Comparison of two different methods for determining flow direction in

Water Science and Engineering, 2009, 2(4): 1-15 doi:10.3882/j.issn.1674-2370.2009.04.001

http://kkb.hhu.edu.cn e-mail: [email protected]

Comparison of two different methods for determining flow direction in catchment hydrological modeling Guang-ju ZHAO*1, 2, Jun-feng GAO2, Peng TIAN3, Kun TIAN4 1. Department of Hydrology and Water Resources Management, Ecology Centre, Kiel D-24118, Germany 2. Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, P. R. China 3. College of Water Resources and Architectural Engineering, Northwest A & F University, Yangling 712100, P. R. China 4. College of Resources and Environment, Northwest A & F University, Yangling 712100, P. R. China Abstract: Digital elevation models (DEMs) are widely used to define the flow direction in distributed hydrological models for simulation of streamflow. In recent decades, numerous methods for flow direction determination have been applied successfully to mountainous regions. Nevertheless, some problems still exist when those methods are used for flat or gently sloped areas. The present study reviews the conventional methods of determining flow direction for such landscapes and analyzes the problems of these methods. Two different methods of determining flow direction are discussed and were applied to the Xitiaoxi Catchment, located in the Taihu Basin in southern China, which has both mountainous and flat terrain. Both the agree method and the shortest path method use drainage networks derived from a remote sensing image to determine the correct location of the stream. The results indicate that the agree method provides a better fit with the DEM for the hilly region than the shortest path method. For the flat region where the flow has been diverted and rerouted by land managers, both methods require observation of the drainage network to determine the flow direction. In order to clarify the applicability of the two methods, both are employed in catchment hydrological models conceptually based on the Xinanjiang model and implemented with PCRaster. The simulation results show that both methods can be successfully applied in hydrological modeling. There are no evident differences in the modeled discharge when using the two methods at different spatial scales. Key words: DEM; flow direction determination; agree method; shortest path method; hydrological modeling; Taihu Basin

1 Introduction In recent years, digital elevation models (DEMs) have been widely used as input data for defining the flow directions in distributed hydrological models for discharge simulation due to their high efficiency in representing the spatial variability of the earth’s surface (Beasely et al. 1980; Beven and Kirkby 1979; Fortin et al. 2001). Numerous grid DEM-based algorithms used for determining flow direction have been developed and implemented in many GIS ————————————— This work was supported by the Studies and Research in Sustainability Program (Deutscher Akademischer Austausch Dienst, DAAD). *Corresponding author (e-mail: [email protected]) Received Sep. 16, 2009; accepted Nov. 16, 2009

softwares for watershed and hydrological analysis (O’Callaghan and Mark 1984; Quinn et al. 1991; Fairfield and Leymarie 1991; Costa-Cabral and Burges 1994; Tarboton 1997). Although the use of grid DEMs is more prevalent due to their simplicity and ease of implementation (Aryal and Bates 2008; Beven et al. 1988; Moore and Grayson 1991), some problems with the approaches that are currently in wide use still exist, especially for large flat areas, where DEMs cannot describe the topography efficiently. Exclusive use of a DEM makes it impossible to determine flow direction in flat areas, because the lack of data on flow paths over flat areas and pits in the DEM means that the DEM cannot represent real river networks explicitly (Hao and Li 2002; Xie et al. 2006). In flat areas with a long cultivation history, many rivers and channels are usually diverted by the land managers for irrigation or other reasons. Channels may run in parallel or in an annular shape within a flat region. In such cases, the flow directions cannot be determined with the DEM. Additionally, the DEM does not include information about lake locations. Therefore, a DEM is not sufficient for deciding whether a constant elevation is either a lake or a flat area. One way to overcome these limitations is to use ancillary data, such as photogrammetric stream lines or a river network derived from remote sensing images (Kenny and Matthews 2005; Jones 2002; Saunders 1999; Turcotte et al. 2001), to provide an accurate picture of the drainage network. The Taihu Basin is a relatively flat region with a well developed river network where the flows have been diverted and rerouted by land managers for irrigation and flood control. For such a region, extraction of the drainage structure and flow direction determination are found to be difficult when existing methods are used, due to inadequate elevation information. The results may not be applicable to hydrological simulation. The purpose of the present study was to compare two different methods, the agree algorithm and shortest path method, for flow direction determination within the framework of modeling the water balance of a catchment with a relatively flat landscape. The first part of the paper provides a brief overview of the methods used for flow direction determination. The agree algorithm and shortest path method using ancillary drainage information from a remote sensing image, as well as the hydrological model, are described in the second section. The Xitiaoxi Catchment in the Taihu Basin, with a mountainous upstream region and a flat alluvial plain downstream was used for a test. The results of the assessment demonstrate the feasibility of the two methods in discharge simulation.

