We present a new parametric autocovariance kernel function for characterizing properties of the mesoscale eddy field and the non-phase-locked internal tide from ocean time series records. We demonstrate that the model captures the important spectral properties, namely the spectral roll-off of the mesoscale continuum and the broad spectral “cusps” centered around the tidal forcing frequencies. The spectral cusp model has three main parameters that characterize the non-phase-locked internal tide: the amplitude, a decorrelation timescale and a shape parameter that captures the rate at which the cusp rolls away. Estimation of the third shape parameter is novel. We argue that an integral timescale is the most suitable characteristic timescale and show how it relates to the parametric decorrelation timescale. A key innovation of this work is that we estimate the parameters in the frequency domain using the debiased Whittle likelihood, thus avoiding the computational demands of estimating the autocovariance in the time domain. We apply our spectral parameter estimation technique to output from idealized and realistic numerical experiments of internal tides propagating through a mesoscale eddy field. We robustly demonstrate that both the non-phase-locked amplitude and integral timescale are influenced by the amplitude of the mesoscale flow field. Furthermore, we reveal that the integral timescale is set by global properties of the eddy field, whereas the shape of the spectral cusp is set by its local properties. The semi-diurnal integral timescale, calculated from a 12-month long, realistically forced ocean basin experiment, was 5–7 d and relatively constant in space.

Previous studies have highlighted the individual importance of diurnal warm layers (DWLs) and surface-layer fronts within the surface boundary layer (SBL) in regulating energy, momentum, and gas exchange between the atmosphere and the ocean. This study investigates the interactions between DWLs and surface-layer fronts using field observations and numerical turbulence models. Our study provides the real-ocean relevance of the coexistence of DWLs and surface-layer fronts in the SBL in an eddy-rich tropical ocean subjected to intense solar heating and weak winds. We found that the presence of a DWL isolates the deeper layers of the SBL from diabatic and frictional surface forcing, causing these layers to quickly become non-turbulent while remaining in a state of marginal stability. This condition suggests that small perturbations from local processes, such as internal tides and waves, can easily trigger instability and turbulence. Additionally, frontal dynamics were observed to deepen the SBL, allowing near-surface diurnal shear associated with DWL dynamics to penetrate to greater depths during nighttime, compared to conditions without a front, thereby facilitating the vertical transport of heat and tracers. Our findings underscore the necessity of accurately representing the interactions between DWLs and surface-layer fronts to enhance the precision of ocean circulation and climate models.

We describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Monte Carlo Markov Chain (MCMC) sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters.

We present an empirical model of the seasonal variability of the internal tide using seasonal harmonics to modulate the amplitude of the fundamental tidal constituents. Internal tide data, from both long-term, in-situ moorings and a mesoscale- and internal tide-resolving ocean model, are used to demonstrate the performance of the seasonal harmonic model for the Indo-Australian Basin Region. The seasonal model describes up to 15 % more of the observed (baroclinic) sea surface height variance than a fixed-amplitude harmonic mode at the mooring sites. The ocean model results demonstrate that the study region, which includes the Australian North West Shelf (NWS), Timor Sea and southern Indonesian Islands, is dominated by standing wave interference patterns due to the presence of multiple generation sites. The seasonal harmonic model reveals that temporal shifts in the standing wave patterns coincide with seasonal variations in density stratification. This shift is particularly evident within distances of 2 - 3 internal wave lengths from strong generation sites. The fraction of the variance of the internal tide signal explained by seasonal modulations is largest in standing wave node regions, contributing to differences in predictive skill of the seasonal harmonic model at two moorings separated by only 38 km. Output of the harmonic model also demonstrated that the seasonally-evolving M2 internal tide propagating southward from Lombok Strait had a small amplitude in October when shear from the Indonesian Throughflow was strongest.