Identifying patterns of correspondence between modeled flow directions and field evidence: An automated flow direction analysis

Transcription

1 ARTICLE IN PRESS Computers & Geosciences 33 (27) Identifying patterns of correspondence between modeled flow directions and field evidence: An automated flow direction analysis Yingkui Li a,, Jacob Napieralski b, Jon Harbor c, Alun Hubbard d a Department of Geography, University of Missouri-Columbia, Columbia, MO 65211, USA b Department of Natural Sciences, University of Michigan-Dearborn, Dearborn, MI 48128, USA c Department of Geography and Environmental Sciences, University of Colorado at Denver and Health sciences Center, Denver, CO 8217, USA d Institute of Geography, School of GeoSciences, University of Edinburgh, Edinburgh, Scotland, EH8 9XP, UK Received 1 June 25; received in revised form 17 April 26; accepted 14 June 26 Abstract Comparison of numerical model output that predicts spatial flow patterns against field observations is a necessity within several areas of the geosciences. However in many cases these comparisons are qualitative or relative in nature. Automated flow direction analysis (AFDA) is a new method designed to provide a systematic comparison between modeled flow patterns and field observations, with particular focus on two-dimensional linear features representing flow directions of natural phenomena. By subtracting vector output of time-dependent models from field-observed directions, the resultant mean residual and variance of the offset between these data sets can be used to identify patterns of correspondence and variation between model-predicted directions and field observations. The technique is demonstrated by comparison of modeled basal ice flow directions of the Fennoscandian Ice Sheet with observed lineations mapped in Northern Sweden. In this example, the analysis provides an effective means to quantitatively validate the modeled basal thermal and flow regime with observed glacial lineations. The technique has potential applications in a wide range of flow vector direction comparisons in the geosciences, for example lava flow, landslides, aeolian and fluvial processes. r 26 Elsevier Ltd. All rights reserved. Keywords: Automated flow direction analysis; GIS; Ice sheet model; Residuals 1. Introduction Understanding spatial and temporal patterns of process dynamics and form evolution is a central component of geoscience research (Ritter et al., 22; Corresponding author. Tel.: ; fax: address: liyk@missouri.edu (Y. Li). Bishop and Shroder, 24). Traditionally, this has been based on field observations, using increasingly advanced measurement and analysis techniques. With improved understanding of process mechanics and the development of advanced computer and IT techniques, many areas of the geosciences now include systematic use of numerical modeling of geologic processes. Realistic modeling typically involves the use of field observations both to constrain 98-34/$ - see front matter r 26 Elsevier Ltd. All rights reserved. doi:1.116/j.cageo

2 142 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) and calibrate model parameters and to validate model output (e.g. Clark, 1997; Clark et al., 24; Ehlers and Gibbard, 23; Napieralski et al., 26). As a result, comparing model output against field observations has become an important issue in many geoscience studies. However, in many areas these comparisons have been qualitative or relative. For example, debris flow run-outs are frequently simulated and compared to field observations, but levels of agreement are generally established by simple, visual comparisons to evaluate whether or not there was a reasonable fit (Rickenmann and Kock, 1997; Ghilardi et al., 21; Laigle et al., 23; Lo and Chau, 23). This lack of systematic comparison and statistical assessment between simulated model outputs and field observations has hindered efforts to assimilate numerical models with field evidence and enhance the understanding of geoscientific processes. Geographic information systems (GIS) are now widely used in examining the spatial and temporal aspects of a variety of geoscience issues (e.g. Bishop and Shroder, 24) and can be used as the foundation for systematic comparisons and statistical assessments of the goodness of fit between model outputs and field observations (Napieralski, 25). In GIS, natural phenomena are represented as a set of geometric objects including points, lines, polygons, and fields (e.g. Longley et al., 21; O Sullivan and Unwin, 23), and the comparison of model outputs against field data can be conceived of as being a comparison of spatial and temporal relationships between these objects. Frequently, linear objects are used to represent both field observations and model output, including features such as rivers, divides, faults, glacial moraines, landslide tracks, drumlins, and any geomorphic feature that provides a sense of the linear/ directional controls on processes. Some linear objects represent the boundaries of natural phenomena, and recent work has focused on developing techniques that compare model output for boundaries that mark the extent of geologic phenomena against model predictions of feature extent (e.g. Napieralski et al., 26). However, other linear objects represent general directional trends of processes or controls, rather than