A regional ocean model for Fram Strait provides a framework for interpretation of the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical levels and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modeling using the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic models gives insights into acoustic propagation during winter and spring. Moreover, overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of purely refracted rays and surface-reflected/bottom-reflected (SRBR) rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of SRBR rays is valuable for choosing appropriate observation kernels for the data assimilation of acoustic tomography data in Fram Strait.

Fram Strait, which is located between Greenland and Spitsbergen, is the only deep-water connection between the Arctic Ocean and the world oceans and an important area for water-mass and sea-ice transports into and out of the Arctic Ocean (e.g., Beszczynska-Möller et al., 2012; de Steur et al., 2009; Langehaug et al., 2013). Therefore, the region is of particular interest for ocean climate monitoring. Since 1996, the Alfred Wegner Institute (API) for Polar and Ocean research and the Norwegian Polar Institute (NPI) have maintained an oceanographic mooring array across the strait along 78°50′N primarily to provide estimates of the heat, mass, and volume transports. However, the flow through Fram Strait is bidirectional and complex, characterized by recirculation of the Atlantic Water (e.g., Marnela et al., 2013), the presence of fronts, eddies, and currents with variable water masses (Walczowski, 2013; von Appen, 2016). The typical spacing between the moorings of the Fram Strait mooring array is about 20 km, while the Rossby radius for the region is 4–6 km. This has made it difficult to provide accurate estimates of the transports. Ilıcak et al. (2016) reported the mean heat transport relative to 0 °C through Fram Strait as 26–50 TW.

A comparative study of global sea ice models showed a large spread in Arctic Ocean temperatures in the models and identified the inflow of Atlantic Water through Fram Strait as a major source of uncertainty (Ilıcak et al., 2016). Fram Strait has an abundance of small-scale eddies, which is a challenge for models to reproduce. As a result, models often fail to simulate the temporal variability in Fram Strait or processes influenced by this small-scale variability, such as the recirculation of the Atlantic Water (Hattermann et al., 2016). However, high-resolution models have made progress reproducing the small-scale variability and the water mass circulations in Fram Strait (Wekerle et al., 2017).

As the measurement of the volume and heat exchanges is difficult to achieve with point measurements because of the small Rossby radius in the region, integral measurements are needed. An ocean acoustic tomography system consisting of three moorings with low frequency, broadband sources, and receivers was installed in Fram Strait during 2010–2012 as part of the Acoustic Technology for Observing the Interior of the Arctic Ocean (ACOBAR) project (Sagen et al., 2017). The mooring triangle was located in the central, deep-water part of Fram Strait (see Fig. 1). The instruments were originally deployed during August–September 2010. During September 2011, moorings A and D were recovered, the batteries replaced, and the moorings redeployed. The final mooring recovery took place during September 2012. The two Teledyne Webb Research swept-frequency acoustic sources transmitted linear frequency-modulated signals with bandwidths of 100 Hz and center frequencies of approximately 250 Hz. Transceiver A transmitted every 3 h every other day; transceiver B transmitted every 3 h every day. The acoustic tomography experiment observes high temporal variability and provides range-depth averaged temperature measurements that are hard to obtain using conventional methods (Dushaw and Sagen, 2017). These range averages overcome the problems of the point measurements and are complementary to them (Dushaw and Sagen, 2016). The interpretation of acoustic travel times in Fram Strait is not as straightforward as in the subtropics, because vertical sound speed profiles are much flatter than at lower latitudes, leading to more unstable ray arrivals and a small temporal spread between different arrivals. Therefore, an ocean model is used in this work to better understand the forward problem and as a first prerequisite step to data assimilation.

FIG. 1.

(Color online) Map of the ACOBAR experiment and Fram Strait, the model domain of the Fram Strait regional model is indicated (red box).

FIG. 1.

(Color online) Map of the ACOBAR experiment and Fram Strait, the model domain of the Fram Strait regional model is indicated (red box).

Close modal

In Sec. II, we present the characteristics of, and results from, an eddy-permitting regional model of Fram Strait. In Sec. III the ocean model fields were used as input to a geometric ray model to simulate the structure and temporal variability of acoustic tomography receptions for comparison with observations. In Sec. IV we synthesize the results to yield insights for inversions and data assimilation of the acoustic tomography observations.

This study uses geometric rays for acoustical forward modeling. The Fortran code used is called “eigenray” and developed by Dushaw and Colosi (1998). The ray code allows range-dependence of sound speed and bathymetry but does not take into account sediments, bottom layers, or surface waves. Sagen et al. (2017) have shown that geometric rays give comparable results to parabolic equation (PE) calculations in Fram Strait. Geometric rays are less computationally expensive as PE calculations and therefore suited for repeated acoustic forward modeling using a time series of daily output fields from ocean models as input. A high-resolution international bathymetric chart of the Arctic Ocean data was used for the ocean bathymetry (Jakobsson et al., 2012).

For evaluation of the ice-ocean model this study uses integrated, i.e., range and depth averaged, ocean temperature measurements obtained by inverting acoustic travel times from the ACOBAR ocean thermometry experiment in Fram Strait (Dushaw and Sagen, 2017; results updated in Dushaw, 2017). Their integrated quality overcomes the problems of point measurements. In a region with a small Rossby radius of deformation, point measurements can be difficult to use to validate models of several kilometers resolution. The acoustically measured depth- and range-averaged ocean temperatures are especially valuable for model evaluation in such regions (Dushaw and Sagen, 2016). In Sec. IV the inversion method used in Dushaw and Sagen (2017) and Dushaw (2017) is discussed. For convenience we provide a short summary of the method. Small mesoscale variability (Dushaw et al., 2016) was added to the World Ocean Atlas 2009 (WOA09) climatology to create a more realistic reference ocean. The reference ocean was used as input to a geometric ray model, which created a multitude of refracted eigenrays between sound source and receiver. This ensemble of eigenrays all sampled the ocean between the ocean surface and 1000–1500 m depth. Measured peaks of the recorded acoustic arrival pattern were then randomly associated with the computed eigenrays for the inversion to sound speed. Technically this was done by choosing the six strongest peaks in the observed arrival pattern. As these occur in the early part of the arrival pattern it was assumed that they correspond to refracted rays. In Sec. IV we will discuss the consequences of when this is not the case. The sound speeds were then converted to temperature. The results of this inversion method are precise range and depth (0–1000 m) averaged temperature estimates, with a formal uncertainty of 75 m°C. This fits well with the observed root-mean-square scatter of the inversion results, which is 80 m°C (Dushaw and Sagen, 2017).

