Maritime shipping constitutes a major source of low-frequency noise in the ocean1,2,3, particularly in the Northern Hemisphere where the majority of ship traffic occurs. At frequencies below 300 Hz, ambient noise levels are elevated by 15–20 dB when exposed to distant shipping4,5,6. Underwater ship noise is an incidental by-product from standard ship operations, mainly from propeller cavitation7. Concerns have been raised over the effects of these increased noise levels on marine life8,9,10,11. Yet, predicting noise levels from ships in a given region and the specific conditions that may increase these levels remains largely unexplored.

The Santa Barbara Channel (SBC), off the coast of southern California (Fig. 1), is a region of intense commercial vessel traffic, concentrated in designated shipping lanes with an average of eighteen ships transiting per day12. Two major ports, Port Hueneme and Port of Los Angeles-Long Beach (POLA), serve ships traveling through the SBC. POLA is the second busiest port in North America and until recently, an estimated 75% of vessel traffic departing from and 65% of traffic arriving at POLA and Port Hueneme traveled through the SBC12.

Figure 1
figure 1

Map of SBC, a region off the coast of southern California (inset).

The location of the HARP (34°16.617′N and 120°01.492′W), AIS receiving station (34°24.5′N and 119°52.7′W), north and southbound shipping lanes (dashed lines) and 100 m bottom contours are shown. The map was created using Matlab- Mapping Toolbox.

Container ships, the focus of this study, are a specific class of large commercial vessels designed to hold containerized cargo (Fig. 2) and represent a highly efficient transport system. These ships are big and fast with comparatively short port time and transport almost 90% of general cargo13. Regionally, container ships represent the majority of the commercial vessels12; globally, they represent 22% of the commercial fleet13. Container ships were introduced in the 1950s and since 1990 container trade has seen a five-fold increase; the fastest growth of any ship-type. In this study, we collected seafloor acoustic measurements of transiting container ships in the SBC to determine what variables (design, operational and oceanographic) relate to the measured levels of underwater noise.

Figure 2
figure 2

Photograph of container ship transiting the SBC (credit J. Calambokidis, Cascadia Research).

Ship design characteristics (e.g. length, gross tonnage), operational condition (e.g. speed) and the oceanographic setting (e.g. month, wave height) collected during each individual ship passage were used as covariates to develop a statistical model to relate the level of underwater noise from ships to these variables. Statistical models were built for broad-band source level estimates (20–1000 Hz) and five low-frequency octave bands using nineteen covariates to determine if measured predictors explain the noise levels, the relationships are significant and ascertain the contributions of different variables. Sound levels from multiple transits of the same ships were also evaluated. The results of this study provide details on ship characteristics and sea conditions that result in higher levels of underwater noise for a relatively new ship-type with continuing growth in global activity13.


Source levels (SL) for 593 container ship transits were estimated from long-term acoustic recording received levels (RL) and a simple transmission loss model using Automatic Identification System (AIS) data for source-receiver range. Forty-five percent of the measured ships made two or more transits and 5% had four or more transits (Fig. 3). Using a suite of operational and oceanographic covariates (Table 1) to predict the SL of these 29 ships, individual ship identification was not selected as a covariate and therefore, did not improve explained deviance in the Generalized Additive Models (GAM) results for any of the modeled frequency bands. There was a slight increasing trend of larger ships having higher broad-band SL; however SL for an individual ship, in some cases, varied by 5–10 dB (Fig. 3). Based on these results, each ship transit was considered an independent event and ship identification was not included as a covariate in the proceeding models.

Table 1 Descriptions of predictor variables used in statistical models
Figure 3
figure 3

Variability individual container ship estimated SL from ships that transited on four or more different occasions.

Boxes bound the 25th and 75th percentiles with the horizontal line at the median. Ends of the vertical whiskers are the highest and lowest values of the data set that are within 1.5 times the inter-quartile range of the box edges. The plus signs represent data outside the range of the whiskers.

