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- Author or Editor: Peter D. Killworth x
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Abstract
Relaxation toward observed values is frequently undertaken in ocean models for numerous reasons. In level models, relaxation of some quantity takes the form of a linear “nudging” term proportional to the difference between observed and computed value of that quantity. In isopycnic models, relaxation of tracers and/or layer depth toward observed values is often employed as an equivalent. This note shows that relaxation of temperature and salinity—and hence density—in a level model is not equivalent to relaxation either of those tracers or of layer thickness in an isopycnic model. Comparison of layer thickness tendencies in the two model types shows that these differ by the ratio of observed vertical density gradient to model vertical density gradient. Only in the special case where the model remains close to observations are the two methods the same to leading order. It is not obvious whether isopycnic or level relaxation is to be preferred.
Abstract
Relaxation toward observed values is frequently undertaken in ocean models for numerous reasons. In level models, relaxation of some quantity takes the form of a linear “nudging” term proportional to the difference between observed and computed value of that quantity. In isopycnic models, relaxation of tracers and/or layer depth toward observed values is often employed as an equivalent. This note shows that relaxation of temperature and salinity—and hence density—in a level model is not equivalent to relaxation either of those tracers or of layer thickness in an isopycnic model. Comparison of layer thickness tendencies in the two model types shows that these differ by the ratio of observed vertical density gradient to model vertical density gradient. Only in the special case where the model remains close to observations are the two methods the same to leading order. It is not obvious whether isopycnic or level relaxation is to be preferred.
Abstract
Attempts to estimate the state of the ocean usually involve one of two approaches: either an assimilation of data (typically altimetric surface height) is performed or an inversion is carried out according to some minimization scheme. The former case normally retains some version of the time-dependent equations of motion; the latter is usually steady. Data sources are frequently not ideal for either approach, usually being spatially and temporally confined (e.g., from an oceanographic cruise). This raises particular difficulties for inversions, whose physics seldom includes much beyond the geostrophic balance. In this paper the authors examine an approach midway between the two, examining several questions. (i) What is the impact of data assimilated continuously to a steady state on regions outside the data sources? (ii) Can remote data improve the long-term mean of a model whose natural response is not close to climatology? (iii) Can an eddy-free model assimilate data containing eddies?
The authors employ an inversion using a simple North Atlantic model, which permits no eddies, but contains better dynamics than geostrophy (the frictional planetary geostrophic equations), and an assimilative scheme rather simpler than those normally employed, almost equivalent to direct data insertion, run to a steady state. The data used are real subsurface data, which do contain eddies, from World Ocean Circulation Experiment cruises in the northern North Atlantic. The presence of noise in these data is found to cause no numerical difficulties, and the authors show that the impact of even one vertical profile can strongly modify the water mass properties of the solution far from the data region through a combination of wave propagation, advection, and diffusion. Because the model can be run for very long times, the region of impact is thus somewhat wider than would occur for assimilations over short intervals, such as a year.
Abstract
Attempts to estimate the state of the ocean usually involve one of two approaches: either an assimilation of data (typically altimetric surface height) is performed or an inversion is carried out according to some minimization scheme. The former case normally retains some version of the time-dependent equations of motion; the latter is usually steady. Data sources are frequently not ideal for either approach, usually being spatially and temporally confined (e.g., from an oceanographic cruise). This raises particular difficulties for inversions, whose physics seldom includes much beyond the geostrophic balance. In this paper the authors examine an approach midway between the two, examining several questions. (i) What is the impact of data assimilated continuously to a steady state on regions outside the data sources? (ii) Can remote data improve the long-term mean of a model whose natural response is not close to climatology? (iii) Can an eddy-free model assimilate data containing eddies?
The authors employ an inversion using a simple North Atlantic model, which permits no eddies, but contains better dynamics than geostrophy (the frictional planetary geostrophic equations), and an assimilative scheme rather simpler than those normally employed, almost equivalent to direct data insertion, run to a steady state. The data used are real subsurface data, which do contain eddies, from World Ocean Circulation Experiment cruises in the northern North Atlantic. The presence of noise in these data is found to cause no numerical difficulties, and the authors show that the impact of even one vertical profile can strongly modify the water mass properties of the solution far from the data region through a combination of wave propagation, advection, and diffusion. Because the model can be run for very long times, the region of impact is thus somewhat wider than would occur for assimilations over short intervals, such as a year.
Abstract
Although data assimilation is now an established oceanographic technique, little work has been done on the interaction of the assimilation scheme and the physics of the underlying model. The way in which even a simple assimilation scheme (here nudging) can significantly alter the response of the model to which it is applied is illustrated here.
Using analytic and semianalytic models, the assimilation of sea surface height, density, and velocity is studied. It is shown that the assimilation can act to alter the high inertia–gravity wave frequency to be the order of the Coriolis parameter, a result that is of relevance to the problems of initialization. The theory also predicts an optimum strength of nudging, normally dependent on wavelength, wave speed, and latitude, which can give convergence of the assimilation on a timescale as short as a day. The results are verified by identical twin experiments using a full primitive equation model, the Free Surface Cox Code, both in barotropic spinup (results presented here) and in a more realistic baroclinic situation (results presented in Part II).
Abstract
Although data assimilation is now an established oceanographic technique, little work has been done on the interaction of the assimilation scheme and the physics of the underlying model. The way in which even a simple assimilation scheme (here nudging) can significantly alter the response of the model to which it is applied is illustrated here.
Using analytic and semianalytic models, the assimilation of sea surface height, density, and velocity is studied. It is shown that the assimilation can act to alter the high inertia–gravity wave frequency to be the order of the Coriolis parameter, a result that is of relevance to the problems of initialization. The theory also predicts an optimum strength of nudging, normally dependent on wavelength, wave speed, and latitude, which can give convergence of the assimilation on a timescale as short as a day. The results are verified by identical twin experiments using a full primitive equation model, the Free Surface Cox Code, both in barotropic spinup (results presented here) and in a more realistic baroclinic situation (results presented in Part II).
Abstract
A preoperational scheme has been implemented to calculate sea surface height fields at 7-day intervals over the North Atlantic. Input data from Argo floats is downloaded and processed in near–real time. The solution method is by Bernoulli inverse. Early results are encouraging. Features of the results are compared with both model and satellite data and show good agreement.
Abstract
A preoperational scheme has been implemented to calculate sea surface height fields at 7-day intervals over the North Atlantic. Input data from Argo floats is downloaded and processed in near–real time. The solution method is by Bernoulli inverse. Early results are encouraging. Features of the results are compared with both model and satellite data and show good agreement.
