Limitations of the advection-diffusion equation for modeling tephra fallout: 1992 eruption of Cerro Negro Volcano, Nicaragua.

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1 University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 2004 Limitations of the advection-diffusion equation for modeling tephra fallout: 1992 eruption of Cerro Negro Volcano, Nicaragua. Kristin Terese Martin University of South Florida Follow this and additional works at: Part of the American Studies Commons Scholar Commons Citation Martin, Kristin Terese, "Limitations of the advection-diffusion equation for modeling tephra fallout: 1992 eruption of Cerro Negro Volcano, Nicaragua." (2004). Graduate Theses and Dissertations. This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact

2 Limitations of the Advection-Diffusion Equation for Modeling Tephra Fallout: 1992 Eruption of Cerro Negro Volcano, Nicaragua. by Kristin Terese Martin A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Science Department of Geology College of Arts and Sciences University of South Florida Major Professor: Charles Connor, Ph.D. Sarah Kruse, Ph.D. Costanza Bonadonna, Ph.D. Date of Approval: November 3, 2004 Keywords: volcanology, volcanic ash, hazard models, Marrabios Range, isomass Copyright 2004, Kristin Terese Martin 1

3 Acknowledgements I would like to thank Dr. Chuck Connor for all his guidance and support over the last few years. Also, this work could not have been accomplished without the help of my other committee members: Dr. Sarah Kruse and Dr. Costanza Bonadonna, as well as, Laura Connor and Ivan Savov. The support of all my family and friends is also greatly appreciated. This research project was funded by the National Science Foundation EAR and the University of South Florida s Latin American and Caribbean Studies Research Award. 2

4 Table of Contents List of Figures...ii Abstract...iii 1. Introduction Cerro Negro Analytical Techniques Granulometry Discussion...8 References...11 Appendices...14 Appendix A: Isopach Map of the 1992 Cerro Negro Tephra Deposit...15 Appendix B: Map of Site Locations and Thicknesses at Each Site...16 Appendix C: Histograms of Granulometry Results at Each Site...17 Appendix D: Density Histogram Plotted for All Sites...50 Appendix E: Isomass Maps for Each Grain Size...51 Appendix F: Table of Thickness, Density, and Isomass for Each Site...59 Appendix G: Table of Granulometry Results for Each Site...62 Appendix H: Spreadsheet of Calculated Settling Velocities i

5 List of Figures Figure 1. Figure 2. Figure 3a. Figure 3b. Figure 4. Location map for the Central American Volcanic Arc showing the location of Cerro Negro Volcano, Nicaragua....3 Isomass map of the entire 1992 tephra deposit...5 Isomass map for the coarse-grained portion of the 1992 tephra deposit.7 Isomass map for the fine-grained portion of the 1992 tephra deposit...7 Graph of calculated settling velocities of particles with varying grain size and density using the method of Suzuki [1983] ii

6 Limitations of the Advection-Diffusion Equation for Modeling Tephra Fallout: 1992 Eruption of Cerro Negro Volcano, Nicaragua. Kristin Martin ABSTRACT: Detailed mapping and granulometric analyses of the 1992 Cerro Negro tephra blanket reveal remarkable departures from the expected distribution of tephra. Isomass maps show that the major axis of dispersion for the eruption was to the SW of the cone and that the coarser-grained particles, ranging from f, were deposited primarily along the major axis of dispersion with deposits thinning off of the axis. Comparable isomass maps for finer-grained particles, f, show that these particles were primarily deposited along the edges of the deposit, off of the major axis of dispersion. Advection-diffusion models for tephra fallout currently widely used in volcanology do not account for this deposition pattern. Rather, it appears that interaction between the wind field, which developed a strong cross flow during the eruption, and the ascending tephra plume resulted in the formation of turbulent structure in the plume. Particles with a settling velocity greater than ~1-2m/s (diameter >0.5 mm) were able to overcome the turbulent structure and settled in a manner predicted by the advection-diffusion equation. Those with lower settling velocities were caught up in turbulent structure and deposited off of the major axis of dispersion, near the edges of the overall tephra blanket. Thus, 5 iii