An eddy-permitting regional z-coordinate model was set up for Fram Strait using the Massachusetts Institute of Technology (MIT) general circulation model (MITgcm) with a horizontal Arakawa C-grid in latitude and longitude and 52 depth levels. The model domain covers the area from 72°93′N to 82°07′N and from 19°30′W to 19°30′E. The depth levels are most densely spaced near the surface with 12 levels within the first 100 m depth and 8 levels between 100 and 200 m depth. The horizontal grid spacing is 4.6 km in the North–South direction, whereas the East–West direction varies from 3 km at the northern boundary to 6.5 km at the southern boundary. This grid spacing is a compromise between the wish to permit the development of eddies and the computational limitation for a model that will also be used for the planned 4DVAR data assimilation of acoustic measurements in Fram Strait. The model is operated in hydrostatic mode with an implicit free surface. A free slip boundary condition is used. The vertical diffusivity and viscosity are parameterized by Laplacian mixing with values of 10−5 m2 s−1. The diffusive operators in the horizontal are biharmonic with values of 1010 m4 s−1, whereas the viscosity is also biharmonic, but with a value of 108 m4 s−1. Mixed layer turbulence is parameterized using the scheme of Gaspar et al. (1990). The sea ice model used has been described in Losch et al. (2010) and Fenty and Heimbach (2013). The sea ice implementation is the same as in the global Estimating the Circulation and Climate of the Ocean (ECCO) state estimate (ECCOv4r3; Forget et al., 2015; Fukumori et al., 2018). The northern, southern, and eastern boundaries were treated as open boundaries. A 10-grid point sponge layer was used on the boundaries with restoring time scales linearly varying from 2 days at the boundary to 5 days at the inner edge of the sponge.

The Arctic Subpolar gyre sTate Estimate (ASTE; Nguyen et al., 2017) provides initial and boundary conditions for the regional model. ASTE is a 2002–2017 medium-resolution ocean-sea ice state estimate for use in climate research. The horizontal grid spacing is approximately 13 km horizontally in Fram Strait and the Arctic. The model employs 50 vertical levels and uses the global ECCO state estimate latest release (ECCOv4r3; Forget et al., 2015; Fukumori et al., 2018) for lateral boundary conditions and the Japanese Reanalysis (JRA-55) for surface forcing. Through minimization of misfits with observations, ASTE represented well the horizontal temperature distribution, the circulation patterns, and the seasonal cycle of Fram Strait. However, biases in the vertical stratification remain. For this study, an early iteration of ASTE was used (hereafter called ASTEi9, where i9 refers to iteration 9 of the optimization). ASTEi9 shows low surface temperatures when compared to observations due to excess sea ice in Fram Strait. It also shows a subsurface maximum temperature at about a 200 m depth instead of the observed monotonically decreasing temperature with depth. This meant that the upper edge of the sound channel, which is observed to be at 600–900 m depth in Fram Strait, was not represented with sufficient accuracy for acoustic modeling in the ASTEi9. Therefore, the ASTEi9 data were bias-corrected with respect to climatology. This was done by comparing the 2010–2012 mean ASTEi9 fields with the mean World Ocean Atlas 2013 (WOA13) climatology. To do this both the ASTEi9 and WOA13 climatology fields were interpolated onto the Fram Strait regional model grid. The temperature and salinity difference between the two mean fields was then subtracted from the ASTEi9 output at all time steps to correct for the bias. The bias-corrected ASTEi9 fields were then used as initial and boundary conditions for the regional Fram Strait model. Additional processing on the meridional flow across the boundaries involved a transport correction to ensure the transport was identical to the ASTEi9 model transports at the respective boundaries in order to account for interpolation issues and bathymetry differences. The transport correction was implemented as a (very small) velocity correction at each respective boundary.

The Fram Strait MITgcm is forced with the Japanese Reanalysis (JRA-55), which has a temporal resolution of 3 h and a horizontal resolution of ∼55 km (Kobayashi et al., 2015). The forcing prescribed includes zonal and meridional components of the wind speed, air temperature, specific humidity, precipitation, and short- and long-wave down-welling radiation.

A snapshot of the model results (Fig. 2) shows the main circulation features in Fram Strait. The warm West Spitsbergen Current flows northward along the western edge of the Svalbard shelves. It splits on the northwestern corner of Svalbard into two branches. One branch continues northward along the western edge of the Yermak plateau, the other branch crosses the Yermak plateau eastward and flows along the northern shelf edge of Svalbard. The West Spitsbergen current sheds eddies on its western side feeding a recirculation of warm Atlantic Water throughout Fram Strait. The eddy shedding and recirculation is most intense between 78°N and 81°N. On the western side of Fram Strait cold polar waters flow south in the East Greenland Current. This current is strongest off the eastern Greenland shelf edge which agrees with observations.

FIG. 2.

(Color online) Model snapshot showing temperature and current field in Fram Strait. Temperatures and currents at 95 m depth on September 12, 2010. Only every fifth velocity vector in each direction is plotted for clarity.

FIG. 2.

(Color online) Model snapshot showing temperature and current field in Fram Strait. Temperatures and currents at 95 m depth on September 12, 2010. Only every fifth velocity vector in each direction is plotted for clarity.

Close modal

The model results from the Fram Strait regional model were compared to the Fram Strait 2002–2008 climatology measured by the 78°50′N mooring section across Fram Strait (Beszczynska-Möller et al., 2012) maintained by the AWI, Bremerhaven and the NPI in Tromsø. The distribution of warm Atlantic Water and Atlantic Recirculated Water in the Fram Strait regional model compares well to the climatology as obtained from Beszczynska-Möller et al. (2012) (Fig. 3). The lower boundary of the Warm Atlantic layer is realistic, and the westward extent of warm water from its core in eastern Fram Strait is largely correct. The regional model also shows a slight temperature maximum at 300 m depth in western Fram Strait that is present in the climatology. However, the cold surface water in western Fram Strait is not cold enough in the Fram Strait regional model. This area is insufficiently sampled by measurements especially during winter. Thus, the World Ocean Atlas likely was biased in this region, and that was then carried over to the Fram Strait regional model. The Fram Strait model showed slightly too cold Atlantic layer temperatures in central Fram Strait. This is consistent with the modeling efforts by Wekerle et al. (2017) where even higher horizontal resolutions than the ones employed in the regional model presented here were necessary to reproduce the full strength of eddy shedding from the West Spitsbergen Current into the central recirculation region. They considered their horizontal resolution of 1 km as eddy-resolving compared to their 4.5 km reference configuration that they considered to be eddy-permitting in Fram Strait.

FIG. 3.

(Color online) Fram Strait temperature cross-section at 78°50′N. Upper panel: long-term mean interpolated mooring measurements (2002–2008) from Beszczynska-Möller et al. (2012). Lower panel: mean model results from Fram Strait regional model (2010–2012).

FIG. 3.

(Color online) Fram Strait temperature cross-section at 78°50′N. Upper panel: long-term mean interpolated mooring measurements (2002–2008) from Beszczynska-Möller et al. (2012). Lower panel: mean model results from Fram Strait regional model (2010–2012).

Close modal

The model evaluation presented so far dealt exclusively with the mean state of Fram Strait. Now, the model is evaluated against a time series of temperature derived from the ACOBAR acoustic tomography experiment. These time series were obtained using inversion techniques on acoustic travel times along three paths between acoustic source and receiver moorings and were published in Dushaw and Sagen (2017). Minor updates to the time series were published by Dushaw (2017). The temperatures obtained by the inversion are range-averaged (167–301 km) along the acoustic paths and depth-averaged over a depth range of 0–1000 m.

In Fig. 4 we compare the inversion results of three ACOBAR acoustic thermometry sections with results from ASTEi9, the Fram Strait regional model, and World Ocean Atlas climatology. The three sections are the 301 km long section ACOBAR B-A, which crosses Fram Strait from west to east at 78°N, the 182 km long section A–D in eastern Fram Strait and the 167 km long section B–D in western Fram Strait (Fig. 1). The modelled temperature fields from the Fram Strait regional model and ASTEi9 were interpolated onto the acoustic paths of the ACOBAR experiment and the 0–1000 m depth. Comparison of range- and depth-averaged ocean temperatures from the two models with the ACOBAR inversion results showed that the bias of the Fram Strait model as compared to ASTEi9 is greatly reduced for sections A–B and A–D (Fig. 4). The bias was slightly reduced for sections B–D. For both sections A–B and B–D (Fig. 4) the model results were closer to the inversion results than the WOA09 climatology. The model results were comparable to the updated 2013 World Ocean Atlas edition (WOA13). WOA09 was used as a baseline in the inversion calculations (Dushaw and Sagen, 2017; Dushaw, 2017), WOA13 was used for the bias correction of the model initial and boundary conditions. In western Fram Strait (sections B–D) the World Ocean Atlas climatologies underestimates the observed temperatures of the acoustic thermometry experiment. Western Fram Strait is sparsely sampled by oceanographic measurements.

FIG. 4.

(Color online) Comparison of range-depth integrated temperatures (0–1000 m depth) along the three sections of the ACOBAR acoustic thermometry experiment: A to B (upper panel), A to D (middle panel), and B to D (lower panel). Inversion results from acoustic thermometry measurement (red dots: inverse result—one point per transmission, blue: cubic-spline smoothed time series; data from Dushaw, 2017). Fram Strait regional model results (gray), ASTE state estimate (cyan), World Ocean Atlas climatology (WOA09: red, WOA13: magenta).

FIG. 4.

(Color online) Comparison of range-depth integrated temperatures (0–1000 m depth) along the three sections of the ACOBAR acoustic thermometry experiment: A to B (upper panel), A to D (middle panel), and B to D (lower panel). Inversion results from acoustic thermometry measurement (red dots: inverse result—one point per transmission, blue: cubic-spline smoothed time series; data from Dushaw, 2017). Fram Strait regional model results (gray), ASTE state estimate (cyan), World Ocean Atlas climatology (WOA09: red, WOA13: magenta).

Close modal

The inversion results for sections A–B show an annual cycle with maximum temperatures in September and minimum temperatures in March–April. The amplitude of the seasonal cycle is about half a degree Celsius. Both the Fram Strait regional model and ASTEi9 show a seasonal cycle. The seasonal cycle in the models is phase shifted by about 50 days relative to the seasonal cycle in the inversion results and the seasonal amplitude in the model results is closer to 1 °C. Sections A to D do not show a discernible annual cycle in the temperature time series derived from acoustic thermometry. It seems that ASTEi9 shows a seasonal cycle for sections A–D, while the Fram Strait regional model shows some long-term variability but no clear seasonality. If there is an annual cycle in the inverse results for sections B–D, it is quite weak. There is no clear seasonal cycle in the models for this section. It should be noted that the thermometry observations cover only years which makes the study of long-term variations difficult. The Fram Strait regional model results show some temperature drift for all three ACOBAR sections (Fig. 4). Most likely this drift stems from the ASTEi9 state estimate which exhibits a similar drift.

The observed temperature time series derived by inversion from acoustic thermometry shows a lot of short-term variation. The short-term variability is especially pronounced in eastern Fram Strait where changes of 0.5 °C over the time span of a few days occur frequently. The Fram Strait regional model (3–6.5 km horizontal resolution) shows more short-term variability than the lower-resolution ASTEi9 state estimate (13 km horizontal resolution), but still strongly underestimates the high-frequency variability observed in the temperature inversions from acoustic thermometry. According to Wekerle et al. (2017), even a higher horizontal resolution of about 1 km would be necessary to get a realistic description of eddy-induced short-term variability in Fram Strait. Another approach could be to reduce the parameterized mixing to increase the variability, but this is outside the scope of this study.

