CN111337548A - High-precision signal-to-noise ratio fitting model and soil humidity inversion method based on same - Google Patents
High-precision signal-to-noise ratio fitting model and soil humidity inversion method based on same Download PDFInfo
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Abstract
The invention discloses a high-precision signal-to-noise ratio fitting model and a soil humidity inversion method based on the model, belonging to the technical field of soil humidity measurement, wherein the high-precision signal-to-noise ratio fitting model is realized based on a GNSS-IR technology, the model models the change of direct signal power and reflected signal power, other characteristic parameters related to soil humidity in the model are all replaced by using fitting parameters, finally, a constraint condition is added to the model to obtain the high-precision fitting model related to signal-to-noise ratio data, the model can obtain all the characteristic parameters by one-step fitting, the model is used for directly fitting the signal-to-noise ratio data of a receiver, an inversion model between the fitting parameters and the soil humidity is established for soil humidity inversion, the signal-to-noise ratio data does not need to be subjected to detrending item operation in advance, and the direct and high-precision fitting modeling of, the flexibility of soil humidity inversion is improved; the problems in the prior art are solved.
Description
Technical Field
The invention relates to a high-precision signal-to-noise ratio fitting model and a soil humidity inversion method based on the same, and belongs to the technical field of soil humidity measurement.
Background
Soil humidity is an important parameter for researching the water circulation of the earth, and accurate and continuous monitoring of soil humidity change has important significance for researching local meteorological condition change, adjusting agricultural production, preventing and reducing disasters. The current soil humidity measuring technology is mainly divided into two types, one is a contact soil humidity measuring method, and the other is a non-contact soil humidity measuring method. The contact measurement method is characterized in that a soil humidity sensor needs to be buried in soil, the soil structure is easy to damage in the burying process, the soil humidity around the sensor can be measured only by the contact measurement method within a range of a few centimeters, the contact measurement method belongs to point measurement, and due to the fact that the soil humidity has high heterogeneity in the space, the measurement results at different points possibly have large differences, and therefore the representativeness of the measurement results is poor. The remote sensing method is a method for measuring the humidity of the non-contact large-area soil by utilizing microwave radiation of the soil or microwave signals scattered by the surface of the soil. With the development of global navigation satellite systems in recent years, a technique of remote sensing using satellite navigation signals scattered through soil has been proposed, and this technique is called GNSS-R technique. Different from the working mode of spontaneous and self-receiving of a traditional active microwave remote sensor, the emission of signals and the receiving of scattered signals in the GNSS-R technology are separated, wherein a microwave emitter navigates a satellite, a receiver is a GNSS-R receiver which is located on the ground or carried on other aircraft platforms, and the distance between the emitter and the receiver is long, so the technology mainly utilizes forward scattered signals of satellite navigation signals to carry out remote sensing.
The GNSS-R technology can be classified into a cooperative mode (i.e., a conventional mode, cGNSS-R for short) and an interference mode (GNSS-Interferometric Reflectometry, GNSS-IR for short) according to the operation mode. Soil humidity measurement in the GNSS-R interference mode mainly utilizes the characteristic that signal-to-noise ratio data recorded by a GNSS receiver is changed in a sine-like function mode. Studies have shown that the sinusoidal-like variation of the snr data is due to the periodic variation of the interference intensity of the directly reflected signal caused by the satellite motion, and the pattern generated by this snr data over time is called the interference pattern. Different interference patterns can be obtained by using antennas with different polarizations to receive interference signals.
As disclosed in the patent publication: CN101900692A discloses a large-area soil humidity measuring method, which relates to a soil humidity measuring method using a vertical linear polarization antenna to receive interference signals. However, the method changes the conventional hardware configuration of the GNSS receiver by using the linear polarization antenna, and is difficult to be widely used. The patent publication numbers are: CN101900692A discloses a soil humidity inversion method based on a low elevation signal received by a Beidou reference station, and relates to a method for measuring soil humidity by using a right-hand circularly polarized antenna to receive interference signals in conventional receiver hardware configuration. The method comprises the steps of firstly carrying out pretreatment operations such as trend removing items on a signal-to-noise ratio, then fitting a standard sine function fitting model with an interference pattern subjected to trend removing items to obtain an initial phase of signal-to-noise ratio oscillation, and establishing an empirical model between the initial phase and soil humidity to carry out soil humidity measurement. However, the standard sine function model with constant amplitude used in the technology has low precision for modeling the actual signal-to-noise ratio because the oscillation amplitude of the actual signal-to-noise ratio is not constant, and the method for modeling the signal-to-noise ratio through two independent fitting processes cannot accurately describe the coupling effect between the straight reflection signals and cannot model the coupling effect between the straight reflection signals.
