# Spectral Adjustment Model's Analysis and Application to Remote Sensing Data

Jose Luis Villaescusa-Nadal, Belen Franch, Jean-Claude Roger, Eric Vermote, Sergii Skakun, Chris Justice

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## To cite this version:

Jose Luis Villaescusa-Nadal, Belen Franch, Jean-Claude Roger, Eric Vermote, Sergii Skakun, et al. Spectral Adjustment Model's Analysis and Application to Remote Sensing Data. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, 12 (3), pp.961-972. 10.1109/JSTARS.2018.2890068. [hal-03469856](https://uca.hal.science/hal-03469856)

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# Spectral Adjustment Model's Analysis and Application to Remote Sensing Data

Jose Luis Villaescusa-Nadal ID, Belen Franch ID, Jean-Claude Roger ID, Eric F. Vermote, Sergii Skakun ID, and Chris Justice

**Abstract**—Differences in the relative spectral response functions of sensors lead to data inconsistencies that should be harmonized before multisensor exploitation. In this paper, we use spectral libraries to simulate satellite data and build models to correct them. We then explore and compare different models for coarse and medium spatial resolution optical sensors, including moderate resolution imaging spectroradiometer, advanced very high resolution radiometer (AVHRR), visible infrared imaging radiometer suite, multispectral instrument aboard Sentinel-2, and Operational Land Imager aboard Landsat 8. We found that optimal correction of different bands depends on the model used. For the green and near infrared bands, a multilinear land cover dependent regression improves the accuracy by up to 80.9%. For the red band, a novel exponential dependence of the spectral band adjustment factor with the normalized difference vegetation index (NDVI) provides an accuracy improvement of up to 72.8%. The best way to correct the NDVI value is to use the corrected NIR and red bands using these models. We apply the proposed methods to 445 BELMANIP2 sites using AVHRR data from the long-term data record from 1982-2017. High NDVI pixels result in 30-year trends varying up to 0.06 when comparing uncorrected to spectrally adjusted NDVI. Further application of these methods to NASA's Harmonized Landsat and Sentinel 2 product shows that for the red band and NDVI, our proposed method provides improved accuracy (54.6% and 62.5%) over the linear spectral adjustment currently used.

**Index Terms**—Advanced very high resolution radiometer (AVHRR), calibration, Landsat, moderate resolution imaging spectroradiometer (MODIS), normalized difference vegetation index (NDVI), relative spectral response, spectral band adjustment factor (SBAF), Sentinel 2, spectral adjustment, surface reflectance, visible infrared imaging radiometer suite (VIIRS).

## I. INTRODUCTION

TO Gain an understanding of land surface processes at a variety of scales, it is increasingly necessary to use data

Manuscript received September 12, 2018; revised November 6, 2018; accepted December 4, 2018. Date of publication January 7, 2019; date of current version March 25, 2019. This work was supported by the NASA grant "Support for the HLS (Harmonized Landsat-Sentinel-2) Project" (NNX16AN88G). (Corresponding author: Jose Luis Villaescusa-Nadal.)

J. L. Villaescusa-Nadal, B. Franch, J.-C. Roger, and S. Skakun are with the Department of Geographical Sciences, University of Maryland, College Park, MD 20742 USA, and NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: jvillaes@umd.edu; befranch@umd.edu; roger63@umd.edu; skakun@umd.edu).

E. F. Vermote is with the NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: Eric.F.Vermote@nasa.gov).

C. Justice is with the Department of Geographical Sciences, University of Maryland, College Park, MD 20742 USA (e-mail: cjustice@umd.edu).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2018.2890068

from multiple Earth observation sensors [1]. By combining similar spatial resolution sensors, we can achieve higher temporal resolutions, increasing our ability to monitor rapidly changing phenomena and increase the opportunity of obtaining cloud-free observations. Additionally, the intercomparison between different sensors of basic parameters such as the surface reflectance is critical to build consistent databases. However, similar bands from different sensors have different spectral ranges and have a different band efficiency (or relative spectral response). This leads to a significant offset in the values measured, even when observing the same target at the same time [2]. Studies have shown differences in the normalized difference vegetation index (NDVI) value due to solely the relative spectral response (RSR). They can result in discrepancies of 6.3% between Quick-Bird and SPOT5 [3] that cause differences in the red and NIR reflectances of 20% and 4%, respectively [4]. It is, therefore, important to place all these sensors on a common radiometric scale, when generating a time series of a certain physical parameter covering different sensor generations and sensor types.

One way to achieve a common radiometric scale is to use an already well-calibrated sensor to calibrate other sensors (i.e., cross calibration) [5]. Cross calibration is a key toward the mission continuity, interoperability, and data fusion [1], [6], and is critical, when the sensor has no onboard reference available or when the vicarious calibrations are limited. This is the case for the advanced very high resolution radiometer (AVHRR) sensors, which started acquiring data in the 1980s. The AVHRR mission provides an unique dataset of 30+ years of global imagery, with daily temporal resolution. However, the time series consists of data from three different sensors onboard 13 different satellites. The RSR function of these sensors differ significantly, resulting in relative differences of around 15% in the red band, 3% in the NIR band, and 6% in the NDVI value, when comparing, for example, NOAA9 with NOAA15 [4]. These differences could result in problems when estimating parameters derived from the whole time-series, as they could produce inconsistencies between the sensors and misleading trends in the data, as will be shown in this study.

Regarding moderate to high spatial resolution, the Landsat series has been providing 16-day imagery since the 1970s. Due to such low temporal resolution of individual moderate spatial resolution satellites, there is a benefit in combining measurements from similar or analogous sensors aboard different satellites [7]. With the launch of Sentinel 2 [8], the combination of Landsat 8 and Sentinel 2 data provides a significant improvement
in temporal resolution [9]. The Harmonized Landsat/Sentinel-2 (HLS) Project, for example, provides a surface reflectance product combining both satellite's measurements at 30-m spatial resolution [10]. In this case, it is important to consider the directional and atmospheric effects resulting from the difference in overpass time and observation angle of each satellite, along with the spectral correction [7].

The purpose of radiometric adjustment is to correct differences due to discrepancies in the RSR function between analogous bands. These differences can only be compared when the spectral responses of the sensors for a given band have enough spectral overlap [11]. Several different ways to correct spectral differences have been reported in the literature and can be generally classified into three main types: band averaging, radiative transfer, and statistical regression. The latter is the most commonly used in the literature and consists in using hyperspectral data convolutions [12], [13], remotely sensed observations [14], [15], or radiative transfer calculation [16] to obtain regression coefficients that establish a relationship between analogous bands.

The most commonly used relationship is the linear regression [13], [16]. It involves using a simple relationship between the reference (ref) and target (tar) sensors to obtain correction parameters which can later be used to correct any target sensor's observation. This method is used in the HLS product [17], using Landsat-8 as a reference. The main reason behind its popularity is its simplicity and practical use, however it overestimates low NDVI values and underestimates high NDVI values, suggesting that its optimal use is for intermediate NDVI values [18]. Previous studies have shown that the reflectance relationships between the red and NIR bands have strong land cover dependencies [19], which are not considered when using the linear regression. They can, however, be corrected as a function of the quadratic NDVI [4], [19], [20]. Differences in the spectral band adjustment factor (SBAF), defined as the ratio between the target and reference reflectance, can increase up to 30% and 40% in the red and NIR bands, respectively [4]. Fan and Liu [11] determined that the SBAF between Landsat TM and Earth Observing One (EO-1) Advanced Land Imager (ALI) is inherently dependent on the NDVI and exhibit nonlinear dependencies. To correct discrepancies between similar NDVI values of soils and sparsely vegetated land cover for varying RSRs, D'Odorico et al. [21] added to the regression model the red and NIR bands, providing further information on the land cover type by means of a multilinear regression. The quadratic approach does not seem to fully correct these nonlinearity problems when the spectral differences are big, and the bands are wide for extreme NDVI values, so we propose an exponential correction function which models the saturation of high NDVI values for pixels with a high leaf area index (LAI) accurately.

