Nesting and data assimilation considerations in regional operational ocean forecasting

ABSTRACT

A combination of nesting and data assimilation setups is explored for lowering analysis and forecast errors in a regional operational ocean model. Original downscaling from the global model and applying 3dVar to a regional model produce unacceptably high errors. The latter are reduced by the introduction of an intermediate assimilative nest with 3dVar and 4dVar assimilations, and by the use of 4dVar assimilation in the regional model. It is found that if only 3dVar assimilation is available, then the intermediate assimilative nest is necessary for lowering errors in the regional model. Alternatively, 4dVar assimilation can be used directly in the regional model or in the intermediate nest. Errors in the regional 3dVar nested in the intermediate 4dVar assimilative nest are comparable to regional 4dVar. Although the latter has lowest errors, there is value in the former, because the intermediate nest could encompass several regional models.

1. Introduction

Regional ocean models are typically run with higher horizontal resolution than the global models that provide their initial and boundary conditions. The boundary conditions for the regional model are usually smooth, having been interpolated from the coarser resolution of the global model fields. Away from the smooth boundary conditions, the regional model solution exhibits small scale variability not seen in the smoother global solution. Several methods have been explored to ensure continuity from the features resolved by the global model to those resolved by the regional model, e.g. Desamsetti et al. (2019) and references therein, Denis et al. (2002) . The contributions of all other sources of errors in regional ocean models (Pham et al. 2016 and references therein) only compound the inaccuracies of the regional solution. These inaccuracies can be significant when compared to observations. Data assimilation therefore also needs to be applied to the regional model to keep it close to observations, particularly because high resolution regional models are susceptible to the double-penalty effect, e.g. Crocker et al. 2020, Gofa et al. (2018), or Rossa et al. (2008). Note that the regional model only ‘knows’ about observations assimilated in the global model through the initial and boundary conditions.

There are several studies using regional ocean models by various groups around the globe: Amo et al. (2021) describe the Iberian Biscay Irish is nested in global CMEMS, Nishikawa et al. (2021) describe a high-resolution model around Japan, O’Dea et al. (2012) describe a regional NEMO for the European North-West shelf, and Chao et al. (2009) describe a regional ROMS for the Monterey Bay, Vandenbulcke et al. (2006) describe a regional model for the Gulf of Lions, and Barth et al. (2005) describe a regional model for the Ligurian Sea, to cite but a few.

This study is motivated by an operational centre setting up a regional domain in the Northeast Atlantic to assimilate all existing ocean observations in the region and new observations from a fleet of gliders that were deployed to sample across ocean fronts of the North Atlantic Current. These observations were assimilated into the Navy coastal ocean model (NCOM, Martin 2000) using the Navy coupled ocean data assimilation (NCODA) 3dVar system (Cummings 2005; Cummings and Smedstad 2013). Both NCOM and the NCODA-3dVar have been validated or operational use (Burnett et al. 2014); the former for regional applications, and the latter for assimilating observations in global ocean forecasting system (GOFS; Metzger et al. 2017) and regional models nested into GOFS. The benefits of high resolution regional models have been studied and reported in the literature. We assume the readers will be familiar with the concept that a high resolution regional model is better suited to represent local dynamics than a global model using lower resolution. The high resolution regional model better represents smaller scale features that are captured by a dense observing network. These features cannot be properly resolved and represented in any coarser resolution global model.

The first run of the regional model nested into the global model GOFS resulted in unacceptably high errors when compared to in situ glider observations, even though the global model was shown to have lower errors in this region. One should keep in mind that the global model was validated with a coarser resolution and observations network, and thus could not account for smaller scale phenomena captured by the gliders. Also, the error statistics of the global model would generally tend to alias the small scale variability, because they are computed as averages over large areas and longer time periods.

