Some statistical properties of theambient noise in the Baltic Sea andits relation to passive sonar

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Some statistical properties of the ambient noise in the Baltic Sea and its relation to passive sonar

Johan Fridstr¨ om A thesis presented for the degree of Master of Science

Royal Institute of Technology

Sweden

2015

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This thesis is part of an EU project financed by LIFE+

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Abstract

The Baltic Sea Information on the Acoustic Soundscape (BIAS) is an European Union financed research project coordinated by FOI. The goal is to determine the soundscape of the Baltic Sea. This study is a part of BIAS and was focused on generating Wenz curves for the Bothnian Sea, which is a part of the Baltic Sea. Wenz curves describe the spectral noise level at different sea states. The investigation of the soundscape was done for both summer and winter conditions when the hydrographical situations differ.

Further investigations of the noise dependencies of the natural and anthropogenic sound sources were performed. Wind and ships were dominating in a broad frequency band.

The influence of ship noise on the ambient noise is dependent of frequency and distance.

Ships within 5 km distance dominates the recorded noise levels and are not part of the ambient noise. At distances longer than 5 km a single ship becomes non-distinguishable and part of the range independent noise floor.

Passive sonar ranges were calculated for two different sources. The range was shown to be clearly dependent on the sea state. With an increase of wind speed from sea state 0.5 to 3 the range increased with about 100%.

The results of this study will be used in BIAS and in related research projects. It may be used for marine biologics but also for development of sonar and underwater systems.

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Sammanfattning

Statistisk beskrivning av Östersjöns ljudlandskap – och dess p˚averkan p˚a räck- vidderna för passiva hydrofonsystem

BIAS är ett EU finaniserat projekt som koordinaeras av FOI och syftar till att beskriva ljudlandskapet i Östersjön. Denna uppsats är en del av BIAS med fokus p˚a att gener- era Wenzkurvor för Bottenhavet, vilket är en del av Östersjön. Wenzkurvor beskriver spektrala ljudegenskaper för olika väderlekar. Kurvorna är framtagna för b˚ade sommar- och vinterförh˚allanden. De dominerande ljudkällornas inverkan p˚a ljudbilden studerades.

Resultaten visar att vind och fartyg ¨ar de dominerande faktorerna.

Fartygens bidrag till bakgrundsljudet visade sig bero p˚a b˚ade frekvens och avst˚andet till mätpunkten. Fartyg innanför en radie p˚a 5 km dominerade de uppmätta ljudniv˚aerna.

Utanför denna radie kunde inte enskilda fartyg med säkerhet idenfieras i ljuddata. Far- tygens ljud försvann in i trafikmullret som ständigt finns i Bottenhavet.

Utifr˚an de olika hydrografiska karaktärerna beräknades räckvidden för tv˚a ljudkällor för en passiv sonar. Räckvidden var klart beroende av väderförh˚allandet. Med en ökad vind- hastighet fr˚an sjötills˚and 0.5 till 3 ökade maximala detektionsavst˚andet för sonaren med ungefär 100%.

Resultaten fr˚an den här studien kommer användas inom BIAS. De kan ocks˚a komma att användas av marinbiologer inom forskning p˚a djurlivet i Östersjön men kan även användas för utveckling av sonarsystem och andra undervattenssystem.

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Preface

The work of this thesis was carried out at Totalf¨orsvarets Forskningsinstitut in Kista, Stockholm. The task was a part of BIAS but also supported by FOI Underwater department. Professor Peter Sigray led the work with good help from PhD Leif K.G. Persson.

First I want to thank the entire Underwater department at FOI for all interesting discussions, nice coffee breaks and a very pleasant stay. Extra thank to PhD J¨orgen Pihl who helped me with sonar calculations. Also PhD Mats Nordin has earned extra gratitude for without any doubt recommended me for this job and for all good and guiding discussions during my entire study time at KTH.

I want to send special thanks to Professor Jakob Kuttenkeuler at KTH for the encour- agement and enthusiastic support during the work and MsD Sebastian Thun´e for all the profitable discussions.

I am most grateful for the help I got from Professor Peter Sigray and PhD Leif K.G.

Persson who have helped me daily by answering question, provided me with good literature, discussed solutions and results but most of all always prioritized my time before their own making the time at FOI in Kista a very stimulating and funny period of my life.

Of course I also want to thank my parents, Inger and H˚akan, who always and doubtless supported me and made it possible to complete the Master Degree in Science. Also my girlfriend Sandra owns my gratitude for all the positive support.

Stockholm June 2015

Johan Fridstr¨om

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1 Glossary and abbreviation

Ambient noise

Ambient noise is the noise background that is observed with a non-directional hydrophone excluding self-noise or identifiable localized source of [22]. In total absence of anthropogenic sounds the term natural ambient noise is used [23].

Anthropogenic

Means that (in this case) noise has its origin in the influence of human activity.

Bandwidth

Bandwidth is the range between frequency upper and lower frequency content of a signal.

It is measured in Hz [23].

Noise

Noise is sound of random nature, which means that the spectrum contains no clear defined frequency components. Noise can also refer to unwanted signals. What is regarded as noise depends on the receiver and the context. [23].

Power Spectral Density:

A power representation of a signal with the amplitude energy/frequency. Often used for stationary random signals [20].

Octave

An octave is a doubling of frequency. Octave band is a frequency band with the mid frequency determining the name [25].

Refraction

The bending of sound due to environmental changes in the medium [5].

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Root mean square

The squared mean value of the signal. It is often used to describe a quantity of a signal with both positive and negative values [1].

Sea States

Sea states is defining different weather conditions at sea. It is ranged from zero to eight based on wind speed and significant wave height [5].

Sound

Acoustic energy radiated through a medium from an object that vibrates. It can be either desired signals or noise [23].

Sound pressure levels

The acoustic pressure relative the reference pressure 1 μPa squared measured in a logarithmic scale. Often used to express sound with a quantity [20].

Stationary

A signal whose statistical properties does not change with time is stationary [20].

Transient signal

A signal with a limited duration and a clear start and stop [25].

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AIS Automatic Identification System

BIAS Baltic Sea information on the Acoustic Soundscape CDF Cumultative Distribution Function

DFT Discrete Fourier Transform DSP Digital Signal Processing

FMV F¨orsvarets Materiellverk (Swedish Defence Material Administration) FOI Totalf¨orsvarets Forskningsinstitut (Swedish Defence Research Agency) HELCOM Helsinki Commission, Baltic Marine Environment Protection Commission HIRLAM High Resolution Limited Area Model

LOFAR Low Frequency Analysis Recorder PSD Power Spectral Density

PSU Practical Salinity Unit [g/kg = ppt]

RMS Root Mean Square

SMHI Sveriges Meteorologiska och Hydrologiska Instut (Swedish Meteorological and Hydrological Instute) SOFAR Sound Fixing and Ranging

SONAR Sound Navigation and Ranging

SPL Sound Pressure Level

SS Sea State

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2 Introduction

The Element of Surprise is an effective tactic in warfare which was described in the Liad by Homeros. In the marine environment covert vessels will undoubtedly have a point of advantage. The Swede Torsten Nordenfelt realized this fact and in 1883 he was the first person to build and design a steam engine driven torpedo-carrying submarine [27].

