Fall Events, Southern Alps, New Zealand

BULL AND BRANDON

LICHEN DATING OF EARTHQUAKE-GENERATED REGIONAL ROCK- FALL EVENTS, SOUTHERN ALPS, NEW ZEALAND

William B. Bull, Geosciences Department, University of Arizona, Tucson, AZ, 58721 Mark T. Brandon, Department of Geology and Geophysics, Yale University, New Haven, CT, 06520-8109

ABSTRACT with diverse climate, altitude, and (Worsely, 1981), which restricts comparison substrate lithology. A regionally con- of results by different workers. In part, the Synchronous regional rockfall sistent lichen growth rate allows use lack of a standard approach has resulted events triggered by large earth- of a single growth-rate equation for from diverse study areas, each of which had quakes in the Southern Alps of New most species of Rhizocarpon subgenus a different purpose, sampling strategy, and Zealand were used to evaluate and Rhizocarpon on the South Island of assumptions. Locke et al. (1979) attribute improve the lichenometry method New Zealand. A nonlinear growth the lack of a universal method to the founder for surface-exposure dating. Digital equation suggests that the first colo- of lichenometry, Beschel (1950, 1957, 1959, calipers were used to measure the nization, on average, occurs in the 5th 1961, 1963), who emphasized only general maximum diameter of the largest li- yr after formation of new rock sur- guidelines instead of a preferred method. chen on many rockfall blocks, using faces (~0.5 m2 unit areas) and is fol- Most workers continue to estimate ages for geomorphic events, such as floods, glacier a fixed-area largest-lichen (FALL) lowed by rapid, exponentially declin- advances, and landslides, based on the single sampling strategy. Regional signifi- ing growth for about 20 yr (great- largest lichen or mean of five largest lichens cance of FALL peaks can be tested growth phase) that is largely com- for the entire deposit. Examples include by confirming the occurrence of a pleted by the 24th yr. Then, linear worthy papers by Matthews (1974), Locke coeval peak at multiple sites, and by growth persists at about 15 mm per et al. (1979), Birkeland (1981), Porter showing an increase in peak size to- century (uniform-growth phase). (1981), Rapp (1981), and Innes (1984, ward the earthquake epicenter. Sig- 1985a). nificance of FALL peaks at a local INTRODUCTION Some recent studies have departed from the site can be described in terms of peak conventional approach by sampling popula- size relative to a uniform density of Lichens can be used to estimate the ages tions of largest lichens on many blocks de- FALL sizes. of surfaces of young rocky deposits or the posited by rockfalls, snow avalanches, glaciers, Measurements of 34000 FALL times of recent exposure of outcrops. Lichen and debris flows (Bull, 1991a, 1994; Matthews sizes on fully exposed rockfall blocks sizes record both the initial time of expo- and McCarroll, 1994; McCarroll, 1993, 1994; and outcrop joint faces at 90 sites al- sure of the rock substrate upon which they Luckman and Fiske, 1995). Bull concentrated low precise dating of geomorphic grow, and subsequent disturbances to on dating of earthquake-generated (coseismic) events of the past 300 to 500 yr. Un- surficial boulders or joint blocks that expose rockfall events in California and New Zealand certainties at the 95% confidence in- fresh substrates for colonization by younger (Bull et al., 1994; Bull, 1996a, 1996b). His terval can be reduced to a level bet- lichens. The ability to record postformation new field and analytical procedures for disturbances also applies to other surface- ter than ±10 yr for ages within the lichenometry were developed in a variety of exposure dating methods, such as weather- geomorphic settings, and have been used to calibrated time range represented by ing rinds and cosmogenic isotopes. the lichen growth equation. Recog- study slush avalanches in northern Sweden Lichenometry directly dates times of spe- (Bull et al., 1995), which has virtually no earth- nition of prehistorical regional rock- cific events, such as earthquakes, by deter- fall events in 1833, 1836, and 1840 quakes. This paper expands on the lessons mining the time of earthquake-generated learned from Bull’s diverse studies to describe demonstrates the excellent resolution landslides. In contrast, radiocarbon strati- a new approach to lichenometry. of this dating method. Precise dates graphic dating estimates the time that or- We seek to advance lichenometry by em- result from exceptionally low mea- ganic matter grew. Deposition of organic phasizing the benefits of large sample sizes. surement errors of lichen sizes rela- matter in fluvial, colluvial, or swamp depos- Digital calipers were used to measure the tive to their growth rate, tightly clus- its at paleoseismic sites is not directly tied maximum diameter of the largest lichen on tered FALL sizes for earthquake-in- to specific earthquake events, because dat- many rockfall blocks in the Southern Alps, duced rockfall events, and substrate able organic matter is created before or af- where outcrops and hillslopes are disrupted exposure times for calibration sites ter seismic disruption of the stratigraphic by large earthquakes. About 34000 lichen- that are known to the year or day. section. size measurements were made at 90 sites in FALL peaks for synchronous rock- Lichenometry dates geomorphic events, the South Island of New Zealand (Fig. 1). fall events are the same for 20 sites and like radiocarbon dating of stratigraphic Measurements were made from 1989 to events, it is in its fifth decade of develop- 1997 and, where necessary, are normalized ment. However, lichenometry continues to *e-mail: [email protected] to 1992 as a reference year. We use the syn- be hindered by a paucity of widely accepted chronous nature of rockfalls throughout [email protected] measurement and analytical procedures much of our 40000 km2 study region to pro- GSA Bulletin; January, 1998; v. 110; no. 1; p. 60-84; 23 figures; 5 tables. 60 Geological Society of America60 Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

cesses loosen blocks that tumble downhill 168° E 172° E during times of seismic shaking. Each rock- N 0 100 200 Km NE fall block may have a different history of detachment from an outcrop, episodic travel WW 1 lichenometry site downhill, local microclimates, and coloni- 5 to 10 lichenometry sites zation by primitive plants. MB ° MU 42 S AR IN NM Regional Rockfall Events TN 2 CG,SK,WA Earthquake-induced landslides are wide- CH spread and common in many alpine moun- MO 1 FH tains. Earthquakes with Mw magnitudes Alpine fault CB AC NB greater than 7 can trigger rockfalls at distances CL of up to 400 km from their epicenters (Keefer, Mt. Cook 1984, 1994; Wieczorek et al., 1992; Wieczorek 44° S and Jäger, 1996). Mw refers to the seismic- moment magnitude scale as defined by Hanks Milford Sound 3 OH and Kanamori (1979). A coseismic landslide is a mass wasting event triggered by, and therefore occurring during or shortly after an earth- Figure 1. Map of the South Island of New Zealand showing the Alpine fault quake. Lichens have been used to date system, and locations of lichenometry sites and historical earthquakes (Table rockfalls (Porter and Orombelli, 1981) and 2). Faults are shown by black lines (Officers of the New Zealand Geological coseismic landslides (Smirnova and Nikonov, Survey, 1983; Van Dissen and Yeats, 1991). Approximate locations of earth- 1990). A coseismic rockfall event is distinc- quake epicenters are AR, Acheron River; CH, Cheviot; IN, Inangahua; MA, tive. It occurs at many sites throughout a re- Marlborough; MO, Motunau; MU, Murchison; NB, New Brighton; NE, gion (Fig. 3), and rockfall abundance increases Nelson; SK, Seaward Kaikoura; TN, Tennyson, and WA, Waiau. The 1855 toward the earthquake epicenter. Coseismic West Wairarapa earthquake, WW, occurred in the southern part of the North rockfall events can be dated by measuring sizes Island. Locations of lichenometry sites are underscored: AC, Acheron rock of lichens with systematic growth rates that avalanche; CB, Craigieburn rock avalanche; CG, Cattle Gully; CL, Clyde colonize the newly exposed rock surfaces (Bull rock avalanche; NM, No Man’s Creek; and OH, Ohau. Circled 1 indicates the et al., 1994; Bull, 1996a, 1996b). general locations of the Arthur’s Pass, Lake Coleridge, and Bealey earth- Moderate earthquakes (Mw = 5.5 to 7), quakes, Falling Mountain rock avalanche, and the Otira Valley, Rough Creek, such as the Mw 6.1 Tennyson earthquake of and Zig Zag sites. Circled 2 includes the North Canterbury and Hossack 1990 in our study area, are accompanied by earthquakes, Raupo Swamp, and the Hope River Bridge landslide. Circled 3 clouds of dust caused by abundant rockfalls includes the Mueller and Tasman glaciers, and the Celmisia and Idyllic sites. near their epicenters. Newly arrived blocks in rockfall deposits are distinctive because vide new insights about factors influencing COSEISMIC ROCKFALL their freshly exposed surfaces have no li- the precision, accuracy, and resolution of LICHENOMETRY MODEL lichenometry as a surface-exposure dating chens. Fresh rockfall blocks are common only within 15 km of the 1990 earthquake method. Synchronous rockfall events at sites New Zealand is well suited for develop- epicenter. with different altitudes, substrate lithologies, ment and testing of the coseismic rockfall Coseismic events dominate the rockfall and climatic settings allowed us to determine lichenometry model. Large earthquakes ca- process in much of the Southern Alps. Many whether or not calibration of lichen growth pable of causing regionally extensive sites where the largest lichen on each block rates based on lichen-size measurements at rockfalls have occurred throughout the is at least 8 mm (Fig. 4) are indicative of a few control sites is valid on a regional Southern Alps. Most earthquakes are widely rockfall deposits that have not received an scale. Our scope also includes the impor- spaced in time relative to the moderately increment of new blocks since the Inangahua tance of site selection, identification of sig- rapid growth of the lichens used in this study, Mw 7.1 earthquake of 1968 (Downs, 1995). nificant peaks in probability-density distri- Rhizocarpon subgenus Rhizocarpon (collec- Hillslope processes are so active in the butions of lichen sizes, calibration of dis- tively referred to as yellow rhizocarpons). Southern Alps that many lichenometry sites tinctive phases of lichen growth, and appli- Unstable outcrops of fractured graywacke only record rockfalls of the past 500 yr (~85 cations of the coseismic rockfall model. sandstone on rugged mountainsides ensure mm); 1000-yr-old rockfall blocks (~165 Discussion follows the flow chart of Figure an ample supply of blocks for talus and de- mm) are rare. The time span of rockfall 2. Event ages are purposely stated in terms bris slopes. Steep hillsides underlain by events that can be dated using lichenometry of lichen size, because age estimates may hard, brittle graywacke typically fail by is influenced by the frequency of rework- change with improvements of the lichen- rockfall and rock-avalanche processes ing of the rockfall deposit. Some blocks are growth equation. We conclude that this ver- (Whitehouse, 1983). Fresh substrates for broken or partially covered by incoming new satile approach to lichenometry can produce new lichens—outcrop joint faces as well as blocks, and fresh substrates are colonized precise age estimates for geomorphic events rockfall blocks—may be created by rain- by new lichens when blocks are overturned in many mountainous regions. storms, freezing of water along joints and or when adjacent soil or rock detritus moves fractures, passage of animals, avalanches, downhill. Additions and redistributions con- and wedging by roots and soil. These pro- tinue until few old blocks remain, their larg-

61 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

Measure and analyse FALL sizes

Select sites and lichens Measure FALL sizes on multiple-event (polymodal) rockfall deposits at many widely spaced sites to see if regional rockfall events are present

Make probability density plots of FALL sizes Identify and classify significant FALL peaks Describe mean size and amplitude of FALL peaks Evaluate factors affecting lichen growth

Calibrate lichen growth rates

Measure many FALL sizes on single-event (unimodal) Determine ages of FALL peaks that record historical landslide and flood deposits, and on cultural features earthquake-generated regional rockfall events Historical events Make seismic-shaking Tree-ring dated events Measure FALL sizes at rockfall 14 sites near earthquake epicenters maps based on FALL Precision C age estimates of surface exposure ages peak amplitudes

Colonization time Duration and rate of great growth Rate of uniform phase growth

Validate coseismic rockfall model

Compare lichenometry and Make new calibration Compare tree-ring and seismic stratigraphy radiocarbon based on radiocarbon lichenometry dates for earthquake ages dated landslides landslides

Apply coseismic rockfall model

Prehistorical earthquakes Geomorphic processes Dating Surface-exposure dating Locating Areal extent of an event Seismic shaking maps

Figure 2. Flow chart showing the method, validation, and applications of the coseismic rockfall lichenometry model. The acronym FALL stands for “fixed-area largest-lichen” and indicates measurement of the size of the largest lichen within a fixed sampling area.

Figure 3. Probability density plots for 8 FALL sizes for Rhizocarpon section A Superficiale growing on rockfall blocks derived from late Holocene glacial moraines 4 near Mt. Cook. Vertical lines denote FALL peaks for regional rockfall events that 0 occurred at both sites. The 108, 115, and 4 135 mm rockfall events at the Celmisia site B occur at other sites in the study region. The 125 mm regional rockfall event typically is 2 strong in a 400 km long area east of the crest of the Southern Alps (Bull, 1996a). Probability density (%/mm) 0 Density plots were constructed using a Gaussian kernel size of 0.5 mm. A. The 100 110 120 130 140 150 Idyllic site is on a moraine of the Mueller Largest lichen maximum diameter (mm) Glacier. n = 45. B. The Celmisia site is on a moraine of the Tasman Glacier. n = 48.

