Land surface reflectance retrieval from optical hyperspectral data collected with an unmanned aerial vehicle platform

Yao-Kai Liu; Chuan-Rong Li; Ling-Ling Ma; Yong-Gang Qian; Ning Wang; Cai-Xia Gao; Ling-Li Tang

doi:10.1364/OE.27.007174

1. Introduction

Satellite-based hyperspectral remote sensing techniques have been widely used on global and large-scale environmental monitoring and management applications [1–4]. However, it must be noted that the coarse spatial resolution of satellite hyperspectral remote sensing data limits the application fields in some cases, such as in precision agriculture and forestry, where finer spatial resolutions are required. Fortunately, civilian applications of unmanned aerial vehicles (UAVs) have been increasing and have been widely used in recent years, which provide an alternative to meeting the demands of finer spatial and temporal resolution owing to the advantages of flexibility, low cost, time efficiency and, most of the all, finer spatial and temporal resolutions for different applications [5]. Recently, hyperspectral sensors carried on UAVs to collect hyperspectral images have been widely used in the fields such as agriculture and forestry [6–8]. However, accurate removal of the atmospheric contributions from the observed signal by the spectrometers to retrieve the surface reflectance is usually the first step when the acquired hyperspectral data are used to study the surface properties and further applications, which is also known as the process of atmospheric correction [9].

The land surface reflectance usually defines as the ratio of radiance leaving the surface in a finite solid angle in the viewing direction to the radiance from a perfect Lambertian reflector under the same illumination conditions as the target. And, many hyperspectral atmospheric correction algorithms have been developed to retrieve the reflectance of surfaces from hyperspectral data during the past two decades. From reviewing the literature, most of the hyperspectral atmospheric correction algorithms can be classified into two categories: empirical atmospheric correction methods and radiative transfer modelling methods [10,11]. The usually used empirical atmospheric correction methods include the flat-field correction method [12], the empirical line method [13] and the cloud shadow methods [14,15]. It is not necessary to conduct the absolute radiometric calibrations of the hyperspectral data when using these empirical methods to estimate the surface reflectance [11]. However, these methods were proved to be strongly dependent on the landscape of the earth’s surface over the duration of the data acquisition [16]. Atmospheric correction methods based on radiative transfer modelling were introduced to estimate the surface reflectance from the at-sensor hyperspectral radiance for decades [17–19]. However, a physical-based algorithm with the radiative transfer model must provide accurate atmospheric components. Additionally, the highest optically active atmospheric components in the solar spectrum range are aerosols and water vapor [9]. In a general situation, there is no available aerosol and water vapor information synchronized with the acquisition of UAV hyperspectral images. Therefore, algorithms for aerosol optical thickness @550 nm (AOT @550 nm) and columnar water vapor (CWV) estimation from the hyperspectral data must be incorporated into atmospheric radiative transfer code to simulate the atmospheric interaction with the solar radiation [19,20].

In this study, we present a physical-based atmospheric correction algorithm for land surface reflectance retrieval based on radiative transfer model MODTRAN 5, with which the aerosol optical thickness@550nm (AOT@550 nm), columnar water vapor (CWV) could also be estimated from the hyperspectral data collected over UAV platform. The study area and data sets are described fully in section 2. Then, the methodology of the AOT@550 nm and CWV atmospheric parameters and land surface reflectance are described in section 3. The results and discussion on the physical-based algorithm applied to synthetic and UAV on-board spectrometer collected hyperspectral data are presented in section 4. Finally, conclusions are drawn in section 5.

2. Study area and data sets

2.1 Study area and field campaign description

The study area was located in the Urad Qianqi (40.88°N, 109.53°E), Inner Mongolia in north China with an average elevation above sea level of approximately 1270 m. The climate of our study area is cold semi-arid with temperatures that range from minus 15 degrees centigrade in winter to 30 degrees centigrade in summer. Additionally, the annual rainfall is approximately 300 mm from spring to summer. The area is mainly covered by economic crops (such as potato, sorghum, maize, sunflowers) and sparse vegetation, which make it quite suitable for remote sensing calibration and validation.

A field campaign organized by Academy of Opto-Electronics, Chinese Academy of Sciences had been carried out at our study area on 3 September, 2011. The aims of the field campaign is to assess the radiometric and spectral calibration performance of the hyper-spectrometer loaded on an UAV platform, which is a part of the “National High Technology Research and Development Program” (also abbreviated to “863” Plan).

2.2 UAV-VNIRIS hyperspectral data

During the field campaign on 3 September 2011, an UAV-VNIRIS sensor was mounted an UAV platform, which was developed to carry payloads for remote sensing applications by the Research Institute of Unmanned Flight Vehicle Design, Beihang University, China. The UAV-VNIRIS hyperspectral data with a spatial resolution of 0.7 m were acquired by the UAV-VNIRIS sensor at approximately 3.5 km altitude above ground level (AGL). Figure 1 shows a subset of the RGB true-color image (RGB corresponding to band 50, band 30 and band 15, respectively) from the center of the UAV-VNIRIS hyperspectral data collected at 06:42 UTC on September 3, 2011. It can be seen from Fig. 1 that fifteen color targets (M1 to M15) with 7 m × 7 m size, four grey targets (R1 to R4) with 15 m × 15 m size, and four hyperspectral targets (H1 to H4) with 15 m × 15 m size were designed, which were used to radiometrically calibrate the hyperspectral data. Additionally, the fan-shaped and three-line white-black targets were designed to evaluate the resolution of the hyperspectral data. The hyperspectral targets were used to validate the retrieved land surface reflectance results from the hyperspectral data. The UAV-VNIRIS sensor is a push-broom scanner that utilizes linear charge-coupled device sensors developed by Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. The sensor covers the visible and near-infrared spectral region from 400 nm to 1000 nm with 128 near-contiguous spectral bands. However, for the UAV-VNIRIS band configuration, channels from 1 to 12 and from 109 to 128 will not be used in our study due to the low signal-to-noise ratios reported by Duan et al. [21]. Therefore, only 96 bands, from channels 13 to 108, will be kept in our methods. Table 1 shows the detailed information on the UAV-VNIRIS sensor.

Fig. 1 A subset of the RGB true-colour image from the UAV-VNIRIS airborne optical hyperspectral data collected at 06:42 UTC on September 3, 2011.

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Table 1. The specification of the UAV-VNIRIS sensor.

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The acquired UAV-VNIRIS hyperspectral data were processed while applying systematic geometric correction, spectral and absolute radiometric calibration. The systematic geometric correction was conducted based on the Global Positioning System and Inertial Measurement Unit (GPS/IMU) data acquired over the flight. A geometric accurate correction was not applied to our used hyperspectral data to maintain the original radiometric information of the hyperspectral data. Absolute radiometric calibration was conducted based on the measured reflectance of the artificial targets and atmospheric parameters [22].