Meanwhile the political arena of Europe got more and more infected by conflicts and in the beginning of the 20^th century became the start of a massive armament.

Submarines were used in naval battles for the first time in history. As a response, new strategies were developed to detect and to combat the submarine threat. It became important to acquire knowledge of the acoustic underwater environment. From a naval point of view it was important not only to address the sources (sound produced by submarines) but also to understand the properties of the ambient noise. The ability to “hide and seek” is strongly linked to these two properties. The Naval activities were however classified and not open to the general public.

The Russians developed early a tool that used radio waves and hydro acoustics to determine the distance to other ships. Their results were published almost simultaneously as the British physicist Joly presented his method for determining distance and direction to underwater sound sources. [7]. The Russian results were not recognized and the literature today is based on results achieved by research performed by researchers in the western countries. The development continued and during the Second World War the listening devices were further developed. This in combination with an increased research in hydro acoustics resulted in a better understanding of the underwater sound environment. Post Second World War a collection of papers written by researchers in the United States about hydro acoustic behaviour were presented. This collection, Physics of Sound in the Sea [2], became the keystone in the following development in the hydro acoustic field.

The civilian society regarded the underwater environment as silent, not at least high- lighted by the documentary movie The Silent World produced by the oceanographers Jaques- Yves Cousteau and Louise Malle. The general public awareness of underwater sound was raised with the observation of the stranding whales, correlated with sonar activities [6]. Presently, the awareness of the sound as a potential “pollution” is growing.

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One of the most fundamental scientific investigation on underwater noise was done by Wenz (1962). He showed that the ambient noise in water depends on many different factors. He summarized in a graph the variety of noise sources and their contribution to the ambient noise. This graph has been in use since then and is commonly known as Wenz curves. His graph is shown in Fig. 2.1 and has been supplemented with hearing ability for some species in the Baltic Sea.

Figure 2.1: Spectral sound levels in deep ocean adapted from the Wenz curves [26][18].

Including anthropogenic and natural sources. The graph also shows the range of hearing thresholds for some animals of the Baltic Sea.

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The graph of Wenz is still valid. It is used by researchers in hydro- acoustics even though the research is based on measurements undertaken in the years before 1962. The “silent world” has however changed during the past fifty years. There are strong indications that the noise levels have increased [9]. An increased density of commercial shipping explains part of this change but also the introduction of new types of propulsion systems. Further, the number of infrastructures at coastal and offshore areas has increased, compared to the levels in the early sixties.

The research underlining the Wenz curves was based on noise in “deep” oceans. The Baltic Sea is a shallow sea and the applicability of the Wenz curves in the Baltic Sea can therefore to some degree be questioned. In his paper it is stated that a rise of the noise intensity of 2-3 dB is expected in shallow waters. It should be underlined that he defined shallow as less than 100 m. Only a minor part of the Baltic Sea is deeper than 100 m, the actual average depth is 54 m. His forecast has been shown to be valid in the deep oceans.

The Baltic Sea is a brackish sea where a strong thermocline develops during summer and it has a complex topography, which differs from the environments that Wenz results were based on. This is one of the motivations for carrying through a study of the Ambient Noise of the Baltic Sea. One of the aims is to present an update of Wenz curves valid for the Baltic Sea. However the generated Wenz curves would only be valid in peace time.

A military conflict in the Northern Europe would probably reduce the shipping in the Baltic Sea which would result in a decrease of ambient noise levels.

As was eluded earlier, anthropogenic generated sound might have a negative impact on the marine life. The focus of this thesis is to better understand the ambient sound and its role in the marine environment. Thus, the same result can be used both in environmental research and for development of underwater systems such as submarines and sonar systems. The work undertaken herein was a part of the Baltic Sea Information on the Acoustic Soundscape project (BIAS). The aim of BIAS was to establish the underwater soundscape in accordance with the Marine Strategy Framework Directive, Descriptor 11, that declares that the member states of the European Union have to establish the baseline of sound levels before 2016 [23]. The Swedish Defence Research Agency (FOI) is coor- dinating the project and a more detailed presentation of BIAS is appended in Appendix A.

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3 Goals and structure of this thesis

This thesis has two goals. The first is to develop tools for characterizing the ambient noise. These were employed on data that were obtained in the Bothnian Sea. The second goal is to quantify the detection range of sound sources, based on the results from the first part.

The structure of this thesis follows the goals. In chapter 4 limitations of the study is presented and is followed by the basic theory of hydro-acoustics which is introduced in chapter 5 and it begins with a general description of acoustics. A presentation of sound sources is given. The Wenz curves are introduced and specific properties of the unique acoustic environment of the Baltic Sea, and the Bothnian Sea in more detail, are discussed. In chapter 6 signal processing theory is presented. The chapter starts with an introduction of stationarity followed by explanations of outliers, correlation and spectral analysis in text and illustrative examples. Chapter 7 contains a presentation of the sonar concept. The passive sonar equation and the use of sonars is described. Chapter 8 consists of a comprehensive description of the methodology. The results are presented and discussed in chapter 9. In the final chapter, chapter 10, conclusions are made and an outlook is given.

All research have been performed for the Bothnian Sea, well away from the coastline and shipping lanes. The following main topics have been investigated:

• Correlation of wind speed, wave height and ambient noise levels.

• Parametrization of the ambient noise.

• Establishment of the Wenz curves.

• Determination of the cumulative range-distribution.

• Establishment of detection ranges as function of frequencies and meteorological conditions for passive sonar.

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4 Limitations

The recordings of the sound data were done with a sampling frequency of 32000 Hz. The Nyquist theorem restricts the analysis to frequencies lower than 16000 Hz. The lower limit of the bandwidth was set by the hardware of the autonomous recorder to 10 Hz.

Limitations in battery and storage capacity only allowed recordings of 23 minutes every hour. The obtained results are not complete and thus associated with statistical errors.

The results presented in this thesis are based on data from Bothnian Sea. The hydrophone was located within 20 km from a shipping line. There were not enough of recordings with no ships within a 20 km radius to statistically determine the natural ambient noise.

At the location of the hydrophone some sea states never occurred. The sediment characteristics are also unknown. The meteorological data used were model based and not obtained from measurements. However, it was provided by SMHI and can for this study be regarded as reliable.

