Topographic variability on Mars: Implications for lava flow modeling

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006je002879, 2007 Topographic variability on Mars: Implications for lava flow modeling L. S. Glaze 1 and S. M. Baloga 1 Received 7 December 2006; revised 23 March 2007; accepted 25 April 2007; published 10 August [1] A new data analysis technique is presented for quantifying topographic variability on the surface of Mars directly from Mars Orbiter Laser Altimeter (MOLA) Precision Experiment Data Record (PEDR) elevation data. The statistic expressing the degree of variability is the mean standard deviation of the residuals resulting from regressions on MOLA PEDR elevation profiles. This topography statistic is determined for ten volcanic areas on the basis of thousands of data points from 181 PEDRs. The topography statistic varies considerably, exhibiting a strong correlation to volcanic area. Despite the correlation with volcanic area, the correlation between topographic variability and slope is weak. Lava flow thickening behavior is quantified with two statistics that are, in turn, used as a rough measure of rheologic change. There is a strong, significant correlation between both flow thickening statistics and topographic variability. These results suggest that the influence of local topographic variability is more important than previously thought in modeling lava flows on Mars. Citation: Glaze, L. S., and S. M. Baloga (2007), Topographic variability on Mars: Implications for lava flow modeling, J. Geophys. Res., 112,, doi: /2006je Introduction [2] How rheologic parameters (e.g., yield strength and viscosity) change during the emplacement of individual lava flows still remains a major issue in planetary as well as terrestrial lava flow studies [e.g., Zimbelman, 1985; Crisp and Baloga, 1990, 1994; Baloga et al., 1995, 1998; Zimbelman, 1998; Harris and Rowland, 2001; Rowland et al., 2004]. Similarly, how flow thicknesses change in response to changing slopes and topographic variability (analogous to roughness ), in the midst of a rheologic change, is one of the fundamental diagnostics of internal (e.g., rheologic character, temperature) versus external influences. Understanding such responses allows us to use observations of the dimensions and morphologies of the remaining deposits, as well as estimates of the underlying slope and its variations, to make inferences about rheologic behavior, flow rates, and variables such as cooling, crystallinity, and composition. [3] Glaze et al. [2003] and Baloga et al. [2003] have both recently indicated the importance of understanding the scale of a lava flow relative to the surrounding topography in extracting inferences about rheologic changes and the interpretation of the style of emplacement. The underlying scientific issue is whether flow emplacement is controlled mainly by the large-scale topographic inclination (i.e., slope) or whether the flow path and emplacement style are substantially influenced by small-scale topography such as that produced by pre-existing lava flows. In addition to the science issues driving our desire to understand the scale of topographic variability, recent efforts have shown that reliable flow thickness profiles can be derived from Mars 1 Proxemy Research, Laytonsville, Maryland, USA. Copyright 2007 by the American Geophysical Union /07/2006JE Orbiter Laser Altimeter (MOLA) Precision Experiment Data Records (PEDRs) [Glaze et al., 2003]. For large flows (significantly thicker than surrounding topographic variation), gridded MOLA data can also be used to find flow thicknesses [Baloga et al., 2003]. However, as the flow thickness approaches the same scale as the surrounding topographic variations, the gridded MOLA data become increasingly unreliable. A quantitative measure of topographic variability may assist in determining when it is appropriate to use gridded data, and when original MOLA PEDR elevations must be used. [4] The as yet unanswered question is What scale of underlying topographic variability is significant for modifying emplacement behavior? Baloga et al. [2003] suggested that the flat topography found on the plains of Mars does not disrupt the emplacement of long thick flows sufficiently to expose the core. Thus there is little cooling of the flow core and minimal bulk viscosity increase over the length of the flow. Conversely, flows over rougher topography tend to be shorter, exhibiting a greater degree of relative thickening and