Computers & Geosciences 36 (2010) 1427–1435
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A modified binary tree codification of drainage networks to support complex hydrological models Tiejian Li a,b, Guangqian Wang a, Ji Chen b,n a b
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
a r t i c l e in fo
abstract
Article history: Received 27 June 2009 Received in revised form 13 April 2010 Accepted 14 April 2010
A new codification method (named a modified binary tree codification method) is developed for coding drainage networks. To express the inner topological structure of a drainage basin, it is necessary to delineate and code digital drainage networks from digital elevation model datasets. In this study, the established software TOPAZ is used to delineate river reaches, and the new codification method is applied, which is based on the application of binary-tree structures and hierarchical zones. A coded drainage network can then be stored in a relational database management system to achieve efficient manipulation of data items for topological operations. The utility of the new codification method is demonstrated by an example applied to the Digital Yellow River Model. The drainage network of the Middle Yellow River in northern China has been coded and the hydrological and soil erosion processes of its sub-basin, the Chabagou River basin, are simulated. Because more details of the drainage network can be efficiently and effectively described, the new codification method can support complex hydrological models and extract more information from hydrological simulations than ever before. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Binary-tree-based codification Digital drainage network Hierarchical zoning Complex hydrological model
1. Introduction In the geosciences, the digital delineation of drainage basins has been rapidly advancing since the 1980s, largely due to improvements in computer hardware, software and the availability of digital elevation model (DEM) data. One of the most important developments of computer software for the geosciences is the availability of a geographic information system (GIS). A GIS can cope with DEM data, such as GTOPO30 DEM data (Gesch et al., 1999), the Shuttle Radar Topography Mission (SRTM)1 DEM data, the National Elevation Dataset (NED) of the United States (Gesch et al., 2002), and the European DEM (EuroDEM),2 to delineate river basins and drainage networks digitally. To simulate the hydrological response of a drainage basin, it is essential to express the topological structure of its drainage network, including river reaches and related hillslope units, which can be extracted from DEM datasets. Several computer software packages, such as WMS (Watershed Modeling System) (Environmental Modeling Research Laboratory, 1998),
n Corresponding author at: Department of Civil Engineering, The University of Hong Kong, Hong Kong, China. Tel.: + 852 28592646; fax: + 852 25595337. E-mail addresses:
[email protected] (T. Li),
[email protected] (G. Wang),
[email protected] (J. Chen). 1 Shuttle Radar Topography Mission, http://www2.jpl.nasa.gov/srtm/. 2 EuroDEM, http://www.eurogeographics.org/content/products-services-euro dem.
0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2010.04.009
TOPAZ (Garbrecht and Martz, 1999), Arc Hydro Tools (Maidment, 2002), GRASS (Geographic Resources Analysis Support System) (Neteler and Mitasova, 2008) provide tools for the extraction of drainage networks. Moreover, numerous studies (e.g., Colombo et al., 2007; Lehner et al., 2008; Verdin and Verdin, 1999) have applied them in order to extract drainage networks from DEM datasets. Verdin and Verdin (1999) applied the GTOPO30 DEM dataset to create a comprehensive reference system, HYDRO1k, for the global river basins. Colombo et al. (2007) extracted the drainage networks for large catchments across the European continent based on the concepts of mathematical morphology. Lehner et al. (2008) developed seamless, high resolution and high quality global hydrographical maps including drainage networks from SRTM DEM datasets. The development of a digital drainage network generally includes two steps, delineation of sub-basins and related river reaches, and codification of them (Verdin and Verdin, 1999). With a DEM dataset, the derivation of topographic parameters (e.g., river reaches) is largely based on the determination of flow directions among grid cells, as in the algorithm of eight flow directions (D8) (e.g., O’Callaghan and Mark, 1984; Quinn et al., 1991; Tarboton, 1997; Tribe, 1992). Presently, compared to the developments in the codification methods, the delineation methods are well explored and have been documented in literature. The lack of development in the codification methods could be because delineation of drainage networks is more fundamental in nature than codification. However, in practice,
