Sergey Gulev and Konstantin Belyaev

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NEW STRATEGY FOR THE DEVELOPMENT OF GLOBAL
GRIDDED AIR-SEA TURBULENT FUXES MINIMIZING
SAMPLING ERRORS USING PROBABILITY DISTRIBUTIONS
Sergey Gulev and Konstantin Belyaev
Outline

• The nature of sampling error in air-sea flux
  fields
• How large sampling uncertainties are?
• A double-exponential distribution (2ePDF)
• the way to account for sampling
  uncertainty
• Minimization of sampling biases using 2ePDF
• Regional energy balances 2D 2eW PDF
• Discussion Conclusions

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A typical VOS-based flux product
VOS measurements SST, Ta, q, SLP
measured Cn (Cl), hw/hs visually estimated V
mixed
Variable corrections SST, Ta, q, V
Parameterizations LW ??SST4 Flw(Cn,Ta,ez), SW
Qo Fsw(Cn,Ta,ez,ho)(1-?), Qh Cp Ct ? (SST-
Ta?)V, Qe L Ce ? (0.622/P) (eo-ez)V, H SW -
LW - Qh - Qe ? Cp ? Cv (V,hw)V2
Averaging, objective analysis and development of
the spatial fields
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Nature of sampling bias in VOS fluxes
Any VOS flux product suffers from the
sampling bias
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Use of NWP for quantifying sampling bias (Gulev
et al. 2004)
6-hourly NWP individual variables
Random sampling error
Random VOS-like sub-sampling
Real-time VOS-like sub-sampling
Total sampling error
Objective analysis error
Re-computation of surface fluxes using bulk
formulae
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Sampling errors in fluxes
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Sampling errors in turbulent fluxes Although it
is clear how to quantify them, it is unclear how
to minimize them A standard approach
in statistics is to derive a PDF and to
integrate it rather than to directly average
poorly sampled data used in precipitation
(Gamma PDF), waves and winds
(Weibull PDF) A problem PDF of
turbulent fluxes is unknown
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Double exponential distribution (2ePDF)
PDF
?
Mean, variance, modal value
?
Parameter estimation
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Climatology of the location and scale parameters
- sensible heat
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a,ß diagram effectively accounts
for different statistical properties of
quantitatively close to each other flux
estimates.
Fluxes in W/m210-3
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2ePDF-derived latent and sensible heat flux
climatology
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Flux differences between 2ePDF and direct
averaging with regular sampling
?mon ? ? 0-5 W/m2
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Sampling errors in the routine and 2ePDF-derived
fluxes latent heat
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If the 2ePDF cannot be properly evaluated, then
The confident intervals for the parameters will
be given as an ellipse
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Estimating regionally integrated heat flux using
2e PDF
Uncertainty in the integrated sensiblelatent
flux
Trenberth Caron 2001
46 /-?
VOS-like sampling ? 0.671014 W
SOC
Koltermann et al. 1999
2e-PDF - reconstruction ? 0.231014 W
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2D-2eW PDF
Qh Cp? Ct( ?T ,V) ?T V
Q, 1011 W
WIND - Weibull PDF
Flux accumulated in ?T,V -classes
SST-Tair -2ePDF
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Estimating regionally integrated heat flux using
two dimensional 2e-Weibull PDF
 
VOS-like sampling ? 0.671014 W
2D-2eW-PDF - reconstruction ? 0.111014 W
2e-PDF - reconstruction ? 0.231014 W
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Conclusions

• A PDF of turbulent fluxes over sea is accurately
  
• approximated by the double exponential
  distribution
• Application of 2ePDF allows for the minimization
  of
• sampling biases from 2 to 7 times
• Confident limits for PDF parameters can be
  evaluated,
• so that we always know the accuracy of the
• estimation of mean fluxes
• A double exponential distribution allows also for
  
• estimation of extreme fluxes
• an accurate estimation of regional energy
  balances
• establishment of proper trimming limits
• 2ePDF is computationally expensive, but effective
  

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