Acoustic forward modeling on the hydrographic fields from the Fram Strait regional model was carried out using geometric rays. In Fram Strait, geometric rays give similar results to parabolic equation calculations (Sagen et al., 2017), with geometric rays being less numerically demanding. A comparison of the predicted acoustic time fronts from forward model runs using both the Fram Strait model and the observed hydrography as input proved that the acoustic model could reproduce some aspects of the observed acoustic arrival patterns. The acoustic forward modeling also managed to reproduce many predicted acoustic propagation paths within the range of their natural variability (Fig. 5). This is especially true for the SRBR arrivals, which are the focus of the research presented here. The model sometimes had an additional surface sound channel extending to section AD (Fig. 5, lower left panel). This causes additional refracted rays, which are trapped in this channel. In a weaker form, similar effects were also reported in Sagen et al. (2017), with refracted rays being predicted to jump from the main sound channel into a surface sound channel in section AD in 2011.

FIG. 5.

(Color online) ACOBAR section AD: Range average sound speed profiles (left panels) and ray paths of first four SRBR arrivals superimposed on sound speed anomaly relative to range-average profiles (right panels). The upper panels show the sound speed field from the CTD survey performed during September 15–17, 2011 and the corresponding ray predictions (Sagen et al., 2017). The middle panels show the sound speed field from the CTD survey performed during July 11–13, 2012 and the corresponding ray predictions (Sagen et al., 2017). The lower panels show the sound speed field from the Fram Strait regional model on September 16, 2011 and the corresponding ray predictions.

FIG. 5.

(Color online) ACOBAR section AD: Range average sound speed profiles (left panels) and ray paths of first four SRBR arrivals superimposed on sound speed anomaly relative to range-average profiles (right panels). The upper panels show the sound speed field from the CTD survey performed during September 15–17, 2011 and the corresponding ray predictions (Sagen et al., 2017). The middle panels show the sound speed field from the CTD survey performed during July 11–13, 2012 and the corresponding ray predictions (Sagen et al., 2017). The lower panels show the sound speed field from the Fram Strait regional model on September 16, 2011 and the corresponding ray predictions.

Close modal

Here we present comparisons of the forward model results based on the regional Fram Strait model with the acoustic observations from the ACOBAR experiment (Sagen et al., 2017). Figure 6 presents time series of signal travel times of the acoustic tomography signal along ACOBAR section A to D (Fig. 1) in eastern Fram Strait. These are compared to the predicted travel times based on hydrographic fields from the Fram Strait regional model. Despite a slight warming model drift the comparison revealed qualitative similarities in the structure and seasonal variability of model and observations, with the overall arrival structures displaying a high degree of stability (Fig. 6). Observations show the purely refracted arrivals with low arrival angles arriving first. They are followed by groups of, respectively 4, 6, and again 6 surface-reflected/bottom-reflected (SRBR) arrivals with alternating upward and downward arrival angles. We classify all arrivals with surface reflections and at least one bottom reflection as SRBR arrivals; SRBR arrivals can also contain one or several upward refractions. The modelled arrivals show the same patterns and number of arrivals. The second set of SRBR arrivals is more intermittent in the model predictions than in the observations. Geometric ray modeling shows that the SRBR arrivals with multiple bottom reflections correspond to very narrow windows in the source angle. These arrivals might therefore be sensitive to scattering or to small path changes due to ocean model biases. Sagen et al. (2017) reported one observed SRBR arrival missing in both geometric ray and PE predictions.

FIG. 6.

(Color online) Observed time series of acoustic arrivals for ACOBAR section AD (upper panel) and predicted time series of arrivals for section AD from Fram Strait regional model (lower panel). For the first deployment year of section AD no arrival angle information is available for the observations. Two arrivals discussed in Sec. IV are indicated by letters: F (violet) and M (green).

FIG. 6.

(Color online) Observed time series of acoustic arrivals for ACOBAR section AD (upper panel) and predicted time series of arrivals for section AD from Fram Strait regional model (lower panel). For the first deployment year of section AD no arrival angle information is available for the observations. Two arrivals discussed in Sec. IV are indicated by letters: F (violet) and M (green).

Close modal

The observed early acoustic arrivals show a seasonal signal. This is also present in the predicted arrivals, but the seasonal cycle is slightly masked by the drift in the ocean model (Fig. 6). Both model and observation show cooling events of about 30–50 days duration, cooling hereby corresponds to longer acoustic travel times. Because the upper ocean cools more than the deeper water the purely refracted arrivals are more sensitive to these cooling events than the SRBR arrivals. This leads to the purely refracted arrivals overlapping or even crossing (becoming later than) the first set of SRBR arrivals. In the ACOBAR observation such cooling events were observed around yearday 830 (relative to 2010) with the sound channel arrivals overlapping with the SRBR arrivals. There is possibly a similar event around yearday 450. However, no arrival angle information is available for the observations during the first year of the experiment (Sagen et al., 2017). It is therefore not possible to see if a similar overlapping of purely refracted arrivals and SRBR arrivals occurred in the observations of this year. The model shows a similar event at yearday 730 and an even stronger event at yearday 470, where the early arrivals are crossing the first set of SRBR arrivals.

Both model and observations show additional early purely refracted arrivals in the case of warming events, for example, at yearday 300 in the model or on several occasions between yearday 670 and 770 in the observations, warming events hereby correspond to periods of shorter acoustic travel times. Short-term warming events in the observations and model are caused by mesoscale variability and therefore generally do not coincide in time. The model shows less short-term variability than the range- and depth-averaged temperatures derived from the acoustic thermometry observations (Fig. 4).

The arrivals for ACOBAR section BD are characterized by greater temporal stability, and the sets of SRBR arrivals with arrival angles of about ±10° are very stable in time (Fig. 7). The late-arriving, high-angle rays are more intermittent than the earlier arrivals in both model and observations, and the early arrivals show a similar response to cooling in model and observations, although not synchronized. Figure 8 shows the complete 2-year dataset from both observations and model in arrival angle vs travel time space. The patterns of observed and predicted arrivals match. Model arrivals are slightly earlier than observed arrivals and the sound channel arrivals are more spread out in travel time for the model predictions compared to the observations. This is likely due to the slight model drift. The two SRBR arrivals between 115.5 and 116 s travel time, one with an upward and one with a downward arrival angle, are more intermittent in the observations than in the model predictions, likely because of smoothness of the model fields. The model predictions show that the early sound-channel arrivals coincide with a first set of deep-going arrivals. These are too close in arrival time and angle to the purely refracted arrivals to be detected separately in the observations. Their presence was therefore unknown before this model experiment and not considered when Dushaw and Sagen (2017) made inverse model estimates of temperature.

