DATA VISUALISATION AND VALIDATION FOR HYDROLOGICAL MODELS

Karsten Rink, Thomas Fischer and Olaf Kolditz1 Helmholtz Centre for Environmental Research, Dept. of Environmental Informatics, Leipzig, Germany

1Dept. of Applied Environmental Systems Analysis, Technical University of Dresden, Germany

ABSTRACT

We propose a data exploration framework for the visualisation and evaluation of hydrological data for the enhancement of numerical simulations. A user-controlled 3D space allows an assessment of large input data sets. Typical examples for inconsistencies between heterogeneous data sets are given and it is demonstrated how these can be detected via a number of modifications done to the scene. Also, the framework allows for the discretisation of the model domain by the generation of finite element meshes based on geo-metric input data. A number of measurements are provided to verify the quality of these meshes and evaluate their adequacy for a subsequent numerical simulation of hydrological processes such as groundwater flow. We demonstrate the application of the framework in two case studies of different scale in central Germany.

KEYWORDS

Visualisation, Data Validation, Mesh Quality, Hydrology, Climate

1. MOTIVATION

The simulation of hydrological processes is a widely researched subject with a large variety of applications. Aspects such as water resource management have become more and more important in recent years. Especially in arid regions it is crucial to develop a sustainable management scheme for agriculture. Other applications include the distribution of chemicals originating from fertilisers, the extraction of geothermal energy or the detection of potential erosion processes in mining areas.

Typical simulations calculate processes such as groundwater discharge and recharge or overland flow. The input data for these simulations are often based on data originating from different sources. Examples are borehole data from drillings for wells or other natural resources, satellite images such as digital elevation models (DEM) or information acquired via precipitation- or groundwater gauging stations. Often these data sets have large differences in scale; the format varies between image raster, point- or vector data as well as time series data. Due to these inhomogeneities along with the wide range of acquisition methods and the application of various post-processing techniques it is not uncommon that there are inconsistencies between any two given data sets. Obviously, if the simulation of processes such as groundwater recharge are based on faulty or conflicting information they might produce erroneous or deceptive results. Therefore, it is necessary for an expert to recognise these potential problems and correct them appropriately. To support this process, we propose a framework defining a simple workflow for the algorithmic and visual validation of hydrogeological data.

In section 2 we give a brief overview over existing approaches to the visualisation of geoscientific data in 3D. Details on the proposed framework are given in Section 3. Section 4 shows the application of the presented techniques on two model regions of different scale. Advantages and drawbacks of our framework are summarised in section 5.

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Figure 1. A typical workflow for setting up a hydrological model based on a variety of input data. Note that this work-flow can vary considerably depending on the existing input data and the processes that should be simulated. At each point

in the workflow correction of either mesh or input data might be necessary. Examples for modifications of input data include the simplification of region boundaries or rivers to avoid unnecessary numbers of small or deformed elements or

the subdivision of stratigraphical layers to allow mesh elements with a good edge ratio (see section 3.2 for details).

2. STATE OF THE ART

While the use of 3D data analysis is extensively used for the analysis of medical imagery or technical models, there exist only few tools for the 3D visualisation of geoscientific data. Most geographic information systems (GIS) offer only a layered 2D view of data sets (Andrienko, 2006). A number of commercial tools offer 3D visualisation of specific types of data for special applications. Examples are the Aquaveo Groundwater Modeling System (GMS1), the ESRI ArcGIS extension 3D Analyst as well as a number of geoscientific CAD tools such as Gocad2 which are often used in the mining or petroleum industry. Most case studies found in literature employ a combination of the above commercial software, combining GIS projects with 3D modelling software for the visualisation of a specific model region (Johnes, 2009; Royse, 2008).

A number of specialised solutions are concerned with the stereoscopy visualisation of geoscientific data in a virtual reality environment (Zehner, 2010) or for modelling for a certain subset of applications such as geothermal fields (Alcaraz, 2011).

