Dongting Lake (111∘40′–113∘10′ E, 28∘30′–30∘20′ N), with a total area of 18 780 km2, is located in the middle reaches of the Yangtze River (Changjiang River; Fig. 1). The areas through which waters of Dongting Lake flow include the districts of Changde, Yiyang, Yueyang, Changsha, Xiangtan, and Zhuzhou in Hunan province as well as three cities in Jinzhou of Hubei Province. Dongting Lake is surrounded by mountains on three sides and its fountainheads are varied and complicated. It is a centripetal water system that fans out from the center. It only flows into the Yangtze River through Chenglingji of Yueyang (Fig. 1).

In the Changjiang River, a large flood occurred in 1860 and 1870, and the Ouchi and Songzi rivers burst their banks. During these events, floods flowed into Dongting Lake along with large quantities of sediment. Deposition of sediment has caused the rapid growth of the bottomlands and highlands, and some of the watercourses, lakes, and bottomlands have been reclaimed. Since then, Dongting Lake shrank from 4350 km2 in 1949 to 2625 km2 in 1995 (as measured by the Changjiang Water Resources Commission in 1995). The total lake area and spillway area is less than 4000 km2, about two-thirds of its former large size. Nowadays, Dongting Lake is commonly divided into the following three parts: East Dongting Lake, South Dongting Lake and West Dongting Lake, among which West Dongting Lake has the largest water area.

Because of its special location and complex river network system, this area is prone to frequent flooding. To protect local communities, numerous economic resources in the forms of labor and money have been spent on dike construction. A total of 266 levees have been built around the Dongting Lake area to prevent flooding, with a total length of 5812 km, the largest levee is 3471 km in length and the second largest is 1509 km in length. Flooding events in this area have caused significant destruction in the past. The costs of damage following individual events in 1996 and 1998 were CNY 15 and 8.9 billion, respectively. The pressure to prevent flooding and the associated damage has been a major factor affecting healthy economic development and living standard improvements in Hunan province.

Flood storage and detention areas, which are important to flood control and the mitigation of flood disasters in key areas, are critical components of a river flood control system. Specifically, effective basin flood control planning requires an understanding of the locations and characteristics of flood storage and detention areas in a region. Overall, planned flood diversions, which guarantee safety in key areas while bringing losses to some other areas, are reasonable and necessary. At present, there are 98 major flood storage and detention areas in China, which are mainly located in the middle–lower plain of the Changjiang River, Huanghe River, Huaihe River, and Haihe River. The Gongshuangcha detention basin, which is one of the largest dry ponds in the Dongting Lake area, is located in the northern part of Yuanjiang county, and it faces South Dongting Lake to the east and Chi Mountain to the west with water in between (Fig. 2). In total, the detention basin is characterized by 293 km2 in storage area, 121.74 km in levee length, and 33.65 m in storage height. It has a storage volume of 1.85 × 109 m3, and is home to 160 000 inhabitants.

We employed the airborne laser-measuring instrument HARRIER 86i, from the German TopoSys Company to acquire aerial photography images of the Gongshuangcha detention basin from 1 to 8 December 2010. The digital camera we used was a Trimble Rollei Metric AIC Pro and the inertial navigation system was an Applanix POS/AV with a sampling frequency of 200 Hz. The laser scanner used was the Riegl LMS-Q680i, with a maximum pulse rate of 80–400 KHz and scanning angle of 45/60.

By processing the point cloud data, we derived a high-resolution DEM of the Gongshuangcha detention basin (Fig. 3). We checked the DEM data quality in terms of plane precision and elevation precision, and the results showed that it could meet the application requirement. The DEM plane position was checked by global positioning system real-time kinematic (GPS-RTK) technology. After conversion parameters were set and control coordinates were confirmed, ground features' plane coordinates, such as the corners of buildings, high-tension poles, telecom poles, and road edges, were measured. We checked 20 ground feature points and the plane position mean square error was 0.44 m. The DEM elevation was checked by class 5 leveling. Using an annexed leveling line or closed leveling line, we calculated the elevation of check points and compared them with a digital terrain model (DTM) and DEM. We checked 70 elevation points, and the elevation mean square error was 0.040 m.

The spatial reference used was the Gauss–Krüger projection coordinate system with Beijing 1954 datum, and the elevation system was based on the 1985 national elevation standard, of which the lowest elevation is 4.55 m and the highest 45.87 m. The general landscape shown in the DEM is flat, and much micro-topography information for levees, dikes, and ridges is retained (Fig. 3).

