1940 to 2023) in
deep water offshore.
The quality of the regression can be assessed by r-
Squared (r² or the coefficient of determination), which
is a statistical measure that determines the proportion
of variance in the dependent variable that can be
explained by the independent variable. In other words,
r-squared shows how well the data fits the regression
model (the goodness of fit).
3.3 Correlation between nearshore and offshore significant
wave heights
Employing 58 extreme wave events from April 2015 to
July 2023, identified by the POT, a linear regression
based on a scatter plot was obtained between the wave
heights recorded in the Santos Pilots ADCP nearshore
and the wave heights of the ERA5 in deep water
offshore.
3.4 Validation of the correlation nearshore x offshore
significant wave heights
The coefficient of correlation obtained according to
explained in item 3.3 was validated with more
nearshore data of 8 extreme wave events comprised
from July 1982 to September 1984 and more 2 extreme
wave events that occurred in May and July 1973.
3.5 Final correlation of the nearshore fairway waves with
the ERA5
A final weighted coefficient, based on correlation
coefficients from items 3.3 and 3.4, was used for the
entire ERA5 series to estimate the nearshore waves.
3.6 Nearshore waves hindcasting from ERA5 with final
correlation coefficient
Two 19-year periods were considered in the
hindcasting analysis, one called remote, from
01/01/1940 to 31/12/1958, and another called present,
from 08/08/2005 to 08/08/2023. The justification for
choosing this 19-year period was that it corresponded
approximately to the lunar nodal period of 18.61 years,
which we have used for the simultaneous study of the
rise in mean sea level on the Brazilian coast. For each
of these very distant periods, the correlation coefficient
previously determined was applied to the ERA5 series
offshore to obtain the estimate of the nearshore wave
height series. In this way, it was possible to perform a
statistical analysis of the frequency of extreme
nearshore waves and compare significant heights and
the number of extreme wave events.
3.7 Extreme value analysis from ordered nearshore
significant wave heights
The Cumulative Distribution Function (CDF) is
considered the most robust relationship for both
interpolation and extrapolation due to its straight-line
structure, as stated in [8]. The probability that any
wave height (H) exceeds a specified value (P(H)) can
be converted into a straight line by transforming the
probability into reduced variates on the ordinates, and
wave heights on the abscissas. The coefficients of the
slope and the intercept of the straight-line relationship
are determined by linear regression analysis. The most
common distributions employed for analysis of
extreme values of ordered statistical in descending
order of significant wave height are the Log-Normal,
Gumbel and Weibull. The reduced variates employed
by these distributions are known as Z, G and W.
For the Log-Normal Distribution, the Z value is
derived from the Standard Normal Probability Tables.
It is calculated using an equation that considers the
mean and standard deviation of ln H (see [8]). The
scatter diagram with linear correlation is given by Z x
ln H. The coefficients of the slope and the intercept of
the straight-line relationship determined by linear
regression analysis are correlated with the mean and
standard deviation of ln H.
For the Gumbel Distribution, the G value is
obtained reducing P(H) according to logarithmic
functions (see [8]). The scatter diagram with linear
correlation is given by G x H. The coefficients of the
slope and the intercept of the straight-line relationship
determined by linear regression analysis are correlated
with G.
For the Weibull Distribution, the W value is
obtained reducing P(H) according to logarithmic
functions (see [8]). The scatter diagram with linear
correlation is given by G x H. The coefficients of the
slope and the intercept of the straight-line relationship
determined by linear regression analysis are correlated
with W. The Weibull Distribution has three
parameters, in addition to slope and intercept
coefficients a third coefficient (α) will require some trial
and error to obtain the best straight line in the scatter
plot.
4 RESULTS
4.1 Adjusting ERA5 wave eights data to match PNBOIA
Fig. 3 shows the linear regression based on a scatter
plot between significant wave height of PNBOIA and
ERA5. It was observed, according to [9], that ERA5
underestimates the actual values, that is necessary to
correct them by multiplying per 1.300. Under these
conditions, a real significant height in deep water of 4.0
m corresponds to ERA5 3.08 m, or in other words,
ERA5 significant heights of 4.0 m will correspond to 5.2
m in real.
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Figure 3. Scatter plot between significant wave height of
PNBOIA and ERA5 model. From this graph, it was possible
to conclude that, in general, ERA5 underestimates the real
significant height of extreme wave events.
4.2 Correlation between offshore and nearshore significant
wave heights
Fig. 4 shows the linear correlation based on a scatter
plot between the significant wave heights recorded in
the Santos Pilots ADCP and the wave heights of the
ERA5 without any adjusting.
Figure 4. Scatter plot between wave heights recorded in
Santos Pilots ADCP and the ERA5. This graph allowed
estimating the effects of significant wave transformations of
offshore extreme wave events in their progression to Santos
Bay.
4.3 Validation of the correlation offshore x nearshore
significant wave heights
Fig. 5 shows the linear correlation based on a scatter
plot between the ERA5 (without any adjusting) x
nearshore data, corresponding to 8 extreme wave
events recorded from July 1982 to September 1984 and
more 2 extreme wave events in May and July 1973, for
validation of the correlation obtained in item 4.2.
Figure 5. Scatter plot between wave heights recorded
nearshore and the ERA5. This regression showed a very
similar linear regression between the significant heights of
offshore and nearshore extreme events with that obtained in
Fig. 4, validating the reliability of the procedures for
evaluating the transformations of wave heights in their
progression towards the coast.
