- of Bay Mau Lake using mathematical models Luu Lan Huong*, Trinh Thi Thanh, Nguyen Thi Thanh Nga College of Science, VNU. - The lake ecosystem of Hanoi has a very important role. - However, the water quality in the lakes of Hanoi is declining. - One of the effective tools for assessing and predicting eutrophycation is the use of mathematical models. - In this paper, we used the Vollenweider model, empirical watershed model and Jorgensen model to determine the eutrophycation of Bay Mau Lake by phosphorous concentration in the lake water. - The results show that Bay Mau Lake is being heavy eutrophication, soluble phosphorus concentration is very high (4.56-7.56mg/l), other phosphorus concentrations is increasing. - We had treated phosphorus concentration of sewage before loading to the lake. - When Cpl decreases up to 90%, the content of PS fluctuates between 0.49 and 0.9mg/l. - Bay Mau Lake.. - Introduction In the recent years, Hanoi’s economic growth rate has increased substantially. - One of these is that the pollution of the lake ecosystem has increased at an alarming level and the water quality has been declining. - Eutrophycation is a phenomenon caused by excess of nutrients, mainly nitrogen and phosphorus, which is reflected in the booming of living algae, particularly the phytoplankton. - In the most serious condition, the lake ecosystem is destroyed, the aquatic organisms cannot survive and the lake is dry. - One of the effective tools for these purposes is the use of mathematical models.. - Research objects Bay Mau Lake is located in Lenin Park at the centre of Hanoi. - The main function of the lake is to make the rainfall equable. - Apply Vollenweider model to determine standard amount of phosphorus loading to the lake annually. - Use the empirical watershed model and the eutrophycation model of Jorgensen to calculate the supplement of nutrients from the basin and compare with standards to determine the lake nutritional condition. - Analyze the dynamic of phosphorus by exchanging phosphorus model of Jorgensen. - Calculating the maximum mass of phosphorus by Vollenweider model Vollenweider model is showed by the following formula: M = 10-9 Lc A, where M: allowable mass of phosphorus (tons/year). - Lc: allowable mass of phosphorus per square meter of lake's surface:. - Calculating the amount of phosphorus loading to the lake 3.1.2.1. - Using empirical watershed model To calculate, we applied technological standards of OECD and Loer [1]. - The main sources of phosphorus include: 1) Diffuse sources. - The amount of P loads from basin (P1) is related to the type of land, land use and intensive cultivation of agricultural land. - The amount of P loads from precipitation is associated with rainfall and lake's area (P2. - The amount of P loads from residential area (P3). - Empirical watershed model is shown by the following equation: A = a0 + a1X1 + a2X2. - anXn , where: A is the total amount of nutrients loading from basin. - a1,a2,...,an: exporting coefficients of phosphorus. - 2) Point sources: the amount of P from sewage (P4). - In the case of Bay Mau Lake, the annual precipitation is 1813mm according to National Hydro-Meteorological Service of Vietnam [2], the phosphorus concentration in rain water is mg/l, lake's area is 18 hectares, the population is 51814 people, the average phosphorus concentration of sewage is 6.206mg/l, the total waste water from sewage is 2,920,000m3. - Thus, the amount of phosphorus can be calculated by empirical watershed model: P kg. - The amount of P loads from land (P1. - The amount of P loads from precipitation (P2. - In the case of Bay Mau Lake, the annual precipitation is 1813mm, the phosphorus concentration in rainwater is mg/l, lake's area is 18 hectares, basin area is 115 hectares, and the population is 51814 people. - Based on these numbers, we have calculated the total amount of phosphorus: P kg/year. - Calculating the content of total phosphorus From the results of phosphorus source discharged into the lake, we can calculate phosphorus concentration. - where TP: average content of total phosphorus. - Lp: amount of phosphorus per square meter, Lp = J/A. - J: total phosphorus loaded to the lake annually. - Estimating content of phosphorus based on the amount of phosphorus loading to the lake calculated by empirical watershed model: Q = 5163530m3, J kg, A = 18ha, LP mg/m2.year, Z = 2.5m, V = 800000m3, tw = 0.155, qs = 16.13. - Estimating content of phosphorus based on the amount of phosphorus calculated by Jorgensen model: Q = 5163530m3, J kg, A = 18ha, LP mg/m2.year, Z =2.5m, V = 800000m3, tw = 0.155, qs = 16.13. - Estimating eutrophic state of Bay Mau Lake by phosphorus parameter By using phosphorus indicator, there are two ways to assess the eutrophycation. - The first one is to compare the total amount of phosphorus discharge into the lake annually with standards specified by Vollenweider model. - the second one is to use eutrophic measurement for phosphorus concentration in the lake. - Estimating eutrophic state by the total amount of phosphorus load We used empirical watershed model and Jorgensen model to calculate the total amount of phosphorus load. - By Jorgensen model, the amount of P load is times higher than the allowable level. - By the empirical watershed model, the amount of P is 282 - 292 times higher than the allowable level. - It shows that the ability of eutrophycation of Bay Mau Lake is very high.. - Estimating eutrophic state by phosphorus concentration From the two above models, the content of phosphorus in the lake exceeds allowable standards (0.03 mg/l) many times [3]. - Therefore, we can conclude that Bay Mau Lake is over eutrophic. - Also, according to research results, the two models have given different results, in which Jorgensen model is more exact in approximating the fluctuation of phosphorus in the lake . - Assessment and prediction of Bay Mau Lake eutrophycation by Jorgensen exchanging phosphorus model 3.2.1. - The model has 7 state variables: PS: Soluble phosphorus, PC: phosphorus in algal cells, PD: phosphorus in detritus, PE: Exchangeable phosphorus in sediment, PI: phosphorus in interstitial water, PB: phosphorus released biologically from sediment, Pzoo: Proportion of phosphorus in fish (Fig. - The content of PS: varies significantly over time. - It proves that the lake is in high eutrophic condition. - This value is approximate with PS measured in fact from 4.56 to 7.56mg/l [4, 6], shows that results of the model can be accepted. - The content of PC: based on the graph, the content of PC gradually rises from February to July, and reaches maximum in July. - From August to November, the content of PC slowly decreases. - Then, the content of PC continues increasing because over nutrient recovers phytoplankton mass. - The content of Pzoo: alters over time, comparing to change of PC shows that the vibration amplitudes of zooplankton and phytoplankton are the same. - But they are contrary, it means that if the content of PC increases, the content of Pzoo decreases. - The content of PD: also changes over time but very slow. - The content of PE: regularly increases over time, especially in winter. - The content of PiN: regularly increases over time but slow (about 0.00083mg/l/month). - The content of PB: regularly increases over time, its growth is higher than PE and PiN, about 0.0042mg/l/month. - This process has provided significant amount of phosphorus to make the lake more eutrophic. - This model simulates the dynamic of PS with the assumption that phosphorus concentration of sewage (Cpl), which has been treated, decreases before discharging into lake. - Therefore, to reduce the content of PS below 0.03mg/l, we should perform a waste water treatment in combination with other methods.. - Decrease of Cpl, PS, and content of PS. - 90 Decreases of PS. - Content of PS (mg/l). - Dynamic of PS content when Cpl decreases:. - Results obtained from mathematical models of total phosphorus amount and phosphorus concentration in Bay Mau Lake show that the lake contains too much phosphorus. - Compared to empirical watershed model, the Jorgensen model gives better result, which is closer to the measured data. - Jorgensen phosphorus exchanging model reflects theoretical rules relating to the lake's ecosystem. - The result of this model is close to the fact. - The content of PS exceeds allowable limit. - The content of other types of phosphorus increases over time. - Phosphorus in the lake is increasing. - When phosphorus concentration of sewage decreases up to 90%, the content of PS fluctuates between 0.49 and 0.9mg/l. - Therefore, to reduce the content of PS below 0.03mg/l, we should perform waste water treatment in combination with other methods