 Namaste and welcome back to the video course on Watershed Management. Today, we will start a new module, module number 4. This module is on mainly on watershed modeling. So, the topics covered in this module are standard modeling approaches and classifications, system concepts for watershed modeling, overall description of different hydrological processes, modeling of rainfall, runoff process, subsurface flows and ground water flow. So, in this module there will be about 7 lectures and today in lecture number 12, we will discuss in this module watershed characteristics. So, in lecture number 12 watershed characteristics, we will discuss some of the topics mainly on watershed characteristics, geometric representation of watersheds, linear aspects, aerial aspects, relief aspects, drainage and discharge. Some of the important keywords for today's lecture, watershed characteristics, geometric representation, drainage, linear, aerial, relief aspects. So, we have already discussed about the watershed characteristics in the first lecture itself when we were discussing about the introduction or introductory aspects on watershed and its management. So, we have seen that there are when we deal with a watershed management, we have to deal with the land, we have to deal with the water and also we have to deal with various resources within the watershed. So, there are number of important characteristics which have to be considered while dealing with a watershed modeling or say watershed management. So, some of the important characteristics I have listed here. So, this includes the size of the watershed. So, we had a brief discussion about the size in the introductory lecture itself. Then shape of the watershed, whether what kind of shape is whether it is say elongated shape or broad type shape. Then physiography of the watershed, so how it is say whether the whatever the various physiographic features within the watershed. Then climates like the rainfall, the say humidity or temperature and various aspects. Then the drainage pattern within the watershed, so that the flow or the runoff will be according to accordingly to vary. Then land use, so what kind of land use is there within the watershed whether it is forested or whether it is agriculture or whether it is say crop land, so like that. Then vegetation, so what kind of vegetation whether it is grass land like this or small small trees like this. Then geology and soils, so the say various hydrological processes taking place within the watershed like infiltration and various other parameters depends upon the geology and soils of the watershed. Then hydrology, so that is already within the climate aspects like rainfall to runoff and various other hydrological processes. Then hydrogeology, so like groundwater and then infiltration and other parameters and then of course the socio economics. So when we are dealing with watershed management, so what is the nature of the people living in that watershed area and what is their economical background, so that what kind of works they are doing or what kind of land use are there within that watershed. So there are number of characteristics which we have to identify and then quantify so that many of these parameters we utilize especially when we say watershed modeling or when we go for watershed management. So this watershed characteristics as I already mentioned earlier, so this watershed characteristics indicate the bio-physical and socio-economic features prevailing in a watershed. So the as we have seen various characteristics are there, so that these characteristics mainly indicates what is the physical nature of the watershed, what are the biological nature of the watersheds and then what are the say hydrogeological nature of the watershed and the socio-economical features which are prevalent within the watersheds. So as I mentioned we have to identify these important watershed characteristics and then we have to say many of the times when we go for watershed modeling or management we have to quantify so that some values for particular parameters like area of the watershed, so length of the channel or the slope or those specific characteristics we may have to give it in say while doing modeling or while doing the say making the plans for watershed management. We have seen many characteristics as far as watershed disconsent, so these characteristics we can broadly classify or categorized into a climate related characteristics, geology and physiography related characteristics, soil related characteristics, land use and cover conditions land use land cover conditions, then watershed hydrology and then socio-economic features of the watershed. So we have seen many parameters in the last slide, so that those parameters and many other parameters also we can classify into say about say 6 classes like a climate, geology, physiography, soils, land use and land cover, watershed hydrology and socio-economical features of the watershed. So now let us see what are the important characteristics within each of these classifications or the each of these groups. So if you consider climate, so as we have seen earlier, so when we deal with the watershed management or when we are going for watershed modeling, so the important aspect is water availability within the watershed and then also various climatological parameters like wind, wind velocity or the temperature or the humidity like that. So the climate parameters mainly includes the precipitation, so the through precipitation or rainfall there will be runoff and that will be the source of water as far as the watershed is concerned and then with respect to temperature, so temperature is another important climate parameter. So with respect to temperature, so there will be say we have to while modeling the watershed we have to quantify many parameters, so like evaporation, then evapotranspiration and then other climate parameters include wind, relative humidity etc. Now if you consider the physiography of the watershed, then we can classify say the watershed or the as per the characteristics of the watershed, we have we can say deal with respect to the size and shape of the watershed. So what is