Geostatistical Space-Time Interpolation Used to Homogenise Hydrological Monitoring Data
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Geostatistical space-time interpolation used to homogenise hydrological monitoring data Robert MARSCHALLINGER The GI_Forum Program Committee accepted this paper as reviewed full paper. Summary Geostatistics has been used to interpolate, in X,Y,time dimensions, groundwater level data collected in the course of a more than 10-years lasting monitoring campaign which has been accompanying a major Austrian railway upgrade project. Georeferenced time series data have been interpolated by 3D Kriging, yielding a space-time voxel array of groundwa- ter level estimates. From this spatiotemporally homogenized data set, time slices are ex- tracted to feed a cartographic animation which communicates, in an intuitive manner, the hydrological situation in the project area. 1 Introduction Part of the Berlin – Palermo Trans-European Transport Networks axis, the Brenner Base Tunnel (“BBT”) holds a key position for future north – south traffic (Fig. 1). On Austrian territory, access to the BBT is provided via the Lower Inn Valley railway, a classical two- track line which has been operative since 1895. With 300 trains per day, the Lower Inn Valley railway is now at the capacity limit. Accordingly, it has been identified as a bottle- neck of future international north-south rail traffic, necessitating a large-scale upgrade pro- gramme. The Brenner Eisenbahn GmbH (“BEG”) has been founded in 1996 to implement all railway upgrade projects for the Brenner axis in Austria (for more details, see www.beg.co.at). Following a step by step approach in the Lower Inn Valley railway up- grade, the BEG has granted highest priority to the section Kundl-Radfeld-Baumkirchen. The length of this technically sophisticated section is approx. 40 km, it comprises two tun- nel chains, subsurface tracks, an acceleration track and links to the existing railway line. Upon completion in 2012, this section will enable trains to run at speeds of up to 250km/h. After environmental impact assessments and the official project approval, the planning for the Lower Inn Valley railway started with drilling campaigns, driving of investigation gal- leries and exhaustive programmes for the preservation of environmental evidence. 2 R. Marschallinger Fig. 1: TEN connectivity outline in Central Europe. Dark lines: operative sections of the TEN axis Berlin-Palermo. Arrows indicate areas of Lower Inn Valley railway up- grade in the Kundl-Radfeld-Baumkirchen area and Brenner Base Tunnel (modified from BEG website, www.beg.co.at ). Geostatistical space-time interpolation 3 2 Hydrogeological overview As outlined above, the Lower Inn Valley railway upgrade project involves large subsurface sections. These are expected to impact the groundwater resources by partially blocking the natural ground water flux, either by temporary building measures or by permanent subsur- face constructions. Therefore, a thorough understanding of the hydrogeological situation is a prerequisite for modelling the impact of the railway update. As usual in alpine valleys, in the Inn valley the hydrogeological situation is quite complex due to the interfacing of basement rocks and the glacial and postglacial sediments. In the lower Inn valley, three hydrogeological units are discriminated (Wanker et al, 2007): 1) Joint acquifers in the hard rock units of the Northern Calcareous Alps. Here, an intercala- tion of highly permeable, karstified limestones and water retaining clay slates prevails. This unit is subject to supraregional drinking water use. 2) Quarternary, low mountain terraces in the Inn valley. Situated at the forefront of the Northern Calcareous Alps, they comprise sequences of slates, sands and gravels. 3) Youngest sedimentary filling of the Inn valley with permeable gravels and intercalated, less permeable delta fan sands. Summing up, the hydrogeological situation in the project area necessitates a dedicated project concept for the planned railway upgrade. To handle the conflicting interests of the railway upgrade project, the local water resources management and individual interests, a large ground water monitoring campaign has been started in 1996, covering the Kundl- Radfeld-Baumkirchen section. Currently, this monitoring programme involves some 420 sources, 200 standpipes, 830 ground water monitoring wells and 100 measurement points in the Inn and its feeder rivers. Most ground water level data have been monitored twice a month, data being stored in a customised database system. 3 Groundwater table XYt modelling & associated process pipeline A subarea of the Kundl-Radfeld-Baumkirchen railway upgrade project has been chosen as testbed for new approaches to communicate the vast amount of available groundwater data. The testbed is approx. 