1. Introduction
Photosynthetically active radiation (PAR) is an important parameter for the terrestrial ecosystem model (Prince 1991; Sellers and Schimel 1993; Running et al. 2004). PAR regulates green vegetation’s photosynthesis and stomatal regulation, which controls the exchange of water vapor and carbon dioxide between vegetation and the atmosphere (Goward et al. 1985; Dai et al. 2004). Terrestrial ecosystem modeling requires PAR dataset for model initiation, calibration, and validation. The needs for PAR datasets with suitable accuracy and spatial–temporal resolution have been articulated by the ecosystem modeling community (Zhao et al. 2006).
Because of the lack of a global network for ground-based PAR measurements, remote sensing has been the only feasible means to estimate PAR at large scales. Methods have been developed to derive PAR from remotely sensed data, and some PAR products have been made available (Eck and Dye 1991; Pinker and Laszlo 1992; Frouin and Pinker 1995; Van Laake and Sanchez-Azofeifa 2004; Rubio et al. 2005; Van Laake and Sanchez-Azofeifa 2005). Reviews of some of the remote sensing–based algorithms is provided by Pinker et al. (1995).
Because of changes in solar zenith angle and atmospheric condition, the magnitude of PAR changes over the course of hours. The high temporal resolution of geostationary satellites, such as the Geostationary Operational Environmental Satellite (GOES) and the Meteorological Satellite (Meteosat), is an advantage in capturing the PAR diurnal variation, as compared with polar-orbiting satellites, which usually take one or two observations at a given place per day. Geostationary satellites have long been used to estimate surface solar insolation and PAR. Gautier et al. (1980) developed a simple physical model to estimate incident solar radiation using first-generation GOES visible data (Gautier et al. 1980), which were later improved by including ozone absorption and introducing an empirical correction for subpixel clouds (Diak and Gautier 1983). GOES observations were used to retrieve total solar radiation and PAR (Gu and Smith 1997), and surface net radiation at The Boreal Ecosystem–Atmosphere Study (BOREAS; Gu et al. 1999) and Amazon basin (Gu et al. 2004). GOES-8, -10, and -12 were used to calculate surface insolation, and the results are validated using insolation data taken at The U.S. Climate Reference Network (USCRN; Oktin et al. 2005). GOES visible band data were used to estimate incoming solar radiation over northwest Mexico (Stewart et al. 1999) and Brazil (Ceballos et al. 2004). Diak et al. (1998) estimated daily solar radiation from GOES-8 visible imagery in an effort to apply satellite data in agricultural management. Incoming solar radiation estimated from GOES-8 imagery is used as part of the input for modeling evapotranspiration from wetlands in north-central Florida (Jacobs et al. 2002).
To retrieve PAR, all existing algorithms require some external knowledge of either the surface or atmospheric condition. This is due to the fact that at-sensor radiance includes a mixed contribution from both the surface and atmosphere, and the PAR retrieval requires a separation of the two. The dependence of these PAR algorithms on external information limited their applicability, especially when the required information is lacking or erroneous.
To address this problem, we developed a new algorithm to estimate incident PAR using at-sensor radiance measured by the GOES visible channel, without any external atmospheric information. The essence of this new algorithm is a simultaneous derivation of land surface and atmospheric parameters. Liang et al. (2006) first proposed the method of estimating PAR using Moderate Resolution Imaging Spectrometer (MODIS) visible band data based on a simultaneous retrieval of surface and atmospheric parameters. In this study, the Liang et al. (2006) method was improved in the following two major aspects: The first improvement is the utilization of a spatial relation for the exclusion of the adverse effects of cloud shadow on surface reflectance retrieval. The second improvement is the incorporation of a bidirectional reflectance distribution function (BRDF) for characterizing surface reflectance. In addition, the impacts of topography on surface incident PAR is also assessed in this article, in order to provide the end user with a topographically corrected PAR dataset.
The rest of this article is organized as follows: Section 2 gives a detailed description of the GOES PAR algorithm. Section 3 evaluates the performance of the new algorithm through validation against ground measurements. Section 4 examines the impacts of topographic impacts on surface PAR at 1-km resolution. Section 5 discusses some problems and possible further improvements.
2. Algorithm description
In addition to solar zenith angle, the amount of solar flux that reaches the earth’s surface is also affected by the scattering and absorption of various atmospheric constituents, including gas absorption, atmospheric molecule Rayleigh scattering, aerosol scattering/absorption, and cloud scattering. Within the PAR spectrum, ozone is the main source of gas absorption. Both ozone and atmospheric molecule Rayleigh scattering can be calculated with relatively high accuracy. As well, atmospheric transmittance over the PAR region is insensitive to the variation of water vapor and zone concentration. A sensitivity study through atmospheric radiative transfer model simulation indicates that atmospheric transmittance over the PAR region changes from 1.0 to 0.9603 with ozone concentration changes from 0 to 17.6862 g m−2, and transmittance changes from 1.0 to 0.9875 when water vapor concentration changes from 0.0 to 6.7258 g cm−2(Liang et al. 2006). The solar zenith angle at the above-described scenario is 0°. The major effects of cloud on atmospheric transmittance are through scattering process, while its absorption within PAR region is negligible (Frouin and Pinker 1995). Thus, the major hurdle in estimating PAR using remotely sensed data is to count for the absorption and scattering caused by aerosol and cloud, which are highly variable in both spatial and temporal domains.
