nm0881: the point we got to last time was that we we'd shown that using these 
observations of atmospheric water vapour transport we could deduce the net 
evaporation or net precipitation at the surface so again those of you who've 
now done done problem sheet one should should be well familiar with this that 
if we if we know the atmospheric transports of water vapour we can deduce E-
minus-P as a function of latitude and so we talked about doing this for a 
particul-, er pa-, particular latitude bands and what i said at the end of last 
lecture is that we can we can carry on this procedure to consider a particular 
latitude longitude box so there's no reason why this technique should be 
restricted to particular latitudes just latitudes so the principle's exactly 
the same if we know the divergence of water vapour coming into the box er we 
can deduce the evaporation minus precipitation so there's er exactly the same 
technique so we can derive er E-minus-P er on a on a 
latitude times longitude grid and the one example that I've got here then is 
from again from these assimilated data sets so these two plots here are the 
annual mean er E-minus-P in millimetres per day er so that these are from two 
two assimilated data sets and that these are one of them just happens to be 
European centre up the road and the other is the U-S er National Meteorological 
Centre and again these are giving us firstly giving us some of the patterns 
that we would expect to see we can see that there's a E-minus-P er is negative 
and over the I-T-C-Z where we would again there's nothing suprising about that 
we've got this band very narrow band it's striking even in the annual mean how 
narrow this band is across the Pacific and across the Atlantic where the 
precipitation is exceeding the evaporation and there's other features that 
we're not going to talk about much for example this this one going er south 
south-east from the Indonesia the South Pacific 
convergence zone which is a feature i don't terribly well understand in the 
atmosphere we can see that er both marked in these plots and we can also see 
the positive regions er and again we'd expect these to me be most positive 
where there's loads of sunlight but loads of water so to evaporate so 
particularly the the subtropical anticyclones over the oceans we expect to see 
large quantities and they're they're in they're in both of the plots assuming 
there's abundant energy available over the desert regions but of course there's 
no water availability so we don't see these strong peaks over over the land 
regions and i won't write it down but again what we expect to see is E-minus-P 
becoming positive er sorry negative as we go into the storm tracks in the 
northern hemisphere so we can see we can see those there too so they're in 
general qualitative agreement but there's er there's some interesting 
interesting differences if we think about the headwaters of a big river 
say the Amazon then what sign would we expect E-minus-P to be over the 
headwaters of the Amazon if you've got a great big river flowing out of it what 
sign would you expect E-minus-P to be yeah so we'd expect strongly negative and 
if we look at the European centre one then we can f-, we find that E-minus-P is 
indeed negative we'd expect the precipitation to exceed rainfall where you've 
got a great big river flowing out of but interestingly over this region in the 
N-M-C analyses it's not negative so it's indicating that there's some er some 
perplexing differences and i've just picked out one example here over the 
headwaters of the Amazon where we think we know the answer because we've we can 
measure the river flow coming out of the region i don't i ha-, i haven't done 
that to try and say E-C-M-W-F is better than N-M-C i've just picked out one i'm 
sure we could pick out other regions of the world where er E-C-M-W-F would be 
worse than than N-M-C so er it'd be 
nice to having said that it would be nice to know how how accurate are ho-, how 
accurate is the er is the E-minus-P data what what we're going to do just to 
finish off this section is just look at a rather nice analyses that i've taken 
from a so it's at the bottom of this sheet again the quite a lot of the quite a 
lot of the papers i'm going to refer to were from the Bulletin of the American 
Meteorological Society which we have in the library in the main library and 
they're often quite readable articles and this is one where the instead of 
looking over the Amazon headwaters where we haven't got much data there's not 
many radiosonde the sense over that part of the world what they've done is to 
look in two regions where er where there are good instrumental records in in 
the United States so good you'd expect a lot of radiosonde offence in these 
regions and they've taken two two basins so this this again is just very much 
an example but er quite an illustrative one is that we'll 
