Anzhou Cao

Inverse Estimation of Open Boundary Conditions in the Bohai Sea

This paper presents an algorithm for the estimation of open boundary conditions (OBCs) which force tides in the interior region by an adjoint data assimilation approach. Assuming that OBCs are position dependent, OBCs can be approximated by linear interpolation among values at certain independent points (IPs). Twin experiments are performed to examine the sensitivity of the model to the IP distribution and interpolation radius. It is proved that the prescribed OBCs can be well recovered with appropriate number of IP and interpolation radius. In the Bohai Sea model domain with horizontal resolution of , the appropriate number of IP is 3 and the interpolation radius is 60′. In the practical experiment, the M2 constituent in the Bohai Sea is simulated by assimilating the T/P data and tidal gauge data. The mean absolute errors in amplitude and phase are 5.0 cm and 5.7°, respectively, and the cochart obtained shows the character of M2 constituent in the Bohai Sea.

Extraction of Internal Tidal Currents and Reconstruction of Full-Depth Tidal Currents from Mooring Observations

AbstractTo obtain internal tidal currents and full-depth tidal currents from limited mooring observations, a method is put forward combining harmonic analysis and modal decomposition. Harmonic analysis is used to separate tidal currents of different constituents, and modal decomposition is used to calculate full-depth tidal currents of each mode. By adding the barotropic tidal currents to all the baroclinic ones, the full-depth tidal currents of each constituent are reconstructed. The feasibility and accuracy of the proposed method is tested by twin experiments. Then, the method is used to extract tidal currents of each mode and to reconstruct full-depth tidal currents for M2 and K1 from a 3-month-long time series of acoustic Doppler current data observed at a station in the northern South China Sea. Results indicate that the total kinetic energy (KE) of M2 is 25% larger than that of K1. For M2, the first baroclinic mode is the dominant one, followed by the barotropic one, and the sum of these modes accou...

Trajectory Estimation of Aircraft in a Double-Satellite Passive Positioning System with the Adjoint Method

A double-satellite passive positioning system is constructed based on the theory of space geometry, where two observation coordinate systems and a fundamental coordinate system exist. In each observation coordinate system, there exists a ray from the observation satellite to the aircraft. One difficulty lies in that these two rays may not intersect due to the existence of various errors. Under this situation, this work assumes that the middle point of common perpendicular between two rays is the actual position of aircraft. Based on the theory of space geometry, the coordinates of aircraft in the fundamental coordinate system can be determined. A dynamic model with the adjoint method is developed to estimate the trajectory of aircraft during the process of rocket propulsion. By assimilating observations, the trajectory of aircraft can be calculated. Numerical experiments are designed to validate the reasonability and feasibility of this model. Simulated results indicate that even by assimilating a small number of observations, the trajectory of aircraft can be estimated. In addition, the trajectory estimation can become more accurate when more observations are assimilated to the model.

On the Equilibration of Numerical Simulation of Internal Tide: A Case Study around the Hawaiian Ridge

AbstractTo investigate the equilibration of numerical simulation (ENS) of internal tide, a three-dimensional isopycnic coordinate internal tide model is applied to simulate the M2 internal tide on idealized topography and around the Hawaiian Ridge. An idealized experiment is carried out on a Gaussian topography, and the temporal variations of the baroclinic velocity and the baroclinic energy flux are analyzed, then ENS is studied, and two criteria are presented. Moreover, the impacts of four parameters [horizontal and vertical eddy viscosity coefficients, bottom friction coefficient, and damping coefficient (to parameterize the nonhydrostatic processes in the model)] on ENS during numerical simulations, the baroclinic velocity, the baroclinic tidal energy, and the baroclinic energy flux are investigated. It appears that ENS for the M2 internal tide is more sensitive to the horizontal eddy viscosity coefficient and the damping coefficient. To further examine the criteria of ENS, a numerical experiment is c...

Estimation of Eddy Viscosity Profile in the Bottom Ekman Boundary Layer

AbstractPrevious studies have shown that strong tidal currents can cause intense turbulent mixing near the seafloor in continental shelf areas. To quantify the turbulent mixing, the eddy viscosity coefficient is generally used. In this study, an estimation scheme is proposed to evaluate the eddy viscosity profile (EVP) in the bottom Ekman boundary layer based on the adjoint method. The estimation scheme is composed of the bottom Ekman boundary layer model and its adjoint model, and a minimization algorithm. The feasibility and effectiveness of the proposed scheme are validated by a series of twin experiments, where the proposed scheme is compared with three other schemes in previous studies. When large measurement errors exist, the proposed scheme performs better than the three other schemes. When large Ekman balance errors exist, the proposed scheme is better than two of the other schemes. The selection of components of the steady current and tidal constituents also influences the performance of the prop...

Harmonic Analysis in the Simulation of Multiple Constituents: Determination of the Optimum Length of Time Series

To investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2 ,S 2 ,K 1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently smallmeansthat HA resultsareindependent of thechoiceof TS,andthe corresponding TS length is regarded as the optimum. Results indicate that the range of 180‐195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimumlengthisindependentofadvection,nodalcorrections,andcomputedarea,andonlydependsonbottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180‐195 days.