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5 Theory Part I: Underwater acous- tics

Underwater acoustics is a broad discipline that encompasses many different applications.

Here the study will be restricted to underwater phenomena that can be divided into source, propagation and receiver. To achieve the aims oceanography and meteorology theories and methods were required.

5.1 Basic acoustic properties

To generate sound a vibrating source and a medium with mass and elasticity are required.

The vibrating source displaces adjacent particles in the medium. The elastic forces of the medium brings the particle back to its initial position. The initial displacement has however forced neighbouring particles to move. The interaction between source and medium results in a sound wave propagating from the source through the medium with a frequency determined by the vibrations of the source. Thus, sound is associated with pressure fluctuations and particle movements [25].

Sound pressure variations and particle motions are related through the impedance of the medium. Eq. 5.1 shows the relation [5]

p = uZ, (5.1)

where p is the acoustic pressure, u is the particle velocity and Z is the acoustic impedance of the medium. The acoustic impedance is dependent on the properties of the medium.

The equation of state for the sound speed is given by the density, salinity and temperature.

The relation is not “obvious” and the sound speed is calculated by using mathematical scripts. By tradition pressure is commonly expressed in relative form both in air and in water. The decibel scale is used where pressure is related to a reference pressure. The underwater sound pressure level is calculated with Eq. 5.2. In this study sound pressure levels (SPL) are used to express the ambient noise and is calculated as follows

SP L = 20 log₁₀ p

p_ref, (5.2)

where p_ref is 1 μPa for underwater acoustics [5]. Note that a different reference pressure is used in air acoustics.

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In statistics a process such as a time series, is either stationary or non-stationary. The condition for stationary processes is that the probability distributions do not change with time. Thus, it does not matter when the signal is recorded; its statistical properties will not change. For example a linearly increasing signal is not stationary since the mean will change with time. Sound might adhere to these two kinds of properties.

Stationary signals are divided into two sub-groups, deterministic and random signals.

At every moment in time the value of a deterministic signal can be predicted, while for random signals only statistical values such as the average is known. Non-stationary signals are divided into continuous and transient signals. It is difficult to give a definition of transients. It is often regarded as a short pulse where short is related to physical phenomena. In contrast, a continuous signal appears during longer time intervals, relative to physical phenomena. A signal can be regarded as transient or continuous depending on the situation. The classification of the signal lies in the eyes of the beholder. A common definition is that transient signals can be dealt with in full, while a continuous signal is analyzed in sections [20]. In this study the ambient noise of the Baltic Sea is investigated and the sound signal is regarded as random in character.

In the paper of Wenz [26], the underwater acoustic sound sources where divided in three categories. In the Bothnian Sea the following sources composes the ambient noise:

• Water motion;

– wind, – waves, – bubbles, – precipitation.

• Man-made (anthropogenic);

– shipping,

– industrial activities.

• Marine life;

– animals.

5.2 Relevant sources of noise in the Baltic Sea

The ambient noise levels depend on wind speed in the frequencies between 200 – 10 000 Hz. Wenz (1962) found that the noise level maximum is in the interval 400 - 800 Hz. The ambient noise below 200 Hz is independent of wind speed except in shallow areas. The noise level in shallow water for the same sea state as for deep oceans is about 5 dB higher [26]. Urick (1983) [22] showed on the other hand that at calm winds the ambient noise levels in shallow water are often lower than in deep and the opposite relation pertains at high wind speeds. Poikonen (2010) [17] showed that the wind speed had a strong influence on ambient noise in shallow seas, especially at lower frequencies. His research was made within the archipelago, at an isolated place with no ship or industrial noise influences.

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Sea States are often used to describe meteorological conditions. Sea states are scaled from zero to eight and each sea state is defined by wind speed and significant wave height. In this thesis the sea states defined by the Swedish Defence Material Administration (FMV) [5] are employed, cf. Table 5.1.

Table 5.1: Definitions of the sea states according to the Swedish Navy [5].

Sea State Wind Speed [m/s] Significant Wave Height [m]

0 0.0-0.2 -

0.5 0.3-1.5 -

1 1.6-3.3 0.6

2 3.4-5.4 0.8

3 5.5-7.9 1.2

4 8.0-10.7 1.9

5 10.8-13.8 2.3

5+ 13.9-17.1 2.7

6 17.2-20.7 -

6+ 20.8-24.4 -

7 24.5-28.4 -

7+ 28.5-32.6 -

Defining sea states based on wind speed is not entirely correct. Water motions generated by wind may vary. The wind speed alone does not suffice to explain the sea state, also wind direction and duration has to be taken into account [26]. To keep the research methods in this study as similar as possible to Wenz (1962) exclusively wind speed was used to define the sea states.

Sairanen (2014) [21] presented results from measurements made in the Finnish Bay, at the border of the archipelago. She showed that there is dependence between wind direction and ambient noise levels, see Fig 5.1. She noted as well a clear correlation between noise and wind speed. Sairanens results are in line with the results presented by Wenz (1962), Urick (1983) and Poiokonen (2010). Her research was part of BIAS. The data origins from the same type of sensors as were used in this study.

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Figure 5.1: Averaged noise levels as a function of wind speed for Jussar¨o, in the Finnish Bay, in January in 1/3 octave bands. Collected from Sairanen (2014) [21].

The result of Poikonen (2010) [17] showed that the ambient noise was dependent on wind speed. He introduced a wind-speed dependent factor. The result was based on measurements in shallow water in the Baltic Sea. The dependence factor was found to be 2.5 for 100 Hz and decreasing to 2 for 500 Hz and higher. These values were higher than those presented by Wenz (1962).

Even in totally calm weather micro sized bubbles in water add up to bigger and bigger bubbles that ascends to the surface, oscillating and generating noise [26]. One of the main sources of natural ambient sound at low frequencies are bubbles created by breaking waves, which in turn are produced by wind. Water droplets are also created from spray and spin drift. Precipitation, such as hail, sleet or water droplets, generates sound when penetrating the water surface. A rule of thumb states that precipitation over 2.54 mm/h (1 in/h) raises the ambient noise levels. At sea state 1 and below when breaking waves are rare, precipitation contributes to the noise levels. For Sea States above 1, no conclusions have been made due to the complexity of separating wind generated spray and spindrift from precipitation noise [26]. The measurement of Poikonen (2010) [17]

was made at an inshore place with no influence of ships. His result therefore shows the meteorological influence on the ambient noise and a strong decrease in the ambient sound levels below 500 Hz. Further, results were presented on correlation between the ambient noise curve with the noise spectrum of oscillating bubble clouds created by waves. The low sound levels of ambient noise below 500 Hz were attributed to the lack of ship and industrial induced noise.