Disclosure of Invention
The invention aims to provide a high-precision signal-to-noise ratio fitting model and a soil humidity inversion method based on the model.
The invention discloses a high-precision signal-to-noise ratio fitting model, which comprises the following steps:
the SNR is the signal-to-noise ratio of an interference signal when the right-hand circularly polarized antenna is used for receiving the interference signal; θ is the satellite altitude, which is a function of time, determined from the satellite ephemeris or ephemeris; sin (θ) is the sine of the elevation angle; a is0Fitting parameters for the signal-to-noise ratio amplification factor; a is1Fitting parameters for the frequency of the signal-to-noise ratio; a is2Fitting parameters to the phase of the signal-to-noise ratio;
and
are each n0And n1An order polynomial, and the constraint conditions shown in the formulas (4) and (5) need to be satisfied; n is0,n1Is determined empirically, but the two satisfy the relationship determined by equation (6);
is a polynomial
The fitting parameters of (1);
is a polynomial
The fitting parameters of (1).
Further, the construction process of the model comprises the following steps: firstly, a theoretical model of the interference signal with the signal-to-noise ratio varying periodically is obtained, and the theoretical model is expressed as follows:
wherein P isd,PrSignal-to-noise ratios of the direct and reflected signals, respectively; theta is the satellite altitude angle;
is the initial phase; f is the oscillation frequency of the signal-to-noise ratio,
h is the effective height of the antenna relative to the reflecting surface, and lambda is the navigation signal carrier wave length;
then, the polynomial of different orders is used to direct signal power PdAnd reflected signal power PrModeling the change of the soil moisture content, substituting the change into the signal-to-noise ratio fitting model in the formula, and replacing other characteristic parameters related to the soil moisture in the model by using fitting parameters;
and finally, adding a proper constraint condition to the model to obtain a high-precision fitting model about the signal-to-noise ratio data, and completing construction of the high-precision signal-to-noise ratio fitting model.
The soil humidity inversion method based on the high-precision signal-to-noise ratio fitting model comprises the following steps of:
step 1: interference signal receiving processing: the receiver is matched with the right-hand circularly polarized antenna to receive and process interference signals, the interference signals are recorded in the form of signal-to-noise ratio data, and meanwhile, the position, time and satellite ephemeris information of the receiver are recorded;
step 2: calculating the satellite elevation angle and azimuth angle: calculating the elevation angle and the azimuth angle of each visible satellite according to the time, the position of the receiver and the satellite ephemeris information;
and step 3: selecting the stars: selecting a satellite with the same azimuth as the measuring area according to the azimuth of the area to be measured relative to the antenna erection position;
and 4, step 4: scale conversion: selecting low elevation signal-to-noise ratio data of the satellite meeting the requirement from the satellites meeting the azimuth requirement, and converting the data from logarithmic scales to linear scales;
and 5: model fitting: directly fitting the high-precision signal-to-noise ratio fitting model with the signal-to-noise ratio data obtained in the step (4) by using a nonlinear least square fitting algorithm to obtain all fitting parameters a at one time2,a1,a0,
Step 6: soil humidity inversion: and (5) utilizing the different fitting parameters obtained in the step (5) to realize different soil humidity inversion operations.
Further, the receiver in step 1 is a GNSS-IR receiver.
Further, the different soil moisture inversion operations in step 6 include a theoretical model-based soil moisture inversion operation and an empirical model-based soil moisture inversion operation.
Further, the soil moisture inversion operation based on the theoretical model comprises the following steps:
fitting parameters in step 5
Substituting the equations (2) and (3) can obtain the estimated signal-to-noise ratio of the direct signal
Signal to noise ratio of reflected signal
Calculating a reflectance | Γ ¬ of soil through the following equation (7)2；
And (3) performing antenna gain correction and soil roughness correction on the reflectivity obtained by the formula (7):
wherein G isd(theta) is the gain of the antenna to the direct signal when the satellite altitude angle is theta; grThe (-theta) is the gain of the antenna to the reflected signal when the satellite height angle is theta; λ is the navigation signal carrier wavelength; sigma is the root-mean-square height of the soil surface and is used for depicting the roughness of the soil; gd(θ)、Gr(-) and σ bothObtained by measurement;
then, the dielectric constant ε of the soil was calculated according to the following formula (9)r；
Finally, the soil moisture was calculated from the soil dielectric constant model, which is shown in the following equation (10).
