NOAA Technical Memorandum NMFS-AFSC-91

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Alaska Fisheries Science Center

June 1998

by

B. L. Wing and J. J. Pella

Time Series Analyses

of Climatological Records

from Auke Bay, Alaska
NOAA Technical Memorandum NMFS

The National Marine Fisheries Service’s Alaska Fisheries Science Center uses

the NOAA Technical Memorandum series to issue informal scientific and

technical publications when complete formal review and editorial processing

are not appropriate or feasible. Documents within this series reflect sound

professional work and may be referenced in the formal scientific and technical

literature.

The NMFS-AFSC Technical Memorandum series of the Alaska Fisheries

Science Center continues the NMFS-F/NWC series established in 1970 by the

Northwest Fisheries Center. The new NMFS-NWFSC series will be used by

the Northwest Fisheries Science Center.

This document should be cited as follows:

Wing, B. L., and J. J. Pella. 1998. Time series analyses of

climatological records from Auke Bay, Alaska. U.S. Dep. Commer.,

NOAA Tech. Memo. NMFS-AFSC-91,90 p.

Reference in this document to trade names does not imply endorsement by

the National Marine Fisheries Service, NOAA.
June 1998

NOAA Technical Memorandum NMFS-AFSC-91

by

B. L. Wing and J. J. Pella

Time Series Analyses

of Climatological Records

from Auke Bay, Alaska

Auke Bay Laboratory

Alaska Fisheries Science Center

11305 Glacier Highway

Juneau AK 99801-8626

U.S. DEPARTMENT OF COMMERCE

William M. Daley, Secretary

National Oceanic and Atmospheric Administration

D. James Baker, Under Secretary and Administrator

National Marine Fisheries Service

Rolland A. Schmitten, Assistant Administrator for Fisheries
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iii

ABSTRACT

Physical environmental data collected by scientists from the Auke Bay Laboratory

of the National Marine Fisheries Service and the U.S. Geological Survey during 1959-93

near Auke Bay, Alaska, are summarized in tabular and graphic formats. Data include sea

surface temperatures, air temperatures, precipitation (rainfall and melted snowfall), water

temperatures for Auke Creek, Auke Lake, and Lake Creek, stream flows from Auke Creek

and Lake Creek, and annual dates of ice-out for Auke Lake. Statistical time series

methods, including spectral analysis for underlying cycles and univariate modeling for

temporal dependence, were used to describe the monthly records for precipitation,

snowfall, average daily high, low, and midrange air temperatures, and sea surface

temperature.

V

CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..iii

INTRODUCTION .............................................. 1

METHODS ................................................... 1

Meteorological Records ...................................... 1

Air Temperatures ..................................... 2

Precipitation ........................................ 2

Auke Bay Saltwater Temperatures ............................... 2

Auke Bay Laboratory .................................. 2

Auke Bay Monitor Station ............................... 3

Auke Lake Watershed Stream Flows and Temperatures ................. 3

Lake Creek ......................................... 3

Auke Creek ......................................... 3

Auke Creek Hatchery .................................. 4

Auke Lake Freeze-Up and Ice-Out ......................... 4

Time Series Analysis ........................................ 4

RESULTS AND DISCUSSION ..................................... 7

Meteorological Records ...................................... 7

Air Temperatures ..................................... 7

Precipitation and Snowfall ............................... 10

Auke Bay Saltwater Temperatures ............................... 13

Auke Bay Laboratory .................................. 13

Auke Bay Monitor Station ............................... 14

Auke Lake Watershed Stream Flows and Temperatures ................. 15

Lake Creek ......................................... 15

Auke Creek ......................................... 15

Auke Creek Hatchery and Auke Lake ....................... 15

Auke Lake Freeze-Up and Ice-Out ......................... 16

ACKNOWLEDGMENTS ......................................... 16

CITATIONS.. ................................................. 17
vi

TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

LIST OF TABLES

Table I.--Monthly averages of daily high temperature (oC) (MADHTs) at Auke

Bay, Alaska, 1963-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Table 2.--Monthly averages of daily low temperature (oC) (MADLTs) at Auke Bay,

Alaska, 1963-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Table 3.--Monthly averages of daily midrange temperature (oC) (MADMTs) at

Auke Bay, Alaska, 1963-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Table 4.--Annual means, extremes, percentage of total variation (%) in weather

variable due to an annual cycle and its statistical significance (p), and slope

of long-term trend and its statistical significance (p), for monthly values of

average daily high (MADHT), low (MADLT), and midrange (MADMT)

temperatures, precipitation, snowfall, and average daily sea surface

temperature (MADSST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Table 5.--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe interannual month

differences in average daily high temperature series, and statistics of the fit . . 30

Table 6.--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe the interannual month

differences in average daily low temperature series (MADLTs), and

statistics of the fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Table 7.--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe the interannual month

differences in average daily midrange temperature series, and statistics of

the fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Table 8.--Monthly precipitation (cm) at Auke Bay, Alaska, 1963-93 . . . . . . . . . . . . 33

Table 9.--Monthly snowfall (cm) at Auke Bay, Alaska, 1963-93 . . . . . . . . . . . . . . . 35

Table 10---Seasonal snowfall (cm) at Auke Bay, Alaska, 1963-93 . . . . . . . . . . . . . . 37

Table 11 .--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe the interannual month

differences in precipitation series, and statistics of the fit . . . . . . . . . . . . . . . 39

Table 12.--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe the interannual month

differences in snowfall series, and statistics of the fit . . . . . . . . . . . . . . . . . . 40
vii

Table 13.--Monthly averages of daily morning observations of sea surface

temperatures (oC) (MADSSTs), Auke Bay Laboratory, 1959-69 . . . . . . . . . . 41

Table 14.--Monthly averages of daily afternoon observations of sea surface

temperatures (oC) (MADSSTs), Auke Bay Laboratory, 1975-93 . . . . . . . . . . 42

Table 15.--Conditional least-squares estimates of the moving-average and

autoregressive parameters necessary to describe interannual month

differences in monthly average daily sea surface temperature series

(MADSSTs), and statistics of the fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Table 16.--Monthly averages of sea surface temperature (oC), Auke Bay Monitor,

1959-93. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Table 17.--Monthly averages of Lake Creek stream flows (m3s

-1), 1963-73 . . . . . . . . 46

Table l8--Monthly averages of Lake Creek stream temperatures (oC), 1963-73 . . . . . 48

Table l9.--Monthly averages of daily Auke Creek stream flows (m3s

-1), 1962-75 . . . . 49

Table 20.--Monthly averages of daily Auke Creek stream temperatures (oC),

1963-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Table 21.--Monthly averages of daily Auke Creek Hatchery temperatures (oC),

1971-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Table 22.--Auke Lake ice breakup dates, 1960-95 . . . . . . . . . . . . . . . . . . . . . . . . . 54

LIST OF FIGURES

Figure 1 .--Auke Bay, Alaska, and vicinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Figure 2a.--Monthly averages of daily high temperature (MADHTs) at Auke Bay

Laboratory, February 1963 through May 1993 . . . . . . . . . . . . . . . . . . . . . . 58

Figure 2b.--Monthly averages of daily low temperature (MADLTs) at Auke Bay

Laboratory, February 1963 through May 1993 . . . . . . . . . . . . . . . . . . . . . . 59

Figure 2c.--Monthly averages of daily midrange temperature (MADMTs) at Auke

Bay Laboratory, February 1963 through May 1993 . . . . . . . . . . . . . . . . . . . 60

Figure 3.--Statistics of annual temperature cycle at Auke Bay laboratory (1963-93)

including daily extremes (lowest low and highest high [0]) and monthly

extrema (high [o], low [•], and series averages [ ] for monthly average

daily high (MADHT), low (MADLT), and midrange (MADMT) air

temperature series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Figure 4.--Annual average of monthly average high (MADHTs [ ] , midrange

