MPO 674 Lecture 15 3/3/15. Bayesian update Jeff Anderson’s Tutorial A | C = Prior based on...
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Transcript of MPO 674 Lecture 15 3/3/15. Bayesian update Jeff Anderson’s Tutorial A | C = Prior based on...
Bayesian update
Jeff Anderson’s Tutorial• A | C = Prior based on previous information C• A | BC = Posterior based on previous
information C and new information B• B = New observational information
A | BC B | AC A | CPosterior Observation Prior
Forecast Model Cycle
MODEL “FIRST GUESS”
OBSERVATION PREPARATION
DATA ASSIMILATION
INITIAL CONDITIONS00 UTC
MODEL “FIRST GUESS”
OBSERVATION PREPARATION
DATA ASSIMILATION
INITIAL CONDITIONS06 UTC
MODEL “FIRST GUESS”
OBSERVATION PREPARATION
DATA ASSIMILATION
INITIAL CONDITIONS12 UTC
MODEL “FIRST GUESS”
OBSERVATION PREPARATION
DATA ASSIMILATION
INITIAL CONDITIONS18 UTC
Integrate 6 hours
Integrate 6 hours
Integrate 6 hours
Integrate 6 hours
FORECAST
Locations of meteorological stations from which Richardson obtained upper-air observations for his first numerical weather prediction. Squares marked 'P' provided atmospheric pressure values; those marked 'M' gave atmospheric momentum.
“Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances and at a cost less than the saving to mankind due to the information gained. But that is a dream.” L. F. Richardson
Cressman Analysis
Three kinds of observation handled by the Cressman successive corrections scheme: height only, wind only, and height and wind together. R is the scan radius and d is the distance from the gridpoint at the center of the circle to the observation: height alone (i index), wind only (j index), height and wind (k index). The radius of influence is R; its value decreases on successive scans.
Cressman Analysis
• Advantages– Simple and computationally fast– Uses forecast information in background field
• Disadvantages– Does not include observation errors (bad obs?)– Does not account for distribution of observations– Level of detail depends on observation density– How to analyze wind versus height?– Does not account for background error
Barnes Analysis
• Advantages– No need for a model– No need to set influence radius– Control of fine-scale analysis
• Disadvantages– Same as for Cressman analysis
Nudging• Adds a “nudging” term to the prognostic equations
for the field variables.
• Initialize with first guess (background field) and integrate forward.
• Nudging term forces integration towards observations.
• Balanced initial conditions.• Good for small-scale obs (e.g. radar).• No covariance matrices.