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  • View in gallery

    BRDF class 1 archetype. Visible BRDF of Sahelian Tiger Bush at 40° solar zenith angle

  • View in gallery

    BRDF class 1 archetype. Near-infrared BRDF of Sahelian Tiger Bush at 40° solar zenith angle

  • View in gallery

    BRDF class 17 archetype. Visible BRDF of dense grass at 40° solar zenith angle

  • View in gallery

    BRDF class 17 archetype. Near-infrared BRDF of dense grass at 40° solar zenith angle

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    North American white-sky albedos. (a) AVHRR channel-1 winter spectral albedos. (b) Channel-1 summer spectral albedo. (c) Channel-2 winter spectral albedo. (d) Channel-2 summer spectral albedo

  • View in gallery

    Summer full band black-sky albedo image. (a) Solar zenith 0°. (b) Solar zenith 80°

  • View in gallery

    (a) Ratio of white-sky infrared broadband albedo to AVHRR channel-2 reflectance (summer). (b) Summer white-sky infrared broadband albedo

  • View in gallery

    BRDF class 8 (dense broadleaf trees–shrubs) summer total shortwave white-sky albedo distribution

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    BRDF class 11 (dense needleleaf trees–shrubs) summer total shortwave white-sky albedo distribution

  • View in gallery

    BRDF class 17 (dense grass-like vegetation–crops) summer total shortwave white-sky albedo distribution

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An Algorithm to Infer Continental-Scale Albedo from AVHRR Data, Land Cover Class, and Field Observations of Typical BRDFs

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  • 1 Department of Geography and Center for Remote Sensing, Boston University, Boston, Massachusetts
  • | 2 Potsdam-Institut für Klimafolgenforschung, Potsdam, Germany
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Abstract

A method to derive bottom-of-atmosphere land surface albedos from Advanced Very High Resolution Radiometer (AVHRR) satellite measurements is presented. The algorithm described uses kernel-based bidirectional reflectance distribution function (BRDF) models of land cover but, in contrast to other kernel-based albedo retrievals, assumes a priori knowledge of underlying surface BRDFs, based on a land cover classification and typical field-measured BRDFs for each class in the land cover classification. The BRDF of each land cover is scaled using AVHRR reflectance measurements to take into account within-class variations of albedo, and the resultant scaled BRDF is integrated to retrieve an albedo. An albedo dataset for North America is produced with this scheme from February and July 1995 monthly maximum normalized difference vegetation index value composite images. Spectral-to-broadband albedo conversion is achieved by using spectral albedos to scale a laboratory-measures vegetation spectral reflectance curve. Both white-sky (bihemispherical reflectance) and black-sky (directional-hemispherical reflectance) albedos are produced. The methodology presented is general and can be used with historical AVHRR. In addition it will be used with data from the moderate-resolution imaging spectrometer sensor aboard the Terra satellite as an ancillary technique to produce global, monthly albedo datasets for use in climatic and atmospheric research.

Corresponding author address: N. C. Strugnell, ArsDigita Ltd., 42 Brook Street, London W1Y 1YB, United Kingdom.

Email: nstrug@arsdigita.com

Abstract

A method to derive bottom-of-atmosphere land surface albedos from Advanced Very High Resolution Radiometer (AVHRR) satellite measurements is presented. The algorithm described uses kernel-based bidirectional reflectance distribution function (BRDF) models of land cover but, in contrast to other kernel-based albedo retrievals, assumes a priori knowledge of underlying surface BRDFs, based on a land cover classification and typical field-measured BRDFs for each class in the land cover classification. The BRDF of each land cover is scaled using AVHRR reflectance measurements to take into account within-class variations of albedo, and the resultant scaled BRDF is integrated to retrieve an albedo. An albedo dataset for North America is produced with this scheme from February and July 1995 monthly maximum normalized difference vegetation index value composite images. Spectral-to-broadband albedo conversion is achieved by using spectral albedos to scale a laboratory-measures vegetation spectral reflectance curve. Both white-sky (bihemispherical reflectance) and black-sky (directional-hemispherical reflectance) albedos are produced. The methodology presented is general and can be used with historical AVHRR. In addition it will be used with data from the moderate-resolution imaging spectrometer sensor aboard the Terra satellite as an ancillary technique to produce global, monthly albedo datasets for use in climatic and atmospheric research.

Corresponding author address: N. C. Strugnell, ArsDigita Ltd., 42 Brook Street, London W1Y 1YB, United Kingdom.

Email: nstrug@arsdigita.com

1. Introduction

In this article we describe a method to derive land surface albedos from satellite-sensed bidirectional reflectances. Bidirectional reflectances are used to constrain an estimate of the bidirectional reflectance distribution function (BRDF) of the underlying surface. The resulting estimated BRDF is integrated to produce the albedo. We present results for visible and near-infrared spectral albedos for the months of February and July 1995 for North America intended as a demonstration the technique.

Albedo is defined as the ratio of reflected solar shortwave radiation from a surface to that incident upon it. Albedo is of particular importance in the land surface energy balance and the earth’s radiation balance that dictates the rate of heating of the land surface under different environmental conditions. Ramanathan et al. (1989) discuss the earth’s climate with respect to radiation balance noting that climate may be extremely sensitive to small variations in radiative forcing, posing stringent accuracy requirements on observations of parameters such as albedo. Although we may use a single value for planetary albedo in simple zero-dimensional climate models to determine a long-term average of global mean temperature, for more sophisticated models we require an accurate map of the earth’s albedo. Lofgren (1995b) compared the climate scenario generated by a general circulation model (GCM) prescribed with a spatially uniform value of albedo to that of a GCM in which albedo was estimated as a function of annual mean precipitation and temperature. The spatially variant albedo resulted in more realistic climate modeling over tropical and subtropical zones, and midlatitude deserts, with little change in midlatitude temperate zones. Lofgren (1995a) goes on to show that, whereas midlatitude climate is not particularly sensitive to perturbation in land surface albedo, precipitation and soil moisture increase with lower surface albedo for low-latitude regions. Lean and Rowntree (1997) in an experiment to determine the sensitivity of the regional climate to Amazonian deforestation found that an increase in forest albedo causes widespread significant decreases in rainfall. Bastable et al. (1993) performed direct measurements of Amazonian forest and pasture albedos and found the latter to be significantly lower than the value then being used in GCMs, possibly due to the presence of soot from burning.

