Data Assimilation of Range- and Depth-Averaged Sound Speed from Acoustic Tomography Measurements in Fram Strait

Florian Geyer aNansen Environmental and Remote Sensing Center, Bergen, Norway

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Ganesh Gopalakrishnan bScripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Hanne Sagen aNansen Environmental and Remote Sensing Center, Bergen, Norway

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Bruce Cornuelle bScripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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François Challet aNansen Environmental and Remote Sensing Center, Bergen, Norway

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Matthew Mazloff bScripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Abstract

The 2010–12 Acoustic Technology for Observing the Interior of the Arctic Ocean (ACOBAR) experiment provided acoustic tomography data along three 167–301-km-long sections in Fram Strait between Greenland and Spitsbergen. Ocean sound speed data were assimilated into a regional numerical ocean model using the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system. The resulting state estimate matched the assimilated sound speed time series; the root-mean-squared (RMS) error of the sound speed estimate (∼0.4 m s−1) is smaller than the uncertainty of the measurement (∼0.8 m s−1). Data assimilation improved modeled range- and depth-averaged ocean temperatures at the 78°50′N oceanographic mooring section in Fram Strait. The RMS error of the state estimate (0.21°C) is comparable to the uncertainty of the interpolated mooring section (0.23°C). Lack of depth information in the assimilated ocean sound speed measurements caused an increased temperature bias in the upper ocean (0–500 m). The correlations with the mooring section were not improved as short-term variations in the mooring measurements and the ocean state estimate do not always coincide in time. This is likely due to the small-scale eddying and nonlinearity of the ocean circulation in Fram Strait. Furthermore, the horizontal resolution of the state estimate (4.5 km) is eddy permitting, rather than eddy resolving. Thus, the state estimate cannot represent the full ocean dynamics of the region. This study is the first to demonstrate the usefulness of large-scale acoustic measurements for improving ocean state estimates at high latitudes.

Significance Statement

Acoustic tomography measurements allow one to observe ocean temperature in large ocean volumes under the Arctic sea ice by measuring sound speed, which is hard to synoptically observe by other methods. This study has established methods for assimilation of depth- and range-averaged ocean sound speed from an acoustic tomography experiment in Fram Strait. For the first time, a 2-yr time series of ocean sound from acoustic tomography has been assimilated into an ocean state estimate. The results highlight the use of ocean tomography in ice-covered regions to improve state estimates of ocean temperature.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Florian Geyer, florian.geyer@nersc.no

Abstract

The 2010–12 Acoustic Technology for Observing the Interior of the Arctic Ocean (ACOBAR) experiment provided acoustic tomography data along three 167–301-km-long sections in Fram Strait between Greenland and Spitsbergen. Ocean sound speed data were assimilated into a regional numerical ocean model using the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system. The resulting state estimate matched the assimilated sound speed time series; the root-mean-squared (RMS) error of the sound speed estimate (∼0.4 m s−1) is smaller than the uncertainty of the measurement (∼0.8 m s−1). Data assimilation improved modeled range- and depth-averaged ocean temperatures at the 78°50′N oceanographic mooring section in Fram Strait. The RMS error of the state estimate (0.21°C) is comparable to the uncertainty of the interpolated mooring section (0.23°C). Lack of depth information in the assimilated ocean sound speed measurements caused an increased temperature bias in the upper ocean (0–500 m). The correlations with the mooring section were not improved as short-term variations in the mooring measurements and the ocean state estimate do not always coincide in time. This is likely due to the small-scale eddying and nonlinearity of the ocean circulation in Fram Strait. Furthermore, the horizontal resolution of the state estimate (4.5 km) is eddy permitting, rather than eddy resolving. Thus, the state estimate cannot represent the full ocean dynamics of the region. This study is the first to demonstrate the usefulness of large-scale acoustic measurements for improving ocean state estimates at high latitudes.

Significance Statement

Acoustic tomography measurements allow one to observe ocean temperature in large ocean volumes under the Arctic sea ice by measuring sound speed, which is hard to synoptically observe by other methods. This study has established methods for assimilation of depth- and range-averaged ocean sound speed from an acoustic tomography experiment in Fram Strait. For the first time, a 2-yr time series of ocean sound from acoustic tomography has been assimilated into an ocean state estimate. The results highlight the use of ocean tomography in ice-covered regions to improve state estimates of ocean temperature.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Florian Geyer, florian.geyer@nersc.no

1. Introduction

The deep ocean strait between Greenland and Svalbard called Fram Strait (sill depth = 2545 m) is of special interest for Arctic oceanography and ocean modeling as it is the only deep connection between the Arctic Mediterranean and the other world oceans. Important water mass exchanges and heat transports occur through this strait, which climate models and ocean analyses need to estimate accurately to correctly represent, e.g., the stratification of the central Arctic Ocean. Warm bias in Atlantic Water inflow through Fram Strait has been identified as a cause for warm model biases in the central Arctic (Ilıcak et al. 2016). The ocean circulation of Fram Strait is complex: there is two-way transport through the strait with the warm and saline West Spitsbergen Current going northward on the eastern side of the strait and the cold and fresh East Greenland Current going southward on the western side of the strait (Fig. 1). The bathymetry in Fram Strait is complex as well, with ridges such as the Knipovich Ridge (a continuation of the Mid-Atlantic Ridge) and deep areas as the 5550 m Molloy Hole. The Fram Strait is north of 75°N, and the Rossby radius of deformation is small, about 4–6 km (von Appen et al. 2016) because of the large Coriolis parameter f and the weak water mass stratification in the area. Hattermann et al. (2016) discuss the importance of eddy shedding from the West Spitsbergen Current caused by baroclinic instabilities. All the above factors contribute to complex recirculation patterns of Atlantic Water within Fram Strait and strong mesoscale eddy activities.

Fig. 1.
Fig. 1.

