CN113076645B - Cosmic ray neutron instrument space characteristic simulation method combining remote sensing data - Google Patents

Cosmic ray neutron instrument space characteristic simulation method combining remote sensing data Download PDF

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CN113076645B
CN113076645B CN202110355076.6A CN202110355076A CN113076645B CN 113076645 B CN113076645 B CN 113076645B CN 202110355076 A CN202110355076 A CN 202110355076A CN 113076645 B CN113076645 B CN 113076645B
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庞治国
江威
覃湘栋
吕娟
付俊娥
路京选
杨昆
李琳
李小涛
曲伟
宋文龙
冯天时
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China Institute of Water Resources and Hydropower Research
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Abstract

The invention discloses a space characteristic simulation method of a cosmic ray neutron instrument combined with remote sensing data, which aims at the problem that the space heterogeneity of the cosmic ray neutron method is difficult to reflect in soil moisture measurement, calculates a normalized vegetation index and a surface temperature by utilizing Landsat8 remote sensing data, provides a soil moisture horizontal direction parameter correction method considering underlying surface condition factors such as surface vegetation and surface temperature, and the like, and simulates a soil moisture vertical correction parameter by combining neutron footprint characteristics and soil types of the cosmic ray neutron instrument, so that three-dimensional space distribution characteristic simulation of soil moisture in an observation range of the cosmic ray neutron instrument is realized, the improvement of the fine degree of soil moisture observation of the cosmic ray neutron instrument is facilitated, the space distribution difference of soil moisture in a measurement area is objectively reflected, and a foundation is laid for the remote sensing authenticity inspection of the soil moisture.

Description

Cosmic ray neutron instrument space characteristic simulation method combining remote sensing data
Technical Field
The invention belongs to the technical field of popularization of measurement technology, and particularly relates to a design of a space characteristic simulation method of a cosmic ray neutron instrument by combining remote sensing data.
Background
Soil moisture is a key parameter in water circulation, energy circulation and biogeochemical circulation, and the current ground observation means of soil moisture is divided into point observation and surface observation according to the space representativeness of observation data. The observation result of point observation is space point data, the space representativeness is small, the space distribution of soil moisture is difficult to accurately describe, and the main methods comprise a drying weighing method, a tensiometer method, a neutron instrument method and a dielectric property method. The observation result of the surface observation can realize the space continuity observation of the soil moisture, and the representative methods include a ground penetrating radar method and a cosmic ray neutron method, wherein the research and the discussion of the cosmic ray neutron method are more.
The cosmic ray neutron method (CRS) is a novel surface soil moisture measuring method appearing in 40 th of 20 th century, and the method is based on the principle that a cosmic ray neutron instrument is used for measuring the number of neutrons generated by cosmic ray particles, and the average soil moisture content in a certain area is estimated according to the relation between the number of neutrons and the soil moisture content. The instrument measurements represent only the mean soil moisture for that range, and it is believed that different distances and depths contribute no difference to the soil moisture results for the observation region. In fact, due to different underlying surface conditions in the measurement source region, the soil moisture has obvious spatial heterogeneity in the region, and the difference of the distribution of the soil moisture in the space cannot be shown only by measuring with an instrument, so that the accurate measurement and application promotion of the cosmic ray neutron method on the soil moisture are restricted to a certain extent, and the spatial characteristic simulation of the soil moisture needs to be carried out by combining with the underlying surface influence factors.
Disclosure of Invention
The invention aims to provide a space characteristic simulation method of a cosmic ray neutron instrument combined with remote sensing data, which fully considers the influence factors of the underlying surface conditions such as surface vegetation, surface temperature, soil type and the like in the underlying surface of a measurement source region, is used for quickly and accurately simulating the three-dimensional space distribution characteristics of soil moisture in an observation range, improves the space precision of a cosmic ray neutron method in soil moisture measurement, and promotes the application depth of the cosmic ray neutron method in soil moisture remote sensing verification.
