I like what you're trying to accomplish, but you are missing a very helpful piece of information in your analysis. I'm sure you noticed how poor of a predictor rain fall is in your assessment of how much water will be added to Lake Oroville. This is largely because Oroville is filled from Sierra Nevada runoff. If a particular storm system is warm (as was the case with the latest one), it will mostly rain in the Sierras. This has a twofold effect: one, the precipitation doesn't stay put at higher elevations (as snow does), and two, it melts the existing snow, causing it to also be added to the downstream water accumulation. So a key part of forecasting is not only to look at expected precipitation, but also the expected snow levels.
"I'm sure you noticed how poor of a predictor rain fall is in your assessment of how much water will be added to Lake Oroville."
Having worked in hydrology (in forecasting) for a year out of college -- yeah -- you might as well use tea leaves and Tarot cards. People can't even predict weather. Let alone: Snowpack + weather.
As a meteorologist, let me offer this apology on behalf of my field: Predicting rainfall is really hard, especially in a particular location. Unlike dynamic variables like temp, pressure, or wind velocity, rainfall depends on just about every term, including sub-grid scale topography. We can have a good idea of how much total water a storm has to be precipitated, but when, where and how it falls is harder.
FWIW, predictions in my neck of the woods (the SF peninsula) are uncannily accurate. Rain is usually predicted with high reliability a week in advance, and we can generally rely on the hour-by-hour predictions a day or two ahead. I realize that our location is particularly easy to predict because of how our weather is dominated by the Pacific ocean, but you've got to take your wins where you can find them.
Most of what you said is the opposite of what the science shows. SF is particularly hard to forecast because its weather is dominated by the Pacific Ocean (in winter at least). In other places we get reasonably reliable 10 day forecasts, but because initial data (observations) are sparse over the ocean, we have less confidence in the forecast here, long range forecasts are less likely to verify. Satellites do help, but it's not like there's a vast network of Doppler radar buoys out there y'know? Anyway, we've gotten good at this despite the ocean, not because of it.
We've gotten a lot better on timing with better satellite data. But so far as precip amounts, and type? Let's just say it is not the exact science we want it to be.
FWIW, I've lived all over the world, and now the bay area. And I am consistently impressed with how good the weather predictions are for the area. So thank you for the hard work. I know I'm impressed.
I've already wondered how meteorology works in terms of computer models. Could you recommend some reading material that would be a good introduction for someone completely new to the field?
Now we have powerful computers and lots of data freely available (well maybe less now thanks to Trump), I've always dreamed of running an old computer model say from the 1980s at home.
The proper approach with uncertainty is an expected value calculation. That way the uncertainty regarding rain within the watershed, the temperature, etc. can all be factored in.
What is missing in this nice analysis is the economic impact. If 200k were evacuated, and roughly estimating they have $100k in real estate each for housing, and say $50k each for business real estate in the flood risk area, that comes to $30B. Assuming some will not be a complete loss, say $15B in real estate loss if the emergency spillway fails (neglecting job and economic activity impacts, etc).
Now if you have a 5% chance of failure in this next storm, the expected value of the loss is $750M.
This value now can be used to decide how much effort should be put into emergency repairs, something less than $750M.
Say these numbers are in the ballpark. Is the emergency repair effort taking place sensible? I suspect not. To avoid a loss in the billions, you'd expect a bigger effort. I'd expect every shotcrete contractor in the western US on hand, rebar being placed by helicopter, steel beams, 50 pieces of heavy equipment, temporary tanks of diesel fuel, and a real sense of emergency. Not seeing it.
Seems like they are dropping super sacks of rock. They might be dropping super sacks of dry mix, but I highly doubt it - the money just wouldn't be there. If they're just looking to armor then the rock would more sense.
Shotcrete and concrete are difficult to place via helicopter. Both need to be pumped (or hand placed) to get a good product, which can't be done via helicopter.
Couldn't you put some kind of plastic membrane over the top of it once it's cured enough to not deform? The reason it needs so long to cure is to make sure the surface is hard enough to withstand erosion from turbulent water flow. If it's not directly exposed to the flow, you should be able to use it much sooner.