associated viscosity increase [Glaze et al., 2003]. [5] This influence of topographic variability has important implications for the validity of theoretical models from which inferences are derived. Specifically, most of the more elementary treatments assume that internal streamlines are parallel, as often seen in the cartoons of flows on an inclined plane. Such an assumption has major ramifications for how models treat internal heat transfer, the character of internal deformation and circulation, and perhaps most importantly, the disruption of the upper crust and radiant heat losses, as well as transient turbulent conditions [Crisp and Baloga, 1990, 1994; Rowland et al., 2004; Glaze and Baloga, 2006]. Thus understanding the influence of ambient topo- 1of9

2 Figure 1. Shaded relief images of MOLA topography depicting areas investigated in this study. (a) Boundaries of all five study areas are shown as black boxes, and approximate locations of the numbered flows in Table 1 are indicated. More detailed shaded relief images of MOLA topography are shown for the areas associated with (b) Pavonis Mons, (c) Arsia Mons, (d) Ascraeus Mons, (e) Elysium Mons, and (f) Alba Patera. For each area the white boxes mark the boundaries of MOLA PEDR regression analysis. Each flow is outlined in black, and numbers correspond to the flow numbers in Table 1. graphic variability relative to the assumptions of theoretical models is of major significance to their validity. [6] Intuitively, it seems that the influence of topographic variability may be in some way measured relative to the thickness of the flow in question, i.e., a 100 m thick flow would be sensitive to larger scale topographic variations than a 10 m flow. However, the data presented here are not consistent with this intuitive concept. Instead, data for all the flows analyzed to date indicate that the degree of influence is directly related to the scale of topographic variability, regardless of overall flow thickness. [7] This paper discusses ambient topographic variability and morphologic characteristics for ten lava flows in five volcanic regions on Mars. These ten flows were emplaced on a variety of slopes and exhibit a range of lengths, thicknesses, and flow morphologies. Figure 1 indicates the locations of each region studied. Table 1 indicates basic characteristics for each flow, including emplacement slope, overall flow thickness (H), whether or not the flow exhibits a distinct channel, and the latitude/longitude range examined for this study. The paper is divided into two sections. The first describes how the topographic variability statistic is computed. The second discusses interpretations of the 2of9

3 Figure 1. (continued) topographic variability in the context of other lava flow characteristics, including source location, slope, and rheology. 2. Topographic Variability [8] Details are presented here for characterizing random variations in topography using MOLA PEDR profiles. The results are based on statistical analysis of thousands of elevation values in 181 MOLA PEDRs. The basic method for quantifying topographic variability in each volcanic area is straightforward, but necessarily time-intensive. The results of the method are robust because of the large number of data points analyzed and the remarkably well-behaved character of the topographies investigated. This approach employs standard linear regression techniques to fit curves to individual MOLA PEDR profiles over several degrees of Table 1. Flow Characteristics Lava Flow Location H Range, m Slope, deg Channel? DL, km Number of PEDRs Latitude Range Longitude Range 1 Pavonis Yes N E 2 Pavonis a Yes N E 3 Arsia No S 2 N E 4 Arsia Yes S 2 N E 5 Ascraeus Yes N E 6 Elysium b No N E 7 Elysium c No N E 8 Elysium c No N E 9 Alba d,e No N E 10 Alba d,e No N E a Baloga et al. [2003]. b Glaze et al. [2003]. c Mouginis-Mark and Yoshioka [1998]. d Schneeberger and Pieri [1991]. e Thicknesses have been corrected for variable flow width. 3of9

