Understanding Earth's Energy Balance and Solar Radiation

so what we look into is basically uh as i was telling you earth energy balance right ah because ah you know ah whatever energy is received by the earth it comes mainly from the sun so whatever is received annually is also dissipated out annually daytime it receives

radiation night it actually back to the cosmos besides that ah you know the seasonal variations are there so that this this shows a kind of a bookkeeping or accounting of the earth energy scenario right

and thats what the diagram was thats what i was looking at in the last class so what we said is hundred percent is ah what is received out of is fifty percent goes right to that atmosphere absorbed by the particles in the atmosphere and some of it comes as diffused

radiation to the ground right and it is reflected back so some of it is reflected back some directly reflected from the diffused you know particles itself the sky i mean particle atmospheric particle itself and then fifty percent is received onto the ground out of which some

percentage goes directly to reflection from the ground itself so if you look at that ah you know fifty percent five percent gets direct reflection from the ground forty percent reflected by absorbed by the atmosphere or reflected back twenty

percent goes as long wave radiation to the sky like a you know as you can see this this one long wave radiation and twenty percent would be evaporation from the sea moisture etcetera right so this is again now fifty percent what is received on the right this

is what is a breakup basically long wave radiation about twenty percent evaporation from the moisture front sea and such things another twenty percent and ah convection radiation you know back from the surface of the earth another ten percent or so

so thats what it is anyway this is not true really ah but it we need not go into further details of it but we understand that now the radiation that falls onto this ground right the basically if it is coming directly normal to the surface normal to the ground surface

the intensity will be highest but if it is coming inclined same amount of energy is falling on larger surface area and as you can see for example the normal surface is b c is the surface area which is on to the horizontal plane or to the ground then c if i have incident

angle s cos theta or cos beta as we are calling it so b is equal to you know b will be basically i i c or i can write it in this manner there is a pen available right so for example i b is a beam radiation thats falling into an area of b and i c is the radiation

on the horizontal surface on the c surface multiplied by c area c area c right area c is the lets say c is this area c is this area i mean width is one i can take so c into one similarly this is b into one so this should be same because energy is same intensity of

radiation is defining watt per meter squared thats what i told you other day so watt per meter square multiplied by the meter square there should be same now what is b by c b by c is cos beta if this is you know the incident angle is defined normal to the surface this

race makes thats what we call as incident angle normal you know so this is incident angle actually which is same as this right this is incident angle so this is same as this so basically it is i b cos beta right so because the area on which it is falling

its not so this is this is this is you know so normal incident radiation is higher intensity will be higher then inclined any time if there is incident angle is more than zero this would be less radiation to this will be less right now ah how do you define incident angle normal

to the surface and the ray angle between normal to the surface and ray thats your incident angle right normal to the surface and ray now since this is normal to this right this is normal to this and ah this one is normal to this one is normal to the ray so this is

normal to the this one this one is normal to the ray so angle between this will be again beta thats what i was just telling now solar constant is the amount of radiation that is available on top of the atmosphere right because atmosphere absorbs so amount

of radiation that comes on top of the atmosphere that we call as solar constant this varies a little bit this varies a little bit because ah suns position distance of the sun from the earth is not same its elliptic orbit so perigee apg and all those so there is the

slight variation besides that sun itself its you know quantity of radiation emitted by the sun that also varies somewhat but approximately one can take is something of the order of around one three nine five watt per meter square some other book you might find slightly

different and so on so thats called solar constant that is received on top of the atmosphere right now thats what i was saying two percent variation in output of the suns output is itself varies and two part point five percent due to distance but

we dont care about it really we are not interested in this we are trying to understand only ok so thats thats what it is right and thats what is you know top of the atmosphere it is more and distance traveled here is less compared to distance travel in this position

so obviously absorbed will be more so it would depend upon and normal surface obviously intensity will be higher compared to inclined surface so these are the issues at atmosphere etcetera etcetera these are

the issues so thats thats what it is so two percent variation thats what i said i already said that so thats again the similar kind of diagram fifty percent you know five percent state away goes out twenty percent is radiated from the diffuse atmosphere diffuse radiation

goes back cloud etcetera twenty five percent absorbed there twenty three percent comes to the ground diffused radiation you know the radiation what is diffuse radiation what is specular and diffuse you see if i have a mirror then rays will be reflected back

right so beam and reflected beam now angle of incident is equals to angle of reflection thats specular on a polished surface but if i have a mat surface something like paper or you know your wood etcetera etcetera it will actually it

will not be it will not be it will not be radiating you know it it will not be reflecting the way that is written there is shown here the pen color i should change actually try to change the pen color over maybe it is changed somewhat it will be actually reflecting in

all direction you dont see your image and you know you mirror you see your image back but on on table or something like that you wont see your image so thats what is happening all getting scattered in all direction i mean it diffuses in all direction there is a completely

diffused surface right so diffused radiation here it gets absorbed by atmosphere and diffused in all direction twenty three percent comes as diffused radiation from the atmosphere twenty seven is a direct radiation and this is what actually it also

dissipate over the year so that was that was that was related to the you know initial discussion of hours and then we will follow continue with from here itself so temperature we have already talked about this effects you know dry bulb thermometer in shade we talked about

sky condition so wind speed and direction this we have already looked into the factors which affect the environment surrounding the building you know solar radiation now how do you measure also we talked about i just didnt mention about this one ah this

is called pyranometer which measures radiation a pyranometer measure measures radiation now there are varieties of type the ah one conventionally been used is who will have a blackened will have a blackened you know blackened oh this color is not black anyway blackened sensing

device right blackened surface there is a dome there is a dome concentric dome there is one dome glass dome here there is another dome there and it has got a heavy base just a small you know quick quick understanding there is a heavy base basis heavy heavy mass

this is blackened actually my color is not showing really black properly it should be black or let me see if i can come close to the black or so go to anyway so this is blackened surface around this which i will have maybe this was better black ok doesnt matter so

its something like this there are two concentric domes there is a sensing device here and a heavy mass there and you have actually what is called thermocouples in series right so basically the hot junction is here cold cold junction is somewhere in the heavy mass and

there will be number of them together series of them right such that temperature difference between these two can easily be sensed so when radiation comes in it is absorbed in that blackened portion and temperature rise occurs there

this is a heavy mass heavy thermal mass so its temperature would not change besides that is also covered by a disk so that it doesnt reciprocate radiation so base doesnt receive radiation it has got a heavy mass its temperature will remain same but ah ah the blackened sensing

area it receives radiation so the difference in temperature which is actually kind of magnified or summed up because there are number of hot junctions and cold junctions that is dependent upon intensity of radiation so it can be calibrated these two glass domes

are put in to reduce down the convective heat transfer also glass traps the radiation so no radiation back can go right so two of them we will ensure that there is no formation of ad or current flow you know air moment etcetera is minimal so thats a pyranometer

anyway again the instruments are not really ah of our and rainfall gauges are there so that you know so we talked about this sometime earlier so this is the parameter and humidity of course as i said absolute terms moisture vapor per unit kg of dry air thats how we

do so thats what we said amount of moisture that can be held in temperature relative humidity measurements of relative humidity i already talked about that hygrometer last class or difference in dry and wet bulb temperature you know in saturated condition dbt minus

wbt is equal to zero this is just a repetition solar radiation measurement i already talked about so now this is this is the environment around right but this environment is not constant these environment changes from what we call

season to season location to location as well as season to season because the environment is mainly governs by the suns radiation thats what we are talking about the energy that comes from the sun so sensible heat is actually measured by temperature changes which you

can sense latent heat is one which occurs because of phase change latent heat occurs where moisture is vaporizing there is latent heat so since we you see its receives energy sensible temperature change you would occur you know suns energy

so temperature surrounding temperature or environmental temperature around the building is a function of the energy received from the sun besides that we have seen the moisture will evaporate so moisture content relative humidity etcetera so all are related to that

and it varies from therefore since suns radiation is not constant every day whatever i get over a period of time lets say month of july and august to december if there is a you know there will be difference of suns radiation because sun another look sun is i mean the

earth is revolving around the sun so therefore its position of this particular location with respect to sun it will go on changing similarly depending upon not pole for example it receives radiation indirect radiation also not direct beam radiation never it receives

there because beyond twenty three point five beyond certain latitude it dosent so its important to look into sun earth relationship to understand this temperature and relative humidity on those parameter and amount of factor variation of those factors right that causes what we

call seasonal variation right seasonal variation and rotation of the earth about its own axis causes what is called diurnal variation daily diurnal variation so we are trying to look into that sun earth relationship then we will understand then we can come to the climate

so you see if you look at sun earth relationship right basically earth has got a banking its inclined you know its inclined to this plane of revolution right plane of its revolution under the sun thats got a banking and thats constant all the time approximately sixty

six point you know twenty three point five is the equal you know this this this angle can be this angle can be twenty three point five so its its got a banking i think its written somewhere exact some summer it will be there so it has got a banking now it is

revolving like this revolving all the time like this so some point it will be normal some of you know and this plane on which it is normal i will keep on varying so we can find out an angle between the equatorial plane which is equator this one diameter equatorial

diameter the center this is north this is south pole so normal to that is a diameter diametrical circle which is equatorial circle and suns rays on particular day falls normal to this point and as it revolves around only a two point of time there is normal to the

equatorial diameter right so this is around twenty first december you find that its normal to twenty three point five southern latitude now what is latitude latitude is the angle at a given location so i you know i have a chord circle i have

a chord circle i have a chord circle here so from the center of the earth if i join a line the angle that will make with the chord circle that we call as latitude so latitude of north pole is ninety degree latitude of north pole is ninety degree latitude of equator

is zero so thats how we vary this latitude angle so latitude angle vary so location of the location of the place you know or or poi[nt]- you know the i i mean location on the surface of the earth any geographical location i can express

it in terms of its latitude latitude longitude these are the one which is this kind of you know i can divide the whole approximately spherical earth into three sixty degrees or one eighty in each direction

and one eighteen west direction right so three sixty degree and divide them into equal angles this three sixty complete circle so these are longitude actually and if you travel from little bit

of digression have you any one of you read a book around the world in eighty days by ag wells phileas fogg well [laughter] ah just digression basically he had a bet and you know some club in england here a bet that i will complete the world go around the world

and come back to london in eighty days and he managed his way through a long story is a book is a novel sort of scientific you know science fiction sort of thing so he moves around even india comes in there so he moves around and then finally reaches there and

according to his watch he found that he is one day late then he suddenly realized as he was traveling he should have changed his time you know he should have changed his time he did not do that so he counted one day more so if you

are moving your you know moving from east to west you have to adjust your clock because when it is twelve noon here let us say in delhi it will be morning somewhere in europe and so on so you got to adjust right he didnt do that adjustment and then suddenly realize

at home he saw the calendar and he is you know servant or somebody has marked it the previously rent to the club of course won the bet thats a there is a story so anyway coming back to this so longitude relates two time what do you call solar time

and standard time standard time is indian standard time is with respect to eighty two point five there is the longitude of allahabad right you know so far its like that so coming back to this as you are saying longitude do we will have a little bit talk about that

sometime later and also so latitude defines a position of a location on the surface of the earth with respect to equatorial diameter in terms of the angle so suns rays falls normal to because it has got a banking this is ah ninety minus twenty

three point five is how much sixty six point five so this banking is sixty six point five since its got a banking with this plane of revolution sixty six point five therefore it can it falls normal here sometime normal

here some you know normal to this equatorial plane only in two times there is twenty first september around twenty first march this is around twenty first june summer solstice and winter solstice and so on equinoxes these are equinoxes so suns you know suns ah i think

this is ah yeah this is this diagram also shows you vernal equinox winter solstice or terminal equinox and summer solstice so it falls normal to this circle which is twenty three point five latitude north on summer solstice they are somewhere around june this

is winter somewhere in australia you will have summer during that period of time so suns radiation falls normal here and during this autumnal and vernal equinox its normal to the equatorial plane so normal winds radiation can be received

only from twenty three point five to twenty three point five i mean north to twenty three point five south so thats why these places who will have relatively warm environment right so what you do is we classify all the latitude into three groups say zero to thirty

thirty to sixty and then thirty to again thirty north to thirty south right and thirty south to sixty south and sixty to ninety that would be right so the one from sixty to ninety they are polar polar climate subtropical and thirty north to thirty south we call it tropical

climate because the environment is warm and i have not possibly defined climate climate is a pattern of temperature relative humidity etcetera at a given location right and weather is a daily data really changes so weather change in weather relates to daily

temperature relative humidity etcetera so when you say todays weather is likely to be rainy we mean but then we talk of monsoon season so climate seasonal variation depends on the climate and everything is related to a sun so thats what it is right so thats what

we looked into even wind flow pattern is because of suns radiation because during the summer solid states the suns radiation will be normal to tropic of cancer that is twenty three point five north that we call as tropic of cancer and see around twenty three point five it

passes through india by the way ah ahmadabad close to ahmadabad and i think agartala who draw a line from ahmadabad to agartala twenty three point five indian latitude varies from eight degree north thiruvananthapuram somewhere around that place is eight to about ah delhis

twenty nine its twenty nine you know and thirty three or so something like that j and k that place so it will be ladakh on those areas would be of this order so this is you know by enlarge indias tropical ah now even the wind movement

is dependent upon the suns radiation because we are in summer solstice around that period of time it will be heating of the sea around the tropic of cancer so the hot you know hot tropical front will start moving up the hot air air gets heated up water vapor you know

so air gets heated up and basically as it heats up the cool air from the subtropical region will tend to move to fill in this gap and then it will move you know it will it the circulation this circulation pattern actually circulation pattern starts so this is tropical

front subtropic high subtropic front etcetera etcetera and polar high so this this is this this also is because of the wind movement is because of this so but there is a model there is slight modification will be there if you moving upward but the

earth is ro earth is rotating so what you call coriolis forces so you find the patterns are something like this you know this is the direction shown as seen from vertically from the top so thats what it is so they you know they are called trade winds actually because

the trade straits man in c they are the first one to recognize this pattern of this wind anyway so wind variation or air movement air wind velocity is at a given location is also related to the climatic scenario or its location and but kind of ready is solar radiation it

receives at latitude and so on altitude is another factor at higher or tier at sea level the radiation is less at higher altitude it can be somewhat higher because of the distance that we talked about absorption by the atmosphere etcetera and this is solar

altitude angle that means when it is falling normal this is the maximum you know where it is normal so depending upon the solar altitude angle will define what is altitude angle of the sun little bit later on so thats what it is so height height also varies so therefore

ah you know at higher altitude you are likely to receive somewhat higher radiation but doesnt mean this will be warmer because there are other factors which makes it cooler one of the ways of finding out of course the all this data are available from meteorological

department there are stations and they measure this all all data could be available but one can even do a little bit of little bit of un for understanding purpose one can look into some sorts of equation and try to look at how you can calculate it out from solar

constant we know the solar constant value so you see its like this beam radiation beam radiation i s c stands for solar constant multiplied by a factor k t k t is given as this is more for understanding but if data is available let us say for new delhi data

is available design data is available then you dont bother to look into this but we understand how it is for example k t is this factor which is a function of t u is the turbidity factor m depends upon you know m is equals to one at sea level for vertical radiation right

and this this you know this this depends upon altitude this is a turbidity factor depends upon whether it is industrial or non industrial how much pollution etcetera so m is one at sea level for vertical radiation with t u equals to let us say one point eight

which is big depending upon turbidity can go to eight value of around eight or so one can find out how much the radiation will be same for a location of thousand meter altitude this m value would change m value will depend upon the distance right altitude altitude

of the ah location and this is depends upon turbidity so if you know solar constant this kind of an empirical formula point nine into m which is a function of the altitude t u is the function of atmospheric pollution or turbidity there it the tabular values are

given for industrial situation this value is higher what it means is point nine into fraction to the power some value right so if you increase that value what will happen to k t value point it will reduce point nine into some power point nine to the power two

is point eight one if it is three that much multiply so it so the value value is high for polluted environment polluted environment industrial situation and this is this again depends upon distance

right this depends upon distance so thats how it is so one can these typical calculations are shown here right these typical calculations are so shown here ok the this m values you know like this this this values are all tabulated so one can actually find it out now this if

i want to find out the radiation so what we have seen is lets look at this parameters a little bit more and lets quantify them then we will define the climate classification of tro tropical climate and so on this understand we define certain angles suppose you want

to find out how much radiation is falling onto a vertical surface or a horizontal surface wall of the building or you know roof or inclined wall or whatever it is then two things i go to know current suns position its intensity of radiation suns position relative to the

surface i am interested in right and all these are done in angular measurements or extension into spherical trigonometry so we define certain angles for example suns position can be defined i can define the position of the sun in the sky volt by two angles one

is called an azimuth angle other is the altitude angle now what is an altitude angle i think this diagram gives you for example this is the sun let us say this is my vertical surface but this is my horizontal plane this is the horizontal plane this is the horizontal plane

right this angle is a altitude angle of the sun if i take suns projection onto the horizontal plane the angle the sun rays makes with this projection we call it altitude angle right i am denoting here by beta right i hope i will be following the same notation if there

is a change let me just correct me so this is called altitude angle of the sun now that you know that thats that has nothing to do the wall so far now i also want to define the position of the sun in the sky volt so what i do i take a reference plane in the

horizontal horizontal plane i take a reference direction so lets say i can take north direction so if i take north direction then the angle the suns ray a projection of the sunray projection of the sun ray on the horizontal plane the angle that projection makes with the geographical

norm it could be i can call it azimuth angle and measure it clockwise well this is one convention i can start from south and measure clockwise so i can you know i have to follow the same convention throughout equations changes when

you because some books for example maybe people in southern hemisphere would like to follow a different convention than people in northern hemisphere so some book you will find that they are actually ah taking from north some might take from the souths but whatever it

is azimuth angle is the angle between reference direction and projection projection of the sunray onto the ground in this case its shown as phi with respect to south so phi is s o h so s o h is taken with

respect to science uh south clockwise it could be with with respect to north also so the formula we use one has to be you know you must know what are you using right so thats thats thats what it is so these are two angles which defines the suns position now i must

define the position of my surface so what i do i draw a normal to the surface i draw normal to the you know normal to the surface i draw a normal to the surface ok let me erase out the previous one so i think this is other a certain thing so this is normal to the surface

now i can find out you know wall azimuth from the same reference or if it is from the south going clockwise anti clockwise then it will be minus so as in wall azimuth right wall azimuth wall azimuth means i draw it normal to the surface

and angle between my reference direction and this but this normal in horizontal plane if it is an inclined surface i will take the projection of the normal want to the horizontal plane for example if this tilted if it is somewhat tilted i take the normal take its

projection onto the horizontal plane and its angle from a reference direction angle between this projection and the reference direction thats the wall azimuth wall wall azimuth wall azimuth thats wall

azimuth so wall azimuth and angle between this normal and the suns projection suns rays projection onto the ground that we call as wall solar azimuth what is wall solar azimuth the difference between the angle between the wall azimuth and

solar solar azimuth the angle between the normal right to the surface or its projection onto the ground and you know projection of the sun straight onto the ground thats we call as wall solar azimuth so wall solar azimuth

he is calling it as gamma which is of course whatever convention you follow it will remain same because you will start from same reference both both the times so this is how we define wall right but i have another angle for the wall or surface to be defined called tilt

angle if it is vertical wall solar azimuth and wall azimuth defines his position wall cell or azimuth defines its position with respect to sun but if it is an if it is an inclined surface then i have something called tilt angle tilt

angle is the angle that surface makes from the with the horizontal tilt angle right so thats tilt angle so thats how define a surface thats how it define so these are solar altitude ok zenith angle is ninety degree minus altitude angle of the sun zenith angle is with the

vertical you know the suns rays making angle suns rays the angle the suns ray is making the vertical that we call as zenith angle so solar altitudes zenith angle wall azimuth i have defined solar azimuth i have defined and wall azimuth i have defined now one more

angle i should define relationship with respect to vertical surfaces and suns ray incident angle what is the incident angle incident angle is the angle between the sun ray and normal to the surface so incident angle will be you see if the normal if it is inclined

surface inclined surface suppose the surface is inclined its normal with something like this suns ray is something like this angle between this two we call it incident angle so far as tilted surface incident angle will mean vertical plane it will not touch the

horizontal ground but for vertical surface you know that incident angle is basically the normal to the surface that is my this to this ray this is what is incident angle right so these are the definition of certain angles which are important for our discussion

and i think ah thats that that would be record so this is shown again just to make it clear no confusion should be there ah so this is the sun this is the solar altitude angle this is the solar azimuth angle again taken from the south here right and you know sun moves

from east to west so it will change from time to time of the day both azimuth angle and altitude altitude angle of the sun it will change from time to time of the day and obviously it will

vary from day to day also we will see that because for example you consider twenty three point five on you know north latitude on twenty first june around that june date whatever i showed you earlier twenty third june or whatever it is the suns ray is normal that

means that twelve noon it will be sharp right at the head but in december it will be somewhat inclined so you see this this angles will keep on varying day to day and as well as time of the day so we will see that how we take count for this i think i have another

diagram showing the same thing this time this is from the north this time you see the reference is north this is the azimuth angle of the sun sun moves from east to the west right and ah sun moves from east to west you know and in its inclined towards the south actually

northern hemisphere and altitude angle is this azimuth angle is this so i think this concept should be clear now there should be no confusion of this so azimuth angle is the angle between sun ray projected on horizontal surface with a reference direction

true north measured clockwise could be what will be using most of the time in our equations that we will be using true north clock wise altitude angle angle between sun ray and we will be using a notation phi and altitude angle angle between sun ray and projection

to the horizontal surface ok right and then wall azimuth i have already defined angle between reference and projection of normal to the wall on horizontal surface and incident angle angle between suns ray and normal to the wall right

wall solar azimuth as i said angle between projection of the normal to the wall on horizontal surface and sun ray projected in the horizontal plane so i think this should be clear this angle should be clear right so incident angle is angle between suns ray normal to the wall

so at this point i think i have defined this all so angles we have defined now next we can follow how do we calculate out this angle how do you estimate this angles for any point we will do that