Marine pollution degree assessment method and system based on pollutant diffusion model

Abstract

The invention discloses a method and system for assessing the degree of marine pollution based on a pollutant diffusion model, and relates to the field of marine environmental assessment. A three-dimensional hydrodynamic model is established using Delft 3D software to simulate the hydrodynamic characteristics of a target sea area, and water quality model parameters suitable for the target sea area are determined by verifying and analyzing the spatiotemporal changes of the tidal level, tidal current, temperature, and salinity of the target sea area, and a three-dimensional water quality model is constructed on the basis of the hydrodynamic model to obtain the main water quality parameters of the target sea area for constructing an assessment matrix, and the water quality quantitative assessment value obtained by the superior and inferior solution distance method is used, and the time series data of the water quality quantitative assessment value of each monitoring point within the monitoring period λ is used as a sample for classification processing to obtain the pollution degree level at the monitoring point of the target sea area, which can effectively reduce the complexity and difficulty of constructing the water quality model, and is conducive to improving the accuracy of the pollution degree assessment result of the target sea area.

Description

Technical Field

[0001] The present invention relates to the field of marine environment assessment, and in particular to a method and system for assessing the degree of marine pollution based on a pollutant diffusion model. Background Art

[0002] In recent years, with the rapid development of supercomputers and partial differential equation numerical solution technology, hydrodynamic-water quality models have been widely used in estuarine and coastal engineering and are the main tools for predicting water environment conditions. In the existing technology, the research on water environment and numerical simulation of water environment in coastal estuaries are mostly focused on the analysis of water environment quality characteristics and the qualitative analysis of the laws of transport and diffusion of related pollutants. The water quality biochemical processes involved in the construction of water quality models are mostly empirical formulas. In the construction process, a large number of water quality parameters must be set first, and then the model must be debugged. Since many water quality parameters are difficult to obtain and the amount of data calculation is huge, the complexity and difficulty of constructing water quality models are greatly increased. To this end, we propose a method and system for assessing the degree of marine pollution based on a pollutant diffusion model. Summary of the invention

[0003] The main purpose of the present invention is to provide a method and system for assessing the degree of marine pollution based on a pollutant diffusion model, which can effectively solve the problems in the background technology.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] Marine pollution assessment methods based on pollutant diffusion models include:

[0006] The 3D water quality model of the target sea area is constructed using Delft 3D software. The construction process includes the following steps:

[0007] Step 11: Use Delft 3D software to establish an initial three-dimensional hydrodynamic model for simulating the hydrodynamic characteristics of the target sea area;

[0008] Step 12: Obtain measured data of tidal currents and tide levels in the target sea area at different periods to verify the hydrodynamics of the model, and obtain measured data of surface temperature and salinity to verify the temperature and salinity of the model;

[0009] Step 13: Reasonably adjust the parameters of the initial three-dimensional hydrodynamic model according to the verification results, determine the hydrodynamic model parameters, and obtain a three-dimensional hydrodynamic model for simulating the hydrodynamic characteristics of the target sea area;

[0010] Step 14: Based on the hydrodynamic model, use the Delft3D-WAQ module to build an initial three-dimensional water quality model of the target sea area, and simulate the water quality parameters and water quality processes of the target sea area through the water quality model;

[0011] Step 15: According to the simulation results, the parameters of the initial three-dimensional water quality model are debugged and sensitivity analyzed to determine the main water quality parameters of the water quality model, including dissolved oxygen, carbon-containing biochemical oxygen demand, suspended matter, non-ionic ammonia, coliform count, inorganic nitrogen, pH, and inorganic phosphate, as well as the values ​​of water quality process data including DO cycle, nitrogen, phosphorus cycle and plant transformation process, to obtain the three-dimensional water quality model of the target sea area, where the water quality process includes reoxygenation process, nitrification process, denitrification process, mineralization process, and plant growth related processes, among which,

[0012] The expression of the reoxygenation process is:

[0013]

[0014] In the formula, It is expressed as the reoxygenation flux value; is the first-order reoxygenation rate value at 20°C; is the water depth value; is the temperature dependence constant of the reoxygenation process; is the water temperature value; is the saturated oxygen concentration value; is the oxygen concentration value;