εr＝2.8603+3.7463·SMC+119.1755·SMC2(10)
Wherein SMC is the volume soil moisture.
Further, the soil moisture inversion operation based on the empirical model comprises:
using the fitting parameters a of step 51,a2Separately establishing an empirical inversion model, wherein a1Oscillation frequency, a, representing the signal-to-noise ratio2An initial phase representing a signal-to-noise ratio; acquiring signal-to-noise ratio data and real soil humidity data for a long time and simultaneously, and processing the signal-to-noise ratio data according to the steps 1 to 5 to obtain the data about a1And a2And finally, establishing a by using a regression analysis technique1、a2Linear or non-linear model with soil moisture SMC.
Compared with the prior art, the invention has the following beneficial effects:
according to the high-precision signal-to-noise ratio fitting model and the soil humidity inversion method based on the high-precision signal-to-noise ratio fitting model, signal-to-noise ratio data of a receiver are directly fitted by the model, then soil humidity inversion is carried out between fitting parameters and soil humidity, the high-precision signal-to-noise ratio fitting model is provided, the model does not need to carry out trend removing operation on the signal-to-noise ratio data in advance, and direct and high-precision fitting modeling on the signal-to-noise ratio data is achieved; the soil humidity inversion method based on the high-precision fitting model is provided, and due to the fact that the characteristic parameters obtained by the model are rich, different inversion methods can be used for different characteristic parameters, and the flexibility of soil humidity inversion is improved; the problems in the prior art are solved.
Drawings
FIG. 1 is a diagram illustrating an exemplary GNSS-IR technique applied to a high-precision SNR fitting model according to the present invention;
FIG. 2 is a schematic diagram of the SNR data change (interference pattern) in an embodiment of the high-precision SNR fitting model of the present invention;
FIG. 3 is a comparison graph of fitting effects of an embodiment of the high-precision SNR fitting model of the present invention and the prior art;
FIG. 4 is a diagram of a comparison of phase estimation errors for an embodiment of the high accuracy SNR fitting model of the present invention and the prior art;
FIG. 5 is a flow chart of a soil moisture inversion method based on a high-precision signal-to-noise ratio fitting model according to the present invention;
FIG. 6 is a soil humidity inversion effect diagram in the soil humidity inversion method based on the high-precision signal-to-noise ratio fitting model.
Detailed Description
The invention is further illustrated by the following figures and examples:
example 1:
the invention discloses a high-precision signal-to-noise ratio fitting model, which comprises the following steps:
the SNR is the signal-to-noise ratio of an interference signal when the right-hand circularly polarized antenna is used for receiving the interference signal; θ is the satellite altitude, which is a function of time, determined from the satellite ephemeris or ephemeris; sin (θ) is the sine of the elevation angle; a is0Fitting parameters for the signal-to-noise ratio amplification factor; a is1Fitting parameters for the frequency of the signal-to-noise ratio; a is2Fitting parameters to the phase of the signal-to-noise ratio;
and
are each n0And n1A polynomial of order and satisfies the formula (4),(5) The constraints shown; n is0,n1Is determined empirically, but the two satisfy the relationship determined by equation (6);
is a polynomial
The fitting parameters of (1);
is a polynomial
The fitting parameters of (1).
The construction process of the model comprises the following steps: firstly, a theoretical model of the interference signal with the signal-to-noise ratio varying periodically is obtained, and the theoretical model is expressed as follows:
wherein P isd,PrSignal-to-noise ratios of the direct and reflected signals, respectively; theta is the satellite altitude angle;
is the initial phase; f is the oscillation frequency of the signal-to-noise ratio,
h is the effective height of the antenna relative to the reflecting surface, and lambda is the navigation signal carrier wave length;
then, the polynomial of different orders is used to direct signal power PdAnd reflected signal power PrModeling the change of the soil moisture content, substituting the change into the signal-to-noise ratio fitting model in the formula, and replacing other characteristic parameters related to the soil moisture in the model by using fitting parameters;
and finally, adding a proper constraint condition to the model to obtain a high-precision fitting model about the signal-to-noise ratio data, and completing construction of the high-precision signal-to-noise ratio fitting model.