These studies, however, do not hypothesize that different bands should be corrected using different models. The sensitivity analysis performed in [19] leads to our hypothesis that the land cover dependencies of bands which overlap with the green peak or red-edge regions in different ways, should be modeled differently. The aim of this paper is to test said hypothesis by comparing the performance of different spectral adjustment

<table><caption>TABLE I
PASSIVE OPTICAL SENSORS CONSIDERED AND THEIR OFFICIAL BAND NUMBER</caption><thead><tr><th>Mission/s</th><th>Sensor</th><th>Green band</th><th>Red band</th><th>NIR band</th></tr></thead><tbody><tr><td>NOAA8, 10</td><td>AVHRR/1</td><td>-</td><td>1</td><td>2</td></tr><tr><td>NOAA7, 9, 11, 12, 13, 14</td><td>AVHRR/2</td><td>-</td><td>1</td><td>2</td></tr><tr><td>NOAA15,16,17,18,19</td><td>AVHRR/3</td><td>-</td><td>1</td><td>2</td></tr><tr><td>Landsat 4, 5</td><td>TM</td><td>2</td><td>3</td><td>4</td></tr><tr><td>Landsat 7</td><td>ETM+</td><td>2</td><td>3</td><td>4</td></tr><tr><td>Landsat 8</td><td>OLI</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Aqua/Terra</td><td>MODIS</td><td>4</td><td>1</td><td>2</td></tr><tr><td>Sentinel 2A/B</td><td>MSI</td><td>3</td><td>4</td><td>8A</td></tr><tr><td>Suomi NPP</td><td>VIIRS</td><td>-</td><td>11</td><td>12</td></tr></tbody></table>

methods on the green, red, NIR, and NDVI. We then apply the selected methods on real data to test their performance. We do this by comparing coincident Landsat 8 and Sentinel 2 images from the NASA's HLS product [10]. We finally analyze the impact of the spectral differences on time series trends by studying AVHRR data. Section II describes the materials used for the study. Section III presents the methodology. Section IV presents the results. Section V presents a discussion of the results and Section VI presents the conclusion.

## II. MATERIALS

### A. Sensors Used

Table I shows the optical sensors and spectral bands considered in this study. Same sensors on different missions have different spectral responses. The RSR functions were downloaded from https://cloudsway2.larc.nasa.gov/ and are shown in Fig. 1.

1) Moderate Resolution Imaging Spectroradiometer (MODIS): The MODIS is an instrument aboard the Terra and Aqua missions, which provides daily measurements at coarse spatial resolution (1 km-250 m). It acquires data in 36 spectral bands, with a very similar RSR for both satellites. It was designed to produce large-scale global measurements. MODIS is widely used in the remote sensing community due to the quality of its calibration [22], [23] and validation [24], [25], so we selected it as a reference sensor. The choice of Aqua over Terra is arbitrary given their almost identical RSR function. In this study, we only consider the red, NIR, and green bands, with band numbers 1, 2, and 4, respectively.

2) Visible Infrared Imaging Radiometer Suite (VIIRS): The VIIRS is an instrument aboard the Suomi National Polar-orbiting Partnership (Suomi-NPP) satellite. It provides daily observations at coarse spatial resolution, similar to MODIS; its purpose is to continue the heritage of the NOAA AVHRR and MODIS products, enabling characterization of the land surface at regional to global scales. We use the I1 and I2 bands, due to the presence of analogous bands in the MODIS or AVHRR sensors.

3) Landsat and Sentinel 2: The Landsat program has been providing information about the Earth at moderate spatial resolution (70-30 m) since the 1970s, increasing our understanding
<figure><img src="image_3.png" /><figcaption>Fig. 1. RSR of the sensors used in this study for the green, red, and NIR bands specified in Table I. The dashed lines show a typical vegetation and bare soil spectra.</figcaption></figure>

of local environmental changes. The most recent satellite, Landsat 8, was launched in 2013 and provides measurements every 16 days. The Sentinel 2A satellite, launched by ESA in 2015, has similar characteristics. The Harmonized Landsat/Sentinel2 product provides a combination of measurements approximately every five days, correcting for geometric, anisotropic, atmospheric, and spectral differences [10].

We downloaded HLS data for seven SURFRAD sites in the U.S. [26] and six sites in Australia (HLS tiles 54HVH, 55HBU, 55HCV, 55HDB, 56HKH, and 56JMQ) where Landsat 8 and Sentinel 2 sensors have coincident observations (131 scenes). The data were corrected for geometric sampling and geographic registration, but in this study were not corrected for directional effects.

The Equator crossing times of the Landsat 8 OLI and Sentinel-2 MSI sensors are close, 10:00 A.M. (L8) and 10:30 A.M. (S2), and the viewing angles from nadir are ±7.5° and ±10.3°, respectively [27]. This means that the illumination conditions for coincident dates are very similar, and the differences in surface reflectance due to the surface anisotropy can be considered negligible for low observation angles. The spectral differences between the L8 OLI and S2 MSI sensors are significant for the green and red bands, but negligible for the NIR bands (see Fig. 1), with band numbers specified in Table I. For these reasons, the use of this product for data on the same site and day allows a reasonable comparison between the two sensors whose difference can be attributed mainly to the spectral differences.

4) *Advanced Very High Resolution Radiometer:* The AVHRR surface reflectance data from 1982 to 2017 were obtained from the long-term data record (LTDR) surface

<figure><img src="image_4.png" /><figcaption>Fig. 2. Distribution of the BELMANIP2 (black dots) sites around the world.</figcaption></figure>

reflectance database [28] produced by NASA's Goddard Space Flight Center and the University of Maryland. These daily data are mapped into a climate modeling grid at 0.05° × 0.05° resolution, corresponding to a 3600 × 7200 pixel array over the globe. It is corrected for directional effects [29], [30], but not for spectral effects [28]. We downloaded AVHRR time series for 445 BELMANIP2 sites. BELMANIP2 sites are an update of BELMANIP1 [31] and were selected because they represent the variability of vegetation types and climatological conditions around the world. The spatial distribution of these sites is shown in Fig. 2.

## B. Spectral Libraries

We considered 615 surface reflectance spectral profiles from ground measurements and atmospherically corrected airborne
<figure><img src="image_5.png" /><figcaption>Fig. 3. NDVI distribution of the surface reflectance spectra used in this study. (a) Before mixing spectral reflectance values. (b) After mixing spectral reflectance values.</figcaption></figure>

visible and infrared imaging spectrometer measurements [32] included in the USGS [33] spectral libraries. These profiles covered a wide range of land covers, including snow, ice, rocks, soils, vegetation, and manmade materials such as asphalt or brick. Overall, they were distributed along the NDVI range from 0 to 0.93 [see Fig. 3(a)].

### III. METHODS

#### A. Algorithm Description

Field measurements are only representative of very specific types of surfaces. When working with coarse resolution data, the measured signal of a given pixel is most often a combination of signals from different surfaces (mixed pixels). Therefore, to make the field measurements more representative of the remotely sensed signal while also increasing the sample size, we simulated random combinations of these spectra. We did this by linearly combining the reflectance spectra of the 615 field measurements. Up to three different field measurements were combined each time to reproduce a coarse resolution remote sensing pixel. We assigned to each one of them a random weight, which represents the percentage cover of that land type in a certain pixel. The number of possible combinations using three different surfaces added up to ~16 million, but we selected a random sample of 500 000 spectra. The NDVI range of the original samples is shown in Fig. 3(a), while that of the combined satellite representative samples is shown in Fig. 3(b).

Having selected the reference hyperspectral data, we applied the spectral adjustment to simulate what the different sensors would measure if only the spectral differences between them were considered. We do this by weighing measured reflectances by their RSR and obtaining the simulated reflectances of each band

$$ \bar{\rho}_{\lambda} = \frac{\int \rho_{\lambda} RSR_{\lambda} d\lambda}{\int RSR_{\lambda} d\lambda} \qquad (1) $$

where $\rho_{\lambda}$ is the spectral library's reflectance, the RSR is the RSR function of the sensor, and $\bar{\rho}_{\lambda}$ the simulated reflectance of the sensor. We calculated the ratio of simulated reflectances from two different sensors; a reference sensor $\bar{\rho}_{\lambda,ref}$ and a target

sensor $\bar{\rho}_{\lambda,tar}$, also known as the SBAF using

$$ \text{SBAF} = \frac{\bar{\rho}_{\lambda,ref}}{\bar{\rho}_{\lambda,tar}}. \qquad (2) $$

