“…Mitchell and Houtekamer (2000) introduced an adaptive formulation of the EnKF, where the model error parameterization was updated by incorporating information from the innovations during the integration. Park and Kaneko (2000) presented an experiment where the EnKF was used to assimilate acoustic tomography data into a barotropic ocean model.…”
The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
“…Mitchell and Houtekamer (2000) introduced an adaptive formulation of the EnKF, where the model error parameterization was updated by incorporating information from the innovations during the integration. Park and Kaneko (2000) presented an experiment where the EnKF was used to assimilate acoustic tomography data into a barotropic ocean model.…”
The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
“…Coastal acoustic tomography (CAT) has been well developed as a coastal sea application of ocean acoustic tomography [1][2][3]. Intensive field measurements by CAT have been performed in coastal seas around Japan [4][5][6] and China [7].…”
A reciprocal sound transmission experiment was carried out during June 10-13, 2015 along a cross-strait line in the Bali Strait with strong tidal currents to measure the vertical section structures of the range-averaged current and temperature at a 3 min interval. The five-layer structures of the range-averaged current and temperature in the vertical section were reconstructed by regularized inversion of the travel time data for two rays. The hourly-mean current showed the generation of nonlinear internal tides with amplitudes of 1.0-1.5 ms À1 and periods of 6 h superimposed on semidiurnal internal tides with amplitudes decreasing from the upper to lower layer. The hourly-mean temperature was characterized by variations with amplitudes of 1.0-1.5 C and periods of 6 and 8 h. The current variations showed an out-of-phase relation between the upper and lower layers while the temperature data varied in-phase for all five layers. The two-day-mean current and temperature showed a stratified structure, varying from À0:6 to À0:1 ms À1 and from 23.8 to 28.0 C, respectively. The five-layer current and temperature were significantly above the inversion errors.
“…[5] Coastal acoustic tomography (CAT) was proposed as the application of Ocean Acoustic Tomography (OAT) to coastal seas, with the goal of continuously monitoring tidal currents in ports, bays, straits, and inland seas without disturbing shipping, fisheries, or marine aquaculture industries [Kaneko et al, 1994;Park and Kaneko, 2000]. Based on CAT, fluvial acoustic tomography (FAT) is designed for continuous measurement of the crosssectional average velocities in shallow rivers using higher frequencies (10-30 kHz).…”
[1] Long-term variations of streamflow in a tidal channel were measured using a Fluvial Acoustic Tomography (FAT) system through one transmission path. FAT is an innovative acoustic technology that utilizes the time-of-travel method to determine velocity between two points from multiple ray paths that traverse the entire cross-section of stream. Due to high spatial variability of flow distribution stationary ADCP measurements were not likely to yield true section-averaged flow velocity and moving-boat ADCP method was therefore used to provide reference data. As such, two short-term moving boat ADCP campaigns were carried out by the authors. In the first campaign, a couple of acoustic stations were added to the FAT system in order to resolve flow angularity in addition to the mean velocity. Comparing the FAT results with corresponding ADCP section-averaged flow direction and velocity indicated remarkable consistency. Second campaign was designed to capture the influence of salt wedge intrusion on the sound propagation pattern. It was found that FAT velocity measurements bias high if acoustic stations lay inside the cooler freshwater layer. Ray-tracing hindcasts suggest that installing acoustic stations inside the salt wedge may significantly improve function of output of the system. Comparing salinities evaluated from long-term FAT travel time records with nodal salinity measurements provided by conductivity-temperature sensors reveals the potential ability of FAT in measuring salt flux.
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