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Bias Adjusted Precipitation Scores Fedor Mesinger NOAA/Environmental Modeling Center and Earth...
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Transcript of Bias Adjusted Precipitation Scores Fedor Mesinger NOAA/Environmental Modeling Center and Earth...
Bias Adjusted Precipitation Scores
Fedor Mesinger
NOAA/Environmental Modeling Centerand
Earth System Science Interdisciplinary Center(ESSIC), Univ. Maryland, College Park, MD
VX-Intercompare MeetingBoulder, 20 February 2007
“The higher the value, the better the model skill is for the particular threshold”
(a recent MWR paper)
Example:Three models, ETS, Bias, 12 months, “Western Nest”
Is the green model loosing to red because of a bias penalty?
BIAS NORMALIZED PRECIPITATION SCORES
Fedor Mesinger1 and Keith Brill2
1NCEP/EMC and UCAR, Camp Springs, MD2NCEP/HPC, Camp Springs, MD
J12.617th Prob. Stat. Atmos. Sci.; 20th WAF/16th NWP (Seattle AMS, Jan. ‘04)
Two methods of the adjustment for bias(“Normalized” not the best idea)
1. dHdF method: Assume incremental change in hits per incremental change in bias is proportional to the “unhit” area, O-
H
Objective: obtain ETS adjusted to unit bias, to show the model’s accuracy in placing
precipitation(The idea of the adjustment to unit bias to arrive at placement accuracy:
Shuman 1980, NOAA/NWS Office Note)
2. Odds Ratio method: different objective
dHdF method, assumption:
can be solved;
a function H (F) obtained that satisfies the three
requirements:€
dHdF
= a (O − H ), a = const,
• Number of hits H -> 0 for F -> 0;
• The function H(F) satisfies the
known value of H for the model’s F,
the pair denoted by Fb, Hb, and,
• H(F) -> O as F increases
A downside: if Hb is close to Fb, or to O,it can happen that
dH/dF > 1 for F -> 0
Physically unrealistic !
Reasonableness requirement:
€
Hb ≤ O(1−e−Fb /O )
“dHdM”method:
O
H
a
b
c
d
F
Assume as F is increased by dF, ratio of the infinitesimal increase in H, dH, and that in
false alarms dM=dF-dH, is proportional to the yet unhit area:
€
dH
dM= b(O − H)
€
b = const
One obtains
( Lambertw, or ProductLog in Mathematica,is the inverse function of
€
z = wew )
€
H(F) = O −1
blambertw bOeb(O−F )
( )
Results for the two “focus cases”,dHdM method
(Acknowledgements: John Halley Gotway, data; Dušan Jović, code and
plots)
Impact, in relative terms, for the two cases is small, because the biases of the three models
are so similar !