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1 GIS and Field-Based Spatiotemporal Analysis for Evaluation of Paleo Ice Sheet Simulations* Jacob Napieralski Department of Natural Sciences, University of Michigan-Dearborn Reconstructing paleo ice sheets is significant for paleoclimate reconstructions and evaluations of sea level low stands. Accurate reconstructions of paleo ice sheet dimensions and dynamics necessitate the combination of field evidence and process modeling. In this study, a GIS-based technique was developed to quantitatively assess model output against geomorphic data. However, implementation of this technique is not straightforward and requires consideration of time-space relationships, data representation, resolution, and analytical design. Combined use of two software tools holds considerable promise for the use, application, and interpretation of refined ice sheet models. Key Words: GIS, glacial geomorphology, ice sheet reconstructions, orientation, spatial analysis. There is general interest in understanding the development of landscapes during the Pleistocene Epoch ( past 2 million years), including the impacts of continental-sized ice sheets that repeatedly covered much of the midlatitudes of the Northern Hemisphere. Reconstructing the spatial extent, timing, and dynamics of these paleo ice sheets is significant for both paleoclimate reconstructions and evaluations of low stands in sea level (Manabe and Broccoli 1985; Boulton, Hulton, and Vautravers 1995; Paillard 1995; Hyde et al. 1999; P. U. Clark and Mix 2002). Although large collaborative efforts have produced estimates for the extent and volume of the former ice sheets (e.g., CLIMAP 1981), there is concern that these approximations, such as estimates of ice sheet thickness, may be flawed. Consequently, there is continued interest in improving paleo ice sheet reconstructions. Ice sheet reconstructions are established using two general approaches: (1) geologic and chronological data, which attempt to diagnose the extent, topography, and general flow patterns of an ice sheet (e.g., Boulton et al. 1985; Peltier 1994; Kleman et al. 1997; Boulton et al. 2001; Ó Cofaigh et al. 2002) and (2) numerical ice sheet models (e.g., Boulton and Payne 1992; Fastook and Holmlund 1994; Siegert et al. 2001; Takeda, Cox, and Payne 2002), which attempt to quantify ice physics to predict the dynamics of present-day or past ice sheets and glaciers. However, the successful use of ice sheet models for climate research is still limited, partly because of an inadequate means by which to integrate and compare output from a numerical model against field data. Such limitations may generate unrealistic simulations of ice sheet inception, growth, and decay, and, as a consequence, inaccurate estimates of ice sheet volume and topography. Differences in predicted ice sheet configurations range from large and thick Last Glacial Maximum (LGM) ice sheets (Payne and Baldwin 1999) to much thinner, and possibly multidomed, LGM ice sheets (Brook et al. 1996; Ballantyne et al. 1998). Recent efforts to compare numerical and geomorphic datasets have utilized predominantly qualitative approaches, or have relied on comparisons that were somewhat limited spatially or temporally. For example, simulations of ice sheet configurations and ice streams were constrained by the distribution of offshore landforms (Dowdeswell and Siegert 1999; Payne *The author thanks his advisor, Dr. Jon Harbor, for support and guidance during this work. The author also expresses gratitude to his research team, including Dr. Yingkui Li, Dr. Alun Hubbard, Dr. Arjen Stroeven, and Dr. Johan Kleman. Without the efforts of this team, this work would have been impossible. The author would also like to acknowledge his committee members Dr. Bernie Engel and Dr. Ken Ridgway. This article was greatly improved due to the suggestions and comments made by four anonymous reviewers. This work was completed while the author was supported as a U.S. Department of Education GAANN fellow, and this material is based on work supported by the National Science Foundation under Grant OPP to Harbor. The Professional Geographer, 59(2) 2007, pages r Copyright 2007 by Association of American Geographers. Initial submission, April 2006; revised submission, August 2006; final acceptance, October Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, and 9600 Garsington Road, Oxford OX4 2DQ, U.K.

