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- Author or Editor: Max Yaremchuk x
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Abstract
The sensitivity of model forecasts to uncertainties in control variables is evaluated using the adjoint technique and the ensemble generated by the reduced-order four-dimensional variational data assimilation (R4DVAR) algorithm within the framework of twin-data experiments with a quasigeostrophic model. To simulate real applications where the true state is unknown, the sensitivities were estimated using model solutions that were obtained after assimilating sparse observations extracted from the true solutions. The numerical experiments were conducted in the linear, weakly nonlinear, and strongly nonlinear (NL) regimes with special emphasis on the NL case characterized by the instability of the tangent linear model. It is shown that the ensemble-based R4DVAR method provides better sensitivity estimates in the NL case, primarily due to the better accuracy of the optimized solutions. The concept of sensitivity in the NL case is also considered within the statistical framework. Using analytical arguments and numerical experimentation, averaging the adjoint sensitivity estimates over an ensemble of model trajectories generated by finite perturbations of the optimal control is shown to provide an estimate similar to that obtained with the adjoint model stabilized by enhanced dissipation. This observation allows for evaluation of the sensitivities of strongly nonlinear optimal solutions by using both the adjoint (4DVAR) and ensemble (R4DVAR) optimization algorithms.
Abstract
The sensitivity of model forecasts to uncertainties in control variables is evaluated using the adjoint technique and the ensemble generated by the reduced-order four-dimensional variational data assimilation (R4DVAR) algorithm within the framework of twin-data experiments with a quasigeostrophic model. To simulate real applications where the true state is unknown, the sensitivities were estimated using model solutions that were obtained after assimilating sparse observations extracted from the true solutions. The numerical experiments were conducted in the linear, weakly nonlinear, and strongly nonlinear (NL) regimes with special emphasis on the NL case characterized by the instability of the tangent linear model. It is shown that the ensemble-based R4DVAR method provides better sensitivity estimates in the NL case, primarily due to the better accuracy of the optimized solutions. The concept of sensitivity in the NL case is also considered within the statistical framework. Using analytical arguments and numerical experimentation, averaging the adjoint sensitivity estimates over an ensemble of model trajectories generated by finite perturbations of the optimal control is shown to provide an estimate similar to that obtained with the adjoint model stabilized by enhanced dissipation. This observation allows for evaluation of the sensitivities of strongly nonlinear optimal solutions by using both the adjoint (4DVAR) and ensemble (R4DVAR) optimization algorithms.
Abstract
Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator 
In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of 
Abstract
Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator
In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of
Abstract
Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.
Abstract
Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.
Abstract
Climatological data on the oceanic and atmospheric variability are inverted to study seasonal variation of the Kuroshio Extension (KE) and the recirculation gyre to the south. The processed datasets include climatological fluxes of heat, salt, and momentum at the ocean surface; Levitus hydrography; TOPEX/Poseidon altimetry; and surface drifter data. A variational data assimilation technique is used to retrieve variability in the open ocean region (18°–42°N, 142°E–160°W) bounded at 1000 m from below. By optimizing the open boundary values of oceanic fields in combination with initial conditions and atmospheric forcing, model solutions that are consistent with various climatological datasets within limits of observational errors were found. Using this technique, the mean geographical positions of the Subtropical Mode Water (STMW) and Central Mode Water (CMW) formation sites were estimated, the structures were analyzed, and estimates of the mode water production rates were obtained. Computations indicate that CMW formation is likely to occur 15°–20° west of the location diagnosed formerly without taking salinity data into the account. The optimized seasonal cycle is characterized by the STMW and CMW production rates of 3.8 ± 0.6 and 3.1 ± 0.5 Sv (1 Sv ≡ 106 m3 s−1), respectively. The KE annual mean transport in the upper 1000 m is diagnosed as 68 ± 7 Sv with a maximum of 79 ± 8 Sv in June–July and a minimum of 56 ± 6 Sv in December–January. Analysis of the heat and salt budgets in the region has shown that atmospheric fluxes are counterbalanced by the horizontal divergence of the advective temperature and salinity transports. In the annual mean, horizontal diffusion plays a minor role in the budgets.