The technical scheme of the invention is as follows: a method for simulating space characteristics of a cosmic ray neutron instrument by combining remote sensing data comprises the following steps:
and S1, acquiring observation data of the cosmic ray neutron instrument, and acquiring Landsat8 earth surface reflectivity data in the observation period according to the measurement range and time of the cosmic ray neutron instrument.
And S2, processing the collected observation data and Landsat8 earth surface reflectivity data to obtain a temperature vegetation drought index.
And S3, carrying out correction parameter simulation in the measurement space of the cosmic ray neutron instrument based on the temperature vegetation drought index.
And S4, according to the corrected parameter simulation result, performing three-dimensional space characteristic simulation on the cosmic ray neutron instrument, and calculating to obtain the spatial distribution of the water content of the soil in the measurement range of the cosmic ray neutron instrument.
Further, step S2 includes the following substeps:
and S21, calculating to obtain a normalized vegetation index NDVI according to the collected Landsat8 earth surface reflectivity data.
S22, inverting the earth surface temperature T by adopting a single window algorithm according to the collected observation data and Landsat8 earth surface reflectivity datas
S23, according to the surface temperature TsAnd calculating the normalized vegetation index NDVI to obtain the temperature vegetation drought index VI.
Further, the calculation formula of the normalized vegetation index NDVI in step S21 is:
Figure BDA0003003283820000021
wherein B is4Band 4, B, representing Landsat8 surface reflectivity data5Indicating the 5 th band of landform reflectivity data for Landsat 8.
Further, the surface temperature T in step S22sThe inversion formula of (a) is:
Figure BDA0003003283820000022
where ε represents the ground of the mixed picture elementEmissivity, τ represents atmospheric transmittance, TbRepresenting the value of the surface brightness temperature, LλRepresenting calibrated spectral radiance, K, of thermal infrared data1And K2Are all constant, TaThe average action temperature of the atmosphere is shown, a and b are reference coefficients, and C and D are intermediate parameters.
Further, the calculation formula of the temperature vegetation drought index VI in step S23 is as follows:
Figure BDA0003003283820000023
wherein
Figure BDA0003003283820000024
Indicating the maximum surface temperature for the corresponding NDVI, ξ + η × NDVI indicating the minimum surface temperature for the corresponding NDVI,
Figure BDA0003003283820000025
are parameters fitted based on the temperature and the characteristic spatial distribution characteristics of the normalized vegetation index.
Further, the correction parameters in the measurement space of the cosmic ray neutron instrument in step S3 include a horizontal correction parameter of the cosmic ray neutron instrument, a horizontal correction parameter considering the surface vegetation and the underlying surface condition of the temperature, and a vertical correction parameter of the cosmic ray neutron instrument.
Further, the simulation formula of the horizontal direction correction parameter of the cosmic ray neutron instrument is as follows:
Figure BDA0003003283820000031
wherein f isH(i) Represents the correction parameter of the ith pixel of the cosmic ray neutron instrument in the horizontal direction, Wr iThe neutron intensity of the ith pixel of the cosmic ray neutron instrument is represented, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument.
Further, the simulation formula of the horizontal direction correction parameter considering the ground vegetation and the underlying surface condition under the temperature is as follows:
Figure BDA0003003283820000032
wherein f isVI(i) Horizontal direction correction parameter for representing i-th pixel of cosmic ray neutron instrument considering surface vegetation and temperature underlying surface condition, VIiThe temperature vegetation drought index of the ith pixel of the cosmic ray neutron instrument is represented, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument.