3. VISUALISATION AND VALIDATION OF DATA

3.1 Assessment of Hydrological Data

We developed a data exploration framework for the visualisation and validation of data and the subsequent simulation of hydrological processes using C++ and Qt. A typical workflow (see figure 1 for an example) for a given model region using our framework begins with the visualisation and subsequent assessment of all relevant input data in the graphical user interface. These data sets usually include the boundary of the model region (often based on river catchments or known boundaries of aquifer systems), digital elevation models acquired via satellite to model terrain of the area and other objects of interest such as river networks or boreholes as well as observation facilities such as precipitation gauging stations. These data sets are arranged in a 3D environment that allows the user to move freely through the visualised objects and manipulate their appearance with a number of tools provided by the framework. If the data sets are considered correct and consistent with each other, it is then possible to generate a mesh discretisation of the domain (i.e. the model region) based on the available geometric information.

1 http://www.aquaveo.com/gms 2 http://www.gocad.org

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(a) (b) (c)

Figure 2. Examples for inconsistencies between data: (a) polylines not quite connected to each other, (b) borehole data with incorrect z-coordinate, (c) stratigraphic layers intersecting each other.

(a) (b)

Figure 3. Assessment of geoscientific data sets in 3D. (a) Course of the river not quite matching the DEM, (b) Differences between borehole stratigraphies and interpolated layers.

Given the combined visualisation of all input data sets a large number of inconsistencies between data sets can be detected by a simple visual inspection. Typically such inconsistencies include given river networks not matching the DEM (Fig. 3a), boreholes starting a large distance above or below the surface (Fig. 2b) or geological layers intersecting each other (Fig. 2c). The reasons for all of these inconsistencies can largely be attributed to the heterogeneity of the data sets as well as different acquisition- and post-processing techniques, differences in the time of data acquisition or simple human errors when cataloguing the data. For most of the mentioned issues our framework merely supports the user in detecting the potential problem. Correction of the data is often problem-specific and can be performed using a GIS or other external software specifically designed for modification of geoscientific data sets. A limited number of problems can also be automatically detected such as river outflows not reaching the boundary of the domain (this is often a requirement as this outflow is a boundary condition for the subsequent simulation) (Fig. 2a) or mesh elements of different subsurface layers intersecting each other (Fig. 2c) which is not possible in reality.

The user is supported in detection of possible errors or inconsistencies by a number of well-proven visualisation techniques. Since the visualisation is performed using the open source graphics library VTK (Schroeder, 2006) a large number of filters for modification of the scene are easy to use and the definition of new filters is straightforward. Note that these are not filters in the same sense as filters in digital signal processing but rather VTK components that receive input data from other components, modify it in some way, and allow the output to be used by other VTK components as part of the VTK visualisation pipeline.

The visualisation of any data set can be made transparent or switched off completely. Each data set can be assigned a specific colour or a user-defined colour table. Since all kinds of soil- and rock-types have predefined colours for visualisation in geological maps, this functionality helps experts in handling borehole

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data or subsurface models. The super-elevation of data sets is useful as the z-dimension of geoscientific data is usually much smaller than the corresponding lateral dimensions. The optional enlargement of data (such as the visualisation of points or lines as spheres or tubes of variable size) is a necessary requirement for visibility of such objects in large domains. For all data sets a subset of the contained objects can be selected for visualisation, i.e. only certain stratigraphic layers of geological data or single rivers in a river network data set and additional scalar data or textures can be mapped onto data sets to add more information to the evaluation process.

3.2 Mesh Quality

Model regions can be defined either in 2D or 3D space, depending on the process that should be simulated. Domain discretisation for 2D models consists of either triangle- or quadrilateral elements; in 3D space the domain is split into tetrahedra, hexahedra or prism (wedge) elements.

Typically, we employ the open source FEM mesh generator GMSH (Geuzaine and Remacle, 2009) for domain discretisation. Our framework has an interface for GMSH that allows to generate either homogeneous or adaptive meshes and to modify parameters such as mesh density or refinement towards selected locations such as observation sites or river networks. Alternatively meshes can be imported from other specialized tools such as Tetgen3, GMS or Gocad.

