It's happened before.Los Angeles is essentially a desert, and like most deserts it is subject ot
Flash Floods. Los Angeles also has an extremely short rainy season, getting just 30 cm of rain each year. Historically, the LA basin has filled up with water quickly and drained quickly because, as you say, it has all those canals. But when water comes down in Southern California, it ends up in LA very quickly because the compacted desert soil has very little absorbance (and the paved regions have even less).
If a shift in weather systems left LA with getting an amount of water from the sky that one normally associates with Seattle (which is extremely possible, 300 cm is not out of the question for a single year), the Los Angeles Basin would turn into a lake. A lake with mountains sticking out of it, but a lake nonetheless.
With the current infrastructure, that would also drain out fairly well. But if the canals were overwhelmed and clogged with debris (even debris carried by the rising flood waters), the drainage might take months. And if the rainfall was repeated the next year, drainage might last all the way into the next rainy season - causing the whole situation to achieve a semi-permanent status.
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Remember, by 2070, noone has been maintaining the LACDA Project (Los Angeles Country Drainage Area) for nearly 60 years. Which means that it probably doesn't work any more. People have by this point built buildings in and around the canals, so when the flood waters rise, there is lots of material to make debris dams out of to keep the flood waters in.
LA Country is considered susceptible to three main natural disasters:
Earthquakes (which LA is very prepared against)
Flood (which LA is
currently somewhat prepared against)
Fire (which LA is moderately prepared against currently)
The problem with the Flood and Fire protection is that these are
collective protections. Once everything gets privatized in the Shadowrun future dystopia, those don't exist anymore. Earthquake protection, on the other hand, is an indivdual protection for each and every building - so it's still there after everything is owned by corporations.
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And yes, raging firestorms could also destroy LA. But then it wouldn't be covered in poisonous water and governmental indifference with all the juicy parallels to New Orleans.
-Frank