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the shortage of efficient and effective codification methods has, to a certain degree, obstructed the application of hydrological models. For example, nowadays, some hydrological models (e.g., SWAT (Neitsch et al., 2005) and HSPF (Bicknell et al., 2001)), which are complex hydrological models, have become more sophisticated after the incorporation of biological, chemical, and other physical processes (Singh and Woolhiser, 2004). Normally, it is required to describe drainage networks with higher resolutions, which results in the demand for coding the connection of river reaches and the structure of a drainage network efficiently. For this propose, an efficient codification method is needed which should have at least two features like (1) identify a river reach directly by the code rather than by an inefficient search and (2) possess obvious topological meaning and judge its topological relationship in a drainage network. Presently, to the best of our knowledge, only the method developed by Pfafstetter has the above two features (Verdin and Verdin, 1999). However, the weakness of the Pfafstetter method, which will be reviewed in the next section, still hinders the effective application of complex hydrological models to largescale drainage networks with high spatial resolutions. By reviewing the existing codification methods and simultaneously overcoming the weakness of the Pfafstetter method, an efficient and effective codification method to support complex hydrological models is developed and reported in this paper. The new codification method is integrated with the established Digital Yellow River Model (DYRIM) (Wang et al., 2007). The DYRIM incorporates multiple models for simulation of hydrological, soil erosion and sediment transport processes in the Yellow River basin. Since the topography of the Middle Yellow River basin is rather complex (Wang et al., 2007), it is necessary to adopt a high-resolution drainage network in the DYRIM. As an example, the codification of the drainage network of the coarse sediment source region in the Middle Yellow River is introduced, and the simulation of the hydrological and the soil erosion processes over a sub-basin of the region is conducted in this investigation.
2. Literature review Garbrecht and Martz (1997) method was used in TOPAZ, to code a drainage network from a basin outlet to every headwater reach recursively. Assigning serial numbers, each reach and all its upper left child reaches are coded from the downstream to upstream of a basin. All its right child reaches are then coded accordingly, which is like a pre-ordered traversal of a binary tree. The allocation of the serial number allows the automated determination of flow routing sequence in a drainage network and this technique has been used for the parameterization of hydrological models (e.g., Lacroix et al., 2002). Nevertheless, the method of applying serial numbers for the codification (Garbrecht and Martz, 1997) may be difficult in describing the topology of a complicated drainage network like the Middle Yellow River basin. Pfafstetter proposed a subdivision and codification method to describe drainage networks for presenting the topological structure of river basins (Verdin and Verdin, 1999). The Pfafstetter approach codes a drainage network from the level of a whole continent, to a whole basin, and then to the level of river reaches of its sub-basins, step by step. At each step, a basin is divided into up to a maximum of 10 sub-basins with ordinal numbers varying from 0 to 9. Numbers 2, 4, 6, and 8 are assigned to the 4 largest tributaries from the downstream to upstream, and numbers 1, 3, 5, 7, and 9 are assigned to the corresponding 5 sub-basins along the mainstem. The one nearest the outlet is designated as 1 and increasing progressively up to the headwater area designated as 9. An endorheic sub-basin is
denoted by 0 (Verdin and Verdin, 1999). Recursively applying the same rules, until the scale of tributaries reaches a predetermined size, a river basin can be divided into different levels of sub-basins. With catenation of the numbers gained at each step, the codes of all the sub-basins (or river reaches) are obtained to identify the river network (Verdin and Verdin, 1999). The Pfafstetter coding system is based on the natural topology of river networks, and it carries topological information with economic number digits applicable to the organization of hydrological data. Verdin and Verdin (1999) applied the Pfafstetter codes to the HYDRO1k, which has been used to study large scale terrestrial hydrological processes (e.g., Chen and Kumar, ¨ ¨ 2001). Furst and Horhan (2009) developed a piece of software with Arc Hydro Tools to code stream network and watersheds using a modified version of the Pfafstetter approach and applied it to code the drainage network of Austria. For the whole of Europe, a pan-European river and catchment database (Vogt et al., 2007) has been developed under the European Union Water Framework Directive (WFD). It is based on the hierarchical Pfafstetter coding system to characterize the structure of a river network and to identify each river reach. Moreover, Jia et