2 174 Volume 59, Number 2, May 2007 and Baldwin 1999; Siegert et al. 2001; Siegert and Dowdeswell 2002), and observed ice flow orientations were assessed by qualitatively comparing model output against geomorphic interpretations of ice flow direction (Näslund et al. 2003). More robust methodologies are needed to compare ice sheet model output to geomorphic and chronologic data to test the predictive capabilities of a model. Numerical models for ice sheet reconstructions require a procedure for comparing output against field data. Frequently, a geographic information system (GIS) is used to visualize and compare field data and model predictions because it provides the capability to amass, and then separate and visualize, enormous amounts of spatial and temporal data. However, there are complexities inherent in field data (e.g., ontological, morphological) and model conceptions. Therefore, the development of a GIS-based system to assess numerical model output with field observations requires consideration of key GIScience issues (Raper and Livingstone 1995; Bishop and Shroder 2004), including data representation, temporal and spatial distributions and relationships, scale limitations, and methodological design. The purpose of this article is to introduce two GIS techniques that compare levels of agreement between geographical data. Although these approaches were developed as separate software tools, together they provide a two-step methodology to compare numerical ice sheet model predictions with geomorphic and chronological data, using the Scandinavian ice sheet (SIS) as an example. Each approach addresses one of two basic issues inherent in comparing ice sheet simulations against interpreted field data: ice extent and ice flow direction. The implementation of this two-step methodology requires consideration of several GIScience issues, which are then briefly discussed. Methodology The emphasis of this article is on the GIS techniques used to test output from a numerical ice sheet model against a suite of geomorphic data. The model runs were compared against field data in two steps using ESRI s ArcGIS and Arc/ INFO s : first, Automated Proximity and Conformity Analysis (APCA), which quantifies the correspondence between moraines and output from each model run ( for details, see Napieralski, Li, and Harbor 2006) and, second, Automated Flow Direction Analysis (AFDA), which establishes the level of correlation between sets of glacial lineations (see Li et al. 2007), and includes drumlins, flutes, or striae that are aligned with localized ice flow patterns (Kleman et al. 1997). Results from the two analyses are then combined to determine which model output(s) best agrees with the field data (i.e., an optimization method between model simulations and field data). Margin Comparisons The APCA uses a system of buffers and overlays to determine the proximity and parallel conformity that exist between interpreted and predicted ice extent. Here, proximity is defined by the total amount of area between linear (including curved) features, and parallel conformity is the overall angle between the predicted and observed features. The area of offset between features (Figure 1A) is calculated by generating multiple buffers around the model output and one buffer around the empirical data (Figure 1B), which are then merged to create a new feature. The buffer rings are automatically designated values that increase outward from the feature, which indicates the proximity of one feature to the other and is used to calculate the area between features. The cumulative plot of these values (Figure 1C) is used to illustrate variations in distance between features in the form of a proximity and conformity diagram ( PCD). The parallel conformity between two linear features is reflected by the slope in the PCD. All other factors being equal, a steep slope indicates relatively good parallel conformity between the features. If the features are perpendicular to each other, then each multiple buffer ring contains the same amount of end moraine and, as a result, the slope of the PCD nears 451. The area under the PCD curve then indicates the overall level of correspondence, as a model run with good proximity and conformity will have a relatively large area under the PCD curve. Using this technique, the values can be normalized and then ranked to determine the model run that best corresponds with the moraines. Flow Direction Comparison The AFDA is based on grid analysis and requires the delineation of sets of glacial lineations