margins. For example, glacial lineations represent basal flow directions and the agreement between modeled basal flow directions and glacial lineations is an important measure of model performance. Comparisons between the directions of linear features can be assessed by calculating residuals (angle difference in directions), and in the ice sheet direction example, model outputs at various time slices in an ice sheet model simulation can be compared to field observations to evaluate the level of correspondence between model outputs and field observations at different times. This paper introduces an automated GIS analysis tool that focuses on the comparison of field and simulation predictions of the directions of linear features, and illustrates use of this tool with ice sheet reconstructions where simulated ice flow directions are validated against field evidence. Although the technique is presented here in the context of glacial geomorphology and ice sheet research, the method may also be adopted to resolve similar issues within other areas of the geosciences. 2. Methodology Ice sheet models have been used to reconstruct paleo-ice sheet dynamics, including the inception, growth and decay of ice sheets and surface and basal thermal conditions (e.g. Boulton and Payne, 1992; Payne and Baldwin, 1999; Hubbard, 1999, 2; Charbit et al., 22; Hulton et al., 22). Three-dimensional ice sheet modeling usually yields a series of time-dependent distributions of ice thickness, surface elevation, isostatic adjustment, mass-balance, thermal regime, surface, englacial and basal velocity. Comparing model-predicted basal flow directions against glacial lineations is a key component to ice sheet model calibration and validation (Napieralski, 25). Three issues need to be addressed in the comparison: (1) quantifying level of correspondence; (2) identifying temporal patterns of correspondence; and (3) validating time consistency between predicted directions and field evidence. Here, we propose an automated flow direction analysis (AFDA) to resolve these issues. AFDA is based on grid analysis, which is available in most GIS software packages. The first step is to make sure the field observations and model outputs are formatted consistently, georeferenced and are gridded to the same resolution and coordinate system. The two data sets are overlaid and subtracted, so that the positive residual for each grid cell is in the range of 1 to 181, where 1 indicates perfect coincident, parallel flow, and 181 indicates that the model predicted ice flow direction is in the opposite direction of the field observation. In order to summarize the level of correspondence between model output and field evidence, the resultant mean and variance of the residual values

3 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) are calculated across the whole field area (domain). This process can be repeated at selected intervals throughout the model s temporal evolution so that the resultant mean and variance of the residuals can be plotted to evaluate the temporal pattern of correspondence between predicted flow directions and field observations (Fig. 1). The residual value as it is used here is a directional data-type which potentially causes problems when the mean and variance of residual values is calculated through ordinary linear statistics (Evans, 1969, 1977, 26; Swan and Sandilands, 1995). Hence, we use vector summation to calculate the resultant mean and variance of the residual values (Fig. 2. Evans, 1969, 1977; Swan and Sandilands, 1995). The basis for this calculation is to treat the directional data as a set of unit vectors (vectors that indicate direction only with the length of 1). Since it is difficult to interpret the ice flow magnitude from the field observed lineations, for the purposes of this study we narrow our focus on the comparison of basal ice flow directions between the ice sheet model and field observations but magnitude comparisons could be developed later for use in other areas of the geosciences. Assuming residual values at different grid cells are given by: a 1 ; a 2 ; a 3 ;...; a n. (1) These residual values can be treated as unit vectors. Each unit vector can be divided into two components at x- and y-axes (x i, and y i ), where x i ¼ sin a i, y i ¼ cos a i. Summing these two components for all unit vectors: x r ¼ X sin a i ; y r ¼ X cos a i. (2) The resultant mean of residual values can be calculated as a ¼ tan 1 ðx r =y r Þ. (3) Glaciated Landscape 18 Mean Residual 9 (A) Model Output a b c d e f g h i j k l m (C) Time Time a Time b Time m (B) (D) 18 Time:d 18 Time:f Fig. 1. Steps of flow direction analysis. (A) Field-based glacial lineations and model outputs are used in analysis. Field-based lineations usually cover parts of study area, whereas model output provides continuous ice flow directions covering whole area. (B) Overlay model outputs and field evidence to produce series residual data sets for different time slices. (C) Plot resultant mean of residual values against their corresponding time slices to identify temporal patterns of correspondence between predicted directions and field observations. (D) Frequency analysis (rose diagram) of selected time slices (e.g. d and f) provides detail information on distribution of residuals across area and can be used to evaluate level of correspondence.