From the above discussion it is clear that accurate representation of surface albedo is desirable if we wish to be able to accurately predict climate changes using GCMs. Currently, albedo in a GCM is represented either by a prescribed parameter, possibly retrieved from coarse resolution remotely sensed data, or as a modeled parameter, generated by coupling a surface–vegetation–atmosphere transfer scheme (SVATS) model to the GCM. The majority of modern GCMs use the latter method although numerical weather prediction models often use prescribed albedo values as albedo is not expected to change significantly over the time period being simulated.

a. Albedo from remotely sensed data

Early investigators proposed various methods to estimate albedo over large areas from aerial photography, airborne scanners, and satellite system [see Starks et al. (1991) and references therein] but with the exception of Kriebel (1979) these methods assumed a Lambertian terrestrial surface, a necessity due to the nadir-viewing sensors used by the investigators. This assumption is still made where albedo measurements are required at such a finescale that only nadir data are available, for example when investigating the urban heat island effect (Soler and Ruiz 1994). Most natural surfaces, however, are anisotropic diffusers of incident radiation and the Lambertian assumption can result in errors of up to 45% in the calculation of albedo (Kimes and Sellers 1985). In order to accurately retrieve albedo from remotely sensed measurements the directional nature of the reflected radiation needs to be taken into account.

The Earth Radiation Budget Experiment (ERBE) sensor is specifically designed to measure top of atmosphere albedo at 40 km resolution and uses a set of 12 scene-dependent empirical models to convert measured directional reflectances to albedo (Barkstrom et al. 1990). To measure surface albedos the effects of the intervening atmosphere must be removed, either by using a regression model (Koepke and Kriebel 1987) or a radiative transfer model (Barker and Davies 1989). Li and Garand (1994) applied sophisticated radiative transfer models to ERBE data in order to derive a parameterization relating surface albedo to top of atmosphere albedo, solar zenith angle, and precipitable water at 2.5° resolution. Csiszar and Gutman (1999) applied Li and Garand’s method to AVHRR global area coverage (GAC) data to produce surface albedos at 0.15° resolution.

The accepted means of describing surface anisotropic effects is the BRDF of Nicodemus et al. (1977):
i1520-0442-14-7-1360-e1
where the subscripts i and r represent incident and reflective directions, respectively, Ω is a direction vector, Ei is the uniform incident irradiance over the surface under consideration, and dLr is the reflected radiance due to the incident irradiance dEi from a small solid angle i in the direction Ωi. BRDF has units of sr−1. Black-sky albedo (synonymous with Nicodemus’ directional-hemispherical albedo) is calculated by integrating fr(Ωi; Ωr) over the reflected radiation hemisphere:
i1520-0442-14-7-1360-e2
White-sky albedo (synonymous with Nicodemus’ bihemispherical albedo) is calculated by integrating fr(ΩiΩr) over both the reflected and incident radiation hemisphere:
i1520-0442-14-7-1360-e3
Lewis and Barnsley (1994) have shown that albedo under real world conditions, where the illumination is a combination of direct and diffuse radiation, can be expressed as
αθiSτρbsθiSτρws
where S(τ) is the fraction of diffuse skylight, a function of optical depth τ. This approximation holds well except for very large solar zenith angles.

From the above discussion it is clear that if we are able to accurately quantify the surface BRDF, we can calculate albedo at any solar zenith angle and under any skylight conditions. This is potentially extremely useful as it allows us to predict surface albedo under cloud cover, which is not currently possible using albedo measurements from remote sensing.

BRDF is not directly measurable, however, we may sample the BRDF by measuring surface reflectance at variable solar and observational angles. These measurements of directional reflectance, called Bidirectional Reflectance Factors (BRFs) can then be used as input into a numerical model of BRDF, the output of which is a function estimating the surface BRDF. Various investigators have proposed BRDF models, in which the BRDF is derived either empirically (Walthall et al. 1985) or theoretically as a function of vegetation canopy structure and leaf and soil reflectance. Theoretical models by, for example, Ross (1981), and Li and Strahler (1992) model a vegetation canopy and its BRDF at various levels of complexity. Lucht et al. (2000b) describe a reformulation of these models (Roujean et al. 1992) through approximations leading to semi-empirical forms that have the virtue of being easily invertible. The resulting Ross Thick Li Sparse Reciprocal model (RTLSR) model allows the user to fit a BRDF to measured BRFs. This model has been chosen to generate the MODIS BRDF and albedo products (Wanner et al. 1995); (Lucht et al. 2000b) and we choose it here for consistency with that dataset. The model has been extensively validated by Hu et al. (1997), Privette et al. (1997), Lucht (1998), and Lucht and Lewis (2000). In the RTLSR model, BRDF is described by two functions and a constant. The values of the constant and the relative weights of each function are determined by fitting the model to observed BRFs. The model can then be used in a forward integrative mode to determine albedos under any illumination conditions. This methodology is also used in albedo retrievals for POLDER instrument (Leroy et al. 1997). Expected relative retrieval accuracies for albedo are between 1.9% and 11.4% (ignoring errors in atmospheric corrections) depending on scene cloudiness and whether one or both instruments are used (Lucht 1998).

b. Method proposal

We propose a method for retrieving surface albedos from remotely sensed directional data. The method may be used to provide global monthly spectral and broadband albedos. Here we demonstrate the method for the North American continent. The albedos are derived by applying a transformation to imagery from the AVHRR sensor, although it is applicable to any wide-scan or multiple-view angle instrument (e.g., MODIS, MISR, MERIS, SPOT VGT, MSG, or GOES). The transformation corrects for bidirectional effects by taking into account the viewing and illumination geometry, and the BRDF of the pixel under consideration, approximated by a typical BRDF for the land cover type occupying that pixel. Simply put, the transformation corrects for the inadequacies of assuming a Lambertian model when deriving albedo from observations of reflectance.