All statistical models significantly improved in explained deviance with the addition of operational and oceanographic covariates. Specifically, the explained deviance using the best-fit model with only design predictors was never greater than 25%. When operating and oceanographic covariates were included, explained variability in SL increased to greater than 39%. Deviance explained was highest for the broad-band best-fit model (56%) and in general fit decreased with increasing frequency band (Table 2).

Table 2 Summary of GAM results for each frequency band. * indicates values for evaluating best-fit model for a given frequency band; ** indicates values used to compare between different best-fit models

In all frequency band models, the operational variable, ship speed (SPD), was included as a covariate and explained the most variability in SL (Table 2; Fig. 4). The additional design, operational and oceanographic covariates and relative importance in the models varied depending on frequency band. The number of covariates included in the best-fit models ranged from 4 to 8; the lower frequency band models included more covariates and in general had higher explained deviance in SL.

Figure 4
figure 4

Generalized additive model functions for ship SL.

For each frequency band model (A-G), functions shown are for the four variables with the most predictive power (Table 3). The rows are ordered according to predictive power (i.e., the first row are the predictors that had the highest predictive power in the step-wise model selection procedure). Functions are scaled relative to the model mean (note different y-axis scales). MTH and TONE were modeled as categorical variables; the width of each bar represents the sample size and dashed lines are two standard error bands.

A measure of ship size (length over all (LOA) or gross tonnage (GT)) was selected as a covariate in predicting SL in all frequency bands (Table 2). Ship length, LOA, was the important design covariate for lower frequency bands, while, GT was the important design covariate for higher frequency bands. For the 124 and 250 Hz models, when ships were shorter than expected based on GT, SL predictions were higher. For the 63 Hz band, when ships had greater horsepower (HP) than expected based on GT, higher SL was predicted. Inclusion of oceanographic covariates varied depending on frequency band model (Table 2). Month (MTH) of the measurement was included as a covariate in all frequency band models; the best-fit models predicted higher SL in the spring. For the lower frequency models (16 and 31.5 Hz) and the broad-band model, wave height and current direction were included as predictors of SL. As wave height increased and when the sea surface current was opposite the direction the ship was traveling, higher SL was predicted. For the higher frequency best-fit models, covariates for ocean surface conditions were not included as covariates.

In some of the frequency band models, range to the seafloor recorder (RAN) and distance to another ship (OTH) were selected as covariates in the best-fit models (Table 2). For example, in the 124 Hz model, ships at closer ranges to the HARP had higher predicted SL. For octave-bands centered at 250 and 500 Hz and the broad-band model, the presence of tones resulted in higher predicted source levels. Narrowband tones were present in 10% of the measured ships (Fig. 5).

Figure 5
figure 5

Spectrogram of received sound spectrum levels during a 1-hour passage of a container ship.

The spectrogram is centered on the CPA of the ship to the HARP, a distance of 3 km. The intense tones present at approximately 350 and 580 Hz are representative of the tones present in 10% of the container ships in this study.


The results of this study reveal how low-frequency noise from commercial maritime vessels relates to a suite of covariates describing the vessel passages. The statistical approach of this study provided a framework to evaluate possible covariates for predicting underwater noise. Covariates differed depending on the frequency band analyzed; however, all models included speed and a measure of ship size, corroborating earlier studies that predicted higher noise levels from faster and larger ships7,14,15. Our results expand on these previous findings by measuring noise from a modern ship-type, the container ship, measuring over a broader frequency range and including additional covariates that describe the oceanographic setting. Although we found substantial variation, even on a ship by ship comparison, considerations of these predictors are important when quantifying the level of ship noise in a particular region. The opportunistic approach of this study can be used to evaluate specific changes in design and measure other ship-types.

