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Animated. Serendipity: The faculty of making fortunate discoveries by accident. R. A. Brown 2003 U. Concepci Ó n. R. A. Brown 2003 U. Concepci Ó n. Model Functions. R. A. Brown 2003 U. Concepci Ó n. There is no theory for the wind generation of water waves.

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  1. Animated

  2. Serendipity: The faculty of making fortunate discoveries by accident R. A. Brown 2003 U. ConcepciÓn

  3. R. A. Brown 2003 U. ConcepciÓn

  4. Model Functions R. A. Brown 2003 U. ConcepciÓn

  5. There is no theory for the wind generation of water waves or for the high wind correlation with backscatter R. A. Brown 2003 U. ConcepciÓn

  6. R. A. Brown 2003 U. ConcepciÓn

  7. Start with the scatterometer backscattero In general, o(u*, , , f, p), where u* is wind stress, f is beam frequency and p is beam polarization. This implies o(u*), plus antenna characteristics. Since u* measurements are not available, use the well-known surface layer relation for over land, u/u* = 1/k ln[z/zo – ] where k is Von Karman’s constant, zo (u*) is a surface roughness parameter and  is a stratification parameter This may be written, with zo(u*),(Ta-Ts),z=10m, U10(u*, Ta–Ts, k) = fn(u*), = fn(o) R. A. Brown 2003 U. ConcepciÓn

  8. Consider a PBL (planetary boundary layer) model • The satellite measures the mean density of the capillaries and short gravity waves on the ocean surface. There is no good theory relating this to anything geophysically worthwhile. • There exists a raw empirical parameterization between surface roughness and near surface winds (for over flat, smooth land surface). • There is a nonlinear analytic solution of the PBL in a rotating frame of reference (but it contains OLE). R. A. Brown 2003 U. ConcepciÓn

  9. Geostrophic Flow VG(u*) effects Thermal Wind Ekman Layer with OLE Nonlinear OLE Non steady-state Advection,centrifugal terms U10(u*) effects Stratification U10 Surface Layer Surface Stress, u*  Variable Surface Roughness Ocean surface R. A. Brown 2003 U. ConcepciÓn

  10. There also exists a solution for the PBL boundary layer (Brown, 1974, Brown and Liu, 1982), where U/VG = ei - e –z[e-iz + ieiz]sin  +U2 where VG is the geostrophic wind vector, the angle between U10 and VG is [u*, HT, (Ta – Ts,)PBL] and the effect of the organized large eddies (OLE) in the PBL is represented by U2(u*, Ta – Ts, HT) U/VG ={(u*), U2(u*), u*, zo(u*), VT(HT), (Ta – Ts), } Or U/VG = [u*, VT(HT), (Ta – Ts), , k, a] =  {u*, HT, Ta – Ts}, for  = 0.15, k= 0.4 and a = 1 VG =  (u*,HT, Ta – Ts) = n(P, , f) Hence VG/u*(k, a, ) and P (u*), = fn(o) R. A. Brown 2003 U. ConcepciÓn

  11. Toward a Model Function (a curve fit to the data) The quality of the model function can be evaluated by the fit of a truncated Fourier cosine series tothe o() (plotted in V, bins) : o=  Ai(V,)cos(-o) = Ao(V,) + A1(V,)cos(-o) + A2(V,)cos2( - o)+ … V can be u*, U10 or VG R. A. Brown 2003 U. ConcepciÓn

  12. Geostrophic Wind VG=P / ( f ) Mid- PBL V = P / ( f) - Fviscous Geostrophic Wind direction 25° (Stable strat.) 18° (neutral stratification) Surface wind 5° (Unstable strat.) -10° to 40° (Thermal Wind Effect) R. A. Brown 2003 U. ConcepciÓn

  13. Model Function History Assume: o  u*  U10 . Get measurements Observe good correspondence; o (U10) Develop U10 o Model Function Get good correspondence; UG [u*(U10)] Develop UGP  U10(o) Model Get good correspondence; P [(U10 (o)] Develop P  oModel Function R. A. Brown 2003 EGS/AGU

  14. The Model Functions In general, o =  { , |V|,  } V may be u*, U10 or VG . U*: There are sparse marine measurements, often with errors of 100%.U*[zo (u*)]. U10: From buoy or GCM surface analyses. Inaccurate at low and high winds. VG: From surface pressure measurements R. A. Brown 2003 U. ConcepciÓn