The albedo datasets so produced provide an improved parameterization of the land surface for use in studies of land surface energy balance, atmospheric radiative transfer, and numerical weather prediction models. They may also be used to constrain radiative transfer models used in GCMs.

2. Methods

a. Reflectance to albedo transformation

Wide-scan angle and multiple-view angle instruments allow us to sparsely sample the BRDF of the land surface by measuring BRFs from multiple view points. Consider a set of n BRF measurements, B:
Bρ0Ωi,0Ωr,0ρ1Ωi,1Ωr,1ρn−1Ωi,n−1Ωr,n−1
We wish to find two transformations, Tbs and Tws that allow us to derive black-sky and white-sky albedos respectively from this set:
i1520-0442-14-7-1360-e6
For a large n at multiple solar zenith angles, we may simply use the RTLSR model to fit a BRDF to the measured BRFs. The RTLSR model takes the form
frΩiΩrc1R1ΩiΩrc2R2ΩiΩrc3
where c1, c2, and c3 are constant weights calculated by the RTLSR inversion process in each waveband under consideration as a function of the observations available. R1(Ωi; Ωr) is a function or kernel describing radiative transfer-type volumetric scattering in the vegetation canopy and R2(Ωi; Ωr) describes geometric-optical scattering (i.e., shadow-casting from the three-dimensional structure of the scene).1 The full formulas for R1(Ωi; Ωr) and R2(Ωi; Ωr) are in Lucht et al. (2000). RTLSR also performs the integrations necessary to determine the ρbs(Ωi) and ρws so in this case of a well-sampled BRDF we may simply substitute the RTLSR inversion process for Tbs and Tws.

Where the BRDF is sparsely sampled, including the limit of measuring only a single BRF (e.g., a single AVHRR observation from a composited image), we can improve the accuracy of the inversion by first making an assumption as to the basic shape of the underlying surface BRDF. Clearly, the BRDF of a given land cover class is variable as we see distinct intraclass variability in brightness. Seasonality and variations in canopy structure cause the largest changes in BRDF but environmental factors such as soil acidity, drainage, prevailing weather patterns, fire, flood, and landslides all contribute to this variability by causing variability in soil color, wetness, canopy greenness, leaf area index, and gap probability among others. Hence, a land cover class such as, boreal needleleaf forest, will have a BRDF that varies from one location to another. It is, however, fair to assume that intraclass BRDFs are broadly similar and that differences are one of degree, rather than substantial changes in the shape of the BRDF function. We further this by grouping within classes land cover types that theory and measurement suggest will have similar BRDFs. Thus boreal needleleaf forest and Mediterranean needleleaf forest occupy different classes in an ecological classification scheme, would occupy the same class in a BRDF-based classification scheme.

Hence, we may define land cover classes within which the BRDF is broadly similar. We refer to the possible BRDFs within this class, caused by variations in the environmental parameters discussed in the previous paragraph, as belonging to a family of BRDFs. By using observed BRFs to select a particular member of this family of BRDFs we may predict the probable BRDF of the pixel under observation, and hence calculate the albedos.

We define a continuous family of surface BRDFs by
FlaflΩiΩraρl,ws
Here, Fl represents the family of BRDFs associated with land cover of type l and fl(Ωi; Ωr) is a typical BRDF for that land cover type. We refer to this BRDF as the archetype as it is representative of the family of BRDFs for the land cover type as a whole. The value ρl,ws is the white-sky albedo associated with fl(Ωi; Ωr). The limit for a ensures that albedos retrieved by integrating some value of Fl can never exceed unity; in practice, we also require that a remain close to unity, otherwise the assumption of similarity made for members of a BRDF family may no longer be fulfilled as the underlying radiation scattering mechanisms change.

We justify the use of a multiplicative factor, a, to generate a family of similar BRDFs from one archetypical BRDFs by considering the changes in directional effects as the overall brightness of a scene changes. As scene brightness increases we tend to see an increase in directional effects: the typical bowl or inverted bowl shape of the BRDF becomes more pronounced as the albedo increases. Conversely, as the overall scene brightness decreases we see a lessening of the directional effects. The phenomenon can be simply explained by noting that a bright scene tends to have a higher contrast between vegetation canopy and soil background that leads to a stronger BRDF. A dark scene will tend to have little contrast in it and hence a weaker BRDF effect. This arises because an important part of the BRDF is caused by the interaction of dark shadows on bright backgrounds; if there is little contrast in the scene, the shadowing process has little effect. Second, BRDF effects that originate from radiative transfer within a vegetation canopy, are more pronounced when absorption is low and low absorption is associated with high scene brightness. For values of a close to unity we expect a multiplicative factor to reproduce this behavior:as the multiplier increases, reflecting an increase in overall scene brightness, the BRDF effect will increase. Using the multiplicative factor we may define a family of BRDF shapes associated with each landcover class, each member of that family being produced by varying a.

A BRDF-based is landcover classification of the earth’s surface, can be obtained by cross-walking classes from a standard ecological classification, we can now associate a family of BRDFs with every pixel on the land surface using an archetypical BRDF that has been accurately retrieved with a ground-based instrument such as PARABOLA (Deering and Leone 1986). The process of cross-walking consists simply of deciding which BRDF class a particular land cover class is equivalent to in a given season. The last step in the procedure is to use remotely sensed data to constrain the value of a in Eq. (9). This allows us to recover a true representation of the surface BRDF and hence albedos for each observed pixel, recovering the variations of albedo within each class from the remotely sensed data.