4 144 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) N ( ) (A) N ( ) (B) Resultant vector E (9 ) 2 Resultant vector E (9 ) Fig. 2. Basis of vector summation method. Each angle is represented as a unit vector. Combining all these unit vectors produces a resultant vector. Angle of resultant vector indicates mean angle and length of resultant vector represents variance of directional data (higher variance results in shorter length). In figure, (A) and (B) have almost same mean angle, but (B) has relatively shorter length for resultant vector due to relatively higher variance of directional data. Since the tan 1 function will produce a value in the range of 9 91, this is converted to a range of 181. Finally, we can also calculate the mean resultant length (R) of unit vectors by: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ¼ ðx 2 r þ y2 r Þ =n, (4) where n is the total number of residual values. The mean resultant length (R) measures the dispersion of the residual values and varies from (no favorite residual) to 1 (all grid cells have the same residual value). Since higher R values indicate less variance (Fig. 2), the variance (s) of residual values can be defined as s ¼ 1 R, where zero indicates that all residual values are identical (Swan and Sandilands, 1995). Field observations typically only cover parts of the model domain. Hence, there will be many empty cells after digitizing the directional data into GIS. These cells can be effectively treated as NoData in GIS, hence only cells with observed directional data are involved in the calculation. Furthermore, modeled ice extent and basal thermal regime also vary temporally throughout a simulation and situations are likely where a model predicts places or times where/when no ice is present (ice free condition) or no ice movement occurs (frozen bed condition). Such scenarios are both frequent and significant outcomes in ice sheet modeling, as the model may predict ice free or frozen bed conditions where glacial lineations exist (a bad fit between model and field data). Hence, the potential to discriminate ice free and frozen bed conditions where observed lineations exist is a critical component of the ice sheet model validation. To account for these situations, values of 1811 and 1821 are assigned to these cells to identify predicted frozen bed and ice free conditions, respectively. The purpose of these two values is to ensure the predicted frozen bed and ice free conditions will be accounted in the resultant mean and variance of residual values. If there are glacial lineations within a series of grid cells, but the ice sheet model predicts these cells as ice free or frozen, then the level of correspondence will be considered poor and treated as the worse possible correspondence between the model and field evidence (i.e. the model fails to reproduce the subglacial conditions required to produce glacial lineations during that specific time slice). Furthermore, the number (area percentage) of these two values is also logged and is used to identify the occurrence of ice free and frozen bed conditions in the last step of the analysis (Fig. 1D). Thus, four parameters: resultant mean, variance, number (area percentage) of ice free condition, and number (area percentage) of frozen bed condition are reported for each time slice and the level of correspondence thereby assessed. Small resultant mean and variance values indicate a good correspondence, whereas high values in the resultant mean and variance represent a poor correspondence. As an ice sheet model yields output for many time slices, statistical parameters can be calculated to evaluate temporal variations of correspondences between model outputs and field observed directions. In this way, a particular or set of time slices can be flagged to examine in more detail the spatial distribution of residuals and the occurrence of predicted ice free and /or frozen bed conditions. In certain instances, it will be critical to examine the detailed spatial distribution of residuals; if there are distinct spatial patterns in residuals, this may be important information for ice sheet model validation. In these instances, additional analyses, including a frequency distribution (rose diagram) for various time slices throughout a simulation will be necessary to fully understand the dynamics of the ice sheet model.

