The Feasibility of Using Tree-Ring Chronologies to Augment Hydrologic Records in Tasmania, Australia

The feasibility of using tree-ring chronologies to augment hydrologic records in Tasmania, Australia

Item Type Thesis-Reproduction (electronic); text

Authors Campbell, Desnee Anne.

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/191702 THE FEASIBILITY OF USING TREE-RING CHRONOLOGIES TO

AUGMENT HYDROLOGIC RECORDS IN TASMANIA, AUSTRALIA

Desnee Anne Campbell

A Thesis Submitted to the Faculty of the

SCHOOL OF RENEWABLE NATURAL RESOURCES In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1980 STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholar- ship. In all other instances, however, permission must be obtained from the author.

SIGNED: Za4fuk_ a, 62,iyide

APPROVAL BY THESIS COMMITTEE

This thes has been approved on the date shown below:

C. W. STOCKTON Associate Professor of Dendrochronology

W. OGGESS Research Associate in The Laboratory of Tree-Ring Research ACKNOWLEDGMENTS

The collection and analysis of tree-ring data used in this thesis project was directly supported by grants ATM 75-15495, ATM 76-24267, and ATM-7823008 from the U. S. National Science Foundation, to Dr. V. C.

LaMarche, Jr., for dendroclimatic research in the Southern Hemisphere.

Some of the unpublished results of this research have been used in this thesis, which was largely undertaken,while the author was working on the

Southern Hemisphere Project at the Laboratory of Tree-Ring Research. Dr.

LaMarche's permission to use these data is gratefully acknowledged.

I would like to thank Brian Watson, of the Hydro-Electric Com- mission of Tasmania, for providing all of the hydrologic data essential to the completion of this study. The dependence upon the postal services of two countries for the transmission of these data provided a lesson in patience.

Special thanks are due to Valmore C. LaMarche, Jr., Malcolm J.

Zwolinski, Charles C. Stockton, William R. Boggess, and Marvin A. Stokes for reviewing the thesis and providing helpful suggestions as well as for their encouragement during the course of the research and writing.

Thank you Linda Drew and fellow graduate students at the Tree-

Ring Laboratory for your help in processing data. I also owe heartfelt thanks to many other friends for their moral support throughout the endeavor. TABLE OF CONTENTS

Page

LIST OF TABLES vii

LIST OF ILLUSTRATIONS ix

ABSTRACT

1. INTRODUCTION 1

2. LOCATION AND PHYSICAL FEATURES 4

Climate 4 Precipitation 7 Temperature 9 Topography 9 Geology and Soils 12 Geology 12 Soils 13 Vegetation 14

3. METHODS 17

Dendrochronology 17 Species and Site Selection 18 Sample Collection and Laboratory Processing . 19 Dating and Chronology Development 20 Chronology Variance Components 22 Time Series Analysis 23 Statistical Characterization 23 Multiple Linear Regression 28 Principal Component Analysis 29 Response Function Analysis 31 Canonical Analysis 35 Tests of Association 37 Correlation Coefficient 39 Sign Tests 40 Reduction of Error 42 Cross-product Means Test 43

4. CLIMATIC DATA 45

Selection of Climatic Station Networks 45 Homogeneity Testing of Temperature and Precipitation Series 46

iv TABLE OF CONTENTS--Continued

Page

Estimation of Missing Temperature and Precipitation Data 46 Eigenvector Analysis 48 Drought 52

5. DENDROCHRONOLOGY 55

Site Characteristics 55 Chronology Statistics 58 Tree-ring Climatic Response Functions 64 Chronology Climatic Response Function Results 66 Site Location and Climatic Sensitivity 69 Eigenvector Analysis 74

6. HYDROLOGY 81

Record Identification 81 Watershed Characteristics 83 Seasonalization and Response Function Analysis 87 Statistical Characterization 88 Eigenvector Analysis 92

7. DENDROHYDROLOGY 97

Regression Analysis 97 Canonical Analysis and Reconstruction 101 Discussion of Reconstructions 105 Association Tests 108 Statistics of Reconstructed Series 110 Drought 113

8. CONCLUSIONS AND RECOMMENDATIONS 115

APPENDIX A: TABLES AND LOCATION MAPS OF CLIMATIC STATIONS 117

APPENDIX B: TREE-RING SITE CHRONOLOGIES 124

APPENDIX C: CLIMATIC RESPONSE FUNCTION PLOTS 140

APPENDIX D: TABLES OF MONTHLY AND SEASONALIZED RUNOFF (IN MILLIMETERS DEPTH) 160 vi

TABLE OF CONTENTS--Continued

Page

APPENDIX E: TABLES OF RECONSTRUCTED SUMMER (NOVEMBER- MARCH) RUNOFF (IN MILLIMETERS DEPTH) 166

REFERENCES 171 LIST OF TABLES

Table Page

1. Correlation between Estimated and Observed Climatic Data 51

2. Drought Duration Intensity for Runs in Excess of Two Years 53

3. Summary of Site and Chronology Information 56

4. Chronology Statistics 59

5. Comparison of Statistics from Tasmanian and Other Chronologies 61

6. Summary of Autocorrelation Analysis of Tree-ring Chronologies 63

7. Summary of Tree-ring Response Function Results 67

8. Summary of Autocorrelation Analysis of Chronology Amplitude Series, 1776-1974 79

9. Streamflow Record Identification 84

10. Summary of Hydrologic Features 84

11. Statistics of Recorded November to March Runoff 89

12. Autocorrelation in Six Lags of Observed November- March Runoff 91

13. Correlations between November-March Runoff Records at Eight Gauging Stations, 1958-1974 93

14. Autocorrelation in Five Lags, Skew, and Kurtosis of Calibration Data Used for November-March Runoff Reconstruction 104

15. Summary of Results of Association Tests between Recorded and Reconstructed Runoff 109

16. Statistics of Reconstructed November to March Runoff for 198 Years 111

vii viii

LIST OF TABLES--Continued

Table Page

17. Summary of Autocorrelation Analysis of November- March Runoff Reconstructions, 1776-1973 112 LIST OF ILLUSTRATIONS

Figure Page

1. Index Map of Tasmania Showing Locations of Tree-ring Sites and Stream Gauging Stations 5

2. Map of Tasmania Showing Climatic Regions 6

3. Climatic Regimes at Selected Stations in Tasmania 8

4. Generalized West-east Profile across Tasmania 11

5. Location Map of Tree-ring SiteS 57

6. Position of Tree-ring Sites within the Altitudinal and Precipitational Range of Three Species 70

7. First Three Eigenvectors of Tree Growth 75

8. Amplitude Series of the First Two Eigenvectors of Tree-ring Chronologies 78

9. Map of Western Tasmania Showing Stream Gauging Station Locations 82

10. Mean Monthly Runoff at Eight Gauging Stations 85

11. First Three Eigenvectors of Seasonalized Summer Runoff . 94

12. Reconstructed and Observed November-March Runoff at Eight Gauging Stations 106

ix ABSTRACT

Monthly streamflow records from 8 gauging stations in western

Tasmania seasonalized to include either the 5 months, November through

March, or the 12 months, April through March, were used as predictands in a series of multiple linear regressions. The predictors were tree- ring eigenvector amplitudes derived from 11 chronologies, representing

4 species, from sites all over the state. Tree-ring widths in both the current and following years were significant in predicting runoff for the November-March period but not for the longer season.

Canonical correlations and regressions calculated between the set of 8 runoff records and the set of 11 tree-ring chronologies accounted for 47% of the variance of the 5-month streamflow during the

1958-1973 calibration period. Estimates of seasonalized summer runoff back through 1776 at 8 gauging stations were obtained by applying canonical regression equations to the 198-year tree-ring record. Three of the reconstructed series were verified using runoff data recorded for at least 8 years outside the calibration period.

The results of this first attempt to employ tree-ring chronologies to extend streamflow records in Tasmania show promise for more widespread future applications of the technique.

X CHAPTER 1

INTRODUCTION

The Australian State of Tasmania, in common with most of the

Western Hemisphere, has only short instrumented climatic and even short-

er hydrologic records. Such short series severely restrict the confi-

dence of planning because available data do not necessarily represent a

random sample from an infinite population, yet most statistical analyses rely on an underlying assumption that they do. Thus population statis-

tics must be estimated from the existing data with reduced reliability

from shorter records. Errors in these estimates due to the shortness of observed records will be retained in any synthetic series generated from them. Rodriguez-Iturbe (1969) stated that if the length of annual runoff record is 40 years or less, there may be an error of up to 20% in the estimation of the mean, up to 60% in the estimation of the variance,

and as much as 200% in the estimation cf the first-order correlation

coefficient.

Extension of the available hydrologic record with proxy data is desirable to increase the accuracy of these estimates. It should be possible, then, to predict with greater confidence the probable magnitude and frequency of hydrologic events associated with an existing record, both in the past and in the future. Until now, rainfall records, the longest of which commence in the 1880's, have provided the only data for hydrologic planning in Tasmania. While reliability of the hydrologic

1 2 predictions is definitely increased, the gain in record length using precipitation data is only a few decades. Recently developed ring- width chronologies from long-lived trees, however, may provide proxy hydrologic data for periods of centuries if it can be shown that a statistically and physically sound relationship exists between tree-ring width and hydrologic parameters (Stockton and Fritts, 1971; Stockton,

1975; Stockton, Meko, and Mitchell, 1978; Stockton and Boggess, 1980).

Extended records from tree rings may be used to judge how well the actual hydrologic data reflect the long-term past conditions and, consequently, how much confidence should be placed in them for predicting future streamflow behavior. Under certain conditions, more reliable estimates of the mean, standard deviation, and first-order autocorrelation coefficient may be made from a reconstructed record (Stockton and

Boggess, 1980). A review of studies prior to 1975 is presented by

Stockton (1975), while Stockton and Boggess (1980) provide a comprehen- sive account of the current "state of the art" of dendrohydrology.

This preliminary study considers 11 tree-ring chronologies ini- tially developed for climatic reconstructions together with flow records from 8 streams in Tasmania. It examines the relationship between tree- ring width and runoff and identifies the strongest link between the two data sets using canonical correlation and canonical regression analysis of the first two eigenvector amplitudes of each set. Cumulative Novem- ber through March seasonalized runoff back to 1776 is estimated at 8 gauging stations by applying the canonical regression equations, derived from the calibration period 1958-1973 to the period of tree-ring record. 3

The purpose of this thesis project is to determine whether long tree-ring series may potentially be used to supplement limited streamflow records in Tasmania and thus provide a sounder base for future hydrologic planning. This evaluation has two forms:

1) the physical reasonableness of the empirically-derived statis-

tical relationship between the available tree-ring records and

recorded streamflow is examined; and

2) the reconstructed hydrologic series are compared with recorded

runoff and drought indices both within and outside the calibra-

tion period using, where possible, verification tests to quanti-

fy the relationships. CHAPTER 2

LOCATION AND PHYSICAL FEATURES

While the runoff records used in this study are from streamflow gauging stations in only the western half of Tasmania, the tree-ring chronologies are from sites scattered over the entire state (Figure 1).

Therefore, general physical characteristics of Tasmania are described, with emphasis on the western region and those features having the greatest effect on runoff characteristics and tree growth.

Tasmania is an island of approximately 68,000 square kilometers, lying 240 km south of the Australian mainland within the latitudes

40 0 30' to 43° 30'S and between 144 ° 30' and 147° 30'E longitude. It is roughly the shape of an equilateral triangle with one side north. King

Island and the Flinders Island group (Figure 2) are politically part of

Tasmania, and data from them were included in the climatic network.

However, as used in this report, Tasmania should be interpreted as the main landmass and Bruny Island to the southeast.

Climate

Tasmania's climate, dominated by prevailing westerlies, is described by Langford (1965) in the Atlas of Tasmania as temperate maritime, typical of west coast areas in mid-latitudes. In summer, especially, the westerlies are partly countered by northeasterlies.

Topography modifies the climate and despite the island's relatively small size, mild continental effects are evident, with nighttime

4 Figure 1. Index Map of Tasmania Showing Locations of Tree-ring Sites and Stream Gauging Stations. -- Numbers are gauging stations and letters are tree-ring sites with tree species symbols as indicated below.

Species code: stars = Phyllocladus aspleniifolius open square = Athrotaxis selaginoides closed square = Athrotaxis cupressoides open circle = Nothofagus gunnii 5

145 ° 146° 147° 148 °

sp 190 km SHT 159

DRR

Z"- PIE gWDF PNL CMT 154 — o 42° - 42 78 LYL

119 4f- —43 °

145° 146° 147° 148°

Figure I. Index Map of Tasmania Showing Locations of Tree-ring Sites and Stream Gauging Stations. 6

146° 402—

91 Launceston 1 1 A .., , ...' INDIAN ts, ...._.,..-" 92 % fi) t 96 .. s, t . t I t '42 I Shannon 42 ° Cape Sorell , v • "i 93 . °— i SwSnsea • • I 1 ,..---V - -, 0;. OCEAN '-../ , I. r: „ •Oatlands 95 s. % I i ...... 1 f , i TASMAN Y Bushy Parki 94 . , SEA 97 x • , , . • % g CLIMATIC REGIONS ...... 1 _, 10 91 Northern Hobart 92 East Coast 93 Midland 94 South Eastern 95 Derwent Valley 96 Central Plateau 97 West Coast (Mountain Region) 98 King Island 99 Flinders Island

44° o 44° 146 148°

Figure 2. Map of Tasmania Showing Climatic Regions. -- The locations of selected stations whose data are used in Figure 3 are shown. 7 cooling occurring in the sheltered interior, particularly in periods of calm weather in winter (Langford, 1965; Gentilli, 1972).

Various divisions of Tasmania's climate have been recognized.

Gentilli (1972) describes seven main physiographic areas and climate types: Bassian Islands, Northern Slopes, Northeastern Block, Western

Slopes, Central Plateau, Eastern Ridge, and Southern Block. He con- cedes, however, that these areas overlap to varying degrees and that blocks and ridges separated from the central plateau have their own local climates. The Australian Bureau of Meteorology divides the island into the climatic regions indicated in Figure 2. Langford (1965) presents a more general description together with rainfall and temperature figures for selected stations, and this is probably a more useful approach here. Figure 3 shows the mean monthly precipitation and mean monthly maximum temperature for 1941-1970 at selected stations used in this study.

Precipitation

The values shown in Figure 3 for Waratah and Cape Sorell are characteristic of west coast regions. Rainfall is received every month with a distinct maximum in winter (June to August) when the westerlies are strongest and most persistent, often causing intense three- to five- day storms. The data for Launceston, also showing a winter maximum, are typical for the whole of northern Tasmania. The other stations show a more even distribution of moisture throughout the year. Very few data exist for the southwest portion of the state, but as far as it is known, 8

300 —•••. .• — 20 • I. • • •• - —10 200 — —0

100

1 ! i1 il HHti 11 1111111 1 1 JMMJ SN JMMJ SN JMMJ SN Wamtah Launceston St Helens

300— .• —20 I. ••••••• —10 200 —

100—

II 1111 111111111111 JMMJ S N JMMJ SN JMMJ S N Cape Sorel I Shannon Swansea

300 — • 46. —20 • •••••••••". —10 200— _ 0

100— 111111111111 111111111111 11111 1111 JMMJSN JMMJ SN JMMJ SN Bushy Park Oattands Cape Bruny

Figure 3 Climatic Regimes at Selected Stations in Tasmania. -- Thirty year, 1941-1970, mean monthly precipitation (mm) (bars), and monthly mean daily maximum temperature ( °C) (dots) for stations located in Figure 2. Temperature records are incomplete for Shannon and Bushy Park. 9 annual totals of about 3000 mm on the ridges and about 2300 mm in the valleys occur. The maximum totals are in the western region and to a

lesser extent in the northeastern highlands, while a distinct rainshadow

is evident in the central, eastern, and southeastern districts. There

is a strong precipitation gradient across the central plateau to the ad-

jacent midlands and Derwent Valley. "The whole is a picture of precipi-

tation yield from a bulk westerly circulation distorted and aggravated

by mountain features" (Langford, 1965, p. 9).

Temperature

Maps of average temperatures for the warmest and coldest months

and of annual extreme temperatures reveal a continental effect on a gen-

erally maritime-influenced climate. This effect, shown by an extreme

temperature range, is most pronounced at the eastern foot of the Western

Tiers and in the upper Derwent Valley. These areas are in the top outer

edge and in the center of the "C" formed by the central highlands. The

hottest months at all stations given in Figure 3 are January and Febru-

ary, a situation which tends to be true for the whole island, although

December temperatures are often almost as high. Minimum temperatures

occur in either July or August.

Topography

Davies (1965), in the Atlas of Tasmania, provides perhaps the

best general description of the island's landforms and has been heavily

drawn upon in the following. The state is a mountainous island having

little of its surface close to sea level with only restricted coastal 10

plains, these being best developed in the extreme northwest and north-

east. Highlands above 1000 m form a large eastward-opening "C" aiound

the center of the island with residual mountains of this altitude in the

northeast corner. There is a central plateau containing many lakes of

glacial origin, although there is no glacial activity today. The west-

east profile shown in Figure 4 is representative of most of Tasmania.

Two general types of mountains may be distinguished. In the

central, eastern, and southeastern areas they tend to be plateau-like, while in the west they are more ridge-like. The plateaus are usually

capped with resistant dolente and represent erosional residuals; the

scarps mostly indicate faulting which exposed softer adjacent rock to

erosion. In the west and northeast, the basement of folded pre-

Carboniferous rocks is exposed and river valleys have formed along the line of strike of the softer rocks. Harder quartz metamorphics and con-

glomerates form ridges whose trends indicate the axis of folding. Thus, river systems of the west, several of which are concerned in this project, show a trellised pattern and drain to the west coast.

Drainage patterns are more complex in other parts of the island, and details will not be covered here. However, a comment made by

Davies (1965, p. 19) concerning three rivers is pertinent to this study:

"The boundary between the Derwent-Huon drainage systems on the pre-

Carboniferous basement is well marked and interesting, for it would seem that, in spite of the fact that the outer edge of the post-Carboniferous rocks is retreating eastward, the Derwent and Huon systems are extending westward by capturing the headwater tributaries of the Gordon and Port 1 1

Rainfall (cm)

1 1 25 200 100 190 100 50 150 75 1:1w 1500 4-1 75

Western Central Midlands NE and E Mountains Plateau Mountains

Figure 4. Generalized West-east Profile across Tasmania. 12

Davey systems." The creation of Lake Gordon and the increase in size of

Lake Pedder through the impoundment of the Serpentine River in 1972 may have altered the rate of this process. Lakes and coastlines are covered by Davies (1965) in his section on landforms, but are not relevant to this thesis.

Geology and Soils

Within any climatic zone, the pattern of soils follows that of the underlying parent material. Thus, where soil surveys have not been made, the more generally available geologic map is the best indicator of likely soil type boundaries. This is the case in the western one- third of Tasmania. However, the geologic map varies in reliability so that the soil map based on it must be interpreted accordingly (Nicolls and Dimmock, 1965). Both geology and soil type will be considered briefly insofar as they indirectly influence runoff and tree growth.

Geology

Lithology, or rock type, and the occurrence of folded and fault- ed structures are probably the two most important geological factors controlling the geomorphology and soil types in a region. Erosion pro- ceeds more rapidly along lines of weakness and in less resistant rocks; the influence of folding and faulting on mountain form and drainage pattern has been noted already. Rock type is also important in determining the type and depth of soil which in turn govern the plant-soil-water relationships at a given site.

Davies (1965) divided the island into two main structure prov- inces: the fault structure of the pre-Carboniferous rocks and the fold 13 structure of the post-Carboniferous rocks and granite. The whole western one-third of Tasmania and part of the northeast comprise the fold structure. Quartzites in the north and west and granites in the northeast are the main parent materials. In the center, east, and southeast

the older rocks are overlain by more or less horizontal Permian and Tri- assic sediments into which dolente has intruded to form somewhat horizontal sheets. Widespread fault movements occurred in the late

Cretaceous or early Tertiary in these areas. A detailed geological his- tory of Tasmania has been presented by Banks (1965).

Soils

Tasmanian soils are invariably leached because of the humid climate, and the majority are acidic. Podzolics of several types are the most widespread soils, and all the Phyllocladus sites sampled were on these. In the north of the state, strongly leached krasnozems on basalt are common. Less severely leached soils are almost restricted to basic igneous rocks in the relatively dry valleys of the center and southeast.

A high organic matter content reflects the high rainfall and low temperatures; a median value of close to 9% for organic matter in the surface

4 inches in 264 samples of various soils throughout the state was found

(Nicolls and Dimmock, 1965). Moor podzol peats, found at some Athro- taxis sites, have been produced by restricted drainage in conjunction with button grass (Mesomelaena sphaerocephalus) at lower elevations on the valley floors of the southwest. Some upland peats also occur, these generally being shallow and rarely more than 60 cm deep. 14

According to Nicolls and Dimmock (1965), the soils in the catchments considered here are either yellow podzolic or skeletal soils and moor peats, the latter association being in the southwestern region, including the Huon and Gordon River catchments. The strongly acidic yellow podzolics may be up to several feet deep and may support native wet sclerophyll forest, but in some cases have been used for pine plantations. The skeletal soils are characteristic of steep slopes on the more siliceous rocks, such as quartzite, where weathered material is rapidly transported, so that bare rock is exposed. These skeletal soils in the west may be associated with moor podzol peats on the valley plains and lower slopes. Their vegetation cover is usually sedgeland dominated by button grass. Most of the western watersheds have this soil association which is often used for reserves or water catchments because of its limited potential for agriculture and forestry. Infil- tration is rapid but restricted in depth so that surface runoff yields tend to be high.