b. Procedure

Recall B, our set of BRF observations described in Eq. (5). We will refer to individual measurements in this set as B0, B1, . . . , Bn−1 where Bk = ρ0(Ωi,k; Ωr,k). We may then use the RTLSR model in the forward mode to retrieve BRFs from the archetypical BRDF for the land cover type under consideration, fl(Ωi; Ωr), at the same viewing and illumination angels as B was measured under. We refer to this set of BRFs as Bl where the subscript l denotes that these BRFs are derived from the BRDF-type land cover map rather than from observations:
Blρl,0Ωi,0Ωr,0ρl,1Ωi,1Ωr,1ρl,n−1Ωi,n−1Ωr,n−1
We then find the value of a that minimizes the difference between B and aBl using the technique of least-mean squares. Specifically, we minimize an error term e2 given by:
i1520-0442-14-7-1360-e11
by setting the condition
i1520-0442-14-7-1360-e12
It follows that
i1520-0442-14-7-1360-e13
Now that we have a value for a we have effectively selected a BRDF from the family described in Eq. (9) and consider the BRDF, afl(ΩiΩr), to be a true representation of the directional qualities of the pixel under consideration. Using the RTLSR model we can determine the albedos of the archetypal BRDF. We refer to these as ρl,bs(Ωi) and ρl,ws for the black-sky and white-sky albedos, respectively. Recalling Eqs. (2) and (3) we may write
i1520-0442-14-7-1360-e14
We may therefore rewrite Eqs. (7) and (8) as
i1520-0442-14-7-1360-e16
where a(B) is given by Eq. (13).

c. Validation

We checked the effectiveness of this approach by applying it to pairs of complete, ground-sensed BRDF measurement. Results are shown in Table 1. For the broadleaf tree land cover type we chose the BRDF of an Aspen stand measured using the PARABOLA instrument (Deering and Leone 1986) as the class archetype. Then as a test BRF dataset on which to execute the methodology we chose Kimes et al.’s (1986) hardwood dataset. Using the RTLSR model in the forward mode we calculate a BRDF from this test dataset. We can then recalculate BRFs from this inversion BRDF and by comparing them with the BRFs in the original dataset, determine an inversion root-mean-squared error, RMSEi. RMSEt is determined by calculating BRFs from the archetype BRDF and comparing them with the BRFs in the test dataset. As would be expected, the values of RMSEt are higher than RMSEi, reflecting differences in the underlying BRDFs. We then calculate a multiplicative factor, a using the process described above. The error calculated using the archetypal BRDF, multiplied by a is given as RMSEa. We can also calculate the errors in albedo with respect to the test dataset. The white-sky albedo error if we simply use the archetypal dataset is given by ϵt and that using the multiplicative factor is ϵa.

From Table 1 we clearly see that the use of the multiplicative factor dramatically improves the albedo retrieval, compared to using the archetypal BRDF for all pixels. For the needleleaf tree landcover type we used a PARABOLA Jack Pine BRDF as the archetype and PARABOLA Black Spruce as the test BRF dataset. The differences in albedos of the two datasets were 17.295% in the red and 19.714% in the near-infrared (NIR). By using the a factor to constrain the archetypal BRDF to the observed test BRFs we reduced this error to 12.534% in the red and 0.357% in the NIR. For dense grass we used a PARABOLA prairie BRDF (Deering and Leone 1990) as the archetype and a PARABOLA mixed grass test dataset. Errors were reduced from 49.431% to 12.020% in the red and from 61.077% to 0.546% in the NIR. The two datasets have similarly shaped BRDFs in the NIR that accounts for the small error. In the visible, however, the two BRDFs appear quite different, which accounts for the larger error. It should be noted that as albedos are usually small in the visible, even quite large relative errors result in only small changes in the surface albedo and hence the radiation budget.

To investigate the robustness of the algorithm we took the archetypal BRDFs in Table 2 and varied the three weights parameterizing the BRDF by up to ±10%, mimicking the variation we might expect in a given BRDF class. We then compared the white-sky albedo of the new BRDFs with those of the archetypal BRDFs. The errors vary according to BRDF class with the largest error seen in the visible band of the urban BRDF (class 25). When all three weights were reduced by 10% in this class the archetypal albedo overestimated the real albedo by 30.4%, however, the constrained inversion albedo only overestimate the real albedo by 8.4%. The class 25 archetype is based on poorly sampled AVHRR data (the only urban AVHRR dataset available at the time of writing). A new urban BRDF dataset from Meister et al. (Meister et al. 1999) will be used in future work. The mean error across all classes using the archetypal albedo to estimate real albedos is 6.61% in the visible and 6.44% in the NIR. Using the constrained inversion errors are reduced to 0.53% in the visible and 0.48% in the NIR.

d. Spectral to broadband conversion

The values ρbs(Ωi) and ρws derived above are spectral albedos within satellite sensor bands; in this study we calculate ρbs(Ωi) and ρws for channels 1 and 2 of the NOAA-14 AVHRR sensor (580–680 nm and 725–1100 nm, respectively). For climatological and LSEB studies we require at least three measures of albedo: the solar total shortwave albedo, αbb across the entire solar spectrum, the solar visible albedo, αvis, calculated for wavelengths less than 695 nm and the solar infrared albedo, αsr calculated for wavelengths greater than 695 nm, and less than 4000 nm.

We estimate the surface reflectance spectrum by fitting a laboratory-measured spectrum to the observed AVHRR reflectances in the visible and NIR. The laboratory spectrum used is dependent on the landcover type.

As we have only two data points (measurements in AVHRR channels 1 and 2) we use a simple linear fit:
ρsλlλB,
where ρl(λ) is the laboratory-measured spectrum, ρs(λ) is the predicted surface reflectance spectrum and A and B are coefficients given by
i1520-0442-14-7-1360-e19
ρVIS and ρNIR are the observed channel-1 and channel-2 AVHRR reflectances. Here, ρ*VIS and ρ*NIR are simulated AVHRR reflectances from the laboratory-measured spectrum, ρl(λ). The simulated reflectances are obtained by convolving the AVHRR instrument response functions with the spectrum.
An albedo, α, over an arbitrary interval, λl, λu can now be calculated by convolving ρs(λ) with a bottom of atmosphere solar irradiance spectrum, I(λ):
i1520-0442-14-7-1360-e21

This method was tested using field-measured reflectance spectra from a variety of sources. We generated simulated AVHRR bands 1 and 2 reflectances from the field-measured data. The AVHRR-like reflectances were then used to retrieve visible, NIR and broadband albedos using the method described above. These albedos were then compared to albedos derived by directly convolving the field-measured spectra with a solar irradiance spectrum. The errors in the visible albedo varied from 15% to 45% with a mean of 25%. To put this into perspective, a typical visible albedo of 0.05 would have an error of ±0.0125. Mean errors in the NIR and total shortwave were much lower, 11% and 10%, respectively. We explain this by noting that most of the field-measured vegetation canopy reflectance spectra available to us were of semidesert and desert shrubs over a very bright soil background. Over darker backgrounds we expect the visible albedo to exhibit errors more in line with those in the NIR and total shortwave, respectively.

