Atmospheric correction for the monitoring of land surfaces

Authors


Abstract

[1] This paper briefly describes the land surface reflectance product (MOD09), the current Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric correction (AC) algorithm and its recent updates, and provides the evaluation of the algorithm performance and product quality. The accuracy of the AC algorithm has been significantly improved owing to the use of the accurate Second Simulation of a Satellite Signal in the Solar Spectrum, Vector (6SV) radiative transfer code and a better retrieval of aerosol properties by a refined internal aerosol inversion algorithm. The Collection 5 MOD09 surface reflectance product computed by the improved AC algorithm was analyzed for the year of 2003 through the comparison with a reference data set created with the help of Aerosol Robotic Network (AERONET) measurements and the 6SV code simulations. In general, the MOD09 product demonstrated satisfactory quality in all used MODIS bands except for band 3 (470 nm), which is used for aerosol inversion. The impact of uncertainties in MOD09 upon the downstream product, such as vegetation indices and albedo, was also evaluated.

1. Introduction

[2] Atmospheric correction (AC) is an important step in deriving land surface properties from satellite data. A surface reflectance signal measured by passive satellite instruments is contaminated by the influence of the atmosphere. Rayleigh and Mie scattering, formation of thin cirrus clouds, and gas absorption are among the processes that prohibit one from seeing the surface behind a blurred image of radiation reflected by the atmosphere. AC is a technique developed to eliminate the influence of these processes on a measured signal.

[3] The Moderate Resolution Imaging Spectroradiometer (MODIS) AC method is a typical example of such technique. It removes the influence of gases and aerosols from MODIS data to produce the MODIS land surface reflectance product (MOD09). The process is managed by the MODIS Land Surface Reflectance Science Computing Facility (LSR SCF) [Vermote et al., 1997, 2002].

[4] By definition, the directional surface reflectance is the ratio between reflected radiance measured in specific observation geometry (zenith and azimuth) within an infinitely small solid angle and irradiance incident on the surface from a direct source of illumination (zenith and azimuth). In an ideal theoretical case, it can be fully decoupled from an atmospheric signal, and thus represents the value that would be measured by a satellite sensor as if there were no atmosphere.

[5] MOD09 presents surface reflectance signals derived from the MODIS level 1B bands 1, 2, 3, 4, 5, 6, and 7, which are centered at 648 nm, 858 nm, 470 nm, 555 nm, 1240 nm, 1640 nm, and 2130 nm, respectively [Vermote et al., 2002]. This product has its own applications in the field of imagery which are aimed at detecting and monitoring changes on the Earth's surface (e.g., anthropogenic impacts, red-green-blue images [e.g., Stöckli et al., 2006]), but mostly serves as primary input for a number of higher-level surface geophysical products such as VI (Vegetation Indices), BRDF (Bidirectional Reflectance Distribution Function)/Albedo, LAI/FPAR (Leaf Area Index/Fraction of Photosynthetically Active Radiation), and Burned Areas and Land Cover [e.g., Knyazikhin et al., 1998; Lucht et al., 2000; Roy et al., 2002].

[6] The MODIS AC algorithm relies on the utilization of look-up tables (LUTs) or precomputed sets of TOA reflectance values to find a solution to an inverse problem. The inverse problem means retrieval of surface reflectance properties on the basis of given TOA reflectance values and atmospheric parameters [Vermote et al., 1997], which is contrary to a direct problem, when TOA reflectance values are modeled on the basis of known surface and atmospheric parameters. The inverse problem is solved under a Lambertian surface approximation; corrections are applied later to account for surface directional effects. In general, the accuracy of resulting product mainly depends on the accuracy of sensor calibration, input atmospheric parameters, LUTs, and operational implementation of an inverse problem or correction for BRDF effects. The algorithm works only with cloud-free or partially cloud-contaminated data. A special cloud mask is applied to remove the influence of thin cirrus clouds.

[7] This paper provides a brief overview of the MOD09 product, describes the basics of the MODIS AC algorithm and its recent updates, and presents the results of the evaluation of the algorithm performance and the product quality. All available information on MOD09, which is not included here, can be found on LSR SCF's Web site at http://modis-sr.ltdri.org.

2. Algorithm Basics

[8] A simulation of the propagation of solar radiation through the atmosphere inside the AC algorithm requires the knowledge of key atmospheric parameters and a tool capable of simulating interactions of photons with aerosols and molecules on the basis of these parameters. This particular tool can be either a semiempirical radiative transfer (RT) model or a theory-based versatile RT code. The choice really depends on the type of application and desired accuracy.

