Proceedings of the Institute of Acoustics

 

Investigating the effect of oceanographic variability on aspects of sonar performance: A simple approach

 

Marcus Donnelly, Systems Engineering & Assessment Ltd.

 

 

1 INTRODUCTION

 

It is well understood that sonar performance depends upon the underwater environment and corresponding acoustic propagation characteristics. These depend upon the variation of sound speed with depth, the sea surface conditions and seabed type. In addition the sonar operating frequency affects the frequency-dependent volume and boundary losses during acoustic propagation. Sophisticated numerical models 1 have been developed to predict acoustic propagation including these effects. Such models can produce accurate results for well understood environmental conditions. However the environment is often highly variable, which makes such models less useful unless they can encompass this variability. This is difficult as (i) they are normally designed to produce extensive and detailed outputs for a deterministic environment (e.g. propagation loss versus range, depth, azimuth and frequency from a given location) and (ii) they may be slow to run repeatedly due to the complex nature of the calculations performed.

 

The aspect of the underwater environment that is usually most accurately known is the variation of temperature and salinity with depth. This can be readily measured using Conductivity Temperature Depth (CTD) sensors by manned or unmanned platforms and is the subject of constant global monitoring by the Argo Float programme. In addition it is routinely predicted using high resolution ocean models which assimilate CTD and other (e.g. remotely sensed) data.

 

A simple approach to understanding the impact of highly variable environments on sonar performance is to limit the acoustic modelling to the calculation of a few important parameters and determine their variability. As most of the oceanographic variability occurs within the mixed layer, the focus of this paper was on surface duct propagation. The following parameters were calculated:

 

• The surface duct depth;

• The range to the first surface bounce of the limiting ray within the surface duct;

• The angle at the sea surface of the limiting ray within the surface duct;

• A parameter representing the sonar beam power in the surface duct.

 

For surface ship hull mounted sonars, the surface duct depth is perhaps the most important environmental parameter governing their performance. The range to the first surface bounce of the limiting ray within the surface duct (i.e. that which turns at the duct depth) is a good indicator of the sonar detection range. Detection with multiple surface bounces is possible, but loss and scattering at each surface bounce reduces the likelihood of this at the typical operating frequencies of such sonars. The angle of the limiting ray at the sea surface determines the vertical beam steer angle necessary to achieve the furthest surface bounce.

 

The last parameter compliments the other three parameters by accounting for a practical aspect of sonar performance – the effect of the beam pattern. It represents the proportion of the (active) sonar beam power transmitted into the surface duct. For example, if much of the angular extent of the beam main lobe is beyond the limiting ray angle, the overall surface duct performance may be poor as relatively little energy is transmitted into the duct. This would be the case for weak or shallow ducts or for wide sonar beams (i.e. small array apertures).

 

The approach taken in this paper was to investigate the variability of the above four parameters using two data sources: the HYCOM ocean model and Argo Floats. Temperature and salinity from these sources was used to calculate the sound speed using standard formulae,² giving the Sound Speed Profile (SSP) as a function of time, latitude and longitude. The parameters listed above were calculated from the SSP using standard geometrical ray formulae.¹ Analysis was conducted on the results to determine the variability of the parameters.

 

 

Figure 1: Schematic diagram of surface duct propagation showing the four parameters of interest. The surface duct depth d corresponds to the maximum sound speed in the SSP. The red curve illustrates the limiting ray, which subtends angle  θ_l at the sea surface and for which the first surface bounce occurs at range _r . Parameter P ′ is represented by the shaded green area within the sonar beam (the green outline).

 

 

2 APPROACH

 

2.1 Parameters

 

A schematic diagram of the parameters is shown in Figure 1. The surface duct depth d was calculated by determing the mixed layer depth and finding the depth of the maximum sound speed between the surface and the bottom of the mixed layer. The mixed layer depth was calculated using the Levitus criterion, i.e. the depth at which the temperature falls to 0.5 ◦ below that at the sea surface.

 

The angle at the sea surface of the limiting ray within the surface duct was calculated from Snell’s law using Equation 1 where c_s is the sound speed at the sea surface and c_d that at the bottom of the duct.