Map of the study area. The black triangle denotes the acoustic paths between the ACOBAR moorings A, B and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots. The background is a snapshot of the temperature field at 95 m depth (model vertical level 12) for 19 Jun 2011 from the Fram Strait state estimate discussed in this publication.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

The Fram Strait has been observed year-round since 1997 by an array of repeatedly deployed oceanographic moorings at 78°50′N maintained by the Alfred Wegener Institute (AWI) and the Norwegian Polar Institute (NPI) (Beszczynska-Möller et al. 2012). This mooring section will hereafter be referred to as the AWI/NPI mooring section. The moorings have a horizontal spacing of 10 km on the upper shelf slope and 30 km in the deep area (Fig. 1). The moorings measure ocean temperature at up to five standard depth levels (Beszczynska-Möller et al. 2012). From September 2010 to September 2012 an acoustic tomography experiment took place in Fram Strait as part of the Acoustic Technology for Observing the Interior of the Arctic Ocean (ACOBAR) project (Sagen et al. 2017). It originally consisted of four acoustic moorings: three moorings were equipped with combined sound sources and acoustic receivers (moorings A–C), and one mooring was receiver only (mooring D). Mooring C was lost as the transceiver fell to the sea floor shortly after deployment (Sagen et al. 2017), but the remaining three moorings A, B, and D measured large-scale average ocean sound speed and temperature along three acoustic paths of 167–301 km length (Sagen et al. 2017; Table 1; Fig. 1). Sound source B transmitted eight times every day and sound source A transmitted eight times every other day. The large-scale measurement of ocean sound speed was considered a complementary measurement to the point measurements from the mooring section with their limited vertical resolution. In Fram Strait sound speed can be easily converted to ocean temperature as the two variables are mostly equivalent (Dushaw et al. 2016a).

Table 1.

Position of moorings in ACOBAR acoustic tomography experiment.

Table 1.

The acoustics in Fram Strait turned out to be as complex as the oceanography. Deep-propagating rays gave stable acoustic arrivals but had ocean bottom reflections that made them unusable for the inversion to ocean sound speed (Geyer et al. 2020). The shallower, refracted rays were scattered by the energetic small-scale oceanic variability in Fram Strait (Dushaw et al. 2016b). Thus, instead of the standard inversion of stable ray arrivals to ocean sound speed and temperature a new statistical approach to the inversions was necessary. This new approach was developed in Dushaw et al. (2016b) and Dushaw and Sagen (2017). The resulting sound speed and temperature data together with a complete overview of the inversion procedure and quality control can be found in Geyer et al. (2020). Important for this study is that the new technique did not yield any depth information for the measured sound speed and temperature from the ACOBAR acoustic tomography experiment, but rather gave range- and depth-averaged ocean sound speed and temperature for 0–1000 m depth.

This work will present the first attempt to assimilate the range- and depth-averaged sound speed measurements from the ACOBAR acoustic experiment into a regional ocean circulation model. Geyer et al. (2020) demonstrated the value of these data for model validation. Here we attempt to assimilate these data into an ocean model and assess the impact of the constraints by comparing to withheld noncollocated AWI/NPI mooring section data. We aim to provide a better understanding of which aspects of the ocean circulation in Fram Strait were captured by the acoustic measurements.

Besides informing Fram Strait dynamics, we also aim to test methods for acoustic assimilation in the region. Previous work by Gopalakrishnan et al. (2021) has shown the feasibility of assimilating acoustic travel times in the Philippine Sea. They employed the Massachusetts Institute of Technology General Circulation Model–Estimating the Circulation and Climate of the Ocean four-dimensional variational (MITgcm-ECCO 4DVAR) assimilation system for that purpose, as we do here. However, the acoustic ray paths in Fram Strait are not stable (Dushaw et al. 2016b) making the assimilation of acoustic travel times problematic in this region. Instead, in this work we aim to see if we can constrain the model by assimilating inversion-based estimates of the range- and depth-averaged sound speeds. Here we determine the extent that assimilation of these depth-averaged inversions results could still yield an improved ocean state.

Regardless of observation type, assimilation in Fram Strait is a challenging task. This region is characterized by energetic small-scale variability (von Appen et al. 2016). The Rossby radius of deformation is 4–6 km in the region, 10 times smaller than in the Philippine Sea. High model resolution is thus needed to resolve these dynamics, and high data density is thus needed to constrain them. Moreover, the data must be dense in time to work with the linearity assumptions in our 4DVAR assimilation system and the length of the time window had to be reduced from 2 months to 20 days. These difficulties also motivated the withholding of the AWI/NPI mooring section to provide comprehensive independent observations for the evaluation of the state estimate.

Section 2 will describe the MITgcm-ECCO 4DVAR assimilation system used for this study. Section 3 will evaluate if the data assimilation worked in a technical sense by comparing the state estimate with the assimilated ocean sound speed time series. Section 4 will evaluate the state estimate using the AWI/NPI mooring section as an independent set of measurements. Section 5 investigates if the ocean state estimate will improve the modeled acoustic arrivals of the ACOBAR acoustic tomography experiment. The discussion in section 6 will try to put the state estimate in an oceanographical context and see if something can be learned from the comparison of acoustic measurements, oceanographic moorings, and the state estimate.

2. Methods

a. Numerical model

The ocean model employed for this data assimilation study is identical to the regional ocean model employed to study the observed acoustic propagation in Fram Strait as measured by the ACOBAR experiment (Geyer et al. 2020). The model used in Geyer et al. (2020) is without data assimilation and will be referred to as the forward model in this manuscript. It is a regional MITgcm-ECCO model with 52 vertical z levels and has a horizontal resolution of approximately 4.5 km. It uses Japanese 55-year Reanalysis (JRA-55; Kobayashi et al. 2015) atmospheric forcing and a preliminary version of Arctic Subpolar Gyre State Estimate (ASTEi9; Nguyen et al. 2017), which was bias corrected using the World Ocean Atlas (WOA13) as boundary conditions (Locarnini et al. 2013; Zweng et al. 2013). The forward model produced oceanographic fields for 2010–12, which were evaluated using both oceanographic and acoustic measurements (Geyer et al. 2020). A more recent version of ASTE, Nguyen et al. (2021) is now available, but for comparability to the forward model solution the bias-corrected ASTEi9 was used as boundary conditions for the data assimilation experiments. The regional ocean model does not include tides; therefore, daily averaged ocean sound speed was assimilated.

b. Assimilation system

The range- and depth-averaged sound speed measurements were assimilated using an adjoint-based MITgcm-ECCO 4DVAR system. An assimilation window of 20 days was selected based on sensitivity experiments and the data assimilation for the ACOBAR period of September 2010–July 2012 was carried out in a nonoverlapping series of 20-day segments. The cost function, defined by the weighted sum of squares of model–data misfit and adjustments to control variables (here temperature and salinity initial conditions: T0/S0, open-ocean boundary conditions, atmospheric forcings), over each 20-day segment was minimized through iterative gradient optimization. The number of iterations required for the convergence of the cost function ranged between 9 and 50 iterations over the series of 20-day segments for the 2010–12 period, with a convergence criterium of the cost descend being less than 1% of the initial cost and small in absolute terms. For the first 20-day assimilation segment, the solution from the forward model was used as the initial conditions, and the end state of the resulting optimized solution was then used as initial conditions for the next 20-day assimilation segment and the procedure is continued for the rest of the 20-day segments for September 2010–July 2012. The optimized solutions from each 20-day segment were then merged to form the long-term 2010–12 state estimate. The length of the assimilation segment was limited by the nonlinearity of the regional ocean model. Attempts to find configurations capable of carrying out the assimilation in segments of 30 days’ length included changing advection schemes, switching from no-slip to free-slip boundary conditions, and varying the viscosity/diffusivity conditions of the adjoint versus the forward run. All such attempts failed in that they did not manage to descend the cost function for a 30-day test segment.

