Analytic Solution and Sensitivity Study for Optical Scintillation Measurements of Boundary Layer Turbulent Fluxes: A Cure for Iteration
Abstract
Scintillometer measurements of turbulence inner scale length and/or refractive index structure functions allow for indirect retrieval of boundary layer turbulent fluxes on large spacial scales and on short temporal scales relative to eddy covariance techniques. For the past several decades, scintillometer measurement strategies have been compared to other boundary layer measurement techniques; they demonstrate advantages in applications such as the validation and parameterization of satellite remote sensing over a wide variety of terrain, as a source of ground level data for input into large scale models, and in agricultural irrigation management. In past analyses of scintillometer data, the relevant set of nonlinear coupled Monin-Obukhov similarity equations has been solved with a cyclically iterative numerical approximation, and analyses of error propagation from source measurements to derived variables have been attempted without explicit solution to this set of equations. A new analytic method of explicit solution is presented which allows for arbitrarily small and easily quantifiable computational error, guaranteed convergence, faster computation, simpler computer code, and, most importantly, which makes the variable inter-dependency explicit, allowing for direct evaluation of global partial derivative terms in error propagation equations. Results from this method show that many sensitivity functions derived in the previous literature are over-estimated in magnitude, in some cases drastically. Past estimates of computational error resulting from the canonical cyclically iterative procedure are re-visited. Explicit variable inter-dependency is shown to resolve spurious correlations in interpretive validations of scintillometer retrievals. General sensitivity functions are expanded for the use of path weighting functions over heterogeneous terrain in a way which is practical for field implementation. Advantages of the new methods are demonstrated in a case study involving a multi-instrument experiment over hilly Arctic tundra in Alaska. Sensitivity multiplication function for errors on sensible heat flux propagated from errors on beam path height measurements for a scintillometer measurement strategy involving an independent friction velocity measurement. zeta is the stability parameter z_eff/L, and u is the normalized beam path position.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFM.A13G0270G
- Keywords:
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- 3294 MATHEMATICAL GEOPHYSICS / Instruments and techniques;
- 3394 ATMOSPHERIC PROCESSES / Instruments and techniques;
- 4490 NONLINEAR GEOPHYSICS / Turbulence;
- 4494 NONLINEAR GEOPHYSICS / Instruments and techniques