Remote sensing for resources development and environmental management: Remote sensing for resources development and environmental management

Damen, M. C. J.

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Multivolume work

Persistent identifier:: 856342815

Title:: Remote sensing for resources development and environmental management

Sub title:: proceedings of the 7th international Symposium, Enschede, 25 - 29 August 1986

Year of publication:: 1986

Place of publication:: Rotterdam; Boston

Publisher of the original:: A. A. Balkema

Identifier (digital):: 856342815

Language:: English

Additional Notes:: Volume 1-3 erschienen von 1986-1988

Editor:: Damen, M. C. J.

Document type:: Multivolume work

Volume

Persistent identifier:: 856343064

Title:: Remote sensing for resources development and environmental management

Sub title:: proceedings of the 7th international Symposium, Enschede, 25 - 29 August 1986

Scope:: XV, 547 Seiten

Year of publication:: 1986

Place of publication:: Rotterdam; Boston

Publisher of the original:: A. A. Balkema

Identifier (digital):: 856343064

Illustration:: Illustrationen, Diagramme

Signature of the source:: ZS 312(26,7,1)

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: Damen, M. C. J.

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: 3 Spectral signatures of objects. Chairman: G. Guyot, Liaison: N. J. J. Bunnik

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: The derivation of a simplified reflectance model for the estimation of LAI. J. G. P. W. Clevers

Document type:: Multivolume work

Structure type:: Chapter

r s,g /r s r ( 7) and J r s.ir s,r ( 8) If we assume that we are able to determine the constants Cj and , merely by measuring the required reflectance values at the same soil moisture content, then equations (2), (3), (6), (7) and (8) offer us five equations with five unknown variables: the corrected infrared reflectance (r! ), soil cover (B) and the soil reflectance in the tliree bands (r , r and r . ). After solving these equations 3 ' g for till 1 correcl4^ r infrared reflectance we obtain: r ! ir r. ir . r v,r r r r V, r r v,g . r y,g ) ( 9) In the situation of bare soil only, r , r and r. , , g r ir equal r Si g f r S/r and r s ^ r , respectively, and equation (9) results in: r£ r =0. In the situation of complete soil cover, rg and r r equal r Vj g and r V/r , respecti vely, and equation (9) results in: r 1 = r ; in . 13T 1IT other words no correction for soil background is applied if the soil is not visible. In order to deduce the relationship between soil cover and LAI, the process of extinction of radiation in a canopy should be considered. If a canopy has a certain extinction coefficient per leaf layer as well as a certain LAI (abbreviated as L in the formulae), the product of both factors equals the mean extinction of that canopy. The mean extinction consists of two components: 1. extinction in the direction of the sensor, indica ted by K.L, where K is the extinction coefficient per leaf layer in the sensor direction; 2. extinction in the direction of the sun, indicated by k.L, where k is the extinction coefficient per leaf layer in the direction of the sun. Consider the process of extinction in a very small part (or element) of the canopy. In the visible spectral bands, extinction in an element occurs when a leaf is hit by radiation. The probability of hitting i elements among n independent elements has a binomial distribution. If the number n of independent elements increases to infinity while the probability of hitting a specific element decreases to zero, the binomial distribution can be approximated by a Poisson distri bution. The Poisson distribution states: P(x=i) = e X . X 1 i = 0,1,2,3,... d°) i; The random variable x is the number of independent elements of the canopy in which extinction occurs; X is the mean or expected number of elements in which extinction occurs. The probability that no element is hit (i=0) equals: P(x=0) = e (11) The probability of soil being visible in the direction of the sensor equals: e~ K * L . The probability of soil being illuminated by the sun equals: e~k.L. If one assumes both events to be independent, the probability of sensing illuminated soil equals: e-K.L * e - k - L = e-< K+k > - L The complementary probability is equal to the appa rent soil cover (new definition). This means that soil cover may be described as: B . -(K+k).L 1 - e (12) Inserting equation (12) into (5) gives: r ' r V (1 -(K+k).L e ) (13) The relationship between LAI and infrared reflec tance (cf. Bunnik, 1978) greatly resembles a "Mitscherlich curve" (y=A-b.exp(-k.t)). In the special situation of such a curve running through the origin (A = b) , the curve defined by y=A. (1-exp(-k.t) ) has only two parameters. For describing the relation ship between the corrected infrared reflectance and LAI (which runs through the origin) an empirical equation similar to equation (13) could be used: r ! ir (1 -O.L (14) parameter r«, being the asymptotic value for the infrared reflectance and a a combination of extinction and scattering coefficients. Both parameters are estimated empirically from a training set. Finally the LAI is solved from equation (14): L = -l/a . ln(l - r i r / r 00>ir ) (15) This is the inverse of the special case of the Mitscherlich function. 4 COMPARING THE MODEL WITH THE SAIL MODEL In this section the model derivations presented earlier will be verified by means of calculations with the more complicated SAIL model (Verhoef, 1984) . This model simulates reflectances as a function of plant variables and measurement conditions (cf. section 2.2). The following variables for the SAIL model have been used: - three soil types: . dry soil (green reflectance = 20.0%, red reflec tance = 22.0%, infrared reflectance = 24.2%); . wet soil (green reflectance = 10.0%, red reflec tance = 11.0%, infrared reflectance = 12.1%); . black soil (green, red, infrared reflectance = 0%) . - spherical leaf angle distribution. - direct sunlight only (solar zenith angle: 45°). - direction of observation was assumed to be vertically downwards. - reflectance and transmittance of a single leaf were assumed to be equal: green reflectance = 8%, red reflectance = 4% and infrared reflectance = 45%. Model calculations were carried out using the follow ing LAI values: 0 (0.1) 1.0 (0.2) 2.0 (0.5) 5.0 (1.0) 8.0. The green, red and infrared reflectance factors were calculated according to the SAIL model for each of the above situations. The SAIL model was also able to calculate the complement of the illuminated soil detectable by the sensor (this equals soil cover with the new definition introduced in this paper). The results obtained with the SAIL model clearly show that the relationship between soil cover, accor ding to the new definition, and green or red reflectance was nearly perfectly linear for a dry soil (figure 3). Similar results were obtained for a wet soil (Clevers, 1986b). These results support the validity of equations (2) and (3) if the new definition of soil cover taking shadow and vegetation together is used. Clevers (1986b) showed that equations (2) and (3) are not valid with the conventional definition of soil cover. In estimating LAI the infrared reflectance is cor rected for soil background and subsequently this corrected infrared reflectance is used for estimating LAI. This latter step may be investigated by using the calculations with the SAIL model for a black background. Then the infrared reflectance does not require correction and the validity of equation (15) may be checked. The results, shown in figure 4, support the validity of this equation for describing the relationship between "corrected" infrared reflectance and LAI at constant leaf angle distribu tion. Results presented by Clevers (1986b) show that distinct leaf angle distributions cause quite distinct

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