CN106909750B - A kind of computational methods of broad-leaved Vegetation canopy reflectivity - Google Patents
A kind of computational methods of broad-leaved Vegetation canopy reflectivity Download PDFInfo
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Abstract
The invention discloses a kind of computational methods and model of broad-leaved Vegetation canopy reflectivity, computational methods comprise the following steps：S1：The parameter of input is identified and classified by input parameter, is divided into blade parameter, Crown canopy parametre and soil parameters；S2：The reflectivity and transmissivity of individual blade are calculated according to blade parameter；S3：Blade parameter in Crown canopy parametre and S2 tries to achieve the extinction coefficient and scattering coefficient of canopy；S4：The associated reflections factor and reflectivity of canopy are tried to achieve according to required canopy delustring and scattering parameter；S5 tries to achieve canopy reflectance spectrum according to the associated reflections factor and reflectivity of canopy.The present invention is by PROSPECT models and SAIL Model couplings, make full use of can get parms in the case of cancel Vegetation canopy reflectivity simulation process in leaf reflectance and transmissivity input process, it is of the invention effectively to simplify parameter acquiring problem and optimized algorithm in Vegetation canopy spectral information simulation process, speed-up computation process, while coupling model is advantageous to vegetation parameter inverting.
Description
Technical Field
The invention relates to evaluation of vegetation health conditions of high-grade highway regions, in particular to a calculation method and a model of broadleaf vegetation canopy reflectivity.
Background
The inversion of vegetation information is always the most promising research field of quantitative remote sensing, and provides a favorable basis for developing vegetation ecological environment monitoring and evaluation research. Numerous vegetation parameter inversion models are proposed by scholars at home and abroad, and can be mainly divided into two categories, namely a statistical model and a physical model, wherein the physical model is favored by excellent wide applicability and stability. The physical inversion model of vegetation information has a rather strong physical basis and does not depend on the specific type of vegetation and the change of the background environment. However, the physical model has the problems that the accuracy is still poor and the calculation amount is large in the large-scale vegetation information inversion, so that the requirements of practical production and application cannot be met, mainly due to two reasons: firstly, the physical model has high requirements on quantitative remote sensing, the surface reflectivity needs to be inverted through a remote sensing image, and a plurality of difficult-to-obtain accurate parameters are used as input parameters of the physical model; on the other hand, most of the current remote sensing physical models are on the canopy scale, and canopy spectra are influenced by factors such as blade spectrum information, soil background reflectivity, canopy structure and the like, so that the accuracy of biochemical parameter inversion is limited, and the difficulty of inversion is increased.
The most studied and applied models in recent years are the prospectt model for broadleaf, LIBERTY model for coniferous, and coronal SAIL model. According to the PROSPECT model, the broadleaf blades are regarded as a composite flat plate model consisting of N layers of rough flat plates containing biochemical substances of the blades and N-1 layers of air, and the reflectivity and the transmissivity of the composite flat plate model are obtained by inputting the concentrations of various pigments, the equivalent water thickness, the white substance concentration and the structural parameters of the blades. The LIBERTY model considers the cells of the needle leaf as standard circular cells, and considers that the needle leaf is formed by stacking numerous leaf cells in the air, and further obtains the spectrum information of the infinite cells by obtaining the optical characteristics of the single cells. The canopy SAIL model is a four-flow approximation to a radiation transmission equation on the basis of a radiation transmission theory, and simulates the reflectivity of a canopy from 400nm to 2500nm by inputting parameters such as a solar zenith angle, a solar azimuth angle, an observation zenith angle, an observation azimuth angle, LAI, soil reflectivity, a hot spot, the reflectivity and the transmissivity of a single blade and the like. Obviously, the output parameters of the broadleaf and conifer models can be used as the input parameters of the SAIL model to realize the coupling of the models, and further realize the simulation of vegetation canopy information. Therefore, researchers at home and abroad successively develop model coupling and application researches, the most current application is that a PROSPECT blade model is coupled with an SAIL canopy reflection model, and the coupling model simulates vegetation canopy reflectivity by using the corrected blade model and canopy model, so that the inversion accuracy and the inversion speed are high. However, most of the conventional PROSAIL models are formed by coupling developed relatively complete initial models, the PROSPECT model and the SAIL model are coupled under the condition that the problems of asymmetry of the upper and lower surfaces of the vegetation blades, hotspot effects and the like cannot be considered, and although the adaptability and the precision are ensured to a certain extent, the problems of insufficient vegetation parameter inversion and the like are still exposed in the practical application process, so that the coupling models are limited by a certain program in the practical application process.
Therefore, it is necessary to design a new calculation method and model for the reflectivity of the broadleaf vegetation canopy.
Disclosure of Invention
The invention provides a calculation method and a model of broadleaf vegetation canopy reflectivity, aiming at the problem that a physical model is limited in the practical application process and solving the problems of parameter acquisition and inversion accuracy of the vegetation physical model in the application process.
The technical scheme of the invention is as follows:
a calculation method of reflectivity of a broadleaf vegetation canopy comprises the following steps:
s1: identifying parameters;
inputting model parameters; and the input parameters are preliminarily divided into three categories: leaf parameters, soil parameters, and canopy parameters; wherein the leaf parameters include pigment content, dry matter content, equivalent water thickness and leaf structure parameters; the soil parameter is the spectral reflectance of the soil; the canopy parameters are the remaining other parameters;
s2: inputting the parameters of the blades in the step S1 into a PROSPECT model to perform single-blade spectrum simulation, and calculating the spectral reflectivity and the transmissivity of each blade;
s3: calculating extinction coefficients and scattering coefficients according to the soil parameters and the canopy parameters in the step S1;
s4: inputting the extinction coefficient and the scattering coefficient obtained by the calculation in the step S3 into an SAIL model, and calculating relevant reflection factors and reflectivities of the canopy, wherein the relevant reflection factors and reflectivities comprise a hemispherical reflectivity in a direct solar direction, a hemispherical reflectivity in an observation direction and a double direct solar reflectivity;
s5: the canopy reflectivity is calculated.
