Interpolating river’s morphological model from cross sectional survey

Abstract

A simple but useful, riverbed-specific interpolation method is reviewed. The newly developed method interpolates a riverbed morphology grid from surveyed cross-secctions representing the special property of the riverbed specifically that gradients across flow direction are much greater than gradients along flow direction. The interpolation is carried with an intermediare step of an auxiliary non-orthogonal but equidistant mesh. The method returnes good results if the riverbank is parallel to the main flow line (typically in the case of low-flow conditions riverbeds). However, it is only limited usable for high-flow condition riverbeds, where the bank (which is usually the dam) is not necessarily parallel to the main flow line. Comparison with some traditional spatial interpolation methods is given. Preliminary results of hydrodynamic and transportation calculations is presented. Introduction and literature overview With the improvement and spreading of computational capacity, 2D and 3D hydrodynamic modelling of complete river reaches is not a speciality any more. While some 10 years ago computational capacity was the usual limiting factor, modellers nowadays struggle with lack of measured data defining boundary and initial conditions. One of the most important boundary conditions is the riverbed morphology (bathymetry). The above sea level elevation of each computational cell should be a modell input for the hydrodynamic calculations. Remote sensing of river bathymetry (with color decoding) is an improving and relatively cheap method despite it’s known drawbacks of vegetable shading along the riverbed and need for on-site measurements for calibration. Techniques for detailed on site survey (e.g. with Acoustic Doppler Current Profiler, ADCP) are also well developed and known but time consuming and rarely carried out. Consequently, river morphology – in many of the cases – has to be interpolated from cross sections surveyed regularly along the river [4]. Widespread GIS software include many interpolation algorithms such as Natural Neighbour, Inverse Distance Weighted, Kriging which don’t take into account the specific property of the river morphology, that gradients along and across the flow direction differ about one order of magnitude. Consequently, riverbedspecific interpolation algorithm has to be applied. Osting developed a suite of software entitled Mesh Elevating and Bathymetry Adjusting Algorithms (MEBAA) in order to adjust the anisotropy to the sinuously changing flow direction. For evaluation both the newly developed method and a traditional interpolation method were applied for both a complete and filtered field data set. In tests using filtered field data, the new algorithm accurately represented natural bathymetry and did so more reliably in areas of sparse field data than the other tested interpolation methods [3][2]. Merwade proposed coordinate transformation, where distance along centerline of the river, and perpendicular distance from centerline are used instead of Cartesian coordinates (z coordinate for elevation keeps unchanged). For the interpolation, he proposed some modifications to the existing methodologies such as inversed distance weighting and spline [2]. Methods When developing the method of interpolation we assumed to have surveyed cross-sections evenly distributed along the river. The goal is to determine elevation for every point of an orthogonal equidistant mesh. According to method developed, this happens is four steps. (1) Cross-sectional data are usually surveyed from a boat, and they do not necessarily fall on one straight line. Thus, in the first step, cross-sectional survey data are orthogonally projected to a straight line (see Fig. 1 left) keeping their original z-value. The straight line is the one connecting the two rear surveyed points. (2) All the straight lines are divided into equal segments, and z-value at the end of each segment is Second Conference of Junior Researchers in Civil Engineering 244 Kardos, M.: Interpolating river’s morphological model from cross sectional survey calculated from the two neighbouring points (see red + signs on Fig. 1. right). Fig. 1. Projection and section interpolation (3) Between two cross-sections a not-orthogonal but equidistant mesh (auxiliary mesh, NOE mesh) consisting of auxiliary crossand longitudinal sections (black lines on Fig. 2) is created, and the z value is determined in every mesh point. Number of auxiliary cross-sections and longitudinal sections are inputs for the program (3 and 8 on Fig. 2., respectively). (4) Z-value of every mesh point of the orthogonal, equidistant mesh is determined from the surrounding four points of the NOE mesh with inverse distance weighting (elevation of red circle point is calculated from the four orange points on Fig. 2.). Fig. 2. 