Sverdrup meets Lambert: analytical solution for Sverdrup’s critical depth

Abstract In his 1953 paper, Harald Sverdrup argued that the development of a spring bloom in ocean depends on juxtaposition two depth horizons: mixed-layer and critical depth. Mixed-layer shallower than favours phytoplankton growth layer vice versa. However, mathematically, left problem unsolved form transcendental equation. spite high number citations this paper has garnered, solution to equation not been found, until now. work, we present an analytical for depth, as originally defined by Sverdrup. The opens with definition description Lambert W function. follows. Sverdrup’s original model is extended include effect light attenuation steady-state biomass mixed derived. expression production at steady state also presented. Two novel variants are defined: optically uncoupled coupled It demonstrated equals irradiance base Competitive exclusion hold linked intensity multi-species competition. Finally, conservation principle found.