Simulating the influence of horizontal gradients on refractivity profiles from radio occultations

Transcription

1 Simulating the influence of horizontal gradients on refractivity profiles from radio occultations a promising approach for data assimilation S. Syndergaard, D. Flittner, R. Kursinski, and B. Herman Institute of Atmospheric Physics University of Arizona, Tucson, Arizona COSMIC workshop, Boulder, CO, August 1 3,

2 How should a derived profile be interpreted? - as a vertical profile at fixed mean event location? - along the locus of the estimated tangent points? - some kind of D average of the atmosphere? Answer: Some kind of D average...

3 What kind of D average? A mapping mimicking the observation geometry and the inversion process assuming spherical symmetry L Lines of integrations z x Atmospheric layers Finite straight lines (L 7 km) Centered at tangent point locations Parallel to propagation directions

4 Theory behind the D mapping Basic requirement: L/ L/ N(x, z)dx = zl z N(r)rdr r z Can be discretized to a linear matrix equation: N = ABN N is the true (D) atmospheric refractivity (model refractivity) B is a finite straight-line forward integration operator A is a finite straight-line Abel-equivalent inverse operator N is the mapped 1D profile

5 Weights on a regular grid Horizontally limited ( 7 km) Horizontally unlimited Longitude [deg] Longitude [deg] Similar to the D resolution kernel by Ahmad and Tyler (1998) Differences: Can be applied for a general occultation geometry Discrete weights within a finite volume

6 A Model of a weather front including moisture Refractivity [N-units] Longitude [deg] Simulated occultation measurements via ray-tracing Inverted using spherical symmetry (Abel transform) Close to worst case scenario in absence of multi-path 3

7 Three ways of evaluating retrieved profiles * In this work: 1. Compared to values along locus of estimated tangent points*. Compared to simple horizontal average centered at longitude 3. Compared to D mapped profile Because of simplified geometry, estimated (assumed) tangent points are vertically aligned at longitude

8 Front base at lon Tangent point D mapped deg. Average Refractivity [N-units] Comparisons Tangent point D mapped Retrieval deg. Average Refractivity error [%] Front base at 1 lon Tangent point D mapped Retrieval deg. Average Refractivity [N-units] Tangent point D mapped deg. Avg. - - Refractivity error [%]

9 Summary of comparisons Worst case results: comparison to tangent point profile gives errors of % comparison to a simple horizontal average does not reduce errors significantly comparison to a D mapped profile reduces errors to 1 % A similar ( 8 %) reduction should be expected on statistical errors subject of future work

10 Accuracy of the D mapping Exact for spherically symmetric atmosphere In general: residual has two major sources 1. The Finite Straight-line Assumption (FSA). Tangent Point Shift (TPS) due to horizontal gradients Let s take a look at the latter...

11 Tangent point shift (TPS) due to horizontal gradients Refractivity [N-units] Longitude [deg] Drift due to satellite movement + bending can be estimated from data (generally on order 1 km) Additional shift due to horizontal gradients can not be estimated from data, only from ray-tracing (on order 1 km or less)

12 Effect of TPS due to horizontal gradients Front base at lon. Front turned 1 8 a Assumed Actual 1 8 b Assumed Actual Refractivity error [%] Refractivity error [%] No conclusive improvement using actual tangent points FSA must account for remaining residual Indicates FSA and TPS effects are of same order of magnitude

13 D mapping as a forward model for data assimilation Attractive features Simple to implement Computations are fast Mapping can be described as a linear matrix operator No need for climatology above the levels of NWP model No need for diffraction/multipath modeling* * When a retrieved profile has been corrected for diffraction and multipath it should be comparable to the D mapped profile

14 Recommendation for COSMIC (CDAAC) Parameters describing estimated tangent point locations as well as propagation directions should be made available along with other derived COSMIC products.