The integrated radiometric correction of optical remote sensing imageries

Abstract Environmental analysis, management and modelling require detailed and precise land‐use/land‐cover discrimination as initial conditions of land surface characteristics. With the ultimate goal of accurate land surface classification analysis, we devised a fully image‐based and physically based correction method (the Integrated Radiometric Correction (IRC) method) considering both the atmospheric and the topographic effects simultaneously, using the information deduced from the satellite images and 5 m resolution DEM data. The overall process is carried out in four steps: (i) calculation of the radiance/irradiance relational expression for horizontal surfaces, (ii) devising the radiance/irradiance relational expression for inclined surfaces, (iii) derivation of solar and land geometric parameters from DEM data, as well as the calculation of the topographic correction factor (A‐factor) and the atmospheric transmittance functions, and (iv) retrieval of the corrected surface reflectance and radiance. Using Landsat/ETM+ satellite data, the performance of the formulated IRC method is evaluated visually and statistically. Visual evaluation of radiometrically corrected images shows significant improvements for each band as well as for various bands composites, while the independence between the corrected surface reflectance and radiance, and the topography (incidence angle (i) or solar illumination (cos i)) is shown by very weak correlation coefficients as compared with non‐corrected data.     

Scattering by Lambertian-leaves canopy: dependence on leaf-area projections

A single-scattering model is constructed for a canopy with Lamber-tian leaves. The azimuthal distribution of the leaves is represented by fractional abundances of the leaf-area in the cardinal directions with respect to the Sun. The canopy bi-directional reflectances are found to be controlled by the projections of the leaf-areas onto horizontal and vertical planes. The sum of the leaf-area projections onto the horizontal plane determines the reflectance to the zenith when the Sun is at the zenith. For a complete canopy this reflectance is where w_xh is the fractional projection onto the horizontal plane of leaf-area of leaf-category x, g_x is the leaf reflectance (assumed equal to the leaf transmittance), and ψ_x, is the zenith angle of the leaf normal for this category. As the view and solar zenith angles deviate from the nadir, the change in the reflectance in the principal plane of the Sun is controlled by ihe difference in the leaf-area projections onto the vertical plane of the leaves with leaf-normals in opposite quadrants in the principal plane. When these two leaf-categories are identical (other than in their azimuths), a large region around the zenith exhibits the Lambertian viewing property, that is, the reflectance does not change with the view or illumination directions. Forward scattering and backscattering, which become intense when both the illumination zenith angle θ₀ and the view zenith angle θ_v are large (approach 90°) while ψ is not small (or when ψ is large while θ₀ and θ_v are not small), are controlled by the sum of these two leaf-area projections. The reflectance has then the limiting value g sinψ(cot θ₀ + cotθ_v), where g and ψ characterize the two leaf categories with normals in the principal plane. This expression represents a generalization of a result obtained for a field of thin vertical cylinders     

Atmospheric optical depth effects on angular anisotropy of plant canopy reflectance

Abstract

A field experiment was conducted to determine whether changes in atmospheric aerosol optical depth would effect changes in bi-directional reflectance distributions of vegetation canopies. Measurements were made of the directionally reflected radiance distributions of two pasture grass canopies (same species, different growth forms) and one soya bean plant canopy under different sky irradiance distributions, which resulted from a variation in aerosol optical depth. The reflected radiance data were analysed in the solar principal plane in two narrow spectral bands, one visible (662 nm) and one infrared (826 nm). The observed changes in reflectance for both wavelengths from irradiance distribution variation is interpreted to be due largely to changes in the percentage of shadowed area viewed by the sensor for the incomplete canopies (pasture grass). For the complete coverage vegetation canopy (soya bean) studied, the effects of specular reflection and the increased diffuse irradiance penetration into the canopy are concluded to be primary physical mechanisms responsible for reflectance changes. Observed reflectivities were found to be lower on a hazy day (higher optical depth with a greater diffuse fraction) than on a clear day, with solar zenith angles at about 58^° on both days, for full-coverage soya bean canopies. The reduced reflectance most likely results from a diminished specular reflection and a greater diffuse radiation penetration into the canopy, which effects an increased energy absorption at large solar zenith angles. The opposite was true for fractional coverage grass canopies at solar zenith angles of about 56^° since the shadowing was less on the hazy day and, therefore, the soil/litter background was more fully illuminated. In the near-infrared waveband the changes in reflectance are much less than in the visible and, therefore, normalized difference vegetation index values differ substantially under clear and hazy sky conditions for the same vegetation canopy conditions. Thus, the influence of atmospheric optical depth must be considered for accurate remote sensing and in situ data interpretation.     

