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Venice of the East

( alt title: A series of unfortunate experiments, item 6224* )

So the Minister for the Environment has determined that the flood incident at Orchard Rd was “caused by an intense storm”. Let’s dive below the surface (groan) of this statement and see where a bit of arithmetic might lead us to. This could be a PSLE maths question some day.

Boon or bane? We report, you decide.
(photo credit: Green Future / Flickr)

The PUB’s webpage on Marina Barrage (http://www.pub.gov.sg/marina/Pages/default.aspx) is most informative. From there, we learn that the barrage has a catchment area of 10,000 hectares, and that during high tide, “giant pumps which are capable of pumping an Olympics-size swimming pool per minute will drain excess storm water into the sea”.

The Minister also acknowledged in Parliament (9 Feb 2009) that any litter thrown into canals in areas as far upstream as Ang Mo Kio will end up in the Marina Reservoir.

Let’s do some sums to see how this works out when it rains. On 16 June, 100mm of rain reportedly fell in 2 hours. So that’s 50mm per hour. If it fell uniformly over the catchment area, that would be 5 million cubic metres per hour.

Of course, not all of the water goes straight into the drainage system: some gets absorbed by the soil in between or under the built-up areas (we’ll come back later to the impact of that). If 75 per cent of the water gets into the drains, then 3.75 million cubic metres per hour flows into the reservoir. 75 per cent is probably too low since that level corresponds to the estimated “runoff coefficient” in Malaysia for a residential area with 8-12 houses per acre [footnote 1]. Now an acre is 43,560 square feet, therefore that density means houses with plot areas from 3630 to 5445 sq ft with a fair amount of garden in between. But let’s assume that 75 per cent is correct.

Since it was high tide, the giant pumps would have to be activated to drain all that water out of the reservoir. If we take it that each pump can move an Olympic-sized swimming pool per minute (50 x 25 x 2m = 2500 cubic metres), then all seven pumps working at that rate will drain 1.05 million cubic metres per hour. That’s 420 swimming pools.

But the  3.75 million cubic metres coming into the reservoir is 1500 swimming pools, or 1080 swimming pools more than can be pumped per hour. Oh dear.

Based on some fancy map analysis, the estimated area of the Marina Reservoir is about 2 sq km depending on how far you follow the Singapore and Kallang Rivers upstream. That’s 2 million square metres.

So, 3.75 million extra cubic metres flowing into the reservoir every hour will increase the water level in the reservoir by 1.875 metres. IF all the pumps are switched on, and working at their full rated capacity even though they need to push against the column of high tide seawater outside the barrage. Any less flow rate, and the reservoir level will increase faster than that. I seem to recall reading that one of the pumps was not turned on…

Putting it another way, the maximum rainfall that can hit the catchment area at high tide without causing the reservoir level to rise is 14mm per hour. Which is only two-thirds of the highest ever 24-hour rainfall recorded in Singapore, which was 512mm in 1978 (that’s an average of 21.3 mm per hour).

This table shows all that with fewer words:

Item Amount Unit Formula
A Catchment area 10,000 hectares
B 100 km2 A / 100
C 100,000,000 m2 A x 10,000
D Rainfall 50 mm / hr
E 0.05 m / hr D / 1000
F Rain volume in catchment area 5,000,000 m3 / hr C x E
G Runoff ratio (% of rain flowing to drains) 75%
H Drained rain volume 3,750,000 m3 / hr F x G
High tide pump capacity:
J Olympic swimming pool volume 2,500 m3 50 x 25 x 2 metres
K Number of pumps 7
L Total pump volume per minute 17,500 m3 / min J x K
M Total pump volume per hour 1,050,000 m3 / hr L X 60
N Pump overload percentage 257% H / L – 1
P Maximum hourly rainfall in catchment area 14 mm / hr M / (C X G) * 1000
Q Undrained (absorbed) water 500 Olympic pools / hr (F – H) / J

You’re most welcome to pick holes in the assumptions. The obvious one that is not reflected is the so-called “hydrologic response” or the delay between the rain falling and the water runoff flowing into the drain system: but then, for highly urbanized environments we would expect this delay to be quite short… because there is not much soil at the surface to soak up the rainwater.

And yes, I said I would come back to the effect of soil absorption. If the normal drainage route (drains > canals > Kallang basin > sea) is walled off, the soil could be retaining more water than before. Which could make it less stable around the old, heavy trees beside the roads. Which could allow said trees to topple over when overloaded with rainwater and strong winds. As tragically happened to a motorist near the junction of Upper Thomson and Yio Chu Kang Roads, and others who were more fortunate to have walked away.

A few questions:

– What assumption for maximum rainfall (mm per hour) was used when designing the Marina Barrage?
– If less than the highest recorded rainfall, why? (bearing in mind that global warming since 1978 is expected to have led to more intense rain storms due to higher evaporation from the sea)
– If the designed maximum rainfall is lower than the highest recorded,
– could the designers have foreseen that rainfall above this level would back-flood the catchment area?
– if they could have foreseen this, which law firm is going to start the suits by flood victims?
– What is the change in soil moisture content in the catchment area since the barrage has been completed?

– If the soil moisture content has increased enough to affect tree stability due to lack of runoff into the sea, which law firm is going to start the suits by tree-fall victims (and their estates)?

*Say it in Cantonese.
Footnote 1: http://eprints.usm.my/8314/1/STUDY_ON_MALAYSIA_URBAN_RAIN_FALL_-_RUNOFF_CHARACTERISTICS.pdf, page 2

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