First, here’s some Oroville dam math:
Drainage Area = 3,624 sq mi
Maximum Water Surface Area = 15,810 acres or 24.7 square miles.
So, the watershed is 147 times bigger than the maximum area of the lake. So if the soil in the watershed was totally waterlogged and there was no snow and now evaporation, then one inch of rain falling uniformly on the entire watershed would raise the lake (with no outflow) by 147 inches or about 12 feet.
Weather Underground is predicting that the next set of storms will arrive in about 24 hours in the wee hours on Thursday and drop 4.75 inches over the subsequent 8 days. If every bit wound up in the lake, that would raise the lake level, with zero outflow, by 4.75 x 147 or about 700 inches or about 58 feet.
On the other hand, they’ve been able to lower the surface level by at least 8 feet per day (and that’s with not insignificant inflows from the last set of storms). So 8 days times 8 feet per day is 64 feet of outflow.
If all goes well on Wednesday (no rain and the main spillway continues to dump 100,000 cfs), then they’ll start rainy Thursday with the lake maybe 26 or 27 feet below the brim of the no-good emergency spillway. So there is hope of making it through the next ten days without overspilling the brim.
If the main spillway holds up.
On the other hand, it could continue to rain heavily in March and well into April.
For example, here in Los Angeles the biggest rain storm I can recall was 15 inches over
Probably the scariest scenario would be a torrential warm rain that also melts the high altitude snow pack. Those are less common in California, but they do happen.
A more philosophical topic:
A common way to get yourself in trouble in a situation where you have multiple safety systems is to assume the odds of each of them failing are independent.
Say, you have three ways to drain a reservoir:
A. You can run 14,000 cubic feet of water per second through power station
B. You can run 65,000 cfs down the main spillway
C. You can run 250,000 cfs over the grandly named Emergency Spillway.
Say the odds of each one failing is 1/100. Then the odds of all three failing at once are 1/100 times 1/100 times 1/100 or one in a million. No problem!
Except, maybe it doesn’t work that quite like that. Maybe if one fails, the others are more likely to fail.
For example, if the main spillway gets damaged, are you sure you can still vent water through the powerplant?
As far as I can tell, the 14k cfs through the power station under the dam has been shut down for several days now, although I’ve read different explanations for why that is, such as worries about debris from the broken main spillway or too much water going down the main spillway into the river and backing up to the power station
And what if you’ve never actually tested your emergency spillway and the only way you’ll ever test it is if both your other outlets are damaged. Maybe the odds of it failing turn out to be more like 80%? But you’ll only find that out when you’ve got big trouble with the other two drains?
Something similar happened with the financial crash of the previous decade.
You couldn’t lose big on mortgages because, it was assumed, you could model defaults like you model deaths for life insurance actuarial purposes. Defaults happen at random. Right? A wave of defaults would be like a wave of cancer deaths. Not gonna happen.
And if your financial company was national, it couldn’t go wrong betting on the housing market, because home prices have never declined nationally, right? (Of course, what happened is that they went up so high in just four states that when home prices in those 4 Sand States plunged in 2007-08, that was enough to drag the whole country into a recession, which then hurt home prices across the rest of the country).
Oroville really needs a second main spillway, located well away from the current spillway, maybe at the other end of the emergency spillway brim, where the boaters’ parking lot is now.
At Oroville, at the moment, the good news is that the lake is down more than 17 feet below the brim at 901 feet of elevation. That’s 9.2 feet in 24 hours.
A reservoir is shaped like a funnel, so the lower the level falls, the faster the decline gets. So they might get down 10 feet in the next 24 hours.
After that it’s going to start raining again, but it probably takes a few days for the rain to trickle out of the hills into the lake. So if the rains aren’t heavy, they may not top out again over the next week, if the main spillway holds up to the pounding its taking.
The dam is about 21 feet taller at 922 feet above sea level than the 1700 foot wide emergency spillway at 901 feet, so it’s hard to see how the dam could be overtopped, short of some kind of combination of earthquake, landslide and tsunami within the lake.
Overtopping the 901 foot brim of the emergency spillway would likely erode away the base of the 30 foot high lip of the lake they built to hold the lake back.
If that collapsed that would dump about 465,000 acre feet into the Feather River about 750 feet below. That’s about 1/8th the capacity of the reservoir, so it’s a lot less cataclysmic than the dam collapsing.
On the other hand, does anybody really know what would happen from 465,000 acre feet of water plunging 750 feet down. Some of the water might boil back upstream and do who knows what to the downstream side of the dam. So, it could be an important question whether the concrete lip of the emergency spillway would fail over several hours (bad) or all at once (real bad).
A minor issue in this current crisis but one that needs some rethinking is how to manage water levels. Looking at the daily chart for the Oroville Reservoir, it looks like the management was trying to keep the water level at about 850 feet, 51 feet below the brim, even after it started raining on February 2. The maximum they can cut the lake down to intentionally by using the main spillway is about 814 feet, or 87 feet below the brim.
Between February 2 and February 6, about 2.6 inches fell. I don’t know how long it takes for most of the water to get into the lake: I’m guessing maybe 36 hours?
Then on Tuesday, February 7th they discovered the main spillway was damaged. On February 8th and 9th over 3 inches of rain fell on Oroville and the lake peaked at 902 feet on Saturday the 11th. I haven’t looked at old forecasts, but I read something from the Department of Water Resources complaining that the rain was heavier than expected over the watershed.
In retrospect, management should have been spilling water by February 2 or 3 to get ready for the week of storms coming. I don’t know how they get compensated for providing water but presumably they get paid more for having water available in hot dry August than sending it down to the sea white it’s raining in February.
Now this is probably all of a moot point regarding the crisis, because if they had been sending more water down the spillway earlier in February, the spillway would probably have been damaged earlier.
But still, all this suggests that maybe the statistical models for managing outflows are overly oriented, especially after the long drought, toward saving water at the risk of a rare catastrophic failure.
They should probably make it a goal for the rest of 2017 to drain the reservoir down to “ogee crest” of the main spillway at 814 feet of elevation, about 87 feet below the emergency spillway’s brim.