Remote sensing reflectance and its relationship to optical properties of natural waters

Monte Carlo simulations of photon propagation through natural water have been utilized to determine the sub-surface remote sensing reflectance, R _RSW (the sub-surface value of the ratio of upwelling radiance from the nadir to the downwelling irradiance) as a function of water type (defined by the ratio of the backscattering coefficient to the absorption coefficient Bb/a), solar zenith angle, and incident radiation distribution (direct or diffuse). R _RSW, as opposed to volume reflectance, R _V (the sub-surface value of the ratio of upwelling to downwelling vector irradiance), is directly applicable to remotely sensed data collected over natural waters. It is shown that, for a nadir viewing direction, (a) R _RSW is essentially independent of solar zenith angle and incident radiation distribution and (b) the dominant factor in determining R _RSW is the optical nature of the water body itself (expressed as Bb/a). A relationship between the sub-surface remote sensing reflectance averaged over solar zenith angle between 15° and 89°, R _RSW and water type is found to predict R _RSW with an r.m.s. error of 9 per cent. Also addressed is the determination of the aquatic optical property, Bb/a, from the sub-surface remote sensing reflectance, R _RSW This capability along with the specific absorption and scattering coefficients of aquatic constituents can, through bio-optical models, be used to estimate the concentrations of these aquatic constituents in non-Case I waters. The empirical relationship obtained to estimate Bb/a (with a r.m.s. error of 9·3 per cent) from the nadir value of the sub-surface remote sensing reflectance is Bb/a = 0·0027 + 987R _RSW ? 34·5( R _RSW)² + 1534( R _RSW)³.     

Wind and cloud cover effects on spectral measurements of flooded rice crops in red and near-infrared SPOT-HRV bands

Wind and cloud cover effects on variabilities of radiance, irradiance and reflectance were analysed using ground-based measurements acquired over flooded rice crops in the red and near-infrared SPOT-HRV bands under variable wind and cloud cover conditions. Overall, spectral measurements were more variable in the near-infrared than in the red band. Wind speed was positively correlated to variability of radiances (r=0.186 (p>0.001)) and reflectances (r= 0.245 (p>0.001)) in near-infrared, but not in red wavelengths. The proportion of diffuse radiation in the total incident solar radiation was positively correlated to the radiance variability in red (r=0.086 (p>0.001)) and near-infrared (r=0.123 (p>0.001)) as well as to the irradiance variability in red (r=0.248 (p>0.001)) and near-infrared (r=0.243 (p>0.001)), but not to the reflectance variability. Such an analysis should be done every time ground spectral measurements are performed under variable weather conditions.     

Diurnal patterns of bidirectional vegetation indices for wheat canopies

The perpendicular vegetation index (PVI) and normalized difference vegetation index (NDVI) were calculated from Mark II radiometer RED (0.63-0.69 μm) and NIR (0.76–0.90 μ) bidirectional radiance observations for wheat canopies. Measurements were taken over the plant development interval flag leaf expansion to watery ripeness of the kernels during which the leaf area index (LAI) decreased from 40 to 2-5. Spectral data were taken on four cloudless days five times (09.30, 11.00, 12.30, 14.00 and 15.30 hours (central standard time, C.S.T.) at five view zenith, Zv (0, 15, 30,45 and 60°) and eight view azimuth angles relative to the Sun, A_v (0, 45, 90, 135, 180, 225, 270 and 315°). The PVI was corrected to a common solar irradiance (PVIC) based on simultaneously observed insolation readings.

The PVIC at nadir view (?=0°) increased as (l/cosZ_s) increased on all the measurement days whereas the NDVI changed little as solar zenith angle (Z_s) changed. Thus, the PVIC responded to increasing path length through the canopy, or the number of leaves encountered, as solar zenith angle changed whereas the NDVI, which has saturated by the time an LAI of 2 was achieved, was nonresponsive.

