Spiralling Inverse Method: A New Inverse Method to Estimate Ocean Mixing

Abstract Here, we introduce the Spiralling Inverse Method (SIM) that provides estimates of the small-scale and mesoscale mixing strength. The SIM uses a vertical integral over a balance between the water mass transformation equation and the thermal wind equation. The result is an equation where all terms, except for the mixing strengths, can be obtained from hydrographic data of temperature and salinity. As an advantage, the SIM estimates the mixing strengths without the need for further knowledge of a reference velocity or streamfunction. Here, we apply the SIM to a small region in the North Atlantic. We find that the estimates obtained by the SIM compare well to observations and other (inverse) estimates of the mixing strength. The SIM therefore has the potential to improve and constrain parameterizations used for climate and ecosystem modeling using readily available hydrographic data. Significance Statement Ocean mixing is a combination of many different physical processes over a large range of scales in time (from seconds to years) and space (from millimeters to 100 km). Most of these processes are too small to compute in climate models and need to be simplified (parameterized). These parameterizations have a strong influence on climate projections, and their shape and magnitude need to be constrained using observations and indirect estimates of ocean mixing strength. The Spiralling Inverse Method (SIM) is a new method to obtain such constraints of mixing strengths using readily available observations of temperature and salinity. We here test the SIM and confirm its potential to improve mixing estimates and therewith ultimately climate simulations.