4 Figure 2. (a) PEDR locations and outline of Flow 6. MOLA PEDRs, from left to right, are 10459, 11792, 11138, 14018, 14345, 12949, 14672, 13691, 14999, 15326, and Note that 10459, 11792, and are almost collocated. Likewise, and are almost collocated. Collocated sets of PEDRs may appear as a single line. (b) Example MOLA elevation profile for PEDR Arrows indicate the lava flow studied here and a crater. Large geologic features, such as the crater, are removed from the elevation data before performing a regression. Such features are removed as outliers when the regression residuals are significantly impacted by leaving them in. (c) MOLA PEDR (with the crater removed) along with a linear regression fit shown by the dashed line. Note that the regression is completely above the elevation data at the northern and southern ends, and completely below the elevation data in the middle. Thus residuals do not reflect the local random topographic variability properly. (d) MOLA PEDR (with crater removed) along with the parabolic regression fit shown as the dashed line. In contrast to the linear regression in Figure 2c, the residuals for the parabolic fit provide a good characterization of the random topographic variability. latitude in each region. The regions were selected because they contain numerous prominent lava flows, although many of the lava flows overlap, intermingle, and cannot be discerned as long solitary, isolated lobate units. [9] Before any statistical analyses can be performed, systematic effects in each PEDR must be removed. This is accomplished with two key steps. First, obvious systematic features are removed (as described below). Next, statistical regression of elevation on distance is performed until approximately normally distributed uncorrelated residuals are obtained. This permits a valid characterization of the residual distribution that can be legitimately interpreted as a statistical measure of the degree of topographic variability at the PEDR sampling scale of 330 m. Flow 6, on the northwest flank of Elysium Mons, has been examined previously by Glaze et al. [2003] and is used to provide a detailed example of the methodology. All statistical calculations, including regression and residual analyses, were conducted using Statgraphics Plus for Windows 1. [10] Figure 2a shows the locations of eleven descending MOLA PEDR profiles in a region north of Elysium Mons (28 31 N, E) that includes flow 6 (Table 1). The outline of flow 6, oriented roughly perpendicular to the MOLA PEDR profiles, is also shown. The elevations along one of those PEDRs (14999) is shown in Figure 2b, with arrows indicating the location of flow 6, and a small crater to the northeast of flow 6. Qualitatively, the thickness of this lava flow is of a similar scale to the ambient topographic variability. In fact, without visible images, it is almost impossible to identify this lava flow in the PEDR data [Glaze et al., 2003]. [11] Before fitting the individual PEDR profiles using regression techniques, each PEDR is examined visually to identify major geologic structures, such as craters, ridges, grabens, and so forth. Determination must be made on a 4of9

5 Figure 3. Histograms of residuals from (a) linear fit of PEDR (shown in Figure 2c) and (b) second-order fit of PEDR (shown in Figure 2d). Residuals for the linear fit are highly asymmetric (left skewed) as compared to the residuals for the parabolic fit, which are very nearly Gaussian and characterize random fluctuations about the regression curve. case-by-case basis whether there is a statistically valid argument for removing large topographic structures. The purpose of removing such structures is to obtain a fit to the ambient topography that produces normally distributed uncorrelated residuals [Sheskin, 1997; Draper and Smith, 1998] suitable for a statistical characterization of the random effects. In general, any feature that produces residual values beyond 3s has been removed. [12] Each of the flow 6 PEDR elevation profiles can be fit by a simple linear regression of the form y = a + bx. Although the R 2 statistic is not a definitive indicator of goodness of fit, it can be used as a guide. The R 2 values for the linear regressions are all quite high. For example, the linear regression on PEDR (Figure 2c) has an R 2 of 98.5%, indicating that the fit describes the bulk of the data. In general, one would not usually attempt a higher-order fit because uncertainties on the fit tend to offset the small improvement in the fit. However, the objective here is not to describe the overall regional slope, but to find a way to characterize the topographic variability around the regional trend. Thus the actual regression is of less interest than the distribution of the residuals (the differences between the measured elevations and those predicted by the regression curve). The residuals for the linear fit in Figure 2b are shown in Figure 3a. The distribution of these residuals only indicates how poorly the linear