Vegetation

A large-scale map of vegetation of Tasmania may be of little value for determining the dominant plant association in any limited area, because each region will actually comprise a mosaic. That is, the vegetation varies floristically and structurally in response to diverse local conditions of altitude, aspect, and soil type produced by the dis- sected mountainous topography of most of the island. Jackson (1965) presents a map based on Davies (1964), which indicates six main categories of vegetation including cleared land, and describes the variation 15 within each of these groups in some detail. However, those associations found on the watersheds and at the tree-ring sites will be the main concern here.

In general, the ecology of many of the island's plant species is poorly documented. Ogden (1978a) gives an account of the distribution and population ecology of two species of Athrotaxis in Tasmania, but the phenology of these and of Nothofagus and Phyllocladus, for which there are tree-ring chronologies, is virtually unknown. The same author presents a diagram showing the preferred altitudinal and annual precipitational ranges of three of these four species (Ogden, 1978b, Figure 6).

This will be considered further in the section dealing with dendroclimatic analyses (Chapter 5).

According to Curtis and Somerville (1949) and Jackson (1965),

Tasmania's vegetation can be grouped into three main formations:

Austral-montane, temperate rain forest, and sclerophyll forest. Stephens

(1941) preferred to subdivide the Austral-montane and sclerophyll forest, a division with which Davies (1964) did not wholly agree. Jackson

(1965), the main reference here, considers that there are at least four other categories which are ecotonal between the three main formations or which do not readily fit into any particular one. These are sedgeland, moorland, coastal heath, and cleared land. Sedgeland, characterized by tussocky growth of monocotyledons and mostly dominated by Mesomelaena sphaerocephala, which may grow to six feet in height, is scattered throughout the western watersheds. Moorland includes non-forest conif- erous shrubs and fell field occurring at altitudes above 1100 m in the 16 north and above 600 m in the south. Krumholz Athrotaxis selaginoides

D. Don (King Billy Pine) and A. cupressoides D. Don (Pencil Pine) at the

Pine Lake site (PNL), respectively, are examples of these two types of moorland.

The other two genera sampled dendrochronologically, Phyllocladus and Nothofagus, best belong to the temperate rain forest formation which has a range from sea level to 1100 m. This forest type is likely to be climax in regions where annual total rainfall exceeds 140 cm or where the summer rainfall is more than 50 "mm per month, as for example at the

Phyllocladus sites, St. Helens (SHT) and Bruny Island (BIT). Gully cor- ridors of rain forest occur within sclerophyll forests of the east coast at altitudes of 450-600 m. Vegetation associations at each of the tree- ring sites have been described by LaMarche et al. (1979).

As mentioned in the soils section, most of the watersheds support wet sclerophyll forest as well as button grass. Jackson (1965, p.

30) considers this forest type to be an ecotonal, fire-maintained dis- climax: "Areas with low soil fertility and aspects exposed to prevailing west to northwesterly winds have greatly increased frequency of fires and this converts potential climatically determined rain forest into sclerophyll forest or under extreme conditions, to open communities of wet scrub, sedgeland or grassland." CHAPTER 3

METHODS

Procedures associated mainly with tree-ring data analysis will be described. Most of these are standard dendrochronological methods which have been well-documented elsewhere (Stokes and Smiley, 1968;

Fritts, 1976). Other, more general, time-series analysis techniques used in this thesis are outlined. Principal component analysis was applied in several ways and the underlying principles, assumptions, and advantages of the technique are discussed. Canonical analysis and multiple linear regression were used in later stages of this investigation for the joint analysis of tree-ring and streamflow data. Climatic response function analysis using both eigenvector analysis and multiple linear regression is briefly outlined. Several tests of association were used to assess the quality of the statistical models used in the reconstructions, and the main features of these measures are given.

Dendrochronology

The 11 tree-ring chronologies used in this thesis are part of a larger set collected for a National Science Foundation-sponsored dendroclimatic project and had already been developed and statistically characterized (LaMarche et al., 1979) when the thesis research was commenced.

The writer was, however, involved in the field collection in 1976 and in the subsequent development and analysis of these chronologies. Some additional analyses, particularly those with climatic data, were used

17 18

for both the original NSF dendroclimatic project and for the dendrohy-

drologic investigation discussed here.

Species and Site Selection

The range of habitats over which a species may grow and repro-

duce is termed its ecological amplitude. Greater variation in ring

width due to climate is expected in tree-ring chronologies derived from

trees of a given species, growing closer to the margins of their ecolog-

ical range where environmental conditions are likely to be more limiting

to physiological processes including growth of the species (Fritts,

1976). Anomalous conditions, wetter or drier, hotter or colder, or a

combination of these conditions throughout a period of up to several

years during which a particular ring's width is influenced, will be re-

corded in trees growing closer to their limiting conditions. In those

trees situated closer to the center of their range, such environmental

conditions will tend to be cushioned. The preferential selection of up-

per and lower tree line sites for sampling is in accordance with this

principle.

The tree-ring samples used in this study are from among the most

recent and extensive collections made in Tasmania. The potential of

several tree species had yet to be confirmed, although Martin, in 1949,

developed a 136-year chronology from Pencil Pine at Mount Field (T. Bird,

personal communication, 1980) and J. Ogden (personal communication, 1975)

and others had demonstrated the dateability of Phyllocladus aspleniifo-

lius (Labill.) Hook, (Celery Top Pine) and King Billy Pine. The distribution of these three species was not documented at the time of 19

collection in 1976 and 1977, but has since been detailed by Ogden

(1978a). The general sampling strategy was to cover as wide a geograph-

ical range as possible while concentrating on the apparently more climatically sensitive Phyllocladus. Unfortunately, there were too few

known accessible stands and not enough time to be as selective as we would have preferred to be, of tree-ring sites in terms of ecological

amplitude.

Sample Collection and Laboratory Processing

A Swedish increment borer 4 mm in diameter and either 400 or

500 mm in length was used to extract cores from at least two radii of

each tree sampled. In areas where logging had been recent or was in-

tended, a chainsaw was used to collect transverse sections (discs) from

stumps or logs of recently-dead trees, or trees were felled for the purpose. The general procedure was to collect, where possible, specimens

from at least ten trees at each site. Preliminary assessment of the

dendrochronological potential of the samples was made in the field.

Clear rings, large year-to-year ring-width variation (sensitivity), ob- vious crossmatching of patterns between radii, both within trees and between trees, and the absence of pronounced growth surges and suppression were preferred.

Cores labeled with site, tree, and radius identification were placed in large-diameter drinking straws for temporary storage and transport to the laboratory. Trees were identified for later location by attaching a numbered aluminum label to them. A detailed site 20

description and site plan of the numbered trees was made. As well as

the general site description, individual tree data including estimated

diameter, height, degree and direction of lean, position on slope, fo-

liage characteristics, scars, and associated vegetation were recorded.

Cambial activity on each sampled radius was recorded to provide an in-

sight into the growing season which had not been defined at the time of

collection.

On return to the laboratory, each core was mounted and each core

or disc surfaced following standard techniques (Stokes and Smiley, 1968;

Ferguson, 1970). Occasionally cores had become twisted during extrac-

tion from the tree, and this twisting seemed to be related to both wood

properties (species) and of the sharpness of the borer used. Where nec-

essary, cores were steamed and straightened before mounting or remount-

ing. The use of water-soluble glue greatly facilitated remounting when

it was required.

Dating and Chronology Development

The surfaced samples were dated using standard crossdating pro-

cedures (Stokes and Smiley, 1968). The year assigned to each ring was

that in which growth commenced. The dated samples were then measured to

the nearest 0.01 mm using a Henson (Bannister model) measuring machine in conjunction with a Bausch and Lomb stereoscopic microscope with crosshairs, mostly at a magnification of 15 or 30 power.

Individual ring-width series typically show a general decline in ring width and variance from the center of the tree to the outside. 21

This phenomenon, which is associated with the increased circumference of the tree with age, is referred to as growth trend. Standardization or indexation of raw ring-width series is a routine procedure used to transform tree-ring data to series that are more stationary in both mean and variance. Therefore, after plotting ring widths for each measured radius, a curve was chosen to fit the data. Standardization is accom- plished by dividing the raw ring widths by the expected or curve value.

Each resultant series has a mean value of one and a variance that is approximately the same throughout its length.

On radii that include the central part of the stem, the ring- width series generally have a negative exponential form, and this is the most appropriate type of curve to use to remove the growth trend. On others, a straight line or polynomial of variable or specified order may be preferred at the discretion of the investigator. The type of curves selected will influence the appearance of the final chronology: a close-fitting polynomial curve will remove more variance than a straight line. An arbitrary decision must be made as to which fluctuations or trends can be attributed to climate and which, if any, to more local effects; hence, the importance of recording detailed site information, especially when other regional chronologies are not available for comparison.

Several types of curves, including negative exponential, straight lines, and polynomials of various orders, were used in the development of the 11 chronologies discussed here. The choice of curves may affect statistics of the final chronologies. 22

Each annual index value in the final or site chronology is the average of all series in which that particular year is represented. The individual cores within each tree are averaged to give a tree chronology, and tree chronologies are averaged to form each site chronology.

That is, a tree-ring site chronology is a mean value function developed from each tree which in turn has been averaged from measured radii within the individual trees (Stockton, 1975, p. 37).

Chronology Variance Components

The total variance in a site chronology may be partitioned to several sources. These include year-to-year variation that is common to all radius samples a 2y, differences in year-to-year variation between 2 corresponding ring indices from tree to tree a t, and differences in 2 some criterion of the sampled cores (radii) u c, which should be significant only if the sampling design incorporated such a variable. Assuming that the variables and errors are independent and that the error is nor- 2 mally distributed with a mean of zero and variance c e, then the total 2 variance for the (site) chronology a T is a sum of the year, tree, core, and error variances. That is:

2 2 2 2 2 a T = a y + a t + a c + a e

2 where a T = total variance of site chronology, 2 a y = variance due to year-to-year index difference,

a 2 t = variance because of index differences between trees,

a 2 c = variance due to differences between cores within a tree, and

a 2e = variance whose source is not identified. 23

The actual values of variance components may differ markedly

from site to site depending on various factors including first-order

autocorrelation which, if high and positive, will tend to increase the 2 a y component. To facilitate comparisons between chronologies, each

component is expressed as a percentage of the total variance. An en-

vironmentally sensitive series will tend to have a high a 2y with the

other sources making small contributions.

Time Series Analysis

Statistical Characterization

The aim of this project is to evaluate the potential of using

time series of tree rings to lengthen existing streamflow series. It

follows that the statistical properties of each series must be estab-

lished so that an appropriate model relating the data sets can be devel-

oped and so that the physical soundness of the resulting empirically

developed reconstruction equation may be judged. The characteristics which need to be known are the probability distributions of the data of

each series and the time dependence or autocorrelation between values within each series. Thus, the mean, variance (and standard deviation),

coefficients of skew and kurtosis, standard error of the mean, and auto-

correlation coefficients for several lags were calculated for the annual

tree-ring and seasonalized runoff records. The discussion and formulae

used to calculate each of these statistics, below, are based on Nie et al. (1975). 24

Mean. The mean is the most common measure of central tendency and is the sum of individual values divided by the number of cases (observations). The formula is:

— E i x - i=1 x

Inthisandthefollowingformulae,x.is the value for a particular year and N is the number of years.

Variance and Standard Deviation. Sample variance, denoted by 2 . s , is the averaged squared deviation from the mean calculated as:

N 2 2 s - N-1

This measure of dispersion about the mean gives additional weight to extreme observations. The standard deviation, s, is the square root of the variance. It has the advantage of a more intuitive interpretation than the variance, since it is based on the same units as the original variables.

Skewness. Skewness is a statistic used to determine the degree to which a distribution of data approximates the normal curve, since it measures the deviation from symmetry. Skewness, s 3 , s calculated as:

3 s3 - i=. 1 ((xi - 25

Skewness will be zero when the distribution is a completely symmetrical bell-shaped curve. A positive value indicates that the cases are clus- tered more to the left of the mean with most of the extreme values to the right. A negative value for s3 indicates clustering to the right of the mean. Confidence limits, a function of sample size (N), may be found from tables such as Snedecor and Cochran (1967, Table A6(i), p.

552) or from graphs such as Wallis, Matalas, and Slack (1974, pp. 13f), for testing the null hypothesis, Ho , that skewness is not significantly different from zero. If Ho is accepted, the data are considered to have a normal distribution.

Kurtosis. Kurtosis, s 4 , measures the relative peakedness or flatness of the curve defined by the distribution of sample data. It is calculated as: 3 s4 _ : 1=1 ((xi - -) / x) - 3

A normal distribution has a kurtosis of zero when s 4 is calculated as above. A positive value indicates that the data have a distribution that is more peaked (narrower), while a negative s 4 indicates a distribution that is flatter than would be true for a normal distribution. As for skewness, confidence limits depending on sample size may be obtained from tables such as Snedecor and Cochran (1967, Table A6(ii), p. 552).

Values for samples of less than 50 observations are not readily available. 26

Standard Error of Means. The standard error of the mean of a sample is a measure of the discrepancy between the sample mean, and the unknown population mean,11. It is used for creating confidence in- tervals of, for example, index values in tree-ring site chronologies.

Standard error can be estimated by dividing the standard deviation, s, by the square root of N, the number of observations:

S.E. - iN

Autocorrelation Analysis. Autocorrelation analysis is used in this thesis to evaluate the dependency structure within individual time series of both tree-ring and runoff records. Observed data, as well as the first few eigenvector amplitude series of each data set and reconstructed runoff values, are examined for serial correlation at several lags.

The autocorrelation coefficient, r between a value in a series at time t and a value in the same series at k time period from t, is calculated in a similar fashion to the Pearson product moment correlation coefficient, described in the section dealing with association tests.

The y terns will be replaced by lagged x terms in the calculation. The autocorrelation function of a particular time series, described by the estimates offor1k several k, is used to assess the probable type of underlying mechanism generating the series. Caution in interpretation is needed, however, because individual estimates of 1k at various lags are not independent (Jenkins and Watts, 1968). 27

Often the first-order autocorrelation coefficient, r1 , along with the mean and variance, is sufficient to characterize a time series.

Several of the tree-ring chronologies used in this thesis, however, have such low r 1 values that if a first-order autoregressive process is assumed, they would appear to be essentially random series, although we know from other analyses that this is not true. The autocorrelation coefficients at higher lags were therefore calculated to give more detailed information on the serial dependence within each chronology.

Likewise, 4 for the first several lags of observed runoff (seasonalized November-March) were calculated, although the limited sample size

(N<30) may allow considerable error in the estimates (Rodriguez-Iturbe,

1969).

Autocorrelation or serial dependence within data reduces the ef- fective number of degrees of freedom used in significance testing and tends to inflate the values of linear correlation coefficients and variance estimates in least-squares analysis. An awareness of the presence and degree of autocorrelation within individual series is important for the formulation of models relating series to each other. Also it is needed in the selection and interpretation of appropriate statistical tests of the strength of the relationship or the performance of the selected model.

Confidence limits for r level may be approximated by -k at the 95% +1.96/1/N, assuming normally-distributed data. If the estimated 4, where k is the number of time lags, lies outside this range, the series is significantly (95%) autocorrelated. 28

Mean Sensitivity. The chronologies were further characterized

by the statistic of mean sensitivity (MS), a measure of the relative

year-to-year change in ring width (Douglass, 1936). This statistic is

calculated as:

2(xt+1 - xt ) MS = 1/n-1 E t=N-1 X t=1 X +X t+1 t

where x is ring width in year t. Values of mean sensitivity range from t zero, when adjacent rings are the same width, to 2.0, when one of a pair

of rings is missing (x=0). As shown, mean sensitivity values are aver-

aged over all pairs of adjacent ring widths in each chronology to give a

mean MS for the site chronology.

Multiple Linear Regression

Stepwise multiple linear regression was used to define the rela-

tive importance of several climatic parameters in determining ring width

and runoff variability. It was also used to develop equations to recon-

struct runoff from tree-ring data. A detailed mathematical explanation

may be found in Ezekeil and Fox (1959). The model used has the form:

Y = B + B X t BkXkt + e t = 1,2 ... N t l 2 2t

where t = the time dimension,

Y = a dependent (predictand) variable linearly related to a t of independent (predictor) variables X series (k-1) 2' X ... Xk , 3 N = the number of observations, and

e = a random error term. 29

One variable at a time is allowed to enter the regression with the significance of each being tested using the F-test with (1,N-1-k) degrees of freedom assuming that the predictor variables are uncorre- lated. Certain statistical assumptions are inherent in the technique.

These are: (1) the expected value of the error term is zero, (2) the error terms have constant variance and are independent and normally distributed, and (3) there are more observations (years of data) than predictor variables which also need to be statistically independent.

Principal Component Analysis

The technique of principal component (or eigenvector) analysis

(Daultrey, 1976) is used to transform variables into orthogonal components. It is especially useful when dealing with limited, highly correlated data sets because it enables the original data to be represented by a smaller number of orthogonal functions (useful in least-squares analysis) and their corresponding amplitudes. The theory underlying principal component analysis and the necessary computations based on a correlation matrix have been described by Daultrey (1976). Examples of its application are provided by Kutzbach (1967) and Sellers (1968).

Eigenvector analysis applied to a time series from a spatial array of m data points results in a set of m eigenvectors. Each eigenvector can be plotted and contoured on a map to depict the spatial variation of the component, and the resulting pattern may be termed a characteristic anomaly pattern for the particular eigenvector (LaMarche and Fritts, 1971). 30

The first few eigenvectors typically account for much of the

variance in the original data, and subsequent analyses generally use a

limited number of these. There is, however, no universally accepted

single criterion for determining how many of these eigenvectors are sig-

nificant (Kshirsager, 1972; Preisendorfer and Barnett, 1977). In this

project, an eigenvector was considered likely to be significant if the

percent variance in the original data set explained by that eigenvector

was greater than that expected by chance. That is, for a set of eight

variables, only those eigenvectors describing at least 12% of the vari-

ance would be retained.

The physical reasonableness of the eigenvector pattern was also

taken into account and, overall, the selection of eigenvectors for fur-

ther analyses must be considered conservative. For example, in the

monthly and annual precipitation analyses, the first four eigenvectors

only, accounting for 86% of the variance, were retained and used in in-

terpolation estimates (see Chapter 4). If the criterion suggested by

Kshirsager (1972) of retaining all eigenvectors whose cumulative eigen-

value product (eigenvalue x percent variance accounted for) were equal

to or greater than 1.0 had been used, 21 eigenvectors accounting for 99%

of the variance in the monthly data and 18 eigenvectors accounting for

98% of the variance in the annual data would have been retained.

The amplitude series associated with each eigenvector of a spa-

tial array shows the importance of the eigenvector through time. The amplitude q of the eigenvector F k in year i is calculated as the sum of 31

theproductsofitselementsf.and the normalized departure of the

quantity p being measured at data point j in year i. That is,

q. = E f p. jk ij ik j=1

The amplitude of an eigenvector is large when the observed anomaly pat-

tern coincides with the characteristic anomaly pattern for that eigen-

vector, if the observed departures are also large. When the absolute

value of the amplitude is large but the sign is negative, the observed

departure resembles the characteristic pattern but is opposite in sign

(LaMarche and Fritts, 1971).

Eigenvector analysis was employed in several ways. Firstly, it was applied to time series of precipitation, temperature, runoff, and

tree-ring indices to display spatial variation in these data. Secondly,

the results of eigenvector analyses were used in an interpolative manner

to estimate monthly temperature and precipitation data for points where none had been recorded (Chapter 4). Thirdly, principal components of

climatic variables were used in the derivation of climatic response

functions.

Response Function Analysis

The concept of the response function was originally developed to express how ring width is related to several climatic variables (Fritts

et al., 1971). Although most commonly applied to tree growth, a re-

sponse function may be used to define the relationship between runoff and climatic variables. It has the general form of a statistical 32

calibration equation which expresses the relative effects, by using as-

sociated weights, of several climatic factors on the dependent variable

(ring width or runoff).

The method of analysis is to compare, in a stepwise multiple

linear regression, annual ring widths or runoff data with eigenvector

amplitudes of monthly precipitation and temperature data together with

"prior growth" or "prior runoff" variables which represent persistence

in the tree-ring or runoff series. Selected principal components of monthly meteorological data are applied to a model of the following

form:

Y = 6 + E + E + ..e + (i) y + cl) y + e, t 0 1 1 2 2 n n t-1 t-n t-n where Y = ring width or runoff in year t, t = regression coefficient for variable, n En E = amplitude as extracted from a correlation matrix of n meteorological data,

cp t _n = regression coefficient of variable y,

= ring width or runoff at time t-n, and Yt-n e = error component (from Stockton, 1975, p. 56).

The number of prior growth (or runoff) variables available to the regression procedure is specified by the researcher and reflects the degree of autocorrelation within the predictand series. Multipli- cation of the amplitudes by their respective eigenvector elements leads to an equation in terms of original data. This is more readily interpreted than the eigenvector amplitudes whose physical relationships to 33 the predictand may not be clear. The modified equation, commonly called a response function, then takes the form:

11 1 Y t = e 0 x 1 (6 1a 8 2 a 12 ) x2 (e a 12 0 2 a 22 ) for the first 2 eigenvectors only, where the a's are the elements of the respective eigenvectors and the x's are the observed values of the climatic variables.

By using the principal components of, instead of the raw climatic data in developing the regression equation, orthogonality of the variables is ensured, a condition which fulfills the assumption of statistical independence of the predictor variables. Fewer variables are needed to represent the climatic data so that the use of transformed data conserves degrees of freedom. Other assumptions, including normality of the input data, are the same as for multiple linear regression.