Off-nadir PVIC ratioed to nadir PVIC increased as the view zenith and solar zenith angles increased (reciprocity in Sun and view angles), and as the view azimuth, A angle approached the Sun position (back scattering stronger that forwardscattering). In contrast, the DNVI was very stable for all view and solar angles consistent with saturation in its response. Even though the PVI is subject to bidirectional effects, it contains more useful information about wheat canopies at LAI > 2 than does the NDVI. The NDVI of the plant canopies changed rapidly at low vegetative cover but its bidirectional sensitivity at low LAI was not investigated.     

Conversion of sub-surface reflectances to above-surface MERIS reflectance

Factors for converting sub-surface reflectances to above-surface MERIS reflectances have been determined both as analytic functions and average numbers for solar zenith angles in the range 30°–75°, wind speeds up to 10 m s^?1, and the spectral domain 400–700 nm. The conversion factors have been obtained by numerical and statistical computations based on field observations of spectral radiance and irradiance, above and below the surface of the sea. The estimated maximum errors of the different algorithms range from ≤0.1% up to 10%, depending on the chosen method and the types of optical quantities that are available. The errors are smallest for solar zenith angles between 30° and 60° and increase when the solar zenith angle approaches 75°. The influence of the wind on the conversion factors is practically negligible. The algorithms, which have been derived for conditions representative of the Skagerrak and the adjacent seas, are assumed to be valid for both Case 1 and 2 waters.     

Reference panel anisotropy and diffuse radiation - some implications for field spectroscopy

Field goniometer measurements were obtained to examine the angular variation in the reflectance of direct beam, diffuse and global radiation from two types of Spectralon^TM panel. The results indicate that optical grade (99% reflective) and grey (20% reflective) SpectralonTM exhibit different non-Lambertian properties with respect to direct beam irradiance. The angular variation in the reflectance of diffuse radiation by the panel appears independent of the panel type but varies with the diffuse to global (D : G) irradiance ratio, especially at large solar zenith angles. The combined effect of the angular response to direct beam and diffuse radiation is that panel reflectance of the global flux shows only slight variation with angle for solar zenith angles up to 55 for optical grade Spectralon^TM. For larger solar zenith angles panel reflectance increases markedly with angle.     

Operational bi-angle approach to retrieve the Earth surface albedo from AVHRR data in the visible band

The inference of surface spectral reflectance using visible observations is complicated mainly because of scattering effects. In the present paper we attempt a solution to the problem of retrieval of surface reflectance from satellite radiance measurements based on a solution of the radiative transfer equation. We have developed an operational method which relies on multiple view angle observations or multiple solar zenith angle observations of the surface to accomplish part of this task in a routine manner. This approach may be used for ERS-2 ATSR visible bands because there will be two view angle observations for the same area at essentially the same time.

This approach can also be used with NOAA satellite AVHRR data by assuming that the distribution of the aerosol does not vary too rapidly as a function of time. Usually it is better to select the AVHRR data from around noon and at dusk in the same day. This approach requires that the visibility of the area should be more than 5 km for multiple solar zenith angle observations applications.     

Irradiance measurement errors due to the assumption of a Lambertian reference panel

Total and diffuse global spectral irradiances, which are often required field measurements in remote sensing, are commonly obtained by measuring the radiance from a horizontal reference panel with assumed Lambertian properties. A technique is presented for determining the error in diurnal irradiance measurements that results from the non-Lambertian behavior of a reference panel under various irradiance conditions. Spectral biconical reflectance factors of a spray-painted barium sulfate panel, along with simulated sky radiance data for clear and hazy skies at six solar zenith angles, were used to calculate the estimated panel irradiances and true-irradiances for a nadir-looking sensor in two wavelength bands. The inherent errors in total spectral irradiance (0.68 μm) for a clear sky were 0.60, 6.0, 13.0, and 27.0% for solar zenith angles of 0°, 45°, 60°, and 75°. The technique can be used to characterize the error of a specific panel used in field measurements and thus eliminate any ambiguity of the effects of the type, preparation, and aging of the paint.     

