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Claude Frankignoul

Abstract

The stochastic character of short time scale atmospheric variables induce unpredictable fluctuations in the climatic system. These fluctuations are treated here as a “forced noise level” to be taken into account in climate modeling. A simple statistical model based on recent work by Hasselmann (1976) is used to estimate the resulting error in the calculated means of climate variables over finite intervals. This error may be large for short record lengths, as illustrated for the sea surface temperature. Some consequences relevant to joint ocean-atmosphere models and climate change experiments are discussed.

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Claude Frankignoul

Abstract

The isotropy of the internal wave field is investigated from short-time spectra of horizontal current measured in the deep sea. A significant anisotropy is detected at high frequencies during most periods of large mean current. The possible cause of this phenomenon is discussed. A theoretical investigation of Doppler distortion of the measurements shows that the Doppler effect cannot produce the observed anisotropy, which is more likely due to the interaction between internal waves and mean shear currents. Data collected during the MODE-0 experiment suggests this anisotropy over short periods of time is produced by the modulation of the internal wave field by the spatial gradients of low-frequency currents, in good agreement with the theory of Müller. The possible influence of critical layer absorption is briefly discussed.

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Claude Frankignoul

Abstract

A simple SST anomaly model is used to demonstrate that midlatitude statistical atmospheric models bias the air–sea fluxes toward positive air–sea feedback and distort the coupling between ocean and atmosphere.

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Peter Müller and Claude Frankignoul

Abstract

To assess the role of direct stochastic wind forcing in generating oceanic geostrophic eddies we calculate analytically the response of a simple ocean model to a realistic model wind-stress spectrum and compare the results with observations. The model is a continuously stratified, β-plane ocean of infinite horizontal extent and constant depth. All transfer and dissipation processes are parameterized by a linear scale-independent friction law (Rayleigh damping). The model predictions that are least sensitive to this parameterization, the total eddy energy and the subsurface displacement, are in good agreement with observations in mid-ocean regions far removed from strong currents. Properties that depend crucially on the parameterization of nonlinearities and topographic effects are not well reproduced. Observed coherences and seasonal modulations provide direct evidence of wind forcing at high frequencies where motions have little energy. Direct evidence at the more energetic low frequencies will be difficult to detect because the expected coherences are small. Altogether, the present results suggest that direct wind forcing may well be the dominant forcing mechanism for central ocean eddies.

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Claude Frankignoul and Nathalie Sennéchael

Abstract

A lagged maximum covariance analysis (MCA) of monthly anomaly data from the NCEP–NCAR reanalysis shows significant relations between the large-scale atmospheric circulation in two seasons and prior North Pacific sea surface temperature (SST) anomalies, independent from the teleconnections associated with the ENSO phenomenon. Regression analysis based on the SST anomaly centers of action confirms these findings. In late summer, a hemispheric atmospheric signal that is primarily equivalent barotropic, except over the western subtropical Pacific, is significantly correlated with an SST anomaly mode up to at least 5 months earlier. Although the relation is most significant in the upper troposphere, significant temperature anomalies are found in the lower troposphere over North America, the North Atlantic, Europe, and Asia. The SST anomaly is largest in the Kuroshio Extension region and along the subtropical frontal zone, resembling the main mode of North Pacific SST anomaly variability in late winter and spring, and it is itself driven by the atmosphere. The predictability of the atmospheric signal, as estimated from cross-validated correlation, is highest when SST leads by 4 months because the SST anomaly pattern is more dominant in the spring than in the summer. In late fall and early winter, a signal resembling the Pacific–North American (PNA) pattern is found to be correlated with a quadripolar SST anomaly during summer, up to 4 months earlier, with comparable statistical significance throughout the troposphere. The SST anomaly changes shape and propagates eastward, and by early winter it resembles the SST anomaly that is generated by the PNA pattern. It is argued that this results via heat flux forcing and meridional Ekman advection from an active coupling between the SST and the PNA pattern that takes place throughout the fall. Correspondingly, the predictability of the PNA-like signal is highest when SST leads by 2 months. In late summer, the maximum atmospheric perturbation at 250 mb reaches 35 m K−1 in the MCA and 20 m K−1 in the regressions. In early winter, the maximum atmospheric perturbation at 250 mb ranges between 70 m K−1 in the MCA and about 35 m K−1 in the regressions. This suggests that North Pacific SST anomalies have a substantial impact on the Northern Hemisphere climate. The back interaction of the atmospheric response onto the ocean is also discussed.

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Claude Frankignoul and Antoine Molin

Abstract

The GISS general circulation model (GCM) is used to investigate the influence of a positive sea surface temperature (SST) anomaly in the subtropical North Pacific on the Northern Hemisphere wintertime circulation. As the set of model data is small, the signal-to-noise ratio is low, and statistical significance is difficult to establish. Only local effects are detected with the univariate t-test, but a multivariate analysis based on hypothesis testing shows that the SST anomaly induces a small signal in the middle and upper troposphere. The same technique is applied to investigate whether the GCM response can be predicted in part from a specification of the SST anomaly, using a simple linear quasi-geostrophic equivalent barotropic model. The model is forced by a vorticity sink proportional to the SST anomaly, as the latter induces condensation heating and upper level divergence. When the barotropic model is linearized about the zonally symmetric part of the mean GCM state in the control runs, no satisfactory prediction of the GCM response is obtained. However, when the zonal variations of the GCM basic control state are taken into account, the linear model prediction is statistically significant, even if only a small fraction of the GCM signal is accounted for. The agreement with the GCM data is best when the equivalent barotropic level is in the upper troposphere, and it depends little on the amount of dissipation. On the other hand, it is very sensitive to the details of the mean flow waviness.

