CN113834792B - MAX-DOAS-based 50m resolution trace gas profile inversion method - Google Patents

MAX-DOAS-based 50m resolution trace gas profile inversion method Download PDF

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CN113834792B
CN113834792B CN202111108376.0A CN202111108376A CN113834792B CN 113834792 B CN113834792 B CN 113834792B CN 202111108376 A CN202111108376 A CN 202111108376A CN 113834792 B CN113834792 B CN 113834792B
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inversion
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CN113834792A (en
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谢品华
郑江一
田鑫
任博
徐晋
李昂
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Hefei Institutes of Physical Science of CAS
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Abstract

The invention provides a MAX-DOAS-based 50m resolution trace gas profile inversion method, which comprises the following steps: s1, inputting an original spectrum, and obtaining O through spectrum fitting 4 Concentration of diagonal column and concentration of gas diagonal column; s is S2. The O is 4 The concentration of the diagonal column is combined with the prior aerosol profile, and the aerosol profile is obtained through first inversion calculation of a Monte Carlo sampling algorithm; s3, the concentration of the gas diagonal column and the gas priori profile of the aerosol profile line are calculated through the second inversion of the Monte Carlo sampling algorithm to obtain the trace gas profile. The method realizes that the trace gas profile resolution is improved from 200m to 50m, greatly reduces the smooth error of an inversion algorithm, and improves the three-dimensional resolution. In addition, the Monte Carlo method is adopted to replace Gaussian Newton iterative solution, and the Monte Carlo solution process enables the solution of the algorithm to be more close to the global optimal solution through adjusting the sampling times, so that the reliability and the precision of the algorithm are improved, and the calculation efficiency of the algorithm is improved.

