1287
1 INTRODUCTION
In recent years, there has been growing interest in
improving energy efficiency in ship operations from
the perspective of reducing environmental impact. In-
operational performance is proposed to be evaluated
by the Annual Efficiency Ratio (AER) using the Carbon
Intensity Indicator (CII) [1]. However, there are many
issues to be addressed, and a review is underway.
Captains operate their vessels in uncertain weather
and sea conditions in order to meet the cargo and
schedule requirements of their shippers. Several issues
need to be addressed to properly manage ship
operations from an energy saving perspective (energy
saving operation management).
First, fuel consumption and CO2 emissions relative
to the work (ton-miles) done by the vessel are used as
energy efficiency indicators by operators in managing
operational performance. The calculation of work can
be done in ton-miles of DWT, GT or Displacement ton-
miles of loaded weight, but which evaluation indicator
is appropriate?
The energy efficiency of each voyage varies greatly
from voyage to voyage, affected by the amount of
cargo carried and the schedule, which caused by
transportation requirements, weather and sea
conditions, and hull fouling. In the CII, such variation
is evaluated using the average AER of energy efficiency
over a one-year period. This treatment is
understandable, since the average of a sufficient
number of data is expected to converge to a certain
value (Central Limit Theorem). However, it is known
that the standard error, which indicates the error of the
mean, depends on the data. It is considered
inappropriate to use a mean value with a large
standard error due to insufficient data. Confirmation of
significance and validity is considered necessary. At
the same time, it will be necessary to consider the
Appropriate Operational Energy Efficiency Indicator
Based on the Significance of the Evaluation for Vessels
in Regular Service
T. Kano, R. Ishizawa & T. Kuitani
NPO Marine Technologist, Tokyo, Japan
ABSTRACT: In recent years, there has been a growing interest in improving energy efficiency during operations
for reducing environmental impact. An indicator for evaluating operational performance, known as CII, has been
proposed, but it has many issues and is currently under review at the IMO. As operational performance is strongly
influenced by shippers’ transport requirements, it is important to select an appropriate energy efficiency indicator
that takes these constraints into account and to verify its validity to evaluate operational performance with high
reliability. Therefore, this study proposes an indicator that considers the physical implications and the influence
of transport requirements, as well as a validation methodology using statistical tests. A comparative evaluation
of the improvement effect of Weather Routing by applying the CII and the proposed indicator, using observed
data from ferries operating daily and with a large number of voyages, showed that the evaluation by the proposed
method is highly significant.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 4
December 2025
DOI: 10.12716/1001.19.04.27
1288
influence of factors of variation and to exclude these as
much as possible to improve significance and validity.
Furthermore, energy efficiency during operation
can be attributed to the shipper's transportation
requirements or to the operator's efforts. Energy
efficiency during operation varies greatly depending
on the amount of cargo carried and the required ship
speed due to the requirement, but even if this results in
poor operational energy efficiency, this is not the
operator's responsibility.
What operators can do from the viewpoint of
energy-efficient operation is to sail in compliance with
the schedule for cargo requested to be transported and
to operate on-time without unnecessary early arrivals.
Appropriate indicators and evaluation methodologies
are considered necessary to evaluate the effects of
improved operations through the efforts of ship
operators.
In order to evaluate reliable operational
performance, it is important to select an appropriate
energy efficiency indicator, and to verify the validity of
the evaluation methodology and verification of the
significance of the evaluation results.
In this study, first, considering the physical
implications of energy efficiency, the authors adopted
the Energy Efficiency of Navigational Index (EENI),
which considers the work done by a vessel in
displacement ton-miles as proposed by the authors in
[2], [3]. Based on previous research [3], propose a
methodology that describes the influence of
displacements of a vessel for evaluating the energy
efficiency of each voyage. Next, introduce an index
suitable for evaluating the effect of energy efficiency
improvements by operators that excludes the effects of
displacement and required vessel speed due to
transport requirements. Finally, the proposed
methodology was applied to the operational data
collected from the ferry in operation, and the energy
efficiency of the ship's basic operation and the effect of
using Weather Routing (WR) [4] [5] as a corrective
action was evaluated by EENI and CII indicators, with
the respective reductions (CO2 emission reductions)
results. At the same time, the reliability (significance)
of the evaluation results will be presented, which was
verified using the Student's t-test [6], one of the
statistical test methods.