                                                                                                             

 

The range to the first surface bounce of the limiting ray within the surface duct was calculated using Equation 2 where κ is the ray constant given by Equation 3 and the sound speed gradient g is given by Equation 4. This assumes a linear sound speed gradient over the duct depth, for which the ray trajectory becomes circular and the ray equations reduce to simple forms. Intermediate sound speed values between the sea surface and duct bottom were ignored for simplicity (this is considered a reasonable approach as the mixed layer is generally isothermal and isohaline, and it also avoids numerical innacuracies which can occur for piecewise-linear ray calculations where g becomes very small between two adjacent depth points in the SSP).

                                                                                                         

                                                                                                            

                                                                                                          

 

The final calculation is of the parameter representing the sonar beam power in the surface duct. The vertical aperture of a hull mounted sonar array is represented here by N omni-directional uniformly shaded unsteered hydrophones on a vertical line with spacing d, for which the beam amplitude response is given by Equation 5 where θ is the elevation angle and k the wavenumber.

                                                                                                              

 

The beam power is proportional to  B², and our chosen parameter is simply the integral of this over solid angle up to the limiting ray angle θ_l . This gives Equation 6, where we have supressed azimuthal integration as the beam pattern is azimuthally invariant and the integral reduces to 2π, which is simply a scaling factor and is therefore ignored.

                                                                                                             

 

Equation 6 is not straighforward to evaluate in closed form, however simplifications can be made. Firstly we assume that the operating frequency is equal to the array design frequency, i.e. k = π/d. Then, if we are concerned only with the main lobe, we can approximate B by B ′ as given by Equation 7 (neglecting the scaling factor N ). The functional forms for B and B′ are almost identical up to the first zero in B at θ = 2/N.

                                                                                                            

 

Using the small angle approximations (sin θ ≈ θ and cos θ ≈ 1) and B′ replacing B in Equation 6 with trignometrical substitutions for the cos 2 term allows straightforward integration, giving Equation 8.

                                                                                                                  

 

P′ takes values between 0 for θ_l = 0 and 1 for θ_l = 2/N . Hence, if θ_l ≥ 2/N , the maximum value of 1 indicates that all of the sonar beam power is in the surface duct. The value will decrease with decreasing duct depth/strength and increasing beamwidth (i.e. decreasing sonar aperture). A value of 0 indicates no surface duct present.

 

A summary of the approximations in the above calculations is as follows:

 

• A linear sound speed gradient is applied over the surface duct (intermediate sound speed values are ignored);

• The sonar operating frequency is equal to the array design frequency;

• The beam pattern sidelobes have been ignored.

 

It is worth highlighting that sound from different ranges will be received at different vertical arrival angles within the duct. The integral approach taken in the derivation of P′ (Equation 8) therefore complements r (Equation 2) which represents the longest likely detection range.

 

A value of N = 8 was used for calculating P′ for all results presented in this paper.

 

 

Figure 2: Bathymetry (left) and average temperature for January (right) around the South East Iceland oceanic front

 

2.2 Variability Analysis

 

The approach to analysing the variability of the four chosen parameters was to calculate the mean and standard deviation over time of the parameters at each location, and then calculate the Coefficient of Variation (CoV) – i.e. the ratio of the standard deviation to the mean – at each location. The CoV was chosen as it shows the relative variability of the different parameters.

 

Two months – January and July 2016 – were chosen for the variability analysis. These were chosen to correspond to winter and summer conditions respectively for the chosen geographical area (see Section 2.3).

 

The analysis was necessarily slightly different for the HYCOM and Argo Float data. For the HYCOM data forecasts are available daily (see Section 2.4), hence at each model output latitude and longitude, 31 time samples of each of the parameters were calculated. For the Argo Float data, profiles are reported when the floats surface, hence a non-uniform space and time distribution of profiles was available. For each month, the profiles reported within the month were binned according to their location into a regular latitude-longitude grid. This allowed the variability analysis to be conducted, however the number of profiles assigned to each grid cell and their temporal separation varied according to those available. This is discussed further in Section 3.