I'm not trying to diminish how difficult it is to get precise estimates...but how precise do you need? A 1ft rise in water levels is almost 5 billion gallons of water. That's a pretty big margin for error.
5 billion gallons / 9350 km² is just 2mm. If that fell in one hour, the flow into the lake would be 5200 m³/s, except it would be lower since it takes time for the water to reach the lake.
The normal flow of the spillway is 4200 m³/s.
Have I done something wrong here, or missed something obvious? 2mm/hr is a pretty moderate rain.
Not all the water (normally!) makes it to the lake, and the average rain over time is probably less than that. Otherwise, no, the math looks fine, but this is why the reservoir is useful as a flood-control system. It can take the fairly large flow caused by even moderate rain, and spread it out over time.
Things get iffy once you have heavy rain for long enough that the soil saturates.
Right. This is different. I never worked in CA hydrology during times when you worry about spill. CA Hydrology was always about allocating a very scarce resource to the people that need it most -- and offering your best prediction of how low reservoirs would go -- and praying snow pack would last. Now? W(who)tf knows.
Actually, there are EXTREMELY good models around rainfall, snowfall, SWE, rainholding capacity, and runoff. The forecasts I see for the Sierra basically nail snow:water ratios and snow levels to within 500ft.
Genuine question here, if predicting the weather for a localized area such as a small region Cali is "tea leaves and Tarot cards", why are we so confident in the prediction of the climate for the entire planet?
Q: If forecasts can’t get next week’s weather right, how can we trust predictions for decades or centuries from now?
A: Weather and climate are not the same. Weather is individual, day-to-day atmospheric events; climate is the statistical average of those events. Weather is short-term and chaotic and is thus inherently unpredictable beyond a few days. Climate is long-term average weather and is controlled by larger forces, such as the composition of the atmosphere, and is thus more predictable on longer timescales. For the same reasons, a cold winter in one region does not disprove global warming.
As an analogy, while it is impossible to predict the age at which any particular man will die, we can say with high confidence that the average age of death for men in industrialized countries is about 75. The individual is analogous to weather, whereas the statistical average is analogous to climate.
OK, I'm going to play devil's advocate. That answer doesn't really seem all that good since it doesn't address the predictability at all.
To use the human lifespan argument, yes we can say the average lifespan for men is 75, but that's looking backwards. How good would we be at predicting future life expectancy? I'd say we're probably pretty bad at it.
Also, yes, we're trying to predict the average temperature of the earth with climate models. However, that average is determined by the climate in a number of different areas.
How good would we be at predicting future life expectancy? I'd say we're probably pretty bad at it.
The fact that businesses selling life insurance make money over the aggregate, despite sometimes losing money in the individual, seems to imply we're decently good at it.
You ask "how good are we at predicting future life expectancy?"
Unfortunately I can't do an analysis right now, so hopefully this qualitative discussion will help answer it for you.
If you look at historical life expectancy, grouped by cohort, you'll see a relatively smooth function with easily identifiable trends. So, group everybody into the year they were born, and graph their average lifespan.
Past trends do not guarantee future performance, however a smooth function implies an underlying order to these observations. This is the core thesis everything else stems from then; we assume there is a relationship between the year someone was born, and their average lifespan.
Now a function relating just the year they were born to their average lifespan is almost certainly too simplistic. Where they were born, their socioeconomic status, and so much more will affect that number. The problem we have is that many of these parameters are hidden to us. Even worse, we can't even say for sure what all the parameters are! What we can do, however, is estimate the effect of these parameters, and even estimate the effect of parameters we don't know exist.
This process is inherently fuzzy, as statistics and modelling from less than perfect knowledge must be, but the models that have been created have proved to have great predictive power. The existence and general profitability of the life insurance industry is evidence to that.