The results of the evaluation by the proposed
method showed high significance. The number of data
required for the required error rate was also less, it is
considered that the proposed indicator is more
appropriate.
2 EVALUATION OF OPERATIONAL
PERFORMANCE
2.1 Energy efficiency for CII
CII uses energy efficiency as an index of CO2 emissions
divided by DWT or GT and voyage distance.
( )
2
- /
FOC CF
VoyageEnergyEfficiencyof CII g CO ton mile
DWTorGT
=
Ｄ
(1)
2.2 Proposed energy efficiency
（
EENI
）
The indexes for CII are defined as CO2 emissions in
relation to DWT ton-miles and GT ton-miles, which can
also be called social work defined by the demands of
society. However, the fuel consumed by a ship is not
consumed only for cargo, but is used to move the
displacement W, which is the total weight of the ship.
For the operational energy efficiency, it is considered
appropriate to use energy efficiency [3], which is
calculated from the FC for the displacement tons x
voyage distance miles, which is the work physically
done by the ship (physical work).
( )
2
EENI /
FOC CF
g CO ton mile
W
= −
Ｄ
(2)
/FOC CF
W Vog
＝
ｈ
(3)
FOC : Fuel Consumption
FOC/h：Fuel Consumption per hour
CF : Conversion factor between fuel consumption and
CO2 emission
W : Displacement(ton)
D : Distance sailed (mile)
Vog : Speed over the ground(knot)
2.2.1 Physical meaning of EENI
According to Kano and Namie [6], the EENI has a
physical meaning, and includes SFC (Specific Fuel
Consumption), total resistance coefficient C_T∇, ship
speed V, water density ρ, and gravitational
acceleration g, ship propulsion efficiency η, and
displacement expressed in volume ▽. In this study,
we assumed EENI is inversely proportion to Wβ, the
displacement W is used instead of the displacement
volume ▽ and is expressed as follows.
2
EENI
W
T
SFC C V CF
=
(4)
Equation (4) expresses the nature of EENI well.
Assuming small changes in SFC, ρ, CF and η, it can
be seen that EENI increases in proportion to the square
of the ship's speed and inversely proportion to W^β.
2
EENI
W
kV
=
(5)
2.2.2 Indicator showing improvements in operations to
transport requirement (OII)
1. Energy efficiency for transport requirement of
EENIr
A transportation requirement specifies the port of
departure and the port of destination as well as the
respective departure and arrival times, which
determines the required ship speed Vr and
displacement W.
Therefore, Energy efficiency for transport
requirement of EENIr is described as follows.
2
EENIr
W
k Vr
=
(6)
1289
2. An indicator showing improvements in operations
responding to transport requirement (OII)
Considering the ratio EENI/EENIr of the observed
EENI and the EENIr for the transport requirement, it
can be said to be the operational improvement ratio OIr
(Operational Improvement Ratio), which indicates
how close the energy efficiency of actual operations has
come to the transport request.
r
r
EENI
OI
EENI
=
(7)
Since it is difficult to specifically identify k, we
propose the following indicator OII (Operational
Improvement Indicator), This indicator means OIr
multiplied by k
2
EENI
OII
Vr
=
(8)
W
k
OIr
=
(9)
2.3 Evaluation of operational energy efficiency
The observed energy efficiency varies depending on
transport requirements from shippers and external
forces such as weather and sea conditions.
Therefore, the evaluation is done by taking the
average value over a certain period of voyage.
For example, CII uses the annual average energy
efficiency rating (AER) as an indicator of operational
performance. The property of the mean value is that it
will converge to a constant value if the number of data
is sufficiently large relative to the variation, even if the
mean value is varied (Central Limit Theorem).
Therefore, it makes sense to use this as an indicator. In
addition, it is considered reasonable to obtain an
average value based on a year's worth of voyage data,
as this incorporates seasonal variations throughout the
year. However, the number of voyages per year varies
from vessel to vessel. In actual evaluations, the average
energy efficiency value is obtained from data on a
limited number of these voyages. In such cases, it is
important to take measures to reduce and evaluate
error. Therefore, we will review the mean error based
on statistical findings.
