# FLOW, EXCEDANCE and PERCENTILESJubilee River Flow SchematicAn attempt to estimate the whole river flow.Where Thames Smooth Waters Glide

Thames flow is usually measured in cubic metres per second: m³/sec.
Its easy to miss what this means. A cubic metre is 1000Kg of water - 1 tonne.
The Thames flow at the Farmoor Gauge at the moment is online as m³/sec.
That's tonnes per minute, or tonnes per hour, or tonnes per day, or Megalitres per day.
Is that a lot or a little? London's water requirement, a good proportion of which comes out of the Thames is about 27m³/sec.
So the flow at Farmoor, in the upper reaches above Oxford, at this moment, is about % of what Londoners use for one purpose, (or another). (To be fair to them they do use it several times!)
But is that a flood or a drought or somewhere in between?
To compare it with other places up and down the river, where the character of the river varies and various inflows from other watercourses add their contributions, and then various reservoirs take it away again , some way of standardising the assessment is required.
The chosen method is Excedance. It is a percentage. (Percentile) The percentage of the time that the present flow is exceeded. That of course results in a somewhat counter intuitive figure in that it is low when the river is in flood and high when it is in drought.
The NRFA give some standard figures to judge the flow against. These are for Farmoor:

This is a drought situation. (95% of the time the flow exceeds this).
The summer norm will be around this figure.
Only don't think this is the mean average because its not!
That's the average, skewed from 50% by the fewer very high flows
Not boating weather! We are getting towards flood!
and very definitely flood conditions!

So how do the NRFA come up with these magic figures? Its not just "suck it and see"! They measure, and how they measure! Online at the moment are 27 numbers some or all of which are applicable to each and every significant place (and in my reckoning there are 101 such places from Ewen to Teddington plus the significant side streams. That makes a database of 2727 figures some of which will change every 15 minutes.
So how are the Excedance percentages calculated? In the case of Farmoor, every day since 7th September 1992 the mean daily flow has been recorded:
6.31, 5.52, 6.81, 23.2, 32.3, 32.7, 36.9, 30.4, 20.3, .... and so on - lots and lots of apparently random numbers. So how to make sense of them? Well the Mean figure is easy enough: add them up and divide by the number of figures. NRFA answer m³/sec.
But what about all those Excedance percentages? This is where computers come in. It simply wasn't feasible in the days of calculators - and one shudders to think of trying to do it by hand, but on a computer is actually quite easy once you understand what is going on.
You simply get hold of all the figures and sort them into order from the largest to the smallest. Then the 50% figure will be exactly half way through your sorted list. That's the Q50% figure. And in that long list the figure halfway through is m³/sec.
So what is the percentile of the present figure m³/sec? You can see by eye how it fits in to the percentiles given. And that is enough for most purposes maybe. But what is its actual percentile? Go through the sorted list and the fraction through the list that you find the nearest figure is, represents the percentile. All you need is a handy list of the 365 x 27 days worth. It can be done, but maybe life is a little short to do it too often.
And you may have noticed that these figures are all comparative. A wet year will shift them. Climate change may alter them significantly. But this last year for which figures are available (the twelve months from September 2017) taken alone would reduce the figures significantly. The Farmoor mean for that twelve months was 13.674m³/sec. One of the issues for hydrologists and meteriorologists is how you cope with a shifting baseline in such data. The longer your period the more stable - but in a time of shifting climate maybe less relevant?
Given the NRFA data this is my current (pun warning!) calculation. The slight discrepancies are not significant but probably caused by selecting very slightly different dates (or treating the blanks differently).

Q0% is the largest daily mean flow in the period and for no day in the data period was that mean flow exceeded.
Q100% is the smallest daily mean flow in the period and every other day in the data period the mean flow was greater.
The NRFA quote their figures (mine in brackets) as: Q5%=52.1 (52.1) ; Q10%= 39.3 (39.4) ; Q50%=9.22 (9.24) ; Q70%=4.03(4.03) ; Q95%=0.96 (0.96) ; Meanflow=14.906 (14.92) (Qmeanflow%= 35%)

Here are the Sutton Courtenay Gauge figures:

Q5%=95.69 (95.69) ; Q10%= 68.4 (68.4) ; Q50%=16 (16) ; Q70%=7.89(7.89) ; Q95%=2.5 (2.5) ; Meanflow=27.495(27.5) (Qmeanflow%= 34%)

And the Reading Gauge figures:

Q5%=129(129) ; Q10%= 93.7 (93.5) ; Q50%=22.9 (22.9) ; Q70%=12.5(12.5) ; Q95%=5.26 (5.26) ; Meanflow=37.764(37.76) (Qmeanflow%= 33%)

And, sorry but you're not going to believe this, the Taplow and Maidenhead figures are not available from the NRFA!
The flow and heights are online but not from NRFA
The Jubilee River and the arguments over its effectiveness in flood prevention, and the question of just how much of the flow should be taken for reservoirs, would seem to me worth the effort to make these available online.
However I do have 24 months worth at Maidenhead. The percentiles would not make sense because they will be skewed by the flow in the Jubilee River.
And I also have 24 months of Taplow and equally the percentiles would not be relevant
But adding Maidenhead and Taplow daily flows, it then becomes possible to create a CLIVEDEN (ie whole channel flow including Taplow and Maidenhead) percentiles table:

Then going downstream we can see what comes out after the Jubilee River reunites with the main channel:

Q5%=173(173) ; Q10%= 128 (128) ; Q50%=40.74 (40.729) ; Q70%=26.65(26.64) ; Q95%=14.79 (14.78) ; Meanflow=59.192(59.19) (Qmeanflow%= 34%)
Here are the Staines Gauge Figures:

Q5%=191(191) ; Q10%= 137 (137) ; Q50%=33.1 (33.1) ; Q70%=17.81(17.81) ; Q95%=10.7 (10.7) ; Meanflow=55.745(55.74) (Qmeanflow%= 33%)
Notice the high flow figures continue to rise as we go downstream, but Q50%, Q70% and Q95% figures are all significantly reduced, presumably by water abstraction. Londoners are drinking the Thames!
TheWalton figures:

Q5%=201 (201) ; Q10%= 143 (143) ; Q50%=33.23 (33.2) ; Q70%=17.3(17.3) ; Q95%=9.8 (9.8) ; Meanflow=58.249(58.25) (Qmeanflow%= 35%)

For Kingston there is an embarrassment of riches, a complete data set since 1883. Only of course the methods have changed since then so here is the 1991-2018 set to match (more or less) the other gauges:

Q5%=216 (227) ; Q10%= 161 (161) ; Q50%=40.2 (33.2) ; Q70%=21.7 (14.7) ; Q95%=7.56 (6.18) ; Meanflow=65.298 (61.83) (Qmeanflow%= 33%)
Whoops, suddenly my figures do not match! The method is proved by the other Gauge figures which are essentially identical - so this must be down to using a different date range. Repeating the exercise with the full range 1883 to 2018 produced the following table:

Q5%=216 (216) ; Q10%= 161 (161) ; Q50%=40.2 (40.2) ; Q70%=21.7 (21.7) ; Q95%=7.56 (7.56) ; Meanflow=65.298 (65.3) (Qmeanflow%= 31%)
So my figures are vindicated! BUT my doubts are raised - should we really be using figures from 1883 for this one Gauge? Wouldn't it be better to use the more or less matching range to match the other gauges? Not only have the measuring methods and physical gauges changed but a whole new regime of pipeline extraction has been implemented.