The working principle of the embodiment is as follows: the high-precision signal-to-noise ratio fitting model is realized based on a GNSS-IR technology, and the GNSS-IR technology is a technology for carrying out remote sensing by utilizing the interference effect of GNSS multipath signals. A typical application scenario is shown in fig. 1.
In fig. 1, the direct signal and the multipath signal reflected by the soil generate interference effect at the antenna to form an interference signal, and the interference signal is recorded in the form of signal-to-noise ratio data after being received and processed by the GNSS receiver. Because the satellite moves continuously, the phase of the direct reflection signal changes periodically due to the continuous change of the path difference of the direct reflection signal, and further the interference intensity of the direct reflection signal changes periodically, and finally the signal-to-noise ratio of the interference signal changes periodically, and the periodic change can be represented by a theoretical model of a cosine-like function:
because the power of the direct signal is attenuated after being reflected by soil, and simultaneously, because the antenna is designed to inhibit multi-path signals entering the antenna from the bottom of the antenna as much as possible, the reflected signal is very weak compared with the direct signal. In this case, the overall trend of the interference signal to noise ratio is determined by the direct signal, and the reflected signal only affects the local variation of the signal to noise ratio.
As shown in FIG. 2, soil moisture affects the change in SNR by affecting the power, effective transmission depth and phase of the reflected signal, where changes in reflected signal power will affect PrEffective transmission depth variation will affect H and thus the signal-to-noise ratio oscillation frequency f, and phase variation will affect
. Therefore, by processing the signal-to-noise ratio data and extracting the three characteristic parameters, an inversion model can be established to invert the soil humidity.
The model of the invention uses polynomials of different orders to direct signal powerPdAnd reflected signal power PrModeling the change of the model, substituting the model into a signal-to-noise ratio fitting model shown in the formula (11), then replacing other characteristic parameters related to soil humidity in the model by using fitting parameters, and finally adding proper constraint conditions to the model to obtain a high-precision fitting model related to signal-to-noise ratio data, wherein the model can obtain all the characteristic parameters only by one-step fitting.
Fig. 3 compares the fitting effect of the snr data of the prior art and the present invention, where fig. 3(a) is the fitting effect of the high-precision snr fitting model of the present invention and fig. 3(b) is the fitting effect of the prior art, and it can be seen that the high-precision snr fitting model of the present invention can well depict the local variation of the snr data.
Fig. 4 further compares the estimation error of the initial phase of the present invention with that of the prior art through simulation, and it can be seen that the estimation error of the initial phase of the high-precision snr fitting model related to the present invention is lower than the result of the prior art under different simulation times.
Example 2:
as shown in fig. 5, on the basis of embodiment 1, the soil moisture inversion method based on the high-precision signal-to-noise ratio fitting model according to the present invention includes the following steps:
step 1: interference signal receiving processing: the receiver is matched with the right-hand circularly polarized antenna to receive and process interference signals, the interference signals are recorded in the form of signal-to-noise ratio data, and meanwhile, the position, time and satellite ephemeris information of the receiver are recorded;
step 2: calculating the satellite elevation angle and azimuth angle: calculating the elevation angle and the azimuth angle of each visible satellite according to the time, the position of the receiver and the satellite ephemeris information;
and step 3: selecting the stars: selecting a satellite with the same azimuth as the measuring area according to the azimuth of the area to be measured relative to the antenna erection position;
and 4, step 4: scale conversion: selecting low elevation signal-to-noise ratio data of the satellite meeting the requirement from the satellites meeting the azimuth requirement, and converting the data from logarithmic scales to linear scales;
and 5: model fitting: directly fitting the high-precision signal-to-noise ratio fitting model with the signal-to-noise ratio data obtained in the step (4) by using a nonlinear least square fitting algorithm to obtain all fitting parameters a at one time2,a1,a0,
Step 6: soil humidity inversion: and (5) utilizing the different fitting parameters obtained in the step (5) to realize different soil humidity inversion operations.
The different soil moisture inversion operations in step 6 include soil moisture inversion operations based on theoretical models and soil moisture inversion operations based on empirical models.
