针对目前基于统计或物理模型方法的升尺度转换研究中存在的不足,以归一化差分植被指数NDVI为研究对象,基于分形理论提出一种连续空间升尺度转换模型CSSM(Continuous Spatial Scaling Model)构建方法.所构建的模型尺度适用范围更广,且具有一定的物理意义.针对已有研究尚未解决的模型构建的最合理尺度层级确定问题,结合原有的统计学四指标评价体系(r、p、rlo、rup),融入了真实性检验应用效能评价指标(Max_of_abs(Error)),建立了一个基于五指标评价体系的模型构建最合理尺度层级确定方法.以北海市沙田半岛Landsat ETM+影像为实验影像,设定r≥0.8,p<0.05,rlo≥r≤rup及Max_of_abs(Error)≤0.05为评价体系的边界条件,从追求模型尺度适用范围更大的角度考虑,确定出该影像模型构建的最合理尺度层级Level=267,则该模型最高可对30 m×267即8 km分辨率遥感影像进行NDVI验证.通过动态调整此评价体系的边界条件,实现了最合理尺度层级取值的敏感性分析.这些工作使得基于分形理论的NDVI's CSSM构建研究更为系统.

Spatial scale transformation is one of the basic and important scientific problems in quantitative remote sensing field. Spatial up-scaling has particularly drawn much attention, as it can effectively help solve difficult problems, e.g., validation of quantitative remote sensing products. However, some issues remain concerning spatial up-scaling research. (1) The transformation formula established by statistical methods has no explicit physical meaning and its available range is limited. (2) The lack of reasonable retrieved physical models hampers the development of up-scaling based on these models. As an important retrieval method, the up-scaling of NDVI also faces these two issues. To address these problems using statistical and physical methods, continuous spatial scaling model (CSSM) of NDVI on the basis of fractal theory was established. The CSSM exhibits a wide available scale range and partial physical meanings. However, the means of determining the most reasonable Level (scale hierarchies) for establishing the model remains an important problem, which is studied in this research.In this research, a precise and rigorous method of determining the most reasonable Level was developed based on a five-index estimation system. The system integrates statistical estimation indices (r, p, rlo, and rup) and an availability-in-validation index [largest error in validation, Max_of_abs(Error)]. It was computed as follows. First, the NDVI CSSM of an image was established on each of the different Levels. Second, the indices (r, p, rlo, and rup) on each Level were compared and analyzed. Third, the most reasonable Level could be computed based on the defined Max_of_abs(Error) to establish the widest scale CSSM.Shatian Byland (Beihai City, Guangxi Zhuang Autonomous Region) was selected as the experimental area because of its variety of ground objects and high spatial heterogeneity. Taking the values (r≥0.8, p<0.05, rlo≥r≤rup and Max_of_abs(Error)≤0.05) as estimation system, the most reasonable Level (Level=267) was computed. On that Level, the model was log₂NDVI=-0.0347log₂1scale-1.1296 and its scale range was from 30 m to 8010 m. Within the range, validating the NDVI image on any up-scale (corresponding to the integral multiple of the 30 m resolution of ETM+ image) could be implemented by the model. Furthermore, the sensitivity of the Level to values of the estimation system was analyzed. The Level would dynamically change when the threshold values of the five-index estimation system were different and the application purpose changed, which meant that the method in the research was steady and rigorous.In this research, the method of determining the most reasonable Level for establishing the CSSM of NDVI was developed based on a five-index [r, p, rlo, rup, and Max_of_abs(Error)] estimation system. This model quantitatively described the transformation relationships of NDVI on continuous scales. On the basis of this result, NDVI validation of different low-resolution images could be implemented rapidly and effectively. This work results in a more systematic research on modeling the CSSM of NDVI.