In 2008, the Changjiang Water Resources Commission approved a report titled the “Comprehensive Treatment Planning of Dongting Lake Area” (Changjiang Water Resources Commission, 2008). The report highlighted the serious threat posed by flooding, which could cause a surplus water volume of 21.8–28 × 109 m3 in the middle and lower reaches of the Yangtze River. It also stressed that the effects of the Three Gorges Project, which greatly influences the conditions for incoming water and sediments, must be taken into consideration. Even though the completion of the Three Gorges Project and the Xiluodu and Xiangjiaba dams on the Chin-sha River enhanced the region's ability to drain floods around Chenglingji (Fig. 1), at the confluence of Dongting Lake and the Yangtze River; the report emphasized that there is an urgent need to construct a 10 × 109 m3 diversion storage zone around Chenglingji.

According to the “Report on the Feasibility of the Flood Control Project of Qianliang Lake, Gongshuangcha and East Datong Lake of Dongting Lake Areas” (Ministry of Water Resources, 2009), flood waters from the events in 1954, 1966, and 1998, in Chenglingji could have been restricted to safely manageable levels if local detention basins were set up to divert 8000–12 000 m3 s-1 of rising waters. For the 1954 flood event, the report shows that the maximum diversion should have been set at 10 000 m3 s-1, with contributions from the Qianliang Lake detention basin (4180 m3 s-1), Gongshuangcha detention basin (3630 m3 s-1), and Datong Lake detention basin (2190 m3 s-1); the corresponding water levels for the dikes should have been set at 33.06, 33.10, and 33.07 m, respectively.

According to the standard design of the Gongshuangcha detention basin diversion, we simulated flood flow using a mode controlled by sluice behavior. The resulting hydrograph acted as the input parameter, with flood flow into the sluice conditioned as follows: when the water level (H) was below 31.63 m, the flow volume into the sluice was 3630 m3 s-1; when H was 31.63–32.60 m, the flow volume was 3050 m3 s-1; when H was 32.60–33.65 m, another flow diversion exit was opened.

The flood routing model employed 2-D unsteady shallow-water equations to describe the water flow, and we used the finite volume method (FVM) and Riemann approximation solver to solve the coupled equations and simulate flood routing inside the detention basin. We used non-structural discrete mesh to represent the computational zone based on the landscape of the area and the location of water conservancy projects. Then to ensure accurate conservation, we used the FVM to decide the bulk, momentum and the equilibrium of density for each mesh element in different periods. To ensure precision, we used the Riemann approximate solver to calculate the bulk and normal numerical flux of the momentum between the mesh elements. The model solves the equations through FVM discretion and converts 2-D problems into a series of 1-D problems with the help of the coordinate rotation of fluxes. The basic principles are as follows.

1.

Basic control equation. The vector expression of conservative 2-D shallow-water equation is as follows:

∂q∂t+∂f(q)∂x+∂g(q)∂y=b(q).

In this expression the conservative vector is q= [h, hu, hv]T, the flux vector of the X direction f(q)= [hu, hu2+gh2/2, huv]T, and the flux vector of the Y direction g(q)= [hv, huv, hv2+ gh2/2]T. h is the height, u and v correspond to the average uniform fluxes of X and Y directions, respectively, g is the gravity, and the source term b(q) is

b(q)=[qw,gh(s0x-sfx)+qwu,gh(s0y-sfy)].

In this expression, s0x and sfx are the river slope and friction slope along the X direction, respectively, s0y and sfy are the river slope and friction slope along the Y direction, respectively, and qw is the net depth of water in each time unit. The friction slope can be calculated through the Manning formula.