al. (2006), Shrestha et al. (2008), and Yang et al. (2004) used the Pfafstetter codes in the division and identification of sub-basins for hydrological and environmental modeling. Each digit of the Pfafstetter code has its topological meaning. For example, the number can indicate the position of a related reach on or off a mainstem, and its location in the downstream or the upstream of a reference section. However, there are two major deficiencies of the Pfafstetter method. Firstly, the areas of subbasins at a certain sub-basin level may differ greatly, which is mainly caused by the separation of sub-basins along the mainstem. At a certain step of separation, sub-basins along the mainstem are separated at the confluence points without any control by the sub-basin size. For example, when two confluence points along the mainstem are close, generally, a relatively small sub-basin between these two points is separated. After a number of separation steps, the difference of sub-basin sizes can be enlarged greatly (e.g., see Fig. 3 in Jia et al., 2006). Secondly, when less-than-9 division is used to code sub-basins, the incomplete Pfafstetter codes will be generated, which will result in the low efficiency in identifying the sub-basin topology. For example, to search the connected downstream sub-basin, which is coded by the incomplete Pfafstetter code, for a given subbasin, the multiple trial-error search operations or a multi-result search would be conducted to run the topological operations using the incomplete Pfafstetter codes. Therefore, it can be concluded that incomplete Pfafstetter codes are not efficient for some topological operations.
3. Development of the new method In this study, a binary-tree-based hierarchical zoning codification method, the so-called modified codification method, is developed to code drainage networks. In this method, codes are assigned to river reaches so as to identify them and to express their hierarchical position in a drainage network. This new method consists of three parts. The first part is the binary-treebased codification of river reaches, the second is the hierarchical zoning of a drainage network, and the third is the database management of the coded drainage network. 3.1. Binary-tree-based codification According to the three-zone watershed concept (Schumm, 1977), a natural drainage network is generally tree-like. If there is
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Fig. 2. A typical section of a drainage network.
Fig. 1. (a) Array-based binary tree. Connected nodes can be directly located by sequential indices. (b) Two-component code for a binary tree. Component L indicates level of a node in tree, and component V (in circles denoting nodes) indicates index of a node in its level L and grows from left to right from 0 to 2L 1 1. Dash circles are vacant nodes.
a confluence point where more than two upstream reaches flow into a downstream reach, virtual reaches can be added at that point to make the drainage network become a binary tree. In computer science, a binary tree is a typical data structure commonly used to implement binary search trees and binary heaps. A complete binary tree is defined as one in which every level is completely filled. Such a tree has a special feature. If all the nodes are numbered in order, level by level, from the root as 0 and node by node from left to right, the indices of the child nodes of a node k are 2k+ 1 and 2k+ 2 (see Fig. 1(a)). Using this numbering system, a tree structure can be compactly stored in a continuously indexed array, with the indices identifying the nodes directly. This is named the array-based binary tree (Kruse and Ryba, 1999). While the nodes of a complete binary tree can be stored and directly located in a continuous array, a drainage network normally is a highly incomplete binary tree. If an array is used to store river reaches, most of the array spaces would not be effectively used. In addition, if the indices are used to code river reaches, the growth of their values would be rapid. In order to overcome the above obstructions in applying the indices of an array-based binary tree to a drainage network, a code with two components (see Fig. 1(b)) is used in this study. The level of a node in the tree is separately recorded as a component L, and the index of the node at level L is recorded as the other component V. Component V is numbered as 0 from left sequentially to right as it is in a complete tree. Therefore, even if there are vacant nodes (see the dash circles in Fig. 1(b)) in the tree, the relationship between parent and child nodes is similar to a complete tree. Namely, if a node at level L has component V equal to Vi, the values of its two children at level L+ 1 are 2Vi and 2Vi +1, respectively (Fig. 1(b)). Generally, each reach in a drainage network has two topological attributes, upstream–downstream and primary–secondary. The primary denotes that the reach is the local mainstem, and the other reach is secondary. Fig. 2 shows a typical section of a drainage network to demonstrate these two topological attributes. In Fig. 2, the reach labeled 1 is the downstream