In this study, a new algorithm is developed to retrieve both surface and atmospheric parameters from at-sensor radiance measured by the GOES imager’s visible channel, and then to calculate surface irradiance within the PAR region. In this new PAR algorithm, the atmosphere condition is characterized by varying aerosol optical depth and cloud extinction coefficient, while atmospheric gases (including ozone) and water vapor are represented by fixed default values. The simplification of using fixed atmospheric gas and water vapor concentration is justified by the relative insensitivity of atmospheric transmittance over PAR region to variations of ozone and atmospheric gases.
Satellite at-sensor radiance contains a contribution from two components—radiance reflected from the earth’s surface and path radiance from atmospheric scattering without contribution from the earth’s surface. The decoupling of surface and atmospheric contributions will allow both atmospheric and surface parameters to be retrieved from the GOES at-sensor radiance. To achieve the decoupling, this new algorithm first retrieves earth surface reflectance through an analysis of a time series of at-sensor radiance.
a. Retrieving surface reflectance using time series of observations
The value of the GOES-12 visible band (0.55–0.75 μm) at-sensor radiance increases with the increase of atmospheric turbidity over most natural surfaces, except snow and ice. Within a long period of time, it is usually valid to assume that there are some points of time when the atmosphere over a given surface location is clear. Under clear atmospheric condition, the relation between at-sensor spectral radiance and surface parameter can be established through atmospheric radiative transfer models, such as Moderate Resolution Atmospheric Transmission (MODTRAN; Berk et al. 1998). This relation allows at-sensor spectral radiance to be converted to spectral surface reflectance under a clear atmospheric condition. The detailed process is as follows: Given a set of clear atmospheric parameters, viewing–illuminating geometry, and spectral surface reflectance, MODTRAN simulations will result in the spectral radiance at the top of the atmosphere (TOA). An integration of the TOA spectral radiance with GOES-12’s visible band spectral response function (SRF) results in at-sensor spectral radiance. In this study, the clear atmosphere is characterized by 100-km visibility at 550 nm with default water vapor and gas (including ozone) concentration values.
Three pairs of values of surface reflectance/at-sensor radiance resulting from the above-described simulation are sufficient to solve for the following three variables: Fd, I0(μ0, μ, ϕ), and
Because GOES-12 visible band at-sensor radiance increases with the increase of atmospheric turbidity over most natural surfaces, except snow and ice (Fig. 1), observations taken under a clear atmosphere will have low values in converted surface reflectance. In most conditions, it is valid to assume, within a reasonably long period of time, that there are observations taken under clear atmosphere. Therefore, for a series of observations at a given pixel, sorting for the lowest values in converted surface reflectance will lead to those observations taken under clear atmospheres.
At a given pixel, a time series of at-sensor radiances are first converted to surface reflectance under a clear atmospheric assumption. The resulting surface reflectance is referred to as nominal surface reflectance hereinafter. High values of nominal surface reflectance represent the following two possible conditions: 1) actual high surface reflectance caused by snow and ice, or 2) a heavy cloud structure. Low values of the converted surface reflectance represent observations taken under clear atmospheric conditions.
There are situations in which a pixel is in the shadow of a cloud structure that is not in the line of view from the ground pixel to the sensor. These shadowed observations tend to have the lowest value in nominal surface reflectance, lower than actual surface reflectance. The underestimation caused by cloud shadowed observations should be excluded from sorting for the actual surface reflectance.
b. Excluding cloud-shadowed observations
Cloud shadow detection algorithms have been developed (Simpson et al. 2000) for cloud screening and other purposes. In this study, cloud-shadowed observations are excluded based on the fact that cloud-shadowed pixels are adjacent to cloud pixels. The distance from a cloud pixel to its shadow on the ground is a function of cloud height, solar zenith angle, and solar azimuth angle (Simpson and Stitt 1998). The knowledge of these angles allows the calculation of the exact position of a cloud pixel’s shadow on the ground surface. Because of the complexity of deriving cloud height, a simpler method is used to exclude cloud-shadowed observations in this study. Because observations with very high solar zenith angle are excluded from deriving surface reflectance, the highest solar zenith angle used is 75°. Visual interpretation of cloud edge and its shadow edge indicated that most shadows are within 10 pixels away from its corresponding cloud structure.
Thus, a two-step cloud shadow exclusion approach is used: First, at a given pixel’s time series, a high value (>0.5) of nominal surface reflectance is identified and a National Oceanic and Atmospheric Administration (NOAA) snow/ice cover map is used to exclude snow/ice pixels. Within the time series, observations with high nominal surface reflectance, which are not identified as snow/ice, are treated as observations under cloud. Second, for each identified cloud pixel, every pixel within 10 pixels of the radius is labeled as a possible cloud-shadowed pixel, and is excluded from subsequent sorting for clear observations.
c. Fitting BRDF model to calculate surface reflectance
A sorting of nominal surface reflectance will result in a set of lowest positive values from the time series of a given pixel. The lowest 10% of the positive values of nominal surface reflectance, excluding those that fall within a 10-pixel radius of identified cloud pixels, are regarded as actual surface reflectance. These actual surface reflectance are used to fit a modified three-parameter linear Ross–Li model in order to characterize the surface bidirectional feature, which in turn will be used to calculate surface reflectance value for the observations taken under an unclear atmosphere.
After the fitting of the BRDF model, the procedure proceeds to compare the values of the standard deviation (σfit) of the fit with a predefined threshold value σmax (σmax = 0.025 in absolute value or σmax = 0.25 in relative value), which represents the maximum value of the standard deviation of the regression that is considered acceptable for successful modeling fitting. When the condition σfit ≤ σmax is fulfilled, the process exits the procedure; otherwise, the surface reflectance value exhibiting the largest absolute departure with respect to the model prediction is eliminated, and the series of surface reflectance values are used to fit the model. This iteration procedure is pursued until either an acceptable fit is obtained or the number of surface data points remaining in the time series becomes too low to ensure a reliable retrieval of the geophysical parameters. After obtained the parameters of the BRDF, values of the surface reflectance at observations under an unclear atmosphere are calculated using the illuminating–viewing angles along with the parameters of the fitted BRDF model.
d. Deriving atmospheric parameters
With surface reflectance calculated for each observation of the time series at a given pixel, the procedure proceeds to derive atmospheric parameters. The atmospheric condition is parameterized by the following two key variables: aerosol optical depth and cloud extinction coefficient. Other atmospheric components, including water vapor, ozone, and gases concentration, are represented by fixed default values. For atmospheric transmittance within the PAR region, cloud has much more significant impact than aerosol. Therefore, the effect aerosol is not considered at the presence of cloud. Thus, atmospheric conditions are divided into two categories—hazy and cloudy, where a hazy atmosphere refers to an atmosphere with aerosol but no cloud. By this configuration, the atmosphere condition is represented by a continuum ranging from the least to most cloudy. A hazy atmosphere is parameterized by varying aerosol optical depth at 550 nm. In an actual MODTRAN simulation, the equivalent value of atmospheric visibility is used in place of the aerosol optical depth. The six values of atmospheric visibility used in this study are 5, 10, 20, 30, 50, and 100 km. The 100-km atmospheric visibility is treated as the clear atmosphere. A cloudy atmospheric condition is parameterized by varying the cloud extinction coefficient at 550 nm. Four different values of cloud extinction coefficients for each of four cloud types are used (Table 1). We found that selecting different cloud types and aerosol types does not significantly affect PAR retrieval. Therefore, in this study, one cloud type (stratus) and one aerosol type (rural aerosol) are used to characterize cloudy and hazy atmosphere respectively.
Under a given illuminating–viewing geometry and surface reflectance, MODTRAN simulation results in an at-sensor radiance value in response to a specified value of aerosol optical depth or cloud extinction coefficient. Extensive simulations have indicated that at-sensor radiance monotonically increase with the turbidity of the atmosphere (except at very high surface reflectance, such as snow/ice). Figure 1 shows the monotonic increase of the GOES-12 visible band at-sensor radiance with the increase of atmospheric turbidity.
This monotonic increase indicates that there is a one-to-one relation between at-sensor radiance and atmospheric turbidity, which enables the retrieval of atmospheric parameter from at-sensor radiance. In other words, under a given illuminating/viewing angle configuration, one value of at-sensor radiance corresponds to only one atmospheric turbidity level, represented by either the aerosol optical depth or cloud extinction coefficient.
e. Generating lookup tables
Although the above-described method is capable of retrieving both surface reflectance and atmospheric parameters, the extreme time-consuming online MODTRAN simulations make it unpractical for large-scale applications. To overcome this obstacle, the lookup tables (LUTs) approach is used.
To create the lookup tables, MODTRAN simulations are conducted for a series of representative configurations of illuminating–viewing geometry and atmospheric conditions. In this study, the following values are used for MODTRAN simulations: a solar zenith angle of 0°, 20°, 40°, 50°, 60°, 70°, 80°, 84°, and 89°; a viewing zenith angle of 0°, 20°, 40°, 60°, 80°, and 85°; and a relative azimuth angle of 0°, 30°, 60°, 90°, 150°, and 180°. The values for atmospheric visibility and the cloud extinction coefficient are the same as those used in section 2d.
For each illuminating–viewing geometry and atmospheric combination, MODTRAN simulations are conducted 3 times, with different surface reflectance values for each run. The three variables in Eq. (2)—path radiance, total transmittance, and atmospheric spherical albedo—are solved as described in section 2a.
The MODTRAN simulation and subsequent derivation of the three variables of Eq. (2) creates entries for the first lookup table, which link at-sensor radiance to atmospheric surface reflectance through the values of three atmospheric parameters: Fd, I0(μ0, μ, ϕ), and
f. Searching LUT to calculate incident PAR
The procedure for calculating incident PAR based on the lookup tables are as follows: 1) For a time series of observations, each at-sensor visible band radiance is first converted to nominal surface reflectance under clear atmospheric condition using entries from the first lookup table and Eq. (2). 2) Cloud pixels are identified based on nominal surface reflectance and with aid of snow map, and then possible cloud-shadowed observations are excluded as described in section 2b. 3) The time series nominal surface reflectances are sorted (excluding snow- and cloud-shadowed observations), and the resulting 10% lowest positive values of nominal surface reflectance are treated as actual surface reflectance. 4) The values of actual surface reflectance, along with their illuminating–view angle information, are used to fit a BRDF model, and the resulting model parameters are used to compute the surface reflectance value at observations taken under an unclear atmosphere. 5) With surface reflectance calculated at each observation, at-sensor radiance at each atmospheric condition, from the clearest to the most heavily cloudy, is calculated based on entries of the first lookup table. The resulting series of simulated values of at-sensor radiance are compared with actual at-sensor radiance values to retrieve the atmospheric parameter as represented by aerosol optical depth or cloud extinction coefficient. 6) With values of both the surface reflectance and atmospheric parameter retrieved, the algorithm proceeds to calculate incident PAR by searching the second LUT. Here the surface reflectance for the GOES-12 visible band region of 0.55–0.72 μm is used to represent the broadband surface reflectance at the PAR region from 04 to 0.7 μm. Based on solar zenith angle and the retrieved aerosol optical depth or cloud extinction coefficient, the value of rs,
g. GOES-12 visible band at-sensor radiance
GOES visible band data used in this algorithm are acquired by GOES-12, which was launched into orbit (75°W, over equator) in 2001. GOES-12 replaced GOES-8 as the operational GOES-East satellite. Both an imager and a sounder are aboard GOES-12. GOES-12 imager’s visible channel (0.55–0.72 μm) has a nominal spatial resolution of 1 km × 1 km at nadir. It is referred to as nominal resolution in the sense that the east–west spatial resolution is actually 0.57 km at nadir because of oversampling. The visible band data used in this study are taken by the GOES-12 imager at 30-min intervals.
Like its predecessors, GOES-12 imager’s visible band does not have an onboard calibration device. Sensor responsivity degradation and postlaunch vicarious calibration have been a constant issue for GOES visible band observations (Weinreb et al. 1997; Knapp and Vonder Haar 2000). GOES-12 visible band data used in this study are of a 16-bits integer count, which are converted to nominal albedo value. Nominal albedo is calculated by calibrated radiance and solar radiance. It is called nominal albedo because it is neither corrected for the solar zenith angle, nor the variation of sun–earth distance. Because visible band radiance is a required input for the GOES PAR algorithm, the visible band radiance is retrieved from converted nominal albedo values by applying the lookup table provided by NOAA.
Because the visible band data used in this work were acquired in mid-2004, more than 2 yr after the launching of the GOES-12 satellite, the on-orbit sensor degradation needs to be taken into account. Vicarious calibrations conducted by NOAA, using star-viewing data, put the GOES-12 imager visible channel responsivity degradation rate at 5.68% yr−1 during the period from 22 January 2003 to 23 January 2005. Based on this calibration result, the visible band radiance values were adjusted by using the degradation rate and number of days since the launch.
3. Validation
To assess the accuracy of the algorithm, the derived PAR values are validated against ground measurements at the following four “FLUXNET” sites (FLUXNET information available online at http://www.daac.ornl.gov/FLUXNET): Canaan Valley, Lost Creek, Metolius, and Willow Creek. The locations of the four validation sites are summarized in Table 2 and Fig. 2. To mitigate the adverse effect of the spatial mismatch between satellite observations and ground sites, a 3 × 3 pixel window centered on the pixel whose latitude–longitude coordinate matches the ground site’s position are used. The arithmetic mean of the derived PAR values at the 9 pixels within the window is used for a comparison with the PAR value measured at the corresponding ground site. To temporally match the observed and derived PAR values, linear interpolations are used to derive the ground-measured PAR value at the times that match the satellite observation. For example, if the satellite observation is taken at timeTsat, which lies between two ground measurements taken at timeTmea_1 and Tmea_2, a linear interpolation is used to derive the ground-measured PAR value at time Tsat based on the measured values at time Tmea_1 and Tmea_2. At all of the four sites, the estimated and measured PAR values are from yeardays 191–198 of 2004.
The resulting instantaneous PAR is taken in watts per meter squared, whereas the PAR ground measurement is in micromoles per meter squared per second. A fixed conversion factor (W m−2 = 4.6 μmol m−2 s−1) is used reach the unit compatibility for the validation (Dye 2004).
The first validation site in Cannan Valley, West Virginia, is located in temperate grassland. The elevation of the site is 1000 m, and the tower is 4 m high. The scatterplot, depicting the comparison between the measured and estimated instantaneous PAR values, along with the fitted linear regression, is in Fig. 3. There are some underestimations and overestimations, though most points are within the vicinity of the one-to-one line. The validation has an RMSE of 197.6 μmol m−2 s−1. RMSE as the percentage of mean estimate is 9.52%, and the bias is −53.46 μmol m−2 s−1.
The second site, in Lost Creek, Wisconsin, is situated at an Alder willow wetland. The flux tower is about 9 m above the ground. The underlying terrain is 480 m above sea level. Figure 4 compares the estimated and measured instantaneous PAR values at this site. The comparison resulted in an RMSE of 141.16, and a bias of −11.09. The liner regression between the estimated and measured PAR resulted in a R2 value of 0.923.
At the third site, Willow Creek, Wisconsin, the dominant vegetation is Alder willow. Figure 5 shows the comparisons between the estimated and measured PAR values, which has an RMSE of 131.44, and a bias of −16.6. RMSE as the percentage of mean estimate is 13.01%.
Validation at the last site of Metolius, Oregon, resulted in the highest bias of the four validation sites (Fig. 6). The bias value of 101.1 points to a systematic underestimation of PAR, which is also indicated by the high R2 value resulting from the linear regression between the estimated and measured PAR values.
Table 2 summarizes the statistics of the validation results at the four sites, and Fig. 7 depicts both the estimated and measured instantaneous PAR values against time, at the same time period as the comparison in Figs. 2 –5.
4. Correcting topographic impacts on incident PAR
Complex surface topography has an impact on the amount of PAR that is actually available for vegetation’s photosynthesis (Winslow et al. 2001). Studies have developed methods to assess and correct topographic effects on PAR or total shortwave radiation at ground level (Dubayah 1992; Dubayah and Rich 1995; Duguay 1995; Varley et al. 1996; Dubayah and Loechel 1997; Kumar et al. 1997; Corripio 2003; Van Laake and Sanchez-Azofeifa 2005). In addition, the topographic impact on incident PAR is closely related with spatial resolution. For instance, the reflected PAR flux from neighboring pixels at a finer resolution becomes a within-pixel phenomenon as resolution grows coarser. Topographic impact on PAR at the within-pixel level is beyond the scope of this article, and therefore is not treated. In this section, a commonly used method is used to evaluate topographic impact on PAR at 1-km nominal resolution at which PAR is retrieved from GOES-12 visible band data. A brief description of the topographic correction method is as follows.
Three parts are considered in the GOES PAR 1-km topographic correction: correction for direct component of PAR based on angular effect, correction of diffuse component for the sky openness, and correction for the reflected direct and diffuse PAR flux from neighboring terrains. It should be noted that the DEM is not included in the PAR retrieval algorithm, which assumes a sea level elevation.
a. Digital elevation dataset
In topographic correction, each pixel is treated as a block of terrain with uniform topographic and reflecting characteristics. The underlying topography is provided by the U.S. Geological Survey (USGS) global 30 arc-second elevation (GTOPO30) digital elevation model (DEM) dataset. GTOPO30 has global coverage with a 30-arc-s spatial resolution. To match the grid of GOES PAR, the USGS GTOPO30 DEM dataset covering the study area is reprojected to the same projection system as that of GOES PAR map with 1-km nominal spatial resolution. The cubic convolution resampling method is used for the reprojection process. Figure 8 shows the USGS GTOPO30 DEM covering the continental United States and part of southern Canada. Elevation at pixels is directly obtained from the DEM, while the slope and aspect at each pixel are calculated based on the elevation values.
b. Angular effects on direct PAR
In calculating the angular effects, the pixels are treated as three-dimensional blocks. At each pixel, the geometric center of the top surface of the three-dimensional block is used the reference point. By treating pixels as three-dimensional blocks, this method assumes the uniform elevation within pixels, therefore ignores the within-pixel elevation variation. This treatment is in keeping with the fact that this article does not treat the topographic impact on the PAR at the within-pixel level.
This method for computing slope and aspect is also used by some commercial remote sensing software packages (ERDAS 1999).
For an arbitrary pixel X, the topographical impact on direct radiation is calculated as an impact factor ranging from 0 to 1, with 0 representing that no direct PAR is actually received because of the terrain’s effect, and 1 representing that 100% of the available direct PAR is actually received. In addition, effects of neighboring terrain’s shadows are corrected by a two-step approach: first, by calculating the shadow of each pixel cast at the given solar zenith and azimuth angle; and second, by testing whether a given pixel is in any pixel’s shadow. If a pixel is in another’s pixel’s shadow, it will be assigned a shadow factor of 0; otherwise, its shadow factor will be 1. The total correction factor for the angular effect on the direct component of PAR is the product of the impact factor and shadow factor.
Figure 9 shows the impact of topography on direct PAR at 1905 UTC 4 May 2005. Within the continental United States, the Rocky Mountain and the Appalachian Mountain range areas reveal the most significant topographical effect on direct PAR.
c. Sky-view factor for diffuse PAR
In this study, the diffuse PAR is treated as of isotropically distributed, therefore topographic impact on diffuse PAR is determined only by the terrain topography. The topographic effect on diffuse PAR is characterized by sky-view factor φsky. At an arbitrary pixel X, φsky is broken down into a subfactor of its eight subdirections, represented by the eight direct neighbor pixels of pixel X. For each neighboring pixel, φsky ranges from 0° to 90°, with 90° representing a fully open sky and 0° representing a completely blocked sky.
At each subdirection, the subfactor is calculated by the elevation of a blocking pixel and the distance from the blocking pixel to pixel X. To find the maximum blocking angle, at each direction, pixels within the distance of the searching radius are examined, and the largest blocking angle is identified. Theoretically, a larger search radius will result in a better chance of finding the maximum blocking angle, but the blocking angle decreases with the increasing distance from a blocking pixel to pixel X. Sensitivity tests indicated that a search radius of 5 pixels is sufficient to ensure that the largest blocking angle is included.
The sky-view factor of pixel X then is calculated as the average of eight subfactors of the eight subdirections. The sky-view factor ranges from 0 to 1, with 0 representing a totally blocked sky, and 1 representing a completely open sky. Figure 10 shows the histogram of the sky-view factor values covering the study area.
d. Reflected direct and diffuse flux from neighboring terrains
Studies had indicated that there is little justification for using a sophisticated method to correct the reflected radiation from neighboring terrains, because the resultant improvement on accuracy is insignificant (Duguay 1995). In this study a simple method developed by Dubayah (1992) is used to account for the reflected radiation from neighboring pixels.
e. The results of the topographically corrected PAR
Validation of topographically corrected PAR is difficult to be carried out because of the lack of ground measurement. This is because pyranometers are usually horizontally oriented regardless of underlying slope. Because it is beyond the scope of this study to carry out field work to validate the topographically corrected PAR, only results based on theoretical calculations are presented. Figure 11 shows the topographically corrected instantaneous PAR covering the continental United States and part of southern Canada, along with corresponding at-sensor radiance GOES-12 visible band images. It can be observed from the imagery that the topographic impact on PAR is much more pronounced in mountainous regions than in relatively flat regions. It is also evident that the topographic impact is much less significant in areas with heavy cloud cover than areas under a clear atmosphere.
5. Discussion
A new algorithm for estimating PAR using GOES visible band data is developed in this paper. Different from the existing GOES PAR algorithms, this new algorithm derives both surface reflectance and atmospheric parameters simultaneously from at-sensor radiance values, without the requirement for external knowledge of surface or atmospheric parameters. Validation against ground measurements indicates that this new algorithm is capable of reaching reasonably high accuracy. When compared with the similar algorithm that was developed to estimate PAR from MODIS visible band data, this GOES algorithm was improved in two important aspects: first, the GOES algorithm counts for the surface bidirectional reflectance using a semiempirical BRDF model while the MODIS PAR is based on assumption of Lambertian surface. Second, this new GOES PAR algorithm utilizes spatial relation to exclude possible cloud-shadowed pixels, while the MODIS method only uses temporal relation for cloud shadow exclusion.
One of the important uses for the GOES-derived PAR product is modeling vegetation’s net primary production (NPP). The needs for high spatial resolution PAR products have been articulated by NPP modeling society (Running et al. 2004; Zhao et al. 2006). The new PAR algorithm’s independence of external information of atmospheric condition, coupled with the high temporal resolution of the GOES observation, makes it possible to provide a daily PAR estimation on production basis.
