an atmospheric correction algorithm for the flex/s3 tandem mission.

AN ATMOSPHERIC CORRECTION ALGORITHM FOR THE FLEX/S3 TANDEM MISSION. N. Sabater(1), J. Vicent(1), L. Alonso(1) , J. Verrest(1) and J. Moreno(1) (1)

Image Processing Laboratory (IPL), University of Valencia (SPAIN), Email:[email protected]

ABSTRACT A new atmospheric correction algorithm is proposed to support data analysis from the ESA’s 8th Earth Explorer Fluorescence EXplorer (FLEX) candidate mission. The Fluorescence Imaging Spectrometer (FLORIS) on board FLEX covers, with a very high spectral resolution, a narrow spectral range, from 500 nm to 780 nm, ideal for vegetation fluorescence detection but insufficient for atmospheric characterization. For this reason, FLEX is planned as a tandem mission with Sentinel-3 (S3). Therefore, to perform the FLEX atmospheric correction, atmospheric parameters such as aerosol optical properties and water vapour content will be estimated from S3 data. Once the atmospheric state has been characterized, a second step deals with the retrieval of surface apparent reflectance, i.e. the surface reflectance modified by the fluorescence radiance emission. The first part of this paper is dedicated to the description of the method, summarising the main steps in the atmospheric characterization and in the succeeding surface apparent reflectance retrieval. In the second part of the paper, different databases have been simulated covering a wide range of atmospheric and surface reflectance properties to show accuracy obtained with the methodology proposed, especially over O2 absorption band spectral regions. The validation task is developed by comparing apparent reflectance retrieved from the atmospheric correction algorithm and those obtained using atmospheric parameters defined in the database creation. In addition, to demonstrate that accuracy obtained from the atmospheric correction is enough to provide a precise chlorophyll fluorescence retrieval, a first fluorescence estimation have been performed for all the cases covered by the simulated databases. 1.

INTRODUCTION

Top of Atmosphere (TOA) radiances acquired by passive optical Earth observation satellites are highly influenced by the presence of atmosphere. The atmospheric correction process, which tries to retrieve the surface reflectance by removing the atmospheric effects, is essential to study and obtain information related to the surface properties. In case of the FLEX mission, this process becomes even more crucial. Thus, the accuracy obtained by the fluorescence retrieval will strongly depend on accuracy achieved by the atmospheric correction. In addition, the low magnitude of the solarinduced chlorophyll fluorescence emitted radiance in

comparison to the reflected radiation makes the process rapidly prone to errors. FLEX’ main payload is the Fluorescence Imaging Spectrometer (FLORIS) instrument. FLORIS has been especially designed to measure the fluorescence signal and focusses on the O2-B and the O2-A absorption bands. Although FLORIS’ exceptional capabilities to measure the fluorescence signal, its spectral range (from 500 nm to 780 nm), however, is insufficient to extract information about the atmosphere and perform an accurate atmospheric correction of the acquired images. To overcome this limitation, FLEX is envisaged to fly as a tandem mission with ESA's Copernicus mission Sentinel-3 (S3). S3 is equipped with the Ocean and Land Colour Imaging spectrometer (OLCI), covering from 400 nm to 1020 nm, and the Sea and Land Surface Temperature Radiometer (SLSTR), covering from the 550 nm to 12 µm with two different viewing angles thanks to its conical scanning. These sensors will provide the information needed to characterize the atmosphere. This paper will describe the proposed atmospheric correction algorithm to process FLORIS data from TOA radiance down to surface apparent reflectance. To that end, atmospheric correction algorithm will make use of S3 data in order to characterize the atmospheric state. Furthermore, different simulated databases showing supportive results related with the accuracy obtained in atmospheric correction, especially at O2-A and O2-B regions, and surface reflectance and fluorescence spectra obtained as final product will be presented. 2.

