Understanding Earth's Energy Balance and Solar Radiation

[Music] so what we look into is basically uh as I was telling you our energy balance

right because you know whatever energy is received by that 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 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 that's what the diagram was that's what I was looking at in the last class so what we

said is 100 percent is what is received out of is 50 percent goes right to that most fair 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 phosphoric particle itself and then 50 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 you know 50 percent 5 percent gets direct

reflection from the ground 40 percent reflected by absorbed by the atmosphere or reflected back 20 percent goes as

norm we have radiation to the sky like you know as you can see this this one long wave radiation and twenty percent

would be evaporation from that see moisture etcetera right so this is again now 50 percent what is received on the

right this is what is a breakup basically long wave radiation about 20 percent you have portion from the

moisture front see and such things another 20% and convection radiation you know back from

the surface of the earth another 10% or so so that's what it is anyway this is not true.really 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's the surface area which is on to the horizontal plane or to the ground then

see if I have incident angle s cos theta or cos beta as we are calling it so B is equal to you know be you will be

basically I I see or I can write it in this manner there's a pen available right so for example IB is a beam

radiation that's falling into an area of B and IC is the radiation on the horizontal surface on the sea surface

multiplied by C area C area C right Area C is the let's say C is this area C is this area I mean with this one I can

take so C into 1 similarly this is B into 1 so this should be same because energy is same intensity of radiation is

defining what per meter squared that's what I told you other day so what 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 that's 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 IB cos beta right so because the area on which it is

falling it's 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's incident necklace more than zero this would be less

radiation to Sigrid Willis right now how do you define incident angle normal to the surface and the Ray angle between

normal to the surface and Ray that's your incident angle right normal to the surface and Ray now since this is normal

to this right this is normal to this and 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 race so angle between this will be again beta that's what I was just telling now solar

constant is the amount of radiation that is available on top of that 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 sun's position distance of the Sun from the earth is not same its elliptic orbit so

perigee APG and all those so there's the slight variation besides that Sun itself it's 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 1 3

9 5 watt per meter square some other book you might find slightly different and so on so that's called solar

constant that is received on top of the atmosphere right now that's what I was saying 2 percent variation in output of

the sun's output is itself varies and 2.5 percent due to distance but we don't care about it really we are not

interested in this we are trying to understand only ok so that's that's what it is right and that's what is you know

top of the atmosphere it is more and distance traveled here is less compared to distance level in this position so

obviously absorbed will be more so it would depend upon and normal surface obviously intensity will be

higher compared to incline surface so these are the issues that most fair etcetera etcetera these issues so that's

that's what it is so two percent variation that's what I said I already said that so that's again the similar

kind of diagram fifty percent you know five percent state ever goes out twenty percent is radiated from the diffuse

atmosphere diffuse radiation goes back cloud etc 25 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 that's specular on a polished surface but if I have a matte surface something

like paper or you know your wood etc 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 that's shown here the pen color I should change

actually try to catch change the pen color over maybe it has changed somewhat it will be actually reflecting in all

direction you don't see your image and you know you mirror you see your image back but on table or something like that

you don't see your image so that's what is happening all getting scattered in all direction I mean it diffuses in all

direction there's a completely diffused surface right so diffused radiation here it gets absorbed by atmosphere and

diffused in all direction 23 percent comes as diffused radiation from the atmosphere 27 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 the initial

discussion of hours and then 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 who in speed in

direction this we 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 didn't mention about this one this is called pyro no meter

which measures radiation a pyro no meter measure measures radiation now there are varieties of type the one conventionally

been used is who lava blackened will have a blackened blackened oh this color is not black anyway blackened sensing

device right back in surface there's a dome there is a dome concentric dome there's one dome glass dome here there's

another dome there and it has got a heavy base just a small you know quick quick understanding there's a heavy base

basis heavy heavy mass this is black and 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 holidays anyway so this is blackened surface around this which I'll

have maybe this was better black okay doesn't matter so it's something like this there are two concentric domes

there's 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 general good Junction is somewhere in the heavy mass and there'll

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 it's temperature would not change besides that is also covered by a disk

so that it doesn't reciprocate radiation so base doesn't receive radiation it has got a heavy mass it's temperature will

remain same but the blackened sensing area it receives radiation so the difference

in temperature which is actually kind of magnified or summed up because there are a 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 will ensure that there is no formation of AD or current flow you know we are movement etcetera is minimal so

that's a perimeter anyway again the instruments are not really of our and rainfall gauges are there so that you

know so we talked about this some time earlier so this is the parameter and humidity of course as I said absolute

terms moisture vapor per unit kg of dry air that's how we do so that's 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 world bulb temperature you know in saturated condition DVT minus WT 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 are normal 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

sun's radiation that's 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 let M t2

occurs where moisture is vaporizing there's latent it so since we you see it's receives energy sensible

temperature change you daugher you know sun's 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 etc 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 let's say month of July and August to

December if there's a you know there'll be difference of sun's radiation because Sun another look Sun is I mean the

artists revolving around the Sun so therefore its position of this particular location with respect to the

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 23.5 beyond certain latitude it done so

it's 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 Bailey

Daniel variation so we are trying to look into that sarnath relationship then we will understand then we can come to

the climate so if you look at sunup relationship right basically Earth has got a banking it's inclined

you know it's inclined to this plane of revolution right plane of its revolution under the Sun that's got a banking and

that's 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 it's it's got a banking I think it's

written somewhere exact some summaries rules yeah 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 not this South Pole so normal to that is a diameter diametrical circle which is

equatorial circle and sun's 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 21st December you find that it's

normal to twenty-three point five five southern latitude now what is latitude latitude is the angle at a given

location so I know I have a quad circle I have a chord circle I have a chord circle here so from the center of the

earth if I join in 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 not police ninety degree latitude of equator is zero so that's how we vary this

latitude angle so let it dangle very so location of the location of the place you know or or point another and I I

mean location on the surface of the earth any geographical location I can express it in terms of its latitude

longitude these are the one which is this kind of you know I can divide the whole approximately spherical art into

360 degrees or 180 in each direction and 118 West direction right so 360 degree and divide them into equal angles this

360 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 80 days by AG wells Phileas Fogg well just digression basically he

had a bet 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 80 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's 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 12:00 noon here

let us say in Delhi it'll be morning somewhere in Europe and so on so you got to adjust right he didn't do that

adjustment and then suddenly realise 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 that's a there's a story so if we come back to this a

longitude relates to 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's the longitude of Allahabad right you know so far it's like that so coming

back to this as you're saying longitude do we have a little bit talk about that sometime later and also so latitude

defines a position of a location on the surface of that with respect to equatorial diameter in terms of the

angle so sun's rays Falls normal to because it has got a banking this is ninety minus twenty-three point five is

how much 0.5 so this banking is sixty six point five since it's 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's 21st September around 21st March this is around 21st June summer solstice and winter solstice

and so on equinoxes desire equinoxes so sons you know sons I think this is 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 23.5 latitude north on summer solstice they're somewhere around June this is

winter somewhere in Australia you'll have summer during that period of time so Suns radiation falls normally yeah

and during this or terminal and vernal equinox it's normal to the equatorial so normal radiation can be deceived only

from twenty-three point five to twenty three point five I mean not to twenty three point five South so that's 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 32 again thirty not to thirty South right and thirty south to

sixty south and sixty to ninety that would be right so that one from sixty to ninety they are polar polar climate

subtropical and thirty not 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 etc so when you say today's weather is likely to be rainy we mean but then we talk of monsoon season

subscribe it seasonal variation depends on the climate and everything is related to a Sun so that's what it is

right so that's what we looked into even wind flow pattern is because of sun's radiation because during the summer

solid states the sun's radiation will be normal to tropic of cancer that is 23.5 not that

we call as Tropic of Cancer and see around 23.5 it passes through India by the way I'm at the bath close to another

world and I think Agartala who draw a line from Amitabha to Agartala 23.5 Indian latitude varies from eight degree

north zero antapuram somewhere around that place is eight to about Delhi's 29 it's 29 you know and 33 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 the zenith by

enlarge India's tropical now even the wind movement is dependent upon the sun's radiation because we are in summer

solstice around that period of crime 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 here gets heated up water vapor you know so

air gets heated up and basically as it heats up the cooler from the subtropical region will tend to move to fill in this

gap and then it will move you know it will the circulation this circulation pattern actually circulation pattern

starts so this is tropical front subtropic height subtropic front etcetera etcetera and polar hi

so this this is this this also is because of that wind movement is because of this so but there is a model there's

slight modification will be there if you moving upward but that is no art 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 that's 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 the swing anyway so when variation or air movement

a our air wind velocity is at a given location is also related to the climatic scenario or look is 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 etc 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 voltage due to angle of the Sun little bit later so that's what it is so height height also varies so

therefore you know at higher altitude you are likely to receive somewhat higher radiation but doesn't mean this

will be warmer because there are other factors which makes it cooler one of the ways of finding out of course that 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 fun 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 it's like this beam radiation beam radiation is C stands for solar constant multiplied by

a factor KT KT is given as this is more for understanding but if data is available let us say for new daily data

is available design data is available then you don't bother to look into this but we understand how it is for example

KT is this factor which is a function of T U is the turbidity factor M depends upon you know M is equals to 1 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 ooh tu because - let us say 1.8 which is big depending upon tabulate

can go to 8 value of around 8 or so one can find out how much the radiation will be same for any location of thousand

meter altitude this M value change embel will depend upon the distance right altitude altitude of the location and

this is depends upon turbidity so if you know solar constant this kind of an empirical formula for 9 into M which is

a function of the altitude tu is the function of atmospheric pollution or turbidity yeah it the tabular values are

given for industrial situation this value is higher what it means is 0.9 into fraction to the power some value

right so if you increase that value what will happen to KT value point it will reduce point 9 into some power point 9

to the power 2 is point 8 1 if it is 3 that much material so it so the value value is high for polluted environment

industrial situation and this is this again depends upon distance right this difference of understood so that's how

it is so one can these typical calculations are shown here right these typical calculations are so shown here

okay 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 let's look at this

parameters a little bit more and let's quantify them then we'll define the climate classification of 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 sun's position its intensity of radiation

sans 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 sans position can be defined I can

define the position of the Sun in the sky wall 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 sun's 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 that's 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 let's

say I can take north direction so if I take note direction then the angle the Sun sir a projection of the sunray

projection of the Sunday on the horizontal plane the angle that projection makes with the geographical

norm it could be I can call it as a Moute 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 throat 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 so some book you will find that they are actually taking from not some might take

from the South's but whatever it is azimuth angle is the angle between reference direction and projection of

the sunray onto the ground in this case it's shown as Phi with respect to South so Phi is Soh so s co H is taken with

respect to science uh south clockwise it could with room north also so the formula we use one has to be you know

you must know what are you using right so that's that's that's what it is so these are two angles which defines the

sun's 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 okay let me raise

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 as he month 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 is DeMuth 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'll take

the projection of the normal or do the horizontal plane for example if this tilted if it is somewhat tilted

I think the normal take its projection onto the horizontal plane and it's angle from a reference Direction angle between

this projection and the reference direction that's the wall wall lazy one wall azimuth that's wall is even so

Elizabeth and angle between this normal and the sun's projection sun's 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 azimuth 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 that's we call as wall solar azimuth so wall solar azimuth he's 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 defense's position wall cell or

azimuth defines its position with respect to Sun but if it is there 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

that's still Tyndall so that's how define a surface that's how it defense so these are solar altitude okay

Zenith angle is 90 degree minus or t2 dangle of the Sun Zenith angle is with the vertical

you know the sun's rays making angle the end of the sun's ray is making the vertical that we call as anything so

Solar altitudes anything dilwale seemeth have defined solar azimuth I've defined and wall azimuth elephant now one more

angle I should define relationship with respect to vertical surfaces and sun's 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 it's normal with

something like this some say 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 right so these are the definition of certain angles who important for our discussion and I think

that's that that would record so this is shown again just to make it clear no confusion should be there 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 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 23.5 on you know north latitude on 21st june around that june date whatever I showed

you earlier 23rd June or whatever it is the Sun say is normal that means that 12:00 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 not this is the azimuth angle of the Sun Sun

moves from east to the west right and Sun moves from east to west you know and in its inclined towards the South

actually northern hemisphere and altitude angle is this is a math analysis so I think this concept should

be clear there should be no confusion of this so azimuth angle is the angle between sun ray projected on horizontal

surface with a reference direction to not measured clockwise could be what will be using most of the time in our

equations that we using to not clock wise altitude angle angle between sun ray and we will be using a notation Phi

and or t2 dangle angle between sun ray and projection to the horizontal surface okay 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 sunset 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 Sunday projected in the horizontal so I think

this should be clear this angle should be clear right so incident angle is angle between Sun strain 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 the sandals for any point we'll do that

[Music] [Music]