The rapid increase in world shipping, along with the increase in ship speed and size, has been correlated with increases in low-frequency ambient noise in the Northeast Pacific5. This study supports this relationship: models in all frequency bands predicted higher SL with increased ship speed and size. Furthermore, ship speed explained most of the variability in container ship SL in all frequency bands and a metric of ship size was included in all models. Ross (1976) reported a similar positive relationship between overall source spectral level above 100 Hz and speed and size of the vessel for ships < 30 kGT, smaller than the ships analyzed in this study. More recent studies relating ship noise to speed did not find evidence for a positive relationship between speed and SL15,16. The lack of a relationship may be an artifact of combining multiple ship-types into a single regression analysis6. Specific ship-types have unique designs (e.g. hull shape, machinery) directly influencing the spectral characteristics of underwater radiated noise6. This study controlled for ship specific differences by performing statistical analyses on only one ship-type, the container ship, to understand predictors of container ship noise levels.

Although a measure of ship size was included as a covariate in predicting SL in all frequency bands, the size variable differed. Ship length was the important design covariate for lower frequency bands, while, GT was the important design covariate for higher frequency bands. Our results also indicated that for ships shorter than expected based on GT had higher predicted source level; these ships are likely post-panamax ships, a design change that allowed for increases in breadth but no change in length. The parameters used in our models were general descriptions of ship design, inclusion of more specific descriptors of propeller and hull design (e.g. block coefficient, resistance, propeller shape) although not part of AIS data stream would likely improve model results and allow for more specific design recommendations.

In addition to ship speed and size, oceanographic variables describing the ocean surface conditions during each ship's transit were included as covariates in the statistical models. Of the seven possible oceanographic variables, month (MTH) of the ship passage was included as a covariate in all models. This predictor was intended to capture differences in radiated noise related to water column properties, specifically sound speed profiles (SSP) which are influenced by seasonal water temperatures that change the propagation characteristics. Given the opportunistic approach of this study, obtaining simultaneous SSP, although ideal for determining propagation loss, was not possible. All statistical models tended to show an increase in predicted radiated noise during the spring months (April, May and June). Spring water column properties in this region provide a possible explanation for this result. During the spring, strong upwelling events occur in this region, introducing cold water to the surface resulting in a more uniform water column17. During the late summer and fall, warmer surface waters trap sound waves when the sound source is within the warm surface layer, resulting in less radiated noise18. Further supporting this explanation is the greater importance of MTH as a covariate in the higher frequency models; as the trapping of sound in the surface layer has a greater effect in the higher frequencies18. Unfortunately, not all months are represented in this study, somewhat limiting the seasonal comparisons. Furthermore, ephemeral coastal oceanographic features such as internal waves could also influence sound propagation in surface waters on shorter time scales19.

Surface current direction was another important predictor of ship noise in the lower frequency models. When the surface current was opposite to a ships' direction of travel, predicted noise levels were higher. This was expected given that for a ship to achieve its optimal operational speed an increase in engine power is needed, potentially increasing radiated noise. In the lower frequency bands, the wave height, dominant wave period and direction of the dominant wave period also influenced predicted noise levels. Increased wave height and decreased wave period create rougher seas, causing ships to roll and pitch, likely resulting in increased cavitation and the predicted radiated noise levels. Weather conditions are known to influence the ambient noise levels at frequencies measured in this study, although at much lower levels than from ships1,3; and in the model selection process, wind speed and direction were not included as covariates in any of the models of radiated ship noise.

For some frequency bands (16, 63, 124 and 250 Hz), an increase in SL level was predicted for ships transiting closer to the HARP. Specific ship behaviors might explain why levels were higher when ships were closer to the HARP. A spatial analysis of ship speed in the region showed that faster ships travel on the outside of the lanes (i.e., closer to the HARP)20. Based on this observation, this variable likely relates to ship speed; however, it might also relate to how sound propagates and interacts with the seafloor at different distances to the receiver. We limited our analysis to individual ships transiting the SBC without other ships (>1hour between passages), but included time between the passing ships as a possible covariate in the models. Only lower frequency bands (31.5 and 63 Hz octave-bands) included this duration as a covariate and inclusion might relate to the propagation of low frequency sound from distant ships.