Similar to the input data, the quality of the domain discretisation needs to be analysed as well. The numerical simulation of hydrological processes is performed using the Finite Element Method (FEM) in 2D or 3D. Therefore, mesh quality affects the convergence as well as the accuracy of the numerical solution to a large extent. Typical sources for problems with finite element meshes are a well-researched problem (Versteeg and Malalasekera, 2007; Gresho and Sani, 2000) and include the mesh itself being too coarse, large jumps in the volume of neighbouring mesh elements or deformed or unsuitable mesh elements. The first problem can be solved by simply adjusting the mesh density using our framework. However, while more mesh elements may give a higher accuracy, they will also slow down computation and require more memory. The process of finding an optimum mesh density is therefore dependent on the size and topology of the model region as well as the type of process that needs to be simulated. The second problem can be safely ignored as it will not occur due to the tools employed for generation of meshes. For determining mesh quality a large number of measurements are found in literature (Knupp, 2000; Shewchuk, 2002). Our framework offers the following options:

• Edge Aspect Ratio: Shortest edge of the element divided by longest edge; • Normalised Volume (only applicable for 3D elements); • Normalised Area: Area of 2D element or minimum surface area of 3D element, respectively; • EquiAngle Skewness, given by

−−−

=opt

opt

opt

optsθ

θθθθθ minmax ,

180max (1)

Where θmax is the maximum angle found between two edges of the element, θmin is the minimum angle and θopt is the optimal angle, i.e. 60° for triangle or tetrahedra elements and 90° for quadrilateral or hexagonal elements.

Mesh element quality can then be visualised either directly by colourisation of the mesh (Fig. 4) or via histogram. As with the aforementioned visualisation options mesh quality values can also be thresholded, allowing the user to specifically select elements with poor quality. Note, that the choice of an adequate quality measure depends on the type of process (i.e. partial differential equation) to be solved numerically. Processes such as groundwater recharge consist mainly of layered flows, meaning that large differences between horizontal and vertical element surfaces might have no effect on a correct result. The simulation of mass transport processes explicitly requires a fine mesh resolution in vertical direction to ensure a stable solution (Courant, 1928).

3 http://tetgen.berlios.de/

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(a) (b) (c)

Figure 4. Visualisation of mesh element quality for a test mesh: (a) Edge Aspect Ratio, (b) Normalised Area and (c) EquiAngle Skewness. High intensities indicate elements with high quality, lower intensities imply low quality.

After verification of both input data and mesh quality, additional information based on measured data such as precipitation or the discharge of rivers can be assigned as boundary conditions, followed by an FEM-based simulation of hydrological processes. We employ the open source FEM simulation software OpenGeoSys for numerical analysis (Kolditz et al., 2008, Wang et al., 2009).

4. CASE STUDIES

Our framework has been used by experts for preparation of simulations in a number of case studies. We would like demonstrate the application for data assessment and validation based on two investigation sites in central Germany: the Selke catchment and the Thuringian Basin.

The Selke river is a tributary of the Bode river and located in the Harz mountains in central Germany. The stream has a length of 64km; its catchment with an area of 468 km2 has been determined by a hydrological analysis (Fig. 5a). Because of its gradient in land use between the agriculture in the lowlands in the northeast of the catchment and the forests in the low mountain ranges in the southwest, this catchment is of special interest for hydrogeological analysis in the scope of the TERENO project (Zacharias et al., 2011) for the prediction of possible impacts of global climate change. A DEM of the area with a pixel size of 90 m is available at the NASA Earth Resources Observation and Science Center. The area is being profoundly instrumented, providing temporal information via precipitation- and runoff-gauging stations. Due to exhaus-tive former mining there are also over 5000 boreholes in the area. Based on the stratigraphic information from these boreholes a subsurface model of the Selke catchment has been interpolated based on the method presented in Sun et al.,2011. After verification of the quality of the model (see Fig. 3b), it can be used as the basis for a subsequent simulation of groundwater discharge and recharge. Boundary conditions and source terms are derived from the information gained from the instrumentation in the area.

