Risk Management: An International Journal 2005, 7 (3), 21–40
The Effect of Weather Factors on the Severity of Fishing Boat Accidents in Atlantic Canada Yue Wu, Ronald Pelot and Casey Hilliard1 Commercial fishing is an inherently risky industry, and the safety of the people and property involved is always a concern of maritime administrations. The purpose of this study is to determine whether certain weather factors affect the severity of fishing incidents. The study area encompasses a broad extent of Atlantic Canadian waters, using fishing boat incidents recorded by Canadian Coast Guard from 1997 to 1999. Weather data from numerous sources were processed to ascertain the conditions during each incident. Statistical analyses were conducted to determine which of the following six weather factors are predictors of incident severity: wave height; sea surface temperature; air temperature; ice concentration; fog presence; and precipitation. Logistic regression established that wave height and ice concentration can predict the likelihood of an incident being classified as distress or non-distress. These results can be instructive for better preventive measures for hazardous weather conditions. Search and rescue personnel can also better anticipate and plan for severe incident occurrences as a function of the weather forecasts. Key Words: Fishing incidents; weather conditions; maritime risk; search and rescue; risk planning Introduction Due to the unpredictable nature of the operating environment, as well as certain economic and competitive drivers, commercial fishing is considered to be one of the most hazardous of occupations. The working conditions fishermen confront every day are far beyond those faced by workers in land-based occupations, leaving aside the possibility of losing their lives. Even the most advanced fishing vessel can be lost at sea. Moreover, compared with other seafaring occupations, the hazards associated with fishing can be extreme. The kind of work which fishermen routinely perform in bad weather has no parallel in the world of seafaring. On a merchant ship such feats as leaping to catch wild cables or ducking out of the way of objects shifting around on deck are normally required only in emergencies, but aboard trawlers they form part of nearly every shooting and hauling of nets. (Warner, 1983:73)
Commercial fishing is thus an inherently risky industry, and the safety of the people and property involved is always a concern. Data show that fishermen continue to be among the most dangerous occupations, having far higher fatality rates than fire fighters, police offices, and truck, taxi, and delivery drivers. (Spitzer, 1999:4-1)
Copyright © 2005 Perpetuity Press Ltd
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Risk Management: An International Journal 2005, 7 (3), 21–40
In the Canadian context: … in 1985, 212 per 100,000 deep sea fishers died, compared with 74 per 100,000 miners, 32 per 100,000 construction workers and 118 per 100,000 forestry workers. (Binkley, 1995:4)
The Canadian Coast Guard (CCG) monitors Canada’s northern and coastal regions and comes to the assistance of seafarers or aviators in distress. Search and rescue (SAR) is essentially a humanitarian activity with the prime purpose of saving lives. Within international agreements for maritime SAR, Canada has three SAR regions (SRRs): Halifax, Trenton and Victoria, the total area of which extends from the Canadian/US border to the North Pole, and from approximately 88 nautical miles out into the Pacific Ocean to 1000 nautical miles into the Atlantic Ocean. Through its SAR division, the CCG compiles records of incidents whenever SAR services are needed, including tasking a vessel or aircraft to render assistance. More than one vessel/aircraft may be tasked to an incident (CCG, 1997). Each time an SAR resource is tasked, a record is generated, and this is then added to the ‘system of information for search and rescue’ (SISAR) database (Canadian Coast Guard, 1998). According to the CCG Maritime SAR Annual Report for 1997, incidents involving vessels or people on board—defined as ‘maritime incidents’—accounted for about three-quarters of all the incidents recorded. Among them, incidents involving commercial fishing vessels were the second leading incident category, amounting to 1250 incidents that year, while the number of lives lost during such incidents was 0.4 per cent higher than the number of lives lost per incident associated with pleasure craft, in spite of the latter engendering over twice as many incidents. This is one indication that fishing incidents often result in more severe consequences than other types of maritime activities. When an incident is reported to the SAR control center, the most available and best-suited SAR resources are tasked. When the incident appears to be serious, referred to as ‘distress’ or ‘potential distress’ incidents, multiple SAR resources, including lifeboats and helicopters, may be tasked, over a period ranging from several hours to days. When an intensive search is conducted, the demand on SAR resources is very high. Conversely, for less serious incidents where no distress or perceived appreciable risk to life is apparent, fewer resources are allocated to the event, unless the situation deteriorates. The relative distinctness of these demands on SAR services is apparent in the CCG Annual Reports (Canadian Coast Guard, 1997; 1999; 2000). Participants in the fishing industry are acutely aware that the vagaries of the weather conditions in which the fishing fleet operates are a major contributor to the occurrence of incidents affecting the vessels and their crews. However, there appears to be a dearth of detailed research on the relationship between weather conditions and the severity of commercial fishing incidents. This article attempts to demonstrate that such an association exists, to determine which are the principal weather factors driving this outcome, and to establish an indicator of severity for SAR resource preparation in certain weather conditions. First, an overview of the literature reflects the principal developments in maritime traffic analysis, particularly those that include aspects of the weather. A detailed explanation of the numerous sources of data and the subsequent preparation and aggregation processes follows. The methodologies for interpolation and creation of the necessary databases for statistical analyses are presented. Finally, a logistic regression model is applied to determine the relationship between weather conditions and incident severity. The importance of these findings to the maritime community and SAR planners is discussed.