look over er to er U-S river basins so the Ohio Tennessee and the upper 
Mississippi and for both these we've got er good radiosonde coverage and so the 
the data going into our assimilated data sets should be should be pretty good 
and we've also got er stream flow measurements so the situation here what do w-,
got here is if this is the if this is the catchment of the river and this is 
this is a river flowing out without with all its tributaries instead of 
calculating the E-minus-P on a nice square box what we're doing is calculating 
the the convergence of water vapour into this er so this is the the boundary of 
the catchment we ca-, we calculate and the divergence or its convergence is 
written on these slides but doesn't matter which calculate the divergence of 
the water vapour transport and we also then measure the stream flow the stream 
flow leaving the catchment so if our system is perfect the amount of rainfall 
the the amount of the amount of water 
leaving the catchment assuming this is the only way that water can get out 
ought to be the same as the amount being the convergence into the catchment so 
we can ask how how how good it is and these are two diagrams which er 
illustrate that so if we just for a moment concentrate on the upper Mississippi 
and the this is the variation of the function of time of year from January back 
through to January and this dashed line is a measured stream flow and this 
solid line is how much how much water is essentially being deposited into the 
into the catchment by by convergence and and this is for the Ohio Tennessee and 
i've just put in the annual averages and what we can see is that er is that 
these numbers don't agree wonderfully well i mean these are errors of maybe 
thirty per cent between the er convergence and the stream flow so even in one 
of these well instrumented areas where we think we've got good data er the the 
difference between and the deduced er convergence of water 
vapour by the atmosphere and stream flow is is only around thirty per cent it 
turns out that the sign differs between this in one case one's getting more 
more convergence and stream flow so where's the water going and in the other 
case er it's the opposite way round now of course there's when you've got two 
sets of measurement there's two sets of measurements could be an error so is is 
this telling us that the stream flow measurement is wrong or is it that the 
convergence measurement were wrong or is there some other way that water can 
get out this catchment the the authors i'm not a obviously not an expert in in 
measuring stream flow the authors conclude er that most of the error er is in 
the E-minus-P so we reckon we can measure stream flow with reasonable accuracy 
so we know how much water was leaving the catchment but we can't measure the 
and that we c-, the implication is that er even our best systems say from the 
European centre aren't getting this er aren't allowing us 
to deduce this convergence of water vapour and hence the E-minus-P with an 
accuracy of better than thirty per cent so this is kind of a limit of how well 
we can do with these techniques okay so er that then concludes this first 
section where we've looked at atmospheric water vapour and its transport and 
what we can deduce from it so we've deduced we've shown that one of the most 
powerful if if somewhat flawed outputs is that we can actually work out what 
the net surface water balance is which is very powerful but obviously we need 
to know how much precipitation's going on so now let's go to the next big 
section this is section section four 
precipitation and i hope a section like this i don't need to motivate why we're 
why we're doing it but what we're going to be concerned with is er is 
essentially how how is rainfall measured which again you'll have touched on in 
first year courses the problems in making those measurements and one of the 
problems we're going to come across which is a major one is the sampling if 
you've got one little rain gauge here trying to represent a huge area around it 
er how how reliable is that tiny little sample and then we'll go on to talk 
about observed distributions of rainfall so let's er spend the first first 
section thinking about techniques for measuring precipitation and of course 
there's many many different techniques we're going to touch on we're going to 
touch on obviously rain gauges radars satellites 
but let's start with the in many ways the simplest which is rain gauges and so 
this this hopefully will build on what you learned in Dr Pedder's course er 
measuring the atmosphere in the first year now we're going to as i said we're 
going to look at loads of different techniques for measuring rainfall but 
there's one distinguishing feature about rain gauges compared to say satellite 
systems and radar does anyone know what it is i mean you might not you might 
think that radars measure rainfall but they don't rain gauges are the only 