The step S2 specifically includes the following steps:
s2.1: calculating an absorption coefficient K; the absorption coefficient is a linear expression of the contents of various chemical substances in the leaves, and the calculation formula is as follows:
wherein c (i) is the concentration of a component i in the leaves, and the component i is a chemical substance such as a pigment, water, a dry substance and the like; k (i) is the specific absorption coefficient of component i; n is a blade structure parameter and represents the layering number of the blade, and can be calculated by adopting the following empirical equation:
N＝(0.9*SLA+0.025)/(SLA-0.1)
wherein SLA is the specific leaf area, which refers to the leaf area per unit dry weight;
s2.2: calculate transmittance at interface:
the transmittance at the interface includes two: one is the transmittance of light from the air into the blade, and one is the transmittance of light from the blade into the air;
natural light can be regarded as unpolarized light, and after reflection, complete polarization occurs, and after transmission, partial polarization occurs in refracted light. According to Snell-Descarats law, the relation between the incident angle and the refraction angle on the contact surface of two media and two refractive indexes can be known, and then the average transmittance t of the light ray from the air with the refractive index of 1 and the incident refractive index of n as a solid angle alpha can be calculated according to the transmittance of the electromagnetic wave given by Schanda through the two media av (α,1, n) let t 12 ＝t av (α,1,n)；
According to the results of Stern's study, the transmittance t of light entering air of refractive index 1 from a blade of refractive index n 21 And t 12 There is a relation t between 21 ＝n －2 ·t 12 Calculating the transmittance at the interface according to the above; the calculation of the transmittance at the interface is prior art and can be done using existing software;
s2.3: calculating the total transmittance tau of light through the flat medium 1 ；
For natural light, the total transmittance tau of the light transmitting the flat plate medium 1 The integral in the whole space of 2 pi of the whole hemisphere is related to the absorption coefficient K and the thickness D of the blade, and the calculation formula is as follows:
wherein t is an intermediate variable;
s2.4: calculating the reflectivity R of a single-layer plate α (1) And transmittance T α (1)：
Performing single-layer flat plate spectrum simulation, wherein the single-layer flat plate spectrum is the core of the whole blade spectrum simulation and mainly comprises the following steps of calculating the reflectivity and the transmissivity of the single-layer flat plate, and the calculation formula is as follows:
s2.5: calculating the reflectivity R of a single leaf α (N) and transmittance T α (N)：
The method comprises the following steps of carrying out blade spectrum information simulation, deeply researching an optical phenomenon of light after the light penetrates through a limited layer flat plate by Stokes, obtaining a calculation theory of the total reflectivity and the total transmissivity of the light after the light penetrates through N layers of flat plates with the same reflectivity and the same transmissivity, and obtaining a simulation formula of the blade spectrum information by applying the theory:
wherein:
the step S3 specifically includes the following steps:
s3.1 shadow compensation:
(1) calculating geometrical factors related to extinction and scattering: firstly, weighting and discretizing according to the probability distribution of general blade inclination angles to obtain a group of discretized blade inclination angles; then, calculating extinction and scattering factors corresponding to each leaf inclination angle; for blade inclination angle theta l The calculation method is as follows:
first, a critical angle β is determined s And beta o The calculation formula is as follows:
wherein the angle between the normal direction of the horizontal plane and the normal direction of the blade is the blade inclination angle theta s Is the zenith angle of the sun, theta o To observe zenith angles;
when the denominator in the calculation formula is not 0 and the calculation result of cos beta is less than 1, directly calculating the values of two critical angles; when the calculation result of cos beta is equal to 1, the two adjacent angles are equal to pi; wherein cos β is broadly referred to as β s And beta o The cosine of (2);
then, the blade inclination angle is calculated as theta l The calculation formulas of the extinction coefficients of the direct solar radiation direction and the observation direction of the single blade are respectively as follows:
wherein, L' = lai/h, lai is the leaf area index, h is the canopy height;
(2) calculating an auxiliary azimuth angle β 1 、β 2 、β 3 : the calculation of the auxiliary azimuth angle mainly depends on the relative inequality relation of two critical angles, and the value taking method comprises the following steps:
| If： | β 1 | β 2 | β 3 |
| ψ≤|β s -β o | | ψ | |β s -β o | | 2π-β s -β o |
| |β s -β o |＜ψ＜2π-β s -β o | |β s -β o | | ψ | 2π-β s -β o |
| ψ≥2π-β s -β o | |β s -β o | | 2π-β s -β o | ψ |
wherein psi is the relative azimuth angle between the sun direction and the observation direction, i.e. the difference between the two azimuth angles;
after three auxiliary azimuth angles are obtained, multipliers related to single-blade reflectivity and transmissivity can be calculated and used for calculating a bidirectional scattering coefficient omega;
(3) calculating the bidirectional scattering coefficient omega (theta) l )：
After the auxiliary azimuth angle is obtained, calculating to obtain a bidirectional scattering coefficient by matching with the single-blade reflectivity and the single-blade transmissivity which are obtained by calculation in the step S2, wherein the calculation formula is as follows:
where ρ, τ, θ l Respectively representing the reflectivity and the transmissivity of the blade and the corresponding blade inclination angle at the moment; let ρ = R in S2 α (N)；τ＝T α (N)。
S3.2, calculating a scattering coefficient after adding the reflectivity and the transmissivity of the blade:
(1) the backscattering coefficients of the diffuse radiation E-and E + are calculated according to the formula:
(2) the forward scattering coefficient calculation formula of the diffuse radiation E-and E + is as follows:
(3) direct solar radiation E S The calculation formula of the backscattering coefficient is as follows:
(4) direct solar radiation E S The forward scattering coefficient calculation formula is:
(5) the calculation formula of the attenuation coefficients of the diffuse radiation E-and E + is as follows:
(6) observation direction radiation E 0 The calculation formula of the backscattering coefficient is as follows:
(7) observation direction radiation E 0 The forward scattering coefficient calculation formula is:
s3.3, calculating the general blade inclination angle distribution probability (blade profile distribution element):
calculating a general blade pitch distribution under the average blade pitch distribution: the blade inclination angle refers to an included angle between the normal direction of a horizontal plane and the normal direction of the blade; different types of vegetation canopy correspond to different vegetation blade inclination angles, while corresponding to the two leaf distribution parameters LIDFa and LIDFb.
In the case of non-ellipsoidal distributions, the probability of a general leaf dip distribution can be calculated from the average leaf dip, the calculation being done by iteration:
x＝2θ
y＝LIDFa·sin(x)+0.5LIDFb·sin(2x)
dx＝0.5(y‐x+2θ)
x＝x+dx
until | dx | < t;
f (θ) =2 (y + θ)/π.
Where θ is a discrete value of the average leaf inclination angle, and F (θ) is a cumulative leaf inclination angle, i.e., a general leaf inclination angle distribution probability.
For the ellipsoidal distribution, the parameter LIDFa represents the distribution angle which is 30 degrees, the parameter LIDFb is 0, and when the general leaf dip distribution probability is obtained, the general leaf dip density function made by Campbell (1986) can be used for obtaining the general leaf dip density function;
s3.4, determining model parameters of the whole canopy;
for any canopy, the blade pitch angle will not be fixed, and will be a continuous process that increases from 0 to 90, so that the model parameters for the entire canopy are determined by calculating the blade pitch angle as θ l General blade pitch distribution probability F (theta) of time l ) The product of the model parameters and the model parameters are added, and the calculation formula is as follows:
Z＝∑F(θ l )Z(θ l )
wherein, F (theta) l ) For angle of inclination of blade theta l Corresponding probability of general blade inclination distribution, Z (theta) l ) For the parameters of a single blade, Z is a modified model Z = ∑ F (θ) through the blade inclination angle l )Z(θ l ) Modified parameters of the whole canopy; z (theta) l ) Denotes k (θ) obtained in steps S3.1 and S3.2 l )、K(θ l )、ω(θ l )、σ(θ l )、σ′(θ l )、s(θ l )、s′(θ l )、 a(θ l )、v(θ l )、u(θ l ) Any one of the above; z accordingly refers to any of all coefficients K, w, σ ', s', a, v, u in the four differential equations of the SAIL model for the entire canopy.
The step S4 specifically includes the following steps:
s4.1: calculating a leaf area parameter; the leaf area parameter is an important index for evaluating the reflectivity of the vegetation canopy, and the parameter calculation formula is as follows:
τ ss ＝e -klai
τ oo ＝e -Klai
ρ dd ＝(e mlai -e -mlai )/(h 1 e mlai -h 2 e -mlai )
τ dd ＝(h 1 -h 2 )/(h 1 e mlai -h 2 e -mlai )
wherein K and K respectively denote the observation direction radiation E 0 Extinction coefficient and direct solar radiation E s The extinction coefficient of (a); lai represents the leaf area index and is a model input parameter;
s4.2: and calculating parameters after the hot spot effect is added, wherein the calculation formula is as follows:
ρ sd ＝C S (1-τ ss τ dd )-D S ρ dd
τ sd ＝D S (τ ss -τ dd )-C S τ ss ρ dd
ρ do ＝C o (1-τ oo τ dd )-D o ρ dd
τ do ＝D o (τ oo -τ dd )-C o τ oo ρ dd
ρ so ＝H o (1-τ ss τ oo )-C o τ sd τ oo -D o ρ sd
the calculation method of each intermediate variable comprises the following steps:
h 1 ＝(a+m)/σ
h 2 ＝(a-m)/σ＝1/h 1
C S ＝[s′(k-a)-sσ]/(k 2 -m 2 )
C o ＝[v(K-a)-uσ]/(K 2 -m 2 )
D s ＝[-s(k+a)-s′σ]/(k 2 -m 2 )
D o ＝[-u(K+a)-vσ]/(K 2 -m 2 )
H s ＝(uC S +vD s +w)/(K+k)
H o ＝(sC o +s′D o +w)/(K+k)
wherein, tau ssoo Correcting parameters for the hot spot effect; because of the problem of solar radiation, particularly the large temperature difference between the soil and vegetation in sparsely populated areas, which is related to their physical surface and meteorological features, a process of temperature correction is required, while possibly providing additional vegetation canopy information. The hot spot effect correction process is as follows:
hotspot correction is performed according to the 2/(K + K) effect, and firstly, parameters are calculated according to given hotspot values:
initial value of given alf is alf =10 6 ，
1) If the hot point value q is larger than 0, the influence of the hot point effect is considered to exist, and at the moment Wherein, theta s Is the zenith angle of the sun, theta o For observing zenith angle,Is the solar azimuth; (if the alpha calculation result is more than 200, the alf value is 200); if the calculation result of alf is 0, calculating the parameter tau under the influence of the shadow-free pure hot spot effect according to the following formula ssoo And a given:
τ ssoo ＝τ ss
if the calculation result of alf is not 0, it is considered to have no influence of hot spot effect, and τ is calculated by the method in 2) ssoo And a sumint;
2) If the hot point value q is 0, the influence of no hot point effect is considered, and the parameter tau under the influence of no hot point effect is calculated by using a cyclic addition method ssoo And a given: the method comprises the following specific steps:
the first step, parameter initialization:
second step, calculating τ iteratively by ssoo And a given:
step 1, judging the value of i:
if i is less than 20, let x2= -log (1-i x fint)/alf;
if i =20, let x2=1;
if i is greater than 20, ending the iteration and making tau ssoo ＝f1；；
Step 2, the following calculations are carried out in sequence:
y2＝‐(K+k)*lai*x2+fhot*(‐exp(‐alf*x2))/alf；
f2＝exp(y2)；
sumint＝sumint+(f2‐f1)*(x2‐x1)/(y2‐y1)；
x1＝x2；
y1＝y2；
f1＝f2；
step 3, making i = i +1, and turning to step 1;
where denotes multiplication.