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The Effect of Weather Factors on the Severity of Fishing Boat Accidents
Risk Management: An International Journal 2005, 7 (3), 21–40
Literature review Due to the frequency and magnitude of weather-related accidents in the maritime milieu, many initiatives have addressed various aspects of environmental conditions. The three main issues for planning and action are to design vessels and equipment for adverse weather conditions (Wolfram and Harris, 1993), to improve information and protocols to deal with bad weather, and to best prepare for response when the inevitable need arises. A holistic approach to evaluating relevant factors and/or problematic areas is to use quantitative risk analysis. In reviewing the assessment and management of risk in maritime transportation, Jason Merrick summarized this concept neatly as follows: Earlier work concentrated on assessing the safety of individual vessels or marine structures, such as nuclear powered vessels, vessels transporting liquefied natural gas and offshore oil and gas platforms. More recently, Probabilistic Risk Assessment (PRA) has been introduced in the assessment of risk in the maritime domain. (2002:381, embedded references excluded)
Fundamentally, risk assessments address the frequency of adverse events, and the type and level of consequences when they do occur (Pelot, 2001). Most studies to date have concentrated on the estimation of the probabilities of various accident types, without much explicit reference to measures of impact. Furthermore, the majority have examined the risks associated with the operation of a single vessel, or a few ships cruising in close proximity, which yields the likelihood of specific events such as collisions and groundings. This precludes the evaluation of total or relative risks across regions, time periods and/or fisheries. Several representative studies are introduced below, most of which incorporate a limited set of weather factors. Few researchers have explicitly studied the effects of weather conditions on maritime incidents and safety. Talley (1999) incorporated three binary variables for weather-related factors, along with numerous other measures, in a study on injury rates arising from shipping accidents. These three factors were: whether adverse weather conditions were key elements in accident initiation; whether fog was present; and whether it was nighttime. Only this latter factor proved to be significant. The required data were extracted from the US Coast Guard’s CASMAIN database. In another study, McCarthy and Talley (2001) focused on recreational boating, with ten of the 27 independent variables represented by binary environmental factors. Five of these were significant predictors of injury to the operators or passengers. To model the probability of accidents for inland waterway transport, Roeleven et al (1995) divided the visibility and wind speed into three classes each, and the current velocity into four classes; hence, 36 circumstance-classes were created to represent weather conditions. In coastal waters and open seas, Wu et al (2005) modeled the fishing incident rate relative to traffic levels as a function of six weather conditions, of which five remained in the regression model: ice concentration; fog presence; wave height; precipitation; and sea surface temperature (air temperature being the one excluded). Aside from testing weather factors, other researchers apply expert judgment to estimate the impact of weather conditions on the type, probability and/or seriousness of maritime accidents. A project conducted by the CCG and Consulting and Audit Canada (CAC) estimated maritime risk by CCG program and waterway to improve efficiency and overall safety (Bushell, 1999). The only environmental factor considered in their risk index was visibility, coarsely estimated according to season. Similarly, Fowler et al (2000) conducted a European study on ‘safety of shipping in coastal waters’ (SAFECO), where individual models were built for different accident types:
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Risk Management: An International Journal 2005, 7 (3), 21–40
collision; powered grounding; drift grounding; structural failure/foundering; and fire/explosion. Weather conditions were introduced in only a few of these models. For the collision model, probabilities of clear and reduced visibility were incorporated. For the drift grounding model, both wind and current were assumed to be constant throughout the drift period. Structural failure frequency is modeled as a function of wind conditions, which is categorized into four groups based on the range of wind speeds. Some studies that deal with weather conditions in combination with other factors use simulation modeling to explore in more detail situational factors leading to incidents. A collaborative National Science Foundation (NSF) project entitled Speaking the Truth in Maritime Risk Assessment, involving Det Norske Veritas, Rensselaer Polytechnic Institute, George Washington University and Virginia Commonwealth University, used simulation to ‘assess the baseline risk of the system and then to test the effect of proposed risk interventions on the system risk’ (Harrald et al, 1998; 1999; 2000). Weather conditions were designated as ‘waterway situation characteristics’, and collapsed into a single factor in the conditional relationships to calculate vessel reliability. Further extensions of this approach integrated the simulation model results with expert judgment techniques to analyze system-wide maritime risk in terms of annual accident frequencies, referred to as ‘system risk simulation’. This process was applied to evaluate the benefits of tug escort schemes, where additional factors included wind, visibility, tugboat positioning and proximity to other vessels for accident probability modeling (Merrick, 2002). Method One of the key challenges in the current analysis is to classify incidents according to severity level. Some previous research (Bushell, 1999; Trbojevic and Carr, 2000) has viewed the risk from the point of socio-economic assessment, interpreting ‘risk’ as the harm that maritime incidents bring to the environment. However, this is only one possible consequence of such incidents. The overall goal of maritime risk analysis is to formulate the likelihood of the incidents, assess their causes and ask how much each cause contributes to the occurrence of an incident. Moreover, maritime traffic comprises a complex system involving many elements, and the consequences of maritime incidents may therefore be assessed using multiple criteria, including impacts on life, property and the environment. In accordance with their mandate, the CCG is primarily concerned with mortality and injury, and its incident severity classification system has been designed to reflect this. Given this central concern, the classification assigned by the CCG in their SAR operations database (SISAR) is adopted here as the measure of consequences. The focus of the paper is to examine the potential role of various weather factors leading to such consequences.
