CN110427733B - Method for obtaining algae concentration based on phosphorus cycle - Google Patents

Method for obtaining algae concentration based on phosphorus cycle Download PDF

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CN110427733B
CN110427733B CN201910857739.7A CN201910857739A CN110427733B CN 110427733 B CN110427733 B CN 110427733B CN 201910857739 A CN201910857739 A CN 201910857739A CN 110427733 B CN110427733 B CN 110427733B
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程瑶
党承华
穆征
赵凤霞
李煜
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Hebei University of Engineering
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Abstract

The invention discloses an algae concentration obtaining method based on phosphorus cycle. The method can effectively simulate the growth and death process of the algae, so that the method has the capability of simulating the change of the algae, and effectively reduces the number of unknown biochemical parameters by using the variables of phosphorus and key nutrient salts. The method can effectively simulate the change process of the algae in the water body, not only does not reduce the simulation precision, but also greatly reduces the model parameters and increases the calculation efficiency because phosphorus is selected as key nutrient-limiting salt.

Description

Method for obtaining algae concentration based on phosphorus cycle
Technical Field
The invention relates to the technical field of algae simulation, in particular to an algae concentration acquisition method based on phosphorus circulation.
Background
At present, excessive discharge of nutrient salts causes the eutrophication degree of lakes and reservoirs to be increased, and water bloom is frequent. Numerical simulation is one of effective methods for analyzing the time-space change of the water bloom in the water body. The existing algae calculation models are numerous and can meet the requirements of bloom simulation, but the models have the following defects:
a. the simulated nutrient salts are numerous and cannot represent the core limit of key nutrient salts;
b. the simulation of the biochemical process is excessive, so that a plurality of ecological parameters which cannot be directly obtained are generated, and the precision of a simulation result is seriously influenced;
c. the operation efficiency is low.
Disclosure of Invention
Aiming at the defects in the prior art, the method for obtaining the algae concentration based on the phosphorus cycle solves the problem of inaccurate analog calculation of the algae concentration.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a method for obtaining algae concentration based on phosphorus cycle comprises the following steps:
s1, establishing a dynamic model of the biological debris;
s2, establishing a kinetic model of the nutrient salt according to the kinetic model of the biological debris;
s3, establishing a dynamic model of algae according to the dynamic model of the biological debris and the dynamic model of the nutrient salt;
and S4, calculating according to the dynamic model of the algae to obtain the algae concentration.
Further, the method comprises the following steps: the dynamic model of the biological debris in the step S1 is as follows:
Figure BDA0002195954770000021
in the above formula, DET is the biomass of the chips, t is the time,
Figure BDA0002195954770000022
to be the rate of change of the concentration of debris,
Figure BDA0002195954770000023
to account for the rate of change of debris due to algae death,
Figure BDA0002195954770000024
snk (DET) is the rate of debris sedimentation;
wherein the rate of mineralised hydrolysis of the fines
Figure BDA0002195954770000025
The calculation formula of (2) is as follows:
Figure BDA0002195954770000026
in the above formula, r DET The crumb based hydrolysis rate.
Further: the kinetic model of the nutritive salt in the step S2 is as follows:
Figure BDA0002195954770000027
in the above formula, PO 4 Is the nutrient salt biomass, t is the time,
Figure BDA0002195954770000028
in order to determine the rate of change of the nutrient salt concentration,
Figure BDA0002195954770000029
the rate of change of nutrient salts caused by the growth of algae,
Figure BDA00021959547700000210
the rate of change of nutrient salts caused by hydrolysis of the crumb;
wherein the rate of change of nutrient salts caused by algae growth
Figure BDA00021959547700000211
The calculation formula of (c) is:
Figure BDA00021959547700000212
in the above formula, the first and second carbon atoms are,
Figure BDA00021959547700000213
is the rate of algae growth;
rate of change of nutrient salts by hydrolysis of debris
Figure BDA00021959547700000214
The calculation formula of (2) is as follows:
Figure BDA0002195954770000031
in the above-mentioned formula, the compound has the following structure,
Figure BDA0002195954770000032
the rate of mineralized hydrolysis of the fines.
Further: the dynamic model of the algae in the step S3 is as follows:
Figure BDA0002195954770000033
in the above formula, P is the biomass of algae, t is the time,
Figure BDA0002195954770000034
is a model of the dynamics of the algae,
Figure BDA0002195954770000035
is the rate at which the algae grow and,
Figure BDA0002195954770000036
is the rate of algal death.