5 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) Program design The proposed flow direction analysis can be implemented in many GIS environments. Here, we present an AML (Arc Macro Language) program which implements all the steps of the analysis (Fig. 3) in the ArcGIS (ArcInfo) environment (ESRI, 1993) Inputs and verification The following inputs are needed to run this program: (1) the field-observed lineation grid (cells without field observed lineation were assigned as NoData ); (2) the start, end time of model outputs, and the step (interval) of time slices; (3) the token used to identify model predicted flow directions at different time slices; (4) the specified values used to identify predicted ice free and frozen Entry Parameters bed conditions. For example, in the model used in this paper, we use 999 and 888 to identify the ice free and frozen bed conditions, respectively; and (5) an output file to record the analysis results. Once all input parameters have been assembled, the program will automatically verify the parameters to make sure every parameter is appropriate for the analysis Convert model outputs to the grid format Based on the specified start time, end time, and the time step (interval), the program automatically finds the model output for a specific time slice and converts it to a GIS grid format. ArcInfo provides commands (ASCIIGRID and FLOATGRID, respectively) to convert ASCII and BIN files to grid formats (create grid data sets). When using the BIN file, the user needs to make sure that there is a corresponding *.hdr file for each *.bin file. After converting the model output to the GIS grid format, the program will check and make sure that both model output and field evidence are at the some resolution and in the same coordinate system. Verification Yes i = No Time= Start_time + i* Step Is the time within the range of start and end time? No End 3.3. Subtract the model output with the field observed flow direction The next step is to overlay the model output grid and the field flow direction grid and use the SUBTRACT operation (model output grid field flow direction grid) to create a temporary grid data set and convert residual values for different grid cells to the range of 181. Yes Read the model output file at the corresponding time slice and covert it to the grid dataset Subtract the model output grid with the field flow orientation grid Summarize cells for the ice free and frozen bed conditions; and calculate the resultant mean and variance of residual values Record the results into the output file i = i + 1 Fig. 3. Flow chart of proposed flow direction analysis implemented in ArcInfo Statistical analysis and record results into the output file First, summarize the numbers of cells where ice free and/or frozen bed conditions occur based on specified values into the output file. Then, as discussed earlier, assign 1811 and 1821 to identify frozen bed and ice free conditions, respectively. Finally, perform the vector summation calculation described earlier for the overlaid grid data set and record the resultant mean and variance of residual values into the output file. After completing one time step, the program repeats these processes to generate statistical parameters for each individual time step and records them into the output file.