62 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

Figure 4. Accumula- tion of rockfall blocks on a stream terrace at the No Man’s Creek site. FALL sizes range from 8 to 104 mm. Person is standing by a light-toned block with 8 mm lichens that dates to 1968. Impact marks leading to the 1968 blocks are still present on the hillslope above the rockfall deposit.

est lichens documenting only the largest of FALL measurements are best displayed measured because growth of their longest the old rockfall events. using a probability density plot (e.g., Fig. axis was constrained by adjacent yellow 3). The prominent peaks in the FALL distri- rhizocarpons. Isolated lichens are less com- FALL Method bution are viewed as a record of short-lived mon on old blocks, so our FALL distribu- events that caused reworking of parts of the tions undersample old thalli. Burial of old Landslide, stream, shoreline, and glacial deposit. Probability density is everywhere blocks by younger blocks also reduces op- and periglacial deposits commonly have normalized to the same units, percent per portunities to measure lichens associated enough cobble- and boulder-size blocks to millimeter, to facilitate comparisons be- with old rockfall events. allow a sampling strategy that we refer to tween density plots. The FALL method also works well for li- as the fixed-area largest-lichen (FALL) The ideal lichenometry sampling strategy chens growing on joint faces of outcrops method. FALL size is defined as the maxi- should attempt to minimize inherent mea- from which the rockfall blocks are derived. mum diameter of the largest thallus, black surement variability by considering sample Typical joint faces in fractured graywacke prothallus rim included, found in a unit area (Innes, 1984, 1985a; Spence and are 0.03 to 0.2 m2, which are smaller in area sample area. The contrast between the con- Mahaney, 1988) and density of lichen thalli. than most blocks in our rockfall deposits. ventional and FALL methods for The ideal data set would result from a sam- lichenometry can be illustrated by consid- pling strategy that measured the largest iso- Site Selection ering a population of lichens growing on a lated lichen in a number of fixed-size sam- recently exposed, glacially polished rock pling areas where conditions for coloniza- Selection of lichenometry sites has a cru- surface. The conventional method would tion and growth were identical but the areas cial influence on precision of age estimates use the largest lichen, or mean of five larg- were otherwise independent of each other. and resolution of closely spaced events. Fac- est lichens measured in a 1 hr search. The Our lichenometry sites depart from this tors to consider in site selection include diver- FALL method would measure the longest ideal strategy, because our unit sampling sity and frequency of geomorphic processes, axis of the largest lichen in each of 100, or area was allowed to vary as a function of lichen species and abundance, quality of thalli, more, sample areas of about the same size block size. Block diameters are generally in substrate smoothness, sizes of rockfall blocks, (for example, 1 m2). The FALL method av- the range of 0.2 to 1 m, and the viable sur- and ability to recognize old, stabilized block erages out the effects of locally variable face area for lichen growth ranges from 0.04 fields where lichen communities are not re- colonization times and growth rates, taxo- to 1 m2. For cool, humid New Zealand, yel- lated to the times of substrate exposure be- nomic misidentification, inherited lichens low rhizocarpons prefer the top and north cause the first generation of lichens has died that predate the surface we seek to date, sides of blocks, which are relatively sunny and has been replaced. and lichens that have merged to form com- and dry. We tried to confine our measure- Diverse landforms may generate, or inter- posite thalli. Note that we use an informal ments to these exposed surfaces to reduce cept and store rockfall blocks. Examples in- terminology, referring to FALL distribu- variations in colonization time and growth clude hillslope benches and concave tions and FALL peaks to avoid more cum- rates. footslopes, ridgecrest saddles, stream terraces, bersome terms such as FALL-size distri- Mosaics of intergrown lichens are rare at alluvial fans, and glacial moraines. bution and FALL-size peak. our sites, but some largest lichens were not Paleoseismologists generally seek rockfall sites

63 Geological Society of America Bulletin, January 1998 BULL AND BRANDON that are sensitive to seismic shaking, such as Fractured outcrop. classes of thallus quality identifies the lower steep hillsides, bouldery glacial moraines, and Fractured outcrop with prominent joint sets limit of acceptable lichen-size measurements rock avalanches with minimal fine sediment. that are vertical and parallel to the hillside. and is a numerical way of identifying sites Seismic shaking is more likely to affect a young Fractured outcrop with multiple joint sets with favorable lichen characteristics. Quality unstable deposit than an older more stable de- undercut by fluvial, glacial, or shoreline erosion. 3 is average, 1 is exceptionally nice, and 4 is posit. Fractured surficial blocks on the distal ridge barely good enough to include in a data set. Rockfall deposits accumulate incremen- of a rock-avalanche deposit. The thallus quality number was appended to tally during times of seismic shaking and Steep-sided young glacial moraine. each measurement. For example, the 2 in storms, or as random rockfall events. Blocks Riser of stream terrace in sandy gravel. 35.672 records an above average quality for detached from outcrops are spread across the Top of talus cone at the angle of repose. a lichen whose digital caliper size was 35.67 surface of talus or debris slopes. Rockfall Block size influences survival of lichens. mm. Noncircular habit, irregular margins, blocks derived from part of a cliff disperse as Tops of large blocks are more fully exposed to slight fuzziness of the prothallus rim at the blocks strike each other, lower outcrops, and sunlight and less affected by fire. Large blocks measuring points, or a nonplanar substrate talus-, debris-, or snow-covered slopes. Rapp are less likely to be buried or overturned but result in a lower quality rating. Thallus-qual- (1960, Fig. 11) documented the routes trav- are more likely to be struck by subsequent ity rating is raised by 1 when several of the eled by 34 disk-shaped rockfall blocks of mica rockfalls. But working on blocks larger than 3 largest lichens on a block are about the same schist at Kärkevagge in northern Sweden. m is time consuming and can be hazardous. size. Thallus quality in our study area is fairly They dispersed into a 170-m-wide swath True linear distances are preferred for li- typical of yellow rhizocarpons, being mainly while traveling 150 to 400 m horizontally and chen-size measurements. Substrates with class 3 with common class 4 and class 2 li- 120 to 220 m vertically. The end product of smooth planar joints, such as quartzitic sand- chens; class 1 is rare. We have noted that the repeated outcrop collapse is a highly stone and fine-grained plutonic rocks, provide widths of FALL peaks increases with decreas- diachronous block field, where overall ages reliable digital- caliper measurements. Ap- ing lichen quality. All four classes of lichen and sizes of rockfall blocks increase proximate sizes of lichens growing on highly quality were included in the data sets, because downslope (Whitehouse et al., 1983). curved river or beach cobbles can be estimated our perception is that peak means are not af- The dominant geomorphic process partly with a flexible ruler. Lichens growing on rough fected by lichen quality even though variance determines the usefulness of lichenometry rock surfaces, such as highly fractured argilla- of the measurements is. sites in alpine mountains. Debris and talus ceous sandstone or porphyritic plutonic rocks A few blocks on glacial moraines, land- cones below chutes and ravines generally may yield unreliable measurements. The best slides, and debris-flows may be derived from should be avoided, unless one wants to study measurements are made on lichens growing sources whose lichens predate the deposit frequency of snow avalanches and debris on smooth surfaces. Rough surfaces or lichens being dated. Identification of these inherited flows triggered mainly by nonseismic events. growing across steps greater than 1 mm should lichens commonly is subjective. The objec- Planar sheets of talus whose blocks are de- be avoided. tive approach used here is to measure all ap- rived from the triangular facets between The ideal coseismic rockfall lichenometry propriate largest lichens, including those that chutes or stream channels may contain a more site is sensitive to both nearby and distant may appear anomalously large or small. We reliable paleoseismic signal because rockfalls earthquakes. Such a site would have: assume that inherited lichens are rare and that may be the dominant process. Moraines gen- Unstable cliffs of fine-grained, strongly they will tend to be incorporated into the high- erally lack the height needed to be a source jointed rock. side tail of the FALL distribution. They should of avalanches, and rainstorm-induced land- Pervasive joints that parallel the cliff face. not significantly affect the means of FALL slides are not likely to occur in moraines con- Abundant blocks with smooth planar sur- peaks. These assumptions can be validated by sisting of permeable gravel. faces. comparing FALL peaks at several sites. Old stabilized block fields, on which sev- A limited size range for most blocks (such Several assumptions pertain to our mea- eral generations of lichens have grown and as 0.5 to 2 m). surements of FALL sizes: The largest lichen died, generally have minimal geochronologic A large repository of blocks close to the on the block was the first to colonize the rock- information. Such blocks may have weath- angle of repose. fall block. Lichen growth has been uncon- ered surfaces or may be largely buried by fine Extensive, thick deposits of blocks devoid strained. The rate of growth is similar to the detritus. Such sites typically have slopes that of plants, which might shade lichens or pro- average for yellow rhizocarpons. are much less than the angle of repose for ta- vide fuel for fires. Important subjective decisions include: lus. Nearly circular, isolated lichens are sug- A local microclimate that favors the species 1. Is the lichen a single thallus or a com- gestive of a first-generation lichen commu- of lichen being measured and that lacks per- posite? This crucial evaluation is easy for a nity. Blocks whose oldest lichens colonized sistent snow cover, which can kill lichens. thallus with concentric rings of areoles, or long after the time of initial substrate forma- where black prothallus rims indicate obvious tion typically have large thalli with highly ir- Lichen Selection and Quality merging of thalli. All gradations exist, so the regular margins, or the lichens may have composite nature of other thalli may go un- grown together to form a mosaic of thalli Slow-growing lichens are preferred for dat- recognized. margins. Block fields that accumulate slowly ing old geomorphic events, whereas fast-grow- 2. Are the margins, long axis, and degree may have a mixture of datable and undatable ing lichens are useful for precise dating of of circularity of the thallus of sufficient qual- blocks, and should be avoided. young, closely spaced events. Rhizocarpon ity to warrant inclusion in the data set? Paleoseismologists may select sites with dif- subgenus Rhizocarpon are the slowest grow- 3. Is the substrate sufficiently smooth and ferent sensitivities to seismic shaking in order ing New Zealand lichens. The moderately slow planar to permit a precise measurement? to identify the fault responsible for a prehistorical growing Rhizocarpon candidum is a white li- Large sample sizes reduce the significance earthquake (Bull, 1997). Potential sites, listed chen with excellent quality thalli (Burrows et of these assumptions and decisions for any in order of increasing sensitivity to seismic shak- al., 1990). single thallus. We prefer samples of at least ing, are: A quality assessment was made with each 50 measurements per rockfall deposit. Massive outcrop with few visible joints. lichen-size measurement. Assigning general 64 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

Digital Caliper Measurements observer’s inability to repeatedly place the mean and a standard deviation of 0.66 mm. caliper blades at exactly the same endpoints. From this, we can estimate the standard de- Some previous studies used dial calipers In Test D of Table 1, fastidious cleaning and viation of a single measurement, 0.47 mm (Matthews, 1974; Innes, 1985a, Bickerton and light lubrication of the caliper and having (0.66 mm × 2–0.5), given that replicate mea- Matthews, 1992), and Innes (1986) noted that one’s hands comfortably braced decreased surements have the same expected value and calipers increase the precision of measure- the variation of sizes from 0.26 mm to 0.17 standard deviation but are otherwise inde- ments made by different observers. Most mm and the standard deviation from 0.06 to pendent. This single-measurement standard lichenometrists use flexible plastic rulers and 0.04 mm. deviation represents the variation due to templates to measure lichens (Locke et al., It would be useful to know whether, after measurement errors alone. Errors increase 1979; Innes, 1985a; Winchester and Harrison, an absence, an observer selects the same li- slightly when a different observer makes the 1994). Assuming a ±1 mm reading, ruler mea- chen on a rockfall block and the same long second measurement. surements degrade lichen-size measurements axis. Figure 5 shows the results of an ex- Our conclusion is that digital calipers can and the lichenometry age estimates, especially periment where replicate FALL measure- reduce measurement errors to an insignificant for slow-growing lichens. Digital calipers are ments were made on marked blocks at sev- level, especially in the context of normal li- clearly preferred for both precision and ease eral sites, with the pair of observations sepa- chen growth. New Zealand yellow of use. They also help reduce unintentional rated by an interval of 1 to 104 days. Mea- rhizocarpons have a growth rate of 1 mm ev- measurement bias. An observer making ruler surement errors show no obvious correla- ery 6 yr during the uniform-growth phase. The measurements is aware of the reading while tion with lichen size. The distribution of measurement-related standard deviation of placing the ruler on the lichen, and must round paired differences is Gaussian and has a zero 0.47 mm is equivalent to a variation of 2.8 yr. to the nearest millimeter. An observer making digital- caliper measurements is not aware of the lichen size until she or he looks at the read- TABLE 1. REPLICATION MEASUREMENTS MADE WITH TWO DIGITAL out. Evaluation of lichen quality continues dur- CALIPERS ON DRY AND WET YELLOW RHIZOCARPONS ing the process of carefully positioning the cali- Test Count Minimum Maximum Mean Standard Standard per blades at the endpoints of the longest axis. size size size deviation error There is no need to look at the digital readout (mm) (mm) (mm) if one sees a fuzzy margin at either endpoint selected for measurement, or if at the last mo- A* 107 9.18 9.44 9.28 0.06 0.01 † ment the observer recognizes coalescence of B 53 9.18 9.38 9.28 0.05 0.01 C§ 59 9.17 9.44 9.28 0.06 0.01 thalli. Bias is also reduced by assigning the # lichen-quality number before looking at the D 252 36.47 36.64 36.56 0.04 0.002 readout, and by never deleting a measurement *Caliper 7123707, dry lichen, minimal operator experience. after looking at the readout of lichen size. Data †Caliper 7123844, on test A dry lichen. loggers further reduce potential for bias, be- §Caliper 7123844, on test A lichen after wetting. cause the observer need not know any of the #Caliper 7123707, dry lichen, experienced operator. lichen sizes until the data set is downloaded into a computer. Determining the largest of several lichens 160 on a block is simple with digital calipers. After measurement of the apparent largest lichen, the caliper blades are placed on the 140 longest axes of other possible largest lichens. 3 σ residuals It is easy to recognize both the largest li- 120 lines chen among several of about the same size and the longest axis of the lichen to be mea- 100 sured. Precision and Replication. Reproduc- 80 ibility of measurements is influenced by in- 1:1 equivalence line strumental and observer errors. Replicate 60 measurement pairs are routinely within ±0.20 mm of each other. A made-at-same- time replication error of ±0.20 mm, or bet- 40 ter, is attainable for >95% of the quality 1 Second measurement (mm) or 2 lichens, 80% to 90% of the quality 3 20 lichens, and about 70% of the quality 4 lichens. Multiple measurements of a thallus 0 diameter indicate that operator errors are 0 20 40 60 80 100 120 140 160 very low (Table 1). Standard deviations of First measurement (mm) repeated measurements of a single lichen (about 0.06 mm) are larger than the Figure 5. Comparisons of 243 replicate FALL measurements ranging from manufacturer’s estimates of instrumental er- 2 to 143 mm. Approximately 90% of the replicate measurements were ror (0.01–0.02 mm) and are caused by the within 1 mm of the original, 74% within 0.5 mm, and 48% within 0.25 mm.