S4.3: calculating the bidirectional reflectivity:
the bidirectional reflectivity comprises two parts, wherein one part has single scattering influence of the hot spot effect, the other part has no multiple scattering influence of the hot spot effect, and the two parts are summed into a final calculation result of the reflectivity influence on the top of the canopy:
ρ so2 ＝ρ so +w*lai*sumint
s4.4: introducing a soil reflection effect:
the soil is located the bottommost of whole canopy reflection system, and the electromagnetic wave can strike soil ground after penetrating the canopy, reflects back the canopy top again after reflecting, forms a part of canopy reflectivity, and the calculation scheme is:
d n ＝1－r s *ρ dd
s4.5: calculating a bi-hemispherical reflectivity factor:
s4.6: calculating the hemispherical reflectivity in the direct solar radiation direction:
ρ sd2 ＝ρ dd +(τ sd +τ ss )*r s *τ dd /d n
s4.7: calculating the hemispherical reflectivity in the observation direction:
ρ do2 ＝ρ do +(τ do +τ oo )*r s *τ dd /d n
s4.8: calculating the dual direct reflectance:
ρ sod2 ＝ρ so +((τ ss +τ sd )*τ do +(τ sd +τ ss *r s *ρ dd )*τ oo )*r s /d n
ρ so3 ＝ρ so2 +ρ so +τ ssoo *r s
wherein r is s Is the soil reflectivity.
The step S5 specifically includes the following steps:
firstly, the basic radiation amounts of the direct solar rays and the scattered atmospheric rays, respectively marked as E, can be obtained according to the database data s And E d ；
Then, a coefficient skyl representing the proportion of the total radiation by the scattered radiation in the atmosphere is calculated:
skyl＝0.847-1.61*sin(90-θ s )+1.04*sin(90-θ s ) 2
and finally, calculating the ratio of the radiation quantity measured in the observation direction to the incident radiation quantity to obtain the reflectivity of the canopy, wherein the formula is as follows:
a calculation model of broadleaf vegetation canopy reflectivity is disclosed, and the formula is as follows:
wherein R is the crown reflectivity, E s And E d The basic radiation amounts of direct solar rays and atmospheric scattered rays are respectively, and skyl is a coefficient representing the proportion of scattered radiation in the atmosphere to total radiation; rho do2 And ρ so3 Respectively the hemispherical reflectivity and the direct reflectivity in the observation direction; the model parameters are solved according to the calculation method of the reflectivity of the broadleaf vegetation canopy.
Has the advantages that:
based on the latest research results of a PROSPECT broadleaf model and an SAIL canopy model, the invention couples the PROSPECT model for simulating broadleaf blade spectral information with the SAIL model for simulating canopy spectral information, fully utilizes the available parameters to save the process of blade spectral simulation, cancels the process of blade reflectivity and transmissivity input in the vegetation canopy reflectivity simulation process, adds a blade model simulation algorithm into the canopy SAIL model to complete the coupling process, and directly simulates the canopy spectrum by vegetation physical and chemical parameters. The latest research result of the physical model is utilized for coupling, so that the precision of the physical model for simulating the spectrum can be greatly improved, the business action capability of the model can be improved, meanwhile, the parameter acquisition problem in the vegetation canopy spectrum information simulation process can be effectively simplified, the algorithm can be optimized, the calculation process can be accelerated, and the inversion capability of the vegetation information can be improved.
Drawings
FIG. 1 is a schematic diagram of the present invention;
FIG. 2 is a diagram of model parameters input by the present invention;
FIG. 3 shows the results of the experiment of the present invention
Detailed Description
The invention is further described below with reference to the accompanying drawings.
According to the method, a SAILH canopy model with improved hot spot effect is used as a basis, a given parameter is classified into a blade parameter and a canopy parameter, then the physical and chemical parameters of the blade are utilized to calculate the basic absorption effect of the blade, the reflectivity and the transmissivity of a single-layer flat plate are calculated and derived by combining the transmissivity under the interface-free absorption effect, and finally the spectral information of the blade under the given structural parameter is derived by utilizing a layering theory; meanwhile, for the canopy parameters, firstly, the leaf profile distribution elements are calculated by using the given leaf inclination angle distribution model parameters, then, the extinction coefficient and the scattering coefficient of the canopy model are calculated by combining the calculated geometric elements and are combined with the leaf profile distribution model, the set of canopy parameters under the complete leaf distribution are obtained through a circulation process, and finally, the reflectivity of the canopy is determined by using the two obtained radiation parameters and the sky scattering coefficient.
The present embodiment further describes the technical solution of the present invention by taking a tree on the highway side, which has a good growth condition and a canopy spectrum easy to measure, as an example. As shown in the attached drawings, the improved physical model PROSAILH calculation method related to the invention is as follows:
the parameters of the tree were determined as follows:
| chlorophyll content | 45.80 | Blade inclination angle distribution type | Inclined type |
| Equivalent water thickness | 0.02 | Leaf area index | 4.30 |
| Dry matter content | 0.02 | Solar zenith angle | 30.00 |
| Structural parameters of blade | 1.30 | Observing zenith angle | 10.00 |
| Hot spot | 8.00 | Relative azimuth angle | 0.00 |
Selecting experimental wavelength of 400nm-2399nm
S1, parameter classification: after obtaining relevant parameters of vegetation, dividing the vegetation into two parts, wherein the parameters of the leaf comprise the pigment content of the leaf, the equivalent water thickness, the dry matter content and the maximum incidence angle (generally 59 degrees); the canopy parameters include leaf dip distribution parameters, leaf area index, sun zenith angle, observation zenith angle, relative azimuth angle, hot spot and background reflectivity of soil.