3 GIS and Field-Based Spatiotemporal Analysis for Evaluation of Paleo Ice Sheet Simulations 175 et al. 1997). Flow fans are spatially delineated representations of glacial landform swarms that serve to aggregate data and include lineations and other interpretations of landform assemblages (Kleman et al. 1997). Several key assumptions are made regarding lineations: 1. Glacial lineations are restricted to basal sliding. 2. Basal erosion is a function of and is orientated in the direction of basal sliding. 3. The formation of glacial lineations is considered negligible during frozen-bed conditions. Each flow fan is digitized so that every grid cell occupying a lineation is given a directional value. The cell size coincides with the resolution of model output (10 km 2 ) and allows for the calculation of the residual (offset) that exists between the direction indicators (Figures 2A and 2B). This residual is calculated as the minimum angle between the two directions; the highest offset is then 1801, which indicates the model is predicting ice flow in the opposite direction. The mean of all the residuals per flow fan, as well as other statistical parameters, is calculated for the total field area. The disparity between predicted basal flow direction and the rasterized flow fans generates residual values that denote the level of agreement for each grid cell. The mean residual for every time slice of a model run is then plotted to assess temporal patterns of correspondence between predicted flow directions and field interpretations (Figure 2C) and a frequency distribution of residual values, along with other statistics, is viewed using a series of rose diagrams (Figure 2D). Figure 1 Steps of Automated Proximity and Conformity Analysis (APCA). (A) Digitize end moraines. (B) Use system of buffers and overlays to calculate the area that exists between linear features. (C) Generate a proximity and conformity diagram ( PCD) to determine which model output best fits empirical data, based on the area under the curve, which considers the proximity and conformity between features. In this example, moraine A generated a higher APCA score for the model run based on a larger area under the curve than moraine B. or flow fans (for details on assumptions and theories, see Boulton and Clark 1990a, 1990b; Kleman 1992; C. D. Clark 1993, 1994; Kleman Application to Scandinavia Field Data Relatively well-defined moraines provide distinct markers for ice marginal positions (see Boulton et al. 2001; Rinterknecht et al. 2004). For this study, four glacial moraines indicating marginal positions during the LGM were digitized from previous geologic reconstructions of Scandinavia ( from Kleman et al. 1997) and three other moraines were used to indicate margin positions during the Younger Dryas Period (YD) (Figure 3). Flow fans were digitized from Kleman et al. (1997) within four main study sites

4 176 Volume 59, Number 2, May 2007 Figure 2 Steps of Automated Flow Direction Analysis (AFDA): (A) Combine glacial lineations and model outputs. (B) Overlay model outputs and field evidence to produce a series of residual datasets for different time slices. (C) Plot the resultant mean of residual values against their corresponding time slices to identify temporal patterns of correspondence between predicted directions and field observations. (D) Analyze selected time slices (e.g., f and j) to provide detailed information on the distribution of residuals to evaluate the level of correspondence. (Source: Figure from Li et al. 2007). in Scandinavia. There are numerous flow fans within the Kiruna, Sweden, site, but only flow fans 31 (synchronous fan from LGM) and 38 (a deglaciation fan from Marine Oxygen Isotope Stage 5d 5a) are reported here (see Kleman et al. 1997). The direction of each lineation was calculated using GIS and was rasterized to fit the model resolution (10 km 2 ) so that only the cells that overlapped a lineation were given a direction value. The mean direction of these lineations was presented in Kleman et al. (1997) so as to summarize the overall flow indicators within each flow fan. Each cell had one value, although if there were flow fans that exhibited cross-cutting characteristics within the same cell then those same cells could exist in a different flow fan, albeit with different direction value. Model Runs A three-dimensional model developed by Hubbard (1999, forthcoming) was used to predict ice flow extent and orientation in Scandinavia during the LGM. The model is thermally coupled and, when basal temperatures approach the pressure melting point, a Weertman-type sliding relation dictates dynamics at the glacier bed (Weertman 1964). Isostatic adjustment relies on the elastic lithosphere-relaxed asthenosphere approach (e.g., Le Meur and Huybrechts 1996; Hagdorn 2003). The model was verified and validated elsewhere (Huybrechts and Payne 1996). The topography was produced from a combination of ETOPO5 and GTOPO30 (global surface and bathymetric digital elevation models) and output was generated in millennia time slices for the preceding 100,000 years (100 ka; ka ¼ thousands of years ago). Model predictions of ice margins were converted to vector format using ESRI s conversion tools (Arc/INFO), and ice flow direction remained in raster format and was limited to the Kiruna study

5 GIS and Field-Based Spatiotemporal Analysis for Evaluation of Paleo Ice Sheet Simulations 177 Figure 3 Distribution of end moraines and glacial lineations used in this study. Moraines #1 4 represent the glacial maximum, moraines #5 7 represent the furthest extent during the Younger Dryas. Glacial lineations within the Kiruna, Sweden, study area were separated and classified into flow fans. (Source: Based on work from Kleman et al. 1997). area. Forty modeling runs were used to produce a range of configurations controlled by the altering of key input parameters, including those associated with topographic representation, isostatic response time, accumulation rates and mass balance elevation, and ice

6 178 Volume 59, Number 2, May 2007 Table 1 Cumulative APCA scores for a subset of modeling runs Moraines LGM1 LGM2 LGM3 LGM4 YD5 YD6 YD7 Age (ka) Run Run Run Run Run Run Run Run Run Notes: APCA ¼ Automated Proximity and Conformity Analysis, LGM ¼ Last Glacial Maximum, YD ¼ Younger Dryas Period. The scores have been normalized so that a value of 1.00 indicates the best APCA score for that particular moraine, and 0.00 indicates the worst fit. APCA scores have only been summed for the estimated period of moraine development (see Figure 3 for locations of the moraines), as provided in the top of the table, and have been calculated using various dating techniques (e.g., see Boulton et al and Rinterknecht et al for more information on time-slice data). dynamics (i.e., flow enhancement and the sliding parameter). Results Margin Comparisons APCA scores were reported only during times of moraine development as determined from previous cosmogenic and radiocarbon dating work (see Table 1). The resulting scores were normalized so that 1.00 indicates the best agreement and 0.00 indicates the worst. The majority of model runs were capable of reproducing the moraines located along the western extent of the ice sheet (LGM1 and YD5), as indicated by their high APCA scores relative to the other moraines. Moreover, this good agreement occurred over an extended period of time, which is not surprising in that the western margin of the ice sheet reached its maximum extent earlier than did the southern or eastern margins, and, because it is restricted by the Norwegian Shelf, it remained relatively stationary for several millennia (Mangerud 2003). In contrast, LGM2 and LGM3, both located near a major Norwegian ice stream (Skagerak), proved difficult to reproduce, and any high APCA scores for these moraines typically resulted in low scores for moraines located on the eastern side of the ice sheet (i.e., LGM4 and YD7). This suggests that the input parameters used to drive the model were unable to generate concordant output for the overall timing of ice sheet growth and decay. The same observation can be made for YD7; any high APCA scores generally correspond with low scores for LGM1. Rarely did all three YD moraines achieve high APCA scores during the same simulation. Thus the model runs could never replicate the field evidence for the Younger Dryas because good agreement along one margin was sacrificed for accuracy along another margin of the ice sheet. In this study, the overall level of agreement between model simulations and field data interpretations was determined by the total APCA scores for all seven moraines (a subset of the forty model runs shown in Figure 4). It is evident that the resultant high APCA scores were caused by reasonably matching all seven moraines; the high APCA scores also could be the result of specific model runs corresponding well with LGM moraines but not with YD moraines. For this study, the sum of APCA scores was used to select the best model runs (nos. 29, 30, 32, and 33) to use in the AFDA analysis. Flow Direction Analysis For this study, AFDA scores were generated for flow fans 31 and 38 and plotted against each corresponding time slice from 100 ka to 10 ka (Figure 5). There were distinct periods when model output corresponded with each flow fan: 85 ka, 66 ka, 38 ka, and 20 ka for flow fan 31 and 75 ka, 48 ka, and 12 ka for flow fan 38. It has been suggested that flow fan 38 probably formed during Marine Oxygen Isotope Stage 5 (115 75