reach, reach 2 is the upper primary reach, and reach 3 is the upper secondary reach. The relationships between reaches 2 and 1, and between reaches 3 and 1, are upstream–downstream, and the relationship between reaches 2 and 3 is primary– secondary. The upstream–downstream relationship represents a nonreversible connection where flow is from the upper reach to the lower reach. The primary–secondary relationship indicates that the flows from two reaches converge toward a confluence point, and, therefore, there is no flow exchange between these two reaches. The binary-tree-based codification approach expresses the relationships of upstream, downstream, primary and secondary reaches in a simple and direct manner. For a certain reach, with the two-component code denoted as (Li, Vi), all its connected reaches can be located directly. Its downstream reach is the one with code (Li 1, Vi\2) (notation ‘‘\’’ is the integer division, returning the integer number only from a division), and the codes of its upper primary and secondary reaches are (Li +1, 2Vi) and (Li + 1, 2Vi + 1), respectively. Furthermore, if Vi is an even number, it is a primary reach at its level, and the secondary reach at the same level has the code (Li, Vi + 1); if Vi is an odd number, it is a secondary reach at its level, and the primary reach at the same level has the code (Li, Vi 1). Compared with possible multiple trial-error searches or a multi-result search when using the incomplete Pfafstetter codes, the modified binary-tree-based codification method improves the efficiency of searching objective reaches, and the structured query language (SQL) for manipulating a reach code database (see Section 3.3) can be applicable. It is worth noting that the modified binary-tree-based codes for an incomplete binary tree cannot be directly generated as an array-based complete binary tree. A procedure to calculate the codes of each reach is used for this new codification method. This procedure consists of the following three steps: (1) for the outlet reach, assign 1 to component L, and 0 to component V; (2) search direct upstream reaches from the current reach (Li, Vi), and assign (Li + 1, 2Vi) to the primary one and (Li +1, 2Vi + 1) to the secondary one following the basic topological relations (see Fig. 2); and (3) repeat the above step to traverse all the reaches. The two direct upstream reaches of a given reach should be located and the primary one should be identified by its larger contributing area during the codification process. Consequently, codification can be implemented when the drainage network is delineated. Algorithms for the above steps can be converted into bitwise operations, which can be fulfilled conveniently by computer programs. Topologically, both the above components of the binary-treebased code can reveal the structure of a drainage network. As in Fig. 1(b), the value of component L is the topological distance of a reach to the basin outlet, which is the independent variable to calculate a topological width function (Claps et al., 1996; Hung and Wang, 2005; Veitzer and Gupta, 2001). A topological width function can be used to analyze the topological configuration of a drainage network or to derive a geomorphological instantaneous
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unit hydrograph (GIUH) (Gupta et al., 1980; Rodriguez-Iturbe and Valdes, 1979) for runoff prediction in ungauged basins (Lee et al., 2006). Values of component V of all the very left reaches in each level are 0, and those consecutive reaches represent the mainstem (see Fig. 1(b)) of a basin, where the outlet is denoted by the root node, (1, 0). The nearer to the bottom right of the drainage network, the greater is the value of component V of the node. Such a node has a farther logical distance to the outlet and mainstem. The value of component V grows from the left to the right from 0 to 2L 1 1 at level L (see Fig. 1(b)). Normally, in practice, there are two limitations of coding the values of component V (Li, 2008). For a drainage network, primary reaches are preferentially arranged to the left in the new codification method. The reaches of a short tributary, which refers to the fact that the number of primary reaches of this tributary is relatively small, are nearer to the left of the binary tree. Therefore, the greater the value of component V, the greater the possibility of an empty tree node (for recording reach attributes), which results in a non-continuous increase of the recorded component V. In contrast, for a sufficiently long tributary, according to the relationships among the reaches (i.e., from the sequence of reaches upstream along a tributary), the value of component V of the first reach in the tributary next to the mainstem is 1, and V increases exponentially to the upper reaches in the tributary away from the mainstem (see Fig. 3). Consequently, component V would be too large to be coded, which will cause digit overflow in codification.
