 Hello everyone, welcome to today's lecture in the course remote sensing principles and applications. In this particular lecture, we will be discussing more details about reflectance, albedo and related quantities which we started in the last lecture. So in the last lecture, I explained you in detail about how the nature of our measurements like the solid angle over which we integrate our measurement will influence our outputs. That is we can consider incoming energy or outgoing energy in different different cases. We can consider to be them coming in one particular direction. We can consider them to be measured over like a conical solid angle or we can measure them or integrate them over an entire hemisphere. So based on these different solid angles we make with respect to our point of observation our output may vary. This thing I told you in the last class and one more thing I told you in the last class is how the source object and the sensor geometry is going to influence our measurements. That is what we call the zenith angle of the source, azimuth angle of the source and zenith angle of the viewing sensor and azimuth angle of the viewing sensor and these two measurements in combination with the solid angle over which we are integrating is going to make the earth surface objects look different. So this is what I explained as source object sensor geometry in the last class. We also defined what reflectance and albedo is. So reflectance the basic definition is irradiance outgoing especially in reflected form. I am not talking about the emitted energy I am just talking about the reflected energy from object of every interest divided by e incoming. So this is what is defined as reflectance and I also said that based on the solid angle of our measurements and the direction in which we look the reflectance can be defined as like different quantities. So the first basic definition of reflectance can contain directional measurements that is the measurements that we made using remote sensing sensors will be from only one particular direction. Sensor can be located here, sensor can be located here exactly over it of the object sensor can be in different directions integrating over the conical solid angle that it subtends on the earth surface. So this is the directional component this is what normally we measure. I also said for applications related to land surface modeling, snow studies, energy balance studies and all we would not be needing this directional component of measurement but we need to measure the total energy that was reflected by an object within the entire hemisphere surrounding it. So what essentially it means our sensor should not be looking from one direction it should quickly move in all directions collect energy within the entire hemisphere which is practically not possible our sensor will not be able to do that especially from satellites. What we do we take this energy that was observed from one different direction we integrate it over using some mathematical functions over the entire hemisphere to get the reflectance of an object within the entire hemisphere and that reflectance that we calculate over the entire hemisphere is what we call albedo. So albedo is defined as the outgoing radiation like albedo is defined as the case of reflectance in which the outgoing radiation or especially I make it more specific the reflected radiation is integrated over a hemisphere surrounding the object of our interest we call it as hemispherical reflectance. So this is with respect to the outgoing reflected radiation this is what we call albedo. Now in the definition of albedo we just talk about the integration angle of outgoing radiation of outgoing radiation also there is one more component of incoming radiation. So what exactly is incoming radiation like how the incoming radiation is integrated is again going to differentiate or classify this albedo further. One thing we talk about what is known as a black sky albedo or we call it as the directional hemispherical reflectance DHR in short directional hemispherical reflectance what is this I already told you that during like very bright extremely clear sunny sky days we can assume the solar radiation to be coming from one particular direction. Assume the sky is totally cleared and no diffuse component is present. Assume this the diffuse component is entirely absent hence the incoming radiation is coming from only one direction. Under such scenarios if we are able to make measurements not make measurements to model the outgoing energy over the entire hemisphere surrounding it in response to this single direction of incoming energy we call it as directional hemispherical reflectance or in a simple parlance we call it as black sky albedo that is the sky is not giving any energy source sky is not acting as energy source the energy sources only the direct solar radiation we call it as directional hemispherical reflectance. On the other hand over most natural cases over like our every day to day life the atmosphere will not behave like a what to say will not behave completely clear atmosphere will do scattering radiation the scattered radiation from the atmosphere will fall on an object. So essentially the total radiation received by the object will have both the direct component and diffuse component. So if we want to calculate the total energy that came in and irradiated on the object then we should take the entire energy that came in within the entire hemisphere surrounding an object right because energy can come in from any direction surrounding the object of our interest one direct sunlight plus diffuse skylight from any possible direction. This sort of incoming radiation that is where incoming radiation is also coming in with an entire hemisphere surrounding an object outgoing radiation also we have to measure over the entire hemisphere surrounding an object and reflectance we measure over or we model over such scenarios we call it as bihemispherical reflectance. So that is bihemispherical reflectance generally it is albedo albedo can be referred to anything but albedo in a broadest sense refers to bihemispherical reflectance. So if you come across a term albedo in any sort of like textbooks related to climate, meteorology, snow, cryosphere studies and all you can always associate it with bihemispherical reflectance ok. And one more point is black sky albedo I already told you there can be another theoretical scenario one of the theoretical scenarios direct sunlight is totally absent whatever the object receives is pure diffuse