The soil moisture inversion operation based on the theoretical model comprises the following steps:
fitting parameters in step 5
Substituting the equations (2) and (3) can obtain the estimated signal-to-noise ratio of the direct signal
Signal to noise ratio of reflected signal
Calculating a reflectance | Γ ¬ of soil through the following equation (7)2；
And (3) performing antenna gain correction and soil roughness correction on the reflectivity obtained by the formula (7):
wherein G isd(theta) is the gain of the antenna to the direct signal when the satellite altitude angle is theta; grAntenna pair for satellite with theta angleGain of the reflected signal; λ is the navigation signal carrier wavelength; sigma is the root-mean-square height of the soil surface and is used for depicting the roughness of the soil; gd(θ)、GrBoth (. about.) and. sigma. can be measured;
then, the dielectric constant ε of the soil was calculated according to the following formula (9)r；
Finally, the soil moisture was calculated from the soil dielectric constant model, which is shown in the following equation (10).
εr＝2.8603+3.7463·SMC+119.1755·SMC2(10)
Wherein SMC is the volume soil moisture.
Example 3:
on the basis of the implementation 2, the soil moisture inversion operation based on the empirical model comprises the following steps:
fitting parameters a with step 51,a2Separately establishing an empirical inversion model, wherein a1Oscillation frequency, a, representing the signal-to-noise ratio2An initial phase representing a signal-to-noise ratio; acquiring signal-to-noise ratio data and real soil humidity data for a long time and simultaneously, and processing the signal-to-noise ratio data according to the steps 1 to 5 to obtain the data about a1And a2And finally, establishing a by using a regression analysis technique1、a2Linear or non-linear model with soil moisture SMC.
As shown in fig. 6, the soil humidity inversion result obtained by the soil humidity inversion method of the present invention is exemplified by the inversion results of GPS 7 and GPS 15. Wherein the curve indicated by the asterisk is the soil humidity measured by using the existing frequency domain reflection soil humidity measurement technology, and in the example, the measurement result is assumed to be the real soil humidity; the curve represented by a triangle is the soil humidity obtained by utilizing the high-precision signal-to-noise ratio fitting model and the soil humidity inversion operation based on the theoretical model, and the soil humidity of two stars is calculated according to the measurement and inversion resultsRoot Mean Square Error (RMSE) of the degree inversion was 0.5cm3/cm3And the correlation coefficient (R) is about 0.7, which shows that the inversion method can track the change of the real soil humidity with higher precision, and proves the usability of the inversion method.
By adopting the high-precision signal-to-noise ratio fitting model and the soil humidity inversion method based on the model, which are described in the embodiment of the invention by combining the drawings, the model is utilized to directly fit the signal-to-noise ratio data of the receiver, and then the soil humidity inversion is carried out between the fitting parameters and the soil humidity, so that the problems in the prior art are solved. The present invention is not limited to the embodiments described, but rather, variations, modifications, substitutions and alterations are possible without departing from the spirit and scope of the present invention.
Claims (7)
1. A high-precision signal-to-noise ratio fitting model is characterized in that: the model comprises:
the SNR is the signal-to-noise ratio of an interference signal when the right-hand circularly polarized antenna is used for receiving the interference signal; θ is the satellite altitude, which is a function of time, determined from the satellite ephemeris or ephemeris; sin (θ) is the sine of the elevation angle; a is0Fitting parameters for the signal-to-noise ratio amplification factor; a is1Fitting parameters for the frequency of the signal-to-noise ratio; a is2Fitting parameters to the phase of the signal-to-noise ratio;
and
are each n0And n1An order polynomial, and the constraint conditions shown in the formulas (4) and (5) need to be satisfied; n is0,n1Is determined empirically, but both satisfy the constraint condition determined by equation (6);
is a polynomial
The fitting parameters of (1);
is a polynomial pn1Fitting parameters of (·).
