**1. Introduction**

The Advanced Very High-Resolution Radiometer (AVHRR) sensor provides a unique global remote sensing dataset that ranges from the 1980s to the present. Among the different products delivered from this sensor, NASA is currently funding the Long Term Data Record (LTDR) project [1] to develop a quality and consistent Climate Data Record (CDR) of AVHRR data with the use of the Moderate Resolution Imaging Spectrometer (MODIS) instrument as a reference. This data record creates daily global surface reflectance products with a geographic projection at coarse spatial resolution (0.05◦). The utility of this long time series has been demonstrated in the literature for a large number of applications such as agriculture [2], burned area mapping [3], Leaf Area Index (LAI) and Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) retrieval [4,5], snow cover estimation [6], global vegetation monitoring [7], and surface albedo estimation products [8–11].

Long-term consistent data records are becoming crucial to provide improved detection, attribution and prediction of global climate and environmental changes, as well as helping decision makers respond and adapt to climate change and other variability in advance [12–14]. The knowledge of surface albedo is of critical importance to monitor land surface processes and plays an important role in energy-budget considerations within climate and weather-prediction models. For this reason, it has been listed as an Essential Climate Variable by the Global Climate Observing System (GCOS) [13,15]. Surface albedo can be derived from satellite data. The most common procedure consists on integrating a BRDF angular model, which can explain the reflectance's anisotropic behavior on different types of surfaces to obtain the black-sky (direct beam) and white-sky (completely diffuse) narrowband albedo. One can then perform narrow-to-broadband conversions to obtain the respective broadband albedos [16] and obtain the actual (blue-sky) albedo by doing a weighted average, using the fraction of diffuse skylight [17].

For this product to be of highest quality, it is critical that the surface reflectance data record has minimal uncertainties in the calibration, geo-location, spectral correction, cloud masking, atmospheric correction and directional effects correction. Issues regarding calibration, cloud masking and atmospheric correction in the AVHRR data have been accurately corrected, after the year 2000, when MODIS data were used as a reference [2]. However, some issues persist for data before this year (1982–2000), such as aerosol and water vapor correction and calibration [1]. These errors propagate resulting in surface reflectance time series with high noise. This is especially true in the red band, where the atmospheric errors are higher, compared to the Near Infrared (NIR) band. Therefore, the BRDF parameters derived from these time series have high uncertainties and might not provide an accurate correction of the directional effects.

To address this issue, the LTDR product uses MODIS retrieved parameters using the Vermote, Justice and Bréon (VJB) method [18,19] and then applies them to AVHRR data. The VJB method uses a pixel's time series (typically 5 years) to compute BRDF parameters (V, R) in a daily manner. This is done with the use of the instantaneous Normalized Difference Vegetation Index (NDVI), which quantifies the vegetation by measuring the difference between NIR and red sunlight. These parameters can later be used to correct the database. This method is based on the assumptions that 1) the target reflectance changes during the year but BRDF shape variations are limited and 2) the difference in surface reflectance between successive acquisitions is mostly explained by directional effects.

Assumption 1 holds true while retrieving the correction parameters with short enough periods, or in other words, if the surface doesn't change significantly over this period. When dealing with AVHRR data, due to the lower number of high-quality observations, a larger number of years is required to make the computation of the BRDF parameters reliable, in which the surface is subject to change. One could argue, however, that because the product is at 0.05◦ spatial resolution, the stability of the pixel through the years is more likely to be maintained. Assumption 2 holds true for MODIS data because the evolution of the view zenith angle during the year is not gradual, so the difference between successive observations is high, and atmospheric errors are low. This means that the time series have high directional effects, which are higher than the atmospheric correction errors. This is not the case for AVHRR data; the difference of view zenith angle between successive observations is low and atmospheric errors are high, especially for the red band. These facts could justify the use of MODIS parameters to correct AVHRR data, however, these also experience propagated uncertainties caused by the different spectral response of the two sensors or calibration issues of AVHRR.

In this paper we explore different approaches to the AVHRR directional effects correction using the VJB method, to optimize it to AVHRR data. Firstly, we find relationships between BRDF correction parameters using different bands and band combinations derived from MODIS data. With this, we aim to minimize the propagation of atmospheric errors to the correction of directional effects. Secondly, we calculate said parameters using 3 years and the whole time series (15+ years). To test the best method, we compare the noise of the normalized surface reflectance to check which one shows the lowest noise in the time series. Section 2 describes the materials used for the study and the methodology employed. Section 3 presents the results. Section 4 presents a discussion of the results and Section 5 presents the conclusion.

## **2. Materials and Methods**