65 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

Single-Event and Multiple-Event Data Sets. Historic Sites, Normalized to 100 Yr. Our experience indicates that FALL distributions 6 A for single-event deposits have large standard de- n = 40 viations (e.g., glacier-outburst flood deposit of µ = 22.1 mm Fig. 6C), compared to the narrow peaks that are 4 π = 32% typical of a multiple-event rockfall deposit (Fig. 1 σ 3). Our measurement standard deviation for a 1 = 0.71 mm single lichen measurement is ~0.47 mm. So, the σ = 4.7 mm within-peak variation displayed in the FALL dis- 2 2 tributions (e.g., Fig. 6) must be due to natural stochastic processes related to colonization, growth, interactions with other lichens, and microclimate. 0 Single-event FALL distributions are typi- 14 B 1890 Tasman Glacier Flood cally unimodal with a bell-shaped form. All of 12 the Figure 6 distributions, except for Figure 6A, n = 175 are significantly different from Gaussian as 10 µ = 22.0 mm 2 judged by the χ test (Press et al., 1992, p. 614). π = 64% 8 1 But the F test (Bevington, 1969, p. 200) indi- σ = 3.2 mm cates that the distributions are better fit by two 6 1 σ = 23.3 mm superimposed Gaussian distributions. In other 2 4 words, the tails of each distribution are longer than would be expected for a single Gaussian 2 distribution. Superimposed Gaussians are used to repre- 0 sent distributions where multiple stochastic 25 C 1913 Whitehorse Flood processes introduce distinctly different mag- n = 430 nitudes of variability to a distribution 20 µ = 19.3 mm (Titterington et al., 1985, p. 22). For example, π

Frequency (count/0.5 mm) = 46% variations in colonization time will result in a 15 1 σ Gaussian distribution with a relatively small 1 = 3.8 mm standard deviation, but spatial variations in lo- σ 10 2 = 7.0 mm cal microclimate might introduce relatively large variations in the growth rates of individual 5 lichens. Variations in sample area from block to block add another source of variation to our 0 data. Nonetheless, when analyzing our FALL 12 1940 Flock Hill Wall distributions we assume that individual peaks D can be represented by a single Gaussian. As a 10 n = 108 result, we are ignoring the stochastic processes µ = 14.8 mm responsible for the long tails of the FALL peaks. 8 π 1 = 68% Multiple-event FALL data sets are charac- 6 σ = 2.5 mm terized by overlapping peaks (Figs. 3, 8, 12A, 1 σ = 15.2 mm 13, and 15). Strong peaks are usually readily 4 2 identified, moderate peaks may appear only as shoulders on the stronger peaks, and weak 2 peaks may not be apparent at all. The overall skewed shape of a polymodal 0 FALL distribution provides information about the 0 1020304050 life-expectancy of the entire lichen population. Maximum Lichen Size (mm) For instance, the distribution for the Zig Zag site (Fig. 7) shows that older lichens with sizes of more Figure 6. FALL distributions for single-event deposits. Each distribution is than 40 mm are dying at a fast rate, presumably best represented by two superimposed Gaussians with different standard due to intermittent destruction of old blocks, and deviations (σ1, σ2) and a common mean (µ). The parameter π1 indicates the increasing competition for dwindling growth fraction of the total distribution included in the first Gaussian (µ, σ1). n is space. The oldest lichens, with sizes of about 135 the sample size. mm, are rare and are estimated to be about 800 yr old. A. Individual FALL measurements for historical stone structures of various ages. The FALL sizes were transformed to a single-age population of 100 FALL Peaks years using equation 10. B. 1890 Tasman Glacier outburst flood deposits. n = 175. Identification of Significant Peaks. Detec- C. 1913 Mueller Glacier outburst flood deposits near Whitehorse Hill. FALL tion and resolution of FALL peaks and preci- measurements made by William Phillips and Nancy Sprague. n = 430. sion of lichenometry ages generally improves D. 1940 wall at Flock Hill (Fig. 14). n = 108.

66 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

Given this convention, the ±3 standard error 3 (SE) variation of a uniform distribution should 38 to 48 mm size be confined to densities less than (p + range of Figure 10 uniform 3 SE) = 2puniform. Thus, peaks that rise above the 2p line would have densities sig- 2 uniform nificantly greater than uniform. In this sense, the reference line remains fixed at 2 puniform, independent of n. An increase in n does buy a 1 decrease in δ, which means an increase in resolution. Daily increments of FALL measurements Probability density (%/mm) 0 on rockfalls at the Cattle Gully site (Fig. 8) 0 20 40 60 80 100 120 140 illustrate the trade-off between detection and Largest lichen maximum diameter (mm) resolution. Eight days of work resulted in a total of 1237 FALL measurements. The Figure 7. Polymodal, skewed FALL distribution for yellow number of daily measurements varied con- rhizocarpons on historical (< 30 mm) and prehistorical rockfall blocks siderably: day 1, 191; day 2, 296; day 3, 219; at the Zig-Zag site. Gaussian kernel size is 0.5 mm. n = 1151. day 4, 59; and days 5 through 8, 472 measurements. In Figure 8, the entire data set is with increasing size of the data set. Small Equation 2 also indicates that an increase compared with that for day 2. Although both data sets reveal only the largest peaks. Thus, in n will bring a decrease in RSE[p(D)]. Pre- histograms have the same general shape, the large data sets are required for confident cision and resolution can be improved by full data set (Fig. 8A) provides greater reso- identification of FALL peaks associated with increasing the size of the data set, either by lution. weak or distant earthquakes. Essential sup- measuring more lichens at a site or by com- Another advantage of scaling the class- porting evidence for the coseismic origin of bining data from several sites. We have interval size is that the relative standard er- a FALL peak is the recognition of coeval found it useful to use a normalized measure rors of the probability density estimates are peaks at multiple study sites. Regional-scale of size, which we call the mean data fre- stabilized. This relationship is illustrated in coverage increases the odds of detecting quency, fm = n/R, where R is the range of Figure 9, which compares replicate data sets related peaks at multiple sites. This section FALL sizes in the measured distribution for Cattle Gully. For this diagram, the his- examines resolution for different sample (e.g., Dmax–Dmin). For example, a data set tograms are plotted using points, and each sizes, defines peak significance, and outlines that had 1500 FALL sizes between 0 to 30 –1 point marks the top center of a histogram criteria for weak, moderate, and strong mm would have fm = 50 mm . Our data –1 bar. The thick line shows the histogram for classes of regional rockfall events. sets have fm ranging from 1 to 119 mm . days 1–8, whereas the daily histograms, Consider the general case of a histogram Our strategy for detecting peaks is to which can be viewed as replicate samples, showing n measurements with FALL size use a uniform distribution of FALL sizes are indicated by different point symbols. indicated by D. The class interval for the as a null hypothesis and to determine Equation 5 was used to determine the class δ histogram is and the count for each histo- which parts of the observed distribution interval for each histogram. The thin lines φ gram interval is given by (D). The prob- have densities different from uniform. In show the 2 SE range from equation 2 for ability density is practical terms, this null case can be the combined data (thick line). In almost all viewed as representative of a FALL dis- cases, the replicate data points lie within the φ()D tribution for lichens growing at a constant 2 SE envelope. This result can be explained p()D = . (1) nδ rate on blocks in a deposit fed by continu- by substituting equation 5 into equation 2, ous rockfall events. The assumption of a which gives constant growth rate is applicable for the Based on the usual assumption that uniform phase of lichen growth as defined φ in the following. If the distribution were 1 samples of drawn at D are approximately RSE[]pD()= . Poisson distributed [valid when the expected uniform, then the expected density, 9pD()R (6) distribution of φ(D) > 9; Taylor, 1982, p. 210], then the relative standard error (RSE) p = 1 R = f n. (3) uniform m This relationship shows that the scaling in- for p(D) is approximated by troduced by equation 5 stabilizes the rela- 1 The relative standard error for puniform is tive standard errors for the probability den- RSE[]pD()= 1 φ ()D = . pD()nδ (2) sities estimated by the histogram method so that they are independent of n. Using this = δ = ( δ) procedure, an increase in n will improve the Equation 2 shows the trade-off for a given RSE[] puniform R n 1 fm . (4) resolution between FALL peaks but not the sample size between detection and resolu- precision of the probability density esti- tion. As δ is increased, RSE[p(D)] will de- We adopt the convention of selecting d so mates. crease, and our ability to detect changes in that RSE(p ) is set to 33 percent, Recognition of minor FALL peaks is cru- probability density will improve. However, uniform which gives cial for detecting coseismic rockfalls over a this improvement comes at the expense of a broad area and for constructing peak-size decrease in resolution because of the larger δ R maps. A seemingly minor peak in a FALL dis- . δ = 9 = 9 f . (5) n m

67 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

5 tribution needs to be identified as (1) a regional A All Data For Cattle Gully feature correlative to coeval peaks, both small 4 and large, at other sites; (2) a local feature; or (3) statistical noise. Correlations between sites 3 provide an essential test of our hypothesis that large earthquakes generate synchronous 2 rockfalls at a regional scale. We recommend UD+3SE the following classification for regional stud- 1 UD ies with more than 20 lichenometry sites. FALL peaks are classed as regional if they are found at a minimum of three other sites. Peaks are 0 termed weak if they rise 2 to 3 standard errors Day #2 Data For Cattle Gully 4 B above the puniform line for a particular site or are present at only 20% to 40% of sites; moderate if 3 to 4 standard errors above puniform

3 or present at 40% to 60% of sites; or strong if Probability Density (%/mm) more than 4 standard errors above puniform or 2 UD+3SE present at more than 60% of sites. Probability Density Plots. Probability 1 UD density plots provide another tool for analysis of FALL distributions. These plots are 0 constructed by converting each measurement 0 1020304050 into a unit Gaussian function and averaging the densities of the overlapping Gaussians FALL Size (mm) (Silverman, 1986, p. 15, 45; Brandon, 1996). Figure 8. Comparison of histograms for different portions of the Cattle The result is analogous to a histogram, but Gully data set; 1 to 48 mm size range. Precision (standard error) for the each observation is represented by a unit estimated probability density has been standardized for the two plots, Gaussian instead of an increment of a histogram bar. Histogram class-interval size is using equation 5, by scaling the class interval relative to n. UD = ex- replaced by a Gaussian kernel size, h, which pected density for a uniform distribution. UD + 3 SE = expected upper defines the width of the unit Gaussian used limit for random variations in density associated with a uniform distri- in constructing the plot. The plot is given by bution. 3 SE indicates three standard errors. 1 A. Days 1 through 8, n = 1,237. pD()= nh 2π B. Day 2, n = 296. n  2  1  D − D  (7) Day 1 ∑ exp  −  i   Day 2  2  h   6 i=1   Daily Variations in Measurements Day 3 Day 4 where Di are the FALL measurements with i 5 Days 5-8 = 1 to n, and p(D) is the probability density All data as a function of D for the entire FALL distri- 4 2 SE limits bution. An advantage of the plot is that it provides a smooth and continuous display of the estimated probability density. The Gaussian 3 kernel size h affects the degree of smoothness. Consider a single Gaussian peak with 2 a standard deviation of σ. When viewed in a probability density plot estimated by the Gaussian kernel method, the peak will have

1 an apparent standard deviation, Probability Density (%/mm) 0 w = h2 +σ2 . 0 1020304050Therefore, as h increases, the apparent width FALL Size (mm) of the peak, w, will increase, and adjacent peaks will merge together (See Brandon, 1996, for details).Selection of an optimal kernel size must balance two competing ob- Figure 9. Probability density of 1,237 measurements in the 1 to 48 mm jectives: to resolve closely spaced peaks and FALL-size range at the Cattle Gully site, with two standard error confi- to guard against excessive random variations dence band. Density estimates for daily data based on equation 5 gener- in density (i.e., noise) that might appear as ally occur within the 95% confidence band for the entire data set. real peaks. A practical estimate for the opti-