S2: resolving spectral information of the blade: after obtaining the corresponding parameters, firstly, the spectral reflectivity and the transmittance of the single blade need to be calculated, and the calculation scheme is as follows:
(1) Calculating an absorption coefficient K: the absorption coefficient is a linear expression of the contents of various chemical substances in the leaves, and the calculation formula is as follows:
(2) Transmittance under no interface absorption was calculated: natural light can be regarded as unpolarized light, and after reflection, it is completely polarized, and after transmission, it is partially polarized. The relation between the incident angle and the refraction angle on the contact surface of the two media and the two refractive indexes can be known according to Snell-Descorts law, and the average transmittance t of the light ray from the air with the refractive index of 1 and the incident refractive index of n in the alpha solid angle can be calculated according to the transmittance of the electromagnetic wave given by Schanda through the two media av (α,1, n) to which a code t is assigned 12 According to Stern's results, light is incident from a blade of refractive index n into an air of refractive index 1, and the air is transmitted through t 21 And t 12 There is a relation t between 21 ＝n －2 t 12 From this, the transmittance at the interface is calculated.
(3) Transmission of light in isotropic media: for natural light, the total transmittance tau of the natural light transmitting through a flat plate medium is the integral in the whole hemispherical 2 pi space, and is related to the absorption coefficient K and the blade thickness D, and the calculation formula is as follows:
(4) Single-layer flat plate spectrum simulation: the spectrum of the single-layer flat plate is the core of the whole blade spectrum simulation, mainly comprises the reflectivity and the transmissivity of the single-layer flat plate, and the calculation formula is as follows:
(5) Single leaf reflectance and transmittance simulations: stokes deeply studies the optical phenomenon after light penetrates through the finite layer flat plate, obtains the total reflectivity and transmissivity after the light penetrates through the N layers of flat plates with the same reflectivity and transmissivity, and obtains a simulation formula of the spectral information of the blade by applying the theory:
wherein:
s3: calculating extinction coefficient and scattering coefficient
(6) And (3) geometric element calculation:
(7) Calculating the leaf profile distribution element:
general blade pitch distribution at average blade pitch distribution: the different types of vegetation canopy correspond to different vegetation blade inclination angles, while corresponding to the two leaf distribution parameters LIDFa and LIDFb. Under the condition of non-ellipsoidal distribution, a general inclination angle can be calculated according to the average leaf inclination angle, the calculation process can be completed by a simple iteration, and the pseudo code is as follows:
x＝2θ
y＝LIDFa·sin(x)+0.5LIDFb·sin(2x)
dx＝0.5(y‐x+2θ)
x＝x+dx
until | dx | < t;
then F (θ) =2 (y + θ)/π
Where θ is the discrete value of the average leaf inclination angle and F (θ) is the cumulative leaf inclination angle.
For the ellipsoidal distribution, the distribution angle is 30 degrees as indicated by the parameter LIDFa, and the parameter LIDFb is 0, which can be obtained by using the leaf dip density function performed by Campbell (1986) when calculating the general angular distribution.
(8) Extinction and scattering coefficient calculation:
shading compensation:
(1) geometrical factor calculations related to extinction and scattering: firstly, weighting and discretizing the blade inclination angle distribution to obtain a set of discretized central angle value blade inclination angle distribution. Then, a set of extinction and scattering factors is calculated corresponding to each leaf inclination angle, and the single calculation scheme is as follows:
first, the critical angle beta is determined s And beta o The calculation formula is：
When the denominator in the calculation formula is determined to be not 0 and the calculation result of cos beta is less than 1, directly calculating the values of two critical angles; when the calculation result of cos beta is more than 1, the two adjacent angles are equal to pi; wherein cos β is broadly referred to as β s And beta o The cosine of (a);
after two temporary boundary angles are calculated, the extinction coefficients of the direct solar direction and the observation direction can be calculated, and the calculation formulas are respectively as follows:
wherein, L' = lai/h, lai is the leaf area index, h is the canopy height;
(2) auxiliary azimuth angle beta for calculating bidirectional scattering coefficient W 1 、β 2 、β 3 And (3) calculating: the calculation of the auxiliary azimuth angle mainly depends on the relative inequality relation of two critical angles, and the value taking method is as follows:
| If： | β 1 | β 2 | β 3 |
| ψ≤|β s -β o | | ψ | |β s -β o | | 2π-β s -β o |
| |β s -β o |＜ψ＜2π-β s -β o | |β s -β o | | ψ | 2π-β s -β o |
| ψ≥2π-β s -β o | |β s -β o | | 2π-β s -β o | ψ |
wherein psi is the relative azimuth angle between the sun direction and the observation direction, i.e. the difference between the azimuth angles of the two directions;
and after three auxiliary azimuth angles are obtained, a multiplier related to the reflectivity and the transmissivity of the single blade can be calculated and used for calculating the bidirectional scattering coefficient W.