fit describes the regional behavior. Increasing the order of the fit to a parabolic regression of the form y = a + bx + cx 2 generally provides an improvement in the R 2 (e.g., to 99.7% for PEDR 14999). Table 2. Topographic Variability: Flow a All PEDRs were fit with second-order polynomial regressions. More importantly, the resulting residuals appear to be randomly distributed. Figure 3b shows a histogram of the residual values resulting from a parabolic regression on PEDR (Figure 2d). As can be seen in Figure 3b, the residuals now have a normal (Gaussian) random distribution suitable for a sound statistical characterization. [13] The flow 6 PEDR profiles are all fit very well by a second-order polynomial regression. Table 2 shows the very high R 2 values for each. It is remarkable that the regional slopes are so well-fit by elementary regressions over such large distances. Furthermore, these regressions are extremely robust, as each is performed on hundreds of points. The second column in Table 2 indicates the number of points used to estimate each regression. The last column of Table 2 lists the standard deviation, s, of the regression residuals for each PEDR. The standard deviation is an indicator of the degree of variability in the topography that is superimposed on the regionally sloping trend. [14] The standard deviations for all eleven PEDRs were averaged to estimate the overall regional topographic variability. The resulting mean standard deviation is 39.4 m for the eleven PEDR profiles shown in Figure 2a. When the residuals are normally distributed, as they are in Figure 3b, 68% of the topographic variability is contained in the range ±39.4 m around the regional trending slope. This confirms the intuitive expectation from Figure 2b that a lava flow between 10 and 40 m thick should be profoundly influenced by the topography. [15] The procedure for estimating the topographic variability described above is repeated for groups of PEDRs crossing the other nine flows in Table 1. The mean s values Table 3. Flow Characteristics Lava Flow Location Mean s, m Dh/DL, m/km DL/(Dh/h o ), km 1 Pavonis Pavonis Arsia Arsia Ascraeus Elysium Elysium Elysium Alba Alba of9

6 Table 4. Topographic Variability: Flow * * * * * * a All PEDRs were fit with third-order polynomial regressions, except those marked with an asterisk (*) (second order). for all ten flows are given in the third column of Table 3. The detailed quantitative values for each area analyzed are given in Tables In some cases, a third-order regression of the form y = a + bx + cx 2 + dx 3 was used in order to obtain normally distributed residuals. Still, it is remarkable that the PEDR elevation data can be fit so well with only second- and third-order polynomial regressions over many degrees of latitude. The order of regression used for each PEDR is provided in the corresponding table. 3. Interpretation [16] The mean s values in Table 3 are listed in order of increasing magnitude. It is interesting to note that the Table 5. Topographic Variability: Flow a All PEDRs were fit with second-order polynomial regressions. Table 6. Topographic Variability: Flow * * * a All PEDRs were fit with second-order polynomial regressions, except those marked with an asterisk (*) (third order). magnitude is very strongly correlated with volcanic region. Whereas it is not surprising that the topographic variability would be similar for the two areas south of Alba Patera, or north of Arsia Mons, it is remarkable that all the values for the three Tharsis volcanoes fall within a range that is distinct from Elysium Mons and Alba Patera. [17] Despite this direct correlation with volcanic region, there is only a weak correlation between mean s and emplacement slope. This weak correlation can be seen either by looking at the fourth column in Table 1 (arranged from smallest to largest mean s) or the scatterplot in Figure 4. The apparent correlation in Figure 4 can be tested statistically using the Pearson Product Moment (PPM) linear correlation coefficient [e.g., Sheskin, 1997]. The PPM is generally represented by r, where r = 0 indicates no correlation, and r = ±1 indicates perfect one-to-one linear correlation (+) or anti-correlation ( ). The PPM for the data in Figure 4 is r = For 10 data points, and 5% significance (i.e., 5% probability of concluding the variables are correlated when in fact they are not), the PPM is evaluated against a critical value of Although the correlation is relatively weak, r is