Further, the method comprises the following steps: the rate of growth of the algae
Figure BDA0002195954770000037
The calculation formula of (2) is as follows:
Figure BDA0002195954770000038
in the above formula, r P P is the algal biomass, the algal basal growth rate.
Further: the basal growth rate r of the algae P The calculation formula of (2) is as follows:
Figure BDA0002195954770000039
in the above formula, r 0 Is the maximum growth rate of the algae,
Figure BDA00021959547700000310
in order to be a function of the temperature limit,
Figure BDA00021959547700000311
in order to be a function of the light confinement,
Figure BDA00021959547700000312
as a nutrient salt limiting function;
wherein the temperature limit function
Figure BDA00021959547700000313
The calculation formula of (2) is as follows:
Figure BDA00021959547700000314
in the above formula, T is water temperature, T 1 Lower temperature limit, T, for proper algae growth 2 The upper limit of temperature suitable for the growth of algae;
light limiting function
Figure BDA00021959547700000315
The calculation formula of (2) is as follows:
Figure BDA0002195954770000041
in the above formula, I Z Solar radiation at a depth Z below the water surface, I opt Optimum illumination intensity for algae growth, wherein the depth under water surface is the solar radiation I at Z Z The calculation formula of (c) is:
I Z ＝I 0 e -(KW+KC·P)D
in the above formula, I 0 The water surface solar radiation is adopted, KW is the extinction coefficient of all substances except algae, KC is an algae extinction coefficient factor, and D is the water depth;
nutrient salt limiting function
Figure BDA0002195954770000042
The calculation formula of (2) is as follows:
Figure BDA0002195954770000043
in the above formula, K P At a phosphate half-saturation concentration, PO 4 Is the concentration of nutrient salt.
Further: rate of death of the algae
Figure BDA0002195954770000044
The calculation formula of (c) is:
Figure BDA0002195954770000045
in the above formula,. Mu. 1 First order death rate for algae, μ 2 Second order death rate for algae.
Further: the calculation formula of the algae concentration in the step S4 is:
Figure BDA0002195954770000046
in the above formula, P n+1 The next time point is the algae concentration, P n At is the algae concentration at the current time, and Δ t is the calculation step length.
The invention has the beneficial effects that: the method of the invention effectively reduces the number of unknown biochemical parameters by using the variable of phosphorus and key nutritive salt, and can accurately calculate the concentration of the algae.
The method can effectively simulate the change process of the algae in the water body, not only does not reduce the simulation precision, but also greatly reduces the model parameters and increases the calculation efficiency because phosphorus is selected as key nutrient limiting salt, and can effectively simulate the growth and death processes of the algae.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of the interaction process of nutritive salt-algae-bio-debris in an embodiment of the present invention;
FIG. 3 is a schematic representation of algae change over time in an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Nutrient salt-algae-bio-debris three-variable circulation mode, as shown in FIG. 2, exogenous input to nutrient salt (phosphate PO) 4 ) The algae (phytoplankton P) ingests nutrient salts (phosphate PO) 4 ) The algae (phytoplankton P) die to form biological debris, and the biological debris DET decomposes to form nutrient salt (phosphate PO) 4 )。
As shown in fig. 1, a method for obtaining algae concentration based on phosphorus cycle includes the following steps:
s1, establishing a dynamic model of the biological debris;
debris is primarily organisms of phytoplankton residues, the kinetics of which are affected by algal death and settlement, so the kinetic model for biological debris is:
Figure BDA0002195954770000051
in the above formula, DET is the biomass of debris, t is the time,
Figure BDA0002195954770000052
to be the rate of change of the biomass of the crumb,
Figure BDA0002195954770000053
for the rate of change of debris due to algae death,
Figure BDA0002195954770000054
snk (DET) is the rate of debris sedimentation;
wherein the rate of mineralised hydrolysis of the fines
Figure BDA0002195954770000055
The calculation formula of (2) is as follows:
Figure BDA0002195954770000061
in the above formula, r DET Is the crumb based hydrolysis rate.
S2, establishing a kinetic model of the nutrient salt according to the kinetic model of the biological debris;
phosphorus plays an important role in the growth of algae. The circulation of phosphorus is mainly based on phytoplankton absorption and debris hydrolysis, so the kinetic model of nutritive salt is as follows:
Figure BDA0002195954770000062
in the above formula, PO 4 Is the nutrient salt biomass, t is the time,
Figure BDA0002195954770000063
in order to determine the rate of change of the nutrient salt concentration,
Figure BDA0002195954770000064
the rate of change of nutrient salts caused by the growth of algae,
Figure BDA0002195954770000065
the rate of change of nutrient salts caused by hydrolysis of the crumb;
algae absorb phosphorus for growth through photosynthesis, so the rate of nutrient salt change caused by algae growth