ATMOSPHERIC CORRECTION ALGORITHM

The presented atmospheric correction scheme is essentially an improved version of the atmospheric correction algorithm originally developed for the Medium Resolution Imaging Spectrometer (MERIS) and the Advanced Along Track Scanning Radiometer (AATSR)[1], predecessors of S3, OLCI and SLSTR instruments. The proposed method relies on the inversion of the parameters that characterizes the atmospheric status by making use of previously computed atmospheric Look-Up-Tables (LUTs) without using any prior information. The well-known MODerate resolution atmospheric TRANsmittance and radiance code (MODTRAN5) was selected to build the LUTs. In all generality, assuming knowledge of viewing and illumination geometry, TOA radiance is modelled by two

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atmospheric components outlined below, being (1) the aerosols load and (2) the columnar water vapour content. Assuming a Lambertian approach, TOA radiance can be described by means of Eq. 1.

2

𝑁

1 2 𝛿𝜆 = ∑ [ ∑ ∑ 𝜑(𝐿𝑆𝐿𝑆𝑇𝑅 − 𝐿𝑆𝐿𝑆𝑇𝑅 𝑠𝑒𝑛 𝑠𝑖𝑚 ) 𝑁 𝑝𝑖𝑥

Ω

(2)

𝜆

𝑀

𝐿 𝑇𝑂𝐴 = 𝐿0 +

(𝐸𝑑𝑖𝑟 𝜇𝑖𝑙 +𝐸𝑑𝑖𝑓 )𝑇↑𝜌𝑎𝑝𝑝 𝜋(1−𝑆𝜌)

(1)

where 𝐿0 is the path radiance, 𝐸𝑑𝑖𝑟 and 𝐸𝑑𝑖𝑓 are the irradiance directly and diffusely transmitted from the sun to canopy level, 𝜇𝑖𝑙 is the cosine of the illumination angle, i.e. the solar zenith angle (𝜃) modified by surface topography, 𝑇 ↑ is the total transmittance, both direct and diffuse, from target to sensor, S is the spherical albedo, and finally 𝜌 and 𝜌𝑎𝑝𝑝 are surface reflectance and surface apparent reflectance respectively. The 𝜌 term in Eq. 1 can be assumed as 𝜌𝑎𝑝𝑝 . This approximation have a low impact both in the atmospheric characterization and in the surface apparent reflectance retrieval and decreases the number of unknown variables. Then, once the atmospheric state is known, an inversion process will provide with the surface apparent reflectance spectrum from TOA radiance. 2.1.

1 𝑂𝐿𝐶𝐼 2 + ∑ 𝜔 (𝐿𝑂𝐿𝐶𝐼 𝑠𝑒𝑛 − 𝐿𝑠𝑖𝑚 ) ] 𝑀 𝜆

where 𝑁 and 𝑀 are the number of bands in SLSTR, not including thermal bands, and OLCI sensors respectively, Ω refers to the dual viewing angle of SLSTR, 𝜑 and 𝜔 are weighting functions defined as ~ 1⁄𝜆2 according to each sensor configuration bands, 𝐿𝑠𝑒𝑛 are OLCI and SLSTR nadir and oblique viewing angle TOA radiances, and 𝐿𝑠𝑖𝑚 are the corresponding simulated TOA radiances for each sensor.

Aerosols optical properties characterization

Generally, atmospheric correction algorithms based on LUTs inversion assume that aerosols model, e.g. urban, rural, maritime, etc., is known, and only Aerosols Optical Thickness (𝜏𝜆 ) is the variable inverted. This fact discretizes the LUT into the limited aerosol types whose optical properties do not necessarily match those of the aerosols in the acquired image [2]. The aerosol retrieval method presented here will instead parameterize the aerosol optical properties through the following variables: Aerosol Optical Thickness at 550 nm (𝜏550 ), Angstrom coefficient (𝛼), and Henyey-Greenstein (HG) (g) parameter of the scattering phase function. First, 𝜏550 represents the aerosol content in the atmosphere. Secondly, the Angstrom law through the Angstrom coefficient models the wavelength dependency of the 𝜏𝜆 (𝛼). Finally, the aerosol scattering isotropy is approximated by the HG phase function through its parameter (g). HG phase function is commonly used in radiative transfer calculation due its simplicity. Nevertheless, other scattering phase functions, as provided by Mie theory, offers a more realistic description of light scattering [3]. In this case, data provided by S3, accordingly to its acquisition geometry, is not sufficient to totally characterize the scattering pattern. Due to that and the fact that FLEX is not dedicated to atmospheric studies, it is not worth using a complex scattering theory to characterize the aerosols optical properties. The aerosol optical properties retrieval is subsequently based on an iterative process Figure 1 that minimizes the cost function Eq. 2.