7 this data set provides the first estimate of the strength of such turbulent structures in advecting plumes, and illustrates the limitations of the typical advection-diffusion models in describing some transport processes. 6 iv

8 1. Introduction The advection-diffusion equation is widely used to forecast tephra dispersal at the world s active volcanoes [Armienti et al., 1988; Barberi et al., 1990; Bonadonna et al., 2002; Carey and Sparks, 1986; Connor et al., 2001; Hill et al., 1998; Macedonio et al., 1988]. Here we test the advection-diffusion equation using medial facies data collected from the sub-plinian April 1992 eruption of Cerro Negro in Nicaragua. We find that the models applying analytical and/or numerical solutions to the advection-diffusion equation do not capture the complexity of the depositional processes during this eruption. These models are particularly poor for describing the distribution of fine-grained particles in the 1992 deposit, which we have mapped in detail. Instead, our findings suggest that complex turbulent structure in the plume has a strong impact on the distribution of fines. The advection-diffusion equation is used to model numerous transport phenomena in the Earth Sciences. Contaminant transport [Anderson, 1979], salt water intrusion [Herbert and Lloyd, 2000; Tejeda et al., 2003], and population distribution [Sibert and Fournier, 1994; Sibert et al., 1999] rely on the advection-diffusion equation to simulate complex transport processes. Because of this wide use, it is critical to understand the limitations of this approach. Our investigation of tephra dispersion offers insights into the limits of applicability of these models for simulating natural phenomena. The advection-diffusion equation is currently in wide use to model tephra fallout from erupting volcanoes. Essentially, the advection-diffusion equation is solved to obtain 71

9 the mass of tephra accumulated at some geographic location relative to the volcanic vent. Horizontal diffusion and advection of the ash particles are governed by atmospheric turbulence, cloud spreading, and wind movement respectively. Vertical transport is determined by the settling velocity of the particles. Most often, the advection-diffusion equation is solved by deriving an analytical solution or partitioning of the sample space into a grid, and numerically integrating the discretized version of the advection-diffusion equation [Armienti et al., 1988; Glaze and Self, 1991; Hill et al., 1998]. All models of tephra dispersion and fallout make simplifying assumptions. For example, in some models the eruption column is treated as a line-source, where some change in particle concentration with height is assumed [Suzuki, 1983; Connor et al., 2001]. Tephra particles are segregated from this column based on their settling velocity, parameters that govern particle diffusion out of the column, and turbulent diffusion. Meteorological data are also incorporated in the model as uniform or stratified wind fields [Lacasse, 2001]. These assumptions, in part, control the modeled map pattern of tephra accumulation and hazard forecasts. Models based on the advection-diffusion equation predict that at a given distance, most of the mass will be deposited along a major axis of dispersion and Gaussian diffusion governs accumulation off the major axis of dispersion. Along the axis, there will be a change in median grainsize with distance from the vent. Larger grains will be deposited proximal to the vent and fines will settle out of the column at a greater distance. The deposit will thin according to exponential thinning [Pyle, 1989]. We test these models by preparing a detailed set of isomass maps for the 2

10 April 1992 eruption of Cerro Negro volcano. This eruption is particularly useful because of a relatively simple windfield and a clear major axis of dispersion. 2. Cerro Negro Cerro Negro is a small volume basaltic cinder cone on the north flank of the El Hoyo volcano complex in the central Marrabios Range of Nicaragua (figure 1). Together with the adjacent Telica, San Cristobal, and Rota volcanoes (to the NW) and Momotombo volcano (to the SE), Cerro Negro is part of the main volcanic front of the Central American Arc. Similarly to Paricutin, Mexico, this volcano formed very recently (first erupted in 1850) and has erupted at least 23 Figure 1: Location map for the Central American Volcanic Arc showing the location of Cerro Negro Volcano, Nicaragua. Black triangles show volcanoes active in the Holocene. times since its formation [Hill et al., 1998; McKnight and Williams, 1997; LaFemina et al., 2004]. These eruptions produced compositionally similar basalt and basalt-andesites [Roggensack et al., 1997] and lava flows reaching several km in length. The crystallinity of the majority 3