7 GIS and Field-Based Spatiotemporal Analysis for Evaluation of Paleo Ice Sheet Simulations 179 APCA Scores YD LGM Run22 Run26 Run29 Run30 Run32 Run33 Run36 Run37 Run39 Model Runs Figure 4 Total Automated Proximity and Conformity Analysis (APCA) scores for the subset of model runs used in this study, based on the cumulative of the highest APCA scores for all seven moraines. Using the graph, it can be determined which model runs best agreed with the seven moraines, individually or cumulatively. In this study, model runs 29, 30, 32, and 33 were deemed the best fits and were used in Automated Flow Direction Analysis (AFDA). YD ¼ Younger Dryas Period; LGM ¼ Last Glacial Maximum. ka) as a result of an elongated west centred ice sheet with its elevation axis parallel to the Scandinavian mountain range (Kleman et al. 1997). A frequency distribution of the data better illustrates the agreement between a flow fan and any given model run. As an example, the agreement between model output and flow fans 31 and 38 from model run no. 30 during time slices of 75 ka and 21 ka was assessed using rose diagrams (Figure 6). During time slice 75 ka, the mean residual was relatively low for flow fan 38 (271), but had a high variance, which indicates the model run was inconsistent with reproducing the whole of flow fan 38. At 21 ka, flow fan 38 exhibited a much higher residual (1011), as most of the predicted ice flow direction conflicted with the flow fan during the LGM. In contrast, the correspondence between the predicted ice flow direction and the interpreted flow fan 31 improved during 21 ka, as the general ice flow direction predicted by the model generally agrees with the field interpretations. Discussion Data Representation It is difficult to compare high spatial resolution field evidence against relatively low spatial resolution model output (e.g., 10 km 2 ). To address Figure 5 The mean residuals for flow fans 31 and 38 were calculated and plotted from 100 ka to 10 ka. Results from Automated Flow Direction Analysis (AFDA) show distinct periods when model output corresponded with field data (figure modified from Li et al. 2007), which occurs when a low mean residual (little offset between predicted and observed) is attained. For example, low mean residuals for flow fan 31 occurred during 85, 66, 38, and 20 ka, and good agreement with flow fan 38 occurred during 75, 48, and 12 ka.

8 180 Volume 59, Number 2, May 2007 Figure 6 Frequency distributions (rose diagram) of residual values from 21 ka and 75 ka BP for flow dataset #31 and #38 (Li et al. 2007). this issue, flow fans were used to capture overall flow patterns. Although there may be an abundance of glacial landforms within a given grid cell, only the average direction of the landforms is used. If cross-cutting characteristics exist, then it is possible the same grid cell will have a direction value for more than one flow fan. The use of flow fans reduces the total amount of data, while capturing the general flow pattern and cross-cutting characteristics of the landscape in a manner in which multiresolution data can still be compared. However, it is important to emphasize that these flow fans are an aggregate interpretation of the actual landform data. This approach does allow for the comparison of geomorphic interpretations against ice sheet model output, which may confirm or provide new insight into the ice sheet dynamics and landscape evolution. In addition, a digitized line in a flow fan may indicate one or more glacial lineations. It is difficult to assume that a good correlation between model output and the flow fan as confirmation of the formative processes because of this uncertainty. For example, opinions differ on the genesis of drumlins and flutings (Boulton 1987; Shaw 1996). Therefore, grouping all streamlined features together may limit the analysis. Finally, the interpretation or opinions used to delineate a flow fan may not be readily agreed