c. Uncertainties of acoustic data

The observations that were assimilated were daily averages of the range- and depth-averaged sound speed time series published in Geyer et al. (2022). This time series had been derived from acoustic travel times by inversion. The inversion results have only a small statistical uncertainty of 0.43 m s−1 for each measurement (Dushaw and Sagen 2016). The statistical errors were regarded as independent for each acoustic transmission; therefore, the uncertainties of the daily averages used for the acoustic data assimilation in this work will be smaller by n, where n is the number of received transmission for a specific day. However, there is an offset of 0.62 m s−1 between the reciprocal measurements from A to B and B to A. This offset was already present in the measured travel times of the acoustic experiment. Sagen et al. (2017) attributed this offset to a source delay. As it is not possible to quantify the source delay more precisely, the offset between the reciprocal paths will be treated as a systematic error of the measurement and is added to the uncertainty estimate of the daily sound speed measurement calculated from the statistical error. The resulting mean uncertainties for the acoustic sound speed measurements for the four acoustic sections are 0.83 m s−1 (section A–B), 0.82 m s−1 (section B–A), 0.79 m s−1 (section A–D), and 0.80 m s−1 (section B–D). These uncertainties in the ocean sound speed measurements are equivalent to temperature uncertainties of 0.10°C (statistical uncertainty) and 0.14°C (estimate of systematic error). The resulting mean uncertainties for the temperature measurements are 0.19°C (section A–B) and 0.18°C (sections B–A, A–D, and B–D). Variograms of the assimilated sound speed time series were calculated and showed a significant loss of predictability after 10 days of less. This can be used as an upper bound of the decorrelation time of the system and shows that the length of the assimilation window (20 days) is long compared to the dynamics of the region.

d. Model controls

The time-dependent model controls (open-ocean boundary conditions, atmospheric forcings) were determined daily with linear interpolation between daily values. The background error covariances for model controls were estimated from the forward model solution for T0/S0 and open-ocean boundary condition, and the NCEP–NCAR reanalysis project (NCEP–NCAR R1; Kalnay et al. 1996) for atmospheric forcings. The NCEP–NCAR reanalysis standard deviation for 2004–10 was hereby used without removing its seasonality and we assume the background uncertainty covariances to be diagonal.

3. Model evaluation I: Comparison to assimilated range- and depth-averaged time series

To evaluate if the data assimilation was successful in a technical sense, time series of sound speed and ocean temperature from the forward model and the state estimate were compared to the assimilated acoustic measurements. Since the range- and depth-averaged sound speed had been assimilated, sound speed will be used for model–data comparison with the statistics of the sound speed and ocean temperature comparison summarized in Tables 24.

Table 2.

Statistical comparison of sound speed and ocean temperature reproduced by the forward model and ocean state estimate with acoustic measurements from the ACOBAR experiment for acoustic sections A–B and B–A (reciprocal paths, range averaged and 0–1000 m depth averaged temperature). The mean uncertainties of the daily averaged measurements are 0.83 m s−1 and 0.19°C for path A–B and 0.82 m s−1 and 0.18°C for path B–A.

Table 2.
Table 3.

Statistical comparison of sound speed and ocean temperature reproduced by the forward model and ocean state estimate with acoustic measurements from the ACOBAR experiment for acoustic section A–D (range averaged and 0–1000 m depth averaged temperature). The mean uncertainties of the daily averaged measurements are 0.79 m s−1 and 0.18°C.

Table 3.
Table 4.

Statistical comparison of sound speed and ocean temperature reproduced by the forward model and ocean state estimate with acoustic measurements from the ACOBAR experiment for acoustic section B–D (range averaged and 0–1000 m depth averaged temperature). The mean uncertainties of the daily averaged measurements are 0.80 m s−1 and 0.18°C.

Table 4.

Biases for the forward model and state estimate were always calculated as the time-mean difference between model and observation for the period 1 September 2010–31 July 2012. The model–observation differences were calculated before taking the mean; therefore, only model data for dates with measurements are used in the calculations. The same approach was taken for the calculation of root-mean-squared (RMS) errors and correlation coefficients, except for the model variances used to scale the correlation coefficients, which were calculated for the whole period of 1 September 2010–31 July 2012.

Figure 2 shows the comparison to the reciprocal measurements from the acoustic sections A–B and B–A. The state estimate reproduces the assimilated sound speed time series on this section well, with the RMS error reduced and the correlation to the sound speed measurements increased (Table 2). The mean bias was small for both the forward model and the state estimate.

Fig. 2.
Fig. 2.

Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at reciprocal acoustic sections A–B and B–A (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bars in the corner denote the uncertainty estimate of the measured time series (A–B: 0.83 m s−1; B–A: 0.82 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

For acoustic section A–D in eastern Fram Strait, the forward model had a strong warm bias (higher sound speed), which is reduced by the state estimate (Table 3), and the state estimate follows the assimilated sound speed time series with a correlation coefficient of 0.95 (Fig. 3), and a more than 70% reduction in the RMS error from the forward model (Table 3). Similarly, the data assimilation improves the modeled sound speed time series for section B–D in terms of bias, RMS error and correlation coefficient (Fig. 4, Table 4).

Fig. 3.
Fig. 3.

Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at acoustic sections A–D (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bar in the corner denotes the uncertainty estimate of the measured time series (0.79 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Fig. 4.
Fig. 4.

Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at acoustic section B–D (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bar in the corner denotes the uncertainty estimate of the measured time series (0.80 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Tables 24 summarize the comparisons for both ocean sound speed and ocean temperature. The temperature statistics are included to allow comparison of the results presented here to those in sections 4 and 6. The results for temperature are very similar to those for sound speed. Only for section B–D the temperature bias is about 0.05°C lower than the sound speed bias would suggest (Table 4). As this small temperature offset is the same for both the forward model and state estimate, it is assumed to be a slight error in the sound speed to temperature conversion by Dushaw et al. (2016a) for the fresher water of western Fram Strait.