3.2. Hierarchical zoning To solve the digit overflow problem and to minimize the possibility of non-continuous increase of the recorded component V in the above binary-tree-based codification approach, the whole drainage network is hierarchically zoned in the new codification method. The relationships of river tributaries are hierarchically represented by a multiway (instead of binary) zone tree (see Fig. 4 for an example). Each zone consists of two components to express its level and sequence in the zone tree. The basin mainstem is at level 0 and the tributaries that originate directly from the mainstem are at level 1, and so forth. The sequences of zones originate from the same zone are serially numbered from the downstream to upstream. In this new codification method, for
convenience, the sequence number of a zone is added by the sequence number of its upper (smaller number) level zone multiplied by 100, and then a single-number zone index is created (see Fig. 4), which is unique for a basin. Accordingly, each river reach can be denoted as (zone index Z, component L, and component V). A zone can be disassembled from the whole drainage network during the binary-tree-based coding process when digit overflow of component V is encountered. Reaches in such a zone are then coded independently and component V’s in the mainstem of the disconnected tributary are all 0, which can avoid digit overflow (see Fig. 3). The tributaries of this zone can be disassembled again in the same way until binary-tree-based codes in each zone do not violate the restriction of the numeric digit, and then a series of zones form the zone tree to secure hierarchical zoning. However, if the drainage network is refined to a higher spatial resolution, new zones may have to be inserted into the zone tree. Though the new codification method can allow the modification of the zone tree and the regeneration of a whole basin’s codes, the upper levels of the zone tree of a large basin should be planned carefully by considering the possible finest drainage network in order to avoid frequent changes of the zone tree. The hierarchical relationship among the zones can be indicated by the zone index defined above. For example, zone index Zi must flow into the upper level zone Zi\100, and the outlet reach in zone Zi must be (Zi, 1, 0). Nevertheless, the code of the confluence point in zone Zi\100 should be recorded separately (see Fig. 4). Therefore, zone indices, binary-tree-based codes, together with the confluence points, can code the overall and detailed structure of all seamlessly coupled zones and their reaches of a basin.
3.3. Management of codification database River reaches of a basin with zone indices and binary-treebased codes can be stored in a Relational Database Management System (RDBMS) (e.g., Oracle) to achieve efficiency of data access. A data table (e.g., named as RReach, see Table 1) is produced to store the topological attributes of reaches. Each record in the table has a unique combination of zone index (ZI), component L (BCL) and component V (BCV), which are used to create the index of the table. To benefit from the efficient structural storage of river
Fig. 3. Digit overflow problem of binary-tree-based codification. Values of component V grow exponentially in a tributary; if a tributary is sufficiently long, component V will exceed a digit limit 2max, which is defined by computer system or programming language. Therefore, a long tributary is disassembled as a zone with own binary-treebased codes to avoid digit overflow.
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Fig. 4. Hierarchically coded zones in a drainage network. Each zone has its order and sequence, which are recomposed to a unitary zone index. Reaches via which higher order zones converge to a lower order one are recorded in (Z, L, V) (e.g., 0, 15, and 1) to make river reaches in drainage network connect as a whole.