slightly greater than the critical value and therefore statistically significant. [18] This weak correlation is interpreted as an indication that volcanoes that have produced lots of lava flows, with a net effect of increasing the topographic variability, eventually exhibit steeper emplacement slopes. Although not quantified in the existing terrestrial literature, this type of correlation is not unheard of on Earth. For example, the slopes of Hualalai, Hawaii (as great as 12 degrees near the summit), are considerably steeper than its neighbor Mauna Loa (typically 7 9 degrees near the summit). Likewise, the topography at Hualalai is qualitatively rougher. On Table 7. Topographic Variability: Flow * * a All PEDRs were fit with third-order polynomial regressions, except those marked with an asterisk (*) (second order). 6of9

7 Table 8. Topographic Variability: Flow * * * * * * * * a All PEDRs were fit with linear regressions, except those marked with an asterisk (*) (second order). Earth, these differences are influenced by eruption conditions (e.g., temperature and magma supply) and the lava composition plays an important role in the extent to which effused flows affect the topographic variability. Unfortunately, the relationship between topographic variability and volcano morphology has not been studied on Earth. It is presently difficult to unravel the effects of eruptive style, topography and composition relative to the growth of the volcano. [19] The influence of topographic variability on the emplacement process itself can also be explored. To statistically quantify changes in rheology along the flow path, two statistics have been developed. The first is a raw measure of the thickening (Dh) along the length of a flow (DL), and is defined as Dh/DL, with units of m/km. The second statistic normalizes the thickening statistic by an initial flow thickness, h o,atl = 0. In general, L = 0 is the most upstream location to which a flow can be definitively traced. This normalized thickening statistic is defined as DL/(Dh/h o ), and has units of km. Both of these statistics are, in essence, rough measures of a potential rheologic change along the length of the flow examined, DL. Estimated values of these two statistics for all 10 flows are given in Table 3. [20] Both thickening statistics are somewhat sensitive to where L = 0 and the flow front are defined in the thickness profiles. However, it is precisely because of this uncertainty that statistical analysis is the best way to approach this problem. The ability to confidently estimate longitudinal Table 9. Topographic Variability: Flow a All PEDRs were fit with second order polynomial regressions. thickness profiles for most lava flows on Mars is at the very limit of what can be interpreted from MOLA data. Thus it is preferable to consider multiple lava flows in a statistical fashion in order to account for uncertainties inherent in the low resolution spatial sampling. [21] Each flow is evaluated in a consistent and methodical way in an effort to minimize the uncertainty. In every case, all available data, including images (primarily Thermal Emission Imaging Spectrometer (THEMIS) data), gridded MOLA digital elevation models, and individual MOLA PEDRs are used to determine the most logical choices for the starting and ending points for L. It should also be noted that two of the flows examined (both at Alba Patera) show significant systematic widening toward the flow front. In these cases the measured flow thicknesses are not as great as they would have been, had the flow remained at a constant width. Thus the thickening statistics for the two Alba flows assume a constant flow width and use corrected thick- Table 10. Topographic Variability: Flow * a All PEDRs were fit with third-order polynomial regressions, except those marked with an asterisk (*) (second order). 7of9