In addition to the measured sound speed time series, the forward model results and the final state estimate, Figs. 24 also display the comparison to iteration 0 (called first-guess or reference solution) of each assimilation segment, i.e., the forward model simulation initialized from the end of the state estimate for the previous 20-day segment which provides the initial cost function for the assimilation. For all sections, there are no available measurements from August 2011 to late September 2011. During this time period the moorings were recovered and prepared for redeployment. For this period the model solution was without data assimilation; i.e., only iteration 0 (reference solution) was simulated for each assimilation segment. This time period also serves as a test that the state estimate will not drift back to the state of the forward model, at least not within 6 weeks. The stability of the corrections by the data assimilation indicates that the state estimate is successful. On the other hand, for sections A–D (Fig. 3) and B–D (Fig. 4), the state estimate drifts during the gap in the observations, not toward the warmer forward model result, but in the opposite direction. The reason for this is unknown, but at section B–D the initial forward simulation (reference run) has this cooling tendency during much of the experiment (Fig. 4, dashed black lines), this cooling is then corrected by the data assimilation in the final state estimate (Fig. 4, red line).

4. Model evaluation II: Comparison to independent data

The oceanographic evaluation of an ocean state estimate is usually done by comparison to independent data, meaning measurements not used in the data assimilation. The long-term oceanographic AWI/NPI mooring data were used for this purpose. This comparison was carried out for temperature, not sound speed, as the salinity data of the moorings below 250 m depth are unreliable (A. Beszczynska-Möller 2022, personal communication). An estimate of ocean sound speed could still have been calculated, as the influence of salinity on ocean sound speed in Fram Strait is small (Dushaw et al. 2016a), but it seemed preferable to compare to a directly measured variable, temperature. The aim of the oceanographic evaluation was mainly to address two questions. First, can the assimilation of temperature/sound speed measurements at one location in Fram Strait improve the large-scale temperatures at another location about 100 km away from the assimilated measurements despite the chaotic nature of the small-scale variability in Fram Strait? Second, what are the limitations of using a range- and depth-averaged measure of temperature or sound speed for the assimilation; i.e., will the lack of depth information cause unrealistic results?

The temperature data from the AWI/NPI mooring section are sparse, especially in the vertical. To facilitate the comparison of model and in situ data, temperature data from the mooring section were interpolated over the period 1997–2016 following the method detailed in Challet et al. (2022). This interpolation method can be decomposed into two steps, both based on ordinary kriging, which estimates the value of a quantity at a point in a region for which a variogram is known (Wackernagel 1995). First, the low-frequency variability of temperature anomalies was estimated at instrument locations where part of the data was missing. When tested on known data, this first kriging algorithm was found to significantly reduce errors compared to using the uncorrected seasonal cycle. The second kriging step estimated daily temperature values at each point of a regular grid with a horizontal resolution of 0.5° and 25 vertical levels. The final interpolated product was quality checked by comparisons with CTD observations (Schauer and Wisotzki 2010; Beszczynska-Möller and Wisotzki 2012) to confirm that the vertical temperature profiles were realistic at depths far from any moored instruments and that the interpolation algorithm was not generating any obvious systematic bias.

The total uncertainty of each interpolated value, thereafter named “pointwise uncertainty,” was calculated. The average pointwise uncertainty is 0.57°C between 6°W and 8°E for the upper 1000 m of the ocean over the period of the ACOBAR experiment. The extension variance of kriging over the whole section was then calculated; it gives a statistical uncertainty of 0.23°C for the range–depth average. This statistical uncertainty on the range–depth average is smaller than the pointwise uncertainty since it is calculated from the temperature estimates on a large number of grid points and part of the kriging errors cancel out. This uncertainty value is however quite sensitive to the choice of the kriging variogram.

An independent estimate of the uncertainty of the range-depth average was obtained from a comparison with CTD observations. The range-depth averaged interpolation error was calculated where and when CTD profiles were available, and the horizontal correlation scale was calculated to estimate the number of independent error profiles over the section. This approach provided an uncertainty for the range-depth average temperature of 0.16°C, which is comparable to the value calculated from the kriging variogram.

The comparison of the time series of range- and depth-averaged temperature at the AWI/NPI mooring section (0–1000 m depth, 6°W–8°E) shows that the state estimate generally matches the measured temperatures better than the forward model (Fig. 5, Table 5). The temperatures from the state estimate are mostly within the range of variability of the measurements, except for a period in the summer of 2011 (July–September 2011), when the temperatures are underestimated by 0.2°–0.4°C. This period overlaps with the period when acoustic measurements were not available, but the temperature underestimation starts one month before the gap in the measurements. Table 5 shows the corresponding reduction of mean bias and RMS error. The bias and RMS error of the state estimate are withing the statistical uncertainty of the measurement. However, the correlation with the measurements did not increase from the forward model to the state estimate. This is likely because of the small spatial scales of the short-term temperature variations in Fram Strait. The state estimate shows more short-term variability than the forward model and is in this respect more similar to the interpolated mooring time series, but the variations of state estimate and mooring time series do not coincide in time.

Fig. 5.
Fig. 5.

Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at the AWI mooring sections (interpolated temperature field at 78°50′N from 6°W to 8°E and 0–1000 m depth). The error bar in the corner denotes the uncertainty estimate of the interpolated mooring time series (0.23°C). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Table 5.

Statistical comparison of forward model and ocean state estimate to the interpolated temperature from the AWI/NPI mooring section (78°50′N, average temperature from 6°W to 8°E and 0–1000 m depth). The uncertainty of the interpolated measured temperature is 0.23°C.

Table 5.

The comparison between the section-averaged time-mean measured and modeled vertical temperature profiles at the AWI/NPI mooring section shows that the forward model overestimates the ocean temperature below 250 m depth by up to 1.5°C (Fig. 6, left panel). The data assimilation cools the ocean in the upper 1000 m for the model. This causes an underestimation of ocean temperatures in the upper 500 m, while temperatures at greater depth are still slightly overestimated. The underestimation of temperature in the state estimate is worst for 50–300 m depth, where it is more than 1.5°C. This shows the limitation of using a depth-averaged acoustic observation for ocean state estimation, where the overall improvement of ocean temperature at 0–1000 m depth is not reflected at all depth layers.

Fig. 6.
Fig. 6.

(left) Section-averaged time-mean measured and modeled vertical temperature profiles at the AWI/NPI mooring section (78°50′N, section averaged over 6°W–8°E); (center) as in the left panel, but for western Fram Strait only (6°–2°W); (right) as in the left panel, but for central and eastern Fram Strait only (2°W–8°E).

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Splitting the section into a western part (Fig. 6, center panel) and a central and eastern part (Fig. 6, right panel) shows that the data assimilation causes the Atlantic Water layers in the state estimates to be cooler than they were in the forward model. This cooling of the Atlantic Water occurs throughout Fram Strait. The underestimation of upper ocean temperatures caused by the data assimilation is concentrated on central and eastern Fram Strait.

Section plots of the bias for the forward model (Fig. 7) and the state estimate (Fig. 8) show that the forward model consistently overestimates ocean temperatures at 400–1000 m depth across Fram Strait. The overestimation is strongest over the continental slopes on both sides of the strait. The data assimilation has reduced this bias in the state estimate by more than half. Both the forward model and the state estimate underestimate the temperatures at 0–300 m depth in central and eastern Fram Strait. The underestimation is much stronger in the state estimate than in the forward model results. Both the forward model and state estimate overestimate the temperature at 0–200 m depth in western Fram Strait; this overestimation is reduced in the state estimate compared to the forward model.

Fig. 7.
Fig. 7.

Bias of forward model relative to interpolated mooring section at 78°50′N.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Fig. 8.
Fig. 8.

Bias of state estimate relative to interpolated mooring section at 78°50′N.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

5. Model evaluation III: Acoustic evaluation

In this work an inversion product derived from acoustic observations was used for the first time to constrain an ocean model. An earlier study in the Philippine Sea had directly used measured acoustic travel times for data assimilation (Gopalakrishnan et al. 2021). This was not possible in Fram Strait, because the complex oceanographic and acoustic conditions make the refracted rays unstable (Dushaw et al. 2016b). It is therefore important to test if the data assimilation of the inversion product, the time series of range- and depth-averaged ocean sound speed, can improve the simulated acoustic arrival pattern. It is not a priori clear if such an improvement can be achieved, as the acoustic propagation, especially of the refracted rays, is dependent on the position and shape of the ocean sound channel, while the assimilated range- and depth-averaged sound speed does not contain any depth-dependent information.

The acoustic observations of the ACOBAR experiment, i.e., the acoustic transmissions between the ACOBAR moorings A, B, and D, were simulated using geometric ray modeling on daily sound speed fields from both the forward model and the ocean state estimate. The “eigenray” Fortran code used for the geometric ray modeling is the same as employed in Geyer et al. (2020). The ocean sound speed fields from the forward model and state estimate were calculated using the sound speed equation of Del Grosso (1974). Ocean temperatures and salinities were slightly smoothed in the vertical before the sound speed calculation using least squares cubic splines. The smoothing was performed to prevent sharp gradient changes close to the surface, which can be problematic for geometric ray modeling.

Figure 9 shows the comparison of simulated and observed arrival patterns for ACOBAR acoustic section B–D. The acoustic arrivals corresponding to refracted acoustic rays (Fig. 9, gray dots) are clearly improved from the forward model to the ocean state estimate. The forward model had predicted the refracted acoustic arrivals about 0.3 s too early, while the state estimate predicts the observed refracted arrivals correctly, both the mean travel time of the arrivals as well as the spread in arrival time and the shape of the arrival distribution in arrival-time/arrival-angle space are improved. Changes in the surface-reflected/bottom-reflected (SRBR) arrivals are small (red and blue dots in Fig. 9). This is expected because these rays are not as sensitive to the ocean sound speed as refracted rays. Similar improvements in the simulated refracted ray arrivals were also achieved for the acoustic sections A–D and A–B (not shown).

Fig. 9.
Fig. 9.

Comparison of (top) observed and modeled acoustic arrival patterns [(middle) state estimate and (bottom) forward model]. The arrival pattern is displayed as a function of acoustic travel time and the arrival angle of acoustic rays from the horizontal. For the modeled arrival pattern, the source angle is indicated by color (red: source angle > 5°; gray: −5° ≤ source angle ≤ 5°; blue: source angle > −5°). Arrivals with low absolute source and arrival angles (gray) correspond to refracted acoustic rays, arrivals with high absolute source and arrival angles (red, blue) correspond to surface-reflected/bottom-reflected (SRBR) rays.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

6. Differences in the horizontal temperature distribution caused by the data assimilation

Horizontal maps of time-mean ocean temperature and currents at 500 m depth are presented for both the forward model (Fig. 10) and the state estimate (Fig. 11). Figure 12 shows a map of the time-mean temperature difference between the two model outputs, i.e., the state estimate minus the forward model results. This illustrates the effect of the data assimilation on the horizontal temperature at 500 m depth. This is the depth with the smallest biases of the state estimate compared to the AWI/NPI mooring section. The biggest difference that can be detected is a cooling of the northward West Spitsbergen Current from about 2° south of ACOBAR mooring A, this cooling is strongest just south of mooring A. It affects several downstream areas: the Atlantic Water inflow to the Yermak Plateau branch, the central area of Fram Strait around mooring D and to the north of it, where the recirculation branch of Atlantic Water is located, as well as the southward-flowing returning Atlantic Water on the western side of Fram Strait. The outer (western) part of the West Spitsbergen Current is also slowed down (indicated by the southward arrows in Fig. 12), while the inner (eastern) part of the West Spitsbergen Current is faster in the state estimate than in the forward model. The cooling caused by the data assimilation reduced the strong warm bias of the forward model compared to both the acoustic section A–D in eastern Fram Strait and the AWI/NPI mooring section. The forward model is more than 0.5°C warmer compared to both measurements (Figs. 3 and 5). Some cooling occurs along acoustic section B–D as well (Fig. 12, Table 4). The state estimate at section B–D is warmer than at sections A–D and A–B/B–A (Fig. 11), a similar temperature difference between the sections was observed by the acoustic measurements (Figs. 24). While the size of the temperature difference varies with depth (Fig. 6), the horizontal structure of the change was quite uniform with depth, so the corresponding temperature difference map at, e.g., 300 m depth or 700 m depth (not shown), looks similar to the map presented here (Fig. 12) except for scaling. This is expected because of the lack of vertical resolution in the observations.

Fig. 10.
Fig. 10.

Time-mean ocean temperature and current field at 500 m depth in forward model (1 Sep 2010–31 Jul 2012). The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Fig. 11.
Fig. 11.

Time-mean ocean temperature and current field at 500 m depth in state estimate (1 Sep 2010–31 Jul 2012). The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

Fig. 12.
Fig. 12.