With high-resolution DEM data, it is not precise to give the floodwater level for the whole DEM grid cells in the mesh element directly because the actual elevation value of each cell in the DEM grid is different. One reasonable way to accomplish this is to calculate the water level of every DEM grid cell through spatial interpolation technology like 1-D hydraulic modeling. There are some common spatial discrete water-level point-based interpolation methods for flood water level including inverse distance-weighted interpolation (Werner, 2001; Moore, 2011) and linear interpolation (Apel et al., 2009). Some of the discrete points interpolation techniques are based on natural neighbors because of their comparatively better performance in evaluating terrain changes; they also have quite obvious advantages in flood level interpolation (Sibson, 1981; Belikov and Semenov, 1997, 2000; Sukumar et al., 2001). Inverse distance-weighted interpolation is a comparatively simple way to get the spatial interpolation data, and it interpolates the values of unknown points given the locations and values of known points. In a high-resolution DEM, we can obtain a water-level value for each central point of every DEM grid cell through interpolation, and compare the water-level value with the elevation value of the DEM grid cell. If the water-level value is higher than that of the DEM grid cell, it means this grid cell is inundated. The inundation depth of the DEM grid cell is the water-level value minus the grid cell elevation value.

It is very important to choose computational mesh nodes as the known interpolated points for the water-level interpolation of DEM grid cells because it is improper to get all the nodes in a hydraulic model involved in water-level interpolation when tens or even hundreds of thousands of computational mesh nodes are involved. Figure 5 shows a non-structural modeling computation mesh (triangulated irregular network, TIN). The computational water-level value of the model can be located on the central point of every triangle (as C1–C13 shows) or on the node of the triangles (as P1–P12 shows) according to different solutions of the equation. For the cell located at row I and column J of the DEM grid, we can decide the location of the cell by the spatial coordinate of the central point. If a DEM grid cell (the black square) is inside P1P2P3, the following methods can be used to choose the nodes for water-level interpolation.

First, obtain the coordinate and its water-level value for the central point C13 of P1P2P3. Then search all the triangles that share the nodes P1, P2, and P3 with P1P2P3, and calculate the coordinate of the central points of these triangles (C1–C12) and their water-level values. The equation for the water level of the grid cell at row I and column J is expressed as z(x)=∑i=113z(Ci)×dix-2∑i=113dix-2.

In this equation, x stands for the central point which is located at row I and column J of the DEM grid, z(Ci) is the water-level value of the NOi known point, C is the central point of the triangle, and the distance between each pair of NOi known point and grid node x is represented by dix raised to the power r, which is set to 2 for spatial data interpolation.

The method mentioned above can interpolate the inside of the actual flood extent. As the water-level elevation of all the known points that are calculated in local areas are equal to the DEM grid cell elevations, values for DEM grid cells that are not inundated can be determined without interpolating, which reduces the number of calculation needed. This method can also be employed for other kinds of computational grids such as quadrilateral grids.

Because much micro-topography information is retained in high-resolution lidar-derived DEM data, many man-made surface features become a part of the DEM; these features include dams, trenches and the surfaces of ponds that cannot be represented on some mid- or low-resolution DEMs (Fig. 6). Suppose that there is a pond surrounded by levees on four-sides. Although the pond becomes inundated during the process of interpolation, it is not actually flooded because the levees do not suffer from the flood. This is a typical false inundation area. Another issue involves ringed mountains; although the elevation of some areas among mountains is lower than flood water level, these areas are not flooded because of the protection of the mountains.

To solve the problem, we can calculate the actual flood extent based on the connectivity principle. However, some judgment methods used to solve the connectivity problem of flat-water and 1-D hydraulic models are based on the entire DEM. These methods cannot be applied to high-resolution DEM data because of the prohibitive DEM size and the computation capability required. Using the seeded region growing method, this produces a difficult amount of data to process, i.e., 8.36 GB (22 000 rows × 51 000 columns × 8 bytes ≈ 8.36 GB); hence, large computer memory sizes would be required to deal with the DEM data of our study area. Moreover, the seeded region growing method is a recursive algorithm with a low efficiency for computations. Thus, problems like recursion might be too deep when dealing with a large amount of data and whereby the stack of a computer can overflow to the extent that computation failures occur. As a result, it is not ideal to employ such neighborhood analysis methods to solve DEM grid connectivity problems when faced with large scales, high resolutions, and enormous amounts of DEM data.

With large amounts of DEM data, it is better to divide the data into strips that can be read easily. As Fig. 7 shows, the DEM data were divided into five strips spatially with each being read one at a time. The results of water-level interpolations were concurrently stored on a raster file with a null value grid equal to the source DEM data. Every time the individual strip water level was interpolated, the result was stored on the corresponding raster file. To process large volumes of DEM data, the memory that was taken up by the previous strip was released before the next data strip was read.

