Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder
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Transcript of Rod Frehlich and Robert Sharman University of Colorado, Boulder RAP/NCAR Boulder
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The Importance of Atmospheric Variability for Data Requirements, Data Assimilation, Forecast Errors, OSSEs and Verification
Rod Frehlich and Robert SharmanUniversity of Colorado, Boulder
RAP/NCAR BoulderFunded by NSF (Lydia Gates) and
FAA/AWRP
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In Situ Aircraft Data
• Highest resolution data
• Many flights provide robust statistical description (GASP, MOZAIC)
• Reference for “truth”
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Spatial Spectra
• Robust description in troposphere
• Power law scaling• Valid almost
everywhere
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Structure Functions• Alternate spatial statistic• Interpretation is simple (no aliasing)• Also has power law scaling• Structure functions (and spectra) from
model output are filtered• Corrections possible by comparisons with
in situ data• Produce local estimates of turbulence
defined by ε or CT2 over LxL domain
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RUC20 Analysis
• RUC20 model structure function
• In situ “truth” from GASP data
• Effective spatial filter (3Δ) determined by agreement with theory
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UKMO 0.5o Global Model
• Effective spatial filter (5Δ) larger than RUC
• The s2 scaling implies only linear spatial variations of the field
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DEFINITION OF TRUTH• For forecast error, truth is defined by
the spatial filter of the model numerics• For the initial field (analysis) truth
should have the same definition for consistency
• Measurement error • What are optimal numerics?
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Observation Sampling Error
• Truth is the average of the variable x over the LxL effective grid cell
• Total observation error • Instrument error = x• Sampling error = x• The instrument sampling pattern and
turbulence determines the sampling error
2 2 2x x xÓ = ó + ä
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Sampling Error for Velocity and Temperature
• Rawinsonde in center of square effective grid cell of length L
1/3u vä = ä = 0.688 (åL)
2 1/3T Tä = 0.450 (C L)
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UKMO Global Model
• Rawinsonde in center of grid cell
• Large variations in sampling error
• Dominant component of total observation error in high turbulence regions
• Very accurate observations in low turbulence regions
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Optimal Data Assimilation• Optimal assimilation requires
estimation of total observation error covariance
• Requires calculation of instrument error which may depend on local turbulence (profiler, coherent Doppler lidar)
• Requires climatology of turbulence • Correct calculation of analysis error
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Adaptive Data Assimilation
• Assume locally homogeneous turbulence around analysis point r
• forecast• observations
Nb o
k kk=1
x(r) = c x (r) + d y (r )∑
oky (r )
bx (r)
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Optimal Analysis Error
• Analysis error depends on forecast error and effective observation error
• forecast error • effective observation
error (local turbulence)
2 22
2 2b eff
Ab eff
=+
beff
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Analysis Error for 0.5o Global Model
• Instrument error is 0.5 m/s
• Large reduction in analysis error for b=3 m/s
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Implications for OSSE’s• Synthetic data requires local estimates of
turbulence and climatology• Optimal data assimilation using local
estimates of turbulence• Improved background error covariance
based on improved analysis• Resolve fundamental issues of observation
error statistics (coverage vs accuracy)• Determine effects of sampling error
(rawinsonde vs lidar)
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Implications for NWP Models• Include realistic variations in
observation error in initial conditions of ensemble forecasts
• Determine contribution of forecast error from sampling error
• Include climatology of sampling error in performance metrics
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Future Work• Determine global climatology and universal
scaling of small scale turbulence• Calculate total observation error for critical
data (rawinsonde, ACARS, profiler, lidar)• Determine optimal model numerics• Determine optimal data assimilation, OSSE’s,
model parameterization, and ensemble forecasts
• Coordinate all the tasks since they are iterative
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Estimates of Small Scale Turbulence
• Calculate structure functions locally over LxL square
• Determine best-fit to empirical model
• Estimate in situ turbulence level and ε
ε1/3
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Climatology of Small Scale Turbulence
• Probability Density Function (PDF) of ε
• Good fit to the Log Normal model
• Parameters of Log Normal model depends on domain size L
• Consistent with large Reynolds number turbulence
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Scaling Laws for Log Normal Parameters
• Power law scaling for the mean and standard deviation of log ε
• Consistent with high Reynolds number turbulence