2.3.1 The term energy efficiency ratio (TER)
From an operational management perspective, we
may wish to evaluate the results over an arbitrary term,
T. The term energy efficiency ratio (TER) for a given
number of voyages (N) over term T is calculated as
follows:
( ) ( )
( )
TER /
N
N
nn
N
FOC CF
g ton mile
W ton Dist mile
=
(10)
2.3.2 Standard error and error rate of TER
When enough data is available, the mean value will
typically converge to a specific error range, as
demonstrated by statistical analysis (Central Limit
Theorem).
The mean (μ) and standard deviation (σ) are,
respectively, obtained from a sufficient number of data.
Then, the difference between the mean value μN
obtained from N data and μ is called the standard error
(SE), which can be obtained by the following equation.
SE
N
=
(11)
And, the standard relative error, ϵSE described as
follows:
SE
SE
=
(12)
From equation (11), the standard error of mean is
expressed as the relationship between the variance,
which indicates variability, and the number of data
from which the mean is calculated, and that the larger
the number of data and the smaller the standard
deviation σ, the smaller this error becomes. In other
words, reliable results with small standard relative
errors can be expected if the number of observed data
is sufficiently large. However, since the number of
voyages per term varies from vessel to vessel, it is
important to evaluate the error in the TER based on the
variance of the data and the number of voyages for
one's own vessel.
2.3.3 The evaluation of operational energy efficiency and
the significance
1. The evaluation of differences in average TERs for
operational energy efficiency
The improvement in operational energy efficiency
due to corrective actions such as WR can be evaluated
by the difference in TER. For example, using the
average TERM of the energy efficiency of M voyages
without WR and the average TERN of the energy
efficiency of N voyages with WR, it can be expressed
as follows.
The improvement rate ε due to corrective action
taken is expressed as follows.
( )
ε
withWR withoutWR
NM
withoutWR
M
TER TER
TER
−
=
(13)
2. Significance of differences in TER
The significance of differences in means can be
determined by performing statistical tests. For
example, the significance can be determined by
determining the P value by performing Student's T test
[7],. In general, a P value is considered significant if it
is less than or equal to 5%. significance of difference in
TER
2.4 Models for energy efficiency in operation
Here, EENI is applied to the evaluation model (a
Wiener-type probability model) proposed in Ref. [3], as
follows. The first term indicates the influence of fouling
on the hull and propeller due to biofouling, etc., and
the bias term increases with time t after docking; the
second term is the term of the ship's original
performance corresponding to the required ship speed;
1290
the third term expresses the variation due to weather
and sea conditions; and the fourth term is a deflection
term hat is caused by directional external forces such
as ocean currents and westerly winds.
( )
0nn
EENI at EENI bZ n cSig= + + +
(14)
where,
a: Effect coefficient of hull fouling and other age-
related deterioration
EENIn0: EENI at calm sea in the condition of the hull at
the time of dockage’s hull cleaning on the nth voyage
b: Effect coefficient of variation due to weather and
wave conditions
Z(n): Variation affected by weather and wave
conditions
c: Effect coefficient of directional factors such as
westerlies, ocean currents
Sig: Sign expressing the deflection of westerly winds,
ocean currents, etc.
To reduce the variations of the observed EENI, this
study as follows. Furthermore, when evaluating the
impact of changes over time, the influence of weather
and sea conditions before and after docking is taken
into account using operational data collected on the
vessel.
1. Removes the effect of differences of displacement
As equation (3), (4) shows, the value of EENI tends
to decrease as the displacement increases. This effect
needs to be excluded in order to evaluate energy
efficiency during operation.
The energy efficiency index (EENI) can be obtained
using the following formula. Since the EENI is defined
for each voyage, the energy efficiency obtained from
the monitoring data is denoted by the lowercase letter
eeni.
/Foc h CF
eeni
W Vog
=
(15)
The effects of wind and waves change from time to
time and the observed EENI includes the effects of
ever-changing wind and waves.
The differences of the displacement in calm
conditions may be made clearer by adopting the
average of monitoring data from the calm sea
conditions (e.g. absolute frontal wind speeds of 5 m/s
or less and wave heights of 1 m or less; it should be
noted that such thresholds vary depending on the size
of the vessel under consideration, etc.).