We use models all the time, and for the most part this goes unquestioned. Regardless of your model of the sun and planets, it better predict the sun rising tomorrow, or else it's got some pretty big gaps. If someone told you they predicted the sun would not rise tomorrow, you'd be rightfully discredulous. But you'd be as equally discredulous if someone told you it was impossible to predict the future, so we really don't know if the sun will come up or not.
We test our models on their predictive power. Even if our models were bad, we don't simply throw them away because they are not perfect. We work to refine them and make them more accurate. Asimov's essay on the relativeness of 'wrong' is well worth the read.
So, life expectancy is a decent model, and is constantly being improved upon as we learn more about the world. Something may come along and cause us all to die, or live forever, but that remote possibility is no reason to throw our hands in the air and say the whole exercise is pointless.
Similarly, our climate models may be inaccurate or not account for some unknown future event, but that is not a reason to stop refining them, nor a reason to say "we can't know the future so this is pointless."
I understand that you can model something and constantly improve it, but that still doesn't inspire confidence in the model's predictive ability.
Maybe a better answer would be: "Yes, weather forecasts are often wrong, but climate modeling from 10 years ago accurately predicted today's global temperatures with a margin of error of +/- 0.5%."
I'd say that's a worse answer, because while it explicitly answers the question, it doesn't address the flawed assumption in the question itself: predictive failure in micro implies predictive failure in the macro.
ofc, answering the question as well would still be useful.
Can you provide any evidence that "climate modeling from 10 years ago accurately predicted today's global temperatures with a margin of error of +/- 0.5%." I don't believe that statement. Perhaps you were saying wouldn't that be great proof if it were true.
Right, you might say that our models predict the sun will rise tomorrow with a high level of confidence but you would have to give a slightly lower level of confidence for the sun rising the day after tomorrow and still lower one million years from now. All models have diminishing predictive power.
I agree with you, however our model of the solar system gives us pretty good confidence about macro level events even into the distant future.
To the specific example of the sun rising - for the sun to stop rising, the earth has to either become tidally locked about the sun, or the earth or sun must be destroyed.
One article[0] says:
Scientists have reliable data on the Earth's rotational speed, based on observations of the sun's position in the sky during solar eclipses, going back some 2,500 years. Although the rotational rate hasn't declined smoothly, over that period the average day has grown longer by between 15 millionths and 25 millionths of a second every year. Even at the faster rate, it will take 140 million years before the Earth's rotation slows enough to necessitate a 25-hour day.
The real crux of this matter is predictive power. We can get a rough understanding of the predictive power of a model by asking the question "at what point does the expected error in our prediction make that prediction meaningless?" For example, how accurate does a population model need to be for us to be willing to use it to predict population distribution in 50 years? It's fair enough to say that our models are not capable of predicting the population distribution in 1 million years, but no model could and it's unlikely we would be able to utilise such a prediction even if it were made.
As I said before, the existence of a profitable life insurance industry is evidence that we are good at making lifespan predictions at the individual level, in aggregate. Every time a policy is written, it's like a wager is being made between the insured and the insurer. Yes the insurers lose some bets, and some years they may even lose a lot of them, but it's clear that the odds are stacked in their favour, for otherwise they would be unable to offer insurance at all.
If you were to bet on what the climate of this planet will look like next year, how would you make your prediction? If you were to offer odds, how would you structure the book to make sure you win?
Yes, the absolute accuracy of climate models is going to diminish over the next 1, 5, 10 years, so the error associated with a specific global average temperature prediction (for example) will increase. That doesn't mean the actual temperature is just going to fluctuate wildly! Next year the global average temperature may decrease. It is extremely unlikely that in 10 years time the average temperature will have decreased, even if there is drastic intervention. Any bookmaker looking to make a profit would be offering odds on how much the temperate increases, not merely on if it increased or not.
Yes, predictive power is going to decrease as time goes on. No, that doesn't mean models are useless, nor that we can't have predictions that become more likely as time goes on.
Another analogy: we can't look at a single atomic of Uranium and tell when it's going to decay - but that doesn't stop us knowing enough about the bulk nucleonics of Uranium to be able to build sophisticated reactors.
