JIA-2019-11

2635 ZHANG Xi-wang et al. Journal of Integrative Agriculture 2019, 18(11): 2628–2643 class among all classes. Alternatively, one can assume the same probability of each class, and then determine it using an iterative method. 3.4. Winter wheat identification model In this section, we design an Abundance-Membership (AM) model to identify winter wheat by integrating the assessed abundances from temporal information and the membership for winter wheat from spectral information. Because the MODIS 250 m data and TM 25 m are strictly registered, each MODIS pixel corresponds to 10×10 TM pixels in the space. Assuming the MODIS data has m rows and n columns in this study area, the abundance image is processed as follows: mn m1 1n 11 AI AI AI AI PAI = Int (100 AI )= Int ... ... ... ... ... 100 (7) where PAI is the processed abundance image at the MODIS scale; AI is the original abundance image; AI ij is the original abundance value of the pixel at the i th row and j th column, 0≤ AI ij ≤1; and Int is a function for a rounding operation. Then, PAI ij is the pixel value of the processed abundance images at the i th row and j th column, 0≤ PAI ij ≤100. For the processed abundance image, the corresponding pixel membership matrix (10×10 membership pixels at 25 m scale) of each MODIS pixel is processed as follows: ( )      = = ijkk ijk 1 ij 1 k ij 11 ij ij ij ij P P P P , , PAI Matrixrank P PAI Matrixrank CT ... ... ... ... ... (8) where CT ij is the calculated threshold for the membership matrix corresponding to the abundance pixel at the i th row and j th column; P ij is the membership matrix corresponding to the abundance pixel at the i th row and j th column; P ijhl is the membership value at the h th row and l th column in this membership matrix, k =10, 1≤ h ≤ k , 1≤ l ≤ k ; and Matrixrank is a function that sorts 100membership values in descending order within thematrix P ij , and outputs the PAI ij thmembership value. Based on the spatial relationship between the abundance and membership data, winter wheat pixels are identified according to the relative size of the membership values in the corresponding matrix. In each matrix, winter wheat is identified by the eq. (9): < ≥ = ij ijhl ij ijhl ijhl CT P 0 CT P 1 RES (9) where RES ijhl is the value of the identified pixel at the h th row and l th column in the membership matrix which corresponds to the abundance pixel at the i th row and j th column. With this method, the memberships are compared in a small matrix of 10×10 pixels, rather than in the entire study area. In other words, this method relies on the relative membership value in the partial space. An example is shown in Fig. 5. Assuming that the abundance value AI ij at the i th row and j th column is 0.58 (Fig. 5-A), and the corresponding matrix is as shown in Fig. 5-B, then the calculated threshold CT ij will be 60. Finally, the pixels whose values are ≥60 are identified as winter wheat (Fig. 5-C). 3.5. Validation Acreage accuracy (Aa) and sampling accuracy (As) are employed to validate the identification results. The former reflects the closeness of the model-identified acreage to the true acreage, and the latter reflects the sampling accuracy of the identified winter wheat. This study considers the official statistics acreages as the true values, and Aa is defined as: ×100 1 Aa (%) − −= Ao Ao A (10) where A is the identified winter wheat acreage in this study area and Ao is the official statistics acreage. AI ij =0.58 + 0.25 0.35 0.40 0.42 0.46 0.50 0.52 0.58 0.61 0.63 = 0.25 0.35 0.40 0.42 0.46 0.50 0.52 0.58 0.61 0.63 0.32 0.41 0.45 0.48 0.50 0.53 0.57 0.61 0.64 0.66 0.32 0.41 0.45 0.48 0.50 0.53 0.57 0.61 0.64 0.66 0.35 0.43 0.47 0.50 0.53 0.56 0.61 0.65 0.67 0.68 0.35 0.43 0.47 0.50 0.53 0.56 0.61 0.65 0.67 0.68 0.36 0.45 0.48 0.52 0.57 0.59 0.65 0.66 0.69 0.71 0.36 0.45 0.48 0.52 0.60 0.60 0.65 0.66 0.69 0.71 0.38 0.50 0.51 0.55 0.58 0.61 0.63 0.68 0.71 0.73 0.38 0.50 0.51 0.55 0.61 0.61 0.63 0.68 0.71 0.73 0.40 0.53 0.56 0.58 0.61 0.65 0.66 0.69 0.73 0.76 0.40 0.53 0.56 0.58 0.61 0.65 0.66 0.69 0.73 0.76 0.40 0.56 0.59 0.60 0.62 0.66 0.68 0.70 0.76 0.79 0.40 0.56 0.59 0.60 0.62 0.66 0.68 0.70 0.76 0.79 0.42 0.50 0.62 0.63 0.66 0.70 0.71 0.73 0.80 0.82 0.42 0.50 0.62 0.63 0.66 0.70 0.71 0.73 0.80 0.82 0.45 0.50 0.65 0.66 0.70 0.72 0.73 0.80 0.82 0.85 0.45 0.50 0.65 0.66 0.70 0.72 0.73 0.80 0.82 0.85 0.50 0.51 0.72 0.72 0.75 0.79 0.80 0.82 0.85 0.90 0.50 0.51 0.72 0.72 0.75 0.79 0.80 0.82 0.85 0.90 A B C 25 m 250 m Fig. 5 An example showing the proposed identification model. A, a single pixel and its value in the abundance image. B, the corresponding 10×10 membership matrix and the membership values. C, the shaded area is the resulting area identified as winter wheat.