Time-mean difference of modeled mean ocean temperatures and currents at 500 m depth between ocean state estimate and forward model (1 Sep 2010–31 Jul 2012), illustrating the effect of the data assimilation. A gray contour line marks the contour of zero temperature difference. Maximum and minimum temperature differences are +0.94° and −1.84°C, respectively. The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

Citation: Journal of Atmospheric and Oceanic Technology 40, 9; 10.1175/JTECH-D-22-0132.1

It is not easy to assess the physical meaning of the differences mapped here, although they are not a priori unphysical and fulfil the criteria of fitting both the assimilated (range- and depth-averaged) temperatures along the acoustic sections, as well as matching within error bars the (not assimilated) measured temperatures at the AWI/NPI mooring section at this depth. On the other hand, the same horizontal pattern of cooling that improved temperatures at 500 m depth leads to too-cold ocean temperatures at 0–300 m depth in central and eastern Fram Strait (2°W–8°E; see Fig. 8). A possible explanation might be that, while the pattern of change might be appropriate at 500 m depth, it should not have occurred so uniformly over the whole water column. There are obvious limitations to the degree of realism that can be achieved by the assimilation of depth-averaged acoustic data, which do not constrain the ocean temperature at 100 m depth relative to 500 m depth, for example.

Ideally, the best possible state estimate for Fram Strait would combine both accurate large-scale measurements of temperature (or sound speed), such as acoustic travel times provide, as well as point measurements containing information about the temperature distribution with depth. Dushaw and Sagen (2016) had shown how these two types of measurements are complementary when combined using objective mapping techniques. The same should apply to data assimilation. It also should be noted that the main biases in this state estimate occur at ocean depths of 0–200 m. This depth range is relatively well covered by instrumentation in the AWI/NPI mooring section; therefore, assimilation of these data can be expected to improve state estimate biases at this depth range.

7. Conclusions

This study presents the first data assimilation of acoustic measurements of ocean sound speed into a numerical ocean model in the Arctic. It demonstrates the utility of acoustic tomography measurements to constrain the unique ocean hydrography in Fram Strait. The overall improvement of the ocean state estimate in Fram Strait was obtained despite the limited resolution of the ocean model (eddy permitting, not eddy resolving), the strongly eddying oceanography, and the complex acoustics in this region.

Using the ACOBAR acoustic tomography measurements to constrain an ocean state estimate of Fram Strait presented unique challenges: The eddying environment causes strong nonlinearity of the ocean circulation which is difficult to match in the ocean state estimate. This limits the segment length that can be used for data assimilation by the 4DVAR method, the decorrelation time of the model system forced a segment length of 20 days for the assimilation. Tests with a segment length of 30 days were not successful. Furthermore, the instability of refracted acoustic ray paths forced the use of range- and depth-averaged time series of ocean sound speed (an inversion product) for the data assimilation instead of using the direct acoustic travel time measurements. This demonstration of nonstandard acoustic measurements in a numerical ocean reanalysis is meant to encourage the more widespread use of acoustic measurements in oceanographic research in the Arctic region or other regions where acoustic ray paths are variable. The developed methodology can be applied in the future for deep basins of the Arctic Ocean, where assimilation of averaged sound speed data from acoustic tomography (provided by recent international projects and observational campaigns) would potentially improve state estimates of ocean temperature and heat content, both being key variables in the context of ongoing Arctic warming.

The assimilation of range- and depth-averaged sound speed improved the overall ocean temperature estimates at the 0–1000-m-depth layer. However, it introduced some increased temperature bias in the upper ocean. We suggest that assimilating both acoustic and oceanographic measurements from moored instruments could address this problem. Higher-resolution models would resolve more of the nonlinear variability in Fram Strait. However, the choice of the 4DVAR assimilation method limits the nonlinearity the Fram Strait model can allow. For a nonlinear oceanographic environment like Fram Strait this also is a limitation of the realism of the ocean model. Other assimilation methods such as the ensemble Kalman filter might allow the assimilation of acoustic measurements while capturing more of the nonlinear small-scale ocean dynamics in Fram Strait. For large-scale basinwide ocean reanalyses this will be less of an issue, as they typically have limited resolution and nonlinearity.

The ACOBAR experiment in Fram Strait was originally conceived to use integrated measurements from different observational platforms “to improve the accuracy of the heat, mass and freshwater transport estimates through the Fram Strait” (https://acobar.nersc.no/). While this goal has not been achieved, this assimilation experiment gives some insight into the usefulness and the limitations of the ACOBAR acoustic measurements. The acoustic observations had been undertaken in the hope that they would accurately capture the temporal variability of large-scale ocean temperature in Fram Strait. They do that, but the lack of correlation of this short-term variability between the ocean state estimate presented here and the AWI/NPI Fram Strait mooring section points to the fact that knowing the short-term variability in one part of Fram Strait does not necessarily allow one to predict it in another. This might be expected for point measurements, but it was more unclear for instantaneous integrated measurements of large ocean volumes, as provided by acoustic tomography. Therefore, it remains to be seen how the high-temporal-resolution measurements that this technique provides can be evaluated oceanographically in an area such as Fram Strait.

This study has shown the abilities and limitations of range- and depth-integrated acoustic tomography measurements for constraining an ocean state estimate of Fram Strait. It will hopefully provide some first insight to how a combination of integral measurements (acoustics) and localized measurements (fixed or mobile platforms) can provide an optimal dataset for improving ocean state estimates in Fram Strait in a sustained and cost-efficient observing system. Dushaw and Sagen (2016) showed that the two types of measurements are complementary when combined using objective mapping techniques. The largest biases in this state estimate, which is purely based on integrated acoustic measurements, occur at ocean depths of 0–300 m. This depth range is relatively well covered by instrumentation in the AWI/NPI mooring section. Therefore, it seems likely that information from the mooring section would be well suited to improve ocean state estimates when combined with the acoustic measurements. This study showed a lack of temporal correlation between the ocean state estimate, which was constrained by the ACOBAR acoustic tomography observations, and the AWI/NPI mooring section. This was most likely due to the limited spatial correlation of short-term variability in Fram Strait. If that is the case, then it would be preferable to have the integrated (acoustic) and localized measurements collocated, to enable the combination of the temporal variability information that they provide. This study is far from being able to provide answers to further questions along such lines. However, it demonstrates the usefulness of integrated acoustic measurements of ocean sound speed and temperature and thus supports the idea that such integrated measurements should form part of regional ocean observation systems.

Acknowledgments.

We want to thank Patrick Heimbach, An Nguyen, and Victor Ocana at The University of Texas at Austin for giving us access to the preliminary iteration 9 of ASTE. This publication was supported by the U.S. Office of Naval Research under the CANAPE-UNDER ICE project (Grant N62909-19-1-2012). 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.