2.3 In situ measurements

In addition to the UAV inflight hyperspectral data, in situ measurements acquired during the field experiment and campaign were used to radiometric calibrate the hyperspectral data and validate the retrieved atmospheric and land surface reflectance results. The in situ measurements include land surface reflectance of the artificial targets and agricultural crops and the aerosol optical thickness, columnar water vapor. Data sets of the land surface reflectance of the artificial targets and agricultural crops were measured before and after the UAV overflight of our study area, within half an hour. The reflected radiance of each of the artificial and natural targets was measured several times using an SVC HR-1024 field portable spectroradiometer (Spectra Vista Corporation (SVC), Poughkeepsie, NY, USA) first. In addition, the reflected radiance of a library-calibrated reference panel was also measured along with the measurements of each of the targets. Then, the land surface reflectance spectra were calculated with the targets and reference panel measurements. Finally, the average land surface reflectance of each artificial target and agriculture crop was calculated from these measurements. All of the acquired surface reflectance values of the artificial and natural targets will be used to radiometrically calibrate the hyperspectral data and validate the retrieved surface reflectance results from the UAV-VNIRIS hyperspectral data.

Measurements of the solar irradiance were also collected during the UAV overflight of our study area by using an automatic sun-tracking photometer CE318 (CIMEL Electronique, Paris, France). The measured solar irradiance was used to calculate the instantaneous aerosol optical thickness and columnar water vapor atmospheric parameters by using a CE318 software package. Figure 2 shows the instantaneous AOT@550 nm, which were estimated from the derived AOT at 340 nm, 380 nm, 440 nm, 550 nm, 670 nm, 870 nm, 1020 nm and 1640 nm. At the same time, the instantaneous CWV was calculated from the solar radiometer measurements at the 936 nm channel as showed in Fig. 3. Finally, the AOT@550 nm and CWV at the time of the UAV overpass of the artificial targets and agriculture crops area were interpolated from the instantaneous AOT@550 nm and CWV. The interpolated AOT@550 nm and CWV is 0.1724 and 1.6964 g/cm², respectively. Both the retrieved AOT@550 nm and CWV based on the CE318 measurements were used to validate the retrieved AOT@550 nm and CWV results from the UAV-VNIRIS hyperspectral data.

Fig. 2 Retrieved AOT at 340nm, 380nm, 440nm, 500nm, 550nm 670nm, 870nm, 1020nm and 1640nm from the automatic sun tracking photometer CE318 measurements on September 3, 2011.

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Fig. 3 Retrieved CWV based on the automatic sun tracking photometer CE318 measured solar irradiance at 936nm.

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3. Methodology

3.1 Theory of physical-based atmospheric correction approach

As has been demonstrated in many research studies [23,24], the radiative transfer modelling method usually results in the best atmospheric correction accuracy in the case of fine-calibrated hyper-spectrometers. Thus, the physical-based atmospheric correction approach with radiative transfer modelling theory will also be adopted here to derive the atmospheric parameters and land surface reflectance. Assuming that the surface is uniform and Lambertian under a horizontally homogeneous atmosphere, the top-of-atmosphere (TOA) radiance observed by the sensors can be expressed by the classic radiative transfer Eq. as in Eq. (1) [25]:

L_{T O A} (λ) = L_{p a t h} (λ) + \frac{ρ_{s} (λ)}{π (1 - ρ_{s} (λ) S (λ))} μ_{s} E_{s} (λ) τ (μ_{s}) τ (μ_{v})

Here, $L_{T O A} (λ)$ is the at-sensor spectral radiance with units W/m²/sr/μm; $L_{p a t h} (λ)$ is the path radiance with units W/m²/sr/μm; $E_{s} (λ)$ is the solar irradiance W/m²/μm; $ρ_{s} (λ)$ is the surface reflectance; $τ (μ_{s})$ is the total transmittance from the sun to surface, which is a function of solar zenith angle; $τ (μ_{v})$ is the total transmittance from the surface to sensor, which is a function of sensor observing zenith angle; $μ_{s}$ and $μ_{v}$ are the cosine values of the sun and viewing zenith angles, respectively; and $S$ is the atmospheric spherical albedo.

It can be explained from Eq. (1) that the radiance at the sensor is composed of two different contributions: the path radiance scattered by the atmospheric molecular and aerosol and the transmitted radiance reflected from the observed land surface. In other words, the hyperspectral sensor observed radiance expressed by Eq. (1) is a function of both atmospheric and land surface reflectance parameters. Therefore, the decoupling of the atmosphere and land surface contributions is essential to estimate both the atmospheric parameters and surface reflectance from the hyperspectral sensor observed radiance. Typically, the atmospheric parameters AOT@550 nm and CWV can be retrieved from the observed hyperspectral data once the surface reflectance characteristics are determined. In contrast, the land surface reflectance can also be retrieved from the observed hyperspectral data if the atmospheric characteristics are given. This approach is the basic theory of atmospheric parameters and land surface reflectance retrieval from optical hyperspectral data. Therefore, two steps should be conducted of the physical-based atmospheric correction approach. First, the atmospheric parameters AOT@550 nm and CWV should be retrieved from UAV hyperspectral data. Then, the land surface reflectance will be derived from the hyperspectral data based on the retrieved atmospheric parameters with a radiative transfer code. Usually, radiative transfer codes such as MODTRAN and 6S are used to make accurate simulations of the radiative transfer modelling. The MODTRAN 5 radiative transfer code was used in this study because of its finer spectral resolution [26].

3.2 Retrieval of atmospheric parameters

The absorption of gases and the aerosol scattering in the TOA radiances must be considered when addressing the atmospheric correction of the hyperspectral remote sensing data. The solar radiation in the soar spectrum on the atmospheric path is subject to absorption by the atmosphere molecules including water vapor, ozone, oxygen and carbon dioxide, which should be carefully considered during the atmospheric correction of hyperspectral data [11]. However, default values of the MODTRAN 5 are used for the ozone and oxygen column content in this study due to its low spatial and temporal variability [27]. With regard to the aerosol scattering, the aerosol optical thickness, angstrom coefficient and refractive index have usually been used for characteristics of the aerosol loading. However, AOT@550 nm has been widely used to characterise the total aerosol content in remote sensing applications [27]. Therefore, it is very important to measure the AOT @550 nm and CWV using ground-based sun photometers during the overpass of the space-borne or airborne spectrometers in order to perform an accurate atmospheric correction. However, it is very impractical to measure these two temporally (also can be demonstrated from Fig. 2 and Fig. 3) and spatially highly variable atmospheric parameters over a large scale area with ground limited sun photometers [20]. Thus, it is essential to estimate the AOT@550 nm and CWV from the hyperspectral data information instead of using simultaneous ground-based measurements over the image acquisitions. For this study, the AOT@550 nm was estimated first based on the collected radiance data in the visible and near infrared region without water vapor, and then, the CWV was estimated in the water vapor absorption bands. Two reasons can be used to explain the determination, as follows. First, the CWV can be assumed to be a constant when estimating the AOT@550 nm in the non-water vapor absorption channels since the hyperspectral sensor observed radiance is not influenced by the changes in the water vapor in these channels. Second, the AOT could have a significant influence on the retrieval of CWV in the channels where the water vapor absorption occurs [9,28,29].