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Julie Deshayes and Claude Frankignoul

Abstract

The response of the upper limb of the meridional overturning circulation to the variability of deep-water formation is investigated analytically with a linear, reduced-gravity model in basins of simple geometry. The spectral characteristics of the model response are first derived by prescribing white-noise fluctuations in the meridional transport at the northern boundary. Although low-frequency basin modes are solutions to the eigenproblem, they are too dissipative to be significantly excited by the boundary forcing, and the thermocline depth response has a red spectrum with no prevailing time scale other than that of a high-frequency equatorial mode, only flattening at the millennial time scale because of vertical diffusivity. The meridional transport is asymmetric about the equator because the northern part of the basin is directly influenced by the boundary forcing while the southern part is mostly set in motion by long Rossby waves. This results in the equator acting as a low-pass filter for the Southern Hemisphere, which clarifies the so-called buffering effect of the equator. In a basin connected by a southern circumpolar channel, the thermocline depth and the transport spectra are redder than in the forced basin and, when a somewhat more realistic stochastic forcing derived from general circulation model simulations is considered, the variability is strongly reduced at high frequency. The linear model qualitatively explains several features of the low-frequency variability of the meridional overturning circulation in climate models, such as its red spectrum and its larger intensity in the North Atlantic Ocean.

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Claude Frankignoul and Peter Müller

Abstract

Stochastic fluctuations in the buoyancy flux at the air-sea interface create density anomalies in the oceanic surface layer, which drive quasi-geostrophic motions in the ocean interior. The efficiency of this forcing mechanism is evaluated by comparison with wind-stress forcing. Stochastic buoyancy forcing is found to be always negligible in the wavenumber-frequency range of oceanic geostrophic eddies. The effect of mass exchange anomalies at the surface is also found to be negligible. The conclusions seem applicable to time scales up to centuries.

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Claude Frankignoul and Peter Müller

Abstract

The quasi-geostrophic response of the ocean to stochastic forcing by wind stress and atmospheric pressure is investigated using a linear, continuously stratified, β-plane oceanic model with a flat bottom. We consider a spectral representation of the forcing and response fields, and we estimate the oceanic response using a vertical normal mode expansion. Model spectra of the wind stress, wind stress curl and surface pressure fields are constructed. In the wavenumber-frequency range of quasi-geostrophic eddies, the observations suggest that because of their short correlation time scale, the forcing fields are, to a reasonable approximation, white in frequency space and symmetric in wavenumber space. Forcing by the wind stress has the dominant role. The oceanic response can be off-resonant or resonant. In the off-resonant case, we predict oceanic wavenumber-frequency response spectra. In case of resonance we estimate total energy transfer rates by integrating the oceanic response over depth and wavenumber (in the range 2π/4000 km−1–2π/50 km−1) and we distinguish between the barotropic and the total baroclinic response, the latter being obtained by summing the contribution of all baroclinic modes.

The barotropic response is resonant at practically all eddy frequencies, and the baroclinic response is resonant at frequencies smaller than the maximum frequency of the first baroclinic Rossby wave. In midlatitudes, we find comparable energy input rates into barotropic and baroclinic modes, of the order of 3 × 10−4 W m−2. In high latitudes the input is comparable for barotropic Rossby waves and smaller for baroclinic ones. The total energy input rate by resonant forcing is only one order of magnitude smaller than the energy input rate from the mean atmospheric circulation into the general oceanic circulation. It is smaller, but comparable with the rate of energy conversion from the mean oceanic circulation into quasi-geostrophic eddies by barotropic and baroclinic instabilities. At medium and high frequencies, the baroclinic response is off-resonant. The model predicts red frequency spectra that are consistent with temperature observations in the central North Pacific. In particular, the seasonal variability of the observed eddy field is reproduced. A comparison with observations in the western North Atlantic also suggests that local stochastic forcing by the atmosphere is an important generating mechanism for the eddies in regions of low eddy activity.

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Pascale Braconnot and Claude Frankignoul

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The multivariate model toning procedure of Frankignoul et al. has been extended to the general time-series case, thus allowing to test ocean model ability at simulating the interannual variability. The method aims at distinguishing between model inadequacies and data uncertainties; model performances are assessed from a misfit evaluated in a space of strongly reduced dimension with basis vectors issued from a double application of common principal component analysis. The testing procedure has been used to investigate the ability of Cane's linear multimode model at simulating the evolution of the 20°C isotherm depth in the equatorial Atlantic during the 1982–1984 FOCAL/SEQUAL experiment. Using Monte Carlo techniques and five different drag laws, 25 equally plausible wind-stress fields were constructed to represent the wind-stress uncertainties consistently with the sample means and variances of the original ship measurements. Even during this well-sampled period, the forcing uncertainties were substantial, with corresponding model response uncertainties as large as the interannual variability; the largest source of uncertainty is the drag coefficient indeterminacy, except in poorly sampled areas where sampling and measurement errors become comparable.

Although the linear multimode model successfully simulates many features of the thermocline depth variability, there are some discrepancies with the observations, as in the Gulf of Guinea where the model poorly reproduces the eastward progression of the equatorial upwelling during summer. The multivariate analysis shows that the model–reality differences, too large to be explained by forcing and initial conditions uncertainties are mostly due to model deficiencies. As the FOCAL/SEQUAL data provide a very stringent test of model performance they are particularly useful for model tuning and intercomparison. The superiority of the two-mode version of the linear model over the two-mode one is thus more clearly established than in a previous comparison with the mean seasonal variations of the suffice dynamic topography, and the LODYC general circulation model is shown to represent the 1982–84 changes in thermocline depth significantly better than the linear model.

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