Methods. In this study the main unit of generalization is the spatial cluster and the main ... Copression Distance metri
SCALABLE GENERALIZATION OF HYDRAULIC CONDUCTIVITY IN QUATERNARY STRATA FOR USE IN A REGIONAL GROUNDWATER MODEL 1
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INVESTING IN YOUR FUTURE
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Jānis JĀTNIEKS , Konrāds POPOVS , Ilze KLINTS , Andrejs TIMUHINS , Andis KALVĀNS , Aija DĒLIŅA , Tomas SAKS 1 2 3 Faculty of Geography and Earth Sciences, Faculty of Physics and Mathematics, Laboratory for Mathematical Modelling of Environmental and Technological Processes. University of Latvia, Riga, Latvia. Contact:
[email protected], www.puma.lu.lv 1140
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Fig. 8. Squared sum of errors against geometries prepared from different clustering solutions using NCD matrix.
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This work aims to present calibration results and detail our experience while integrating a scalable generalization of hydraulic conductivity for Quaternary strata into the regional groundwater modelling system for the Baltic artesian basin – MOSYS V1.
Methods
spatial clustering results into the MOSYS finite-element mesh geometry and resolving structure conflicts, arising from different lithological structures, geological columns selected from the most typical borehole log in this cluster. 100
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In this study the main unit of generalization is the spatial cluster and the main criteria for finding adequate representative borehole columns is the Normalized Copression Distance metric – a nonparametric datamining technique calculated by CompLearn ncd utility (Cilibrasi, 2007). Spatial clusters were obtained from flattened completelink hierarchical clustering dendrogram representations, supplying cluster membership identifiers for each borehole. Using Voronoi tesselation and GIS dissolve spatial analysis functionality on this data spatial clusters were obtained in GIS format. The procedure is described in detail in “Lithological Uncertainty Expressed by Normalized Compression Distance” by Jatnieks et al. 2012. Full overview of the experiment workflow with software components and key stages is shown in Figure 1. We used two experiment matrices for hierarchical clustering. One where spatial clusters are obtained from Normalized Compression Distance (further identified as NCD matrix) matrix alone and a second where matrix is combined with range normalized Euclidean distance matrix of borehole locations in BalticTM93 projection (further identified as NCD+E experiment matrix).
Fig. 3. Algorithm for calculating Z values for including
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Fig. 4. After the algorithm described in Fig. 3 creates the layer structure into the model geometry, the respective conductivity values are assigned to mesh elements, created by the new placeholder layers. The cluster membership for each of mesh elements is determined by intersecting the element centroids, shown here in white with spatial clusters in GIS Shapefile layer. Log scale for conductivity values on Y axis.
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Fig. 12. Selected experimental model geometries and their response to
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Results
The experiment geometries based on NCD matrix perform each of the geometries derived from different logical clustering better overall. solutions using NCD matrix. The various Quaternary representations tested have a measurable effect on model results - the worst geometries, such Number of logical clusters against squared sum of head errors - NCD+E matrix as NCD+E 7, 3 and others with low logical cluster count, perform more than twice as bad compared to the best NCD clustering based geometries. NCD clustering based geometries with the better initial calculation results (in Figures 8 and 10), such as the 12 and 13 cluster variants, also tend to respond better to optimization with MOSYS auto-calibration routine (Figure 12). Some the geometries with lower results from intial model run, Fig. 10. Squared sum of errors against geometries prepared from show very minimal improvement with calibration (Figure 12). different clustering solutions using NCD+E matrix. For our experiment territory, consisting of formerly glaciated Squared error sum distribution by clustering solution and associated experimental geometry structure - NCD+E matrix Number of logical clusters after dendrogram flattening territory of Latvia, the best performing generalizations have 12 and 13 clusters. This could have been successfully deduced from the clustering dendrogram in Figure 2. The best performing model geometry before applying the NCD metric based clustering solution, had squared error sum of 814 meters. The best NCD clustering geometry provides 9.7% improvement to 735. This may seem modest in nominal terms. It isn't, because the experimental Quaternary strata were inserted in a previously calibrated model geometry with initial conductivity values as estimates. Model autocalibration works by multiplying D2nr D2ar D2br D3gj D3am D3pl D3slp D3dg D3ogkt D3stel D3jnsk C1 P Q layer material properties with coefficients determined by the the Scipy L-BFGS-B routine (Zhu et al. 1997). Since this works on a Fig. 11. Squared error distribution by model calibration layers for layer basis, the proportional differences in conductivity values each of the geometries derived from different logical clustering between elements in each layer remain constant. Ideally, the solutions using NCD+E matrix. model geometry area built using clustering and the rest of the The response of the selected new model geometries to territory would be calibrated seperately. This could yield further calibration indicates their influence on the underlying improvements. model strata, not just improved performance in the part References 1. Bennett, C. H., Gacs P., Li M., Vitanyi P., Zurek W. 1998, Information Distance, IEEE Transactions on Information Theory, of the model representing the Quaternary deposits. 44(4), 1407-1423., IEEE. R. 2007., Statistical Inference Through Data Compression, ILLC Dissertation Series DS-2007-01, Institute for Geometries NCD 12c, NCD 13c were calibrated further, 2. Cilibrasi, Logic, Language and Computation, Universiteit van Amsterdam. including the remaining bedrock layers as optimization 3. Klints I., Virbulis J., Timuhins A., Sennikovs J. and Bethers U., Calibration of the hydrogeological model of the Baltic Basin, EGU Geophysical research abstracts EGU2012-10003 [this section poster board A255]. parameters and yielding further decrease of squared 4. Artesian Takčidi, E. 1999. Datu bāzes "Urbumi" dokumentācija [Documentation of the database "Boreholes"]. Valsts ģeoloģijas Rīga. [In Latvian]. error sum, used as overall fitness function for model 5. dienests, Valner, L. 2003. Hydrogeological model of Estonia and its applications. Proc. Estonian Acad. Sci. Geol., 52, 3, 179-192. performance against observed pressure heads. 6. Virbulis, J., Bethers, U., Saks, T., Sennikovs, J. & Timuhins, A. Hydrogeological model of the Baltic Artesian Basin. Journal. [Under revision]. Examples of crossections from NCD 12c structure are 7. Hydrogeology C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (1997), ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560. shown in Figures 6 and 7. 1750 1700 1650 1600 1550 1500 1450 1400 1350 1300 1250 1200 1150 1100 1050
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The cover of Quaternary sediments, especially in formerly glaciated territories usually is the most complex part of the sedimentary sequences. In regional hydro-geological models it is often assumed as a single layer with uniform or calibrated properties (Valner, 2003). However, the properties and structure of Quaternary sediments control the groundwater recharge: it can either direct the groundwater flow horizontally towards discharge in topographic lows or vertically, recharging groundwater in the bedrock. Building a representative structure of Quaternary strata in a regional hydrogeological model is important as this affects all the underlying strata.
