Phytoplankton play a central role in the planetary cycling of important elements and compounds. Understanding how phytoplankton are responding to climate change is consequently a major question in Earth Sciences. Monitoring phytoplankton is key to answering this question. Satellite remote sensing of ocean colour is our only means of monitoring phytoplankton in the entire surface ocean at high temporal and large spatial scales, and the continuous ocean-colour data record is now approaching a length suitable for addressing questions around climate change, at least in some regions. Yet, developing ocean-colour algorithms for climate change studies requires addressing issues of ambiguity in the ocean-colour signal. For example, for the same chlorophyll-a concentration (Chl-a) of phytoplankton, the colour of the ocean can be different depending on the type of phytoplankton present. One route to tackle the issue of ambiguity is by enriching the ocean-colour data with information on sea surface temperature (SST), a good proxy of changes in three phytoplankton size classes (PSCs) independent of changes in total Chl-a, a measure of phytoplankton biomass. Using a global surface in-situ dataset of HPLC (high performance liquid chromatography) pigments, size-fractionated filtration data, and concurrent satellite SST spanning from 1991 to 2021, we re-tuned, validated and advanced an SST-dependent three-component model that quantifies the relationship between total Chl-a and Chl-a associated with the three PSCs (pico-, nano- and microplankton). Similar to previous studies, striking dependencies between model parameters and SST were captured, which were found to improve model performance significantly. These relationships were applied to 40 years of monthly composites of satellite SST, and significant trends in model parameters were observed globally, in response to climate warming. Changes in these parameters highlight issues in estimating long-term trends in phytoplankton biomass (Chl-a) from ocean colour using standard empirical algorithms, which implicitly assume a fixed relationship between total Chl-a and Chl-a of the three size classes. The proposed ecological model will be at the centre of a new ocean-colour modelling framework, designed for investigating the response of phytoplankton to climate change, described in subsequent parts of this series of papers.