Model configuration

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Model configuration
2-layer spectral PE model, run at T127 (truth),
T63, and T31. Model state is vorticity,
divergence, and layer thickness of Exner
function. Wavenumber 2 terrain peaked at
45NS. No land/water. Forced by Newtonian
relaxation of interface Exner fn (top layer) to
prescribed state. Del8 hyperdiffusion, 6-hour
e-folding timescale for shortest resolvable
scale. Error doubling times are 3.78 days, 2.16,
1.88 at T127, T63, and T31.
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Westerly upper jets in midlatitudes, more
pronounced at T127, Easterly in tropics, less
pronounced at T127. Subtropical easterlies at
low levels.
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Model Error at T31

• Model Err M31(T x127(t) ) T x127(t1)
  where M is the forward model operator at T is the
  truncation operator, and superscript denotes
  resolution of state and/or forecast model.
• x127(t1) M127 x127(t)

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Evaluating model errors in low-resolution
version of high-resolution model (here in full
PE model)
t 0
t 12h
(compare)
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Model errors show some temporal continuity,
assocd with jet-stream dynamics.
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Model errors larger at T31, but they grow faster
at T63. Peaked at baroclinic scales by 2 days.
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Data Assimilation Methodology

• EnSRF
• Additive (different flavors, next pg) or
  covariance inflation (uniform across domain).
  Additive is random sample from time series of
  some forecast aspect.
• Cov localization with 5000 km cutoff,
  Gaspari/Cohn. No vertical localiz.
• 208 members

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8.75 J/(kg K) obs error std dev for
interface height obs
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Range of Experiments

• 1) T127 Perfect Model (1 )
• 2) Covariance inflation (diverged)
• 3) Restarted covariance inflation (10)
• 4) Perfect additive error (no infl, true samples
  of error)
• 5) T63 additive 1.2
• 6) T63 analogs 1.2
• 7) T63 no bias correction 1.2 (4, 5, and 6 bias
  corrd)
• 8) 24-h tendency 0.25
• 9) climatology 0.25
• 10) 3D-Var 1.40 (samples of actual errs from
  expt 5)

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Errors
Err (KE) Spread (KE) Err ( ??2) Spread ( ??2) Err ( ??12) Spread ( ?? 1 2)
T127 perfect 3.67 3.96 5.37 5.51 1.17 0.97
Cov inflation - - diverged - - -
Restarted cov inflation 5.62 5.47 7.74 5.04 1.83 2.31
Perfect additive error 4.92 4.85 7.10 6.81 1.25 0.86
T63 additive 4.93 4.81 7.14 6.62 1.28 0.82
T63 analogs 4.96 4.76 7.10 6.52 1.27 0.82
T63 no bias corr. 4.96 5.00 7.17 6.67 1.30 0.88
24-h tendency 5.08 4.18 7.21 5.53 1.45 1.14
Climatology 5.56 5.36 7.30 5.89 1.98 1.93
3D-Var 5.76 N/A 8.16 N/A 1.73 N/A
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Why are covariance inflation errors higher than
additive error?

• Model error not in subspace of forecast ensemble?
  (fiddled around a lot with this to come up with
  good explanatory graphic, to no avail).

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