 

2.3 Geographical area

 

The geographical area selected for the analysis was around the Iceland-Faroe oceanic front. This is a well known area of strong oceanographic variability due to the mixing of relatively warm, saline waters from the North Atlantic ocean with cold, fresh waters from the East Iceland Current. The bathymetry in the area (from the General Bathymetric Chart of the Oceans (GEBCO) Digital Atlas⁵) is shown in the left hand plot of Figure 2, and the average sea surface temperature for January (from the World Ocean Atlas⁴ 2013 (WOA13) Version 2) is shown in the right hand plot. The front forms in the vicinity of the ridge running from north-west to south-east between Iceland and the UK Faroe Islands, where the two water masses meet. As shown in the right hand plot, the temperature changes dramatically across the front.

    

 

Figure 3: Argo Float profile reporting locations (black circles) plotted over bathymetry for January 2016 (left) and July 2016 (right)

 

2.4 Data Sources

 

The Hybrid Coordinate Ocean Model (HYCOM)³ and data server provides oceanographic forecast data including temperature and salinity. The GLBu0.08 dataset is used here, for which the data is provided at 40 standard depth levels on a high resolution (0.08 ◦ by 0.08 ◦) grid. The data server provides 3-hourly forecasts and retains daily previous forecasts. The daily forecast data was used here as historical data was needed for comparison with measured Argo Float data.

 

Argo Floats are freely drifting profiling floats which measure the temperature and salinity of the upper 2000m of the ocean. There are more than 3000 floats currently deployed. Argo data was accessed from the US National Oceanic and Atmospheric Administration (NOAA).⁴

 

As noted earlier, the Argo Float profiles are non-uniformly separated in location and time as each profile is reported when a float surfaces. There were 55 profiles available in January 2016 and 54 in July 2016, the locations of which are shown in Figure 3.

 

The HYCOM and Argo Float data were used for the variability analysis. The GEBCO Digital Atlas⁵ and WOA13⁴ were used in understanding the general properties of the Iceland-Faroe front (see Figure 2).

 

The HYCOM, Argo Float and WOA13 data were accessed⁴ over the Internet using the Open Data Access Protocol (OpenDAP).⁶

 

 

3 RESULTS

 

3.1 Variability examples

 

An immediate appreciation of the potential for variability in this geographical area is given by calculating the four parameters from the HYCOM predictions for two consecutive days (16^th and 17^th January 2016 were arbitrarily chosen) and plotting the percentage difference, as shown in Figure 4. Over this 24 hour period alone, around 50% difference is observed around the front (and there are higher isolated values). In Figure 5, the maximum percentage difference between any two consecutive days in January is shown at each location. There were 30 samples used at each location (that for the 28^th January was not included in any of the analysis as the HYCOM data appears anomalous at all locations for depths greater than 25m on that day). The greatest changes visible in Figure 5 are around the front and in the shallow water regions. At these locations the parameters are clearly changing from near-zero to a maximum value or vice-versa (i.e. the changes are up to +-100%). As these maximal changes can occur over a single 24 hour period, potentially significant changes could be expected within a few hours at a single location.

 

                                               

Figure 4: Percentage difference for parameters d, θ l, r and P ′  between HYCOM predictions for 16^th and 17^th January 2016   

  

 

 Figure 5: Maximum percentage difference for parameters d, θ l, r and P′ between contiguous HYCOM predictions

 

Figure 6: Variability of surface duct depth d for January 2016 from HYCOM data

 

The surface duct depth d is the controlling factor for the other parameters, so it is instructive to look at its variability first. The variability of d as predicted using HYCOM data for January 2016 is shown in Figure 6. The mean, standard deviation and CoV were calculated as described in Section 2.2. The surface duct depth is greatest for the North Atlantic waters to the south-west of the area. Most of the variability is in the vicinity of the front, though it is also present to the south. There is also some strong localised variability north of eastern Iceland. The variability of d for July 2016 from HYCOM data is shown in Figure 7. The mean values are considerably lower for summer than for winter, as would be expected due to the much shallower mixed layer. The CoV is quite high, reaching 1 (i.e. duct depth varying between 0 and twice the mean) in some areas. The high variability is generally in areas where the mean value is low.