4.4 Final correlation of the ERA5 series to the nearshore
fairway
A final weighted coefficient of 0,66 was used to
correlate nearshore wave series to ERA5. It is to be
noted that the coefficients obtained in items 4.2 and 4.3
are quite similar, denoting a good consistency of the
analysis.
4.5 Nearshore waves hindcasting from ERA5 model
The hindcasting analysis compares the remote period
from 01/01/1940 to 31/12/1958 to the present period
from 08/08/2005 to 08/08/2023. Considering the limit of
significant height on the fairway established by the
Maritime Authority's Pilotage Regulations for the total
suspension of traffic regarding waves, i.e. 3.0 m, Fig. 6
shows that only 3 situations occurred in the remote
period against 19 situations in present days. These
numbers demonstrate how dramatically it has
increased the frequency of extreme nearshore events
and permit to compare the significant heights of the
most extreme.
4.6 Extreme value analysis from ordered nearshore
significant wave heights
Tab. 1 shows the results obtained from the extreme
value analysis.
Table 1. Values of significant wave heights (m) for extreme
value analysis in the fairway. Typical return periods of
significant wave heights for projects in Port Engineering
DISTRIBUTION
PRESENT PERIOD
(RETURN PERIOD - YEARS)
50
75
100
50
75
100
Log-normal
3.33
3.38
3.41
3.66
3.70
3.73
Gumbel
3.70
3.81
3.89
3.83
4.10
4.16
Weibull
3.89
4.06
4.19
4.13
4.26
4.35
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Figure 6. Chronology and intensity of extreme wave events
of total interruption of traffic on the fairway.
5 ASSESSMENT OF LIMITATIONS AND
RELIABILITY OF FINDINGS
Wave records on the Brazilian coast, which has
approximately 8,500 km of development, are still
relatively sparse and scarce in terms of sufficiently long
historical series with few gaps. In the case of this study,
the PNBOIA measurements in Santos, which lasted for
90 months, had an effective rate of 84.17%, i.e. the gaps
represented 15.83%, which allowed a sampling period
of approximately 76 months, or 6.3 years. This
effectiveness rate can be considered suitable, one of the
best of the PNBOIA, in terms of representations of the
wave climate. For the ADCP measurements, during the
period of 99 months, the effectiveness rate was 95.10%,
due to the excellent maintenance provided by the
Maritime Authority's Pilotage.
Wave measurements from the 1980s and, especially,
those from the 1970s were subject to greater
inaccuracies and failures, but since they were used
more for validating the correlation coefficient between
offshore and nearshore wave heights, they resulted in
a correlation coefficient very close to that obtained with
ADCP measurements. This finding, in itself, is an
indication of the reliability of this adjustment, despite
the different accuracies of the different recording
equipment.
The ERA5 data has certainly become more accurate
since the early 1980s, when satellite data became more
accessible to the general public. The atmospheric
synoptic information from the most remote data for
estimating wind parameters (speed, fetch and
duration) was still often produced manually. Despite
these limitations, the ECMWF sought to improve this
information in order to make it suitable for
oceanography applications. Despite these limitations,
the findings showed a comparatively significant
increase in extreme wave events over the last 8
decades, and the wave estimates for extreme wave
events with return periods of 50 to 100 years were
consistent with this trend.
6 CONCLUSIONS
This hindcasting study quantitatively demonstrated
the impact of climate change on the extreme wave
event regime in the fairway of the Port of Santos, the
most strategically important port in the South Atlantic.
Using the historical series from 1940 to 2023 of the
oceanographic model ERA5, at a grid point located in
deep water, it was possible to identify offshore extreme
wave events with significant wave heights greater than
4.0 m in correspondence with an oceanographic buoy
that operated nearby between 2011 and 2018. By
associating the offshore extreme wave events with the
events recorded by an ADCP located nearshore in the
vicinity of the fairway, it was possible to obtain, and
successively validate independent nearshore wave
data, a correlation coefficient between the significant
heights of the offshore and nearshore extreme events.
By comparing two 19-year periods, one without
climate change (1940 to 1958) and one under its
influence (2005 to 2023), these effects can be clearly
demonstrated. In fact, the extreme wave events that
lead to the total interruption of maritime traffic
through the fairway have increased more than 6 times,
and the severity of wave heights in these extreme wave
events has also increased (by about 10%). Finally, a
statistical analysis of extreme wave height values for
return periods of 50, 75 and 100 years revealed
increases of 3.8% to 9.9% depending on the statistical
distribution used and the return period considered.
The awareness of stakeholders and operators in the
port sector in Brazil has not yet been sufficiently
mobilized in terms of the reality that we are already
274
facing with climate change, and which will probably
have a greater impact in the coming decades. Planning
to face this new reality is still in its beginning, with little
dissemination of systematized information about these
impacts from managers to the workforce directly
involved in operations. This is the practical significance
of this study, that is, the applicability of the findings to
areas such as port operational safety and
environmental downtime management.
ACKNOWLEDGMENTS
The authors would like to thank Zenith Litoral Hidrografia
Ltda and Santos Pilots for providing the ADCP data
maintained by the Santos Pilotage. We extend our gratitude
to the National Oceanographic Data Bank of the Navy
Hydrography Center, of the Hydrography and Navigation
Directorate of the Brazilian Navy for providing the Santos
Buoy data of the National Buoy Program. The first author
expresses gratitude towards the support received from the SP
Águas – São Paulo State Water Agency of the Secretariat of
Environment, Infrastructure and Logistics of the São Paulo
State.
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