代写 graph statistic software Optik 124 (2013) 586–589

Optik 124 (2013) 586–589
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Topographic imaging simulation of optical remote sensing based on Landsat TM data
Hui-ping Qina,b,∗, Wei-ning Yib, Jin-ji Maa, Xu-xing Dinga, Xiang-bing Zhua
a Anhui Normal University, Wuhu 241000, Anhui, China
b Key Laboratory of Optical Calibration and Characterization, Chinese Academy of Science, Hefei 230031, Anhui, China
article info
Article history:
Received 26 August 2011 Accepted 20 December 2011
Keywords:
Topographic imaging simulation Mountain terrain
Look-up table
Digital elevation model
1. Introduction
Simulation of optical remote sensing imaging is widely used in civil and military applications with the quantitative development of optical remote sensing. The simulated data can be used to assess the parameters of new sensors and the influence of the imaging environment, and preprocess images, and so on. In optical remote sensing images, mountain terrain severely affects the image qual- ity as the sunlit surface receives much more irradiance than the shadow parts without considering the topographic effect. Many studies have focused on the topographic correction or the simu- lation of optical remote sensing imaging but not on topographic imaging simulation [1,2].
The topographic simulation of optical remote sens- ing actually simulates the sun–atmosphere–topographic surface–atmosphere–sensor process. In this study, the retrieved reflectance on the slope surface was corrected to the plane surface with the scs+c method. Then the corresponding irradiance on the slope surface at the imaging time was simulated and a look-up table was set up. Based on the retrieved reflectance and irradiance results, the reflected radiance on the pixel surface was calculated with a radiative transfer equation in which the directional char- acter was considered. The apparent radiance image at the sensor was the simulation result, which was the sum of reflected radiance and upward path radiance.
∗ Corresponding author at: Anhui Normal University, Wuhu 241000, Anhui, China. E-mail address: pinghui4600@sina.com (H.-p. Qin).
0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.12.058
abstract
In this study, topographic imaging simulation was realized based on the Landsat TM image and DEM data. Firstly, the surface reflectance was retrieved with the scs+c correction method. Secondly, the slope sur- face irradiance look-up table was set up by combining the radiative transfer equation and bi-directional reflectance ratio with the plane surface irradiance at different slopes, aspects, image acquisition times and elevations with 6 s radiative transfer software. Finally, the apparent radiance reaching at the sensor, cov- ering the Liaoning mountain terrain, was simulated at 8 am, 12 pm and 16 pm on 11 August, respectively.
© 2012 Elsevier GmbH. All rights reserved.
2. Methods
2.1. Data
A Landstat 7 TM image, acquired on 10 September 2007, which includes mountains, lake, forest and plane ground, was selected as the data source. The solar elevation angle and azimuth are 47◦and 147.7◦, respectively. The image was geocorrected precisely. The digital numbers were transformed to radiance using a linear cal- ibration equation. Gain and offset were acquired from the header files of the image. The DEM data with a resolution of 30m was acquired from the United States Geological Survey (USGS). It was registered with the Landsat image. The original image at band 4 and DEM data are shown in Figs. 1 and 2, respectively.
2.2. Terrainsurfacereflectanceretrieval
There are many empirical and physical topographic correction methods, such as cosine correction, statistical–empirical correc- tion, Minnaert correction, c correction, scs correction and scs+c correction [3]. The scs+c method was selected for its robust cor- rection effects and computational simplicity. The expression is:
cos Scos􏰖s +c
􏰕h=􏰕t cosi+c (1)
2.3. Terrainsurfaceirradiation
In terrain areas, the topography affects the illumination of the surface and causes energy redistribution so that spectra may be