The number of variables allowed to enter the multiple regression can be controlled by the investigator by specifying either the amount of variance in the original data set to be reduced, or an upper limit to the number of eigenvectors allowed to enter the regression and by specifying the F-level of entry and deletion of the variables. For the tree- ring climatic response functions, 80% variance reduced and an F-level of 1.0 for both entry and deletion of variables in the regression was stipulated. For the runoff response functions, a fixed number of eigenvector amplitudes, depending on the analysis period, were permitted to enter the regression. Again, the regression was allowed to proceed with variables entering until the F-level of entry was reduced to 1.0. 34

At an F-level of 1.0, the entering variable has 50% probability of entering the regression by chance. Although Fritts (1976) uses an

F-level criterion of F = 1.0, a more conservative F-level is used here to select the climate response function equation (step) for interpretation. The significance of the F-level of the variable entering at step k is tested with (1,N-1-k) degrees of freedom. The last step chosen is significant at least at the 90% level if the entering variable is climatic, and at the 95% level if the entering variable is prior growth.

That is, there is less than 10% or 5% probability, respectively, of a higher F-value occurring at the selected step.

In response function analysis, temperature and precipitation variables are considered separately and treated as statistically independent of each other after they are forced to be orthogonal in the principal component analysis. In reality, the two types of climatic data are often highly correlated so that the physical reasonableness of the response function must be considered when it is interpreted. Cli- matic response function plots (Appendix C) are the usual way of graphic- ally presenting the results of response function analysis. Standard normal variates of ring-width indices or runoff values are plotted against partial regression coefficients of the variables, temperature, precipitation, and prior growth or prior runoff. Bars indicating 95% confidence limits of each weight or coefficient for each variable, calculated from their respective standard errors (Draper and Smith, 1966), are also shown. A more detailed discussion of the assumptions and 35 applications of response function analysis is found in Fritts et al.

(1971).

Canonical Analysis

Canonical analysis is a multivariate parametric statistical technique that includes both canonical correlation and canonical regression (Glahn, 1968; Clark, 1975). In many respects it is analogous to eigenvector analysis with two sets of data considered together. Canoni- cal correlation specifies orthogonal modes of intercorrelation between two sets of variables while canonical regression is used to determine, from canonical correlation, a set of regression coefficients which may then be applied to one set of variables to predict separately variables in the second set. Glahn (1968) and Clark (1975), for example, present detailed mathematical descriptions of canonical correlation analysis which will not be repeated here, while Fritts (1976) summarizes the major steps only. The method used to develop transfer functions from canonical analysis for reconstructing runoff from tree-ring chronologies is essentially the same as Stockton et al. (1978) used in estimating Palmer Drought Severity Indices.

According to Fritts (1976), canonical analysis is used for four main purposes. They are:

1) to obtain covarying modes of behavior between two sets of

variables,

2) to eliminate small-scale modes which have the lowest covariance

between sets, 36

3) to maximize the number of degrees of freedom in the final analy-

sis, and

4) to gain efficiency and stability by solving equations for a re-

duced number of variables.

Thus, the advantages of using canonical analysis are essentially those outlined for principal component analysis.

According to Poole and O'Farrell (1971), the successful and appropriate use of canonical analysis relies on several assumptions about the input data, two of which are more important than others. The first of these, that the data are normally distributed, becomes critical at two stages in the analysis: when the canonical weights are calculated and when the raw data are standardized prior to being post-multiplied by canonical weights to form canonical scores (also called canonical variates). Accordingly, the skew (s 3) and kurtosis (s 4 ) of the amplitude series of both the runoff data and tree-ring chronologies, in the 1958-

1973 calibration period, were calculated and tested against the values for the normal distribution (Chapter 7).

The other main consideration in using canonical analysis con- cerns multicollinearity in the data which, if it is present, may be a source of major error. The use of amplitudes rather than raw data the- oretically overcomes this problem.

Each canonical analysis results in three measures:

1) a set of latent roots, A's, which have values from 0 to 1.0,

2) a set of pairs of canonical vectors or canonical weights, and

3) a set of pairs of canonical scores or variates. 37

The latent roots, together with the associated indices of statistical significance, indicate the magnitude of patterns which are common to both data sets. The first X describes the maximum correlation between a weighted linear combination of predictand variables and any weighted linear combination of predictor variables, the second X describes the next highest possible correlation and so on for as many latent roots as there are variables in the smaller data set. The vectors or weights indicate the degree of involvement of each variable in each pattern and as such are somewhat analogous to eigenvector weights. The canonical scores or variates, in this case, reflect the involvement of each year's data in each of the common patterns and are related to the amplitudes derived from eigenvector analysis.

The correlation between two sets of canonical scores is equal to the square root of the corresponding latent root, X. The runoff data set used in this thesis had two variables only, the first and second amplitudes of seasonalized November to March streamflow, so that only two canonical correlation coefficients were calculated. Four variables, the first two amplitudes for t and t+1 years, comprised the tree-ring data set. Both canonical correlation coefficients were used in the canonical regression and subsequent reconstruction of runoff from tree rings.

Tests of Association

Tests of association are used to measure how closely one series is related to another. They may be employed to assess the predictive power or reliability of regression models used for reconstructing one 38 series, the predictand, from one or more predictors. When tests of association are made between reconstructed series and observed data, a distinction must be made between the dependent data used in the calibration period and independent data, which are observations not included in the calibration data. A satisfactory performance of a model during the calibration period is essential for reliable reconstruction, but the model must be tested with independent data to verify its reliability

(Anderson, Allen, and Cady, 1972).

The tests of association used in this thesis employ statistics to measure various types of similarity between pairs of series including independent predictand estimates and corresponding observed predictand values. The use of several different association tests in verification minimizes the limiting effects of any particular one. Several statistics are calculated: the correlation coefficient for untransformed and first-differenced pairs of series, the count of agreements in sign of differences from the mean and of first differences, and the reduction of error (RE) and the cross-product means. Each of these may be interpreted by comparison with a standard by hypothesis testing, except for RE which does not have known confidence limits. Each of these statistics is calculated for the 8 paired series of estimated and observed

November-March runoff in the 16-year calibration period. Only 3 of the

8 series have at least 8 years of independent data, the minimum number of observations necessary for verification (Gordon, in preparation).

Correlation Coefficient

The Pearson product-moment correlation coefficient, symbolized

by r, is a widely used measure of the relationship between two variables.

Mathematically, it is defined as the ratio of covariation to the square

root of the product of the variation in x and the variation in y, where

x and y symbolize the two variables whose correlation is calculated.

This corresponds to the formula:

- (Yi - r N 2 % 1=1 - TO2) (E.1=1 (Y. - 3) )} 2

where x. = the i th observation of variable x,

y. = the i th observation of variable y,

N = the number of observations,

= E.1=1 x./N1 = mean of variable x, and

= E i=1 y i /N = mean of variable y.

The correlation coefficient has a range from +1.0, indicating

perfect positive agreement to -1.0, indicating perfect inverse agree-

ment. A zero value occurs when the two data sets are completely unre-

lated. The correlation coefficient is used to measure the association

between two sets of climatic data, between runoff series from different

stream gauging stations, and also as a measure of similarity between re-

constructed and observed runoff series.

When used in verification tests to measure how well one series

is reconstructed from the other, r has two deficiencies. First, r is 40 insensitive to bias of the estimates and second, it is sensitive to long-term trends within the independent observed series and reconstructed series outside the calibration period. The second r statistic used, calculated from the first-differenced series, however, is relatively unaffected by trends and thus provides a measure of how well the year-to- year variations correspond between the reconstructed and observed series. The degrees of freedom used in significance tests of the null hypothesis Ho:p (the true or population value of r) = 0 against the alternative Ha:p>0 are N-2 for r and ri-3 for lid or the first-differenced series. A more detailed discussion of these statistics for verification is found in Gordon (in preparation).

As used in verification tests, the rejection of Ho and accep- tance of Ha for r implies that the model provides an acceptable reconstruction of the temporal pattern of the predictand. As used to compare other pairs of series, rejection of the null hypothesis implies that there is a stronger association between the two series than would be expected by chance alone.

The correlation coefficient is also used to measure association between items lagged in time and is then referred to as the autocorrelation (or serial correlation) coefficient, as described in the section on autocorrelation analysis.

Sign Tests

The verification procedure used in this investigation employs the sign test in two ways. First differences, the sequence obtained by subtracting each value in the time series from its immediate successor, 41 are calculated for the observed and for the estimated data. The signs of these first differences of corresponding values in the two time series are compared, and similarities (both positive or both negative) are tabulated. The magnitude of the first differences is not taken into account, and this application gives information only about the direction of the interannual variations. The second application of the sign test uses departures from the mean. A series of cross-products is formed, and the number of positive and negative products (of deviations) is found.

If the reconstructed series resembles the observed, the probability of a positive result (both series moving in the same direction or on the same side of the mean, respectively), 4, is greater than the probability of a negative result, p_. The null hypothesis, then, to test if p+ is significantly greater than p_, is Ho :p+ = p_ = .5. The alternative is Ha :p+ >p- . Cumulative distribution tables for the binomi- al distribution with parameter p = .5 (for N<45) or the normal distribution for N>45 using a Z score formed from N_ or N+ is used to find the critical level of N or N as outlined by Gordon (in preparation). H o may be rejected in favor of Ha if N_ N-crit or > N+crit Statis- tical textbooks may also contain tables of significance values for the sign test (e.g., Snedecor and Cochran, 1967, Table A8, p. 554).

Both applications of the sign test, described here and used to check runoff reconstructions, are tested for significance in the above manner. The first-differenced method, because it emphasizes the association between series at high (year-to-year) frequencies, is relatively 42 unaffected by trends and persistence in the data; it disregards the relationship of the values to the mean. The difference from the mean application measures association at all frequencies, but may be affected by trend in the data. It is useful to apply both types of sign test to verification as each gives different types of information about the relationship between the estimated and predictand data.

Reduction of Error

This statistic, applied to the dependent data set, is equiva- lent to the square of the correlation coefficient which is a measure of the percent variance calibrated by the relationship with the predictor or independent data set. It has possible values from a maximum of 1.0 to a minimum of minus infinity. In the absence of knowledge of significance levels, Fritts (1976) considers any positive values to be encouraging.

The computations for the reduction of error (RE) are:

RE = 1 - SSR/SSM where SSR = the sum of squares of the residuals (differences between the actual data and the statistical estimates), and

SSM = the sum of squares of the differences of the actual data from the mean of the dependent set used for calibration.

Statistical tests for positive values of RE are the same as those for r 2 the square of the correlation coefficient. The reduction of error statistic has the disadvantage that one very bad estimate can offset the effect of several very good estimates (Fritts, 1976), especially when 43 the sample size, N, is small. Gordon (in preparation) deals with the use of this statistic for verification in greater detail.

Cross-product Means Test

The cross-product means test (Fritts, 1976), used in verification tests, takes into account both the sign and magnitude of the departure from the calibration mean. It is computed from the product of the departures of the actual and estimated values from the mean value, with the positive and negative products averaged separately. The two average cross-products, M+ and M_, correspond to the agreeing and disagreeing estimates. The difference between the absolute values of 11+ and M is tested with the t statistic as: 2 2 (m+ M ) - ) + s_ t= + - - , SE = 2 N N_ SE + where SE = the standard error of the differences between the two mean values,

of positive and negative cross-products, N+ and N = the number respectively, 2 s and s 2 = the corresponding sample variances, and

or population mean values of the posi- p+ and p_ = the hypothetical tive and negative cross-products.

The value of t computed from the above equation is compared with

the critical value obtained from a table of percentage points for the

t-distribution (e.g., Snedecor and Cochran, 1967, Table A4, p. 549).

+ N > 30, the table is entered with (N + N -2) degrees of When N+ _ + freedom at the one-sided 95% probability level. A value of t that is

greater than the tabulated critical level indicates that the mean of the

positive products is significantly greater than the mean of the negative

products.

Since the sample sizes available for verification are small

(N+ + N < 30), the statistic calculated from the above equation devi-

ates from the t-distribution, and significance testing depends on an

adjusted number of degrees of freedom (d.f.). Welch's approximation

(Bickel and Doksum, 1977, p. 218) is used to give the adjusted d.f. as

follows:

2 2 -1 k = ( q + ) N +1 N - 1 +

2 2 where q = s +/(N + SE ). Gordon (in preparation) describes underlying assumptions in the use of the cross-product means test and the implica-

tions of violating these assumptions. In particular, the use of the t-

distribution assumes that the positive and negative cross-products are

normally distributed. This condition is not true, since the products

are considered separately and are therefore bounded on one side by a

zero value. When M+ and M are both large relative to the standard deviations of the cross-products, this departure from the assumption of

normality is less important (Gordon, in preparation). CHAPTER 4

CLIMATIC DATA

Monthly precipitation and temperature observations in Tasmania rarely begin before 1900 and many start much later. There are fewer temperature than precipitation stations, and both are poorly represented

in the relatively sparsely settled Western or Mountain region and in the

Midland, as the districts are defined by the Australian Bureau of Meteo-

rology (Figure 2). Among the few analyses of Tasmania's climate are two

reports, Watson and Wylie (1972) and Watson (1978), by the Hydro-

Electric Commission (HEC) of that state. The first report analyzes

long-term rainfall records, and the second describes the climate of the

lower Gordon River region, an area of concern to this thesis.

Monthly total precipitation (mm) and monthly averages of daily

maximum temperature ( ° C) data were obtained from the Australian Bureau

of Meteorology, the source of all climatic data ubed. Daily maximum

temperatures, rather than daily means, were selected because they were

considered to be more important in influencing tree growth.

Selection of Climatic Station Networks

In any study of this nature, a compromise in the selection of

data between length of record and number of stations must be made. All

available records were screened for length and completeness, and all

stations with data missing for 24 or more consecutive months were 45 46 rejected. The common analysis period of 30 years, 1941-1970, was selected and homogeneity tests, outlined below, were performed on the data. All precipitation records were found to be homogeneous and, after elimination of temperature records from a few stations, networks of 78 precipitation and 15 temperature stations, including those on Flinders

Island and King Island, were available for further analysis. The few estimates of monthly data needed to complete the series were made using a weighted regression on surrounding stations, as described below.

Analyses by Watson and Wylie (1972) 'suggest that the mean of the 30 years of annual precipitation used in this thesis is likely to be higher and the range less than for the longer term (1884-1970) mean annual precipitation.

Homogeneity Testing of Temperature and Precipitation Series

Graphical analysis tests for homogeneity of the climatic data were made to assess the "uniform representativeness of the data for conditions in rather large geographical areas" (Mitchell et al., 1966, p.

8). For the temperature records, year-by-year differences between the series being evaluated and at least two other series were computed and the cumulative differences between pairs of station records were plotted. The absence of spikes or abrupt changes in the gradient of the line of best fit through the points indicated that the records were relatively homogeneous.

A double-mass technique (Kohler, 1949), whereby series of cumulative annual total precipitation of the station record under test and 47 series from other stations were plotted, was used to check homogeneity of precipitation records. Again, a departure from or gradient change of an approximately straight line indicated inhomogeneity in at least one of the records in the pair (Kohler, 1949; Mitchell et al., 1966;

LaMarche and Stockton, 1974; Fritts, 1976).

Estimation of Missing Temperature and Precipitation Data

Few estimates were needed to complete the 30-year record in each network and, where necessary, the same method was applied to both monthly total precipitation and monthly daily maximum temperature. For each station whose record was missing data, the interpolation station, 3 to 5 index stations to cover all directions around it, were selected. The station record to be estimated was then used as the dependent variable and the other station records as a set of independent variables in a series of stepwise multiple linear regression analyses performed separately for each month (Draper and Smith, 1966), for either temperature or precipitation. The results of these regressions were applied to estimate each missing monthly value (Y1 ) of temperature or precipitation using the following formula:

Œ4Y4 Y 1 - a 2Y2 a3113 a 5Y5 (1 611 6 K where a value for station 1 is being estimated from 5 other station records (for the particular month) whose partial regression coefficients are the a's and K is a constant derived in the regression analysis. 48

The estimation technique takes into account the seasonal vari-

ations in dominant weather patterns which may influence a station from

different directions in different months. Thus, the order in which each

index station enters the multiple regression and its relative regression

weight may change from month to month. This flexibility is not possible with alternative estimation methods relying on a fixed ratio over all

months between the incomplete series and those used for estimation of

missing values.

A. B. Pittock (personal communication, 1979) found the multiple

regression technique, described above, to be superior to the normal-

ratio method (Paulhus and Kohler, 1952; McDonald, 1957) and to the

normal-ratio method weighted by the inverse of the distance when each

procedure was applied to the Tasmanian precipitation data. The criteri-

on used for this evaluation was the percentage variance of the actual

observations at the interpolated station accounted for by the estimates.

Temperature estimates were not made with either of the normal-ratio methods for comparison with the multiple regression technique.

Appendix A contains maps which show the location of the selected

networks and tables, which list the corresponding catalogue number (Aus-

tralian Bureau of Meteorology), name, latitude, and longitude of the

climate stations whose records were used in this thesis.

Eigenvector Analysis

A principal component analysis was performed separately on each

grid using monthly mean daily maximum temperature and mean monthly precipitation. The results of these analyses were used to generate 49 estimates of precipitation and temperature records close to tree-ring sites and watersheds (Figure 1). The first three eigenvectors of maximum temperature, for each month, accounting for about 86% of the variance in the original data, were plotted on a set of 36 maps and then contoured. The first 4 eigenvectors of monthly precipitation, also accounting for 86% variance, were contoured on another set of 48 maps.

Interpolations from these contours to tree-ring sites and stream gauging station catchment midpoints were made for each month for each eigenvector of temperature and precipitation. Each interpolated eigenvector value associated with a tree-ring site or catchment midpoint was then multiplied by its respective eigenvector amplitude, and the products summed for each month for either temperature or precipitation. The results are standard normal variates considered to be the best possible estimates of climatic data where nearby instrumental records are unavailable (V. C. LaMarche, Jr., personal communication, 1980).

As far as is known, this technique of estimating data has not been re- ported in the literature.

Stidd (1967) used eigenvectors to estimate mean monthly precipitation values for 60 stations in Nevada. He found that station elevations significantly affected the eigenvector values so that his inter interpolations needed to be adjusted to a mean elevation. Consequently, the linear correlations (Pearson product-moment 0 between the altitude of stations used in the Tasmanian networks and each of the first three eigenvectors for January and for July were measured. These calculations were made for both monthly mean daily maximum temperature and mean 50

monthly total precipitation. There were, however, no significant cor-

relations so that corrections for station elevation were unnecessary.

The validity of the interpolated estimations was checked in 2

ways. Firstly, estimates were made at 6 precipitation stations with

complete 30-year, 1941-1970, records, and at 4 temperature stations with

at least 16 years of data (N=16, 17, 22 and 30), excluded from the data

networks (Appendix A). Correlations were then calculated between the

estimated and actual data. For the 30-year records, r greater than .46

is significantly different from zero at the 99% confidence level. For

the average length of temperature records (N=19), r greater than .58 is

significant at the 99% level. Since all values shown (Table 1) exceed

the 99% confidence limits (assuming independence), it can be accepted

that the estimated series are highly correlated with the observed. Al-

though precipitation tends to be less spatially homogeneous (more vari-

able) than temperature, the higher density of stations in Tasmania

allows better estimation of precipitation when an interpolative proce-

dure is used.

Secondly, wherever climatic stations were close to tree-ring

sites or stream-gauging stations, separate climatic response functions were calculated using both recorded data and the interpolated estimates

of temperature and precipitation. In most cases, the results were simi-

lar enough for confidence to be placed in this method of estimating climatic data. ▪

0:1 aJ

c.) a) co

a 0

cri a) N- 4_1 U)

0 .0 cd

a) a 3-1 0 .0 ..0 (i) 1—) 0

cn1 co co ai

a) co Co Lf $.4 cd r•-• cd co •H c.n o ;.T.1 3-4 • c-r) CO

c•-1 a) cnI

0 -.1- a) O N-I-4 -0 F.T.4

0 -H 0 on 0 cd co co cd • II

0.) }-1 $-4 0 52

Drought

"The term hydrologic drought is defined as a deficiency in water

supply or precipitation in time, area or both. Any hydrologic drought

involves duration, areal extent, severity, probability of recurrence and

location in absolute time" (Watson and Wylie, 1972, p. 7). These work-

ers calculated drought duration intensity values for several stations in

the precipitation network, for runs in excess of two years, using the

parameters defined by Yevjevich (1967):

duration = run minus length of negative deviations,

severity = run minus sum of negative deviations, and

intensity = severity/duration.

The computational formula is:

drought intensity - X - / N SD where X = annual rainfall,

X = mean annual rainfall,

SD = standard deviation of annual rainfall, and

N = duration of deficiency in years.

Unlike the monthly Palmer drought severity index (PDSI),

(Palmer, 1965), temperature is not included as a variable in the indices calculated by Watson and Wylie (1972). Values for three stations,

Franklin, Gormanston, and Waratah (Appendix A), which respectively are not far from the catchments of or gauging stations 119, 78, and 159, were extracted from Watson and Wylie (1972, Figure 10) and are presented in Table 2. These data may be relevant to later discussions of runoff

Table 2. Drought Duration Intensity for Runs in Excess of Two Years.