68 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS mal size of the Gaussian kernel is about 0.6 30 times the standard deviation of the measure- A S ment error (Brandon, 1996). For our case, S this rule of thumb suggests h ≈ 1.5 mm. The 20 M S inference is that when h is set to less than S M M this value, the density plot will contain sig- W M nificant noise. When h is greater than this 10 value, peak resolution will be significantly degraded. The large Zig Zag data set (mean data fre- 0 –1 38 40 42 44 46 48 mm quency, fm = 21 mm ) in Figure 10 illustrates the influence of kernel size on the es- S timated density plot for h = 0.1 to 2.5 mm. 16 B Also labeled are nine regional peaks that S were found at three or more sites in our 12 South Island study area. The density plot S with h = 2.5 mm (Fig. 10D) fails to show 8 any detailed structure because two real peaks have been merged into a single composite 4 peak. The h = 1.0 mm plot (Fig. 10C) shows two strong peaks. The h = 0.5 mm plot (Fig. 0 10B) reveals a third strong peak at 47 mm S and a modest shoulder at 42 mm. The h = C 0.1 mm plot (Fig. 10A) shows all nine re- 12 S gional FALL peaks, but eight low amplitude peaks and three shoulders have also been introduced. The price of the extra resolution 8 is extraneous noise. Additional work may

show that some of the minor peaks belong Probability density (%/mm) 4 in the regional category, or that some repre- sent local events, but we suspect that many are related to noise introduced by a relatively 0 small kernel size. Density plots for this paper were prepared D using kernels with h = 0.1 to 2.0 mm, depend- 8 ing on the size of the data set and the need to generalize or show details. Our experience indicates that h = 0.1 mm works well for data –1 4 sets with fm > 20 mm . Like the histograms, uniform density can be used as a reference for the probability density plots. Equations 3.8 and 3.9 in 0 Silverman (1986) were used to determine 38 40 42 44 46 48 mm the expected mean and standard error for the density estimated by the Gaussian kernel Figure 10. Effects of different kernel sizes (h in equation 7) on resolution and method for a sample drawn from a uniform precision of FALL peaks in density distributions of 211 yellow rhizocarpons distribution. Given the reasonable assump- in the 38 to 48 mm size range at the Zig-Zag site. See Figure 7 for the full tion that R>>h, then the expected value for distribution. Gaussian kernel sizes of 2.5 (D), 1.0 (C), 0.5 (B), and 0.1 (A) puniform is mm result in progressively more detailed probability density plots. Strengths of significant peaks are noted as weak, W, moderate, M, or strong, S. = puniform ~1Rh fm nh (8) limit needed to separate real peaks from sus- mic-shaking event has a size that should with a standard error of pected noise. Once again, we have shown scale approximately with the intensity of that detection of FALL peaks is improved local shaking. Factors that affect coseismic f by increasing n. Conversely, a decrease in h rockfall production include the magnitude, SE()p ≈ 1 = m . (9) uniform nRh2 nh will make it more difficult to separate real distance, and propagation characteristics of peaks from statistical noise. the earthquake, amplification characteristics Mean and Size of FALL Peaks. The of seismic waves in local materials, topo- The upper limit of variation in the density abundance of earthquake-generated graphic focusing of seismic energy, and out- for a uniform distribution would lie at about rockfalls is a function of the intensity, di- crop resistance to seismic shaking. Fractured puniform + 3 SE(puniform). This limit is rection, and duration of seismic shaking. graywacke is the dominant rock type on the viewed as a rough indicator of the detection Thus, a FALL peak resulting from a seis- typically steep slopes of our study area.

69 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

,y , Keefer’s (1994) calculations for Peru indi- TABLE 2. HISTORICAL EARTHQUAKES away). Relative intensities, as represented IN THE NORTHEASTERN PART cate that 99% of the volume of coseismic OF THE SOUTH ISLAND OF NEW ZEALAND by peak sizes, increase toward the earth- landslides is caused by earthquakes larger quake epicenters (Figs. 3 and 11 in Bull et Earthquake Main shock Approximate than Mw 6, and 92% larger than Mw 7. name date magnitude al., 1994). Decomposition of a 20-site re- Approximately 30 significant peaks are (Ms) gional data set yields the same FALL means present in the FALL distribution for the Zig- Arthur’s Pass 1994.46 6.7 for the three regional rockfall events as es- Tennyson 1990.34 6.1 Zag site (Fig. 7). All of these peaks are in- Hossack 1973.31 5.5 timated from the small Rough Creek data ferred to have formed during regional rock- Inangahua 1968.39 7.4 set (Fig. 11). Acheron River 1960.14 5.4 fall events because the peaks for these events Seaward Kaikoura 1955.45 5.1 are present at multiple sites. We interpret the Cheviot 1951.03 5.5 Waiau 1948.39 6.4 peaks to be a record of at least 30 earth- Lake Coleridge 1946.48 6.4 FACTORS AFFECTING LICHEN quakes with Mw > 7 during the past 800 yr. Arthur’s Pass 1929.22 7.1 GROWTH Murchison (Buller) 1929.46 7.8 We employed a commercially available Motunau 1922.98 6.4 computer program (PeakFit by Jandel Sci- Cheviot 1901.89 7 Lichenometric ages commonly are esti- North Canterbury 1888.67 7.1 entific) to estimate the mean, width, and size Hurunui 1881.93 >6.5 mated with minimal knowledge as to how of FALL peaks in the density plots (see Figs. Nelson 1893.12 6.7 lichen growth varies with local microcli- New Brighton 1869.43 5.7 11, 21, and 22). The general problem of fit- Bealey 1866.08 >6.5 mate, altitude, temperature and precipitation, ting Gaussian peaks to density plots is dis- West Wairarapa 1855.06 8.2 duration of snow cover, competition with Marlborough 1848.79 7.4 cussed in Brandon (1992, 1996). The mean Note: Data taken primarily from Eiby (1968), other plants; or with substrate characteris- of the fitted peak is used to estimate the age Cowan (1989), Downs (1995), and Aitken and tics such as smoothness, lithology, and de- Lowry (1995). See Figure 1 for approximate of a rockfall event, whereas the peak size locations of earthquake epicenters. gree of weathering. Intuition leads one to provides an index of the intensity of the expect local variations in growth rates that event at each site. Peak sizes for older events components. The dominant peak has a mean would require a new calibration of lichen are reduced due to reworking by younger of 16.27 ± 0.04 mm (95% confidence level). growth at every study site. Limited knowl- events (Figs. 7 and 12A). This bias can be A linear calibration curve introduced below edge about the factors affecting lichen minimized by normalizing the peak size by indicates that the age estimates for the three growth has also tended to undermine the the number of FALL measurements within peaks are close to the times of historical credibility of lichenometry. We believe it is a larger range around the peak. We use a ±3 earthquakes in 1881, 1929, and 1968 (Table important to determine the extent of the re- mm range in constructing our peak size 2). The largest peak records the 1929 gion for which a particular calibration is maps introduced below. Arthur’s Pass earthquake, with an epicenter valid. We examine here the effects of fire Data from the Rough Creek site (Fig. 11) about 25 km away. The two smaller peaks and prolonged snow cover that can kill many provide an example of decomposition of a appear to record coseismic rockfalls asso- lichens at a site, the growth rates of differ- density plot into component Gaussians. Two ciated with the 1881 Hurunui earthquake ent yellow rhizocarpons, the effects of vari- shoulders suggest a mixed distribution. De- (epicenter 65 km away) and the 1968 able microclimate at one site, and the varia- composition of the plot reveals at least three Inangahua earthquake (epicenter 130 km tion in lichen growth rates at 20 sites with diverse macroclimates.

16.27±0.04 mm Snowkill and Firekill Events 0.08 Lichenometrists making earthquake stud- Gaussian probability ies should be aware that fires and perennial density plot snowfields can kill lichens over a large area. The vulnerability of lichens to persistent 0.04 ± snow cover is an asset for alpine climate 23.16 0.09 mm studies (Benedict, 1990, 1993), but it can Peak mean Peak area be problematic for studies of regional-rock- 8.50±0.39 mm (±2σ) (% of total area) fall events because climate changes can pro- 8.50 ±0.39 mm 9 duce regional changes in the extent of perennial snow cover. Examples of snowkill 8.81 ±0.06 mm 0 events have been recognized in the high re- 10 20 30 16.27 ±0.04 mm 63 gions of the Sierra Nevada of California

Probability density (%/mm) Largest lichen size (mm) (Curry, 1969) and the Rocky Mountains of 16.29 ±0.02 mm Colorado (Benedict, 1990, 1993), at mod- Rough Creek data set n = 28 23.16 ±0.09 mm 28 Regional data set n = 3,404 23.18 ±0.04 mm

Figure 11. Decomposition of probability density plot of FALL sizes on historical coseismic rockfalls at Rough Creek. The density plot shows three peaks with mean sizes that are the same as for three regional rockfall events from the large Figure 15B data set. n = 28. Kernel size is 0.5 mm. Modified from Figure 2 in Bull, et. al, (1994).

70 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

100 erate altitudes in the Cascade volcanoes of Washington A (Porter, 1981) where snowfields can persist for several 80 years, and at low altitudes in the Arctic (Andrews et al, 1976; Williams, 1978; Koerner, 1980). Snowkill is not a 60 problem at our New Zealand sites, which are at altitudes of only 380 to 1620 m, but firekill has occurred at a few sites. 40 Univariate scattergrams provide an easy way to detect the consequences of lichen-kill events. A scattergram is 20 constructed by plotting FALL size as a function of observation number as one makes a sequence of lichen-size 0 measurements while traversing a rockfall deposit. A de- 0 100 200 300 400 500 600 posit that accumulated during frequent events with ap- First Sequence of observations Last proximately uniform dispersal to all parts of the deposit will have a scattergram that shows a similar pattern of FALL density across the entire traverse. For example, the density pattern of Figure 12A is characterized by uni- 200 B formly scattered measurements between 10 and 60 mm and a gradual but systematic decrease in density above 150 60 mm. This decrease is attributed mainly to the removal Snowkill domain of old lichens by death or burial and the introduction of younger blocks with fresh surfaces (also suggested by Fig. 100 7). In contrast, a snowkill or firekill event is revealed by a scattergram that has an abrupt decrease in density with 50 increasing FALL size. The transition marks the time of the lichen-kill event. The FALL distribution of Figure 12B illustrates a

Largest lichen maximum diameter (mm)0 Largest lichen maximum diameter (mm) 0 50 100 150 200 250 300 350 400 450 lichenometry transect on a glacial moraine in the Sierra First Sequence of observations Last Nevada of California that was affected by snowkill during the past 1000 yr. The density of the first 200 FALL 140 sizes decreases gradually to 150 mm, above which lichens are sparse (much like the desirable situation portrayed in 120 C Figure 12A). FALL sizes at observations 200 to 420 in the traverse are much smaller; none are larger than 76 100 mm, and most are smaller than 28 mm. We infer a snowkill ± 80 event immediately prior to 28 mm time (A.D. 1816 10 yr). The high density of FALL sizes between 5 and 28 60 mm suggests that renewed colonization may have been restricted to local areas at first. The moraine may not have 40 been entirely free of persistent snow cover until A.D. 1870 20 to 1915. This 19th century snowkill event is coeval with the Little Ice Age in the Sierra Nevada.

Largest lichen maximum diameter (mm) 0 Our Cattle Gully site shows a good example of a firekill 0 200 400 600 800 1000 1200 event. The scattergram (Fig. 12C) shows two density do- First Sequence of observations Last mains; the transition at 47 mm dates to about A.D. 1700. Pieces of charred, rot-resistant Totara wood on the Cattle Gully hillslopes suggest that fire may have killed many 4 lichens, perhaps when Maoris used fires for clearing travel D routes and flushing game (McGlone, 1979). The density 2 plot (Figure 12D) shows that FALL peaks <47 mm were unaffected by the firekill event. For instance, the 31 mm Probability density (%/mm) 0 0 20 40 60 80 Largest lichen maximum diameter (mm) Figure 12. Evaluation of possible snowkill and firekill at lichenometry sites. (A) Univariate scattergram for traverse observations in the 0 to 100 mm size range at the Zig Zag site, altitude of 950 m. No obvious anomalies suggestive of either snowkill or firekill are present; n = 692. (B) Univariate scattergram of Lecidea atrobrunnea at the Chickenfoot moraine lichenometry site at an altitude of 3540 m in the Sierra Nevada of California. A domain of anomalous FALL density between observations 200 and 420 of the traverse suggests snowkill; n = 481. Tom Moutoux and Bill Phillips helped measure FALL sizes. (C)Univariate scattergram of Rhizocarpon subgenus Rhizocarpon for the Cattle Gully site, altitude of 500 m, reveals two domains of FALL densities above and below the 47 mm line, which dates a firekill event that removed many lichens; n = 1388. (D) Cattle Gully data shown as a density plot. The consequences of the firekill event can be seen as an abrupt transition to lower density of FALL sizes larger than 47 mm. Gaussian kernel size of 0.5 mm; n = 1364.

