## 1 Introduction  
With the continuous expansion of human activities and the growth of industrial and agricultural production, the problem of freshwater scarcity has become increasingly prominent [1]. The United Nations 2030 Agenda identifies the shortage of freshwater resources as a key factor restricting global sustainable development in the 21 st century [2]. While central cities can efficiently address freshwater issues through collective water supply systems, remote rural or island areas often suffer from severe water supply challenges due to inadequate infrastructure. To tackle this challenge, researchers have begun focusing on the collection and utilization of rainwater as a vital means of replenishing water resources. Rainwater collection and utilization have been successfully implemented in various regions; for example, in rural areas of India, rainwater is collected by installing troughs on rooftops,saving 25% of non-potable water usage [3]. In Jordan, the rainwater collected from residential rooftops can meet 5.6% of the total annual domestic water consumption [4]. However, in most areas, collected rainwater is limited to non-potable uses, representing a significant waste of resources in tropical island regions where freshwater resources are already scarce. These areas, constrained by their unique geographical structures, face particularly acute freshwater shortages. Existing freshwater resources often fail to meet the production and living needs of island residents. However, the region experiences abundant rainfall; if collected rainwater can be effectively treated and converted into drinking water, it would significantly alleviate the water shortage for island residents. Rainwater is influenced by both human and natural factors and often contains a substantial amount of pollutants. Common pollutants include suspended particulate matter (turbidity), nitrogen and phosphorus nutrients (such as ammonia nitrogen (NH\({}_{3}\)-N) and total phosphorus (TP)), organic pollutants (such as total organic carbon (TOC) and humic acid), heavy metals (such as Pb\({}^{2+}\) and Cu\({}^{2+}\)), and pathogenic microorganisms [5]. If these pollutants are consumed directly without treatment, they may threaten human health. Biological slow filtration (BSF) technology, initially developed by [PERSON] from the United Kingdom, offers advantages such as a simple process flow, low water production costs, convenient management and maintenance, and the ability to remove pollutants without the need for additional purification and disinfection agents. This technology has gradually been promoted and applied in resource-scar areas [6]. BSF is a complex physical, chemical, and biological process that integrates filter media filtration, biological adsorption/degradation, electrostatic adsorption, and chemical precipitation, resulting in the joint removal of pollutants by filter media and microorganisms [7; 8]. This technology has unique advantages in rainwater treatment: its slow filtration rate (0.1-0.3 m/h) provides sufficient time for microbial metabolism and is suitable for treating rainwater with a low pollutant load but complex composition. Additionally, the feature of not requiring chemical agents mitigates the risk of secondary pollution, making it particularly suitable for remote islands with limited resources [6]. Existing studies have demonstrated that BSF can effectively remove pollutants such as turbidity, NH\({}_{3}\)-N, and organic matter from rainwater. For instance, [PERSON] et al. treated slightly polluted cellar water using a BSF system with volcanic rock filter media, achieving a turbidity removal rate exceeding 97% during the stable period [9]. [PERSON] et al. utilized Moringa seeds, coconut shells, and lava as filter media in the BSF system to treat rainwater, successfully removing significant amounts of Escherichia coli, total dissolved solids (TDS), Fe, Pb\({}^{2+}\), Cd\({}^{2+}\), and NH\({}_{3}\)-N [10].