8 Table 11. Topographic Variability: Flow a All PEDRs were fit with second-order polynomial regressions. nesses that accommodate all volume changes at each step in the thickness variable. [22] The longitudinal thickness profiles used in this study were determined using one of two techniques. Thicknesses for the broad, thick flows were determined by taking cross flow profiles from the 128 pixel/degree MOLA gridded data set. These flows are wide enough that any smoothing artifacts of the gridding process should not alter estimates of flow thickness significantly. Individual MOLA PEDR profiles were used for narrower (few km) flows that have only a few ground shots across the width of the flow. [23] Figure 5 shows the relationship between the two flow thickening statistics and topographic variability as described by the mean s. Visually, both thickening statistics appear to show some correlation with s.the PPM for Dh/DL versus s is r = 0.828, and for DL/(Dh/h o )versuss, jrj =0.805.Bothof these PPMs are relatively strong, and statistically significant (again, compared to the critical value of 0.632). It is interesting to note that the absolute thickness of the flow, incorporated in the second statistic, does not seem to have much of an effect on the correlation with topographic variability. In other words, lava flows tend to thicken directly in response to the topographic variability, regardless of how thick the flows are. This Table 12. Topographic Variability: Flow * * * * * a All PEDRs were fit with third-order polynomial regressions, except those marked with an asterisk (*) (second order). is in direct contrast to intuition that might lead one to think that the response of a lava flow to topography should in some sense be related to the flow thickness. [24] The most straightforward interpretation of the apparent correlation between topographic variability and thickening behavior is that an increase in the overall topographic variability tends to increase the disruption of streamlines within the flow, and possibly the upper surface crust. The subsequent cooling of the interior results in an increase in the internal viscosity of the lava, which causes a greater degree of thickening per unit length. Further, it is possible that high topographic variability might actually be the cause of the halting, stagnating behavior suggested at Elysium Mons [Mouginis-Mark and Yoshioka, 1998] in contrast to the long, unperturbed flows north of Pavonis Mons [Baloga et al., 2003]. Or, perhaps, the high topographic variability of the preexisting surface is the result of eruption rates that are highly time variable, indicating a very different eruptive style at Elysium Mons as compared to the Tharsis shield volcanoes. [25] The strong correlation between topographic variability and rheology may have a profound impact on how lava flows are modeled. To date, most models (if not all) have assumed that lava flows are emplaced on a relatively smooth inclined plane, i.e., surface roughness can be ignored. However, this study seems to indicate that the local topographic variability affects the flow rheology during emplacement, possibly by initiating eddies (non-parallel flow) or by disrupting the lava flow crust, affecting the ability to retain internal core heat. Thus the topography may be a stronger influence on rheology than previously assumed. 4. Conclusions [26] A new data analysis technique has been presented for quantifying the topographic variability of the surface of Mars. The statistic expressing the degree of topographic variability is the mean standard deviation of the residuals resulting from regressions on MOLA PEDR elevation profiles surrounding a specific lava flow. The topographic variability statistic is very closely correlated with volcanic centers. Of the sites examined, the mean s is smallest (smoothest) at the Tharsis volcanoes (Pavonis, Arsia, and Ascraeus Montes), increasing at Elysium Mons, and largest Figure 4. Scatterplot of emplacement slope versus mean s. Visual inspection of the data suggests a weak correlation between slope and topographic variability, but sites with large topographic variability occur on a range of slopes. 8of9

9 Figure 5. Scatterplots of (a) raw and (b) normalized thickening statistics versus mean s. Both thickening statistics are strongly correlated with topographic variability. This strong correlation suggests topographic variability has a significant influence on rheologic changes (and thus flow thickening behavior) during emplacement. The correlation coefficients for both cases are very similar, implying the overall flow thickness (used for the normalized statistic in Figure 5b) is not a determining factor in how strongly the topographic variability affects rheologic changes during emplacement. on the southeast flanks of Alba Patera. The mean s is descriptive of broad areas at each volcano, and these broad areas themselves appear to be fairly similar across the volcanoes. [27] There is also a weak, but significant, correlation between topographic variability and slope; i.e., as slopes increase, so does the topographic variability. One