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This paper considers the initial stage of radiatively driven convection, when the perturbations from a quiescent but time-dependent background state are small. Radiation intensity is assumed to decay exponentially away from the surface, and we consider parameter regimes in which the depth of the water is greater than the decay scale of$$e$$of the radiation intensity. Both time-independent and time-periodic radiation are considered. In both cases, the background temperature profile of the water column is time-dependent. A linear analysis of the system is performed based on these time-dependent profiles. We find that the perturbations grow in time according to$$\exp [(\sigma (t) t)]$$, where$$\sigma (t)$$is a time-dependent growth rate. An appropriately defined Reynolds number is the primary dimensionless number characterising the system, determining the wavelength, vertical structure and growth rate of the perturbations. Simulations using a Boussinesq model (the Stratified Ocean Model with Adaptive Refinement) confirm the linear analysis. 

ABSTRACT MotivationHere, we make available a second version of the BioTIME database, which compiles records of abundance estimates for species in sample events of ecological assemblages through time. The updated version expands version 1.0 of the database by doubling the number of studies and includes substantial additional curation to the taxonomic accuracy of the records, as well as the metadata. Moreover, we now provide an R package (BioTIMEr) to facilitate use of the database. Main Types of Variables IncludedThe database is composed of one main data table containing the abundance records and 11 metadata tables. The data are organised in a hierarchy of scales where 11,989,233 records are nested in 1,603,067 sample events, from 553,253 sampling locations, which are nested in 708 studies. A study is defined as a sampling methodology applied to an assemblage for a minimum of 2 years. Spatial Location and GrainSampling locations in BioTIME are distributed across the planet, including marine, terrestrial and freshwater realms. Spatial grain size and extent vary across studies depending on sampling methodology. We recommend gridding of sampling locations into areas of consistent size. Time Period and GrainThe earliest time series in BioTIME start in 1874, and the most recent records are from 2023. Temporal grain and duration vary across studies. We recommend doing sample‐level rarefaction to ensure consistent sampling effort through time before calculating any diversity metric. Major Taxa and Level of MeasurementThe database includes any eukaryotic taxa, with a combined total of 56,400 taxa. Software Formatcsv and. SQL.