Station Period' Drought Intensity (a) Franklin 1885-1892 0.85 1894-1900 0.55 1918-1921 0.67 1939-1943 0.56 1948-1951 0.74 1964-1967 0.78

(b) Gormanston 1897-1900 0.99 1901-1903 0.43 1905-1908 0.44 1917-1922 0.67 1931-1933 0.80 1935-1938 0.50 1948-1951 0.97 1958-1961 1.17

(c) Waratah 1884-1894 0.75 1896-1900 0.40 1917-1922 0.48 1924-1927 0.81 1948-1951 1.16 1958-1961 1.06 1964-1967 1.27 1 Gormanston rainfall record begins in 1895, others in 1884. Last year of record is 1970 for all three stations. 54 reconstruction at the three gauging stations (Chapter 7). According to Watson and Wylie (1972), the longest period of extended, extensive drought in Tasmania for their period of analysis (1884-1970) was 1886- 1902. CHAPTER 5

DENDROCHRONOLOGY

The ring-width series (chronologies) available for this study were collected for a project to reconstruct past climate (LaMarche et al., 1979). The sites were selected to cover a wide geographic range and to include several species, so that the data are not necessarily from optimum locations for comparison with runoff. However, within a limited area, actual tree sites were chosen to maximize the climatic signal, a stragegy that would have been followed had the samples been collected specifically for a dendrohydrologic study. As a general pol- icy, a minimum sample size of ten trees was considered to be desirable, but several of the series are comprised of data from fewer trees (Table

3).

Site Characteristics

The general physical characteristics of Tasmania have been outlined in Chapter 2. The tree-ring sites (Figure 5) are generally in high rainfall areas and frequently include dense forest stands, very different from the environments found to be best suited for dendrochronological research in the southwestern part of the United States. Yet, these sites appear to yield chronologies sensitive to precipitation and temperature variations. The apparent paradox is thought to be explained by the soils in which the sampled trees grow. These soils tend to be shallow and often are coarse-textured. They have high infiltration

55 ▪ •

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ci) ro4 1-4 44 H H cd CD 1:4 H >4 g O H 4.1 z L) Z ,17,11 cri U PD O 0 "0 Ca H ai .1-1 0 H X 0 U cd 0 0 H 0 4 ▪ C.) -S -ci PLI <4 4-) i ci) o cf) -L) E H 0 1:14

14,5 ° 146° 147° 148°

145° 146° 147 0 148°

Figure 5. Location Map of Tree-ring Sites. -- Species code: stars = Phyllocladus aspleniifolius, open square = Athrotaxis selaginoides, closed square = Athrotaxis cupressoides, open circle = Nothofagus gunnii. 58 capacities so that local soil-moisture deficits may occur despite the high precipitation. In addition, the sites (except Pine Lake) from which the chronologies were derived are on slopes and can be considered to be well-drained. The Pine Lake site occurs on a relatively level relict block-field with a shallow water table.

Two Athrotaxis sites, Mount Field and Pine Lake, are at 1200 m elevation and have coarse, rocky soils derived from dolente. Most of the trees sampled at Mount Field are growing on steep, east-facing slopes while those at Pine Lake are scattered among large dolente boulders on only very slight slopes. The moderate gradients of Wein- dorfer Forest and the adjacent Cradle Mountain site are west-facing.

The soil depth was not measured but appears to be greater than at the other sites; the forest floor is covered with organic matter including logs in various stages of decay.

The seven Phyllocladus chronologies were developed from sites with a range of parent materials, slopes, and aspects. All these sites except Holly Range Road have fairly shallow soil; at Holly Range Road a deeper clayey soil has formed on schist. The Dove River Stand, unlike others sampled, is relatively even-aged, and the cored trees are generally younger than those from which the other ten site chronologies were derived. Further details, including the associated plant species of each individual site, may be found in LaMarche et al. (1979).

Chronology Statistics

Table 4 shows four of the most important statistics used to

characterize tree-ring chronologies. These are the first - order serial 59

0 cli ).4 tel 0-) cr) Cr% 0 a) a) N C) T-1 .1- on CJ b 0 A

(i) c_) 0 cd 0 c.) › cd N N CV 4-) 4-1 k (1) 0C

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0 7-, Cl) 0 3 H (-) CO H Tn C D (-n Cr) rn h- cf) c,-) 4-) o c-4 'd 4-1 0 H 13.) C ,․) o co 0 4-) 0 CO N c-4 N H N $.4 Cl) cd •r-1 0 0 •Hl 4-) 14-1 .64 C/d (d cn W ci) H • Cd N

0 0 0 ?) 4-1 0 I P 1-1 444 .44 4--) al cd Lr) Lf) CSN CO cc) 0 0 C/) -0 r1 r-i - LC 1-4 cr, c:r% Ce) cl') Cr, 4-4 %.0 Lin cc) tr) N N H vo )-4 -H )-0 -1-1 0 a) $.4 -H 6 PT-1 ci] $-) -H o CI) 0 a) W CO CO

COQ) 4-) H 44 P4 1-4 Fx-1 W 4 Cd •H 1-1 Z H H cf) 6 g P-1 1-1 C-1 p cf) 60 correlation coefficient (rd'- ) standard deviation (s), standard error (SE), and mean sensitivity (MS). Analysis of variance results are pre-

sented for 6 of the 11 chronologies, the others having too few paired

radii or being composite chronologies whose component series were ana-

lyzed separately (LaMarche et al., 1979). Although these results are

not used directly in the thesis, they aid in the interpretation of some

later analyses. Within the set of 11 chronologies, only Phyllocladus (7

sites) is well-replicated.

Table 5 compares the values of mean sensitivity (MS), first-

order serial correlation (r- 1 ), and the percent variance in the chronol- 2 ogy accounted for by year-to-year variation (a y), from Tasmanian chron-

ologies with those from other areas. The mean values of MS and r1 from

Tasmania are intermediate between mean values of these statistics from

the eastern and western United States. Average values of these or any

other statistics may have little meaning unless the range of values is

also presented. Accordingly, the maximum and minimum values for these

and percent variance due to a 2 y, extracted from recent dendrochronologi-

cal reports (Stockton, 1975; Cook, 1976; Duvick, 1979) are also given.

The analysis periods are not equal for all these data, but approximately

100 years of data were included in each series. The Tasmanian chronolo-

gies have slightly higher MS than those of Cook (1976) and Duvick (1979),

and all have higher values than the average for the eastern United

States. The first-order serial correlation of the Tasmanian chronolo-

gies shows an extreme range and some unusually low values. 2 The mean percent variance accounted for by a y, but not the minimum, is lower in the Tasmanian chronologies than in any other series 61

Ln cs4 o0 cr) 4-1 o cd 4-) cu c-n0c5-, c!, Q) Ln ce-) -d- cv Q) crs u) H 4 Cs CD r-- 0 N Q) 7, "0 esi c..) b N- cr-) Ln cf) cd 0 0 cd r--4 cd c.) -H cd E r4 $.4 a) • • cd CO h 0 cr, o ts3 Q) Lr cN cr, N u) N $.4 • I a) -0 0 o 4-1 r1 1 0 Ca 1+4 0 •H CC1 0 0 •-1 0c Ln on cn a.) ,c) t4-1 • 4, z cll I cd 6 w r-1 CU $-1 CJ Q) Eh c) • c:7\ r•-• •H LI Q) ccl •H a) 4 1 Li-) a.1 to •-) 4J 0Q)cd C!, o co $-1 L10 C..) a) "ti •H r-1 0 4-1 -H <4 cd ••-1 • 0 o $-1 o cn N 0 0 •r-i O .' cd ci-.i. $.4 • cd 4-) C_) co 1-1 2 Q) Q) 0 .o 00 o Cr 1-1 $-1 4-1 0-1 4-1 t4-i 4-1 cu • c0 0 $-4 .0 • a) t4-1 4-1 t-I-1 C!, Q-4 •,-1 • 4-) OD u^) cf) al 0 Z Cl) •r4 0 $.4ci) 44 0 • .1-1 0 0 -H c-n N cri 0 0 0 4-) 4 cd W -H c.) cn za) g Cd 4-1 a) 0 • • cd $-1 co 0 04-i (4-1 3-1 1-1 C.) 0 cd co cd "c) co c..) 0 •r1 14-t a) 0 •, • .Ni 0 CU r4 , •ri 01 ...-. CI) 1:10 • In .-1• --co Fi'l-c n 0 P-4 0 1-4 04 CnI N- .••-•, a) a) a) a) 0 m 01 a. 4_) 4.) .0 4.-) •H $-1 0 CO 0 • C.) n—i ,---, r-- co cd co ni Car-4 0 cO a...... ,.․) cr, cd 4-1 a) 4-1 44 04 c.ci)) N- ,--1 rxi cf) cf) op co 1-1 ^ 0 CN ••••• 0 (1) • 4 0 CU .1-1 0 1-1 •ri CU '0 O.) "d •r-100U0.10g a .W -....., .- 0 O0 CU bp CU S-1 C.) '17 CU ..- c.) Lml cd 4.4 ni 4..) 0 eA0 .1-1 3-1 Cd 1-1 •-1 C) ,.- -H 5. $.4 -H $.4 -,-1 0 -0 0 0 › (0 a) 0 a) 0 bJ) 0 o cd cd a) cd 4-1 0 ni › › 0 u0E-+H cn c.) A H <4 <4 N 'st 62 considered. This statistic as a measure of climatic sensitivity is discussed later in this chapter.

Autocorrelation coefficients at lags of more than one year were calculated for the Tasmanian chronologies because the first-order correlation coefficients, of at least some of the series (Table 4, CLH, BIT, and SHT), are inconsistent with climatically sensitive records. Low r1 values suggest that the ring-width series are generated by approximately

random (white noise) stochastic processes, but the value of rk (Table

6), where k is the lag in years, confirms the existence of trend within

the chronologies. The pattern of rk values and their failure to fall within the 95% confidence limits for a random process (±1.96/VN), ex-

cept after many lags, is evidence that the underlying process generating

the chronologies is most like a mixed autoregressive-moving average pro-

cess (Watts, 1967).

In this respect, the Tasmanian chronologies give similar correl-

°grams to chronologies from Arizona and New Mexico (Stockton, 1975).

That is, the autocorrelation function was probably generated by the

process:

+ a v + a vt-3 + z + B, z + z Yt a lYt-1 t-2 .3" t t-1 2 t-2

where y t = ring width index at time t and

z t = a random variable at time t.

Stockton (1975), however, found that in most cases, his data could be

adequately fit by a less complex, second-order, autoregressive model:

Yt = a lYt-1 agt-2 z t •

co in H H 0 Il Il Cl) "0 cn N- H ,.0 0 0 Ln c.! ,.0 C H 0 4-1 c...) 0 H-1 ..1 Cs) N r-1 1-1 C1/4.1 -1 C1/41 Eccio •-n A A A al Pl, 3-i 0 1"--. CH) ....1- 00 0 r--1 0 cc. %.0 c), cn 4-) 0 0 )--I )--1 0 H H H 0 o 0 0 5 cd •H "0 r-1 000 4-4 ai .1-1 "G a) 4-1 a) 'G G. 0 u • 4-4 Cr) C•1/41 Q 1-1 C1/41 N Q C1/4.1 G 0 a) 4-) c.) 4 Z •)-1 a) 4-1 u) "G

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Cd "0 4 a) H ro H C) GI co Q cv a\ c-4 v;) c), 0w cz) cc) cc) cv N cv -1- Q N •r 4 '0 • 10 •r 4 a) 0 .0 4-} 4-1 a1 Z cci Q) 4J ai ccj .J'—'• 4-1 •)-1 4 a) 4-) -G c.) cc) N. on N. co •.t 0 P. 0 a) u) H H esi tr) N Cc) L L CN1 n.0 Gi H 4-) H cl 0 4 •)--) crf c.) 0 c) Z cci E G 0 0bd) 00(1)0 410 H Ln H 0 Ln 0, on c 0- 4-1 0.1 •,-1 a) H L oc) in cn os! H 1/40 1/4.0 0 T--1 Cl) 'd r-1 $-ItO a) cd a) I a) c\I c)5 -0 'G a) $-4 o 0 a)p ad 440 14 4-4 .1..) /1 /1 /1 /1 r•-•, C1/41 03 0 1/40 CO cD co G) 0 U) 0 1/40 C1/4.1 Q CNI 1/40 Cr) 1/40 CD 'V C.) 3D ci) N. ov N 1/40 on -1- .4- -t II Z cci a) 4-1 a) H 0 0 0 0 0 0 0 0 0 0 0 0. I4-4 O - Li") 1-1 S. 00 4-1 CL) E-• 7, N- C1/41 C1/4.1 -1- cc) cr, 04-4H 0 ••-i W 4-4(4) 44 • cd cd a) u) a) 04 a) a) -0 0 -G Z ›, c.) TI 0 0 4-3 a) 0 ›N /1 /1 /-... /1 /1 /1 /1 s /1 /1 ci -H trà $.4 W Ct) Cl) tn Cri C/3 Cr] CO -ii = cn 0 P. 3 d) C.7 g g <4 g c.) u) cci - 4 ci Q) 1--1 H 0 = = H g g a) H u) 4-1 4.4 JU 0 <4 Z P4 P. ID-1 P-1 P-) •G P.4 •H G a) 0 a) a) a) HG ....• •...... - ...... --, -....- s...., ,.._., ....) c.) 0 5 3 -0 Cl) 0 a) H H O o E •H $.4 H Pt-1 g w a g x a H H rr3 CQ 44 4 0 0 .0 Z H 71 14 Z H = cl) 0 4-1 Z 0 H 0R C A4 1-4 Z C.) Cz-i s:0 C/) 1-1 N Cr) 64

It is thought that this is likely to be true of the chronologies used in this thesis. A more detailed examination of the time series properties of these and other tree-ring chronologies from Tasmania is expected to be made by T. Bird (personal communication, 1980).

Table 6 shows the autocorrelation coefficient for each of the 11 chronologies for up to 8 lags, although values for 20 lags were calculated. There is a tendency for the Athrotaxis chronologies, CMT, PNL, and MTF, to have higher first-order correlation coefficients than the other chronologies. These high values appear to dampen more regularly; for example, in CMT a constant ratio of about 1.25 is maintained between rk and 11+1 for the first 4 lags. The values for Phyllocladus fluctu- ate greatly, and several increase from r 1 to r 2 . The consistently higher r, in the three Athrotaxis chronologies suggests that there may be a difference in ring-width generating processes between this genus and

Phyllocladus; generalizations cannot be made about Nothofagus, since this genus is represented in only one chronology, WDF.

Tree-ring Climatic Response Functions

The general procedure of climatic response function analysis has been outlined in Chapter 3, and the response to climate of trees growing in a variety of limiting environments has been detailed by Fritts

(1976). Models have been developed to describe how climate affects physiological processes within a tree and through these processes the relative width of the annual ring (Fritts, 1976, Figures 5.8 to 5.10, pp. 227-238). The models recognized as generally applicable to northern hemisphere species on moisture-limited sites may need modification for 65

Tasmanian conditions. Some of the sites sampled do not appear to be moisture-limited and do not conform in several respects to criteria of ideal tree-ring sites as outlined in classic dendrochronological theory

(Stokes and Smiley, 1968; Fritts, 1976). Despite these differences in growing conditions, it appears that most of the principles of dendrochronology can be applied to the development of new chronologies from diverse species and areas such as those found in Tasmania.

Although the phenology of the tree species used in this project is poorly documented, it is probable that, as for Pinus spp. for which

Fritts's models were developed, summer is the season of most tree growth. It is generally considered that environmental conditions prior to the actual growing season can influence ring width, so these must be included in any climate-tree growth analysis. Therefore, an 18-month period from the beginning of October preceding the likely growing season through March of the year in which the annual ring is completed was included in the response function analyses. The conventional computer programs used in these analyses were modified so that meteorological data for parts of three consecutive calendar years could be used. This modification was needed because summer (the growing season) in the southern hemisphere extends from one calendar year to the next, while in the northern hemisphere it occurs within a single calendar year. Three years of prior growth were included as variables to compensate for autocorrelation within the tree-ring series (Fritts et al., 1971). Vari- ables were allowed to enter the regression equation until the F-level of entry was reduced to 1.0. 66

Chronology Climatic Response Function Results

The analyses use a regression model which allows the entry of eigenvectors of climate accounting for up to 80% variance in the original temperature or precipitation data. In most of the response functions, this means that 10 to 12 climatic variables and a possible 3 prior growth variables give a maximum of about 15 predictors. Since 3 years of prior growth were included in the regression model, N for the

30-year (1941-1970) analysis period is 27. The significance of the F- level of entry of each variable is tested using the F test with (1,

26 - k) degrees of freedom at step k. When the variable enters the regression at less than 95% but more than 90% significance, the step is accepted if the variable is climatic, but a previous step is chosen if the entering variable is prior growth.

Table 7 summarizes the results of climatic response functions for the set of 11 chronologies, using temperature and precipitation data for the 18-month period October t-1 year to March t year, 3 years of prior growth and constraints on the entry of variables, described above. The percentage variance calibrated by the regression attributable to climate and to prior growth and the number of regression steps included are also tabulated in Table 7. Graphs of the response functions for all chronologies are presented in Appendix C. In only 2 chronologies, LYL and BIT, was there more than 50% variance in the chronologies explained by the 18 months of climatic variables in the calibration period 1941-1970. 6 7

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++++ I I 1 on

+ I

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+ a.) H + + oIo 0

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D. a) 0 Z Lin 4f) r--

E-4 H rz-1 H n E-1 •• •• 1:4 ›-t H 6 tz0 L) 1:41 C/) 68

Positive (+) and negative (-) correlations between tree growth and climatic variables are tabulated for each month, together with the totals, to give an indication of the "mean response." Positive correlations mean that warmer or wetter conditions are, in a particular month, associated with wider than average rings, while negative correlations mean that these conditions are associated with narrower rings.

The most consistent result is for a negative correlation with temperature of the summer and positive correlation with temperature of the winter prior to the expected growing season. The MTF Athrotaxis cupressoides chronology behaves differently from all others; the only other chronology of this species, from Pine Lake (PNL), showed no significant correlations with climate and prior growth variance accounted for the total variance explained. There is a generally positive association between ring width and precipitation of both the previous and current summers and a strong negative relationship with July (mid- winter) precipitation. This negative response may be indicative of a positive response to solar radiation. Wetter winters are associated with cloudy conditions which possibly limit photosynthesis and lead, in part, to narrow ring widths in the subsequent season (T. Bird, personal communication, 1980).

The response function analyses whose results are presented serve mainly as a guide to the most promising associations between runoff and ring-width data. Only one species, Phyllocladus aspleniifolius, is well-replicated, and generalizations about the response to climate of

the other three species cannot be made; the results of eigenvector 69 analysis, however, suggest a species differentiation in the mode of chronology variation.

A further set of climatic response functions whose results are not presented in this thesis, using a model excluding prior growth variables, gives generally higher percentages of calibrated climatic variance in these 11 chronologies (V. C. LaMarche, Jr., personal communication, 1980). It is not clear, at present, which model is more appropriate for analyzing the relationship between ring width and monthly

climatic variables. Further experimentation with various models may

clarify this.

Site Location and Climatic Sensitivity

When compared with Ogden's (1978b) ecological range diagram, a modified version of which is presented in Figure 6, all of the 11 sites except Cradle Mountain are close to the margins of either the altitudinal or precipitational ranges or both. Some of the sites, Dove River

Road, Pieman River, and Lyell Highway (Figure 6, C, D, E), apparently lie outside the ranges given by Ogden, a reflection of the inadequacy of a generalized vegetation map to represent local variations in plant associations. Estimates of annual precipitation used in Figure 6 are from several sources, including interpolation from a detailed map by Watson and Wylie (1972).

The Phyllocladus sites span a wide altitudinal and precipitational gradient: the A. cupressoides sites are from upper elevational and lower rainfall ends of their range, while the A. selaginoides site at Cradle Mountain is perhaps representative of that species under 70

1200-

100 200 300 Regional Annual Precipitation (cm)

Figure 6. Position of Tree-ring Sites within the Altitudinal and Pre- cipitational Range of Three Species. -- Species code as in Figure 5 and site code as in Figure 7. Diagram is adapted from Ogden (1978b, Figure 6, p. 349). 71 optimum growing conditions. Although data for Nothofagus gunnii were not presented by Ogden (1978b), this species, as a component of the temperate forest association, has an altitudinal range from sea level to

1100 m (Jackson, 1965) and could be approximated in Figure 6 by the range for Phyllocladus. The Weindorfer Forest (WDF) site would thus be one of the highest and wettest locations at which Nothofagus gunnii could be expected if only Jackson's generalization is used. T. Bird

(personal communication, 1980), however, states that N. gunnii is found in exclusively high and wet areas so that WDF is a typical rather than extreme site for the species.

There are several measures of the climatic sensitivity of a chronology. Mean sensitivity (MS) (Douglass, 1936) is a relatively reliable indicator of the likely dendroclimatic potential of tree-ring index series in arid areas. Percent of variance due to year-to-year 2 differences in mean index (a y) in a set of chronologies often reflects the MS, higher values of each indicating greater sensitivity. In response function analysis, the more climatically sensitive chronologies might be expected to have a greater number of climatic variables significant to growth (ring-width index). The variance due to climate, calibrated by the response function using an appropriate set of climatic data, may be the most powerful measure of the dendroclimatic (or dendrohydrologic) quality of a chronology.

The relationship between mean sensitivity calculated after stan- 2 dardization, a y, and calibrated climatic variance is not as clear in 72 the Tasmanian chronologies as in those from drier areas of the southwestern United States. The Phyllocladus chronologies have consistently higher MS than those of the other three Tasmanian species, which are less well-replicated. The cl 2y values, where calculated, do not reflect the rankings of the mean sensitivity (Table 4). The percent variance calibrated by the response functions also is inconsistent with that pre- 2 dicted from a knowledge of the mean sensitivity and a y. 2 Values of a y are not available for the two chronologies with the highest MS values, St. Helens (.47) and Holly Range Road (.28). De- spite their relatively high mean sensitivities, these two chronologies have less than 40% climate variance calibrated by the two significant

(95%) response function steps (Table 7). The Mount Field chronology, however, with an MS of only .13, the lowest in the set of 11 chronologies, has 42% climatic variance calibrated by 4 significant response function steps (Table 7).

The position of each tree-ring site within the ecological range for its species should be reflected in the response function analysis.

Those sites closer to the drier parts of the range, other things being equal, would be expected to have a greater number of significant monthly precipitation variables than would a higher rainfall site. Only the

Phyllocladus sites can be considered, and even then there are too few sites with comparable conditions at present to adequately test if this principle holds in Tasmania. The 18-month (October, t-1, to March, 0 response functions for the drier site, St. Helens, has 15 precipitation elements significant, while the wetter site, Dove River Road, at 73

slightly higher altitude, has 12. The Lyell Highway chronology is a

composite from a site at approximately 360 m in the Franklin River

Valley and another on Mt. Arrowsmith at about 800 m, close to the upper

altitudinal range for Phyllocladus (Ogden, 1978b). The position of

sites shown in Figure 6 represents an average altitude and rainfall.

Response functions show, as expected, significant regression weights for

more months of temperature for the Lyell Highway chronology than for

that from Pieman River, a site receiving approximately the same annual

rainfall but at a lower elevation.

These results suggest that the general principle of climatic

sensitivity in relation to ecological amplitude holds, at least in the

Phyllocladus used in this study. There were too few paired radii mea-

sured to perform a statistically valid analysis of variance on all of

the 11 sites, but in general, the most limited sites would have been 2 expected to produce chronologies with the largest a y or chronology

variance when this was expressed as a percentage of the total variance

in each chronology.

Stockton (1975), in a study in the southwestern United States,

states that among other things, the ideal chronology for potential use 2 in hydrologic reconstructions would have a high a y and high mean sen-

sitivity. It must be noted, however, that the criteria used to judge

the dendroclimatic or dendrohydrologic quality of tree-ring chronologies

may not be entirely applicable to those from very wet sites. Cook

(1976) observed, in his study of chronologies from the eastern United

States, that climatic sensitivity may be more closely related to edaphic

site factors than to geographic location. This comment may be 74 especially relevant to the Tasmanian chronologies, as has been shown by the inconsistent relationship between the usual measures of sensitivity.

Eigenvector Analysis

A principal component analysis for the 199-year period, 1776-

1974, was conducted on the set of 11 site chronologies. Eigenvectors were extracted from a correlation matrix and the elements of the first three, accounting for 58% of the total variance, are plotted in Figure

7. The weights of each of these eigenvectors for each chronology would be expected to reflect the major sources of variation within each chronology. It seems, indeed, that these results may be reasonably interpreted in terms of overall climatic influences.

Higher order eigenvectors, representing smaller amounts of total variance, would be expected to reflect more local influences such as site characteristics within a species group. The eigenvector patterns shown in Figure 7 and the results of response-function analysis confirm and complement one another. To a certain degree they also validate the empirically derived relationships between runoff and tree rings (Chapter

7), since both types of series are climatically influenced.

The most important mode of variation is common to all chronologies. This is indicated by the small range of weights for the first eigenvector at all sites. The three Athrotaxis sites (Figure 7, A, H,

I) have weights closer to zero, which may reflect a difference in chronology variation due to tree genus or to frequency of variance since the Phyllocladus chronologies are characterized by high year-to-year Figure 7. First Three Eigenvectors of Tree Growth. -- Eigenvectors were extracted from the correlation matrix of 11 tree-ring chronologies from Tasmania. The 3 eigenvectors together represent 58.3% of the total variance of the chronologies in the 199-year period, 1776-1974.

A = CMT Athrotaxis selaginoides B = WDF Nothofagus gunnii C = DRR Phyllocladus aspleniifolius D = PIE Phyllocladus aspleniifolius E = LYL Phyllocladus aspleniifolius F = HRR Phyllocladus aspleniifolius G = CLH Phyllocladus aspleniifolius H = PNL Athrotaxis cupressoides I = MTF Athrotaxis cupressoides J = BIT Phyllocladus aspleniifolius K = SHT Phyllocladus aspleniifolius 75

EIGENVECTOR 1 34.8%

EIGENVECTOR 2 14.4%

.60 .40 .20 o

EIGENVECTOR 3 9.1%

TREE-RING SITE CHRONOLOGY

Figure 7. First Three Eigenvectors of Tree Growth. 76 variation, and the Athrotaxis chronologies show more low frequency variation.

The second eigenvector, accounting for 14.4% of the variance, identifies the second most important mode of variation among the 11 chronologies. It is dominated by the Athrotaxis chronologies, whose weights are more than double those for the Phyllocladus and Nothofagus chronologies.

The third eigenvector may indicate a geographical gradient which is probably climatically determined. The sites to the northwest tend to be positively weighted, while those to the east and south (Figure 7) tend to be negatively weighted. The result for the Dove River Road site is an exception to this generalization and may be related to stand characteristics. The Dove River stand is dense, young, and even-aged, which suggests that natural thinning and other stand development processes may not have been in operation long enough for these trees to emerge from the understory. The chronology developed from the Dove River site is the shortest in the set of 11. Other chronologies are from apparently- mature, mixed-aged forests.

The first three eigenvector amplitudes were used as independent variables in a series of multiple regression analyses with seasonalized runoff and with amplitudes of seasonalized runoff. The results of these regressions indicated that only the first two eigenvectors of the 11 tree-ring chronologies were significant in predicting runoff, so that the subsequent canonical analysis omitted the third tree-ring 77 eigenvector from the predictor data set. Plots of the first two chronology amplitude series are shown in Figure 8.

Table 8 shows the autocorrelation coefficients, rk for k = 1 to

8, of the amplitude series of the first 3 chronology eigenvectors computed for the 199-year period, 1776-1974. The values for rk reflect the general appearance of the plots of the series shown in Figure 8. That is, the first amplitude series contains much high frequency variation while the second amplitude series demonstrates more low frequency variation. The autocorrelation coefficient of the first amplitude fluctu- ates about zero within the 95% confidence limits for a random process, except for r 20 which has a value of .24. In the second amplitude series, r becomes negative at the 27 th —k lag and in the third series it be- th comes negative at the 14 lag. In both the second and third amplitude series, rk then remains negative until r49 , the highest order autocorrelation coefficient calculated.

When Table 8 is compared with Table 6, it appears that the amplitude series of the first eigenvector of tree growth has an autocorrelation structure more like the Phyllocladus chronologies, and that the second eigenvector amplitude tends to be more like the Athrotaxis chronologies. Indeed, the general appearance of the two sets of tree-ring indices, plotted against time, resembles that of the first two amplitude series, as suggested by the tables of rk (Tables 6 and 8).

The first and second amplitude series, but not the third, were used in canonical analysis with runoff data and in the subsequent reconstructions of November-March streamflow. The possible effect of the 78

OW 1 • W MM MW MM MW MW MW MW MW MW MW MW MW MW MW MO MW MW OW A) Amplitude of first eigenvector, EV#1.

OW 1797 MM MW MM MW MO MW MW MW MW MW MW MM MM MM MW MW NW MW B) Amplitude of second eigenvector, EV#2. YEAR

Figure 8. Amplitude Series of the First Two Eigenvectors of Tree-ring Chronologies.

-.1- -4' r•-• 1-4

n0 0 CV Cc) . z.

▪ ClJ qQ CS 0 cY • +1 u Cj u c‘i 4-J CD cc) Cc) E • Cd 1-1 1-1 cn • 1 (,) Lr) o o cr1 c WO -0 .0

o o II o • • L.r) • CSn (1) G CO •r•I 3-1 • Q) • .W CA

• L) r1 tuj c*-) cn Ln crl 4-4 0 O 14-1 4 cd

$-4 0 Cr's

n-1 N cr) bD I)) a) W "d "ce 0 0 0 4-1 4-J ›, •n•-i •ri 80 relatively high and persistent (through many lags) autocorrelation in the second chronology amplitude, on the reconstructed runoff series, is discussed in Chapter 7. At this stage, it has not been determined how much of this persistence may be attributed to biological factors and how much to climatic and physical environmental factors. CHAPTER 6

HYDROLOGY

All hydrologic data used in this project were supplied by Mr.

Brian Watson of the Hydro-Electric Commission (HEC) of Tasmania.

Watson's judgment that these records were all of natural flow and hence suitable for this feasibility study was relied upon. All streamflow values have been expressed as depth In millimeters for easier comparison of series from different-sized drainage basins. The Australian water year, unlike that of the United States, is the calendar year. Where seasonalized data are used, the year in which the season begins is assigned to the data. For example, when the cumulative total of November through March is used, as in the final reconstructions, the year of

November is assigned to the data in the same way as the growing season described previously for the tree-ring data.

Record Identification

Each streamflow record series may be identified by location description, by index number (Australian Water Resources Council, AWRC) catalogue, record number, and, in most cases, gauging station number.

The stream gauging station number has been used here because it is the shortest identification and it is the convention used by the HEC. The locations of stream gauging stations and their catchments are shown in

Figure 9.

81 82

40 Florentine R. above Derwent Junction 46 Gordon R. below Huntley Ck. 78 King R. at Crotty 119 Huon R. above Frying Pan Ck. 154 Pieman R. above Heemskirk R. 159 Arthur R. below Rapid R. 183 Franklin R. below Jane R. 10087 Derwent R. below L. St. Clair

Gauging Station Figure 9. Map of Western Tasmania Showing Stream Locations. -- Broken lines indicate catchment boundaries. 83

The station record identified as 10087 and described as Derwent

River below Lake St. Clair on the data list could not be matched with a

HEC station number on the map of catchment areas provided. However, the station labeled 10131 on Watson's map and keyed as Lake St. Clair has been taken to be approximately the same location. Therefore, the catchment boundary of station 10131 is assumed to be that for the runoff series identified as 10087. The HEC gauging station numbers do not appear in the AWRC catalogue (1976), but cross-listing of catchment descriptions, location (latitude and longitude), size of drainage basin and period of record, in all other cases, allows precise identification of series by the HEC station number (Tables 9 and 10).

Watershed Characteristics

The watersheds on the study area range in size from 254 to 2539 sq km. Slope and length measurements (Watson, 1979), available for only four of the eight catchments, are given in Table 10. All records are from stream gauging stations in the western half of Tasmania. Five of them are from westward-draining systems, the others from predominantly eastward-draining systems.

All catchments experience a winter-dominant precipitation re- gime, although this is less pronounced in the more eastern Derwent,

Florentine, and Huon River systems which also receive lower annual rain- falls (Figures 2, 3, and 9). All records have their maximum flows during winter months and their minima during the summer. There is a tendency for a local minimum in June in most of the eight records (Fig- ure 10). The range in runoff depth varies considerably between stations, 84

Table 9. Streamflow Record Identification. AWRC Gauging Lati- Longi- Index Record Station Gauging tude tude Number Number Number River Station (S) (E) 304015 7850 40 Florentine Above Derwent 42°26' 146 ° 32' Junction 308002 12050 46 Gordon Below Huntley 42 ° 40' 146 °21' Creek 309001 78 King Crotty 42 °08' 145 ° 38' 306002 12450 119 Huon Above Frying 43 °02' 146° 51' Pan Creek 310008 154 Pieman Above Heemskirk 41 0 48 145 °12' River 312003 159 Arthur Below Rapid 41 007' 145 °07' River 308004 183 Franklin Below Jane 42 ° 27' 145 ° 44' River 304028 10087 10131? Derwent Below Lake St. 42 °07' 1460 13' Clair

Table 10. Summary of Hydrologic Features. Meanl Mean Physical Characteristics Annual Annual Station Record Runoff Flood Area Length 2 Slope 2 Number Period (mm) (m3/s) (km2 ) (km) (m/km) 40 1922-33 884 450 1951-75 778 46 1952-76 1546 246 458 61 2.9 78 1924-78 2419 418 449 46 4.8 119 1949-75 1314 2098 154 1955-77 1802 1716 2539 114 3.33 159 1955-77 1047 1746 183 1958-77 1885 1094 1590 102 5.7 10087 1958-77 1946 254 'April to March totals. 2 From Table 3 in Report on Gordon River Basin (B. Watson, personal communication, 1979). 85

Station 40 300 f Apr-Mar I- Nov-Mar 200

100

J FMAMJ JAS ONDJ FM

Station 46 300 Apr-Mar Nov-Mar-----I 200

n n .N.RIn11 , •• •• 100 1--I FMAMJJASONDJ FM

Station 78 300 Apr Mar

I- Nov-Ma r 200

100 ••n••n•••

J FMAMJJ ASONDJ FM

Station 119 300 Apr-Mar I-Nov-Mar-I 200

100

FMAMJJASONDJ FM

MONTH

Stations. -- Fifteen Figure 10. Mean Monthly Runoff at Eight Gauging months are included to show seasonalization. 86

Station 154 300 - Apr- Mar 4— Nov-Mar --I 200

100 -

F----1- J F MAMJ JASON DJ FM

Station 159 300 - I Apr-Mar I— Nov-Mar —I 200

100

FMAMJ JA SON DJ FM

Station 183 300 I Apr-Mar I-- Nov-Ma r --4 200

100

FMAMJJASONDJ FM

Record 10087 300 I Apr-Mar

}—Nov-Mar —4 .01nn•••••

200 -

100

F-E. J FMAMJJASONDJ FM

MONTH

Figure 10, continued. 87

but it is beyond the scope of this report to discuss the many factors

which influence total runoff in a particular watershed (Satterlund,

1972). The soils of the catchments, as described in Chapter 2, are gen-

erally shallow. Information on vegetation cover in the watersheds is

limited to general vegetation association descriptions. The extent of

land clearing and artificial revegetation is unknown, but it is thought

to be minimal. Wildfire is the main influence changing vegetational

characteristics (T. Bird, personal communication, 1980).

Seasonalization and Response Function Analysis

The association between streamflow and tree growth arises from

their response to a common environment and in particular to climate.

The period April to March, the probable period of greatest climatic in-

fluence on annual ring width based on climatic response function analy-

sis (Appendix C), was selected instead of the calendar year total for

input to the runoff response function analyses. The April-March cumu-

lative monthly totals were used together with climatic data for the period April (t-1) to March (t) where t year is the start of the runoff season. Estimates, made to the midpoint of catchments using the method described in Chapter 4, were the climatic data used for all stations except 154 and 159, whose records were obtained after the other analyses had been completed. Temperature and precipitation estimates made for the tree-ring site PIE (Figure 1) were compared with the runoff record for the Pieman River at gauging station 154. Data from the precipitation station Edith Creek and temperature station Waratah Post Office 88

(Appendix A) were compared with gauged runoff record 159 (Arthur River

below Rapid River).

The expected relationship between runoff and climate, positive

for precipitation and negative for temperature, was present at all

stations (Appendix C). One year of prior runoff was included in the

response function regression model, but in no case was it statistically

significant in predicting current cumulative April-March streamflow.

After comparison with the tree-ring response functions, a short-

er runoff season, November to March, was chosen for further analyses.

It seemed that summer runoff had a stronger link to tree growth than did

runoff for the total year. Subsequent dendrohydrologic analyses with both the 12- and 5-month series supported this speculation.

Statistical Characterization

The main purpose of determining the basic distributional characteristics of each series was to check the validity of the assumptions on which planned subsequent statistical techniques were based. This en- tailed determining if the runoff records were approximately normally distributed, by examining the skewness and kurtosis and testing whether individual series were significantly serially correlated, a consideration in the choice of regression models for later dendrohydrologic analyses.

Statistics for only the November-March seasonalization are presented as it was only the shorter period for which reconstructions were made. The values for several of the more important statistics for the period of record of each station are shown in Table 11. These • • 0 • •

ci) C r--ee) c0 O Ln CO C N co ce) CO 4-4 cn )--I

cd 3 01 0 c C co cr. o d)c co co If. ,--i •--I

0p...000000000

CO-1 CO CTI ..1- CO Cr.) n0 N E n O '—j cl) CD C \I O CO CO 01 in CYN -H rH 1-1 r--I 1-1 1-1 t—I CV T--1 z

0 0 0 0 N 0 0 0 0 • N Cr) N n-1 r-- )-1 ce, N. 1-1 s.0 01 CO CO 1-1

CN N Cr)

CO CO 1-1 Cs1 tr) CNI Cr) N- N. N. I-1 N N. V) N. 1-1 rH r—I r-I

• C) L.r)

CO • 0 N. C N N- CO n.0 r Cr) N CO Cr) )--1 re) s..c) ce) c"-) ce)

crn • N

co cr) 0 co If) CO 0 N- 90

statistics differ slightly from those for the 16-year calibration period, which is shorter for all records except 10087.

Table 11 shows that there is a considerable variation in the

November-March runoff between station records. Station 40, the Floren- tine River above Derwent Junction, has a discontinuous record so the statistics in each period were calculated separately, giving large dif- 4 ferences in s3, and s estimates as well as a higher maximum in the longer period. Station 78, gauging the King River at Crotty, has the greatest mean and maximum streamflow depths. Station 159, Arthur River below Rapid River, has the smallest. The longer portion of the station

40 record departs from a normal distribution while the records for stations 159 and 10087 are only marginally normally-distributed. All other records approximate normal distributions.

Table 12 shows that none of the recorded November-March runoff series is significantly (95%) autocorrelated. There is a tendency (5 of the 8 series), however, for r 2 to be negative and for 4 to be alter- nately positive and negative. This pattern is more pronounced in the

12-month April-March seasonalized data (not presented). Pittock (1975) showed that there is a correlation between rainfall in southern Aus- tralia including Tasmania and the Southern Oscillation Index (S.O.I.).

Several workers have shown that the S.O.I. has a period of from 2 to 5 years (Trenberth, 1975). It is possible, therefore, that the fluctu- ating signs of the autocorrelation coefficients of seasonalized runoff series reflect a quasi-biennial fluctuation in rainfall records, although this has not been investigated. As with the tree-ring 91

Table 12. Autocorrelation in Six Lags of Observed November-March Runoff.

Autocorrelation Coefficients 1 Station N 1.96 r2 Number (yrs) Il 1_-3 1-4 1:5 4 /N kl 40 25 .09 -.17 0.02 0.01 0.22 .13 .39 1

46 24 .13 .29 .17 .10 .10 .07 .40 1

78 55 -.14 .04 -.20 .21 .05 -.13 .26 1

119 27 .17 -.22 -.22 .06 -.17 -.17 .38 1

154 23 .12 -.21 -.16 0 -.09 .07 .41 1

159 21 .13 -.15 .06 .20 .02 .15 .43 1

183 20 -.11 -.25 -.18 .25 -.06 0 .44 1

10087 21 .09 -.35 -.07 .12 .01 -.03 .43 1 lAssuming normally-distributed variables, ±1.96/141 defines the 95% confidence interval for a white noise process and k is the number of lags for to fall within this interval; k = 1 to 6 except for station 78, 15 lags was calculated. for whichup-rk to 92

chronologies, r 2 for the November-March runoff often has a greater abso-

lute value than r 1 so that I -1 values alone do not adequately describe the serial correlation present in most of the records.

Table 13 demonstrates the high correlations between the

November-March records from all 8 gauging stations. Correlations be-

tween the April-March records (not presented) are, in general, higher

and follow a similar pattern except for record 10087, which is relative-

ly poorly correlated (r < .6) with all the others. A value of r greater

than .48 indicates correlation significantly different from zero at the

95% level (Snedecor and Cochran, 1967, Table All, p. 557). These sta-

tistics will be discussed and compared with those of the reconstructed

series in Chapter 7.

Eigenvector Analysis

An eigenvector or principal component analysis was performed on

runoff data seasonalized to include either 5- or 12-month totals from 8

gauging stations, which were used as variables, for the 17-year pe-

riod, 1958-1974. The first 3 eigenvectors extracted from correlation

matrices accounted for 98.1% of the variance in the 5-month records and

97% in the 12-month series. Only the results for the November-March

season are given (Figure 11), since it was the amplitudes of these

eigenvectors that were used in reconstructing runoff.

All eight records show strong common behavior, as shown by the very high variance accounted for by the first eigenvector and the almost

identical values for this component in all series. The amplitudes of 93

Table 13. Correlations between November-March Runoff Records at Eight Gauging Stations, 1958-1974.

Station 40 46 78 119 154 159 183 10087 40

46 .87

78 .81 .96

119 .88 .93 .85

154 .83 .94 .98 .85

159 .74 .65 .74 .60 .81

183 .85 .97 .97 .89 .96 .72

10087 .90 .98 .95 .92 .96 .97 .97 Figure 11. First Three Eigenvectors of Seasonalized Summer Runoff. -- Eigenvectors were extracted from the correlation matrix of November to March cumulative monthly totals from 8 runoff records from Tasmania in the 17-year period, 1958-1974.

A = Station 40, Florentine River above Derwent Junction B = Station 46, Gordon River below Huntley Creek C = Station 78, King River at Crotty D = Station 119, Huon River above Frying Pan Creek E = Station 154, Pieman River above Heemskirk River F = Station 159, Arthur River below Rapid River G = Station 183, Franklin River below Jane River H = Record 10087, Derwent River below Lake St. Clair 94

EIGENVECTOR 1 88.6%

.6 . .20 o -.20 n n •• ...,....,..,e„..e,.— .----n•••••'''''''''...'"*.""""'".qk...n.IIh -.4.0 -.6

EIGENVECTOR 2 6.0%

EIGENVECTOR 3 3.5%

ABC D EF GH

GAUGING STATION RECORD

Figure 11. First Three Eigenvectors of Seasonalized Summer Runoff. 95 the first eigenvector thus provide a sound estimate of the mean response of all watersheds involved.

The record from station 159 exhibits a different secondary mode of variation from the others with a large negative value for the second eigenvector. This is possibly attributable to the location of Arthur

River watershed in the path of summer northeasterlies (Chapter 2). The other stations would be much less influenced by these storm systems.

