We first resampled and reclassified each land cover dataset into the same legend and spatial resolution (1/120 degree), denoted by **b**_{k,x,y}. We then combined them into a prior global land cover (**a**_{x,y}). The pixels with high consistence were then extracted and denoted by C_{x,y}. Finally, we updated the probability distribution of each pixel (
${\mathit{a}}_{\text{x},\text{y}}^{u}$) using Bayes theory and got the posterior global land cover map (
${C}_{x,y}^{T}$).

#### 3.1. Reclassification and Resampling

To facilitate fusion of different land cover maps, they need to be homogenized into a common legend, and in this study we selected the IGBP classification system (

Table 3). The 17 categories of IGBP land cover legend embrace the climate independence and canopy component philosophy presented by Running

et al. [

35], and are compatible with classification systems for environmental modeling for providing landscape information [

10]. The correspondence between the IGBP and other legends is rarely 100% [

24] and some classes have partial overlap [

19]. Simple conversion can produce errors. Thus, in this study every land cover type was translated to a state probability vector representing the probability it belongs to each IGBP land cover type. The state probability vector makes it possible to convert one land cover type to more than one IGBP land cover types and reduce error caused by land cover legend conversion.

Different land cover legends (UMD (

Table 4), FAO LCCS (

Table 5) and UN LCCS (

Table 6)) were converted to the IGBP legend according to comparison of legend definitions, pixel-by-pixel statistical comparison and previous comparison studies [

36–

38]. Because of insufficient information, each land cover type was converted to several IGBP land cover types equi-probably. Considering possible classification mistakes, we assumed that each pixel of every land cover map was classified into a wrong class with 50% probability. That is to say, in state probability vector of a certain land cover class, the total probability for all specified IGBP classes is 50%. This assumption will not substantially change the classification of each pixel but will allow for assessing the uncertainties of classification of land cover maps.

All the global land cover maps need to be projected to the same projection (geographical projection in this study) and resampled to the same spatial resolution (1/120 geographical degree in this study). The state vector of each resampled pixel was the average of original pixels’ state vectors, weighted by their area overlapped with resampled pixel. For example, when resampling from 300 m to 1 km, which does not fit with each other, as shown in

Figure 2, land cover state probability vectors of resampled pixels were combined based on the overlapped area with original pixels. By this method, no information will be lost when resampling.

Finally, all the global land cover data-sets were homogenized. The state probability vector of pixel located in the x-th path of y-th line in k-th land cover map is represented by **b**_{k,x,y}, of which b_{k,x,y}(i) stands for the probability it belongs to the i-th IGBP class.

#### 3.2. Generate Prior Global Land Cover Map

A prior global land cover needed by the Bayes method was generated by aggregating information provided by the existing land cover products, in which the prior state probability vector of pixel (x, y) is denoted by

**a**_{x,y}. Therefore, we need to combine probability distributions

**b**_{k,x,y} in existing land cover products into one. Without any other information available, simple axiomatic approaches [

39] were used, such as linear opinion pool,

and logarithmic opinion pool

where N is the number of land cover maps used (N = 5 in this study). w_{k} is the weight of the k-th land cover map (w_{k} = 1 in this study). β is normalizing constant. The prior land cover class is denoted by C_{x,y}, which was derived from

where M is the number of classes in the common legend (M = 17 for IGBP legend in this study). The parameter **a**_{x,y}(C_{x,y}) represents classification certainty for pixel (x, y). Without further information about which method is more accurate, both linear and logarithmic opinion pools were used when generating prior global land cover map in this study and their differences were also compared.

#### 3.3. Update State Vector of Each Pixel

The state probability vector of each pixel in the prior global land cover map was updated based on Bayes theorem. The updated probability for pixel (x, y) can be written as conditional probability given classifications of existing land cover products:

where
${C}_{x,y}^{T}$ is the true class of pixel (x, y), which is unknown, and t = 0,1,2, …, M − 1. The symbol ∩ denotes joint probability, C_{k,x,y} denotes the maximum likelihood land cover class in the state probability vector of pixel (x, y) in the k-th land cover map, which means **b**_{k,x,y}(C_{k,x,y}) = max_{0≤}_{i}_{<}_{M} **b**_{k,x,y}(i). According to Bayes formula, above conditional probability can be written as:

where

α is a normalizing constant.

$P({C}_{x,y}^{T}=t)$ is the prior probability that true class of pixel (x, y) is

t and identical to

**a**_{x,y}(

t). Given the assumption that each land cover map is independent,

Equation (5) can be rewritten as

Here,
$\alpha {\prod}_{k=1}^{N}P({\mathit{b}}_{k,x,y}\mid {C}_{x,y}^{T}=t)$ is the updating coefficient of prior state vector **a**_{x,y}(t).

For any k = 1,2, …, N in the updating coefficient, we have

As we do not know the true class
${C}_{x,y}^{T}$ for any pixel (x, y), we assume that for any pixel (x, y)
${C}_{x,y}^{T}={C}_{\text{x},\text{y}}$ if its certainty **a**_{x,y}(C_{x,y}) is higher than a given threshold. This threshold varies for different classes and is defined as the upper quartile of certainties for each class, so we have:

where

h_{t} is the certainty threshold for class

t. In other words, we figured out the probability in

Equation (8) by summarizing under condition of

C_{x,y} =

t and

**a**_{x,y}(

C_{x,y}) >

h_{t}.

After substituting

Equation (8) into

Equation (5) and normalization, we obtained the updated state vector

${\mathit{a}}_{\text{x},\text{y}}^{u}$. Furthermore, the posterior global land cover map

${C}_{x,y}^{p}$ was derived from: