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Transcript of Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater -...
![Page 1: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/1.jpg)
Multi-Model or Post-processing: Pros and Cons
Tom Hopson - NCAR
Martyn Clark - NIWA
Andrew Slater - CIRES/NSIDC
![Page 2: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/2.jpg)
2 Questions:
1) How best to utilize a multi-model simulation (forecast), especially if under-dispersive?
a) Should more dynamical variability be searched for? Or
b) Is it better to balance post-processing with multi-model utilization to create a properly dispersive, informative ensemble?
2) How significant are the gains of a multi-model approach over utilizing a single best model with a few “tricks”?
a) Blending two post-processing approaches (quantile regression and logistic regression)
b) Applying “poor-man’s” data assimilation
![Page 3: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/3.jpg)
Outline
Explore these two questions using multi-model simulations for the French Broad River, NC of MOPEX
I. Multi-model: Framework for Understanding Structural Errors (FUSE)
Pre-calibration results => under-dispersive
II. Calibration procedure Introduce Quantile Regression (“QR”; Kroenker and Bassett,
1978)
III. Discussing of Question 1) -- how best to utilize multi-model
IV. Question 2 -- multi-model vs single-best model single-best model calibration procedure: Logistic Regression
employed under QR framework
![Page 4: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/4.jpg)
PRMS SACRAMENTO
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
FUSE: Framework for Understanding Structural Errors
![Page 5: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/5.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
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wltθ fldθ satθ
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Define development decisions: upper layer architecture
![Page 6: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/6.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
B
qif
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wltθ fldθ satθ
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wltθ fldθ satθ
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Define development decisions: lower layer / baseflow
![Page 7: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/7.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
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pe
S1T S1
F
S2T
S2F
A
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qbB
q12
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wltθ satθ
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Define development decisions: percolation
![Page 8: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/8.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
B
qif
qbA
qbB
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wltθ fldθ satθ
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wltθ satθ
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Define development decisions: surface runoff
![Page 9: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/9.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
B
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wltθ fldθ satθ
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wltθ satθ
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Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Build unique models: combination 1
![Page 10: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/10.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
B
qif
qbA
qbB
q12
wltθ fldθ satθ
lzZ
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q12
S2
S1
wltθ fldθ satθ
GFLWR lzZ
uzZ
S2
S1
e p
q12
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qb
e p
wltθ satθ
S1TA
fldθ
lzZ
uzZqsx
qif
qb
S1TB S1
F
q12
S2
Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Build unique models: combination 2
![Page 11: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/11.jpg)
PRMS SACRAMENTO
ARNO/VICTOPMODELwltθ fldθ satθ
lzZ
uzZ
pe
S1T S1
F
S2T
S2F
A
S2F
B
qif
qbA
qbB
q12
wltθ fldθ satθ
lzZ
uzZ
e p
qsx
qb
q12
S2
S1
wltθ fldθ satθ
GFLWR lzZ
uzZ
S2
S1
e p
q12
qsx
qb
e p
wltθ satθ
S1TA
fldθ
lzZ
uzZqsx
qif
qb
S1TB S1
F
q12
S2
Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.
Build unique models: combination 3
78 UNIQUE HYDROLOGIC MODELSALL WITH DIFFERENT STRUCTURE
![Page 12: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/12.jpg)
Example: French Broad RiverBefore Calibration => underdispersive
Black curve shows observations; colors are ensemble
![Page 13: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/13.jpg)
Goal of “calibration” or “post-processing”P
roba
bilit
y
calibration
Discharge
Pro
babi
lity
Skillful ensemble post-processing should correct:• the “on average” bias• as well as under-representation of the 2nd moment of the empirical forecast PDF (i.e. corrected its “dispersion” or “spread”)• ensemble represents a random-draw from an (unknown) PDF of hydrologic uncertainty
goal: produce calibrated ensemble forecast that has as much information content (i.e. “narrow PDF”) as possible
“spread” or “dispersion”
“bias”obs
obs
ForecastPDF
ForecastPDF
Discharge
![Page 14: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/14.jpg)
Our approach: Quantile Regression (QR)
Benefits
1) Less sensitivity to outliers
2) Works with heteroscedastic errors
3) Optimally fit for each part of the PDF
4) “flat” rank histograms
![Page 15: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/15.jpg)
Calibration ProcedureUse QR to perform a fit on 78 quantiles individually (recall:
78 FUSE models simulations).
For each of quantile:
1) Perform a “climatological” fit to the data=> simulation always as good as “climatology”
2) Starting with full regressor set, iteratively select best subset using “forward step-wise cross-validation”
– Fitting done using QR– Selection done by:
a) Minimizing QR cost functionb) Satisfying the binomial distribution=> Verification measures directly inform
the model selection
3) 2nd pass: segregate forecasts into differing ranges of ensemble dispersion, and refit models => forcing skill-spread utility
Pro
babi
lity
Discharge
obs ModelPDF
Regressor set for each quantile:
1) - 78) All individual 78 model simulations79) ensemble mean80) ensemble standard deviation81) ranked ensemble member (sorted ensemble that corresponds to quantile being fit)
![Page 16: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/16.jpg)
Example: French Broad RiverBefore Calibration After Calibration
Black curve shows observations; colors are ensemble
![Page 17: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/17.jpg)
Raw versus Calibrated PDF’s
Blue is “raw” FUSE ensemble
Black is calibrated ensemble
Red is the observed value
Notice: shift in both “bias” and dispersion of final PDF
(also notice PDF asymmetries) obs
![Page 18: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/18.jpg)
Rank Histogram Comparisons
After quantile regression, rank histogram more uniform
(although now slightly over-dispersive)
Raw full ensemble After calibration
![Page 19: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/19.jpg)
Calibration: Rank Histogram and Skill-Spread Information
SSr =rfrcst −rrefrperf −rref
X100%
(reference forecast uncalibrated FUSE ensemble)
Rank Histogram Skill Score = 0.86
Skill-Spread Skill Score = 0.75
![Page 20: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/20.jpg)
Frequency Used forQuantile Fitting of Method I:
Best Model=76%Best Model=76%Ensemble StDev=13%Ensemble Mean=0%Ranked Ensemble=6%
What Nash-Sutcliffe implies about Utility
![Page 21: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/21.jpg)
Sequentially-averaged FUSE models (ranked based on NS Score) and their resultant NS Score
Notice the degredation of NS with increasing # (with a peak at 2 models)
For an equitable multi-model, NS should rise monotonically
Maybe a smaller subset of models would have more utility? (A contradiction for an under-dispersive ensemble?)
What Nash-Sutcliffe implies about Utility (cont)
-- degredation with increased ensemble size
![Page 22: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/22.jpg)
Initial Frequency Used forQuantile Fitting:
Best Model=76%Best Model=76%Ensemble StDev=13%Ensemble Mean=0%Ranked Ensemble=6%
What Nash-Sutcliffe implies about Utility (cont)
Reduced Set Frequency Used for Quantile Fitting:
Best Model=73%Best Model=73%Ensemble StDev=3%Ensemble Mean=32%Ranked Ensemble=29%
…using only top 1/3 of modelsTo rank and form ensemble mean …… earlier results …
Appears to be significant gains in the utility of the ensemble after “filtering” (except for drop in StDev) … however “proof is in the pudding” …Examine verification skill measures …
![Page 23: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/23.jpg)
Skill Score Comparisonsbetween full- and “filtered” FUSE
ensemble setsPoints:
-- quite similar results for a variety of skill scores
-- both approaches give appreciable benefit over the original raw multi-model output
-- however, only in the CRPSS is there improvement of the “filtered” ensemble set over the full set
post-processing method fairly robustMore work (more filtering?)!