FIG. 7.

(Color online) Observed time series of acoustic arrivals for ACOBAR section BD (upper panel) and predicted time series of arrivals for section AD from Fram Strait regional model (lower panel). For the first deployment year of section AD no arrival angle information is available for the observations.

FIG. 7.

(Color online) Observed time series of acoustic arrivals for ACOBAR section BD (upper panel) and predicted time series of arrivals for section AD from Fram Strait regional model (lower panel). For the first deployment year of section AD no arrival angle information is available for the observations.

Close modal
FIG. 8.

(Color online) Observed acoustic arrival pattern for ACOBAR section BD as a function of travel time and arrival angle (upper panel). Predicted arrival pattern as a function of travel time and arrival angle for section BD from Fram Strait regional model (lower panel), color coded by source angle. Red: source angle >5°; gray: −5° ≤ source angle ≤5°; blue source angle <−5°.

FIG. 8.

(Color online) Observed acoustic arrival pattern for ACOBAR section BD as a function of travel time and arrival angle (upper panel). Predicted arrival pattern as a function of travel time and arrival angle for section BD from Fram Strait regional model (lower panel), color coded by source angle. Red: source angle >5°; gray: −5° ≤ source angle ≤5°; blue source angle <−5°.

Close modal

For ACOBAR section BA there is more differences between the observed acoustic arrivals and the predicted arrival pattern based on the Fram Strait regional model (Fig. 9). However, a close look reveals that these differences are mostly caused by predicted high-angle arrivals that are not registered in the observations. As these steep arrivals correspond to ray paths with multiple bottom reflections it can be assumed that the acoustic energy in these ray paths is attenuated by bottom interaction. Other than the missing arrivals the predicted arrival structure is again very similar to the observations. The high-angle arrivals observed at 207.2–208 s travel time correspond in arrival time and angle to the predicted SRBR arrivals from the Fram Strait regional model. Both model and observations show the early purely refracted arrivals to be more widely spread for section BA than for the shorter sections AD and BD, but the spread is much more pronounced in the observations. The additional spread in the observations is assumed to be caused by scattering by small-scale oceanographic variability (Dushaw et al., 2016), a process that is not captured by the regional model except for the largest scales.

FIG. 9.

(Color online) Observed time series of acoustic arrivals for ACOBAR section BA (upper panel) and predicted time series of arrivals for section BA from Fram Strait regional model (lower panel). The observed arrivals in the upper panel were used by Dushaw (2017) for the inversion to ocean temperature presented in Fig. 4.

FIG. 9.

(Color online) Observed time series of acoustic arrivals for ACOBAR section BA (upper panel) and predicted time series of arrivals for section BA from Fram Strait regional model (lower panel). The observed arrivals in the upper panel were used by Dushaw (2017) for the inversion to ocean temperature presented in Fig. 4.

Close modal

The Fram Strait regional model predicts SRBR rays with positive arrival angles of about 10° that are overlapping in travel time with the purely refracted arrivals. These SRBR arrivals were observed to arrive earlier than the purely refracted rays during seasonal cooling events (yearday 400–550 and 800–850 relative to 2010) (Fig. 9). During summer, when hydrographic sections were taken, these SRBR arrivals were not present in either acoustic observations or forward model predictions based on the hydrographic sections (Sagen et al., 2017). Thus, using ocean model fields as input to the acoustic raytracing enables us to identify and explain aspects of the arrival pattern variability that could not be explained before.

The comparison of arrival angle/travel time figures (Fig. 10) illustrates how ray predictions on the regional ocean model make it possible to also identify patterns in the acoustic observation that were not understood before. For example, occasional arrivals observed at 206.4 s travel time and −8° arrival angle can be identified as the intermittent arrival pattern predicted by the regional model at 206.25–206.5 s travel time and −9° arrival angle. Another arrival pattern at 206.4–207 s and at angles of +10° and −10° is predicted by the regional ocean model. These arrivals are generally overlapping with the purely refracted arrivals in the observations and not separable from these in the dot plots. Only during cooling events in winter time the arrival with +10° arrival angle separate from the purely refracted arrivals as discussed above (Fig. 9). Despite this overlap, the set of arrivals can be identified in the arrival angle/travel time plot (Fig. 10), because of the tilt between the positive and negative arrival angles, with the positive arrival angles arriving about 100 ms earlier than the negative arrival angle arrivals. Thus, we can prove that SRBR arrivals have in fact been observed as part of the main acoustic arrival for section BA, without being recognized as belonging to different ray paths (Sagen et al., 2017). This is very important information for inversions, as it proves that the assumptions employed by Dushaw and Sagen (2017) and Dushaw (2017) that all early arrivals belong to purely refracted rays does not hold for some acoustic tomography sections in Fram Strait.

FIG. 10.

(Color online) Observed acoustic arrival pattern for ACOBAR section BA as a function of travel time and arrival angle (upper panel). Predicted arrival pattern as a function of travel time and arrival angle for section BA from regional Fram Strait (lower panel), color coded by source angle. Red: source angle >5°; gray: −5° ≤ source angle ≤5°; blue: source angle <−5°.

FIG. 10.

(Color online) Observed acoustic arrival pattern for ACOBAR section BA as a function of travel time and arrival angle (upper panel). Predicted arrival pattern as a function of travel time and arrival angle for section BA from regional Fram Strait (lower panel), color coded by source angle. Red: source angle >5°; gray: −5° ≤ source angle ≤5°; blue: source angle <−5°.

Close modal

Travel time measurements from the acoustic tomography experiment in Fram Strait had been inverted to obtain time series of depth-range average sound speed and temperature (Dushaw and Sagen, 2017; Dushaw, 2017). For this inversion it was assumed that the early or main acoustic arrival was caused by sound traveling along purely refracted ray paths. As we have shown in Sec. III, this is not always the case. If the SRBR arrivals are prominent in the first arrival group and if their temporal variability is different than the variability of the refracted rays and if the SRBR arrivals are not excluded from the inversion, then we must assume that they can cause errors in the inversion results. Here we perform a worst-case test on the size of the possible error caused by the overlapping of refracted and SRBR arrivals. We have chosen three winter days from section BA, yeardays 459-461 (relative to 2010) containing 21 received acoustic transmissions. For this section and these days, the high-angle SRBR arrivals are arriving earlier than the lower-angle refracted arrivals (see Fig. 9). If the SRBR arrivals are interpreted as part of the refracted arrival for the inversion, they will cause a positive temperature bias to the inversion result. The original inversion scheme used the strongest early arrivals without regard to arrival angles (Dushaw, 2017). We rerun the inversion using only arrivals with arrival angles smaller than +5° and larger than −7°. This excludes especially the early SRBR arrival observed at section BA during winter. The results of this worst-case test are listed in Table I. Twenty-one received acoustic transmissions are used for this test. The early SRBR arrivals are among the strongest arrivals (which are used by the inversion scheme) for 7 of the received acoustic transmissions, 6 of these occur on yearday 461. This day can therefore serve as an indication of the maximum bias that can be expected from the use of SRBR arrivals in the inversion. The maximum bias observed on yearday 461 is noteworthy, but not dramatic. It is less than twice the expected theoretical uncertainty of the daily mean temperatures resulting from the inversion. The other two days are indicative of the uncertainty of the inversion result caused by the spread of the arrivals. Further testing revealed that the inversion scheme will rarely use the early SRBR arrival as the scheme picks only the six strongest arrivals for each received transmission to calculate the temperature inverse. Thus, we conclude that while it is best to use a condition on arrival angles in the future, the existing time series of inverted temperatures will only be biased by more than the expected theoretical uncertainties in a limited number of extreme cases.

TABLE I.

Results of testing the influence of SRBR arrivals on the inversions. Daily mean temperatures in this table are derived by the inversion method described in Dushaw and Sagen (2017) and Dushaw (2017). Standard deviations of daily mean temperatures were calculated from the spread of the temperatures of up to 8 received transmissions per day. In parentheses the expected uncertainties derived from the theoretical inverse uncertainty of 70 m°C for each received transmission are listed for comparison.

Yearday relative to 2010459460461
Number of acoustic receptions 8 (7 after excluding high-angle arrivals) 
Daily mean temperature [°C] from inversion using all arrivals 0.5352 ± 0.0431 0.5589 ± 0.0162 0.6605 ± 0.0141 
 (±0.0313) (±0.0247) (±0.0247) 
Daily mean temperature [°C] from inversion where steep rays are excluded 0.5170 ± 0.0367 0.6000 ± 0.0226 0.5954 ± 0.0119 
(±0.0313) (±0.0247) (±0.0265) 
Bias [°C] (difference between the two inversion results) 0.0182 ± 0.0566 −0.0411 ± 0.0278 0.0651 ± 0.0184 
 (±0.0443) (±0.0350) (±0.0362) 
Yearday relative to 2010459460461
Number of acoustic receptions 8 (7 after excluding high-angle arrivals) 
Daily mean temperature [°C] from inversion using all arrivals 0.5352 ± 0.0431 0.5589 ± 0.0162 0.6605 ± 0.0141 
 (±0.0313) (±0.0247) (±0.0247) 
Daily mean temperature [°C] from inversion where steep rays are excluded 0.5170 ± 0.0367 0.6000 ± 0.0226 0.5954 ± 0.0119 
(±0.0313) (±0.0247) (±0.0265) 
Bias [°C] (difference between the two inversion results) 0.0182 ± 0.0566 −0.0411 ± 0.0278 0.0651 ± 0.0184 
 (±0.0443) (±0.0350) (±0.0362) 

Sagen et al. (2017) showed that the early arrivals of acoustic receptions in Fram Strait were unstable. These arrivals correspond to purely refracted rays covering a depth range of approximately 0–1000 m. Sagen et al. (2017) also reported that the later SRBR arrivals are more stable than the purely refracted arrivals. The publication discusses the possibility of using these SRBR arrivals, which are usually ignored for inversions or data assimilation due to concerns about the sensitivity of these ray paths to the location of their bottom interaction. The regional ocean model for Fram Strait presented here gives the opportunity to study the time variability of the SRBR rays.

The prominent SRBR arrival F (see Fig. 6) is chosen as a test case for ray stability. This arrival corresponds to a bundle of rays with 6 surface reflections and 5 lower turning points/bottom reflections covering a depth range of approximately 0–2000 m (Geyer et al., 2018). The arrival is well defined and traceable, for the model data it is identified using travel time, source angle, and arrival angle of the geometric rays. There is substantial variability to the lower turning points and bottom reflections of the rays contributing to the arrival F (Fig. 11). This is reflected in a ray path length spread of more than 400 m. The time variability of the path length is also pronounced. Both jumps and gradual variations of path lengths are observed. An example for a jump occurs at yearday 30, when the shorter ray branch suddenly changes more than 200 m in length. Gradual variations are especially pronounced at yeardays 400–500. They are spanning ray path length variations of 300 m. This test was repeated with a second SRBR arrival (arrival M, see Fig. 6) yielding comparable results. The path length variations are somewhat smaller, on the order of 100 m, the variability of the bottom-reflection locations is larger than for arrival F, with two distinctly different groups of rays with identical number of turning points and reflections contributing to the arrival.

FIG. 11.

(Color online) SRBR arrival F, geometric ray model results using regional Fram Strait ocean model fields as input. Travel time (upper panel), ray path length (middle panel), and ray paths (lower panel). Ray paths are only plotted every 150th day for better readability.

FIG. 11.

(Color online) SRBR arrival F, geometric ray model results using regional Fram Strait ocean model fields as input. Travel time (upper panel), ray path length (middle panel), and ray paths (lower panel). Ray paths are only plotted every 150th day for better readability.