There are two states for every grid cell during DEM grid interpolation; these include un-inundated and might-be-inundated states. This is typical binary raster data. If we perform run-length compressed encoding to the sequential might-be-inundated DEM grid cells in raster rows, we can mark all the might-be-inundated cells and store them in memory. Run-length encoding is a typical compressed method for raster data (Chang et al., 2006; He et al., 2011), which encodes the cells with the same value in compression. Every run-length only needs to mark the cells with where it starts and where it ends, which reduces the data storage needs remarkably. Figure 7 shows the run-length compressed encoding of the might-be-inundated DEM grid cells. Area A in blue is the real inundation extent where there are three islands. There is a false inundation area inside the middle island. The following are the equations for the run-length data and run-length list on the raster: Run length data set={RLList: RLList=(RowIndex, RLNum, RLS)},RLS={RL:RL=(RLIndex, StartCol, EndCol)}.

As Eq. (5) shows, the run-length data are mainly comprised of the RLLists on every raster row. The list represents the run-lengths of current raster rows, on which there are RowIndex, RLNum, and RLS. In Eq. (6), RLS consists of all the run-lengths on one raster row, and each run-length carries its RLIndex, StartCol, and EndCol.

After finishing DEM grid water-level interpolation and storage of run-length compressed encoding of inundated cells data, the connectivity issue of the DEM grid cells can be solved by run-length boundary tracing technology (Quek, 2000). To prove the connectivity of two inundated cells of the DEM randomly, only a judgment of connectivity for the corresponding run-lengths is needed. Both the right and left borders of a run-length are traced vertically and horizontally. If the two run-lengths are connected, then their borders can be traced to form a closed loop.

In Fig. 8, three inundated cells in a raster field are marked in purple. To prove the connectivity between inundated cell 1 and inundated cell 3, the run-length of inundated cell 1 (the first run-length on the raster row) and inundated cell 3 (the fourth run-length on the raster row) must be found. If these run-lengths are connected, the boundary trace from the left of the run-length of 1 (as is shown on the graph) will be to the right of 3 as long as it is on the left of 1.

If the boundary trace from the left of the run-length of inundated cell 1 meets the right of the run-length of inundated cell 3, the cells are connected. Likewise, if the run-length of 1 and the run-length of 2 cannot meet each other by boundary tracing, they are not connected. Based on mutual exclusion, as long as we know that 1 is the real inundation area, all the areas connected to 1 are real inundation areas, and all the areas connected to 2 are false inundation areas. As a result, the run-lengths have carried the information of connectivity between inundation grid cells, and the connectivity problem can be worked out through boundary tracing. Compared with the seeded region growing method, this method only requires searches along the run-length borders to prove the connectivity between cells, thus allowing for far faster computation speeds.

Based on the method mentioned above, we can remove false inundation areas during run-length boundary tracing and obtain an accurate map of flood extent and depth. Figure 9a shows the run-length boundary tracing and flood extent, in which run-lengths are marked with red rectangles. The DEM data only include 25 raster rows, and the model computation mesh is only expressed by four triangles; thus, the run-lengths have been simplified. The water-level value of the central point of the mesh element is calculated by model computation, so we can calculate the flood extent by tracing the boundaries of the run-lengths, which can be searched for on the central points of all of computational model elements.

Take Fig. 9a for example, the inundated central point of triangle ABC can be found on the first run-length on the 11th raster through its spatial coordinate. From the left of this run-length, the outer boundary of the flood extent can be traced (Fig. 9a) and from the right of this run-length, one of the inner boundaries of flood extent can be traced (Fig. 9b). The outer boundary of the entire flood extent can be also traced through boundary tracing of the run-length that can be searched for from the central point of triangle CDE (the 9th row). To avoid repetition of run-length tracing, and to mark real inundated run-lengths, it is important to set two labels along two sides of the run-length to indicate whether a run-length has been traced previously. Run-lengths are marked as traced once one of the sides is traced. Therefore, boundary tracing of the run-length where the central point of triangle CDE was located was not performed when the run-length of the central point of triangle ABC had been traced.