3. Results

We used this procedure to derive summer and winter albedo datasets for continental North America. Satellite observational data used consisted of 1-km AVHRR imagery in the form of 30-day maximum NDVI reflectance value composites for February (winter) and July (summer) of 1995 (Eidenshink and Faundeed 1994). A BRDF-based landcover classification was produced using the global ecological classification of AVHRR data made available by the United States Geological Service (USGS) (Loveland et al. 2000). Associate archetypal BRDFs were generated from directional measurements over a wide variety of landcover types, taken principally with the PARABOLA instrument.

a. Data

1) AVHRR measurements

The 1-km AVHRR data are distributed as 10-day maximum value composites (MVCs) calculated to maximize the normalized difference vegetation index (NDVI) and therefore minimize cloud cover. The dataset contains reflectances in the two reflective shortwave bands and three bands describing the view and illumination geometry: the relative azimuth, view zenith, and solar zenith. The data are distributed in the Goodes’ homolosine projection (Steinwand 1994), unfortunately, pixel boundaries are aligned to meridians rather than whole kilometers in the Goodes’ map grid. The data therefore have to be resampled (by the nearest neighbor method) to align it to the landcover dataset (described subsequently).

Visual inspection of the composites for North America reveals that the 10-day compositing period is not long enough to eliminate cloud cover in some areas—notably mountainous areas of central America. We therefore composited three consecutive 10-day periods to produce monthly composites. We found the monthly composites to be free of cloud except for small areas of central America in the summer scene. The monthly compositing period also fits in well with the stated aim:to provide monthly albedo datasets. Unfortunately, in cloud-minimization the MVC algorithm will also minimize the amount of snow-covered pixels in the scene—it will generally choose snow-free pixels over snow-covered ones. Thus, scenes during the winter months underestimate the amount of snow-covered landmass, showing as snow-covered only pixels that are such for every day of the month in question. Additionally, as snow typically can have a slightly lower NDVI than clouds, there is a possibility that no surface albedo is retrieved at all. The retrievals of albedo over snow-covered areas should therefore be treated with caution. The data as supplied is atmospherically corrected for Rayleigh scattering and ozone absorption only. We therefore applied an additional aerosol and water vapor correction to the data for a standard U.S. continental atmosphere using the 6S program (Vermote et al. 1997). We assumed a low (0.15) constant aerosol optical depth at 550 nm, arrived at by assuming a visibility of 45 km, which might be a typical visibility on a very clear day. Allowing the aerosol optical depth to vary by ±0.02 results in a median ±8.5% error in AVHRR channel 1 for winter (February) solar zenith angles and a median ±1.8% error for summer (July) solar zenith angles. There is a negligible error in the NIR.

2) Landcover classification

As described earlier we require a global landcover classification in terms of typical surface BRDFs. Currently no such database exists so we took an existing ecological land cover classification and cross-walked it to a BRDF-based classification. The BRDF classification system is shown in Table 2.

The classification is designed to break up land surfaces into three distinct groups: discrete canopies (classes 1–11) where we can distinguish individual crowns in the canopy that have a shadowcasting effect, layered canopies (classes 12–19) where the canopy is continuous and dominated by volume scattering, and backgrounds (classes 20–25). The full classification system, which will be described in more detail in a forthcoming paper, consists of 36 classes, each consisting of a combination of scene elements. For the purposes of simplification, redundant classes (such as separate classes for dense canopies on differing soil background), or ecologically unlikely classes (such as sparse broadleaf trees on a dark barren soil background) have been left out, leaving us with the 25 classes seen here.

Next, we cross walked an existing global classification, the USGS land cover classification database to the BRDF classification. The USGS land cover classification database is a 1-km global surface classification derived from AVHRR and ancillary data and available in a variety of classification systems. We chose the Olson classification (Olson 1994) as it provides a flexible global classification system—systems such as USGS/Anderson classification (Anderson et al. 1976) provide a classification that varies in class definitions by continent, systems related to SVATS such as the SiB (Sellers et al. 1986) or Biosphere–Atmosphere Transfer Scheme (Dickinson et al. 1986) classifications are limited in number of classes and tend to amalgamate ecologically quite distinct cover types into the same class. The Olson classification on the other hand contains 94 classes covering all significant global ecosystems.

Lookup tables were constructed to assign a BRDF class to each of the Olson classes. As the Olson classification is ecological rather than structural it has no seasonal dependence, however, the BRDF of a canopy is clearly influenced by seasonal changes as the growth and senescence of green vegetation changes the scattering characteristics of the canopy. For this reason, two lookup tables were constructed, for the winter and summer months included in the study. The winter lookup table typically mapped Olson classes containing deciduous trees to the “barren” BRDF classes, classes 3 or 4 in Table 2 as appropriate. Although we cannot reprint the lookup table due to space constraints, examples are shown in Table 3.

Table 3 shows that during the winter month we may map the Olson class to either of two BRDF classes, dependent on the presence of snow. If the visible AVHRR reflectance of the pixel under consideration is higher than 70% we assume that the pixel is snow covered and the relevant BRDF class is chosen. A pixel that has summer snow will be indicated as permanent snow in the Olson classification and BRDF class 23 (smooth snow) will be used.

