Geostatistical Space-Time Interpolation Used to Homogenise Hydrological Monitoring Data

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 groundwater level estimates. From this spatiotemporally homogenized data set, time slices are extracted 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 programme. 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 upgrade, 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 tunnel 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 upgrade 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 subsurface 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 available. 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 observations, 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 observation 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 increments, 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 groundwater 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, are forwarded to a desktop database, which allows the convenient extraction and output of time slices at user defined time increments. One time slice, in the context of the XYt modelling universe, is a section through the voxel array parallel to the XY plane (cf. Fig. 7). From the database, time slices are output as ASCII raster data of estimates and standard deviations, which can be easily read by contouring software for colour coding. In the cur- rent study, data have been contoured and colour coded by Golden Software Surfer and then aggregated to cartographic animations (= Animated GIF format) in Adobe Image Ready.

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Fig. 6: Experimental semivariograms of groundwater levels in the investigation area. Large diagram: semivariogram parallel to XY plane (northing/easting in Fig. 5, abscissa: lag distance in meters). Small, inserted diagram: semivariogram in time di- rection (Z in Fig. 5, abscissa: time lags (days), seasonal changes are clearly visible). Both the spatial and temporal component have been approximated with a Gaussian variogram model. Variogram models for indication only to convey dimensions of the search ellipsoids applied in Kriging.

As the testbed is densely sampled in space and time, the search ellipsoid dimensions can be kept small enough for working with a separable space-time covariance approach while fully covering the volume of interest in the space-time modelling universe with Kriging estimates (XY dimension 250m, t dimension 60 days). However, this approach holds for the testbed situation only; generalizing it for larger, less exhaustively sampled areas of the Lower Inn Valley Upgrade, spatio-temporal modelling with non-separable covariance (e.g., Cressie and Huang, 1999) is a preferable choice.

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Fig. 7: XYt model universe, with orthogonal slices extracted from the voxel array of Kriging estimates of groundwater level heights. Plane parallel to XY represents one time slice, with level heights coded in shades of grey. Time series columns are indicated for XYt reference. Same view and software as in Fig. 5.

4 Conclusions

Space-time Kriging followed by cartographic animation of the results, is considered a prac- tical and traceable method to analyze and visualize aquifer reactions. In the testbed considered here, the proposed process pipeline turned out to be a reliable and economic approach to communicate the complex behaviour of the groundwater system and the impacts by the Lower Inn Valley railway upgrade. Extending the coverage of the model to less densely sampled areas of the railway upgrade, a non-separable approach to modelling the spatiotemporal covariance structure of the groundwater levels will be taken into account, using published extensions to GSLIB for geostatistical space-time modelling (e.g., De Cesare et al. 2002). Geostatistical space-time interpolation 9

Acknowledgements

The author would like to thank the BEG [www.beg.co.at ] for providing monitoring data as well as one anonymous reviewer for his constructive feedback on non-separable space-time covariances.

Software used in the process pipeline

Geostatistics : GSLIB, www.statios.com ; SGEMS www.sourceforge.net Desktop databas e: Microsoft Visual Fox Pro, www.microsoft.com Grid/contouring : Golden Software Surfer, www.goldensoftware.com Animation compiler : Adobe Image Ready, www.adobe.com

References

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