Description

MAX-DOAS-based 50m resolution trace gas profile inversion method
Technical Field
The invention relates to the technical field of environmental monitoring, in particular to a 50-meter resolution trace gas profile inversion method based on MAX-DOAS.
Background
With the progress of urban treatment, the situation of atmospheric pollution is increasingly severe, and the real-time monitoring of atmospheric pollutants is particularly important in the treatment process of pollutants. MAX-DOAS (multi-axis differential absorption spectroscopy) is widely used as an important means for ground based telemetry, which can continuously and automatically work and provide a three-dimensional profile of contaminants (aerosols, sulfur dioxide, nitrogen dioxide, formaldehyde, gaseous nitrous acid, etc.).
However, the current MAX-DOAS trace profile-based inversion method still has some obvious drawbacks:
1. the existing MAX-DOAS inversion algorithm has a profile stereo resolution of 200 meters, which means that the high-value stereo distribution condition of the gas cannot be clearly positioned, and especially the real stereo distribution condition cannot be displayed for some gases distributed near the ground (such as gaseous nitrous acid and the like). Meanwhile, the three-dimensional resolution is too high, the smooth error proportion in the inversion error is usually more than 70%, and the accuracy of the algorithm is greatly reduced.
2. The existing MAX-DOAS gas profile inversion algorithm is designed for meeting the minimum value function, and the iteration solution based on the Gaussian Newton method is adopted without exception. However, the iterative solution method has three important defects:
1) The efficiency is low; the conventional iterative solving algorithm (such as Prinam) uses the maximum iteration for 20 times to solve the profile, which greatly increases the matrix operation amount, so that the solving efficiency of the algorithm is very low and too much solving time is consumed.
2) Singular values occur; the iterative process of the algorithm adopts a uniform iterative step length, so that singular values usually appear in the inversion of a high layer (more than 1 km), which limits the application of the iterative algorithm to high resolution.
3) The precision is poor; the iterative process adopts a threshold value judging method, and the threshold value is adopted by two methods: a maximum iteration number threshold and a minimum cost function threshold, which means that the profile of the iterative solution is a local optimal solution and the most accurate global optimal solution cannot be obtained; at the same time, the maximum number of iterations also results in the occurrence of singular values.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a 50m resolution trace gas profile inversion method based on MAX-DOAS, wherein an aerosol extinction coefficient profile is inverted through a first step of a Monte Carlo method, a trace gas vertical profile is inverted through the aerosol extinction coefficient profile, and an inversion error is greatly reduced through a two-step inversion method of the Monte Carlo method, so that the reliability and the accuracy of an algorithm are improved.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows:
a MAX-DOAS based 50 meter resolution trace gas profile inversion method, the inversion method comprising the steps of:
s1, inputting an original spectrum, and obtaining O through spectrum fitting 4 Concentration of diagonal column and concentration of gas diagonal column;
s2, the O 4 Diagonal column concentration combined with aerosolThe experimental profile is subjected to first inversion calculation through a Monte Carlo sampling algorithm to obtain an aerosol profile;
s3, the concentration of the gas diagonal column and the gas priori profile of the aerosol profile line are calculated through the second inversion of the Monte Carlo sampling algorithm to obtain the trace gas profile.
Further, the main flow of the monte carlo sampling algorithm is as follows:
inputting the concentration of the inclined column and the prior profile into a radiation transmission model, and generating a weight function of the concentration of the vertical column of the gas and each layer;
then, carrying out normalization processing on the weight function and the prior profile, inputting the weight function and the prior profile into a Monte Carlo random sampling calculation flow, and calculating to obtain an optimal line type;
the optimal line shape is multiplied by the concentration point of the vertical column to obtain a three-dimensional profile.
Further, the concentration of the inclined column is O 4 Diagonal column concentration or gas diagonal column concentration.
Further, the prior profile is an aerosol prior profile or a gas prior profile.
Further, the monte carlo random sampling calculation flow is as follows:
firstly, generating a random sampling sequence between 0 and 1 according to the input maximum sampling times, wherein the sequence is a weight factor;
characterizing different random sampling line types by combining weight factors, recording a cost function under the line types, and storing the cost function;
and after the sampling process is finished, searching the minimum cost function in the sampling process by adopting a sequencing method, and outputting the corresponding line shape and weight factors, namely the optimal line shape.
Further, the two inversion calculation process of the Monte Carlo sampling algorithm is as follows:
a minimization cost function is used:
wherein y is MAX-DOAS observed value, FFor radiation transmission model simulation values, ε y Representing the error of the observed value y, x p A priori profile, epsilon, representing atmospheric composition p Representing error terms of a priori profile, wherein m and n respectively represent the number of layers of the high grid points of the gridding model;
the inversion requires the use of a radiation transmission model to simulate the true three-dimensional distribution state of the gas in the atmosphere, and the simulation value of the atmosphere radiation transmission modelThe method is affected by various influences of observation, weather and observation errors, and is simplified into the following model during calculation:
F(y)＝K(y，b)+ε (2)；
in the aboveThe weight function under each elevation angle is represented, and y, b and epsilon respectively represent three influencing factors of observation, weather and observation errors; the weight function K concrete form may represent the partial derivatives of the model for each component as:
wherein the method comprises the steps ofIndicating elevation angle of +.>Analog value of time,/->Indicating the number of layers of the height lattice points;
solving (1) by adopting a Monte Carlo random sampling model, and adopting a weight factorThe relation between the model and the prior is measured, and the expression form of the solution is as follows:
wherein K and VCD are the simulated outputs of the radiation transmission model, which integrate the results of the observation and simulation, x p For a priori profile, box represents the number of height grid points of the Box model, ea represents the number of observation elevation angles, |K|and|x p The I represents the first order norms of the weight function and the prior profile respectively, the corresponding line type can be obtained through normalized divisor construction, and for the value x at the same cost function α And (3) withThe method meets the following conditions:
||x α -x||→0 (7)；
the error of the algorithm can be divided into a priori error S P Measurement error S M And model error S K Total error S total Obeying an error transfer formula in which a priori the error S P Error from model S K By a weight factorAnd (3) calculating:
total error S total Obeying an error transfer formula, it can be expressed as:
the beneficial effects are that: according to the invention, 50m resolution atmospheric trace gas profile inversion is realized for the first time, 200m resolution is improved to 50m, and inversion errors are greatly reduced. According to the invention, a brand new higher-efficiency solving algorithm is adopted, and the Monte Carlo sampling algorithm is adopted to solve, so that the multi-point problem caused by the traditional Newton iteration method is avoided, meanwhile, the algorithm solving efficiency is greatly increased, and the solving precision and reliability are improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention. In the drawings:
FIG. 1 is a flow chart of a MAX-DOAS based 50m resolution trace gas profile inversion method according to an embodiment of the present invention;
FIG. 2 is a main flow chart of a Monte Carlo sampling algorithm of a 50m resolution trace gas profile inversion method based on MAX-DOAS according to an embodiment of the present invention;
fig. 3 is a flow chart of monte carlo random sampling calculation for a MAX-DOAS based 50m resolution trace gas profile inversion method according to an embodiment of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention will be described in detail below with reference to the drawings in connection with embodiments.
Example 1
See fig. 1: the embodiment relates to a 50m resolution trace gas profile inversion method based on MAX-DOAS, which comprises the following steps:
s1, inputting an original spectrum of light,obtaining O by spectral fitting 4 Concentration of diagonal column and concentration of gas diagonal column;
s2, the O 4 The concentration of the diagonal column is combined with the prior aerosol profile, and the aerosol profile is obtained through first inversion calculation of a Monte Carlo sampling algorithm;
the state of the first inversion aerosol of this embodiment employs a resolution of 200m.
S3, the concentration of the gas diagonal column and the gas priori profile of the aerosol profile line are calculated through the second inversion of the Monte Carlo sampling algorithm to obtain the trace gas profile.
The second time for inverting the vertical profile of the trace gas in this example, a resolution of 50m is used.
In summary, the trace gas profile resolution is improved from 200m to 50m, which greatly reduces the smoothing error of the inversion algorithm and improves the stereo resolution. In addition, the Monte Carlo method is adopted to replace Gaussian Newton iterative solution, and the Monte Carlo solution process enables the solution of the algorithm to be approximate to the global optimal solution in an infinite way through adjusting the sampling times, so that the reliability, the precision and the solution rate of the algorithm are greatly improved, and the efficiency of the algorithm is improved.
See fig. 2: in a specific example, the main flow of the monte carlo sampling algorithm is as follows:
inputting the concentration of the inclined column and the prior profile into a radiation transmission model, and generating a weight function of the concentration of the vertical column of the gas and each layer;
then, carrying out normalization processing on the weight function and the prior profile, inputting the weight function and the prior profile into a Monte Carlo random sampling calculation flow, and calculating to obtain an optimal line type;
the optimal line shape is multiplied by the concentration point of the vertical column to obtain a three-dimensional profile.
It should be noted that, all MAX-DOAS profile inversion algorithms approach the optimal solution by adopting an iterative method, and this embodiment innovatively proposes a solution expression form, and directly shows two factors of influence of the solution: the model affects the vertical column concentration and weight, and a prior profile affects only the line shape. The embodiment introduces the concept and characterization of the line type, and uses the concept of the line type to express the three-dimensional distribution state of the gas, and the concentration of the vertical column and the line type are separately processed, so that the solving process is clearer and more concise.
In addition, the normalization processing method of the embodiment adopts the first-order norm normalization processing prior profile and the weight function, thereby effectively preventing the influence of errors of digital size on the solving process and solving the problem that singular values appear in inversion when the prior profile is inaccurate.
In one embodiment, the concentration of the diagonal column is O 4 The prior profile is an aerosol prior profile or a gas prior profile.
See fig. 3: in a specific example, the monte carlo random sampling calculation process is as follows:
firstly, generating a random sampling sequence between 0 and 1 according to the input maximum sampling times, wherein the sequence is a weight factor;
characterizing different random sampling line types by combining weight factors, recording a cost function under the line types, and storing the cost function;
and after the sampling process is finished, searching the minimum cost function in the sampling process by adopting a sequencing method, and outputting the corresponding line shape and weight factors, namely the optimal line shape.
It can be understood that in this embodiment, the optimal weight factor is solved by using the monte carlo method to represent the line type, the Meng Daka lo method is a method of adopting random sampling to solve the mathematical model, and this sampling process is highly related to the calculation process of the computer, so that the solving speed of the computer is greatly improved, the utilization rate of the CPU is also effectively improved, and the solving speed of the profile is greatly improved.
The setting of the weight factor sampling interval of the embodiment limits the weight factor between 0 and 1, so that the solution form has practical physical significance, the influence of overflow of the weight factor value on inversion is effectively avoided, the inversion algorithm is enabled to be converged without singular value.
In a specific example, the two inversion calculation process of the monte carlo sampling algorithm is:
a minimization cost function is used:
wherein y is MAX-DOAS observation value, F is radiation transmission model simulation value, epsilon y Representing the error of the observed value y, x p A priori profile, epsilon, representing atmospheric composition p Representing error terms of a priori profile, wherein m and n respectively represent the number of layers of the high grid points of the gridding model;
the inversion requires the use of a radiation transmission model to simulate the true three-dimensional distribution state of the gas in the atmosphere, and the simulation value of the atmosphere radiation transmission modelThe method is affected by various influences of observation, weather and observation errors, and is simplified into the following model during calculation:
F(y)＝K(y，b)+ε (2)；
k in the above formula represents a weight function under each elevation angle, y, b and epsilon respectively represent three influencing factors of observation, weather and observation errors; the weight function K concrete form may represent the partial derivatives of the model for each component as:
wherein the method comprises the steps ofIndicating elevation angle of +.>Analog value of time,/->Indicating the number of layers of the height lattice points;
solving the formula (1) by adopting a Monte Carlo random sampling model, and measuring the relation between the model and the prior by adopting a weight factor alpha, wherein the expression form of the solution is as follows:
wherein K and VCD are the simulated outputs of the radiation transmission model, which integrate the results of the observation and simulation, x p For a priori profile, box represents the number of height grid points of the Box model, ea represents the number of observation elevation angles, |K|and|x p The I represents the first order norms of the weight function and the prior profile respectively, the corresponding line type can be obtained through normalized divisor construction, and for the value x at the same cost function α And (3) withThe method meets the following conditions:
||x α -x||→0 (7)；
the error of the algorithm can be divided into a priori error S P Measurement error S M And model error S K Total error S total Obeying an error transfer formula in which a priori the error S P Error from model S K By a weight factorAnd (3) calculating:
total error S total Obeying an error transfer formula, it can be expressed as:
the foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.