We then proceeded to build the models described in detail in Section III-B and retrieve the corresponding regression coefficients, using MODIS/Aqua as a reference. These coefficients were applied to the surface reflectance data to allow the comparison of the different methods over different sensor combinations. This comparison is assessed in terms of the accuracy, precision, and uncertainty (APU) metrics [34]. The accuracy represents the mean bias of the estimates, against reference data. It is also known as the mean bias error. The precision represents the repeatability of the estimate, and it computes the standard deviation of the estimates around the reference values corrected for the bias (accuracy). Finally, the uncertainty, or root mean square error (RMSE), is the deviation of the estimate from the reference.

The surface reflectance bands analyzed are the green, red, and NIR, but we also compute the corrected NDVI. The two schemes generally used in the literature for NDVI correction are the distributed and lumped schemes. The former initially corrects the spectral bands and then calculates the NDVI from them (3), while the latter computes an intercalibration equation from the NDVI (NDVI-to-NDVI) [18], [35]

$$ \text{NDVI}_{\text{corrected}} = \frac{\rho_{\text{NIR,corrected}} - \rho_{\text{red,corrected}}}{\rho_{\text{NIR,corrected}} + \rho_{\text{red,corrected}}}. \qquad (3) $$

In the case that our hypothesis is valid and different methods are used to correct different bands, we can calculate the NDVI using the distributed scheme through the NIR band corrected using one model, and the red band corrected using a different model.

#### B. Spectral Methods Description

The empirical regression models and SBAF methods that have been tested in this paper are the following.

1) Linear Model:

$$ \bar{\rho}_{\lambda,ref} = a + b \cdot \bar{\rho}_{\lambda,tar}. \qquad (4) $$

2) Multilinear Regression Model 1 (MR1): Strong land cover dependencies have been observed in the red and NIR bands' intercalibration, but none have been reported for the green band, so analogous to the red and NIR multilinear regression

$$ \bar{\rho}_{\text{(red,nir),ref}} = \beta_1 \bar{\rho}_{\text{red,tar}} + \beta_2 \bar{\rho}_{\text{nir,tar}} + \beta_3 \text{NDVI} + \beta_4 \text{NDVI}^2 + \epsilon. \qquad (5) $$

We model the green band in the following way:

$$ \bar{\rho}_{\text{green,ref}} = \beta_1 \bar{\rho}_{\text{green,tar}} + \beta_2 \bar{\rho}_{\text{nir,tar}} + \beta_3 \text{NDVI} + \beta_4 \text{NDVI}^2 + \epsilon. \qquad (6) $$

We avoided the inclusion of both green and red bands in the same model, given their high correlation ($R > 0.9$) to reduce the significant multicollinearity effects.
3) Multilinear Regression Model 2 (MR2): To characterize the land cover dependencies without the use of the NDVI, which becomes saturated at high LAI values (dense vegetation canopies), we propose a second version of the multilinear regression model which considers products and second-order polynomials of the spectral bands

$$ \bar{\rho}_{(g,red,nir),ref} = \beta_1 \bar{\rho}_{(g,red),tar} + \beta_2 \bar{\rho}_{nir,tar} + \beta_3 (\bar{\rho}_{(g,red),tar} * \bar{\rho}_{nir,tar}) + \beta_4 (\bar{\rho}_{(g,red),tar})^2 + \beta_5 (\bar{\rho}_{nir,tar})^2 + \epsilon. \quad (7) $$

To ensure that “black” surfaces have the same values for both target and reference sensors, both multilinear models are fit without a constant term.