Thank you, that helped quite a bit. It makes sense, as predicting when a single individual will die (a single area will have <x> weather), is different than, the observed trend is males live to avg. 75 years. Makes sense to the layman!
For the same reason that, even though it's 'tea leaves and tarot cards' trying to predict the exact geometry of surface waves in a square meter of ocean, we can predict the time and height of a high tide with high accuracy.
Imagine a cannonball, on its flight through the air. Attached to it is a feather. We can't predict the fluctuations of the feather, as it is whipsawed by the airstream of the cannonball, but this has almost no effect on the trajectory of the composite.
Do a search for "Lorentz attractor". It's the result of an early numerical weather model.
The weather is a particular point on the twisted surface; it is impossible to calculate what point you'll reach at a given time, for reasons that you'll find in a search for "Lyapurnov exponent".
The climate is the butterfly shape. If you run the simulation with different parameters, you can look and see how this changes.
The Lorentz equations are much simpler than a realistic weather model, but the same principles apply to the complicated models, and to the laws of physics that the atmosphere actually follows.
The analyses do not appear to take the size of the watershed into account either. A large watershed drains into this reservoir. As such, distant storms can still have a large impact on the water levels. Time to concentration (the amount of time it takes for water to flow through the watershed) will play a large roll in the inflow rate.
And the expected temperature of the falling precipitation, and a whole lot of other meteorological stuff which is involved, so in reality this dataset, while admirable for effort, is really useless as there are way, way, way too many unaccounted-for variables.
Thanks for the suggestion. We had a discussion internally as to why inflows are higher this seasons compared to previous periods with comparable precipitation levels. We thought it might be due a multiple storms this season or because of discharges from the upstream reservoirs.
The timespan we used in the SQL query calculates the inflow/precipitation ratio based on the last few weeks and we use that as an input into the estimate.
The 1997 flooding in CA was mostly due to this issue of warm rain + snowmelt, so searching around for information about that might be good.
This guy seems to have testified about this flooding damage and claims 30 inches of rain around Oroville, with 18 inches of coincident melting, thus exceeding their worst-case scenario.
Oroville itself is at 900 feet altitude, but the Oroville watershed extends into the Sierra Nevadas, including alpine valleys at 5000 feet. The Sierras have record snowpack this year (150 inches in places, so I hear).
Oroville is both north and west of where you are. Significant rain shadowing occurs east of the Sierra. and I think the "5000ft high" watershed number for Oroville may be low.
Yep all true. There's probably not any snow below even _6,000 or 7,000ft_ in the Sierras right now because the last storm, which was warm/rainy, melted it. This is another reason why the next storm won't put as much water into the reservoir.
I'm having trouble pulling that map up, but I believe there's snowpack at 5500' and above right now, and there's a huge amount of land upstream of Lake Oroville that is above 5500'. My data is this: here's an Instagram tagged at Emigrant Gap (5200') taken four days ago.
I would note, as one example, the ground saturation is insane. I have a sloped backyard in Moraga, CA that goes to a creek which has been running non-stop since the first rains. It's been 3 days of sun and the ground is squishy and it's totally damp under the house. Pre-existing ground saturation will play a part in how fast the rain gets to the lake.
I was young, but I was there and remember it well. That flood was crazy. I remember being boxed in with my uncle and he had to do some crazy stuff to his truck's air intake on the fly just so we could get through a deep puddle and out of the box. In retrospect, we probably shouldn't have driven through deep water.
I could find one instance of a word beginning with "ero". An article elsewhere was highlighting the possibility of catastrophic erosion. Outflow rates should have an associated catastrophic failure probability estimate and then we can get a realistic cap on sustained outflows.
Outflow rates should have an associated catastrophic failure probability estimate
The emergency spillway was originally rated for 350,000 cfs (cubic feet per second), but when it came into use, the erosion started causing a risk of catastrophic failure at just 6,000 - 12,000 cfs (this is what prompted the evacuation order, and the re-opening of the primary spillway to its capacity).
The catastrophic failure probability estimates simply haven't stood up to real-world testing.