11 of the Cerro Negro lavas is in the order of 50%, with abundant phenocrysts of olivine, plagioclase, and pyrocene. Since 1968 the volcano has undergone 4 large tephra eruptions; 1968, 1971, 1992, The 1968 eruption of Cerro Negro released 9.7 x 10 6 m 3 of pyroclastic material [Hill et al., 1998]. The largest tephra eruption occurred in 1971, with 3.0 x 10 7 m 3 of tephra erupted. The 1992 eruption of Cerro Negro consisted of two distinct phases. The first eruptive phase lasted for approximately 6 hours and was the most energetic phase of the eruption with a maximum column height of ~7 km above sea level. The second phase of the eruption lasted for 17 hours and was less energetic than the previous phase, with a column height of 1-4 km above sea level and a bent over plume. The entire eruption produced 2.3 x 10 7 m 3 of tephra. The most recent large tephra eruption took place in The maximum column height was between km and the tephra fall volume was estimated as 2.16 x 10 6 m 3 [Hill et al., 1998]. As expected, the volatile contents of tephra samples from 1992 eruption are with elevated H 2 O contents (4.2-6 wt %) in respect to the less explosive eruption of 1995 ( wt %) [Roggensack et al., 1997]. The tephra released during all of these eruptions settled along a major axis of dispersion to the west of Cerro Negro. This poses a significant hazard to the secondlargest city in Nicaragua, Leon, which is located to the west of the volcano, very near the axes of dispersion for all four eruptions. Past eruptions have caused building collapse, contaminated water supplies, agricultural damage, and other public health concerns in Leon [Hill et al., 1998]. 4

12 3. Analytical Techniques The 1992 tephra blanket is particularly well-preserved because it is buried by the 1995 tephra deposit. We sampled the 1992 tephra blanket of Cerro Negro in 80 locations ranging from 1-13 km from the volcano. At each location, a trench was dug until the base of the 1992 deposit was reached, readily identified by a sudden change in color, grainsize, and occasionally by the presence of roots. The thickness of the deposit was measured and samples of the deposit were collected for granulometric analysis. Figure 2: Isomass map of the entire 1992 tephra deposit. The contour interval is 100 kg/m 2. Circles represent sample locations. Map shown in UTM coordinates, datum NAD27. Solid black line represents location of the major axis of dispersion. Contouring was done using Generic Mapping Tool (GMT). There was no evidence of reworking of the tephra as the thickness measurements taken were in agreement with thickness measurements taken at some sites directly after the 1992 eruption. Cumulate deposit density was measured in the field at each of the 80 sites, which is 1186 ± 133 kg/m 3. These data provide an estimate of total mass per unit area at 5

13 each site, and these estimates were contoured across the region (figure 2). Near vent mass is considerably thicker than shown, as our sample pits could not reach the base of the deposit where thickness exceeded 2m. Similarly, the contour map is not interpolated to thin distal areas because the deposit in the distal region, >13 km from the vent, is eroded or disturbed. 3.1 Granulometry Isomass maps were prepared for individual grain sizes at 0.5f intervals from each of the 80 sites. These isomass maps reveal several important features of the deposit. First, median grainsize decreases with distance from the vent, as expected (figures 3a and 3b). At coarse grain sizes, -4.0 thru 1.0f, a maximum in accumulation occurs along the major axis of dispersion. The location of this maximum is increasingly distant from the vent along the major axis of dispersion for successively finer grain size fractions (figure 3a). A similar result was observed at Ruapehu volcano, New Zealand, and interpreted to be caused by turbulent structure in the weak plume [Bonadonna et al., submitted]. The most surprising result, however, is that the maxima in the fine-grained fraction, (>1.0f ), of the deposit are not evenly distributed along the major axis of dispersion. Accumulation of fine-grained particles is actually greatest off the major axis of dispersion (Figure 3b). Maximum accumulation tends to occur approximately 2-3 km off of the major axis of dispersion. This result is consistent for each grain size fraction finer than 1.0f. 6