2.1. Theoretical Background

[9] In the idealized case of a Lambertian surface and within narrow spectral bands outside of main absorption features of water vapor, the top-of-atmosphere (TOA) reflectance can be calculated as:

equation image

where ρTOA is the reflectance at the top of the atmosphere; θs is the solar zenith angle, θv is the view zenith angle, and ϕ is the relative azimuth (or the difference between the solar and view azimuth angles); P is the atmospheric pressure; Aer = {τA, ω0, PA}, where τA is the aerosol optical thickness, ω0 is the aerosol single scattering albedo, and PA is the aerosol phase function; UH2O is the integrated water vapor content, UO3 is the integrated ozone content; Tg designates the gaseous transmission by water vapor (TgH2O), ozone (TgO3), or other gases (TgOG); m is a parameter calculated as 1/cos(θs) + 1/cos(θv); ρatm is the atmosphere intrinsic reflectance, Tratm is the total atmosphere transmission (downward and upward), Satm is the atmosphere spherical albedo, and ρs is the surface reflectance to be retrieved by the atmospheric correction procedure.

2.2. Input Parameters

[10] The key atmospheric parameters which are input in a dedicated RT code include the following [Vermote and Saleous, 2006]:

[11] 1. Aerosol characteristics (vertical profile (optional), aerosol optical thickness (AOT), single scattering albedo (SSA), particle size distribution, and refractive indices): AOT is retrieved from MODIS data with the help of the internal aerosol inversion algorithm (section 4). SSA, size distribution and refractive indices are the parameters of one of four preassigned aerosol models, which is also selected by the internal aerosol algorithm. The vertical profile is in most cases assumed to be exponential. AOT needs to be retrieved at the spatial resolution of 1 km owing to its high spatial variability, while the other aerosol parameters can be retrieved at a coarser resolution with little loss of accuracy. Uncertainties in AOT retrievals depend on atmospheric conditions. The goal is to retrieve AOT with an accuracy of 0.01, in correlation with the Aerosol Robotic Network (AERONET) accuracy requirements.

[12] 2. Atmospheric pressure: This parameter is obtained from the combination of the 1-degree resolution 6-h time step Numerical Weather Prediction Model (NWP) provided by the National Center for Environmental Prediction Global Data Assimilation System (NCEP GDAS) and the 1-km resolution Digital Elevation Model (DEM) provided by the U.S. Geological Survey (USGS). The DEM is used to map surface pressure data at a higher resolution within each meteorological data grid cell. The accuracy of the final pressure is assumed to be 10 mbar [Vermote and Saleous, 2006].

[13] 3. Ozone concentration: This parameter is extracted with the accuracy of ±0.02 cm·atm from experimental measurements performed by a UV ozone sounder (e.g., NASA's Total Ozone Mapping Spectrometer (TOMS)) at a coarse spatial (1 deg.) and temporal (1 day) resolution.

[14] 4. Column-integrated water vapor content: This content is derived from the MODIS near-infrared band 18 (931–941 nm) and 19 (915–965 nm) at 1 km spatial resolution using the two-band ratio described by Gao and Kaufman [2003]. Such an approach determines the instantaneous water vapor content at the time of acquisition with an accuracy of 5–10%. Meteorological data from NCEP GDAS are used when required MODIS data are not available.

[15] The above mentioned parameters were listed by the order of effect on the reflectance products. After having been retrieved, they are used as an input for the MODIS AC algorithm.

2.3. RT Code

[16] Currently, LUTs of the MODIS AC algorithm rely on the Second Simulation of a Satellite Signal in the Solar Spectrum, Vector (6SV), an advanced RT code specifically designed to simulate the reflection of radiation by a coupled atmosphere-surface system. Its input conditions include spectral and geometrical configurations of a number of major satellites, including ASTER, AVHRR, ETM, MODIS, POLDER, and VIIRS.

[17] The code has been extensively validated since the release of its β-version in May 2005 [Kotchenova et al., 2006; Kotchenova and Vermote, 2007]. On the basis of this validation effort, its accuracy is stated to be within 1%, which complies well with the standard RT code accuracy requirement [Muldashev et al., 1999]. The 6SV code also has a significant advantage compared to scalar codes in avoiding errors caused by the assumption of a nonpolarizing atmosphere. In the visible spectrum, these errors can be as large as 7% for a simple case of a mixed atmosphere with molecular and aerosol constituents [Kotchenova et al., 2006].

