DEM

Digital Elevation Models

定义Surface analysis implies the analysis of continuous spatial variation. The most common application of surface analysis is Digital Elevation Modelling, which is widely employed in GIS. A DEM is a representation of three-dimensional (3D) space. DEMs are used for creating a surface of elevation data showing the rises and falls across a landform.

# surface: representations of continuous values across space. For data that are not continuous, surfaces must be created from the point, line, or polygon data.

分类In GIS, DEMs are modelled by regular grids( altitude matrices ) and triangular irregular networks( TINs ). The preference for one or the other depends on the kind of data analysis that needs to be carried out.
有关第一种分类方法Altitude matrices are the most common form of discretized elevation surface( 离散高程面 ), which is a regular grid of numbers which represent elevation above an arbitrary datum( 假定基面，such as mean sea level ). The advantage of this one is easy to be manipulated, that is the reason which has become the most available form of DEM. Grid DEMS are ideal for visualization in landscape that do not have abrupt changes, like cliffs, and data that are sampled almost regularly across a landscape.
第一种分类方法缺点The disadvantages of altitude matrices include:

a) The large amount of data redundancy in areas of uniform terrain( 均匀地形 )

b) The inability to adapt to areas of differing relied complexity without changing the grid size

c) The exaggerated emphasis along the axes of the grid for certain kinds of computation such as line-of-sight calculations( 感觉就是过度依赖网格 )

第二种分类方法 TIN is a surface of triangular elements. Small triangles can be clustered around the data-rich, highly variable areas, and large triangles can be used to represent regions of very little undulation. TINs can avoids the redundancies of the altitude matrix and can be more efficient for many types of computation. Unlike altitude matrices, TINs allows extra information to be gathered in areas of complex relief without the need to gather huge amounts of redundant data from areas of simple relief.( 允许在复杂地形区域收集额外信息，而无需从简单地形区域收集大量冗余数据 ) Cause the grid cell size is constant across a surface, whereas the TIN element can alter in size between data-rich (small triangles) and data-poor (large triangles) locations
由于TINs triangular的引入会使模型离散化，这种离散化会影响分析结果
TINs与vector polygons的区别是，前者无需make provision for islands of holes
Altitude matrices can be converted to TINs, other, vice versa
DEM data sources:

a) Ground survey

b) Creating digital elevation models from stereo aerial photography and satellite images( photogrammetry, radar-based systems, laser-based systems )

c) Interpolating from digitized contours to an altitude matrix

d) Geometry correction for altitude matrices and other raster data

e) Digital orthophotos( updating orthophotos )

A grid surface is usually created from a point layer, through interpolation methods, which estimate values for unknown locations based on values at known locations to create a continuous surface. Interpolation is based on one of the basic principles of geography, known as Tobler’s Law( all things are related, but near thins are more related than distant things )

谨遵医嘱

surface analysis指对连续空间变化的分析
surface表示空间中的连续值，除了数字图像外，很少用这种方式捕捉数据。对于非连续数据，必须从point、line或polygon创建曲面
points是基本要素，non-point data( lines + polygon转化为point形成surface
spatial autocorrelation: self-similarity in nearby values (Tobler’s Law), is the relationship between objects based on the difference in their distance and values
point interpolation: is the process of predicting the value of attributes at unsampled sites from measurements made at point locations in the same area or region. Predicting the value of an attribute sites outside the area covered by exciting observations is called extrapolation是根据在同一区域或区域的点位置进行的测量来预测未采样点属性值的过程。预测兴奋观测覆盖区域外的属性点的值称为外推
point interpolation is used to convert data from point observations to continuous fields so that spatial patterns sampled by these measurements can be compared with the spatial patterns of other spatial entities. Areal interpolation is used to transfer data values from one set of zones or areas to another, areal weighted overlay is often used to combine two different sets of zones and transfer counts from one set of zones to another. 点内插法用于将点观测数据转换为连续场，以便将这些测量数据采集的空间模式与其他空间实体的空间模式进行比较。区域插值用于将数据值从一组区域或区域传输到另一组区域，区域加权叠加通常用于组合两个不同的区域集，并将计数从一组区域传输到另一组区域
interpolation is necessary when:

a) when the discretized surface has a different level of resolution, cell size, or orientation from that required当离散曲面的分辨率、单元大小或方向与所需的不同时

# the conversion of images from one gridded tessellation, with a given size and/or orientation, to another, this procedure is generally known as convolution将具有给定大小和/或方向的图像从一个网格化细分转换为另一个网格化细分，此过程通常称为卷积

b) when a continuous surface is represented by a data model that is different from that required

# the transformation of a continuous surface from one kind of tessellation to another

c) when the data we have do not cover the domain of interest completely

# the conversion of data from sets of sample points to a discretized, continuous surface

we must distinguish situations with dense sampling networks from those with sparse sampling networks, or data collected along widely spaced transects我们必须区分密集采样网络和稀疏采样网络的情况，或沿宽间距横断面收集的数据 Dense sampling networks are common when creating hypsometric surfaces(DEM), where the source data are cheap and the attribute can be observed directly密集采样网络在创建高度计曲面（DEM）时很常见，因为源数据便宜，可以直接观察属性
the continuous surface obtained from interpolation can be used as map overlays in a GIS of displayed in their own right. The surfaces can be represented by the data models of contour lines, discrete regular grids, or by irregular tiles. the data structures used are regular grids, contour lines or triangular irregular networks(TINs)

# because the interpolated surfaces vary continuously over space, regular gridded interpolations must be represented by a data structure in which each grid cell can take a different value, therefore space-saving raster data structures such as run-length codes and quadtrees cannot easily be used

the original data may be collected as point samples distributed regularly or irregularly in space, or they can be taken from already gridded surfaces such as those obtained by remote sensing