Close modal

From these results it can be concluded that SRBR arrivals in Fram Strait are unstable. As the refracted arrivals in Fram Strait are also unstable (Sagen et al., 2017; Dushaw and Sagen, 2017) it is not possible to use an assimilation scheme based on resolved, stable, identified arrivals for assimilating the measured acoustic travel times in Fram Strait. Dushaw and Sagen (2017) [with some minor technical updates in Dushaw (2017)], had developed a stochastic method that allowed the inversion of the acoustic thermometry measurements despite the lack of stable arrivals. They employed stochastically assigned sets of rays from a multitude of refracted ray paths derived by adding scattering by adding small meso-scale variations to the ocean profiles.

Considering the novelty of this approach it seems easier to use the inverse results derived by this method such as depth-range averaged temperatures or sound speeds (Dushaw and Sagen, 2017; Dushaw, 2017) for data assimilation in this region. This would separate the methodical uncertainties related to ray stability from the process of data assimilation. An alternative method would be to develop a ray-based assimilation system for non-stable rays using the stochastic method of Dushaw (2017).

Assimilation of path-average ocean observations such as acoustic thermometry observations or of depth-range averaged temperatures or sound speeds derived from acoustic thermometry observation by inversion should provide an improved description of water-mass exchanges through Fram Strait as they overcome the limitations of point measurements in an ocean environment were the Rossby radius of deformation is smaller than the technically and financially achievable horizontal resolutions of long-term moored oceanographic observation systems.

We want to thank Patrick Heimbach, An Nguyen, and Victor Ocana at the University of Texas, Austin, for giving us access to preliminary iteration 9 of ASTE. We also thank An Nguyen for useful discussions on ASTE. We want to thank Brian Dushaw for access to his inversion code and discussions about our tests. This paper relied on access to data collected and processed in the EU funded project ACOBAR (Grant No. 212887). The analysis of the data was carried out in the Norwegian Research Council projects ACOBAR II: Analysis and publication (Grant No. 226997) and UNDER-ICE (Grant No. 226373). The time series of range-depth averaged ocean temperature and the underlying measured travel times are formatted using international standards as a contribution from the H2020 project Integrated Arctic Observation System (INTAROS). INTAROS has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 727890. The data will be available through the Norwegian Marine Data Center. The completion of this paper was supported by institutional basic funding from the Norwegian Ministry of Climate and Environment and by support from the U.S. Office of Naval Research under the Canape-Under Ice project (Grant No. N62909-19-1-2012). The U.S. Office of Naval Research also supported a research visit by F.G. at Scripps Institution of Oceanography through the ONR Visiting Scientist Program (Grant No. 17-6-003). B.C. and H.J.V. were supported by ONR under the ONR Canape grant. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the Office of Naval Research. M.R.M. was supported by NASA NNX16AH67G, NSF OPP-1750035, NSF PLR-1425989.