When using the GOES-derived PAR estimates in NPP modeling, it is worth noting that cautions have been taken to ensure the compatibility between PAR and other model parameters and inputs. It is often the case that a flat surface is assumed in NPP modeling, irrespective the underlying terrain. When flat surface is assumed, the topographically corrected PAR that is estimated can directly used with other gridded biophysical variables. Note that such treatment introduces errors due to the fact that the flat surface assumption results in a smaller surface on sloped areas. However, this problem can be easily mitigated by calculating the actual area of the sloped pixel before using the topographically corrected PAR.
To evaluate the new GOES PAR algorithm, it makes sense to compare its performance with the existing PAR algorithms. The algorithm developed by Van Laake and Sanchez-Azofeifa (2005) to estimate instantaneous PAR using MODIS standard products reaches the relative accuracy of 5.7%–7.3% at two validation sites. Liang et al.’s (2006) algorithm reaches the relative accuracy from 4% to 21% at seven validation sites. In comparison, the estimation accuracy of the new GOES PAR algorithm is relatively low (14.59%–22.22%), which is at least in part caused by the lack of onboard calibration for GOES’s visible band. On the other hand, the high temporal resolution gives GOES an advantage in integrating instantaneous PAR to daily PAR.
Further improvement for the GOES PAR algorithm is necessary. The topographic correction has not been validated because of the lack of ground measurements. The error associated with the DEM used for topographic correction may introduce extra uncertainty into the topographically corrected PAR. Future studies should consider using topography data with greater accuracy in order to improve the accuracy of topographic correction. For instance, the DEM generated by the shuttle radar topography mission (STRM) at 30-m spatial resolution, with global coverage between 60°N and 56°S, is an alternative to the GTOPO30 DEM.
The uncertainty involved in validating PAR value from 1-km remote sensing data against ground-based point measurements is another issue that needs to be addressed. Concerns have been raised about using ground-based measurement to validate model performance at grid level (Li et al. 2005). More sophisticated validation methods, including intercomparison among different remote sensing PAR products and comparison with meteorological reanalysis datasets, will be evaluated in future work.
Acknowledgments
The study was supported in part by U.S. NASA under Grants NAG512892 and NNG05GD10G, managed by Dr. Diane Wickland at NASA Headquarters. The authors thank Dr. R. Pinker for providing the code for calculating GOES angular information.
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The change of the GOES-12 visible band at-sensor radiance with atmospheric turbidity. The y axis represents GOES-12 at-sensor radiance (W m−2 μm−1), and the x axis represents the atmospheric turbidity index. The atmospheric turbidity index of 1–4 represents the cloudy atmosphere, and 5–10 represents the hazy atmosphere, with 1 standing for the most cloudy and 10 standing for the most clear conditions. Simulation was carried out with surface reflectance = 0.1, solar zenith angle = 40, sensor zenith angle = 155.0, and relative zenith angle = 0.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
The change of the GOES-12 visible band at-sensor radiance with atmospheric turbidity. The y axis represents GOES-12 at-sensor radiance (W m−2 μm−1), and the x axis represents the atmospheric turbidity index. The atmospheric turbidity index of 1–4 represents the cloudy atmosphere, and 5–10 represents the hazy atmosphere, with 1 standing for the most cloudy and 10 standing for the most clear conditions. Simulation was carried out with surface reflectance = 0.1, solar zenith angle = 40, sensor zenith angle = 155.0, and relative zenith angle = 0.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
The change of the GOES-12 visible band at-sensor radiance with atmospheric turbidity. The y axis represents GOES-12 at-sensor radiance (W m−2 μm−1), and the x axis represents the atmospheric turbidity index. The atmospheric turbidity index of 1–4 represents the cloudy atmosphere, and 5–10 represents the hazy atmosphere, with 1 standing for the most cloudy and 10 standing for the most clear conditions. Simulation was carried out with surface reflectance = 0.1, solar zenith angle = 40, sensor zenith angle = 155.0, and relative zenith angle = 0.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Illustration of the four FLUXNET sites used for validating the instantaneous PAR estimated using GOES visible band data: Metolius, OR; Lost Creek, WI; Willow Creek, WI; and Canaan Valley, WV. The latitude and longitude of the four sites are given in Table 2.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Illustration of the four FLUXNET sites used for validating the instantaneous PAR estimated using GOES visible band data: Metolius, OR; Lost Creek, WI; Willow Creek, WI; and Canaan Valley, WV. The latitude and longitude of the four sites are given in Table 2.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Illustration of the four FLUXNET sites used for validating the instantaneous PAR estimated using GOES visible band data: Metolius, OR; Lost Creek, WI; Willow Creek, WI; and Canaan Valley, WV. The latitude and longitude of the four sites are given in Table 2.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Scatterplot between estimated instantaneous PAR (x axis) and measured instantaneous PAR (y axis) at Canaan Valley. The solid line is the 1:1 line, and the dashed line is the fitted linear regression line.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Scatterplot between estimated instantaneous PAR (x axis) and measured instantaneous PAR (y axis) at Canaan Valley. The solid line is the 1:1 line, and the dashed line is the fitted linear regression line.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Scatterplot between estimated instantaneous PAR (x axis) and measured instantaneous PAR (y axis) at Canaan Valley. The solid line is the 1:1 line, and the dashed line is the fitted linear regression line.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Lost Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Lost Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Lost Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Willow Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Willow Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Willow Creek site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Metolius site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Metolius site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