[0015] The expression of nitrification process is:

[0016]

[0017] In the formula, is the nitrification rate; is a constant background rate value; is the value of the kinetic constant; is the kinetic constant of NH4, , is the NH4 concentration value; is the half-saturation parameter value of NH4; is the kinetic constant value of DO, , is the DO concentration value; is the oxygen half-saturation parameter value;

[0018] The expression of denitrification process is:

[0019]

[0020] In the formula, is the denitrification rate; is the kinetic constant value of nitric acid;

[0021] The mineralization process expression is:

[0022]

[0023] In the formula, is the mineralization flux value; is the substance concentration value; is the value of the temperature dependence constant of mineralization;

[0024] The expression of plant growth related processes is:

[0025]

[0026] In the formula, is the maximum growth rate of the plant; It is a nutrient limiting factor; is the light limiting factor; is the sunshine factor; is the temperature factor; is the actual concentration value of the nutrient;

[0027] According to the constructed three-dimensional water quality model, the main water quality parameters of the target sea area at time t within the monitoring period λ are obtained. , which is represented by the jth main water quality parameter value of the i-th monitoring point in the target sea area at time t, where i=1,2,...,n; j=1,2,...,m;

[0028] Construct an assessment matrix using the main water quality parameters obtained as elements , The superior and inferior solution distance method is used to obtain the water quality assessment value of each monitoring point at time t during the monitoring period. The acquisition process includes the following steps:

[0029] Step 31: Divide the water quality parameters into extremely large parameters, extremely small parameters, interval parameters and intermediate parameters according to the degree of influence on water quality;

[0030] Step 32: Perform forward processing on the extremely small parameters, interval parameters and intermediate parameters in the evaluation matrix to obtain the forward-processed evaluation matrix. The forward processing formula is:

[0031] For very small parameters: ;

[0032] For intermediate parameters: ;

[0033] For interval parameters: ;

[0034] In the formula, Represents the data value before normalization; represents the data value after normalization; M represents the maximum value of the data value before normalization; q represents the minimum value of the data value before normalization; , They represent the lower and upper limits of the data interval of the intermediate parameter before forward transformation respectively; , They are respectively represented as the lower limit and upper limit of the optimal data interval of the intermediate parameter; Step 33: Standardize all elements in the evaluation matrix after the forward processing, and the standardization formula is: , get the standardized evaluation matrix , ;

[0035] Step 34: Define the distances between the water quality evaluation value of the i-th monitoring point at time t and the optimal water quality and the worst water quality as and , ; , where Expressed as the weight of the jth main water quality parameter; , are the maximum and minimum values ​​of the jth main water quality parameter among all monitoring points at time t, respectively;

[0036] Step 35: According to and The calculation result of obtains the water quality assessment value of the i-th monitoring point at time t ,in, ;

[0037] The time series data of the water quality assessment value of each monitoring point within the monitoring period λ is used as a sample for classification processing to obtain the pollution degree level at the monitoring point in the target sea area. The classification process includes the following steps:

[0038] Step 41, using the time series data of water quality assessment values ​​to create a sample set, denoted as { , ,... , , ,... , ..., , ,... },in, ;

[0039] Step 42, obtain the mean and standard deviation in the sample set, and use the mean and standard deviation to standardize the data in the sample set. The standardization formula is: , in which z is the standard parameter, σ is the variance of the sample data, and μ is the mean of the sample data;

[0040] Step 43, after completing the standardization, the standard parameters are used to The numerical interval is adjusted to [0,1], and the function value of f(k) is used to classify the water quality assessment value. The classification mechanism is:

[0041] when When the water quality assessment value is classified as level one;

[0042] when When the water quality assessment value is classified as Level II;

[0043] when When the water quality assessment value is classified into three levels;

[0044] By analogy, when When the water quality assessment value is classified as level r;

[0045] in, , They are The minimum and maximum values ​​of the function values, f(k)1, f(k)2,,, f(k) r are the middle values ​​of f(k), and f(k) min <f(k)1<f(k)2<,,,<f(k) r <f(k) max , r is a positive integer;

[0046] Step 44, using the classification results of the water quality assessment values, classify the pollution levels at the target sea area monitoring points, and the classification mechanism is:

[0047] When the water quality assessment value is classified as level one, the pollution level is level one;

[0048] When the water quality assessment value is classified as Level 2, the pollution level is Level 2;

[0049] By analogy, when the water quality assessment value is classified as level r, the pollution level is level r.

[0050] The present invention has the following beneficial effects:

[0051] Compared with the existing technology, a three-dimensional hydrodynamic numerical diffusion model is established by using Delft 3D software to simulate the hydrodynamic characteristics of the target sea area. The temporal and spatial changes of the tidal level, tidal current, temperature and salinity of the target area are verified and analyzed to determine the water quality model parameters suitable for the target area. A three-dimensional water quality model is constructed on the basis of the hydrodynamic model to obtain the main water quality parameters of the target sea area for constructing the evaluation matrix. The water quality quantitative evaluation value obtained by the superior and inferior solution distance method is used. The time series data of the water quality quantitative evaluation value of each monitoring point within the monitoring period λ is used as a sample for classification processing to obtain the pollution degree level at the monitoring point in the target sea area. This can effectively reduce the complexity and difficulty of constructing the water quality model, and is conducive to improving the accuracy of the pollution degree assessment results of the target sea area. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the method for assessing the degree of marine pollution based on the pollutant diffusion model of the present invention;

[0053] Figure 2 It is a flow chart of the process of constructing a three-dimensional water quality model of the target sea area in the solution of the present invention;

[0054] Figure 3 The material relationship framework in the three-dimensional water quality model constructed for the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with specific implementation methods, wherein the accompanying drawings are only used for exemplary descriptions and represent only schematic diagrams rather than actual drawings, and should not be understood as limiting the present invention. In order to better illustrate the specific implementation methods of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product.

[0056] The implementation process of the technical solution of the present invention includes the following steps:

[0057] Step 1: Use Delft 3D software to build a 3D water quality model of the target sea area. The construction process includes the following steps:

[0058] Delft 3D software was used to establish an initial three-dimensional hydrodynamic model for simulating the hydrodynamic characteristics of the target sea area.

[0059] Obtain measured data of tidal currents and tide levels in the target sea area at different times to verify the hydrodynamics of the model, and obtain measured data of surface temperature and salinity to verify the temperature and salinity of the model;

[0060] According to the verification results, the initial three-dimensional hydrodynamic model is reasonably adjusted to determine the parameters of the hydrodynamic model, and a three-dimensional hydrodynamic model is obtained for simulating the hydrodynamic characteristics of the target sea area;

[0061] Specifically, the hydrodynamic model uses orthogonal curve grids, finite difference method for discretization, and alternating implicit method for solution to obtain offshore topographic data of the target sea area and water depth topographic data of the nearshore sea area; the hydrodynamic model uses nested grids to establish a large-area two-dimensional model, set the number of calculation grids and the maximum grid resolution and minimum resolution, and select the predicted water level time series for interpolation of the open boundary conditions in the offshore; the model is calibrated using historical data of tide level and tidal current measurements to determine the Manning coefficient and horizontal eddy viscosity coefficient, and the model is verified using historical data of tide level and tidal current measurements. On the basis of reasonable verification, accurate boundary conditions are provided for the three-dimensional model established in the small area, the number of calculation grids and the number of vertical layers of the small area model are determined, and the initial temperature field and salinity field are given at the same time. For the temperature and salinity boundary conditions of the small area model, linear interpolation of the data of the adjacent measured stations is used, and the bottom friction coefficient and horizontal eddy viscosity coefficient are consistent with the large area model;

[0062] Based on the hydrodynamic model, the Delft3D-WAQ module is used to construct an initial three-dimensional water quality model of the target sea area, and the water quality parameters and water quality processes of the target sea area are simulated through the water quality model;

[0063] According to the simulation results, the parameters of the initial three-dimensional water quality model are debugged and sensitivity analyzed to determine the main water quality parameters of the water quality model, including dissolved oxygen, carbon-containing biochemical oxygen demand, suspended matter, non-ionic ammonia, coliform count, inorganic nitrogen, pH, and inorganic phosphate, as well as the values ​​of water quality process data including DO cycle, nitrogen, phosphorus cycle and plant transformation process, to obtain the three-dimensional water quality model of the target sea area, where the water quality process includes reoxygenation process, nitrification process, denitrification process, mineralization process, and plant growth-related processes.

