Monday 13 November 2023

Rains and returning period

Auckland's 1-in-200 years flood was given the name Anniversary Weekend flood 2023 on wiki...or simply just the Anniversary flood. The scars are still visible around, and recently a review has just been concluded from the Metservice side. The conclusion is that their rain prediction is poor.

Um...thank you.

I think most Aucklanders aren't surprised as the forecast tends to underestimate rains heavily all the time, where longer forecasts on precipitation are merely better than flip of a coin. We used to read radar directly because we can pinpoint the location of interest and is more accurate in general. We can at least tell whether a region is going to rain in an hour while the forecast can't!

When I wrote about the flood earlier this year, I said it's not a good time to talk about the 1-in-N-years thing because it's not the right time to do so. I think we are in the position to do it now especially when a comparable event happened later this year: the torrential rainfall over Hong Kong on early September 2023: record breaking 158mm in one hour, 800mm+ widely over the Island over 12-24 hours. A rare city wide flood that immediately recalls what happened over Auckland some times ago. It ended up being described as a 1-in-500-years event but was taken as excuse to inability of the government.

There are too many things we can talk about the two storms here like crisis management or building standards but I just want to focus on the numerical and scientific bits here as below.

Auckland's major flood on 27 January was caused by atmospheric river dragged near NZ by remnants of Tropical Depression 06F and blocked or forced stationary by a nearby anticyclone/high. At the same time, Hong Kong's flood was caused by the remnants of Typhoon Hanna (11W), stuck in a saddle field right above Hong Kong so that rain bands kept sweeping in.

The similarity is clear: both floods were caused by remnants of tropical systems that are stuck so that the affecting period is prolonged. But then it seems like this is the only recipe for such rainfall: normal lows can't be that powerful so it must be something related to tropical systems; mature systems (e.g. typhoons) are primarily driven by higher atmospheric features and seldom stuck like that so it has to be as weak as depressions or lows as remnants of the previous systems. Even so we need that to get stuck over an extended period (e.g. 12h) and provide enough water vapor to the system for that to work. Without considering other more extreme events like volcanic eruption/nuclear winters etc, is there any other possible way to produce such rainfall?

I suspect that the long tail on rainfall distribution over considerable period of time -- is not normal, because it is only produced under a specific combination of meteorological events. The distribution is composed of some 'common raining events', then events like what caused the above floods that is responsible for part of the tail, then more extreme event for the rest of the tail. Just think of adding three unequal Poisson (not saying these distribution is Poisson of course) distributions together and what would you get? Of course these are more speculation than anything, but that should allow us to get into what causes these rainfall outliers.

The next thing we should think about is the returning period which is the most talked about. If the distribution is not even normal how can we calculate the returning period? Another problem is, even with the returning period on our hands how should we set standards using that? 

The 1-in-500-years claim of the Hong Kong flood is based on the peak 1 hour rainfall 158.1mm which exceeds the 500 years mark (~155mm) on the 1hr rainfall returning period table. Auckland's 1-in-200-years flood is based on NIWA's claim but I can't find any numerical evidence supporting that. They were referring to the specific flood on 27 Jan so it might be 24hrs cumulative rainfall (or least 12, considering this is how long it lasted). Of course the flood is record breaking in all timeframes like the monthly precipitation of 539mm easily exceeding any of the months in the last 170 years. 

It is clear that the officials picked 200 and 500 respectively because this is the greatest that can be interpreted out of the numbers so that it sounds as serious as possible. But to those who want to use the returning period for risk management what's the proper timeframe to look at?

Unlike water level for dams where the returning period is duration independent, drainage capacity isn't and could have very different implication over different timeframe. A 1-in-200-years 2mins rainfall may sounds scary but is nothing to the drainage. The returning period of monthly rainfall is also pretty useless for drainage system because all you care is whether or not you can handle the spike. If the 538mm rainfall is distributed evenly then we will receive ~0.7mm of precipitation per hour nonstop for a month. Bad to have in the summer but no big harm at all.

Now suppose we take 1hr and 12hr rainfall into consideration more than anything else. Does it make the returning period a reliable indicator? On one side you say yes because it covers flash floods that are  immediately visible as well as the whole raining period that the system is designed to withstand. But consider this: a typhoon just swept through Hong Kong exactly a week before the flood that introduces significant amount of trash into the drainage which of course weakens its capability to drain. Should we take the two as independent event? If not, is it necessary to take returning period of longer timeframe back into consideration? Same thing happened to Auckland as a subtropical low hit Auckland 4 days after bringing more precipitation, then there came Gabrielle early February that again broke the still sagged SH1.

The lesson here is that the returning period is a highly on-paper number, easily manipulated by the data interpreter, highly confusing to the public and hard to use as a reliable reference. The bottom line is that it's something that you can always calculate and compare...but that's it. 

Oh and before I conclude it's unfair not to say something for the forecast institutes. Precipitation forecasting is a very complicated task even in 2023: it is very random in locality and intensity. The difference between rain and no rain could just be hundreds of meters apart, and there is no point to forecast upon such precision. Even if we can tell if it's going to rain or not, the cloud may develop or dissipate at any moment. This is particularly true in case of heavy rains. Just look at the radar -- the chances of actual heavy rain is much higher than finding signals of "heavy rains" on the chart! These are true limitations of technology up to now and are things that can't improve overnight. Still I am grateful that they are thinking to improve. Let us hope that floods like that don't ever happen again.

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