Figure 1 Aerosols optical properties retrieval scheme iterative process. First iteration is exclusively dedicated to estimate the g parameter value, i.e. to characterize the scattering phase function isotropy. Once and approach for g is obtained, second and third iterations will lead to find AOT and 𝛼 values. This last step, second and third iteration, is a repetitive process that finishes when the AOT value keep stable between successive iterations. In addition, a refinement of g value is performed as part of this second iterative process. Moreover, while atmospheric properties remain nearly constant for wide areas, surface properties tend to present a more heterogeneous spatial pattern. This natural contrast is then introduced mathematically as a boundary condition. Thus, pixels included in the minimization cost function summation of Eq. 2, must be selected to be representative of the diversity in surface reflectance while atmospheric conditions are fixed. Therefore, taking into account 𝐿𝑠𝑖𝑚 dependency, several approximations are introduced to calculate and minimize the cost function of Eq. 2. - To estimate surface reflectance an auxiliary reflectance spectra database is used. This database stores a wide variety of spectra from bare soil, different vegetation types to synthetic materials and water. Surface


-

2.2.

reflectance spectrum will be one which minimize the cost function (Eq.2). The absorption feature of water vapour can be neglected out of the water vapour absorption bands. So, a standard value of water vapour content is assumed during this part of the algorithm.

2.3.

Then, the final expression used to obtain apparent reflectance is Eq.4.: 𝜆𝑓

𝐿 𝑇𝑂𝐴 = ∫ (𝐿0 ∗ 𝑓)𝑑𝜆 𝜆𝑖

Apparent reflectance retrieval.

Once the atmospheric state has been characterized, it is necessary to invert the reflectance spectrum from the TOA radiance expression. However, the expression in Eq. 1 cannot be used to derive surface reflectance. Since mathematically the product of convolutions differs from the convolution of products, i.e. 〈𝑎 ∗ 𝑏〉 ≠ 〈𝑎〉 ∗ 〈𝑏〉, the Taylor expansion of Eq. 1 will be calculated until first order Eq.4. Additionally, a mathematical magnitude, the “apparent reflectance”, i.e. true reflectance modified by fluorescence emission, is defined as Eq.3. 𝜌𝑎𝑝𝑝 = 𝜌 +

𝜋𝐹 𝐸𝑇𝑂𝐶

(3)

where 𝜌𝑎𝑝𝑝 and 𝜌 are apparent and true reflectance respectively, F is fluorescence radiance and 𝐸𝑇𝑂𝐶 is total irradiance at TOC. Therefore, two approximations are assumed to obtain surface apparent reflectance.  Performing the Taylor expansion of TOA radiance expression from Eq.1.  Assuming all the surface reflectance terms of Eq.1 equal to surface apparent reflectance. This approach has a low impact in the solutions and simplify the number of unknown variables.

𝜆𝑓

+ ∫ (𝜋𝑇𝐸𝑇𝑂𝐶 𝜌𝑎𝑝𝑝 ∗ 𝑓)𝑑𝜆

(4)

𝜆𝑖 𝜆𝑓

Columnar water vapour retrieval algorithm.