14 a: b: Figure 3: (a)- (top) Isomass map for the coarse-grained portion of the 1992 tephra deposit. The plotted values are the sum of the isomass values of grain sizes -4.0 thru 1.0f (16mm < d < 0.5mm). The deposition of these larger grains was focused along the main axis of dispersion. Contour interval is 100 kg/m 2. Map shown in UTM coordinates, datum NAD27. Solid black line represents location of the major axis of dispersion. Contouring was done using Generic Mapping Tool (GMT). (b) - (bottom) Isomass map for the fine-grained portion of the 1992 tephra deposit. The values plotted are the sum of the isomass values of the grain sizes 1.5 thru 3.5f (0.35mm < d < 0.09 mm). Maxima in deposition of fines occur off the major axis of dispersion. Contour interval is 20 kg/m 2. Map shown in UTM coordinates, datum NAD27. Solid black line represents location of the major axis of dispersion. Contouring was done using Generic Mapping Tool (GMT). 7

15 4. Discussion The reported partitioning of tephra fallout along and about the major axis of dispersion cannot be explained using traditional models of tephra dispersion that rely on advection and diffusion from a simple source. Instead, turbulent structure [Cunningham et al., in press] and perhaps subtle bifurcation of the plume [Ernst et al., 1996] are possible structures controlling distribution of tephra fallout. For example, incipient vortex counter rolls [Fric and Roshko, 1994] in the advecting plume may cause the pattern we observe in fine-grained tephra fallout. If so, we can calculate the upward velocities of these turbulent structures by considering the settling velocities of particles as a function of grain size. The settling velocity, v o, as a function of grain size, particle density, and shape can be approximated by using the methods relationship as described in Suzuki [1983]: v o ( φ) = 9ηρ 0.32 f + 81η 2 ρ ρ 0.64 f tephra gφ ρ tephra ρ air gφ ρ f (1) where? tephra is the density of tephra particles, g is gravitational acceleration,? is air viscosity,? air is air density, and p f is particle shape factor p p + p b c f = (2) 2 p a 8

16 where subscripts a, b, and c refer to the diameter of the particle along the principle axes: and p a > p b > p c [Suzuki, 1983]. The values for? tephra and p f were varied and the settling velocities recalculated to provide a range of settling velocities for each grain size (Figure 4). Settling Velocity at Sea Level (m/s) Phi Units 1000 kg/m kg/m kg/m3 Figure 4: Calculated settling velocities of particles with varying grain size and density using the method of Suzuki [1983]. Particle shape factor was estimated at The settling velocity calculated for the fine particles which were mainly deposited off of the major axis of dispersion is < 1-2 m/s. Coarse tephra grains (>0.5mm) have settling velocities >1-2 m/s (equations 1 and 2). Maxima for these grain sizes fall on the major axis of dispersion for the 1992 deposit (figure 3a). Fine tephra grains (<0.5 mm) have settling velocities (v o ) of ~ 2 m/s or less and are redistributed in the deposit with maximum thickness 1-3 km off the major axis of dispersion. This suggests that turbulent structures in the plume had maximum upward 9

17 velocities ~ 1-2 m/s, and that these rotating cells were of diameter ~1-3 km, depending on where the particles fell out of the vortices. The occurrences of such structures in volcanic plumes injected into a windfield are predicted by fluid dynamic simulations [Fric and Roshko, 1994; Cunningham et al., in press]. Here we show that such structures actually impact tephra deposition, resulting in complexity in these deposits that are not predicted by the advection-diffusion equation. As the scale of turbulent structures depends on the relative velocities of the plume and windfield [Fric and Roshko, 1994], models of tephra deposition and related hazards may benefit from consideration of scale and velocity of these features of volcanic plumes. 10