(3) And (3) calculating a bidirectional scattering coefficient: after the auxiliary azimuth angle is obtained, the bidirectional scattering coefficient can be calculated by matching the single-blade reflectivity and the single-blade transmissivity which are calculated in the S2, and the calculation formula is as follows:
where ρ, τ, θ l Respectively representing the reflectivity and the transmissivity of the blade and the corresponding blade inclination angle at the moment; let ρ = R in S2 α (N)；τ＝T α (N)。
Model parameter solution
(9) Calculation of scattering coefficient (addition of reflectance and transmittance of the blade):
(1) the calculation formula of the backscattering coefficients of the diffuse radiation E-and E + is as follows:
(2) the forward scattering coefficient calculation formula of the diffuse radiation E-and E + is as follows:
(3) direct solar radiation E S The calculation formula of the backscattering coefficient is as follows:
(4) direct solar radiation E S The forward scattering coefficient calculation formula is:
(5) the calculation formula of the attenuation coefficients of the diffuse radiation E-and E + is as follows:
(6) observation direction E 0 AfterThe calculation formula of the scattering coefficient is as follows:
(7) observation direction E 0 The forward scattering coefficient calculation formula is:
for any canopy, the blade pitch angle will not be fixed, and is a continuous process that increases from 0 to 90, so when determining the model parameters of the whole canopy, the calculation method is that the blade pitch angle distribution function is added after being multiplied by the probability function F (theta) and the model parameters, and the calculation formula is:
Z＝∑F(θ l )Z(θ l )
wherein, F (θ) l ) For angle of inclination of blade theta l Corresponding probability of general blade inclination distribution, Z (theta) l ) For the parameters of a single blade, Z is a corrected model of blade inclination angle Z = ∑ F (θ) l )Z(θ l ) Modified parameters of the whole canopy; z (theta) l ) Denotes k (θ) obtained in step 1) and step 2) l )、K(θ l )、ω(θ l )、σ(θ l )、σ′(θ l )、s(θ l )、s′(θ l )、 a(θ l )、v(θ l )、u(θ l ) Any one of the above; z accordingly refers to any of all coefficients K, w, σ ', s', a, v, u in the four differential equations of the SAIL model for the entire canopy.
S4: calculating relevant reflection factors and reflectivities of the canopy, wherein the relevant reflection factors and reflectivities comprise a hemispherical reflectivity in a direct solar radiation direction, a hemispherical reflectivity in an observation direction and a double direct solar radiation reflectivity;
(1) Addition of leaf area coefficient: the leaf area index is an important index for evaluating the reflectivity of the vegetation canopy, and the parameter calculation formula is as follows:
τ ss ＝e -klai
τ oo ＝e -Klai
ρ dd ＝(e mlai -e -mlai )/(h 1 e mlai -h 2 e -mlai )
τ dd ＝(h 1 -h 2 )/(h 1 e mlai -h 2 e -mlai )
(2) And (3) calculating parameters of the solution: the parameters after adding the hot spot effect are complex, and the calculation formula is as follows:
ρ sd ＝C S (1-τ ss τ dd )-D S ρ dd
τ sd ＝D S (τ ss -τ dd )-C S τ ss ρ dd
ρ do ＝C o (1-τ oo τ dd )-D o ρ dd
τ do ＝D o (τ oo -τ dd )-C o τ oo ρ dd
ρ so ＝H o (1-τ ss τ oo )-C o τ sd τ oo -D o ρ sd
the calculation method of each variable comprises the following steps:
h 1 ＝(a+m)/σ
h 2 ＝(a-m)/σ＝1/h 1
C S ＝[s′(k-a)-sσ]/(k 2 -m 2 )
C o ＝[v(K-a)-uσ]/(K 2 -m 2 )
D s ＝[-s(k+a)-s′σ]/(k 2 -m 2 )
D o ＝[-u(K+a)-vσ]/(K 2 -m 2 )
H s ＝(uC S +vD s +w)/(K+k)
H o ＝(sC o +s′D o +w)/(K+k)
(3) Correction of the hotspot effect: because of the problem of solar radiation, particularly the large temperature difference between the soil and vegetation in sparsely populated areas, which is related to their physical surface and meteorological features, a process of temperature correction is required, while possibly providing additional vegetation canopy information. The hot spot effect correction process is as follows:
hotspot correction is performed according to the 2/(K + K) effect, and firstly, parameters are calculated according to given hotspot values:
initial value of given alf is alf =10 6 ，
1) If the hot point value q is greater than 0, the influence of the hot point effect is considered, and at the moment Wherein, theta s Is the zenith angle of the sun, theta o For observing the zenith angle,Is the solar azimuth; (if the alpha calculation result is more than 200, the alf value is 200); if the calculation result of alf is 0, calculating the parameter tau under the influence of the shadow-free pure hot spot effect ssoo And a mint, the calculation formula is:
τ ssoo ＝τ ss
if the calculation result of alf is not 0, it is considered to have no influence of hot spot effect, and τ is calculated by the method in 2) ssoo And a sumint;
2) If the hot-point value q is 0, it is considered to be free from the influence of hot-point effect, and cyclically addedThe method calculates the parameter tau without the influence of the hot spot effect ssoo And a given: the method comprises the following specific steps:
the first step gives the initial parameters in the loop:
fhot＝lai*sqrt(K*k)；
x1＝0；
y1＝0；
f1＝1；
fint＝(‐exp(‐alf))*0.05；
sumint＝0；
the second step is to calculate parameters:
finally let τ ssoo ＝f1；
An x in the code indicates multiplication;
in the program calculation, the intermediate parameter x2 in the first 19 times of the cycle is calculated according to a given formula and substituted into the following formula to calculate the sumint, the intermediate parameter x2 in the 20 th time of the cycle is set to be 1 and substituted into the following formula to calculate the sumint, and the tau is set ssoo Equal to f1 calculated in the 20 th cycle.