Effects of the atmosphere on the detection of surface changes from Landsat multispectral scanner data

The atmospheric effects on radiometric data recorded in the Landsat multispectral scanner system (MSS) bands are compiled for cases of representative and ideal atmospheric conditions. The effects are expressed as a difference between the Earth's surface spectral reflectivity, a₀, and the surface-atmosphere system spectral reflectivity, a_s, derived from the satellite data,

a_s?a₀ = ?a₀[l+(l/μ₀)](B+W) + 2a² ₀B + g(μ₀)B/2μ₀

where μ₀ is the cosine of the solar zenith angle, B and W are the backscattering and absorption optical thickness respectively, and the function g( μ₀) is the anisotropy of backscattering to the zenith from the direct beam. This formula is accurate only for an atmosphere of low optical thickness. Also, the equation applies only to large areas having a uniform reflectivity, because adjacency effects due to reflection from the terrain surrounding the object pixel and subsequent scattering by the atmosphere are not considered.

It is concluded that in the quantitative monitoring of surface changes from satellites, scattering effects predominate in some applications (for example, bathy-metric mapping of coastal waters), whereas absorption effects predominate in other applications (for example, monitoring desert fringe areas). Different measurements are more appropriate for assessing the scattering effects than for assessing the absorption effects.

These effects on the monitoring of surface changes by the use of Landsat MSS data are discussed in terms of departures of the actual atmosphere at the time of a satellite passage from a ‘minima’ atmosphere having no aerosols and characterized by gaseous absorption corresponding to minimal water vapour amounts.     

The Rayleigh lookup tables for the SeaWiFS data processing: Accounting for the effects of ocean surface roughness

In the atmospheric correction of ocean colour remote sensing, it is important to account for the effects of ocean surface roughness (wind speed) in the computation of Rayleigh radiance lookup tables, in particular, for the large solar and/or sensor zenith angles (>～60°). In the paper, both simulated and the SeaWiFS-retrieved results that demonstrate the effects of the ocean surface wind speed on the Rayleigh radiance computations for the various solar and sensor-viewing geometries as well as on the performance of atmospheric corrections are presented and discussed. An improved set of Rayleigh lookup tables, in which the Rayleigh scattering radiance is also a function of the sea surface wind speed, were generated and implemented into the SeaWiFS data processing system in May 2000.     

View azimuth and zenith,and solar angle effects on wheat canopy reflectance

Since crop canopies are not lambertian reflectors, their reflectance varies with sun and view positions. It is not always possible or convenient to make reflectance measurements from the nadir position nor at the same time of day. Therefore, ways of estimating nadir reflectance from off-nadir views and for various solar zenith angles are needed. In this study, spectral measurements were made with a Mark II radiometer five times during the day on each of four dates from 15° interval zenith and 45° azimuth positions for wheat canopies during the development interval stem extension to watery ripeness of the grain. The ratio of off-nadir [R(Z_v,A_v)] to nadir [R(0)] radiance in NIR band (0.76–0.90 μm) was described by the regression equation: $\text{R(Z}{}_{\mathrm{v}}\text{,A}{}_{\mathrm{v}}\text{)}\text{R(0)}\text{= 1.0 + [β}{}_0\text{+ β}{}_1\text{sin}\text{(}\text{A}{}_{\mathrm{v}}\text{2}\text{) + β}{}_2\text{(1/}\text{cos}\text{Z}{}_{\mathrm{s}}\text{)]}\text{sin}\text{Z}{}_{\mathrm{v}}$ where A_v is view azimuth angle relative to the sum position, Z_s is solar zenith angle, and Z_v is view zenith angle. The coefficient of determination was 0.70 or higher. The equation describes the observations that 1) the ratio of off-nadir to nadir radiance increases or decreases as view zenith angle increases depending on view azimuth angle; backscattering is stronger than forwardscattering and the pattern is azimuthally symmetric about the principal plane of the sun; and 2) the rate of change in the radiance ratio increases with increasing solar zenith angle. The coefficients, β₀, β₁ and β₂, changed as the canopies grew. Although the equation needs to be more fully tested, it should help summarize and compare various angular observation data taken in crop fields.     

