Kriging and the Drift of Salinity Risk Mapping

Transcription

1 Kriging and the Drift of Salinity Risk Mapping Tim J. Peterson 1, Craig Clifton 2, Henry Chaplin 3 1 Environmental Engineer, Sinclair Knight Merz, Victoria, Australia 2 Associate, Sinclair Knight Merz, Victoria, Australia 3 GIS Specialist, Sinclair Knight Merz, Victoria, Australia Abstract: Salinity management relies heavily upon the mapping of the watertable to predict regions at risk of salinity. Current mapping techniques often ignore the influence of topography to interpolate using only the reduced water level (RWL) at each bore. The result, frequently, is an exaggerated area of shallow watertable and as such salinity risk. Current methods also do not provide any measure of map reliability or bias. Kriging with external drift (KED) is a valuable technique for improving the mapping of the shallow watertable but has received little application in salinity management. It is a geostatistical technique which, in this application, allowed local topography to be considered in the interpolation between bores. KED was applied to Victoria s North Central Catchment Management Authority (NCCMA) region to produce RWL and depth to watertable maps (DTWT) for the years 2000, 2020 and 2050 (Peterson et al. 2002). Focusing only on the Avon-Richardson sub-catchment of the NCCMA, this paper compared the year 2000 DTWT map from KED to that from the 1998 National Land and Water Resources Audit (NLWRA). The NLWRA DTWT map was produced from hand contouring of bore RWL. To adequately compare the two maps the climatic and hydrogeological changes from 1999 to 2000 were assessed and the only significant change was a decline in the RWL of approximately 0.5 metres. Additionally, cross-validation of the KED model quantified its bias. The NLWRA technique was unable to estimate the bias or the spatial reliability. The NLWRA estimated the area shallower then 2 metres as up to 4.7 times that of KED and misrepresented hydrogeological processes. In numerous regions the differences between the two methods was far beyond the extent of the RWL decline or model bias. As these discrepancies frequently occurred at regions of high reliability on the KED map, the NLWRA maps was concluded as the least plausible and KED to be a valuable reproducible technique for salinity management that also provides a measure of map reliability and bias. Keywords: Salinity planning, watertable mapping, kriging with external drift, geostatistics. 1. INTRODUCTION The management of secondary salinity relies heavy upon maps of the current and future depth to the watertable (DTWT). Although also dependent upon other factors, such as soil type and local geology, the DTWT is the most widely used indicator for salinity risk assessment. The salinity management plans of all of Victoria s Catchment Management Authorities are based upon DTWT maps. All DTWT maps are produced from mapping of the RWL surface and its substraction from the digital elevation model (DEM). Due to the spatial paucity of the shallow groundwater monitoring network, particularly within dryland farming regions, DTWT mapping is highly dependant upon the interpolation technique. Common RWL mapping techniques include: Hand-contouring of bore observations with underlaid topographic map; Linear interpolation, such as triangulation, based only on bore observations; Non-spatial relationships between RWL and reduced natural surface elevation (RLNS) For an unconfined aquifer flowing under a topographic gradient, the water table is a subdued replica of the ground surface above (Desbarats et al. 2002). A common deficiency of the above methods is the inability to include both this process and the spatial distribution of bores to quantitatively estimate the RWL. Also rarely is any cross-validation of the interpolation model performed to either calibrate it or estimate the model bias or uncertainty. Bore monitoring networks are often also clustered around irrigation regions and know saline discharge areas. Therefore at each location the RWL estimate will be based upon a differing quantity and proximity of data and as such will differ in reliability. Salinity management decisions would benefit from such information but none of the above methods provide an estimate of reliability beyond noting the location of the bore data.

