Data - Soil sequences

Transcription

1 A Data - Soil sequences Thicknesses (cm) of named tephras (i = 1,..., 22) observed at locations (j = ). r j denotes the distance from the vent (km), θ j denotes the angular direction from the vent (radians anticlockwise from east). Approximate ages for the named tephra formations are reported as given in Alloway (1989) and Alloway et al. (1995). The thicknesses are obtained from descriptions of the reference sections in Alloway (1989) or, where not specifically stated, have been measured from scale figures showing the section stratigraphy. In situations where the figures in Alloway (1989) do not separate the different beds, the total thickness is apportioned so that the thickness of the dominant phase(s) is proportional to that observed in the reference sections. Name Manganui.c (3.1 ka) Inglewood.b (3.6 ka) Korito.b (4.1 ka) Tariki.f ( ka) Tariki.e ( ka) Waipuku (5.2 ka) Kaponga.f ( ka) Konini.b (10.1 ka) Mahoe.a ( ka) Paetahi.a ( ka) Tuikonga.d ( ka) Koru.a ( ka) Pukeiti (26.2 ka) Waitepuku.a ( ka) Mangatoki.a (4.4 ka) Kaponga.d ( ka) Kaihouri.h ( ka) Poto.a ( ka) Mangapotoa.a ( ka) Waitui (55.0 ka) Araheke ( ka) Te Arei (75.0 ka) ID i ID j r j θ j Thickness (cm)

2 B Data - Core sequences Resulting arrangement of tephra thicknesses and estimated ages across the six sediment cores: Lake Umutekai (Um), Lake Rotokare (Ro), Near Source (NS), Eltham Swamp (El), Lake Rangatauanui (Ra) and Auckland (Au). There is no tephra number 27 in the Umutekai and Rotokare records and no tephra number 4 in the Rangatauanui record as these are the rhyolitic Stent Ash sourced from the Taupo Volcanic Centre ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Manganui.c 3577± ± ± Continued on next page

3 Continued from previous page ± ± ± ± Inglewood.b 4019± ± ± ± ± ± ± ± ± Korito.b 4804± Mangatoki.a 4840± ± ± ± ± ± ± ± ± ± Tariki.f 5344± Tariki.e 5412± ± ± Waipuku 5664± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Kaponga.f 6944± ± ± ± ± ± ± ± Continued on next page

4 Continued from previous page ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Kaponga.d 10738± ± ± ± ± ± ± Continued on next page

5 Continued from previous page ± ± ± ± ± Konini.b 12354± ± ± Mahoe.a 13036± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Kaihouri.h 18316± ± ± ± ± ± ± ± ± Paetahi.a 22770± ± ± ± ± Poto.a 25637± ± ± ± ± Tuikonga.d 29030± ± ± ± ± ± ± ± ± Koru.a 29522± Continued on next page

6 Continued from previous page ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Pukeiti 31725± ± ± ± Waitepuku.a 32456± ± ± ± ± ± ± ± Mangapotoa.a 33679± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Continued on next page

7 Continued from previous page ± ± ± ± ± ± ± ± ± ± ± ± ± Waitui 51189± ± Araheke 58524± ± Te Arei 67161± ±

8 C WinBUGS code model{ for (j in 1:nSites){ for (i in 1:nTephras){ thick[i,j] ~ dlnorm(mu[i,j],0.3156)i(0,cens[i,j]) mu[i,j] <- log(0.5*g[i,j]*exp(f1[i,j])+(1-0.5)*g[i,j]*exp(f2[i,j])) g[i,j] <- exp(a[j])*pow(v[i],(c[i]+1)/3)/pow(r[j]+d[i]*pow(v[i],1/3),c[i]) f1[i,j] <- alpha1[i]*cos(theta[j]-phi1[i])+beta1[i]*cos(2*(theta[j]-phi1[i])) f2[i,j] <- alpha2[i]*cos(theta[j]-phi2[i])+beta2[i]*cos(2*(theta[j]-phi2[i])) DATA # cens[i,j] = censoring variable, # cens[i,j] = 0.05 for missing tephras in the sediment cores, cens[i,j] = 100 otherwise # r[j] = distance (in km) of location j from the vent # theta[j] = angular direction (radians) of location j from the vent # thick[i,j] = thickness (in cm) of tephra i observed at location j # q[i] = probability of observing two lobes # nsites = 39 # ntephras = 270 #### # prior for the presence of 2 lobes for (i in 1:nTephras){ X[i] ~ dbern(q[i]) # if x = 0 one lobe, if x = 1 two lobes. # prior for the site-specific effect # for the coring sites for (j in 1:6){ a[j] ~ dnorm(0,0.0001) # for the exposed locations for (j in 7:nSites){ a[j] ~ dnorm(7.9137,302.68) # prior for the volume V[i] (in cubic km) # for the named tephras V[1] ~ dlnorm( ,138.72) V[2] ~ dlnorm( ,44.178) V[3] ~ dlnorm( ,94.214) V[4] ~ dlnorm( ,33.996) V[5] ~ dlnorm( ,87.722) V[6] ~ dlnorm( ,89.698) V[7] ~ dlnorm( ,87.749) V[8] ~ dlnorm( ,37.672) V[9] ~ dlnorm( ,26.886) V[10] ~ dlnorm(-1.685,40.336)