(1) Aerosol optical thickness retrieval
It can be known from the radiative transfer modelling theory in section 3.1 that there are two prerequisites to retrieving the AOT@550 nm from the UAV-VNIRIS hyperspectral data. First, the land surface reflectance of the pixels selected to retrieve the AOT@550 nm should be very low in order to reduce the reflectance influence on the AOT@550 nm inversion. Second, the land surface reflectance of the selected pixels should be estimated accurately. Based on these two prerequisites, some methods have been developed to estimate the AOT@550 nm from the remote sensing data in recent years. For example, Kaufman proposed the classic dense dark vegetation (DDV) method to estimate the AOT@550 nm from the MODIS remote sensing data by assuming an empirical relationship between the visible and shortwave infrared channels [30]. However, the DDV method is limited to the remote sensing data that include the 2.1 μm band, assuming that the observed data in the 2.1 μm band is not affected by the atmospheric effect, which is not strictly satisfied, especially for atmospheric conditions with heavy aerosols. Therefore, the DDV method developed by Kaufman is improved in this paper to estimate the AOT@550 nm from the hyperspectral data while only covering visible and near infrared wavelengths. First of all, thresholds of ratio vegetation index (RVI) and multiple TOA reflectance were adopted here to determine the DDV pixels [31]. However, the TOA reflectance instead of land surface reflectance was used to calculate the RVI, which defines as ratio of the near-infrared and red TOA reflectance (RVI = ρ_nir /ρ_red). Pixels satisfy the condition expressed as RVI≥3 and 0.1≤ρ_nir≤0.25 and ρ_red≤0.04 will be determined as DDV pixels. Then, a linear relationship of the land surface reflectance in the red and blue channels for the DDV pixels can be expressed as Eq. (2).
$ρ_{s}^{r e d} = k \cdot ρ_{s}^{b l u e}$
Here, $k$ is a ratio coefficient between the land surface reflectance in the red and blue channels. $ρ_{r e d}^{s}$ and $ρ_{b l u e}^{s}$ is the land surface reflectance in the red and blue channels, respectively. Then, a cost function $f (τ_{550}, k)$ between the land surface reflectance at the red and blue channels can be formed as in Eq. (3).
$f (τ_{550}, k) = \sum_{i = 1}^{c h n} {(ρ_{s}^{r e d, i} - k ρ_{s}^{b l u e, i})}^{2}$
According to Eq. (1), the land surface reflectance $ρ_{s}^{r e d, i}$ and $ρ_{s}^{b l u e, i}$ at the selected blue and red multiple channels can be expressed by Eq. (4).
$ρ_{s}^{i} = \frac{L_{T O A}^{i} - L_{P a t h}^{i}}{(L_{T O A}^{i} - L_{P a t h}^{i}) S_{i} + μ_{s} E_{s} τ (μ_{s}) τ (μ_{v}) / π}$
where $i$ denotes the selected blue and red multiple channels. The path radiance $L_{P a t h}^{i}$ , atmospheric spherical albedo $S_{i}$ and total transmittance from sun to ground to sensor $τ_{i} (μ_{s}) τ_{i} (μ_{v})$ are simulated with MODTRAN 5 radiative transfer code with different AOT@550 nm inputs.
The AOT@550nm estimation based on a linear relationship between blue and red bands of DDV pixels were also reported in the previous studies [32–34]. However, as an improved aerosol optical thickness @ 550nm retrieval approach in this study, there are two improvements compared to the previous studies. For one thing, a blue-red relationship with multiple blue (bands 15-19) and red (bands 48-52) bands instead of single blue and red band were used due to the continuous and finer spectral resolution of the hyperspectral data. For another thing, the coefficient between blue and red relationship were determined with ground measured land surface reflectance of varies vegetation types as reported in the previous studies. However, the coefficient varies with different sensor designation and vegetation types. Thus, in addition to the AOT@ 550nm, the coefficients between blue and red relationship were set as an unknown parameter and estimated from the cost function as expressed in Eq. (3). In this study, we used an optimization algorithm to solve the cost function of Eq. (3). Firstly, empirical values of k and AOT @550nm were configured before the iteration process. Then, the cost function was calculated based on the MODTRAN 5 simulation by adjusting AOT @ 550 nm and k. Then, both the AOT@550 nm and k coefficient can be determined while the iteration results satisfy the convergence condition.
(2) Columnar water vapor retrieval
Even though aerosols have significant effects on the transmittance, water vapor also plays an important role and must be eliminated when estimating the land surface reflectance from the hyperspectral data accurately. The retrieval of CWV from the hyperspectral data is usually conducted by assessing the water vapor absorption features in the visible and near infrared (VNIR) spectrum range. Many methods, such as the continuum interpolated band ratio (CIBR) [35,36] and atmospheric precorrected differential absorption (APDA) [37], have been proposed to retrieve CWV by assessing the strong water vapor absorption features centred at 0.94 μm and 1.14 μm. Another slightly strong water vapor absorption band located at 0.82 μm can also be used to estimate CWV when the water vapor absorption at longer wavelengths is not registered or has a poor signal-to-noise ratio (SNR) for some hyper-spectrometers. Similar study on water vapor content retrieval from hyperspectral data near 820nm was also used by Zhang et al. [38].
In this study, the water vapor absorption band near 0.82 μm was selected to retrieve the CWV since the ideal absorption band near 0.94 μm for water vapor retrieval has a lower signal-to-noise ratio (SNR) for the UAV-VNIRIS hyperspectral data. As an improved method, we used an effective apparent reflectance expressed as Eq. (5):
$ρ_{e f f} = \frac{π (L (μ_{v}) - L_{p} (μ_{v}))}{μ_{s} E_{0}} = \frac{ρ_{s}}{1 - ρ_{s} S} τ (μ_{s}) τ (μ_{v})$
Assuming the atmospheric spherical albedo $S < < 1$ , Eq. (5) can be simplified to become Eq. (6):
$ρ_{e f f} = ρ_{s} τ (μ_{s}) τ (μ_{v})$
According to a previous study, the land surface reflectance water vapor absorption and non-absorption channels show a linear relationship [39]. Then, CWV can be estimated based on the ratio of effective apparent reflectance $R (c w v)$ between the water vapor absorption and non-absorption channels, as expressed by Eq. (7).
$R (c w v) = \frac{ρ_{e f f}^{a}}{w_{1} * ρ_{e f f}^{1} + w_{2} * ρ_{e f f}^{2}}$
where $ρ_{e f f}^{a}$ is the effective apparent reflectance at the water vapor absorption, and $ρ_{e f f}^{1}$ and $ρ_{e f f}^{2}$ are the effective apparent reflectance of the reference channels around the water vapor absorption channel, which are free from water vapor absorption. Additionally, $w_{1}$ and $w_{2}$ are the band weighted coefficients, which can be determined with the wavelength distance between selected water absorption bands and reference bands as Eq. (8) and (9) expressed. Furthermore, in order to reduce the noise and random error impacts from the observed hyperspectral data, two of the most sensitivity water vapor absorption bands near 0.82μm were selected based on water vapor sensitivity factor analysis. In this study, channels centred at 0.815μm and 0.82μm that correspond to the 85th and 86th channels of the UAV-VIRIS hyperspectral data, respectively, were selected as the water absorption channels. While, channels centred at 0.775μm and 0.865μm of the UAV-VIRIS hyperspectral data were selected as the reference channels.
$w_{1} = \frac{λ_{2} - λ_{a}}{λ_{2} - λ_{1}}$ $w_{2} = \frac{λ_{a} - λ_{1}}{λ_{2} - λ_{1}}$
where $λ_{2}$ and $λ_{1}$ is the wavelength of reference bands, while, $λ_{a}$ is the wavelength of water vapor absorption bands.
According to the Eq. (7), the ratio value of the effective apparent reflectance between the water absorption and non-absorption channels should be transformed to the columnar water vapor. Firstly, 30 records land surface reflectances from ASTER spectral library including crops, forests, sands, artificial targets, grass were selected as the background land surface reflectance. And, 1000 CWV values within 0 to 6 g/cm² were generated randomly. Then, 30000 records of TOA radiance were simulated using MODTRAN 5 radiative transfer code with the input of land surface reflectance and CWV combinations. Then, ratio value $R (c w v)$ of the effective apparent reflectance between the water absorption and non-absorption channels were calculated with the simulated TOA radiance as express by Eq. (7). Finally, polynomial regression model with coefficient of determination (R²) larger than 0.995 and RMSE less than 0.006 will be used to fit the calculated $R (c w v)$ and CWV. Therefore, a 4th polynomial regression model was selected to fit the various effective apparent reflectance ratios and CWV for 0.815μm and 0.82μm water absorption channels. The R² and RMSE is 0.9966 and 0.005415 for Eq. (10). While, R² and RMSE is 0.996 and 0.005662 for Eq. (11).
$y = 0.00018 x^{4} - 0.0045 x^{3} + 0.044 x^{2} - 0.2 x + 1$ $y = 0.00027 x^{4} - 0.0055 x^{3} + 0.048 x^{2} - 0.2 x + 0.98$
where y is the effective apparent reflectance ratio, which is unitless, and x is the CWV with unit g/cm². The units in Eqs. (10) and (11) of the $x^{4}$ , $x^{3}$ , $x^{2}$ $x$ is cm⁸/g⁴, cm⁶/g³, cm⁴/g², and cm²/g, respectively. Figure 4 shows the scatter plot between the effective apparent reflectance ratio and CWV for the two selected water absorption channels. Then, the columnar water vapor can be estimated based on the regression model once the effective apparent reflectance ratio is determined from the UAV-VIRIS hyperspectral data.

