## 1. Introduction

[2] The mixed layer of the ocean is commonly considered as the region near its surface with vertically quasi-uniform oceanic tracers (temperature, salinity and density) above a layer of more rapid vertical changes. The intense vertical turbulent mixing near the surface penetrates a short distance into the top of the pycnocline and is the cause of the observed vertical uniformity. The vigorous vertical turbulence is generated mainly by the action of the horizontal momentum and the vertical buoyancy fluxes derived from the atmospheric energetic motions. Variations of these fluxes are well documented [e.g., *Kalnay et al.*, 1996; *Roads et al.*, 2003] and these force variations of the mixed layer depth, *h*_{mix}, on daily to interannual timescales. The heat budget of *h*_{mix} is of particular interest because it governs the evolution of the sea surface temperature (SST), which is the most important ocean parameter influencing the atmosphere. It is important to know not only the SST evolution but also how deep the homogeneous thermal energy column penetrates into the stratified ocean. The main objectives of this paper are to present a new computation of the global distribution of *h*_{mix}, to verify the skill of this method based on both global observations and the output of ocean general circulation models (OGCMs) and to analyze the effect of *h*_{mix} anomalies on seasonal-to-interannual ocean-atmosphere interaction.

[3] As a point of departure, consider the global coupled atmosphere-ocean model of *Alexander et al.* [2000]. In its locally one-dimensional upper ocean *h*_{mix} is time dependant and there is a flux of thermal energy out of the bottom of the mixed layer. According to *Alexander et al.* [2000] the evolution of SST anomalies, δ(SST), is dominated by three terms:

where *h*_{mix} ≡ 1/η, overbars define a temporal mean, and δ( ) defines the departures from the mean; *c*_{p} is the specific heat and ρ the density of seawater. The entrainment heat flux is proportional to the product of the entrainment rate *w*_{e} and the temperature jump at the base of the mixed layer Δ*T*. Therefore changes in δ(SST) are forced by the time integration of highly energetic short-term anomalous variations of surface fluxes, δ(*F*), the entrainment rate at the base of the mixed layer and, of capital importance for this study, anomalous *h*_{mix}.

[4] *Dommenget and Latif* [2002] point out that the variability of *h*_{mix} on seasonal to longer timescale should also be an important parameter to consider in climate model diagnostics. In our context the second term on the right hand side of equation (1) gives a direct way to estimate the sensitivity of SST evolution in an anomalous *h*_{mix} field. A monthly mean δ(*h*_{mix}) anomaly during midlatitudinal spring and summer of 5 m would result in 0.25 K month^{−1} δ(SST) change (with δ(η = −_{mix}^{−2}δ(*h*_{mix}) a monthly mean _{mix} = 50 m, = 200 W m^{−2}, *c*_{p} = 4000 J kg^{−1} K^{−1} and ρ = 1026 kg m^{−3}). This monthly change of SST is well within its observational accuracy on a global basis [*Reynolds and Smith*, 1994]. The closure of *Alexander et al.* [2000] is the importance of anomalous *h*_{mix}, beside heat flux variations, during spring and summer north of 20°N.

[5] The impact of anomalous entrainment out of the mixed layer base to the SST tendency is indirectly through *h*_{mix}. The stored anomaly of thermal energy beneath the seasonal thermocline can last for many years, which in our context is represented by the third term on the right hand side of equation (1). Thermal anomalies of the previous winter become entrained into the current winter mixed layer as the mixed layer deepens in the fall [*Alexander et al.*, 2000]. The implementation of this “reemergence mechanism” could also directly extend the persistence of winter SST anomalies to several years [*Alexander and Deser*, 1995; *Deser et al.*, 2003]. Therefore, to quantify, understand and ultimately predict ocean-atmosphere interactions on seasonal-to-climate relevant timescales it is crucial that the sensitivity of anomalous SST to changes of *h*_{mix} be well modeled in comparison to observations.

[6] A more complicated set of processes, as wind stress changes that force horizontal currents to advect thermal energy from place to place seem to explain a portion of the observed SST changes in the El Niño–Southern Oscillation (ENSO) regime in the tropical Pacific [*Jin*, 1997]. Additional changes are caused by the mixed layer depth anomalies, including turbulent fluxes out of the mixed layer bottom [e.g., *Wang and McPhaden*, 2001], internal waves, and ocean eddies. To be useful in climate analyses and climate modeling, the uncertainty of the *h*_{mix} must match the uncertainty of SST observations, or in our context, that all terms in equation (1) have comparable errors. The two major reasons for the lack of observed *h*_{mix} are the insufficient number of observations, both in spatial and temporal senses, to average the effects of internal waves and ocean mesoscale [e.g., *Moisan and Niiler*, 1998] and that *h*_{mix} is not a directly measurable quantity. The ocean mixed layer depth *h*_{mix} is most commonly defined as that depth where the temperature (potential density) has decreased (increased) from the surface value by a constant amount Δ. For climatological profiles on a global scale it is found that the Δ criterion introduces an error of 20 m in *h*_{mix} [*Kara et al.*, 2000b], which is several times larger than the error of the terms in equation (1) introduced by SST or flux errors. The error in *h*_{mix} seems to be reduced when applying the threshold method to individual profiles [*de Boyer Montégut et al.*, 2004].

[7] The main focus in this paper is to establish a new criterion for *h*_{mix} that can be used globally to study the large-scale processes of thermal energy storage in the upper ocean in both observations and in OGCM simulations. In this respect *h*_{mix} should be considered in a similar way that the high-quality SST is currently used for a diagnostic of the upper ocean processes. We require from the introduced criterion that it minimizes systematic errors between estimates of *h*_{mix} based on measured data and the output of OGCMs and that applications of the criterion to both data sets provide comparable statistics for *h*_{mix}, respectively. This analysis should make model-data comparison more stringent because not only must SST be correct, but also its first vertical moment, or *h*_{mix}. We use the global historical hydrographic measurements with both high and low vertical resolutions, including the World Ocean Circulation Experiment (WOCE) data set, and a full OGCM output to determine whether calculations of *h*_{mix} and its variability can be improved.

[8] The paper is organized as follows: In section 2 we present the data and discuss the difficulties in estimating *h*_{mix} from these data; we then introduce a new criterion for estimating an *h*_{mix} (which we refer to as *h*_{mix/c}) and test the sensitivity of *h*_{mix/c} to the assumptions made in our new criterion and also compare our results with the more traditional Δ criterion. In section 3 we introduce a “quality index” and discuss the quality of the observed *h*_{mix/c}. In section 4 we describe some characteristics of *h*_{mix/c} and its space and time variability over ocean basins. In section 5 we apply our algorithm for *h*_{mix} to the output of the Massachusetts Institute of Technology (MIT)/OGCM/Estimating the Circulation and Climate of the Ocean (ECCO) model in an assimilation mode and compare *h*_{mix/c} to the diagnosed planetary boundary layer depth in the model *K*PP parameterization. A summary of our results is given in section 6.