interpretation of this correlation is that volcanoes that produce lots of lava flows influencing the topographic variability, eventually produce steeper emplacement slopes. If additional study (including terrestrial examples) reveals that this is a common characteristic, it would have profound implications for the growth of volcanoes on Mars, particularly the role of effusive phases. [28] Flow thickening behavior has also been quantified using two simple statistics, the first is a raw measure of thickening, defined as Dh/DL, and the second, defined as DL/Dh/h o, is normalized by the flow thickness at a specified starting point. These two statistics can be used as a rough measure of rheologic change over the distance DL, and then compared to topographic variability. [29] There is a strong significant correlation between both flow thickening statistics and topographic variability. This suggests that topographic variations are important in lava flow emplacement dynamics. The magnitude and influence of these variations have been previously unrecognized or underrepresented in flow modeling. [30] Understanding the influence of ambient topographic variability on the thickness profile of a lava flow is essential for unraveling rheologic changes during emplacement. The basic topographic variability measure presented here, based on the standard error of regression, can be used along with regional slope and rheologic character (i.e., changes in yield strength or viscosity) to better understand the influence of topography on lava flow emplacement. These results suggest that future theoretical studies more thoroughly explore the influence of topographic variations along the flow path, their influence on internal circulation within the flow, the disruption of the upper crust, and ultimately the thermal dynamics of lava flow emplacement on Mars. [31] Acknowledgments. This work was supported by grants from the National Aeronautics and Space Administration Mars Data Analysis Program (grants NNG04GN05G and NNX06AD98G). The authors would like to thank David Senske and Scott Rowland for helpful comments and suggestions. References Baloga, S. M., P. D. Spudis, and J. E. Guest (1995), The dynamics of rapidly emplaced terrestrial lava flows and implications for planetary volcanism, J. Geophys. Res., 100(B12), 24,509 24,519. Baloga, S. M., L. S. Glaze, J. A. Crisp, and S. A. Stockman (1998), New statistics for estimating the bulk rheology of active lava flows: Puu Oo examples, J. Geophys. Res., 103(B3), Baloga, S. M., P. J. Mouginis-Mark, and L. S. Glaze (2003), Rheology of a long lava flow at Pavonis Mons, Mars, J. Geophys. Res., 108(E7), 5066, doi: /2002je Crisp, J. A., and S. M. Baloga (1990), A model for lava flows with two thermal components, J. Geophys. Res., 95(2), Crisp, J. A., and S. M. Baloga (1994), Influence of crystallization and entrainment of cooler material on the emplacement of basaltic aa lava flows, J. Geophys. Res., 99(6), 11,819 11,832. Draper, N. R., and H. Smith (1998), Applied Regression Analysis, 3rd ed., 736 pp., Wiley-Interscience, Hoboken, N. J. Glaze, L. S., and S. M. Baloga (2006), Rheologic inferences from the levees of lava flows on Mars, J. Geophys. Res., 111, E09006, doi: /2005je Glaze, L. S., S. Baloga, and E. R. Stofan (2003), A methodology for constraining lava flow rheologies with MOLA, Icarus, 165, Harris, A. J. L., and S. K. Rowland (2001), FLOWGO: A kinematic thermo-rheological model for lava flowing in a channel, Bull. Volcanology, 63, Mouginis-Mark, P., and M. T. Yoshioka (1998), The long lava flows of Elysium Planita, Mars, J. Geophys. Res., 103(E8), 19,389 19,400. Rowland, S. K., A. J. L. Harris, and H. Garbeil (2004), Effects of Martian conditions on numerically modeled, cooling-limited, channelized lava flows, J. Geophys. Res., 109, E10010, doi: /2004je Schneeberger, D. M., and D. C. Pieri (1991), Geomorphology and stratigraphy of Alba Patera, Mars, J. Geophys. Res., 96(B2), Sheskin, D. J. (1997), Handbook of Parametric and Nonparametric Statistical Procedures, 719 pp., CRC Press, New York. Zimbelman, J. (1985), Estimates of rheologic properties for flows on the Martian volcano Ascraeus Mons, Proc. Lunar Planet. Sci. Conf. 16th, Part 1, J. Geophys. Res., 90, suppl., D157 D162. Zimbelman, J. (1998), Emplacement of long lava flows on planetary surfaces, J. Geophys. Res., 103(B11), 27,503 27,516. S. M. Baloga and L. S. Glaze, Proxemy Research, Farcroft Lane, Laytonsville, MD 20882, USA. (lori@proxemy.com) 9of9