9 GIS and Field-Based Spatiotemporal Analysis for Evaluation of Paleo Ice Sheet Simulations 181 upon; consequently, model runs should be compared against all variations of a particular flow fan. Space-Time Dependency Testing a numerical ice sheet model requires consideration of both time and space, as the formative events responsible for glacial landforms occur over varying scales. The reliability of the APCA depends on the ability to compare model runs against moraines that are situated in different segments of the ice sheet. Furthermore, the spatial extent of the model runs should be tested against interpreted field data from distinct time periods (e.g., LGM, YD), which allows for better comparison of the timing of ice sheet growth, maxima, and decay. The more moraines used in the analysis, the more detail the APCA will provide regarding levels of correspondence. The age (and uncertainty) associated with the dating techniques used for moraines will influence the APCA, and as the techniques continue to evolve these dates will need to be modified. If the certainty decreases with regards to moraine age, this will likely affect the window size used to extract APCA scores (generally 1 millennium for LGM moraines in this study, 0.5 for YD moraines). The AFDA quantifies the agreement between interpreted flow fans over a broad area to simulated subglacial conditions during specific time slices. If a flow fan developed in a time-transgressive manner, then it is unlikely that the mean residual approach would capture this effectively. Rather, the AFDA can be modified to evaluate the deglaciation patterns of nonsynchronous fans by dividing the flow fans into grid cell zones that are situated in an inward-transgressing manner. In this study, the flow fans are assumed to be synchronous, or formed during some event, such as ice streaming. Resolution Limitations As discussed earlier, the resolution of the numerical model is usually the limiting factor since model output is typically in kilometers but glacial landforms can be measured at smaller scales. Thus, model resolution influences the use and interpretation of APCA and AFDA. For example, the model applied here had a 10-km resolution, which fails to capture critical subgrid topographic interactions, especially in the initial stages of mountain inception and in the subsequent reduced mass transfer to lower elevations through deep valleys and fjords less than 10 km wide. This can have a profound influence on the evolving three-dimensional ice sheet geometry, as illustrated by the contrast between the simulation of the Patagonian Ice Sheet (Hulton et al. 2002; Hubbard et al. 2005). Increasing the model resolution, coupled with advancements in the model performance, will improve the ability to capture small-scale ice flow characteristics that play an important role in the inception and decay of mountain-centered ice sheets, and will exhibit sufficient detail to compare smaller flow fans. Analytical Design and Interpretation The design of APCA and AFDA can be modified to reflect changes in the interpretations of field data or different resolutions as modeling capabilities continue to improve. Alterations of buffer and overlay characteristics, for example, can increase or decrease the APCA sensitivity to fluctuations in correspondence between datasets. Likewise, AFDA can be modified to reflect newly acquired field data and to adjust with evolving process-based models. As an example, a weighting scheme can be developed to emphasize the levels of correspondence during specific times or in particular locations. If matching a particular moraine or set of moraines is key to testing the model, then the APCA scores generated for those moraines can be weighted to have a more influential impact on the analysis and results. Conversely, if modeling runs reproduce the position of the LGM moraines more accurately than YD moraines, then the APCA scores generated for the YD moraines can be weighted more heavily in order to better differentiate between model runs. However, when various sizes and distributions of field data are used in GIS tools like APCA and AFDA, care must be taken when interpreting the results from a statistical perspective. Flow fans will vary in size and moraines may be generalized and extensive in length (hundreds to thousands of kilometers in length), and this must be taken into consideration when evaluating the results from statistical analyses. The approach taken in this work compares ice extent as a primary test of agreement between model simulations and geomorphic data. In contrast, regional ice flow patterns may actually be considered a better primary test of corre-