2 Overview of methods for flow direction determination 2.1 Conventional method The most widely implemented and effective approach for flow direction determination and automated drainage recognition is probably the D8 (deterministic eight nodes) method (Martz and Garbrecht 1992). The D8 algorithm was first presented by O’Callaghan and Mark (1984). It assumes that a water particle in each DEM cell flows towards one and only one of

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Guang-ju ZHAO et al. Water Science and Engineering, Dec. 2009, Vol. 2, No. 4, 1-15

its neighboring cells, which is the one in the direction of steepest descent. After single flow directions are determined, some other important characteristics, such as the watershed boundary and river network, can be derived directly. There is no doubt that the D8 algorithm is very simple and convenient, and has wide applicability in hydrological analysis (Jenson and Domingue 1988; Martz and Garbrecht 1993). However, the D8 algorithm cannot provide an accurate match of the modeled to the real flow directions. The major limitations are, first, that only eight possible directions cannot represent the real flow directions, especially for groundwater, the paths of which are quite broad and diffuse (Costa-Cabral and Burges 1994; Pan et al. 2004; Quinn et al. 1991), and second, that there is incontinuity of drainage across flat areas or anywhere there is a pit in the DEM.

2.2 Other algorithms Single flow direction algorithms have been criticized because they cannot model flow dispersion (Costa-Cabral and Burges 1994; Quinn et al. 1991). Researchers have attempted to remove this limitation by using multi-flow direction algorithms where the outflow from one cell passes not only to its neighbor of steepest descent but also to other neighbors (Aryal and Bates 2008; Holmgren 1994; Quinn et al. 1991; Tarboton 1997; Wolock and McCabe 1995). The multi-flow direction algorithm (MD8) proposed by Quinn et al. (1991) allocates flow fractionally to all lower neighboring cells in proportion to their slopes. Although this method tends to produce more reasonable results than the D8 algorithm by avoiding concentration to distinct lines, the main disadvantage is that the flow from one cell is routed to all neighboring lower cells and thus dispersed to a large degree, even for a convergent hillslope. Costa-Cabral and Burges (1994) presented an elaborate set of procedures called the digital elevation model network (DEMON). The DEMON algorithm generates flow in each source pixel and follows it down a stream tube until the edge of the DEM or a pit is encountered. The method shows the differences between convergent and divergent areas more accurately than both single and multi-flow direction algorithms. Tarboton (1997) addressed the Dinf (known as D∞) approach to describe infinite possible single-direction flow pathways. However, like the single flow direction algorithm, the Dinf algorithm has trouble in defining flow direction in flat areas. Seibert and McGlynn (2007) developed a new triangular multi-flow direction algorithm (MD∞) for a range of flow routing and topographic index applications. Previous study has demonstrated that the multi-flow direction algorithm might be more appropriate for overland flow analysis, while the single flow direction algorithm is superior in zones of convergent flow and large drainage areas with well-developed channels (Martz and Garbrecht 1992; Quinn et al. 1991).

2.3 Strategy for optimizing DEM for flow direction determination As described previously, the DEM employed for hydrological analysis presents researchers with challenges in several types of landscapes, particularly where pits and large