Therefore, a coefficient of βis identified using the
least squares method for the relationship between the
measured eeni at calm sea conditions per voyage and
the displacement. Using this coefficient, the eeni can be
converted to the same displacement and compared.
2. Removes the effect of changes over time
According to References [3], the effect of change
over time coefficient ‘a’ is determined by the difference
in average EENI for X months before and after docking,
as shown in equation (16).
before after
EENI EENI
a
T
−
=
(16)
where
before
EENI
is the average EENI before docking,
after
EENI
is the average EENI after docking and T is the
time difference between dockages.
Figure 1. Changes over time for EENI
3 APPLICATION FOR A FERRY
In this section, the proposed evaluation method is
applied to a ferry operating on the following regular
routes to evaluate the energy efficiency of the vessel
and the energy saving effects of using WR (eE-
NaviPlan) [5] as a corrective measure and not using
WR (eE-NaviPlan).
3.1 Overview of target ship
Figure 2 shows Ship A (Table1) and the regular route.
This ferry is operated by Miyazaki Car Ferry Co., Ltd.
(Miyazaki Car Ferry, 2024) [8] and operates daily
between Miyazaki (A) and Kobe (B) according to the
schedule in Table 2, with one round voyage every two
days. It becomes. Additionally, sailing times differ for
outbound and return voyage from Monday to
Saturday and Sunday. The sailing time differs between
Monday-Saturday and Sunday for outbound and
return trips.
Figure 2. Ship A and regular route
Table 1. Principal specifications
Ship Name
Route
L [m]
B [m]
GT [ton]
NAV.DIST
[N.M]
TAKACHIHO
Miyazaki-
Kobe
194
27.6
14006
267
Table 2. Cases, Ship’s Schedule and Required Speed of Ship
A
Cases & Schedule
Port A
Port B
Nav.Time
REQ.Speed
Case1 Monday – Sunday
19:10
→
7:30
12:20
21.6
Case2 Monday – Saturday
8:40
←
19:10
13:30
19.8
Case3 Sunday
8:40
←
18:00
14:40
18.2
Table 3. Incidence (Xi) of each case
Dockage
… …
EENI
Dockage
7/14
6/14
1/14
1291
3.2 Investigation
3.2.1 Impact of displacement on EENI
Figure 3 shows the relationship between the
observed eeni at calm sea conditions and the
displacement between 20 May and 15 June 2023 in the
Case 1. Here, the frontal absolute wind speed is less
than 5 m/s and the wave height is less than 1 m
predicted by the JMA (Japan Meteorological Agency)
were defined as calm conditions, respectively. The
figure shows that the value of eeni is smaller and
improve energy-efficient in operation the larger the
displacement. The approximate curve obtained by the
least-squares method is shown as a solid line in the
figure. The results show that α = 37971 and β = -0.847
for the vessel as following equation.
0.847
84120eeni W
−
=
(17)
Figure 3. eeni and displacement
3.2.2 Impact of displacement on EENI
1. Variation in EENI and CII of the ferry
Table 4 shows the results of the evaluation of the
standard deviation and other statistics of EENI
excluding the effects of CII and drainage volume based
on one year of data (28 Jun 2023~28 Nov 2023) recorded
in the abstract logbook of the subject vessel. The EENI's
variance, standard deviation, standard error and
standard relative error are relatively better than those
of the CII, with smaller values of 29%, 15%, 16% and
4% respectively. The frequency distribution of each is
also shown in the Figure 4. Although similar in shape,
the kurtosis is greater for EENI.
Table 4. Statistics values of AER for EENI and CII
Figure 4. Frequency distribution of EENI and CII
Figure 5 shows the relationship between the
standard error rate and the number of voyages
determined by equation (12). It shows that the number
of voyages required to reduce the error rate below 1%
requires data from at least 67 voyages for EENI and 72
voyages for CII. EENI requires about 7% less data than
CII.
Figure 5. Standard error rate and number of voyages
2. Variation in EENI and CII of the ferry in each case
The subject vessel has different orientations and
speed requirements for each Case, as shown in Table 2.
Table 5 shows the statistics values for each Case,
including the standard deviation for each Case, which
is about 30-50 % smaller than the aforementioned
results, and therefore the data is more coherent. The
frequency distribution of each Case is also shown in the
Figure 6.