Data sources The relevant data sets acquired for this research fall into two main categories: incident data and weather data. Incident reports: SISAR. The SISAR database captures pertinent information concerning SAR missions conducted within Canadian areas of maritime SAR responsibility. SISAR is an extensive historical data set; it has been in existence since 1988, but only since 1993 has it been consistent and well filled out. For the analysis in this paper, only commercial fishing incidents in Atlantic Canada that occurred during the period 1997–99 were extracted from the SISAR database and subjected to thorough data-cleaning processes, including geographical verification, logical consistency checks, and complex matching procedures between the weather, vessel and incident data sets (Hilliard and Pelot, 2002).
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The SISAR incident database is a fairly detailed record of the incidents, including date, time and location, incident type, cause and severity, response summary (action taken), details on the vessels involved, and atmospheric conditions at the time (wave height, wind speed, wind direction, wind-against-current, visibility, ceiling, air temperature, sea temperature, clouds, ice, date and time of observation, position of observation, weather comments, atmospheric conditions, and tide states). Atmospheric conditions, a mandatory field, records the selection from the following list of available choices: clear skies, fog/mist, freezing rain/drizzle, hail, overcast, partly cloudy, rain, snow, squall, other and unknown (Canadian Coast Guard, 1998). Unfortunately, the quality of the SISAR weather table is inadequate for analysis, owing to low fill rates, inconsistencies and errors. Nevertheless, it provides a basis for limited verification of the weather data amassed directly for this study, as described below. On the other hand, SISAR is an invaluable source of information on the incidents themselves. It is used to pinpoint them both spatially and temporarily, as well as to categorize different vessel types involved. Incidents are classified according to their severity and the demand for SAR services. There is a distinction between maritime incidents and other categories (eg humanitarian assistance). Maritime incidents are classified as follows: •
M1: distress incidents, where a vessel or person is threatened by grave and imminent danger and requires immediate assistance;
•
M2: potential distress incidents, where the potential exists for a distress incident if timely action is not taken;
•
M3: incidents resolved in the uncertainty phase, where no distress or perceived appreciable risk to life is apparent; or
•
M4: false alarms and hoaxes that cause the SAR system to react but then prove unjustified or fabricated, such as a mistaken report of a flare (this category is excluded from analyses).
Weather data: AES40 wind and wave model data. Even for non-mariners, it is easy to appreciate that wave conditions on the open ocean are amongst the most important factors affecting the safety of maritime traffic. In particular, wind-waves2 can have a relatively high amplitude and frequency, which can play an important role in the movement and stability of the vessel. Due to the stochastic nature of waves, researchers use specific terminology to quantify the characteristics of waves, such as height, direction, frequency and total spectrum (Earle and Bishop, 1984). Based on consultation with experienced mariners, the wave height was selected for analysis as a key factor, quantified by the significant wave height (H1/3).3 The AES40 North Atlantic Wind and Wave hindcast model was developed at Oceanweather Inc with support from the Climate Research Branch of Environment Canada (Swail and Cox, 2000), for the continuous period 1958–2003, at six-hour intervals starting at midnight every day. The model covers the region of latitude 40° to 60° N and longitude 73.33° to 45.83° W, divided into grid squares 0.625° of latitude by 0.833° of longitude in extent. The data set is generated by running the Pierson-Moskowitz sea-states model in the North Atlantic region. The overview of this dataset (Swail et al, 1999; 2000) includes a statistical evaluation verifying that the model results agree quite well with the in situ and satellite data, concluding that: the wind and wave data are considered to be of sufficiently high quality to be used in the analysis of long return period statistics, and other engineering applications. (Swail et al, 2000:1)
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Intuitively, wind speed could also be considered an important factor affecting the safety of maritime activities. However, it has been omitted from the current model for several reasons. First, the wind speed and wave height are not independent factors: stronger winds generally result in bigger waves. Secondly, based on incident reports and expert opinion, the waves are more directly linked to adverse consequences, and therefore, given a choice, wave measures take precedence over wind factors for inclusion in the model. Finally, for the preparation of the AES40 hindcast data, the wave height at a particular grid point is functionally generated by inputting local wind speed, as well as influences from adjacent grid points. Therefore in the AES40 Wind and Wave model outputs there is a high correlation between wave height and wind speed, as shown in a scatter plot of these two variables (Figure 1).