Ice is known to generate noise in a broad frequency range [26]. Urick (1983) [22] showed that an ice covered sea could work as a band-pass filter. High and low frequencies are

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filtered out. Sairanen (2014) [21] noted a decrease in sound pressure levels due to ice in the Baltic Sea. Unfortunately, during 2014 the Bothnian Sea was never covered with ice and therefore it was not possible to investigate ice in this study.

In acoustics sound sources can be assumed small if the distance to the source is much larger than the extension of the source. This was the case in this study where the ma- jority of ships were at a distance 5 km or longer.

Anthropogenic sound can further be categorized as intentionally or unintentionally. Ship- ping noise is unintentionally sound generation, since the noise from shipping is a by- product of its activity. Seismic surveys, on the other hand, may be regarded as intentionally generated noise since the sound is used to map out the sediment structure.

Shipping noise is a combination of noise generated by cavitation, turbulence and vibrations from on-board machinery. Propulsion systems are the most dominant part. The noise generated from ships are classed as low (1-10 Hz), medium (10-500 Hz) and high (500 Hz - 20 kHz) frequencies [26]. The higher frequency components in shipping noise are not affecting the ambient noise levels with any significance but due to the high attenuation of high frequency sound in water, it is only affecting the close vicinity of the ship.

It is important to distinguish between nearby and distant shipping. Distant shipping noise is the noise from ships at a distance where a single ship cannot be attributed to the sound levels. The opposite prevails for a nearby ship. The sound levels will be dominated by the ship and the source can be identified. Thus, ship noise dominates at frequencies between 20-500 Hz but it has an influence on the ambient noise in the interval 10-1000 Hz [26]. At a well-defined shipping lane this distance will show where the sound levels will be range dependent. Outside this distance the sound will be determined by the distant shipping. The results by Sairanen (2014) [21] showed a clear “knee” where ships didn’t significantly influence the ambient noise, see Fig. 5.2.

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Figure 5.2: Averaged noise levels as a function of distance to ships during January in the Finnish Bay in 1/3 octave bands. Collected from Sairanen (2014) [21].

In Fig. 5.2 the “knee” is clearly visible at 4-5 km distance. At lower distances the sound pressure levels are increasing and at longer distances they are independent on the distance to the ships.

Ships generate sound below 50 Hz that emanates from the propeller and the hull. The sound levels have be shown to be dependent on the depth of the two sources, i.e. the draught of the ship. Due to boundary conditions the sources in the water will create image sources at the water surface, which will add the noise level up, also known as the Lloyd-mirror effect [26].

Industrial generated noises such as pile-driving, hammering and other intermittent activities may be regarded as ambient noise and not, depending on the purpose of the measurements. Offshore wind farm generated noise may however be regarded as ambient noise since it is always present.

Animals are known to produce sound to communicate, orient and to hunt. The sounds have many different characters. The cod is for example known to produce grunts, especially when spawning. Other animals such as whales produce a repertoire of sounds, both short pulses and longer continuous songs. Biological noise varies with time, location and frequency and is an important part of the ambient noise [26].

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5.2.1 Sound propagation, refraction and absorption

Sound propagates outwards from a sound source as a spherical wave. Since the Baltic Sea is shallow the waves will interact with both the surface and the seabed. The propagation will be altered and the spherical symmetry will be lost. Under certain circumstances the spreading will become cylindrical. Measurement of attenuation shows that often the spreading falls between the spherical and cylindrical geometry [5].

Sound waves produce relative motion between water particles. The kinetic energy is transformed to heat due to friction force. This transformation of energy is called absorption and is especially relevant for high frequencies and long propagation distances [5].

Urick (1983) [22] gave three explanations for the absorption. First, magnesium sulfate in the water absorbs the kinetic energy of sound. Second, the shear viscosity and third the volume viscosity contributed to absorption. Urick concluded that absorption increases with increasing salinity and frequency. He also introduced the absorption depth-factor that decreases the absorption with 2 percent with every 300 m of depth. The end product, the absorption coefficient, is approximately 0.02 dB/km at 500 Hz and 1 dB/km at 10 kHz for the Baltic Sea with salinity of 7 PSU, practical salinity unit, and a temperature of 5 ^◦C [5]. Even at distances of 100 km the absorption is less than the errors introduced by the methodology. The absorption in shallow seas is rather dependent of the bottom characteristics. Sea floors such as clay increase the absorption of sound massively [22].

The low salinity, the short propagation distances of the Baltic Sea and the dominating absorption by the sediment makes the Baltic Sea soundscpae environment complex.

The phenomena investigated in this study are related to frequencies between 10 Hz and 10 kHz, shallow depth and low salinity. The absorption in the Baltic Sea is dominated by the properties of the sediment; thus, absorption in water can be neglected.

As presented in chapter 5.1, sound speed increases with increasing salinity, pressure and temperature. The temperature has the largest impact on sound speed. During summer season the surface layer in the Baltic Sea is heated by the influx of the sun, which results in a temperature rise at the surface, the so called thermocline is developed, often located at 15- 20 m depth. At larger depth a halocline (change in salinity) is separating the bottom layer from the other water volume all year around [5]. This results in a high sound speed at the surface and at the bottom layers and lower sound speed in between the two layers. Sound waves that propagate between two layers will refract towards the center of the water column and thus be trapped therein. This phenomenon is named a sound channel and the most known is the Sound Fixing and Ranging (SOFAR) channel, found at a depth about 1000 m, in the deep oceans [22]. Sound might travel long distances in these channels. In a SOFAR channel ship sounds can propagate up to a few 1000 km [26]. Sound channels acts as a low-pass filters but too low frequencies components of sounds are cancelled out [22]. The top boundary tends to keep air borne sounds from entering the channel. Sound channels are well known by both Navies and whales, the former using it for surveillance and the later for communicating long distances. The Baltic Sea is somewhat more complex and has a seasonal component that has to be taken into account. Under certain circumstances sound channels exists, especially during the summer seasons [5].

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5.3 Ambient noise

After the second World War the field of underwater theatre started to be systematically exploited. The Physics of sound in the sea was published the same year as Knudsen et al. (1945) investigated the noise dependency of the sea states and Wenz (1962) updated their results almost 20 years later.

The curves of Wenz are spectral presentations based on average sound pressure levels produced by a number of independent noise sources. Wenz based his research on the results by Knudsen and he described Knudsens result as Knudsen curves. Today, the result are known as Wenz curves and is illustrated in Fig. 2.1.

A less used graph presented by Wenz describe average noise levels for deep and shallow water at no traffic and average traffic situations. This graph shows clearly that shipping noise is dominant in 20-500 Hz frequency band as presented in chapter 5.1. It is included in Fig. 2.1. The traffic noise fields (pale blue and blue) are corresponding to these results.