(MADMTs [ ] , and low (MADLTs [•] daily air temperatures at Auke

Bay, Alaska, 1963-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 5.-Sample autocorrelation function (SACF) of interannual month

differences in logarithm-transformed monthly average daily high air

temperatures (MADHTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
viii

Figure B.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed monthly average daily high air

temperatures (MADHTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Figure 7.--Sample autocorrelation function (SACF) of interannual month

differences in logarithm-transformed monthly average daily low air

temperatures (MADLTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Figure 8.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed monthly average daily low air

temperatures (MADLTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure 9.--Sample autocorrelation function (SACF) of interannual month

differences in logarithm-transformed monthly average daily midrange air

temperatures (MADMTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure l0.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed monthly average daily midrange air

temperatures (MADMTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Figure 11a.--Total monthly precipitation at the Auke Bay Laboratory, February

1963 through May 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Figure 11 b.--Monthly snowfall at the Auke Bay Laboratory, February 1963 through

May1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 12.--Statistics of annual precipitation cycle at Auke Bay Laboratory

(1963-93) from monthly precipitation (cm) (maximum [o], mean [ ] , and

minimum [•]) for total precipitation, calendar-year snowfall

(January-December), and seasonal snowfall (July-June) . . . . . . . . . . . . . . . . 7 1

Figure 13.--Annual total precipitation at Auke Bay, 1963-93 . . . . . . . . . . . . . . . . . . 72

Figure 14.--Sample autocorrelation function (SACF) of interannual month

differences in logarithm-transformed precipitation at Auke Bay . . . . . . . . . . . 73

Figure 15.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed precipitation at Auke Bay . . . . . . . . . . . 74

Figure 16.--Annual total snowfall at Auke Bay, 1963-93 . . . . . . . . . . . . . . . . . . . . 75

Figure 17.--Sample autocorrelation function (SACF) of interannual month

differences in logarithm-transformed snowfall at Auke Bay . . . . . . . . . . . . . . 76

Figure 18.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed snowfall at Auke Bay . . . . . . . . . . . . . . 77

Figure 19a.--Statistics of daily sea surface temperatures at the Auke Bay

Laboratory float . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Figure 19b.--Statistics of daily sea surface temperatures at the Auke Bay

Laboratory float for 1959-69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Figure 19c.--Statistics of daily sea surface temperatures at the Auke Bay

Laboratory float for 1975-93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
ix

Figure 20.--Monthly averages of daily sea surface temperatures (MADSSTs) at

Auke Bay Laboratory, February 1975 through May 1993 . . . . . . . . . . . . . . . 81

Figure 21 .--Annual average of monthly average daily sea surface temperatures

(MADSSTs) at Auke Bay, Alaska, 1975-93 . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 22.--Sample autocorrelation function (SACF) of interannual differences in

logarithm-transformed monthly average daily sea surface temperatures

(MADSSTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 23.--Sample partial autocorrelation function (SPACF) of interannual month

differences in logarithm-transformed monthly average daily sea surface

temperatures (MADSSTs) at Auke Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Figure 24.--Statistics of annual sea surface temperature cycles (1959-93) at Auke

Bay monitor station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 25.--Statistics of annual Lake Creek stream flow cycle (1963-73) . . . . . . . . . 86

Figure 26.--Statistics of annual Lake Creek temperature cycle (1963-73) . . . . . . . . . 87

Figure 27.--Statistics of annual Auke Creek stream flow cycle (1962-75) . . . . . . . . . 88

Figure 28.--Statistics of annual Auke Creek temperature cycle (1963-93) . . . . . . . . . 89

Figure 29.--Statistics of annual Auke Creek hatchery temperature cycle (1971-92) . . . 90
INTRODUCTION

Auke Bay is a small (11 km2) embayment of the fjord system in southeastern

Alaska, located approximately 130 km inland of the open ocean, 16 km northwest of

Juneau, Alaska, and 5 km west of the Juneau International Airport (Fig. 1).

Meteorological data for the latter two locales extend back to the 1880s and 1940s,

respectively (Lomire 1979). Auke Bay is subject to a northern maritime climate, having

moderate temperatures, high precipitation, and predominant southeasterly winds. Average

monthly insolation varies greatly with day length and cloud cover density, ranging from

20 g cal cm-2day-1 in midwinter to 340 g cal cm-2day-1 in midsummer (Bruce et al. 1977).

Diel photoperiod ranges from 6.4 hours at the winter solstice to 18.3 hours at the summer

solstice. The mountainous terrain of southeastern Alaska causes considerable local

weather variation over short distances, as is evident from comparing Auke Bay weather

records to those of nearby Juneau and the Juneau International Airport. Auke Bay is

protected by the surrounding hills from the prevailing southeasterly winds and in the

winter from the severe, north winds associated with periods of strong atmospheric high

pressure in the interior of northwestern Canada.

Auke Bay and vicinity have been the locale of biological research since the 1950s.

The National Marine Fisheries Service and the University of Alaska have research

laboratories at Auke Bay. The U.S. Fish and Wildlife Service, U.S. Forest Service, U.S.

Geological Survey, and the Alaska Department of Fish and Game have used the area for

experimental studies. The research and management projects in the Auke Bay vicinity

have resulted in a diverse time series of environmental data. Few of these data sets have

been summarized or are readily available to the general research community.

This report presents tabular and graphic summaries and time series analyses of the

physical data gathered by scientists from the Auke Bay Laboratory of the National Marine

Fisheries Service and U.S. Geological Survey since 1959. These summaries supplement,

and update previously published data from Auke Bay by Bruce et al. (1977) and Coyle

and Shirley (1990).

METHODS

Meteorological Records

Weather observations have been taken daily at the Auke Bay Laboratory (lat.

58o22.88’N, long. 134o38.67’W) for the National Weather Service Cooperative Observer

Program since February 1963. Daily air temperatures and precipitation were recorded at

1630 hours according to procedures in the Weather Bureau Observing Handbook (ESSA

1970). Although daily climate records have been obtained, the series began before general

availability of computers and only the monthly summaries have been transferred to

computer-readable media. Extreme daily high and low temperatures have also been

recorded.
2

Air Temperatures

Maximum, minimum, and current air temperatures were measured by liquid-inglass thermometers from February 1963 through July 1988. Beginning in August 1988,

air temperature observations were taken with an electronic maximum/minimum system.

The liquid-in-glass thermometers serve as backup during frequent electric power outages.

Since October 1979, a paper-recording battery-powered hygrothermograph has served as

backup to both standard systems for occasions when an observer is unavailable. All air

temperatures were recorded in degrees Fahrenheit to the nearest whole degree. For this

report the temperatures have been converted to the Celsius scale.

Precipitation

Daily precipitation observations from a standard 8-inch (20.3 cm) nonrecording

gage were recorded to the nearest 0.01 inch. Precipitation includes the water equivalent of

any snowfall or ice pellets. Daily snowfall and snow on the ground were measured with

standard 12-inch and 36-inch rulers. Snowfall was recorded to the nearest 0.1 inch and

snow on the ground recorded to the nearest whole inch. For this report, average

precipitation records were converted to centimeters. Snow-on-the-ground data have not

been analyzed for this report.

Auke Bay Saltwater Temperatures

Auke Bay Laboratory

Daily sea surface temperatures (SSTs) for the Auke Bay Laboratory from January

1959 through April 1963 were taken on the beach at a private residence adjacent to the

laboratory. These temperatures were normally taken between 0700 and 0800 hours with a

mercury-in-glass thermometer at the water’s edge. From May 1963 through 1969, the

temperatures were taken off the laboratory float (roughly l0-20 m beyond the 0 tide line)

and on a less regular schedule according to specific project needs. In 1975, daily sea

surface temperature observations were reinstituted at the Auke Bay Laboratory float. To

assure continuity of the data, sea surface temperatures were taken at the end of the normal

work day (1630) and included as part of the daily weather observations.

The large gaps in these data resulted from changing priorities, personnel, and

programs.
3

Auke Bay Monitor Station

The Auke Bay Monitor oceanographic station (lat. 58o21.97’N, long. 134o4O.OO’W)

has been a reference for research projects in Auke Bay since 1960. Located near the

middle of Auke Bay, it is considered representative of much of the bay (Bruce et al. 1977,

Coyle and Shirley 1990). Oceanographic data were collected there on varying and

irregular weekly to quarterly schedules according to the needs of specific projects.