 

The variability of d in January 2016 from the Argo Float data is shown in Figure 8, with the data processed as described in Section 2.2. The colour scales are the same as in Figure 6 for ease of comparison. There were 55 profiles available in January (see Section 2.4), processed into 7.5◦ by 7.5◦ cells for Figure 8. The two left hand cells were each assigned 18 profiles and the upper right hand cell 19 (no profiles were available in the lower right hand cell). Hence, whilst a coarse grid resolution, the number of profiles in each non-empty cell is approximately equal. Comparison of Figure 8 with Figure 6 shows that the broad trends are actually quite similar, e.g. the mean and standard deviation are highest to the south west and the highest variability is to the north west. In Figure 9 the cell size is decreased to 5◦ by 5◦, for which the number of profiles in each non-empty cell varies between 2 and 14. In some areas the agreement with the trends of Figure 6 is improved, e.g. the slightly higher mean values to the north east. The peak variability is further south in the Argo Float data, though it still corresponds to an area of relatively high variability from the HYCOM data. The same plot for July 2016 is shown in Figure 10, with the same colour scales as Figure 7. Again, the trends for the two data sources are broadly similar, with both absolute values and distribution comparing reasonably well. In both cases the variability is higher to the west, though it is more spread out in latitude for the Argo Float data than for the HYCOM data.

 

 

Figure 7: Variability of surface duct depth d for July 2016 from HYCOM data

 

 

Figure 8: Variability of surface duct depth d for January 2016 from Argo Float data, grid cell size 7.5 ◦

 

It should be noted that as HYCOM assimilates Argo Float data, some level of agreement between the two data sources should be expected. The extent of that agreement is not the subject of this paper – it simply provides confidence that the higher resolution HYCOM predictions should represent the expected variability in the area.

 

 

Figure 9: Variability of surface duct depth d for January 2016 from Argo Float data, grid cell size 5◦

 

 

Figure 10: Variability of surface duct depth d for July 2016 from Argo Float data with grid cell size 5 ◦

 

                                                   

Figure 11: Mean of all parameters for January 2016 from HYCOM data   

           

 

 Figure 12: CoV of all parameters for January 2016 from HYCOM data

 

3.2 Variability of all parameters

 

The mean and CoV of the four parameters during January 2016 are plotted for the HYCOM data in figures 11 and 12 and for the Argo Float data in figures 13 and 14. The same sets of results are plotted for July 2016 in figures 15, 16, 17 and 18. A grid cell size of 5 ◦ was used for all Argo Float data.

 

The means of all parameters are significantly higher for January than for July as would be expected from the deeper mixed layer. The CoV from the HYCOM data reaches ~0.6 for January in the vicinity of the front. The variability of the four parameters is spatially correlated as would be expected, though it is slightly lower for θ l, r and P ′ than for d. The Argo Float data for January shows higher variability than the HYCOM data, with the highest CoV values reaching ~0.8.

 

In July the variability from the HYCOM data is higher than in January, with θ l, r and P′ following the trend for d shown in Figure 7, once again with d showing the highest variability of the four. For the Argo Float data (54 profiles were used) the CoV of d is slightly lower than the other three parameters in Figure 18. The Argo Float data gives a higher CoV to the east than the HYCOM data. The CoV to the west is high in both datasets and highest in the Argo Float data. Although the reduced number of samples in the Argo Float data compared with the HYCOM data must be taken into account, it is interesting to note that the high CoV grid cells in Figure 18 have different numbers of samples yet give similar CoV values. The westernmost cells had 15,12 and 6 samples going from north to south and the easternmost mid-latitude cell had 3.

 

                                         

Figure 13: Mean of all parameters for January 2016 from Argo Float data   

    

 

 Figure 14: CoV of all parameters for January 2016 from Argo Float data

 

                                       

Figure 15: Mean of all parameters for July 2016 from HYCOM data 

 

 

Figure 16: CoV of all parameters for     July 2016 from HYCOM data

 

                                                   

Figure 17: Mean of all parameters for July 2016 from Argo Float data 

 

 

Figure 18: CoV of all parameters for July 2016 from Argo Float data

 

 

4 SUMMARY

 

The variability of four parameters of importance for underwater acoustics and sonar performance has been investigated in the vicinity of the Iceland-Faroe oceanic front using two data sources for the months of January and July 2016. The parameters – surface duct depth, limiting ray angle, range to first surface bounce and a parameter representing the sonar beam power in the surface duct – were chosen as they are all important for surface duct sonar performance, where oceanographic variability is typically strongest.