technique that actually measure how much water is reaching the surface so we're 
going to look at lots of other techniques where people talk about measuring 
rainfall but they're not actually measuring rainfall they're deducing it 
indirectly so these are the the only technique that actually measures the 
rainfall reaching the surface and don't be tricked into thinking otherwise when 
you read read about some other techniques in in books so it's 
er and the other thing that we'll find is that every other technique radars and 
satellite techniques they are absolutely rely on rain gauges so er so that's 
the other important point no other techniques can rely on them so we can go to 
some fancy high tech solutions with radars and satellites but at the end of the 
day er they can't do without er our old Victorian technology er types again a 
lot of this you'll hopefully know know very very well the the main type of rain 
gauge are storage gauges where these are generally read these are s-, simple er 
collectors of rainfall and they're normally just read er once per day matters 
up to even at operational weather sites 
sm0882: sorry i 
nm0881: that that you that you measure only once per day from a rain gauge i 
mean certainly on a site like ours they're only read once a day 
sm0882: yeah you you you then for the standard five inch gauges but the 
nm0881: mm 
sm0882: there are automatic loggers which actually do what the 
nm0881: yeah well i understand you so these these are what so so at some sites 
they would be measured twice a day but say on our our climatological web 
climatological site 
we'll only use them once a day so and then obviously the the second type of 
gauge which i'm not going to talk about much in this these lecture courses the 
the automatic gauge gauges for example the there's various different models but 
the the c-, whoop let's get it right the tilting syphon er gauge that we have 
on our on our met site which i hope you've all all seen and the these of course 
give give the amount er plus the timing of the rainfall so they give us extra 
information as i say i'm not going to talk too much about these these have real 
advantages also in t-, in terms of and when we get to talk about radars is that 
these can be set up so they can actually transmit the data they're recording so 
they'll you'll get data in real time coming back for a from an automatic rain 
gauge if they're properly set up but the other thing about them is that they're 
rather complex pieces of equipment there's lo-, many more things that can go 
wrong with a an automatic rain gauge 
than a than a storage gauge so they're less robust in many ways but we'll going 
to over the world as a whole it's these these kind of rain gauges that are 
dominant and the ones that are used most in in trying to understand the 
hydrological cycle so let's just sit back and think about rain gauges a little 
bit sorry did i failed to count properly sorry so so the first point is that 
rain gauges are the storage gauges er are the most common i think Strangeways 
in his book estimates something like two-hundred-thousand of them across the 
world but there's there's a lot of problems we have to be aware about with rain 
gauges and again some you will have touched on the first is that there's a 
there's a whole zoo of different rain gauges which are routinely used and so so 
this is potentially problems is that there are about fifty in routine use er 
around the world and the these what i've reproduced here is just a a subset of 
er nine of these nine of these different ones and i'm not going 
to look at them i-, in any great detail and the [sneeze] the U-K one happens to 
be this one and and these are ones used in in d-, b-, various other countries 
as er is indicated there and they all differ in in in characteristics they 
differ in er in size they differ in they can differ in in the shape of the 
collector things that also matter er er is the material they're made out of and 
that can have an impact on whether the surface tension forces cause little 
droplets just to sit in the gauge or run down into the collecting bottle and so 
some of those things are are indicated on this diagram er i should say one i 
don't believe this figure if it one of the figures it it tells us that the 
first number indicates the code gives the orifice of the gauge area and i don't 
think it's correct for this s-, one so i'm not sure quite what the units are 
but nevertheless the main point about this is that we've got this whole zoo of 
of different gauges and so er th-, the reason why this is a 
problem is that is that they're they're not not all er easily compared if 
you're getting rainfall measured by one gauge you can't immediately compare 
that to measurements from another gauge another problem can come if you're 
looking at trends in rainfall is if there's a slow changeover from one of these 
gauge types to another er you have to be damn sure you know that if you're 