The question that drives this study is whether the analyses and forecasts can be improved in the regional model. We will investigate this question from two perspectives:

1. the role of the rough downscaling: would an assimilative intermediate model/nest (with an intermediate resolution) between the global and regional model help reduce analyses and forecast errors in the regional model?

2. the role of the data assimilation method: can the 4dVar in the regional model and or in the intermediate nest help reduce the errors in the regional model compared to 3dVar?

We believe the answer to these questions will provide guidance on how to properly set-up operational regional models and best utilise both 3dVar and 4dVar, if the latter is available.

This paper explores the roles of nesting (and thus the source of boundary conditions) and data assimilation choice between 3dVar and 4dVar in order to improve the accuracy of analyses and forecasts in a regional ocean model. An assimilative intermediate model between the global and regional models has the potential to reduce the errors of the regional model, especially in highly dynamic regions like the one used in this study. Even though the nesting ratio between the global and regional models may be adequate for typical cases, a regional model will benefit from a higher resolution parent assimilating data at shorter correlation scales to better capture the small scale features when they are prevalent. This in turn will help improve the accuracy of the initial and boundary conditions of the regional solution. The goal of this study is not to carry out a thorough investigation of nesting (many studies have done that already), nor to compare 3dVar and 4dVar by providing reasons why one approach does better than the other. Lorenc and Rawlins (2005) explored and provided those reasons. We are taking a pragmatic approach on how to use these methods best for the sole purpose of lowering analysis and forecast errors of a regional model. It is our view that lowering the forecast errors in operational forecasting is of paramount importance. We will detail the experiments setup in section 2, results from numerical experiments in section 3, followed by a discussion in section 4 and brief summary in section 5.

2. Experiments setup

The region of interest, shown in Figure 1, is a portion of the North Atlantic that covers longitudes 48° to 13.1° degrees West and latitudes 33° to 67.92° North. A peculiar feature of the ocean circulation in this domain is the remnant of the Gulfstream meanders entering near its southwestern boundary. The regional model is based on the Navy coastal ocean model (NCOM, Martin (2000)) at a 2 km horizontal resolution, and uses the same parameterisation of physics (viscosity, diffusion, … etc.) from the global NCOM (Barron et al. 2006, 2007; Kara et al. 2006). Initial and boundary conditions for the regional model are taken from GOFS, which is based on the Hybrid Coordinates ocean model (HYCOM, Chassignet et al. 2007). The global model has a resolution of 1/12.5° (∼9 km at the equator, ∼7 km at mid-latitudes). The nesting ratio between the global and regional models is thus approximately 3-to-1.

Figure 1. The regional model domain boundaries (black box) and bathymetry. The full domain shown is that of the intermediate model, and the white box is the area where GOFS was evaluated against floats along around the southwestern boundary.

Both NCOM and GOFS use the NCODA 3dVar system to assimilate satellite sea surface temperature (SST), satellite sea surface height anomalies (SSHA) in the form of synthetic temperature and salinity profiles through the improved synthetic ocean profile system (ISOP, Helber et al. 2013) for GOFS and the modular ocean data assimilation system (MODAS, Fox et al. 2002) for NCOM, in situ temperature and salinity profiles from ARGO floats (Roemmich et al. 2014), XBTs, and a recently deployed fleet of gliders in the study region. The 3dVar FGAT option is used only for the assimilation of SST, both for the global and regional models. Combined observation and representation errors for the regional model are set to 0.05 m, 0.224°C and 0.1 psu for SSH, temperature, and salinity respectively. In situ profiles (e.g. from gliders) are thinned for 3dVar assimilation in the global and regional models; the thinning is a function of the background correlation length scale. The default value removes profiles that are within 3/4 correlation length scale of a selected profile. This also applies to the regional model 4dVar assimilation, with the additional thinning in time, where profiles also have to be at least one hour apart from each other. With this thinning, assimilated observations are still correlated, but the iterative minimisation process still converges more satisfactorily than if a less stringent thinning were applied.