Further, the simulation formula of the correction parameter of the cosmic ray neutron instrument in the vertical direction is as follows:
Figure BDA0003003283820000033
wherein
Figure BDA0003003283820000034
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter in between is set to be,
Figure BDA0003003283820000035
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The weight coefficient between the weight of the first and second groups,
Figure BDA0003003283820000036
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumenthAnd zh+1M is the discrete layering quantity of the soil, and H represents an empirical parameter set according to different soil types; weight coefficient
Figure BDA0003003283820000037
The calculation formula of (2) is as follows:
Figure BDA0003003283820000038
wherein Wz(r) represents the neutron intensity at any radial distance r at a depth z, z*(r) represents the effective depth of the measurement result of the cosmic ray neutron instrument when the radial distance is r, and the calculation formula is as follows:
Figure BDA0003003283820000041
where ρ isbdThe volume weight of soil particles is shown, and SM represents the soil mass water content measured by a cosmic ray neutron instrument.
Further, in step S4, the calculation formula of the soil moisture content in the measurement range of the cosmic ray neutron instrument is:
Figure BDA0003003283820000042
wherein
Figure BDA0003003283820000043
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The SM represents the soil mass water content measured by a cosmic ray neutron instrument, fH(i) Representing a correction parameter of the ith pixel of the cosmic ray neutron instrument in the horizontal direction, fVI(i) Represents the horizontal direction correction parameters of the ith pixel of the cosmic ray neutron instrument in consideration of the surface vegetation and the underlying surface condition of the temperature,
Figure BDA0003003283820000044
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter therebetween.
The invention has the beneficial effects that:
(1) aiming at the application requirement of carrying out fine monitoring on soil moisture by utilizing a cosmic ray neutron instrument, the invention fully utilizes remote sensing data to calculate bedding surface factors such as vegetation and surface temperature, provides a soil moisture content horizontal direction parameter correction method considering bedding surface condition factors such as surface vegetation and surface temperature, and simulates a soil moisture vertical correction parameter by combining the neutron footprint characteristic and the soil type of the cosmic ray neutron instrument, and carries out three-dimensional space characteristic simulation on the cosmic ray neutron instrument.
(2) The method for simulating the spatial characteristics of the cosmic ray neutron instrument, provided by the invention, has strong spatial adaptability, can reflect the spatial distribution difference characteristics of soil moisture in a measurement area, and lays a foundation for multi-scale authenticity verification of remote sensing of soil moisture.
(3) The method can be used for quickly and accurately simulating the soil moisture spatial distribution characteristics in the observation range, improves the spatial precision of the cosmic ray neutron method in soil moisture measurement, and promotes the application depth of the cosmic ray neutron method in soil moisture remote sensing verification.
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Fig. 1 is a flowchart of a method for simulating spatial characteristics of a cosmic ray neutron instrument by using remote sensing data according to an embodiment of the present invention.
Fig. 2 is a block diagram showing a flow chart of a method for simulating spatial characteristics of a cosmic ray neutron instrument by using remote sensing data according to an embodiment of the present invention.
FIG. 3 is a schematic diagram showing the matching between the measurement footprint of the cosmic ray neutron instrument and the remote sensing pixel according to the embodiment of the invention.
Detailed Description
Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It is to be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, not to limit the scope of the invention.
The embodiment of the invention provides a space characteristic simulation method of a cosmic ray neutron instrument by combining remote sensing data, which is shown in fig. 1-2 and comprises the following steps of S1-S4:
and S1, acquiring observation data of the cosmic ray neutron instrument, and acquiring Landsat8 earth surface reflectivity data in the observation period according to the measurement range and time of the cosmic ray neutron instrument. In the embodiment of the invention, the observation data and Landsat8 earth surface reflectivity data are downloaded from the website of the United states geological exploration bureau.
And S2, processing the collected observation data and Landsat8 earth surface reflectivity data to obtain a temperature vegetation drought index.
The step S2 includes the following substeps S21-S23:
and S21, calculating to obtain a normalized vegetation index NDVI according to the collected Landsat8 earth surface reflectivity data.
In the embodiment of the invention, the vegetation condition of the underlying surface is represented by a normalized vegetation index NDVI, and the calculation formula is as follows:
Figure BDA0003003283820000051
wherein B is4Band 4, B, representing Landsat8 surface reflectivity data5Indicating the 5 th band of landform reflectivity data for Landsat 8.