Abstract
Climatological data on the oceanic and atmospheric variability are inverted to study seasonal variation of the Kuroshio Extension (KE) and the recirculation gyre to the south. The processed datasets include climatological fluxes of heat, salt, and momentum at the ocean surface; Levitus hydrography; TOPEX/Poseidon altimetry; and surface drifter data. A variational data assimilation technique is used to retrieve variability in the open ocean region (18°–42°N, 142°E–160°W) bounded at 1000 m from below. By optimizing the open boundary values of oceanic fields in combination with initial conditions and atmospheric forcing, model solutions that are consistent with various climatological datasets within limits of observational errors were found. Using this technique, the mean geographical positions of the Subtropical Mode Water (STMW) and Central Mode Water (CMW) formation sites were estimated, the structures were analyzed, and estimates of the mode water production rates were obtained. Computations indicate that CMW formation is likely to occur 15°–20° west of the location diagnosed formerly without taking salinity data into the account. The optimized seasonal cycle is characterized by the STMW and CMW production rates of 3.8 ± 0.6 and 3.1 ± 0.5 Sv (1 Sv ≡ 106 m3 s−1), respectively. The KE annual mean transport in the upper 1000 m is diagnosed as 68 ± 7 Sv with a maximum of 79 ± 8 Sv in June–July and a minimum of 56 ± 6 Sv in December–January. Analysis of the heat and salt budgets in the region has shown that atmospheric fluxes are counterbalanced by the horizontal divergence of the advective temperature and salinity transports. In the annual mean, horizontal diffusion plays a minor role in the budgets.
Abstract
The mean seasonal cycle of the western boundary currents in the tropical North Pacific Ocean is studied diagnostically by combining atmospheric climatologies with drifter, satellite altimetry, and hydrographic data in the framework of a simplified numerical model incorporating geostrophy, hydrostatics, continuity, and tracer conservation. The approach enables the authors to diagnose the absolute 3D velocity field and to assess the seasonal cycle of sea surface height (SSH)/total transports. Errors are estimated by considering multiple datasets and averaging over the results of the corresponding diagnostic computations. Analysis shows that bifurcation of the North Equatorial Current (NEC) occurs at 14.3° ± 0.7°N near the Philippine coast. Meridional migration of the NEC bifurcation latitude is accompanied by quantitative changes in the partitioning of the NEC transport between the Kuroshio and Mindanao Current. In February–July, when the NEC transport is 58 ± 3 Sv (Sv ≡ 106 m3 s−1), the Kuroshio transport is 12%–15% higher than the Mindanao Current (MC) transport. In the second half of the annual cycle the situation is reversed: in October the NEC transport drops to 51 ± 2 Sv with the MC transport exceeding the Kuroshio transport by 25%. The net westward transport through the Luzon Strait is characterized by a minimum of 1.2 ± 1.1 Sv in July–September and a maximum of 4.8 ± 0.8 Sv in January– February. A statistically significant correlation is established between the monthly SSH/streamfunction anomalies north of 10°N and the Ekman pumping rate associated with the northeast monsoon developing in the region in October–December. The result provides an indication of the fact that local monsoon is likely to be an important mechanism governing seasonal variation of the NEC partitioning and water mass distribution between the tropical and subtropical North Pacific.