1.
Beszczynska-Möller
,
A.
,
Fahrbach
,
E.
,
Schauer
,
U.
, and
Hansen
,
E.
(
2012
). “
Variability in Atlantic water temperature and transport at the entrance to the Arctic Ocean, 1997-2010
,”
ICES J. Marine Sci.
69
,
852
863
.
2.
de Steur
,
L.
,
Hansen
,
E.
,
Gerdes
,
R.
,
Karcher
,
M.
,
Fahrbach
,
E.
, and
Holfort
,
J.
(
2009
). “
Freshwater fluxes in the East Greenland Current: A decade of observations
,”
Geophys. Res. Lett.
36
,
L23611
, .
3.
Dushaw
,
B. D.
(
2017
). “
Estimating temperature in Fram Strait using DAMOCLES and ACOBAR acoustic tomography data by exploiting small-scale variability
,”
NERSC Technical Report 378
, Nansen Environmental and Remote Sensing Center, Bergen, Norway (November 6, 2017),
43
pp.
4.
Dushaw
,
B. D.
, and
Colosi
,
J. A.
(
1998
). “
Ray tracing for ocean acoustic tomography
,”
Appl. Phys. Lab. University of Washington, APL-UW TM
3-98,
31
pp.
5.
Dushaw
,
B. D.
, and
Sagen
,
H.
(
2016
). “
A comparative study of moored/point and acoustic tomography/integral observations of sound speed in Fram Strait using objective mapping techniques
,”
J. Atmos. Oceanic Tech.
33
,
2079
2093
.
6.
Dushaw
,
B. D.
, and
Sagen
,
H.
(
2017
). “
The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography
,”
J. Acoust. Soc. Am.
142
(
6
),
3541
3552
.
7.
Dushaw
,
B. D.
,
Sagen
,
H.
, and
Beszczynska-Möller
,
A.
(
2016
). “
On the effect of small-scale variability on the acoustic propagation in Fram Strait: The tomography forward problem
,”
J. Acoust. Soc. Am.
140
,
1286
1299
.
8.
Fenty
,
I.
, and
Heimbach
,
P.
(
2013
). “
Coupled sea ice–ocean-state estimation in the Labrador Sea and Baffin Bay
,”
J. Phys. Oceanogr.
43
(
5
),
884
904
.
9.
Forget
,
G.
,
Campin
,
J.-M.
,
Heimbach
,
P.
,
Hill
,
C. N.
,
Ponte
,
R. M.
, and
Wunsch
,
C.
(
2015
). “
ECCO version 4: An integrated framework for non-linear inverse modeling and global ocean state estimation
,”
Geosci. Model Develop.
8
,
3653
3743
.
10.
Fukumori
,
I.
,
Heimbach
,
P.
,
Ponte
,
R. M.
, and
Wunsch
,
C.
(
2018
). “
A dynamically consistent, multivariable ocean climatology
,”
Bull. Am. Meteor. Soc.
99
,
2107
2128
.
11.
Gaspar
,
P.
,
Grégoris
,
Y.
, and
Lefevre
,
J. M.
(
1990
). “
A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and Long-Term Upper Ocean Study site
,”
JGR Oceans
95
(
C9
),
16179
16193
.
12.
Geyer
,
F.
,
Sagen
,
H.
,
Cornuelle
,
B.
, and
Gopalakrishnan
,
G.
(
2018
). “
Setting up and testing a regional model for Fram Strait that can be used for the assimilation of acoustic tomography data
,”
NERSC Technical Report 389
, Nansen Environmental and Remote Sensing Center, Bergen, Norway (June 15, 2018),
34
pp.
13.
Hattermann
,
T.
,
Isachsen
,
P. E.
,
von Appen
,
W.-J.
,
Albretsen
,
J.
, and
Sundfjord
,
A.
(
2016
). “
Eddy-driven recirculation of Atlantic Water in Fram Strait
,”
Geophys. Res. Lett.
43
(
7
),
3406
3414
, .
14.
Ilıcak
,
M.
,
Drange
,
H.
,
Wang
,
Q.
,
Gerdes
,
R.
,
Aksenov
,
Y.
,
Bailey
,
D.
,
Bentsen
,
M.
,
Biastoch
,
A.
,
Bozec
,
A.
,
Böning
,
C.
,
Cassou
,
C.
,
Chassignet
,
E.
,
Coward
,
A. C.
,
Curry
,
B.
,
Danabasoglu
,
G.
,
Danilov
,
S.
,
Fernandez
,
E.
,
Fogli
,
P. G.
,
Fujii
,
Y.
,
Griffies
,
S. M.
,
Iovino
,
D.
,
Jahn
,
A.
,
Jung
,
T.
,
Large
,
W. G.
,
Lee
,
C.
,
Lique
,
C.
,
Ju
,
J.
,
Masina
,
S.
,
George Nurser
,
A. J.
,
Roth
,
C.
,
Salas y Mélia
,
D.
,
Samuels
,
B. L.
,
Spence
,
P.
,
Tsujino
,
H.
,
Valcke
,
S.
,
Voldoire
,
A.
,
Wang
,
X.
, and
Yeager
,
S. G.
(
2016
). “
An assessment of the Arctic Ocean in a suite of interannual CORE-II simulations. Part III: Hydrography and fluxes,”
Ocean Model.
100
,
141
161
.
15.
Jakobsson
,
M.
,
Mayer
,
L. A.
,
Coakley
,
B.
,
Dowdeswell
,
J. A.
,
Forbes
,
S.
,
Fridman
,
B.
,
Hodnesdal
,
H.
,
Noormets
,
R.
,
Pedersen
,
R.
,
Rebesco
,
M.
,
Schenke
,
H.-W.
,
Zarayskaya
,
Y.
,
Accettella
,
A. D.
,
Armstrong
,
A.
,
Anderson
,
R. M.
,
Bienhoff
,
P.
,
Camerlenghi
,
A.
,
Church
,
I.
,
Edwards
,
M.
,
Gardner
,
J. V.
,
Hall
,
J. K.
,
Hell
,
B.
,
Hestvik
,
O. B.
,
Kristoffersen
,
Y.
,
Marcussen
,
C.
,
Mohammad
,
R.
,
Mosher
,
R.
,
Nghiem
,
S. V.
,
Pedrosa
,
M. T.
,
Travaglini
,
P. G.
, and
Weatherall
,
P.
(
2012
). “
The International Bathymetric Chart of the Arctic Ocean (IBCAO) Version 3.0
,”
Geophys. Res. Lett.
39
,
L12609
, .
16.
Kobayashi
,
S.
,
Ota
,
Y.
,
Harada
,
Y.
,
Ebita
,
A.
,
Moriya
,
M.
,
Onoda
,
H.
,
Onogi
,
K.
,
Kamahori
,
H.
,
Kobayashi
,
C.
,
Endo
,
H.
,
Miyaoka
,
K.
, and
Takahashi
,
K.
(
2015
). “
The JRA-55 reanalysis: General specifications and basic characteristics
,”
J. Met. Soc. Jpn.
93
(
1
),
5
48
.
17.
Langehaug
,
H. R.
,
Geyer
,
F.
,
Smedsrud
,
L. H.
, and
Gao
,
Y.
(
2013
). “
Arctic sea ice decline and ice export in CMIP5 historical simulations
,”
Ocean Model.
71
,
114
126
.
18.
Losch
,
M.
,
Menemenlis
,
D.
,
Campin
,
J. M.
,
Heimbach
,
P.
, and
Hill
,
C.
(
2010
). “
On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations
,”
Ocean Model.
33
(
1–2
),
129
144
.
19.
Marnela
,
M.
,
Rudels
,
B.
,
Houssais
,
M.-N.
,
Beszczynska-Möller
,
A.
, and
Eriksson
,
P. B.
(
2013
). “
Recirculation in the Fram Strait and transports of water in and north of the Fram Strait derived from CTD data
,”
Ocean Sci.
9
,
499
519
.
20.
Nguyen
,
A.
,
Ocaña
,
V.
,
Garg
,
V.
,
Heimbach
,
P.
,
Toole
,
J.
,
Krishfield
,
R.
,
Lee
,
C.
, and
Rainville
,
L.
(
2017
). “
On the benefit of current and future ALPS data for improving Arctic coupled ocean-sea ice state estimation
,”
Oceanography
30
(
2
),
69
73
.
21.
Sagen
,
H.
,
Worcester
,
P. F.
,
Dzieciuch
,
M. A.
,
Geyer
,
F.
,
Sandven
,
S.
,
Babiker
,
M.
,
Beszczynska-Möller
,
A.
,
Dushaw
,
B. D.
, and
Cornuelle
,
B.
(
2017
). “
Resolution, identification, and stability of broadband acoustic arrivals in Fram Strait
,”
J. Acoust. Soc. Am.
141
(
3
),
2055
2068
.
22.
von Appen
, W.-J.
,
Schauer
,
U.
,
Hattermann
,
T.
, and
Beszczynska-Möller
,
A.
(
2016
). “
Seasonal cycle of mesoscale instability of the West Spitsbergen Current
,”
J. Phys. Oceanogr.
46
(
4
),
1231
1254
.
23.
Walczowski
,
W.
(
2013
). “
Frontal structures in the West Spitsbergen current margins
,”
Ocean Sci.
9
(
6
),
957
975
.
24.
Wekerle
,
C.
,
Wang
,
Q.
,
von Appen
,
W.-J.
,
Danilov
,
S.
,
Schourup-Kristensen
,
V.
, and
Jung
,
T.
(
2017
). “
Eddy-resolving simulation of the Atlantic Water circulation in the Fram Strait with focus on the seasonal cycle
,”
JGR Oceans
122
,
8385
8405
.