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Linear aspects of drainage network is also referred as linear aspect of channel system. This includes the analysis of stream’ order, stream length and length of overland flow, mainly.
Aspect # 1. Stream Order:
It is the classification system of stream/river ranks in the watershed. The most important aspect of physical geography is the study of natural environment and resources, one of which is the water. Because of this reason, the geographers, geologists and hydrologists consider the stream order to study and measure the size of waterways falling in the watershed.
The stream is the water flow path over the earth’s surface. The stream order provides a kind of stream classification, e.g., the smallest stream in the watershed has lower most order. On the other hand, the largest stream includes highest order. The lowest order streams may be the tributaries or rivulets, while highest order stream is the outlet of watershed.
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The concept of stream order was proposed by Newell Strahler in the year 1952. He was a Geoscience Professor at Columbia University (New York). He outlined the stream order as the way to define the size of perennial and recurring streams. In classification of streams using stream order the size of stream was from first order to the largest 12th order stream. In which, the first order stream was the smallest stream, feeding the water to the larger streams.
The first and second order streams generally lie on the steep slopes and deliver the flow quickly into next higher order streams. The third order stream forms head stream. Regarding size and strength the fourth to sixth order streams are classified as the medium streams, while larger streams up to 12th order are considered to be the river. The world’s largest river Amazon in South America is of 12th order; the Ohio River in the United States is of 8th order stream and the Mississippi river is 10th order stream.
The stream order also reflects the slope steepness and size of the stream. As compared to first order stream (smallest stream) the high order steams (medium and large rivers) have greater slope steepness and size, both. Since, the size is more, of bigger streams therefore, flow velocity is low. The highest order stream has larger volume of runoff and debris, because it receives all the flow from the network of smaller order streams lying at upper reaches.
Importance of Stream Order:
The classification of stream as per stream order (size) is very important for geographers, geologists, hydrologists and other professional/scientists to have an idea about the size and strength of a specific waterway within stream network.
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In addition, few more importances are also outlined as under:
i. Classification of stream order allows the professional/scientists to conduct a better study on evaluation of amount of sediment production from the area; and also use of streams/rivers as natural resources.
ii. Stream order helps the people like biogeographies and biologists to predict the types of lives living in the waterway.
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iii. It also provides a kind of guidelines to determine the river contamination and number and types of organisms present in the stream.
iv. Nowadays, the stream order has also been used in GIS to map the river network in watershed/region. In GIS the vectors (lines) are used to represent the streams.
v. The stream order is an effective tool to classify the important waterways, and is a step in understanding and managing the differences between streams of different sizes.
vi. Stream order also provides the information about flow direction in the watershed system.
Stream order is a dimensionless term. The designation of stream orders of drainage basin is the first step in analysis of drainage basin. The stream orders are designated in terms of Ist, IInd, IIIrd orders and so on.
These are explained as under:
1. The smallest finger tips like tributaries are the Ist order streams.
2. When two Ist-order streams are joined in one, then resulting stream segment is termed as IInd-order stream.
3. If two IInd-order streams join together, then a IIIrd-order stream segment is formed.
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One point should always be kept in view that, when a lower order stream segment joins to the high order stream segment, then the order of resultant stream segment does not change, but high order of stream is remained as it is. The highest order stream is also called trunk order stream, through which all discharge of watershed passes to the outlet.
The order number of streams is related to the size of watershed, channel dimension and to the stream discharge. Since, the order number is dimensionless, therefore two dissimilar drainage systems can be compared with respect to a given parameter on the basis of stream order numbers. Various stream orders are shown in Fig. 27.5.
It states that the number of stream segments of each order form an inverse geometric sequence with the order number, expressed as under –
Where,
Nu = number of stream segments of order ‘u’. The Nu of any order is fewer than for the next lower order, but more in numbers than the next higher order.
Rb = bifurcation ratio, defined as the ratio of number of stream segments of a given order u to the number of stream segments of next higher order, expressed as under –
In which, Nu + 1 is the number of stream segments of next higher order than the order ‘u’. The ‘Rb‘ is not precisely the same of order u to the next, because of variations in geometry of the watershed, but tends to be constant throughout the series.
k = order of the trunk stream segment, i.e. highest stream order existing in the watershed.
The plotting of logarithm of Nu and stream order results a linear relationship with small deviation from the straight line for most of the drainage basins. The average value of Rb for a given channel network can be computed by determining the slope of straight line (Rb = anti log b). The ‘Rb‘ estimated so, indicates that there is Rb times as many channel segments of any given order as of the next higher order stream segment.
The bifurcation ratio lies between 3.0 and 5.0 for those watersheds in which geological formations do not distort the drainage pattern of the watershed. A high ‘Rb’ is expected in the regions of steeply dipping rock strata, where narrow valleys are confined between the ridges. An elongated basin (Fig. 27.6 a) has higher ‘Rb‘ than the normal basin (b) and approximately the circular basin (basin c). The variation in Rb shows the effect on maximum flood discharge of the watershed. The elongated watershed, which comprises higher Rb would result a lower but extended peak flow, while round watershed with low Rb produces sharp peak flow.
If bifurcation ratio (Rb) and trunk order (k) of stream are known, then total number of streams of all orders of a drainage network can be computed by using the following equation developed by Horton (1945) –
Aspect # 2. Stream Length:
The extent of stream length in a watershed denotes the characteristics size of different components of drainage system and its contributing area. The stream length is determined by using the device in which one is called ‘chartometer’. For this, the watershed map showing the drainage system is required. The channel length obtained so represents the true length, which is little less due to projection on horizontal plane. However, the stream length can also be computed, by using the following equation –
In which, L̅u is the mean length of channel of order ‘u’ and Nu is the total number of stream segments of order ‘u’. The L̅u increases as the order number decreases.
The stream length is used to determine the basin perimeter, basin length, drainage density etc.
Length Ratio:
It is defined as the ratio of mean length of stream segment (L̅u) of order ‘u’ to the mean length of stream segment of next lower order (L̅u – 1), expressed as –
The ‘RL‘ is dimensionless. Horton (1945) mentioned that the length ratio tends to be constant throughout successive orders stream segment in the watershed.
Law of Stream Length:
It states that the mean length of stream segment of successive order basin approximates a direct geometric sequence represented by following expression.
Thus, from the equation 27.14 the length ratio (RL) is determined as antilog of ‘a’, which is called regression coefficient of the line fitted by least-square method or by inspection to the plot of logarithm of stream lengths and their respective orders.
The law of stream numbers and stream lengths can be combined, together which results an equation for the total channel length of given order ‘u’. The equation is given as under –
Aspect # 3. Length of Overland Flow:
The overland flow and surface runoff are quite different hydrological phenomenon in which overland flow refers to that flow of precipitated water which moves over the land surface leading to the stream channels. The channel flow reaching to the outlet of watershed is referred as the surface runoff. The overland flow is significant in the smaller watersheds, whereas runoff is in bigger watersheds. The length and depth of overland flow are small. The flow characteristics of overland flow is in laminar condition.
Horton defined the length of overland flow as the length of flow path projected on the horizontal plan from a point on drainage divide to the adjacent stream channel, as shown in Fig. 27.11. It is one of the most important watershed characteristics, affects both to the hydrologic and physiographic development of watershed. The length of overland flow is calculated as half of the reciprocal of the drainage density, i.e. –
Where,
Lg = length of overland flow
Dd = drainage density
Horton (1945) also derived the following relationship for Lg by accounting the effect of stream slope and slope of valley sides, given as –
Where,
θc = channel slope
θg = average ground slope