The regional model is initialised on 1 May 2019, and starts assimilating observations right away using 3dVar. The assimilation window is set to 24 h. Although this paper focuses on comparing assimilation results from 1 June to 30 June 2019, the entire assimilation experiment runs through 31 August 2019. All comparisons are based on 24-hr forecast RMS error profiles against real T/S profiles from ARGO and gliders.

The 24-hr forecast RMS errors are computed from the differences between the model forecast and the observations during the 24 h after the analysis, where the observations are compared to the nearest model forecast in time. The RMS errors of the regional model against in situ observations in the month of June 2019 (Figure 2) show that errors remain relatively high: temperature errors exceed 1°C in most of the upper 600 m, and salinity errors exceed 0.2 psu in the upper 100 m. These high errors have significant adverse effects on tactical decisions. Since we cannot address all the possible reasons why errors remain high in the regional model, our effort focuses on two arguably main reasons: (i) erroneous boundary conditions from the global model, (ii) high nesting ratio, and (iii) inefficient use of in situ data in the regional model. The first two will be addressed by introducing an intermediate assimilative model domain into which the regional model is nested, and the third will be addressed by using a 4dVar assimilation.

Figure 2. 24-hr forecast RMS errors of temperature (a) and salinity (b) for the month of June 2019 from the regional model nested into the global model.

2.1. Errors in the boundary conditions

An evaluation of GOFS by the same 24-hour forecast RMS against available floats in a small area around and along the southwestern boundary, referred to as the ‘western boundary focus area’ (dashed red box in Figure 3a below) for the month of June 2019, shows that the global model has high errors in that region. Temperature errors are above 2^e C in the upper 200 m, and above 1°C between 200 and 600 m, while salinity errors range 0.2–0.5 psu in the upper 400 m. With currents speeds sometimes reaching 1 m/s in this area, these boundary errors will rapidly propagate and contaminate the solution in the interior of the domain.

Figure 3. The Rossby number (a) computed from GOFS model outputs, temperature (b) and salinity (c) RMS error profile of GOFS in the western boundary focus area (dashed red box in (a)).

Not surprisingly, the western boundary focus area where these rather large errors are located, is also the area with the largest Rossby numbers, compared to the rest of the regional model domain. This area has strong currents, as it is the area where the Gulfstream turns into the North Atlantic Current. Considering the high Rossby numbers and the errors of GOFS in this same area, it is not unreasonable to assume that the errors in the regional model seen in Figure 2 may be due, at least in part, to errors at the boundaries. Note that the Rossby number shown in Figure 3 is computed as the Coriolis-normalized depth-averaged vertical vorticity in the upper 100 m from GOFS model outputs, for 14 June 2019.

A way to improve accuracy of the boundary conditions is to introduce an intermediate model into which the regional will be nested. An intermediate model approach is not new in regional ocean modelling or downscaling in general. Chao et al. (2009) used an intermediate model to go from their US West coast ROMS to the Monterey Bay, keeping a 3:1 nesting ratio; Vandenbulkce et al. (2006) used an intermediate North-Western Mediterranea model to go from the entire Mediterranea sea to their regional Gulf of Lions, using nesting ratios of 5:1, Barth et al. (2005) used an intermediate Liguro-Provençal model to go from the Mediterranean Sea model to their regional Ligurian Sea model.

The question of nesting ratios has been explored to some extent by Spall and Holland (1991) with nesting ratios varying from 3 to 7, and the conclusion that the higher ratios tend to degrade the regional model solution. Blayo and Debreu (2005) recommend nesting ratios between 2 and 5, from a study that was mostly focused on open boundary conditions from the perspective of characteristic variables. Although the 3–1 ratio seems to have become conventional, the prevailing local dynamics, especially around the boundaries of the nested model, should determine what the efficient nesting ratio should be. Many studies using a 3:1 or higher nesting ratio do not have a major meandering current flowing into their boundaries, e.g. Chao et al. (2009) and Amo et al. (2021).