4) SBAF Quadratic NDVI: Equation (8) shows the regression approach for the green, red, and NIR bands, using the SBAF

$$ \text{SBAF} = \frac{\bar{\rho}_{\lambda,ref}}{\bar{\rho}_{\lambda,tar}} = a + b \cdot \text{NDVI} + c \cdot \text{NDVI}^2. \quad (8) $$

5) SBAF Exponential NDVI: An exponential fit is proposed (9), which is steeper in the high and gentler in the low NDVI values, to account for the NDVI saturation for high LAI values [36]

$$ \text{SBAF} = \frac{\bar{\rho}_{\lambda,ref}}{\bar{\rho}_{\lambda,tar}} = a \cdot e^{b \cdot \text{NDVI}} + c \cdot e^{d \cdot \text{NDVI}}. \quad (9) $$

### C. Propagation of Uncertainties

When these adjustment equations are used with real data to correct for spectral effects, uncertainties from the surface reflectance measurements are propagated to the corrected reflectance. This means that, even if we found theoretically that a certain model performed better in terms of uncertainty than another model, this might not be the case operationally. For this reason, we simulate surface reflectance data with a 5% uncertainty and analyze the propagated uncertainties for the different models considered. Equation (10) shows the propagated uncertainty ($\sigma_f$) of a function f(x,y). ($\sigma_x, \sigma_y$) are the uncertainties of x and y, and $\sigma_{x,y}$ is the covariance between x and y

$$ \sigma_f^2 = \left| \frac{\partial f}{\partial x} \right|^2 \sigma_x^2 + \left| \frac{\partial f}{\partial y} \right|^2 \sigma_y^2 + 2 \left( \frac{\partial f}{\partial x} \right) \left( \frac{\partial f}{\partial y} \right) \sigma_{x,y}. \quad (10) $$

### D. HLS Product

To select low observation angles for Landsat 8, we use the image metadata and extract the images that compose a specific HLS image. We then identify the pixels from the tile with a close to nadir observation (viewing angle < 2°) using the trajectory overpass and tile geolocation. We do the same with Sentinel 2 images and select those pixels which overlap for both sensors. Overall, we obtained 1.7 × 10⁷ coincident pixels. From these, we masked pixels with high aerosol values to minimize atmospheric effects.

<figure><img src="image_6.png" /><figcaption>Fig. 4. SBAF dependence between MODIS Aqua (reference) and NOAA14 (target) based on the simulated data. The quadratic fit is shown in blue and the exponential fit in red.</figcaption></figure>

### E. AVHRR Time Series

In this section, we computed the NDVI value from the different sensor's surface reflectance which combines AVHRR/2 and AVHRR/3 measurements from the NOAA 7, 9, 11, 14, 16, and 18 satellites to produce a 36-year NDVI time series. We then corrected the time series using the different spectral adjustment parameters explained in detail in the following section and performed a Mann-Kendall correlation coefficient test [37], [38] to analyze the significance of the trends for each method. We used the Sen's slope method [39] to compute said trends and compared their value for the different methods proposed. The slope's confidence intervals were obtained by using the 95 and 5 percentiles of the individual slopes [40].

## IV. RESULTS

### A. Model Comparisons With Simulated Data

To justify the use of the SBAF exponential model as a correction to the SBAF quadratic model, Fig. 4 shows the SBAF dependence with the NDVI between simulated MODIS/Aqua data as a reference sensor and AVHRR/2 (NOAA14) as a target sensor. The blue line represents the quadratic fit, and the red line the exponential fit. The former shows some problems for low (<0.2) and high (>0.7) NDVI values, which are correctly modeled by the latter, evidenced by a decrease of RMSE and MAE of ~3%.

Table II shows the absolute values (x10⁻³) and percentage improvements in the APU values for the green, red, and NIR bands of four different sensors (L8, NOAA14, VIIRS, and S2) using the spectral adjustment regression methods considered in this paper. The retrieved coefficients for every sensor combination are available at http://ltdri.org/salsa/. MODIS/Aqua is used as the reference sensor. The improvements are calculated with respect to the spectrally uncorrected surface reflectance data, and the method that shows the highest increase for each case is highlighted. In the green band, the highest improvement in the accuracy is given by the SBAF exponential method, and the highest improvement in the precision and uncertainty is given by the MR1. In the case of S2, for example, the APU values increase
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