Auke Lake Watershed Stream Flows and Temperatures

Auke Bay receives most of its freshwater input from the Mendenhall River, and

three small watersheds drained by Auke Creek, Auke Nu Creek, and Waydelich Creek

(Fig. 1). Several small permanent streams and intermittent streams contribute to the runoff

to Auke Bay. Temperatures and stream flows were recorded by stream gages on Lake

Creek (1963-73) flowing into Auke Lake, Auke Creek (1962-75) flowing from Auke

Lake, and the Mendenhall River (1965-79) and its tributary Montana Creek (1963-76)

(Chapman 1982, U.S. Geological Survey 1963-76). Zieman et al. (1990) compared

stream flows of Auke Creek, Auke Nu Creek, and Waydelich Creek only for March

through June (1986-89).

Lake Creek

Lake Creek is the largest stream flowing into Auke Lake. Its 6.5 km2 (2.5 mile2)

watershed is relatively low and mostly hemlock-spruce forest with some open muskeg.

The low-gradient first 1.5 km of the creek includes most of the known stream spawning

area for salmonids inhabiting Auke Lake. Stream flows and temperatures were recorded

continuously by a U.S. Geological Survey stream gage from October 1963 through

September 1973.

Auke Creek

Auke Creek, the outflow from Auke Lake to Auke Bay, has a 10 km2 (4.0 mile2)

watershed. Surface water from Auke Lake to Auke Creek passes through a shallow

lagoon. The narrow entrance to the lagoon is often less than 50 cm deep during extended

low runoff periods. The exit from the lagoon passes through a narrow channel over a

bedrock sill. Water depth at the sill is often less than 30 cm. The stream is short (0.65

km) and has a steep gradient (average 26 m km-1). The upper portion of the stream was

modified to increase salmon spawning area in 1963, but pink salmon do not consistently

spawn in the modified area.

Auke Creek temperatures and stream flows were recorded continuously by a U.S.

Geological Survey stream gage at the upper end of the creek from October 1962 through
4

September 1975; thereafter, stream temperatures were recorded at the Auke Creek

Hatchery weir at the lower end of the creek. Currently, temperatures are taken each

morning with liquid-in-glass thermometers.

Auke Creek Hatchery

Until 1990, temperatures of inflow water to the Auke Creek Hatchery were

recorded each morning by liquid-in-glass thermometers at the hatchery trough. The water

was drawn from 6 m (20 feet) depth in Auke Lake and flowed though an insulated 35 cm

diameter pipe to the hatchery. Flow rate into the hatchery was approximately 0.06 m3

 s

-1

(0.5 cfs). Although some heat exchange occurred during flow through the pipe, heat

exchange was considered minimal. Therefore, Auke Creek Hatchery temperatures were

probably representative of the Auke Lake temperatures at 6 m through the spring of 1990,

when the Auke Bay Laboratory ceased using water from the same pipe line for domestic

and experimental use.

Auke Lake Freeze-Up and Ice-Out

Specific records of freeze-up or ice-over (date of first complete ice cover) were not

routinely maintained. Several individuals kept private records of the last day of the year

that float planes could land and take off from Auke Lake.’

Ice-out (last day of ice on the lake) was followed more closely than freeze-up

because it is associated with the emigration of fish from Auke Lake. The dates of ice-out

from 1960 through 1995 were taken from field notes of Auke Bay Laboratory fishery

biologists.

Time Series Analysis

Weather variables with the longest periods of observations from the Auke Bay

climate data were examined by statistical time series methods using the SAS SPECTRA

(spectral decomposition), AUTOREG (autoregressive error models), and ARIMA

(autoregressive integrated moving-average models) procedures (SAS Institute, Inc. 1993).

Those variables available and analyzed were monthly consolidations of daily recordsaverages or totals (depending on the variable)-for air temperatures, precipitation (rainfall

and melted snowfall), and snowfall from February 1963 to January 1993 inclusive (30

years of nearly continuous monthly records for each variable with no series missing more

than 5 of the 360 months) and sea surface temperature from February 1975 to January

1993 inclusive (18 years of continuous monthly records). Over the span of observation

1

Lief Lie, National Weather Service, Juneau, Alaska. Pers. commun., 3 Dec. 1992.
5

(say T months), the monthly values for any variable or its transform will be denoted as z,;

fitted values from ARIMA modeling, by and the residual from the fit, by 

= 1, 2, . . . . T. The forecast value for one month beyond the span T will be denoted as 

SPECTRA was used to decompose the total variation in a time series into cyclical

components of time (months). That proportion of the total variation due to the annual

cycle was extracted and tested for statistical significance using an F-test for a known

period (Fuller 1976). Missing values (except at the beginning of the series) were

estimated by cubic spline interpolation using the SAS EXPAND procedure before analysis

of untransformed variables by SPECTRA.

AUTOREG was used to fit and test statistical significance of linear trend models to

annual totals (precipitation and snowfall) or averages (temperatures). The procedure

allowed for estimating autocorrelation structure in residuals about the line. The DurbinWatson statistic was used to test for serial correlation of residuals. These regression

analyses omitted the beginning year of each series (1963 for precipitation, snowfall, and

air temperatures; 1975 for sea surface temperature) because the January observation was

missing.

Standard Box-Jenkins methods of time series modeling (Box and Jenkins 1976,

Pankratz 1983) were used to further describe the time series using the SAS ARIMA

Procedure (SAS Institute, Inc. 1993): 1) examination of the sample autocorrelation

function (SACF) and sample partial autocorrelation function (SPACF) to identify candidate

ARIMA (autoregressive integrated moving-average) models; 2) estimation of parameters of

the model(s) chosen; and 3) checking for adequacy of the model(s) by testing whether the

time series of residuals were distinguishable from white noise using the SACF and SPACF

of residuals and the Ljung-Box (1978) statistic. The conditional least-squares method was

used for parameter estimation. When residual analyses indicated a proposed model was

inadequate, the model was revised, parameters reestimated, and adequacy rechecked.

Statistics were computed up to a maximum lag of 60 months for precipitation and

temperature series, up to a maximum lag of 35 months for snowfall (5 of the 12 months,

May through September, with no or very low snowfall were omitted from the series), and

up to a maximum lag of 45 months for SST, thereby meeting the usual recommendation

not to exceed a lag equal to one-fourth of the total observations.

In a preliminary examination, the SACF and SPACF for monthly time series of

each weather variable were computed using interannual month differences 

intra-annual month differences or the combined differences 

 for untransformed and logarithm-transformed observations. So that the

logarithm transformation (which can be applied only to positive values) could be used,

monthly precipitation and snowfall measurements (cm) were increased by 1 cm and

monthly temperature measurements (oC) were increased by 20°C. Interannual month

differences of logarithm-transformed observations were chosen for analyzing all the time

series because reasonably simple SACFs and SPACFs that were helpful for modeling (Box

and Jenkins 1976) generally resulted.

After the models were chosen by standard Box-Jenkins methods, their forecast

accuracy was compared with that from simpler models in which one or more of the
6

coefficients of the chosen models were omitted. Forecast performance for each weather

variable during the last 5 years was the basis of the comparison. For each test year and

weather variable, the chosen models, as well as the simpler models, were fit by conditional

least squares to data available at the beginning of the test year. The parameter estimates

and the weather variable values preceding the test year were used to forecast the weather

variable for each of the 12 months of the test year. These forecasts were compared with

the actual values of the weather variable; the mean square of forecast errors (average

squared errors) was used as a summary statistic.

The autocorrelation coefficients of the SACF are denoted as {rk

, k = 1, 2, . . . , K),

and the partial autocorrelation coefficients of the SPACF are denoted as { k = 1, 2, . . . ,

K}. Precision of autocorrelation coefficients was determined from the approximation for

standard error (SE) (Bartlett 1946),

Precision of partial autocorrelation coefficients was approximated by (Box and Jenkins

1976)

(1)

(2)

In Equations (1 and 2), n is the number of values in the time series, reduced for missing

values and losses during differencing.

Forecast equations for weather variables were derived using the difference

equations approach (Box and Jenkins 1976). The one-month ahead forecast equations

were included to clarify important temporal relationships within time series. Although

these equations could be used in forecasting one-month ahead and they could be modified

easily to forecast an arbitrary number of months ahead (see chapter 10 of Pankratz 1983),

the time elapsed after the final information included requires updating with the most recent

observations available from the National Weather Service, Western Regional Climate

Center, on the internet (http://www.wrcc.dri.edu/summary/climsmak.html (22 Jan. 1998)).