71 Geological Society of America Bulletin, January 1998 BULL AND BRANDON peak was the result of a large nearby earth- for the Alpicola data set, relative to those valley-floor community are Placopsis quake (Bull, 1997). The FALL distribution for the other yellow rhizocarpons. Studies perrugosa, Rhizocarpon geographicum, shows peaks >47 mm, indicating that some by Innes (1988) in southwest Norway also Parmelia adpicta, Placopsis parellina, lichens survived the firekill event. Peakfitted indicated a relatively longer colonization Teloschistes velifer, Rhizocarpon sp., and means for this part of the distribution can time followed by faster long-term growth Lecidea sp. (Orwin, 1970, 1971). North- be correlated with regional rockfall events, rates for Section Alpicola (1985a, 1985c). west-facing walls get full exposure to after- but the peak sizes have been so corrupted noon sun and to fierce northwest winds that by fire damage that they cannot be used in Microenvironment descend the eastern slopes of the Southern peak-size maps. Alps when storms pass to the south. Influence of local microclimate was as- Sizes of yellow rhizocarpons were mea- Relative Growth Rates of Yellow sessed at a site with extreme contrasts. Ver- sured for each accessible cobble (unit Rhizocarpons tical walls of stream-worn graywacke sample areas were only ~0.01 m2) on the cobbles, held in place by wire mesh, were wall with the greatest microenvironmental Taxa of New Zealand yellow rhizocarpons constructed in 1940 to protect a highway at contrasts (Fig. 14). Lichen cover in 1992 on comprise several sections within the the Flock Hill site. Common lichens in this the exposed north side was less than 40%, Rhizocarpon subgenus Rhizocarpon of the genus Rhizocarpon (Innes, 1985b). Each sec- 12 tion of Rhizocarpon subgenus Rhizocarpon Section Rhizocarpon has many species. Laboratory identification of 8 yellow rhizocarpon species (Benedict, 1988; Poelt, 1988) is time consuming and is not prac- 4 tical when measuring thousands of lichens. Instead, similar-appearing classes of bright 0 greenish yellow lichens were distinguished in 4 Section Superficiale the field employing criteria similar to those used by Winchester (1989) and Werner (1990). Our field-based classifications were based on 2 color, size, density and textural patterns of are- ola; size, morphology, and density of apoth- Probability density (%/mm) ecia (reproductive structures); and width of 0 prothallus rims. Representative samples were 100 110 120 130 stained and studied with a binocular micro- Largest lichen maximum diameter (mm) scope by William Phillips (1993, personal commun.). Most keyed out as Rhizocarpon Figure 13. Comparison of FALL distributions for different large yellow section Rhizocarpon and are presumed to rep- rhizocarpons growing on rockfall blocks derived from late Holocene resent several species. moraines of the Mueller (Idyllic site) and Tasman (Celmisia site) Gla- FALL peaks for different types of lichens were compared to see if there were noticeable ciers near Mt. Cook. Vertical lines denote FALL peaks for regional rock- differences in growth rate. Rhizocarpon sec- fall events that occur at about the same location in the distributions for tion Superficiale is a common lichen of good two different Sections of Rhizocarpon subgenus Rhizocarpon. Gaussian quality found on moraines (Fig. 3) in glacier kernel sizes are 0.5 mm. n = 18 and 74. forelands and on landslide deposits along the east side of the central Southern Alps (Bur- rows et al., 1990; Orwin, 1970). The good 10 match of FALL peaks for Rhizocarpon sec- A. Exposed lichens 8 tion Rhizocarpon with those for Rhizocarpon B. Sheltered lichens section Superficiale (Fig. 13) suggests that visually different yellow rhizocarpons have 6 similar growth rates, with one notable excep- tion. 4 Rhizocarpon section Alpicola was mea- 2 sured only at the Otira Valley site and noted at the Ohau site; both sites are at relatively Probability density (%/mm) 0 high altitudes (1300 m) and have extremely 0 5 10 15 20 25 30 humid climates. Relative to sections Largest lichen maximum diameter (mm) Rhizocarpon and Superficiale, section Alpicola requires triple the colonization time, grows twice as fast during the great- Figure 14. Microenvironmental control of lichen growth rates for yellow growth phase, and has a slightly faster rhizocarpons growing on a wall. Plot A: lichens fully exposed to sunlight (105%) uniform phase growth rate (see the and gale-force winds; n = 108. Plot B: lichens sheltered from wind and discussion of Fig. 18 below). These differ- afternoon sun; n = 178. Mean sizes of decomposed FALL peaks are 14.28 ences are enough to offset the FALL peaks mm for Plot A, and 15.94 mm for plot B. Gaussian kernel size is 2.0 mm.

72 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS and FALL sizes ranged from 4 to 23 mm. range from less than 12 to 15 °C, and mean not correlate with altitude (northern Swe- The cooler, wetter microenvironment of the July temperatures range from much less than den: Denton and Karlen, 1973; Bull et al., sheltered southeast side also supported a few 1 to about 4 °C (New Zealand Meteorologi- 1995. Sierra Nevada of California: Bull et shrubs. Lichen cover was more than 80%, cal Service, 1985). al., 1994). This conclusion does not indicate and FALL sizes ranged from 3 to 29 mm. Precipitation, temperature, snow cover, the absence of a climate effect. More likely, Comparison of the peak means indicates and length of growing season are all factors it means that the within-site variance for about 20% faster growth for the sheltered that might affect lichen growth. All of these yellow rhizocarpon growth rate is signifi- lichens. Wider prothallus rims of lichens factors are strongly correlated with altitude. cantly greater than the between-site variance growing in sheltered microclimatic settings Thus, any relation between local climate and caused by local climates. Note that yellow account for part of the size contrast. Our lichen growth rate should be revealed by rhizocarpons in New Zealand grow one and study supports Benedict’s (1967) conclusion examining lichen data sets collected at dif- one half times as fast as those in the Sierra that shelter from sun and wind promotes ferent altitudes. We combined data sets from Nevada, but only half as fast as those in faster growth of yellow rhizocarpons. 20 lichenometry sites with mean annual pre- Sweden. These intercontinental differences Complications caused by different growth cipitation ranging from less than 500 mm to might be due, at least in part, to genetic dif- rates in sheltered and exposed microenviron- more than 5000 mm and a distribution of ferences that have evolved between these ments were subsequently avoided by measur- altitudes shown in Figure 15A. Regional widely separated rhizocarpon populations. ing only exposed lichens. The various genera variations in lichen growth rate would cause of lichens on the rockfall blocks generally pre- a broadening of the FALL peaks, but this is PHASES OF LICHEN GROWTH fer specific exposure and moisture regimes not apparent for the peaks in Figure 15B. (Jochimsen, 1973). Fortunately, New Zealand Thus we conclude that, with the excep- Lichens pass through three phases of yellow rhizocarpons generally prefer the sun- tion of Section Alpicola, the growth histo- growth—colonization, great growth, and niest, driest parts of rockfall blocks. However, ries and growth rates of many different spe- uniform growth (Beschel, 1961; Innes, outcrops typically are shady and wet compared cies of New Zealand yellow rhizocarpons 1985a). Colonization is defined as the aver- to rockfall blocks. Yellow rhizocarpons are not are remarkably similar, despite marked age amount of time between exposure of the present on many outcrops, and where present, variations in altitude, local climate, and sub- substrate and the appearance of the first li- they are likely to grow in partially sheltered strate lithology. Substrate-exposure ages can chen. Colonization generally entails the de- conditions. The apparently wider range of lo- be estimated accurately using a single livery of spores to the substrate surface, the cal microclimate for exposed yellow growth curve, because the data used to cali- establishment of an initial symbiosis of the rhizocarpons that were measured on outcrops brate the curve are representative of yellow algae and fungi, and the growth of the na- may explain their 2% faster growth rate rela- rhizocarpons of the study region. Other stud- scent lichen to a visible size. Colonization tive to those growing on rockfall blocks (Bull, ies have also concluded that growth rate does time is expected to be a function of the area 1997). 0.3 Substrate Lithology and Altitude A We found yellow rhizocarpons on the fol- 0.2 Figure 15. Probability lowing substrate lithologies: quartzitic density plots for com- graywacke sandstone, argillaceous and tuf- bined data sets of 20 0.1 faceous graywacke sandstone, andesitic basalt, sites in 20,000 km2 of syenite, quartz-biotite schist, and phyllite. the northern part of the Elongate lichens are more common on foli- Probability density (%/ m) 0 South Island of New ated rocks, but peak means are the same as 250 500 750 1000 1250 1500 1750 Zealand underlain by Altitude in meters those at nearby sites with nonfoliated substrate quartzitic greywacke lithologies. Foliated rocks appear to constrain 4 sandstone, syenite, and lichen growth only in the short axis direction. argillaceous greywacke New Zealand yellow rhizocarpons have mini- B sandstone. mal differences in growth rates on noncalcareous substrates. A parallel conclu- 3 A. Site altitude ranges sion was reached by Innes (1985c) in a study from 380 to 1620 m; of lichen sizes on gravestones with diverse Gaussian kernel size is lithologies in Scotland. 20 m. The wide variation of climate present at 2 B. Distribution of the 90 lichenometry sites must be consid- FALL sizes; Gaussian ered in the event that more than one cali- kernel size is 0.5 mm. n bration is required to define growth of 1 = 5,650. Rhizocarpon subgenus Rhizocarpon. Study- Probability density (%/mm) site climate ranges from weakly seasonal humid to extremely humid, and from moderately seasonal mesic to frigid (classifica- 0 tion of climate after Bull, 1991b, Table 2.1). 0 1020304050 Largest lichen maximum diameter (mm) Mean annual precipitation ranges from 700 to 5500 mm, mean January temperatures

73 Geological Society of America Bulletin, January 1998 BULL AND BRANDON available for colonization. A larger surface 30 should have a higher probability for receiv- ing an initial viable spore in a shorter pe- 25 riod of time, assuming that all other factors Figure 16. Best-fit solution for are equal. The strategy of using an approxi- average the four-parameter lichen- mately constant sampling area should help 20 colonization age growth equation for New ensure that the time needed to colonize each Zealand yellow rhizocarpons. block surface is, on average, the same. Yel- 15 linear growth Great-growth phase is below rhizocarpons on 12 year-old New tween the dashed lines. Colo- Zealand substrates were large enough to be

FALL size (mm) 10 nization time is shown by off- classed by Orwin (1970, 1971) as multi-observation dataset set of the great-growth curve Rhizocarpon geographicum or Rhizocarpon single observation dataset from the origin. Superficiale. 5

We introduce here a complete equation that great growth incorporates the three basic phases of lichen 0 growth, 0 25 50 75 100 125 150 Surface Age (yr)  −K()τ −τ  D = D 1 − e 0  + C(τ − τ ), tributions were generated using the dard deviation are equal for this distribution: 0  0 (10) τ µ τ σ τ GASDEV routine of Press et al. 1992. Given 0 = ( c) = ( c). The example in Figure τ this procedure, a single FALL measurement 17A uses 0 = 5.4 yr, which is equal to the where τ is the substrate-exposure age in has unit weight, and multiobservation FALL estimate given in Figure 16. The coloniza- years, and D is the size of the largest lichen peaks are weighted according to their peak tion-time distribution (Figure 17A) can be on that surface in millimeters. The equation size and peak width. The residuals after the transformed into a predicted FALL distri- τ bution at 150 yr (Fig. 17B) using the lichen contains four parameters: 0 is the mean regression indicate that the standard devia- colonization time, K represents the nonlin- tion of a single lichen size measurement in growth curve given by equation 10, assum- ear component of the growth rate during the a FALL peak is σ(D) ~ 2.4 mm. The ob- ing colonization to be the only factor influencing the structure of the peak. The calcu- great-growth phase, D0 is the excess lichen served lichens with known substrate-expo- size produced by great-growth, and C rep- sure ages form a set of lichen sizes, D obs, lated standard deviation for the transformed i σ resents the constant growth rate during the where i = 1,...n, and the corresponding sizes distribution is = 0.9 mm. This example uniform-growth phase. predicted by equation 10 are designated shows that block-to-block variations in colo- Equation 10, as illustrated in the Figure D calc. The best-fit parameters are deter- nization time can cause a maximum varia- i ± 16, provides a complete description of all mined by minimizing Σ(D obs – D calc)2, tion in FALL size of ~ 2.1 mm (equal to i i ± σ phases of growth. Calibration of equation as summarized in Table 4. 3 ) around the FALL mean. This means 10 requires FALL data sets for substrates of The coseismic rockfall model assumes that the colonization process alone produces known ages that cover both the great and that the largest lichen on each rockfall block variations in FALL sizes equal to an appar- ± ± σ uniform phases of growth. The Figure 16 was the first to colonize the fresh substrate. ent age variation of ~ 18 yr (~ 3 ). analysis is based on data sets summarized Thus, it is important to consider the prob- About 20 to 30 yr may be needed for ini- in Table 3 and Figure 6. Historic stone struc- ability distribution of times needed for the tial colonization of all blocks generated by tures, such as tombstones, provide 40 single first lichen to colonize. Colonization can be a given New Zealand rockfall event (Fig. observations (Fig. 6A). Large viewed as a Poisson process if the average 17A). The resulting lichen-size distribution multiobservation data sets include the 1890 rate of colonization is everywhere constant. for rock surfaces younger than 30 yr will Tasman and 1913 Whitehorse glacier out- This assumes that the average flux of spores have a large-side bias because those lichens burst floods and the cobbles in the 1940 across the study area remains constant in that will eventually make up the small-side Flock Hill wall (Figs. 6, B–D). Note that time and space, that all favorable surfaces part of the distribution have yet to become the peak means for the multiobservation data have an equal probability of being colonized, established. A partial solution to this sam- sets show much less scatter than that for the and that the colonization events are inde- pling problem is to use equation 10 to trans- single-observation data because of the re- pendent and randomly distributed across all form all young lichens to a common age duction in variance that comes with averag- favorable surfaces. The distribution of first (Fig. 17A). The transformation equation is, ing the many lichen measurements in each events for a Poisson process is described by the exponential distribution (equivalent to multiobservation data set. D()τ = D()τ + These data collectively define a growth the gamma distribution with α = 0; see r − τ − τ − τ (12) curve for the past 150 yr. The parameters Selby, 1970, p. 572; Press et al., 1992, p. K 0 K − K r + τ − τ D0e ()e e C()r , for equation 10 were estimated using stan- 282), dard methods for nonlinear least-squares estimation (Press et al., 1992). Weighting of 1 −τ τ (τ ) = c 0 the different types of data was accomplished p c τ e , (11) 0 τ by converting each FALL peak calibration where is the known substrate-exposure τ τ point (Table 3) into a Gaussian-distributed age, r is the reference age ( r = 150 yr in τ set of FALL sizes with a mean, standard where p is the probability density as a func- Fig. 17B), D( ) is the measured lichen size, τ τ τ τ deviation, and count equal to the mean, tion of colonization time c, and 0 is the and D ( r) is the predicted size at r. width, and count of the FALL peak. The dis- mean colonization age. The mean and stan-

74 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

TABLE 3. CALIBRATION SITES AND DATA USED TO DEFINE GREAT-GROWTH AND UNIFORM GROWTH PHASES FOR RHIZOCARPON SUBGENUS RHIZOCARPON IN THE STUDY REGION ON THE BASIS OF FALL MEASUREMENTS