5km*2,5km wide (Fig. 2). A total of 145 wells have been manually monitored each other week since 1996. In selected wells, continuous data logging is avail- able. The ground water level in the testbed is dominantly influenced by the seasonal water level variations of the Inn river and by industry water extraction. Small feeder rivers, local precipitation, water extraction by public water providers and households are of subordinate importance (Fig. 3). From these data, standardized, colour-coded groundwater table maps are created which show the groundwater level in regular intervals. These maps are com- piled to cartographic animations of groundwater level fluctuations. The animations aim at giving a straightforward and intuitive overview of the huge monitoring data set, unravelling the hydrological impact of the railway upgrade building measures (Fig. 4). 4 R. Marschallinger Fig. 2: Testbed, approx. 5km*2.5km wide. Existing track and upgrade of the Lower Inn Valley railway is shown as white, broken line which parallels the Inn river. Ground water monitoring sites are black crosses; they are unevenly distributed in the testbed, with clustering in places. The village Kundl is visible to the right of the image centre. When creating standardized groundwater table height maps from a real-world set of obser- vations, issues arise from missing observations in time and space (Marschallinger, 2006). Usual problems are: • Locally variable number of observation points, with data clustering (cf. Fig. 2). • Temporally varying number of observation points due to condensation of the ob- servation network, staff outages or technical problems with automatic data loggers during a measurement campaign (compare Fig. 3). To visualise the ground water table variations it is convenient to interpolate between the original monitoring data, i.e., to fill existing gaps in X,Y,t space with estimates. The result of interpolation algorithms is usually a regular 2D or 3D grid of estimates, which can be visualised as groundwater level contours and colour coded raster images, or as isosurfaces and voxel renderings. In hydrology, several interpolation methods are in use, e.g., triangula- tion with linear interpolation, minimum curvature and moving average algorithms (Davis, 2002). Among the moving average algorithms, geostatistical Kriging is considered a reli- Geostatistical space-time interpolation 5 able technique for interpolating hydrological data. It honours the spatial variability of input data, yielding robust estimates and associated standard deviations (Blöschl, 2006). Fig.3: Time series graphs of two fundamentally different monitoring sites in the testbed. Time interval is about 6 ½ years (abscissa), same scaling of level axes (ordinate). The lower graph is practically free of human interference, reflecting the seasonal changes of in the Inn water levels (highest in early summer). The upper graph is from an industrial site in the testbed. Here, the natural fluctuations are biased by water extraction. Kriging can be performed in 2D or 3D space. For example, in mining engineering, Kriging is routinely used to estimate 3D block models of reserves from samples, given xyz coordi- nates and associated grade values (Akin & Siemes, 1988). Principally, when interpolating groundwater table heights, 3D Kriging can be performed with time as the third dimension (Schafmeister, 1999). When monitoring data are available at reasonably small time incre- ments, the temporal autocorrelation can be used to buffer missing observations in the time series and to stabilise interpolation results in the X,Y,t model universe. Fig.4: Process pipeline for 3D space-time kriging of testbed groundwater levels and sub- sequent output of time slices (see text for details). In the project considered here, as a major step in the process pipeline (Fig. 4), a homogene- ous space-time data set is created from the inhomogeneous monitoring data by 3D Kriging 6 R. Marschallinger (Software: GSLIB). Missing observations in space and time (compare Fig. 5) are counter- balanced by spatially and/or temporally close monitoring data. Fig. 5: XYt (easting, northing, time) model universe for 3D kriging the testbed groundwa- ter level variations. Time series are represented as columns paralleling the time(=Z) axis, with each groundwater level datum plotted as a colour coded dot. In places, automatic data logging is available, resulting in tiny sampling intervals (displayed like continuous lines). Prior to geostatistical estimation, such 3D model space view is useful for explorative data analysis. Modified from Marschallinger (2008). Slant view from SE (SGEMS software). GSLIB outputs one voxel array of groundwater level estimates, and one voxel array of associated Kriging standard deviations. The voxel arrays, in the form of GSLIB ASCII files,