going to not if the trends you see are are real trends in rainfall rather than 
a a trend in use from one type to another so that's er big big potential 
problem and the second problem about rain gauges i said that they're they're 
the only technique that actually measure rainfall but they're they're they're 
imperfect collectors of rainfall and what this second diagram does is just sort 
of shows some some of the different things that we have to worry about er when 
when we're thinking about rain getting into a rain gauge so one of the things 
that can happen is that rain falls into the into the mouth 
of the gauge forms a little droplet and during the during the day that water is 
evaporated up into the atmosphere and that obviously depends on the input of 
the sun and the wind rather than going into the gauge we've got other things if 
we're going to accurately know how much rainfall has gone on we need to know 
what size our gauge is now if someone if someone when they're mowing the lawn 
on the ga-, on the on the on the site manages to bash their rain gauge with a 
er lawnmower and i gather that's not er uncommon then you you end up with your 
[laugh] with your rain gauge being something less than less than circular so 
there's there's there's various different er different er sources of error 
and let's just er note note some of them potential errors include things like 
precision of manufacture do we really know accurately what the area is course 
that's c-, if you've got a a bottle full of water and we need to convert that 
to rainfall we need to know precisely how big the the collecting er orifice is 
we've got er evaporation from the gauge and again this isn't insignificant it's 
about er in some gauge it the er it's reckoned at about point- two millimetres 
per rainfall event there's a kind of a rough figure is lost just through 
evaporation another other ones that can be important depending on the gauge 
type is water either falling into the gauge and splashing out again or the 
opposite falling out of the gauge and splashing splashing in so those 
are referred to as outsplash and insplash and well all these and various ones 
i've listed there are er all of of order cause an error of order of about one 
per cent and it's reckoned reckoned that er the kind of random error due to a 
the collection of all these things a random error er to all all these things is 
about point about point-six to one millimetres per day so the random error in 
daily rainfall is what i'm trying to say is around point-six to one millimetres 
so very small rainfall amounts we have to be quite careful about how big the 
error is now the biggest error in terms of measuring rainfall is is is 
windspeed biggest by far so the biggest error source is wind and so we're going 
to spend a few minutes just er thinking about this and i've got to have a er 
and the kind of error that we're talking about so that s-, the U-K rain gauge 
the standard Met Office one has a has a has it's top at er three-hundred 
millimetres again as you all very familiar with and the 
kind of error we have ha-, have for this one is is about ten per cent at at 
four metres per second and is er and the error sorry the error is and that this 
error increasingly linearly with with wind speed so generally it's a unless 
someone has clouted their rain gauge with a with a lawnmower it's generally 
larger than than these error sources here and this this is kind of for a 
typical lowland site in in mountainous regions of course you've got more er 
wind but but more particularly 'cause in mountainous areas a lot of the 
rainfall is from is from drizzle which is small raindrops we can find errors er 
of about fifty per cent and so why where do these errors come about from second 
handout ooh sorry so again as many of you will be familiar that the reason why 
this error comes about is that the gauge itself provides a a block on the flow 
and the the air which is blocked by the the er rain gauge has to go somewhere 
and so in general there'll be an acceleration of of of the air 
both around the gauge and for our purposes most importantly is over the gauge 
so what this means is that droplets drops raindrops that would otherwise be 
falling into the gauge are swept swept from it and the situation is worse in 
mountainous areas because there's they if if you've got a large droplet with a 
not lot of inertia it doesn't care too much about the wind speed but if you've 
got a small droplet with er with not much i-, inertia so a drizzle droplet will 
tend to be more susceptible to the effects of this acceleration so that's the 
the physical cause then is the er the acceleration of the flow er due to the er 
due to the effect of the gauge itself so this is a classic example in physics 
of the measurement actually perturbing what we want to measure so the presence 
of a rain gauge is is disrupting the measurement so so what are the possible 