Calendric date of Characteristics of lichenometry calibration site FALL Standard Peak width Peak size historical deposit peak mean error of peak (standard (count) (yr, A.D.) lichen size mean (mm) deviation, (mm) mm) 1983.21 Boulder bar deposited at the mouth of the Charwell River gorge during rainy El Niño year. 6.149 0.3140 1.88 36 Measured in 1997.38. 1982.90 Construction of road on Puhi Peaks farm exposes fractured graywacke. Measured in 6.751 0.2566 1.41 30 1997.41. 1981 Construction of infiltration gallery leaves cobble piles on the floodplain of Charwell River. 7.619 0.4955 2.10 18 Measured in 1997.38. 1975.20 Cobble and boulder bar deposited at the mouth of the Charwell River gorge at time of 9.011 0.3660 2.23 37 Cyclone Alison flood. Measured in 1997.38. 1969.61 Boulders removed from field on terrace of the Charwell River. Measured in 1997.38. 10.24 0.2763 2.01 53 1957 Boulder and cobble bar deposited at the mouth of the Charwell River gorge. Measured in 12.85 0.3130 2.75 77 1997.38. 1955.45 Mass movement deposits near earthquake epicenter. Not witnessed, but local residents 11.51 0.1230 0.615 25 described coseismic landslides. Age of earthquake known to the day. Measured in 1992. 1940.5 Wall near Flock Hill studied by Orwin (1970, 1971). Age estimate is time of construction 14.28 0.1803 1.42 62 date for this flood protection wall (±0.5 yr). Measured in 1992. 1929.46 Mass movement deposits near earthquake epicenter. Not witnessed, but photographs were 16.27 0.0408 0.809 393 taken after the earthquake of the Rough Creek landslides and the 60 × 106 m3 Falling Mountain rock avalanche. Date of Arthur’s Pass earthquake was 1929.22, but 1929.46 date of much larger Murchison earthquake is used in the calibration. Measured in 1992. 1913.25 Outburst flood deposit of the Mueller Glacier. Eye witnesses date destruction by this flood 17.92 0.2051 4.02 384 to the day. Measured in 1992. 1890 Outburst flood deposit of the Tasman Glacier. Not witnessed, but guides use the vegetation- 22.61 0.1626 0.920 32 free flood deposit as a new access route to the glacier. Age estimate is ±0.5 yr. Measured in 1992. 1881.93 Mass movement deposits near earthquake epicenter. Other control points used for an 23.16 0.1205 2.07 295 assumed age, which then was verified by a rockfall-abundance map that shows that greatest seismic shaking occurred near the epicenter of the earthquake, whose age is known to the day. Measured in 1992. 1855.06 Mean lichen size from 20-site regional data set (n = 3866). Other control points used for 27.38 0.0953 0.286 9 an assumed age, which then was verified by a rockfall abundance map that shows that greatest seismic shaking occurred near the epicenter of the earthquake, whose age is known to the day. Measured in 1992. 1848.79 Same as for the 27.38 mm FALL peak. 28.47 0.0696 0.400 33 Note:N PeakPk means, standard ddidhdifd errors, widths, and sizes are from decomposed ddilThddfhkiidhkidhdiid density plots. The standard error for the peak mean is estimated as the peak width divided by the square root of the peak size. It approximates the uncertainty in the peak mean that would be observed in analysis of many replicate FALL distributions.

TABLE 4. CALIBRATION OF LICHEN GROWTH EQUATIONS

Description AB (= –C) το Do K (mm) (mm/yr) (yr) (mm) (yr–1) Four parameter equation using data in Table 3, and 310.183 –0.1525 5.43 7.22 0.1219 40 single observation data; 54 calibration points, (±0.0030) (±2.2) (±0.33) (±0.0353) 1524 lichens, σ(D) ≈ 2.4 mm. Two parameter equation using sites older than 1956 307.289 –0.1510 N.A. N.A. N.A. in Table 3; 8 calibration points, 1233 lichens, σ(D) (±46.6) (±0.0244) ≈ 2.5 mm. Two parameter equation using sites older than 1956 311.889 –0.1535 N.A. N.A. N.A. in Tables 3 and 4; 19 calibration points, 3438 lichens. Note: Uncertainties given at ±1 standard error. N.A. = not available.

75 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

20 CALIBRATION OF LICHEN GROWTH A Equation 10 uses great-growth and uni- 15 form-growth data sets to estimate four li- Exponential Distribution chen growth parameters. Calibration based τ τ τ τ Figure 17. The distribu- p( c) = (1/ o) exp(- c / o) only on uniform-growth data sets, together 10 τ σ tion for lichen coloniza- with a simplified version of equation 19, o = = 5.4 yr tion time as predicted by uses the widely available linear regression the first arrival times for 5 method a Poisson process.

Probability Density (%/yr) A. Predicted distribution D = A + Bt, (20) 0 for arrival times of the 0 10203040first lichen. where D is the dependent variable and t the Colonization Time (yr) B. Distribution of lichen independent variable. A and B are fit param- sizes after 150 years, as- eters that relate to equations 18 and 19 ac- 140 τ suming that the only cording to A = D0 + C (tp – 0) and B = –C. 120 B variation is in coloniza- Use of equation 20 requires that the peak means are larger than great-growth sizes, 100 Size Distribution at 150 Yr tion time shown in Figure which for New Zealand is D > 9.4 mm. Mean size = 29.5 mm 17A. 80 The markedly different calibration plots SD = 0.9 mm for Rhizocarpon section Alpicola from the 60 Otira Valley site in the Southern Alps, and 40 Lecidea atrobrunnea in the Sierra Nevada 20 of California illustrate how the linear regres-

sion method can be used to evaluate dura- Probability Density (%/mm) 0 tion of lichen colonization time, and mag- 0 5 10 15 20 25 30 35 nitude and rate of great growth (Fig. 18). FALL Size (mm) Projection of the slow linear growth rate line for R. Alpicola intersects the time axis at A.D. Equation 10 can be simplified if lichen For the uniform growth phase, equation 2027. A 1968 control point constrains the growth has reached the uniform-growth 10 simplifies to great-growth segment of the growth curve phase. First, we need to introduce ζ, which and indicates a colonization time of about indicates the degree of completion of the 20 yr (four times longer than other yellow = ( − τ ) + τ great-growth phase as represented by the D D0 C 0 C (16) rhizocarpons). The uniform growth-rate line first term in equation 10, for L. atrobrunnea intersects the time axis at A.D. 1941, indicating a colonization time of >50 yr. The amount of great growth for −K ()τ −τ ζ = − 0 (13)  D    1 e . τ = τ − 0 + 1 L. atrobrunnea apparently is only half of that  0    D. (17)  C   C for R. Alpicola. Field studies of lichens on With infinite time, ζ will approach 1.0 as- young substrates confirm that L. ymptotically, which means that the first term For field applications, we prefer to estimate atrobrunnea has a long colonization time, in equation 10 has gone to 0. Using equa- the time of substrate-exposure in calendar short great-growth phase, and rapid uniform τ ζ tion 13 and solving for as a function of years. The year when the surface of the rock- growth compared to R. Alpicola. gives fall block was first exposed is defined by t Precise calibration of lichen growth is and the year when the lichen was measured possible in the Southern Alps because of (1) digital-caliper lichen-size measurements, (2) ln( 1 − ζ) is defined by tp. Equations 16 and 17 can τζ( ) = τ − τ large data sets, (3) substrate-exposure dates 0 . (14) be converted by substituting tp – t for . K for landslide and flood deposits that are known to the year or day, and (4) minimal   We define great growth to correspond to the D = D + Ct()− τ − Ct between-site variation of lichen growth  0 p 0  (18) amount of time needed to complete 90% of rates. Ideally, all FALL measurements used the excess growth, Do, produced by great in calibration equation 20 should be made growth. Lichen size at the end of great in the same year. FALL sizes measured in growth is different years can be normalized, but only  D   1  t =  0 + ()t − τ  −   D after an initial uniform growth rate has been  C p 0   C (19) estimated. For example, measurements of C ln() 0.1 ζ = − D( = 0.90) 0.9D0 . (15) New Zealand yellow rhizocarpons made 6 K Equation 19 sets the stage for a simple cali- yr apart would require a correction of 0.9 bration procedure. mm (6.0 yr × 0.15 mm/yr = 0.90 mm). For Figure 16, τ (90%) = 24 yr and D(ζ = FALL measurements on deposits of 0.90) = 9.4 mm. At this point, there is only known age provided eight control points to 10% excess growth that will occur, equal to calibrate the uniform phase growth rate for another 0.7 mm increase in lichen size. yellow rhizocarpons (sites with dates older

76 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS than 1956 in Table 3). These include the Flock 50 Hill wall, two glacier-outburst flood deposits, three landslide deposits, and two points where FALL peaks can be correlated to a regional Rhizocarpon rockfall event caused by a known earthquake. 40 One of the landslide sites was at Rough Creek Section Alpicola (Fig. 11) where coseismic rockfalls were pho- D = 321.8-0.159t tographed in 1929. Two 1929 earthquakes oc- 30 R^2 = 0.998 curred only 3 months apart at two widely separated epicenters (Table 2). These were the Arthur’s Pass event: Ms ~7.1, depth <15 km, right-lateral surface displacement; and the 20 Murchison event: Ms ~7.8, depth <20 km, re- verse-oblique surface displacement (Speight, Lecidea atrobrunnea 1933; Dowdrick and Smith, 1990; Cowan, D = 447.6 - 0.231t 1994). 10 R^2 = 0.998

A map of rockfall abundance based on sizes Largest lichen modal size (mm) 1968 of best-fit FALL peaks (Fig. 19) provides additional confirmation for the 1929 date for the 16 0 mm FALL peak at the Rough Creek site. Re- 1700 1740 1780 1820 1860 1900 1940 1980 2020 sponse to seismic shaking associated with the Calendric age, A. D. Arthur’s Pass earthquake appears to have been particularly intense near the epicenter. The Figure 18. Comparison of growth rates for Rhizocarpon section alpicola Murchison earthquake caused more widespread at the Otira Valley site in the Southern Alps of New Zealand, and Lecidea and stronger seismic shaking. The climate is too wet for yellow rhizocarpons near the Murchison atrobrunnea from the Sierra Nevada of California, using linear regres- epicenter, so the peak-size map is incomplete near sion equation 20. Intersection of uniform phase regression lines with the the epicenter. X axis constrains the maximum substrate-exposure date. Patterned lines Peak-size maps were used to confirm assign- show likely great growth curves and substrate-exposure dates. Data sets ments of earthquake dates to specific FALL are normalized to a 1992 measurement year. peaks for two calibration points. Rockfall abundance for the 28.47 mm peak was greatest near the epicenter of the 1848 Marlborough earthquake (Fig. 1, Table 2), but decreased to minimal values 150 km to the southwest. In 168° E 172° E marked contrast, the great 1855 West Wairarapa earthquake (27.38 mm peak) caused 0 100 200 Km N large rockfalls more than 500 km from its epicenter in the southern part of the North Island. The Figure 20A calibration was determined >80% Ms 7.8 by the linear-regression method. Weighting of the data was accomplished in the same way as 42 °S 60 - 80% Ms 7.1 for Figure 16, by generating for each FALL 40 - 60% peak a Gaussian-distributed set of FALL sizes with a mean, standard deviation, and count < 40% equal to the mean, width, and count of the peak. Relative size of The number of calibration points N = 9, whereas the number of data points n = 1524. rockfall event The best-fit equation is

D = 307.289 – 0.1510t, (21) which is relative to an observation year of A.D. 1992. Uniform-phase growth is clearly linear at 15.1 mm per century. Substrates exposed at A.D. 0 would have a FALL mean of 307 mm in A.D. 1992, assuming that the lichens were still alive. (Note that A.D. 0 is not formally recog- Figure 19. Peak-size map for the 16 mm regional rockfall event at 53 nized on the calendar scale, but it would be lichenometry sites showing the combined effects of seismic shaking in- equivalent to 1 B.C. given that this is the calen- duced by the 1929 Ms magnitude 7.1 and 7.8 earthquakes (Table 2). Con- dar year that preceded A.D. 1). The heavy gray tours show the percentage of the 16 mm modeled peak size relative to all curve shows the nonlinear curve of Figure 16 for comparison. FALL sizes between 13 and 19 mm.

77 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

30 200 C A 175 25 150 20 125

15 100

75 Observation Year (1992)

FALL size (mm) 10

50 Observation Year (1992) 5 25

0 0 1840 1880 1920 1960 2000 1000 1200 1400 1600 1800 2000 Calendric age, A.D. Calendric age, A.D.

30 30 B D 20 20 25

100 10 25 10 500 100 500 0 0

500 100 500 -10 25 -10 confidence interval (yr.) 100

95% 25 -20 -20

-30 -30 1400 1500 1600 1700 1800 1900 2000 1000 1200 1400 1600 1800 2000 Calendric age, A.D. Calendric age, A.D.

Figure 20. Calibration results illustrating the importance of data set size and age range in calibrating the lichen growth equation. Data are from Tables 3 and 5 and were restricted to sites older than 1956 to ensure that the calibration was entirely within the uniform-growth phase. Note that the heavy gray line in parts A and C shows, for comparison, the 4-parameter growth curve of Figure 16. A. Calibration using eight historic calibration points spanning 150 years. Regression results were calculated using D as the dependent variable and t as the independent variable. The plot symbols are larger than the two standard error uncertainties for age and FALL size. B. The 95 percent confidence interval for an estimated lichenometry age using the calibration in part A. The contoured values 25, 100, and 500 refer to the number of FALL measurements used to estimate the FALL peak to be dated. C. Calibration using a combined data set of 19 calibration points, both historic and prehistoric, spanning a 1000 years. Regression results were calculated with t as the dependent variable and D as the independent variable. Error bars show the one standard error uncertainties. D. The 95 percent confidence interval for an estimated lichenometry age. The contoured values 25, 100, and 500 refer to the number of FALL measurements used to estimate the FALL peak to be dated.

