Tnm l

Samples (50–100 mL) were collected at defined time intervals for analysis. First, the pH value was analyzed using a pH meter (Orion Star™ A211, Thermo scientific, USA). The samples were then vacuum-filtered through a pre-weighed GF/C filter paper (47 mm, Whatman, USA) to analyze the biomass based on the procedures in Standards Methods¹⁹ . The productivity of microalgal biomass was calculated as follows^{20 (link)}: $$P_{\mathit{Biomass}}(\mathrm{g}{\mathrm{L}}^{-1}{\mathrm{d}}^{-1})=({\mathrm{C}}_2-{\mathrm{C}}_1)/({\mathrm{t}}_2-{\mathrm{t}}_1)$$ where P_biomass is the biomass productivity (g L^-1d^-1), C₁ and C₂ are the concentrations of biomass at times t₁ and t₂.
Water analysis was conducted using the filtrates. Filtrates were filtered again using a 0.45 µm polyvinylidene fluoride (PVDF) syringe filter for total nitrogen (TN) and total phosphorus (TP) analysis. The TN values were analyzed using a TN analyzer (TNM-L, Shimadzu, Japan) equipped with a Total organic carbon (TOC) analyzer (TOC-LCPH, Shimadzu, Japan). The TP concentration was analyzed using water test kits (HS-TP-H and HS-TP-L, Humas, Korea) according to the manufacturer’s instructions.

Concentrations of dissolved organic C (DOC) and dissolved total N (DTN) in filtered ice samples were determined on a total organic C analyzer (Shimadzu TOC-L_CPH, Kyoto, Japan) coupled with a total N measuring unit (Shimadzu TNM-L). The ammonium-N (NH₄⁺-N), nitrate-N (NO₃^–-N), and phosphate-P (PO₄^3–-P) contents of the same samples were quantified on a photometric meter (Gallery^TM Plus Discrete Analyzer). According to six replicate standards, the CV for the DOC, DTN, NH₄⁺-N, NO₃^–-N, and PO₄^3–-P analyses were 3.71%, 7.38%, 0.20%, 0.26%, and 0.35%, respectively. The corresponding detection limits for the same analyses were 51.40 μg L^–1, 39.12 μg L^–1, 1.19 μg L^–1, 3.13 μg L^–1, and 4.95 μg L^–1. Dissolved organic N (DON) was calculated for each sample as the difference between concentrations of DTN and dissolved inorganic N (DIN; sum of NH₄⁺-N and NO₃^–-N).