Abstract A mathematical model is framed for a goldfish recirculating aquaculture system based on unsteady-state mass balance for prediction of the concentration of total ammonia nitrogen (TAN), nitrite-nitrogen (NO2-N), nitrate-nitrogen (NO3-N), dissolved oxygen (DO) and total suspended solids (TSS). The goldfish were stocked at 100 numbers per m3 of rearing water volume of 5 m3 tank capacity in the years 2009 and 2010 and the model was calibrated and validated. The recirculation flow rate was fixed at 29,000 L/day. The model parameters were estimated as kTAN (mg of TAN generated per kg of feed): 20,000, M (mortality rate): 0.002 day−1, α (percentage of feed conversion to suspended solids): 23.8, koxy (mg of oxygen required for fish respiration per kg of feed applied in unit time): 300,000, kb (partial nitrification in the culture tank): 0.86 and the reaction rate constants, k1 and k2: 84.65 day−1 and 42.03 day−1 respectively and temperature growth coefficient (TGC): 5.00 × 10-5. The model efficacy was adjudged by estimation of the coefficient of determination (R2), root mean square error (RMSE), Nash-Sutcliffe modelling efficiency (ENS) and graphical plots between predicted and observed values.

中文翻译：

---

金鱼循环水养殖系统（GRAS）的数学模型

摘要 建立了基于非稳态质量平衡的金鱼循环水养殖系统的数学模型，用于预测总氨氮（TAN）、亚硝酸盐-氮（NO2-N）、硝酸盐-氮（NO3-N）、溶解氧 (DO) 和总悬浮固体 (TSS)。2009 年和 2010 年以每立方米 5 m3 水箱容量的养殖水体积 100 条放养金鱼，并对模型进行了校准和验证。再循环流量固定为 29,000 升/天。模型参数估计为 kTAN（每千克饲料产生的 TAN 毫克数）：20,000，M（死亡率）：0.002 天-1，α（饲料转化为悬浮固体的百分比）：23.8，koxy（所需氧气的毫克数）单位时间内每公斤饲料的鱼类呼吸量）：300,000，kb（养殖池中的部分硝化作用）：0。86 和反应速率常数 k1 和 k2：分别为 84.65 天-1 和 42.03 天-1，温度增长系数 (TGC)：5.00 × 10-5。通过对决定系数 (R2)、均方根误差 (RMSE)、Nash-Sutcliffe 建模效率 (ENS) 和预测值与观测值之间的图形图的估计来判断模型功效。