6 146 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) Application of this technique The case example compares basal ice flow directions predicted by an ice sheet model against field-observed glacial lineations in northern Sweden to identify temporal patterns of correspondence between model outputs and field observations Study area and flow direction data Northern Sweden was a core area for continental ice sheets during the Quaternary period (Ljungner, 1949; Mangerud et al., 1996; Kleman, 1992; Kleman and Stroeven, 1997). The relative abundance of glacial lineations, such as striae, flutes, till fabrics and glacio-tectonic fold, provides evidence of the varying flow patterns during the last glaciation, especially the last glacial maximum (LGM) (Fig. 4). Two flow direction data sets were extracted: #31 and #38 (numbers assigned to different data sets are based on Kleman et al., 1997) (see Fig. 4). Both data sets are composed of various landforms that provide evidence of ice flow direction, but the chronology of landforms is relative (dependent on the presence of cross-cutting features or dating techniques). The directions of the lineations within the flow-sets had a predominant flow direction either to the northeast (#31) or the southeast (#38). The glacial lineations were digitized from Kleman et al. (1997). In their work, a map illustrating the generalized distribution of glacial lineations was developed from the compilation of numerous field and remote sensing studies. This map was georeferenced and digitized so that each lineation was designated a direction value (in degree) and then labeled according to the corresponding flow fan. Each flow fan was extracted as an individual vector data set, then rasterized to correspond with model output (cell size of 1 km). Generally, there was no conflict with designating a grid cell a direction as the original map was generalized and cross-cutting features were extracted to form different flow fans. Glacial lineations were digitized whilst the grid domain was visible in order to identify if a lineation was crossed two or more grid cells. Once the flow fans were digitized and rasterized, they were interpolated to correspond with the nodes of the model domain Ice sheet model and model outputs A three-dimensional ice sheet model (Hubbard, 1999, 2) was used to simulate the Fennoscandian 3 '"E 18 '"E 33 '"E 48 '"E N W E S 7 '"E Flow Dataset #38 7 '"N study Area 65 '"E 65 '"N 6 '"N 6 '"E Flow Dataset #31 55 '"N 55 '"E 18 '"E Fig. 4. Map of study area and two flow data sets (#31, #38) used for automated flow direction analysis. Flow data sets were separated and classified based on their directions and landform characteristics (from Kleman et al., 1997). Data set #38 represents a predominant flow direction to southeast, whereas #31 indicates a predominant flow direction to northeast.

7 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) Ice Sheet during the last glaciation, driven by the GRIP oxygen isotope curve and calibrated using present-day patterns of precipitation, temperature, and observed geothermal heat flux (Na slund et al., 25). The spatial resolution of this model is 1 km. Modeled basal flow directions for pre-identified domains were output in ArcGIS readable files for different time slices Flow direction analysis AFDA was used to analyze model output run from 15 to 1 ka BP (1. ka interval). Four parameters (resultant mean, variance, area percentage of ice free condition, and area percentage of frozen bed condition) between predicted and observed flow directions were calculated for each time slice. These parameters are plotted against their corresponding time slices to illustrate the temporal patterns of correspondence between model and field observations during the simulated period (Fig. 5). The fluctuations in correspondence reflect the changes in ice sheet configuration (e.g. size and shape) during the past 15 ka, which directly affect ice flow direction, as well as influence the occurrence of ice free and/or frozen bed conditions. There were distinct periods when model output has the highest levels of correspondence with each flow data set. Flow-set #31 achieved good correspondence (lower resultant mean and variance of residual values, lower occurrence of ice free and /or frozen bed conditions) around 86, 66, 38, and 21 ka BP, while #38 was characterized by higher mean residuals during same periods. Model output had high correspondence values with #38 around 75, 46, and 12 ka BP, when the model corresponded poorly with the other flow-set #31. This is to be expected, as the general flow direction for #38 is predominantly southeast, but north for flow data sets #31. It provides supporting evidence that flow-sets #38 and #31 formed at different phases of glaciation (see Kleman et al., 1997). The flow direction analysis indicates the presence of constant ice cover over the area of interest, as well as a complex basal thermal history with varying flow directions. To analyze the results in more detail, a frequency distribution (rose diagram) of residual values was extracted from 75 and 21 ka BP (Fig. 6). At 75 ka BP, the resultant mean of residual values was much lower for #38 (27.41) than for flow data set #31 (.91). For this particular time slice, although the whole area was completely ice covered Mean residual ( ) (A) Mean residual ( ) Residual variance (x1) Time (ka B.P.) Residual variance (x1) Mean residual ( ) (C) Mean residual ( ) Residual variance (x1) Time (ka B.P.) Residual variance (x1) 1 Ice free conditions (%) Frozen bed conditions (%) (B) Time (ka B.P.) Ice free conditions (%) Frozen bed conditions (%) Ice free conditions (%) (D) 1 Ice free conditions (%) 8 Frozen bed conditions (%) Time (ka B.P.) Frozen bed conditions (%) Fig. 5. Temporal variations of calculated resultant mean and variance of residual values (A (#38) and C (#31)) between predicted directions and flow data sets and occurrence of ice free and frozen bed conditions (B (#38) and D (#31)) for flow data set #31 and #38 from 15 ka to 1 ka BP. Results show opposite temporal patterns of level of correspondence between flow data sets #31 and #38.