The histograms of monthly flow (Figure 10), however, do not single out station 159, although the correlations of this record with others are

lower (Table 13). Only 6% of the total variance in the whole set of

records is accounted for by the second eigenvector, and 11-12% might be

expected to be due to chance alone. Despite this, the second eigenvec-

tor of the seasonalized summer (November-March) runoff was found to be

significantly correlated with tree-ring width.

The third eigenvector seems to show a north-south gradient with

the higher positive values to the north (C,E), negative values to the

south (A,D), and several stations showing insignificant weights for the

component. The third eigenvector was made available to the multiple re-

gression analyses, but was excluded from the later canonical analysis

with tree-rings.

A further set of eigenvector analyses using months as variables

at each station for the period of record was carried out to study the

main regimes of monthly flow. As expected, the first eigenvector was

similar to the average monthly runoff (Figure 10), although the vari-

ance it accounted for ranged from 17.5% for record 78 to 30.8% for 96 record 159. Approximately 70% of the variance in this set of analyses was explained by the first 5 eigenvectors for all series. These data would perhaps be more useful if the streamflow for a longer season than the 5 months used here was considered. CHAPTER 7

DENDROHYDROLOGY

The dendrochronology and the hydrology of the study area have been documented. The relationship of tree growth and of runoff to monthly temperature and precipitation have been examined through response functions. The tree-ring series has been shown to have varying degrees of autocorrelation, while no significant year-to-year persistence exists in the runoff records. Relationships between runoff and tree-ring series now need to be defined. Climate acts similarly on both systems, and the response function results suggest that tree-ring records will relate more closely to summer runoff than to runoff for any other season or to total annual runoff. The existence of autocorrelation within the tree-ring chronologies indicates that important differences in the persistence structure exist and that compensation for these differences by lagging of dependent variables may be appropriate.

Regression Analysis

The amplitude series derived from the tree-ring eigenvector analysis (Figure 8) are the tree-ring data used in the following regression analyses. Individual stream gauging station data seasonalized to include the 12-month cumulative total monthly runoff for April through

March or the 5-month total November through March were used as the dependent variable in a series of multiple linear regression analyses.

The independent variables were the first three eigenvectors of tree

97 98

growth lagged so that runoff in t (current) year was compared with ring

width in t-1, t, and t+1 years.

Ring widths for three years were included to account for auto-

correlation existing within the tree-ring chronology amplitudes (Table

8). If a substantially longer runoff records had been available, it may

have been desirable to include one or two lagged runoff variables on the

right-hand side of the regression equation since the autocorrelation

structures of the observed runoff series (Table 12) indicate that a

second-order autoregressive process may be responsible for their gener-

ation. It was, however, necessary to restrict the number of variables

in the regression model to conserve degrees of freedom.

If only those tree-ring variables entering at significant (95%)

F-levels are considered, the first and second eigenvector of t+1 year,

and the first eigenvector of the t year consistently entered the regres-

sion equation. In several cases, the second eigenvector in t year was

also included. For the 5-month (November-March) seasonalized total, the

first 3 variables entered the regression for each of the 8 gauging sta-

tions. For the 12-month seasonalized (April-March) total, the same

variables tended to enter the regression equation, but in several in-

stances the F-levels of entry were not significant.

These regression results confirm independently the results of

the response functions in that the relationships between tree growth and

runoff were stronger in the summer months. The sign of the correlation

coefficient, as each tree growth variable entered, was also consistent with information given by the response functions of the two main genera 99

of the trees whose ring-width indices were included. That is, the am-

plitude of eigenvector 1 of tree growth was correlated positively with

current summer runoff and negatively with runoff in the previous summer.

The second eigenvector amplitude was positively correlated with runoff

both in the previous and current summers. In no case were the t-1 year

tree-ring data significant in predicting runoff in year t.

It is apparent from the runoff climatic response functions (Ap-

pendix C) that lower temperatures and higher rainfall are associated

with higher runoff. The first eigenvector of tree growth is slightly

dominated by Phyllocladus, a genus which favors a cooler, more moist

previous summer for growth. The second tree-ring eigenvector is strong-

ly dominated by the two Athrotaxis species whose wider rings are asso-

ciated with warmer, drier conditions both in the current growing season

and in the previous summer. Since the sign of both tree-ring eigenvec-

tors is negative (Figure 7), a negative amplitude value indicates in-

creased tree growth. Therefore, a positive value for the second eigenvector emplitude indicating reduced tree growth for a given year corresponds to a higher runoff or has a positive correlation with runoff, as indicated in the regression analyses. For the first eigenvector, the negative correlation with runoff in the summer prior to the growing season is expected, although the positive relationship in the current summer could not be predicted from the indefinite result of the Phyllo- cladus response function in the growing season (Table 7). The positive correlations between the second amplitude of tree growth and runoff for 100

both summers are predictable from the climatic response function analyses.

This research set out to investigate the relationships between

runoff and tree rings. Analyses to this stage indicated that the most

promising associations would involve the summer period. Therefore, fur-

ther analyses concentrated on the November to March season. Since the

first eigenvector of this 5-month series (for 1958-1974) accounts for

89% of the variance in the recorded streamflow at 8 gauging stations, it

is reasonably representative of the overall or mean response of the set

of stations. It, as well as the second and third eigenvectors, was used

as the dependent variable in a multiple regression analysis with the in-

dependent variables being the first 3 eigenvector amplitudes of tree

rings for t and t+1 years. The results of these regressions confirmed

those for individual stations, but the F-levels at which the variables,

the first 2 eigenvectors of the t+1 and then the current year, entered were considerably improved. A second set of regressions using the 12- month seasonalized runoff was also carried out with the same set of tree-ring data.

The first two eigenvector amplitudes of the 5-month period were significantly correlated with tree growth, but only the third amplitude of the 12-month seasonalization entered the regression equation at significant (95%) F-levels (e.g., F = 4.0). It should be noted that the patterns of the second eigenvector of the 5-month runoff seem to be the same as those of the third eigenvector of the 12-month runoff. The equations resulting from the regression analyses were: 101 for the five-month data,

C iy = -1.6257 2xt+1 + 0.6786C 1xt+1 - 0.8836 (1)

C 2 y = 0.3408 2x t + 0.3597 (2)

and for the twelve-month data,

C 3y = 0.1989 9 xt + 0.2100 (3) where C ny's = the amplitudes of runoff for year t, and

E nx's = the amplitudes of tree rings for years t, t+1.

The correlation between the amplitudes reconstructed from the

transfer functions or regression equations and the actual amplitudes derived from the principal component analysis of runoff were (1) 0.725 for the first amplitude of November-March runoff, (2) 0.567 for the second amplitude of November-March runoff, and (3) 0.442 for the third eigenvector of April-March runoff.

It was originally intended to terminate this project after the initial regressions because of the scarcity and shortness of runoff records and the relatively sparse but wide spatial coverage of tree- ring sites. The results of the regression between runoff amplitudes and tree-ring amplitudes, however, encouraged an attempt at preliminary runoff reconstructions.

Canonical Analysis and Reconstruction

The regression equations shown above can be used to reconstruct the two runoff amplitude series separately. Also, the two amplitudes 102 can be optimally combined by performing a canonical correlation analysis. For one matrix, the amplitudes of the first two eigenvectors of

November-March seasonalized runoff were used, and for the other, the first two eigenvector amplitudes of the tree-ring data lagged to include t+1 as well as t or current year. This gave a total of six variables in the analysis.

Following the technique that Stockton et al. (1978) used for

Palmer Drought Severity Index (PDSI) reconstructions, canonical equations were derived and solved for the calibration period 1958-1973. The canonical equations were:

E ly = 1.810E ixt + .1715 2 x + .5627ç ixt+1 - .8786 2 xt+1 (4)

E 2 y = -.3949E ix t + .2773E 2 xt - .1064E 1xt+1 + .4110E 2 xt+1 (5)

These two canonical regression equations explained 46.6% of the variance in the two amplitudes of November-March runoff for the calibration period.

Equations (4) from the canonical and (1) from the multiple linear regression (MLR) may be compared. Both emphasize the importance of the eigenvectors in t+1 year, showing that the first eigenvector of runoff has a strong positive correlation with chronology eigenvector 1 and a strong negative correlation with chronology eigenvector 2. Likewise, equations (2) and (5) should be comparable, but the F-level constraint allowed only one variable to enter the MLR analysis and this is not the 103

one most highly correlated with the second amplitude of runoff according

to the canonical analysis results.

Solutions to the above canonical regression equations were ap-

plied to and runoff amplitudes estimated for the period of tree-ring

record, 1776-1973. These reconstructed amplitudes were transformed to normalized runoff values at each of the eight gauging stations in the

original runoff eigenvector network, by applying eigenvector weights.

The program RECONA (available at the Laboratory of Tree-Ring Research,

University of Arizona, Tucson) was used for this transformation. The

calibration mean and standard deviation were then inserted to estimate the reconstructed values.

One assumption made in using canonical analysis (see Chapter 3)

is that the input data are normally distributed. The skew (s 3) and kur- 4 tosis (s ) of the calibration data were, therefore, examined, there being too few observations to test normality through x2 and contingency analysis. Table 14 shows that one of the four series, the first amplitude of November-March runoff, is significantly negatively skewed and 4 has a more peaked distribution than the normal. The s 3 and s of the other amplitude series fall within the 95% confidence limits for the normal distribution for 16 observations. A negative skew in the first amplitude of runoff corresponds to a positive skew in the observed data, because the first eigenvector of November-March runoff is negatively weighted at all stations. The departure from normality in the first amplitude series may be due to skew in records from stations 40, 159, and 10087 and kurtosis in station 40 (Table 11). Station 40 is not, 104

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The implications of the use of a negatively-skewed, peaked series in canonical analysis are not fully understood. The violation of the assumption of normality affects the standardization of the series and the calculation of canonical weights which indicate the degree of involvement of each station record in each of the two patterns (of variation) common to the tree-ring and runoff data sets. It is thought that the results of the canonical analysis are probably valid, but that they need to be interpreted cautiously.

Table 14 also shows the autocorrelation structure of each of the data sets used in canonical analysis. None of these series is significantly autocorrelated within the 16-year calibration period, although r l for the second chronology amplitude (r 1 = .48) is close to the 95% significance level (r 1 = .49) for 16 observations. It must be emphasized 3 that the estimates s , s 4 , and Ilk shown in Table 14 may not be very reliable because of the limited sample size (N = 16) on which they depend.

Discussion of Reconstructions

The reconstructed series are plotted in Figure 12 together with the corresponding observed record. Tables of values used in these plots are presented in Appendices D and E. 106

STATION 40

° oilo rim MM mm mm ti40 mM mm m5111 mk mm mm ism mM mkt m'44) to mm 19M

dAtt\,,A,,\AAJOrv\

1860 Mio lobo mM Mu) Lek 1932 Lsk

STATION 119

-0

o ow om mm mm mm mm mu) mm mm mm mw mm mm mm mm mm m4 0 mk tok mM

YEAR

Figure 12. Reconstructed and Observed November-March Runoff at Eight Gauging Stations. -- Broken vertical lines indicate calibration period. 107

STATION 154

• 4 nk nbo mk ieo mm mm Mk Mk MW m% mk mk NW MM MM Mk Mk mk mk L9M

STATION 159

ow nm Lew mio Mk mk ma mk mk mm mm mm mw WM Mk MW Mk mk Lak mM

STATION 183 :L

a om nm mm mm mm ok mk mm 4M mk mk mki94o mk Mk MQ to MW Mk

STATION 10087

nia mk dip mm ma mk mm 4 0 Mk mm mw mm mm mm ma Mk mm tik

YEAR

Figure 12, continued. 108 Association Tests

Good agreement between the reconstructed record and observed values in the calibration period is a prerequisite for valid reconstruc-

tions. Several tests of association between variables, outlined in

Chapter 3, were performed on data in the 16-year calibration period,

1958-1973. There were 5 measures of association to which significance

tests were applied, in addition to the calculation of the reduction of error (RE). Verification using independent runoff data outside the cal-

ibration period was possible at only 3 of the gauging stations, a minimum of 8 years being considered necessary for verification. The tests were applied using the subroutine VERIFY at the Laboratory of Tree-Ring

Research, University of Arizona. The total possible number of test passes was 5. The results of verification tests, in the calibration as well as in the independent years, are presented in Table 15.

In the calibration period, stations 119, 154, and 10087 were the only three that passed all association tests, each of the others failing at least one of the sign tests. Stations 40 and 159 showed the poorest correspondence between estimated and observed data with only 36% and 30% variance calibrated, respectively; all the other stations had at least

50% variance calibrated, with the results for station 119 (Huon River above Frying Pan Creek) being the best. This station had 65% variance calibrated, corresponding to a correlation coefficient, r, of .83.

In the verification period, station 78 had a relatively low but still statistically significant r and a marginally significant first difference sign test. An examination of the plotted reconstructed time

109

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series for this station suggests that the record was quite well-

duplicated except for the period 1937-1942 when the estimated series has

very little variance and a lower mean than for most of the record. This

period is reconstructed similarly at all eight stations.

Statistics of Reconstructed Series

Tables 16 and 17, showing several statistics of the 8 recon-

structed records may be compared with Tables 11 and 12 for the corres-

ponding observed records. The values for the reconstructed series are better estimates of the population statistics because a larger number of

observations (N = 198) are used than for the observed series (N = 11 to

54). Judging by the skewness (s 3 ) and kurtosis (s 4 ) coefficients, which

are all close to zero, the reconstructed series all approximate normal

distributions. The means and ranges are neither consistently higher nor

lower than those of the corresponding observed series. An examination of Figure 12 reveals a failure of the reconstructions to estimate the higher runoff values, even in the calibration period.

Autocorrelation (Table 17) is higher and more persistent in the reconstructed records than in the observed, and this reflects the serial dependence within the tree-ring series used to estimate the long-term runoff records. The values of r (k = 1 to 5) are all positive except for station 159 (rl = -.28) in the reconstructed record reflecting more the autocorrelation structure of the tree-ring chronologies and chronology amplitudes (Tables 6 and 8) than that of the observed runoff records (Table 12). The tendency for high November-March runoff totals to be followed immediately by low ones, evident from Table 12, with I 1 111

Table 16. Statistics of Reconstructed November to March Runoff for 198 Years. Mean Standard (mm) Deviation Maximum Minimum Skewness Kurtosis Station -f s (mm) (mm) s3 s4 40 184.9 59.7 369.0 0 -.06 -.01

46 365.4 143.9 810.0 0 .04 -.30

78 547.1 166.4 1058.0 3.0 -.09 .07

119 336.2 111.9 677.0 0 -.02 -.13

154 362.1 115.3 717.0 0 -.08 .04

159 159.5 37.6 265.0 45.0 -.23 .12

183 460.1 144.9 905.0 0 -.07 0

10087 419.9 156.5 904.0 0 0 -.19

•• ▪

112

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Stockton (1975) discusses the conditions under which the estimates of the mean and variance of the reconstructed series will be superior to those from the shorter observed record, and he reviews the work of several others who have addressed the question. One of the conditions necessary for an improved estimate of the mean is that of the absence of autocorrelation. The problem of introduction of autocorrelation into the reconstructions from highly autocorrelated tree-ring series needs to be resolved to determine whether the apparent serial correlation in the reconstructed series is climatically or biologically determined. Until this is clarified, a statement about the relative qualities of the means and variances calculated from the recorded and from the estimated series cannot be justified.

Drought

The reconstructed series for stations 78, 119, and 159 were examined for periods of low flow and compared with drought data from Gor- manston, Franklin, and Waratah, respectively (Figure 12, Table 2).

These drought data can be considered to be independent checks of the validity of the reconstructions. It must be kept in mind, however, that the reconstructions are for only a 5-month season spanning parts of two calendar years so that they do not coincide with the 12-month calendar year on which the drought indices are based. Nevertheless, since the drought data are for periods of two years or more, periods of prolonged 114 low summer streamflow might be expected to be reflected in more intense droughts even though the comparisons are necessarily qualitative.

Gormanston and Station 78. The drought 1905-1908 is possibly reflected in the King River record at Crotty with decreasing summer runoff in 1907-1909. In the intense drought periods, 1931-1933, 1935-1938, and 1948-1951, the reconstructed values are all below the long-term mean, but the 1917-1922 drought is not indicated.

Franklin and Station 119. The reconstructed record is below the mean in the period 1884-1889, the first part of a prolonged drought as shown by Table 2. Again, the 1917-1922 drought is not echoed in the runoff series, so perhaps the periods which were exceptionally dry were in the winters rather than summers of those years. The dry periods of

1948-1951 have below-average runoff in the reconstructed record of Huon

River at station 119.

Waratah and Station 159. Arthur River, gauged at station 159, has the lowest year-to-year variation of all records both in the observed and in the reconstructed series. The only drought period fully reflected is 1964-1967. CHAPTER 8

CONCLUSIONS AND RECOMMENDATIONS

This investigation was handicapped by paucity of data. Within the bounds of statistical validity many apparent links between tree rings, climate, and hydrology could not be explored further without at least better replication of tree-ring chronologies. Nevertheless, almost half the variation in a set of eight summer streamflow records could be predicted from the main components of the available tree-ring chronologies in Tasmania. The tree-ring sites are widely spaced and are not ideally located to give information about the watersheds with which they are compared. It is possible, therefore, that the relationships between tree rings and runoff, shown in this study, could be considerably strengthened with more strategic selection of tree-ring sites.

There is evidence that the various tree species respond differently to climate so that greater representation of all dateable species may give added information about climate and hydrology in particular seasons. While summer runoff was most strongly related to tree growth in this investigation, streamflow for a 12-month period was also correlated with tree growth.

The use of tree rings to reconstruct hydrologic records has tra- ditionally been restricted to dry climates. This study presents tenta- tive evidence that tree-ring chronologies developed from temperate rain forest species may also provide proxy hydrologic information. The

115 116 reconstructions of streamf low made here may have inflated serial correlations and this problem needs to be addressed if future dendrohydrologic studies are undertaken. The limited data available for verification suggest that the records estimated from the tree-ring series are reasonable.

In Tasmania, dateable trees up to 2000 years in age are known.

One of the chronologies available to this study extends back to 1028, but only the most recent part of this could be used when a common period was selected. The possibility of deVeloping long chronologies from sites located in watersheds for comparison with the existing hydrologic records, coupled with evidence presented in this study, offers considerable potential for using tree-ring chronologies to augment streamflow records in Tasmania. APPENDIX A

TABLES AND LOCATION MAPS OF CLIMATIC STATIONS

117 118

. 15 1451 ° 146° 147°

0 50 100

41° 0

• • 14 5 4 1 42° .D 6 42° - 13 • ca 8

12 P • 10 43° - 43° Î

147° 148° 145° 146° il

1 1 i 1

Figure A.1. Location Map of Temperature Stations. -- See Table A.1 for corresponding names and Australian Bureau of Meteorology catalogue numbers. 119

Table A.1. Temperature Stations. Sequence Catalogue Latitude Longitude Number Number Name o , s o 1 91022 Cressy Research 41 43 147 05

2 91057 Low Head Lighthouse 41 03 146 47

3 91094 Stanley Post Office 40 46 145 18

4 91104 Launceston Airport 41 33 147 13

5 92033 St. Helens Post Office 41 20 148 14

6 92038 Swansea (Maria St.) 42 07 148 04

7 92045 Eddystone Point Lighthouse 41 00 148 21

8 93014 Oatlands Post Office 42 18 147 22

9 94010 Cape Bruny Lighthouse 43 30 147 09

10 94029 Hobart Regional Office 42 53 147 20

1 1 94041 Maatsuyker Island 43 40 146 16

12 94056 Risdon 42 50 147 19

13 97000 Cape Sorell Lighthouse 42 12 145 10

14 97014 Waratah Post Office 41 26 145 31

15 98001 Currie Post Office 39 56 143 52 120

75.