The intermediate model used here is based on NCOM dynamics and has twice/half the resolution of the global/regional model (thus providing a nesting ratio of 2-to-1), while being itself nested into the global model. The boundaries of the intermediate model are the outer edges of Figure 1. Note that the regional model also assimilates observations within its domain, an approach that is different from the one used in Usui et al. (2015) or Hirose et al. (2019) where observations were not assimilated in the regional model (inner nest). Besides providing better boundary conditions to the regional model, the purpose of this assimilative intermediate model is also to more accurately constrain the Gulfstream remnant flowing into the domain at higher resolution than the global model, because it has a strong impact on the circulation of the regional model. Two data assimilation methods are used in the intermediate domain: one is the 3dVar system that is used in the global model (GOFS) and in the regional model (cf. the comparison above), and the other is the NCOM-4dVar system of Ngodock and Carrier (2014). The 4dVar will also be used for assimilation in the regional domain in a later comparison. Here it is used as a means to improve the boundary conditions for the regional model by improving the solution of the intermediate model.

2.2. Inefficient use of in situ observations

In situ profiles observations consist of mainly ARGO profiles (a few dozen daily) for the first 17 days of June 2019, and a little over 200 glider profiles daily starting on June 18. As already mentioned above, the processing of in situ profile observations for 3dVar discards observations within 3/4 of a background error correlation scale. This is done for practical purposes to achieve fast convergence of the cost function minimisation process. In general, there is no need to thin or discard observations for 3dVar. Yet, assimilating observations that are very close to each other in space introduces correlations in the observation space, i.e. non-zero off-diagonal values in the matrix to be inverted, which negatively affects the convergence of the iterative inversion process, and thus the time of execution of the assimilation, which is critical in the operational context. The thinning process may not be detrimental for ARGO profiles, because of their coarse distribution on a daily basis (Figure 4a). However, when dozens of gliders are deployed (in this case on 16 June 2019) and observations are recorded at a high temporal frequency, only a small amount of in situ profiles is actually assimilated with the 3dVar system. The introduction of the 4dVar addresses this issue of inefficient use of in situ observations since profiles can be processed every hour (or even every 15 min) for assimilation with 4dVar, thus significantly increasing the number of assimilated in situ profiles, see Figure 4(b). The difference in situ profile observations assimilated by 4dvar versus 3dvar is mostly due to accounting for the time dimension in processing the observations for 4dvar, specifically for gliders reporting more frequently. Before the gliders started reporting, both 3dvar and 4dvar assimilated basically the same number of in situ profile observations from floats on a daily basis, due to their coarse spatial distribution.

Figure 4. (a) the spatial distribution of all float observations in the regional model for all the month of June 2019 (blue circles), and for the day of June 14, 2019 (black bullets), and (b) time series of total in situ profiles (black), and the number of in situ profiles assimilated in 3dVar (blue) and 4dVar (red).

The spatial correlation length scale of the background error covariance is set to the Rossby radius of deformation, and is used for thinning observations in space in both 3dVar and 4dVar. The two systems have the same thinning in space; the only difference is that since 4dVar includes the time dimension, observations are also thinned in time. Theoretically, the observations can be assimilated in the 4dVar as frequently as the model time step itself. However, 4dVar accounts for two types of time correlations: the one introduced by the time-dependent model error covariance, and the inherent correlation (in time) resulting from the integrations of the adjoint and tangent linear models. Thus, assimilating observations that are too close in time introduces non-zero off-diagonal elements in the matrix to be inverted, which degrade its conditioning and thus negatively affects the convergence. The latter is critical for the time of execution of the system in the operational context. We have found by experience that the 1-hour time separation between observations is sufficient for efficient convergence of the minimisation within operational time constraints. Also, 4dVar with an appropriate assimilation window, propagates the information from the observations locations to other parts of the model domain according to the dynamics of the background.