9 V[11] ~ dlnorm( ,48.753) V[12] ~ dlnorm( ,15.453) V[13] ~ dlnorm( ,161.17) V[14] ~ dlnorm( ,142.66) # for the named tephras that do not have isopach diagrams for (i in 15:22){ V[i] ~ dlnorm( ,3.7521) # for the unnamed tephras for (i in 23:nTephras){ V[i] ~ dbeta( , ) # prior for c[i] # for the named tephras for (i in 1:14){ clog[i] ~ dlnorm( ,5.1758) c[i] <- clog[i]+2 # constraint c > 2 # for the remaining tephras for (i in 15:nTephras){ clog[i] ~ dlnorm(-1.160,2.604) c[i] <- clog[i]+2 # constraint c > 2 # prior for d[i] # for the named tephras for (i in 1:14){ d[i] ~ dlnorm( ,5.2213) # for the remaining tephras for (i in 15:nTephras){ d[i] ~ dlnorm(0.1798,1.1485) # prior for the shape parameters alpha1[i] alpha2[i] beta1[i] beta2[i] for (i in 1:nTephras){ V1[i] ~ dgamma( , ) # variable for difference alpha1-4*beta1 V2[i] ~ dgamma( , ) # variable for difference alpha2-4*beta2 W1[i] ~ dgamma(1.4556,3.6992) # variable for beta1 W2[i] ~ dgamma(1.4556,3.6992) # variable for beta2 alpha1[i] <- 4*W1[i]+V1[i] # constraint alpha > 4beta beta1[i] <- W1[i] # if there is only 1 lobe (X = 0) then alpha2 = alpha1 and beta2 = beta1. alpha2[i] <- (1-X[i])*alpha1[i]+ X[i]*(4*W2[i]+V2[i]) beta2[i] <- (1-X[i])* beta1[i] + X[i]* W2[i]

10 # prior for the wind directional parameters phi1[i] and phi2[i] # for the named tephras angle1[1] ~ dbeta(116.07,58.377) angle1[2] ~ dbeta(172.82,62.382) angle1[3] ~ dbeta(181.3,80.407) angle1[4] ~ dbeta(99.237,77.905) angle1[5] ~ dbeta(228.44,154.44) angle1[6] ~ dbeta(49.174,20.009) angle1[7] ~ dbeta(164.32,81.006) angle1[8] ~ dbeta(77.758,77.758) angle1[9] ~ dbeta(93.247,93.247) angle1[10] ~ dbeta(92.478,61.08) angle1[11] ~ dbeta(100.39,35.174) angle1[12] ~ dbeta(11.487,3.5526) angle1[13] ~ dbeta(36.38,7.3343) angle1[14] ~ dbeta(87.87,37.23) angle2[1] ~ dbeta(11.915,29.058) angle2[2] ~ dbeta(13.237,27.513) angle2[3] ~ dbeta(20.896,39.176) angle2[4] ~ dbeta(3.7532,8.8708) angle2[5] ~ dbeta(11.601,20.691) angle2[6] ~ dbeta(14.41,35.051) angle2[7] ~ dbeta(4.8731,8.8458) angle2[8] ~ dbeta(11.957,48.479) angle2[9] ~ dbeta(7.0225,21.197) angle2[10] ~ dbeta(43.648,111.36) angle2[11] ~ dbeta(1,1) # one lobe for Tuikonga angle2[12] ~ dbeta(3.4986,6.6165) angle2[13] ~ dbeta(1,1) # one lobe for Pukeiti angle2[14] ~dbeta(1,1) # one lobe for Waitepuku # for the remaining tephras for (i in 15:nTephras){ angle1[i] ~ dbeta(2.0909,2.0776) # beta distribution on interval 0-1 angle2[i] ~ dbeta(2.0909,2.0776) # convert beta distributions to -pi/2 - pi/2 interval. for (i in 1:nTephras){ phi1[i] <- (angle1[i]-0.5)*( ) # create temporary variable for the absolute difference phi1 - phi2 Y[i] <-abs( (angle1[i]-0.5)*( ) -(angle2[i]-0.5)*( )) # if only one lobe (X = 0) then phi2 = phi1, if two lobes (X = 1) then phi2 is some angle Y from phi1. # if phi1 > 0 then phi2 is south of phi1, If phi1 < 0 then phi2 is north of phi1. phi2[i] <- phi1[i]+(-step(phi1[i])+(1-step(phi1[i])))*y[i]*x[i]

11 Frequency D Models for eruptive volume Density functions and parameter estimates for a range of distributions fitted to the logarithm of the posterior mean volume estimates (km 3 ) Volume Data Mixture of Normals Mixture of Lognormals Mixture of Weibulls Mixture of Weibulls Mixture of Lognormals Mixture of Normals p = ± p = ± p = ± k 1 = ± µ 1 = ± µ 1 = ± δ 1 = ± σ 1 = ± σ 1 = ± k 2 = ± µ 2 = ± µ 2 = ± δ 2 = ± σ 2 = ± σ 2 = ± log L log L log L AIC = AIC = AIC =