That information is also of importance for navies since the hydro acoustic profile changes with a war scenario, and it is above all the shipping that changes.

5.3.1 Rule of fives

In the frequency interval of 500 Hz- 5 kHz Wenz (1962) formulated an empirical formula that described the behaviour of the ambient noise. The rule was formulated based on research done in deep water without any information of wind direction and duration or the bottom characteristics [26]. The estimate was named rule of fives and has been applied on others research with good accuracy. The first rule says that between 500-5000 Hz the ambient sea-noise spectrum levels decrease 5 dB per octave with increasing frequency.

The second rule says that between 500- 5000 Hz the ambient sea- noise spectrum levels increases 5 dB with each doubling of wind speed in the range 2.5- 40 knots.

5.3.2 Acoustics of the Baltic Sea

The Baltic Sea is located in Northern Europe. Border states are Sweden, Denmark, Finland, Russia, Poland, Lithuania, Estonia, Latvia and Germany. The Baltic Sea can be divided into seven sub regions, which are illustrated in Fig. 5.3 [24]. This study is performed in the Bothian Sea and many Baltic Sea characteristics are the same for the Bothnian Sea.

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Figure 5.3: The map illustrates the division of the Baltic Sea in sub regions. It is collected from HELCOM [9].

The Baltic Sea is a small isolated sea only connected with the North Sea through Baelt and ¨Oresund. Baelt and ¨Oresund are both narrow sounds which restricts the exchange of water between the Baltic Sea and the North Sea. Althought the Baltic Sea has a rich inflow of fresh water from rivers, lakes and precipitation. This in combination with the low inflow of ocean water makes the salinity of the Baltic Sea low compared to the oceans.

The water in the Baltic Sea is not salt, but brackish. The salinity varies in the Baltic Sea both with location and time of year. Bothnian Sea is located north in the Baltic Sea and is much less saline than the southern parts. For comparison, the salinity in Bothnian Sea is about 5 PSU and 8 PSU at Bornholm Deep at the same time [24].

The Baltic Sea is also shallow compared to the oceans with a maximum depth of about 459 m at Landsortsdjupet. The mean depth is about 54 m, which is less than what Wenz referred to as shallow. Also the coastline with the many islands and the stratification patterns of the water makes the sea unique [18].

The bottom characteristic varies through the Baltic Sea. In the Bothnian Sea, pertinent to this study the seabed consists of strata formed at the quaternary period. Below a 100 m thick layer from Ordovician is found and below that a layer formed at the Cambrian period. A bit east of the study area the bottom consists mostly of Jotninan sandstone [24].

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The warming of the Baltic Sea is often rapid and a thermocline is created at a depth of 15- 20 m. At the autumn, the surface temperature drops and the influence of the thermocline weakens. Together with the commonly recurring autumn storms the thermocline disap- pears and the top layer of the Baltic Sea gets well mixed. This is essential for oxygenation of the water. During winter the thermocline is absent. The mixing can be expected to be effective down to a depth of 70 m. At 60 - 70 m a halocline is present dividing the top layers and the saline bottom layer [24]. The halocline and the thermocline make up the two boundaries that constitute the sound channel in the Baltic Sea. Their presence will change the wave propagation of low frequency sound and has to be taken into account.

The oceanographically characteristics of the Baltic Sea environment and the fact that the Baltic Sea is one of the most densely trafficked seas [9], makes the ambient noise situation unique. The noise levels are expected to differ compared to the large oceans [18].

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6 Theory Part II: Signal processing and analysing

Recorded information from physical properties often results in complex signals in the presence of unknown noise. To understand the signals, conversion into digital form followed by analysis using various algorithms called digital signal processing (DSP) and time series analysis, is required. It causes a need of careful planning and a conceived strategy.

To realize a complete analysis all prior knowledge of recorded physical and noise properties is vital [1]. In this study the recorded signals and noise are an electrical quantity delivered by transducers that transforms the acoustical pressure to electrical energy. The electrical quantity is in a linear relation with the acoustical pressure and therefore sounds are also referred to as both signals and noise in this thesis.

In real life the recording of a significant amount of acoustic sounds require large data storage space. The data is often unmanageable to handle and interpret. To extract fea- tures that describe the data, signal processing methods were applied. Signal processing methods were also applied to make quality check of the data. To describe the signal it has to be described in both time and frequency domain.

6.1 Stationarity

The knowledge of statistical properties of recorded data is fundamental in time series analysis. An important statistical property is stationarity of the probability distribution.

Stationarity answer the question of how much is the statistical underlying mechanism expected to temporal vary. Stationarity is fulfilled in systems that achieved a steady-state [19]. Commonly used statistical methods such as correlation and Fourier transform are only valid if the assumption of stationarity holds true within the estimation window [1].

Thus, it is important to test whether the signal is stationary or not and to what degree.

From a philosophical point of view a signal is either stationary or non-stationary. The requirement is that the statistical estimate of the stationary process does not change over time [19]. This can be illustrated with an example: A time series is divided in two data sets x₁, ..., x_n and x_1+t, ..., x_n+t. If the probability density function of the two sets are equal, then the sets are strict stationary, if not, they are non-stationary [12].

In an practical perspective stationarity can be classed as strict stationarity, n:th order stationarity or wide-sense stationarity. Strict stationarity means that the joint probability does not change over time, and neither does the mean or variance. Not all random

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processes and real recorded data fulfill this requirement but shows stationary behavior.

The weakest form of stationarity is the wide-sense stationarity which is also called weak stationarity. Wide-sense stationarity means that the mean of the signal (first order statistical moment) is constant and the covariance is only dependent on the time lag (second order statistical moment), not time itself [12]. A stronger form of stationarity is n:th order stationarity and means that all statistical moments up to order n are stationary.

In spectral analysis, second order forms a break point between strict and n:th order stationarity, which implies that the stationarity of a signal does not contribute significantly more to the concept of stationarity with a higher order. Thus, the stationarity of second order is comparable with strict stationary and higher orders are not further investigated in this study [19].

Temporal stationarity is a function of time and amount of data samples. However, the contribution of the sound sources changes both temporally and spatially which affects the stationarity of the signal. Also the amount of samples affects the validity and the significance of stationarity. Levonen (2005) [11] concluded that a time window of 1.5 s was appropriate to use in underwater acoustic ambient noise analysis. Choosing an appropriate size of time window is important since if poorly selected, the time series may deviate to much from the assumed stationarity and the results gets invalid [19]. Levonen (2006) [12] also presented that the ambient acoustic noise in a shallow bay of the Baltic Sea was stationary for 0.4 s and with decreasing depth the stationarity decreased. Levonen (2003) [10] also showed that stationarity of ambient noise may have a dependency on time-of-day.