S22, inverting the earth surface temperature T by adopting a single window algorithm according to the collected observation data and Landsat8 earth surface reflectivity datas
Figure BDA0003003283820000052
Wherein epsilon represents the ground surface emissivity of the mixed pixel and is obtained by calculation through the empirical relation of normalized vegetation index or vegetation coverage; tau represents the atmospheric transmittance and is obtained by calculation through an empirical formula according to the atmospheric moisture content provided by a meteorological observation station near a test area; t isbRepresenting the value of the surface brightness temperature, LλRepresenting calibrated spectral radiance, K, of thermal infrared data1And K2All are constants which can be obtained from header information of the downloaded data, TaThe average action temperature of the atmosphere is represented, and meteorological data provided by meteorological observation stations near the test area are obtained based on an empirical formula; a and b are reference coefficients, in the embodiment of the invention, a is-67.355351, and b is 0.458606; c and D are both intermediate parameters.
S23、According to the surface temperature TsAnd calculating the normalized vegetation index NDVI to obtain the temperature vegetation drought index VI.
In the embodiment of the invention, the temperature vegetation drought index VI is closely related to soil moisture by comprehensively considering the surface vegetation and the surface temperature in the underlying surface, and the calculation formula is as follows:
Figure BDA0003003283820000061
wherein
Figure BDA0003003283820000064
Represents the maximum surface temperature corresponding to NDVI, representing extreme dryness (VI ═ 0),
Figure BDA0003003283820000065
represents the minimum surface temperature corresponding to NDVI, representing extreme wetness (VI ═ 1),
Figure BDA0003003283820000066
are parameters fitted based on the temperature and the characteristic spatial distribution characteristics of the normalized vegetation index.
And S3, carrying out correction parameter simulation in the measurement space of the cosmic ray neutron instrument based on the temperature vegetation drought index.
In the embodiment of the invention, the correction parameters in the measurement space of the cosmic ray neutron instrument comprise correction parameters in the horizontal direction of the cosmic ray neutron instrument, correction parameters in the horizontal direction considering the conditions of surface vegetation and a temperature underlay surface and correction parameters in the vertical direction of the cosmic ray neutron instrument.
(1) The simulation formula of correction parameters of the cosmic ray neutron instrument in the horizontal direction is as follows:
Figure BDA0003003283820000062
wherein f isH(i) Represents the correction parameter of the ith pixel of the cosmic ray neutron instrument in the horizontal direction, Wr iRepresent universeThe neutron intensity of the ith pixel of the ray neutron instrument, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument.
In the embodiment of the present invention, under an ideal condition that the standard air pressure is set (P0 ═ 1013.25hPa) and there is no vegetation on the ground, the variation rule of the neutron intensity detected by the CRS in the horizontal direction can be quantitatively analyzed as follows:
Figure BDA0003003283820000063
wherein WrRepresenting the neutron intensity of the sub-region, r representing the radial distance of the sub-region from the cosmic ray neutron instrument, F1~F8All represent relevant parameters calculated by an empirical formula and can be obtained by combining meteorological parameters and observation parameters of the cosmic ray neutron instrument.
The neutron intensity of each pixel center can be calculated by using the neutron intensity, and as shown in fig. 3, the neutron intensity of the pixel center represents the value of the whole pixel.
(2) The temperature vegetation drought index VI combines factors such as vegetation and surface temperature, and can well represent the relative state of soil moisture, so that the simulation formula of the horizontal direction correction parameter considering the surface vegetation and the temperature underlying surface condition in the embodiment of the invention is as follows:
Figure BDA0003003283820000071
wherein f isVI(i) Horizontal direction correction parameter for representing i-th pixel of cosmic ray neutron instrument considering surface vegetation and temperature underlying surface condition, VIiThe temperature vegetation drought index of the ith pixel of the cosmic ray neutron instrument is represented, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument.
