Where Thames smooth waters flow

This is the basic known online Thames flow data from which the rest must be deduced -

There are also Tributaries with known flows; several Tributaries and recycled water outlets with unknown flows; and intakes for reservoirs with unknown flows.
I have also developed a method of estimating flow by finding the historic drops in the downstream reaches and finding the percentile of the current drop. The assumption is then made that this same percentile will apply to the flow. These percentiles are referred to as "QR" in the table.
I have erred on the side of guessing where I cannot prove - so though I have used 3 decimal places - some of it should be taken with a pinch of salt! DO NOT USE FOR ANYTHING SERIOUS!

There is a significant error in the EA gauge figures (unless I have totatally misunderstood them - in which case I apologise!). The drop in each reach between the level below each lock and the level above the next lock is frequently negative. And this is not just a case of the odd cm which might be down to reading errors.
I take the downstream reach drop to be (TGPZ + READING) - (SHWL + READING)
TGPZ=Tail Gate Pile Zero; SHWL= Standard High Water Level
For example at the moment Rushey Lock downstream reading is 1.671 and its TGPZ is 62.682
source: here (Click 'key information')
Shifford Lock upstream reading is 0.065 and its SHWL is 64.355
(1.671 + 62.682) - (0.065 + 64.355) = - 0.067
Since I doubt the river is flowing backwards this must be an error of at least 7 cm.
Looking at the Downstream Reach Drop Percentile figures (based on the existing EA reference figures) - hover over QR% for Rushey - below) you will see that QR68% is 0. ie the drop is negative for 31% of the time.
The QR99% figure is -0.13; so I have "normalised" the drop figures, in this case by 13cm.
This seems to make the drop in cm per Km make sense (and rarely go negative). To a greater or lesser extent this applies to all but one or two locks (the exceptions appearing to have a positive bias). The wooden spoon goes to the Shifford downstream reach with an error of 36cm. However I have not used that as my example because there appears to be a disagreement about Northmoor SHWL. I have 61.971 and the 36 cm figure is based on that. However EA now say 62.182 which would make the correction 57cm! I can only assume that the Tail Gauge Pile Zero figures are relative to the lock sills, but that their translation into ODN was not correctly managed.
[As I said - if its me that has it wrong, my apologies - and please explain!]

Estimations of Thames Flow from online data

AIM:
This page contains a complete (if necessarily inaccurate in some details) assessment of Thames flow. My aim is to be as complete and accurate as the limited online information will allow.
If there is an error in the online information, the figures here may compound it. If these figure imply a Tsunami sweeping down the Thames then chances are there is an error!
DATA:
The raw material is just nine online FLOW GAUGES available, LEVELS for every point on the River, and just fourteen Q95% Q70% Q50% & Q10% PERCENTILES available from the NRFA. There are also HISTORIC DATA on flows and levels available in various places. The links GM RL EA NRFA after the place names show the main sources. I have tried to make the estimations 'fail gracefully' when one or more sources fail to update

SOURCES:
From that data (and other fixed data such as relative heights and distances) the table is produced. Known online figures are bold and underlined as links to where they came from. Hovering over these figures will show that they are described as 'SOURCES'.

ESTIMATIONS:
The 'ESTIMATIONS' are in bold italics. The principle assumption used is that the percentile derived from an online source also applies here. Where the site is between known sources it seems a fairly secure assumption. Ewen is a special case where it seems unlikely that the Farmoor percentile applies as far upstream as that. An alternative Q is found from the downstream drop (see below). At Ewen also there are only three percentiles given (Q95% being dry). They were graphed and a full set of 100 percentile points estimated by eye. Whether the results are reliable remains to be seen. Nobody should use the results for any serious purpose!

GUESTIMATIONS:
The remaining gaps (where no percentiles are available online) were filled in by smoothing the results between known sources, allowing also for the flows from tributaries where known. There were classed as 'GUESTIMATES' and shown in italics.

SURPRISES:
There are surprises! The peak flow in low flow times is in the Cliveden Reach. Thereafter the flow diminishes due to substantial intakes for Reservoirs. These intake flows are difficult to handle because nothing is available online. All that can be done is to note where flow is lost and allocate that between the intakes in that section.

PERCENTILES:
Note that the PERCENTILES used are contrary to usual expectation. They are Percentile Excedance figures -
The Q95% is a low flow exceeded 95% of the time. Below this is drought.
The Q10% is a high flow exceeded only 10% of the time. Above this is flood.
The average flow is above Q50%. (Because the figures are biased by the huge peak flows)

METHOD:
The method for finding percentiles from historic flow data is to sort all the data into order. Then find the figure at each percent. (For example given 1000 figures the Q1% is the 10th, Q2% the 20th etc). Then given a Q% percentile the flow can be estimated.

REACH PERCENTILES:
In any given reach there will be a drop related to the flow. By finding this drop and getting Percentiles it is theoretically possible to use that to find the flow for any reach for which the NRFA four percentile figures are known. However the accuracy required is not available - and some reaches are simply not long enough. The full set of calculated percentiles are shown by hovering over the Qr% figure (or 'x' where it seems totally wrong!) Though the levels are given in metres to 3 decimal places, it is apparent that the accuracy is probably worse than ± 2 cm. However this is work in process ...

Note the error: Sunnymead Intake is BELOW Old Windsor Weir. The weir is not as marked.

This intakes diagram is from 1981 -