 

Data from the HYCOM ocean model was used to calculate the variability between daily updates for each month – 31 updates for July and 30 for January (one sample was ignored due to anomalies) – on a high resolution (0.08 ◦ by 0.08 ◦) grid. The smaller number of samples for the Argo Float data – 55 profiles for January and 54 for July across the area of interest – were binned according to their location into a regular latitude-longitude grid with resolution 5 ◦ by 5 ◦. Despite the different resolutions, the approach allowed both the absolute values and spatial trends in the variability to be analysed and compared. The broad trends for the two data sources were observed to be similar.

 

The Coefficient of Variation (CoV) over time was used as the principal measure of variability. In general, the CoV was highest in July, reaching a value of 1 in some locations. This implies that the sonar detection range varies between near zero (i.e. when the surface duct vanishes) and twice the mean value. This is clearly significant, and as the CoV is based on the standard deviation, the extremes in variability could be greater still, as indicated by Figure 5. The mean values of the four parameters were higher in January than in July as the mixed layer is deeper in January. The maximum CoV in January as predicted from the HYCOM data was ~0.6 and geographically constrained to the frontal position. The Argo Float data for January gave higher CoV values (~0.8) to the west of the front. The sonar performance could be summarised from these results as good in January with significant variability and poor in July with extreme variability.

 

The CoV results presented correspond to the temporal variability as a function of location; clearly these are also related to the strong spatial variability visible in the plots. Hence, a non-stationary sonar would experience both temporal and spatial variability.

 

 

5 CONCLUSIONS

 

The results show that the oceanographic variability from the chosen data sources around the Iceland-Faroe front has a significant effect on surface duct sonar performance. The Coefficient of Variation for July 2016 implies that the sonar detection range at any one location can routinely vary between near zero and twice its mean value. In January 2016 the detection range variation is lower but still significant at ~60-80% of the mean.

 

It is concluded that rapidly calculating and visualising the variability of important parameters over a wide area of interest can allow for a good understanding of the environmental variability and its impact upon underwater acoustics and sonar performance. Such an approach is complementary to detailed underwater acoustic modelling, e.g. calculation of propagation loss versus range, depth, azimuth and frequency from a given location. For example, detailed modelling could follow once an optimum area for sonar deployment has been identified using the approach demonstrated here.

 

A feature of the approach demonstrated in this paper is rapid access of high quality oceanographic data from Internet sources for the variability analysis. The four parameters analysed here were appropriate for surface duct sonar performance; different parameters could be chosen for other aspects of sonar performance whilst retaining the basic methodology of rapid, wide-area analysis and visualisation using simple parameters calculated from readily available oceanographic data.

 

 

6 ACKNOWLEDGEMENTS

 

This work was funded by Systems Engineering & Assessment Ltd.

 

The author acknowledges the United States National Oceanic and Atmospheric Administration (NOAA), the HYCOM Consortium and the GEBCO organisation for making available the data used in this study.

 

 

7 REFERENCES

 

1. F.B. Jensen at el, Computational Ocean Acoustics, AIP Press, 1994.

2. C-T. Chen and F.J. Millero, Speed of sound in seawater at high pressures (1977) J. Acoust. Soc. Am. 62(5) pp 1129-1135.

3. Funding for the development of HYCOM has been provided by the National Ocean Partnership Program and the Office of Naval Research. Data assimilative products using HYCOM are funded by the U.S. Navy. Computer time was made available by the DoD High Performance Computing Modernization Program. The output is publicly available at http://hycom.org.

4. These data were acquired from the US NOAA National Oceanographic Data Center (NODC) on 25 th September 2016 from http://www.nodc.noaa.gov/.

5. The GEBCO_2014 Grid, www.gebco.net.

6. J. Gallagher et al, The Data Access Protocol - DAP 2.0, ESE-RFC-004.1.2, October 2007.