Figure BDA0002195954770000066
The calculation formula of (2) is as follows:
Figure BDA0002195954770000067
in the above formula, the first and second carbon atoms are,
Figure BDA0002195954770000068
is the rate of algae growth;
the algae debris is converted into phosphate through hydrolysis and mineralization processes, so that the change rate of nutrient salt caused by the hydrolysis of the debris
Figure BDA0002195954770000069
The calculation formula of (c) is:
Figure BDA00021959547700000610
in the above formula, the first and second carbon atoms are,
Figure BDA00021959547700000611
the rate of mineralized hydrolysis of the fines.
S3, establishing a dynamic model of the algae according to the dynamic model of the biological debris and the dynamic model of the nutrient salt;
water quality models rarely model specific species of algae. Algae may be grouped into one or several groups. The kinetic model of algae is influenced by growth and death, and is as follows:
Figure BDA0002195954770000071
in the above formula, P is the biomass of algae, t is the time,
Figure BDA0002195954770000072
is a model of the dynamics of the algae,
Figure BDA0002195954770000073
is the rate of growth of algae，
Figure BDA0002195954770000074
Is the rate of algae death.
The growth of algae is influenced by water temperature, nutrient salts, light and basal growth rate, so the growth rate of algae
Figure BDA0002195954770000075
The calculation formula of (2) is as follows:
Figure BDA0002195954770000076
in the above formula, r P P is the algal biomass, the algal basal growth rate.
Basal growth rate r of algae P The calculation formula of (2) is as follows:
Figure BDA0002195954770000077
in the above formula, r 0 The maximum growth rate of the algae is set as,
Figure BDA0002195954770000078
in order to be a function of the temperature limit,
Figure BDA0002195954770000079
in order to be a function of the light confinement,
Figure BDA00021959547700000710
as a nutrient salt limiting function;
the growth of the algae is influenced by the temperature, and the algae grows fastest in a certain proper temperature interval. Above or below this temperature, the growth rate of the algae is affected. Temperature limit function
Figure BDA00021959547700000711
The calculation formula of (c) is:
Figure BDA00021959547700000712
in the above formula, T is water temperature, T 1 Lower temperature limit, T, for proper algae growth 2 The upper limit of temperature suitable for the growth of algae;
the growth of algae is also influenced by light (solar radiation). Light limiting function
Figure BDA0002195954770000081
The calculation formula of (2) is as follows:
Figure BDA0002195954770000082
in the above formula, I Z Solar radiation at a depth Z below the water surface, I opt Optimum illumination intensity for algae growth, wherein the depth under water surface is the solar radiation I at Z Z The calculation formula of (2) is as follows:
I Z ＝I 0 e -(KW+KC·P)D
in the above formula, I 0 The water surface solar radiation is adopted, KW is the extinction coefficient of all substances except algae, KC is an algae extinction coefficient factor, and D is the water depth;
the limiting nutrient salts that algae growth is subject to are mainly nitrogen, phosphorus and silicon. The mass ratio of nitrogen and phosphorus in domestic water is generally more than 15, and the water is a typical phosphorus-limited water body. Therefore, phosphorus in the water body is key nutrient salt for limiting the growth of algae, and a Michaelis-Menton model is selected to describe the relationship between the growth of algae and the phosphorus concentration and a nutrient salt limiting function
Figure BDA0002195954770000083
The calculation formula of (c) is:
Figure BDA0002195954770000084
in the above formula, K P At a phosphate half-saturation concentration, PO 4 Is the nutrient salt concentration.
Death of algae is a nonlinear process, so the rate of algae death
Figure BDA0002195954770000085
The calculation formula of (2) is as follows:
Figure BDA0002195954770000086
in the above formula,. Mu. 1 First order death rate for algae, μ 2 Second order death rate for algae.
And S4, calculating according to the dynamic model of the algae to obtain the algae concentration.
The calculation formula of the algae concentration is as follows:
Figure BDA0002195954770000087
in the above formula, P n+1 The next time point is the algae concentration, P n At the current time, the algae concentration is calculated as Δ t.
The values of the parameters in the present invention are shown in table 1.
TABLE 1 ecological parameters and suggested values
Figure BDA0002195954770000091
As can be seen from the data in FIG. 3, the method of the present invention effectively reduces the number of unknown biochemical parameters with the variables of phosphorus and key nutrient salts, and allows accurate calculation of algae concentration.
The method can effectively simulate the change process of the algae in the water body, not only does not reduce the simulation precision, but also greatly reduces the model parameters and increases the calculation efficiency because phosphorus is selected as key nutrient limiting salt, and can effectively simulate the growth and death processes of the algae.

