Should a local bias correction be applied to climate scenario data?

Not to the change factors themselves. A delta-change projection supplies a difference (or ratio) between two model climates, in which the systematic model bias largely cancels; a reanalysis-to-observation correction is an absolute level correction and does not belong on a delta. Correct the baseline instead, then apply the delta on top:

Details

ERA5 hourly -> extract_era5_lake_met()
            -> fit_met_bias_correction(era5, obs)
            -> apply_met_bias_correction(full record)
            -> met_to_daily()                      # corrected baseline
            -> delta-change: extract_climate_point(), monthly change factors,
               add / multiply onto the baseline
            -> disaggregate_met_to_hourly()        # if sub-daily is needed

See vignette("scenario-workflow", package = "metscale") for a runnable end-to-end example on Lake Rotorua.

Applying the local correction to the baseline before the delta-change step is what makes the composition well defined, whatever kinds the two adjustments are: the NIWA CCAM change fields are additive in degC for temperature, percentage for rainfall, wind and humidity, and additive in W m-2 for shortwave, while fit_met_bias_correction() picks the transform per variable. Do not try to fold the local correction in after the delta - correct first, shift second.

A caveat worth carrying: both steps assume stationarity. A correction fitted over a few years of observations is being asserted to hold under a future climate. Prefer method = "scale" over quantile mapping for a baseline that will be projected, since a fitted CDF extrapolates poorly outside its training range.

See also

bias_correct_daily_baseline(), fit_met_bias_correction(), extract_climate_point(), disaggregate_met_to_hourly()