2. The model of claim 1, wherein the model is a fit model of high accuracy signal-to-noise ratio: the construction process of the model comprises the following steps: firstly, a theoretical model of the interference signal with the signal-to-noise ratio varying periodically is obtained, and the theoretical model is expressed as follows:
wherein P isd,PrSignal-to-noise ratios of the direct and reflected signals, respectively; theta is the satellite altitude angle;
is the initial phase; f is the oscillation frequency of the signal-to-noise ratio,
h is the effective height of the antenna relative to the reflecting surface, and lambda is the navigation signal carrier wave length;
then, the polynomial of different orders is used to direct signal power PdAnd reflected signal power PrModeling the change of the soil moisture content, substituting the change into the signal-to-noise ratio fitting model in the formula, and replacing other characteristic parameters related to the soil moisture in the model by using fitting parameters;
and finally, adding a proper constraint condition to the model to obtain a high-precision fitting model about the signal-to-noise ratio data, and completing construction of the high-precision signal-to-noise ratio fitting model.
3. A soil humidity inversion method based on a high-precision signal-to-noise ratio fitting model is applied to the high-precision signal-to-noise ratio fitting model according to any one of claims 1-2, and is characterized in that: the method comprises the following steps:
step 1: interference signal receiving processing: the receiver is matched with the right-hand circularly polarized antenna to receive and process interference signals, the interference signals are recorded in the form of signal-to-noise ratio data, and meanwhile, the position, time and satellite ephemeris information of the receiver are recorded;
step 2: calculating the satellite elevation angle and azimuth angle: calculating the elevation angle and the azimuth angle of each visible satellite according to the time, the position of the receiver and the satellite ephemeris information;
and step 3: selecting the stars: selecting a satellite with the same azimuth as the measuring area according to the azimuth of the area to be measured relative to the antenna erection position;
and 4, step 4: scale conversion: selecting low elevation signal-to-noise ratio data of the satellite meeting the requirement from the satellites meeting the azimuth requirement, and converting the data from logarithmic scales to linear scales;
and 5: model fitting: directly fitting the high-precision signal-to-noise ratio fitting model with the signal-to-noise ratio data obtained in the step (4) by using a nonlinear least square fitting algorithm to obtain all fitting parameters at one time
Step 6: soil humidity inversion: and (5) utilizing the different fitting parameters obtained in the step (5) to realize different soil humidity inversion operations.
4. The soil moisture inversion method based on the high-precision signal-to-noise ratio fitting model according to claim 3, characterized in that: the receiver in the step 1 is a GNSS-IR receiver.
5. The soil moisture inversion method based on the high-precision signal-to-noise ratio fitting model according to claim 3, characterized in that: the different soil moisture inversion operations in the step 6 comprise soil moisture inversion operations based on a theoretical model and soil moisture inversion operations based on an empirical model.
6. The soil moisture inversion method based on the high-precision signal-to-noise ratio fitting model according to claim 5, characterized in that: the soil moisture inversion operation based on the theoretical model comprises the following steps:
fitting parameters in step 5
Substituting the equations (2) and (3) can obtain the estimated signal-to-noise ratio of the direct signal
Signal to noise ratio of reflected signal
Calculating a reflectance | Γ ¬ of soil through the following equation (7)2；
And (3) performing antenna gain correction and soil roughness correction on the reflectivity obtained by the formula (7):
wherein G isd(theta) is the gain of the antenna to the direct signal when the satellite altitude angle is theta; grThe (-theta) is the gain of the antenna to the reflected signal when the satellite height angle is theta; λ is the navigation signal carrier wavelength; sigma is the root-mean-square height of the soil surface and is used for depicting the roughness of the soil; gd(θ)、GrBoth (. about.) and. sigma. can be measured;
then, the dielectric constant ε of the soil was calculated according to the following formula (9)r；
Finally, the soil moisture was calculated from the soil dielectric constant model, which is shown in the following equation (10).
εr＝2.8603+3.7463·SMC+119.1755·SMC2(10)
Wherein SMC is the volume soil moisture.
7. The soil moisture inversion method based on the high-precision signal-to-noise ratio fitting model according to claim 5, characterized in that: the soil moisture inversion operation based on the empirical model comprises the following steps:
using the fitting parameters a of step 51,a2Separately establishing an empirical inversion model, wherein a1Oscillation frequency, a, representing the signal-to-noise ratio2An initial phase representing a signal-to-noise ratio; acquiring signal-to-noise ratio data and real soil humidity data for a long time and simultaneously, and processing the signal-to-noise ratio data according to the steps 1 to 5 to obtain the data about a1And a2And finally, establishing a by using a regression analysis technique1、a2Linear or non-linear model with soil moisture SMC.
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