Data availability statement.

The temperature and sound speed time series from acoustic tomography on which this paper is based are published in Geyer et al. (2022): https://doi.org/10.1016/j.dib.2022.108118. They are archived at the Norwegian Marine Data Centre under https://doi.org/doi:10.21335/NMDC-NERSC-1237754860. These data were collected and produced by the ACOBAR project (Sagen et al. 2017; Dushaw and Sagen 2017; Geyer et al. 2020). Data are made freely available by NERSC as part of the Horizon 2020 INTAROS project. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement 727890. The regional model state estimate dataset on which this paper is based is too large to be retained or publicly archived with available resources. Documentation and methods used to support this study are available from florian.geyer@nersc.no at Nansen Environmental and Remote Sensing Center.

REFERENCES

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    • Search Google Scholar
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    • Search Google Scholar
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    • Search Google Scholar
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    • Search Google Scholar
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  • Gopalakrishnan, G., B. D. Cornuelle, M. R. Mazloff, P. F. Worcester, and M. A. Dzieciuch, 2021: State estimates and forecasts of the northern Philippine Sea circulation including ocean acoustic travel times. J. Atmos. Oceanic Technol., 38, 19131933, https://doi.org/10.1175/JTECH-D-20-0178.1.

    • Search Google Scholar
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  • Hattermann, T., P. E. Isachsen, W.-J. von Appen, J. Albrechtsen, and A. Sundfjord, 2016: Eddy-driven recirculation of Atlantic Water in Fram Strait. Geophys. Res. Lett., 43, 34063414, https://doi.org/10.1002/2016GL068323.

    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
  • Locarnini, R. A., and Coauthors, 2013: Temperature. Vol. 1, World Ocean Atlas 2013, NOAA Atlas NESDIS 73, 40 pp., https://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol1.pdf.

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    • Search Google Scholar
    • Export Citation
  • Nguyen, A. T., H. Pillar, V. Ocaña, A. Bigdeli, T. A. Smith, and P. Heimbach, 2021: The Arctic Subpolar Gyre State Estimate: Description and assessment of a data-constrained, dynamically consistent ocean-sea ice estimate for 2002–2017. J. Adv. Model. Earth Syst., 13, e2020MS002398, https://doi.org/10.1029/2020MS002398.

    • Search Google Scholar
    • Export Citation
  • Sagen, H., and Coauthors, 2017: Resolution, identification and stability of broadband acoustic arrivals in Fram Strait. J. Acoust. Soc. Amer., 141, 20552068, https://doi.org/10.1121/1.4978780.

    • Search Google Scholar
    • Export Citation
  • Schauer, U., and A. Wisotzki, 2010: Physical oceanography during POLARSTERN cruise ARK-XX/2. PANGAEA, accessed 5 September 2023, https://doi.org/10.1594/PANGAEA.742660.

  • von Appen, W.-J., U. Schauer, T. Hattermann, and A. Beszczynska-Möller, 2016: Seasonal cycle of mesoscale instability of the West Spitsbergen Current. J. Phys. Oceanogr., 46, 12311254, https://doi.org/10.1175/JPO-D-15-0184.1.

    • Search Google Scholar
    • Export Citation
  • Wackernagel, H., 1995: Ordinary kriging. Multivariate Geostatistics, H. Wackernagel, Ed., Springer, 74–81, https://doi.org/10.1007/978-3-662-03098-1_11.

  • Zweng, M., and Coauthors, 2013: Salinity. Vol. 2, World Ocean Atlas 2013, NOAA Atlas NESDIS 74, 39 pp., https://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol2.pdf.

Save
  • Beszczynska-Möller, A., and A. Wisotzki, 2012: Physical oceanography during POLARSTERN cruise ARK-XXVI/1. PANGAEA, accessed 5 September 2023, https://doi.org/10.1594/PANGAEA.774196.

  • Beszczynska-Möller, A., E. Fahrbach, U. Schauer, and E. Hansen, 2012: Variability in Atlantic Water temperature and transport at the entrance to the Arctic Ocean, 1997–2010. ICES J. Mar. Sci., 69, 852863, https://doi.org/10.1093/icesjms/fss056.

    • Search Google Scholar
    • Export Citation
  • Challet, F., F. Geyer, L. Bertino, and R. P. Raj, 2022: Physical oceanography of the Fram Strait: Improving general understanding and models through the use of mooring interpolation products. NERSC Tech. Rep. 420, 57 pp.

  • Del Grosso, V. A., 1974: New equation for the speed of sound in natural waters (with comparison to other equations). J. Acoust. Soc. Amer., 56, 10841091, https://doi.org/10.1121/1.1903388.

    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., and H. Sagen, 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 Technol., 33, 20792093, https://doi.org/10.1175/JTECH-D-15-0251.1.

    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., and H. Sagen, 2017: The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography. J. Acoust. Soc. Amer., 142, 35413552, https://doi.org/10.1121/1.5016816.

    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., H. Sagen, and A. Beszczynska-Möller, 2016a: Sound speed as a proxy variable for temperature in Fram Strait. J. Acoust. Soc. Amer., 140, 662630, https://doi.org/10.1121/1.4959000.

    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., H. Sagen, and A. Beszczynska-Möller, 2016b: On the effects of small-scale ocean variability on acoustic propagation in Fram Strait: The tomography forward problem. J. Acoust. Soc. Amer., 140, 12861299, https://doi.org/10.1121/1.4961207.

    • Search Google Scholar
    • Export Citation
  • Geyer, F., H. Sagen, B. Cornuelle, M. R. Mazloff, and H. Vazquez, 2020: Using a regional ocean model to understand the structure and variability of acoustic arrivals in Fram Strait. J. Acoust. Soc. Amer., 147, 10421053, https://doi.org/10.1121/10.0000513.

    • Search Google Scholar
    • Export Citation
  • Geyer, F., H. Sagen, B. Dushaw, A. Yamakawa, M. Dzieciuch, and T. Hamre, 2022: A dataset consisting of a two-year long temperature and sound speed time series from acoustic tomography in Fram Strait. Data Brief, 42, 108118, https://doi.org/10.1016/j.dib.2022.108118.

    • Search Google Scholar
    • Export Citation
  • Gopalakrishnan, G., B. D. Cornuelle, M. R. Mazloff, P. F. Worcester, and M. A. Dzieciuch, 2021: State estimates and forecasts of the northern Philippine Sea circulation including ocean acoustic travel times. J. Atmos. Oceanic Technol., 38, 19131933, https://doi.org/10.1175/JTECH-D-20-0178.1.