The Columnar Water Vapour (CWV) is derived based on a differential absorption technique using OLCI data [4]. In essence, differential absorption techniques 𝐿 calculates the ratio 𝑅 = 𝑜𝑢𝑡⁄𝐿 between radiances 𝑖𝑛 inside (𝐿𝑖𝑛 ) and outside (𝐿𝑜𝑢𝑡 ) the water vapour absorption band. Particularly, in OLCI this ratio is calculated at 940 nm. While 𝐿𝑖𝑛 is directly TOA radiance acquired inside the absorption band, 𝐿𝑜𝑢𝑡 is obtained by linear regression from the reference channels, i.e. channels close to the absorption band but not affected by it. The CWV is retrieved by a LUT inversion, using Brent’s method to minimize the cost-function between the sensed and simulated ratios 𝜒 = 𝑅𝑠𝑖𝑚 − 𝑅𝑠𝑒𝑛 . The simulated ratio uses the previously derived aerosol properties and approximates the surface reflectance in the measurement spectral channel as a linear interpolation between the reference channels. The retrieval is done on a pixel-wise basis due to the high spatial variability of this parameter.

3

2 + ∫ (𝜋𝑇𝐸𝑇𝑂𝐶 𝑆𝜌𝑎𝑝𝑝 ∗ 𝑓)𝑑𝜆 𝜆𝑖

Where f is the Instrumental Spectral response Function (ISRF). 3.

SIMULATED DATABASES

In order to test the developed algorithm, two different simulated databases, DB1 and DB2, of 240 images each have been created. Simulations have been performed by coupling two radiative transfer codes. One at surface level, being the Soil Canopy Energy Balance (SCOPE)[5], which gives surface reflectance and fluorescence, and MODTRAN5 at the atmosphere level. Coupling these two codes, taking into account the adjacency and the BRDF effects of surface reflectance, the simulated data have been derived using the procedure described in [6]. In this way, canopy reflectance spectra and associated fluorescence signals can be characterized by configuring several biophysical parameters such as leaf chlorophyll content and Leaf Area Index (LAI) and photosynthesis parameters. For the atmospheric characterization, several input parameters have been considered: e.g., the atmospheric temperature profile, the aerosols optical properties, the Columnar Water Vapour (CWV), etc. Figure 2 shows a schematic description of databases basic structure. In each DB, five different surface reflectance and fluorescence spectra have been simulated remaining identical in the 240 different atmospheric cases covered. Then, to study the impact of reducing the surface reflectance heterogeneity, DB1 covers from bare soil to dense vegetation spectra while DB2 only considers spectra from vegetation. Vegetation scenes have an especial interest for FLEX mission objectives.

Figure 2. Schematic view of databases structure. Both DBs cover 240 different atmospheric cases. DB1 include


4

bare soil spectrum. DB2 only contains vegetation spectra. In addition, Figure 3 summarizes surface reflectance spectra used in DB1 and DB 2.

Figure 4 Errors in HG parameter retrieval (scattering phase function definition) and subsequent errors in O2apparent reflectance. Errors are estimated as the difference between real and retrieved magnitude. Figure 3 Surface reflectance spectra used in the simulation of DB1 and DB2. Black spectra corresponds to VEG1, VEG2, VEG3 and VEG4 common in both databases. Bare soil and VEG0 are highlighted in different colors. In Tab. 1 atmospheric input values of the generated atmospheric LUTs are summarized.

Variable

𝜏550

𝛼 g 𝐶𝑊𝑉 SZA VZA RAA 𝐸𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 Model atmosphere

Value 0.05-0.16-0.25 0.79-1.39-1.54-1.74-2.5 0.4-0.75-08-0.9 1.2-2.4(𝑔⁄𝑐𝑚2 ) 45° 0,55° 0° (100-1500)m Mid Latitude Summer

Table 1. Summary of database atmospheric properties. Now, only one vertical temperature profile has been considered in simulated DBs being a limitation in the test study. In future DBs more atmospheric vertical profiles will be included. 4.

RESULTS

In this section, results obtained from the atmospheric correction and from the fluorescence retrieval are presented. On one hand, relative errors in the scattering phase function estimation and the subsequent errors in the apparent reflectance for the O2-A region from DB1 are shown in Figure 4. It can be highlighted how the worse estimation of the scattering phase function parameter, g, leads to the worse accuracy in apparent reflectance. The high impact of this parameter makes necessary a first iteration especially dedicated to approach the g parameter before retrieving the other optical parameters, see Figure 1.