Fig. 4 The scatter plot between the effective apparent reflectance ratio and CWV for (a) 0.815μm water absorption at band 85 and (b) 0.82μm water absorption at band 86.

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3.3 Land surface reflectance retrieval

By rearranging Eq. (1), the surface reflectance can be expressed as follows:

ρ_{s} = \frac{π (L_{T O A} - L_{p a t h})}{π (L_{T O A} - L_{p a t h}) S + μ_{s} E_{s} τ (μ_{s}) τ (μ_{v})}

To retrieve the surface reflectance from the UAV-VIRIS TOA radiance by Eq. (10), three atmospheric parameters, $L_{p a t h}$ , $S$ and $F$ , at different view zenith angles, solar zenith angles, AOT, and CWV for a determined atmospheric and aerosol model must be calculated first. Here, $F$ is equal to $μ_{s} E_{s} τ (μ_{s}) τ (μ_{v})$ for simplification. Once the atmospheric parameters AOD and CWV have been determined from the UAV-VIIRS data themselves, the three atmospheric parameters can be calculated from the MODTRAN simulated TOA radiances with three surface reflectances, 0, 0.5 and 1.0.

It would be highly time consuming to derive the surface reflectance for each spectral channel of each pixel from hyperspectral data due to the MODTRAN 5 computations. According to estimation based on our experience, it would cost about 1 minute to calculate land surface reflectance of 128 bands for each pixel. However, it only costs 0.000189 seconds when using a LUT method. Therefore, a method by using a pre-calculated look-up table (LUT) has been adopted in this study. LUT approach has been widely used to reduce the calculation time when running radiative transfer code [19,40]. The designed LUT in this study consists of seven inputs and three output parameters. The input parameters as showed in Table 2 consist of the sun zenith angle (SZA), view zenith angle (VZA), relative azimuth angle (RAA), flight height (FH), ground elevation (ELEV), AOT@550 nm and CWV. The three output parameters are the $L_{p a t h}$ , $S$ and $F$ . The breakpoints of the input parameters were defined as shown in Table 2, and the same weights were given in the generation of the samples. In addition to the seven free parameters, the other input variables must be set previously to drive the MODTRAN 5 radiative transfer code. In this study, the mid-latitude summer and the rural aerosol model are used as the atmospheric model and aerosol model, respectively. Considering the low spatial and temporal variation, the total ozone column content and the carbon dioxide mixing ratio are both set to default values. The DIScrete Ordinate Radiative Transfer (DISORT) was used in the scattering calculation of the MODTRAN 5 code. Finally, the breakpoint positions of the seven free input parameters produce a total of 329280 simulations. Once the seven input parameters have been determined, the three atmospheric parameters can be extracted from the LUT by means of a linear interpolation. In this study, we selected the multidimensional Lagrange interpolation method to interpolate the atmospheric parameters from LUT according to the comparison of the multidimensional Lagrange and multidimensional inverse distance weighted interpolation method by Hu et al. [41]. Analysis on the interpolation accuracy suggests that the standard deviation value of relative error is about 1% when comparing the interpolated $L_{p a t h}$ , $S$ and $F (μ_{s} E_{s} τ (μ_{s}) τ (μ_{v}))$ to the values calculated directly based on MODTRAN 5 simulations. Once the three atmospheric parameters were interpolated from LUT, the land surface reflectance for each pixel of the UAV-VNIRIS hyperspectral data then could be retrieved by using Eq. (12). Figure 5 shows the flowchart of the land surface reflectance retrieval algorithm.