This intemet web site includes daily observations for 1961-97, which were not available

for our time analyses. Also, the logarithm transformation requires special methods to

translate forecasts to original measurement scales (see section 10.3 of Pankratz 1983).
7

RESULTS AND DISCUSSION

Meteorological Records

Daily meteorological records were nearly complete from February 1963 through

December 1993. The accompanying tables and figures summarize the monthly means,

maxima, and minima.

Air Temperatures

The monthly averages of daily high temperature (MADHTs) (Figs. 2a, 3; Table l),

daily low temperature (MADLTs) (Figs. 2b, 3; Table 2), and daily midrange temperature

(MADMTs); that is, the temperature midway between the daily high and low for the

24 hours preceding the observation (Figs. 2c, 3; Table 3), exhibited lesser variation

superimposed on annual cycling. The annual cycles were discerned easily (p < 0.001) and

accounted for more than 80% of the total variation in each temperature series (Table 4).

January was the coldest month (-4.16oC) and July was the warmest month (13.12oC) by

average MADMT (Table 3). Annual variation was evident from l-month shifts of

monthly extremes such that in exceptionally cold winters, December or February was

colder than January; in exceptionally warm summers, August was warmer than July.

Daily extremes showed that frost occurred in all months except August, and that

temperatures occasionally approached or fell below -20°C from December through March

(Table 2). Above freezing temperatures occurred in all months. Maximum daily air

temperatures approaching or exceeding 30°C were recorded in June, July, and August

(Table 1).

Annual averages of the three temperature series (MADHT, MADLT, and MADMT)

between 1963 and 1993 (missing months were estimated by cubic spline interpolation)

contained an irregular upward trend (Table 4, Fig. 4). Annual average MADHT ranged

from a low of 7.43oC in 1972 to a high of 10.96oC in 1993 (Table 4, Fig. 4) with a series

average of 8.52oC (+0.77oC). Annual average MADLT ranged from a low of 0.33oC in

1972 to a high of 3.88oC in 1981 (Fig. 4) with a series average of 1.9OoC (+0.91oC).

Annual average MADMT temperatures ranged from a low of 3.85oC in 1972 to a high of

7.31oC in 1993 (Fig. 4) with a series average of 4.91oC (+0.84oC). Slopes of the trend

lines (Table 4, Fig. 4) for MADHT, MADLT, and MADMT showed that temperatures

increased over the 29 years fitted (1964-92) at a rate of 0.029oC yr-1 (SE = 0.014, p =

0.057), 0.066oC yr-1 (SE = 0.016, p < O.OOl), and 0.047oC yr-1 (SE = 0.015, p < O.OOl),

respectively. The Durbin-Watson statistics equaled 1.887, 1.638, and 1.717 for the three

series, respectively, and provided no evidence of lag-l autocorrelation in residuals from

the fitted lines.

Interannual month differences in the logarithm-transformed high, low, and

midrange temperature series produced SACFs and SPACFs indicating presence of an

annual component composed of pure or mixed moving-average and autoregressive

processes. For the MADHTs, the SACF (Fig. 5) had a large negative spike (r12 = -0.516,
8

SE = 0.062) at a lag of 12 months and no further significant values at lag multiples of 12

months. The SPACF (Fig. 6) had a slowly decaying (more slowly than exponential decay)

series of spikes at lag multiples of 12 months. For the MADLTs, the SACF (Fig. 7) had

an apparent oscillating series of spikes (significant spikes are starred in the following

coefficients) at lag multiples of 12 months: r12* = -0.515, SE = 0.058; r24, = -0.104, SE =

0.071; r36* = 0.207, SE = 0.073; r48 = 0.026, SE = 0.076; and r60* = -0.20, SE = 0.077.

The SPACF (Fig. 8) for the MADLTs had a slowly decaying (more slowly than

exponential decay) series of spikes at lag multiples of 12 months. For MADMTs, the

SACF (Fig. 9) had a large negative spike (r12 = -0.516, SE = 0.059) and no further

significant spikes at lag multiples of 12 months. The SPACF (Fig. 10) had slowly

decaying spikes at multiples of 12 months.

Intra-annual variation for the high, low, and midrange temperature series included a

first-order autoregressive process. The SACFs had decaying coefficients at lags 1 month

through 3 or more months, and the SPACFs had significant coefficients at lag 1 month,

followed by a cutoff at higher lags. An initial model consisting of a first-order moving

average process for interannual variation and a first-order autoregressive process for intraannual variation was fit to each temperature series and tested for adequacy. Generally, the

SACF and SPACF of the residuals indicated either or both interannual and intra-annual

variation were more complex than provided for in the initial model.

For MADHTs, an intra-annual autoregressive term at lag 6 months was added after

examination of the SACF and SPACF for residuals of the initial model. Statistics of the

fit (Table 5) showed all coefficients (excluding the constant) were significant and weakly

correlated. The l-month ahead forecast for transformed high temperature (MADHT) in

January 1994 (Table 5) included linear terms of the transformed MADHT for the previous

January (1993), the difference in transformed December MADHTs of the two previous

years (1992 and 1993), the difference in transformed July MADHTs of the two previous

years (1992 and 1993), and the residual for the previous January (1993). A general

forecast equation for any month would show that events 1, 6, 12, 13, and 18 months

previous to that month were of value for predicting MADHTs. Little or no additional

information occurred in the residuals as evidenced by their SACF and SPACF (not

shown). Two autocorrelation coefficients (at lags of 47 and 50 months) for residuals from

this final MADHT model were statistically significant (three were expected by chance);

and five partial autocorrelation coefficients (at lags of 22, 32, 47, 50, and 60 months) for

the residuals were significant (three were expected by chance). The Ljung-Box test

supported the conclusion that the residuals were indistinguishable from white noise for

lags up to 60 months (Table 5).

For MADLTs, an interannual autoregressive term at lag 36 months was added to

the initial model. Statistics of the fit (Table 6) showed all coefficients (excluding the

constant) were significant and all but one pair were weakly correlated. The one-month

ahead forecast for transformed low temperature (MADLT) in January 1994 (Table 6)

included linear terms of the transformed MADLT for the previous January (1993), the

difference in transformed December MADLTs of the two previous years (1992 and 1993),

the difference in transformed January MADLTs of three and four years previous (1990
9

and 1991), and the residual for the previous January (1993). A general forecast equation

for any month would show events 1, 12, 13, 36, and 48 months earlier than that month

were of value to predicting MADLTs. Little or no additional information occurred in the

residuals as evidenced by their SACF and SPACF (not shown). Two autocorrelation

coefficients (at lags of 47 and 60 months) for residuals from this final low temperatures

model were statistically significant (three were expected by chance); and four partial

autocorrelation coefficients (at lags of 47, 49, 58, and 60 months) for the residuals were

significant (three were expected by chance). The Ljung-Box test supported the conclusion

that the residuals were indistinguishable from white noise for lags up to 60 months (Table

6.h

For MADMTs, an interannual autoregressive term at lag 36 months was added to

the initial model just as had been done for MADLTs. Statistics of the fit (Table 7)

showed all coefficients (excluding the constant) were significant and all but one pair were

weakly correlated. Just as was the case for the low temperature series (MADLTs), the

one-month ahead forecast for the transformed midrange temperature (MADMT) in January

1994 (Table 7) included linear terms of the transformed MADMT for the previous January

(1993), the difference in transformed December MADMTs of the two previous years

(1992 and 1993), the difference in transformed January MADMTs of 3 and 4 years

previous (1990 and 1991), and the residual for January 1993. A general forecast equation

for any month would show that events 1, 12, 13, 36, and 48 months prior to that month

were of value to predicting MADMTs. Little or no additional information occurred in the

residuals as evidenced by their SACF and SPACF (not shown). One autocorrelation

coefficient (at lag of 47 months ) for residuals from this final midrange temperatures

model was statistically significant (three were expected by chance); and three partial

autocorrelation coefficients (at lags of 47, 58, and 60 months) for the residuals were

significant (three were expected by chance). The Ljung-Box test supported the conclusion

that the residuals were indistinguishable from white noise for lags up to 60 months (Table

7).

The SACFs and SPACFs for residuals of the final models for the three temperature

series indicated possible need of additional terms with high lags. The SACFs for

MADHTs, MADLTs, and MADMTs contained significant coefficients at lags of 47 and

50 months, 47 and 60 months, and 47 months, respectively. Also, the corresponding

SPACFs contained significant coefficients at the following lags: 22, 32, 47, 50, and

60 months; 47, 49, 58, and 60; and 47, 58, and 60 months. All functions shared a

significant coefficient at lag of 47 months. However, when the final models were

augmented by an autoregressive term with lag of 47 months, this fitted coefficient was not

statistically significant for any of the three series.

The final models for the three temperature series shared first-order moving-average

terms for interannual variation and first-order autoregressive terms for intra-annual

variation. The midrange and low temperature series shared an autoregressive coefficient

of 36 months lag, whereas the high temperature series contained an autoregressive

coefficient of 6 months lag.
10

Test-year forecasts from the final models and three simpler models supported

certain of the simpler models. For MADHTs, mean square of forecast errors by the final

model (parameterized by was smallest in two test years; that of the next

simpler model (parameterized by was smallest in one test year; and that of

the simplest model (parameterized by was smallest in two test years as well as

overall (5 years combined). For MADLTs, the mean square of forecast errors by the final

model (parameterized by was smallest in two test years; that of the next

simpler model (parameterized by was smallest in two test years as well as

overall (5 years combined); and that of the simplest model (parameterized by 

was smallest in one test year. For MADMTs, the mean square of forecast errors by the

final model (parameterized by was smallest in one test year; that of the

next simpler model (parameterized by was smallest in two test years as well

as overall (5 years combined); and that of the simplest model (parameterized by 

was smallest in two test years. For high, low, and midrange daily temperatures, the final

model was surpassed in overall (5 years combined) forecast accuracy and matched in

certain years for best forecast accuracy by one of the simpler models.

Precipitation and Snowfall

Precipitation was recorded as the monthly sum of amounts of liquid water collected

daily (rainfall and melted snowfall). Precipitation (Fig. lla, Table 8) and snowfall (Fig.

11b, Table 9) were computed for each month of the calendar year (January through

December). In addition, snowfall was computed for the snow year of July through June

(Table 10). Although this snow year differs from the U.S. Geological Survey hydrological

year of October through September, it placed the rare September snowfalls at the

beginning of the oncoming winter rather than the end of the passing summer. Mean

monthly precipitation ranged from 7.27 cm in April to 22.02 cm in October (Fig. 12).

The monthly extremes were 0.18 cm in February 1989 and 41.81 cm in September 1991.

The annual cycle was discerned easily (p < 0.001) but accounted for only about 32% of

the total variation (Table 4). Snowfall occurred from September through May (Fig. 12),

although May, September, and October normally received only trace amounts. Mean

monthly snowfall for November through April was 39 cm. January has the highest

average snowfall (mean of 71 cm with a range of 5 cm in 1987 to 180 cm in 1982). The

annual cycle was evident (p < 0.001) but accounted for only about 43% of total variation.

Annual precipitation between 1963 and 1993 (Table 8) ranged from a low of

128.45 cm in 1965 to a high of 215.39 cm in 1991. Average annual precipitation was

157.93 cm (SD = +43.46 cm). The annual series contained an irregular upward trend,

interrupted about the time of the 1982-83 El Niño (Fig. 13). Slope of the trend line

(Table 4) showed that precipitation increased over the 29 years (1964-92) fitted at a rate

of 1.128 cm y-1 (SE = 0.400, p < 0.01). The Durbin-Watson statistic was 1.914 and

provided no evidence of lag-l autocorrelation in residuals from the fitted line.

Interannual month differences in logarithm-transformed precipitation values

produced simple SACF and SPACF (Figs. 14, 15). An annual component of the
11

transformed precipitation series was included as a first-order moving-average process: the

SACF had a highly significant spike (r12 = -0.489, SE = 0.055) at lag equal to 12 months

(and no further significant autocorrelation coefficients at higher lag multiples of

12 months); and the SPACF decayed toward zero at lags of 12, 24, and 36 months.

Inconsistent with the simple first-order annual moving-average process was the slow decay

(slower than exponential decay) of the simple partial autocorrelation coefficients at lags of

48 and 60 months. None of the remaining sample autocorrelation coefficients were

significant. The simple first-order annual moving-average model was fit to the series of

interannual month differences in annual precipitation. The SACF and SPACF of the

residuals indicated an autoregressive coefficient of lag equal to 48 months was needed:

both functions contained significant coefficients at that lag.

A revised model with a moving-average parameter of lag equal to 12 months and

autoregressive parameter of lag equal to 48 months was fit. Both the annual movingaverage parameter, (p < 0.001) and autoregressive parameter (p < 0.05) were

detected (Table 11); but the estimate for p did not differ significantly from zero. The

parameter estimates were weakly correlated. The one-month ahead forecast for

transformed precipitation in January 1994 (Table 11) included linear terms of the

transformed precipitation during the previous January (1993), the difference in transformed

January precipitation 4 and 5 years earlier (1989 and 1990), and the residual for the

previous January (1993). A general forecast equation for any month would show events

12, 48, and 60 months in advance of the current month were of value to predicting

precipitation. Contrary to the temperature series, precipitation of the previous month was

not useful in prediction. Apparently little or no additional information occurred in the

residuals as evidenced by their SACF and SPACF (not shown); none of the residual

autocorrelation coefficients nor partial autocorrelation coefficients was significant. The

Ljung-Box test supported the conclusion that the residuals were indistinguishable from

white noise for lags up to 60 months (Table 11).

Test-year forecasts from the final model (parameterized by and a

simpler model (parameterized by were inconclusive: the mean square of

forecast errors of the simpler model was smaller in four of the five test years, but the

overall (5 years combined) mean square of forecast errors of the final model was smaller.

Annual snowfall (calendar year) between 1963 and 1993 (Table 9) ranged from a

low of 50.55 cm (1987) to a high of 438.66 cm (1971) with an average of 236.28 cm

(SD = +99.41 cm). The series contained an irregular downward trend until the mid-1980s,

whereafter snowfall rose above the long-term mean in 1989, 1990, and 1991 before falling

below the mean again in 1992 and 1993 (Fig. 16). Slope of the trend line (Table 4,

Fig. 16) indicated snowfall decreased over the 29 years fitted (1964-92) at a rate of 3.8 15

cm yr

-1 (SE = 2.165, p < 0.1); however, this slope was not statistically significant at the

usual 0.05 level. The Durbin-Watson statistic was 1.452 and was inconclusive regarding

lag-l autocorrelation in residuals from the fitted line. Inclusion of first-order

autocorrelated error into the model structure did not alter the slope substantially (decrease

in snowfall of 3.771 cm yr-1) , but reduced its statistical significance (SE = 2.773,

p < 0.19). Differences in annual snowfall in successive years reached more than 250 cm
12

twice (1970-71 and 1988-89) and more than 100 cm 11 times (Table 9). Snowfall during

the snow year (July through June, but essentially late September through early May)

ranged from a low of 84.58 cm (1976-77) to a high of 421.64 cm (1975-76) the

preceding year, with an average of 223.78 cm (SD = +109.14 cm) (Table 10).

No snow fell during June, July, and August, and average snowfall for May and

September was less than 0.2 cm. Therefore, these 5 months were omitted from the time

series for ARIMA modeling, and snowfall for the remaining 7 months was analyzed.

Interannual (7 months) differences in logarithm-transformed snowfall produced simple

SACF (Fig. 17) and SPACF (Fig. 18). The functions provided clear indication of an

interannual moving-average process of order 1: the SACF had a highly significant spike

at lag of 7 months (r7, = -0.531, SE = 0.077), and the SPACF decayed regularly at lag

multiples of 7 months. Less clear from the two functions was the process within years:

the SACF had three significant spikes at lags of 2, 9, and 26 months, and the SPACF had

significant spikes at nonannual lags of 2, 6, 19, and 30 months. The SACF and SPACF

spikes at lag 2 months (r2 = 0.262, SE = 0.070 = 0.262, SE = 0.070) exceeded three

standard errors, and were further remarkable for absence of adjoining significant values.

Intra-annual processes of moving average, autoregressive, and their mixture up to order 2

were fit; an autoregressive coefficient for a lag of 2 months best described the series.

Statistics of the fit of an annual, first-order, moving-average process and an intra-annual

autoregressive process with a lag of 2 months (Table 12) indicated the annual movingaverage parameter, was highly significant (p < 0.001) and its estimate was only weakly

correlated with that of the other parameters; that is, the constant and the autoregressive

coefficient of lag 2 months, . The estimate of the intra-annual autoregressive parameter,

 was also significant (p < 0.01). A general forecast equation for any month (Table 12)

would show that snowfall 2, 7 (= 1 year), and 9 (= 1 year and 2 months) months in

advance of that month was of value to predicting snowfall. The estimate for did not

differ significantly from zero. Little or no additional information occurred in the residuals

as evidenced by their SACF and SPACF (not shown). None of the residual

autocorrelations to lag 35 months (5 years) was significant at 0.05, although that at lag

26 months would have been significant at = 0.10; about two significant tests were

expected from sampling error even when all autocorrelations were actually zero. The

Ljung-Box test confirmed that the residuals were indistinguishable from white noise for

lags up to 35 months (5 years) (Table 12).

Test-year forecasts from the final model (parameterized by and a

simpler model (parameterized by ) supported the final model: the mean square of

forecast errors for the final model was smaller in three of the five test years, and the

overall (5 years combined) mean square of forecast errors for the final model was smaller

as well.
13

Auke Bay Saltwater Temperatures

Auke Bay Laboratory

Sea surface temperatures of Auke Bay are affected by several factors, most

important of which are daily solar heating, the annual cycle of cooling and heating,

exchange of water with adjacent channels, exposure to wind mixing, proximity to streams

and surface freshwater sources, and rain and snowfall conditions. Because the Auke Bay

Laboratory is located in the northeastern corner of Auke Bay and is well protected from

the prevailing southeasterly winds, surface waters at the Auke Bay Laboratory float are

poorly mixed by the winds, strongly influenced by the outflow of Auke Creek, and subject

to accumulation of a freshwater lens during heavy rains and snowfall. Surface

temperatures at the Auke Bay Laboratory tend to be lower in the winter and higher in the

summer than those in either the middle of Auke Bay (see Auke Bay Monitor Station

below) or the more exposed waters of Lynn Canal and Stephens Passage (Williamson

1965, Jones 1978). Sea surface temperatures for 1959-69 were taken in the morning,

whereas temperatures were recorded in the afternoon from 1975 to present. Some

differences in the temperatures of these two series are apparent (Figs. 19a-19c). Because

these differences may have been caused by die1 warming effects, the 1959-69 data (Table

13) were summarized separately from the 1975-93 data (Table 14).

According to Hagen2

, oscillations in the daily recorded Auke Bay sea surface

temperatures and in a 4-day running average of these values did not appear to be related to

tidal cycles. The oscillations of the averaged data could be artifacts of smoothing called

the Slutzky-file effect (Kendall and Stuart 1966).

Monthly averages of daily sea surface temperatures (MADSSTs) fluctuated very

regularly (Fig. 20), with 92% of the variation explained by the annual cycle (p < 0.001,

Table 4). MADSST ranged from a minimum of 2°C in February to a maximum of 16°C

in July. Annual average of MADSSTs between 1975 and 1992 ranged from a low of

6.9oC in 1976 to a high of 8.9oC in 1993 (Fig. 21). Long-term average of MADSSTs was

8.1oC. The annual series began with lowest annual temperatures in 1975 and 1976 and

thereafter fluctuated with increasing variation (Fig. 21). The slope of the trend line

suggested sea surface temperature increased over the 17 years fitted at a rate of 0.031 oC

year

-1, but that increase was not statistically significant (SE = 0.019, p < 0.12). The

Durbin-Watson statistic was 1.768 and provided no evidence of lag-l autocorrelation in

residuals from the fitted line.

Interannual month differences in logarithm-transformed MADSST produced simple

SACF and SPACF (Figs. 22, 23). The annual component of the transformed MADSST

series was a first-order moving-average process: the SACF had a highly significant spike

(r12 = -0.405, SE = 0.092) at lag equal to 12 months (and no further significant

autocorrelation coefficients at higher lag multiples of 12 months), and the SPACF decayed

2Hagen, P. T. 1988. Time series analysis of sea surface temperatures in Auke Bay, Alaska. Juneau Center

for Fisheries and Ocean Sciences, University of Alaska-Fairbanks, 29 p., unpublished.
14

toward zero at lags of 12, 24, and 36 months. The intra-annual component was a firstorder autoregressive process; the SACF appeared to decay exponentially from lags 1

through 5 months (those for lags of 1 and 2 months were highly significant); and the

SPACF had a spike at lag of 1 month [ = 0.520, SE = 0.0701. In addition, the SACF

had one additional significant coefficient at lag equal to 13 months, and the SPACF had

three significant coefficients at lags of 13, 23, and 25 months; roughly two significant

coefficients were expected from sampling variation for either case if all remaining actual

coefficients were zero. The simple model with first-order annual moving-average and

first-order intra-annual autoregressive terms was fit to the series of interannual month

differences in MADSST. Statistics of the estimation (Table 15) indicated the annual

moving-average parameter, and the intra-annual autoregressive parameter, were

highly significant (p < 0.001). The estimate for was significantly different from zero,

although its value was small, meaning a slight deterministic trend underlay the differenced

series. All parameter estimates were weakly correlated. The one-month ahead forecast for

transformed SST in January 1994 (Table 15) included linear terms of transformed SST

during the previous January (1993), the difference in transformed December SST of the

two previous years (1992 and 1993), and the residual for the previous January (1993). A

general forecast equation for any month would show that events 1, 12, and 13 months

prior were of value in predicting sea surface temperature. Apparently little or no

additional information occurred in the residuals, as evidenced by their SACF and SPACF

(not shown). None of the residual autocorrelations to lag 45 months were significant at

 = 0.05 (about two significant tests were expected by chance), although that at lag of

10 months would be significant at = 0.10 (roughly four significant tests at this level

would have been expected by chance alone). The Ljung-Box test (Table 15) supported the

conclusion that the residuals were indistinguishable from white noise for lags up to

45 months.

Mean square of forecast errors for the final model (parameterized by )

was smallest in all 5 test years as compared to that of the simpler model (parameterized by

Auke Bay Monitor Station

Although the records for sea surface temperature extend back to 1959, the

observations were not taken on a regular schedule nor was the method of observation

constant (Table 16). The irregular nature of the data did not permit clear interpretation of

interannual variation; therefore, only the means and extremes for the annual surface

temperature cycle at the Auke Bay Monitor Station are presented (Fig. 24).
15

Auke Lake Watershed Stream Flows and Temperatures

Lake Creek

Average daily discharge of Lake Creek (1963-73) was 0.36 m3s-1 (12.9 cfs)

(U.S.G.S. 1974). Average daily discharge is lowest (0.10 m3s-‘) from December through

February and highest in May (0.81 m3s

-1) following the annual increase in runoff from

melting snow (Fig. 25). Maximum instantaneous stream discharges up to 27.75 m3s

-1

(980 cfs) typically followed heavy rains in September and October (Table 17). No

measurable surface flow occurred during hard winter freezes and summer dry spells (e.g.,

March, June, and July 1969).

The available temperature records (Table 18, Fig. 26) for October 1963 through

September 1973 showed that Lake Creek was strongly influenced by seasonal snow melt

and runoff. Lake Creek stream temperatures were generally lower than Auke Creek and

Auke Lake throughout the year. Freezing or near-freezing conditions occurred from

November through early May of most years, when flows were at annual minima and often

not evident as a surface flow at the gage site.

Auke Creek

Average daily discharge of Auke Creek (1962-75) was 0.49 m3s

-1 (17.8 cfs)

(U.S.G.S. 1976). Average daily discharges are lowest from December through March

(0.22-0.26 m3s

-1) and highest in May (0.89 m3

s

-1) following the annual increase in runoff

from melting snow (Fig. 27). Stream discharges ranged from no measurable surface flow

during hard winter freezes and summer dry periods to maximum instantaneous flows up to

9.85 m3s

-1 (348 cfs) following late summer and early fall rain storms (Table 19).

Auke Creek stream temperatures, like those of Lake Creek, were strongly

influenced by seasonal snow melt and runoff. Temperatures were at the annual minima

from late December through mid-March, when stream flows were lowest and Auke Lake

was ice-covered (Table 20, Fig. 28). Maximum temperatures occurred from June through

August during periods of low runoff and when the surface waters of Auke Lake were

strongly warmed by incident sunlight.

Auke Creek Hatchery and Auke Lake

Temperature of the freshwater flow into the Auke Creek Hatchery was lowest in

January and February and highest in July and August (Table 21, Fig. 29). Temperatures

were near 3°C from late November through late April, approximately the same period as

total ice cover on Auke Lake. During winter, daily temperatures varied from 1.9oC to

3.8oC. During the warmest part of the summer, temperatures averaged near 8.OoC and

ranged from near 5.OoC in early July to near 14.OoC in late July and early August.
16

Auke Lake Freeze-Up and Ice-Out

Dates of freeze-up and ice-out are indicators of heat loss and accumulation in Auke

Lake and of autumnal and vernal turnover. Freeze-up (complete ice cover) does not occur

until after turnover in November and surface waters cool to 0°C. Frequently, ice formed

intermittently around the edge of the lake for several days to 2 weeks before the lake iced

over completely. November 25 was the average last day of float plane operations in Auke

Lake and was usually 2 weeks before the lake froze over completely.3 Freeze-up

occurred as early as 15 November (1963) to as late as 2 January (1994).

Ice-out is associated with the vernal turnover and often is quite rapid. Auke Lake

may go from less than 10% open water to over 95% open water within 3 or 4 days. For

our purposes, we have determined ice-out as the day the lake surface was 90% open water.

Ice-out (Table 22) on Auke Lake normally occurred in late April or early May; 20 April

was the average date of ice-out for the 33 years of available data. Earliest date of ice-out

was 11 January 1978 and latest ice-out date was 20 May 1972.

ACKNOWLEDGMENTS

Many people assisted in gathering data for this report. Special appreciation is due

to the late John Hagmeir, who recorded the daily sea surface temperature at Auke Bay

from 1959 through 1962, and Jessie D. Jones, who reinitiated the series in 1975. Roy

May recorded the daily weather from 1963 through 1965, and Gerald Olson recorded daily

weather from 1966 through 1979. S. G. “Jerry” Taylor has been responsible for obtaining

the Auke Creek hatchery and stream temperatures since 1974. The dedication of these

volunteers ensured the remarkable completeness of these time series data.

3

Lief Lie, National Weather Service, Juneau, Alaska. Pers. commun., 3 Dec. 1992.
17

CITATIONS

Bartlett, M. S. 1946. On the theoretical specification of sampling properties of auto

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Fish Wildl. Serv. Data Rep. 8, 41 p.
19

Zieman, D. A., L. D. Conquest, K. W. Fulton-Bennett, and F? K. Bienfang. 1990.

Interannual variability in the physical environment of Auke Bay, Alaska, p.

99-128. In D. A. Zieman and K. W. Fulton-Bennett (editors), APPRISEInterannual variability and fisheries recruitment. The Oceanic Institute, Honolulu,

HI.

TABLES

Table 1 .--Monthly averages of daily high temperature (oC) (MADHTs) at Auke Bay, Alaska, 1963-93.

Table 2.--Monthly averages of daily low temperature (oC) (MADLTs) at Auke Bay, Alaska, 1963-93.
Table 2.--Continued.

‘Mean is the average of the MADLTs, Max. is the highest MADLT, Min. is the lowest MADLT, Extreme is the lowest daily low temperature observed.
Table 3.--Monthly averages of daily midrange temperature (oC) (MADMTs) at Auke Bay, Alaska, 1963-93.
Table 3 .--Continued.

‘Mean is the average of the MADMTs, Max. is the highest MADMT, Min. is the lowest MADLT.
Table 4.--Annual means, extremes, percentage of total variation (%) in weather variable due to an annual cycle and its

statistical significance (p), and slope of long-term trend and its statistical significance (p), for monthly values of

average daily high (MADHT), low (MADLT), and midrange (MADMT) temperatures, precipitation, snowfall, and

average daily sea surface temperature (MADSST).
30

Table 5.--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe interannual month differences in average daily high

temperature series, and statistics of the fit.

One-month-ahead forecast equation for transformed temperature of January 1994 from

December 1993 (T = 360):
31

Table 6.--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe the interannual month differences in average

daily low temperature series (MADLTs), and statistics of the fit.

One-month-ahead forecast equation for transformed temperature of January 1994 from

December 1993 (T = 360):
32

Table 7.--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe the interannual month differences in average

daily midrange temperature series, and statistics of the fit.

One-month-ahead forecast equation for transformed temperature of January 1994 from

December 1993 (T= 360):
Table 8.--Monthly precipitation (cm) at Auke Bay, Alaska, 1963-93.
Table 8.--Continued.
Table 9.--Monthly snowfall (cm) at Auke Bay, Alaska, 1963-93.
Table 9.--Continued.
Table l0.--Seasonal snowfall (cm) at Auke Bay, Alaska, 1963-93.
Table l0.--Continued.
39

Table 11 .--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe the interannual month differences in

precipitation series, and statistics of the fit.

One-month-ahead forecast equation for transformed rainfall of January 1994 from December

1993 (T= 360):
40

Table 12.--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe the interannual month differences in snowfall

series, and statistics of the fit.’

One-month-ahead forecast equation for transformed snowfall of January 1994 from

December 1993 (T= 210):
Table 13.--Monthly averages of daily morning observations of sea surface temperatures (oC) (MADSSTs), Auke Bay Laboratory, 1959-69.

Means were calculated only for those months with five or more observations.
Table 14.--Monthly averages of daily afternoon observations of sea surface temperatures (oC) (MADSSTs), Auke Bay Laboratory,

1975-93.
43

Table 15.--Conditional least-squares estimates of the moving-average and autoregressive

parameters necessary to describe interannual month differences in monthly

average daily sea surface temperature series (MADSSTs), and statistics of the fit.

One-month-ahead forecast equation for transformed temperature of January 1994 from

December 1993 (T = 216):
Table 16.--Monthly averages of sea surface temperature (oC), Auke Bay Monitor, 1959-93.
Table 16.--Continued.
Table 17.--Monthly averages of Lake Creek stream flows (m3

s

-1), 1963-73. The observed instantaneous maximum flow was

27.75 m3

s

-1, on 23 August 1966.
Table 17.--Continued.
Table 18.--Monthly averages of Lake Creek stream temperatures (oC), 1963-73.
Table l9.--Monthly averages of daily Auke Creek stream flows (m3

s

-1), 1962-75. The observed instantaneous maximum observed flows are 9.85

m

3

s

-1 on 2 November 1949 for 1947-50 records and 6.59 m3

s

-1 on 29 September 1970 for 1962-75 records.
Table l9.--Continued.
Table 20.--Monthly averages of daily Auke Creek stream temperatures (“C), 1963-93.
Table 20.--Continued.
Table 21 .--Monthly averages of daily Auke Creek Hatchery temperatures (oC), 1971-93.
54

Table 22.--Auke Lake ice breakup dates, 1960-95.
FIGURES

57

Figure 1 .--Auke Bay, Alaska, and vicinity.



Figure 3.--Statistics of annual temperature cycle at the Auke Bay Laboratory (1963-93)

including daily extremes (lowest low and highest high [0]) and monthly extrema

(high[o], low [•], and series averages[ ]) for monthly average daily high (MADHT),

low (MADLT), and midrange (MADMT) air temperature series.
Figure 4.--Annual average of monthly average high (MADHTs [ ] ), midrange (MADMTs [ ] ), and low (MADLTs [•]) daily air

temperatures at Auke Bay, Alaska, 1963-93. Missing monthly values were estimated by cubic spline interpolation. Solid

horizontal lines are the overall annual means. Dashed lines are the trends.
Figure 5.--Sample autocorrelation function (SACF) of interannual month differences in logarithm-transformed monthly average daily

high air temperatures (MADHTs) at Auke Bay. The interval covering 2 standard errors is indicated.
Figure 6.--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed

monthly average daily high air temperatures (MADHTs) at Auke Bay. The interval covering 2 standard errors is

indicated.
Figure 7.--Sample autocorrelation function (SACF) of interannual month differences in logarithm-transformed monthly

average daily low air temperatures (MADLTs) at Auke Bay. The interval covering 2 standard errors is

indicated.
Figure 8--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed monthly

average of daily low air temperatures (MALDTs) at Auke Bay. The interval covering 2 standard errors is indicated.
Figure 9.--Sample autocorrelation function (SACF) of interannual month differences in logarithm-transformed monthly average daily

midrange air temperatures (MADMTs) at Auke Bay. The interval covering 2 standard errors is indicated.
Figure l0.--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed monthly

average daily midrange air temperatures (MADMTs) at Auke Bay. The interval covering 2 standard errors is indicated.


Figure 12.--Statistics of annual precipitation cycle at Auke Bay Laboratory (1963-93) from

monthly precipitation (cm) (maximum [O], mean [ ] , and minimum [•]) for total

precipitation, calander-year snowfall (January-December), and seasonal snowfall

(July-June).
Figure 13.--Annual total precipitation at Auke Bay, 1963-93. Missing monthly values were estimated by cubic spline interpolation.

Solid horizontal line is the overall mean, and the dashed line is the trend.
Figure 14.--Sample autocorrelation function (SACF) of interannual month differences in logarithm-transformed precipitation at Auke

Bay. The interval covering 2 standard errors is indicated.
Figure 15.--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed precipitation

at Auke Bay. The interval covering 2 standard errors is indicated.
Figure 16--Annual total snowfall at Auke Bay, 1963-93. Missing monthly values were estimated by cubic spline interpolation.

Slope of the trend line was not significant (p > 0.05). Solid line is the overall annual mean, and dashed line is the trend.
Figure 17.--Sample autocorrelation function (SACF) of interannual month differences in logarithm-transformed snowfall at Auke Bay.

The interval covering 2 standard errors is indicated.
Figure l8--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed snowfall at

Auke Bay. The interval covering 2 standard errors is indicated.
Figure 19a.--Statistics of daily sea surface temperatures at the Auke Bay Laboratory float. Comparison of the moving 4-day averages

for 1959-69 ( ) and 1975-93 (o). Temperatures during 1959-69 were measured in the morning, whereas

temperatures during 1975-93 were measured in the afternoon.
Figure 19b.--Statistics of daily sea surface temperatures at the Auke Bay Laboratory float for 1959-69. Minimum (+), mean (-), and

maximum (0).
Figure 19c.--Statistics of daily sea surface temperatures at the Auke Bay Laboratory float for 1975-93. Minimum (+), mean (-), and

maximum (0).

Figure 21.--Annual average of monthly average daily sea surface temperatures (MADSSTs) at Auke Bay, Alaska, 1975-93. The

solid line is the overall annual mean, and the dashed line is the trend.
Figure 22.--Sample autocorrelation function (SACF) of interannual differences in logarithm-transformed monthly average

daily sea surface temmperatures (MADSSTs) at Auke Bay. The interval covering 2 standard errors is indicated.
Figure 23.--Sample partial autocorrelation function (SPACF) of interannual month differences in logarithm-transformed monthly

average daily sea surface temperatures (MADSSTs) at Auke Bay. The interval covering 2 standard errors is indicated.
Figure 24.--Statistics of annual sea surface temperature cycles (1959-93) at Auke Bay monitor station

average (-) and extreme days (maximum [0] and minimum [+]).

including 7-day moving
Figure 25.--Statistics of annual Lake Creek stream flow cycle (1963-73), including extreme days (maximum [O] and

minimum [•]) and monthly extremes (high [•], low [ ], and series average [ ] ). Minima of no surface flow are not

shown.
Figure 26.--Statistics of annual Lake Creek temperature cycle (1963-73), including 4-day moving average (-) and daily extremes

(maximum [0] and minimum [+]).

Figure 28.--Statistics of annual Auke Creek temperature cycle (1963-93), including 4-day moving average (-) and extreme days

(maximum [0] and minimum [+]). August-October minima appear to be instrumental errors.

RECENT TECHNICAL MEMORANDUMS

Copies of this and other NOAA Technical Memorandums are available from the

National Technical information Service, 5285 Port Royal Road, Springfield, VA 22167 (web

site: www.ntis.gov). Paper and microfiche copies vary in price.

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PACUNSKI, Ft. E., P. A. LIVINGSTON, and B. S. MILLER. 1998. Food of flathead sole Hippoglossoides

elassodon in the eastern Bering Sea, 27 p. NTIS number pending.

WILKINS, M. E., M. ZIMMERMANN, and K. L. WEINBERG. 1998. The 1995 Pacific west coast bottom

trawl survey of groundfish resources: Estimates of distribution, abundance, and length and age

composition, 138 p. plus Appendices. NTIS No. PB98-136252.

FRITZ, L. W., A. GREIG, and R. F. REUTER. 1998. Catch-per-unit-effort, length, and depth distributions

of major groundfish and bycatch species in the Bering Sea, Aleutian Islands, and Gulf of Alaska regions

based on groundfish fishery observer data, 179 p. NTIS No. PB98-139298.

SINCLAIR, E. H. (editor) 1997. Fur seal investigations, 1996, 115 p. NTIS No. PB98-131790.

SINCLAIR, E.H. (editor). 1997. Fur seal investigations, 1995, 188 p. NTIS No. PB98-131808.

KINOSHITA, R. K., A. GREIG, and J. M. TERRY. 1998. Economic status of the groundfish fisheries off

Alaska, 1996, 91 p. NTIS No. PB98-126170.

LAAKE, J., D. RUGH, and L. BARAFF. 1998. Observations of harbor porpoise in the vicinity of acoustic

alarms on a set gill net, 40 p. NTIS No. PB98-117641.

RUTECKI, T. L., M. F. SIGLER, and H. H. ZENGER JR. 1997. Data report: National Marine Fisheries

Service longline surveys, 1991-96,64 p. NTIS No. PB98-108822.

MARTIN, M. H. 1997. Data report: 1996 Gulf of Alaska bottom trawl survey, 235 p. NTIS No. PB98-

103930.

LAUTH, R. R. 1997. The 1996 Pacific West Coast upper continental slope trawl survey of groundfish

resources off Washington and Oregon: Estimates of distribution, abundance, and length composition,

156 p. NTIS No. PB97-208912.

LAUTH, R. R. 1997. The 1995 Pacific West Coast upper continental slope trawl survey of groundfish

resources off southern Oregon and northern California: Estimates of distribution, abundance, and length

composition, 110 p. NTIS No. PB97-208920.

LAUTH, R. R., M. E. WILKINS, and P. A. RAYMORE JR. 1997. Results of trawl surveys of groundfish

resources of the West Coast upper continental slope from 1989 to 1993,342 p. NTIS No. PB97-208904.

HILL, P. S., D. P. DEMASTER, and R. J. SMALL. 1997. Alaska marine mammal stock assessments,

1996, 150 p. NTIS No. PB97-203277.

CHUMBLEY, K., J. SEASE, M. STRICK, and R. TOWELL. 1997. Field studies of Steller sea lions

(Eumetopias jubatus) at Marmot Island, Alaska, 1979 through 1994,99 p. NTIS NO. PB97-203376.

OSMEK, S., J. CALAMBOKIDIS, J. LAAKE, P. GEARIN, R. DELONG, J. SCORDINO, S. JEFFRIES, and

R. BROWN. 1997. Assessment of the status of harbor porpoise (Phocoena phocoena) in Oregon and

Washington waters, 46 p. NTIS No. PB97-198436.

WING, B. L., C. W. DERRAH, and V. M. O’CONNELL. 1997. Ichthyoplankton in the eastern Gulf of

Alaska, May 1990,42 p. NTIS No. PB97-174379.