2 Kriging is a geostatistical technique for interpolating sparse data. It relies upon a spatial statistical model, or variogram, of the average difference between all observations as a function of separation distance. The model is also able to be calibrated against observations. Kriging with external drift (KED), unlike ordinary kriging, improves the estimate by including a secondary spatially continues variable that has a linear relationship to the primary variable. Thus KED allows watertable mapping based on the spatial distribution of bore data and the RLNS. Unlike all of the above methods kriging and KED also provides a map of reliability. The Victorian NCCMA contracted Sinclair Knight Merz for the North Central Salinity Audit to reassess the current and future risk of salinity. KED was employed to map the current DTWT and both KED and ordinary kriging (OK) to map the best, worst and most-likely DTWT in 2020 and 2050 (Peterson et al. 2002). Although KED has had some application to watertable mapping (see Desbarats et al. 2002) this is the first know application to salinity management in Australia. This paper compares the year 2000 DTWT maps from KED and the NLWRA to highlight the benefits of and deficiencies of KED. In the following is a non-technical overview of kriging and KED followed by the techniques used for the National Land and Water Resources Audit for Victoria. For an in-depth discussion of KED see Deutsch et al. [1998] and Goovaerts [1997]. 1.1 Introduction to Ordinary Kriging (OK) Four steps are required to complete OK: Experimental Variogram An experimental variogram is a line plot of the average squared difference between all data points as a function of separation distance. It is a statistical model of how related two data points are as function of separation distance and at what distance apart they hold no relation. Multiple variograms also allow the inclusion of isotropic scenarios Model Variogram The model variogram is a set of distribution functions which best fit the experimental variogram. These distribution functions are the fundamental input to kriging. The experimental variogram is derived from a sample dataset, not from the population. It therefore is only a sample of the study area s actual variogram. As a result the model is based not only upon the experimental variogram but also upon the physical processes operating within the study area and the configuration of the monitoring network Cross-validation of model variogram Cross-validation is an iterative processes very similar to calibration whereby the quality of the variogram model is repeatedly assessed and modified. Each data point is removed from the dataset, estimated using the model variogram and surrounding data and re-inserted to the dataset. The mean error, bias and location of inadequate errors is thus quantified and the model reviewed until satisfactory Ordinary kriging (OK) OK is the implementation of the model to produce the map. OK uses the best linear unbiased estimate (BLUE) algorithm. Datapoints within a user-set search radius of each estimation point are selected and, using the variogram, the variance of each is derived based on their distance from the estimation point. The algorithm then derives a weighting for each data-point to minimise the variance at the estimation point. Multiplication of each datapoint by its weighing and summing with the other points produces the estimate. This process is repeated for every grid cell of the map. 1.2 Introduction to Kriging with External Drift (KED) KED requires the same four steps as OK but the variogram is not based upon the raw data but its value after the influence of the secondary variable is removed, that is RLNS. In this study it was removed using the spatial variogram to obtain a direction least influenced by the regional topography. When kriging the influence of the secondary variable is replaced. For each estimation point a linear equation between RLNS and RWL is derived, which is based only upon the data within the search radius. A first estimate of the RWL is derived using this equation and the RLNS at the estimation point. A processes similar to step four above uses the residual variogram to adjust this first estimate, and produce the final RWL estimate. The requirements of KED is that the secondary variable be known at every point of estimation