In addition, CWV values obtained from DB1 are summarized in Figure 5. It can be observed a better accuracy obtained from pixel 1 in DB1, corresponding to a bare soil spectrum, compared with the rest of pixels (vegetated spectra). The reason of this behaviour is explained by the approach assumed to define reflectance inside water vapour absorption band. At 940nm, deep inside the absorption band, reflectance is estimated as a linear regression of reflectance in reference bands. While bare soil reflectance shows a linear trend in this spectral region, vegetated spectra will move away from linear behaviour as leaf liquid water content increases. Despite these approximations assumed, errors in the water vapour retrieval are below 2% in all cases. A comparison between apparent reflectance spectra obtained from atmospheric correction and theoretic apparent reflectance is shown in Figure 6. In this figure, errors obtained in O2-A and O2-B regions have been calculated as a mean difference between retrieved and theoretical apparent reflectance. In addition, to show the impact of reducing surface spectra heterogeneity, from DB1 to DB2, Figure 6 shows errors obtained in DB1 as shadowed areas indicating the highest and the lowest limits together with errors achieved in DB2. In addition, it must be indicated that theoretic apparent reflectance have been obtained doing the inversion fixing the atmospheric parameters to the ones that were used as input in the simulation.


5

Figure 5 Columnar water vapor retrieval results showed as a boxplot from DB1.

Figure 7 Apparent reflectance spectra obtained from the atmospheric correction algorithm. (a) Worst case, (b) Best case.

Figure 6 Apparent reflectance errors obtained in O2-A and O2-B regions from DB2. Shadowed areas indicate the highest and lowest limit of errors from DB1. Furthermore, apparent reflectance spectra from two extreme cases, the worst and the best atmospheric correction performance are plotted in Figure 7. Noise simulation has been included according to the technical specifications of FLORIS instrument [7]. Finally, fluorescence first estimation inside O2-A and O2B regions have been performed to show the impact in fluorescence of errors committed in atmospheric correction. It must be taken into account that results from fluorescence showed in Figure 8 are only a first order estimation of fluorescence and not corresponds with the full fluorescence spectrum that will be provided by FLEX full retrieval algorithm.

Figure 8 Boxplot of fluorescence first estimation for O2A and O2-B absorption bands. It can be seen that fluorescence values obtained deep inside the absorption bands for all cases matches considerably well with input fluorescence values used in the simulation. Due to the high sensibility of fluorescence retrieval to errors caused by in atmospheric correction, errors in apparent reflectance below 4% in O2-A and 10% in O2-B seems to indicated a good first estimation in fluorescence.


5.

photosynthesis, fluorescence, temperature and energy balance,” Biogeosciences Discuss., vol. 6, no. 3, pp. 6025–6075, Jun. 2009.

CONCLUSSIONS

An atmospheric correction algorithm for the FLEX/S3 tandem mission has been presented in this work. Many encompassing aspects make it efficient and autonomous. First, there is no need for using additional or external information. By using only TOA radiances from a combination of instruments, the algorithm is able to characterize the atmosphere. Information provided by S3 sensor is essential to fully characterize the atmospheric state. Secondly, there is no need to perform a previous aerosol model classification. Aerosols will be defined by their optical properties, i.e. 𝜏𝜆 , 𝛼 and g which will be retrieved by the algorithm. Thirdly and finally, the accuracy achieved by the atmospheric correction algorithm proposed seems to guarantee a good estimation of subsequent fluorescence retrieval from the FLEX mission. ACKNOWLEDGMENTS This work has been supported by ESA’s Tandem Mission Performance Analysis and Requirements Consolidation Study (PARCS) 4000105078/11/NL/AF project and by the Spanish Ministry for Science and Innovation under the project AYA2010-21432-C02-01. REFERENCES [1]

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