Multiple recordings of individual ships on different transits provided a comparison of SL from the same ship (Fig. 3). The 5–10 dB variability suggested that either operational conditions and/or the oceanographic settings had a significant influence on the radiated noise. This result, although important for understanding conditions that might lead to higher noise levels from ships, presents a challenge for targeting individual ships to reduce overall noise from the noisiest ships. One important covariate, the presence of spectral tones, might result in significant reductions in noise. Ships with tones had higher predicted noise levels in both the broad-band and high frequency octave bands (250 and 500 Hz). The cause of these tones is unknown, but may relate to propeller damage which may increase radiated noise and potentially decrease efficiency of the propulsion system7. Identifying these ships and eliminating the cause of the tones would result in a significant reduction in noise.

The age of a ship was a covariate in the 31.5 Hz octave band model: older ships produced more noise in this band. Most of the ships analyzed in this study were built between 2000 and 2005 (47%), 19% were built after 2005 and the remaining ships were built prior to 2000; the oldest container ship included was built in 1971. Changes to the propulsion system in newer ship builds might explain the decreased amount of low-frequency radiated noise, even though newer ships travel at faster speed and are, on average, larger. Container ship design has seen continued improvements both in the reduction of ship resistance through the water and increased propulsion and machinery efficiency21. Improvements include dampening of engine vibrations, changes in hull design and a reduction in the number of engine cylinders21. Propeller damage or fouling on older ships might also explain the higher levels of radiated noise predicted for older ships.

Given that ship speed was the most important covariate in predicting SL, ship speed reduction should result in lower radiated sound levels. However, ship SL is an instantaneous estimate of radiated noise and strategies to reduce noise from shipping must consider the cumulative noise exposure, especially when slowing ships in a particular region. One method to calculate cumulative exposure is Sound Exposure Level (SEL) or the integration of the noise over a specific duration:

There is a trade-off between traveling slower (decrease in SL) and spending more time in an area (increase time) for the SEL calculation. For example, a 294 m container ship was recorded traveling at 10 m/s and 5 m/s (Fig. 6A). The SL for this ship was 5 dB less for the slower passage, but the time spent in the area increased two-fold resulting in a 3 dB increase in noise; therefore, the net reduction in SEL was only 2 dB for the slower ship. To calculate the net reduction in SEL for any speed the following equation was derived using the relationship between speed and SL (Fig. 6A) and the ship's operational speed (service speed):

where, i is a specific speed iteration, spdo is the known operational speed of the ships and SLo is the estimated ship source level at operational speed. In this example, the spdowas 12 m/s and SL was 183.2 dB re: 1 μPa @ 1 m. The maximum net reduction in SEL occurred when the ship traveled at 4 m/s (7.7 knots) or 35% of operational speed (Fig. 6B). Noise reduction efforts could focus on ships with tones, older ships and reducing vessel speeds. However, vessel speed reduction should consider cumulative noise, specifically the trade-off between SL reduction and time spend in a region and the feasibility of a ship traveling at speeds slower than their operational speed.

Figure 6
figure 6

(A) Relationship between broad-band SL and speed for a 294 m container ship that transited the region on four separate days (10/17/2008, 11/21/2008, 04/10/2009 and 05/14 2009). Equation for the linear relationship and goodness of fit value (R2) are shown. (B) The net reduction in SEL for the container ship in (A) for different speeds. The derived curve is based on the relationship between SL and speed (A) and known operation speed of 12 m/s (23.3 knots). The gray part of the curve indicates that these speeds are likely not possible for a container ship.

