Geometrical Force Balance in Glaciology

The analytical force balance traditionally used in glaciology relates gravitational forcing to ice surface slope for sheet flow and to ice basal buoyancy for shelf flow. It is unable to represent stream flow as a transition from sheet flow to shelf flow by having gravitational forcing gradually passing from being driven by surface slope to being driven by basal buoyancy downslope along the length of an ice steam. This is a serious defect, because ice streams discharge up to 90% of ice from ice sheets into the sea. The defect is overcome by using a geometrical force balance that includes basal buoyancy, represented by the ratio of basal water pressure to ice overburden pressure, as a source of gravitational forcing. When combined with the mass balance, the geometrical force balance provides a holistic approach to ice flow in which resistance to gravitational flow must be summed upstream from the calving front of an ice shelf. This is not done in the analytical force balance, and it provides the ice-thinning rate required by gravitational collapse of ice sheets as interior ice is downdrawn by ice streams.

The Value of Adding Optics to Ecosystem Models: A Case Study

Many ecosystem models have been developed to study the ocean's biogeochemical properties, but most of these models use simple formulations to describe light penetration and spectral quality. Here, an optical model is coupled with a previously published ecosystem model that explicitly represents two phytoplankton (picoplankton and diatoms) and two zooplankton functional groups, as well as multiple nutrients and detritus. Surface ocean color fields and subsurface light fields are calculated by coupling the ecosystem model with an optical model that relates biogeochemical standing stocks with inherent optical properties (absorption, scattering); this provides input to a commercially available radiative transfer model (Ecolight). We apply this bio-optical model to the equatorial Pacific upwelling region, and find the model to be capable of reproducing many measured optical properties and key biogeochemical processes in this region. Our model results suggest that non-algal particles largely contribute to the total scattering or attenuation (> 50% at 660 nm) but have a much smaller contribution to particulate absorption (< 20% at 440 nm), while picoplankton dominate the total phytoplankton absorption (> 95% at 440 nm). These results are consistent with the field observations. In order to achieve such good agreement between data and model results, however, key model parameters, for which no field data are available, have to be constrained. Sensitivity analysis of the model results to optical parameters reveals a significant role played by colored dissolved organic matter through its influence on the quantity and quality of the ambient light. Coupling explicit optics to an ecosystem model provides advantages in generating: (1) a more accurate subsurface light-field, which is important for light sensitive biogeochemical processes such as photosynthesis and photo-oxidation, (2) additional constraints on model parameters that help to reduce uncertainties in ecosystem model simulations, and (3) model output which is comparable to basic remotely-sensed properties. In addition, the coupling of biogeochemical models and optics paves the road for future assimilation of ocean color and in-situ measured optical properties into the models.