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flat areas exist. The fundamental issue is always the same: the vertical or horizontal DEM resolution and accuracy do not adequately capture the topographic information necessary to accurately determining flow direction. If these areas are not handled properly, the result can be a disconnected drainage network or a connected drainage network that is not representative of known hydrological features. Therefore, some methods have been introduced to overcome these limitations (Kenny and Matthews 2005; Hutchinson 1989). The stream-burning approach involves converting scale-consistent vector stream data to a raster format and digging the DEM using the raster drainage networks at a fixed depth (Callow et al. 2007; Saunders 1999). Although this procedure has weaknesses, attention to several key points in the process can dramatically improve the accuracy of extracted river networks and watershed boundaries (Kenny et al. 2008). Hellweger (1997) proposed an agree procedure for surface reconditioning in the vicinity of the stream lines, which has been applied in Arc Hydro Toolbox (Maidment 2002). This approach was compared with the shortest path method in the present study. Turcotte et al. (2001) used a digital river and lake network (DRLN) as an input in addition to the DEM. The use of ancillary data related to the location of rivers and lakes makes it possible to obtain a fit between the DRLN and the modeled drainage structure. Kenny and Matthews (2005) proposed a method for aligning raster flow direction data with photogrammetrically mapped hydrology. It produces a very accurate flow direction grid and provides a highly concurrent relationship between the photogrammetrically derived hydrology and the flow direction grid. Thus, additional data related to the position of rivers is very helpful to determine the flow direction in flat areas, such as the Taihu Basin, with lakes and numerous artificial channels.

3 Methodologies For this study, remote sensing images were used for drainage network extraction. Compared with other methods, a remote sensing image provides an accurate and coherent link between the derived hydrological regime and the real river network. The work reported here made use of the Xinanjiang model implemented with PCRaster to compare two different flow direction determination methods for hydrological modeling (Wesseling et al. 1996; Zhao et al. 1980; Zhao 1992).

3.1 Flow direction determination methods 3.1.1 Agree method The agree algorithm is a modified approach to the stream-burning method created by Hellweger (1997), using ARC/INFO’s Arc Macro Language. It uses a raw DEM and a singleline stream vector as inputs. A user-specified horizontal buffer distance and depth as well as stream-burning at a selected depth are used for reconditioning the raw DEM. The method involves modifying the raster elevation values not only in the stream network, but also in 4


buffered proximity. In the reconditioning process, within user-specified riparian zones, DEM elevation values are adjusted to provide a linear down-gradient path to the stream-burned network. A complete description of the method and a simple example can be found in Hellweger (1997). 3.1.2 Shortest path method The shortest path method uses a known drainage network to define the flow direction in each grid. It is a multi-step automated process: From a user-defined catchment outlet, the network is traced upwards, capturing the entire upstream network. The upstream searching process is shown in Fig. 1. As shown in Fig. 1(a), the watercourse grids with values of 1 are extracted from a remote sensing image. Fig. 1(b) shows the resulting watercourse grid flow direction. The cell on the left of MV is the outlet, from which the water will flow out of the area. Afterwards, the drainage network is assumed to be a source grid to search the nearest raster cell, and the water will flow into the source cell. As shown in Fig. 1(c), the values of the cells are assigned differently depending on the distance to the nearest water body (the cell size is assumed to be 2). The flow directions of the cells are the routes from the cells themselves to the nearest water body cells, symbolically shown in Fig. 1(d). However, the main problem with this algorithm is that there are some cells that have equal distances to different water body cells (Fig. 1(c)). In that case, the flow direction has to be chosen from one of those randomly.

Fig. 1 Process of flow direction determination using shortest path method

3.2 Hydrological modeling To compare the applicability of the two approaches in hydrological modeling, both methods were applied to the simple raster-based PCR-XAJ model, which is implemented within PCRaster, a dynamic environment modeling language, and based on the Xinanjiang model concept (Zhao et al. 1980). The DEM and the river network were used to create a local drainage direction map according to the two algorithms mentioned above. The hydro-climatic variables, precipitation and evaporation, were interpolated with inverse-distance weighting (IDW). The mechanism of runoff generation and separation in the Xinanjiang model was employed in the pervious areas (i.e. paddies, forests, arable land, and orchards). Guang-ju ZHAO et al. Water Science and Engineering, Dec. 2009, Vol. 2, No. 4, 1-15

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The Xinanjiang model has been widely applied in the humid regions in southern China as a basic tool for rainfall-runoff simulation, flood forecasting and water resources management (Zhao 1992). In the model, watershed heterogeneity is described with a parabolic curve representing the water storage capacity of the soil (Zhao et al. 1980): b

