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

Abstract

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 M 2 , S 2 , K 1 , and O 1 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 small means that HA results are independent of the choice of TS, and the 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 optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom 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.

Estimation of Bottom Friction Coefficient in Multi‐Constituent Tidal Models Using the Adjoint Method: Temporal Variations and Spatial Distributions

“…Following Gao et al. (2015), the 2D multi‐constituent tidal model was run for 30 days from 1 January 2010 (16 January 2010, in some of the following sensitivity experiments) with the hydrostatic state (i.e., ζ = u = v = 0), and the initial 15 days was spun up, which is sufficient to separate the simulated four principal tidal constituents (Cao et al., 2015). The adjoint model was run for 15 days backward in time from 31 January 2010 (15 February 2010, in some of the subsequent sensitivity experiments).…”

“…As shown in Fang et al (2004), M 2 , S 2 , K 1 , and O 1 are the principal tidal constituents in the BYECS, so these four principal tidal constituents (only M 2 or M 2 and K 1 in some of the following sensitivity experiments) were simulated. Following Gao et al (2015), the 2D multi-constituent tidal model was run for 30 days from 1 January 2010 (16 January 2010, in some of the following sensitivity experiments) with the hydrostatic state (i.e., ζ = u = v = 0), and the initial 15 days was spun up, which is sufficient to separate the simulated four principal tidal constituents (Cao et al, 2015). The adjoint model was run for 15 days backward in time from 31 January 2010 (15 February 2010, in some of the subsequent sensitivity experiments).…”

Two-Dimensional Numerical Simulation of Tide and Tidal Current of Eight Major Tidal Constituents in the Bohai, Yellow, and East China Seas

“…The hindcast run started at 0:00 on 1 October 2019, with a time step of 2 min, and the total duration of the simulation is 450 days. Cao et al [42] suggest that for the simultaneous simulation of multiple tidal constituents, the appropriate time span of sea level anomaly (SLA) series for harmonic analysis is approximately 1 year. As the model requires a stable process, the initial 90-day-long data of the simulation are not available.…”

Estimation of the Manning’s n coefficient in multi-constituent tidal models by assimilating satellite observations with the adjoint data assimilation

“…Following Wang et al (2021b), the 2D multi-constituent tidal model was run for 30 d from 1 January 2010 and the initial 15 d was spun up. The simulated results in the final 15 d were analysed to separate the simulated four principal tidal constituents (Cao et al, 2015). The adjoint model was run for 15 d backward in time from 31 January 2010 with the same horizontal resolution and time step.…”