Table 2. The breakpoint positions of the Look-up table (LUT) for the 6 input parameters.

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Fig. 5 Flowchart of the land surface reflectance retrieval from UAV-VNIRIS hyperspectral.

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4. Results and discussion

4.1 Results and validation of the atmospheric parameters with synthetic data

To evaluate the effectiveness of the improved aerosol optical thickness @ 550 nm and columnar water vapor retrieval methods mentioned in section 3.2, a radiative transfer code MODTRAN 5 was used to simulate the TOA spectral radiance hyperspectral data set with the UAV-VNIRIS sensor band configuration, as described in section 2.2. For the AOT@550nm retrieval accuracy evaluation, there are total 30 TOA spectral radiances were generated with MODTRAN 5 radiative transfer code. For each generated TOA spectral radiance for AOT@550nm retrieval, the spectral surface reflectance of a dense dark vegetation pixel combined with a randomly generated AOT@550nm value from 0.05 to 1.0 were configured to the MODTRAN 5 simulation. While, there are total 60 TOA spectral radiances were generated with MODTRAN 5 radiative transfer code for CWV retrieval accuracy evaluation. Similarly, for each generated TOA spectral radiance, the spectral surface reflectances of two pixels corresponding to dense dark vegetation and bare soil surface combined with a randomly generated CWV value from 0.5 g/cm² to 5.5 g/cm² were configured to the MODTRAN 5 radiative transfer code simulation. In addition to the spectral surface reflectance, AOT@550nm and CWV for each simulation of the synthetic data set, other essential input parameters configured to drive MODTRAN 5 code are shown in Table 3. Other parameters not shown in Table 3 use the default values [26].

Table 3. Essential input parameters configured to drive MODTRAN 5 code to simulate the synthetic data set

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Then, the improved atmospheric parameter retrieval methods introduced in section 3.2 were used to retrieve both the AOT@550 nm and CWV from the synthetic data sets. Figure 6 shows comparisons between the theoretical and retrieved AOT@550 nm with synthetic hyperspectral data sets for specified dense dark vegetation land surface conditions. The comparison results demonstrate that our improved algorithm retrieved at AOT@550 nm was well consistent with the theoretical values with a R² of 0.9492. In addition, the root-mean-square error (RMSE) between the theoretical and retrieved AOT@550 nm results is 0.0205, which indicates that our improved AOT@550 nm retrieval algorithm is effective at deriving the AOT@550 nm atmospheric parameter from simulated optical hyperspectral data.

Fig. 6 Comparisons between 30 theoretical and retrieved AOT@550 nm with synthetic hyperspectral data sets.

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Based on the regression model between the effective apparent reflectance ratio and CWV as shown in Fig. 4, CWV atmospheric parameters were also retrieved from synthetic optical hyperspectral data for two selected water absorption channels. Then, the averaged CWV were compared with the theoretical CWV input values when simulating the synthetic optical hyperspectral data sets. Figure 7 shows the scatters and fit lines between the theoretical and retrieved values for the vegetation and bare soil land surface conditions, respectively. The results show that the retrieved results usually agree well with the theoretical values when the CWV values are smaller than 3.5 g/cm², with R² values of 0.9948 and 0.9972 and RMSE values of 0.0904 g/cm² and 0.1893 g/cm² for vegetation and bare soil land surface conditions, respectively. For different surface type corresponding to vegetation and bares soil surface, it can be noted that the CWV retrieval RMSE for vegetation surface is larger than the CWV retrieval RMSE for bare soil surface. The reason may due to the non-Lambertian characteristics of the surface reflectances for the vegetation surface, which is more apparent than the bare soil surface. However, there are larger differences between the theoretical values and the retrieved values when the CWV values are larger than 3.5 g/cm², with R² values of 0.9037 and 0.8988 and RMSE values of 0.5190 g/cm² and 0.6267 g/cm² for the vegetation and bare soil land surface conditions, respectively. It can be seen from Fig. 6(b) that the retrieved CWV results from both the vegetation and bare soil land surface type synthetic hyperspectral data sets are obviously smaller than the theoretical values in high humidity atmospheric conditions, with a CWV value larger than 3.5 g/cm². It is interesting to note that from the regression model, between the effective apparent reflectance ratio and CWV, as shown in Fig. 4, the effective apparent reflectance ratio tends to be stable when the CWV is larger than 3.5 g/cm² for both of the selected water vapor absorption channels. In other words, there are several retrieved CWV values when using these models for retrieving CWV in high humidity vapor contamination atmospheric conditions with a CWV larger than 3.5 g/cm². That situation maybe is the reason for the large retrieval errors. In additional, MODTRAN 5 can apply a truncation of water vapor when it exceeds the physically possible amount regarding the given atmospheric vertical profile [42], which is probably why the effective ratio is non sensitive to the CWV above 3.5 g/m². Therefore, the introduced CWV retrieval method in our study is limited to the estimated CWV from the hyperspectral data collected in high humidity vapor atmospheric conditions with the CWV larger than 3.5 g/cm². Other models or spectral intervals should be used in this case should be figured out in the future work.

Fig. 7 Comparisons between theoretical and retrieved CWV with synthetic hyperspectral data sets: (a) without high humidity atmospheric conditions; (b) with high humidity atmospheric conditions.

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4.2 Results and validation of the atmospheric and land surface reflectance with the UAV-VNIRIS hyperspectral data set

To further evaluate the robustness of our improved atmospheric and land surface reflectance parameter retrieval algorithm as described in section 3, the introduced method was tested on the absolutely radiometric calibrated UAV-VNIRIS airborne optical hyperspectral data collected on September 3, 2011. First, according to the rule of DDV pixel selection, eight regions of interest (ROIs) as marked at Fig. 8(a) with green rectangles were selected from the UAV-VNIRIS airborne optical hyperspectral data as the DDV pixels to derive the AOT@550 nm with our introduced algorithm, as expressed by Eq. (3). Four of the eight vegetation ROIs were also been used to derive the CWV. Another four bare soil ROIs as marked at Fig. 8(a) with dark rectangles were also selected to derive the CWV from the two selected water vapor absorption channels with established regression models. There are total 12 × 12 pixels for each selected ROI. Both of retrieved AOT@550nm and CWV for each ROIs were showed in Table 4. To validate the retrieval error of the atmospheric parameters, the CIMEL photometer ground measurements of AOT@550 nm and CWV were compared with the retrieval results based on the selected ROIs from the UAV-VNIRIS hyperspectral data, as shown in Table 4. Then, the RMSE between retrieved atmospheric parameters for each ROIs and measured atmospheric parameters were calculated. The result shows that the RMSE is 0.0310 and 0.1852 g/cm² for AOT@550 nm and CWV, respectively. The final AOT@550nm and CWV averaged from the eight ROIs retrieval results is 0.142 and 1.557g/cm². And, the standard deviation of the retrieved AOT@550 nm and CWV is 0.0068 and 0.1303.

