In describing the drainage net of the Humber River (Ontario), the various parameters used (stream length, number, order: basin area: mean annual discharge) were found to have clear linear relationships. These relationships could not have arisen by chance, and, hence, reflect the regularity of the erosional processes at work. Product moment correlation analysis was also employed between stream length and basin area

Roberts, Michael C.

English

University of Northern Iowa

Proceedings of the Iowa Academy of ScienceVolume 70 | Annual Issue Article 561963Some Empirical Regularities of the Humber RiverDrainage NetMichael C. RobertsState University of IowaCopyright © Copyright 1963 by the Iowa Academy of Science, Inc.Follow this and additional works at: https://scholarworks.uni.edu/piasThis Research is brought to you for free and open access by UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academyof Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu.Recommended CitationRoberts, Michael C. (1963) "Some Empirical Regularities of the Humber River Drainage Net," Proceedings of the Iowa Academy ofScience: Vol. 70: No. 1 , Article 56.Available at: https://scholarworks.uni.edu/pias/vol70/iss1/56Some Empirical Regularities of the Humber River Drainage Net1 MICHAEL c. ROBERTS Abstract. In describing the drainage net of the Humber River ( Ontario ) , the various parameters used ( stream length, number, order: basin area: mean annual discharge) were found to have clear linear relationships. These relationships could not have arisen by chance, and, hence, reflect the regu-larity of the erosional processes at work. Product moment correlation analysis was also employed between stream length and basin area. The Davisian approach to describing drainage nets in terms of a time sequence has been found to have certain deficiencies (Chorley, 1962). To avoid these shortcomings, quantitative geomorphology attempts an examination of the morphologic characteristics of the landscape, leaving aside all notions of cyclical development. Thompson ( 1942), writing on the mor-phologic approach as against that based solely on the genetic viewpoint in the field of biology, notes that a mathematical definition of form is not only precise but allows further deriva-tions to be made. Such is the case in geomorphology. The pur-pose of this paper is to describe the empirical relationships that hold between certain variables of the River Humber drainage net. ONT p.R\0 TH!: LOCATIDf' Of 1111: "'*91:11 IUVl!:R ~ tN IOVTICltN ONTAIUO Figure 1. The shaded area outlines the drainage basin of the Humber River. J Department of Geography, State University of Iowa, Iowa City 321 1Roberts: Some Empirical Regularities of the Humber River Drainage NetPublished by UNI ScholarWorks, 1963322 IOWA ACADEMY OF SCIENCE [Vol. 70 LOCATION OF STUDY The Humber River has its headwaters on both the Niagara Escarpment and the Oak Ridges interlobate moraine. It flows into Lake Ontario on the west side of the city of Toronto" The triangular shaped drainage basin reflects the path taken by the two major tributaries that make up the Humber drainage system. The total area of the basin is 344 square miles. DATA SOURCES The basin has a complete coverage of topographic maps at a scale of 1:50,000. Every stream was classified according to the ordering system of Strahler ( 1957 ) . A word is in order about this system, which is both operational and useful. First order streams are defined as the smallest unbranched tributar-ies. Second order streams are formed by the confluence of two first orders; the process of combining lower orders to form higher ones is continued to the desired degree. Once the streams were identified, it was possible to outline their associated basins, which were measured using a polar planimeter. The complete 100 50 10 5 4 3 3 2 STREAM ORDER Figure 2. The relation of number o.f streams and stream order within the Hu1nber drainage basin. The lines fitted to the observations represent the smaller drainage basins within that of the Humber. (This applies to Figures 3 and 4 as well). 2Proceedings of the Iowa Academy of Science, Vol. 70 [1963], No. 1, Art. 56https://scholarworks.uni.edu/pias/vol70/iss1/561963] fil ...J ! ~ G z w _J HUMBER RIVER 323 r------------------.100 50 :o 5 Region C Region D ·5 234 1234 2 3 4 2 3 STREAM ORDER Figure 3. The relation of stream lengths and stream order within the Humber drain-age basin. Humber basin was subdivided into four regions based on fourth order streams; this was done to permit more detailed infer-ences. THE NATURE OF THE MORPHOLOGIC RELATIONSHIPS The morphologic parameters used in this study are stream length, number, order, and basin area. These can be expressed in quantitative terms· and hence are applicable to examination by statistical techniques. The graphs (see figures 2, 3, 4) illus-trate the visual relationships between these parameters. Using data from streams in New York state, Horton ( 1945) was so impressed by the regularity, shown by figure 2 in this case, that he called it "The Law of Stream Numbers". In their work on experimental stream models, Ore and White ( 1958) have substantiated this finding of Horton. All told, these plots of the various geomorphic variables show a regularity so marked that it cannot result from chance, but must be related to processes that operate in an orderly fashion. If the variates stream length and basin area are examined in a 3Roberts: Some Empirical Regularities of the Humber River Drainage NetPublished by UNI ScholarWorks, 1963324 IOWA ACADEMY OF SCIENCE [Vol. 70 50 J IO 5 ·5 1234 I 234 1234 123 STREAM ORDER Figure 4. The relation of basin area and stream order within the Humber drainage basin. frequency distribution, they have a distinctive lognormal dis-tribution. It will be research into the understanding of the gen-eration of these lognormal distributions that will contribute to the explaining of the regularities shown by the graphs. An alternate way of examining the relationships illustrated by the graphs is by developing some simple equations (Leopold and Miller, 1956) such that between stream order 0 and the number of sh·eams N there is the relation. O=klogN 1. or 0 a log N 2. and in a similar fashion 0 a log L 3. OalogA 4. where L is stream length, and A is basin area. The exponential relationships take the form, 0 a Nk 5. OaU 6. 0 a Ak 7. 4Proceedings of the Iowa Academy of Science, Vol. 70 [1963], No. 1, Art. 56https://scholarworks.uni.edu/pias/vol70/iss1/561963] HUMBER RIVER 325 where k is some exponent having a particular value for each equation. Table l. The regression Region A Region B Region C Region D lines fitting the stream length/basin y c = .25 + .80 x y c = .44 + .46 x Y• = .24 + 1.10 X Ye = .33 + .77 X area data Table 2. Correlation coefficients of stream length/basin area. Region A Region B Region C Region D .81° .70" .79" .93" " Significant at the 1% level of significance. The parameters in this study can be analyzed by using simple regression, and, in fact, stream length and basin area were cor-related. The obvious intuitive notion that there will be a high relationship (see tables 1 and 2) was borne out, though the lack of a perfect 'r' implies that other factors must be hypo-thesized as influencing the development of these particular river valleys. One explanation would be that the initial Pleisto-cene surface on which the streams first flowed had a number of undulations, so that the river started to flow in a partly form-ed "valley". Another hypothesis, though a rather unlikely one in this area of southern Ontario, would be that the river valleys were once part of an overflow channel complex. --------------------.ioo,ooo -yr I0,000 0 0 • ·"7 0 i Humber ot Weston 8 Ill ~~mber cbovt "'6'oodbr!dg1 a: ..: ~ .. Q (~umbtr at Pint Grove 1000 10 100 1000 DRAINAGE BASIN AREA(SQ.MILESl Source; Brush, 1961. Figure 5. Logarithmic graph showing the relation of discharge (of mean annual flood) and drainage basin area. To form a link between the purely morphological variables and the actual flow of the river, an additional parameter was introduced into the study - mean annual flood discharge. This 5Roberts: Some Empirical Regularities of the Humber River Drainage NetPublished by UNI ScholarWorks, 1963326 IOWA ACADEMY OF SCIENCE [Vol. 70 is an important variate, because it is during this time of high discharge that most of a river's erosive work is carried out (Leopold and Miller, 1956). However, to incorporate this data into the studv it was necessary to use the records of other southern Onta;io streams. These were not avaifable, so that it necessitated the use of data from the nearest area of similar climate and river regimes, which in this case was the northern Appalachians (Brush, 1961). Plotting basin area against mean annual flood discharge on log-paper a linear relationship re-sults ( see figure 5). The fit of the data from the three gaging stations on the Humber gets better as the drainage area at the respective station also increases. CONCLUSION The hydrologic and morphologic variables selected for study show distinctive linear relationships that reflect the regularity of the processes at work in stream flow. The correlations be-tween stream flow and basin area were found to be high and significant, though a full explanation would require the oper-ationalizing of variables that are, as yet, only in the qualitative stage of recognition. Literature Cited Brush, L. M., 1961, Drainage Basins, Channels, and Flow Characteristics of Selected Streams in Central Pennsylvania: Professional Paper No. 282-F, U.S. Geological Survey, pp. 145-181. Chorley, R. J., 1962, Geomorphology and General Systems Theory: Pro-fessional Paper No. 500-B, U.S. Geological Survey, pp. 1-10. Horton, R. E., 1945, Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology: Bulletin of the Geological Society of America, Vol. 56, pp. 275-370. Leopold, L. B., and Miller, J. P., 1956, Ephemeral Streams-Hydraulic Factors and Their Relation to the Drainage Net: Professional Paper No. 282-A, U.S. Geological Survey, pp. 1-37. Ore, H. T., and White, E. D., 1958, Compass, Vol. 36, No. 1, p. 23. Strahler, A. N., 1957, Quantitative analysis of watershed geomorphology: American Geophysical Union Trans., Vol. 38, pp. 913-920. Thompson, D'A. W., 1942, On Growth and Form: Cambridge University Press, pp. 1026-1030. Preliminary Investigation of the Little Sioux River Valley DAVIDE. PEDERSEN and ROBERT A. LOHNES Purpose The purpose of this paper is to describe the aerial extent, thickness, and nature of the materials that comprise the modem alluvium and terrace sediments of the Little Sioux River valley. This paper is part of a study conducted in the spring and sum-mer of 1962 which was concerned with the alluvial morphology 'Department of Geology, Iowa State University. 6Proceedings of the Iowa Academy of Science, Vol. 70 [1963], No. 1, Art. 56https://scholarworks.uni.edu/pias/vol70/iss1/56

Some Empirical Regularities of the Humber River Drainage Net

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Some Empirical Regularities of the Humber River Drainage Net

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