18 References: Anderson, M.P., Using Models to Simulate the Movement of Contaminants through Groundwater Flow Systems, Critical Reviews in Environmental Control, 9(2), , Armienti, P., G. Macedonio, and M.T. Pareschi, A numerical model for simulation of Tephra transport and deposition: applications to May 18 Mount St. Helen Eruption, J. Geophys. Res., 93, , Barberi, F., G. Macedonio, M.T. Pareschi, and R. Santacroce, Mapping the tephra fallout risk: an example from Vesuvius, Italy, Nature, 344, , Bonadonna, C., G. Macedonio, and R.S.J. Sparks, Numerical modeling of tephra fallout associated with dome collapses and Vulcanian explosions: application to hazard assessment on Montserrat, in The eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999, edited by T.H. Druitt, and B.P. Kokelaar, , Geological Society, London, Memoir, Bonadonna, C., J.C Phillips, and B.F. Houghton, Modeling tephra fall from a Ruapehu weak plume eruption, in press. Carey, S.N., and R.S.J. Sparks, Quantitative models of the fallout and dispersal of tephra from volcanic eruption columns, Bul. Volcanol., 48, , Connor, C.B., B.E. Hill, B. Winfrey, N.M. Franklin, and P.C. LaFemina, Estimation of volcanic hazards from tephra fallout, Natural Hazards Review, 2, 33-42, Cunningham, P., S.L. Goodrick, M.Y. Hussaini, and R.R. Linn, Coherent vortical structures in numerical simulations of buoyant plumes from wildland fires, submitted to 5 th Symposium on Fire and Forest Meteorology on January 26, Ernst, G.G.J., R.S.J. Sparks, S.N. Carey, and M.I. Bursik, Sedimentation from turbulent jets and plumes, J. Geophys. Res.-Solid Earth, 101(B3), , Fric, T.F., and A. Roshko, Vortical structure in the wake of a transverse jet, J. Fluid Mechanics, 279, 1-47,

19 Glaze, L., and S. Self, Ashfall dispersal of the 16 September 1986, eruption of Lascar, Chile, calculated using a turbulent diffusion model, Geophys. Res. Lett., 18, , Herbert A.W., and J.W. Lloyd, Approaches to modeling saline intrusion for assessment of small island water resources, Quarterly J. Engineering Geology and Hydrogeology, 33(1), 77-86, Hill, B.E., C.B. Connor, M.S. Jarzemba, and P.C. LaFemina, 1995 eruptions of Cerro Negro, Nicaragua and risk assessment for future eruptions, Geol. Soc. Am. Bull., 110, , Lacasse, C., Influence of climate variability on the atmospheric transport of Icelandic tephra in the subpolar North Atlantic, Global and Planetary Change, 29, 31-55, LaFemina, P., Connor, C.B., Hill, B.E., Strauch, W., and Saballos, J.A, Magma-tectonic interactions in Nicaragua: the 1999 seismic swarm and eruption of Cerro Negro volcano, J. Volcanology and Geothermal Research, 137(1-3), , Macedonio, G., Pareschi, M.T., Santacroce, R.A., Numerical simulation of the Plinian fall phase of 79 A.D. eruption of Vesuvius, J Geophys. Res. 93(B12), , McKnight, S. B. and S.N. Williams, Old cinder cone or young composite volcano? The nature of Cerro Negro, Nicaragua: Geology, 25(4), , Pyle, D. M., The thickness, volume and grainsize of tephra fall deposits, Bul. Volcanol., 51, 1-15, Roggensack, K., R.L. Hervig, S.B. McKnight, and S.N. Williams, Explosive basaltic volcanism from Cerro Negro Volcano, Nicaragua: the influence of volatiles on eruption style, Science, 277, , Sibert, J. R., J. Hampton, D. A. Fournier, and P. J. Bills An advection-diffusionreaction model for the estimation of fish movement parameters from tagging data, with application to skipjack tuna (Katsuwonus pelamis). Canadian Journal of Fisheries and Aquatic Sciences, 56, pp Sibert, J.R. and D.A. Fournier, Evaluation of advection-diffusion equations for estimation of movement patterns from tag recapture data, Proceedings of the First FAO Expert Consultation on Interactions of Pacific Ocean Tuna Fisheries, Summary report and papers on interaction, , R. S. Shomura, J. Majkowski and S. Langi (eds.) FAO Fisheries Technical Paper 336/1, 326,