⎛ W′ ⎞ f = 1 − ⎜1 − (1) ⎟ ⎝ Wmax ⎠ where f is the fraction of the watershed with a water storage capacity less than or equal to W ′ , Wmax is the maximum value of the tension water capacity of the whole watershed, and

b is a shape parameter that controls the spatial variability of W ′ within a range between 0.1 and 0.4 (Zhao 1992). The areal mean tension water capacity W can be obtained: Wmax W W = ∫ (1 − f ) dW ′ = max 0 1+ b Then, the value of the tension water storage AU is calculated as follows: 1+ b ⎡ ⎛ W W ⎞ ⎤ AU = ∫ (1 − f ) dW ′ = W ⎢1 − ⎜1 − ⎟ ⎥ 0 ⎢⎣ ⎝ Wmax ⎠ ⎥⎦ where W is the areal mean tension water storage , and 1 (1+ b ) ⎤ ⎡ ⎛ W ⎞ ⎥ W = Wmax ⎢1 − ⎜1 − ⎟ ⎢ ⎝ Wmax ⎠ ⎥ ⎣ ⎦

(2)

(3)

(4)

Runoff will not generate until the soil moisture of the unsaturated zone reaches maximum capacity. Thus, runoff yield Rt at time t can be calculated as follows: If Pt − Et + AU ≤ Wmax (5) then, 1+ b

⎛ P − Et + AU ⎞ Rt = Pt − Et − W + W + W ⎜1 − t ⎟ Wmax ⎝ ⎠

(6)

Otherwise, Rt = Pt − Et − W + W

(7)

where Pt and Et are the amounts of precipitation and evaporation at time t, respectively. The runoff in the water bodies and urban areas is calculated separately. In this study, the overland flow was calculated with one-dimensional kinematic wave equations, available as a built-up function in PCRaster software. The equations include (Chow et al. 1988): The continuity equation: ∂Q ∂A + =q ∂x ∂t The momentum equation: Sf = S0 3

(8)

(9)

where Q is the surface discharge (m /s), A is the cross-sectional area of the flow discharge

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(m2), q is the amount of lateral inflow per unit flow length (m2/s), x is the length of the slope (m), t is the time (s), Sf is the friction gradient, and S0 is the slope of the surface. The continuity equation can also be written in the following form: t t +Δt Qit++Δ At +Δt − Ait+1 qit++Δ1 t − qit+1 1 − Qi + i +1 = (10) Δx Δt 2 where Δt is the time step, and i is a cell index. According to the Manning equation (Chow et al. 1988), the surface flow rate is S 1/ 2 R 2 / 3 V= f n (11) A R= P where n is the Manning roughness of the surface, R is the hydraulic radius (m), and P is the wetted perimeter (m). Based on Eqs. (8), (9) and (11), A is obtained by the following equation: A = aQ β (12)

(

where a = nP 2 / 3

S0

)

0.6

and β = 0.6 . The channel flow is also modeled by the kinematic

function and the details can be found in the LISFLOOD model manual (van der Knijff and De Roo 2008). The interflow and groundwater routing are modeled as simple, linear storage. The polders are considered points in the simulation.

4 Study site and data set The Xitiaoxi Catchment, covering more than 2 200 km2, is located upstream of Taihu Lake in southern China (Fig. 2). The Xitiaoxi River is one of the most important tributaries in the Taihu Basin, supplying 27.7% of the water volume of Taihu Lake (Chen et al. 2009). There are two large reservoirs (the Fushi and Laoshikan reservoirs) in the upper Xitiaoxi Catchment (Fig. 2). The whole catchment is characterized by a semitropical climate with mean annual rainfall of about 1 465 mm. The precipitation in the Xitiaoxi Catchment is dominated by the Asian summer monsoon. The catchment has various kinds of topography: mountainous and hilly areas with a maximum elevation of 1 585 m (above mean sea level), where the stream flows very fast, and also low alluvial plains where the drainage network is well developed. The distribution of the elevation in Fig. 3 illustrates that a large flat region is located in the lower Xitiaoxi Catchment, where the landscape is representative of the Taihu Basin. The cumulative probability curve indicates that more than 60% of the catchment is below 200 m (above mean sea level). In this region, the river flows have been diverted and rerouted by land managers for irrigation or flood control.


