Error Analysis of Retrieved Aerosol Optical Depth due to Adjacency Effect for ROCSAT-2 RSI Bands

1 Department of Information Management / Geographic Information Management and Research Center, Transworld Institute of Technology, Yunlin, Taiwan, ROC * Corresponding author address: Dr. Chien-Hui Liu, Department of Information Management / Geographic Information Management and Research Center, Transworld Institute of Technology, Yunlin, Taiwan, ROC; E-mail: chliu@tit.edu.tw The adjacency effect (AE), caused by the scattering of reflected radiance from an inhomogeneous surface, is known to introduce a blurring effect on remotely sensed data, especially for high spatial resolution data. The retrieval of aerosol optical depth (AOD) by the dark target (DT) method usually neglects the AE. Hence, significant errors may be induced in aerosol retrieval. In this study, the errors of retrieved AOD due to AE by the DT method for very high spatial resolution data of 8 m in the multi-spectral bands of ROCSAT-2 RSI are investigated. A fast, accurate simple atmospheric correction model is applied. Target size is considered the same as the spatial resolution. The errors are mainly studied for both low and medium contrasts, in both clear and hazy skies for both continental and urban aerosol models. The results indicate that for the continental model, AE may cause significant retrieval errors for AOD over DTs for medium contrast in both skies in blue and red bands. Error becomes negligible if the inhomogeneous surface is for low contrast in clear sky. It is larger for the urban model where there is more absorption than for the continental model, due to the less sensitivity of top-of-atmosphere reflectance to AOD for DTs in inhomogeneous surfaces. This suggests that AE be considered for medium contrast in both skies, especially for urban-industrial regions for ROCSAT2 RSI. (


INTRODUCTION
Remote sensing of aerosols has been of considerable interest, because of the fact that increasing atmospheric aerosol concentrations scatters more sunlight back into space, increases planetary albedo and decreases the temperature of the Earth (McCormick and Ludwig 1967).
Researchers have estimated that an increase in the tropospheric aerosol optical depth (AOD) of 0.1 would decrease the temperature about 1°C on Earth's surface (Hansen and Lacis 1990).Owing to its highly spatial and temporal variability, accurate determination of AOD is also very important to correct the atmospheric effect of remotely sensed data and retrieve surface reflectance.An increase in AOD of 0.2 can decrease the surface reflectance by 0.02 in the green band of SPOT high resolution visible (HRV) for the target reflectance of 0.03, when AOD is 0.33 (see Fig. 7, Liu et al. 1996).Consequently, it is of great importance to retrieve AOD accurately from remotely sensed data, especially for the very high spatial resolution data of 8 m in the multi-spectral bands of the ROCSAT-2 remote sensing instrument (RSI) (Table 1), which was launched on May 21, 2004.The Dark Target (DT) method, which was first proposed over one and-a-half decades ago by Kaufman and Sendra (1988) (KS88), is probably the most popular method to retrieve AOD from remotely sensed data.Since the top-of-atmosphere (TOA) signal contains larger atmospheric reflectance and the surface reflectances are very low in the visible bands for DTs, the errors of retrieved AOD due to the errors of the assumed reflectances over DTs are expected to be much lower than those over bright targets.The DTs are identified by taking advantage of the low opacity of most aerosol types in the mid-IR bands.Their reflectances in the blue and red bands are estimated using constant regression coefficients with reflectances in mid-IR band (Kaufman et al. 1997).The reflectance of the background surrounding the DT is considered the same as that of DT.Then, the lookup table approach, given in the specified aerosol model, can be used to determine AOD (Ouaidrari and Vermote 1999).This method has been operationally applied to Earth observing system (EOS) moderate resolution imaging spectroradiometer (MODIS) data (Kaufman et al. 1997) and Landsat thematic mapper (TM) data (Ouaidrari and Vermote 1999).For sensors without mid-IR bands, such as SPOT HRV and ROCSAT-2 RSI, DTs can be identified as the pixels with low near-IR signal and high vegetation index (KS88).Their reflectances can be assumed by reasonable values in the visible bands.
The adjacency effect (AE) has a systematic nature, which brightens the dark target and darkens the bright target at the TOA level (Lyapustin 2001;Lyapustin and Kaufman 2001).It originates from the reflected radiance of the surrounding areas, out of the field of view, and is scattered by the atmosphere into the field of view (Kaufman 1989), thus causing a blurring effect and reducing the contrast of an image.Therefore, it becomes very important for remote sensing applications when dark or bright targets are used.Significant errors of retrieved surface reflectance at the red wavelength due to AE can be up to 0.07 at the viewing zenith angle of 53.1° in a hazy sky even at 1 km resolution (Lyapustin and Kaufman 2001).Therefore, it is suggested that AE be taken into account not only in the atmospheric correction algorithms but also in aerosol retrieval.Nevertheless, the AOD retrieval algorithms of EOS-MODIS (Kaufman et al. 1997) and Landsat TM data (Liang et al. 1997) did not consider the AE over DTs.
Consequently, there is ample room for improvement of these algorithms (Vermote et al. 2002), especially for the multi-spectral data of ROCSAT-2 RSI with a pixel size of 8 m.
Recently, a new DT method of aerosol retrieval for Landsat enhanced thematic mapper plus (ETM+) has been developed (Lyapustin et al. 2004).Based on 3D radiative transfer theory, it can remove the positive error of retrieved AOD in 1D theory due to AE over inhomogeneous surface.This method simultaneously retrieves the aerosol model and AOD.Furthermore, their results show that the accuracy of aerosol retrieval can be significantly improved based on socalled surface climatology, which describes the regional and seasonal distribution of the regression coefficients.On the contrary, these coefficients are considered as constants in MO-DIS algorithm.Since the spectral characteristics of RSI are very similar to those of ETM+ (Table 1), albeit their lack of middle infrared bands, their study may be very helpful for aerosol retrieval from ROCSAT-2 RSI data.
Table 1.Comparison of the central wavelengths and spectral ranges of ROCSAT-2 RSI and Landsat ETM+ bands.
a. determined from the moments method (Palmer and Tomasko 1980;Asrar 1989); (please note that there is a small deviation (~0.004 µm) in near-infrared from the central wavelength denoted in Liu (2003), which should be corrected as equivalent wavelength) b. full width at half maximum; c. available from http://geo.arc.nasa.gov/sge/health/sensor/sensors/landsat.html.
In this paper, a study analyzing errors of retrieved AOD due to AE for ROCSAT-2 RSI bands is presented.Only the DT method is considered, although contrast reduction method also obtains satisfactory results for SPOT HRV (Lin et al. 2002) and NOAA AVHRR (Liu et al. 2002) data.Numerical simulations are conducted using a fast and accurate simple atmospheric correction model (SACM) (Liu 2003).The retrieved AOD errors due to AE are also studied at different solar, viewing zenith angles and relative azimuthal angles in different levels of haziness.Both continental and urban aerosol models (CM and UM) are considered.Though target size affects error, it is considered the same as the spatial resolution of ROCSAT-2 RSI in this study, as the error of retrieved AOD due to AE in the red band 0.65 µm for different spatial resolutions has been excellently studied by Laypustin and Kaufman (2001).