3 and be continuous. Also the relationship between primary (RWL) and the secondary (RLNS) variable must be linear. 1.3 Methodology for the National Land and Water Resources Audit for Victoria. The NLWRA for all but the Wimmera, which includes the Avon-Richardson, mapped the risk of salinity occurring within any grid cell. Only in the Wimmera was the DTWT explicitly mapped. Standing water levels were compiled on 1:100,000 map sheets and a watertable surface manually interpolated from topographic contours and watertable elevation contours from the Murray-Darling Basin Hydrogeological Map Series. The 1998 depth to water table map for the Wimmera study was produced by using these watertable contours and point data from the it s final bore dataset. (Sinclair Knight Merz et al. 2000). The maps were digitised at a 350 metre grid cell resolution. 2. STUDY AREA dryland and irrigation salinity and declining river health, water quality and biodiversity. The North Central Salinity Audit was one of the key data collection projects within the region s NAP Foundation Program. It provided baseline information on salinity and groundwater and the potential impacts of salinity on key regional environmental, agricultural, infrastructure and social assets. The information collected provides a basis for evaluating long-term impacts of NAP and other natural resource management investments in the region. The salinity audit built upon previous regional scale work under the Murray-Darling Basin Salinity Audit (Murray-Darling Ministerial Council 1999; Sinclair Knight Merz 1999) and National Dryland Salinity Assessment (Sinclair Knight Merz and Agriculture Victoria 2000; National Land and Water Resources Audit 2001) In the following only the Avon-Richardson catchment is reported upon. This was required to adequately represent the detail within the format of a conference paper. Also, only the year 2000 map is presented. The North Central Catchment Management Authority (NCCMA) region is bordered by the Murray River to the north and the Great Dividing and Mt. Camel Ranges to the south and east (see Figure 1). It covers an area of approximately three million hectares, around 13% of the State of Victoria. It includes four major river catchments: the Campaspe, Loddon, Avoca and Avon-Richardson. The Campaspe and Loddon rivers drain directly into the Murray River. The Avoca River drains into a series of terminal lakes and wetlands (the Avoca Marshes). The Avon-Richardson catchment is internally drained, with most surface water draining into Lake Buloke in the north of the catchment. It supports dryland agriculture and is characterised by broadacre land uses, such as cropping and grazing. Average district rainfall ranges from less than 400 mm/year in the north of the region to over 1000 mm/year in the high elevation areas in the south and south-east. Rainfall is winter spring dominant. Summers are warm and dry and winters generally cool and moist. Average rainfall declines and average temperature increases from south to north across the region and from the east to west (especially in the region s southern half). The NCCMA region is one of twenty-one priority areas nominated under the National Action Plan for Salinity and Water Quality (NAP). It is a region facing significant challenges, in terms of Figure 1. The study area: Victoria s North Central Catchment Management Authority. 3. METHODOLOGY 3.1 Data Collection and Preparation The data sources comprised only of the NCCMA 25 metre resolution DEM and bore RWL data. All bores within a five kilometre buffer of the NCCMA boundary from both the

4 Victorian State Groundwater Management System and the Conservation and Land Protection Research (CLPR) networks were collated. Of this dataset only those meeting the following criteria were used: surveyed location; average DTWT less than 20 metres; if a nested bore only the shallowest in the nest was selected. The data was de-nested as kriging requires a unique value for each location. Using a database the hydrograph from each bore was manual inspected and erroneous observations removed. Any period of very high frequency observations was also averaged to a single average observation in order not to incorrectly bias the arithmetic average DTWT for the year As many bores were not surveyed for elevation the RWL was derived by subtracting the DTWT from the DEM. The final bore dataset comprised of those with at least one observation within the calendar year. Where multiple observations existed during the year the arithmetic average was used. 3.2 DTWT Mapping for the Year Using the year 2000 bore dataset the linear relationship between RLNS and RWL was first verified. The experimental residual variogram was derived using a surface variogram, which defined the angle of minimum variance. This method assumed that the variogram is isotropic. The following variogram parameters where further adjusted to produce the smoothest variogram: lag spacing; search angle; angle of tolerance and bandwidth. Outlier variance data points were then removed via visual inspection. The model variogram was fit to the experimental variogram visually but with consideration of the reliability of each variogram point, a focus on shorter range points and the spatial clustering of data throughout the CMA. The nugget (random underlying variance in the data) was assumed low due to hydrogeological processes ensuring the RWL of neighbouring bores is often high correlated. Both the experimental and model variograms were derived using Variowin (Pannatier 1996). Cross-validation involved adjustment of the model variogram and search criteria to produce a mean and median error closest to zero; minimum skew of errors and a random distribution of errors against the observed DTWT. The search radius was also kept low to ensure the RWL versus RLNS relationship reflected the local topography. The crossvalidation and the KED used the Deutsch et. al. (1998) KED algorithm. Using the cross-validated model and KED a map of the year 2000 RWL, at 100 metre resolution, was produced and its subtraction from the DEM produced the DTWT map. Mapping of the KED variance produced an indication of reliability. Prior to mapping the variance it was reclassified into the following five percentile classes of reliability; 10 th for very high; >10 th and 25 th for high; >25 th and 50 th for moderate; >50 th and 75 th for low and >75 th for very low. Importantly, the reliability estimate from KED is dependent only upon the spatial distribution of data, not the value at each point. Also it is not derived from the crossvalidation. Therefore it is only an indication of reliability. 4. RESULTS In figure 2 is the experimental and model residual variogram. At each point on the experimental variogram the number of bore pairs is displayed. The model variogram is Gaussian with range 61,200 metres, sill of 965 and nugget of 20. Beyond the range the difference between two pairs of bores is greater then 95%. Figure 2. Variogram for the 2000 DTWT Map. Note: the sill is the height on the y-axis at which variogram is approximately horizontal. In table 1 is a summary of the cross-validation of the model variogram. Throughout the entire NCCMA the mean DTWT error was estimated as metres shallower that observed. The distribution of errors was only slightly skewed from a normal distribution. Table 1. Summary of variogram crossvalidation. Statistical Parameter Est. Obs. DTWT (m) Mean m Median m Standard Deviation 3.0 m Skew 0.31 m

5 Figure 3. KED derived depth to water table map of the Avon-Richardson sub-catchment in Figure 5. NLWRA depth to water table map of the Avon-Richardson sub-catchment in In figure 3 is the KED derived DTWT map of the Avon-Richardson. Figure 4 provides an estimate of the reliability of the KED derived DTWT map. In figure 5 is the NLWRA DTWT map of the Avon-Richardson. It was derived using hand contouring from a comparable bore dataset, and is unable to produce a map of reliability. Additionally, there are no artesian regions as when hand-contour such regions are easily identified and, based on judgement, removed. The circled regions are those that differ significantly to the KED map. A difficulty in comparing the two DTWT maps is that the KED was derived for the year 2000 while the NLWRA for Inspection of the rainfall residual (derived from the entire 84 years of rainfall data) in figure 6 indicates that from 1999 to 2000 the annual rainfall in districts 81 and 88 was respectively only 67 mm/year and 30 mm/year above the average. Figure 4. Reliability of KED derived depth to water table map of the Avon-Richardson subcatchment.

6 Cumulative Rainfall Residual (mm) BoM District No. 81 (Average of 433 mm/yr) BoM District No. 88 (Average of 731 mm/yr) Figure 6. Rainfall residual of the two Bureau of Meteorology (BoM) rainfall districts within the Avon-Richardson. In table 2 are the RWL trends at selected shallow bores throughout the Avon-Richardson. Together they cover from upstream of the confluence of the Avon and Richardson Rivers to north of Lake Buloke. Also all of the bores but number 34 is within major discharge region. Despite the above average rainfall from 1999 to 2000 the RWL at most of these bores continues to decline. Table 2. RWL trends inclusively from 1999 to 2000 at selected CLPR bores. Bore ID RWL Trend (m/year) RWL Change (m) In figure 7 is fraction of the Avon-Richardson within each DTWT class as estimated by each map. The most significant differences are: the NLWRA estimated 10% of the area having a DTWT less than 2 metres while the KED map estimated only 4%; and the NLWRA estimated 72% deeper than 5 metres while the KED map estimated 78%. Artesian, 2% <2m, 2% >10m, 43% 2-5m, 18% 5-10m, 35% >10m, 55% <2m, 10% 2-5m, 18% 5-10m, 17% (a) KED Map (b) NLWRA Map Figure 7. Percentage Area of the Avon- Richardson within each DTWT class. 5.0 DISCUSSION In the following the results from KED are first discussed followed by a comparison with the NLWRA DTWT map. 5.1 DTWT Mapping using KED Prior to developing the experimental variogram the RWL versus RLNS relationship was confirmed, which had a very high correlation of The angle of minimum variance is the direction in which the RWL is least influenced by regional topography and as such is perpendicular to the direction of lateral flow. The minimum variance was 85 o from north which is encouragingly towards and in the downstream direction of the Murray River, the major discharge site of the NCCMA. A reliable variogram was derived by the fact that each point contained a large and comparable number of data pairs and it reached a stable sill. If the regions topographic trends had not been adequately removed a sill would not have been observed. In testing the assumption of the variogram being representative of the entire NCCMA a variogram was derived for both the plains and highlands, which were defined respectively at north and south of Donald. The range of the lowlands variogram was noticeably greater than that of the highlands. The variogram in figure 2 was an approximate merging of the two. In the interests of maintaining a seamless map at such a boundary the NCCMA was not divide and krigged separately. Visual inspection of figure 2 suggests the model fits well to all data points, except that at 32,000 metres separation. A Gaussian model best fitting the experimental variogram and was also what is expected when kriging a watertable surface as two neighbouring bores are likely to having a very comparable RWL (Desbarats et al. 2002). The nugget was made lower than that observed as the first data point comprised mostly of bores within the irrigation regions. Irrigation increases the spatial variance and such the nugget. A nugget was required to ensure a mathematically stable Gaussian model. The skew and non-zero mean and median errors from the cross-validation results in table 2 suggest a model bias. Inspection of the observed versus estimated DTWT indicated the DTWT was over estimated when shallower than

7 4 metres and underestimated when deeper then 8 metres. Additionally inspection of the randomness of errors (estimated minus observed DTWT) highlighted a poorly correlated trend of slightly decreased error with increased observed DTWT. Thus, despite an approximately zero mean error the distribution of errors were not random. This slight deviation from an assumption of KED is most likely due to the single variogram not being entirely representative of the NCCMA region. This is difficult to confirm without repeating KED using the northern and southern variograms mentioned above but is suggested by the northern having the greatest expanse of near uniform DTWT and the southern a far more varied DTWT. Inadequacy of the single variogram in northern regions would produce, and as is observed, an overestimate of the DTWT when shallow. Inadequacy of it in northern regions would produce, and again as is observed, an underestimate of DTWT when deep. The map in figure 3 is the result of an iterative process of also adjusting the search parameters to omit artificial linear structures. Despite this artificial structures still remain in the far south, far north and north eastern boundaries of the Avon-Richardson. All of these regions are identified in figure 4 as of low reliability. The correlation between the regions of high reliability being also of shallow DTWT is due only to historically groundwater bores more often being drilled in regions of shallow DTWT. The bias identified from the cross-validation of the overestimation of the DTWT when shallower than 4 metres causes the extent of the shallow DTWT to be slightly underestimated. In regions of few neighbouring bores the DTWT estimate will be most sensitive to the variogram range, which as mention above is the likely cause of the model s bias. Regions mapped as of high or very high reliability will therefore be least bias and the overestimation the shallow DTWT minimised. All regions of shallow DTWT, with the exception of immediately downstream of the confluence of the Avon and Richardson rivers and far upstream on the Avon River, are of high or very high reliability and as such its extent is not likely to be underestimated. 5.2 Comparison of DTWT Maps Prior to comparing the NLWRA and KED DTWT maps the significance of them being for different years, that is 1998 and 2000 respectively, must be assessed. From 1999 to 2000 the rainfall was 67 mm/year above average (district 81) which in comparison to the previous 20 years is a minor deviation. The seasonal distribution of rainfall from 1999 to 2000 was also well within the 95 th to 5 th percentile range of the monthly average rainfall. Despite the above average rainfall the hydrographs from numerous bores near the confluence of the Avon and Richardson Rivers and downstream to Lake Buloke illustrate, from 1998 to 2000, a modestly declining RWL. At this confluence and at Lake Buloke flood recharge also occurs. In 1996 an approximate 1 in 10 flood occurred though within one years the RWL at many bores within the flood extent returned to the pre-flood RWL. Therefore the lower watertable of the KED map is not caused by changes either in rainfall or flooding from 1999 to The declining bore RWL does complicate the comparison but as discussed below it is far exceed by the differences between the two maps. In figure 7 is a gross comparison of the area within each DTWT class. Most significant to salinity management is the NLWRA estimate of the area shallower than 2 metres as 2.6 times that of KED. In the KED map, if the artesian regions of low reliability in the far south, north and north east were omitted then the area of watertable shallower than 2 metres increases to a difference of over 4.7 times. In the NLWRA map (figure 