8 148 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) Dataset: #31 Time slice: 21ka Mean residual: 1.2 Variance (x1):.72 Ice free condition:.% Frozen bed condition:.% Dataset: #31 Time slice: 75ka Mean residual:.9 Variance (x1):.98 Ice free condition:.% Frozen bed condition:.% (A) 18 (B) Dataset: #38 Dataset: #38 Time slice: 21ka Time slice: 75ka Mean residual: 11. Mean residual: 27.4 Variance (x1): 7.16 Variance (x1): Ice free condition:.% Ice free condition:.% Frozen bed condition: 2.2% Frozen bed condition: 3.8% (C) 18 (D) 18 Fig. 6. Frequency distributions (rose diagram) of residual values at time slice 21 ka and 75 ka BP for flow data set #31 and #38. (% ice-free condition), 3.8% of the grid cells across flow-set #38 were modeled with a frozen bed. Hence, flow-set #38 received a relatively higher variance of 11.4 compared to # 31 at.98, where no cells were frozen. In contrast, flow data set #31 obtained relatively good correspondence with field data during 21 ka BP, with a resultant mean residual of 1.21 and the variance of.72 (a result of predicted ice flow direction corresponding with field data and % of predicted frozen bed or ice free conditions). AFDA is also capable of examining temporal variations of the occurrence of frozen bed and ice free conditions during the last 15 ka. For example, the model used in this case study generally predicts that ice free conditions only occurs at the beginning of the model run (15 1 ka BP) and there is consistent ice coverage over both flow-sets between 1 1 ka BP However, frozen bed conditions were more prevalent across flow-set #38 (Fig. 5), as the occurrence of frozen bed conditions ranged from 1% to 11% of the grid cells during 1 1 ka BP. The flow direction analysis used here provides a useful quantitative assessment of the level of correspondence between predicted basal ice flow directions and field observations over a broad area at specific time periods. 5. Discussion The automated flow direction analysis (AFDA) method presented here focuses on assessing the correspondence between model output and field observed directions at different time periods. The method provides a flexible and effective way to automatically calibrate and validate the basal

9 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) dynamics and thermomechanics of ice sheet models; a critical task because such validation is an on-going process dealing with large quantities of modeled and observed directions. It is also able to identify the occurrence of predicted ice free and/or frozen bed conditions, which is an important asset to ice sheet reconstructions. Furthermore, the proposed method has the potential to provide new insights into ice sheet dynamics and patterns of glacial landform development. For example, temporal variations in the level of correspondence between predicted directions and field evidence can provide chronological constraints on potential periods of glacial lineation development. This information can be used to verify the time consistency between predicted directions and dated glacial lineations. Even if no time constraints for glacial lineations exist, the comparison can provide insight into the relative order of timing of the formation of these lineations. In addition, AFDA can be combined with APCA, which is used to determine the general proximity and parallel conformity between linear features representing ice marginal positions (Napieralski et al., 26), to provide a comprehensive toolbox for ice sheet model validation. For example, the user can first apply the APCA method to the ice marginal comparison between predicted ice extent and end moraines, then use the AFDA to verify the ice flow characteristics and subglacial regime. Therefore, optimum models or model parameters can be selected by ranking the levels of correspondence both from the ice margins and glacial lineation comparisons. As a result, these two techniques provide an innovative opportunity to validate ice sheet models based on geomorphic evidence. Several issues do though need to be considered in the application of this technique. First, although the resultant mean residual