METHODOLOGY
SACM is implemented to estimate the errors of retrieved AOD, δτ a , due to AE for ROCSAT-2 RSI bands.The look-up table of environment function, defined as the probability of scattered photons reaching the sensor from assumed uniform circular target over inhomogeneous surface in the second simulation of the satellite signal in the solar spectrum (6S) (Vermote et al. 1997), is compiled with radius of 4 m in SACM, i.e. half of spatial resolution of ROCSAT-2 RSI.The rmse values of TOA reflectances ρ TOA simulated by SACM are less than 0.001 (about 0.0008 and 0.0006 in blue and red bands) for both CM and UM, when compared with 6S for wide ranges of parameters.Numerical studies have been conducted to estimate the induced errors of retrieved AOD due to the rmse of ρ TOA by SACM.A DT with the reflectances ρ c of 0.01 in the blue band is assumed at a solar zenith angle (θ s ) of 30°, viewing zenith angle (θ v ) of 45° and the relative azimuthal angle (φ ) of 0°.Two contrasts over DT are considered.The low contrast (LC) and medium contrast (MC) denote that DT is surrounded by the background with its reflectance ρ b = 0.06 and ρ b = 0.12, respectively.The results show that the induced errors are only 0.005 and 0.010 in clear sky (τ a = 0.23) and hazy sky (τ a = 0.76) for MC, respectively, when aerosol is CM.As for UM, the errors are about 0.01 for LC and MC in clear sky, respectively, however, the errors can be 0.07 and up to 0.14 for LC and MC in hazy sky, respectively.Therefore, though for both contrasts the errors are negligible for CM in both skies as well as for UM in clear sky, they will be significant in hazy sky for UM, especially for MC.One should note that it is because UM with single scattering albedo ω 0 of 0.65 is more absorptive than CM with ω 0 of 0.90 in blue band.Detailed explanation of the significant errors for UM in hazy sky will be presented in the later section.For simplicity, these errors are neglected in the following discussion.Hence, the estimated AOD errors due to AE should be moderate in the latter conditions.
Numerical simulations under different conditions are conducted to study the errors of retrieved AOD.Visibilities (VIS) are set to 23 km (clear sky) and 5 km (hazy sky), which correspond to the τ a values of 0.23 and 0.76 at 550 nm, according to 6S. θ s are set to 30° and 60°.θ v is fixed as 45° by the design of ROCSAT-2 RSI.The values of φ are set to 0°( backscattering) and 180° (forward-scattering).To assess the errors, relative error δτ a / τ a (%), absolute standard error (ASE) and relative standard error (RSE) (%) are used.The value of δτ a is defined as the estimated AOD minus the true AOD; RSE is defined as the ratio of standard error of estimated AOD to true AOD.In the numerical experiments, the true AOD is used to simulate ρ TOA by considering AE; the estimated AOD is then retrieved by inverting ρ TOA with all the same parameters given in the simulation of ρ TOA , except assuming the uni- form surface ( ρ b = ρ c ).