(3) The simulation formula of the correction parameters of the cosmic ray neutron instrument in the vertical direction is as follows:
Figure BDA0003003283820000072
wherein
Figure BDA0003003283820000073
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter in between is set to be,
Figure BDA0003003283820000074
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The weight coefficient between the weight of the first and second groups,
Figure BDA0003003283820000075
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumenthAnd zh+1The weighting coefficients of the soil types are m, the discrete layering number of the soil is m, H represents an empirical parameter set according to different soil types, and recommended values of H are shown in table 1 because the infiltration rates and the water storage capacities of different soil types are different.
TABLE 1H recommendation table
Type of soil Rate of infiltration Water retention property H value recommendation
Sand soil Is quicker Is poor 0.55~0.65
Loam soil In general In general 0.75~0.85
Clay clay Is slower Is preferably used 0.9~1.0
Weight coefficient
Figure BDA0003003283820000076
The calculation formula of (2) is as follows:
Figure BDA0003003283820000077
wherein Wz(r) represents the neutron intensity at any radial distance r at a depth z, z*(r) represents the effective depth of the measurement result of the cosmic ray neutron instrument when the radial distance is r, and the calculation formula is as follows:
Figure BDA0003003283820000078
where ρ isbdThe volume weight of soil particles is shown, and SM represents the soil mass water content measured by a cosmic ray neutron instrument.
And S4, according to the corrected parameter simulation result, performing three-dimensional space characteristic simulation on the cosmic ray neutron instrument, and calculating to obtain the spatial distribution of the water content of the soil in the measurement range of the cosmic ray neutron instrument.
In the embodiment of the invention, the calculation formula of the soil water content in the measurement range of the cosmic ray neutron instrument is as follows:
Figure BDA0003003283820000081
wherein
Figure BDA0003003283820000082
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The SM represents the soil mass water content measured by a cosmic ray neutron instrument, fH(i) Representing a correction parameter of the ith pixel of the cosmic ray neutron instrument in the horizontal direction, fVI(i) Represents the horizontal direction correction parameters of the ith pixel of the cosmic ray neutron instrument in consideration of the surface vegetation and the underlying surface condition of the temperature,
Figure BDA0003003283820000083
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter therebetween.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (6)

1. A method for simulating space characteristics of a cosmic ray neutron instrument by combining remote sensing data is characterized by comprising the following steps:
s1, acquiring observation data of the cosmic ray neutron instrument, and acquiring Landsat8 earth surface reflectivity data in the observation period according to the measurement range and time of the cosmic ray neutron instrument;
s2, processing the collected observation data and Landsat8 earth surface reflectivity data to obtain a temperature vegetation drought index;
s3, carrying out correction parameter simulation in a measurement space of a cosmic ray neutron instrument based on the temperature vegetation drought index;
s4, according to the correction parameter simulation result, performing space ray neutron instrument three-dimensional space feature simulation, and calculating to obtain the soil water content space distribution in the measurement range of the space ray neutron instrument;
the correction parameters in the measurement space of the cosmic ray neutron instrument in the step S3 include correction parameters in the horizontal direction of the cosmic ray neutron instrument, correction parameters in the horizontal direction considering the conditions of surface vegetation and temperature bedding surface and correction parameters in the vertical direction of the cosmic ray neutron instrument;
the simulation formula of the horizontal direction correction parameter considering the ground vegetation and the bedding surface condition under the temperature is as follows:
Figure FDA0003322648510000011
wherein f isVI(i) Horizontal direction correction parameter for representing i-th pixel of cosmic ray neutron instrument considering surface vegetation and temperature underlying surface condition, VIiThe temperature vegetation drought index of the ith pixel of the cosmic ray neutron instrument is represented, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument;
the simulation formula of the correction parameter of the cosmic ray neutron instrument in the vertical direction is as follows:
Figure FDA0003322648510000012
wherein
Figure FDA0003322648510000013
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter in between is set to be,
Figure FDA0003322648510000014
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The weight coefficient between the weight of the first and second groups,
Figure FDA0003322648510000015
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumenthAnd zh+1M is the discrete layering quantity of the soil, and H represents an empirical parameter set according to different soil types; weight coefficient
Figure FDA0003322648510000016
The calculation formula of (2) is as follows:
Figure FDA0003322648510000021
wherein Wz(r) represents the neutron intensity at any radial distance r at a depth z, z*(r) represents the effective depth of the measurement result of the cosmic ray neutron instrument when the radial distance is r, and the calculation formula is as follows:
Figure FDA0003322648510000022
where ρ isbdRepresenting the volume weight of soil particles, and SM representing the soil mass water content measured by a cosmic ray neutron instrument;
the calculation formula of the soil water content in the measurement range of the cosmic ray neutron instrument in the step S4 is as follows:
Figure FDA0003322648510000023
wherein
Figure FDA0003322648510000024
Indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The SM represents the soil mass water content measured by a cosmic ray neutron instrument, fH(i) Representing a correction parameter of the ith pixel of the cosmic ray neutron instrument in the horizontal direction, fVI(i) Representing the ith pixel consideration of cosmic ray neutron instrumentHorizontal direction correction parameters of the surface vegetation and the temperature underlay surface condition,
Figure FDA0003322648510000025
indicating the vertical depth z of the ith pixel of the cosmic ray neutron instrumentpAnd zp+1The correction parameter therebetween.
2. The method for simulating the spatial signature of a cosmic ray neutron instrument as recited in claim 1, wherein said step S2 includes the sub-steps of:
s21, calculating to obtain a normalized vegetation index NDVI according to the collected Landsat8 earth surface reflectivity data;
s22, inverting the earth surface temperature T by adopting a single window algorithm according to the collected observation data and Landsat8 earth surface reflectivity datas
S23, according to the surface temperature TsAnd calculating the normalized vegetation index NDVI to obtain the temperature vegetation drought index VI.
3. The method for simulating spatial signatures of cosmic ray neutron instruments according to claim 2, wherein the normalized vegetation index NDVI in step S21 is calculated by the following formula:
Figure FDA0003322648510000026
wherein B is4Band 4, B, representing Landsat8 surface reflectivity data5Indicating the 5 th band of landform reflectivity data for Landsat 8.
4. The method for simulating the spatial signature of a cosmic ray neutron instrument as recited in claim 2, wherein the surface temperature T in step S22sThe inversion formula of (a) is:
Figure FDA0003322648510000031
wherein epsilon represents the ground surface emissivity of the mixed pixel, tau represents the atmospheric transmittance, TbRepresenting the value of the surface brightness temperature, LλRepresenting calibrated spectral radiance, K, of thermal infrared data1And K2Are all constant, TaThe average action temperature of the atmosphere is shown, a and b are reference coefficients, and C and D are intermediate parameters.
5. The cosmic ray neutron instrument spatial feature simulation method according to claim 2, wherein the calculation formula of the temperature vegetation drought index VI in step S23 is:
Figure FDA0003322648510000032
wherein
Figure FDA0003322648510000033
Indicating the maximum surface temperature for the corresponding NDVI, ξ + η × NDVI indicating the minimum surface temperature for the corresponding NDVI,
Figure FDA0003322648510000034
mu, xi and eta are parameters fitted based on the characteristic space distribution characteristics of the temperature and the normalized vegetation index.
6. The method of simulating the spatial signature of a cosmic ray neutron instrument according to claim 1, where the simulation formula for the horizontal correction parameters of the cosmic ray neutron instrument is:
Figure FDA0003322648510000035
wherein f isH(i) Represents the correction parameters of the ith pixel of the cosmic ray neutron instrument in the horizontal direction,
Figure FDA0003322648510000036
the neutron intensity of the ith pixel of the cosmic ray neutron instrument is represented, and n represents the number of pixels in the measurement range of the cosmic ray neutron instrument.
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