2D interpolation Results and discussion The algorithm was tested on the Paks – Mohács reach of the Danube. Discharge here varies between 900 and 6400 m3/s, causing a water level change of more than 8 m-s. Width of the stream at medium water is about 500 meters. Flow direction is here from north to south (from above to down on the figures). Cross-sections for low flow conditions were measured every 500 m-s with ADCP. Cross-sections for high flow conditions were created by combining low flow ADCP-measurements with field measurements. High flow crosssections were available for a 10 km-reach every 100 m-s. Creation of both the low and the high-flow morphology was handled as separate tasks. On Fig. 3 the present algorithm is compared with two “built-in” functions of ESRI ArcGIS software: “Topo Second Conference of Junior Researchers in Civil Engineering 245 Kardos, M.: Interpolating river’s morphological model from cross sectional survey to Raster” based on [1] and “Natural Neigbour”. None of the built-in functions reproduces the stringiness property of the riverbed. Fig. 3. Comparison with other algorithms: „Topo to Raster” (left) and Natural Neighbour (centre) To evaluate the algorithm calculation with a full dataset was compared to calculation with a reduced dataset. Reduced dataset meant in this case, that only every fifth cross-section survey data was taken into account. After running the algorithm with both datasets, the two grid’s difference was calculated. Result is shown on Fig. 4., where the color scale is the difference in meters restricted to -1 to 1 meters. Axes show coordinates according to Hungarian Datum. Fig. 4. Difference between grids calculated from full and reduced datasets On Fig. 4. the three cross-sections used in both datasets are well recognizable beacause of the white (meaning 0 m difference). Difference between the two grids is below 1,0 m between the two cross-sections in the central part of the river, where most of the discharge happens. Higher differences occur around the riverbank areas representing low percentage of the discharge. The algorithm seemed to deliver acceptable results when calculating the low-flow conditions riverbed. However, the resulting grid seemed to be quite problematic when calculating the high-flow conditions riverbed. High-flow cross-sections are usually 1,5-2,0 km-s long, and the distance between them was 100200 m-s, meaning usually cross-sections crossing one another. Even when eliminating these overlapping parts, the orthogonal directions defined by them seemed too much emphasized (see Fig. 5 (c)). Second Conference of Junior Researchers in Civil Engineering 246 Kardos, M.: Interpolating river’s morphological model from cross sectional survey (a) (b) (c) (d) Fig. 5. Comparison of aerial photo (a), low-flow riverbed (b) and high-flow riverbed before (c) and after (d) manual correction Main cause for the discrepancies shown on Fig. 5 (c) is that the algorithm interpolates between the two rear points of two adjacent cross-sections. Since rural points of the high-flow condition cross-sections are at the dam, which can follow any lining, auxiliary longitudinal sections not necessarily follow the center line or main flow line of the river. This can be corrected manully, which is rather time consuming. Manual correction leaded to Fig. 5 (d). A special problem was faced when trying to interpolate an area of two parallel reaches. The case presented here is the one of the island called Uszódi-sziget situated in the 1524. riverkilometer of the Danube (see Fig. 6 (a)). The smaller problem here was lack and inaccuracy of measured data, the greater one that crosssections weren’t orthogonal to the flow direction. Fig. 6 (b) represents the result of an automatical run of the algorithm. Small black points (appearing as black lines) represent input measured data, surveyed partially from water, partially on field, as already mentioned. As visible, data is partly missing exactly from the side branch, and cross sections are not orthogonal to the flow direction of the smaller branch. Solution was densification of cross-sections with new on site survey project (see red lines on Fig. 6 (c)). The three newly surveyed cross-sections were still not enough to represent the Uszód side branch, so they were transformed, and all of them used many times, as marked with yellow triangles on Fig. 6 (a). After that the algorithm was runned for the main branch and for the side branch separatly, and as a last step, the two grids were joined „manually”. The resulting grid represented adequately the riverbed morphology of both arms (see Fig. 6 (c)). On Fig. 7. preliminary results of the hydrodynamical and transport modell calculations are presented. On the left side the velocity field is visualised and on the right side the concentrations due to a constant inflow of a pollutant on the right side of the river some 1000 m-s above the island. Evaluation The newly developed interpolation method calculates the DEM of a riverbed much more accurately than many common interpolation methods not specified for riverbed interpolation. The method is leading to a satisfying result when distance between cross-sections is greater than their extension, but is problematic, when (1) distance between cross-sections is too dense compared to their width (2) cross-sections are not orthogonal to the flow direction (3) bank of river defined by the endpoints of the cross-sections is not parallel to the flow direction. In the above cases manual correction (which also means loss of data) can improve the resulting grid. Acknowledgement Special thanks to Zsolt Kozma who is owner of the original idea and developer of the source code described above. The work reported in the paper has been developed in the framework of the project „Talent care and Second Conference of Junior Researchers in Civil Engineering 247 Kardos, M.: Interpolating river’s morphological model from cross sectional survey cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP4.2.2.B-10/1--2010-0009. The work reported in the paper has been partially funded by the ENVISHEN project supported by the Hungarian National Development Agency.

7 Figures and Tables

Cite this paper

@inproceedings{Kardos2013InterpolatingRM, title={Interpolating river’s morphological model from cross sectional survey}, author={M{\'a}t{\'e} Kardos}, year={2013} }