Steady-state solutions of nitracline with the evolution of subsurface chlorophyll maximum in typical stable water columns

In typical stable water columns, nitrate exhibits a strong vertical gradient in the euphotic zone, which is conventionally referred to the nitracline. The subsurface chlorophyll maximum layer (SCML) commonly emerges at the bottom of the euphotic zone and can reshape the nitracline. The correlation between the SCML and the nitracline layer has been widely reported in the literature, but the analytic solution for the relationship between them is not well established. By incorporating a piecewise function for the approximately Gaussian vertical profile of chlorophyll, we derive the analytical solutions from the system of phytoplankton and nutrient, whereby the three important measurable parameters (depth, steepness and thickness of the nitracline) are used to characterize the nitracline: 1) the thickness of SCML is inversely related to the nitracline thickness, and a thinner SCML corresponds to a steeper nitracline; 2) the nitracline depth, located below the SCML depth, shoals with an increase in the light attenuation coefficient and a decrease in surface light intensity; the light level at the nitracline depth is positively correlated to the maximum rate of new primary production, an indicator of the rate of new primary production; 3) the nitracline steepness is positively influenced by vertical nitrate gradient below the nitracline depth, but is negatively related to vertical diffusivity in the stratified deep layer. In addition, the analytic result shows that the nitrate concentration decreases with depth from the bottom of the surface mixed layer to the upper boundary of the nitracline layer.