An examination of spectral band ratioing to reduce the topographic effect on remotely sensed data

Spectral hand ratioing in the form of radiance,/radiance, was examined as a proposed means for reducing the topographic effect from muitispectral data. The topographic effect is defined as the variation in radiances from inclined surfaces compared with radiance from a horizontal surface as a function of the orientation of the surfaces relative to the light source and sensor position (Holben and Justice 1980). A ground based nadir pointing two channel radiometer filtered for the red and photographic infrared portions of the electromagnetic spectrum was used to measure the topographic effect from a uniform surface inclined from horizontal to 60°, at 16 compass points, for several solar elevations.

Spectral band ratioing reduced the topographic effect by more than a factor of 6 (i.e. 83 per cent) on the radiance data sets obtained in this study. The greatest proportional reduction of the topographic effect due to ratioing occurred where the topographic effect in the radiance was most pronounced, i.e. for slopes parallel to the principal plane, and least reduction for slope orientations perpendicular to the principal plane. A residual topographic effect was observed after ratioing the radiance data. This was reduced on an average of 50 per cent for all slopes and aspects by subtracting the diffuse skylight component from the radiances.

Band ratioing of muitispectral satellite and aircraft data can be expected to be less successful than results presented in this study because of stronger additive radiance factors and sensor calibration and quantization effects. The degradative effects of Landsat sensor calibration and quantization are demonstrated for a range of. surface reflectances and irradiance levels.     

Simulated directional radiances of vegetation from satellite platforms

The effects of off-nadir viewing, canopy geometry and density, solar zenith angle, and atmospheric condition on the radiance and normalized difference index (ND) of a grass canopy as viewed from a satellite are examined via simulation techniques. Two wavelengths, 0·68 and 0·80 μm, are considered. Results indicate that off-nadir viewing effects are more pronounced in the red than in the I.R., but that the ND index tends to eliminate much of the variability seen in the individual bands. The magnitude of off-nadir viewing effects is also shown to be a function of canopy geometry. Overall variability of the ND tends to decrease with increasing biomass at given sun and view angles, but increases with increasing solar zenith angles. Atmospheric haze masks useful surface information by intensifying scattering effects.     

Linear polarization measurements of a wheat canopy

Abstract

The amount of linearly polarized light reflected by a wheat canopy was measured using a polarizing filter attached to a radiometer at two wavelengths (478 nm and 668 nm) and three view zenith angles (60°, 70°, 80°). Measurements were carried out in the anti-solar direction in the principal plane, with relative azimuth between Sun and view directions being 180°. It is found that the degree of polarization (DOP) and mean polarized radiance (R¯ _Q ) between stages is statistically significant at view zenith angles of 70° and 80°, in the blue wavelength region. It is concluded that DOP and R¯ _Q are better indicators of the onset of heading stage. Calculations of polarized reflectance using Fresnel reflection equations are also presented.     

Multiple view zenith angle observations of reflectance from ponderosa pine stands

Bi-directional reflectance factors (BRF(λ)) from dense and sparse ponderosa pine (Pinus ponderosa) stands, derived from radiance data collected in the solar principal plane by the Advanced Solid-State Array Spectroradiometer (ASAS), were examined as a function of view zenith angle (0_rpar;. BRF(λ) was maximized with 0_ nearest the solar retrodirection, and minimized near the specular direction throughout the ASAS spectral region. The dense stand had much higher BRF anisotropy (maximum BRF/minimum BRF) in the red region than did the sparse stand (relative differences of 5·3 versus 2·75, respectively), as a function of 0_, due to the shadow component in the canopy. Anisotropy in the near-infrared (NIR) was more similar between the two stands (2·5 in the dense stand and 2·25 in the sparse stand); the dense stand exhibited a greater hotspot effect than the sparse stand in this spectral region. Two common vegetation transforms, the NIR/red ratio and the normalized difference vegetation index (NDVI), both showed a θ _ dependence for the dense stand. Minimum values occurred near the retrodirection and maximum values occurred near the specular direction. Greater relative differences were noted for the NIR/red ratio than for the NDVI. The sparse stand showed no obvious dependence on 0_ for either transform, except for slightly elevated values toward the specular direction.     

