[Questions] How to avoid bias adjustment for climate indicators

[saschahofmann]

Setup Information

• Xclim version:
  0.55

Context

This is not necessarily a xclim question but I would love to hear your opinion on this: We are looking into ways to avoid bias adjusting for several reasons and think that for indicators that are averaged over a period or where extreme values are computed (read with return periods) this might even be the best option.

For any indicator that's not threshold-based or multivariate, the approach is, of course, straight-forward, we can just compute the change of the projection relative to the historic period and apply this change/climate change signal to the value for the same historic period in the reference period.

Now, for threshold-based indicators, e.g. days above 35 degrees, it becomes a little bit more tricky but we think it'd be correct to compute the corresponding percentile of this threshold in the reference and extract the value for this percentile in the historic period of the projection data and then apply this threshold.

We are still discussing how this would look for SPEI or FWI but maybe a simple mean scaling BA would be enough for these type of indicators?

Steps To Reproduce

$ pip install foo --bar

[coxipi]

Hi Sascha! Interesting idea. I'm not sure about the first proposal, I would have to re-read it carefully. But for the second one:

Now, for threshold-based indicators [...] we think it'd be correct to compute the corresponding percentile of this threshold in the reference and extract the value for this percentile in the historic period of the projection data and then apply this threshold.

I think this is OK, but this would only reproduce the correction you get by adjusting the mean of a distribution. Any change in the shape of the distribution (as allowed by quantile mapping) cannot be represented by this approach, no?

[saschahofmann]

Interesting to me, mapping the thresholds to quantiles sounds like we are doing QuantileMapping just not on the data?

What change of distribution do you mean? Between historical-future?

[coxipi]

Sorry, I don't seem to get notifications for discussions.

Interesting to me, mapping the thresholds to quantiles sounds like we are doing QuantileMapping just not on the data?

Suppose you just have an indicator that counts the number of time steps that exceeds a condition. Suppose your threshold corresponds to the 60th percentile in your reference data, ref_q60. Then, when you find the 60th percentile in your simulation data (only historical data for now), hist_q60, and find the number above this threshold, hist > hist_q60

This would effectively be the same as:

1. Find ref_q60 and hist_q60.
2. Adjust hist: hist -> hist' = hist + (ref_q60 - hist_q60)
3. Find number of days with hist' > thresh == ref_q60

That's because
hist' > ref_q60 (bias adjusted way)
can be expanded as
(hist) + (ref_q60 - hist_q60) > ref_q60 => hist > hist_q60 (find the appropriate threshold -- what you suggest)

Thus, for this specific computation, you will get the same results as if you had used a single adjustment factor (ref_q60 - hist_q60) and applied it on the simulation data.

What change of distribution do you mean? Between historical-future?

Partly, but I meant mainly the difference between the simulation and the reference. In the example above, you use a single adjustment factor, so it's effectively just performing a translation on the distribution.