[0064] The expression of the reoxygenation process is:

[0065]

[0066] In the formula, It is expressed as the reoxygenation flux value; is the first-order reoxygenation rate value at 20°C; is the water depth value; is the temperature dependence constant of the reoxygenation process; is the water temperature value; is the saturated oxygen concentration value; is the oxygen concentration value;

[0067] The expression of nitrification process is:

[0068]

[0069] In the formula, is the nitrification rate; is a constant background rate value; is the value of the kinetic constant; is the kinetic constant of NH4, , is the NH4 concentration value; is the half-saturation parameter value of NH4; is the kinetic constant value of DO, , is the DO concentration value; is the oxygen half-saturation parameter value;

[0070] The expression of denitrification process is:

[0071]

[0072] In the formula, is the denitrification rate; is the kinetic constant value of nitric acid;

[0073] The mineralization process expression is:

[0074]

[0075] In the formula, is the mineralization flux value; is the substance concentration value; is the value of the temperature dependence constant of mineralization;

[0076] The expression of plant growth related processes is:

[0077]

[0078] In the formula, is the maximum growth rate of the plant; It is a nutrient limiting factor; is the light limiting factor; is the sunshine factor; is the temperature factor; is the actual concentration value of the nutrient;

[0079] Step 2: Based on the constructed three-dimensional water quality model, obtain the main water quality parameters of the target sea area at time t within the monitoring period λ , which is represented by the jth main water quality parameter value of the i-th monitoring point in the target sea area at time t, where i=1,2,...,n; j=1,2,...,m;

[0080] Step 3: Construct an assessment matrix based on the main water quality parameters obtained , The superior and inferior solution distance method is used to obtain the water quality assessment value of each monitoring point at time t during the monitoring period. The acquisition process includes the following steps:

[0081] Step 31: Divide the water quality parameters into extremely large parameters, extremely small parameters, interval parameters and intermediate parameters according to the degree of influence on water quality;

[0082] It should be noted that for the main water quality parameters involved in this plan, including dissolved oxygen, carbon-containing biochemical oxygen demand, suspended matter, non-ionized ammonia, coliform count, inorganic nitrogen, pH, and inorganic phosphate, refer to the water quality standard requirements in the "Technical Specifications for Quality Assessment of Seawater, Marine Sediments and Marine Organisms" and "Seawater Quality Standards", as shown in the following table.

[0083] Table 1 Comparison table of seawater quality standards

[0084]

[0085] According to the above table, for dissolved oxygen in water quality parameters, the larger the content value, the higher the water quality grade and the better the water quality, and its parameter type is an extremely large parameter. For parameters such as carbon-containing biochemical oxygen demand, suspended matter, non-ionic ammonia, coliform count, inorganic nitrogen and inorganic phosphate, the smaller the value, the higher the water quality grade and the better the water quality, and its parameter type is an extremely small parameter. For pH, when it is within the range of 7.8 to 8.5, the water quality grade is the highest and the water quality is better, and it is an interval parameter.

[0086] Step 32: Perform positive processing on the extremely small parameters, interval parameters and intermediate parameters in the evaluation matrix to obtain the positive evaluation matrix. The positive processing formula is:

[0087] For very small parameters: ;

[0088] For interval parameters: ;

[0089] In the formula, Represents the data value before normalization; represents the data value after positive conversion; M represents the maximum value of the data value before positive conversion; m represents the minimum value of the data value before positive conversion; , They represent the lower and upper limits of the data interval of the intermediate parameter before forward transformation respectively; , They represent the lower and upper limits of the optimal data interval of the intermediate parameters respectively;

[0090] Step 33: Standardize all elements in the evaluation matrix after the forward processing. The standardization formula is: , get the standardized evaluation matrix , ;

[0091] Step 34: Define the distances between the water quality evaluation value of the i-th monitoring point at time t and the optimal water quality and the worst water quality as and , ; , where Expressed as the weight of the jth main water quality parameter; , are the maximum and minimum values ​​of the jth main water quality parameter among all monitoring points at time t, respectively;