Claims (4)

1. A method for obtaining algae concentration based on phosphorus cycle is characterized by comprising the following steps:
s1, establishing a dynamic model of the biological debris;
s2, establishing a kinetic model of the nutrient salt according to the kinetic model of the biological debris;
s3, establishing a dynamic model of algae according to the dynamic model of the biological debris and the dynamic model of the nutrient salt;
s4, calculating according to the dynamic model of the algae to obtain the concentration of the algae;
the dynamic model of the biological debris in the step S1 is as follows:
Figure FDA0003903453440000011
in the above formula, DET is the biomass of the chips, t is the time,
Figure FDA0003903453440000012
to be the rate of change of the biomass of the crumb,
Figure FDA0003903453440000013
to account for the rate of change of debris due to algae death,
Figure FDA0003903453440000014
snk (DET) is the rate of debris sedimentation;
wherein the rate of mineralisation and hydrolysis of the debris
Figure FDA0003903453440000015
The calculation formula of (2) is as follows:
Figure FDA0003903453440000016
in the above formula, r DET Is the crumb based hydrolysis rate;
the kinetic model of the nutritive salt in the step S2 is as follows:
Figure FDA0003903453440000017
in the above formula, PO 4 Is the nutrient salt biomass, t is the time,
Figure FDA0003903453440000018
the rate of change of the nutrient salt concentration is,
Figure FDA0003903453440000019
the rate of change of nutrient salts caused by the growth of algae,
Figure FDA00039034534400000110
the rate of change of nutrient salts caused by hydrolysis of the crumb;
wherein the rate of change of nutrient salts caused by algae growth
Figure FDA0003903453440000021
The calculation formula of (2) is as follows:
Figure FDA0003903453440000022
in the above formula, the first and second carbon atoms are,
Figure FDA0003903453440000023
is the rate of algae growth;
rate of change of nutrient salts by hydrolysis of debris
Figure FDA0003903453440000024
The calculation formula of (c) is:
Figure FDA0003903453440000025
in the above-mentioned formula, the compound has the following structure,
Figure FDA0003903453440000026
is the rate of mineralized hydrolysis of the fines;
the dynamic model of the algae in the step S3 is as follows:
Figure FDA0003903453440000027
in the above formula, P is the biomass of algae, t is the time,
Figure FDA0003903453440000028
is a model of the dynamics of the algae,
Figure FDA0003903453440000029
is the rate at which the algae grow and,
Figure FDA00039034534400000210
is the rate of algal death;
the calculation formula of the algae concentration in the step S4 is as follows:
Figure FDA00039034534400000211
in the above formula, P n+1 The next time point is the algae concentration, P n At is the algae concentration at the current time, and Δ t is the calculation step length.
2. The method of claim 1, wherein the rate at which the algae grow is determined by the algae concentration obtaining method based on the phosphorus cycle
Figure FDA00039034534400000212
The calculation formula of (c) is:
Figure FDA0003903453440000031
in the above formula, r P P is the algal biomass, the algal basal growth rate.
3. The method of claim 2, wherein the basal growth rate r of the algae is set according to the algae concentration P The calculation formula of (2) is as follows:
Figure FDA0003903453440000032
in the above formula, r 0 The maximum growth rate of the algae is set as,
Figure FDA0003903453440000033
in order to be a function of the temperature limit,
Figure FDA0003903453440000034
in order to be a function of the light confinement,
Figure FDA0003903453440000035
as a nutrient salt limiting function;
wherein the temperature limiting function
Figure FDA0003903453440000036
The calculation formula of (c) is:
Figure FDA0003903453440000037
in the above formula, T is water temperature, T 1 Lower temperature limit, T, for proper algae growth 2 The upper limit of temperature suitable for the growth of algae;
light limiting function
Figure FDA0003903453440000038
The calculation formula of (2) is as follows:
Figure FDA0003903453440000039
in the above formula, I Z Solar radiation at a depth Z below the water surface, I opt Optimum illumination intensity for algae growth, wherein the depth under water surface is the solar radiation I at Z Z The calculation formula of (2) is as follows:
I Z ＝I 0 e -(KW+KC·P)D
in the above formula, I 0 The water surface solar radiation is adopted, KW is the extinction coefficient of all substances except algae, KC is an algae extinction coefficient factor, and D is the water depth;
nutrient salt limiting function
Figure FDA00039034534400000310
The calculation formula of (2) is as follows:
Figure FDA00039034534400000311
in the above formula, K P At a phosphate half-saturation concentration, PO 4 Is the nutrient salt concentration.
4. The method of claim 3, wherein the rate of algal death is by rate of algal death
Figure FDA0003903453440000041
The calculation formula of (2) is as follows:
Figure FDA0003903453440000042
in the above formula,. Mu. 1 First order death rate, μ for algae 2 Second order death rate for algae.
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