After boundary tracing through all the central points of the inundated computational mesh elements, some of the run-lengths were only traced by one side, such as rows 5–8 and 12–17 in Fig. 9b. These were located at the islands of the flood extent. Traverse procedures were used through the run-lengths to search the islands for the flood extent. Once one side of a run-length was traced (while the other was not), all the islands were found by tracing from the untraced side and performing boundary tracing (Fig. 9c). By this time, there were only two kinds of run-length procedures. One was where each side of the run-length was traced, and the other was where neither side of the run-length was traced. The extent of untraced run-lengths showed the false inundation areas, and the false inundation extent was automatically removed by boundary tracing. Meanwhile, flood extent and depth were interpolated automatically from the traced run-length (Fig. 9d).

According to the principle mentioned above, we obtained 50 periods worth of flood extent and depth data for the Gongshuangcha detention basin of the Dongting Lake area. Figure 10 (period nos. 10, 30 and 50) shows the comparison between the result from the 2-D hydraulic model and the results from the proposed method mentioned above. The resolution of the 2-D hydraulic model mesh was above 100 m, whereas the proposed method mentioned above interpolates the water level through a 1 m high-resolution DEM. As a result, although the whole flood extent only differed by a small amount, the distributions of flood depth were very different from each other. The maximum inundation depth calculated by our method was 70 cm higher than that of the 2-D hydraulic model.

Figure 11 shows the inundation for period no. 50 and its regional enlarged view. In Fig. 11a, the high-resolution aerial remote sensing image taken by the airborne lidar system is shown, and its spatial resolution was 0.3 m. From this image we can see the distribution of farmlands, roads, channels, levees, and houses clearly, among which there are houses that have been constructed along the rivers and levees. Figure 11b and c show the 2-D hydraulic model's and our method's regional enlarged view of the inundation area, respectively. The mesh resolution of the 2-D hydraulic model was coarser compared with the geographic features of roads and houses, so the results can only prove that the flood depth of that area was lower while the ponds on the left of the image could not be expressed. It also was not capable of showing the flood conditions for every house. However, with the help of our method, important geographic features can be clearly expressed. From Fig. 11c, it is obvious that not only the flooding condition of channels, ponds, and levees are clearly expressed but also the differences of flood depths between the ridges of paddy fields. In Fig. 11c, there are three linear areas which were not inundated. From Fig. 11d, we can determine that those are levee crests on which houses and roads are being constructed.

We compare the flood extents calculated from the 2-D hydraulic model and the proposed method described above for 50 different periods. In the 2-D hydraulic model, the flood extent was calculated by adding up every inundated triangle's area from the hydraulic computational mesh, while in the proposed method, the flood extent was calculated by summing every real inundated cell area based on 1 m resolution DEM data. It was expected that the flood extent calculated from the 2-D hydraulic model would be larger than that from the method proposed in this paper (Fig. 12). The 2-D hydraulic model cannot take micro-topography information into full consideration, and many details cannot be shown on the model computational mesh, such as some secondary levees, ponds, and steep slopes. We therefore will get a smaller area result because we can get rid of the parts in the computational mesh whose elevation values are higher than the interpolated water levels.

Among the 50 periods, the flood area calculated by the 2-D hydraulic model surpassed that of our method by 5–17 %. In the 50th period, the flood area from the 2-D hydraulic model was 6 km2 larger than that from the proposed method.

As for the inundation volume, the result calculated by the 2-D hydraulic model were smaller than those calculated by our method (Fig. 13). Specifically, according to the previous graphs, the maximum inundation depth and the regional inundation depth calculated by our method were larger than the depths calculated by the 2-D hydraulic model, which means that all of the digital topography could be higher if we employ model computational mesh to express the topography directly. The differences in the results ranged from 3 to 8 %, and in the 50th time period, the inundation volume difference was 9.689 × 106 m3.

The precision of digital topography is a key factor for flood simulation and analysis. Spatial resolution and vertical precision are both important for mapping the flood extent and depth. Employing high-resolution topography data can make up for errors of a 2-D hydraulic model.

With high-resolution topography data, flood simulation data can be analyzed from the basis of topography and geographic elements because some of the most important micro-topography information is accounted for by digital topography data, especially that of levees, ponds, and man-made structures. Once we take the factors from the flood extent and depth map into consideration, we can obtain the results with more precision.

However, there are trade-offs involved. With more manmade structures in the high-resolution digital topography, new problems might occur because some false topography information might be involved. For example, airborne lidar point cloud data cannot be distinguished easily from data for channels, bridges over reaches, or viaducts over roads. The redundant information may affect the simulation and analysis results for floodplain flow models. To remove redundant information, later treatments are needed and this might complicate the situation.