Seasonal Cycles of Phytoplankton Expressed by Sine Equations Using the Daily Climatology from Satellite-Retrieved Chlorophyll-a Concentration (1997-2019) Over Global Ocean

The global coverage of Chlorophyll-a concentration (Chl-a) has been continuously available from ocean color satellite sensors since September 1997 and the Chl-a data (1997-2019) were used to produce a climatological dataset by averaging Chl-a values at same locations and same day of year. The constructed climatology can remarkably reduce the variability of satellite data and clearly exhibit the seasonal cycles, demonstrating that the growth and decay of phytoplankton recurs with similarly seasonal cycles year after year. As the shapes of time series of the climatology exhibit strong periodical change, we wonder whether the seasonality of Chl-a can be expressed by a mathematic equation. Our results show that sinusoid functions are suitable to describe cyclical variations of data in time series and patterns of the daily climatology can be matched by sine equations with parameters of mean, amplitude, phase, and frequency. Three types of sine equations were used to match the climatological Chl-a with Mean Relative Differences (MRD) of 7.1%, 4.5%, and 3.3%, respectively. The sine equation with four sinusoids can modulate the shapes of the fitted values to match various patterns of climatology with small MRD values (less than 5%) in about 90% of global oceans. The fitted values can reflect an overall pattern of seasonal cycles of Chl-a which can be taken as a time series of biomass baseline for describing the state of seasonal variations of phytoplankton. The amplitude images, the spatial patterns of seasonal variations of phytoplankton, can be used to identify the transition zone chlorophyll fronts. The timing of phytoplankton blooms is identified by the biggest peak of the fitted values and used to classify oceans as different bloom seasons, indicating that blooms occur in all four seasons with regional features. In global oceans within latitude domains (48 degrees N-48 degrees S), blooms occupy approximately half of the ocean (50.6%) during boreal winter (December-February) in the northern hemisphere and more than half (58.0%) during austral winter (June-August) in the southern hemisphere. Therefore, the sine equation can be used to match the daily Chl-a climatology and the fitted values can reflect the seasonal cycles of phytoplankton, which can be used to investigate the underlying phenological characteristics.