the size whether it is a major watershed or it is a sub watershed or it is a minor watershed or micro watershed like that with respect to size and then what is the shape of the watershed. So especially shape is very important, so according to the shape the runoff characteristics within the watershed will change. Then another important physiographical parameter is elevation, so you can see that the watershed say within the watershed the elevation or the various the slope is changing from one location to another location. So the elevation according to elevation we can identify the conduces of the watershed and then we can say see various parameters related to that and then slope and aspects. So slope is of course with respect to the elevation aspect of the various points within the watershed. Then aspect means it is it can be linear aspects, aerial aspects or the say the height related aspects. So these details we will be discussing later. Then another important characteristics is related is geology. So like the drainage features then pattern density etcetera, then what kind of rock is there within the watershed say what is the nature of the rock whether it is it is then sedimentary or metamorphic what kind of rock is there. So like that say geological parameters are also very important when we deal with the watershed modeling or related to watershed management. Now as far as soils are concerned say within the watershed say what is the depth of the soil, so that is very important since accordingly see the agricultural activities or accordingly the say the infiltration parameters that you vary. Then what is the type of soil whether it is sandy type soil or the loamy type or clay type what kind of soil then soil infiltration capacity. So we discussed earlier that when the same rainfall to runoff process say infiltration is one of the important parameter which is controlling the runoff process. So we have to identify the infiltration capacity of the soil within the watershed. Then soil erosiveness so we already seen earlier the erosion and sedimentation problems within a watershed. So say depending upon the nature of soil and other parameters the there will be more or less or say what type of erosion problems can be there within the watershed. And then finally, the land use and land cover conditions. So land use say accordingly the say for example, many parameters like man-in-surface coefficients or the agricultural pattern all those things will be according to the land use and land cover. So land use types like forest, grass lands, agricultural lands, urban lands etc. Then the ownership pattern say the land is concerned whether it is government lands, private lands, industrial lands. So accordingly say the various things what we can do within the watershed it will vary. Then forest land conditions whether it is major type of forest or say what kind of weather thick forest or thin forest. Then range land condition and types then agriculture practices within the watershed. Then say whether there is there are roads in the watershed like road network and what are the conditions of that road. Then recreational like resort whether the watershed area is used for resort purpose, wildlife, fish resources etc. So these are some of the important aspects or important characteristics which we have to consider as far as land use and land cover conditions are concerned. Then as far as watershed hydrology is concerned say another important classification watershed hydrology. So we have to see with respect to the hydrological aspects of the area. So what are the erosion conditions along streams you can see that this stream is said too much error on the bands. So that accordingly the various conditions within the watershed will vary. And then whether say with respect to rainfall whether there are any flooding problems within the watershed and how much is the quantity of say runoff taking place within a stream like this. So, these are some of the important characteristics which we have to consider as far as watershed hydrology is concerned. Then finally the socio-economic features of the watersheds. So as far as socio-economic features are concerned say like water use and needs say as far as the people living in the watershed water is concerned like water source of water then what are the uses of the water like domestic use or irrigation or industrial or for power generation purpose etc. Then water use problems so when with respect to the usage of water within the watershed whether say with respect to the conditions available within the watershed whether there can be problems of erosion or flooding or siltation then as far as water supply for the domestic supply or industrial supply then what is the condition of the quality of the waters like water quality. Then another important aspect is which we have to deal always is the economical aspects so that means the income generation activities associated within the watershed. So as we have discussed earlier in any of the watershed management programs the economical status of the people or the income generation facilities available within the watershed whether through it may be through agricultural activities or it is through various mining activities or whatever kind of activities which are which are possible within the watershed. So that is also an important characteristics like economic characteristics which we have to consider when we go for a watershed management or watershed modelling. So now say with respect to the various watershed characteristics which we have considered so now say some of the important characteristics we will be discussing in detail since some of these characteristics are very important especially when we go for watershed modelling say modelling means it can be rainfall to runoff modelling or ground water modelling or many of the other processes what are taking place within the watershed. So let us have a brief look into the important watershed characteristics what are their definitions and what way we will be utilizing as far as the watershed modelling is concerned. So first one is the drainage area of the watershed. So as far as a watershed is concerned the area of the total area of the watershed is most important factor. So the drainage area is the most important as far as the hydrological design is concerned when we deal with especially with various land is one of the resource and then with respect to water also we have to deal with how much is the area of the watershed so called drainage area. So this drainage area reflects the volume of water generated from the rainfall. So if say for example if 100 mm of rainfall takes place within a watershed so we can identify how much is the volume of water available with respect to this 100 mm rainfall by considering the drainage area. So normally what we can do the volume of water available for runoff may be assumed as product of rainfall depth and the drainage area. So this is a simple calculation but that may not be so accurate but say generally we can take it as the depth of the rainfall or depth of water available multiplied by the drainage area that will be the volume of water available for runoff within the watershed. Of course various losses will be there so that we have to consider with respect to the rainfall available or so called excess rainfall. Then another important characteristics which we have to consider especially in watershed modeling is so called watershed length. So watershed length is defined as the distance measured along the main channel from the watershed outlets to the basin divide. So you can see that if this is the watershed which we consider here so here is the basin divides and if somewhere here is the watershed outlets then so this is the length say from the watershed divide to the outlets. So that is the definition of the watershed length. So you can see that this watershed length increases as the drainage increases so that is obvious when the drainage increases the watershed length also increases. So this is one of the important aspect as far as the hydraulic computations are consents since the time of concentration and then runoff generation depends upon the watershed length. Then this watershed length L is measured along the principal flow path. So if this is the main channel available within the watershed so this here or in this watershed this is the main channel then say the watershed length is measured along the principal flow path. So while going for watershed modeling this drainage area A and watershed length L both measures of watershed size. So say what is the watershed size so that depends upon the drainage area and the watershed length. So this A and L they may reflect the different aspects of the size of the watershed. So as we have discussed A indicate the potential for rainfall to provide the say corresponding volume of water and L is used in computing the time parameter. So as I mentioned time of concentration or the time required for water to reach from the divide water divide to the water outlet. So it is a measure of travel time of water through a watershed. So two important parameters as far as the watershed modeling is consents these parameters are drainage area and the watershed length. Then some other important parameters like a watershed slope. So the slope according to the slope say when the precipitation takes place the runoff will be evolved according to the watershed slope. So the flood magnitudes reflect the moment of the runoff. So slope is an important factor in the momentum. So according to the slope of the say you can see that depending upon what is the slope. So here you can see that a steep slope as far as this watershed consents. So according to the slope there will be more momentum as far as the runoff is consents and a watershed slope reflects the rate of change of elevation with respect to distance along the principal flow path. So for the watershed consents if this is the principal flow path so accordingly so the watershed slope reflects the rate of change of elevation. So the slope S is equal to delta E by L where delta E is the difference in elevation that means between n points of the principal flow path and L is the hydraulic length of the flow path. So if this is our concerned watershed so S can be defined as say if this is our main channel. So here what is the height here and what is the outlet height and then we can identify what is the difference in elevation between these two points and then we can identify what is the hydrologic length. So slope will be watershed slope will be delta E by L. Then another important characteristics is watershed shape. So watershed shape come an infinite say as far as watershed shape is consents there can be infinite variety of shapes it can be broad type or elongated type or somewhat circular type. So there can be number of types of shapes and the shapes are supposedly reflects the way that runoff will bunch up at the outlet. So you can see that if there is a narrow shaped watershed then the runoff will be much much say it will take in small period of time but if it is a broad type watershed like this. So they need more time to for that all this say the runoff will be bunching up at the outlet. So watershed shape is an important parameter. So say for example a circular shaped watershed would result in the runoff from various parts of the watershed reaching outlet at the same time. So the shape is very important whether it is say somewhat circular type or the broad type or rectangle type or a square type or narrow elongated type. So accordingly the various especially when we are going for watershed modeling. So accordingly the runoff process the say for example time of concentration will vary or say the total runoff will vary according to the shape of the watershed. So now as far as the watershed shape is consents there are number of important parameters which we have to consider. So basin shape and related watershed parameters. So the watershed parameters that reflect the basin shape includes the length to the center of area. So that is the distance say in miles or kilometers measured along the main channel from the basin outlet to the point on the main channel opposite the center of area. So this is the definition as far as length to the center of area of the watershed is consents. So this depicts one of the parameter as far as the basin shape is consents. Then another important parameter is shape factor. So we can define the shape factor as L into LCA to the power 0.3 where L is the length of the watershed in miles and LCA is the length of center of area. So as shown here so shape factor is equal to L into LCA to the power 0.3. Now another important aspect is the circulatory ratio. So the circulatory ratio is the as far as basin shape is concerned. Circulatory ratio means the ratio of basin area to the area of circle having equal perimeter as the perimeter of drainage basin. So that means circulatory ratio is defined as the ratio of the basin area AU divided by the area of a circle which has equal perimeter as the perimeter of the drainage basin. So generally depending upon the watershed the circulatory ratio can vary from 0.6 to 0.7. Then as far as shape is concerned another important say parameter is so called elongation ratio. So as I mentioned this shows what is the shape like say narrow type or broad type watershed. So the elongation ratio it is the ratio of the diameter of a circle say DC having same area as the basin to the maximum basin length. So the elongation ratio R is equal to DC by LBM where DC is the diameter of a circle having same area and then LBM is the maximum basin length. So as far as the basin shape is concerned this 4 important factors or 4 important parameters like length of the center of area then shape factor circulatory ratio and the elongation ratio. So now again let us come back to some of the other important watershed characteristics or say called the watershed factors. So as we can see if you go to any of the watershed we can see that say when we go from one location of the watershed to another location the various features or the various geographical or geographical all these features are varying from one location to another location. So you can see that say this is a watershed say here you can see the say like the relief is changing the slope is changing then say the land use is changing so all the parameters are changing from one location to another location and then in the direction wise also. So that is why we can say that any of the watershed is say as when we go for watershed modeling watershed we have to consider highly heterogeneous and anisotropic. So as far as any parameters concerned all these parameters will be varying from one location to another location in the length wise or any location wise. So now like say other parameters like a land cover so you can see that this watershed so here grass is there then other location say plants are there or some other location trees are there. So the land cover is changing and land use is concerned say some of the area may be covered by the agriculture land some of the area may be forest land so according to the land use will be varying and then especially when we go for watershed modeling one of the important aspects in a scientific modeling is what we have to consider is the roughness of the area say when we are transforming the rainfall to runoff various hydrological process which we have to consider. So when we go for physical modeling the runoff depends upon the roughness of the watershed. So this roughness can vary according to the various parameters like land cover, land use and the type of soil. And then as far as soil is concerned some of the important soil characteristics like a texture of the soil how is the texture then what is the soil structure then say of course the as far as runoff is concerned how is the soil moisture and then especially when we go for various modeling say we can classify the various soil type within the watershed into various group. So that kind of classification we call it as so hydrological soil groups. So this aspect will be discussing in some later lectures. So hydrological soil groups accordingly we can identify various parameters like say the initial soil moisture or the hydrologic conductivity as far as the soil is concerned. So like that number of soil characteristics which we have to deal as far as the watershed is concerned. Now again coming back to the watershed is concerned the channels within the that means the drainage or the channels within the watershed is say very important in watershed modeling. So the channel geomorphology so is one of the important aspect which we have to consider. So channel geomorphology is concerned say some of the important aspect which we have to consider include channel length. So this is as we already discussed earlier. So this channel length is used frequently in hydrological computations. So when we say we have to identify what will be the runoff available at the outlet of the watershed we have to see what is the length channel length. So accordingly we will be routing the flow what is happening as far as the rainfall to runoff within the watershed. Then the distance measured along the main channel from the watershed outlet to the end of the channel that is the channel length as far as say as we discussed. So this is channel length is the distance measured along the main channel from the watershed outlet to the end of the channel. And channel slope channel slope is equal to delta E g by L c where delta E c is the difference in elevation between the points defining the upper and lower ends of the channel and L c is the length of the channel between the same two points. So if this is the channel so from one end to the other end what is the length and what is the elevation difference. So from that we can calculate the channel slope. And most of the watershed due to the heterogeneity channel slope will be keep on changing if the channel slope is keep on changing from one point to another point then say we can take somewhat an average of the channel slope. So if the channel slope is not uniform a weighted slope may provide an index that reflects effect of slope on the hydrological response of the watershed. So as I mentioned say when they are rainfall to runoff process taking place. So this we have to route the flow and then we have to also consider the channel slope. So the say how much is the hydrological response that depends upon the channel slope. Now say when we deal with the watershed modelling we have to say represents the various features within the watersheds by considering the say the length aspects or the aerial aspects and then the elevation aspects like that. So the geometric representation of watershed is very important in watershed modelling. So there are basically two concepts generally are used as far as the geometric representation is concerned. The first one is called a grid method and the second one is called a conceptual method. So both of these methods we will discuss in detail. So in the grid method what we do? So we generate say as far as the watershed area is concerned if we know the boundary of the watershed. So what we can do? We can say put the watershed boundary say within a rectangular or triangular grids. So in the grid method we represent the grid just like a triangular grid or rectangular grid. So the stream channel system so say as we have seen the watershed modelling is concerned we have to consider the overland type flow and the channel type flow. So the stream channel system based upon the slope channel dimensions and conditions we have to deal. So say in the grid we can use the triangular or rectangular grid and the flow in elemental areas say like if this is the rectangular grid which we consider. So the flow from one element to other element travel to channel and finally to the watershed outlet. So if this is the watershed outlet which we consider. So we can consider grid like represented here and then the flow is concerned the flow travels say one grid to another grid and to finally to an adjacent channel and finally to the outlet of the watershed. So as I mentioned say watershed is concerned we have to see the overland flow and the channel flow. So the overland flow and channel flow mainly overland flow we can consider with respect to the either rectangular grids or triangular grids and these grids will be connected to the channel, generally channel flow we consider as one dimensional flow and overland flow either we can consider as one dimensional strip type flow or two dimensional flow. So this overland flow strips will be connected to the channel flow and so that we can identify say when the rainfall to run no process taking place we can route the flow from say one overland strip to another strip and then that will be joining to a stream and through the stream we can finally route the flow to the outlet of the watershed. So various steps which we have to consider as far as the geometry representation is concerned the steps are listed here. So we can consider rectangular grid system say like you can see that this is if this is the outlet of the watershed. So this is a rectangular system which we can consider. So rectangular grid system is superimposed on topographic map of the watershed. So we can get the topographic map of the watershed from which we can identify the boundaries of the watershed. So then we can superimpose on a grid system like this and the grid size say the watershed boundaries of the channels approximated by grid segments. So what is the grid segment accordingly we can approximate the boundaries of the watershed. You can see that since when we consider especially rectangular grid system we cannot exactly represent the variation of the boundary of the watershed. So we can approximate it but if we use triangular grid then we can better way we can represent the irregular boundaries as far as the watershed is concerned. Then say overland units are grid units inside watershed boundaries and channel units may create grid units. You can see that so this can be a channel unit which is going to the outlet of the watershed and these are all the overland units. So that will be slowly merging to the coming to the say channel segment is concerned. So if this is the main channel so you can see that various small small channel will be there and that will be coming under these grids and that will be finally joined to the main channel. So the principle flow direction of each overland flow is determined by the landscape. So you can see that the landscape say what is a landscape like what is the slope what is the size of the watershed what is the shape of the watershed accordingly the principle flow direction will vary and what is used to flow in the direction of land slope to next overland flow unit or adjacent channel. So we will be considering cascade type flow conditions and the say so that this cascade of the overland flow will be joining the to the channel. So that the so in the grid representation so we have already seen earlier grid method the grid method say we can have the following these steps as far as the geometric representation is concerned. So as I mentioned if this is our watershed so the overland flow is concerned we consider as the various grids say either one dimensional or two dimensional grids is one dimensional strips and in two dimensional grids. So these grids you can see that it will be like this it will be keep on joining to the important channels. So this is represent channel is represented as a one dimensional say like this and then the overland flow is considered as an element like this either in two dimension or one dimension and this will be joining. So this is the way we do in the representation as far as the grid method is concerned. Now the next one is the conceptual methods. So in the conceptual methods watershed geometry is defined using a network of various elemental sectors like a plane, triangular section, converging section, diverging section and the of course the channel. For example if this is the watershed then you can see that if this is the channel is represent and then we can consider various planes then sometimes triangular shapes or the converging this converging or diverging like that. And when we join all these say the sectors like a plane, triangular or whatever the sectors which we consider then when we join together we have the complete watershed. So the plane is defined by the length and width and that can be either horizontal or inclined and then the said it is defined by the slope length and area so like that. So then as far as the converging section is concerned you can see that depending upon the variation of the shape of the watershed and the slope we may use converging section or diverging section. And then many times it will be better to use triangle elements so that you can easily represent the irregular shape of the watershed. And then as far as channel element is concerned the by hydraulic geometry like cross sectional area, wetted perimeter, hydraulic radius, width etcetera we will be considering as far as the channel element is concerned. So as far as this watershed is concerned this is the channel so we will be considering the like what is the cross sectional area of this channel and what is the wetted perimeter, hydraulic radius, width etcetera and the bed profile. So the channel section is concerned it can be either rectangle section as you should rectangular trapezoidal, parabolic or semicircular or triangular section so like that various sections are possible as far as the channel section is concerned. So now the geometric approach we can assemble all these elements together so that the entire watershed can be represented by one or another kind of the elements. So we assemble all this geometry elements by topographic characteristics like graved direction of flow, land use, vegetation, roughness and the channel network. So that is very clear from this figure. So then there are basically two methods to do this assembly so first one is based on the topographic characteristics like a different portions of watersheds are represented by the geometric elements and then 1 to 1 correspondence between a portion of watershed and the element representing it. So we do this assemblage based upon the topographic characteristics and the second one is we can consider the geomorphic characteristics of the watershed. So here we use this geomorphic characteristic to develop a network representation like this so that the model flow paths are analogous to the watershed flow paths. So the assembly can be done either based upon the topographic characteristics or the geomorphologic characteristics. So as far as geomorphological characteristics are concerned we have to deal the quantitative land form analysis like a flowing water and associated mass gravity movements acting over long periods of time. So how the flow is taking place and then associated mass gravity movements all these we have to consider and this is responsible for development of surface geometry. So a watershed can evolve according to the flow pattern what is happening within the watershed. So we have to assess what kind of variation is taking place within the watershed and then as far as geomorphological characteristics of watershed is concerned we have to systematically describe the watershed so a systematic description of watershed is required and geometry and its stream channel system we have to identify and we have to measure the linear aspects of drainage network. So how much is the length of the drainage system and then like aerial aspects of the drainage basin and then relief aspects or elevation aspects of the channel network within the watershed. So these are some of the important characteristics as far as the geomorphological features of the watershed. So we have detailed discussion as far as the linear area and relief aspects of the watershed is concerned. So first let us look into the linear aspects of drainage network. So we can see that when we deal with a watershed so this is a watershed or this is a watershed which I have drawn. So the stream order means stream order indicates the degree of stream branching with a watershed so you can see that this is the main stream so you can see that there will be number of branching. So the first order means there will not be any branch so unbranched tributary so you can see that these are all first branch where one is indicated that is the first branch. So this original watershed is concerned this is a blue line indicates the first branch first order. And second order so two or more first order so you can see that two or more first order will be keep on joining so this is so called a second order. So this one whatever is indicated in blue is the second order and third order means two or more second order streams are coming together. So this is the third order as far as the stream order is concerned. So like that nth order stream is formed by two or more stream of orders n minus one and a stream of lower order. So that is the nth order of the stream. So according to this we can now have various definitions like a bifurcation ratio. So bifurcation ratio is the ratio of number of stream of any order to the number of stream of the next lower order. So if nu is the order of the watershed as far as the watershed is concerned nu is the number of stream of youth order then the bifurcation ratio is nu divided by nu plus 1. So where nu plus 1 is the number of stream of u plus 1 order. So we have already seen the stream order so bifurcation ratio means the nu divided by nu plus 1. So this indicates say whether it is what is the way the watershed say the nature of the watershed whether it is in steep or whether it is mildest steep. So this represent the effect on maximum flood discharge of the watershed. So bifurcation ratio based upon the stream order is one of the important indicator as far as the maximum flood discharge to the outlet of the watershed is concerned. Then say bifurcation ratio and the principal order k of stream of watershed are known then total number of streams of all orders of a drainage network we can identify as sigma is equal to 1 to k, nu is equal to r b k minus 1 divided by r b minus 1. So this depends upon the bifurcation ratio and the stream order. So then another important definition as far as the linear aspect is concerned it is called the law of stream numbers. So this relate the number of stream of order u that means nu to bifurcation ratio and the principal order k. So nu is equal to r b to the power k minus u. So where r b is the bifurcation ratio and nu is the stream of order u. So that is called the law of stream numbers. So these are some of the definitions which indicates what is the linear nature of the as far as the drainage is concerned drainage pattern is concerned how it is changing from one watershed to another watershed. We can quantify in terms of this definition as far as the watershed nature is concerned. Then stream length we can define as it reveals the characteristics of various components of drainage network and it is contributing surface area. So if l u is the mean length of the channel of order u so l u bar is equal to sigma is equal to 1 to n l u divided by nu where nu is the stream order of u. So that is another definition stream length. Then some other definitions like a stream length ratio so that is the average length of stream of any order to average length of stream of next order lower order. So r l is equal to l u bar divided by l u minus 1 bar so that is called stream length ratio. Then law of stream lengths that relates average length of stream order u to stream length of ratio r l and the average length of first order streams. So l u bar is equal to l into r l to the power u minus 1. Then another definition like law of stream number and stream lengths can be combined to yield an equation for finding the total channel length. So the total channel length we can identify based on the law of stream number and the stream lengths. So sigma i is equal to 1 to n l u is equal to l 1 bar into r b to the power k minus u into r l to the power u minus 1. So these are some of the important linear aspects. So we can quantify the drainage pattern as far as the length of the drainage pattern or the variations within the watershed by using the linear aspects. So now let us look into aerial aspects of the watershed. So this indicates the arrangement of aerial elements like a stream basin and inter basin. So this is the stream basin and this is called inter basin. So stream basin means area of stream basin. So this is the stream then what is the corresponding area. So that is the stream basin. The inter basin area is the contributing surface flow directly to the stream of higher order. So that is the definition of inter basin area. So the total basin area say a u of order u it is the total area projected on a horizontal plane contributing overland flow to the stream of given order plus all the tributaries of lower order. So a u is equal to sigma is equal to 1 to n a 1 plus sigma is equal to 1 a 2 plus like that plus sigma is equal to 1 to a 0 2 plus sigma is equal to 1 a 0 3 like that. So this represent the stream basin area as I mentioned here and this represents what is put in this red color that represent the inter basin area. So the total basin area we can identify like this. Then say very similar to the linear aspects. So aerial aspects also we can have lower stream areas. So that relates uneven area of basin of order u to the mean drainage area of first order a 1 and the system area rate r a. So a u bar is equal to a 1 bar into r a power u minus 1 where r a is the average basin area of stream of one order to average area of basin of next lower order. So this is analogous to the lower stream length as we have seen in the previous slide. And then we can have a relationship between the basin area and the stream length l is equal to m into a to the power n where l is the stream length a is the basin area. And for the considered watershed m and n are some constants. Then based upon this area and say the drainage pattern we can have some relationship as far as the drainage and discharge is concerned. So the relationship between drainage and drainage area and discharge can be represented as q is equal to j into a to the power m where j and m are some constants. And this m can vary from generally from 0.5 to 1. So these are some of the as far as drainage and discharge is concerned and then basin shape is the shape of projected surface area on the horizontal plane of basin shape. And it has significant impact effect on stream discharge characteristics as consents and basin can be characterized by some important factors like a form factor circulatory ratio and the elongation ratio. So this definition we have already seen earlier but within the context of basin shape let us have a look again. So the form factor means it is a ratio basin area to the square of basin length and then circulatory ratio is a ratio basin area to the area of circle having equal perimeter as the perimeter of drainage basin AU by AC. So this can vary from 0.6 to 0.7 depending upon the watershed. Then elongation ratio is the ratio of diameter of a circle DZ having same area as basin to the maximum basin length LBM. So this is the elongation ratio. So this define the so called basin shape. So this aspect also we have seen earlier. Now another important aspect as far as the watershed is concerned it is so called drainage density. So this indicates the ratio of total length of all stream of all order within a watershed to the total area of the watershed. So that we can be defined as drainage density can be defined as sigma i is equal to 1 to K sigma r is equal to 1 to N LU divided by AU where say this gives say what is the total the ratio of total length of all stream to what is the area of the watershed. So the high value of the drainage density indicates a relatively high density of streams and there is a rapid stream response will be there say for example this watershed is concerned there may be rapid stream response. In constant of channel maintenance it is the inverse of drainage density. So we can define another term called constant of channel maintenance. So that is E is equal to 1 by drainage density. Then also another term as far as drainage and discharge is concerned drainage is concerned we can define stream frequency it is the number of stream segments per unit area of the watershed. F is equal to i is equal to 1 to K nu divided by A K. So where N nu is the number of stream segments of youth order and A K is the basin area of the principal order K. So this is as far as the stream frequency is concerned. Now the last aspect is so called relief aspect that is based upon the elevation. So relief is the elevation difference between the reference points located in the drainage basin. So maximum relief is the elevation difference between the highest and lowest point within the watershed. And the maximum basin relief means elevation difference before basin outlet and highest points located in the perimeter of the basin. So that is so called a basin maximum basin relief and we can also ratio call relief ratio that is the H by L where H is the relief horizontal distance on which relief was measured L. So this is the ratio of relief H to the horizontal distance L. So then also as we defined earlier say we can have a relative relief. So that is H by P into 100 where H is the maximum basin relief and P is the basin parameter. And then so according to the elevation the channel slope will be also we have to consider the slope of a channel segment increases with increase in orders. And say we can combine the law of stream and with respect to slope like this. So it relates the average slope of stream of order U to average slope of first order stream and stream slope ratio says U bar is equal to S1 bar into RS to the power U minus 1. And another important aspect which we can use is called goodness number as far as watershed is concerned. It is a product of relief H and the rainier density. So that is this is one of the important parameter which is used to characterize a watershed. So R is equal to the relief into rainier density H into dd. Then finally another number called geometric number also we can use that is H into dd that means the ruggedness number divided by the say so called geometry it is called geometric number that is the ratio H dd divided by the ground slope SG. So then before closing this lecture so when we deal with since we have now seen the various aspects like a linear aspect, aerial aspects and then the relief aspects. So accordingly the as far as watershed variation is concerned the as far as the relief variation is concerned we can have analysis called hypsometry analysis. So this gives a relationship between the horizontal cross sectional area of watershed and it is elevation. So this is a curve plotted with relative height H by H so on the y axis and relative areas A by A where H is the height of given contour capital H is the relief A is the cross sectional area of contour and capital A is the total watershed area. So this curve is so called a hypsometric curve. So for the given watershed we can develop this hypsometric curve. This is very useful to compare the elevation characteristics as far as the watershed is concerned. So accordingly the slope can be identified and the runoff process also we can identify. So slope of hypsometry could be changed with stages of watershed developments. So then according to the developments taking place within a watershed we can classify the watershed into three stages one is so called an equilibrium stage, second one is called equilibrium stage and third one is called a monotonic stage. So this in equilibrium stage is a young stage so that watershed is under development process so you can see that the watershed is still keep on evolving so various things are keep on happening so no equilibrium is reached. Second one is the equilibrium stage so this is a mature stage of watershed where steady state conditions are reached so all the parameters are concerned there is not much changes taking place. Then third one is so called a monotonic stage so this isolated bodies of resistant rocks as you can see here from prominent hills are found above subdued surface so that is so called a steady column monotonic stage so three important stages as far as the development of watershed in equilibrium equilibrium and monotonic. So this if you do a hypsometric analysis we can identify how these stages will be varying so this figure shows this is taken from the book of Ranveer Singh. So this is relative area a by a v is plotted on x axis and relative height h by h so this top curve black color curve indicate in equilibrium stage and the middle one red color indicate equilibrium stage and the last one called monotonic stage so accordingly we can identify. So some of the important reference used for today's lecture watershed planning and management as we are seeing and then some of the other references so as you shall before closing the lecture say one tutorial question which you can attempt. So critically analyze the important characteristics of a typical agriculture watershed so illustrate various parameters and try to quantify them and discuss the order of importance as far as the agriculture watershed discrepancy and if you self evaluation questions like classify the various watershed characteristics and its importance in watershed management describe different methods of geometric representation of watersheds. Then I describe linear aspects of watershed and its importance in geomorphological study of watershed then discuss relief aspects of watershed and its importance in geomorphological study and what is hypsometric analysis of watershed. So all these questions if you go through the lecture so all these things we have discussed and some assignment questions like what are the important watershed factors to be considered in watershed management in watershed analysis what are the important channel geomorphology and parameters to be considered illustrate the geometric representation of watershed step by step and describe the aerial aspects of watershed and its importance in geomorphological study and what are the different stages of watershed developments. So all these questions you can get answered when you go through this today's lecture. Then finally one unsolved problem so for your watershed where you are living you can identify the various characteristics and then list them in order of importance then analyze the linear aspects of the watershed analyze the aerial aspects and relief aspects. So you can collect various data related to elevation area channel length slope etcetera and then you can make a say a matrix which illustrate the importance of each characteristics in the watershed management plans. In today's lecture we were discussing about the various important watershed characteristics. So in the next lecture we will be discussing the watershed delineation and various methodologies. So this is the module on watershed modeling. Thank you.