146 ° 147°

41 °

42 °

43°

39 148° 146° 47 147°

Figure A.2. Location Map of Precipitation Stations . -- See Table A.2 for corresponding names and Australian Bureau of Meteorol- ogy catalogue numbers. Stars indicate those precipitation stations for which drought indices are available. 121

Table A.2. Precipitation Stations. Sequence Catalogue Latitude Longitude Number Number Name o , s o I E 1 91004 Branxholm Post Office 41 10 147 44 2 91007 Bridport Post Office 41 00 147 24 3 91010 Burnie (1) 41 03 145 54 4 91011 Wool North 40 42 144 42 5 91013 Carrick 41 33 147 00 6 91022 Cressy Research 41 43 147 05 7 91032 Epping (Forton) 41 44 147 19 8 91033 Frankford West 41 19 146 44 9 91038 Golden Valley 41 38 146 42 10 91044 Irishtown 40 55 145 09 11 91053 Lilydale 41 12 147 12 12 91057 Low Head Lighthouse 41 03 146 47 13 91073 Nietta South 41 24 146 04 14 91074 Edith Creek 40 59 145 05 15 91092 Smithton Post Office 40 51 145 07 16 91094 Stanley Post Office 40 46 145 18 17 91102 Ulverstone 41 09 146 11 18 91104 Launceston Airport 41 33 147 13 19 91105 Wilmot 41 23 146 10 20 91109 Yolla 41 08 145 43 21 91195 Moltema (Craythorne) 41 27 146 31 22 92000 Rossarden (Aberfoyle) 41 39 147 45 23 92001 Apslawn 41 58 148 11 24 92003 Bicheno 41 53 148 18 25 92005 Bream Creek 42 48 147 50 26 92013 Frome Dam 41 08 147 54 27 92019 Lake Leake 42 01 147 48 28 92020 Lewis Hill 41 50 147 57 29 92024 Mathinna 41 29 147 53 30 92029 Ormley 41 43 147 50 31 92033 St. Helens Post Office 41 20 148 14 32 92034 St. Marys 41 35 148 11 33 92037 Swan Island 40 44 148 12 34 92038 Swansea (Maria St.) 42 07 148 04 35 92043 Triabunna 42 31 147 55 36 92045 Eddystone Point Lighthouse 41 00 148 21 37 92047 Stonehouse 42 16 147 41 38 93014 Oatlands Post Office 42 18 147 22 39 94010 Cape Bruny Lighthouse 43 30 147 09 40 94014 Colebrook 42 32 147 22 41 94023 Franklin Post Office 43 05 147 01 42 94025 Glenorchy Reservoir 42 51 147 15 43 94026 Killora (Grasmere) 43 07 147 19 44 94030 Hobart Botanical Gardens 42 52 147 19 45 94032 Southport 43 26 146 58 46 94034 Kempton 42 32 147 12 47 94041 Maatsuyker Is. 43 40 146 16 122

Table A.2, continued. Sequence Catalogue Latitude Longitude Number Number Name o v s o 1E 48 94056 Risdon 42 50 147 19 49 94060 Runnymede 42 38 147 37 50 94061 Sandford 42 56 147 31 51 94075 Tasman Is. Lighthouse 43 15 148 00 52 95003 Bushy Park (Hops Res. Stn.) 42 43 146 53 53 95008 Hamilton 42 33 146 50 54 95010 Lake Fenton 42 42 146 36 55 95012 Millerbrook (Ouse) 42 29 146 43 56 95017 Sharpes Siding, Tyenna 42 43 146 42 57 95018 Tarraleah 42 18 146 27 58 96002 Bronte Park 42 08 146 30 59 96003 Butlers Gorge 42 17 146 16 60 96015 Lake St. Clair 42 06 146 13 61 96021 Shannon (Hydro-Electric Commission) 42 03 146 45 62 96022 Steppes (Old Post Office) 42 06 146 54 63 97000 Cape Sorell Lighthouse 42 12 145 10 64 97003 Gormanston 42 04 145 36 65 97006 Lake Margaret 42 00 145 36 66 97008 Queenstown 42 04 145 34 67 97011 Rosebery 41 46 145 32 68 97014 Waratah Post Office 41 26 145 31 69 97016 Zeehan Post Office 41 53 145 20 70 98000 City of Melbourne Bay 40 01 144 07 71 98001 Currie Post Office 39 56 143 52 72 98003 Harwell 39 55 143 57 73 98004 Naracoopa 39 55 144 08 74 98013 Yambacoona 39 42 143 56 75 99001 Deal Island 39 30 147 20 76 99006 Palana (The Hermitage) 39 46 147 54 77 99008 Whitemark 40 07 148 01 78 99009 Wingaroo 39 51 148 01 123

Table A.3. Independent Climatic Records. 1 Catalogue Latitude Longitude Years of Number Name ° 'S o I E Data TEMPERATURE

91049 Launceston (Pumping 41 30 147 12 16 Station)

91064 Moina 41 30 146 06 17

94008 Hobart Airport 42 50 147 32 22

95003 Bushy Park (Hops 42 43 146 53 30 Research)

PRECIPITATION

91061 Meander 41 42 146 36 30

91081 Railton 41 20 146 25 30

92042 Tower Hill 41 32 147 52 30

93007 York Plains (Hanroyd) 42 16 147 35 30

94002 Bagdad P. 0. 42 38 147 13 30

96023 Waddamana 42 08 146 45 30 analysis whose data were used ' Station records not used in eigenvector to verify interpolations made using results of monthly principal component analysis, 1941-1970. APPENDIX B

TREE-RING SITE CHRONOLOGIES

124

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CLIMATIC RESPONSE FUNCTION PLOTS

140 141

MAX TEMPERATURE (CIEG Cl

1719P+49:r—f-1016.Pc'

ONOJFMAMJJASONOJTMmmw TOTAL PRECIPITATION (MM)

Esi-f

-0.4- ONOJFIIRMJJOISONOJF reNTI15

(CMT) Figure C.1. Climatic Response Function for Cradle Mountain Chronology. -- Regression step 3, F-level of entering vari- to- able = 3.29 (less than 10% probability of a higher F), tal variance explained = 65%, climatic variance = 22%, prior growth variance = 42%. 142

MAX TEMPERATURE (DEG C)

I -0.4 -- ONOJFilfiriJJASONOJF11 WV TOTAL PRECIPITATION (MM)

0 _

204 - 1=17.1dTF:F=}471=1 1-04-

if) ONOJFriAriJJASONOJF ri II:04TM

IIPRIOR GROWTH

1 - 2 -

-0.4- in 123 LA0( YEARS)

Figure C.2. Climatic Response Function for Weindorfer Forest (WDF) Chronology. -- Regression step 3, F-level of entering variable = 4.08 (less than 10% probability of a higher F), total variance explained = 56%, climatic variance = 21%, prior growth variance = 35%. 143

N 0.4_ MAX TEMPERATURE (0EG Cl 1 o.:- / -

2 -

-0.4- 41 ONOJFMAMJJASOMOJFM rIONT115 TOTAL PRECIPITATION (MM)

1 0.2- - Z _ 2 0.0- 2 - I -0.2 -

in ONOJTMAMJJASONOJFM t101111$5

PRIOR GROWTH

-0.4- 123 UV YEARS) Figure C.3. Climatic Response Function for Dove River Ro ad (DRR) Chronology. -- Regression step 1, F-level of entering van- able = 6.29 (less than 2.5% probability of a higher F), total variance explained = climatic variance = 20%. 144

W MAX TEMPERATURE (0EG Cl

2 1=9TiTLII-FigeL,H--1 r.2_ •-- —0.4 — en ON0Jrt1AMJJR5ONDJTt1 MONTHS TOTAL PRECIPITATION (MM)

10.2 —— 6 _ 2 0.0- E _ p, 2_ Hk'vT441714 r - —0.4 — 0 ONOJFMAt1JJASONOJFM MONTI%

PRIOR GROWTH

.2_ r ..I —0.4 — in 123 URNYEAR6) Figure C.4. Climatic Response Function for Pieman River (PIE) Chronology. -- Regression step 3, F-level of entering variable = 3.36 (less than 10% probability of a higher F), total variance explained = climatic variance = 40%. 145

MAX TEMPERATURE (0EG C)

*0 ONOJFritinJJR3ONOJFn riONTrtS

PRIOR GROWTH

-0.4— Fota 123 LA04 YEARS ) Figure C.5. Climatic Response Function for Lyell Highway (LYL) Chro- nology. -- Regression step 5, F-level of entering variable = 3.49 (less than 10% probability of a higher F), total variance explained = climatic variance = 62%. 146

MAX TEMPERATURE (DEG C)

O - 2 o.o- ii 1=1,HA:El=61H B -

4.4 ONOJFAA AJJASONOJF /1 MORITZ

W TOTAL PRECIPITATION (MM) g 0.4-

6 _ 2 0.0 - 2 — 171.271.17LH"Tsi

r) ONOJFMAAJJASONOJf11 MOANS

PRIOR GROWTH

.2 0.0 2 1 _0.2__

in 123 U1C4 YEARS )

Figure C.6. Climatic Response Function for Holly Range Road (HRR) Chronology. -- Regression step 2, F-level of entering variable = 4.33 (less than 5% probability of a higher F), total variance explained = climatic variance = 26%. 147

N MAX TEMPERATURE (GEG C) 0.4 -

i- 0.0-

r.2_

04.4- ONOJFMAMJJASONOJF A MONTHS

g 0.4_ TOTAL PRECIPITATION (MM)

6 _ 2 - 0.0- 2 -

1.- -0.4 --, in ONI3JrARAJJASONOJFri MONTHS

PRIOR GROWTH

M _ 2 0.0

YEARS)

Hill (CLH) Chronolo- Figure C.7. Climatic Response Function for Clear gy. -- Regression step 4, F-level of entering variable = 9.91 (less than 1% probability of a higher F), total variance explained = 64%, climatic variance = 35%, prior growth variance = 29%. 148

MAX TEMPERATURE ( OEG C)

2 0.0 8

0- -0.4 - in 0N0Jf11FIMJJ1160140JFM MONTHS

TOTAL PRECIPITATION (MM)

0.2 -

0.0

ONOJFMAMJJASONOJFM roams

RIOR GROWTH

12 3 UWW0DINS1 Climatic Response Function for Pine Lake (PNL) Chro- Figure C.8. variable nology. -- Regression step 1, F-level of entering 39.13 (less than 0.5% probability of a higher F), total variance explained = prior growth variance = 60%. 149

N MAX TEMPERATURE (DEG Cl

1 04-- i— ox-

.2 -

-0.4 - iv) ONOJF,111t1JJASONOJFM 11014T115

0.4_ TOTAL PRECIPITATION (MM)

1 - b _ 2 0.0 8 _ 1 1 ill=1 ., 7 7P

0 .4- 0- 0N0Jr/111t1JJASONOJFM MONTHS

PRIOR GROWTH

2 - r.2 :

1 2 3 LI10( YEARS ) (MTF) Chronol- Figure C.9. Climatic Response Function for Mount Field ogy. -- Regression step 4, F-level of entering variable = 5.46 (less than 5% probability of a higher F), total variance explained = 56%, climatic variance = 42%, prior growth variance = 14%. 150

W MAX TEMPERATURE (0E& Cl 0.4 -

in ON0JfnAMJJASONOJrn INNS

PRIOR GROWTH g0.4 -

0.2 _-

123 LA04 YEARS

Figure C.10. Climatic Response Function for Bruny Island (BIT) Chro- nology. -- Regression step 4, F-level of entering variable = 3.02 (less than 10% probability of a higher F), total variance explained = climatic variance = 64%. 151

•I-, ONOJFM11r1JJFISONOJIrt1 roams

r.2_ .m.,

.,7 , ONOJF,11:1,1JJASONOJFM MONTHS

La PRIOR GROWTH 1 OA -

10.2 - - I - 2 -

-0.4 - n 123 LAN YEARS )

Figure C.11. Climatic Response Function for St. Helens (SHT) Chronol- ogy. -- Regression step 2, F-level of entering variable = 6.43 (less than 2.5% probability of a higher F), total variance explained = 36%, climatic variance = 22%, prior growth variance = 14%. 152

MAX TEMPERATURE (0EG Cl • _ 2 0.0 - e _

W TOTAL PRECIPITATION (MM) 0.4 -

0.2--

RHJJASONOJFH MONTHS

PRIOR GROWTH 0.4-

0.2 -

0.0 - § -

LAG( YEARS )

Figure C.12. Climatic Response Function for Gauging Station 40. -- Regression step 4, F-level of entering variable = 4.91 (less than 5% probability of a higher F), total variance explained = climatic variance = 84%. 153

MAX TEMPERATURE (DEG Cl

LT4-1,,,,,FLI

n AMJJA5ON0JFM MONTI15

ArIJJASONDJ Fn reN1113

PRIOR GROWTH

i UICATEARE)

Figure C.13. Climatic Response Function for Gauging Station 46. Re- gression step 4, F-level of entering variable = 10.31 (less than 10% probability of a higher F), total variance explained = climatic variance = 86%. 154

MAX TEMPERATURE (0EG C

(a AMJJFISONDJFM MICRO TOTAL PRECIPITATION (MM)

0.2 —-

2 0.0

to AMJJRSONO.Iftl rIONTIti

PRIOR GROWTH N 0.4—

0.2 —

-- Figure C.14. Climatic Response Function for Gauging Station 78. Regression step 2, F-level of entering variable = 11.80 (less than 2.5% probability of a higher F), total variance explained = climatic variance = 92%. 155

W MAX TEMPERATURE (DEG Cl 04. —

0.2 :

TOTAL PRECIPITATION (MM)

0.2 _: 2 0.0 2 -

V) 1:111JJASONOJFM MOND'S

PRIOR GROWTH 0.4

0.2 : M _

n- LAG( YEARS )

Figure C.15. Climatic Response Function for Gauging Station 119. -- Regression step 2, F-level of entering variable = 4.59 (less than 5% probability of a higher F), total variance explained = climatic variance = 59%. 156

MAX TEMPERATURE (0EG C)

MJJASONDJFA

/ 0.4_, TOTAL PRECIPITATION (MM)

— n _ 2 - 0.0 2 -

AAJJASONDJFA WITM

PRIOR GROWTH

ZS _

to 1 LAG(YEMS)

Figure C.16. Climatic Response Function for Gauging Station 154. -- Regression step 3, F-level of entering variable = 3.72 (less than 10% probability of a higher F), total variance explained = climatic variance = 89%. 157

MAX TEMPERATURE (DEG Cl

0.2 —

" — 0.0 e _ r.2_

ou3 —0.4 —b

IIJJRSONDJF fl MIMS

PRIOR GROWTH 0.4 —

0.2 —

- —0.2-0.2-

Figure C.17. Climatic Response Function for Gauging Station 159. -- Regression step 3, F-level of entering variable = 6.48 (less than 2.5% probability of a higher F), total variance explained = climatic variance = 92%. 158

W MAX TEMPERATURE (DEG Cl

0.2

A AJJASONOJFA norms

PRIOR GROWTH 0.4 —

0.2 - I 0.0 -

1 LACAYEAR0)

Figure C.18. Climatic Response Function for Gauging Station 183. -- Regression step 3, F-level of entering variable = 7.61 (less than 2.5% probability of a higher F), total variance explained = climatic variance = 94%. 159

MAX TEMPERATURE (DEG Cl g04- .

0-2

TOTAL PRECIPITATION (MM) 0.4 -

0.2

2 0.0

to AMJJASONOJF11 room

PRIOR GROWTH M 0.4

0.2 _- 2 0.0- 8 r.2_

LACA VMS)

Figure C.19. Climatic Response Function for Gauging Station Record 10087. -- Regression step 3, F-level of entering variable = 29.66 (less than 0.5% probability of a higher F), total variance explained = climatic variance = 94%. APPENDIX D

TABLES OF MONTHLY AND SEASONALIZED RUNOFF (IN MILLIMETERS DEPTH)

Table D.1. Runoff at Gauging Station 40, Florentine River above Derwent Junction. YEAR JAN FEB MAR APR MAY JNE AY AUG SEP OCT NOV DEC12M0 10.5M0

1922 15 13 46 70 56 68 80 31 22 78 80 48 726 324 1923 96 56 45 24 161 192 94 77 136 125 126 58 1180 371 1924 83 59 45 106 72 133 98 124 110 132 114 51 1026 251 1925 23 37 26 23 24 47 42 121 82 145 31 64 660 175 1926 16 43 20 30 77 69 106 106 110 108 146 70 908 302 1927 20 36 30 27 102 97 112 104 66 38 52 13 653 108 1928 21 13 8 22 56 22 116 120 303 221 129 47 1133 273 1929 49 19 30 114 31 104 143 85 104 69 63 86 904 253 1930 75 15 15 24 28 27 91 42 137 74 110 38 766 342 1931 68 35 92 64 76 137 173 158 153 156 74 22 1100 184 1932 23 45 19 72 34 110 36 42 60 56 72 34 673 264 1933 45 42 70 68 88 75 47 102 90 89 23

1951 11 18 92 56 49 108 124 71 46 88 37 740 195 1952 28 26 15 55 65 284 149 60 124 86 79 28 982 157 1953 16 18 18 56 49 89 141 103 149 53 84 103 926 284 1954 23 32 42 29 88 98 59 130 78 60 34 28 646 104 1955 16 16 10 26 54 53 80 137 61 70 134 40 744 262 1956 50 21 18 57 39 103 90 124 85 73 117 96 906 335 1957 72 24 26 51 100 48 49 23 55 117 66 106 702 257 1958 29 26 31 66 258 147 82 191 52 126 76 47 1115 193 1959 22 24 23 54 33 70 58 107 44 82 28 44 568 120 1960 15 21 11 94 107 68 74 43 59 57 65 21 622 120 1961 12 10 11 14 42 87 86 53 58 37 41 37 517 140 14 22 26 26 57 198 113 99 137 98 55 22 857 128 1962 153 1963 16 15 21 28 23 37 42 77 104 22 22 12 486 1964 58 31 31 21 78 53 132 166 147 87 57 84 924 240 42 20 39 74 147 125 86 51 83 81 42 29 780 133 1965 108 1966 19 16 29 77 108 46 74 74 75 44 33 30 606 1967 19 12 17 25 27 32 44 55 75 59 76 69 531 213 1968 27 24 17 53 116 131 100 140 131 157 2C 3 93 1237 411 34 49 35 87 54 87 105 131 94 48 29 52 748 142 1969 160 1970 29 15 18 46 72 32 210 196 163 96 47 38 975 1971 34 27 14 26 82 94 87 81 107 150 92 38 820 191 148 1972 27 16 19 33 34 38 159 85 120 55 35 30 671 1973 37 18 29 73 165 106 66 66 141 69 41 42 822 137 1974 25 14 14 20 21 62 144 113 120 52 29 67 722 191 1975 46 18 30 59 182 119 180 160 96 89 110 43

*APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT

160 161

Table D.2. Runoff at Gauging Station 46, Gordon River below Huntley Creek. YEAR JAN FEB MAR APR MAY JNE JLY AUG SEP OCT NOV DEC*12MC *5M0

1953 17 27 30 190 122 191 278 176 294 9 0 186 198 1938 596 1954 14 63 136 69 213 214 106 256 108 131 56 53 1279 181 1955 27 37 9 85 153 122 190 257 100 141 279 47 1508 460 1956 101 10 24 163 52 214 190 266 124 145 251 221 1851 698 1957 136 28 63 160 235 108 70 37 116 233 169 221 1539 560 1958 55 39 97 146 499 237 154 324 88 229 109 76 1951 275 1959 12 34 45 139 93 169 142 238 86 153 43 90 125 3 231 1960 15 67 17 228 205 149 157 57 101 113 e5 17 1139 128 1961 6 7 13 45 124 221 155 85 132 68 85 81 1137 3C5 1962 1 58 80 71 146 445 223 210 215 183 115 20 1727 233 1963 14 22 62 96 58 81 127 146 204 21 59 19 1183 449 1964 210 76 87 53 212 104 277 320 304 152 132 183 1956 537 1965 89 23 110 163 289 261 171 60 212 115 89 46 1497 227 1966 25 28 40 198 248 77 142 119 129 57 73 59 1189 220 1967 34 11 44 89 62 72 91 129 145 137 191 130 1174 447 1968 44 54 28 154 274 70 179 270 262 322 406 13 2257 727 1969 48 110 58 197 106 156 216 214 188 72 24 121 1364 216 1970 30 11 30 147 164 61 435 320 261 176 60 75 1762 198 1971 35 21 7 68 194 203 152 159 204 273 155 43 1537 283 1972 39 8 38 87 83 95 368 148 266 90 57 87 1491 355 1973 98 23 91 189 352 192 99 122 280 106 97 9 0 1591 251 1974 36 11 17 44 29 148 278 211 260 89 46 184 1473 414 1975 92 15 79 133 376 184 288 234 129 146 18' 46 1770 281 1976 22 11 21 80 204 225 172 182 74 84 57 239 *APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT 162

Table D.3. Runoff at Gau in Station 78 Kin River at Crotty. YEAR JAN FEB MAR APR MAY JNE JLY AUG SEP OCT NOV DEC 1012M0 4, 5M0

1924 330 186 358 261 298 349 324 272 103 2864 759 1925 92 217 74 199 47 162 168 305 277 352 72 248 2142 634 1926 53 147 113 146 401 182 314 337 159 104 95 56 2109 465 1927 53 147 113 146 401 182 314 337 159 104 95 56 2024 380 1928 98 71 61 127 231 129 351 357 583 455 270 126 3051 819 1929 214 44 165 260 116 284 316 196 262 191 159 262 2329 703 1930 205 36 42 135 120 81 314 214 328 169 265 139 2236 877 1931 226 99 148 156 279 264 382 373 337 329 178 44 2672 554 1932 91 166 75 267 94 331 83 208 155 197 224 162 2276 942 1933 156 154 246 207 282 182 125 266 232 249 35 41 1710 169 1934 28 19 46 126 92 62 218 168 254 286 147 90 1955 748 1935 126 181 203 237 362 355 318 300 144 175 188 42 2215 325 1936 19 18 58 304 126 159 204 568 321 287 199 103 2837 868 1937 377 70 121 180 321 32 343 168 174 115 84 90 1924 590 1938 176 167 73 127 221 349 141 182 251 170 91 377 2028 587 1939 21 51 49 171 115 228 248 442 491 235 192 270 2953 1022 1940 171 281 109 120 95 366 325 215 219 132 241 125 2175 703 1941 48 48 243 80 273 262 285 225 254 351 252 104 2476 746 1942 218 101 70 226 235 157 331 287 402 153 65 99 2240 449 1943 110 110 65 331 256 322 325 192 177 89 149 111 2296 603 1944 121 103 119 288 171 358 258 170 279 160 243 166 2790 1106 1945 100 188 411 87 126 248 261 377 317 328 152 63 2440 697 1946 134 168 179 128 191 215 499 537 314 246 138 155 3187 546 1947 85 39 128 116 218 599 336 371 292 356 172 100 2881 592 1948 51 41 230 119 535 399 318 287 298 382 197 232 3124 786 1949 104 181 72 180 163 104 323 260 171 220 166 199 2091 670 1950 178 35 94 72 81 56 122 122 169 132 129 117 1162 409 1951 28 36 100 321 261 64 355 275 112 189 280 199 2336 759 1952 154 84 42 174 225 702 278 196 353 219 250 95 2628 478 1953 40 47 47 345 233 318 403 256 380 158 227 266 2942 848 1954 25 104 227 170 352 291 202 366 186 156 105 96 2069 347 1955 68 ,50 28 155 273 167 313 422 149 225 320 88 2369 665 1956 208 12 38 304 75 321 283 404 218 242 294 304 2757 910 1957 147 52 114 270 422 183 103 109 178 325 237 267 2403 812 1958 84 59 166 157 640 314 268 450 124 341 182 111 2792 498 1959 21 109 75 211 140 259 222 353 123 183 61 137 1902 412 1960 38 133 42 264 345 279 271 108 131 193 216 29 1906 316 1961 15 23 33 136 207 324 218 122 178 138 103 107 1835 512 1962 16 107 179 80 215 603 283 322 249 270 165 38 2400 378 1963 30 39 106 154 92 114 167 249 292 45 124 55 3.826 714 1964 271 136 129 81 282 164 381 509 382 191 146 241 2712 723 1965 124 29 184 197 371 389 211 100 277 148 157 72 2086 394 1966 45 46 74 283 361 139 248 181 133 79 125 68 1777 351 1967 67 24 69 135 88 108 137 193 205 169 209 177 1643 608 1968 59 86 77 244 435 365 295 445 336 425 488 148 3498 955 1969 109 120 90 280 167 162 343 299 269 97 48 191 1948 331 1970 42 18 32 230 259 137 553 467 364 249 77 104 2543 282 1971 51 37 15 129 270 286 191 245 293 407 206 94 2314 492 1972 91 25 76 160 129 144 463 228 330 129 94 121 2133 552 1973 129 57 152 270 478 245 172 220 356 142 145 162 2293 412 1974 54 23 27 98 98 224 358 346 364 145 83 315 2345 752 1975 172 26 157 187 563 277 401 276 216 179 227 56 2494 396 1976 35 16 63 173 362 271 247 253 108 117 96 468 2398 868 1977 115 27 162 305 304 235 267 265 98 242 214 230 2358 643 1978 63 97 39 164 165 53 393 ',APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT 163

Table D.4. Runoff at Gauging Station 119, Huon River above Frying Pan Creek. YEAR JAN FEB MAR APR MAY JNE JO. AUG SEP OCT NOV DEC*12M0 45M0

1949 94 132 53 115 52 73 220 136 79 90 86 117 1136 371 1950 97 22 50 55 45 48 44 70 09 56 77 44 628 222 1951 16 23 62 220 150 50 202 181 64 92 156 91 1363 403 1952 57 71 29 122 120 456 174 86 190 148 140 53 1583 285 1953 24 31 38 128 100 168 258 146 279 77 179 154 1664 508 1954 18 52 105 69 184 256 98 242 98 95 61 50 1232 190 1955 34 31 14 91 131 127 154 205 85 108 235 62 1285 385 1956 59 11 18 113 67 248 170 209 101 129 208 183 1645 606 1957 108 36 73 120 192 66 62 53 153 176 122 179 1333 511 1958 53 40 118 94 355 194 134 310 88 184 85 82 1627 269 1959 19 38 46 105 98 137 123 181 71 114 37 58 1013 184 1960 17 55 17 240 237 121 135 64 89 99 113 19 1181 195 1961 15 18 31 47 122 217 158 74 113 73 69 67 1083 280 1962 24 60 60 58 136 345 181 173 198 162 90 25 1469 217 1963 21 30 51 94 55 75 109 117 156 18 51 22 995 372 1964 158 69 72 43 166 87 208 265 181 108 115 177 1573 514 1965 85 29 108 167 249 213 133 79 167 112 110 49 1397 276 1966 24 31 63 167 200 83 178 119 102 64 73 47 1131 217 1967 31 22 44 73 76 69 110 113 114 116 157 115 1067 396 1968 30 63 31 149 243 278 154 219 232 240 315 104 2127 612 1969 47 77 69 181 90 150 179 162 168 64 52 130 1306 313 1970 59 18 54 101 146 54 401 276 225 174 63 76 1621 243 1971 46 46 13 66 154 181 127 140 166 237 116 38 1306 235 1972 33 13 35 76 81 84 219 107 170 60 40 63 1027 231 1973 52 24 52 139 241 149 82 91 164 74 73 66 1152 211 1974 27 24 23 35 38 125 283 161 181 58 47 147 1229 349 1975 74 15 66 84 223 149 211 214 100 128 119 27 *APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT 164 Table D.5. Runoff at Gauging Station 154, Pieman River above Heems- kirk River. YEAR JAN FEB MAR APR MAY PIE JLY AUG SEP OCT NOV DEC*12M0 *5M0

1958 72 50 161 139 547 276 213 376 119 286 153 104 1959 2356 400 22 68 54 164 106 203 197 276 112 155 54 113 1548 335 1960 29 105 35 243 274 212 198 82 117 163 172 27 1545 256 1961 16 16 27 86 167 273 174 91 136 108 94 85 1440 404 1962 16 76 134 78 165 535 253 257 218 231 143 34 2051 1963 20 314 29 89 121 75 93 138 212 234 51 83 35 1516 593 1964 250 108 117 77 252 133 328 386 351 176 128 226 2350 647 1965 115 29 149 185 318 345 197 87 238 137 119 53 1800 293 1966 34 34 54 233 309 106 199 148 116 65 93 68 1453 276 1967 47 17 52 114 70 98 119 153 166 143 175 147 1371 508 1968 56 75 55 205 360 302 222 347 295 366 421 132 2910 813 1969 82 102 76 237 138 160 292 277 237 81 37 146 1688 266 1970 33 18 33 185 236 83 486 373 285 216 64 96 2222 358 1971 46 30 124 103 231 250 179 221 249 355 181 74 1987 399 1972 76 16 52 124 100 118 432 203 287 111 73 91 1815 440 1973 121 43 113 212 388 216 145 168 307 113 122 115 1882 333 1974 48 22 26 63 39 159 300 279 319 114 68 247 1867 594 1975 132 23 123 157 453 243 334 254 172 159 191 45 2107 336 1976 34 18 49 133 296 229 213 220 82 96 78 352 1915 645 1977 84 22 110 239 202 182 215 216 78 *APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT

Table D.6. Runoff at Gauging Station 159, Arthur River below Rapid River. YEAR JAN FEB MAR APR MAY JNE JLY AUG SEP OCT NOV DEC*12M0 • 5M0

1958 61 24 81 130 219 263 166 344 109 293 178 70 1862 330 1959 8 39 34 171 65 171 144 269 130 207 42 102 1425 271 1960 16 90 20 273 244 189 208 82 142 156 165 15 1484 192 1961 4 5 3 86 135 232 190 128 164 103 92 89 1374 334 1962 3 49 100 61 138 526 250 303 231 277 146 30 2059 271 1963 11 24 61 91 40 76 122 283 267 41 95 4 1468 547 1964 217 132 99 46 231 169 313 401 381 197 130 208 2314 574 1965 96 11 130 185 303 274 144 100 204 120 91 62 1547 216 1966 20 16 26 194 223 77 172 147 146 70 103 71 1279 251 1967 52 5 20 79 51 74 122 152 204 170 214 173 1377 523 1968 47 41 50 206 336 300 221 362 294 400 488 139 2972 854 1969 67 107 54 191 119 132 265 255 178 97 52 163 1535 295 1970 33 9 40 184 174 106 456 372 297 294 100 94 2164 279 1971 41 15 29 78 237 209 167 198 278 361 211 87 1937 409 1972 79 6 26 89 74 93 372 238 317 96 77 74 1645 366 1973 104 28 83 225 382 200 155 165 315 111 71 142 1830 275 1974 45 6 12 54 44 172 317 267 273 153 63 209 1799 519 1975 109 12 125 145 451 215 376 218 185 163 196 34 2015 263 1976 9 0 24 94 263 196 163 194 94 100 66 298 1629 527 1977 54 12 99 147 194 139 148 301 84 181 131 190 1846 653 1978 29 68 236 152 145 50 •APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT 165

below Jane Table D.7. Runoff at Gauging Station 183, Franklin River River. YEAR JAN FEB MAR APR MAY JNE JLY AUG SEP OCT NOV DEC*12m0 *5m0

1955 205 127 312 422 104 190 233 72 501 1956 164 15 19 245 99 299 239 398 171 168 234 213 2265 646 1957 101 29 69 216 354 159 88 63 1 31 239 173 183 1776 527 1958 44 28 99 110 520 244 210 357 94 278 155 66 2147 335 1959 15 71 28 161 78 195 168 324 92 152 37 106 1437 266 1960 21 82 20 222 287 237 235 112 116 156 170 37 1606 240 1961 9 9 15 99 144 284 205 88 119 107 73 78 1384 337 1962 12 53 121 53 176 493 239 294 212 226 126 24 1930 236 1963 18 18 51 93 56 94 159 223 262 28 88 25 1375 462 1964 153 108 89 55 241 184 385 485 312 149 122 172 2309 498 1965 81 15 107 149 339 349 200 91 200 115 95 43 1657 215 1966 16 23 39 190 254 97 238 160 106 54 85 56 1328 229 1967 47 11 31 TO 50 74 121 159 150 134 156 117 1149 391 1968 43 35 41 200 383 326 259 410 280 350 381 87 2883 674 1969 62 87 58 194 149 129 292 136 229 58 46 132 1435 247 1970 37 11 21 186 224 128 481 452 340 182 51 64 2181 188 1971 38 25 10 91 242 259 176 221 257 318 157 71 1916 351 1972 78 14 32 86 89 109 411 228 249 102 65 58 1610 336 1973 72 34 108 190 358 196 138 184 300 96 85 104 1726 264 1974 46 15 15 76 56 178 308 335 329 115 64 222 1940 543 1975 114 20 122 143 483 205 355 240 192 147 186 39 2054 289 1976 27 12 26 106 293 224 178 259 84 70 47 304 1737 522 1977 . 57 20 94 188 242 196 220 248 58 173 116 147 *APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT

Derwent River Table D.8. Runoff for Gauging Station Record 10087, below Lake St. Clair. YEAR JAN FEB MAR APR MAY JNE JLY AUG SEP OCT NOV DEC*12m0 *5m0

1955 108 218 364 71 101 103 45 282 1359 1956 79 26 29 147 125 191 169 231 136 80 99 79 280 30 32 82 177 94 88 47 78 117 69 56 867 183 1957 40 178 15 15 29 39 270 122 157 201 48 173 91 29 1189 1958 644 12 8 11 34 13 41 25 70 71 211 32 67 26 47 1959 138 14 31 10 98 174 159 174 106 94 97 94 24 1039 1960 36 731 139 1961 8 6 6 49 52 138 160 77 56 60 31 134 62 21 1150 123 1962 il 20 42 23 103 312 170 168 117 12 19 15 62 169 169 170 22 31 11 809 184 1963 16 11 148 69 46 58 143 142 287 266 190 109 39 56 1343 1964 27 863 93 20 8 25 47 186 190 122 62 101 61 39 23 1965 60 26 793 128 1966 10 9 13 50 97 52 219 127 76 43 51 597 160 1967 23 9 10 13 21 40 96 102 92 74 53 24 15 17 96 224 201 173 301 145 181 189 50 1662 341 1968 142 22 46 34 76 103 77 190 200 135 35 43 45 959 1969 1197 140 1970 34 10 10 62 106 89 256 278 179 87 38 33 96 57 1261 213 1971 31 28 12 59 150 198 106 179 176 181 35 14 12 28 30 54 238 174 117 48 26 16 793 105 1972 47 65 1197 169 1973 23 14 26 91 238 178 118 158 182 62 35 13 10 64 60 211 282 208 200 84 43 136 1435 327 1974 38 1975 66 17 64 63 304 115 268 153 143 99 99 *APRIL OR NOVEMBER OF GIVEN YEAR THROUGH MARCH OF NEXT APPENDIX E

TABLES OF RECONSTRUCTED SUMMER (NOVEMBER-MARCH) RUNOFF (IN MILLIMETERS DEPTH)

Table E.1. Reconstructed Seasonalized Summer Runoff at Station 40, Florentine River above Derwent Junction. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 108 201 174 216 1780 269 199 228 249 135 136 138 126 185 197 1790 238 278 201 277 244 185 187 205 207 232 1800 267 255 256 369 215 290 260 179 184 228 1810 192 229 301 231 234 143 295 253 256 296 1820 161 223 192 231 158 267 167 232 152 212 1830 250 206 192 109 160 130 195 176 195 113 1840 230 234 143 226 124 155 80 189 229 51 1850 176 188 231 107 138 158 219 94 143 0 1860 171 136 158 221 130 125 219 263 147 156 1870 231 173 147 205 166 232 186 173 148 126 1880 161 74 165 223 102 131 141 112 68 283 1890 185 176 237 172 241 152 144 213 130 159 1900 240 278 180 259 252 197 241 211 163 79 1910 312 276 301 188 253 275 236 196 174 159 1920 223 249 286 236 216 144 197 145 216 118 1930 204 153 221 141 97 149 183 88 134 116 1940 130 128 135 111 153 23 98 131 226 104 1950 150 183 74 216 140 209 264 101 15 2 89 1960 96 192 186 240 248 113 143 209 230 177 1970 169 152 138 147

166 167

Table E.2. Reconstructed Seasonalized Summer Runoff at Station 46, Gordon River below Huntley Creek. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 177 390 343 436 1780 568 409 471 521 259 240 245 217 360 396 1790 494 601 422 588 520 383 367 414 423 479 1800 571 541 550 810 470 620 562 370 361 470 1810 391 471 650 505 487 288 621 552 549 643 1820 331 452 391 473 312 554 334 479 291 426 1830 520 430 380 188 292 230 381 348 382 199 1840 457 487 275 453 230 280 114 357 470 16 1850 323 372 475 190 240 294 439 157 247 0 1860 297 238 293 440 237 215 431 558 288 290 1870 467 349 268 409 320 474 370 339 271 221 1880 293 99 296 448 173 219 251 177 81 580 1890 378 355 487 349 493 298 263 430 239 299 1900 495 595 373 543 540 404 502 448 314 122 1910 652 611 656 401 528 592 502 400 338 301 1920 450 522 616 500 447 271 386 275 428 214 1930 398 293 445 271 144 271 352 137 226 188 1940 221 211 232 172 269 0 125 217 451 173 1950 272 346 103 418 263 419 552 183 272 127 1960 138 361 368 495 520 210 248 418 486 350 1970 324 271 240 256

Table E.3. Reconstructed Seasonalized Summer Runoff at Station 78, King River at Crotty. YE AP/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 334 591 518 634 1780 781 588 668 724 411 410 417 383 548 580 1790 695 807 593 803 712 550 552 602 610 679 1800 777 744 747 1058 635 839 758 533 545 667 1810 567 670 871 678 683 434 852 738 746 857 1820 484 653 568 676 475 774 499 679 456 622 1830 728 607 566 336 476 395 574 524 573 348 1840 670 683 432 661 381 463 256 557 669 176 1850 521 555 676 332 417 473 641 297 430 3 1860 505 410 472 647 395 379 641 764 444 466 1870 673 516 441 603 494 678 551 514 445 383 1880 478 240 488 653 317 395 423 344 222 817 1890 548 524 692 514 702 457 434 625 396 474 1900 699 805 537 754 735 581 704 622 486 254 1910 897 804 870 560 737 799 690 579 517 474 1920 652 727 828 689 634 435 581 437 631 362 1930 598 460 647 428 301 447 542 279 404 355 1940 393 388 406 340 456 96 302 396 660 322 1950 450 540 239 630 424 615 766 316 455 279 1960 298 564 550 700 723 350 430 613 689 526 1970 502 454 416 439 168 Table E.4. Reconstructed Seasonalized Summer Runoff at Station 119, Huon River above Frying Pan Creek. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 191 351 320 389 1780 492 373 418 457 260 239 243 221 330 361 1790 435 520 386 507 459 355 337 375 382 423 1800 497 472 482 677 427 532 492 347 332 417 1810 360 417 556 454 431 285 529 487 481 552 1820 318 401 359 418 300 478 316 423 281 382 1830 455 390 348 204 277 232 345 324 347 212 1840 402 430 271 400 237 267 145 325 417 105 1850 298 342 419 207 237 280 390 181 241 0 1860 273 236 278 389 239 220 382 486 282 277 1870 412 328 260 369 302 418 341 317 262 226 1880 277 133 277 397 192 219 248 188 118 494 1890 350 332 428 329 432 289 257 385 242 285 1900 435 515 349 472 475 370 441 406 298 155 1910 550 533 562 373 460 513 446 366 315 288 1920 399 456 531 444 401 266 350 269 381 224 1930 357 282 396 269 165 262 323 164 224 197 1940 222 213 230 184 257 33 143 218 398 191 1950 262 318 138 370 261 376 479 203 261 153 1960 159 327 340 434 456 223 241 375 428 326 1970 304 260 237 247

Table E.5. Reconstructed Seasonalized Summer Runoff at Station 154, Pieman River above Heemskirk River. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 215 399 341 424 1780 525 386 446 484 261 269 274 251 366 384 1790 465 538 385 540 470 356 366 400 404 454 1800 519 496 495 717 408 565 502 343 362 445 1810 371 448 586 439 455 272 579 484 495 574 1820 307 438 373 454 306 524 323 454 296 416 1830 488 397 376 211 318 258 385 344 383 220 1840 455 455 277 446 240 310 158 377 447 96 1850 354 368 453 206 277 313 431 182 288 0 1860 350 271 313 438 254 248 435 511 284 308 1870 454 334 291 403 325 455 363 337 293 248 1880 320 147 330 440 198 264 279 226 137 560 1890 357 341 465 332 473 294 285 418 254 312 1900 469 539 346 507 486 381 471 404 319 151 1910 615 529 582 357 496 533 455 380 342 311 1920 439 487 554 455 419 282 390 283 426 227 1930 404 299 435 273 194 295 363 172 270 233 1940 260 259 269 225 307 49 205 265 447 203 1950 299 363 144 430 273 412 516 192 305 177 1960 194 383 363 470 483 216 288 411 462 345 1970 331 303 276 294 169 Table E.6. Reconstructed Seasonalized Summer Runoff at Station 159, Arthur River below Rapid River. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

17769 119 189 149 184 1780 208 154 183 193 110 139 142 134 169 162 1790 190 198 141 213 174 134 163 168 167 188 1800 196 193 182 265 131 218 181 127 162 183 1810 149 186 222 143 181 101 238 165 183 211 1820 Ill 189 151 193 127 220 132 188 132 182 1830 200 152 166 104 162 132 177 150 174 106 1840 208 183 118 199 107 162 94 188 186 59 1850 185 162 190 94 150 153 191 91 160 45 1860 203 144 154 200 121 132 204 198 117 149 1870 199 134 146 177 147 194 157 148 146 126 1880 164 92 176 195 98 150 143 135 95 247 1890 140 139 197 131 203 123 142 180 119 148 1900 196 204 130 205 179 150 191 145 144 78 1910 260 176 211 120 203 198 168 154 155 144 1920 192 196 208 171 167 129 180 127 193 104 1930 189 135 191 117 118 149 172 94 154 135 1940 144 151 147 137 166 69 152 154 203 105 1950 153 178 85 208 124 182 209 81 161 110 1960 124 193 158 197 192 91 160 181 192 149 1970 153 160 149 161

Table E.7. Reconstructed Seasonalized Summer Runoff at Station 183, Franklin River below Jane River. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 274 494 436 534 1780 664 498 566 615 345 339 345 316 459 489 1790 589 689 506 683 607 467 464 508 516 574 1800 662 633 637 905 546 715 648 453 457 565 1810 480 567 743 582 580 368 723 633 637 733 1820 412 550 481 571 400 655 422 575 382 524 1830 616 516 477 279 395 327 481 441 481 289 1840 562 580 363 556 318 383 208 463 566 142 1850 431 467 572 277 343 393 539 245 353 0 1860 414 338 392 543 329 313 537 650 375 388 1870 568 437 366 507 414 572 464 432 369 317 1880 396 193 403 549 262 323 351 280 177 689 1890 465 443 585 435 593 385 360 527 331 396 1900 592 687 457 639 627 493 597 531 408 208 1910 759 691 744 479 625 682 589 490 433 397 1920 549 616 707 587 538 364 487 366 530 302 1930 501 385 545 359 244 370 453 228 331 290 1940 323 317 334 276 375 66 238 323 555 266 1950 373 450 194 526 355 517 650 265 376 225 1960 240 469 463 592 614 294 353 516 583 443 1970 420 375 343 361 170

Table E.8. Reconstructed Seasonalized Summer Runoff for Record 10087, Derwent River below Lake St. Clair. YEAR/ DECADE 0 1 2 3 4 5 6 7 8 9

1776 217 458 393 501 1780 641 460 535 588 293 288 294 263 419 451 1790 560 668 467 662 578 425 424 472 480 544 1800 639 607 611 904 509 697 622 410 417 534 1810 440 536 728 549 549 317 707 605 611 716 1820 364 518 441 541 353 633 376 544 334 490 1830 590 479 438 221 349 275 443 398 443 232 1840 533 549 312 525 263 337 144 425 535 70 1850 391 427 541 218 293 348 507 184 305 0 1860 373 288 346 511 276 259 505 626 324 342 wo 53e 392 318 471 370 542 423 389 321 263 1880 352 128 360 518 203 272 301 224 Ill 671 1890 423 400 556 391 565 336 311 493 277 349 1900 563 666 414 615 600 454 569 494 362 143 1910 748 668 728 437 599 660 558 451 390 350 1920 518 590 687 557 503 314 450 316 497 246 1930 466 337 513 308 184 323 413 166 280 235 1940 271 265 283 220 329 0 181 272 524 207 1950 326 410 128 494 304 482 626 204 329 164 1960 181 431 422 564 586 236 305 481 554 400 1970 376 328 293 313 REFERENCES

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