solutions to this er well there are there are various ones er one is to derive 
is simply do lots of measurements and derive 
correction factors so if you know the wind speed at your meteorological site 
and the rainfall you can use the wind speed to er to make a correction so 
that's actually done er quite routinely in the big big analyses of global 
rainfall i-, in some but not all of them the other technique is to put some 
kind of shield around the rain gauge which is indicated by er by some of the 
gauges here and so the idea of the gauge oh sorry the idea of the shield is is 
that it er doesn't cause so much distortion of the air flow over the over the 
gauge another one that's sometimes used but you need loads of space is 
something called a a turf wall so wall so what this is er kind of a cross 
section through the turf wall what you do is have a standard rain gauge er 
still th-, three-hundred millimetres above ground level but you surround it by 
a a turf wall some distance away from it and again that's supposed to reduce 
the editi-, er ed-, th-, the eddying and the acceleration of the air over the 
gauges reduced 
because er it it's sheltered so that's one one other technique but all all 
these gauge types have the problem in that they're trying to measure rainfall 
from from a gauge which is stuck typically thirty thirty centimetres above the 
ground so it's not measuring at ground level and you've got an acceleration of 
the flow so probably the best er solution is the one that again we can see on 
our own met site outside is the er is to put the gauge at ground level or the 
gauge opening 
at ground level so flush with the surface and surround it by a a pit with a 
grating on so let's just think about this design for a second the obviously 
putting it at ground level is is a solution but if we if we just put it at 
ground level on normal normal ground then you'd have terrible trouble with 
water splashing and running into the gauge so you want to have an area around 
the gauge where er where the rain can't bounce off so you you sink you you put 
it in surrounded by a pit but if you just left that pit open then er you'd have 
all kinds of eddying due to the sudden change in surface from the from the 
grass to a er to a deep pit so the the idea of the grating is to er not really 
give much er insplash but it gives you a a more smooth aerodynamic surface so 
you don't get too much eddying so this is generally regarded as the best 
solution it's not always a practical solution 
particularly if you're er in a rocky area and need to [laugh] dig a dig a deep 
pit to do this and it also has to be looked after you have to er make sure this 
pit is kept kept clear and weed free and if you want to which i do encourage 
you to do read a little more about this i i refer to this book b-, er a book by 
Ian Strangeways earlier in the course he's written a few nice little articles 
for Weather so these are just a few pages long so this one's er just a few 
years old now so i'd encourage you to go and read that and er he also talks 
about er his experiments with rather more bizarre types of gauge which might be 
er sort of gauges of the future so how how much difference do these these make 
well it it's typically so er er one of these er these pit gauges they typically 
measure er for a for a U-K site they'll typically measure something like three 
to six per cent more than a standard gauge and again in mountainous areas where 
we tend to have stronger winds and often smaller raindrops it 
can be er can be as much as twenty per cent so they're much more much much more 
efficient collectors of rainfall but i should stress that this kind of rain 
gauge is much much less common than the the standard the more standard type 
that we're used to seeing now there's two other kinds of precipito-, well 
there's a two two other things that we have to worry about with measuring 
rainfall it's very easy to put a rain gauge out on the on on the land but how 
any ideas how you'd measure r-, rain in the o-, on the ocean so two-thirds of 
the planet is covered by ocean and we need to know the rainfall there 
sm0883: buoys maybe 
nm0881: yeah do you think that would work very well 'cause the one of the 
problems these things are rocky you need to keep keep your gauge level and 
you've got a lot of a lot of waves splashing in and things like that so they 
don't tend to work terribly well any other ideas measuring rain in the ocean 
sm0884: put them on ships 
nm0881: pardon 
sm0884: put them on ships 
nm0881: well you can but you've got real 
problem there is keeping the ship steady and er it it tends to be many metres 
above the surface so it's not really regarded as very reliable i mean there's 
two things that tend to be done er one is just to use stations in island re-, 
er island stations and hope that they're somehow representative of the 
surrounding region which is a a a big assumption a-, another thing that's being 