Atmospheric effects on radiometric imaging from satellites under low optical thickness conditions

An approximate explicit formula has been developed for the Earth-atmosphere system nadir-beam reflectivity a₈,

$\text{a}{}_{\mathrm{s}}\text{=r}\text{1?}\text{1}\text{μ}{}_0\text{+1}\text{(B+W)+2aB}\text{+(a?r)F+}\text{g(μ}{}_0\text{2μ}{}_0\text{B}$

, where r is the object pixel reflectivity, a is the effective reflectivity of the surrounding terrain, μ₀ is the cosine of the solar zenith angle, B, F, and W, respectively, are the backward-scattering, forward-scattering, and absorption optical thickness, and g(μ₀) is the anisotropy of atmospheric backscattering to zenith from the direct beam. This formula is accurate only for limiting cases of low optical thickness and should not be used for quantitative atmospheric correction unless [(B + W + F)/μ₀] < 0.1. Still, the expression affords a good insight into atmospheric effects on radiometric imaging and may be useful under circumstances when B, W, and F are not measured during a satellite pass. The significance of the terms 2aBr and (a—r)F, which describe the adjacency effect, i.e., the effects of reflection from the terrain surrounding the object pixel and subsequent scattering, is discussed, (a₈—r) is calculated from this formula and analyzed in terms of how this difference affects the possibility and the accuracy of measuring the surface albedo and of thematic mapping by matching the measured multispectral radiometric data against compiled spectral signatures. Subsequently, the derivative da₈/dr is analyzed, showing how the atmosphere decreases this derivative for low reflectivities, thereby reducing discrimination capability for thematic mapping in any mode. Finally, contrast transmittance through the atmosphere, which affects the possibilities of photointerpretation is discussed. The adjacency effects lead to ambiguity in the concept of contrast transmittance, which is resolved through the use of several definitions.     

Novel synthesis formulas to design square patch frequency selective surface absorber based on equivalent circuit model

A new procedure is presented to design electromagnetic absorbers based on resistive square patch frequency selective surface (FSS) over grounded dielectric. The periodicity (p) and the distance between two adjacent squares in the lattice (w) are two unknowns to be solved, given the thickness and permittivity of the substrate, surface impedance of the square patches and the desired reflectivity in some specified frequency. Equivalent circuit model and transmission line method are employed here. Previously reported analysis formulas to calculate the square patch FSS admittance are exploited and novel synthesis formulas are extracted based of them. The final synthesis equations to calculate p and w are presented in term of polynomials. Usually an absorber is supposed to have a maximum reflectivity r in a frequency band [f₁, f₂]. The (p, w) pairs for reflectivity less than r in f₁, define an area in p‐w plane. The intersection of the so‐called area with the similar one defined by f₂ specifies all possible (p, w) pairs. Finally the results are tested and verified by the commercial full wave simulator Ansys‐HFSS as well as some experimental design. There is a good agreement between the expected results with the full wave analysis and practical test.     

Extraction of spectral hemispherical reflectance (albedo) of surfaces from nadir and directional reflectance data

Abstract

A radiative transfer model was used to explore how the error in inferring spectral hemispherical reflectance (p_λ) from nadir reflectance values varies as a function of wavelength, solar zenith angle, leaf area index and leaf orientation distribution. Secondly, a technique using multiple spectral nadir reflectance values to infer p_λ for a single wavelength was tested using field data. In addition, several techniques that use multiple off-nadir view angles taken in azimuth planes (called strings of data) were tested using field data. These latter techniques were very accurate (with errors less than 4 percent of the true value)and are ideally suited to present and future sensor systems that scan in a known azimuth plane (e.g. Advanced Very High Resolution Radiometer (AVHRR) and other scanning radiometers) or view fore and aft in a known azimuth plane (e.g. Advanced Solid-State Array Sensor (ASAS)Moderate Resolution Imaging Spectrometer (MODIS)High Resolution Imaging Spectrometer (HIRIS)), a brief analysis was performed to explore the effects of errors in hemispherical reflectance on terrestrial energy budget and productivity calculations.