3) Field BRDFs

The archetypal BRDFs, fl(Ωi; Ωr), in Eq. (9) were mostly obtained from ground-based measurements. Table 3 provides a brief description of each data source and any relevant references. It should be noted that not all of these archetypal BRDFs were ideal; a review of the literature failed to provide suitable ground-based BRF measurements for most of the sparse, discrete canopy types (BRDF classes 1–6), which are the most difficult to measure in the field. We therefore substituted BRF measurements obtained by airborne instruments: Sahelian Tiger Bush (used for class 1) was imaged using the Advanced Solid-state Array Spectroradiometer (ASAS) and South American Cerrado, used as the archetype for classes 2–6 was imaged using the Cloud Absorption Radiometer (CAR) in a ground-scanning mode. The urban BRDF (class 25) was derived from multiple late summer AVHRR images of the New York, New York, and Boston, Massachusetts, metropolitan areas as no other datasets were available at the time (D’Entremont 1999).

The remaining archetypes were measured using ground-based radiometers, principally the PARABOLA instrument, a sphere-scanning radiometer described by Deering and Leone (1986). Earlier instruments used for classes 12 and 20 are described in the references given in Table 3.

Next, we retrieved BRDFs from the field-measured data using the RTLSR model discussed earlier. The BRDF produced by the RTLSR is parameterized by the weights c1, c2, and c3 in Eq. (8). Using the RTLSR model in the forward mode we may plot the BRDF at any given solar zenith angle. Examples are shown in Figs. 1, 2, 3, and 4.

The spectral characteristics of the various instruments used to collect surface BRDFs, and of the AVHRR sensor are shown in Table 4. Clearly there is some difference between the instruments, both in where the visible and near-infrared bands are centered, and the bandwidths. The error columns in Table 4 show the relative under- or overestimation of reflectance by the various sensors compared to the AVHRR sensor. The values used to calculate the errors are the mean values of a typical broadleaf vegetation reflectance spectrum in the bands of the various instruments under consideration. The reflectance spectrum used was the Johns Hopkins University deciduous vegetation spectrum from the ASTER spectral library (Salisbury 1998). We see from the table that AVHRR reflectances in the visible are underestimated by up to 17.84% by the other instruments used in the study. This is due to the AVHRR visible band overlapping slightly with the green reflectance peak of vegetation. AVHRR therefore overestimates the red band reflectance that we usually equate with visible reflectance. In the near infrared there is much closer agreement between the reflectances measured by the various sensors. Although these discrepancies appear severe they are not relevant as they do not affect the shape of the BRDF. The shape of the BRDF is determined by physical factors such as the angular distribution of leaves and the relative reflectance and transmittance of leaves within a given bandwidth.

In using BRDFs inferred from ground-based measurements as archetypes we are assuming that the BRDF of a given landcover type is invariant with scale. This assumption has a varying degree of validity depending on the land cover type and at the 1-km scale of AVHRR measurements there will always be a degree of mixing within pixels. Lucht et al. (2000a) conclude albedo is scale invariant to AVHRR resolution for a semi-desert landscape as do Stroeve et al. (1997) for an ice cap. Schaaf and Strahler (1994) report scale invariance for albedos over a spruce forest and Minnis et al. (1997) show consistent trends in surface albedo and top of atmosphere albedo from GOES data. Lewis et al. (1999) showed that point measurements of albedo in the Sahel exhibit good agreement with values derived from ASAS overflights and BRDF modelling. Taken together these studies suggest that we can directly compare measurements of BRF and albedo from different resolution sources for broadly homogeneous surface. At the scale of ground-based measurements (20 m) most land cover types are homogeneous so to produce archetypes at scales at which heterogeneity becomes an issue, some form of mixture modeling would be necessary. In the interests of simplicity we have assumed homogeneity at 1 km. This assumption holds true for large areas of the earth’s surface including deserts, ice caps, grasslands, boreal forest, and some type of tropical forest. The assumption of heterogeneity is most severely challenged in areas of mosaic agriculture.

b. North American spectral albedos

Using the methodology and data described above we produced red and near-infrared spectral albedo maps for North America using AVHRR imagery from February and July 1995. Figure 5 shows spectral white-sky albedo from AVHRR channel 1 and AVHRR channel 2. Both sets of albedo maps use a false-color scheme in which blues represents low albedos, yellows and oranges intermediate to high albedos and reds very high albedos that are only associated with snow- or ice-covered areas.

1) Channel-1 spectral albedos

Figure 5a shows the winter AVHRR channel-1 (red) white-sky albedo map for North America. Unbroken snow and ice bands produce high albedos (red) over much of arctic Canada, the Canadian central plains, and the northwestern mountain ranges. We also see moderately high albedos (yellow) in the southwestern United States and northern Mexico that reflect the sparse vegetation and bright soils in these regions. There is also a band of lower albedo across the boreal and mixed forest bands in Canada and the northeastern United States. Although this area is snow covered (its albedo is higher in winter than summer), canopy elements such as evergreen trees obscure the snow and reduce the overall brightness. This contrasts with the central plains and the tundra zones where there are no large canopy elements to obscure the snow layer.

Figure 5b shows the summer AVHRR channel-1 (red) white-sky albedo. The scene is darker overall with only the relatively barren southwest retaining the high albedos seen in the winter scene. We also see some areas of high albedo appearing in central America due to persistent cloud not removed by the compositing process. Snow effects persist only in the Greenland ice-cap and the large Alaskan and Canadian ice caps of the northwest. Albedos are consistently lower over the eastern United States, particularly in the midwestern areas where once bare soils have been replaced by darker crops.

2) Channel-2 spectral albedo

Figure 5c shows the winter AVHRR channel-2 (near-infrared) white-sky albedo in which we see the same snow effects as in Fig. 5a. In the Canadian boreal zone we see an elevated NIR albedo due to both ground snow and evergreen vegetation. Over most of the United States we see low NIR reflectances due to the predominantly deciduous vegetation.

Figure 5d shows summer AVHRR channel-2 (near-infrared) white-sky albedo. Here, we see an increase in albedo over most of the United States as a result of deciduous vegetation greening up. The NIR albedo of the boreal zone is reduced compared to the winter map;this is due to the absence of snow.

c. North American broadband albedos

Climate models and SVATS usually require broadband albedos extending well outside the ranges of the AVHRR sensors. Specifically they require the visible albedo (300–700 nm), the infrared albedo (700–3000 nm) and the total shortwave solar albedo (300–3000 nm). The spectral to broadband conversion we have described require reflectance spectra and a bottom of atmosphere solar irradiance spectrum. We selected eight reflectance spectra covering different vegetation types, bare soils, and snow from the ASTER spectral library (Hook et al. 1998) and associated each BRDF class with a relevant spectrum. A clear-sky bottom of atmosphere solar irradiance spectrum retrieved using an ASD FieldSpec FR spectroradiometer was used in the albedo calculation described by Eq. (21).

1) Full-band albedos

Figure 6a shows the summer full band black-sky albedo for nadir solar zenith. The patterns we see are broadly similar to the AVHRR channel-2 albedos shown earlier with high values in areas of dense deciduous forest, and low values in urban areas. Figure 6 shows the same area but for a solar zenith angle of 80°. Albedos over the whole scene increase with the increase in solar zenith angle, an effect that is responsible for the diurnal variation of surface albedo that has been widely reported in the literature [see Minnis et al. (1997) for a definitive discussion].

4. Discussion

a. Interpretation of results

Figure 7 shows an image of the ratio between the July shortwave infrared broadband albedo and the July AVHRR channel-2 reflectance for the northeastern United States and part of Canada. As the regionally different values of the ratio show, reflectance alone is a poor measure of albedo and even schemes relying on a supposed linear relationship between reflectance and albedo are flawed and we must take into account surface BRDF and view and illumination geometry.

Figure 7 demonstrates the relative contributions to infrared albedo from variations in surface brightness and land cover. Surface brightness provides the major contribution to albedo, as shown by the limited range of values in the ratio map, whereas land cover and view geometry cause variation in the amount of under or overestimation of albedo. We also note that the ratio is generally close to unity so we believe that our original assumptions in using a multiplicative factor for the BRDF adjustment holds. View geometry effects result in abrupt changes in the ratio, demonstrated by the blue/yellow banding in northern Maine. The fact that we can see these geometric effects in the ratio image points to the fact that they are present in the raw AVHRR reflectance data but absent (or strongly reduced) in the calculated albedo data. An albedo calculated purely from the reflectance data without taking into account view and illumination geometry would perpetuate these effects, resulting in errors in the results.

Although the effect is view geometry dependent we can see from Fig. 7 that the albedos of urban areas such as Montreal, New York, and Boston are heavily overestimated by the AVHRR-measured reflectances (dark blues). Over the remainder of the scene AVHRR reflectances overestimate albedo to a much lesser degree with the reflectances and albedos being in closest agreement over forested areas of northern New England (oranges).

The insets in Fig. 6 show the change in albedo of New York, with varying solar zenith angle. Although the albedo of most of the city increases with increasing solar zenith angle as we would expect, the albedo of the most built up area, New York, does not increase. Roujean et al. (1992) describe a BRDF model in which the surface is simulated by a random distribution of rectangular protrusions, a situation that describes Manhattan, New York, well. It was shown that the albedo derived from this BRDF model is constant or decreases with increasing solar zenith angle. We see this behavior replicated for Manhattan, New York.

Table 5 summarizes the summer total shortwave white-sky albedos over the entire continent. These albedos behave largely as expected: needleleaf trees have a lower albedo than broadleaf trees, and the surface brightness is a good indicator of the overall albedo, particularly for sparse vegetation. The “litter” BRDF class (class 19) has a surprisingly high albedo. This is probably because this class was used to represent the Olson tundra classes that may have either some residual slow or high summer greenness. Table 6 summarizes the summer total shortwave black-sky albedos at local solar noon by International Geosphere–Biosphere Programme classification (Belward and Loveland 1995), which is widely used by biogeographers. The effects of snow are again apparent with higher albedos in winter than in summer for classes such as Evergreen Needleleaf Forest and Mixed Forest.

Figures 8, 9, and 10 show areal histograms for three important BRDF classes. That the histograms are all single peaked and broadly Gaussian implies that our assumptions as to the make up of these BRDF classes are correct. However, the distributions also graphically show that using a single value of albedo for a given land cover type, as is often the case in GCMs, is incorrect. The means and standard deviations for each class are provided in Table 5 and these values should be of use in developing a statistical understanding of the effect on GCMs of uncertainty in albedo measurements.

b. Error analysis

Estimating confidence in remote sensing data is difficult without external data for comparison. In the case of global albedo there is no current external dataset at 1-km resolution with which we can directly compare our work. However, we have attempted to estimate the errors inherent in each step of the algorithm and can use these to give overall estimates of error.

A margin of error (±0.02) in the aerosol optical depth results in a 8.5% error in the AVHRR channel-1 measured reflectance in winter and a 1.8% error in summer. Errors in AVHRR channel 2, however, are negligible. The second source of error is the BRDF inversion algorithm. The discussion of errors in section 2c give a theoretical error of 0.53% in AVHRR channel 1 and 0.48% in AVHRR channel 2 but experimentation with the Black Spruce and Jack Pine PARABOLA datasets suggested a higher error of about 15% in channel 1. Assuming no correlation between errors we obtain a 16% error in AVHRR channel-1 albedo (there is only ±1% difference between the summer and winter errors after adding the effects of the 15% error discussed in section 2c and a 0.48% in channel-2 albedo).