Table 5. Statistics values of AER for EENI of each Case
Figure 6. Frequency distribution of EENI
The Figure 7 shows the relationship between the
number of voyages and the standard error rate against
the EENI obtained for each Case. It can be seen that the
number of voyages required to reduce the standard
error rate below 1% is significantly reduced from 67
voyages when all data are handled to 14, 33 and 27
voyages in Case 1, Case 2 and Case 3.
1292
Figure 7. Standard error rate and number of voyages of each
case
3.3 Application of the proposed mode
3.3.1 The effect of changes over time
From the relationship between displacement and
average of EENI, the following table compares the
difference 30days before and after docking for EENI at
a displacement of 16000 tons for each Case. Case 3
was excluded for analysis because of the small number
of 3 data.
Table 6. Average of EENI before and after dockage and
number of data
3.3.2 WR service for the ferry
The WR service ‘eE-Navi Plan’ provided by NPO
Marine Technologists [9] is a system that supports
voyages by sending voyage plans (arrival/departure
ports, arrival/departure times, etc.) from ships to shore
in advance, and then providing optimal control
variables and a weather forecast information
(weather/sea condition prediction). The system
supports navigation by providing optimum control
variables (RPM/wing angle), etc. from shore to ensure
that the ship arrives in time for the planned arrival
time.
This system enables ships to sail at the minimum
necessary speed without being late for the required
arrival time, avoiding unnecessary early arrivals,
avoiding the rush-to-wait phenomenon and avoiding
offshore waiting, thereby achieving a significant
reduction in CO2 emissions from vessels and on-time
operation. CO2 emissions from vessels can be
significantly reduced and on-time operations can be
achieved.
It is also possible to check the monitoring data
transmitted from the ship and the results of analyses of
voyage planning and fuel savings, which will be useful
for improving the efficiency of future operations.
3.3.3 Evaluation on improvements from WR as a
corrective action
The average EENI (Energy Efficiency of
Navigational Index) at a displacement of 16000 tons
and corrected changes over time）of the vessel's basic
operational performance with WR (BAU; Business As
Usual) and without WR (Project) can be determined by
equation (10) using the operational data corresponding
to the respective schedules, where the deflection and
time-dependent terms have been removed. Eventually,
the improvement rate ε due to WR can be calculated by
equation (13).
1. Data to be analyzed
The operational data for the analysis was obtained
from 2023/6/28~2023/11/30 after leaving the dock,
taking into account that the performance will not
completely return to the level immediately after
entering service. During this period, Ship A was
provided with WR services, but as the WR planning
and operations were not properly planned and
operated, so on September 14, 2023, the captain and
crew were explained how to operate it. Since then, the
voyage planning and operation had generally been
done correctly. The voyages where the WR was
correctly planned and operated as shown in Table 7 for
the use of the WR are defined as those voyages where
the WR was used (w/o WR) and those where the WR
was not used (w/o WR).
Table 7. Number of data with / without WR
Num. of Data
w/WR
W/o WR
Case1
22
49
Case2
29
33
Case3
3
8
Total
54
90
2. Evaluation result
Table 8 shows the average EENI values with and
without the use of WR per Case. The effectiveness of
the WR calculated by the equation (13). Furthermore,
the significance of this reduction effect was statistically
tested by Student's t-test (Student, 1992).
The significance of the evaluation results of each
reduction effect can be determined by the p value, and
it is often determined that it is significant if this value
is 5% or less. For Case1, the p-value is less than 5%,
indicating high significance and 95% reliability. For
Case2, the p-value is 6.7%, it is above 5% but also below
10%, which is considered to be an acceptable range.
However, in Case3, the p value exceeds 70%, so it is
unreasonable to judge it as significant. This may be due
to the fact that the amount of data for the evaluation
was as small as 3 and 8 data.
Therefore, the results of Case3 were excluded and
the value of the EENI reduction effect obtained by
averaging the ratios of Case1 and 2 as 7:6 respectively,
was evaluated as the reduction in operational energy
efficiency due to WR during the evaluation period. The
results show that the operational energy efficiency has
been reduced by 2.9%.