Figure 1. Sample scatter plot of significant wave height and wind speed (N = 706): sample data at 12 pm, 1 July 1998
Significant wave height (m)
4
3
2
1
0 0
2
4
6
8
10
12
14
16
Wind speed (m/s)
Weather data: other data. Several other weather features may play a role when operating in the maritime environment, including sea surface temperature (SST), air temperature, precipitation, ice concentration, and fog. Through the Climate Diagnostics Centre of the National Oceanic and Atmospheric Association (National Oceanic and Atmospheric Association/Cooperative Institute for Research in Environmental Sciences, 2003) in the US, extensive databases related to various weather features are available. These data are primarily interpolated, modeled values based on real observation data. For this analysis, those datasets with the highest available spatial and temporal resolution were selected to achieve the greatest possible accuracy. These diverse datasets cover different time spans and geographic extents, with varying resolutions of grid sizes and time frequencies. The details of each weather dataset used in this research are shown in Table 1.
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Table 1. Definition, scope and sources of weather data Variable name
Dataset
Time span
Time interval
Geographic range
Grid size
Source
Wave height
AES40 North Atlantic Wind and Wave Climatology
1958–98
Every six hours
40° ~ 60° N, 0.625° x 73° 20’~ 45°50’ W 0.833°
Oceanweather, via Climate Research Branch of ECa
SSTb
NCEPc OId SST 1981– V2 present
Weekly mean
89.5° S – 89.5° N, 0.5° – 359.5° E
1° x 1°
CDCe-NOAAf
Air temperature
NCEP/NCARg reanalysis
1948–2002 Every six hours
90° S – 90° N, 0° – 357.5° E
2.5° x 2.5° CDC-NOAA
Precipitation
CPCh merged analysis of precipitation
01/1979– 12/1999
Monthly mean
88.75° S – 88.75° N, 2.5° x 2.5° CDC-NOAA 0° – 357.5° E
Ice NCEP OI V2 concentration
1981–99
Weekly mean
89.5° S – 89.5° N, 0.5° – 359.5° E
1° x 1°
Boundary layer height
ECMWF 40 years re-analysis
1957–2002 Every six hours
90° S – 90° N, 0° – 357.5° E
2.5° x 2.5° ECMWF i
2 m dewpoint temperature
ECMWF 40 years re-analysis
1957–2002 Every six hours
90° S – 90° N, 0° – 357.5° E
2.5° x 2.5° ECMWF
CDC-NOAA
a. Environment Canada; b. Sea surface temperature; c. National Center for Environmental Prediction (formerly NMC); d. Optimal interpolation; e. Climate Diagnostics Center; f. National Oceanic and Atmospheric Administration; g. National Center for Atmospheric Research; h. Climate Prediction Center; i. European Centre for Medium-Range Weather Forecasts.
In addition to these acquired variables, one derived variable was also needed for analysis. The presence of fog is a major concern among mariners (Markell, 2003), yet no systematic historical fog records are available for use in this study. Although this deficiency is almost intractable, methods have been developed recently to estimate the presence of fog. Using rules based on machine learning, the existence of fog was determined to be related to sun angle, boundary layer height (European Centre for Medium-range Weather Forecasts, 2004), sea surface temperature, and dew-point temperature (Tag and Peak, 1996). Fog is assumed to be present when the following conditions are met: •
sun angle > 53.7° (from zenith);
•
inversion base height (boundary layer height) <= 285 metres;
•
sea surface temperature <= 20.5°C; and
•
(dew-point temperature minus sea surface temperature) > -2.6°C
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The sun angle, ( Θ ), required for this evaluation, can be calculated as follows (Duffie and Beckman, 1974): cos Θ = sinδ * sinΦ + cosδ cosΦ cosω
Where
δ = 23.45 sin(360 * (284 + n) / 365) n = day of year Φ = latitude, (north positive) ω = (12 – T) * 150 T = time of day (24h)
The time of day in these equations refers to the local time. The time of day entered in the SISAR and weather databases is in Greenwich Mean Time (GMT) format, and therefore an offset of -4 hours is applied to correct to local Atlantic (Canada) time. For this analysis, fog is represented by a binary variable: 1 or 0 respectively for the presence of fog or not. Data preparation Since the distribution of incident positions is not regular, temporal and spatial interpolation are required to associate the gridded weather information with each incident recorded in SISAR. The whole process involves three stages: matching incidents with gridded weather data; spatial interpolation/extrapolation; and temporal interpolation. In this process, the order of spatial or temporal interpolation makes no difference in the results, since the grid point values are spatially independent with respect to the time windows and the interpolation procedure is linear. The steps in this preparation process are explained in the Appendix. Matching. To calculate the weather conditions at the time of each incident, a matching process is required to associate an incident with its adjacent weather grid points. This means that the study area must not extend beyond the scope of the gridded weather areas, and that intervening land must be accommodated for the matching process. The study area (Figure 2) was therefore defined as the intersection of the areas for which weather datasets (AES40, NCEP, CPC and ECMWF) have been obtained, and also considering the NAFO4 and SAR jurisdictional boundaries (Shahrabi, 2003), and a general bathymetric chart of the oceans, which includes a 1:250,000 scale landmass (General Bathymetric Chart of the Oceans, 2003). Between 1997 and 1999, 2817 fishing incidents of severity level M1, M2 and M3 occurred within this study area. The incident matching is performed first with the most spatially restricted data set, the AES40. The initial step in the process relies on the provision that the incident and adjacent grid points be connectable by a direct line (ie not crossing land). The number of visible adjacent weather grid points determines whether automated matching with line-of-sight, automated matching without line-of-sight, or manual matching techniques are invoked. A few incidents were deleted from the analysis due to awkward locations and complicated local features which made it impossible to find good associations with the gridded weather data, culminating in a final tally of 2748 usable incident records. Table 2 summarizes how many of these incidents could be matched with weather points, sorted by the number of weather points matched and the dataset under consideration.