Calculating broadband albedos introduces another source of error during the narrow to broadband conversion. The error in the broadband conversion was estimated to be 25% in the visible, 11% in the NIR, and 10% in the total shortwave. We assume that the AVHRR channel-1 signal accounts for 90% of the error in the visible albedo, that the AVHRR channel-2 signal accounts for 90% of the error in the NIR albedo and that both channel contribute equally to the total shortwave error, resulting in a visible albedo error of 29%, an NIR albedo error of 11%, and a total shortwave albedo error of 13%. These are again relative errors and we emphasize that as visible albedos are generally low (≪0.1), absolute errors in the visible are of the order of ±0.015. Typical absolute errors in the NIR and total shortwave are ±0.03.

c. Future work

This study provides a prototype of a 1-km albedo product derived from AVHRR data. Comparing this dataset to the existing albedo parameterizations used in GCMs we see several advantages. Existing models may use prescribed values, ranging from the extreme simplicity of the CCSAS model (Marchuk 1979), which uses only two different values for sea and land, to systems that use seasonally varying albedos for a number of different land cover classes such as the GISS model (Hansen 1983). More recent models such as CCM3 use a fully coupled land surface model that calculate upwelling and downwelling fluxes (and hence albedo) using a canopy radiative transfer model. Our approach will provide albedos on a yearly basis at 1-km resolution. Although current GCMs do not operate at this resolution, the higher resolution allows better estimates of the mean albedo of heterogeneous GCM cells to be made. The dataset provides albedos at any solar zenith angle and albedos under varying degrees of cloud cover can also be retrieved by weighting the sum of white-sky and black-sky albedos with a cloud-cover factor.

1) Refinements

This paper demonstrates a prototype of what will become a global dataset. We aim to improve the database in several ways:

  • Currently we use only one AVHRR observation per pixel. By using multiple observations per pixel per month we aim to substantially improve the accuracy of the dataset. This will require using selected daily AVHRR data and cloud clearing algorithms rather than the current MVC process.
  • We will eventually produce monthly albedo datasets. This requires careful design of the lookup tables used in translating landcover types to BRDF types. The same lookup tables cannot be used for all areas of the globe as seasonality varies with hemisphere, latitude, and continentality.
  • In addition to white-sky albedos we will provide the black-sky albedo in the form of the coefficients of a polynomial describing the black-sky albedo as a function of solar zenith angle (Lucht et al. 2000b). In this way users may calculate surface albedo under any illumination conditions without reference to the underlying BRDF models as a weighted linear combination of white-sky and black-sky albedo, the weights varying with atmospheric conditions.
  • With the launch of NASA’s Terra satellite we have access to extremely high quality directional measurements from the MODIS and MISR instruments along with a much improved land cover product (Justice et al. 1998). By using MODIS reflectance and land cover products we will improve the accuracy of the albedo datasets and provide a product that will complement and act as a fallback product for the operational MODIS albedo product (Strahler et al. 1996).

2) Uses

The dataset was initially developed as a constraint for atmospheric radiative transfer models but has wider applicability in GCMs. The 1-km resolution is higher than the cell resolution of current GCMs that makes the dataset useful for studying subpixel accuracy, flux averaging, and general spatial scaling and variability in these models. An important use of the work will be to provide globally summarized albedos for each of the 94 Olson ecological classes, including monthly means and ranges. Together with MODIS data, the method provides the operational MODIS fallback product, however its real importance is when applied to the unique 18-yr AVHRR time series.

Acknowledgments

This work was funded by the NASA Earth Sciences Climate and Radiation Research and Analysis Program under R. Curran through JPL Subcontract 960916/97 as part of a research project into influences upon top-of-atmosphere radiative fluxes. We gratefully acknowledge the Principal Investigator of this project, Ralph Kahn. Additional funding was provided by NASA under NAS5-31369 as part of the Terra-MODIS project. Wolfgang Lucht was partially funded by the German Federal Ministry of Education and Research under project 01LA98280. We thank Alan Strahler for continued support at Boston University. We also thank two anonymous references for their helpful comments.

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Fig. 1.
Fig. 1.

BRDF class 1 archetype. Visible BRDF of Sahelian Tiger Bush at 40° solar zenith angle

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 2.
Fig. 2.

BRDF class 1 archetype. Near-infrared BRDF of Sahelian Tiger Bush at 40° solar zenith angle

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 3.
Fig. 3.

BRDF class 17 archetype. Visible BRDF of dense grass at 40° solar zenith angle

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 4.
Fig. 4.

BRDF class 17 archetype. Near-infrared BRDF of dense grass at 40° solar zenith angle

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 5.
Fig. 5.

North American white-sky albedos. (a) AVHRR channel-1 winter spectral albedos. (b) Channel-1 summer spectral albedo. (c) Channel-2 winter spectral albedo. (d) Channel-2 summer spectral albedo

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 6.
Fig. 6.

Summer full band black-sky albedo image. (a) Solar zenith 0°. (b) Solar zenith 80°

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Ratio of white-sky infrared broadband albedo to AVHRR channel-2 reflectance (summer). (b) Summer white-sky infrared broadband albedo

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 8.
Fig. 8.

BRDF class 8 (dense broadleaf trees–shrubs) summer total shortwave white-sky albedo distribution

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 9.
Fig. 9.

BRDF class 11 (dense needleleaf trees–shrubs) summer total shortwave white-sky albedo distribution

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Fig. 10.
Fig. 10.

BRDF class 17 (dense grass-like vegetation–crops) summer total shortwave white-sky albedo distribution

Citation: Journal of Climate 14, 7; 10.1175/1520-0442(2001)014<1360:AATICS>2.0.CO;2

Table 1.

Constrained Inversion Accuracy. LC Type is the landcover type and band under consideration, RMSEi is the inversion error of the test dataset, RMSEt is the difference between the test dataset and the archetype dataset, RMSEa is the difference between the test dataset and the scaled archetype BRDF afl(Ωi, Ωr), a is the value of the multiplicative factor, ϵt is the relative difference between the test data albedo and the archetype albedo, and ϵa is the relative difference between the test data albedo and the scaled archetype albedo

Table 1.
Table 2.

BRDF land cover classes and archetypical BRDF data sources. Sources marked with a † were retrieved using the PARABOLA instrument

Table 2.
Table 3.

Some examples of cross-walking between the Olson classification and seasonal BRDF classifications

Table 3.
Table 4.

Instrument characteristics

Table 4.
Table 5.

Total summer shortwave white-sky albedos by BRDF land cover class

Table 5.
Table 6.

Broadband black-sky albedos summarized by IGBP class

Table 6.

1

Strictly speaking, BRDF and the terms in Eq. (8) are dependent on wavelength, however, in the interests of simplicity we have omitted the wavelength dependence from all equations. The reader should assume an implicit wavelength dependence in all equations relating to BRDF.

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