1293
Table 8. EENI savings from WR in Ship A
3.4 Operational Improvement Indicator (OII)
Table 9 shows the Operational Improvement Indicators
(OII) for Cases 1 and 2. These indicators show how far
the energy efficiency of the actual operation has come
in relation to the transport requirements. This shows
that Case 2 is less energy efficient than Case 1 due to its
larger value. This may be due to the influence of ocean
currents and prevailing winds.
Table 9. OII （Operational Improvement Indicator）
4 CONCLUSION
Energy efficiency during operations, which is
considered to represent operational performance, is
strongly influenced by the transport requirements of
shippers and daily changing weather and sea
conditions on a voyage-by-voyage basis, and has a
large degree of variation, so in order to conduct a
reliable evaluation of operational performance, it is
necessary to select appropriate evaluation indicators
and to verify the validity of the evaluation method and
evaluation results using these indicators. The following
are some of the key issues that need to be addressed.
In this study, the following results were obtained on
operational performance, using observation data from
ferry that operate daily and for which data on a large
number of voyages are available, and investigating the
validity of the evaluation indices, methods and
evaluation results.
1. EENI was shown to be appropriate as an index for
evaluating energy efficiency during operations.
2. Component-separated models were introduced,
which influence the effects of changes over time,
such as hull fouling, and the effects of deflections,
such as ocean currents and prevailing westerly
winds, and energy efficiency on a voyage-by-
voyage basis, such as weather and sea conditions.
The model was applied to evaluate the effects of
changes over time on the data before and after
docking, and by treating Case separately for each
route/schedule, it was possible to evaluate the
energy efficiency of the operation with reduced
variation.
3. Energy efficiency during operations can be derived
from transport requirements from shippers, or from
operational improvements made by captains and
other operators. Operational improvement
indicator (OII) was proposed, suitable for
evaluating the impact of energy efficiency
improvements by operators, excluding the impact
of transport requests.
4. A comparison of EENI and CII statistics derived
from ferry operation data shows that EENI has less
variation than CII, and the number of data required
for a standard relative error of 1% is also 7% less 67
for EENI than compared to 72 for CII. The proposed
EENI indicator is considered to be an appropriate
and reasonable indicator for the evaluation of
operations.
5. Furthermore, the effectiveness of the WRs used on
this ferry as a measure to improve operational
efficiency was evaluated and a reduction of 2.9%
was achieved with acceptable confidence (p-value
≤ ７％）
6. Although the study was conducted for ferries in
regular service, the proposed indicators and
methodologies are considered to be applicable to
tramp vessels, so the next step is to evaluate the
applicability of the proposed indicators and
methodologies to tramp vessels.
REFERENCES
[1] IMO, ‘2023 IMO Strategy on reduction of GHG emission
from ships’,
https://wwwcdn.imo.org/localresources/en/OurWork/En
vironment/Documents/annex/MEPC%2080/Annex%2015
.pdf ,2024
[2] ISHIZAWA, R., KANO, T., ‘Evaluation of energy saving
using weather routing operational data for coastal
ferries’, Proceedings of the Asia Navigation Conference,
2024.
[3] KANO,T., ISHIZAWA, R., ‘Evaluation on Energy Savings
Effect of Corrective Actions Using Monitoring
Operational Data for Ferries’, Proceedings of the 2025
Managing CII and Associated Challenges, The Royal
Institute of Naval Architects, UK.
[4] THE GROUPE OF WEATHER ROUTING RESERCHER.,
‘Weather routing -Optimal voyage plan based on weather
and marine forecast information-’, Seizando-Shoten
Publishing, 1992.
[5] SATO, K., KANO, T., ‘Eco-shipping project with speed
planning system for Japanese coastal ships’, Journal of
the maritime university of szczecin, 2016.
[6] KANO, T., NAMIE, S. ‘A study on estimation
methodology of GHG emission from vessels by using
energy efficiency index and time series monitoring data’,
Proceedings of the conference on maritime-port
technology, 2014.
[7] STUDENT, ‘The Probable Error of a Mean’,
BIOMETRIKA, 1908.
[8] MIYAZAKI CAR FERRY.,
https://www.miyazakicarferry.com/, 2024
[9] MARINE TECHNOLOGIST., eE-NaviPlan,
https://mtl.or.jp/activity/, 2024.
