Estimating uncertainties on a Gulf Stream mixed-layer heat budget from stochastic modeling

Highlights

• Winter mixed-layer cooling in the GS similar with ERA40 or CORE forcing

• In contrast significant differences on the heat budget terms due to forcing

• OGCM uncertainties estimated from an ensemble of 33 simulations

• Large uncertainties on the mixed-layer heat budget terms along the GS path

• Ensemble spread of advection and vertical diffusion due to mesoscale decorrelation

Abstract

This study aims to explore the robustness of the mixed-layer heat budget as estimated from an eddy-permitting model with respect to uncertainties in atmospheric forcing. We illustrate how statistics from an ensemble can be used in a first step towards the calculation of error bars of any simulated quantity, such as the mixed-layer heat budget. The statistics from an ensemble of 33 simulations are derived in order to infer information on the model errors space and time variability of the main terms of the heat budget. The ensemble is generated by perturbing the wind forcing and the incoming solar radiation as uncertainties on these fields are expected to be a main source of errors for the surface layer representation in the model at monthly to seasonal scales. We focus on the mixed-layer in the Gulf Stream system during the deepening period (Sept.–March). The results indicate that large errors are expected at the Gulf Stream front location and just north of it. The largest errors are found on the zonal and meridional advection and vertical diffusion terms: they can locally reach values that are larger than the terms themselves. We observe a rapid increase with time of the errors for both these terms. The error growth is mainly due to the mesoscale decorrelation. The impact of wind errors on southward Ekman transport and surface turbulence generates uncertainties on the vertical diffusion term just north of the Gulf Stream front.

We work with an eddy-permitting configuration similar to those used in ocean reanalysis projects (e.g. SODA, and GLORYS). Our results suggest that for such configurations, at monthly to seasonal time scales, the impact of uncertainties in the atmospheric forcing is weak on the mixed-layer cooling but very large on the zonal and meridional advection and vertical diffusion heat budget terms. In consequence, the estimate of these quantities from ocean reanalyses is not robust with respect to the atmospheric forcing and should be provided with error bars.

Introduction

Estimating and understanding the ocean surface mixed-layer heat content distribution and the physical mechanisms that rule it is fundamental to oceanic studies, whatever the time scale considered. Indeed the superficial heat content results from and constrains different processes that in turn affect the oceanic circulation as well as heat, fresh water and momentum fluxes between the ocean and the atmosphere (see for instance Dong and Kelly, 2004). Moreover the surface water hydrological properties are transferred to deeper layer through subduction that takes place when the mixed-layer shoals.

In many studies dedicated to heat budget estimations, numerical models are used to provide information on the terms that are poorly or not observed, such as 3D advective terms and those related to vertical physics. These latter are expected to play a fundamental role. Diffusivities and vertical velocities cannot be usually inferred from observations with the necessary precision, unless the experiment is dedicated to the investigation of these processes. In previous studies, heat budgets have been estimated from the oceanic and atmospheric mixed-layer measured variables and have been compared to numerical simulations, in experiments such as SEMAPHORE (Caniaux and Planton, 1998), Subduction (Spall et al., 2000) and POMME (Paci et al., 2007, Giordani et al., 2005).