is generally an acceptable way to evaluate the level of correspondence, the distribution underlying the mean value could be important. For example, a high resultant variance indicates a wide distribution of residual values across the area. In this case, even if the resultant mean residual is low, it is not a good fit. The occurrence of ice free and/or frozen conditions where glacial lineation exists also indicates a poor fit even the other area having low values in the resultant mean and variance of residual values. Second, caution should be taken when selecting flow data sets. One assumption of using field evidence to validate an ice sheet model is that glacial lineations within each flow data set formed during the same period. Thus, glacial lineations in each flow data set should have developed during the same period. If not, they should be separated into different data sets in order to produce more reliable results. In addition, the size of the field area and number of lineations potentially affect the level of correspondence; Larger field areas and more glacial lineations increase the variability of the results. Third, spatial resolution will affect the outcome because the analysis is limited to the quality of field data and the capabilities of the numerical model. For example, the case-study presented here uses a grid cell resolution of 1 km. If this resolution is increased to 1 km, then more detail can be distinguished, and more field evidence included. Hence, model validation will be performed at a higher standard if the model output and field data are at higher spatial resolutions. However, it is also essential to understand that the limitations of the model are also important, as the model may not be able to discriminate changes in flow direction at very fine resolutions. On the other hand, if the resolution is coarser, for example, the resolution is greater than 1 km in this case study, then the field evidence becomes more generalized and only provides a limited verification for model output. Although the proposed method stems from the need to validate ice sheet models with glacial lineations, it need not be limited to this specific application. It is also useful to resolve other geoscience issues such in aeolian, fluvial and tectonic processes, where field observed directions are used to calibrate and validate geologic processes models. For example, models can be used to predict wind directions in a specific area, and the simulated results can be validated by comparing to field observed alignments of sand dunes which indicate dominant wind directions in the area. Due to the differences in the model structure and output format, as well as different application issues, some modifications to AFDA may be needed to fit in with new issues and geologic processes. Acknowledgments This paper was supported by National Science Foundation Grant No OPP to Harbor. We thank Dr. Chris Clark and Bryn Hubbard for reviewing and providing numerous constructive

10 15 ARTICLE IN PRESS Y. Li et al. / Computers & Geosciences 33 (27) suggestions. ALH acknowledges support from the above NSF grant & Royal Society of Edinburgh. Appendix A. Supplementary materials Supplementary data associated with this article can be found in the online version at doi:1.116/ j.cageo References Bishop, M.P., Shroder Jr, J.F., 24. Geographic Information Science and Mountain Geomorphology. Springer-Praxis Books in Geophysical Sciences, Heidelberg, 486pp. Boulton, G.S., Payne, A.J., Mid latitude ice sheets through the last glacial cycle: glaciological and geological reconstructions. In: Duplessy, J.C., Spyridakis, M.T. (Eds.), Long-Term Climatic Variations, NATO ASI Series I 22, pp Charbit, S., Ritz, C., Ramstein, G., 22. Simulations of northern hemisphere ice-sheet retreat: sensitivity to physical mechanisms involved during the last glaciation. Quaternary Science Reviews 21, Clark, C.D., Reconstructing the evolutionary dynamics of former ice sheets using multitemporal evidence, remote sensing and GIS. Quaternary Science Reviews 16, Clark, C.D., Evans, D.J.A., Khatwa, A., Bradwell, T., Jordan, C., Marsh, S.H., Mitchell, W.A., Bateman, M.D., 