3. Numerical results

We will now discuss the results the four experiments carried out in this study. They consist of the original regional model with 3dvar data assimilation and boundary conditions from the global model GOFS (Exp1), the regional model with 3dvar assimilation an boundary conditions from 3dvar assimilative intermediate model (Exp2), the regional model with 3dvar assimilation and boundary condition from 4dvar assimilative intermediate model (Exp3), and the regional model with 4dvar assimilation and boundary conditions from GOFS. The experiments are summarised in Table 1. Note that we did not carry out any GOFS model runs; we only used the GOFS output files when the experiments needed them.

Table 1. Summary of numerical experiments carried out in this study.

Regional model experiment	Data assimilation type	Source of boundary conditions	Line colour in the Figure 2, Figures 5–7
Exp1	3dvar	GOFS	Solid black
Exp2	3dvar	Intermediate model (3dvar nested into GOFS)	Solid blue
Exp3	3dvar	Intermediate model (4dvar nested into GOFS)	Dashed blue
Exp4	4dvar	GOFS	Solid red

3.1. 3dvar comparison: when a 4dVar is not available

The intermediate model introduced above is initialised on 1 March 2019; its initial and boundary conditions are drawn from the global model. We carry out 3dVar assimilation in this model on a daily cycle, similar to the assimilation in the global and the regional models. The regional model is nested into this 3dvar assimilative intermediate model (Exp2) starting on 19 May 2019, just as with nesting into the global model. We now compare in Figure 5 the 24-hr forecast RMS error profile of the original assimilative regional model with boundary conditions from the global model (Exp1), to the new assimilative regional model with boundary conditions from the intermediate model (Exp2). Note that these two regional models runs are driven by the same surface forcing fields, assimilate the same observations, and only differ in the origin of their initial and boundary conditions. There is a noticeable improvement in the error profiles in Figure 5: improvements in the temperature errors extend from the surface to 1000 m, sometimes exceeding 0.5°C, e.g. around 400 m depth. The gains in salinity errors are marked in the upper 100 m (0.15 psu), and become modest from 100 to 600 m. This experiment highlights the benefits of having an intermediate assimilative model, with higher resolution than the global model, to provide initial and boundary conditions to the regional model. This of course means that an operational centre should maintain (keep running) both the intermediate and the regional models. We argue that the gains in forecast accuracy and its impact on tactical decision making should outweigh the logistical considerations of keeping the intermediate model.

Figure 5. Same as Figure 2, except for the inclusion of 24-hr forecast RMS error profile from Exp2.

3.2. The 4dVar improvements

When an operational centre is fortunate to have a 4dVar system, it is usually applied to regional models of rather small sizes, primarily because of the significantly higher computational demands of the 4dVar. Note that there is no global operational ocean 4dVar system to our knowledge. If there was a global 4dVar, its resolution would have to be coarser in order to fit within operational constraints; and this may lead into having to use two or more intermediate steps in order to properly scale down the resolution to the regional domain. The 4dVar system at our disposal is applied to both the intermediate and regional models. The first application aims at providing more accurate initial and boundary conditions to the regional model, and the second application will be discussed in an analysis of alternatives. We already know from theory and various previous studies that the 4dVar solution will be more accurate than its 3dVar counterpart either for the intermediate or the regional model, so the comparison between the 3dVar and 4dVar solutions is not our focus. Rather, we are interested in the potential improvements of the initial and boundary conditions provided to the regional model by the 4dVar solution for the intermediate model, and this from the 3dVar perspective. It is important to note that due to its higher computational cost, the 4dVar assimilations are not carried out at the native model resolutions: the intermediate model 4dVar uses a reduced resolution of 8 km, and the regional model 4dVar uses a reduced resolution of 6 km. Note that the reduced resolutions are only used to compute the analysis increments; the background solutions still use the native model resolutions. These settings provide significant computational savings without sacrificing the analyses accuracy.