Fig. 8 The false colour RGB images of the retrieved land surface reflectance images: (a) the artificial target area; (b) the agricultural crop areas.

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Table 4. Validation between retrieved and measured atmospheric parameters.

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It can be concluded that our method’s retrieved AOT@550 nm and CWV values are close to the ground measurements, although both our method’s retrieved AOT@550 nm and the CWV are lower than those of the ground measurements. The vertical distribution of aerosols and water vapor could be the major error source in AOT@550 nm and CWV retrieval from the observed UAV-VNIRIS airborne optical hyperspectral data. As is known, the atmospheric effects, including aerosols and water vapor, usually distribute over the whole atmospheric path. However, the UAV-VNIRIS sensor payload on the UAV platform was collected at a low flight height (4.77 km) of the atmospheric path. Therefore, the atmospheric effects above the flight height of the atmospheric path cannot be retrieved from the airborne collected data. At the same time, the ground measurements with the sun photometer were collected in the whole atmospheric path. For this reason, the retrieved AOT@550 nm and CWV from the UAV-VNIRIS airborne optical hyperspectral data were underestimated when compared with the AOT@550 nm and CWV retrieved from the ground measurements in the whole atmospheric path. Similar conclusions were also drawn by the study of Guanter et al. when retrieving the aerosol and water atmospheric parameters from airborne hyperspectral data [9]. Furthermore, it is interesting to note that the retrieved CWV results based on vegetation ROIs are slightly larger than these with bare soil ROIs, which may due to the surface evaporation above the vegetation types more apparent.

Based on the retrieved AOT@550 nm and CWV from the UAV-VNIRIS hyperspectral data, the surface reflectance is retrieved from the absolutely radiometric calibrated UAV-VNIRIS hyperspectral data with the method, as described in section 3. It should be noted that we used the same retrieved AOT@550 nm and CWV for all of the pixels land surface reflectance retrieval, considering that our study area is small and that the aerosol and water vapor were assumed to be relatively stable over a small spatial scale. For a large scale of over 3 square kilometres, the AOT@550 nm and CWV atmospheric parameters should be retrieved separately for each small block. Figure 8 shows the retrieved surface reflectance with RGB colour channels corresponding to band 50, band 30 and band 15 for the artificial targets and agricultural crop areas.

The spectra of four different artificial targets measured during the over flight using the SVC HR-1024 portable field spectrometer were used to validate the retrieval accuracy. As showed in Fig. 9, the spectral surface reflectance retrieved using estimated AOT @550 nm and CWV as well as the spectral surface reflectance retrieved using local CIMEL photometer measurements were compared with the ground measured surface reflectance for the four hyperspectral targets (namely, H1, H2, H3 and H4 marked in Fig. 1). In addition, similar comparisons for two low agricultural crops (namely, potato marked with black dash rectangle and sorghum marked with solid rectangle in Fig. 8) were also conducted and showed in Fig. 10. Other retrieved agriculture crop land surface reflectances were not validated here due to the difficulty and large uncertainty in collecting an accurate canopy reflectance of high agricultural crops such as maize and sunflower. It can be seen from Fig. 9 and Fig. 10 that the retrieved surface reflectance with our improved method has a high consistency with the at-ground measured surface reflectance. It can also be noted that the UAV-VNIRIS optical hyperspectral data has undergone atmospheric correction for VNIR aerosol scattering and the water absorption band near 820 nm atmosphere window by our retrieved AOT@550 nm and CWV. For another reason is the underestimation of AOT@550 nm and CWV, which may correspondingly affect the land surface reflectance retrieval accuracy especially in the aerosol scattering and water vapor absorption bands. It also can be seen from Fig. 9 and Fig. 10 that the calculated surface reflectance based on CIMEL photometer measurements at the water vapor absorption bands are more close to the ground measurements. Furthermore, spectral calibration error of the hyperspectral data, which may result in the difference of retrieved surface reflectance in the spectral range especially at the atmospheric absorption channels. Therefore, only the 86 channels that retrieved land surface reflectances, from channels 13 to 108, were validated with the in situ measured values.

Fig. 9 Comparison of the surface reflectance retrieved using estimated AOT@550 nm (0.142) and CWV(1.557g/cm²) as well as the surface reflectance retrieved using local CIMEL photometer measured AOT@550 nm (0.1724) and CWV(1.6964g/cm²) with the ground measured surface reflectance for the (a) H1, (b) H2, (c) H3 and (d) H4 artificial targets as shown in Fig. 1.

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Fig. 10 Comparison of the surface reflectance retrieved using estimated AOT@550nm (0.142) and CWV (1.557g/cm²) as well as the surface reflectance retrieved using local CIMEL photometer measured AOT@550 nm (0.1724) and CWV (1.6964g/cm²) with the ground measured surface reflectance for the (a) potato marked with black dash rectangle and (b) sorghum marked with solid rectangle as showed in Fig. 7 (b).

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Differences between measured and retrieved surface reflectance from UAV-VNIRIS airborne optical hyperspectral data as a function of the wavelength for artificial targets and agriculture crops are shown in Fig. 11 and Fig. 12, respectively. It can be stated from Fig. 11 and Fig. 12 that the differences between measured and retrieved results are less than 0.1 when discarding bad signal-to-noise ratio channels from band 13 to band 108. In order to evaluate the accuracy of retrieved land surface reflectance, both of the mean absolute error (MAE) and RMSE between retrieved and ground measured values were calculated and showed in Table 5. As showed in Table 5, compared with ground measured surface reflectance, the MAE of retrieved surface reflectance based on ground measured AOT@550nm and CWV for the four artificial targets and two agriculture crops is 0.0175, 0.0025, 0.0115, 0.0109, 0.0109 and 0.0074, respectively. While, compared with ground measured surface reflectance, the MAE of retrieved surface reflectance based on estimated AOT@550nm and CWV for the four artificial targets and two agriculture crops is 0.0217, 0.0031, 0.0169, 0.0170, 0.0128 and 0.0088, respectively. Besides, the RMSE between the retrieved and measured surface reflectances were also calculated for the four artificial targets and two agricultural crops without including bad signal-to-noise ratio channels. As showed in Table 5, the RMSE of retrieved surface reflectance based on ground measured AOT@550nm and CWV for the four artificial targets and two agriculture crops is 0.0155, 0.0062, 0.0117, 0.0116, 0.0118 and 0.0105, respectively. While, the RMSE of retrieved surface reflectance based on estimated AOT@550nm and CWV for the four artificial targets and two agriculture crops is 0.0176, 0.0070, 0.0139, 0.0151, 0.0128 and 0.0115, respectively.