(4) And (3) calculating the bidirectional reflectivity: the bidirectional reflectivity comprises two parts, one part is provided with a hot spot effect, the other part is not provided with the hot spot effect, and the two parts are summed into a final calculation result:
ρ so2 ＝ρ so +w*lai*sum
(5) Introduction of soil reflex action: the soil is located at the bottommost part of the whole canopy reflection system, electromagnetic waves penetrate through the canopy and then can be emitted to the soil ground, the electromagnetic waves are reflected to the top of the canopy again after being reflected, and a part of the canopy reflectivity is formed, and the calculation scheme is as follows: 1-r s *ρ dd
(6) Calculating a double hemisphere reflectivity factor:
(7) Calculating the hemispherical reflectivity in the direct solar radiation direction:
ρ sd2 ＝ρ dd +(τ sd +τ ss )*r s *τ dd /(1－rs*ρ dd )
(8) And (3) calculating the hemispherical reflectivity in the observation direction:
ρ do2 ＝ρ do +(τ do +τ oo )*r s *τ dd /(1－rs*ρ dd )
(9) Calculating the dual direct reflectance:
ρ sod2 ＝ρ so +((τ ss +τ sd )*τ do +(τ sd +τ ss *r s *ρ dd )*τ oo )*r s /(1－rs*ρ dd )
ρ so3 ＝ρ so2 +ρ so +τ ssoo *r s
s5: calculating the reflectivity of the canopy:
the basic radiation amounts of the direct solar rays and the scattered atmospheric rays can be obtained according to the data of the database, and are respectively E S And E d Next, the atmospheric scattering coefficient skyl parameter is calculated:
sskyl＝0.847-1.61*sin(90-θ s )+1.04*sin(90-θ s ) 2
the calculation method of the reflectivity of the canopy is the ratio of the radiation quantity measured in the observation direction to the incident radiation quantity, and the formula is as follows:
the calculated vegetation reflectivity is shown in figure 3.
The selected physical and chemical parameters of the vegetation in the expressway area and the spectrum used for comparison are measured values, and the model simulation result utilizes RMSE to determine the problems of usability and precision.
Through detection, the simulated spectrum information Root Mean Square Error (RMSE) of the model is 0.15706, and the simulation result of the simulation algorithm is available and has high precision.
The described examples are intended to be a part, rather than a whole, of the present invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without making any inventive step, are within the scope of the present invention.
Claims (3)
1. A method for calculating the reflectivity of a broadleaf vegetation canopy is characterized by comprising the following steps:
s1: identifying parameters;
inputting model parameters; and the input parameters are preliminarily divided into three categories: leaf parameters, soil parameters, and canopy parameters;
s2: inputting the PROSPECT model according to the blade parameters in the step S1 to perform single-blade spectrum simulation, and calculating the spectral reflectivity and the transmittance of a single blade;
s3: calculating an extinction coefficient and a scattering coefficient according to the soil parameters and the canopy parameters in the step S1 and the spectral reflectivity and the transmissivity of the single blade obtained in the step S2;
s4: inputting the extinction coefficient and the scattering coefficient obtained by the calculation in the step S3 into an SAIL model, and calculating the related reflection factor and the reflectivity of the canopy;
s5: calculating the reflectivity of the canopy;
the step S2 specifically includes the steps of:
s2.1: calculating an absorption coefficient K:
wherein c (i) is the concentration of component i in the leaf; k (i) is the specific absorption coefficient of component i; n is a blade structure parameter and represents the layering number of the blade; n is calculated using the following empirical equation:
N＝(0.9*SLA+0.025)/(SLA-0.1)
wherein SLA is the specific leaf area, which means the leaf area per unit dry weight;
s2.2: calculate transmittance at interface:
calculating the average transmission t of light rays from the air with refractive index 1 to the blade with refractive index n at solid angle alpha av (α,1, n), let t 12 ＝t av (α,1,n)；
S2.3: calculating the total transmittance tau of light through the flat medium 1 ；
Wherein t is an intermediate variable, K is an absorption coefficient, and D is the thickness of the blade;
s2.4: calculating the reflectivity R of a single-layer plate α (1) And transmittance T α (1)：
Wherein n is the refractive index of the blade;
s2.5: calculating single leaf reflectance R α (N) and transmittance T α (N), i.e., the total reflectance and transmittance of light passing through the N layers of flat plates of the same reflectance and transmittance:
wherein:
the step S3 specifically includes the following steps:
s3.1 shadow compensation:
(1) calculating geometrical factors related to extinction and scattering:
firstly, weighting and discretizing according to the distribution probability of the general blade inclination angle to obtain a group of discretized blade inclination angles (namely, the included angle between the normal direction of a horizontal plane and the normal direction of a blade); then, calculating extinction and scattering factors corresponding to each leaf inclination angle; for blade inclination angle theta l The calculation method is as follows:
first, a critical angle β is determined s And beta o The calculation formula is as follows:
wherein, theta s Is the zenith angle of the sun, theta o Observing a zenith angle;
when the denominator in the calculation formula is determined to be not 0 and the calculation result of cos beta is less than 1, directly calculating the values of two critical angles; when the calculation result of cos beta is equal to 1, the two adjacent angles are equal to pi; wherein cos β is broadly referred to as β s And beta o The cosine of (a);
then, the blade inclination angle is calculated as theta l The calculation formulas of the extinction coefficients of the direct solar direction and the observation direction of a single blade are respectively as follows:
wherein, L' = lai/h, lai is the leaf area index, and h is the canopy height;
