An expression is derived for the surface salt input needed to induce complete convective overturning of a polar water column consisting of 1) a layer of sea ice, 2) a freezing temperature mixed layer, 3) a pycnocline with linearly varying temperature and salinity, and 4) deep water with fixed temperature and salinity. This quantity has been termed the bulk stability by Martinson. The bulk stability is found to consist of three components. The first two make up Martinson's salt deficit and are

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... e salt input needed to increase the density of the mixed layer and the pycnocline layer to that of the deep water (the mixed layer stability and pycnocline layer stability, respectively). The third component is Martinson's thermal barrier: the potential for pycnocline heat to melt ice, reducing the surface salinity. It is found that when the pycnocline density gradient due to temperature offsets more than one half of that due to salinity, the pycnocline layer stability is negative. Consequently, it is possible for a stably stratified water column to have zero or negative bulk stability.