78 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

Preliminary Long-Term Calibration regional rockfall event. The Table 5 FALL calibration points (Tables 3 and 5) for sites peaks are shown in Figure 7. Radiocarbon older than 1956, define lichen growth as Prehistoric (before A.D. 1840) FALL peaks age estimates of trees buried by the Clyde, that can be correlated with reasonably well- Acheron, and Craigieburn rock avalanches D = 311.889 – 0.1535t. (22) dated paleoseismic events provide useful in- (Burrows, 1975; Whitehouse, 1981; sight in two ways. They can be used to vali- Whitehouse, 1983), together with FALL Equations 21 and 22 are nearly identical, date equation 21, and to illustrate how a measurements on the rock avalanches pro- which indicates that the constant rate asso- change in the range of ages for calibration vide three calibration points. ciated with the uniform-growth phase ap- control points affects the uncertainties of This regression calculation is different pears to extend back for 1000 yr. lichenometry age estimates (Fig. 20B). The from the previous one because the uncer- We have some reservations about the 11 prehistoric calibration points include nine tainties associated with time are greater than long-term calibration because all the age radiocarbon age estimates and two forest those associated with FALL size. As such, estimates for the prehistoric control points disturbance events (Table 5). the regression equation must be recast so that have potential problems. Three of the radio- Cowan and McGlone (1991) concluded t is the dependent variable, and D is the in- carbon ages may be 30 to 100 yr older than that episodes of silt deposition in Raupo dependent variable. Weighting in this case the landslides they date. Except for the swamp (Fig. 1) were related to paleoseismic was done by generating for each FALL peak Acheron sample, chunks of wood, instead disruption of hillslopes that drained into the a bivariant Gaussian-distributed set of FALL of only the outermost tree rings, were dated. swamp. Pollen in the peat above each silt sizes and ages equal in number to the count Dates for the Raupo Swamp silt layers as- layer records a transition from disturbance- of each peak. FALL size was varied to mimic sume that peat-accumulation rates have been type plants, such as the shrub Discaria the mean and width of the associated FALL constant. The forest disturbance events are toumatou, to plants indicative of stable peak. Age was varied according to the means not dated to the year; rimu (Dacrydium hillslopes. Calibrated radiocarbon ages were and uncertainties cited in Table 5. Average cupressinum) does not cross date (the den- used to calculate the peat-accumulation rate uncertainties were used for those ages with drochronology method used to make sure in order to date the coseismic silt layers. Age unequal uncertainties in order to ensure sym- that annual growth rings are not missing or estimates for five silt layers, and older land- metric distributions as required for the re- duplicated). In light of this, simple ring slide-buried trees in the banks of the nearby gression method. A peak width of 2.5 mm counts were made to estimate germination Hope River range from A.D. 1260 to 1782; was assumed for all of the FALL peaks in ages or time of damage. We prefer to use each most probable age (without individual Table 5. equation 21 for events back to A.D. 1848 and uncertainty ranges) is within ±30 yr of a The combined historic and prehistoric equation 22 for events older than A.D. 1848. lichenometry estimate for the age of a strong

TABLE 5. DATA FROM PREHISTORIC SITES THAT WERE USED FOR A LONG-TERM CALIBRATION OF THE GROWTH OF RHIZOCARPON SUBGENUS RHIZOCARPON Calendric age Peak mean Peak size Dating method used to estimate calendric age estimate (yr, A.D.) lichen size (count) Lichenometry site characteristics (mm) 1782 +73 –42 40.25 560 Radiocarbon age for coseismic silt layers in a peat bog along the Hope River segment of the Hope fault (Cowan and McGlone, 1991), compared with lichenometry age for a regional rockfall event. 1743 ±50 43.53 410 Major disturbance event in a rimu forest described by Conere (1992) and modeled by Bull (1996a). 1729 ±5 47.20 250 Tree-ring counts on 25 podocarps on fault scarp near Haupiri (Andrew Wells, Lincoln University, New Zealand, 1997, personal commun.), compared with lichenometry age for a regional rockfall event. 1728 +53 –93 47.50 270 Radiocarbon age for coseismic silt layers in a peat bog along the Hope River segment of the Hope fault (H. Cowan, 1994, personal commun.), compared with lichenometry age for a regional rockfall event. 1659 ±40 54.50 300 Radiocarbon age for wood buried by the Clyde rock avalanche (Whitehouse, 1983). 1634 +52 –31 64.50 150 Radiocarbon age for coseismic silt layers in a peat bog along the Hope River segment of the Hope fault (Cowan and McGlone, 1991), compared with lichenometry age for a regional rockfall event. 1530 +37 –21 80.30 130 Radiocarbon age for coseismic silt layers in a peat bog along the Hope River segment of the Hope fault (Cowan and McGlone, 1991), compared with lichenometry age for a regional rockfall event. 1435 ±40 84.27 140 Radiocarbon age for twigs buried by the Acheron rock avalanche (Burrows, 1975). 1402 +46 –21 100.50 23 Radiocarbon age for coseismic silt layers in a peat bog along the Hope River segment of the Hope fault (Cowan and McGlone, 1991), compared with lichenometry age for a regional rockfall event. 1260 ±50 121.50 16 Radiocarbon age of wood in the Hope River Bridge landslide, dated by the old solid carbon counting method (Cowan and McGlone, 1991). 998 ±40 166.26 6 Radiocarbon age for wood for part of the Craigieburn rock avalanche (Whitehouse, 1981). Lichen data from Craigieburn rock avalanche and nearby sites. Radiocarbon ages are consistent with weathering- rind dating of 8 synchronous rock avalanches studied by Griffiths (1983) and modeled by Bull (1996a). Note: Measurements were made in 1992, or normalized to 1992. Age uncertainties are ±1 standard error.

79 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

LICHENOMETRY AGE ESTIMATES eters, which means that the degrees of free- ing associated with the two older earthquakes. dom are 17. Once again, the Student t distri- The A.D. 1833 event occurred along the Our coseismic rockfall model allows a ro- bution was used to estimate confidence inter- Conway segment of the Hope fault, as is sug- bust appraisal of lichenometry as a dating vals from the standard error determined for gested by the Figure 23A peak-size map, and method. This section addresses several key ques- the predicted time, t. confirmed by FALL measurements on dis- tions: How is the precision of lichenometry age The estimated confidence intervals include rupted outcrops within 4 km of the fault trace estimates affected by the sizes and age range of the uncertainties associated with the calibra- (Bull, 1997). The other event appears to be the calibration control points? What are the ad- tion line and the uncertainties of the estimated smaller and occurred in A.D. 1836 near the vantages of having many independent age de- mean for the FALL peak to be dated. For Fig- western edge of the study area. The simple terminations for an event, instead of only one ure 20B, the confidence intervals expand pattern of peak size associated with the 29 age estimate? Which field and data analysis greatly for extrapolations beyond the A.D. mm FALL event (Fig. 23B) clearly suggests methods should be used to describe and date 1848 to 1955 calibration range. Within the seismic shaking associated with a single large regional rockfall events that are closely spaced calibration range, it is possible to estimate li- A.D. 1840 earthquake in the central part of the in time? What is the accuracy of the chen ages to better than ±10 yr for FALL study area, perhaps along the Awatere fault. lichenometric approach to surface-exposure peaks with more than 25 measurements. By Peak sizes for the A.D. 1840 event are anoma- dating in New Zealand? comparison, the extended calibration shown lously low near the Conway segment of the in Figure 20 (C and D) has a much tighter Hope fault, most likely because the A.D. 1833 Uncertainties uncertainty. FALL peaks with 100 to 500 earthquake had already dislodged most of the measurements can be dated to a precision of unstable blocks. The internal consistency of Figures 20B and 20D show the 95% confi- better than ±15 yr back to ages of A.D. 1000 the two peak-size maps and the three FALL dence intervals for the two calibrations. The and older. Figure 20 illustrates the important peaks of Figure 22 supports the hypothesis methods used for calculating these intervals role that the calibration curve plays in influ- of three earthquakes in 7 yr. are discussed in Mandel (1964, p. 278–281) encing the uncertainty for an estimated Lichenometry age estimates can be tested and Draper and Smith (1966, p. 21–24). The lichenometry age. The uncertainty of an age using independent historical or tree-ring dated appropriate procedure to be used is influenced estimate for a FALL peak can be improved events known to the year. Comparison of his- by the different ways that the calibrations were by increasing the number of measured lichens, torical earthquake dates with lichenometry done, with D as the dependent variable in Fig- but beyond about 100 to 200 lichen-size mea- age estimates for Figure 15B modeled peaks ure 20A and t as the dependent variable in surements, the uncertainty becomes limited suggests a mean difference of 3 ± 4 yr. This Figure 20C. by the quality of our calibration. departure is about the same as noted for ac- Equation 12.25 from Mandel (1964) was curacy of lichenometry in the Sierra Nevada used to calculate the 95% intervals for Fig- Resolution of California, 2 ± 4 yr (Bull, 1996b). ure 20B. For this case, his variable N is the total number of lichens (1233) in the eight We examined the resolution of the APPLICATIONS calibration points. There are eight indepen- coseismic rockfall model, initially using a dent calibration points and two fit parameters, large FALL data set combined from four sites The FALL approach to surface-exposure dat- which means that the degrees of freedom are that are only 2 to 4 km from the Conway seg- ing can be used in other geomorphic studies to six. The Student t distribution was used to ment of the Hope fault (Fig. 21). The 28.70 determine the frequency of hillslope, fluvial, estimate confidence intervals from the stan- mm peak probably records the oldest histori- coastal, glacial, and periglacial processes. dard error determined for the predicted time, cal earthquake for this study area, one that Closely spaced geomorphic events can be dated t. had an epicenter approximately 110 km away with much better precision than by radiocarbon The calculation for the 95% intervals in (Table 2). Applying equation 21 or 22, this dating. Examples include rockfall accumulation Figure 20D follows that of equation 1.4.7 peak dates to about 1845. The 29.43 and 30.36 rates (Luckman and Fiske, 1995), frequency of from Draper and Smith (1966). Their vari- mm peaks predate the first substantial influx debris flows (Rapp, 1981; Innes, 1983), and able s is estimated from the residuals from of European colonists into New Zealand in landslide-hazard evaluation (Bull, et al., 1994). the regression calculation (i.e., the misfit be- 1840. Two events in the 29–31 mm range are FALL measurements can decipher the compos- tween observed and calculated t). Their vari- recorded at many sites; mean peak sizes are ite nature of young glacial moraines, stream- able n = 3438 is the total number of lichens 29.5 and 30.4 mm at 47 and 46 sites, respec- terrace treads, and beach ridges. Glacial mo- measured in the 19 calibration points. We in- tively. raines that appear to have been emplaced at one creased the standard error of t given by their Decomposition of the density plot of esti- time typically have several distinct lichen-size equation 1.4.7 by the amount mated ages for the combined 47 site data set peaks (Proctor, 1983; Bull et al., 1995, Fig. 8). (Fig. 22) into its component Gaussians reveals Reliability of lichenometric dating of geo- Bσ()D m , a third and smaller peak that is not apparent at morphic processes is best where substrate-ex- the Hope fault sites (Fig. 21). Estimated posure time is the same for all blocks and is where B is the slope of the calibration line, calendric ages for the three presumed poor where many blocks have inherited li- σ(D) is the standard deviation of a single size prehistorical earthquakes are about A.D. 1840, chens. Blocks carried on the surface of a gla- measurement for lichens in a FALL peak, and 1836, and 1833. Are these closely spaced peaks cier may have lichens that predate their depo- m is the number of lichen measurements in real, or they are merely noise? sition in a moraine. In contrast, large rock ava- the unknown FALL peak to be dated. This The hypothesis of three regional coseismic lanches and block slides generally exhume modification accounts for the influence that rockfall events during a 7 yr time span be- deep-seated joint blocks. Furthermore, there the number of lichens in the unknown FALL tween A.D. 1833 and 1840 can be tested with is minimal chance of survival of inherited li- peak has on the uncertainty of the estimate peak-size maps to locate the epicentral regions chens if the landslide detritus is mixed dur- lichenometry age. σ(D) was estimated to be for the three earthquakes. The peak-size pat- ing rapid transport over long distances. Well- ~ 2.5 mm. For Figure 20D, there are 19 inde- tern for the 30 mm event (Fig. 23A) is sug- mixed rock avalanches and block slides will pendent calibration points and two fit param- gestive of a composite pattern of seismic shak- typically result in a single FALL peak with

80 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

30 deposits. Like most glacial moraines, the FALL distributions for such debris flows Gaussian probability commonly are highly skewed toward larger 25 density plot FALL sizes, making it difficult to distinguish 28.70 ± 0.03 mm the peak that records the event date from older and younger peaks. 20 29.43 Event magnitude is revealed by the areal ±0.05 mm extent of lichens belonging to a specific FALL distribution. Examples include epi- 15 sodes of slush-avalanche deposition on a fan (Bull et al., 1995), trimlines on bedrock that record closely spaced advances of a valley 10 glacier (Mahaney, 1987), and bouldery flood deposits. 30.36 ± 0.04 mm Lichenometry adds new dimensions to studies of prehistoric earthquakes. Dating of Probability density (%mm/) 5 earthquakes has been limited mainly to dig- ging trenches across fault scarps and dating 0 the times of stratigraphic disturbance caused 31.0 by surface ruptures (e.g., McCalpin, 1996, 28.5 29.0 29.5 30.0 30.5 p. 47–75). Access to fault scarps is not Largest lichen maximum diameter (mm) needed in the lichenometric approach to paleoseismology, and, because of this, re- Figure 21. Three principal FALL peaks modeled for a probability den- cent earthquakes associated with blind thrust sity plot composed of data combined from the Stone Jug and Goat faults and offshore subduction zones can be studied. For example, Bull (1996a, Fig. 13) used peak-size maps to describe patterns of seismic shaking associated with three Al- 125 pine fault earthquakes, even though none of his lichenometry sites were within 20 km of Gaussian the fault trace. Systematic regional trends probability depicted by peak-size maps (see Figs. 19 and 100 density plot 23) provide the same level of information as Modified Mercalli Intensity maps (Cowan, 1991; Downs, 1995). Surface-exposure dating methods avoid 75 two inherent problems with stratigraphically based isotopic dating. Dated organic matter either predates or postdates the time of an 50 earthquake, and isotopic production rates may vary, resulting in multiple apparent ages for a single young sample (Stuiver and Probability density (%/mm) Reimer, 1993). Thus, lichenometry can be 25 more precise than radiocarbon dating, and may also be more reliable and credible than 1835 1837 1841 stratigraphic radiocarbon dating of earthquakes. Periods of nondeposition are diffi- 0 cult to recognize at stratigraphic 1825 1830 1835 1840 1845 paleoseismic sites (Cowan and McGlone, Calendric age, A. D. 1991) but are crucial because earthquake(s) Figure 22. Decomposition of a density plot of times of regional rockfall that occur during a depositional hiatus may events at 47 lichenometry sites suggests that three coseismic events not be recognized. Omission of one or more events can seriously bias an earthquake-re- virtually no inherited lichens (Bull et al., 1994, currence evaluation (Bull, 1996b). Fig. 5). Small, shallow mass movements The coseismic-rockfall lichenometry ap- generally contain blocks with inherited li- proach to paleoseismology is best used in chens; their FALL data sets tend to be mountain ranges characterized by lichens polymodal. Half the blocks on debris-flow growing on smooth, planar rock surfaces, levees may have inherited lichens if blocks historical earthquakes with Mw magnitudes from source hillslopes are shoved of 6 to >8, and unstable outcrops as indi- downslope with minimal mixing, or are incorporated from nearby older debris-flow