3. Collection 5 Product Description

[18] The latest available collection of MOD09 is Collection 5. Its content has been slightly changed compared to that of Collection 4 to satisfy the user's changing requirements. Thus, the Daily Quality product computed at 1-km resolution was incorporated into the Daily Surface Reflectance product at 500-m resolution. The short names of the Daily Surface Reflectance products at 500-m and 1-km were modified accordingly to reflect this change. Also, a new Daily product was created on the basis of a Climate Modeling Grid (CMG) with a resolution of 0.05°. This product was mainly designed to be used in climate simulation studies. The complete list of final products is presented in Table 1. Figure 1 shows an example Surface Reflectance Daily L3 Global 0.05 Deg CMG, acquired by MODIS Terra on 4 December 2000.

Figure 1.

The MODIS Surface Reflectance Daily L3 Global 0.05 Deg CMG product extracted from data acquired by MODIS Terra on 4 December 2000.

Table 1. MOD09 Collection 5 Product
Product NameTerraAqua
  • a

    CMG, Climate Modeling Grid; L2G, level 2 product (top-of-atmosphere backscattered reflectance of filtered pixels (no cloud shadows and residual cloud contamination) over a sinusoidal grid; L3, composited level 2 product.

Surface Reflectance Daily L2G Global 250 mMOD09GQMYD09GQ
Surface Reflectance Daily L2G Global 500 m and 1 kmMOD09GAMYD09GA
Surface Reflectance 8-Day L3 Global 250 mMOD09Q1MYD09Q1
Surface Reflectance 8-Day L3 Global 500 mMOD09A1MYD09A1
Surface Reflectance Daily L3 Global 0.05Deg CMGaMOD09CMGMYD09CMG

[19] The quality of Collection 5 MOD09 has been significantly improved compared to that of Collection 4. The LUT format was modified to include a preassigned set of four different aerosol models, to perform a more accurate interpolation of atmospheric parameters, and to use MODIS ocean bands for a more accurate retrieval of aerosol properties over land.

4. Internal Aerosol Inversion

[20] The current MODIS internal aerosol inversion algorithm is an advanced version of pioneer algorithms applied to AVHRR, LANDSAT and MODIS data [Kaufman et al., 1997] and the so-called “dark and dense vegetation technique (DDV)” [Holben et al., 1998] in the sense that it is based on two main principles underlying these methods. First, it uses shorter wavelengths, where the atmospheric contribution dominates a top-of-atmosphere (TOA) signal, to estimate aerosol properties. Second, it relies on an empirical spectral relationship to estimate surface reflectance in the aerosol retrieval band. However, the current algorithm also incorporates a number of changes that have significantly improved its performance. These changes include the following:

[21] 1. A more robust “DDV technique” which relies on a relationship between blue (470 nm) and red reflectances (670 nm) to retrieve the aerosol optical thickness. This relationship was developed using MODIS data collected over 40 AERONET sites distributed globally and represented by different land cover types [Vermote and Saleous, 2006].

[22] 2. The use of four additional wavelengths (490 nm, 443 nm, 412 nm, and 2130 nm) for the inversion of aerosol type from a set of four preassigned aerosol models (smoke low absorption, smoke high absorption, urban polluted, and urban clean) created on the basis of AERONET climatology. The type retrieval is done by minimizing a residual function.

[23] 3. Improved LUTs calculated with the help of the accurate 6SV RT code [Kotchenova et al., 2006; Kotchenova and Vermote, 2007].

[24] The performance of the modified algorithm is illustrated below with a more detailed description of change 2. Let us consider two MODIS TOA images collected by MODIS Terra over the Alta Floresta (9.87°S, 56.10°W) and Mongu (15.25°S, 23.15°E) AERONET sites on 13 September 2003 at 14h10GMT and 14 September 2003 at 8h20GMT, respectively (Figures 2 and 3) . The corresponding RGB surface reflectance images are shown on the right. The tables above the images show AOT and water vapor values retrieved from the MODIS band 3 data and measured by AERONET at 550 nm, together with the number of “good” observations (the term “good” is explained in section 5.2). In both cases, this number is equal to 0, which means the presence of a large atmospheric contribution and possible uncertainties in the retrieved surface reflectance images.

Figure 2.