As in Fig. 3, but at the Metolius site.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Comparison of estimated instantaneous PAR (μmol m−2 s−1, solid circles) against measurements (solid triangles) at the four sites: Canaan Valley, Lost Creek, Willow Creek, and Metolius.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Comparison of estimated instantaneous PAR (μmol m−2 s−1, solid circles) against measurements (solid triangles) at the four sites: Canaan Valley, Lost Creek, Willow Creek, and Metolius.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Comparison of estimated instantaneous PAR (μmol m−2 s−1, solid circles) against measurements (solid triangles) at the four sites: Canaan Valley, Lost Creek, Willow Creek, and Metolius.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
USGS GTOPO30 DEM projected to Lambert azimuthal equal area projection, with center of projection at 30°N, 90°W. The image covers the continental United States and part of southern Canada.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
USGS GTOPO30 DEM projected to Lambert azimuthal equal area projection, with center of projection at 30°N, 90°W. The image covers the continental United States and part of southern Canada.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
USGS GTOPO30 DEM projected to Lambert azimuthal equal area projection, with center of projection at 30°N, 90°W. The image covers the continental United States and part of southern Canada.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Topography’s effect on direct PAR through the angle between solar illumination direction and the normal to the terrain slope. The dark color represents low percentage of incident direct PAR that is actually received on the terrain surface, and the bright color represents a higher percentage. Note that the topographic effect on direct PAR is dependent on time of day and day of year. This image is of 1905 UTC 4 May 2004.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Topography’s effect on direct PAR through the angle between solar illumination direction and the normal to the terrain slope. The dark color represents low percentage of incident direct PAR that is actually received on the terrain surface, and the bright color represents a higher percentage. Note that the topographic effect on direct PAR is dependent on time of day and day of year. This image is of 1905 UTC 4 May 2004.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Topography’s effect on direct PAR through the angle between solar illumination direction and the normal to the terrain slope. The dark color represents low percentage of incident direct PAR that is actually received on the terrain surface, and the bright color represents a higher percentage. Note that the topographic effect on direct PAR is dependent on time of day and day of year. This image is of 1905 UTC 4 May 2004.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
The histogram of values of sky-view factor covering the same area as that of Figs. 8 and 9. The sky-view factor ranges from 0.3 to 1.0, with mean value of 0.98 (x axis) and std dev of 0.019. The y axis is the percentage value.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
The histogram of values of sky-view factor covering the same area as that of Figs. 8 and 9. The sky-view factor ranges from 0.3 to 1.0, with mean value of 0.98 (x axis) and std dev of 0.019. The y axis is the percentage value.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
The histogram of values of sky-view factor covering the same area as that of Figs. 8 and 9. The sky-view factor ranges from 0.3 to 1.0, with mean value of 0.98 (x axis) and std dev of 0.019. The y axis is the percentage value.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
PAR (μmol m−2 s−1) derived using GOES visible band data (left) without and (right) with topographic correction. The five pairs of images are from yeardays 191, 192, 193, 194, 195, respectively (from first to fifth row) of 2004. The times of the five pairs of images are all at 2000 UTC. The impact of topographic impact is more pronounced at the absence of cloud than at the presence of cloud. Mountainous areas see more topographic impact than relatively flat areas.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
PAR (μmol m−2 s−1) derived using GOES visible band data (left) without and (right) with topographic correction. The five pairs of images are from yeardays 191, 192, 193, 194, 195, respectively (from first to fifth row) of 2004. The times of the five pairs of images are all at 2000 UTC. The impact of topographic impact is more pronounced at the absence of cloud than at the presence of cloud. Mountainous areas see more topographic impact than relatively flat areas.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
PAR (μmol m−2 s−1) derived using GOES visible band data (left) without and (right) with topographic correction. The five pairs of images are from yeardays 191, 192, 193, 194, 195, respectively (from first to fifth row) of 2004. The times of the five pairs of images are all at 2000 UTC. The impact of topographic impact is more pronounced at the absence of cloud than at the presence of cloud. Mountainous areas see more topographic impact than relatively flat areas.
Citation: Journal of Applied Meteorology and Climatology 47, 3; 10.1175/2007JAMC1475.1
Cloud extinction coefficient (km−1) at 550 nm.
The summary of site locations and validation statistics at the four validation sites.