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Figure 2. Maritime weather study area with commercial fishing incidents (1997–99)
Table 2. Matched incident counts by database and technique
Dataset AES LOSa
Minimum number of weather points matched One point Two points Three points Four points matched matched matched matched 2346
1766
1063
464
AES no LOS
229
157
46
4
AES manual
173
21
0
0
Total AES
2748
ICE LOS
2424
1732
1218
550
ICE no LOS
309
130
42
8
ICE manual
15
0
0
0
Total ICE
2748
SST LOS
2424
1732
1218
550
SST no LOS
309
130
42
8
SST manual
15
0
0
0
Total SST
2748
a. Line-of-sight
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Interpolation/extrapolation. Once all the incidents were matched to the relevant weather data points, routines were run to calculate representative weather conditions at the actual incident location. For matches with the AES, ICE and SST datasets, incidents that could not be matched via line-of-sight to weather points were nevertheless assigned average data values from adjacent, valid weather grid points. Coverage of grid points for the following variables falls both on land and sea, hence any incident location can be associated with four neighboring points and no special treatment for spatial interpolation is needed: air temperature; precipitation; boundary layer height; and dew-point. All matches with other weather datasets, and those with line-of-sight or manually selected for AES, ICE and SST data were run through the interpolation routines as shown in the Appendix. When the spatial interpolation and averaging were completed, temporal averaging was employed to interpolate the weather data to the time of the incident. Ice concentration and SST are stored as weekly means, which are applied to all incidents within the corresponding week. Similarly, precipitation is only available as a monthly mean. All other data values were interpolated temporally, accommodating the distinct temporal resolutions of diverse weather factor databases. Model building General assumptions. Prior to building the risk model, several general assumptions must be clarified, as follows (not in order of importance): •
other potential contributing factors to incident occurrences are ignored in this study, including human error, mechanical failure, or instrument failure;
•
the hindcast weather data collected from AES40 and NOAA, and the fog estimate using ECMWF, are truly representative of the weather conditions encountered in the actual situation; and
•
the reports in the SISAR database about the instant and location of the occurrence of the incidents are accurate.
Model structure. Although weather can influence maritime activities in many ways, including mariners’ behaviour and decisions as well as traffic levels, this study focuses on the effect of weather conditions on incident severity, irrespective of other antecedents. Specifically, to ascertain how the outcomes of certain events are associated with potential contributing factors, statistical dependence techniques are adopted. In this instance, the dependent variable is the severity level of maritime incidents as classified in SISAR (M1, M2 and M3), and the values for each weather field form the independent variables, including a binary variable in the case of FOG, with the remaining weather fields comprising continuous variables. Among the 2748 incidents falling into the study area that could be matched with gridded weather data, fewer than five per cent are classified at M1 severity level, and less than seven per cent at M2. Although this is a favorable situation for the CCG, it is less so for the current analysis, as the small numbers render the statistic analysis less robust. Despite these small values, the severe incidents are spread across the full spectrum of wave heights (see Figure 3). In order to partially compensate for this imbalance in event numbers, in this analysis the M1 and M2 distress incidents are grouped as serious consequence (SEVERITY = 1), while SEVERITY = 0 is assigned to the remaining M3 incidents. This way, the dependent variable, incident severity level, can now be represented as a binary variable. Binary logistic regression (Hosmer and Lemeshow, 2000) can be invoked to try to establish a relationship between incident severity and the independent variables detailed in Table 3.
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Figure 3. Histogram of incidents by incident classification vs wave height
Proportion of incident total
35% 30%
M3
25%
M2
M1
20% 15% 10% 5%
3.25~6.75
2.75~3.25
2.25~2.75
1.75~2.25
1.25~1.75
0.75~1.25
0.25~0.75
0~0.25
0%
Wave height (metres)
Table 3. Weather factor variables for logistic regression analysis Variable field name
Variable description
Data type
Function in model
SEVERITY
Severity of incident indicator
Binary
Dependent
WAVEHT
Wave height (m)
Continuous
Independent
AIRT
Air temperature (ºC)
Continuous
Independent
ICECONC
Ice concentration (%)
Continuous
Independent
PRECIP
Amount of precipitation (mm/day)
Continuous
Independent
SST
Sea surface temperature (ºC)
Continuous
Independent
FOG
Fog existence indicator
Binary
Independent
Analysis When the relationship between one response (ie dependent) variable and one or more explanatory (ie independent) variables is the goal of a multivariate analysis, regression methods are invoked. The type of the dependent variable is the key element in choosing the appropriate regression method; if the dependent variable is categorical, logistic regression is recommended. Multivariate linear regression methods describe the direct relationship between the continuous response variable and explanatory variables, whereas logistic regression yields the probability of each level of the categorical response variable as the outcome of the regression. When the dependent variable takes on more than two levels, multinomial logistic regression may be used; whereas binary logistic regression (usually simply referred to as logistic regression) is suitable for our analysis, since the dependent variable has only two levels (SEVERITY = 1/0) (Hair et al, 1998). The concept of logistic regression is to use a transformation function, namely the logit function g(x),
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to map the unit interval of probability (0,1) onto the real domain (- ∞ , + ∞ ) so that we can carry out the regression on the independent variables, which can be continuous or categorical. The form of the logit function is
( 1–θθ )
g (θ ) = ln
where θ represents the mean of the response variable, and
( 1–θθ ) is called an ‘odds ratio’. When the response variable can assume only two values, 1 or 0, θ is actually the probability of a positive event (ie response = 1) (Hosmer and Lemeshow, 2000).
75 ~ 6.
25 3.
25
~ 3.
75 75 2.
~ 2.
25 25 2.
1.
1.
75
~ 2.
~ 1.
25 25
~ 1.
75 0.
75
~ 0.
0.
25
0. 2 0~
75
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 5
Proportion of incidents
Figure 4. Proportion of incidents by severity (SEVERITY = 1 combines M1 and M2) vs wave height (m)
Wave height (m)
SEVERITY = 1
SEVERITY = 0
Although not immediately apparent in Figure 3, the proportion of severe incidents in each category is increasing with wave height as shown in Figure 4, indicating a possible relationship between these variables. To establish a possible relationship between the probability of SEVERITY being high (ie distress) (θ) and the weather conditions, where xi represents the measure of weather factor i at the time and location of each incident, the odds ratio acts as the dependent in the binary logistic regression model:
θ ln 1 – θ
(
) = β + Σβ x 0
i i
i
Generally, there are three choices of methods for including independent variables into a multivariate regression model: enter (all), whereby combinations of variables are examined for retention; forward selection, where variables are included sequentially based on their contribution to prediction; and backward elimination, where variables with insignificant explanatory power are sequentially removed from the entire set. A stepwise forward selection procedure was performed using SPSS (Norusis, 2002), a conservative approach which is suitable when orthogonality of the independent variables is not guaranteed. Several hypotheses tests on the appropriateness and adequacy of the model were run, using a significance level of α = 0.05.
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Hypothesis test 1: to determine if at least one of the weather factors’ coefficients in the model is not equal to zero. H0: all regression coefficients for the weather factors are equal to zero (ie β i = 0, for all i = 1 to 6); Ha: at least one weather factor regression coefficient is not equal to zero. Null model –2 log likelihood
Full model –2 log likelihood
Chi-square (change in null and full model –2 log likelihood)
p-value
Reject H0
1961.128
1921.675
39.452
0.000
Yes
Since the p-value is less than α = 0.05, the null hypothesis is rejected. Therefore, there is at least one weather variable which has a significant effect on the variability of the dependent variable. Hypothesis test 2: to determine if the fit of the model is adequate using the Hosmer and Lemeshow Test (Norusis, 2002). H0: the model is adequate; Ha: the model is not adequate. Chi-square
p-value
Reject H0
6.950
0.542
No
Hence, the fitted model is adequate. Hypothesis test 3: to determine the statistical significance of each of the independent weather factors in explaining the variability of the dependent variable SEVERITY. H0: the weather factor is not significant in explaining the variability of the dependent variable SEVERITY; Ha: the weather factor variable is significant in explaining the variability of the dependent variable SEVERITY. Risk factor variable
Risk factor variable coefficient (β)
p-value
Reject H0
Constant
-2.588
0.000
Yes
WAVEHT
0.403
0.000
Yes
ICECONC
0.018
0.000
Yes
From the coefficient table, only wave height and ice concentration contribute significantly to the occurrence of an incident with SEVERITY=1, classified as M1 and M2 in SISAR. Out of all the maritime fishing incidents included in this study, the likelihood of high consequence incidents is predicted by:
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exp(–2.588 + 0.403WAVEHT + 0.018ICECONC) 1 + exp(–2.588 + 0.403WAVEHT + 0.018ICECONC)
θ=
The sensitivity of the incident severity likelihood θ to these two predictor variables is presented in Figure 5. The likelihood of a high-severity incident increases with wave height and ice concentration respectively. However, an interaction effect between the two independent variables is also apparent; at low ice concentration, the severity likelihood grows at an increasing rate with wave height, whereas at high ice concentrations the growth rate drops off. Figure 5. Sensitivity chart for probability of high SEVERITY (θ) incidents by wave height (m) and ice concentration (percentile)
0.8
θ) Prob. of high Prob.of Highseverity Severity((?)
0.7 0.6
0.7-0.8 0.6-0.7 0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0-0.1
0.5 0.4 0.3 0.2 0.1 0 0
1
2
3
Wave height (m)(m) Wave Height
40 4
Ice Ice Concentration concentration (%) (%)
20 5
6
0
Discussion This study has demonstrated that certain weather factors can discriminate between distress incidents and less severe maritime fishing events. The strong relationship between wave height and maritime incidents, confirmed through the above model, is expected following discussions with mariners and meteorologists. Waves, or the presence of ice with the potential for accompanying freezing spray, can all adversely affect the stability and mobility of vessels. Large waves and pack ice might inflict damage to vessels or injury to the crew, or cause control of the vessel to be lost— any of which may be classified as a distress situation, requiring immediate assistance from the SAR system. The results of this study should be considered in the context of a larger ongoing maritime risk model (Pelot, 2001). One objective is to provide a spatial and temporal representation of risks associated with maritime traffic (including shipping, fishing, passenger vessels, recreational boating, etc). Amongst the many potential factors which influence the occurrence or severity of
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incidents, the weather is postulated to have a significant impact. This study has confirmed that certain weather factors are indeed significant determinants in the severity of incidents, and this provides another piece in the puzzle towards a better understanding of the maritime risk picture. The results of this study can be used directly to undertake proactive measures. These may include better education of mariners about the potential consequences of certain weather conditions so that they can either avoid them or prepare better for such circumstances; improved issuance of warnings under adverse weather conditions, such as the Small Craft Warnings currently disseminated in Canada; and perhaps a higher state of readiness by responders under certain extreme weather conditions when higher distress incidents are to be expected. These results can be instructive for other preventative measures, such as changing the regulations for commercial fishing season openings if certain weather conditions are unacceptable, or better education of mariners on when to curtail trips. The logistic regression model can be invoked to predict the likelihood that the consequences will be severe, given that a fishing vessel in the study area is involved in an incident. Aggregating across all fishing traffic at a given time, and the expected number of incidents associated with this activity level based on historical records, the value derived from the regression yields an overall estimate of the proportion ‘θ’ of these incidents expected to be severe. SAR resource planning can also be reviewed, in the light of better anticipation of such severe incident occurrences as a function of the weather forecasts. Finally, the insights gained through this analysis can serve to inform planning future studies. As in many risk analyses, significant predictors are often sought and found, but this does not imply that they are direct causative factors in the occurrence of an adverse event. For example, knowing that the presence of ice is significantly related to the level of severity of maritime incidents does not explain how or why they are related, but does suggest that future research can focus on a more detailed model of fishing in icy conditions, and on which aspects aggravate the outcome of an accident. Appendix. Calculating weather variables for each incident occurrence In order to associate each SISAR fishing vessel incident with the gridded weather datasets from AES40 and NOAA, spatial and temporal interpolation procedures are essential steps in preparation for the statistical analysis. The aim is to calculate and store the weather variables corresponding to the particular time and location of each incident in a single database record, ready to be imported into SPSS (Norusis, 2002). Since the weather information from the AES40 and NOAA datasets are recorded at regular spatial and temporal intervals, the order of interpolation makes no difference to the final result if linear interpolation is used.
A.1 Overall procedure for data processing The following lists the steps for extracting information from AES40 and NOAA dataset prior to the actual interpolation procedures: 1.
Check the neighborhood of the incident location: read the latitude and longitude of the location, then locate the nearest four grid points (ie which unit grid it falls into). Connect each grid point with the incident to see if the connection intersects with landmass (ie confirm line-of-sight (LOS) between the incident location and the neighboring grid points).
2.
For each incident (identified by Event #) and each weather dataset, store the indices of grid points in the following format:
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Weather grid cell coordinates Event #
Lower left
Lower right Upper left
Upper right
Event1 …
Index1 …
Index2 …
Index4 …
Index3 …
3.
Read the time of the incident: identify in which time interval it occurred (eg six-hour spans for AES40), and extract the weather point data at both the beginning and the end of this period, using the relevant unit grid corner indices from the preceding step.
4.
Spatial interpolation procedure: find the most informative combination of values from the gridded weather point data by linear interpolation or closeness approximation. For details, see section A2 below.
5.
Temporal interpolation procedure: the preceding spatial interpolation is conducted at both instants at the beginning and the end of the time window bracketing the incident, then a linear interpolation in time yields the value of the weather factor at the time of the incident.
6.
Store the results: the interpolated result for each weather factor is stored in a field of the record for the associated incident, such that each incident record ultimately possesses a complete set of weather conditions.