(2) calculating an auxiliary azimuth angle beta 1 、β 2 、β 3 : the value taking method comprises the following steps:
wherein psi is the relative azimuth angle between the sun direction and the observation direction, i.e. the difference between the two azimuth angles;
(3) calculating the bidirectional scattering coefficient omega (theta) l )：
After the auxiliary azimuth angle is obtained, the single-blade reflectivity R calculated in S2 is matched α (N) and transmittance T α (N) and the transmissivity are calculated to obtain a bidirectional scattering coefficient, and the calculation formula is as follows:
where ρ, τ, θ l Respectively representing the reflectivity and the transmissivity of the blade and the corresponding blade inclination angle at the moment; ρ = R α (N)；τ＝T α (N)；
S3.2, calculating a scattering coefficient after adding the reflectivity and the transmissivity of the blade:
(1) the backscattering coefficients of the diffuse radiation E-and E + are calculated according to the formula:
(2) the forward scattering coefficient calculation formula of the diffuse radiation E-and E + is as follows:
(3) direct solar radiation E S The calculation formula of the backscattering coefficient is as follows:
(4) direct solar radiation E S The forward scattering coefficient calculation formula is:
(5) the calculation formula of the attenuation coefficients of the diffuse radiation E-and E + is as follows:
(6) observation direction radiation E 0 The calculation formula of the backscattering coefficient is as follows:
(7) observation direction radiation E 0 The forward scattering coefficient of (2) is calculated as:
s3.3, firstly, aiming at each blade inclination angle theta obtained by discretization in the step (1), calculating the corresponding general blade inclination angle distribution probability F (theta):
under the condition of non-ellipsoidal distribution, calculating the probability of general leaf inclination angle distribution according to the average leaf inclination angle, wherein the calculation process is finished by the following iteration:
x＝2θ
y＝LIDFa·sin(x)+0.5LIDFb·sin(2x)
dx＝0.5(y-x+2θ)
x＝x+dx
until | dx | < t;
f (θ) =2 (y + θ)/π;
wherein LIDFA and LIDFb are leaf distribution parameters; theta is a discrete value of the average leaf inclination angle, and F (theta) is a cumulative leaf inclination angle, namely a general leaf inclination angle distribution probability;
for the ellipsoidal distribution, calculating general leaf inclination angle distribution probability F (theta) by using a Campbell leaf inclination angle density function;
s3.4, determining model parameters of the whole canopy;
multiplying the leaf inclination angle distribution probability corresponding to each leaf inclination angle obtained in the discretization in the step (1) with the model parameters respectively and then adding the multiplied leaf inclination angle distribution probabilities to obtain new model parameters, wherein the calculation formula is as follows:
Z＝∑F(θ l )Z(θ l )
wherein, F (theta) l ) For angle of inclination of blade theta l Corresponding probability of general leaf inclination distribution, Z (theta) l ) Denotes k (θ) obtained in steps S3.1 and S3.2 l )、K(θ l )、ω(θ l )、σ(θ l )、σ′(θ l )、s(θ l )、s′(θ l )、a(θ l )、v(θ l )、u(θ l ) Any one of the above; z accordingly refers to any of all coefficients K, w, σ ', s', a, v, u in the four differential equations of the SAIL model for the entire canopy.
2. The method for calculating the reflectivity of a canopy of broadleaf vegetation according to claim 1, wherein the step S4 specifically comprises the steps of:
s4.1: calculating a leaf area parameter:
τ ss ＝e -klai
τ oo ＝e -Klai
ρ dd ＝(e mlai -e -mlai )/(h 1 e mlai -h 2 e -mlai )
τ dd ＝(h 1 -h 2 )/(h 1 e mlai -h 2 e -mlai )
wherein, lai represents the leaf area index and is a model input parameter;
s4.2: and calculating parameters after the hot spot effect is added, wherein the calculation formula is as follows:
ρ sd ＝C S (1-τ ss τ dd )-D S ρ dd
τ sd ＝D S (τ ss -τ dd )-C S τ ss ρ dd
ρ do ＝C o (1-τ oo τ dd )-D o ρ dd
τ do ＝D o (τ oo -τ dd )-C o τ oo ρ dd
ρ so ＝H o (1-τ ss τ oo )-C o τ sd τ oo -D o ρ sd
the calculation method of each intermediate variable comprises the following steps:
h 1 ＝(a+m)/σ
h 2 ＝(a-m)/σ＝1/h 1
C S ＝[s′(k-a)-sσ]/(k 2 -m 2 )
C o ＝[v(K-a)-uσ]/(K 2 -m 2 )
D s ＝[-s(k+a)-s′σ]/(k 2 -m 2 )
D o ＝[-u(K+a)-vσ]/(K 2 -m 2 )
H s ＝(uC S +vD s +w)/(K+k)
H o ＝(sC o +s′D o +w)/(K+k)
wherein, tau ssoo And the sum is a hot spot effect correction parameter;
s4.3: calculating the bidirectional reflectivity:
the bidirectional reflectivity comprises two parts, wherein one part has single scattering influence of the hot spot effect, the other part has no multiple scattering influence of the hot spot effect, and the two parts are summed into a final calculation result of the reflectivity influence on the top of the canopy:
ρ so2 ＝ρ so +w*lai*sumint
s4.4: introducing a soil reflection effect:
d n ＝1－r s *ρ dd
s4.5: calculating a bi-hemispherical reflectivity factor:
s4.6: calculating the hemispherical reflectivity in the direct solar radiation direction:
ρ sd2 ＝ρ dd +(τ sd +τ ss )*r s *τ dd /d n
s4.7: calculating the hemispherical reflectivity in the observation direction:
ρ do2 ＝ρ do +(τ do +τ oo )*r s *τ dd /d n
s4.8: calculating the dual direct reflectance:
ρ sod2 ＝ρ so +((τ ss +τ sd )*τ do +(τ sd +τ ss *r s *ρ dd )*τ oo )*r s /d n
ρ so3 ＝ρ so2 +ρ so +τ ssoo *r s
wherein r is s Is the soil reflectivity.
3. The method for calculating the reflectivity of a canopy of broadleaf vegetation according to claim 2, wherein the step S5 specifically comprises the steps of:
firstly, the basic radiation quantities of the direct solar rays and the scattered atmospheric rays are obtained according to the data of the database and are respectively marked as E s And E d ；
Then, a coefficient skyl representing the proportion of the total radiation by the scattered radiation in the atmosphere is calculated:
skyl＝0.847-1.61*sin(90-θ s )+1.04*sin(90-θ s ) 2
and finally, calculating the ratio of the radiation quantity measured in the observation direction to the incident radiation quantity to obtain the reflectivity of the canopy, wherein the formula is as follows:
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