An efficient depression processing algorithm for hydrologic analysis

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Abstract

Depression filling and direction assignment over flat areas are critical issues in hydrologic analysis. This paper proposes an efficient approach for the treatment of depressions and flat areas, based on gridded digital elevation models. Being different from the traditional raster neighborhood process which is time consuming, a hybrid method of vector and raster manipulation is designed for depression filling, followed by a neighbor-grouping scan method to assign the flow direction over flat areas. The results from intensive experiments show that there is a linear relationship between time efficiency and data volume, and the extracted hydrologic structures of flat areas are also more reasonable than those proposed by the existing methods.

Introduction

Because it is a fundamental problem in digital terrain analysis, the extraction of hydrologic structures plays an important role in applications such as hydrologic analysis, mineral deposition, land erosion, pollution diffusion analysis, etc. (Wolock and McCabe, 1995; Chen, 1991; Freeman, 1991; Moore et al., 1994; Li et al., 2004). Ridges and valleys are the basic features in hydrologic structure information. The most popular application extracts them from gridded digital elevation models (DEMs) and almost all the methods are based on the flow routing model (O’Callaghan and Mark, 1984; Jenson and Domingue, 1988; Tarboton et al., 1991; Moore et al., 1994). In such a model, the main task is to derive three matrices from the original DEM: the depressionless elevation matrix, the flow direction matrix and the flow accumulation matrix.

Depressions and flat areas are common in gridded DEMs; most of them are the result of mistakes, whereas some represent real terrain features, e.g., quarries and grottoes. The majority are spurious features, which arise from interpolation errors during DEM generation, truncation of interpolated values, and the limited spatial resolution of the DEM grid (Martz and Garbrecht, 1993). Depressions and flat areas must be dealt with as a precondition of flow route tracing, but the process is time consuming. So far, a number of methods have been developed for handling the depressions and flat areas of DEMs. Band (1986) simply increases the elevation of these cells until a downslope flow path to an adjacent cell becomes available. O’Callaghan and Mark (1984) attempted to treat them by smoothing the data. Jenson and Domingue (1988) and Martz and de Jong (1988) presented a method for filling depressions by increasing the elevation of cells in it to the elevation of the lowest overflow point on the depression boundary. However, these methods are effective only for the simplest cell, they change the nature of the terrain, and they may produce new depressions. Martz and Garbrecht, 1995, Martz and Garbrecht, 1998 proposed algorithms that considered both higher and lower terrain effects in dealing with depressions and flat areas. Thus, they produce more realistic results in applications. However, they still consider each depression separately and thus recursive detecting and filling processes may be required. The inherent problems of the efficiency and accuracy of these approaches have hindered their application in the processing of large-scale DEMs. Aiming at solving these problems, a hybrid method for depression filling using both vector and raster processes is proposed in this paper.

A raster process does not record the relationship of two objects (such as the depression and flat area) directly and searches its adjacent objects only through four or eight neighbors. On the other hand, a vector process considers the vector characteristics of the objects and treats an object as a whole. The hybrid method will be discussed in detail in the next section. Section 3 deals with the direction of flow over flat areas, assigned by applying a neighbor grouping scan method. Intensive experimental analysis is illustrated in Section 4. Finally, a few concluding remarks are given in Section 5.

Section snippets

Detecting depressions

There are three kinds of depression in gridded DEMs: single-point depressions, stand-alone depressions and compound depressions. The compound depressions include all complex topographic situations, such as looping depressions (adjacent depressions flowing into each other), depressions within flat areas, and truncation of depressions and flat areas at the edge of the DEM. Compound depressions have been recognized as one of the chief obstacles in the extraction of hydrologic structures (Jenson

Assigning flow direction over flat areas based on a neighbor-group scan

Assigning the direction of flow over flat areas is another stubborn problem in the computation of the flow accumulation matrix from gridded DEMs. The reasons why flat surfaces can arise in a grid DEM include sampling precision, data interpolation, some real terrain features, and the result of filling depressions (O’Callaghan and Mark, 1984; Freeman, 1991). To date, many methods of assigning the direction of the flow over flat areas have been devised. The main disadvantages of existing methods

Experimental analysis

The approach proposed above was implemented using Microsoft Visual C++ and tested with real DEMs of various sizes. A comparison of the results was carried out between the proposed method and one of the existing methods (the Spatial Analysis Tools of ArcGIS V9.0 developed by ESRI Inc.). The main purpose of the experiment was to investigate the efficiency and accuracy of the approach. The data sets used in the experiment were the square grid DEMs (with a 5 m grid cell size) obtained from aerial

Conclusion

This paper presents a new method to fill depressions by adopting vector processes combined with traditional eight neighborhood raster processes and assigns the direction of the flow over flat surfaces by applying a neighbor-grouping scan method. The approach has been tested with real DEMs, and the results show that it is efficient and its accuracy is better than existing methods. It is therefore more appropriate for the processing of large-scale DEMs, which can be used for spatial

Acknowledgments

This paper is supported by the National Basic Research Program of China (2004CB318206 and 2002CB312101), and the Hubei Outstanding Young Researchers Foundation of China (2004ABB018).

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