[0092] Step 35: According to and The calculation result of obtains the water quality assessment value of the i-th monitoring point at time t ,in, ;

[0093] Step 4: Use the time series data of the water quality assessment value of each monitoring point within the monitoring period λ as samples for classification processing to obtain the pollution level at the monitoring point in the target sea area. The classification process includes the following steps:

[0094] Step 41, using the time series data of water quality assessment values ​​to create a sample set, denoted as { , ,... , , ,... , ..., , ,... },in, ;

[0095] Step 42, obtain the mean and standard deviation in the sample set, and use the mean and standard deviation to standardize the data in the sample set. The standardization formula is: , in which z is the standard parameter, σ is the variance of the sample data, and μ is the mean of the sample data;

[0096] Step 43, after completing the standardization, the standard parameters are used to The numerical interval is adjusted to [0,1], and the function value of f(k) is used to classify the water quality assessment value. The classification mechanism is:

[0097] when When the water quality assessment value is classified as level one;

[0098] when When the water quality assessment value is classified as Level II;

[0099] when When the water quality assessment value is classified into three levels;

[0100] By analogy, when When the water quality assessment value is classified as level r;

[0101] in, , They are The minimum and maximum values ​​of the function values, f(k)1, f(k)2,,, f(k) r are the middle values ​​of f(k), and f(k) min <f(k)1<f(k)2<,,,<f(k) r <f(k) max , r is a positive integer;

[0102] Step 44, using the classification results of the water quality assessment values, classify the pollution levels at the target sea area monitoring points, and the classification mechanism is:

[0103] When the water quality assessment value is classified as level one, the pollution level is level one;

[0104] When the water quality assessment value is classified as Level 2, the pollution level is Level 2;

[0105] By analogy, when the water quality assessment value is classified as level r, the pollution level is level r.

[0106] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for assessing the degree of marine pollution based on a pollutant diffusion model, characterized in that: include: Construct a three-dimensional water quality model of the target sea area using Delft 3D software; According to the constructed three-dimensional water quality model, the main water quality parameters of the target sea area at time t within the monitoring period λ are obtained. , which is represented by the jth main water quality parameter value of the i-th monitoring point in the target sea area at time t, where i=1,2,...,n; j=1,2,...,m; Construct an assessment matrix using the main water quality parameters obtained as elements , The superior and inferior solution distance method is used to obtain the water quality assessment value of each monitoring point at time t during the monitoring period. ; The time series data of the water quality assessment value of each monitoring point within the monitoring period λ is used as a sample for classification processing to obtain the pollution degree level at the monitoring point in the target sea area; The process of constructing a three-dimensional water quality model of the target sea area includes the following steps: Step 11: Use Delft 3D software to establish an initial three-dimensional hydrodynamic model for simulating the hydrodynamic characteristics of the target sea area; Step 12: Obtain measured data of tidal currents and tide levels in the target sea area at different periods to verify the hydrodynamics of the model, and obtain measured data of surface temperature and salinity to verify the temperature and salinity of the model; Step 13: Reasonably adjust the parameters of the initial three-dimensional hydrodynamic model according to the verification results, determine the hydrodynamic model parameters, and obtain a three-dimensional hydrodynamic model for simulating the hydrodynamic characteristics of the target sea area; Step 14: Based on the hydrodynamic model, use the Delft3D-WAQ module to build an initial three-dimensional water quality model of the target sea area, and simulate the water quality parameters and water quality processes of the target sea area through the water quality model; Step 15: According to the simulation results, the parameters of the initial three-dimensional water quality model are debugged and sensitivity analyzed to determine the values ​​of the main water quality parameters and water quality process data of the water quality model, and obtain the three-dimensional water quality model of the target sea area; The process of obtaining water quality assessment values ​​includes the following steps: Step 31: Divide the water quality parameters into extremely large parameters, extremely small parameters, interval parameters and intermediate parameters according to the degree of influence on water quality; Step 32: Performing forward processing on the extremely small parameters, interval parameters and intermediate parameters in the evaluation matrix to obtain a forward-processed evaluation matrix; Step 33: Standardize all elements in the evaluation matrix after the forward processing. The standardization formula is: , get the standardized evaluation matrix , ; Step 34: Define the distances between the water quality evaluation value of the i-th monitoring point at time t and the optimal water quality and the worst water quality as and , ; , where Expressed as the weight of the jth main water quality parameter; , are the maximum and minimum values ​​of the jth main water quality parameter among all monitoring points at time t, respectively; Step 35: According to and The calculation result of obtains the water quality assessment value of the i-th monitoring point at time t ,in, ; The pollution degree classification process includes the following steps: Step 41, using the time series data of water quality assessment values ​​to create a sample set, denoted as { , ,... , , ,... , ..., , ,... },in, ; Step 42, obtain the mean and standard deviation in the sample set, and use the mean and standard deviation to standardize the data in the sample set. The standardization formula is: , in which z is the standard parameter, σ is the variance of the sample data, and μ is the mean of the sample data; Step 43, after completing the standardization, the standard parameters are used to The numerical interval is adjusted to [0,1], and the function value of f(k) is used to classify the water quality assessment value. The classification mechanism is: when When the water quality assessment value is classified as level one; when When the water quality assessment value is classified as Level II; when When the water quality assessment value is classified into three levels; By analogy, when When the water quality assessment value is classified as level r; in, , They are The minimum and maximum values ​​of the function values, f(k)1, f(k)2,,, f(k) r are the middle values ​​of f(k), and f(k) min <f(k)1<f(k)2<,,,<f(k) r <f(k) max , r is a positive integer; Step 44, using the classification results of the water quality assessment values, classify the pollution levels at the target sea area monitoring points, and the classification mechanism is: When the water quality assessment value is classified as level one, the pollution level is level one; When the water quality assessment value is classified as Level 2, the pollution level is Level 2; By analogy, when the water quality assessment value is classified as level r, the pollution level is level r.