    • Search Google Scholar
    • Export Citation
  • Hattermann, T., P. E. Isachsen, W.-J. von Appen, J. Albrechtsen, and A. Sundfjord, 2016: Eddy-driven recirculation of Atlantic Water in Fram Strait. Geophys. Res. Lett., 43, 34063414, https://doi.org/10.1002/2016GL068323.

    • Search Google Scholar
    • Export Citation
  • Ilıcak, M., and Coauthors, 2016: An assessment of the Arctic Ocean in a suite of interannual CORE-II simulations. Part III: Hydrography and fluxes. Ocean Modell., 100, 141161, https://doi.org/10.1016/j.ocemod.2016.02.004.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437471, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kobayashi, S., and Coauthors, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 548, https://doi.org/10.2151/jmsj.2015-001.

    • Search Google Scholar
    • Export Citation
  • Locarnini, R. A., and Coauthors, 2013: Temperature. Vol. 1, World Ocean Atlas 2013, NOAA Atlas NESDIS 73, 40 pp., https://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol1.pdf.

  • Nguyen, A. T., V. Ocaña, V. Garg, P. Heimbach, J. M. Toole, R. A. Krishfield, C. M. Lee, and L. Rainville, 2017: On the benefit of current and future ALPS data for improving Arctic coupled ocean-sea ice state estimation. Oceanography, 30 (2), 6973, https://doi.org/10.5670/oceanog.2017.223.

    • Search Google Scholar
    • Export Citation
  • Nguyen, A. T., H. Pillar, V. Ocaña, A. Bigdeli, T. A. Smith, and P. Heimbach, 2021: The Arctic Subpolar Gyre State Estimate: Description and assessment of a data-constrained, dynamically consistent ocean-sea ice estimate for 2002–2017. J. Adv. Model. Earth Syst., 13, e2020MS002398, https://doi.org/10.1029/2020MS002398.

    • Search Google Scholar
    • Export Citation
  • Sagen, H., and Coauthors, 2017: Resolution, identification and stability of broadband acoustic arrivals in Fram Strait. J. Acoust. Soc. Amer., 141, 20552068, https://doi.org/10.1121/1.4978780.

    • Search Google Scholar
    • Export Citation
  • Schauer, U., and A. Wisotzki, 2010: Physical oceanography during POLARSTERN cruise ARK-XX/2. PANGAEA, accessed 5 September 2023, https://doi.org/10.1594/PANGAEA.742660.

  • von Appen, W.-J., U. Schauer, T. Hattermann, and A. Beszczynska-Möller, 2016: Seasonal cycle of mesoscale instability of the West Spitsbergen Current. J. Phys. Oceanogr., 46, 12311254, https://doi.org/10.1175/JPO-D-15-0184.1.

    • Search Google Scholar
    • Export Citation
  • Wackernagel, H., 1995: Ordinary kriging. Multivariate Geostatistics, H. Wackernagel, Ed., Springer, 74–81, https://doi.org/10.1007/978-3-662-03098-1_11.

  • Zweng, M., and Coauthors, 2013: Salinity. Vol. 2, World Ocean Atlas 2013, NOAA Atlas NESDIS 74, 39 pp., https://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol2.pdf.

  • Fig. 1.

    Map of the study area. The black triangle denotes the acoustic paths between the ACOBAR moorings A, B and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots. The background is a snapshot of the temperature field at 95 m depth (model vertical level 12) for 19 Jun 2011 from the Fram Strait state estimate discussed in this publication.

  • Fig. 2.

    Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at reciprocal acoustic sections A–B and B–A (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bars in the corner denote the uncertainty estimate of the measured time series (A–B: 0.83 m s−1; B–A: 0.82 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

  • Fig. 3.

    Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at acoustic sections A–D (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bar in the corner denotes the uncertainty estimate of the measured time series (0.79 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

  • Fig. 4.

    Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at acoustic section B–D (0–1000 m depth). Ticks on the x axis denote the first day of the respective month. The error bar in the corner denotes the uncertainty estimate of the measured time series (0.80 m s−1). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

  • Fig. 5.

    Comparison of ocean state estimate, forward model, and measured range- and depth-averaged sound speed at the AWI mooring sections (interpolated temperature field at 78°50′N from 6°W to 8°E and 0–1000 m depth). The error bar in the corner denotes the uncertainty estimate of the interpolated mooring time series (0.23°C). The iteration 0 (dashed black line) is the so-called first-guess or reference solution of each 20-day assimilation segment, which illustrates the effect of the assimilation for each segment when compared to the optimized solution (solid red line).

  • Fig. 6.

    (left) Section-averaged time-mean measured and modeled vertical temperature profiles at the AWI/NPI mooring section (78°50′N, section averaged over 6°W–8°E); (center) as in the left panel, but for western Fram Strait only (6°–2°W); (right) as in the left panel, but for central and eastern Fram Strait only (2°W–8°E).

  • Fig. 7.

    Bias of forward model relative to interpolated mooring section at 78°50′N.

  • Fig. 8.

    Bias of state estimate relative to interpolated mooring section at 78°50′N.

  • Fig. 9.

    Comparison of (top) observed and modeled acoustic arrival patterns [(middle) state estimate and (bottom) forward model]. The arrival pattern is displayed as a function of acoustic travel time and the arrival angle of acoustic rays from the horizontal. For the modeled arrival pattern, the source angle is indicated by color (red: source angle > 5°; gray: −5° ≤ source angle ≤ 5°; blue: source angle > −5°). Arrivals with low absolute source and arrival angles (gray) correspond to refracted acoustic rays, arrivals with high absolute source and arrival angles (red, blue) correspond to surface-reflected/bottom-reflected (SRBR) rays.

  • Fig. 10.

    Time-mean ocean temperature and current field at 500 m depth in forward model (1 Sep 2010–31 Jul 2012). The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

  • Fig. 11.

    Time-mean ocean temperature and current field at 500 m depth in state estimate (1 Sep 2010–31 Jul 2012). The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

  • Fig. 12.

    Time-mean difference of modeled mean ocean temperatures and currents at 500 m depth between ocean state estimate and forward model (1 Sep 2010–31 Jul 2012), illustrating the effect of the data assimilation. A gray contour line marks the contour of zero temperature difference. Maximum and minimum temperature differences are +0.94° and −1.84°C, respectively. The black triangle denotes the acoustic paths between the ACOBAR moorings A, B, and D. The locations of the AWI/NPI oceanographic mooring section are denoted by yellow dots.

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