6.2 Outliers

An outlier is a data observation or value that lies at an abnormal distance from the mean of other values in a data set. The recorded data in BIAS consists of samples within a certain amplitude range and normally less than 1% of all values are exceeding this range.

These extreme values are treated here as outliers.

Outliers are known, or strongly suspected, to be due to effects that are not from a physical underwater acoustical measured quantity [4]. One such effect is electronic noise in the recording system. When dealing with signal processing, measures for determine whether the signal contain outliers and to what extent is needed. Due to large data sets automatic processing methods for outlier removal is appropriate.

Great care has to be taken when defining outliers. However, the outliers might be a result of the experiment and should therefore be included in the data for signal processing. It could also be ”a result of gross deviation from the prescribed experimental procedure” as Grubbs (1969) [8] stated it. If the outlier is a bi-product that has nothing to do with the assumed measured signal the outlier should be removed prior the estimation of underwater acoustical measures [8].

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Some recorded data may contain many multiple outliers. In such case the cause of the outliers has to be identified. There is a risk that identified outliers belong to the actual signal, and if so, the sorting of outliers has to be done manually.

6.3 Correlation

Correlation functions are used in statistics and signal processing to determine relation- ships between two different sets of measured data. However, some care has to be taken.

Correlation estimates should be based on a physical assumption that is a known or hypothesized relation. Two time series with no physical relation will often produce a correlation that could be used to interpret the relation. Two functions of correlation are mainly used, auto-correlation and cross-correlation. The former measure how well future values can be predicted using older data. The latter is often used to reveal the similarity of two signals as a function of the time delay between them. Both signals and noise are often analyzed with cross-correlation. Auto-correlation may be used to find specific tones in the noise, which is relevant to the use of sonar systems [1].

The correlation is estimated as the integral of the product of the two signals. Two identical signals generate a value of one at zero delay, and opposite totally different signals are un-correlated and generates a value of 0 [1]. Cross correlation is further explained with an example of two identical signals where one is time delayed with 20 samples displayed in Fig. 6.1.

Figure 6.1: Example of cross-correlation between two signals of random character. The red line indicates zero time lag and the blue line indicates the correlation at each time lag.

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The location of the peak indicates that the two signals are well correlated at a delay of 20 samples. By changing the order of the signals in the cross-correlation function, the peak would shift to the negative side of zero on the x-axis [20]. The order is important due to the causality of many phenomena.

6.4 Spectral analysis

For an extended analysis of noise and signals, estimation of the spectral content is required. Recorded time series are presenting an amplitude, in this case the acoustic pressure, at every sampled time stamp. The frequency domain representation of the data is independent of time but returns the amplitude and phase for each frequency. Visual inspection of a data set in time domain tells when different pressure fluctuations appear while a spectral analysis returns at what frequency it does. The energy for a signal is conserved i.e. the energy is equal in both time and frequency domain in accordance with Parseval’s identity [1]. Spectral analysis is a standard method to inspect both the noise and signal contents in recorded data. For a broader understanding of signals and noise both temporal and spectral analysis are required. It need to be emphasized that spectral analysis is only a preliminary data analysis tool. Spectral estimates should not be used to answer specific questions about data such as whether a sonar pulse is present, but only suggest possible hypotheses. Detection is a statistical tool and should not be mixed with spectral analysis.

6.5 Fourier analysis

In spectral analysis the use of the Fourier transform is essential. The analysis is based on that an arbitrary periodic signal could be written as a sum of sine and cosine functions to be Fourier series. Jean- Baptiste Fourier formulated this early in the 19^thcentury. His theories became well used and further developed. Today non-periodic signals may also be expressed with a sum of sine and cosine elements by using Fourier transform [20].

6.6 Power Spectral Density

A convenient way of presenting signal and/or noise power is to estimate the power as a function of frequency by use of Power Spectral Density (PSD) displays. The PSD display may look different depending on type of underlying signals in the recorded time series, i.e. short spikes are displayed as broadband components. It is established when analysing and displaying stationary continuous signals to use the PSD as the amplitude squared as a function of frequency, e.g. V²/Hz [20].

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6.7 Bandwidth

The bandwidth of recorded data is the difference between the uppermost (highest) and lowest frequency component of a signal, i.e. if a signal consists of frequency components 10 – 50 Hz the signal bandwidth is 40 Hz [25].

Octave bands are common in acoustics. The mid frequency in each octave band is the doubling of the prior octave band. Historically, sound pressure levels are usually divided into 1/3 octave bands. The reason behind this is that a 1/3 octave band represents the critical bandwidth of a human ear. The 1/3 octave bands are defined in Eq. 6.1 where the mid (centre) frequency f_m gives the name to the 1/3 octave band [25].

f_u,l = f_m2^±(1/6) (6.1)

The bandwidth off each 1/3 octave band increases with increased frequency. The ratio between the band frequency and the bandwidth is constant. Consequently, the 1/3 octave band is suited to display in a logarithmic scale [20].

The ambient noise is in most cases described in 1 Hz bands but in some cases also in 1/3 octave bands. In a technical point of view 1 Hz bands are easier in many applications to interpret but in sonar applications 1/3 octave band is sometimes handy.

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7 Theory Part III: Passive sonar

Water is a most effective medium for transport of sound. A ship can be detected long before it is visually observed at the surface. Individual ships can be heard at 1000 km distance provided that a sound channel exists [22]. Navies utilized this fact and have been developing different means to “listen” to underwater sound. The most common sensor for both listening and transmitting sound is the sonar. This word is well known but few know that it is an abbreviation for Sound, Navigation and Ranging (SONAR). There are two types of sonars, passive and active. Passive sonars are dealt with in this study. A passive sonar is also called listening sonar since it detects sound radiated from the target (source). Active sonars generate sound-pulses that travels through the sea hitting the target and returns to the sonar as an echo, cf. radar. Active sonars are used by naval war ships to locate submarines while submarines use passive sonars to locate other ships [22].

Active underwater echo ranging was developed before the First World War to detect icebergs at far distances. At the outbreak of the First World War the interest of sonars in military application amplified. Both active and passive sonars were developed during the war. A passive listening device called the Eel, consisted of twelve air tubes mounted along a neutral buoyant line array towed by ships, was used to locate submarines [22].

Using cross bearings with a group of 2-3 Eels it was possible to obtain a “fix” on a sound source. Active sonars were employed in the hunt of German submarines but without success. The breakthrough of active sonars had to wait till the Second World War [22].

After The First World War German papers on underwater acoustics became public and results were presented on the behaviour of sound propagation due to salinity and temperature gradients. The paper was far ahead in time and was unrecognised for 60 years [22].