  15. Evolution of a Pressure Model Function Observation (sailors): Surface stress related to surface wind Surface roughness correlates to Surface (Log-layer) wind Observations: PBL Model = Surface wind + Ekman Layer with OLE works well to produce PBL wind profiles, turning Surface wind correlates to Gradient Wind & P Observation: Satellite P correlate with NWC Pressures Backscatter correlates with P R. A. Brown 2003 U. ConcepciÓn

  16. Patoux 2003 U. ConcepciÓn

  17. Toward a Surface Pressure Model Function • Fortunately, there exists a relation • U10/u* = F(z, zo, stratification…). • Established over Land, assumed over the Ocean . • Verified in 25 years since Seasat. • A Scatterometer doesn’t measure Winds. It measures Capillaries & Short Gravity waves, related to zo., u* There’s an Easy Extrapolation to: • Fortunately, there exists a relation • UG/u* = F(z, zo, stratification, , ……). • Established in UW PBL_LIB • Verified in 20 years scatterometer data R. A. Brown 2003 U. ConcepciÓn

  18. Scatterometer Model Functions 1-4 VG VG VG VG 1-3 KM Thermal Wind Effects Stratification Effects 2 1 U10 U10 U10 10-100m 4 3 U* U* P o o Ocean Surface Models: 3 (PMF) 1970 2000 4 (fill-in) 1974 2001 1 (classic) 1950 1973 2 (inverse) 1970 1974 1982 1982 Theory Scat MF R. A. Brown 2003 U. ConcepciÓn

  19. Practical Aspects of Model Functions Winds Buoys: Sparse distribution; Point measurement; Miss High Winds, Low Wind Directions Ships: Only Met. Ships OK; Very Sparse GCMs: Bad Physics in PBL Model; Too low High Winds, Too high Low Winds…... Pressures From Buoys, ships: sparse. Accurate measurement in low and high wind regimes GCM product has good verification, interpolation scheme Scale is compatible with scatterometer footprint U* Few Measurements; So what? From over-land formulas? From GCM PBL? R. A. Brown 2003 U. ConcepciÓn

  20. Practical Aspects of a Surface Stress Model Function Surface ‘Truth’ Limits Ship stress: Very Sparse and inaccurate. Buoy stress: Very Sparse and inaccurate; a point; misses high stress. PBL stress: Parameterization of land & sea based data. Stratification effects on u*(U10). Usual high and low winds problems. R. A. Brown 2003 U. ConcepciÓn

  21. Practical Aspects of a Wind Model Function Surface ‘Truth’ Limits Ship winds: Sparse and inaccurate except Met. Ships. Buoy winds: Sparse; a point; miss high winds, low wind directions. GCM winds: Bad physics in PBL Model; Toolow high winds, too high low winds. R. A. Brown 2003 U. ConcepciÓn

  22. Practical Aspects of a Pressure Model Function • Surface ‘Truth’ Limits • Buoy and ship pressures: Accurate in low and high wind regimes; sparse • GCM: • Good verification; compatible scale R. A. Brown 2003 U. ConcepciÓn

  23. CONCLUSIONS-1 • The surface layer relation, hence U10 {u*(o ) }works well • There is almost no surface truth buoy or GCM surface winds with U10 > 25 m/s * The U10 model function can be extrapolated to about 40 m/s • There are indications that o responds to the sea state for U10 > 40 m/s. (H-pol > 60?) * Winds > 30 m/s need an asterisk indicating a kluge • The JPL Model function still misses very high winds (Wentz model doesn’t) R. A. Brown 2003 U. ConcepciÓn

  24. The PBL relation VG{U10 [u*(o )] } works well CONCLUSIONS-2 * GCM PBL models still have wrong (diffusion vs advection) physics, too-low winds, too low pressure gradients * Scatterometer derived pressure fields can be used to choose the best direction ambiguity, substitute an average U10 or a very high wind. * Similarly, the pressure fields can be used to correct (smooth) o single or small area (rainy) anomalies R. A. Brown 2003 U. ConcepciÓn

  25. Programs and Fields available onhttp://pbl.atmos.washington.eduQuestions to jerome@atmos.washington.edu or neal or rabrown@atmos.washington.edu • The direct PBL model: PBL_LIB, an analytic solution for the PBL flow with rolls, U(z) = f( P, To , Ta) --- available for ftp • The inverse PBL model: Takes U10 and calculates surface pressure fields P (U10 , To , Ta) ---ibid • Pressure fields directly from the PMF: (2003) P (o) along all swaths * Surface stress fields from PBL_LIB corrected for stratification effects along all swaths (2004) R. A. Brown 2003 U. ConcepciÓn

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