MODIS TOA (left) reflectance and (right) surface reflectance RGB images. The MODIS data were collected over the Alta Floresta AERONET site on 13 September 2003. AOT and WV are the values of aerosol optical thickness and water vapor content (g/cm2) measured by AERONET and retrieved by the MODIS AC algorithm; delta means the measured variability; std means the standard deviation; DTaot designates the difference in time between two AERONET observations which bracket the MODIS acquisition; and nb obs is the number of “good” MODIS observations. SLA, SHA, UP, and UC are abbreviations for smoke low absorption, smoke high absorption, urban polluted, and urban clean aerosol models, respectively. The AERONET site is located in the center of the image.

Figure 3.

MODIS TOA (left) reflectance and (right) surface reflectance RGB images. The MODIS data were collected over the Mongu AERONET site on 14 September 2003. The abbreviations used are explained in the caption for Figure 2. The AERONET site is located in the center of the image.

[25] In the case of Mongu the AOT value agrees very well with that retrieved by the algorithm (i.e., 0.982 versus 0.990) and the standard deviation (std AOT) in the MODIS retrieval is relatively low (∼0.05). In the case of Alta Floresta the retrieved and measured AOT values agree less well (0.862 versus 0.960), but with the standard deviation in the MODIS retrieval being rather high (∼0.26), we may attribute the difference to a larger spatial variability of the AOT.

[26] The retrieved AOT values are then used to compute surface reflectances for the four above mentioned aerosol models at the four additional wavelengths (412 nm, 443 nm, 490 nm, and 2130 nm). For each model, we calculate the average quadratic difference (model residual) between the retrieved, ρs, and predicted surface reflectances as:

equation image

where ρsred is the surface reflectance retrieved at 670 nm by using the optical thickness derived from 470 nm, and ai,red are empirical spectral coefficients between the 412-nm, 443-nm, 490-nm, 2130-nm bands and the 670-nm band.

[27] The aerosol model which is characterized by the smallest residual is then selected. Thus, the smoke low absorption model was selected for the Alta Floresta site (Figure 2) and the smoke high absorption one was chosen for the Mongu site (Figure 3). Both findings are quite reasonable considering the fact that Alta Floresta is located in a forest biomass burning area and Mongu belongs to a savanna burning area. Moreover, in those particular cases, the single scattering albedo (SSA) at 670 nm inverted by AERONET was 0.905 for Alta Floresta and 0.83 for Mongu, and these SSA values compare well with the model values of 0.92 (smoke low absorption) and 0.85 (smoke high absorption).

5. Accuracy of Collection 5 MODIS Surface Reflectance Product

5.1. Error Budget

[28] The best way to estimate the sensitivity of surface reflectance to uncertainties in input key atmospheric parameters is to create a theoretical error budget which would provide a realistic estimate of the impact of each uncertainty.

[29] Such a budget has recently been created by Vermote and Saleous [2006]. They simulated TOA reflectances using the 6SV code for a number of atmospheric and geometrical scenarios and estimated the influence of uncertainties in each input parameter on the final product. In total, they considered uncertainties in the instrument calibration (±2%), atmospheric pressure (±10 mb), water vapor content (±0.2 g/cm2), ozone content (±0.02 cm·atm), retrieved AOT values (resulted from the aerosol inversion), and selection of the aerosol model (urban polluted, smoke low absorption, smoke high absorption, or urban clean) (See section 2.2 for the explanation of the uncertainties). Ten different geometrical combinations and 3 values of AOT (0.05: clear, 0.3: average, 0.5: hazy) were used in the analysis.

[30] In summary the overall theoretical accuracy of the atmospheric correction method considering the influence of all error sources at once is given in Table 2. The overall accuracy of surface reflectance varies in dependence of the band and AOT. Under clear atmospheric conditions it does not exceed 0.006 in reflectance unit. Using the limited, but representative range of variation in surface conditions, the product error bars were conservatively set to 0.005+0.05ρ for the surface reflectance, and 0.02 + 0.02VI for the vegetation indices.

Table 2. Overall Theoretical Accuracy of Retrieved Surface Reflectances and Vegetation Indicesa
Reflectance/VIForestSavannaSemiarid
ValueAerosol Optical DepthValueAerosol Optical DepthValueAerosol Optical Depth
ClearAvgHazyClearAvgHazyClearAvgHazy
  • a

    Considering the error source on calibration, ancillary data, and aerosol inversion for three values of aerosol optical thickness (0.05: clear, 0.3: average, 0.5: hazy). The selected sites are Savanna (Skukuza), Forest (Belterra), and Arid (Sevilleta). The uncertainties are considered independent and summed in quadratic.

ρ1 (645 nm)0.0240.00520.00590.00650.080.00530.00620.00670.140.00570.00740.0085
ρ2 (870 nm)0.29310.0040.01520.02460.22260.00350.01030.01640.23240.00410.00950.0146
ρ3 (470 nm)0.0120.00520.00510.00520.040.00520.00520.00530.070.00510.00530.0055
ρ4 (550 nm)0.03750.00490.00550.00640.06360.00520.00580.00640.12460.00510.0070.0085
ρ5 (1240 nm)0.30830.00380.0110.01790.2880.00380.00970.01580.29290.00450.00930.0148
ρ6 (1650 nm)0.15910.00290.00520.00840.24830.00350.00660.01040.30850.00550.00810.0125
ρ7 (2130 nm)0.0480.00410.00280.00420.160.0040.00360.00530.280.00560.0060.0087
NDVI0.8490.030.0340.040.4710.0220.0280.0330.2480.0110.0150.019
EVI0.3990.0050.0060.0070.2030.0030.0050.0050.1190.0020.0040.004

5.2. Error Budget Verification

[31] To check the quality of the Collection 5 MOD09 product, we have analyzed a year of Terra data (2003) collected over 150 AERONET sites. The analysis consisted in processing subsets of Level 1B data, acquired by MODIS over AERONET sites, by an algorithm similar to the standard AC algorithm and comparing them to a specifically created reference data set. This reference data set consisted of surface reflectance values simulated by the 6SV RT code filled with AERONET measurements (AOT, distribution of particles, refractive indices, and water vapor content). To enhance the accuracy of the performed analysis, we considered only those AERONET measurements which were taken within 30 min of MODIS measurements. A surface reflectance value produced by the standard algorithm (or observation) was considered “good” if the difference between this value and the reference value fell within the MODIS theoretical uncertainty of 0.005+0.05ρ, where ρ is the surface reflectance.

[32] The percentage of “good” observations for each MODIS band was then plotted on a global map in the form of circles centered on AERONET sites. Here we show the results for bands 1 and 2 (Figures 4 and 5) . In Figures 4 and 5, the circle color is a function of the percentage of “good” observations for a given site, and the circle radius is a function of the number of clear-day observations coinciding with AERONET measurements (divided by the cosine of the view zenith angle to account for fewer observations off-nadir) used for this site.

Figure 4.

Comparison between the MODIS band 1 surface reflectance and the reference surface reflectance data set for all available AERONET data of 2003. The circles show locations of AERONET sites. The circle radius is proportional to the number of observations. The circle color shows what percentage of comparisons falls within the MODIS theoretical one-sigma error bar (green > 80%, 65% < yellow < 80%, 55% < magenta < 65%, red < 55%).

Figure 5.

Same as Figure 4 but for band 2.

[33] Detailed results for six AERONET sites characterized by different land cover types are shown in Figure 6. The selected sites include: Alta Floresta (9.87°S, 56.10°W, forest biomass burning), Mongu (15.25°S, 23.15°E, savanna burning), Bratts Lake (50.28°N, 104.70°W, prairies), Hamburg (53.57°N, 9.97°E, industrial zone), Jabiru (12.66°S, 132.89°E, wooded area), and HJAndrews (44.24°N, 122.22°W, temperate coniferous forest). The results are presented in the form of a bar chart. Each bar corresponds to one of the MODIS seven bands (1–7), and the height of a bar designates the percentage of “good” observations for a given band for the year 2003. The infrared band product (bands 2 and 5–7) demonstrate very good quality, while the quality of visible band product (bands 1, 3 and 4), especially that produced for band 3 (blue), is in some cases (e.g., Hamburg, bands 3–4, or HJAndrews, band 3) not good at all. The reason for that is strong atmospheric contribution in the visible spectrum, which makes atmospheric correction less accurate.

Figure 6.

Detailed results for six AERONET sites characterized by different land cover types. Each bar corresponds to one of the seven MODIS bands. The height of a bar designates the percentage of “good” observations for a given band for the year 2003.