Abstract
The mean seasonal cycle of the western boundary currents in the tropical North Pacific Ocean is studied diagnostically by combining atmospheric climatologies with drifter, satellite altimetry, and hydrographic data in the framework of a simplified numerical model incorporating geostrophy, hydrostatics, continuity, and tracer conservation. The approach enables the authors to diagnose the absolute 3D velocity field and to assess the seasonal cycle of sea surface height (SSH)/total transports. Errors are estimated by considering multiple datasets and averaging over the results of the corresponding diagnostic computations. Analysis shows that bifurcation of the North Equatorial Current (NEC) occurs at 14.3° ± 0.7°N near the Philippine coast. Meridional migration of the NEC bifurcation latitude is accompanied by quantitative changes in the partitioning of the NEC transport between the Kuroshio and Mindanao Current. In February–July, when the NEC transport is 58 ± 3 Sv (Sv ≡ 106 m3 s−1), the Kuroshio transport is 12%–15% higher than the Mindanao Current (MC) transport. In the second half of the annual cycle the situation is reversed: in October the NEC transport drops to 51 ± 2 Sv with the MC transport exceeding the Kuroshio transport by 25%. The net westward transport through the Luzon Strait is characterized by a minimum of 1.2 ± 1.1 Sv in July–September and a maximum of 4.8 ± 0.8 Sv in January– February. A statistically significant correlation is established between the monthly SSH/streamfunction anomalies north of 10°N and the Ekman pumping rate associated with the northeast monsoon developing in the region in October–December. The result provides an indication of the fact that local monsoon is likely to be an important mechanism governing seasonal variation of the NEC partitioning and water mass distribution between the tropical and subtropical North Pacific.
Reconstruction of the Rheological Parameters in a Sea Ice Model with Viscoplastic RheologyAbstract
We analyzed the feasibility of the reconstruction of the spatially varying rheological parameters through the four-dimensional variational data assimilation of the sea ice velocity, thickness, and concentration into the viscoplastic (VP) sea ice model. The feasibility is assessed via idealized variational data assimilation experiments with synthetic observations configured for a 1-day data assimilation window in a 50 × 40 rectangular basin forced by the open boundaries, winds, and ocean currents and should be viewed as a first step in the developing the similar algorithms which can be applied for the more advanced sea ice models. It is found that “true” spatial variability (∼5.8 kN m−2) of the internal maximum ice strength parameter
Abstract
We analyzed the feasibility of the reconstruction of the spatially varying rheological parameters through the four-dimensional variational data assimilation of the sea ice velocity, thickness, and concentration into the viscoplastic (VP) sea ice model. The feasibility is assessed via idealized variational data assimilation experiments with synthetic observations configured for a 1-day data assimilation window in a 50 × 40 rectangular basin forced by the open boundaries, winds, and ocean currents and should be viewed as a first step in the developing the similar algorithms which can be applied for the more advanced sea ice models. It is found that “true” spatial variability (∼5.8 kN m−2) of the internal maximum ice strength parameter
Abstract
Acoustic tomography (AT) and satellite altimetry (SA) measure properties of the ocean state with high temporal resolution. That makes these data suitable for long-term monitoring of mesoscale features in the open ocean regions, where the open boundaries are the major sources of model forecast uncertainties on timescales larger than 1 week. In this paper, a finite-difference quasigeostrophic model of an open ocean region is considered as a possible tool for interpolating AT–SA data in space and time. The assimilation algorithm is based upon the 4D variational data assimilation scheme controlled by the initial and boundary conditions of the model. The model configuration used in the simulations corresponds to the AT array deployed by the Japan Marine Science and Technology Center (JAMSTEC) in the region of the Kuroshio Extension in 1997. Twin data experiments show that mesoscale features in an area of 1000 km × 1000 km can be effectively monitored by five acoustic transceivers, measuring reciprocal travel times. The quality of assimilation is studied as a function of the position of the transceivers in the vertical and the effective number of monitored rays. It is shown that reciprocal travel time observations (differential tomography) in combination with SA provide a significant improvement of the quality of assimilation.
Abstract
Acoustic tomography (AT) and satellite altimetry (SA) measure properties of the ocean state with high temporal resolution. That makes these data suitable for long-term monitoring of mesoscale features in the open ocean regions, where the open boundaries are the major sources of model forecast uncertainties on timescales larger than 1 week. In this paper, a finite-difference quasigeostrophic model of an open ocean region is considered as a possible tool for interpolating AT–SA data in space and time. The assimilation algorithm is based upon the 4D variational data assimilation scheme controlled by the initial and boundary conditions of the model. The model configuration used in the simulations corresponds to the AT array deployed by the Japan Marine Science and Technology Center (JAMSTEC) in the region of the Kuroshio Extension in 1997. Twin data experiments show that mesoscale features in an area of 1000 km × 1000 km can be effectively monitored by five acoustic transceivers, measuring reciprocal travel times. The quality of assimilation is studied as a function of the position of the transceivers in the vertical and the effective number of monitored rays. It is shown that reciprocal travel time observations (differential tomography) in combination with SA provide a significant improvement of the quality of assimilation.