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Fig. 2 Locations of Xitiaoxi Catchment and hydro-climatic stations

A Landsat 7 Enhanced Thematic Mapper (ETM) image acquired on October 11, 2001 was used to extract the river network and land use maps. The land use information was used for runoff generation and Manning roughness coefficient derivation based on the literature (Chow et al. 1988). The DEM (Fig. 2) was used to derive Fig. 3 Distribution and cumulative probability of the hydrologic parameters of the elevation in Xitaoxi Catchment catchment, i.e., the slope and local drainage direction (LDD). A grid size of 200 m × 200 m was selected for daily discharge simulation to avoid producing a large number of pixels and the requirement of much more computation time. Continuous daily rainfall

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data from eight rain stations in the catchment are available (Fig. 2). Of these stations, the Hengtangcun Station and Fanjiacun Station (with drainage areas of 1 308 km2 and 1 914 km2, respectively) are also streamflow stations. However, the model used in the study did not considered the spatial heterogeneity of soil types due to the unavailability of data for the catchment.

5 Results and discussion 5.1 Visual analysis Fig. 4 shows flow direction maps in a rugged region and a flat region established using both the agree and shortest path methods. The blue cells show a single-line stream interpreted from a remote sensing image, and the other pixels with various colors represent different elevations. The white flow vectors with arrows denote the flow directions of each grid cell. As shown in Fig. 4, both the agree and shortest path methods produce flow directions consistent with the stream lines. This is due to the additional input information on the position of lakes and estuaries. It allows for the derivation of a fully connected and hierarchically structured river network that is consistent with lakes and other water types.

Fig. 4 Flow direction maps for rugged region and flat region

The modeled flow directions extracted from the improved DEM show the real surface flow directions in the non-watercourse grids (Fig. 4(a)) in terms of water particles flowing to the steepest neighboring cell. In contrast, the shortest path method does not provide a perfect match with the DEM in the rugged region (Fig. 4(b)). In addition, it can generate significant errors in arid regions without well-developed drainage networks. Shown in Figs. 4(c) and (d) are the flow directions extracted for the flat region using both methods. It can be clearly seen that both methods produce numerous parallel flow directions. In a previous study, Callow et al. (2007) compared flow direction definition in the stream-burning and agree methods. They found that stream-burning was the simplest method, using the lowest number of cells and performing well in replicating stream length and position, while the agree method fundamentally changed the landscape represented by the DEM. Our study indicates that the shortest path method, unlike the agree method, completely changed the way that the flow direction was determined by the DEM. Guang-ju ZHAO et al. Water Science and Engineering, Dec. 2009, Vol. 2, No. 4, 1-15

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Fig. 5 illustrates two typical problematic areas for flow direction determination: a lake and an annular river network. The green arrow lines denote flow directions, the blue cells are a raster of the stream network, and the bright blue vector polygon shows the lake area.

Fig. 5 Flow direction determination for annular river and lake using different methods

Figs. 5(a) and (c) show the flow directions in an annular river network (see the area with the red circle in Fig. 2) generated by two methods. As we can see, both methods divided the continuous stream line into two sections (emphasized by the black rectangles in Figs. 5(a) and (c)). This was caused by the pitfall of the D8 algorithm that the flow in a grid has only one direction. For natural loops where the river bifurcates and forms circular drainage, one main flow path must be conserved entirely while the other flow path must be disconnected at the point where the bifurcation occurs (Saunders 1999; Turcotte et al. 2001). Such instances are very common in the Taihu Basin, and are challenges for hydrological modeling. Figs. 5(b) and (d) show the flow directions in water body grid cells. Due to the available stream line and lake information, the flow directions produced by both methods seem reasonable. However, the D8 approach cannot be used to model flow directions in lakes; the results may not represent the real conditions in the lake (Jones 2002).

5.2 Discharge simulation using different flow direction determination methods The hydrological model was calibrated and validated for the whole catchment at both the Hengtangcun and Fanjiacun stations. After the initial warm-up period (1978-1979), the daily streamflow records from a continuous period of 20 years (1980-1999) at both stations were used for calibration (1980-1989) and validation (1990-1999). The Nash-Suttcliffe efficiency CNS (Nash and Suttcliffe 1970) and the correlation coefficient R2 were calculated at a daily resolution to evaluate the hydrological model performance. Both the calibration and validation results show a good agreement between measured and modeled daily discharge at Hengtangcun Station in terms of high values for the correlation coefficient (R2 > 0.8) and Nash-Suttcliffe efficiency (CNS > 0.78). The modeled results at Fanjiacun Station are slightly worse than those at Hengtangcun Station. Fig. 6 shows one section of the hydrographs of the measured and modeled discharges at

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Hengtangcun and Fanjiacun stations in the validation period. Both of them illustrate that some peaks of the modeled values are much higher than the measured discharge, while the modeled values are lower after the peaks. The cause may be the two reservoirs located upstream of the catchment. The reservoirs are used for irrigation in the dry season and flood control in the rainy season. This also explains some missing peaks in the modeled data during the dry season.

