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Sergey Gulev and Konstantin Belyaev

Explore the use of double-exponential distributions for minimizing sampling biases in air-sea flux fields, improving regional energy balances and reducing uncertainties in VOS-based flux products. Discusses estimation methods and practical applications.

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Sergey Gulev and Konstantin Belyaev

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  1. 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

  2. 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

  3. Nature of sampling bias in VOS fluxes Any VOS flux product suffers from the sampling bias

  4. 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

  5. Sampling errors in fluxes:

  6. 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

  7. Double exponential distribution (2ePDF) PDF:  Mean, variance, modal value:  Parameter estimation:

  8. Climatology of the location and scale parameters - sensible heat

  9. GS Subtrop Atl Trop Atl α,β – diagram – effectively accounts for different statistical properties of quantitatively close to each other flux estimates. Fluxes in W/m2×10-3

  10. 2ePDF-derived latent and sensible heat flux climatology

  11. Flux differences between 2ePDF and direct averaging with regular sampling mon   0-5 W/m2

  12. Sampling errors in the routine and 2ePDF-derived fluxes: latent heat

  13. If the 2ePDF cannot be properly evaluated, then … The confident intervals for the parameters will be given as an ellipse

  14. Estimating regionally integrated heat flux using 2e PDF Uncertainty in the integrated sensible+latent flux Trenberth & Caron 2001 46 +/-? VOS-like sampling: Δ = 0.67*1014 W SOC Koltermann et al. 1999 2e-PDF - reconstruction: Δ = 0.23*1014 W

  15. 2D-2eW PDF Qh = Cp· ·Ct( T ,V)·T· V Q, 1011 W WIND - Weibull PDF SST-Tair -2ePDF Flux accumulated in T,V -classes

  16. Estimating regionally integrated heat flux using two dimensional 2e-Weibull PDF VOS-like sampling: Δ = 0.67*1014 W 2D-2eW-PDF - reconstruction: Δ = 0.11*1014 W 2e-PDF - reconstruction: Δ = 0.23*1014 W

  17. 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 algorithm is under development

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