24. Map and GIS database of glacial landforms and features related to the last British ice sheet. Boreas 33, Ehlers, J., Gibbard, P., 23. Extent and chronology of glaciations. Quaternary Science Reviews 22, ESRI, Arc Macro Language, Developing ARC/INFO Menus and Macros with AML. Environmental Systems Research Institute, Redlands, CA. Evans, I.S., The geomorphology and morphometry of glaciated mountains. In: Chorley, R.J. (Ed.), Water, Earth and Man. Methuen, London, pp Evans, I.S., World-wide variations in the direction and concentration of cirque and glacier aspects. Geografiska Annaler A 59, Evans, I.S., 26. Local aspect asymmetry of mountain glaciation: a global survey of consistency of favoured directions for glacier numbers and altitudes. Geomorphology 73, Ghilardi, P., Natale, L., Savi, F., 21. Modeling debris flow propagation and deposition. Physics and Chemistry of the Earth 26, Hubbard, A., High-resolution modeling of the advance of the Younger Dryas ice sheet and its climate in Scotland. Quaternary Research 52, Hubbard, A., 2. The verification and significance of three approaches to longitudinal stresses in glacier flow models. Geographic Annalers 82A, Hulton, N.R.J., Purves, R.S., McCulloch, R.D., Sugden, D.E., Bently, M.J., 22. The last glacial maximum and deglaciation in southern South America. Quaternary Science Reviews 21, Kleman, J., The palimpsest glacial landscape in northern Sweden Late Weichselian deglaciation landforms and traces of older west-centered ice sheets. Geografiska Annaler 74A, Kleman, J., Stroeven, A.P., Preglacial surface remnants and Quaternary glacial regimes in northwestern Sweden. Geomorphology 19, Kleman, J., Hättestrand, C., Borgström, I., Stroeven, A., Fennoscandian paleoglaciology reconstructed using a glacial geological inversion model. Journal of Glaciology 43, Laigle, D., Hector, A., Hu bl, J., Rickenmann, D., 23. Comparison of numerical simulation of muddy debris-flow spreading to records of real events. In: Proceedings of the Third International Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment (DFHM) Conference, Savos, Switzerland, pp Ljungner, E., The east-west balance of the Quaternary ice caps in Patagonia and Scandinavia. Bulletin of the Geological Institute of Uppsala 33, Lo, K.H., Chau, K.T., 23. Debris-flow simulations for Tsing Shan in Hong Kong. In: Proceedings of the Third International Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment (DFHM) Conference, Savos, Switzerland, pp Longley, P.A., Goodchild, M.F., Maguire, D.J., Rhind, D.W., 21. Geographic Information Systems and Science. Wiley, Chichester, UK, 536pp. Mangerud, J., Jansen, E., Landvik, J., Late Cenozoic history of the Scandinavian and Barents Sea ice sheets. Global and Planetary Change 12, Napieralski, J.A., 25. Integrating a numerical model of the Scandinavian ice sheet with field data using GIS. Ph.D. Dissertation, Department of Earth and Atmospheric Sciences, Purdue University. Napieralski, J.A., Li, Y.K., Harbor, J., 26. Comparing predicted and observed spatial boundaries of geologic phenomena: Automated Proximity and Conformity Analysis (APCA) applied to ice sheet reconstructions. Computers and Geosciences 32, Näslund, J.O., Jansson, P., Fastook, J.L., Johnson, J., Andersson, L., 25. Detailed spatially distributed geothermal heatflow data for modeling of basal temperatures and meltwater production beneath the Fennoscandian ice sheet. Annals of Glaciology 4, O Sullivan, D., Unwin, D.J., 23. Geographic Information Analysis. Wiley, Hoboken, N.J, 448 pp. Payne, A.J., Baldwin, D.J., Thermomechanical modeling of the Scandinavian ice sheet: implications for ice-stream formation. Annals of Glaciology 28, Rickenmann, D., Kock, T., Comparison of debris flow modeling approaches. In: Proceedings of 1st International Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment (DFHM) Conference, San Francisco, CA, pp Ritter, D.F., Kochel, R.C., Miller, J.R., 22. Process Geomorphology, 4th ed. McGraw-Hill Higher Education, New York, NY, 546 pp. Swan, A.R.H., Sandilands, M., Introduction to Geological Data Analysis. Blackwell Science, Oxford, 466 pp.