RESULTS AND DISCUSSIONS
Figures 1a, b, c, and d illustrate δτ a / τ a (%) due to AE for different ρ c and ρ b in different VIS in the blue and red bands of ROCSAT-2 RSI for CM.θ s , θ v and φ are 30°, 45° and 0°, respectively.The values of ρ c and ρ b are all from 0.00 to 0.12 for both visibilities and both bands.For a given ρ c , δτ a / τ a increases monotonically as ρ b increases in both bands and both VIS.On the other hand, δτ a / τ a decreases monotonically as ρ c increases for given ρ b .If the background is brighter than the target, i.e., ρ b > ρ c , τ a is over-estimated (δτ a > 0) due to the under-estimation of ρ b .On the contrary, τ a is under-estimated (δτ a < 0) due to the over- estimation of ρ b , if the target is brighter than the background.These errors are all due to the negligence of the scattered radiance reflected from the inhomogeneous surface, i.e. uniform surface assumption.Since this phenomenon is quite similar to those cases of θ s = 60° and/or φ = 180°, their figures are neglected.However, quantitative analysis will be discussed as in the following.The values of δτ a / τ a range from -253.3% to 118.3% and -323.0% to 110.0% for blue and red bands in clear sky, and they range from -101.8% to 66.7% and -162.5% to 70.0% for both bands in hazy sky.In fact, δτ a are enhanced in the hazy sky compared with those in the clear sky, because of the negligence of the stronger scattered radiance reflected by the inhomogeneous surface.
To better understand the values of δτ a , ASE and RSE (%) of the retrieved τ a due to AE over DT at various θ s , φ , different contrasts, and in different VIS in the blue and red bands of ROCSAT-2 RSI are studied.Both CM and UM are considered.The reflectance of DT, ρ c , is considered to range from 0.01 to 0.06, since there will exist various degrees of darkness of DT used in remote sensing AOD.The definitions of DT and these two contrasts over DT are similar to those of Lyapustin and Kaufman (2001).In the following discussion, ASE_AOD and RSE_AOD represent the ASE and RSE of the retrieved τ a .
First, CM is considered.As shown in Table 2, RSE_AOD (ASE_AOD) increases as VIS increases (decreases) and/or contrast increases.When θ s and φ are 30° and 0°, respectively, RSE_AOD can increase from 18.19% to 31.20% as VIS increases from 5 km to 23 km for LC in the red band; it can be up to 96.66%, which is the maximum RSE_AOD, for VIS = 23 km and MC in the same band.In the blue band, the maximum RSE_AOD is 99.88% for the same VIS and contrast.When the viewing direction is changed from backscattering to a forwardscattering direction, the RSE_AOD is decreased.This is because of the less scattered radiance from the inhomogeneous surface in the forward-scattering direction.When θ s increases to 60°, the RSE_AOD due to AE is decreased.This is because the increasing atmospheric reflectance over DT dominates the ρ TOA (Lyapustin and Kaufman 2001).When θ s and φ are 60°a nd 180°, ASE_AOD are almost negligible (less than 0.1) except for VIS = 5 km and MC in both bands.In general, the differences of ASE_AOD in both bands are small (less than 0.05).
As shown in Fig. 3 of Lyapustin and Kaufman (2001), the SE_AOD reached up to maximum value 0.31 for MC (average ρ b = 0.11) at the nadir view, in the hazy sky (τ a = 0.8) for a spatial resolution of 25 m, in the red band.Compared with their study, it is not surprising that the maximum ASE_AOD can be up to 0.45, for a VIS of 5 km and MC in the red band, when θ s and φ are 30° and 0° (Table 2).It is likely due to the higher resolution (8 m) in this work.
The behavior of the ASE_AOD with VIS, θ s and contrast over DT, as described above, is also consistent with their study.It is also interesting to note that for a given contrast, when τ a increases from 0.23 (VIS = 23 km) to 0.76 (VIS = 5 km) (about three times larger), the ASE_AOD increase is only about twice as large.However, for a given VIS, when the contrast Table 2.The absolute and relative standard errors (%, in parenthesis) of the retrieved τ a due to AE for DTs ( ρ c = 0.01~0.06)at various θ s , φ , differ- ent contrasts, and for different VISs in km in the blue and red bands of ROCSAT-2 RSI.Continental aerosol model is considered.LC and MC denote that the dark target is surrounded by ρ b = 0.06 and ρ b = 0.12, respectively.
increases from LC ( ρ b = 0.06) to MC ( ρ b = 0.12) (only twice as large), the ASE_AOD in- creases approximately threefold.This indicates that the ASE_AOD due to AE is about twice as sensitive to the contrast variation than τ a variation.
For UM, RSE_AOD for LC in clear sky increases to 84.00% as compared with 32.29% for CM in the blue band for θ s = 30° and φ = 0°.It is because sensitivity of TOA reflectance to τ a for more absorptive UM is less than that for CM in the case of LC.Look-up tables of TOA reflectance as a function of τ a (Fig. 2) for CM (solid curve) and UM (dashed curve) for ρ c = 0.03 in the case of MC could explain this result.θ s , θ v and φ are 30°, 45° and 0°, respectively.LUTs are determined as ρ c = ρ b = 0.03.The labeled values of horizontal lines are TOA reflectances for different VISs and aerosol models for ρ c = 0.03 and ρ b = 0.12.As VIS decreases from 23 km to 5 km, TOA reflectance increases from 0.1604 to 0.2117 for CM, however, it increases only from 0.1398 to 0.1467 for UM.One could also notice that no feasible value of τ a , which ranges from 0.05 to 2.0, could best fit the TOA reflectance for UM in case of MC in clear and hazy skies.When the sky is hazy, no feasible value of τ a could be retrieved for LC.Although UM is more absorptive, the large scattered radiance from the inhomogeneous surface should be accounted for by the large or even no feasible , as compared to 12, when θ s , θ v and φ are 30°, 45° and 0°, respectively.
the case for CM.These results also explain the reason why the induced errors of retrieved AOD due to the rmses of ρ TOA by SACM are significant in hazy sky for UM, especially for MC, as mentioned above.This reveals the difficulty of aerosol remote sensing over urbanindustrial regions, where highly inhomogeneous surfaces exist with the small size of sparsely distributed DTs (Lyapustin et al. 2004).