component. Practically speaking such scenario may happen during like highly cloudy days extremely cloudy completely dense clouds covering us which obscures the sun totally like during monsoon season and all we might have observed such scenario the sky will be completely covered with dark clouds filled with like rain water and it may be going to rain anytime under such scenarios we will not be able to see the sun. So practically speaking sunlight is completely obscured and whatever light we receive during that time is entirely diffuse in nature. So direct radiation is almost absent whatever we receive is entirely diffuse in nature. If we measure reflectance of an object under such circumstances where it is irradiated only by diffuse skylight we call that particular reflectance as white sky albedo. So please remember there are like lot of different different things here and this is for your own knowledge. First thing I told you directional hemispherical reflectance where only direct skylight is considered direct sunlight is considered diffuse component is removed. Second case the most practical thing we encounter in our everyday life is every object will be receiving energy both from direct sunlight and diffuse skylight. If we measure albedo under such circumstances we call it as bi hemispherical reflectance there can be some circumstances where the diffuse skylight only is present direct sunlight is absent we measure reflectance under such circumstances that is we measure bi hemispherical reflectance only under such circumstances but the albedo is has a name of white sky albedo that is white sky albedo is albedo measured without direct sunlight component. I write the word measured but practically this will not be measured this will be modeled using some functions whereas black sky albedo is albedo without sorry this should be without without direct sunlight without any diffuse component. So, black sky albedo means the incoming energy has only direct component white sky albedo means the incoming energy has only diffuse component but measured over a entire hemisphere so no direct component but always remember if we say the word albedo then the outgoing radiation is measured in the entire hemisphere surrounding an object. So, if we are talking about measuring outgoing radiation reflected radiation in any one particular direction as we normally do in remote sensing things we call it as reflectance but if we convert this reflectance into the entire hemisphere surrounding an object of interest we call it albedo and even this albedo we can further subclassify it as white sky albedo and black sky albedo whether diffuse or direct component is present. And also one more thing to notice we talked about lot of things measuring energy quantities albedo reflectance and so on. They can be measured with respect if we talk about wavelengths of measurements over the wavelengths with which we measure they can be measured over like either small spectral bands like only green band 0.5 to 0.6 only red band 0.6 to 0.7 like the small bands we can measure or we can measure even over like larger bands I want to measure over entire IR 0.7 that is near infrared band 0.7 to 1.4 micrometers that is possible. So, the quantities such as reflectance albedo and even the earlier terms like gradient flux density and everything whatever measurements we can we are going to make we can measure in any different bandwidths we can measure in small small bandwidths or we can talk over in like entire visible range entire infrared range and so on. So, if you are talking about like small bandwidths like only red green blue small portion of NIR we call it as spectral measurements like what is the reflectance in red band what is the albedo in green band and so on. If we talk about like very broad wavelength entire visible 0.4 to 0.7 I talk about albedo of an object in the visible bandwidth reflectance of an object in the entire NIR bandwidth and so on. So, the measurements can be made over like a large wavelength range or over like a small wavelength range also based on our needs our sensor characteristics please remember that. And also one more thing is the actual albedo that is the actual true biohemispherical albedo can be calculated as a linear combination of white sky and black sky albedos. So, this is like later in the course we will be talking about lot of data products available so these albedos are available from satellites for sensors such as modus where if we take they will give us white sky and black sky albedo for converting them to normal biohemispherical reflectance or normal albedo we can treat them as like a linear fractions and do it. Then next important property that we should always have in mind is DRTF that is bidirectional reflectance distribution function. What is this? In the last lecture when I when we discussed about the source object and sensor geometry I told you that objects will look different when we observe the object from different different directions. So, we know objects will look different but I also told for some measurements we need to integrate over the entire hemisphere we should not be having directional measurements we should be having like a total hemispherical integrated measurement. How is that possible? How to model the object's behavior when we look from different different angle that mathematical function which helps us to model this directional property of an object is called BRDF bidirectional reflectance distribution function. So, what is the definition of BRDF? BRDF is defined as the radiance of an object that is reflected or outgoing from an object reflected radiance to the ratio of the incoming energy that is incoming irradiance that is the radiance going out of an object divided by the irradiance received by the object. This is the basic definition of BRDF but here I have I have lot of angular elements attached with it. What are these? The angular elements here gives us the direction in which incoming energy is coming and the direction in which outgoing energy reflected energy is going out. Theta i and phi i indicate the zenith and azimuth angles of incoming radiation whereas theta r and phi r are the zenith and azimuth angles of outgoing radiation. So, I just repeat zenith angle is angle measured with respect to the normal to the surface or with respect to vertical I will say with respect to vertical is what we call zenith angle and azimuth angle is the angle the horizontal angle we measure with respect to some reference direction. Normally we take it as a like the direction we measure clockwise from north we call it as azimuth like east is 90 degree, east is at 90 degree azimuth from north, south is at 180 degree azimuth from north and so on. So, from any one particular reference direction the horizontal angle we measure is called azimuth the angle we measure from the vertical line is what we call zenith and I also told you in the last class that if we have these two angles zenith and azimuth angles we can fix the direction of incoming radiation and also the outgoing radiation. If we have theta i and phi i we can fix the direction of incoming radiation. Similarly, if we have theta r and phi r we can fix the direction of outgoing radiation. So, this BRDF is a mathematical function which relates which will tell us how an object will behave for incoming radiation and outgoing radiation in almost all possible combinations for a given theta i and phi i and for a given theta r and phi r what is the ratio dL by dE this is BRDF. So, essentially it is kind of like one function mathematical function. So, there are like different ways to get this BRDF using like ground measurements and all people use like instruments different instruments for this and measure the objects property using like different different different different directions and derive this BRDF. What is the benefit of deriving this BRDF? Once we have this BRDF defined for an object it will be helpful for us in calculating the different directional reflectances and different albedo quantities. Like I said what the sensor measures is directional it may it integrates energy over a cone. I also said for some applications we will be needing albedoes which is energy integrated over the entire hemisphere. How to go about it? We should know the BRDF of an object. If we know the BRDF of an object there are like mathematical functions anyway the functions we are not going to discuss in this course there are different mathematical ways in which we can convert this directional conical measurement from a sensor into a hemispherical measurement that is possible and BRDF helps us in achieving this. So, BRDF is an intrinsic reflection property of the object. How an object will look if we look from one particular direction and when the object is irradiated from one different direction. So, before we proceed further I have a question for you. Can you just think of what will be the BRDF value for a Lambertian surface? Please pass the video and relate it to the earlier relationships we talked in radio mentoring and try to guess an answer for this. Please pass the video and think for few seconds. The answer for the question I asked is the BRDF of a truly Lambertian surface will be 1 by pi. For a Lambertian surface is not actually a function it is actually a constant that is 1 by pi. Why because for Lambertian surface we know E is equal to L pi BRDF is defined as L by E. So, if we take this L by E as BRDF then BRDF will become 1 by pi this is only for purely Lambertian surfaces. Just remember one thing at this stage it is very easy to get confused between BRDF and reflectance but they are entirely different they are not one and the same. Just look at the definition of these quantities. Reflectance is defined as E reflected divided by E incoming. So, both the terms are radiant flux density here also is radiant flux density here also is radiant flux density. Essentially this is watt per meter square units this is watt per meter square units they cancel out each other and reflectance has no units. Now, we look at the definition of BRDF. BRDF is defined as radiance in a given direction divided by irradiance from a given direction. So, if we look at this radiance has a unit of watt per meter square per radian radiance is unit is this please refer back to the previous slides where we defined radiometric quantities watt per meter square per solid angle. So, watt per meter square per radian is its units E is the units of watt per meter square these will cancel out and BRDF will have a unit of per radian. So, this is the unit of BRDF. So, conceptually speaking BRDF is a function which we integrate over the angles of our observation are we from which angle are we observing with which theta i and phi i with which theta r and phi r are we observing. If we integrate BRDF over these angle combinations we will get reflectance. So, BRDF is a function which is like you can think it as like the least what to say the maximum limit in which we can go and see above an object of interest. So, this is like the finest derivative of an object like a single point on object. So, it is like concept of integration and differentiation you have one point you integrate or a function defined over one point. So, you integrate it over an area you get the surface area right that is the process of integration same thing you define reflectance for like one particular point that is BRDF you integrate it over like the different solid angles over which you work that will give you reflectance. So, reflectance has no units BRDF has a unit of first gradient SR raise to power minus 1 and BRDF is a intrinsic property of a surface and it is a function and we need to integrate it in order for us to get reflectance whereas reflectance we can measure it basically. So, reflectance denotes how much energy came out. So, it is kind of we can measure and the purpose of BRDF is to convert other various directional it is over which we measure and take them to different different quantities. BRDF helps us to understand in detail about how object will look if we look from different different angles if we supply energy from different different angles or if we look from different different angles how an object will look. BRDF will help us to understand that model that we are not going very much in detail about conversion of different reflectance quantities and all but just for your understanding I define all these quantities. So, if you come across such quantities Albedo directional hemispherical reflectance, bi-hemispherical reflectance BRDF and so on in various like papers you read or remote sensing textbooks you read you should be remembering or you should be knowing what is what that is the purpose of telling this. So, in summary in this particular lecture we have discussed again we discussed what a reflectance is what Albedo is how Albedo is classified further such as white scale Albedo and black scale Albedo and also we define one more important property called BRDF bi-directional reflectance distribution function. With this we end this lecture. Thank you very much.