The use of forced numerical simulations however raises the question of the confidence one can have in the simulation and in particular in the atmospheric forcing used. Different sources of uncertainties are expected to influence the air/sea exchanges: uncertainties in the atmospheric fields (air temperature, wind, humidity, etc.) and uncertainties in the parameterizations and parameters in the bulk formulae used to couple oceanic and atmospheric variables. These uncertainties are considered as potentially critical, a fact that has led to several attempts to derive atmospheric forcing products that lead to more realistic ocean simulations. For instance, Large and Yeager (2004) combined information from satellite data, historical precipitation records, and in situ observations with the NCEP/NCAR reanalysis (Kalnay et al., 1996) to generate the so-called CORE product. Hybrid forcing fields have been built from CORE and the ERA40/ECMWF reanalysis (Uppala et al., 2005) variables to force global interannual simulations within the context of the DRAKKAR project (Brodeau et al., 2010). Other efforts are put into estimating uncertainties in atmospheric variables stemming from different reanalyses in an attempt to derive upper bound estimates of uncertainties (Chaudhuri et al., 2013). At last, data assimilation methods can provide adjustments to the atmospheric forcing fields along with the ocean state estimation process (e.g. Ayoub, 2006, Wunsch and Heimbach, 2007). Sensitivity of the surface layers in an OGCM to changes in wind forcing has been discussed in the study of Cravatte and Menkes (2009) in the equatorial Pacific cold tongue region. They compare mixed-layer heat budgets in the cold tongue area from simulations forced with five different wind products. They conclude that heat budget estimated from one simulation only (i.e. with a unique wind forcing) must be cautiously examined since the estimation is not robust with respect to the choice of forcing. The response of a model to the uncertainties in the forcing in terms of superficial heat content is deemed critical for seasonal predictions; but it is poorly known qualitatively or quantitatively. There is however a growing interest in the oceanographic community to provide budget for uncertainties on simulated or forecasted ocean quantities (e.g. Kim et al, 2011).

Several attempts have been made in the past to compute the heat budget in the upper layers of the Gulf Stream jet and recirculation system (e.g. Dong and Kelly, 2004, Kelly et al., 2010, Schiller and Ridgway, 2013) at interannual to seasonal scales, relying on observations or numerical simulations. However, to our knowledge, none have explored the robustness of these ‘one shot’ budgets to errors in the atmospheric forcing, although inaccuracies in wind stress and more generally of air-sea flux estimates are recognized as impacting significantly estimates of convection and heat transports (e.g. Wang and Carton, 2002, Marshall and CLIMODE Group, 2005). In a different context, Lucas et al. (2008) showed the large sensitivity of the temperature field in the upper 200 m in an area of the separated Gulf Stream to uncertainties in the atmospheric forcing fields. The interplay between horizontal advective effects, vertical mixing triggered by convection or wind generated turbulence, and mesoscale activity makes the ocean response to atmospheric perturbations very complex over seasonal time scales.

Within such a context, we propose to illustrate the way stochastic modeling can be used to provide estimates of the uncertainties given known error sources on simulated quantities, to apply the method to the study of the mixed-layer heat budget in the separated Gulf Stream region and analyze the physical processes leading to such uncertainties. We focus here on the mixed layer heat budget in the Gulf Stream extension region during the cooling period in an eddy-permitting simulation. With such a configuration (i.e. eddy-permitting) we target the space–time scales range typical of present reanalysis products (such as SODA (Carton and Giese, 2008), GLORYS from MERCATOR-Océan (Ferry et al., 2010) and global data assimilation systems such as ECCO (Wunsch et al., 2009)) that are widely used in climatic studies. We first show that using two different atmospheric reanalyses to force an ocean model yields different estimations of the mixed-layer temperature budget terms. Given such sensitivity, one can expect errors on the budget to arise from uncertainties in the atmospheric fields used to force the ocean model. We propose an ensemble approach inherited from ensemble data assimilation methods, to quantify and to characterize the uncertainties on the budget terms due to those in the atmospheric forcing. The ensemble spread, computed as the standard deviation about the ensemble mean, gives an estimate on the uncertainties on the model results. We then discuss the possible physical processes at work to explain the space-time structure of the obtained uncertainties or ‘error bars’.

The paper outline is as follows: in Section 2, we describe our experimental framework and give a general overview of the main features of the surface circulation in the reference run. Section 3 presents the stochastic modeling approach and the method of generating the ensemble. In Section 4, we analyze the mixed-layer depth and net heat flux at the surface in the different simulations. Section 5 is dedicated to the analysis of the mixed-layer heat budget and of its sensitivity to atmospheric perturbations. We conclude in Section 6.