CONCLUSIONS
In this study, the errors of retrieved AOD due to AE by the DT method for ROCSAT-2 RSI bands are investigated with aid of the fast and accurate SACM.Target size is considered the same as the spatial resolution.The results show that the induced error of retrieved AOD by SACM are negligible for CM in both skies as well as for UM in clear sky; however, they are significant in hazy sky for UM, especially for MC.AE becomes negligible if the inhomogeneous surface is not highly reflective; however, it may cause large RSE_AOD up to 100% and 55% for MC over DTs in clear and hazy skies in blue band for CM, as θ s and φ are 30° and 0°.RSE_AOD is larger for UM compared with CM, due to the lesser sensitivity of TOA reflectance to τ a .This suggests that AE be considered for MC in both skies, especially for urban- industrial regions.

Fig. 1 .
Fig. 1.Relative errors of retrieved aerosol optical depth δτ a / τ a (%) due to AE for different target reflectances ρ c and background reflectances ρ b in different VISs in the blue and red bands of ROCSAT-2 RSI for continental aerosol model.(a) and (b) are in the blue band; (c) and (d) are in the red band.VISs are 23 km in (a), (c) and 5 km in (b), (d).θ s , θ v and φ are 30°, 45° and 0°, respectively.

Fig. 2 .
Fig. 2. TOA reflectance as a function of τ a in blue band of ROCSAT-2 RSI.Solid and dashed curves (look-up tables (LUT)) and lines are for continental and urban aerosol models, respectively.LUTs are determined as ρ c = ρ b = 0.03.The labeled values of horizontal lines are TOA reflectances for different VISs and aerosol models for ρ c = 0.03 and ρ b = 0.12, when θ s , θ v and φ are 30°, 45° and 0°, respectively.