A.2 Spatial interpolation procedures The interpolations necessary for estimating weather conditions for the incident points may be broken down into categories according to the number of AES40 and NOAA weather data points local to the incident point. Because the AES40 and NOAA data are gridded, the assumption will be made that each incident falls within a grid unit. This means that for each incident point, there will be between one and four weather data grid points from which an interpolation will be calculated, as shown in Figure A1. The calculations for each case follow. X and Y denote the longitude and latitude respectively, and Z represents the weather variable being processed. In all cases, M1 = X2 – X1 is the width of the grid cell (∆ longitude) and M2 = Y2 – Y1 is the height of the grid cell (∆ latitude). Figure A1. Various scenarios for matching incident positions with weather grid points in the presence of land
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0B0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 D 00000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00 00 00 00 00 00 00 00A00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 C 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000
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Procedure 1: when only 1 grid point is visible (point A in Figure A1) Use the Z value for the single grid point found. Procedure 2: when only 2 grid points are visible (point B in Figure A1) Case 1:
Both grid points are on the same latitude. Input weather grid points: Z11 (X1, Y1), Z21 (X2, Y1) Incident point: Z00 (X0, Y0) Z00 =
Case 2:
X0 – X1 (Z21 – Z11) + Z11 M1
Both grid points are located on the same longitude. Input grid points: Z11 (X1, Y1), Z12 (X1, Y2) Incident point: Z00 (X0, Y0) Z00 =
Case 3:
Y0 – Y1 (Z12 – Z11) + Z11 M2
The two grid points to be used are along the diagonal of the grid. Input grid points: Z12 (X1, Y2), Z21 (X2, Y1) Incident point: Z00 (X0, Y0) A line from the incident location Z00, perpendicular to the diagonal from Z12 to Z21 meets at point Z’. The interpolated weather variable at Z’ will be assigned to the incident: Z00: Z’ (X’, Y’). Line between Z12 and Z21: M2 X’ – M1Y’ – M2 X1 + M1Y1 = 0 Normal to above: M1X’ – M2Y’ – M1X0 + M2Y0 = 0 Solve the above equations for X’ and Y’ Z’ =
√(X’ – X2)2 + (Y’ – Y1)2 (Z12 – Z21) + Z21 √ M12 + M22
Procedure 3: when only three grid points are visible (point C in Figure A1) Case 1:
Incident point within three grid points Input grid points: Z12 (X1, Y2), Z21 (X2, Y1), Z22 (X2, Y2) Incident point: Z00 (X0, Y0) Given three points in a plane, where two of them have the same X value, and two have the same Y value (as in this case), the following standard algebraic expression yields the unknown dependent variable Z00, given the dependent variable values at the three vertices (Z12, Z21, Z22):
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Risk Management: An International Journal 2005, 7 (3), 21–40
X0 – X1 Y0 – Y2 Z00 – Z12 X2 – X1 Y2 – Y2 Z22 – Z12 = 0 X2 – X1 Y1 – Y2 Z21 – Z12 Case 2:
Incident point outside three grid points: use the two visible grid points along the diagonal (following Procedure 2, Case 3) and ignore the third grid point.
Procedure 4: when all 4 grid points are visible (point D in Figure A1) Input grid points: Z11 (X1, Y1), Z22 (X2, Y2), Z12 (X1, Y2), Z21 (X2, Y1) Incident point: Z00 (X0, Y0) Solve the following equation: Z00 =
Y0 – Y1 M2
[
]
X0 – X1 X – X1 (Z22 – Z12) + Z12 – 0 (Z21 – Z11) – Z11 M1 M1
+
X 0 – X1 (Z21 – Z11) – Z11 M1
Notes 1
Yue Wu is a PhD candidate and Ronald Pelot is an Associate Professor in the Department of Industrial Engineering, and Casey Hilliard is a Computer Programmer/Analyst in the Maritime Activity and Risk Investigation Network (MARIN) Laboratory, at Dalhousie University, Halifax, Nova Scotia; email:
[email protected]. This project was supported by the Canadian Coast Guard, the GEOIDE National Centre of Excellence, and the Natural Sciences and Engineering Research Council. William Perrie from the Bedford Institute of Oceanography offered invaluable suggestions, while William Richards and Val Swail of Environment Canada provided access to essential data. This research relied on excellent technical assistance by members of the MARIN research group in the Department of Industrial Engineering, Dalhousie University. The authors also very much appreciate having had access to the free extensive databases available online through NOAA, including the Optimum Interpolation (OI) SST V2 data and the NCEP Reanalysis data. Their location and URL are respectively: NOAA-CIRES Climate Diagnostics Center, Boulder, CO, USA, and http://www.cdc.noaa.gov/.
2
Waves can be categorized into two types, wind waves and swell waves. Three factors influence the generation of wind waves: wind speed, duration of wind, and fetch (sea area across which the wind blows). As wind waves move beyond the fetch, they become swell waves (also known as ‘swell’). The transformation of wind waves to swell waves also occurs when the wind over the fetch dies off.
3
Significant wave height: the average height (trough to crest distance) of the one-third highest waves. An experienced observer will most frequently report heights equivalent to the average of the highest one-third of all waves observed (see at http://www.crh.noaa.gov/dtx/?page=glossary/s).
4
Northwest Atlantic Fisheries Organization.
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