20 Suzuki, T., A theoretical model for dispersion of tephra, Arc Volcanism: Physics and Tectonics, D. Shimozuru and I. Yokoyama, Eds., Terra Publishing Co., , Tejeda I., R. Cienfuegos, J.F. Muñoz, and M. Durán, Numerical modeling of saline intrusion in the Salar de Atacama, J. Hydro. Engineering, 8(1), 25-34,

21 Appendices 14

22 Appendix A: Map of Site Locations and Thicknesses at Each Site 15

23 Appendix B: Isopach Map of the 1992 Cerro Negro Tephra Deposit 16

24 Appendix C: Histograms of Granulometry Results at each Site 17

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57 Appendix D: Density Histogram Plotted for All Sites 50

58 Appendix E: Isomass Maps for Each Grain Size 51

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66 Appendix F: Table of Thickness, Density, and Isomass for Each Site Site Easting Northing Layer Mass Thickness Density Isomass (m) (m) (g) (cm) (m) (kg/m 3 ) (kg/m 2 ) A B A B A B A B A B A B Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed A B B A B Mixed Mixed Mixed Mixed Mixed B Mixed Mixed Mixed A B A B

67 Appendix F (Continued) A B Mixed A B Mixed A A B Mixed A B A B Mixed Mixed Mixed Mixed A B A B A Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed A top B A Bottom Mixed

68 Appendix F (Continued) A B Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed Mixed A B Mixed A B Mixed Mixed Mixed Mixed Mixed Mixed

69 Appendix G: Table of Granulometry Results for Each Site Sample Name: A B A B A Total Measured Weight (g): Weight of each Phi Size (g): > Calculated Weight (g):

70 Appendix G (Continued) B A B A B A B

71 Appendix G (Continued) M M M M M M M

72 Appendix G (Continued) M A B B A B M

73 Appendix G (Continued) M M M M

74 Appendix G (Continued) Sample Name: B C M M M Total Measured Weight (g): Weight of each Phi Size (g): > Calculated Weight (g):

75 Appendix G (Continued) A B A B A B M

76 Appendix G (Continued) A B A B A B A

77 Appendix G (Continued) B M (Fine) A B A B M

78 Appendix G (Continued) Sample Name: M M M A B Total Measured Weight (g): Weight of each Phi Size (g): > Calculated Weight (g):

79 Appendix G (Continued) A B A B M M M

80 Appendix G (Continued) M M M M M M

81 Appendix G (Continued) M M M

82 Appendix G (Continued) Sample Name: M M A Top B Total Measured Weight (g): Weight of each Phi Size (g): > Calculated Weight (g):

83 Appendix G (Continued) A Bottom M A B M M M

84 Appendix G (Continued) Sample Name: M M M M M Total Measured Weight (g): Weight of each Phi Size (g): > Calculated Weight (g):

85 Appendix G (Continued) M A B M A B M

86 Appendix G (Continued) M M Fine M M M

87 Appendix H: Spreadsheet of Calculated Settling Velocities Settling Velocities calculated with Given Densities? ash= 900? ash= 1000? ash= 1100? ash= 1200? ash= 1300? ash= 1400? ash= 1500 v o (f) = v o (f) = v o (f) = v o (f) = v o (f) = v o (f) = v o (f) = Phi Size: