The position of the coastlines in the study area was visually interpreted based on various features on standard false-color remote sensing images, such as tones, textures, spatial mor- phologies, and distribution characteristics, referring to topographic maps of the study area, field observations, and other supplementary information。 Different interpretation standards were applied for the different coast types (Chang et al。, 2004; Ma et al。, 2007; Sun et al。, 2011)。In particular, artificial coasts directly border seawater and generally feature regular land-sea demarcation lines, like ports and enclosed embankments; the sea side of the artifi- cial coast was regarded as the artificial coastline。 For sandy coasts that are generally flat, sandy sediments are carried by the spring tide and often deposited to form a ridge that is parallel to the shore; the position of this ridge was regarded as the location of the coastline。 For muddy coasts that have been developed or encompass a relatively small area, the coast- line was regarded as the piding line between tidal flats and other surface features, such as vegetation, shrimp ponds, and roads, because at the height of spring tide, seawater cannot cross this piding line。 For muddy coasts without artificial development, the exposed land above the average high tide line during spring tides and the tidal flat below the average high tide line during spring tides will typically be portrayed in different colors in remote sensing images; the piding line between these two types of land was regarded as the coastline。 For bedrock coast, the locations where ocean capes and upright cliffs directly contact with sea- waters were regarded as the coastline。

To ensure that the unchanged portions of the coastlines were strictly consistent in position between two consecutive time periods, the coastline distribution in 2000 was visually inter- preted and digitized using the ArcInfo software platform to generate the coverage vector data。 Subsequent coastline measurements used the earlier coastline as the background data, and only the changed portions of coastlines were updated。 This approach effectively avoided the “double eyelid” phenomenon that would occur if the coastline dynamics had been di- rectly extracted from remote sensing images with different spatial resolutions that had been obtained at different times。

2。3Method of calculating the fractal dimensions of  coastlines

There are two methods for calculating the fractal dimensions of coastlines: the  pider method (Mandelbrot, 1982) and the box-counting method (Liebovitch, 1989)。 This study utilized the box-counting method to calculate these fractal dimensions。 The fundamental notion of the box-counting method is to use non-overlapping square  grids  of  different lengths to continuously cover the coastline that must be measured。 When the length of the square grid (k ) changes, the number of grids needed to cover the entire coastline, Nk (k ) will shift accordingly。 According to fractal theory:

摘要：本研究利用遥感和地理信息技术研究了从2000到2012年间，中国北方大陆海岸线的空间分布，并用盒计数法计算了海岸线的分形维数。此外，我们分析了在海岸线的长度的时空变化和分形维数的特征、长度的变化与分形维数的变化之间的关系以及中国北方的海岸线变化的驱动力。在研究期间，研究区的海岸线以每年53。16公里的速度增加了637。95公里。在区域一级，河北和天津的海岸线长度变化最为显著。在时间上，中国北部海岸线的增长速度在2008之后加快。最显著的增长是在2010和2011之间，以每年2。49%的速率增长。中国北方海岸线的分形维数在研究期间不断增加，而最剧烈的增长发生渤海地区。历史海岸线长度与分形维数（相关系数为0。9962）之间存在较强的正线性关系。通过对大量的当地海岸线变化的统计分析，可以发现，当地的海岸线长度的增加（或减少），在大多数情况下将导致整个海岸线分形维数的增加（或减少）。土木工程建设是驱动我国北方海岸线变化的最重要因素。港口建设、渔业设施和盐工厂三大建设活动的关系。与人类活动相比，河口沉积和侵蚀等自然过程的影响相对较小。