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NOAA Technical Memorandum ERL GLERL-107

EARLY 20TH CENTURY LAKE SUPERIOR BASIN PRECIPITATION ESTIMATES

R.A. ASSEL, D.C. NORTON, F.H. QUINN

NOAA, Great Lakes Environmental Research Laboratory, Ann Arbor, MI

Great Lakes Environmental Research Laboratory

Ann Arbor, Michigan

September 1998

NAT OI NAL OCEANIC AND ATMOSPHERIC ADMINISTRAT OI N

U.S.DEPARTMENT OF COMMERCE UNITED STATES

DEPARTMENT OF COMMERCE

William Daley

Secretary

NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

D. James Baker

Under Secretary for Oceans

and Atmosphere/Administrator

Environmental Research

Laboratories

James L. Rasmussen

Director
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NOTICE

Mention of a commercial company or product does not constitute an endorsement

by the NOAA Environmental Research Laboratories. Use of information from

this publication concerning proprietary products or the tests of such products for

publicity or advertising purposes is not authorized. This is GLERL Contribution

No. 1048.
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CONTENTS

PAGE

ABSTRACT ........................................................................................................................................... 5

1. INTRODUCTION ............................................................................................................................. 5

2. METHODOLOGY AND APPLICATION TO THE LAKE SUPERIOR BASIN ............................ 6

2.1 General Description ...................................................................................................... 6

2.2 Data Sources and Gridding Method............................................................................. .6

2.3 Calculating the Ratio for All Cells Within the Basin .................................................... 7

2.4 Calculating the Basic Precipitation from the Ratios ..................................................... 7

2.5 Evaluating Station Density in the Canadian Basin ....................................................... 7

2.6 Error Analysis ............................................................................................................... 8

2.7 Ratio and Thiessen Precipitation Comparisons with St. Marys

 River Flow .................................................................................................................... 9

3. SUMMARY AND CONCLUSIONS ................................................................................................ 9

4. ACKNOWLEDGMENTS ............................................................................................................... 10

5. LITERATURE CITED .................................................................................................................... 11

Tables

Table 1. Total Over-Land Lake Superior Basin Precipitation (mm)................................................... 12

Figures

Figure 1. Location Map of the Great Lakes. ....................................................................................... 14

Figure 2. Three-year running average annual precipitation using the Thiessen method and St. Marys .

 River flow per unit surface area of Lake Superior. ............................................................. 15

Figure 3. Map of Lake Superior hydrologic basin. ............................................................................. 16

Figure 4. Station Density. .................................................................................................................... 17

Figure 5. Annual precipitation for the overland areas of U.S. and Canadian

 portions of the Lake Superior basin...................................................................................... 17
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Figure 6. Average annual precipitation grid for the 1961-1990 period. ............................................ 18

Figure 7. Average annual ratios grid(basin precipitation/cellular precipitation)

 for the 1961-1990 period. ................................................................................................... 19

Figure 8. Locations of Canadian and U.S. precipitation stations. ..................................................... 20

Figure 9. Precipitation over the Canadian portion of the Lake Superior drainage basin. ................. 21

Figure 10. Precipitation over the Canadian portion of the Lake Superior drainage basin. ................. 21

Figure 11. A comparison of 3-year running averages of annual precipitation

 estimates for the Lake Superior basin. ............................................................................... 22

Figure 12. Cumulative annual successive year slopes from double mass

 curves (precipitation/flow). ................................................................................................ 22
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EARLY 20TH CENTURY LAKE SUPERIOR BASIN PRECIPITATION ESTIMATES

Raymond A. Assel, David C. Norton, and Frank H. Quinn

Abstract. A method to provide improved estimates of the annual value of over-land

areally weighted Lake Superior basin precipitation is described and compared with the

traditional Thiessen method. The method consists of calculating the ratio of areally

weighted precipitation to precipitation at individual grid cells in the basin during periods

when station density is high. The ratios are used in conjunction with data collected during

the late 19th and early 20th centuries to generate improved basin precipitation estimates.

The “ratio method” provides precipitation estimates for that period that are more in

agreement (relative to the Thiessen method) with trends in flow for the outlet of Lake

Superior.

1. INTRODUCTION

The Laurentian Great Lakes are an important natural resource containing about 95% of the United States

and 20% of the world’s fresh surface water supply; about one-eighth of the U.S. population and onethird of Canada’s population live within the Lakes drainage basin. Lake Superior, located between the

46th and 49th parallel and having a surface area of 82,100 km2

 and a mean depth of 149 m, is the largest,

the farthest upstream, and the furthest north of the five Great Lakes (Figure 1). Long-term precipitation

data are important in climate and water resources studies of the Great Lakes (Quinn, 1981) and in

developing models that are useful tools for weighing regulation policy options (Croley, 1989). A historical review showed annual precipitation over the Canadian portion of the Lake Superior basin to be less

than the precipitation over the U.S. portion during the first half of this century, and greater than the U.S.

precipitation during the second half of this century (T. Bullock -personal communication, 1995, Environment Canada, Atmospheric Environment Service, Downsview, Ontario, Canada).This could have

major significance for Great Lakes water resource studies. It is likely that gage undercatchment and low

station density both contributed to the lower estimates of Canadian basin precipitation. The scope of this

study, however, is limited to consideration of the problem of low station density.

An independent assessment of precipitation changes can be undertaken using the Lake Superior outflow

through the St. Marys River. Three-year moving averages of Lake Superior’s overland basin precipitation and outflow are highly correlated between 1920 and 1990 ( r = 0.81), but the correlation is much

lower betewen 1880 and 1920 ( r = 0.18). Prior to about 1910, over-land precipitation on the Lake

Superior basin was consistently less than the outflow through the lake’s outlet, the St. Marys River

(Figure 2). This relationship started to change between 1910 and 1920, at the same time the number of

precipitation gages installed on the Canadian side of the basin were increasing, bringing into question

whether the precipitation data prior to about 1920 are representative. It should be noted that the natural

flow through the St. Marys River was altered by construction of navigation locks, hydropower diversion

canals, and compensating works (gates controlling river flow) in the late 19th and early 20th centuries

(Quinn, 1978). However, the effect of these modifications on the St. Marys River flow were not of

sufficient magnitude to cause the observed change in the relationship between river outflow and overland basin precipitation (Figure 2). The objective of this study is to provide improved estimates of over-
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land Lake Superior basin precipitation (Croley and Hunter, 1994) for the late 19th and the early 20th

centuries by the development of improved estimates of basin precipitation when station density is low.

Approximately 67 percent of the Lake Superior basin lies in Canada (Figure 3). Thus, estimates of

areally weighted precipitation have been more dependent upon the location, number, and accuracy of the

precipitation gages in Canada than on those in the U.S. Previous studies indicate that Canadian gages

have underestimated precipitation (snowfall in particular) prior to 1940 (Metcalfe et al., 1997), and both

U.S. and Canadian gages have underestimated precipitation in the first half of the 20th century

(Groisman and Easterling, 1994). However, it was beyond the scope of this study to develop and apply

correction factors to precipitation data. We believe that Thiessen weighting of sparse Canadian gage

data during the late 19th and early 20th centuries (Figure 4) adversely affected estimates of total basin

precipitation and contributed to the observed dichotomy of annual precipitation between U.S. and

Canadian sub-basins (Figure 5) in the late 19th and early 20th centuries. A method was developed to

estimate catchment precipitation that is independent of station locations. It is described and compared to

the traditional Thiessen method (Croley and Hartman, 1985). Both methods are compared to Lake

Superior outflows to evaluate the better estimate.

2. METHODOLOGY AND APPLICATION TO THE LAKE SUPERIOR BASIN

2.1 General Description

The method used to estimate areally weighted precipitation consists of the following steps: (1) a

cartesian grid (described below) is applied to a lake basin, and precipitation is estimated for each grid

cell from available (irregularly spaced) station data in contemporary years when the number of stations

is much higher than it was in the early 20th century. The grid is necessary because some of the earlier

stations were discontinued or moved, and we needed to relate precipitation at the discontinued station

location with contemporary basin average precipitation; (2) a ratio of total basin precipitation to precipitation at every grid cell is calculated; (3) the ratios and available station data in prior years are used to

calculate multiple basin precipitation estimates; (4) the median of the calculated basin precipitation

estimates is selected (for reasons explained later) as the basin precipitation.

2.2 Data Sources and Gridding Method

Gridded estimates of monthly precipitation for the Lake Superior drainage basin were calculated from

monthly precipitation data [sources include: Earth Info., 1996; Assel et al., 1995; Atmospheric Environment Service, 1994] using a software package called Surfer (Golden Software, Inc. 1995). The grid

consists of a 760 x 516 matrix of 1-km x 1-km cells (Figure 3). Kriging, a relatively well-known interpolation methodology, has been used to estimate regional precipitation (Dingman et al., 1988). Kriging,

employing a one component linear variogram with no drift (contained in the Surfer software package),

was used to convert station data to grid cell data. Kriging generates a good overall interpretation of

irregularly spaced data sets and is an exact interpolator, i.e., it does not smooth the input data. Monthly

precipitation grids were generated for the 1961-1990 base period, a period when station spatial density

was high. The 30-year gridded average annual precipitation spatial pattern (Figure 6) resembles the

long-term (1931-1960) annual precipitation in Phillips and McCulloch (1972).
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2.3 Calculating the Ratio for All Cells Within the Basin

The Lake Superior drainage basin was used as a mask to differentiate between cells inside and outside

the basin (Figure 3). A spatial average for each month “j” and year “y” (Avg.jy) was calculated over all

the cell values inside the basin. The ratio of the average basin precipitation to that at each cell “i” was

then calculated for that month and year:

Rijy = Avg.jy /Pijy, where Pijy is the precipitation at cell “i” for month “j”, and year “y”.

Not surprisingly, an average of the monthly ratios (Figure 7) was largest in the northwest and smallest in

the southeast portion of the basin, i.e., the inverse of the precipitation spatial pattern shown in Figure 6.

Monthly groupings of the thirty grids (e.g., all January grids for 1961 to 1990, all February grids for

1961-1990, etc.) were sorted (largest to smallest) for each cell (from the 760 x 516 cell matrix). The

median ratio “m” for the years 1961-1990 at each cell “i” and month “j” (ij) was selected and output as a

grid, establishing 12 monthly median ratio grids. The median of the precipitation ratios was selected

because it is a more robust estimator of centrality than the average in non-normally distributed populations. Since the frequency distribution of precipitation tends to be skewed toward higher values (Cong

et al., 1993), the cell ratios derived from the precipitation cellular values will tend to reflect skew characteristics in corresponding (although opposite) distribution shapes.

2.4 Calculating the Basin Precipitation from the Ratios

To estimate basin precipitation (BPijy) for month “j” of year “y” using grid cell “i”, we multiply the total

monthly precipitation in cell “i” (either station data or data estimated from Kriging) for that month and

year, (Pijy) with the median precipitation ratio for that month and grid cell:

BPijy = ij x Pijk

The assemblage of basin precipitation estimates (for all grid cells with rain gage data) was then sorted,

and the median value (a second median) was selected as the estimated monthly precipitation value.

Annual basin precipitation values were calculated as the sum of the monthly values. Our preliminary

analysis of these data indicated that using this second median rather than an average reduced the impact

of any erroneous or otherwise non-representative station data. In using this method to estimate precipitation during the first half of the 20th century, it is implicitly assumed that spatial and seasonal precipitation patterns over the Lake Superior basin have not changed significantly from that of the 1961-1990

base period.

2.5 Evaluating Station Density in the Canadian Basin

In order to evaluate inaccuracies derived from low station density, the Canadian portion of the basin was

isolated for examination. The examination focused on the 1961-1990 period data to obviate

undercatchment uncertainties so as to explore only network and method differences. A representative

assemblage of stations reporting around 1910 were identified and plotted (Figure 8) along with the

closest stations with good records for the 1961-1990 period. The greater density and continuity among

U.S. stations is notable. During the 1961-1990 period, four of the five Canadian stations closed in the

early 1970’s, and new adjacent stations had to be used. Thiessen-weighted monthly precipitation was
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computed for the Canadian basin using all (18-34) reporting Canadian stations, and separately for the

selected-station network. In Figure 9 it is evident that precipitation estimates from the selected-station

network rather consistently underestimate the all-station network. Selected-station ratioed values were

also calculated, and they spanned the all-station Thiessen values.

Using paired t-tests with a 5% confidence level, it was determined that the selected-station network

Thiessen method yielded statistically different basin precipitation than the all-station Thiessen values

and the selected-station ratioed values. However, the selected-station ratioed values were statistically

the same (at the 5% confidence level) as the all-station Thiessen values. Therefore, in this evaluation,

the ratio method proved to be superior to the Thiessen method when limited to a small station network

representative of that which existed in the early part of this century.

Gridding using all Canadian station data yielded another estimate of Canadian basin precipitation.

Although statistically different, these values are broadly comparable (Figure 10) to ratioed values computed using a combined selected Canadian and selected U.S. station network (Figure 8). The reasonable

fit lends credence to the methodology used in this study, i.e. the utilization of precipitation from U.S.

stations as proxy data (geographically external but climatically related) to aide in estimating Canadian

Basin precipitation.

2.6 Error Analysis

The remaining analysis focuses on the entire Lake Superior drainage basin. The grid ratios used in this

study were calculated from 30 years of data: 1961-1990; the root mean square error (RMSE) of annual

precipitation using these ratios was 40 mm, and the standard deviation of the gridded data about its 30-

year mean (819 mm) was 89 mm. The method of cross-validation (Ferguson, 1976) was used to obtain

an unbiased estimate of the RMSE of annual precipitation for station networks from 1961 to 1990. In

our application of cross-validation, we used gridded precipitation for the even years from 1961-1990 to

calculate the ratios, and then used the station precipitation for the odd years (again between 1961 and

1990) and the even-year ratios to estimate annual precipitation. The process was then repeated using the

odd years to calculate the ratios and the even years’ station precipitation to calculate the annual catchment precipitation. The RMSEs increased by less than 18% over the independent data (47 mm and 46

mm, respectively). Thus, applying the ratios to independent data did not result in a large increase in its

RMSE value. This lends credence to the RMSE of the ratio method using all years of data to derive the

ratios. Precipitation values throughout the text have been rounded to the nearest millimeter.

Existing station networks (number and location of stations in the Lake Superior basin) from each year

(1880-1960) were used to calculate annual precipitation for the 1961-1990 base period to evaluate the

ratio method’s utility to simulate basin precipitation when station networks had less stations and different spatial configurations. The station networks from 1880 to 1960 were used to select cell precipitation

values from the gridded data and to calculate the annual precipitation for each year of the 30 years

(1961-1990), using the ratio method. Results were compared to the actual gridded precipitation estimates using all available stations. The RMSE ranged from a minimum of 22 mm to a maximum of 68

mm, and the average RSME was 37 mm (median, 36 mm). These values lend further credence to the

ratio method for calculating precipitation when the number of stations is much smaller and the distribution pattern is different (less evenly distributed) than the 1961-1990 network.
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2.7 Ratio and Thiessen Precipitation Comparisons with St. Marys River Flow

During the contemporary period (1961-1990), the ratioed values compared well to the Thiessen values;

the RMSE of the Thiessen estimated precipitation was virtually the same as that of the ratioed estimated

precipitation (40 mm). Not surprisingly, contemporary estimates of basin precipitation from both methods tend to converge to the same value. A plot of the 3-year running mean of the ratioed data, plus and

minus the RMSE for the 1880-1960 annual ratioed precipitation, provides an estimate of the uncertainty

in estimated average basin precipitation in years with low station density (Figure 11). Note that the

Thiessen values clearly fall outside the ratio error bounds during a majority of years prior to about 1910,

and the values are also at or below the lower limit of the lower error bound most years between 1910

and 1930. A three-year moving average of Lake Superior’s overland basin precipitation and outflow

between 1880 and 1920 is much more highly correlated for the ratio-estimated precipitation ( r = 0.57)

than is a similar correlation for the Thiessen-estimated basin precipitation (r=0.18). This and a discussion on double mass curves given below provides evidence that the ratio method produces the more

representative estimate of actual basin precipitation for the late decades of the 19th and early decades of

the 20th century.

Double mass curves were generated for both the Thiessen and ratioed precipitation versus the St. Marys

flow. The slopes between successive years were computed and then plotted as cumulative sums (Figure

12). Since the relationship (slope) between basin precipitation and outflow is assumed to be constant

through time, deviations from the predominate slope indicate lower accuracy estimates. Because flows

are accurately measured, these deviations can be attributed to precipitation estimate inaccuracy. The

impact of anthropogenic flow changes is believed to be small enough to be ignored here. The slopes of

the Thiessen and ratioed values remain constant from about 1930 onward. If a line is drawn through the

recent Thiessen slope, that line continues and coincides with the ratioed slope from the 1920’s back to

the origin, indicating that the ratioed values are more correct than the Thiessen values during that period.

Since there was an increase/change in the precipitation gage network around 1931, ratioed values are

recommended from 1880-1930 and Thiessen values from 1931 onward.

A tabular summary of the 1880-1930 ratio-generated estimates of monthly and annual over-land precipitation for the Lake Superior basin is given in Table 1. Annual Thiessen estimates of precipitation

(Croley and Hunter, 1994) are also provided (Table 1) for comparison with the ratio-generated annual

values.

3. SUMMARY AND CONCLUSIONS

A ratio of precipitation at each grid cell to that over the entire Lake Superior basin was developed for a

30-year base period in order to define a relationship between precipitation at a point and precipitation

over the entire Lake Superior basin. The ratios were calculated to estimate monthly Lake Superior basin

precipitation in the first half of the 20th century. Prior to about 1930, differences in the ratio-estimated

basin precipitation and St. Marys River outflow were smaller than similar differences for Thiessen

precipitation estimates. A double mass curve analysis of basin precipitation and St. Marys River outflow

demonstrated that prior to about 1930, ratio estimates of basin precipitation were more consistent with

St. Marys River outflow than Thiessen estimates of basin precipitation. Therefore, we conclude that

prior to about 1930, the ratio method produced better basin precipitation estimates relative to the

Thiessen method. However, we should caution that the ratio method is not a panacea for producing

better estimates of areally averaged precipitation. The assumptions about precipitation distribution
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patterns not changing significantly over time, errors in precipitation data associated with changes in

precipitation gages, gage exposure, or gage accuracy, while beyond the scope of this study, are clearly

important factors to be considered in a future study. It should be emphasized that when one is faced with

a sparse rain-gage network, independent but related observations such as the St. Marys River flow data,

are extremely helpful and perhaps even critical in evaluating the utility of different methods of calculating areal precipitation. If the downward trend in the number of precipitation stations for the Lake

Superior basin that started about 1980 continues (Figure 4), the ratio method may be useful in the future

to obtain more representative estimates of basin precipitation (relative to the Thiessen method). Finally,

a discontinuity observed in the Canadian station data beginning in 1975 when new gages were installed,

while not adversely affecting the historical ratio-estimated precipitation in this study, has implications

for contemporary precipitation and is currently under study.

4. ACKNOWLEDGMENTS

T. Bullock of Environment Canada, Downsview, Ontario, participated in the early stages of this

study by identifying the differences in precipitation between U.S. and Canadian sub-basins of Lake

Superior. The Cooperative Institute for Limnology and Ecosystem Research Project “Great Lakes Ice,

Precipitation, and Temperature Data Rescue” data were used in our analysis. This is GLERL contribution number 1048.
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5. LITERATURE CITED

ASSEL, R. A., C. E. SELLINGER, D. E. Meyer, and R. N. Kelley. Great Lakes States Monthly Precipitation Data - Beginning of Record to 1990. NOAA TM ERL GLERL-86, Great Lakes Environmental

Research Lab, Ann Arbor, MI, 39 pp. (1995).

Atmospheric Environment Service. Climatological Station Data Catalogue, Ontario. Environment

Canada, Downsview, Ontario (1994).

Cong, S., Y. Li, J. L. Vogel, and J. C. Schaak. Identification of the Underlying Distribution Form of

Precipitation by Using Regional Data. Water Resources Research 29 (4):1103-1111 (1993).

CROLEY, T. E. II, and T. S. HUNTER. Great Lakes Monthly Hydrologic Data. NOAA TM ERL

GLERL-83, Great Lakes Environmental Research Lab, Ann Arbor, MI, 53 pp. (1994).

CROLEY, T. E. II. Verifiable Evaporation Modeling on the Laurentian Great Lakes. Water Resources

Research 25 (5):781-792 (1989).

CROLEY, T. E. II, and H. HARTMAN. Resolving Thiessen Polygons. J. of Hydrol. 76:363-379 (1985).

Dingman, S. L., D. M. Seely-Reynolds, and R.C. Reynolds III. Application of Kriging to Estimating

Mean Annual Precipitation in a Region of Orographic Influence. Water Resour. Bulletin 24 (2):329-339

(1988).

Earth Info. NCDC Summary of the Day. East and Central CDs. Boulder, CO (1996).

Ferguson, G.A. Statistical Analysis in Psychology & Education, Fourth Edition. McGraw-Hill, New

York, New York, (1976).

Golden Software, Inc. SURFER for Windows. Boulder, CO (1995)

Groisman, P. Y., and D. R. Easterling. Variability and Trends of Total Precipitation and Snowfall over

the United States and Canada. J. Climate 7:184-205 (1994).

Metcalfe, J. R., B. Routledge, and K. Devine. Rainfall Measurement in Canada: Changing Observational Methods and Archive Adjustment Procedures. J. Climate 10:92-101 (1997).

Phillips, D. W., and J. A. W. McCulloch. The Climate of the Great Lakes Basin. Climatological Studies

No. 20, Environment Canada, Toronto, Ontario, Canada (1972).

QUINN, F. H. Lake Superior Regulation Effects. Water Resour. Bulletin 14(5):1129-1142 (1978).

QUINN, F.H. Secular Changes in Annual and Seasonal Great Lakes Precipitation, 1854-1979, and Their

Implications for Great Lakes Water Resource Studies. Water Resour. Res. 17(6):1619-1624 (1981).
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Table 1. Total Over-Land Lake Superior Basin Precipitation (mm). Ratio Monthly and Annual Values for 1880-1930 with Reference Thiessen

Annual [TH].

 Year J F M A M J J A S O N D Ann TH

 1880 63 69 27 63 116 158 85 104 86 80 46 34 931 807

 1881 32 53 30 23 88 68 63 84 265 95 93 18 912 764

 1882 35 91 54 49 45 97 106 99 98 135 36 48 893 717

 1883 47 32 13 34 68 126 137 52 55 73 75 58 770 653

 1884 26 48 30 68 72 33 96 144 130 142 34 73 896 786

 1885 37 22 33 25 47 92 93 65 61 32 63 37 607 574

 1886 80 75 35 48 43 111 51 40 117 86 56 34 776 685

 1887 33 36 15 51 39 63 115 33 54 90 54 45 628 622

 1888 61 29 41 44 76 94 47 102 72 58 38 30 692 665

 1889 49 49 31 59 63 49 113 78 92 32 30 79 724 724

 1890 68 60 31 33 67 81 120 88 70 47 25 24 714 675

 1891 39 55 51 41 17 37 101 81 70 65 54 62 673 608

 1892 37 28 28 43 78 58 67 85 42 57 57 23 603 562

 1893 41 57 37 65 49 71 88 46 55 72 36 68 685 637

 1894 42 16 83 65 91 56 51 50 74 116 61 37 742 656

 1895 59 31 18 33 85 89 56 54 137 36 39 53 690 661

 1896 67 22 30 88 123 55 50 71 42 97 129 34 808 671

 1897 88 46 44 30 56 73 143 72 47 70 37 37 743 640

 1898 32 46 36 14 88 139 88 64 54 90 47 30 728 634

 1899 42 30 38 47 119 132 72 108 97 84 16 61 846 656

 1900 35 27 24 36 23 53 131 135 181 63 39 29 776 701

 1901 30 21 65 28 42 122 139 65 71 73 51 42 749 674

 1902 33 29 21 41 70 82 97 68 63 74 78 75 731 654

 1903 36 36 55 43 102 36 146 102 91 101 55 50 853 716

 1904 35 43 58 22 74 67 80 77 110 96 23 64 749 668

 1905 38 22 45 41 84 120 99 68 123 87 77 28 832 730

 1906 46 25 38 25 85 139 40 89 77 75 91 54 784 665

 1907 68 29 45 49 71 37 77 98 108 42 42 26 692 678

 Year J F M A M J J A S O N D Ann TH
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Table 1. Cont.

 Year J F M A M J J A S O N D Ann TH

 1908 24 73 50 61 126 105 91 34 86 32 40 45 767 708

 1909 36 68 31 53 59 35 147 82 65 59 90 77 802 702

 1910 33 40 7 48 48 15 81 71 80 52 41 39 555 589

 1911 36 53 37 21 86 71 154 81 89 54 83 65 830 847

 1912 33 12 10 58 96 52 55 99 86 45 28 60 634 671

 1913 29 40 71 40 74 88 142 58 92 89 47 8 778 734

 1914 48 32 31 85 47 96 77 109 70 34 53 24 706 625

 1915 48 37 15 28 78 151 74 63 112 85 96 51 838 777

 1916 101 23 59 79 83 147 47 84 135 81 31 44 914 802

 1917 25 28 79 36 34 86 59 76 56 92 16 51 638 618

 1918 38 28 12 36 104 55 71 74 79 89 74 53 713 697

 1919 30 57 28 57 47 67 66 70 75 87 118 32 734 675

 1920 41 20 70 50 40 127 104 47 58 51 56 64 728 679

 1921 26 30 62 61 67 46 129 57 99 37 40 54 708 701

 1922 37 85 48 70 71 106 113 54 63 31 66 47 791 669

 1923 57 29 50 27 35 82 111 57 59 46 28 42 623 598

 1924 45 38 22 62 55 59 92 127 74 35 46 43 698 660

 1925 25 37 25 25 41 98 65 62 98 51 34 40 601 612

 1926 31 42 55 22 31 116 105 79 159 90 113 53 896 815

 1927 32 44 38 41 108 73 113 41 73 59 82 79 783 728

 1928 39 18 35 66 39 122 118 122 114 112 24 28 837 766

 1929 83 23 47 40 57 70 74 41 115 77 43 55 725 687

 1930 36 45 28 28 78 111 65 16 113 62 57 32 671 663

 Year J F M A M J J A S O N D Ann TH
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Figure 1. Location Map of the Great Lakes.
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Figure 2. Three-year running average annual precipitation using the Thiessen method and St. Marys

River flow per unit surface area of Lake Superior.

500

700

900

1100 Precipitation (mm)

1880 1900 1920 1940 1960 1980

Thiessen 3-yr avg. St. Marys River Flow
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Figure 3. Map of Lake Superior hydrologic basin with 1 x 1 km grid cell indicated along the horizontal

and vertical axes. The Canadian sub-basin has dark shading while the U.S. sub-basin has light shading.

The western juncture of the sub-basins was defined along the nearest drainage basin to the international

divide.
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Figure 4. Station Density. The annual total number of station-months of data divided by 12 (months)

per unit area (KM2). The transitory increase and decrease in stations in the mid-to-late 1940s - early

1950s is attributed to temporary stations that were started following the end of the second World War.

Figure 5. Annual precipitation for the overland areas of U.S. and Canadian portions of the Lake Superior basin, derived from the Thiessen polygon method to estimate catchment precipitation.

0

0.5

1

1.5

(Station-Years / Square Km) X 1000

1880 1900 1920 1940 1960 1980

CA Basin U. S. Basin Entire Basin

550

650

750

850

950

Precipitation (mm)

1880 1900 1920 1940 1960 1980

Canadian Basin U. S. Basin
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Figure 6. Average annual precipitation grid for the 1961-1990 period.
19

Figure 7. Average annual ratios grid(basin precipitation/cellular precipitation) for the 1961-1990 period.
20

Figure 8. Locations of Canadian and U.S. precipitation stations representative of 1910 and selected

(closest) reporting 1961-1990 stations.
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Figure 9. Precipitation over the Canadian portion of the Lake Superior drainage basin. Two Thiessen

weighted estimates, one using all Canadian stations (All) and a second using the selected station network

(Selected) composed of 5 stations (see Figure 8).

Figure 10. Precipitation over the Canadian portion of the Lake Superior drainage basin. Gridded estimates (Grid) using all Canadian stations, and ratioed estimates (Ratio) using the selected U.S. and

Canadian stations given in Figure 8.

550

650

750

850

950

1050

Precipitation (mm)

1960 1965 1970 1975 1980 1985 1990

Year All Selected

550

650

750

850

950

1050 Precipitation (mm)

1960 1965 1970 1975 1980 1985 1990

Year CA Grid Ratio
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Figure 11. A comparison of 3-year running averages of annual precipitation estimates for the Lake

Superior basin using the Thiessen method and the ratio method along with its error bars for the 1880-

1960 period.

Figure 12. Cumulative annual successive year slopes from double mass curves (precipitation/flow)

where precipitation in mm was computed by the Thiessen and ratio method using all available Canadian

and U.S. stations and St. Marys River flow per unit surface area of Lake Superior.

600

700

800

900

1000 Precipitation (mm)

1880 1890 1900 1910 1920 1930 1940 1950 1960

Ratioed Thiessen Ratioed Error

0

10

20

30

40

50

Cumulative Slope

1880 1900 1920 1940 1960 1980

Year Thiessen Ratio