Visual assessment of these data sets in three dimensions is straightforward. The domain discretisation of the surface including all of the aforementioned input data (Fig. 5b) consists of about 42.000 prism- and tetrahedra-elements (Fig. 5c). While this might not seem overly complex one has to keep in mind that each pixel of the DEM covers 8100 m2 while the mean area covered by elements is about 11.000 m2.

Obviously it not possible to validate the correctness of the data from the 2D layered view that GIS tools offer. Conversely, many modelling software products for subsurface structures do not support the import of geographic data. The combination of these aspects in the present framework allows a more straightforward workflow for experts and additionally allows the direct numerical simulation of hydrological processes based on the imported data (Fig. 5d).

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(a) (b)

(c) (d)

Figure 5. Data visualisation for the Selke river case study: (a) Input data including the boundary of the model region, the river network and observation sites. The large markers symbolise groundwater- and precipitation gauges, the small

markers are boreholes. (b) Section of the adaptive mesh generated from the input data. The marked objects represent rivers and boreholes. (c) Super-elevated visualisation of the surface mesh of the model region including boreholes. (d)

Result of groundwater recharge process simulation.

The second case study is concerned with the Thuringian Basin in the scope of the INFLUINS research project. The scope of this project is the investigation of coupled dynamics of near surface and deep flow patterns of fluids as well as mass transport of chemical species in a sedimentary basin. The Thuringian basin is located in Thuringia in central Germany and covers an area of approximately 14.000 km2. The geometric model covers the three triassic units Buntsandstein, Muschelkalk and Keuper (Kober, 2009). Since the model region is considerably larger than the Selke catchment study presented in the first example, the resulting mesh consists of 159.038 nodes and 608.504 tetrahedrons. Boundaries of outcrops are included in the mesh as well as fault lines and important rivers (Fig. 6). Visual assessment of a model of this scale is tedious and a general overview over element quality provided by a histogram is helpful for evaluation of the mesh before the numerical simulation of processes.

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(a) (b)

(c) (d)

Figure 6. Visualisation from the Thuringian Basin case study: (a) Input data consisting of outcrops, fault lines and river network. (b) Surface view of model region showing the three most dominant stratigraphic layers in the basin as well as the river network. (c) Visualisation of the 3D model used for subsequent mass transport simulation. (d) Histogram of

EquiAngle Skewness mesh element quality showing all elements within acceptable bounds (i.e. with s<0.8).

5. CONCLUSIONS AND OUTLOOK

We presented a framework for the visualisation and assessment of hydrogeological data. It combines and augments the capabilities of data visualisation found in GIS and geological CAD modelling software, thus allowing experts to evaluate the whole range of data required for the simulation of hydrological processes. A number of inconsistencies between data sets can be detected either algorithmically or via visual assessment. An adaptive domain discretisation of the model region can be conducted with the optional inclusion of geometrical objects derived from the input data. The quality of generated meshes can be analysed based on a number of established criteria and the result can be written in the form of a histogram or visualised directly on the data.

While the automatic correction of data sets goes beyond the scope of the present framework we will include additional functionality to at least automatically detect and indicate a wider range of potential problems in the future, allowing the user to recognize existing inconsistencies easier. This will prove especially helpful in large scale modelling such as the simulation of fluid dynamics of the Thuringian Basin. At this point the only course for the correction of low quality mesh elements is performing a re-meshing of the whole domain. An automatic correction of such elements is another goal planned for implementation in the framework.

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ACKNOWLEDGEMENTS

The research was supported by the Helmholtz Association with the program “Earth and Environment” and the TERENO initiative (Terrestrial Environmental Observatories) as well as the INFLUINS project (Integrierte Fluiddynamik in Sedimentbecken). The authors would also like to thank Feng Sun, Andreas Musolff, Christian Schmidt, Wenqing Wang, Alraune Zech and Björn Zehner for providing data and additional information for the presented case studies.

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