Towards a Robust and Model- Independent GNSS RO Climate Data Record Chi O. Ao and Anthony J. Mannucci 12/2/15CLARREO SDT Meeting, Hampton, VA1 © 2015 California Institute of Technology. Government sponsorship acknowledged. Jet Propulsion Laboratory California Institute of Technology Pasadena, CA, USA

Objectives A major source of uncertainty in stratospheric refractivity retrievals comes from the high- altitude initialization of bending angles (BA) in the Abel integration. Typically an a priori model (e.g., MSIS, weather analysis/forecast, etc.) is used above some altitude to “smooth” the noisy BA measurements. Our goal is to eliminate the use of models in climate-oriented RO retrievals and provide rigorous uncertainty estimates. 12/2/15CLARREO SDT Meeting, Hampton, VA2

12/2/15CLARREO SDT Meeting, Hampton, VA3 Refractive Index = 1+N Impact parameter a = n(r) r Bending angle Abel inversion

12/2/15CLARREO SDT Meeting, Hampton, VA4 median 10 %-tile 90 %-tile BA noise at km from COSMIC BA noise vs. Average BA Ao et al., GRL, 2012 Noise ~ Signal BA stops decreasing (residual ionosphere?)

The “Smoothing” Solution Noisy BA at high altitudes are smoothed by replacing it with an a priori. “Optimized” algorithms consist of a blend of observed BA and a priori, with weights determined by uncertainties in observation and model. “Advanced” algorithms adjust the a priori with bias corrections based on the measurements to minimize systematic biases. 12/2/15CLARREO SDT Meeting, Hampton, VA5

The “Averaging” Solution If only averaged refractivity is required, it is possible to average BA first and invert the averaged BA [Ao et al., GRL, 2012 and Gleisner and Healy, AMT, 2013]. This reduces the random noise and allows BA at higher altitudes to be used, thus reducing the need for a priori. But BA -> N is not entirely linear. In addition N -> T is highly non-linear. 12/2/15CLARREO SDT Meeting, Hampton, VA6

The “Hybrid” Solution A “hybrid” solution can be considered where the averaged BA is used only at high altitudes where it is truly needed. This eliminates the need for an a priori, minimizes nonlinearity errors at lower altitudes, and improves single-profile retrieval. Similar idea has been proposed [Pirscher- Scherllin et al., AMT, 2015]. 12/2/15CLARREO SDT Meeting, Hampton, VA7

Data-Based Approach to High-Altitude BA Initialization “Raw” Bending Angle Profile BA “Climatology” Merged BA Profile Refractivity Profile Temperature Profile Refractivity “Climatology” Temperature “Climatology” Averaging 12/2/15CLARREO SDT Meeting, Hampton, VA8 < 60 km > 60 km

BA Climatology Construction Infer BA at high altitudes from a large number of RO profiles (e.g., monthly zonal means). Use a simple approximation of BA at high altitudes. (Here we assume BA varies exponentially as ~ A exp(-(h-60km)/H)). Estimate A, H as a function of time (year, month) and latitude. 12/2/15CLARREO SDT Meeting, Hampton, VA9

A, H from Monthly Data 12/2/15CLARREO SDT Meeting, Hampton, VA10 Ionosphere-corrected COSMIC BA from km height was used for the exponential fit. Median values at each 5 degree latitude bands are shown below. BA at 60 km Scaleheight

Polynomial Fit (Degree 6) 12/2/15CLARREO SDT Meeting, Hampton, VA11

BA Climatology (A) 12/2/15CLARREO SDT Meeting, Hampton, VA12 Global annual mean = 4.58 micro-rad

BA Climatology (H) 12/2/15CLARREO SDT Meeting, Hampton, VA13 Global annual mean = 7.44 km

New vs. Old Refractivity Difference 12/2/15CLARREO SDT Meeting, Hampton, VA14 Jan 2008 NH SH GlobalTrop

New vs. Old Refractivity Difference 12/2/15CLARREO SDT Meeting, Hampton, VA15 July 2008 NH SH Global Trop This suggests significant bias in our old processing in the extratropics, especially in the winter, likely due to higher stratopauses.

Uncertainty Characterization Uncertainty in the derived BA climatology leads to uncertainty in refractivity. Let A=A±dA and H=H±dH. – Upper bound: (A+dA)*exp(-(z-zo)/(H+dH)) – Lower bound: (A-dA)*exp(-(z-zo)/(H-dH)). We estimate dA (dH) from RSS of – Standard error of monthly average – Polynomial fit residual Simple analytical expression can be derived for corresponding refractivity uncertainty profiles. 12/2/15CLARREO SDT Meeting, Hampton, VA16

Uncertainty in A (dA) 12/2/15CLARREO SDT Meeting, Hampton, VA17 Global annual mean = micro-rad

Uncertainty in H (dH) 12/2/15CLARREO SDT Meeting, Hampton, VA18 Global annual mean = km

Uncertainty Bounds 12/2/15CLARREO SDT Meeting, Hampton, VA19 Blue lines show estimated uncertainties

12/2/15CLARREO SDT Meeting, Hampton, VA20 If A is well-constrained, H can be relatively unconstrained, depending on accuracy desired.

Summary A hybrid approach incorporating RO-based BA “climatology” at high altitudes was proposed to address a major source of refractivity uncertainty above ~ 30 km. The monthly BA “climatology” was approximated using a simple exponential with height. The latitude variation is approximated with 6-degree polynomial fits of the two exponential parameters. Uncertainties in refractivity due to high altitude initialization can be estimated rigorously with this approach. 12/2/15CLARREO SDT Meeting, Hampton, VA21

Additional Considerations COSMIC-2 will have ~ 2x higher SNRs and thus lower BA noise. How much will that improve stratospheric retrievals? – How much of the observed noise at high altitudes is due to ionosphere? – If noise can be neglected, up to what altitudes can we trust the observed BA? 80 km? 12/2/15CLARREO SDT Meeting, Hampton, VA22

Relevance to CLARREO Pathfinder COSMIC-2A (low inclination, 2016) and COSMIC-2B (polar, 2018) could provide the RO observations lacking in the Pathfinder mission. Could COSMIC-2 provide the sampling and accuracy needed to achieve the CLARREO science goals? 12/2/15CLARREO SDT Meeting, Hampton, VA23