A 3dVar assimilative experiment is thus carried with the regional model, using initial and boundary conditions from the 4dVar assimilative intermediate model (Exp3). Results are compared to the original 3dVar assimilative regional model (Exp1), and to the regional 3dVar assimilative model from Exp2. The 24-hr forecast RMS error profiles are shown in Figure 6. Noticeable improvements of up to 0.25^o C are seen in the temperature errors between 100 and 600 m; improvements are also seen in the salinity error profiles from 100 m to 400 m. Thus, at least for both subsurface temperature and salinity, the 4dVar gains in accuracy in the intermediate model translate into gains in accuracy in the regional model.

Figure 6. Same as Figure 5, except for the additional RMS profile from Exp3.

As mentioned above a second 4dVar assimilative experiment is carried for the regional model. This regional model 4dVar experiment gets its initial and boundary conditions from the global model (Exp4). All three regional 3dVardvar assimilative solutions are now compared to the regional 4dVar assimilative solution, using the same 24-hr forecast RMS error profile (Figure 7). The main point of this comparison is to evaluate the 3dVar solutions with improved initial and boundary conditions against the regional 4dVar. However, since we have already discussed the accuracy of the 3dVar solutions relative to each other, we restrict this comparison between the regional 4dVar and the best of the regional 3dVar solutions, namely the one with initial and boundary conditions from the intermediate 4dVar assimilative model (Exp3). As seen in Figure 7, both solutions from Exp3 and Exp4 have virtually the same the accuracy from the surface to about 100 m; the 4dVar solution (Exp4) becomes more accurate by some 0.15°C from 100 m to about 350 m, but then becomes less accurate than the 3dVar (Exp3) by 0.1°C from 350 m to about 600 m. Below 600 m, the 4dVar and the two 3dVar solutions From Exp2 and Exp3 have the same levels or errors. Salinity errors from Exp4 improve in the upper 200 m, but degrade between 200 and 800 m. We note that the difference in salinity errors between Exp4 and Exp3/Exp2 from 200 m to 800 m is not significant, as it is less than 0.05 psu, which is lower than the observation error for salinity (0.1 psu) used in all assimilation experiments.

Figure 7. Same as Figure 6, except for the additional RMS error profile from Exp4.

4. Discussion

Although improved initial and boundary conditions from the 4dVar assimilative intermediate model bring the performance of the 3dVar assimilative regional model on par with the 4dVar assimilative regional model, one should keep in mind that the latter is still hampered by inaccuracies in the boundary conditions taken from the global model. There is no doubt that the accuracy of the regional 4dVar would improve if provided with improved initial and boundary conditions from the assimilative intermediate model, just as was done for the regional 3dVar. But since it is not likely that an operational centre that is fortunate to have a 4dVar system would carry out 4dVar assimilation for both the intermediate and regional models, a pragmatic choice has to be made. The considerations guiding the pragmatic choice are (1) 4dVar is more accurate than 3dVar, (2) an intermediate model is needed (hopefully this study has shed some light to this regard), (3) it is computationally expensive to run a 4dVar, much more for both the intermediate and regional models. What strategy should a centre adopt then? The 3dVar assimilative regional model nested into the 4dVar assimilative intermediate model (option 1), or the 4dVar assimilative regional model nested into the 3dVar assimilative intermediate model (option 2).

When a centre has only one regional domain, the discussion and results above showed that a 4dVar in the regional model is able to overcome inaccuracies of the boundary condition from the global model without the hassles of going through an intermediate model. In what follows an assumption is made that operational centres routinely run several high resolution smaller regions/domains nested in coarse resolution global or larger domains. An intermediate model domain can be defined to encompass several smaller operational domains. If the regional model domains are spread around the globe, a few more intermediate model domains can be defined, with the general idea that each intermediate domain will encompass several regional domains. In this case it is obvious that running a 4dVar assimilation for each regional domain will demand more resources than running only one 4dVar on the intermediate domain. The latter will provide more accurate boundary conditions to all the regional domains contained in the intermediate domain simultaneously, and a 3dVar assimilation for each regional domain will follow.