Variability in SL that remained unexplained by our statistical models may be related to the depth of the propeller, the main sound source. A shallower source depth will decrease the effect of the dipole source; thereby decreasing the amount of radiated sound from the ship. In other words, the closer the source is to the sea surface the lesser the strength of the dipole7. Source depth will vary depending on the particular design of a ship and the load conditions during a specific transit. Unfortunately, AIS does not provide information on the load conditions of the ship; therefore, it was not possible to include this covariate in the models. The models included the ship's specified optimal draft. This variable, however, was not selected as a covariate in any of the models, suggesting that ship draft was not a good proxy for the actual depth of the source. Perhaps other metrics, such as the number of loaded containers, might be more accurate prediction of propeller depth. In general, container ships leaving POLA (i.e., northbound) are not as loaded as when they enter22. Measurements reported in this study are from ships departing POLA (northbound), potentially over representing ships that are not fully loaded and underestimating the radiated noise from fully loaded ships, likely with a deeper source.


Acoustic recordings

High-frequency acoustic recording packages (HARPs) were deployed in the SBC, approximately 3 km from the northbound shipping lane (Fig. 1). HARPs are bottom-mounted instruments containing a hydrophone, data logger, battery power supply, ballast weights, acoustic release system and flotation23. The hydrophone is tethered to the instrument and buoyed approximately 10 m above the seafloor. All acoustic data were converted to absolute sound spectrum levels using Fast-Fourier Transforms (2000 Hz sampling rate, 2000 samples, 0% overlap, Hanning window) and based on hydrophone calibrations performed at Scripps Institution of Oceanography Whale Acoustics Laboratory and at the U.S. Navy's Transducer Evaluation Center facility in San Diego, California. The amount of time used in the sound spectrum level calculation was equal to the time it took the ship to travel its own length, as suggested by Bahtiarian (2009) and detailed in the Acoustical Society of America (ASA) standard (ANSI/ASA S12.64-2009/Part 1).

Opportunistic acoustic recordings of passing ships were collected October-November 2008 and March-October 2009, excluding August. Long-term acoustic recordings were combined with ship passage information from AIS24 to estimate ship source level using the same methods described in McKenna et al. (2012)6. Received sound levels were measured at the closest point of approach (CPA) of each ship transiting the northbound shipping lane to the HARP (Fig. 1). CPA distances ranged from 1.6 to 4.6 km. Total broad-band noise level (20-1000 Hz) and noise levels in standard octave bands, centered at 16, 31.5, 63, 124 and 500 Hz were calculated by summing the mean squared pressure values in each 1-Hz frequency bin and converted back to sound pressure levels expressed as decibels referenced to a unit sound pressure density in sea water (1 μPa). To estimate SL for each transiting ship, approximated sound transmission loss (TL) at the CPA distance (typically ~3 km) was added to the measured ship RL at CPA. A spherical spreading transmission loss model was used (i.e., TL = 20*log10 (Range[m]); see McKenna et al., 20126 for justification). By using a long duration measurement and broad frequency band, interference patterns resulting from the dipole source near the surface and bottom reflection were averaged out, providing an estimate of SL. All acoustic data matching the CPA times were evaluated for the presence of a single ship and eliminated if another ship passed within 1-hour or if vocalizing marine mammals were present.

Ship operational variables

The AIS data provided information on the operating conditions of each ship transit. Four variables were collected and used as covariates in the statistical models: speed SPD, range to the receiver RAN, time to the next ship passage OTH and the proportion of the service speed the ship was traveling at PSPD (Table 1). The speeds reported by AIS, are speeds over ground, not actual speed of the ship relative to surface currents. The AIS speeds were adjusted to actual speed based on the surface current speed and direction. Archived surface current data were obtained from the University of California Santa Barbara, surface current mapping project25. One additional operational variable gathered from the acoustic data was the presence of narrow-band frequency tones TONE. This was a simple binomial variable, present or absent.

Ship design variables

Only ships classified as container ships greater than 100 m in length were included in this analysis. For these ships, seven additional ship design variables were gathered from the World Shipping Encyclopedia26 by matching the unique ship identification from AIS with this database. The seven variables collected were ship identification ID, gross tonnage GT, service speed SSPD, length overall LOA, draft DFT, horse power HP and year built YB (Table 1). Many of the ship design variables are highly correlated (Fig. 7) and to avoid ambiguous model results, the residuals from linear fits between variables were used as covariates in the models.

Figure 7
figure 7

Comparison of container ship design characteristics.

(A) Distributions of design variables (B) Correlations of different design characteristics, including gross tonnage (kGT), ship length, horse power (kHP) and drafts are shown for 593 container ships.

Oceanographic variables

Sea conditions during each ship passage were obtained from archived data at the National Oceanic and Atmospheric Administration, station 46053 (32°14.9′N 119°50.5′W)27. The six oceanographic conditions measured during the same hour as the passage of each ship included: ocean surface current direction CDIR, wind direction WDIR, wind speed WSPD, significant wave height WVHT, dominant wave period DPD and dominate period wave direction MWD (Table 1). The month of the acoustic measurement MTH was also included as a general representation of water column properties.

Statistical approach

For each frequency band, generalized additive models (GAM)28 were used to relate ship source level to the ship characteristics described above. GAMs are well suited for modeling distribution data since the constraint of linearity is lifted and a more flexible approach to the relationship between covariates can be taken. We fit GAMs using the step.gam software package (R Project for Statistical Computing 2.12.2). The shapes of the distributions of source levels in each frequency band were used to choose identity link functions (Fig. 8). Each predictor variable was evaluated with and without smoothing splines where the number of knots for smoothed functions was constrained to either 2 or 329. The best-fit model was selected using Akiake's Information Criterion (AIC):

where, (L(Θ|y) is the likelihood of the parameters given the data y and P is the number of parameters. The best-fit model minimizes AIC by maximizing the log-likelihood, with penalties for the number of parameters included30. For purposes of evaluating covariates in the models, we used a step-wise approach and present the delta AIC value for each covariate relative to the null model AIC value (Table 3). AIC is a powerful model selection technique, but only compares models during the selection process and does not give any indications of the significance of a particular model fit to the data or allow for comparisons between different models (in this case the frequency band models). Therefore, the best-fit model for each frequency band was also verified using an analysis of explained deviance, comparing the residual deviance of several models using a chi-square method. The best-fit model was one that minimized both AIC and residual deviance. Each model result is summarized by AIC values, percent explained deviance and expressed as an equation:

where, SLFq band is the response variable the model is predicting, predictor 1 represents a linear covariate, s() represents a smoothing function for a given predictor, x represents the number of knots (i.e., smoothing constraints) and y represents the number of knots in a subsequent smoothing function.

Table 3 Comparison of delta AIC values from the step-wise GAM procedure for the best-fit model in each frequency band (blank boxes indicate that the covariate was not included in the best-fit model). AIC values are compared to the null model and greatest delta AIC values indicate the most improvement from the null model
Figure 8
figure 8

Distribution of estimated container ship SL by frequency band.

The number of bins equals the square root of the number of ship transits, with a fitted normal distribution. The skewness (measure of asymmetry of the data around the mean, negative indicated left skew) and kurtosis (measure of outliers, where 3 is considered normal) are shown in the upper left corners.

All model trials were run separately for each frequency band (e.g. broad-band and four octave bands). Using the GAM approach, we first modeled a subset of ships, specifically individual ships that had four or more transits, to determine if specific ship (as a categorical variable and random effect in a generalized linear model) improved model fit. If not, each ship transit was considered an independent event. Only operational and oceanographic covariates were included in these trials given that the design variables did not change for individual ships. A second set of GAMs were used to determine what design variable described the most variability in estimated SL; using the step-wise approach delta AIC values were used to determine the covariate that explained the most variability. The resulting design variable was then used to transform the other ship design variables into residuals of the main design variable (rGT, rSSPD, rLOA, rDFT, rHP, rYB). After the correlated designed variables were transformed, a third set of GAMs were run with all predictor variables (Table 1) to relate ship SLs to the covariates.