Fig. 11 Differences between measured and retrieved surface reflectance from UAV-VNIRIS airborne optical hyperspectral data as a function of the wavelength for the (a) H1, (b) H2, (c) H3 and (d) H4 artificial targets.

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Fig. 12 Differences between measured and retrieved surface reflectance from UAV-VNIRIS airborne optical hyperspectral data as a function of the wavelength for the (a) potato agriculture crop and (b) sorghum agriculture crop.

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Table 5. Validation between retrieved and measured land surface reflectance

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The results in Table 5 also show that the averaged MAE and RMSE of measured and retrieved surface reflectance based on estimated AOT@550nm and CWV is 0.0134 and 0.0130. While, the averaged MAE and RMSE of measured and retrieved surface reflectance based on ground measured AOT@550nm and CWV is 0.0101 and 0.0112. It can be noted that both the averaged MAE and RMSE of retrieved surface reflectance based on estimated AOT@550nm and CWV is slightly larger than the results of retrieved surface reflectance based on ground measured AOT@550 nm and CWV. The uncertainties of the AOT@550 nm and CWV estimation error may influence the performance of the physical-based atmospheric correction approach on land surface reflectance retrieval. Therefore, sensitivity analysis of the land surface reflectance retrieval with the physical-based atmospheric correction approach were conducted. Sensitivity analysis suggests that the land surface reflectance retrieval uncertainty associated with the uncertainty of the AOT@550 nm and CWV estimation error as showed in Table 4 is 0.0043 and 0.0142, respectively. In addition, the retrieved surface reflectance error could be caused by the relative signal-to-noise ratio and absolute radiometric calibration errors. The vicarious absolute radiometric of the UAV-VNIRIS instrument used in our study is about 5%, which may cause about 5.64% land surface reflectance retrieval error. Furthermore, the use of LUT could also cause the land surface reflectance retrieval error, as reported by Hu et al. [41]. Analysis on the LUT interpolation accuracy suggests that the standard deviation value of relative error is about 1% when comparing the LUT interpolated values to the MODTRAN 5 directly simulations. And, this 1% error when using LUT may cause about 1.1% land surface reflectance retrieval error. The surface bidirectional reflectance distribution (BRDF) properties could also impact the accuracy of the surface reflectance retrievals under certain conditions [42]. For the retrieved reflectance of vegetation crops, the BRDF effects due to the heterogeneity of the vegetation crop canopy could cause the retrieval error even though the viewing angle in the agricultural crop area is nadir. With regard to the retrieved reflectance of an artificial target, the BRDF effect also could affect the retrieved accuracy due to the artificial targets not being in the centre position of the hyperspectral image scene.

Another important point that affect the retrieval results is the adjacency effect, which has a significant role in the atmospheric correction of hyperspectral remote sensing data, especially for acquired airborne hyperspectral images [43,44,21]. The adjacency effect tends to mask the pixel seen by the hyperspectral sensors, derives mainly from the atmospheric scattering due to the aerosol loading in the collected hyperspectral images. Therefore, the diffuse and direct radiation component should be required in order to determine the contribution from the surrounding pixels to the pixel reflectance. Also, aerosol types and atmospheric model should be determined carefully according to the actual environment when using MODTRAN 5 radiative transfer code. Improper selected aerosol types and atmospheric model may result in large retrieval error. Overall, the validation results demonstrate that the retrieved land surface reflectance based on the retrieved AOT@550 nm and CWV key atmospheric parameters is a good way to address the conditions when it is difficult to collect the atmospheric parameters at the ground. It provides a quick and easy way to acquire the surface reflectance from UAVs platform observed hyperspectral data for further quantitative remote sensing applications.

5. Conclusions

Recently, spectrometers carried on UAVs to collect hyperspectral images have been widely used in the fields of agriculture, forest, ecology, oil, oceanography and atmospheric studies. However, the atmospheric correction of hyperspectral images collected over UAVs to recover the land surface reflectance is usually the first step in studying the surface properties and in conducting further applications. In this study, a physical-based atmospheric correction algorithm was introduced using MODTRAN model, with which the aerosol optical thickness @550 nm, columnar water vapor and surface reflectance could be automatically retrieved from the UAV collected hyperspectral data. For the AOT@550 nm retrieval algorithm, the DDV method developed by Kaufman is improved in this paper to estimate the AOT@550 nm from the hyperspectral data for covering only the visible and near-infrared wavelengths. For the CWV retrieval algorithm, an effective apparent reflectance ratio was introduced, and regression models with CWV were established for selected water vapor channels. Off-line radiative transfer calculations are performed by a MODTRAN 5 radiative transfer code to build a pre-calculated LUT that includes seven free input variables and three output parameters.

The physical-based atmospheric correction algorithm was tested on both synthetic and airborne collected optical hyperspectral data. The RMSE between theoretical and retrieved AOT@550 nm with synthetic hyperspectral data sets for specified dense dark vegetation land surface conditions is 0.0205 while the typical variation of this parameter is about 0.0209. At the same time, the RMSE between the theoretical and retrieved CWV values is 0.0904 g/cm² while the typical variation of this parameter is about 0.0923 g/cm² for vegetation land surface conditions. And, the RMSE between the theoretical and retrieved CWV values is 0.1893 g/cm² while the typical variation of this parameter is about 0.1932g/cm² for bare soil land surface conditions. However, obvious error occurs when retrieving the CWV from airborne optical hyperspectral data collected in high humidity atmospheric conditions with a CWV larger than 3.5 g/cm². The introduced method in this study was also applied to UAV-VNIRIS hyperspectral data collected on September 3, 2011. The RMSE between retrieved atmospheric parameters for each ROIs and measured atmospheric parameters is 0.0310 and 0.1852 g/cm² for AOT@550 nm and CWV, respectively. And, the standard deviation of the retrieved AOT@550 nm and CWV is 0.0068 and 0.1303. Based on the retrieved AOT@550 nm and CWV atmospheric parameters, land surface reflectances were retrieved from the absolutely radiometric calibrated UAV-VNIRIS hyperspectral data and then compared with the ground measurements. The RMSE between the retrieved and measured land surface reflectances were less than 0.0299 and 0.0158 for the tested artificial targets and agriculture crops, respectively. Overall, the validation results demonstrate that the retrieved land surface reflectance based on the retrieved AOT@550 nm and CWV key atmospheric parameters is a good way to address the conditions when there is no available aerosol and water vapor information synchronised with the acquisition of the UAV hyperspectral images. Furthermore, the encouraging results indicate that the introduced physical-based atmospheric correction approach on the basis of accurate radiative transfer model MODTRAN can be used to retrieve the atmospheric components and surface reflectances reliably and automatically from the UAV hyperspectral images. It provides a quick and easy way to acquire the surface reflectance from UAVs platform observed hyperspectral data for further quantitative remote sensing applications.