We did not carry out 4dVar assimilation experiments for the regional model with initial and boundary conditions coming from either 3dVar or 4dVar intermediate model. The main reason for this omission is the fact that 4dVar will provide a more accurate solution than 3dVar given the same initial and boundary conditions. The 3dVar and 4dVar assimilation results from the regional model nested into the global model suffice to substantiate this position, in addition to Lorenc and Rawlins (2005).

As mentioned above, the resolution of the intermediate model was set to 4 km, while 4dVar increments were computed with a resolution of 8 km. Present global or large basin scale modelling is increasing in horizontal resolution. For example the present operational global HYCOM is run at 1/12th degree, with plans to transition to 1/25th degree. These approximately represent the reduced and full resolutions in our 4dVar experiments. Thus given enough computational resources, it is foreseeable to carry out a global 4dVar computing increments at a reduced resolution than the global model itself, which will likely eliminate the need of an intermediate 4dVar assimilative model.

The results presented here apply to the particular system studied and have not been shown to be generally applicable to all regional models. This study highlights the importance of the source and location of boundary conditions for regional models, especially when strong nonlinear dynamics are present around the boundaries.

Finally, a recent study by Shapiro and Gonzalez-Ondina (2022) presents a simple and computationally inexpensive method for assimilating observations in a regional model, especially when systems such as 3dvar or 4dvar are not available.

5. Summary

Regional operational ocean forecasting may be negatively affected by (i) errors coming from global models, (ii) high nesting ratios, and (iii) inefficient use of in-situ observations. It was established that significant errors came from the global model through the southwestern boundary of the regional model, an area with strong inflow currents and high Rossby numbers. Also, the observations thinning for 3dVar left a significant portion of in-situ glider profiles. This study looked into the first two issues by introducing an intermediate assimilative model into which the regional model of interest was nested, and the last issue was addressed by using a 4dVar assimilation system instead of the 3dVar that originally used in the regional domain as well as in the global. Both approaches, i.e. the intermediate model and the 4dVar, significantly improved the accuracy of the regional model’s forecast. Care should be taken in selecting the location of boundaries of a regional model, especially when strong nonlinear dynamics are present.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was sponsored by the Office of Naval Research Program Element 62435N as part of the ‘‘Local Analysis Through Tactical Ensonification’’ project. This paper is NRL paper contribution number NRL/JA/7320-20-5021.

Notes on contributors

Hans Ngodock

Dr. Hans Ngodock is an oceanographer with the Naval Research Laboratory. He received his PhD in Applied Mathematics and inverse modeling from the Université Joseph Fourier (France) in 1996. His expertise is in the implementation of advanced data assimilation algorithms into numerical models, with applications to single and coupled models of the ocean, atmosphere, waves and acoustics.

Matthew Carrier

Dr. Matthew Carrier is an oceanographer with the Naval Research Laboratory. He received his PhD in Meteorology and data assimilation The Florida State University in 2008. His expertise is in the implementation of advanced data assimilation algorithms into numerical models, with applications to single and coupled models of the ocean, atmosphere, waves and acoustics.

John Osborne

Dr. John Osborne is an oceanographer with the Naval Research Laboratory. He received his PhD in Physical Oceanography and data assimilation from Oregon State University in 2014. His expertise is in ocean modeling and the implementation of advanced data assimilation algorithms into numerical models, with applications to single and coupled models of the ocean, atmosphere, waves and acoustics.

Scott Smith

Dr. Scott Smith is an oceanographer with the Naval Research Laboratory. He received his PhD in Aerospace Engineering from The University of Colorado in 2002. His expertise is in ocean modeling and the implementation of advanced data assimilation algorithms into numerical models, with applications to single and coupled models of the ocean, atmosphere, waves and acoustics.