Claims (5)

1. A MAX-DOAS based 50 meter resolution trace gas profile inversion method, the inversion method comprising the steps of:
s1, inputting an original spectrum, and obtaining O through spectrum fitting 4 Concentration of diagonal column and concentration of gas diagonal column;
s2, the O 4 The concentration of the diagonal column is combined with the prior aerosol profile, and the aerosol profile is obtained through first inversion calculation of a Monte Carlo sampling algorithm;
s3, the aerosol profile line is combined with the gas diagonal column concentration and the gas priori profile line is subjected to second inversion calculation through a Monte Carlo sampling algorithm to obtain a trace gas profile line;
the two inversion calculation processes of the Monte Carlo sampling algorithm are as follows:
a minimization cost function is used:
wherein y is MAX-DOAS observation value, F is radiation transmission model simulation value, epsilon y Representing the error of the observed value y, x p A priori profile, epsilon, representing atmospheric composition p Representing error terms of a priori profile, wherein m and n respectively represent the number of layers of the high grid points of the gridding model;
the inversion needs to use a radiation transmission model to simulate the real three-dimensional distribution state of gas in the atmosphere, the simulation value F of the atmosphere radiation transmission model is affected by various observation, weather and observation errors, and the calculation is simplified into the following model:
F(y)＝K(y，b)+ε (2)；
k in the above formula represents a weight function under each elevation angle, y, b and epsilon respectively represent three influencing factors of observation, weather and observation errors; the weight function K concrete form may represent the partial derivatives of the model for each component as:
wherein i represents an analog value when the elevation angle is i, and j represents the number of layers of the altitude lattice point;
solving the formula (1) by adopting a Monte Carlo random sampling model, and measuring the relation between the model and the prior by adopting a weight factor alpha, wherein the expression form of the solution is as follows:
wherein K and VCD are the simulated outputs of the radiation transmission model, which integrate the results of the observation and simulation, x p For a priori profile, box represents the number of height grid points of the box model, ea represents the number of observation elevation angles, |K|and|x p The I represents the first order norms of the weight function and the prior profile respectively, the corresponding line type can be obtained through normalized divisor construction, and for the value x at the same cost function α And x, satisfy:
||x α -x||→0 (7)；
the error of the algorithm can be divided into a priori error S P Measurement error S M And model error S K Total error S total Obeying an error transfer formula in which a priori the error S P Error from model S K Calculated by a weight factor alpha:
total error S total Obeying an error transfer formula, it can be expressed as:
2. the MAX-DOAS-based 50 meter resolution trace gas profile inversion method of claim 1, wherein the main flow of the monte carlo sampling algorithm is:
inputting the concentration of the inclined column and the prior profile into a radiation transmission model, and generating a weight function of the concentration of the vertical column of the gas and each layer;
then, carrying out normalization processing on the weight function and the prior profile, inputting the weight function and the prior profile into a Monte Carlo random sampling calculation flow, and calculating to obtain an optimal line type;
the optimal line shape is multiplied by the concentration point of the vertical column to obtain a three-dimensional profile.
3. The MAX-DOAS-based 50 meter resolution trace gas profile inversion method of claim 2, wherein the diagonal column concentration is O 4 Diagonal column concentration or gas diagonal column concentration.
4. The MAX-DOAS-based 50 meter resolution trace gas profile inversion method of claim 2, wherein the a priori profile is an aerosol a priori profile or a gas a priori profile.
5. The MAX-DOAS-based 50 meter resolution trace gas profile inversion method of claim 2, wherein the monte carlo random sampling calculation procedure is:
firstly, generating a random sampling sequence between 0 and 1 according to the input maximum sampling times, wherein the sequence is a weight factor;
representing different random sampling line types by combining weight factors, recording a cost function under the line types, and storing;
and after the sampling process is finished, searching a minimum cost function in the sampling process by adopting a sequencing method, outputting corresponding line shapes and weight factors, and representing the optimal line shape of the profile.
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WO2008103486A1 (en) * 2007-02-23 2008-08-28 Duke University Scaling method for fast monte carlo simulation of diffuse reflectance spectra
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