81 Geological Society of America Bulletin, January 1998 BULL AND BRANDON

sodes of avalanche and debris-flow activity 168° E 172° E triggered by major storms. Outcrops and detritus exposed by construction of trans- 0 100 200 Km N portation and utility routes across mountain ranges also may be used to determine if a 60 - 80% single calibration can be used at many sites. 42 °S 40 - 60% 20 - 40% CONCLUSIONS < 20% Lichenometry has several advantages and Relative size of limitations. The cost per age estimate is rockfall event small, and ages are obtained quickly where lichen growth rates are calibrated. Slow- and fast-growing lichens are common on rock substrates in much of the world, and use of several genera allows validation of age estimates (Winchester, 1984; Bull, 1996b). ° 44 S Limitations include the experience required A to select suitable study sites and the time needed to collect large data sets. Lichenometric dating generally is limited to the past 500 yr. Taxonomic identification of ° ° 168 E 172 E hundreds of measured lichens is not practi- 0 100 200 Km N cal, even at the section level. Furthermore, few lichenometrists have the botanical skills needed to detect subtle differences at the > 50% species level. 42 °S 40 - 50% The potential of lichenometry to date geo- 30 - 40% morphic events of the past 500 yr precisely 20 -30% is best achieved by: < 20% 1. Making FALL measurements with digital calipers in order to increase precision and Relative size of reduce bias. rockfall event 2. Measuring the long axes of elliptical thalli, which record optimal lichen growth. 3. Measuring only exposed lichens to minimize microclimatic effects on lichen growth rates. 44° S 4. Measuring large FALL data sets and B using peak-fitting methods to estimate the mean, area, and width of significant peaks. 5. Calibrating lichen growth rates with sites dated to the year or day. Examples in- Figure 23. Peak-size maps for three regional events. Contours show the clude tree-ring analyses of a forest killed by percentage of the 29 mm or 30 mm modeled peak size relative to all FALL a prehistorical landslide or volcanic erup- sizes between 27 and 33 mm. tion (Smiley, 1953, Yamaguchi, 1985; Bull A. Map for the 30 mm FALL event indicates two areas of highest seismic et al., 1994) or historical substrate-exposure shaking on the edges of the study region. events. B. Map for the 29 mm FALL event shows one area of seismic shaking in the 6. Determining the spatial validity for center of the study region. calibration of lichen growth rates by comparing FALL distributions on substrates cated by the presence of talus and debris FALL sizes on dated landslide, flood, vol- formed at the same time at different altitudes slopes. Lichenometry has been used to esti- canic, and glacial deposits; and on highway, and climatic settings, and on different rock mate earthquake recurrence intervals, as railroad, and trail cuts, or dam embankments types. well as the time that has elapsed since the that mimic rocky hillslopes (Bull et al., Our study of synchronous earthquake-gen- most recent earthquake (Bull, 1996a). The 1995). Synchronously exposed rock surfaces erated rockfalls helps to remove a persistent local fault responsible for a prehistorical in nonseismic mountain ranges can also be cloud of uncertainty that has hovered over earthquake can be identified by using frac- used to assess the influence of regional cli- lichenometry. Calibration of lichen growth is tured bedrock sites that respond only to in- matic gradients on lichen growth rates. Ex- not necessary at every study site because fac- tense, local shaking (Bull, 1997). amples of potentially useful geomorphic tors such as substrate lithology and smooth- Our calibration method can also be used surfaces include extensive historical flood ness, mean annual precipitation and tempera- in nonseismic regions by measurement of gravels and lava flows, and regional epi- ture, and length of growing season do not no-

82 Geological Society of America Bulletin, January 1998 LICHEN DATING OF NEW ZEALAND ROCKFALL EVENTS

ticeably affect colonization times or growth peaks with >100 measurements, can be re- p.1044–1062. ± Beschel, R. E., 1963, Geobotanical studies on rates of many species of Rhizocarpon subge- duced to better than 10 yr. The level of preci- Axel Heiberg Island in 1962, in Müller, F., nus Rhizocarpon growing at 90 sites in the sion achieved depends on proximity of the ed., Axel Heiberg Island Preliminary Report 1961–62: Montreal, Canada, McGill Univer- Southern Alps of New Zealand. However, mi- peak being dated to the age range of the cali- sity, p. 199–215. croclimate does influence growth rates; yel- bration points, but can be improved where Bevington, P. R., 1969, Data reduction and error low rhizocarpons are larger where partly multiple independent lichenometry age esti- analysis for the physical sciences: New York, McGraw-Hill, 336 p. shaded and sheltered. The influence of local mates are available, or when the age range of Bickerton, R. W. and Matthews, J. A., 1992, On microclimate can be reduced by only measur- calibration sites is increased. the age of lichenometric dates—An assessment based on the ‘Little Ice Age’ moraine ing those lichens with a similar degree of ex- sequence of Nigardsbreen, southern Norway: posure to sun and wind. ACKNOWLEDGMENTS The Holocene, v. 2, p. 227–237. Regionally constant lichen growth rates Birkeland, P. W., 1981, Soil data and the shape of the lichen growth-rate curve for the Mount greatly simplify calibration procedures. This work was supported by the National Cook area: New Zealand Journal of Geol- Calibration data sets with both great-growth Geographic Society, the U. S. National Sci- ogy and Geophysics, v. 23, p. 443–445. Brandon, M. T., 1992, Decomposition of fission phase and uniform phase control points can ence Foundation, and the Department of Geo- track grain age distributions: American Jour- use equation 10 to describe the average colo- logical Sciences, University of Canterbury, nal of Science, v. 292, p.535–564. nization time, the nonlinear component of New Zealand. We are especially grateful to Brandon, M. T., 1996, Probability density plots for fission-track grain-age samples: Radia- growth during the great-growth phase, li- the many New Zealand farmers and the uni- tion Measurements, v. 26, p.663–676. chen size at the end of the great-growth versity and governmental scientists who gen- Bull, W. B., 1991a, New Ways of dating earthquakes on the oblique-slip Hope fault, New phase, and the constant growth rate during erously assisted with advice, equipment, and Zealand: Geological Society of America the uniform-growth phase. Calibration data permissions. Trevor Chinn, Hugh Cowan, Abstracts with Programs, v. 23, no 5, p.168. Bull, W. B., 1991b, Geomorphic responses to cli- sets consisting only of uniform-growth Fanchen Kong, Elsa McGilvary, Mauri matic change: New York, Oxford University phase control points can use equation 21 to McSaveney, Tom Moutoux, Elise Pendall, Jarg Press, 326 p. define lichen age as the sum of all three Pettinga, William Phillips, Nancy Sprague, Bull, W. B., 1994, Avoiding pitfalls in lichenometry: Geological Society of America phases of lichen growth, and to make gen- Kirk Vincent, and Mark Yetton provided valu- Abstracts with Programs, v. 26, no 7, p. 96. eral estimates of colonization time and able discussions during this 7-year project, and Bull, W. B., 1996a, Prehistorical earthquakes on the Alpine fault, New Zealand: Journal of amount of great growth. Reporting of ages measured some of the lichens. Fanchen Kong Geophysical Research, Solid Earth Special in calendric years eliminates the need for a provided probability density plots of FALL Section, Paleoseismology, v. 101(B3), p. master reference year, such as the A.D. 1950 measurements and modeled component dis- 6037–6050. Bull, W. B., 1996b, Dating San Andreas fault radiocarbon dating reference year. Uniform- tributions that were used to prepare peak-size earthquakes with lichenometry: Geology, v. phase growth rate does not change with the maps. Review comments by Bill Locke, Wil- 24, p. 111–114. Bull, W. B., 1997, Lichenometry—A new way of year in which FALL measurements were liam McCoy, and John Innes provided impor- dating and locating prehistorical earthquakes, made, but the constant A in equation 20 that tant insights as to how to improve the organi- in Sowers, J. M., Noller, J. S, and Lettis, W. R., eds., Dating and earthquakes: Review of describes growth since the year B.C. 1 (= A.D. zation and logic of this paper. Quaternary geochronology and its applica- 0) is a function of measurement year. tion to paleoseismology: U.S. Nuclear Regu- Lichenometry does not match the dating latory Commission Report NUREG/ CR REFERENCES CITED 5562, p. 3-67–3-76. resolution of dendrochronology, but it can Bull, W. B., King, J., Kong, F., Moutoux,T., and be much more precise and accurate than ra- Aitken, J. J., and Lowry, M. A., 1995, More earth- Phillips, W. M., 1994, Lichen dating of quakes explained: New Zealand Institute of coseismic landslide hazards in alpine moun- diocarbon dating, especially for the past 300 Geological and Nuclear Sciences Informa- tains: Geomorphology, v. 10, p. 253–264. yr. Like dendrochronology, lichenometry is tion Series 35, 30 p. Bull, W. B., Schlyter, P., and Brogaard, S., 1995, Andrews, J. T., Davis, P. T., and Wright, C., 1976, based on an empirical relation between age Lichenometric analysis of the Kärkerieppe Little Ice Age permanent snowcover in the slush-avalanche fan, Kärkevagge, Sweden: and a biological phenomenon. Complex eastern Canadian Arctic: Geografiska Geografiska Annaler, v. 77A, p.231–240. botanical dating methods are not easily sum- Annaler, v. 58A, p. 71–81. Burrows, C. J., 1975, A 500 year old landslide in Benedict, J. B., 1967, Recent glacial history of the Acheron River Valley, Canterbury: New marized by laws of physics, such as those an alpine area in the Colorado Front Range, Zealand Journal of Geology and Geophys- describing the decay of radioactive isotopes. U.S.A. 1. Establishing a lichen growth curve: ics, v. 18, p. 357–360. Journal of Glaciology, v. 6, p. 817–832. Nevertheless, lichenometry has excellent Burrows, C. J., Duncan, K. W., and Spence, J. R., Benedict, J. B., 1988, Techniques in 1990, Aranuian vegetation history of the potential as a surface-exposure dating lichenometry—Identifying the yellow Arrowsmith Range, Canterbury. II. Revised method for disciplines as diverse as archae- rhizocarpons: Arctic and Alpine Research, chronology for moraines of the Cameron v.20, p. 285–291. Glacier: New Zealand Journal of Botany, v. ology, geomorphology, and Benedict, J. B., 1990, Lichen mortality due to late- 28, p. 455–466. paleoseismology. lying snow: Results of a transplant study: Conere, B. M., 1992, Population dynamics of a Arctic and Alpine Research, v. 22, p. 81–89. Our approach improves the resolution and lowland rimu forest, South Westland, New Benedict, J. B., 1993, A 2000-year lichen-snowkill Zealand [Master’s thesis]: Christchurch, precision of lichenometry. Excellent resolu- chronology for the Colorado Front Range, New Zealand, University of Canterbury, 102 tion is suggested by the consistent ability to USA: The Holocene, v. 3, p. 27–33. p. Beschel, R. E., 1950, Flechten aus Altersmaastab Cowan, H. A., 1989, An evaluation of the late separate pairs of regional rockfall events only rezenter, moränen (Lichens as a yardstick of Quaternary displacements and seismic haz- 6 yr apart. Events only 2 to 4 yr apart may be age of late-glacial moraines): Zeitschrift für ard associated with the Hope and Kakapo Gletscherkunde und Glazialgeologie, v. 1, p. dated, and the epicentral regions of the earth- faults, Amuri District, North Canterbury 152–161. [M.Sc. thesis]: Christchurch, New Zealand, quakes that caused them can be located, when Beschel, R. E., 1957, A project to use lichens as University of Canterbury, 230 p. indicators of climate and time: Arctic, v. 10, one takes the additional steps of preparation Cowan, H. A., 1991, The North Canterbury earth- p. 60. quake of September 1, 1888: Journal of the of FALL peak-size maps and making FALL Beschel, R. E., 1959, Lichenometrical studies in Royal Society of New Zealand: v. 21: p. 1– measurements on outcrops near suspect fault West Greenland: Arctic, v. 11, p. 254. 12. Beschel, R. E., 1961, Dating rock surfaces by li- Cowan, H. A., 1994, Field Guide to New Zealand zones. We conclude that the 95% confidence chen growth and its application to the glaci- active tectonics: General Assembly of the level uncertainties for New Zealand ology and physiography (Lichenometry), in International Association of Seismology and Raasch, G. O., ed., Geology of the Arctic: Physics of the Earth’s Interior, 27th, Royal lichenometry ages of the past 600 yr, using Toronto, University of Toronto Press,

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