thought about is actually just measuring which is amazing is is measuring the 
noise due to the raindrops hitting the surface so there are now people trying 
to develop acoustic techniques of actually having little microphones under the 
ocean literally listening to the pitter-patter of the rainfall so they're very 
much at the at the research level er and er they can be interfered with by by 
all kinds of things so that that's a problem th-, th-, the other problem i'm 
just going to touch on er briefly is is of course measuring snow snowfall which 
in certain parts of the world is a a large part of 
the rainfall again we're not well large part of the precipitation is is that 
gauges are of of of limited use and of course one of the most severe problems 
in these situations is is drifting where all you're doing is redistributing 
snow that's already fallen which ends up in your gauge and you don't know 
whether it's it's just due to drifting or whether it's due to er er whe-, 
whether it's real precipitation or whether it's due to drifting and also it 
doesn't take that much snowfall in some some areas to overtop top the gauge 
'cause obviously snow's a lot less dense so it doesn't take so much snow to 
actually fill up your fill up the top of your er rain gauge so those are some 
problems there's er so there's various other techniques that er try to be used 
one is to try and er one is that you simply forget the gauge and you just 
measure the depth of snow and and assume the volume oh sorry assume assume a 
density but even the density of snow depends very much on its form and how 
old it is or actually er take take a core of the snow and ju-, and just melt it 
and so you measure the and and calculate the rainfall or calculate the the the 
precipitation there are more subtle techniques being being being used in some 
areas and one one of these is er is that we know that the earth is a natural 
source of radioactivity and there's for example gamma rays being emitted just 
by natural radioactivity in the earth and and snow is quite a good absorber of 
those er o-, of gamma rays and so i-, if you if you measure how much 
attenuation you've got of the normal gamma rays you'd expect say measured by an 
aircraft you get can get some idea of the volume of of snow so that's a kind of 
a a very modern technique and you you probably wouldn't use that just for a a 
little area but for getting some kind of aerial average picture you can get 
some idea of the w-, the er snow water content there and i'm not going to to do 
any more and talk about this if you're interested in them 
then both er two of the books that i i've referred to Ward and Robinson and 
Strangeways er go into quite a lot of detail about snow measuring techniques 
it's really quite an interesting area and of course if in some continelt-, ar-, 
continental areas it's an important contribution to the er to the whole 
hydrological cycle okay now what we're not going to touch on here which is a 
which is a serious issue is is as i said before a rain gauge only only measures 
a a very small fraction of the total area and if say we want to know the 
rainfall over the U-K how many rain gauges do we need is it one ten a hundred a 
thousand and what we're going to do have to do later is to c-, try and come up 
with some quantative way of saying how how densely do we need to pack our rain 
gauges to get a reasonable er indication of the of the total rainfall and of 
course that will be er dependent on whether er on on the particular weather we 
have for example whether it's er frontal or or convective so 
we'll come back to that because that's and that's a very important part of 
hydro-meteorology is how you reliably average the the next technique we're 
going to touch on er for measuring rainfall is one that we can see on the telly 
every night of the week these days is radar and i'm not going to labour the 
technical side of radar the Met students will get it i think in their third 
year from Dr namex what i'm going to just going to do is is put it in the 
context of er as a hydrological cycle so er the real routes of of the radar 
growth of c-, of course radars grew out of the Second World War but it's only 
been since i guess the er mid-nineteen-seventies er we've seen a a massive 
growth 
in the use of radars for rainfall growth in rainfall radars and particularly in 
developed countries and the U-K now is is pretty well covered by by by radars 
and er what we're going to do is look at look at some of the prob-, some of the 
advantages and disadvantages of radars one of the big problems we're going to 
find is that they don't actually measure rainfall they're measuring the water 
while it's still up in the atmosphere which isn't telling you about how much is 
actually hitting the ground and we have to go through a lot of assumptions to 
to deduce that so and that's a convenient place to leave it leave it for now 
and see you nine o'clock tomorrow morning