5) the circles numbered one to three are shallow features present only in the NLWRA map. These features differ to the KED map by over one DTWT class and are all of a very high to high reliability class and as such could not be accounted for by the declining RWL from 1999 to 2000 or the KED model bias. The circles numbered four and five are shallow features which are also represented but are clearly shallower in the KED map. Again these two features are of a very high reliability class. The only features that are present only on the KED map are those already identified as of very low reliability at the far north, far south and northeast boundaries. In the NLWRA map the DTWT surrounding lowland shallow regions increases over a very short distance to deeper then 10 metres. Considering the topography is very flat and the geology relatively uniform such hydrogeological processes are unlikely. In comparison in the KED map shallow regions are surrounded by a gradual progression through the DTWT classes. Asides from making the NLWRA map questionable this also understates the risks to

8 salinity management as it suggests such shallow groundwater mounds would dissipate more quickly and the surrounding region is not as at a greater risk of salinity. 6.0 CONCLUSION Clear differences have been proven between the DTWT maps of each method, and while proving which is correct is an unsuitable question, proving the most plausible is suitable. Of the two techniques discussed only for KED is the model calibrated and refined in an iterative process prior to mapping. Although this did identify model bias, which could not be overcome, the NLWRA in contrast applied a technique without any calibration or estimate of its bias. Additionally only for KED is a map of reliability produced to explicitly illustrate each location is not of equal reliability. The most significant differences between the two maps are that the NLWRA map: identified major regions of high salinity risk not identified by KED; overestimated the area of shallow watertable; and unrealistically representation some hydrogeological processes. As a result of all three discrepancies occurring in regions of high reliability on the KED map and their estimate being derived from a non-calibration model the KED map is considered the most plausible. Despite the deficiencies of the NLWRA map it s technique does allow consideration of geological features and the omission of low reliability features such as those of the far northern and southern in the KED map. Additionally this technique is also considerably less time-consuming. Such benefits make it a useful technique to complement KED during the model development and cross-validation. In the Avon-Richardson, salinity management decisions based upon the NLWRA map would have both incorrectly identified and overestimated the risks. Prioritisation within the Avon-Richardson catchment and between other catchments would have been misguided and future salinity risks potentially amplified. If the current DTWT map is also to be used as a baseline to gauge the effectiveness of management actions then the mapping technique must be reproducible, which of the two methods only KED offers. Finally, via the variogram KED extracts more information from the bore network than hand-contouring. Therefore with KED a less extensive salinity bore monitoring network is required. 1.4 Acknowledgments The authors are grateful to Mark Reid and David Heislers from the Centre for Land Protection Research for their support and their supply of bore monitoring data; Brain Barnet for useful discussions and Camille McGregor for initial project planning. 1.5 References Desbarats, A. J., Logan, C. E., Hinton, M. J., D. Sharpe R., On the kriging of water table elevations using collateral information from a digital elevation model, Journal Of Hydrology, 255 (1) 25-38, Deutsch, C. V., Journel, A. G., GsLib: Geostatistical software library and user s guide. Oxford University Press, Second edition, New York, NY, Goovaerts, P., Geostatistics for Natural Resource Management, Oxford University Press, New York, Murray-Darling Basin Ministerial Council, The salinity audit of the Murray-Darling Basin. Murray-Darling Basin Ministerial Council. Australia,1999. National Land and Water Resources Audit, Australian dryland salinity assessment 2000, National Land and Water Resources Audit, Australia, Pannatier, Y., VARIOWIN: Software for Spatial Data Analysis in 2D, Springer-Verlag, New York, NY, Peterson, T., Clifton, C., McGregor, C., Chaplin, H., Heislers, D., Reid, M., Smith, N., North Central Salinity Audit: current and future risk area, Sinclair Knight Merz, Australia, Sinclair Knight Merz, Agriculture Victoria, National Land and Water Resources Audit Theme 2 dryland salinity: extent and impact of dryland salinity in Victoria. Report to the National Land and Water Resources Audit, Australia, Sinclair Knight Merz, Ultimate salt loads to the Murray River, Department of Natural Resources and Environment. Melbourne, Australia,1999.