During the Second World War, the United States developed a simple and cheap sonar system that was mass-produced. The sonar system was placed on-board many surface ships of the United States and played an important role in the victory of the Atlantic Battle [22].

The development of advanced sonar systems has been followed by more silent submarines.

The development during the Cold War was no exception. The active sonars became better and cheaper and eventually they found their way to the commercial market. Active sonars became standard on merchant and fishing ships, both for depth control and fish location. Today it is also standard system on-board pleasure boats to measure the depth [22].

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7.1 Purpose and use of passive sonar

The purpose of using passive sonars is to locate ships without revealing the location of the sonar carrier. Presently, submarines are equipped with a few different passive sonars placed at different locations on the hull. Buoys can also be equipped with passive sonars.

These can be dropped into the ocean from ships and aircrafts. Buoys have a limited capacity since the battery charge is limiting the operation time. An expensive alternative is to place fixed passive sonar systems in the oceans that constantly survey the water volume. A surface ship towing a long passive sonar array keeps the submarine uncertain if it is hunted or not. To effectively detect submarines at low frequencies these arrays has to be many hundred meters long [5].

7.2 Passive sonar equation

In this chapter an introduction to passive sonars is presented. The theory and results herein are all gathered from open sources. No classified information is presented in this thesis. A simple passive sonar model (SOFAR) was employed and used in the estimates of detection ranges.

The sonar equation for passive sonars is a starting point for estimating detection ranges of a ship. The sonar equation is presented in Eq. 7.1 and consists of five terms which are presented in Table 7.1.

The sonar equation is based on the assumption that wave propagation is exponential.

Thus, it is possible to relate the different terms as a sum of logarithmic values. This relation is automatically fulfilled for sound pressure values that are defined as logarithm of a relative pressure (in dB relative to 1 μPa). The sonar equation is defined as follows

T L = SL − N L − (−DI) − DT (7.1)

where the variables are defined in Table 7.1.

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Table 7.1: The parameters of the passive sonar equation and brief explanations of them.

All parameters are measured in dB. The table is a recreation of table 2.1 in Urick (1983) [22].

Term Equation Explanations

Transmission loss TL = 10 log

₁₀ ^I_I^s

t

I

_s

= Signal intensity at 1 m I

_t

= Signal intensity at target Source level SL = 10 log

₁₀ _I^I^k

ref

I

_k

= Source intensity at 1 m I

_ref

= Reference signal intensity Noise level NL = 10 log

₁₀ _I^I^N

ref

I

_N

= Noise intensity*

I

_ref

= Reference signal intensity Directivity index DI = 10 log

₁₀ ^P_P^Nekv

NS

P

N_ekv

= Power generated by ndh*

P

NS

= Actual Power generated Detection threshold DT = 10 log

₁₀ _P^P^R

N0

P

_R

= Signal power needed P

_N₀

= Noise power

* Non-directional hydrophone.

TL is the difference of the source intensity and the intensity at a range r. It depends on geometrical spreading of sound, anomalies in water and the current absorption.

SL is the intensity level 1 m from the source measured in 1 Hz band compared to the reference intensity. The reference intensity is calculated for a signal consisting of a plane wave with rms 1 μPa.

NL is the unwished surrounding noise level. In this study NL is the ambient noise measured in 1 Hz -bands. It changes with sea states.

To reduce the influence of noise, multiple hydrophones can be employed mounted in an array configuration. By keeping the main axes of the array orthogonal to the target direction the ambient noise is reduced relative to the source level. The source to noise ratio is improved and the source can be detected at longer ranges [5]. With an array length of 25 m, 5 dB directivity gain (DI) can be achieved at a frequency of 100 Hz.

Detection Threshold (DT) is the signal to noise ratio needed to detect a target with a certain confidence. It is set by the operator. With a decrease of DT an increase of false alarms will follow and with increased value of DT an increased probability to miss the target is followed [5]. It is thus a trade off. Experience from operations shows that a DT of about 9 dB is a good choice. In this study broadband detection was employed since no specific tone was assumed for the target. If the target is producing a specific tone that is known by the operator, it is optimal to apply a sharp filter that detects changes in frequency amplitude (narrow band detection) [5].

Both noise level (NL) and transmission loss (TL) are dependent on weather, location and hydrography, which in turn are dependent on time of year. The environmental parameters have to be deduced by in situ measurements or calculated for each position and situation. The transmission loss is even more difficult to determine than the ambient

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noise since it depends on spreading, sediments, anomalies and the hydrography. For example if the hydrophone is placed within a sound channel and the target is outside the TL will be higher than if the target also was located in the channel. To investigate the local transmission loss a numerical estimate was calculated using a LOFAR sonar. The frequency of the source was 100 Hz and the water depth was 70 m. The sonar was located at 63 m depth. The sound channel was present in the middle of the water column. The results are shown in Fig. 7.1. The sound is trapped in the middle of the water column.

Figure 7.1: Transmission loss in the Bothnian Sea in January. The illustration indicates the transmission loss for differrent source placement in the xy plane. The colour-bar indicates the values of each colour. The values are in dB re 1 μPa. Result computed with software SonaCalc.

This result visualizes the behaviour of sound in water in the Bothnian Sea. According to this result it is most favourable for a submarine to stay in the pale blue areas, since that is where the transmission loss is the greatest. In this case that would be almost at the surface and at the bottom. a depth of 34 m would should be avoided since the transmission loss is less strong at that level to a distance of about 10 km. These results are important for the submarine operator.

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8 Method

The aim of this study was to establish the sound levels of the ambient noise and investigate the detection ranges for a basic sonar surveillance system. To achieve these aims a number of data sets were used. The recorded sound data as well as wind, wave, hydrography and AIS data were used. For the estimation of detection ranges the sonar equation was used where background levels were taken from the own produced results.

8.1 Data collection

The sound data used in this study was measured 2014 by the BIAS project. Meteoro- logical and ocean data were produced by SMHI and pre-processed by AquaBiota Water Research. The AIS data was supplied by HELCOM.

8.1.1 Noise recordings

The hydrophone used was of the type SM2M logger from Wildlife Acoustics and was placed at N 61.75738^◦, E 19.31642^◦. It was anchored at the sea bottom at 63 m depth.

The deployment position was chosen to be outside the shipping lane. The sampling frequency was 32 kHz. The rig was deployed in November 2013. The recording started at the 1^st of January and ended 31^st of December. The recording time was limited to three months where after the memory was full the sensor had to be replaced. This procedure was repeated throughout the 2014. The recording length was 23 minutes every hour every day for a year. The main component of the rig was the autonomous recorder that contained a hydrophone, amplifier, filter unit, A/D converter and a storing unit. A sketch of the rig is showed in Fig. 8.1 [23].