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Introduction
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Normalized Compression Distance and hierarchical clustering as an approch for scalable generalization of Quaternary sediment lithological structure in the MOSYS regional groundwater modelling Fig. 2. Complete-link agglomerative hierarchical system for the Baltic artesian basin territory. clustering dendrogram for Normalized Compression Distance matrix of serialized borehole log lithological structures.
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Fig. 1. Overview of the full experiment workflow for using
Optimization runs for Quaternary strata in 5 model geometries for each of NCD and NCD + E matrices
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B This degree of similarity and the spatial heterogeneity of the cluster polygons can be varied by different flattening of the hierarchical cluster model into variable number of clusters. Such an approach provides a scalable generalization solution. It can be scaled from broad to more detailed generalization, depending on model and structural characteristics of the modelling territory, with the help of the clustering dendrogram (Figure 2). Using the dissimilarity matrix of the NCD metric, a borehole, most similar to all the others from the lithological structure point of view, can be identified A from the subset of all cluster member boreholes. The log structure of this borehole then is applied Fig. 5. Spatial distribution of vertical permeability values in the throughout the territory of the corresponding spatial MOSYS V1 modelling system mesh in the clustering experiment cluster. The spatial locations of the same logical clusters can be disjoint - in different parts of the territory in Latvia. Screenshot fragment of MOSYS visualization modelling territory and have the same borehole log platform HiFiGeo, log scale, EPSG:25884 projection. column, representing the lithological structure throughout spatial clusters with the same logical cluster identifier. Hori162 model geometries Vertical zontal were prepared, incorporating Class Lithology conduc- conductivity, tivity, m/day different candidate m/day 1 sandstone 5 1 representations of Quaternary sandstone2 1 0.5 low strata made from spatial conductivity clusters with the most typical sandstone3 high 50 20 borehole column, selected conductivity 4 limestone 30 10 using NCD metric. The limestone-low 5 1 0.1 borehole log column conductivity dolomite-high lithological structure is 6 100 30 conductivity 7 dolomite 30 10 Fig. 6. Middle fragment of vertical crossection AB (overview in Figure composed using aggregate domerite 5) across the Vidzeme region, showing horizontal permeability values lithology types as shown in 8 (clayey 0.1 0.01 dolomite) on the right Y axis in Quaternary represented by 8 modelling system Table 1 with their 0.0000 9 clay 0.00001 layers (only Q layers shown, for simplicity). Left Y axis - Z values in 1 conductivity values. 10 loam 0.001 0.001 To integrate these 11 sandy loam 0.001 0.001 meters above sea level. Distance from crossection A point on X axis. silt 0.01 0.01 results into the geometry 12 13 sand 5 5 of regional groundwater 14 gravel 20 20 10 10 model MOSYS V1, the 15 gypsum peat 10 10 algorithm, shown in Figure 16 gyttja and biogenic 0.0003 0.0003 3, calculates mesh point 17 other sediments heights in meters above sea 18 soil 1 1 other 1 1 level for every mesh point in 19 20 concrete 0 0 every newly created Table 1. Initial Quaternary layer. conductivity values After the layer surface from lithology calculations, the mesh classifier, used for element cluster memebership generalization of is determined by intersecting borehole log Fig. 7. Previous implementation of Quaternary strata in the MOSYS V1 element centroids (white dots structures for this modelling system consisted of 4 layers - two sets of aquifer-aquitard in Figure 4) with the spatial study. transitions. The arrow indicates the border between the previous clusters. Quaternary implementation (left) and the new Quaternary The performance of resulting geometries is implementation, using hierarhical clustering of Normalized detailed in Figures 8-11. For both matrix variants Compression Distanece, on the right. (NCD and NCD+E) 82 model geometries, based on different flattenings of cluster dendrogram (Figure This provided insight in their sensitivity to calibration 2) were prepared and run in MOSYS V1 modelling through further optimization of hydraulic conductivity values environment. From the inital model run results in in Quaternary strata (Figure 12). The model geometry, in Figures 8 and 10, 3 better perfoming, one which the Quaternary clustering experiment geometries were median and also the worst performing geometry integrated, had already been calibrated until convergence was run through MOSYS autocalibration routine before these experiements. (Klints et al. 2012). 6440000
This work was supported by the European Social Fund project "Establishment of interdisciplinary scientist group and modelling system for ground-water research", 2009/0212/1DP/1.1.1.2.0/09/APIA/VIAA/060
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