Modeling ocean deep convection

Abstract The goal of this study is to assess models for Deep Convection with special emphasis on their use in coarse resolution ocean general circulation models . A model for deep convection must contain both vertical transport and lateral advection by mesoscale eddies generated by baroclinic instabilities. The first process operates mostly in the initial phases while the second dominates the final stages. Here, the emphasis is on models for vertical mixing. When mesoscales are not resolved, they are treated with the Gent and McWilliams parameterization. The model results are tested against the measurements of Lavender, Davis and Owens, 2002 (LDO) in the Labrador Sea. Specifically, we shall inquire whether the models are able to reproduce the region of “ deepest convection ,” which we shall refer to as DC (mixed layer depths 800–1300 m). The region where it was measured by Lavender et al. (2002) will be referred to as the LDO region. The main results of this study can be summarized as follows. (1) 3° × 3° resolution. A GFDL-type OGCM with the GISS vertical mixing model predicts DC in the LDO region where the vertical heat diffusivity is found to be 10 m 2 s −1 , a value that is quite close to the one suggested by heuristic studies. No parameter was changed from the original GISS model. However, the GISS model also predicts some DC in a region to the east of the LDO region. (2) 3° × 3° resolution. A GFDL-type OGCM with the KPP model (everything else being the same) does not predict DC in the LDO region where the vertical heat diffusivity is found to be 0.5 × 10 −4 m 2 s −1 which is the background value. The KPP model yields DC only to the east of the LDO region. (3) 1° × 1° resolution. In this case, a MY2.5 mixing scheme predicts DC in the LDO region. However, it also predicts DC to the west, north and south of it, where it is not observed. The behavior of the KPP and MY models are somewhat anti-symmetric. The MY models yield too low a mixing in stably stratified flows since they predict a critical Richardson number Ri (cr)=0.19 which is five times smaller than the value Ri (cr)=O(1) needed to obtain realistic ML depths. However, as discussed above, in unstable stratifications the MY models yield better results. On the other hand, the KPP model, which was motivated primarily by the need to overcome the MY “too low mixing” in stable stratification, yields at coarse resolution, no DC in the LDO region. In this respect, the GISS model, yields both a correct Ri (cr)=O(1) in stable stratification and correct results in the unstable configuration in the LDO region. (4) 1/3° × 1/3° resolution. In this case, KPP predicts mixed layer depths up to 1.7 km inside the LDO region where at coarse resolution none existed. However, the model still produces DC at locations outside the LDO region where it is not observed. However, since these regions are intermingled with very shallow mixed layer depths, the resulting mean mixed layer depths turn out to be less than 800 m almost everywhere outside the LDO region. (5) 1/12° × 1/12° resolution. In this case, KPP predicts mixed layer depths up to 3 km both inside and outside the LDO region. These regions are, here too, intermingled with very shallow mixed layer depths with resulting mean mixed depths greater than 800 m both inside and outside the LDO region. In conclusion, as for a model for deep convection to be used in coarse resolution, these results indicate that the GISS mixing model fares well with observations in both stable and unstable stratifications but overestimates its geographical extent. This leads to the problem of future improvements of the model. It must be generalized to include the following physically important features: (a) rotation that becomes important in the later phases of deep convection when it acts to slow down the rate of mixed layer deepening, (b) non-locality , in particular skewness which is large (negative) in the initial phases of deep convection and becomes small in the final stages, and finally, (c) a new model to treat lateral advection by baroclinic eddies that in the final stages of deep convection dominates over vertical transport.