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Figure 8.1: Sketch of the BIAS standard rigs. The rig to the left uses the Loggerhead sensor and the rig to the right the Wild Life Acoustics. 1 hydrophone, 2 extra buoyancy, 3 & 7 autonomous loggers, 4 acoustic releasers, 5 anchors, 6 buoys [23].

Calibration of the system was completed both before the first and after the last deployment. The aim of the calibration was twofold; first to control the quality of raw data and second, more important, to establish the sensor sensitivity, that is the relation between the pressure variations and the recorded data. The calibration gave the sensitivity in bins/μPa. The reason for this “odd” entity is that the recorded sound was stored in a wav-file, which scales data in 2¹⁶ bins. To convert the bins to pressure the scaling factor was needed [23].

The hydrophone is connected to two separate channels. Thus, here was the option to amplify one of the internal amplifiers of the autonomous sensor. This has to be done with care. A too high gain results in clipping when strong sound sources pass, which will have an uncorrectable effect on the sound average estimate. On the contrary, if a too low gain is set, the signal-to-noise ratio might be too low [23]. The first channel was set to zero amplification and the second to 12 dB.

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8.1.2 Meteorological data

The meteorological data was pre-processed by AquaBiota Water Research but was origi- nally produced by SMHI. The data used was significant wave height, ice thickness, salinity and temperature of the water for every sixth hour as well as wind speed data for every hour. The meteorological data were model based estimates for a position close to the actual hydrophone position.

8.1.3 AIS data

AIS, Automatic Identification System, is a world-wide system that makes it possible to identify and track ships from other units or land-based stations. The purpose of the system is to increase the safety at sea. The Swedish Maritime Administration is responsible for AIS data distributed within Sweden. HELCOM is the data holder for all AIS data to be used in BIAS. The BIAS project has allowance to use the data for 2014. The AIS data was stored in a text-file format containing date, time, speed, position, dimensions of ship, draught, type of ship and cargo.

8.2 Signal processing

There is a number of processing steps that can be applied to a time series. The different options at hand will affect the estimated properties. How to choose and implement processing methods lies in the hands of the processor. Every set of data can be measured, processed and analysed in multiple ways. There are no rules to adhere to. The methods employed are often based on experience from earlier studies.

8.2.1 Pre-processing

Pre-processing was performed to prepare data before estimating the statistical properties. It was also done to make sure there were no artefacts affecting the estimates. The purpose of the recordings was to measure the ambient noise. Some signal content should not be regarded as ambient noise signals [16]. Electronic spikes are an example of that and should be removed before starting to estimate the properties of the time series. A second example is the ambient noise recorded during deployment of the rig, even if it can be regarded as ambient noise it was not in this study, and it was removed.

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The processing started with grouping the data into monthly periods. In the first pre- processing test the number of files was counted to make sure no recordings were missing.

In the second test the length of each file was controlled, to make sure that the sensor had been working properly. Files with substantial difference in length were removed from the data set. Each noise recording was also controlled for non-numerical values such as NaNs (not-a-number) and infs (too high value for a numerical representation). All non- numerical values were excluded from the set [16]. If the sound was too loud the recorded data became clipped when the amplitude of the signal was higher than the maximum allowed value of the Analog-to-Digital converter. Clipping was checked for both positive and negative values.

8.2.2 Grubbs’ test

Self-noise is an unwanted product of the instrument and has to be dealt with. The first step in this process was to optically inspect the time series for anomalies. When anomalies were found they were inspected both by plotting them and by listening to the sound.

The different types of anomalies were identified and an algorithm was designed that automatically identified and removed the anomalies. A commonly occurring anomaly were spikes. These were small groups of outliers much stronger than the surrounding signal.

The algorithm that was developed to remove spikes was based on Grubbs’ test [8]. This is a test which results in identification of outliers in a time series. The significance level of 5% was used. The algorithm was built up in seven consecutive steps:

1. The data set was divided in windows of maximum 1000 samples.

2. The data within each window was sorted in ascending order; x₁, x₂, x₃, . . . , x_n. 3. The ratio of w/s was calculated, where

s = std(x₁, x₂, x₃, . . . , x_n.) and w = x_n− x₁.

4. The value of w/s was compared with the value 7.33 collected from table 3 in Pearson (1964) [15]. If it didn’t exceed, the process started over with a new time window in step 1, if it did, the process continued with step 5.

5. The value T₁ was compared to pV, where T₁ was defined according to Eq. 8.1 and pV according to Eq. 8.2. T₁ was calculated as

T₁ = ±[x_mean− x_n]

s (8.1)

if the value exceeded pV, calculated as

pV = N_stdn − 1

√n s

t²

(n − 2 + t²), (8.2)

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it was classed as an outlier and the second largest value, x_n−1, in the set was tested.

If not, the process restarted with the next time window in step 1. pV was calculated according to Dan (2013) [4], where n is the number of samples (in this case 1000), t is a constant value set to 1.645 and N_std is the number of standard deviations [4]. A high value of N_std results in high certainty that all outliers identified were outliers but with a risk that some outliers were not found. A low value results in data identified as outliers even if they were not. In this case N_std was set to 5.

6. All x_i corresponding to a too high T₁ were classed as spikes and were removed from the data set and replaced, i.e. a piece of the data set without spikes was cut-out and used to replace spikes. Many different methods can be applied to replace data.

After a few tests this method was selected due to good stationarity result.

7. The procedure was repeated with the next time window.

8.2.3 Kolmogorov-Smirnov two sample test of stationarity

In signal processing strict stationary signals are rare. The Kologorov- Smirnow two sample test, also known as the KS-test, are often used to test whether a signal is stationary or not [11].

The test is based on distribution functions of the two sets. The cumulative distribution function (CDF) is calculated for each set. They are compared and if there is a non- significant difference between the CDFs, the sets are said to be strict stationary with a certain confidence. This was calculated with Eq. 8.3 [3],

T_KS = sup|CDF₁− CDF₂|, (8.3)

where 1 and 2 denotes the different sets tested. Then a null- hypothesis as H₀ = ”the two sets are stationary”

was stated. H₀ should be rejected with the significance level α, if TKS was greater than (1-α), [3] [12]. The level of significance may be decided by the user and is often set to a maximum level of 5 %, which was used in this study. A 1.5 second window was used.

8.2.4 Averaging

Noise was recorded with a sampling frequency of 32 kHz. The file corresponded to 23 minutes recording. The file size was 175 MB and it was found to be difficult to handle more than a few files simultaneously. To reduce the computational time the data was decimated by calculating averages over a pre-specified time length. Two different methods were used for averaging; twenty seconds means (20 s means) and PSD averaging.

Some statistical properties of theambient noise in the Baltic Sea andits relation to passive sonar