GREEN -- full calibrated multi-modelBLUE -- “filtered” calibrated multi-modelReference -- uncalibrated FUSE set
![Page 24: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/24.jpg)
Calibration Procedure (cont)I. Method I (FUSE multi-model) regressor set for each 78 quantiles:
1) sorted associated ensemble member; 2) ensemble median; 3) ensemble standard deviation; 4) all 78 models
II. Method 2 (FUSE best member) regressor set for each 78 quantiles:
First step - use Logistic Regression (LR)– Calibrate CDF over prescribed set of climatological quantiles using FUSE best member
-- for each day: resample 78 member ensemble
1) best member; 2) persistence; 3) associated Logistic Regression ensemble member
![Page 25: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/25.jpg)
Calibration Procedure-- single best model
Use QR to perform a fit on 78 quantiles individually (recall: 78 FUSE models simulations).
For each of quantile:
1) Perform a “climatological” fit to the data=> simulation always as good as “climatology”
2) Starting with full regressor set, iteratively select best subset using “forward step-wise cross-validation”
– Fitting done using QR– Selection done by:
a) Minimizing QR cost functionb) Satisfying the binomial distribution=> Verification measures directly inform
the model selection
3) 2nd pass: segregate forecasts into differing ranges of ensemble dispersion, and refit models => forcing skill-spread utility
Pro
babi
lity
Discharge
obs ModelPDF
Regressor set for each quantile:
First step - use Logistic Regression
– Calibrate CDF over prescribed set of climatological quantiles using FUSE best member
-- for each day: resample 78 member ensemble
1) best member; 2) persistence; 3) associated Logistic Regression ensemble member
![Page 26: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/26.jpg)
Regression Variable Usagefor Best-member method)
Best Model 34%
Persistence 66%
Logistic regress q 86%
0 0.2 0.4 0.6 0.8 1
Precent Used
Log Reg
Persistence
Best Model
Regressors
Regressor Usage
![Page 27: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/27.jpg)
Example: French Broad RiverI. Multi-Model Method II. Best-member Approach
Black curve shows observations; colors are ensemble
![Page 28: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/28.jpg)
GREEN -- Multi-modelBLUE -- Best-ModelReference -- uncalibrated FUSE set
Skill Score Comparisonsbetween multi-model versus single best model calibrated ensembles
Points:
-- quite similar results for a variety of skill scores
-- both approaches give appreciable benefit over the original raw multi-model output
-- CRPSS shows an improvement of the single model over the full set
post-processing method fairly robust
![Page 29: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/29.jpg)
2 Questions revisited:1) How best to utilize a multi-model simulations (forecast),
especially if under-dispersive?a) Should more dynamical variability be searched for? Orb) Is it better to balance post-processing with multi-model utilization to
create a properly dispersive, informative ensemble?“Answer”: adding more models can lead to decreasing skill of the
ensemble mean (even if the ensemble is under-dispersive)
2) How significant are the gains of a multi-model approach over utilizing a single best model with a few “tricks”?
a) Blending two post-processing approaches (quantile regression and logistic regression)
b) Applying “poor-man’s” data assimilation“Answer”: quantile-regression-based calibration is fairly robust and can do
a lot with just a single model, especially if a variety of approaches are utililized
=> Benefit of moving beyond model ensemble calibration alone, to include “kitchen sink”, including “blending” of different techniques
![Page 30: Multi-Model or Post- processing: Pros and Cons Tom Hopson - NCAR Martyn Clark - NIWA Andrew Slater - CIRES/NSIDC.](https://reader035.fdocuments.us/reader035/viewer/2022081519/56649f155503460f94c29bdf/html5/thumbnails/30.jpg)
Summary
Quantile regression provides a powerful framework for improving the whole (potentially non-gaussian) PDF of an ensemble forecast
This framework provides an umbrella to blend together multiple statistical correction approaches (logistic regression, etc.)
“step-wise cross-validation” calibration approach used here ensures forecast skill greater than climatology and persistence (by utilizing both in the regression selection process)
The approach here improves a forecast’s ability to represent its own potential forecast error:
– More uniform rank histogram– Guaranteeing utility in the ensemble dispersion
(=> more spread, more uncertainty)