Table 1 Possible columns in drainage network table RReach in a relational database management system. Parameter/ variable
Data type
Note
ZI BCL BCV Longitude
Integer Integer Integer Float
Latitude Elevation
Float Float
Reach length Reach slope Left area Left slope Righty Sourcey
Float Float Float Float Float Float
Zone index Component L of the binary-tree-based code Component V of the binary-tree-based code Longitude of the representative point of a river reach Latitude of the representative point of a river reach Elevation of the representative point of a river reach Length of a river reach Mean bed slope of a river reach Area of the hillslope left to a river reach Mean slope of the hillslope left to a river reach Properties of the hillslope right to a river reach Properties of the source hillslope of a headwater river reach
reaches, the parameters of each reach (e.g., geographic coordinates, reach length, and mean river bed slope) and corresponding hillslopes (e.g., area, mean slope, and vegetation cover) can be stored in table RReach (see Table 1). Consequently, all parameters of hydrological models can be stored and managed integrally. In addition, water level, flow discharge, water quality data, and other variables and model simulation results can be stored in additional tables connected to the related river reach by the table index. In the RDBMS, structured query language (SQL) and predefined application programming interface (API) can be used to query, update, insert and delete data items (Melton and Simon, 1993), which can improve the convenience and efficiency of data access for geographical analysis and complex hydrological modeling. For example, flow routing and contaminant transport need to be simulated from upstream to downstream. If the simulation follows the descending order of zone index and component L,
no dependency conflict will happen. Therefore, the following SQL statement to access river reaches can be used: SELECT n FROM RReach ORDER BY ZI, BCL DESC. Moreover, to obtain the topological width function (i.e., width¼f(distance)) of a zone, the SQL statement can be written as follows: SELECT BCL AS Distance, COUNT(n) AS Width FROM RReach GROUP BY BCL ORDER BY BCL. In fact, for hydrological model simulations, the access demands of datasets for securing watershed attributes, model parameters, and simulation variables are indeed more plentiful than those described above. However, with the basic topological relationships recorded by the binary-tree-based codification method developed in this paper, these access demands can be achieved efficiently and effectively. The advantages of the new codification method in expressing the structure of drainage networks and manipulating the access demand of database make it possible to apply complex hydrological models to large-scale and high-resolution drainage networks. In the following section, an example is provided to show the value of the new codification method.
4. Example application In this example, the Middle Yellow River basin is coded and the hydrological and soil erosion processes over its sub-basin, the Chabagou River basin, are simulated by a complex hydrological model, the DYRIM. The new codification approach is integrated into the DYRIM to manage large-scale and high-resolution drainage networks, to store complex hydrological model parameters and simulation results in a database, and to enhance the effectiveness and efficiency of the DYRIM (Li, 2008). Different topographical forms are distinguished in the DYRIM for the simulation of hillslope rainfall–runoff relationship, hillslope soil
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erosion, gravitational soil erosion at gully slopes, flow routing and sediment transport in channels (Wang et al., 2007).
4.1. Codification of the Middle Yellow River The Middle Yellow River passes thoroughly the Loess Plateau in northern China (Fig. 5). In the rolling Loess Plateau region, the complex topography with numerous gullies and channels (see Fig. 6) results in high reach density of a drainage network. Due to its high soil erodibility, this region is the principal source of sediment production for the Yellow River and one of the key areas for sediment research (Chien et al., 1980). Fig. 5(a) shows
the identified coarse sediment source area in the Middle Yellow River with an area of 78 600 km2 by using the criterion of specific soil erosion greater than 5000 ton/km2/yr and specific soil erosion of coarse sediment (diameter no less than 0.05 mm) greater than 1300 ton/km2/yr (Xu et al., 2000). To obey the physical mechanisms of hydrological and soil erosion processes and thus to produce highly accurate results, a high-resolution drainage network in this region needs to be delineated and coded. Then, the hydrological and related processes on hillslope and channel units are simulated. The new codification method is applied to the Middle Yellow River basin. More specifically, it is applied to the region from Hekouzhen to Longmen along the mainstem and the upstream
Fig. 5. Hierarchical structure of Yellow River basin: (a) Shaded region shows extent of coarse sediment source area in Middle Yellow River basin. (b) Main tributaries covering coarse sediment source area are shown with zone indices, and Chabagou River basin locates near doted region. (c) Drainage network of Chabagou River basin is shown with rainfall and runoff gauging stations. (d) A part of Chabagou drainage network is displayed to show connection between map and data records.
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Fig. 6. Picture of gullies in coarse sediment source area (see Fig. 5) photographed in northern Shaanxi Province of China.
