Transcript Idealized Testing: An Example using Quantile Mapping Joe Barsugli What is Quantile Mapping? • A bias correction technique that corrects for the whole distribution.

Idealized Testing: An Example
using Quantile Mapping
Joe Barsugli
What is Quantile Mapping?
• A bias correction technique that corrects for the whole
distribution of values, not just the mean
• Has been used in weather forecasting to adjust forecast
model output
• Used in the BCSD and BCCA downscaling method
• We will focus on the “BC” in these methods
BC
One GCM; and Bias Corrected data using
quantile mapping
GCM
1950
2000
2050
2100
36 GCM runs from 16 GCMs ;
A2 emissions scenario
GCM
BC
When run through a hydrologic
model the amounts shown here lead
to approximately 1 billion cubic
meters of additional flow at Lee’s
Ferry in the Bias Corrected Runs
The percent change in the future for the bias corrected data is
modified from, and can even differ in sign from, the GCMs.
This is not true everywhere, and depends on the details of the
probability distributions.
Q: Can we use idealized testing to better understand what
features of the probability distribution contribute to this
effect?
Assume that precipitation follow a Weibull Distribution (this has been assumed in
many publications for daily precipitation going back to at least Dan Wilks’s work in the
late 1980’s)
We will be looking at
distribution like this one
Quantile mapping formulas are solvable with pencil and paper for the Weibull
distribution.
If we assume that the Past and Future GCM data, as well as the past observed data
are all from Weibull distributions with different parameters, then we can compute the
bias corrected future data, which is also a Weibull distribution. We can then see if the
same “wettening effect” happens, and under what combination of parameters.
BC change -8.6%
GCM change -10.4%