**1. Introduction**

Land surface albedo, which is defined as the fraction of incident solar radiation (0.3–5.0 μm) reflected by land surfaces [1], is widely used in ground energy balance analysis, weather climate prediction, and climate change research [2,3]. Existing global albedo products include the Advanced Very High-resolution Radiometer (AVHRR) [4–6], Earth Radiation Budget Experiment (ERBE) [7], Moderate-Resolution Imaging Spectroradiometer (MODIS) [8], Multi-angle Imaging SpectroRadiometer (MISR) [9], POLarization and Directionality of the Earth's Reflectances (POLDER) [10–12], Meteorological Satellites (Meteosat) [13], and Global Land Surface Satellite (GLASS) [14], are all conventional production. Their spatial resolution ranges from several hundred meters to several kilometers, which is much larger than the characteristic patch size for forest management, the typical field size of global agriculture, or the dominant extent of impervious surfaces in urban areas [15]. There is ye<sup>t</sup> demand for new land surface albedo estimation methodologies which span longer time periods without sacrificing high spatio-temporal resolution.

Previous researchers have proposed various techniques for estimating high spatial resolution albedo with satellite imagery. Liang [16], for example, used an extensive radiative transfer model as a conversion formula for calculating total shortwave albedo, total-, direct-, and diffuse-visible, and near-infrared broadband albedos for several narrowband sensors. He [17,18] later applied the algorithm to the Chinese environment and disaster monitoring and forecasting small satellite constellation (HJ) data and Landsat series data to derive 30 m resolution albedo data. The results were validated at Surface Radiation (SURFRAD), AmeriFlux, Baseline Surface Radiation Network (BSRN), and Greenland Climate Network (GC-Net) sites; the direct estimation algorithm did provide accurate albedo estimations for different land cover types with root mean squared errors (RMSEs) ranging from 0.022 to 0.034 for snow-free surfaces. Shuai et al. [19] proposed an algorithm for generating land surface albedo at 30 m resolution using Landsat and the anisotropy information from Moderate-Resolution Imaging Spectroradiometer (MODIS) observations. Their estimated albedos showed an absolute accuracy of ± 0.02–0.05, RMSE less than 0.03, and a bias less than 0.02 by comparison against field measurements. Zhang [20] used the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) to blend spatial information from fine-resolution shortwave albedo images and temporal information from coarse-resolution shortwave albedo images to successfully estimate high spatio-temporal resolution albedos. These methods all center on the use of Landsat imagery to obtain high spatial resolution albedos. However, Landsat data sets are affected by the long satellite return cycle and cloud contamination, and do not readily provide surface albedo data with high temporal resolution or time series albedo data.

Data assimilation is an effective approach to time series land surface parameter estimation. It is a mechanism to integrate various direct or indirect observation information types of varying resolution and from different sources to automatically adjust the model trajectory which provides accurate dynamic model state and model predictions. The Kalman filter algorithm was first developed in 1960 and later used to estimate time series soil moisture, leaf area index (LAI), and other surface parameters [21,22]. Li [23] proposed the Dual ensemble Kalman Filter (Dual EnKF) to estimate a time series LAI; Dual EnKF represents an updated LAI estimation with more sensitive parameters (LAI, Markov parameter, weight of the first price function, and weight of the second price function) in the dynamic model. Zhou [24] built a data-based mechanistic assimilation technique by coupling a revised universal data-based mechanistic model (LAI\_UDBM) with a vegetation canopy radiative transfer model (PROSAIL). The Ensemble Kalman filtering algorithm was applied to enhance the LAI estimation accuracy.

Many other researchers have achieved notable results in this field. Shi [25] used the China Land Soil Moisture Date Assimilation System (CLSMDAS) to perform an assimilation experiment on soil moisture based on the EnKF and Land Surface Process Model; their results reasonably reflected the spatial and temporal distribution of soil moisture. Jin [26] used the EnKF algorithm coupled with the canopy radiative transfer model (ACRM) to accurately predict time series LAI data from a phenological model. Xu [27] proposed an algorithm that integrated Direct Insertion (DI) and Deterministic Ensemble Kalman Filter (DEnKF) methods to assimilate snow depth with surface albedo; the solution was shown to improve the precision of snow depth simulations. Although the EnKF assimilation method has been widely used in the inversion of many surface parameters, it has not ye<sup>t</sup> been applied to the estimation of land surface albedos.

In this paper, we propose a time series high-resolution land surface albedo estimation algorithm based on the ensemble Kalman filter. The albedo dynamic model was established based on historical MODIS albedo products and Thematic Mapper (TM) observations, and albedo data was recursively updated via the EnKF method.

#### **2. Study Areas and Data**
