Correlated signals and causal transport in ocean circulation

Abstract

This article presents a framework for interpreting the time‐lagged correlation of oceanographic data in terms of physical transport mechanisms. Previous studies have inferred aspects of ocean circulation by correlating fluctuations in temperature and salinity measurements at distant stations. Typically, the time lag of greatest correlation is interpreted as an advective transit time and hence the advective speed of the current. In this article, we relate correlation functions directly to the underlying equations of fluid transport. This is accomplished by expressing the correlation functions in terms of the Green's function of the transport equation. Two types of correlation function are distinguished: field–forcing correlation and field–field correlation. Their unique relationships to the Green's function are illustrated in two idealized models of geophysical transport: a leaky pipe model and an advective–diffusive model. Both models show that the field–forcing correlation function converges to the Green's function as the characteristic (time‐ or length‐) scale of forcing autocorrelation decreases. The leaky pipe model provides an explanation for why advective speeds inferred from time‐lagged correlations are often less than the speed of the main current. The advective–diffusive model reveals a structural bias in the field–field correlation function when used to estimate transit times.

On the origin and propagation of Denmark Strait overflow water anomalies in the Irminger Basin

“…The direct correlation from the Denmark Strait sill to Angmagssalik gives similar time scales of 8–16 days and mean current speeds of O( ). These speeds probably underestimate the real mean flow, as lagged correlations reflect the combined effect of all advective‐diffusive transports and not only the advection [ Jeffress and Haine , ]. Within the uncertainty of the time lags (which is about 2 days), these results are in reasonable agreement and also conform with other studies (e.g., Eulerian estimates from moorings as in von Appen et al .…”

Shear dispersion and delayed propagation of temperature anomalies along the Norwegian Atlantic Slope Current

“…(Furevik, 2001; Sundby and Drinkwater, 2007;Yashayaev and Seidov, 2017). A related method for analysing propagation uses temperature or salinity correlations between two locations along the flow: The time lag for which the correlation reaches its maximum, is interpreted as a mean transit or advection time between the points (Jeffress and Haine, 2014). Using this approach, Skagseth et al (2008) analyse mooring records of temperature in the Svinøy section and in the Barents Sea Opening (BSO) and find a maximum in correlation at a lag (or transit time) of two years, corresponding to a propagation speed of about 2 cm s −1 .…”

Estimating sea-surface temperature transport fields from stochastically-forced fluctuations

“…We refer to (9) as the global method because ′ ′ c c T contains all × M M covariances in the system. In practice the covariance matrices of high dimensional systems often have high condition numbers and cannot be inverted accurately, so measures are taken to reduce the dimensionality of the system.…”

“…The local method assumes spatial locality in the linear operator in order to reduce the dimension of the inverted covariance matrix in (9). This approach assumes that the dominant physical processes in  can be expressed as local spatial derivatives, such as advection and diffusion.…”

“…This approach has provided a foundation for quantifying the transport of a variety of tracers in geophysical reservoirs [4][5][6]. If SST arises from a stochastic atmospheric forcing [7] and is advected and diffused over certain temporal and spatial scales [8], then the transport response function is related to correlation functions by the covariance structure of the atmospheric forcing [9].…”