# Presentation: 408283

## Sounding the Troposphere by LEO-LEO Occultation: A Simulation Retrieval System and Performance Analysis Results 

- Stephen Leroy1, Chi O. Ao
- Jet Propulsion Laboratory
- California Institute of Technology

- 1Done in part while visiting the Danish Meteorological Institute

## Inheritance and Requirements

**GPS Occultation **
- All operational experience in level 2 retrieval gained from GPS occultation
- Unresolved problems: negative-refractivity bias, horizontal gradients, nonphysical retrievals
- Unresolveable issues: wet-dry ambiguity (though no need to resolve for NWP)

**To ACE+**
- Make a system which is a first draft retrieval system and performance analysis system
- Simulate multipath, diffraction, high-accuracy amplitude
- Simulate systematic and random noise: stability and power issues
- Retrieve physically-constrained geophysical parameters (T, p, pw, ρcloud, rrain, O3, u, gain)

## Steps in Performance Analysis

**GPS Occultation**
- Atmospheric parameters (T, p, pw) to real index of refraction (*n*)
- Simulate bending using Abel transform / multiplane diffraction integrals
- Geometry to simulate phase
- Superimpose noise on s/c measurement of phase
- Invert to real index of refraction using geometry / Egorov, then Abel transform
- Obtain atmospheric parameters by assuming T or pw or by variational assimilation

**Intersatellite Link Occ’n **
- Atmospheric parameters (T, p, pw, ρcloud, rrain, O3, u) to complex *n*
- Simulate bending and attenuation using Abel transforms
- Simulate phase using inverse canonical transform
- Superimpose noise on receiver measurements of correlation products (open-loop)
- Invert to complex *n *profiles using forward canonical transform, Abel transforms
- Obtain physically constrained atmospheric parameters using linearly constrained least squares

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## SimDistribution (115 occ’ns)

**Properties:**
- Multiple transmitters
- Multiple receivers
- Mutual occ’ns
- Oblate Earth
- NetCDF output
- Circular orbits
- Variable inclination, altitude, ascending node, anomaly

## SimNCEPAtmosphere

**Properties**
- Uses NCEP analysis starting at any time
- Millimeter-wave Propagation Model
- User-selected frequencies
- Accounts for clouds, rain (future: ozone, wind)
- NetCDF input/output

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## The Inverse Canonical Transform

**Methods of simulating observations**
- Raytracing (1-D, 2-D, 3-D)
- Ideal for computing phase
- Difficult to simulate amplitude
- Handles multipath, but not guaranteed to find all rays
- Cannot handle diffraction
- 2-D and 3-D version handle spherically nonsymmetric structures
- Multiplane (2-D)
- Computes phase, amplitude very precisely
- Handles multipath, find all rays
- Handles diffraction completely
- Handles along-track asymmetric in atmosphere
- Very expensive at high frequency

**Forward canonical transform**
- Given phase and amplitude, compute bending angle and atmospheric attenuation
- 1-Dimensional
- Accounts for multipath and diffraction
- Does not handle spherically nonsymmetric structures
- Computationally inexpensive, two FFTs
- The canonical transform has an analytic inverse which produces phase and amplitude from atmospheric bending and attenuation
- (Gorbunov, 2000)

## The Canonical Transform

- Complex field ux(y), Fourier transform ux(η)

- Impact parameter p
- Orientation angle ξ
- Attenuation –ln A(p)

*x*

## The Inverse Canonical Transform, cont’d

- The forward canonical transform (from Gorbunov) transforms from y,ky coordinates to p,ξ coordinates:
- The inverse canonical transform transforms from p,ξ coordinates to y,ky :

## Abel Transform Integrals

**Forward model **
**for attenuation!**
- (Need corrections
- for some geometric
- effects)

**Forward model **
**for bending!**
- (Need correction for
- incident ray
- orientation)

## Example simulation

## Example simulation, cont’d

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## Adding Error

- Sources of error:
- Gain drift dg/dt in dB/s
- Signal-to-noise ratio, σ = (vs/c/dy)1/2 / SNR

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## Abelian inversions

- Inversion for real part of refractivity
- Inversion for imaginary part of refractivity

## The simulation-retrieval system

**NCEP Analysis**

- Complex
- refractivity
- profile

**Simulated**
**observation**

- Bending,
- attenuation
- profiles

- Complex
- refractivity
- profile

**Profile of**
**geophysical**
**variables**

- MPM

- Inverse
- canonical transform

- Add noise, systematic
- and random

- Integrate
- bending;
- absorption

- Level 2
- retrieval

- Bending,
- attenuation
- profiles

- Abel integrals

- Forward canonical transform

- Complex
- electric
- field

## Retrieval of geophysical variables

- Constraints, such as hydrostatic equilibrium, nonnegative water vapour, etc., must satisfy **H**(**x**)=0.

- Minimize  χ2 with respect to data and constraints:

**Solution: Factorize**

- Remove the constraint space described by the eigenvectors **e***H* from the retrieval space (**JO**-1**J***T*). Then retrieval can be done for each level, starting from the top of the atmosphere. Same as **linearly constrained least squares**: Minimize

- Topmost layer: 0DVAR using a climatology of pressure and temperature.
- Subsequent layers: linearly constrained least squares, hydrostatic equilibrium mandatory.
- Added generality: make it possible to retrieve a subset of geophysical variables; use up to 10 frequencies, but subset by frequency and real/imaginary part for each level.

- subject to

## Boundary layer χ2

- Boundary layer χ2

- Bending and absorption

- Absorption only

## Example level 2 retrieval w/ errors

## Example (unrelated) level 2 retrieval

## Summary/Work-to-be-done

- Complete forward and inverse canonical transform
- Include line parameterizations for ozone
- Series of runs at 10.3, 17.2, 22.6 GHz
- Series of runs with a “calibration tone” (3-5 GHz)
- Try different gain drifts (0.01-0.10 dB/30s) with and without calibration tone to determine how much the calibration tone helps
- Different SNRs (100-1000) with different sets of frequencies to determine sensitivity in the presence of clouds