###### Abstract
Moreover, the number and types of selected PolSAR parameters for investigating temporal variation are also limited, such as SAR backscattering and ratios, polarimetric decomposition parameters, polarimetric coherences and phase differences. Meanwhile, fewer polarimetric observables inputting to layer combinations might achieve better results in crop applications [38]. Few efforts have been made in optimal combination of SAR features for crop classification. The common way for constructing a feature set is to stack all polarimetric observables from various sources [7; 17; 27; 39]. In addition, comparable or even better crop classification results might be obtained by combining fewer images on dates of critical phenology [10; 27]. However, such research topics have not been well studied for crop classification using SAR time-series data. The usual approach for combination of multitemporal SAR images is adding images one by one sequentially along the SAR acquisition time [39; 40]. Classification accuracies usually approach saturation as the number of images increases. Recently, a forward selection procedure was proposed for searching the optimal combination of SAR images that make the best tradeoff between classification and number of images [7]. In this procedure, the SAR images for classification were gradually selected and included in the image set (starting with an empty image set) with an increment step of one acquisition date. The tests with an L-band PolSAR time-series indicated that the combination of SAR images achieving the best crop classification accuracy could be arbitrary selections from the SAR dataset [7]. The concept of the forward selection procedure can be expanded in search of the optimal combination of polarimetric observables for crop classification, i.e., forward feature selection. Moreover, the optimal combination of both factors, i.e., polarimetric observables and SAR images, will be an interesting topic. The motivation of this research work was to evaluate the potential of time-series polarimetric C-band RADARSAT-2 images acquired in the same beam mode across a full growing season for crop monitoring and classification. The major scientific innovations and goals of this research can be summarized as follows. First, the responses and seasonal patterns of 27 widely used polarimetric observables, categorized into ten groups, were quantitatively analyzed for different crop types, providing comprehensive analyses of radar signatures over an agricultural area. Second, using the well-known Random Forest (RF) algorithm, crop classifications with single groups of polarimetric observables were conducted and their accuracies compared. Third, the concept of optimal combination for crop classification was applied and expanded to both SAR images and polarimetric observables. As a result, the forward selection procedure was applied and expanded for searching the optimal combination of polarimetric observables, SAR images or both, respectively. This concept was exploited to achieve the best tradeoff between classification accuracy and number of parameters, image acquisitions or both factors. Moreover, it could be transferable to SAR data at other frequencies, other incidence angles or other agricultural areas. In addition, the variable importance for crop classification was quantified across 27 input variables as well as over acquisitions. For testing purposes, an agricultural area with various crop types in southwestern Ontario, Canada, was selected as the test site. Seven fully polarimetric SAR images acquired in the same beam mode (with the same spatial resolution and incidence angles), covering the entire growing period of major crops of the region, were exploited.