2. The method for assessing the degree of marine pollution based on the pollutant diffusion model according to claim 1 is characterized in that: The main water quality parameters include dissolved oxygen, carbon-containing biochemical oxygen demand, suspended matter, non-ionized ammonia, coliform count, inorganic nitrogen, pH, and inorganic phosphate; The water quality process includes DO cycle, nitrogen and phosphorus cycle and plant transformation process.

3. The method for assessing the degree of marine pollution based on a pollutant diffusion model according to claim 1 is characterized in that: The forward processing formula is: For very small parameters: ; For intermediate parameters: ; For interval parameters: ; In the formula, Represents the data value before normalization; represents the data value after normalization; M represents the maximum value of the data value before normalization; q represents the minimum value of the data value before normalization; , They represent the lower and upper limits of the data interval of the intermediate parameter before forward transformation respectively; , They represent the lower and upper limits of the optimal data interval for the intermediate parameters respectively.

4. The method for assessing the degree of marine pollution based on a pollutant diffusion model according to claim 1 is characterized in that: Water quality processes include reoxygenation, nitrification, denitrification, mineralization, and plant growth-related processes, among which: The expression of the reoxygenation process is: ； In the formula, It is expressed as the reoxygenation flux value; is the first-order reoxygenation rate value at 20°C; is the water depth value; is the temperature dependence constant of the reoxygenation process; is the water temperature value; is the saturated oxygen concentration value; is the oxygen concentration value; The expression of nitrification process is: ； In the formula, is the nitrification rate; is a constant background rate value; is the value of the kinetic constant; is the kinetic constant of NH4, , is the NH4 concentration value; is the half-saturation parameter value of NH4; is the kinetic constant value of DO, , is the DO concentration value; is the oxygen half-saturation parameter value; The expression of denitrification process is: ； In the formula, is the denitrification rate; is the kinetic constant value of nitric acid; The mineralization process expression is: ； In the formula, is the mineralization flux value; is the substance concentration value; is the value of the temperature dependence constant of mineralization; The expression of plant growth related processes is: ； In the formula, is the maximum growth rate of the plant; It is a nutrient limiting factor; is the light limiting factor; is the sunshine factor; is the temperature factor; is the actual concentration of nutrients.

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