Fig. 1. Original image at band 4.
different for the same class on different slopes and aspects. We considered the atmospheric scattering and adjacent effect quan- tificationally based on the scs+c model [4], and integrated the Proy radiative model [5] into the physical model of Sandmeier and Itten [6] by substituting the adjacent radiance for the initial adjacency effect. The revised physical model is written as:
irradiance were all calculated with 6 s radiative transfer software [7].
When the location is fixed, the total solar irradiance is related with the slope, aspect, time and elevation of the pixel. Various alti- tudes were used as inputs based on the DEM with an interval of 200 m [8]. An Eg look-up table of Lingyuan was set up at the orig- inal image acquisition time and simulation time. The irradiance corresponding to the original image at band 4 is shown in Fig. 3.
2.4. Radiationreflectedbyterrainsurface
For a given satellite band, assuming a Lambertian ground reflectance, the surface reflected radiance [9] can be calculated by
Lreflect = 􏰕hEg􏰙 (3) 􏰘
In fact, the actual pixel mixed with different objectives is non- Lambertian, especially the surface in the rugged terrain. Dymond and Shepherd [10], Wen et al. [12] and Cheng et al. [13] have induced a factor ˇ to calculate the surface reflectance based on the non-Lambertian assumption so that the reflected radiance could be expressed as:
[ˇ(􏰗EIh(cos i/cos 􏰖s cos S) + 􏰗EDh K(cos i/cos 􏰖s cos S)) + EDh (1 − K)Vd + Ea] Lreflect=􏰕h 􏰘
(4)
inwhichˇ=(cosi+cose)/(cos􏰖s +cos􏰖v).
When the irradiance look-up table corresponding to the pixels is
set up, and the reflectance on the plane surface is retrieved, the radi- ance reflected by the ground surface can be calculated according to Eq. (4).
2.5. Radiationreceivedbysensor
The radiance received by a sensor consists of three parts: path radiance Lp, radiance Lreflect reflected by objective pixel, and adja- cent reflected radiance. The adjacent radiance was ignored for its tiny effect and complex calculation process; then the radiance received by the sensor can be expressed as:
􏰙􏰕 Eg
L↑ =Lp +Lreflect =Lp + h (5)
H.-p. Qin et al. / Optik 124 (2013) 586–589 587
Eg = Ed + Ef + Ea
􏰃
cosi 􏰂 cosi
+Efh(1−k)Vd
=􏰗Edh + 􏰗Efhk cos􏰖s cosS
cos􏰖s cosS 􏰚􏰘LN cosTM cosTNdSN
(2)
+ d2
N MN
where Eg is the total solar irradiance on an slope surface; 􏰗 is a binary value with zero for a shaded pixel and 1 for a sunlit pixel; Ed, Ef and Ea are the direct, scattering and adjacent irradiance on a slope surface, respectively; Edh and Efh are the direct and scatter- ing irradiance on a plane surface, respectively; Vd is the sky-view factor; LN is the apparent radiance of pixel N reaching the satellite sensor; k is the anisotropy index; i and 􏰖s are the illumination and solar zenith angle, respectively; S is the slope.
The two-way transmittance of direct and scattering light, path radiance, the downwards sky scattering irradiance and the direct
Fig. 2. DEM data.
􏰘
3. Results
3.1. Correctionresult
Fig. 4 shows the topographic correction result. Fig. 4(a) is the cor- rected image. Fig. 4(b) is the scatter diagram of 400 points selected randomly. The scatter diagram shows the relationship between cor- rected reflectance and cosi, in which the linear relationship should be eliminated. In the visual, the three-dimensional effect is weak- ened in the corrected image than the original image. In Fig. 4(b), kh and ka are the slopes of the fitted lines, respectively. The linear coef- ficient between corrected reflectance and cosi is eliminated against the original image.
3.2. Simulationresult
Based on the correction results and the slope surface irradiance, the apparent radiance images were simulated at 8 am, 12 pm and 16pm on 11 August, respectively. The solar zenith and azimuth corresponding to the time are (59.6◦, 96.6◦), (26.6◦, 174.3◦) and (55.7◦, 259.5◦), respectively. The azimuth was set at zero in the true north and increased by degrees clockwise in this study. The simulation results are shown in Fig. 5, in which the RGB image was merged together with second three bands of TM image.

588 H.-p. Qin et al. / Optik 124 (2013) 586–589
Fig. 3. Terrain surface irradiance at imaging time and simulating time: (a) irradiance of original image; (b) irradiance at 8 am on 11 August; (c) irradiance at 12 pm on 11 August; (d) irradiance at 16 pm on 11 August.
4. Discussionandconclusion
In rugged terrains, topography affects both the surface irradi- ance and the reflected radiance. The real reflectance of objects was retrieved by reducing the three-dimension effects and the reflectance distortion with topographic correction method. The irradiance on the slope object, considering the atmospheric
scattering and the adjacent effect, finally was simulated at the image acquisition time. According to the corrected reflectance and simulated irradiance, the radiance at the sensor was achieved.
In conclusion, the simulation model presented in this study achieved satisfactory results that the simulated image factually described the specific topographic characteristics and differences
Fig. 4. Scs+c correction result of TM at band 4: (a) corrected image and (b) scatter diagram of 400 pixels.

H.-p. Qin et al. / Optik 124 (2013) 586–589 589
Fig.5. OriginalRGBimageandsimulatedRGBresultsofTMon11August:(a)originalRGBimage;(b)simulationresultat8am;(c)simulationresultat12pm;(d)simulation result at 16 pm.
of the image at different solar angles. The result allows us to draw the conclusion that topographic imaging simulation can be used to get the simulation image at any time for sensor quality evaluation and image preprocessing.
But there are some approximations in this paper. For exam- ple, the atmospheric parameters in radiative transfer software 6 s, such as model atmosphere, water vapour, aerosols, which were estimated values on the day of image acquisition, would reduce the accuracy of the simulation. The scs+c topographic correc- tion method did not quantificationally consider the atmospheric scattering and adjacent irradiance. Meanwhile, the calculation of radiance at the sensor which did not consider the adjacent reflected radiance also induced errors. Although a DEM smoothing was intro- duced to achieve better results, some errors could not be totally avoided. There are some errors caused by the image registration, low resolution or mismatch of the resolution of the DEM with the imagery. All these need to be improved to raise the accuracy of simulation.
Acknowledgements
This work was supported by Anhui Provincial Key Sci- ence Foundation for Outstanding Young Talent under Grant No. 2012SQRL029ZD, Anhui normal university innovation fund under Grant No. 2011cxjj09 and the Anhui Province natural science foun- dation under Grant No.090414173.
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