Abstract
A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances 
The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.
Abstract
A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances
The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.
Abstract
A version of the reduced control space four-dimensional variational method (R4DVAR) of data assimilation into numerical models is proposed. In contrast to the conventional 4DVAR schemes, the method does not require development of the tangent linear and adjoint codes for implementation. The proposed R4DVAR technique is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. Performance of the method is demonstrated in a series of twin-data assimilation experiments into a nonlinear quasigeostrophic model utilized as a strong constraint. When the adjoint code is stable, R4DVAR’s convergence rate is comparable to that of the standard 4DVAR algorithm. In the presence of strong instabilities in the direct model, R4DVAR works better than 4DVAR whose performance is deteriorated because of the breakdown of the tangent linear approximation. Comparison of the 4DVAR and R4DVAR also shows that R4DVAR becomes advantageous when observations are sparse and noisy.
Abstract
A version of the reduced control space four-dimensional variational method (R4DVAR) of data assimilation into numerical models is proposed. In contrast to the conventional 4DVAR schemes, the method does not require development of the tangent linear and adjoint codes for implementation. The proposed R4DVAR technique is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. Performance of the method is demonstrated in a series of twin-data assimilation experiments into a nonlinear quasigeostrophic model utilized as a strong constraint. When the adjoint code is stable, R4DVAR’s convergence rate is comparable to that of the standard 4DVAR algorithm. In the presence of strong instabilities in the direct model, R4DVAR works better than 4DVAR whose performance is deteriorated because of the breakdown of the tangent linear approximation. Comparison of the 4DVAR and R4DVAR also shows that R4DVAR becomes advantageous when observations are sparse and noisy.
Abstract
A variational data assimilation algorithm is developed for the ocean wave prediction model [Wave Model (WAM)]. The algorithm employs the adjoint-free technique and was tested in a series of data assimilation experiments with synthetic observations in the Chukchi Sea region from various platforms. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars (HFRs) within a geographic sector, and SWH from satellite altimeter along a geographic track. Numerical experiments demonstrate computational feasibility and robustness of the adjoint-free variational algorithm with the regional configuration of WAM. The largest improvement of the model forecast skill is provided by assimilating HFR data (the most numerous among the considered types). Assimilating observations of the wave spectrum from a moored platform provides only moderate improvement of the skill, which disappears after 3 h of running WAM in the forecast mode, whereas skill improvement provided by HFRs is shown to persist up to 9 h. Space-borne observations, being the least numerous, do not have a significant impact on the forecast skill but appear to have a noticeable effect when assimilated in combination with other types of data. In particular, when spectral data from a single mooring are used, the satellite data are found to be the most beneficial as a supplemental data type, suggesting the importance of spatial coverage of the domain by observations.
Abstract
A variational data assimilation algorithm is developed for the ocean wave prediction model [Wave Model (WAM)]. The algorithm employs the adjoint-free technique and was tested in a series of data assimilation experiments with synthetic observations in the Chukchi Sea region from various platforms. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars (HFRs) within a geographic sector, and SWH from satellite altimeter along a geographic track. Numerical experiments demonstrate computational feasibility and robustness of the adjoint-free variational algorithm with the regional configuration of WAM. The largest improvement of the model forecast skill is provided by assimilating HFR data (the most numerous among the considered types). Assimilating observations of the wave spectrum from a moored platform provides only moderate improvement of the skill, which disappears after 3 h of running WAM in the forecast mode, whereas skill improvement provided by HFRs is shown to persist up to 9 h. Space-borne observations, being the least numerous, do not have a significant impact on the forecast skill but appear to have a noticeable effect when assimilated in combination with other types of data. In particular, when spectral data from a single mooring are used, the satellite data are found to be the most beneficial as a supplemental data type, suggesting the importance of spatial coverage of the domain by observations.