Fig. 6 Hydrographs of daily measured and modeled discharge at two stations from 1990 to 1994

After the model calibration and validation, the parameters were fixed for comparison of the two different methods of determining the flow direction. The results are given in Figs. 7 and 8. Fig. 7 shows the daily discharge from 1990 to 1994 modeled using two flow direction methods, where Qa and Qs are the daily discharges modeled with the agree method and the shortest path method, respectively. It can be clearly seen that there is no significant difference between the modeled discharges of the two methods at both stations. Both approaches produce virtually identical results in daily discharge simulation. This finding is in agreement with the work of Wolock and McGabe (1995), who compared single and multi-flow direction algorithms for computing topographic parameters in TOPMODEL and found no variation in total runoff in terms of the model’s fit to observed streamflow data at different optimized hydraulic parameters, despite marked differences in the topographic index histograms.


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Fig. 7 Modeled discharges at two stations based on different flow direction determination methods

To further evaluate whether the two approaches are applicable to discharge simulation, 64 sub-basins in the Xitiaoxi Catchment with different slopes and areas were selected for comparison. Fig. 8 shows the correlation between modeled discharges using both methods. It can be clearly seen that most coefficients are higher than 0.98, indicating that the discharges modeled by the two flow direction determination methods are almost identical.

Fig. 8 Correlation of modeled discharges using two flow direction determination methods

Previous study indicates that environmental and hydrological models have many sources of error and uncertainty (Wechsler 2007). The uncertainty in determination of flow directions and flow paths is perhaps one of the less serious of them. Although variations of flow length (determined by flow direction) may lead to significant changes in the time lag between precipitation and peak flow discharge that may result in a much different hydrograph (Wu et al. 2008), the results of our study present almost identical hydrographs from both methods. Quinn et al. (1995) suggest that if only the hydrograph at the catchment outlet is required, then the use of a coarse DEM employing any of the algorithms will suffice and that any inaccuracy will be compensated for by the calibrated parameters (Aryal and Bates 2008; Wolock and McCabe 1995). This can explain why variances between the modeled discharges using two flow direction approaches in most sub-basins are less than 0.5%.

6 Conclusions This study introduced two approaches, the agree approach and the shortest path approach, to automatically defining flow directions for hydrological modeling based on known stream networks. The results indicate that both methods can be successfully applied to discharge simulation, even in some regions where the morphology of rivers and channels has been greatly influenced by land managers. Both approaches use a DEM and a stream vector as inputs and obtain a good agreement between observed and modeled drainage structures. It is difficult to automatically extract drainage networks of the flat landscape of the Taihu

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Basin from DEMs. Using a remote sensing image to derive the river network is much easier, more efficient and useful for complementing the limitations of some other methods. The image provides more information on the location of lakes and wetlands, which cannot be completely extracted from DEMs. The agree approach overcomes some limitations of the widely used D8 algorithm and provides good accuracy for rugged areas. Obviously, the improved DEM yields a good fit with a raw DEM and can also provide for acceptable flow direction assignment results. The shortest path approach, a non-physical method, completely changes the way that the flow direction is determined by the DEM. However, this algorithm is a good option for hydrological modeling in a flat catchment. Although the simulation results did not show any changes, the flow directions determined by the shortest path approach in the non-watercourse region do not represent the real water flow directions. The hydrological simulation shows that the predictions of discharge from the catchment with the two methods are identical. Furthermore, there are no marked differences in modeled mean daily discharge with different spatial scales and landscapes. In this instance, only one catchment with well-developed drainage networks has been tested, and the methods are applied in the Xinanjiang model at a daily scale. The differences between the flow directions determined by different methods do not have a significant effect on the prediction of total discharge. However, additional work is still needed to test and validate the suitability of these flow direction determination methods at different spatial and temporal scales. The methods should also be validated by other models with a much wider range of terrain types.

Acknowledgements The climatic data and DEM were collected by the Nanjing Institute of Geography and Limnology of the Chinese Academy of Sciences.

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