However, several points should be paid attention when using our introduced approach. For one thing, BRDF effect should be considered in future work, especially for the heterogeneous vegetation canopy, according to the results and analysis in this study. For another thing, adjacent effects were not considered in this study, which may result in the land surface reflectance accuracy for acquired high spatial resolution UAVs hyperspectral data. Additionally, the AOT @550 nm retrieval algorithm is limited to the areas with dense vegetation. It also must be noted that the aerosol type and atmospheric model should be selected carefully when using our introduced approach. Future work on AOT @550 nm inversion should consider the brightness area in order to extend the application of the UAV hyperspectral images. Furthermore, an apparent CWV estimation error occurs on humid atmospheric conditions with CWVs larger than 3.5 g/cm², which should also be paid attention to when applying UAV hyperspectral image atmospheric corrections.

Funding

National Key Research and Development Program of China (2016YFB0500400); National Natural Science Foundation of China (41601398).

Acknowledgments

The authors would like to appreciate the technical editor and anonymous reviewers for their constructive comments and suggestions on this study.

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Parameter	Value
Instantaneous field of view	0.2 mrad
Field of view	11.5°
Spectral range	400–1000 nm
Spectral resolution	5 nm
Spatial resolution	1 m @ 5 km flight altitude
Number of bands	128
Swath width	1 km @ 5 km flight altitude
Width of the imaging array	1000 pixels
Digitisation	12 bits
Signal-to-noise ratio	≥40 dB

Parameter	Value	Instruction
MODEL	2	Mid-Latitude Summer (45° North Latitude).
ITYPE	2	Vertical or slant path between two altitudes.
IEMSCT	2	Radiance model.
IMULT	−1	With multiple scattering。
LLFLTNM	UAV-VNIRIS.flt	User-defined UAV-VNIRIS sensor filter function.
IHAZE	1	RURAL extinction, default VIS = 23 km.
GNDALT	1.27	Altitude of surface relative to sea level (km).
H1ALT	4.77	Altitude of the UAV platform (km).
OBSZEN	180	Sensor zenith angle (°).
V1	350	Initial wavelength (nm).
V2	1200	Final wavelength (nm).
PARM	44.08	Solar zenith angle (°).

	AOT@550nm		CWV (g/cm²)
	Retrieved	Measured	Retrieved	Measured
ROI_1	0.1523	0.1724	1.6295	1.6964
ROI_2	0.1348	0.1724	1.7211	1.6964
ROI_3	0.1405	0.1724	1.6745	1.6964
ROI_4	0.1317	0.1724	1.6328	1.6964
ROI_5	0.1473	0.1724	1.3575	1.6964
ROI_6	0.1395	0.1724	1.5469	1.6964
ROI_7	0.144	0.1724	1.4082	1.6964
ROI_8	0.146	0.1724	1.4855	1.6964
RMSE	0.0310		0.1852

Parameter	Value
Instantaneous field of view	0.2 mrad
Field of view	11.5°
Spectral range	400–1000 nm
Spectral resolution	5 nm
Spatial resolution	1 m @ 5 km flight altitude
Number of bands	128
Swath width	1 km @ 5 km flight altitude
Width of the imaging array	1000 pixels
Digitisation	12 bits
Signal-to-noise ratio	≥40 dB

Parameter	Value	Instruction
MODEL	2	Mid-Latitude Summer (45° North Latitude).
ITYPE	2	Vertical or slant path between two altitudes.
IEMSCT	2	Radiance model.
IMULT	−1	With multiple scattering。
LLFLTNM	UAV-VNIRIS.flt	User-defined UAV-VNIRIS sensor filter function.
IHAZE	1	RURAL extinction, default VIS = 23 km.
GNDALT	1.27	Altitude of surface relative to sea level (km).
H1ALT	4.77	Altitude of the UAV platform (km).
OBSZEN	180	Sensor zenith angle (°).
V1	350	Initial wavelength (nm).
V2	1200	Final wavelength (nm).
PARM	44.08	Solar zenith angle (°).

Land surface reflectance retrieval from optical hyperspectral data collected with an unmanned aerial vehicle platform

Abstract

1. Introduction

2. Study area and data sets

2.1 Study area and field campaign description

2.2 UAV-VNIRIS hyperspectral data

2.3 In situ measurements

3. Methodology

3.1 Theory of physical-based atmospheric correction approach

3.2 Retrieval of atmospheric parameters

3.3 Land surface reflectance retrieval

4. Results and discussion

4.1 Results and validation of the atmospheric parameters with synthetic data

4.2 Results and validation of the atmospheric and land surface reflectance with the UAV-VNIRIS hyperspectral data set

5. Conclusions

Funding

Acknowledgments

References

Cited By

Figures (12)

Tables (5)

Equations (12)

Optics Express

Input parameters	Breakpoints
Input parameters	#1	#2	#3	#4	#5	#6	#7	#8
AOT@550	0.05	0.1	0.2	0.6	1.0
CWV (g/cm²)	0.1	0.5	1.0	2.0	3.5	5.0
SZA (°)	0	10	20	30	40	50	60	70
VZA (°)	0	10	20	30	40	50	60
RAA (°)	0	30	60	90	120	150	180
FH (km)	1.0	2.0	3.0	4.0	5.0
ELEV (km)	0	1.0	2.0	4.0

	Retrieved with measured AOT@&CWV		Retrieved with estimated AOT&CWV
	MAE	RMSE	MAE	RMSE
H1	0.0175	0.0155	0.0217	0.0176
H2	0.0025	0.0062	0.0031	0.0070
H3	0.0115	0.0117	0.0169	0.0139
H4	0.0109	0.0116	0.0170	0.0151
Potato	0.0109	0.0118	0.0128	0.0128
Sorghum	0.0074	0.0105	0.0088	0.0115
Mean	0.0101	0.0112	0.0134	0.0130