10 182 Volume 59, Number 2, May 2007 spondence, since these patterns also reflect ice sheet configuration, such as the position of the ice divide or dome, and subglacial conditions. This would require a set of flow fans that, based on relative or absolute dating, provide evidence of a known shift in ice flow direction during distinct stages of glaciation. If this approach is needed, then AFDA can be used to compare and rank model runs as a primary test, followed by APCA. Conclusion Glaciers and ice sheets are vital components of the global climate system, and estimating the extent and behavior of paleo ice sheets may be improved by appropriately reconstructing ice sheet extents and subglacial processes. As CLI- MAP (1981) estimates of the thickness and volume of global ice sheets during the LGM have recently been questioned and new reconstructions have been recommended (Mix, Bard, and Schneider 2001), it is vital that such reconstructions agree with geomorphic and chronological field evidence and their interpretation. The methodology presented here is a first step toward accomplishing this, enabling a quantitative comparison of modeled timing, extent, and general ice sheet flow patterns against suites of interpreted field data. Good correspondence between datasets can help evaluate the capability of a model to reproduce patterns of ice flow during varying stages. As a result, it is conceivable to use APCA and AFDA as tools to quantitatively assess an ensemble suite of numerical experiments through geographical scrutiny to explore model uncertainties and sensitivities, and to improve the use and application of such modeling technology. Literature Cited Ballantyne, C. K., D. McCarroll, A. Nesje, S. O. Dahl, and J. O. Stone The last ice sheet in North- West Scotland: Reconstruction and implications. Quaternary Science Reviews 17: Bishop, M. P., and J. F. Shroder Jr Geographic information science and mountain geomorphology. Chichester, U.K.: Praxis. Boulton, G. S A theory of drumlin formation by subglacial sediment deformation. In Drumlin symposium, ed. J. Menzies and J. Rose, Rotterdam, U.K.: A. A. Balkema. Boulton, G. S., and C. D. Clark. 1990a. A highly mobilized Laurentide ice sheet revealed by satellite images of glacial lineations. Nature 346: b. The Laurentide Ice Sheet through the last glacial cycle: The topology of drift lineations as a key to the dynamic behaviour of former ice sheets. Transactions of the Royal Society of Edinburgh. Earth Sciences 81: Boulton, G. S., P. Dongelmans, M. Punkari, and M. Broadgate Palaeoglaciology of an ice sheet through a glacial cycle: The European ice sheet through the Weichselian. Quaternary Science Reviews 20: Boulton, G. S., N. Hulton, and M. Vautravers Ice-sheet models as tools for palaeoclimate analysis: The example of the European ice sheet through the last glacial cycle. Annals of Glaciology 21: Boulton, G. S., and A. Payne Simulation of the European ice sheet through the last glacial cycle and prediction of future glaciation. Technical Report SKB 93-14, Swedish Nuclear Fuel and Waste Management. Boulton, G. S., G. D. Smith, A. S. Jones, and J. Newsome Glacial geology and glaciology of the last mid-latitude ice-sheets. Journal of the Geological Society of London 142: Brook, E. J., A. S. Nesje, J. Lehman, G. M. Raisbeck, and F. Yiou Cosmogenic nuclide exposure ages along a vertical transect in western Norway: Implications for the height of the Fennoscandian ice sheet. Geology 24: Clark, C. D Mega-scale glacial lineations and cross-cutting ice-flow landforms. Earth Surface Processes and Landforms 18: Large-scale ice-moulding: A discussion of genesis and glaciological significance. Sedimentary Geology 91: Clark, P. U., and A. C. Mix Ice sheets and sea level of the last glacial maximum. Quaternary Science Reviews 21:1 7. CLIMAP Project Members Seasonal reconstruction of the earth s surface at the last glacial maximum. Map and Chart Series, Vol. 36. Geological Society of America. Dowdeswell, J. A., and M. J. Siegert Ice-sheet numerical modeling and marine geophysical measurements of glacier-derived sedimentation on the Eurasian Arctic continental margins. Geological Society of America Bulletin 111: Fastook, J. L., and P. Holmlund A glaciological model of the Younger Dryas event in Scandinavia. Journal of Glaciology 40: Hagdorn, M Reconstruction of the past and forecast of the future European and British ice sheets and associated sea level change. Unpublished PhD diss., University of Edinburgh, Scotland. Hubbard, A High-resolution modeling of the advance of the Younger Dryas ice sheet and its climate in Scotland. Quaternary Research 52:27 43.

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