Table 2 Results from six gauging stations in Chabagou River basin (see Fig. 5(c)) for study period of July–September in 1967 Station 2
Contributing area (km ) Measured runoff (m3/3 months) Simulated runoff (m3/3 months) Runoff error (%) Measured peak flow dischargea (m3/s) Simulated peak flow dischargea (m3/s) Peak flow dischargea error (%) NSE of daily flow discharge Measured sediment runoff (ton/3 months) Simulated sediment runoff (ton/3 months) Sediment runoff error (%) NSE of daily sediment concentration a
Caoping
Dujiagoucha
Xizhuang
Sanchuankou
Tuoerxiang
Shejiagou
187 7.34 106 7.38 106 5.4 18.1 18.9 4.2 0.89 3.64 106 3.45 106 5.3 0.55
96.1 4.39 106 3.65 106 17 10.1 11.1 9.9 0.75 2.32 106 2.30 106 1.1 0.35
49.0 1.75 106 1.63 106 7.2 4.20 4.38 4.3 0.84 9.08 105 8.67 105 4.5 0.48
21.0 5.44 105 6.47 105 19 1.01 0.99 1.9 0.88 2.15 105 1.84 105 14 0.46
5.74 1.67 105 2.85 105 71 0.424 0.757 79 0.92 7.53 104 10.4 104 38 0.62
4.26 1.52 105 1.17 105 23 0.451 0.201 56 0.58 5.57 104 1.85 104 67 0.55
All flood peaks are counted on August 26, 1967.
parts of the two tributaries of the Yellow River, Jing River and the Beiluo River (Fig. 5(b)), covering the coarse sediment source area (He et al., 2009; Li, 2008). The DEM dataset used to delineate the study area is at a resolution of 100 m 100 m, which is the scale of 1:250 000, obtained from the National Fundamental Geographic Information System of China. The TOPAZ model is used to delineate the drainage network, and then the river reaches are coded. Firstly, crude drainage networks are separately extracted from different DEM blocks. Secondly, the reaches in each block are coded. Finally, these coded reaches are aggregated as a complete drainage network. Accordingly, the delineated study area consists of 92 zones with 7 levels, including more than 120 000 river reaches and 300 000 hillslopes with an average area of about 0.37 km2. Among them, there are 24 zones at the first level and 25 zones at the second level (e.g., Fig. 5(b)). All the coded river reaches of the Middle Yellow River basin, along with their properties, are stored in an RDBMS, Oracle. A sample of data items of the refined Chabagou River basin (Fig. 5(c)) is shown in Fig. 5(d).
4.2. Complex hydrological simulation of the coded basin The processes of hydrology and soil erosion are simulated over a sub-basin of the Middle Yellow River basin, the Chabagou River basin (Fig. 5(c)), to verify the necessity of the application of the new codification approach. The Chabagou River basin, with an area of 205 km2, is re-extracted from a 50 m 50 m resolution DEM dataset. The refined drainage network (Fig. 5(c)) consists of 4912 reaches and related hillslopes with an average area of 1.67 ha, and is coded by the new codification approach (e.g., Fig. 5(d)). The hydrological and erosion models in the DYRIM are established for each river reach (e.g., reach a in Fig. 5(d)) and its corresponding hillslope units. The DYRIM utilizes a database with
the data structures introduced in Section 3.3 to organize the simulation units and to handle its inputs and outputs. Facilitated by the simple rules of the modified binary-tree-based codes, the DYRIM can efficiently determine the simulation sequence of the units and transfers data from upper to downstream. Therefore, this complex hydrological model can handle a rather great number of river reach/hillslope units. In fact, a number of studies (e.g., Liu et al., 2006; Xie et al., 2008; Xu et al., 2008; Yang et al., 2005; Ye et al., 2008) have taken place to explore the hydrological and erosion processes over the Chabagou River. However, due to the lack of an effective codification method to code the details of the Chabagou Drainage network, all of these studies lack the capacity of producing a continuous simulation of the hydrological and erosion processes (Li, 2008), resulting in difficulty in understanding the rainfall– runoff relationship and related sediment production. In this example, the study period covers the 3-month flood season from July to September in 1967, and the simulation time step is 6 min. The DYRIM is calibrated by using the observations of runoff and sediment concentration at Caoping station near the basin outlet (Fig. 5(c)). Then, the observations from five other gauging stations upstream of the Caoping station are used to validate the model performance. Table 2 lists the control drainage areas of these six stations, and the observation and simulation results. From Table 2, it can be observed that the simulations include rather considerable errors at two stations, Tuoerxiang and Shejiagou. This may be due to these two stations with the smallest contributing area among these six stations and the lack of spatial variations of some DYRIM parameters, which will cause more sensitive of the simulation over these two contributing areas. With the details of the basin drainage network by using the new codification method, the distribution of soil erosion from different sources, i.e., hillslope, gully, and channel, in the simulated period can be produced (see Fig. 7). It is worth noting that channel erosion
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Fig. 7. Simulated distributions of soil erosion from different sources: (a) hillslope erosion, (b) channel erosion, and (c) gravitational (i.e., gully) erosion.
refers to the result of the eroded soil minus the sediment deposition that occurred in the river channels. Statistics show that the proportions of sediment production over the basin from hillslope erosion, gravitational gully erosion, and channel erosion are 80%, 7%, and 13%, respectively. Such proportions from the different sources over the Chabagou basin, which are valuable to soil erosion prevention over the region, are for the first time available in literature due to the use of high resolution units facilitated by the new codification method. However, the distributions of soil erosion in Fig. 7 cannot be validated directly due to the shortage of observations. With the comparable simulation of streamflow and sediment at six stations (see Table 2), these proportions would be reasonable to a certain extent.
5. Conclusions A new codification method for drainage networks to support complex hydrological models is developed in this paper. This method preserves the efficiency of the binary-tree-based codes in expressing the topological structure of drainage networks. It is applicable to large scale drainage networks through usage of a hierarchical zoning scheme. With the zoning scheme, combination and decomposition of drainage networks can be achieved flexibly. Coded drainage networks are stored in a Relational Database Management System (RDBMS) to make use of large storage capacity and efficient manipulation of data items in RDBMS, resulting in efficient topological operations. Codes of each reach, along with all the attributes of the channel reach and related hillslopes, are stored together. Therefore, the obstacle to accessing databases in applying complex hydrological models, which has often occurred before the development of this new codification method, can be overcome.
The new codification method is validated through its application to the coarse-sediment source area in the Middle Yellow River in North China. With the DYRIM, the efficient simulation of hydrological and soil erosion processes in the Chabagou River basin, a sub-basin in the coarse-sediment source area, is achieved. More information of hydrological simulation, than ever before, is obtained for the applied watershed. However, hydrological and soil erosion simulations in the whole Middle Yellow River, the Loess Plateau, are complicated, and further explorations should be undertaken. To make use of increasing computational power, parallel algorithms are commonly used. However, physical processes in hydrological models inevitably consist of some non-parallelizable components. Since sub-drainage networks are separated by drainage divides, which do not have upstream–downstream relationships, decomposition of the whole drainage network can be simulated synchronously. This is expected to result in high parallel efficiency. With the new codification method, the parallelization of hydrological models, based on the decomposition of drainage networks, can be easily and efficiently achieved. However, to support complex hydrological models this new method may face difficulty on occasions where other methods (e.g., the Pfafstetter method) are used. Only a tree-like drainage network has been fitted for the new method. Also, when the resolution of a drainage network changes, the zone tree needs modification, which may result in an inconvenient application usage of the new codification method.
Acknowledgements This research was supported by the National Key Basic Research Program of China (Grant no. 2007CB714100), the Open
T. Li et al. / Computers & Geosciences 36 (2010) 1427–1435
Research Fund Program of State Key Laboratory of Hydroscience and Engineering (Grant no. sklhse-2008-A-02), and the Chinese Postdoctoral Science Foundation (Grant no. 20080440392). The authors are also grateful for the valuable review comments and suggestions from the two anonymous reviewers.
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