Walking by the Thames yesterday morning I couldn't help noticing how low the tide was. Not just a low tide but a spring tide (which is the extreme tide we tend to get in the days just after a full moon or new moon).
Had I come along six hours later I'd have noticed how high the tide was, almost lapping up to the top of the river wall. That's a heck of a lot of extra water filling a formerly empty space. And that got me wondering how much more water there is at high tide than low tide, and that's what today's post is about.
Within London, how much more water is there in the River Thames at high tide than low tide?
Things to note
• To keep things manageable I'm restricting this to Greater London, i.e. from Hampton Court to Aveley Marshes.
• The Port of London Authority publishes a magnificent set of tide tables annually, including pages of additional data about depths, delays and mileage, and I shall be using this pdf shamelessly.
• The cross section of the Thames is highly irregular, but I'm going to pretend it isn't.
• In particular the bed of the Thames slopes, it isn't flat, but the advantage of asking about the difference between high and low tides is that this doesn't involve the bottom of the river.
• Yes, the answer is going to be very approximate, but hopefully the final estimate will be of the right order of magnitude.
First things first. The width of the Thames isn't constant, it varies considerably from source to estuary. Even within London the width expands enormously from around 80m as it flows in from Surrey to 700m as it flows out to Kent. There's a lot more water in the Thames out east than out west. To aid my calculation I've needed to estimate the width all the way down, for which I've used Google Maps, drawn lines across the river and averaged them out.
This map shows the approximate width of the Thames at various points.
The width roughly doubles from Richmond to Putney, then roughly doubles again from Putney to Greenwich and roughly doubles again from Greenwich to Erith. If you're only used to seeing the Thames in central London you may not realise how different a river it is elsewhere.
What I did next is straighten out the Thames, all 35-odd miles of it, then chop it up into sections. I pretended all these were rectangles, all very thin and very long, calculated their areas and added them up. My resulting estimate is that the surface area of the Thames in London covers around 17 square kilometres, or approximately six square miles. That's about the same size as the London borough of Hammersmith and Fulham, should it ever completely flood.
Next I needed to know the depth of Thames, specifically the depth at high tide and the depth at low tide. Thankfully the Port of London Authority is on the case with a list of depths at various navigationally important points including Chiswick, Westminster and North Woolwich. It also gives these depths for spring tides and neap tides - the highest and lowest in the monthly cycle - and calculates an annual average. I took the figures for MHWS (Mean High Water Spring) and MLWS (Mean Low Water Spring) and subtracted these to find the difference.
This map shows the range (in metres) of a typical spring tide.
The difference between high and low tide is roughly 5m at Brentford, 6m at Wandsworth and Erith and about 6½m between Westminster and Woolwich. The maximum value (on days with a typical spring tide) is 6.7m in the Pool of London by the Tower. But the Thames is only tidal as far as Teddington Lock, above which the depth of water is all down to natural flow downstream. This means I can disregard the Thames above Teddington when making my calculation.
n.b. The difference at neap tides is rather smaller, around 4-4½m throughout.
n.b. If all you want is the average change in river height on an average day then this is about 5-5½m everywhere below Hammersmith. Again the peak is in central London.
n.b. This is why London's river piers float up and down with a hinged walkway, because they fall five metres and rise five metres twice a day.
Knowing these depths allowed me to work in three dimensions. I took each of my chopped up rectangles and multiplied by the relevant depth to calculate a volume, then added up the volumes of the resulting watery cuboids. It's all horribly approximate but I can now give you an answer to my original question.
Q: Within London, how much more water is there in the River Thames at high tide than low tide? A: 100 million cubic metres
If it's a spring tide then it's more like 110 million and if it's a neap tide it's more like 80 million, but I'm happy to approximate this to one significant figure overall which is 100 million.
Let's convert those 100 million cubic metres to other units.
Q: Within London, how much more water is there in the River Thames at high tide than low tide? A: 100 billion litres A: 0.1 cubic kilometres A: 700 million bathfuls A: 40 thousand Olympic sized swimming pools
One last catch is that high tide and low tide don't occur at the same time at all points along the Thames. The closer you are to the North Sea the earlier they happen, with a significant difference from one side of London to the other.
This map shows how times vary on a day when high tide at London Bridge is at noon.
High tide takes 15 minutes to sweep up the estuary from the edge of Kent to Beckton, and another half hour to meander through Greenwich to central London. To reach Putney takes another half hour, then half an hour more to the limit of tidal navigation at Teddington. Times for low tide vary similarly downstream from London Bridge but are considerably slower upriver, delayed by the natural outward flow of the Thames. Low tide at Hammersmith is a full two hours later than at London Bridge, and Teddington (incredibly) three.
With different parts of the Thames rising and falling at different times this means the total volume of water in the river doesn't change uniformly, so my earlier guess will be an underestimate. But it's still a decent ballpark figure, and still a heck of a lot of water.
Indeed it's London's great disappearing act - twice a day 100 billion litres of water just drains away.