[34] Figure 7 shows the results of the analysis for MODIS band 4 data measured in July 2003 for the AERONET sites used in Figure 6. The surface reflectance retrieved from the MODIS data were plotted against those extracted from the reference data set. In addition to the results of the comparison, each plot shows the total number of observations, Nobs, and the percentage of “good” observations. Nobs is quite high for Mongu (1553), Jabiru (1482) and HJAndrews (1376), which can be explained by a high number of clear day observations in July 2003: 22, 22 and 25, respectively. On the contrary, there were only 2 clear days in July for Hamburg, and thus its Nobs is really low (117). The percentage of “good” observations for all sites correlates well with the results for band 4 shown in Figure 6. All sites except for Hamburg are characterized by a high percentage of “good” observations.

Figure 7.

Results of the comparison between the surface reflectances retrieved from MODIS band 4 data by the standard algorithm and those extracted from the reference data set for six different AERONET sites. The MODIS data used were collected in July 2003. Nobs means the total number of observations for the given month, and “% of good” means the total number of “good” observations.

[35] Globally, over 4988 cases covering about a quarter million individual reflectance values were analyzed. The average percentage of “good” observations for bands 1, 2, 3, 4, 5, 6, and 7 was equal to 88.66%, 94.34%, 50.52%, 79.34%, 96.50%, 97.87%, and 98.62%, respectively (http://ltdri1.geog.umd.edu/cgi-bin/mod09_2003_c005.cgi). The relatively poor results for band 3 (470 nm) are mainly associated with uncertainties in the spectral empirical relationship between reflectances in the blue and red (670 nm) bands. The reflectance in this band should be used with caution or not used at all if possible. The very nature of the atmospheric correction algorithm makes the reflectance in this band quite ambiguous as it is also used to invert the aerosol optical thickness. This is a not a big concern at this stage since most downstream products rely primarily on the reflectance in the red or longer wavelengths.

5.3. Downstream Products: VI and Shortwave Albedo

[36] It is useful to estimate the impact of uncertainties in surface reflectances directly on the downstream products as errors are not spectrally independent. To achieve this goal, an analysis similar to that illustrated in Figures 47 has been performed for two vegetation indices, NDVI (Normalized Difference Vegetation Index) and EVI (Enhanced Vegetation Index). NDVI is the normalized ratio of the NIR and red bands:

equation image

where ρNIR is the reflectance of band 2, and ρred is the reflectance of band 1.

[37] EVI is calculated as

equation image

where G = 2.5 is the gain factor, L = 1 is the canopy background adjustment factor, and C1 = 6.0 and C2 = 7.5 are the aerosol resistance weights [Huete et al., 2002].

[38] Globally, 97.11% of retrieved NDVI values and 93.64% of retrieved EVI values fell within the theoretical MODIS one-sigma error bar (±(0.02 + 0.02·VI)) (which means that the error in a given index value is 0.02 plus 2% of the index value). A map illustrating the NDVI results is presented in Figure 8. It shows that the error on NDVI is always lower than the largest possible error related to the uncertainties of individual bands (red and near-infrared).

Figure 8.

Comparison between NDVI and the reference data set for all available AERONET data of 2003. The meaning of circle radius and color is explained in the caption for Figure 4.

[39] We also estimated the influence of uncertainties on the albedo product. For this purpose, we analyzed one year (2003) of radiation data collected at a radiation tower site located near the AERONET site in Lamont, OK. White-sky and black-sky albedo values were derived from the standard reflectance product following the approach described by Liang et al. [1999].

[40] These two albedos are the extreme cases of completely direct and completely diffuse illumination. Black-sky albedo, αbs, is defined as albedo in the absence of a diffuse component:

equation image

where Ω0 is the incident solar beam direction, Ωr is the direction of reflected radiation, λ is the wavelength, and fr0, Ωr, λ) is the BRDF of considered surface. White-sky albedo is defined as albedo in the absence of a direct component when the diffuse component is isotropic:

equation image

The actual albedo is then interpolated between these two as a function of the fraction of diffuse skylight which, in its turn, is a function of AOT [Schaaf et al., 2002]. A particular AOT value is converted to the fraction of diffuse skylight by using a special look-up table created by the MODIS BRDF/Albedo Group for broad spectral bands (visible, NIR and shortwave).

[41] The derived albedos were then compared with those obtained using the reference data set. Figure 9 shows the results of this comparison for the short wave (SW) albedo for the period of 16 days. It also shows that the real albedo value (0.161) extracted from experimental measurements and averaged over 16 days correlates well with the black sky and white sky albedo range (0.156–0.158). Figure 10 illustrates the results of the comparison between the reference albedo, the albedo derived from MOD09 and the experimentally measured albedo (both daily and averaged over 16 days) for days 221–341 of the year 2003. The albedo values derived from MOD09 agree very well with the experimental measurements, which confirms a good quality of the MOD09 products.

Figure 9.

Results of the comparison between the SW albedo values derived from the standard MOD09 product and that derived from the reference data set. The albedo was measured at a radiation tower site (20 km x 20 km) located near the AERONET location in Lamont, OK. The value of 0.161 is an experimentally measured albedo averaged over 16 days.

Figure 10.

Results of the comparison of the SW albedo values derived from the standard MOD09 product, obtained using the reference data set, and experimentally measured by an albedo meter for days 221–341 of the year 2003. WS means “white-sky albedo,” and BS means “black-sky albedo.” The site average albedo was calculated by averaging daily values over a period of 16 days.

6. Statistical Analysis of the Accuracy of MOD09

[42] A more comprehensive and synthetic evaluation of the performance of the surface reflectance and vegetation indices versus the references values obtained over the AERONET sites could be conducted by computing the statistical metrics defined by the NPOESS project to evaluate the Earth Data Record (EDR). The three quantities used to track the performance of the product are accuracy, precision and uncertainty (APU). The accuracy (A) statistically represents the mean bias of the estimates, μe, versus the truth data, μt, and is computed as:

equation image

The precision, P, is representative of the repeatability of the estimate and is computed as the standard deviation of the estimates around the true values corrected for the mean bias (accuracy), that is:

equation image

Finally, the uncertainty, U, represents the actual statistical deviation of the estimate from the truth including the mean bias is computed as:

equation image

It is worth noting that it is only necessary to compute the accuracy and the precision, because the uncertainty, U, satisfies:

equation image

Figures 1113 show the Accuracy, Precision and Uncertainty computed for the validation data set used in section 5. The APU metrics has been binned by range of reflectance or VI to better reflect the performance of the product for different surface conditions. Also shown is the suggested specification for reflectance and VI uncertainties which was mainly derived from the error budget analysis (0.005+0.05ρ, 0.02+0.02VI). In general, the performance of the products is slightly better than the expected errors derived from the error budget, which confirms the validity of the conservative error analysis.

Figure 11.

Accuracy (red line), precision (green line), and uncertainty (blue line) over the directional surface reflectance in MODIS band 1 binned in 0.01 increments of reflectance. Also shown are the number of points in each bin (blue bars) with the value on the left and the error budget of suggested uncertainties (magenta line).

Figure 12.

Accuracy (red line), precision (green line), and uncertainty (blue line) over the directional surface reflectance in MODIS band 2 binned in 0.01 increments of reflectance. Also shown are the number of points in each bin (blue bars) with the value on the left and the error budget of suggested uncertainties (magenta line).

Figure 13.

Accuracy (red line), precision (green line), and uncertainty (blue line) over the directional surface reflectance in MODIS NDVI binned in 0.05 increments of NDVI. Also shown are the number of points in each bin (blue bars) with the value on the left and the error budget of suggested uncertainties (magenta line).

7. Conclusions

[43] The performed validation analysis has confirmed a good quality of the MOD09 product and provided the user with a quantitative measure of the MODIS AC algorithm improvement. The algorithm has undoubtedly benefited from its recent significant changes, such as a better retrieval of aerosol characteristics and the use of the accurate vector RT code. However, before one can make a general conclusion about the overall quality of the MOD09 products, the analyses presented here should be extended to include the other years of data.

[44] Although the error budget and the comparison to the reference data set derived from AERONET are necessary steps in the evaluation of the atmospheric correction algorithm, the study of the accuracy should be extended to include comparison to systematic ground measurement such as the Albedo network and the independent analysis of vegetation index time series. Also, the results will need to be updated to include nonuniform and non-Lambertian surface cases, as soon as the AC algorithm handles such cases.

[45] In general, uncertainties in atmospherically corrected product (MOD09) are not the only source of errors in downstream products. While evaluating the quality of downstream products, it is necessary to account for errors unrelated to atmospheric correction (e.g., LAI uncertainty due to biome segmentation, BRDF uncertainty due to the use of linear kernel models, etc.) and to analyze for which bands further improvement in atmospheric correction will not lead to any significant improvement in downstream products.

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