This document proposes a new radiometric concept called a cross-beam interferometer to retrieve 3D profiles of atmospheric temperature and water vapor density. It would use two antennas separated by a distance to measure brightness temperatures from different atmospheric volumes independently, without being subject to the cumulative effects of the radiative transfer equation. Theoretical development and initial simulation results exploring the technique's spatial resolution and sensitivity to antenna spacing are presented. Open issues that require further study include calibration methods, estimating radiometric resolution for water vapor content retrieval accuracy, and applying retrieval techniques like "onion peeling" to simulated atmospheres.

1. A RAdiometEr Concept to Retrieve 3-D Radiometric Emission from Atmospheric Temperature and water vapor DENSITY X. Bosch-Lluis1, H. Park2, A. Camps2, S.C. Reising1, S. Sahoo1, S. Padmanabhan3, N. Rodriguez-Alvarez2, I. Ramos-Perez2, and E. Valencia2 1. Microwave Systems Laboratory - ECE, Colorado State University, Fort Collins, CO, USA. 2. Remote Sensing Lab, Dept. Teoria del SenyaliComunicacions, UniversitatPolitècnica de Catalunya and IEEC CRAE/UPC, Barcelona, Spain.3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA. E-mail: xbosch@mail.colostate.edu IGARSS’11 – Vancouver, Canada, 29thJuly 2011 FR3.T03: Microwave Radiometry Missions and Instrument Performance III

2. Presentation Outline Motivation Introduction to Atmospheric Sounding New Concept Proposal Theoretical Development Simulation Results Future Lines and Conclusions

3. Motivation Radiometric measurements of the atmosphere provide brightness temperatures according to the radiative transfer equation. Retrieval algorithms are used to obtain information on profiles of atmospheric parameters such as water vapor content (WVC). Weighting functions and in-situ measurements from radiosondes (RAOB) are required to perform such retrievals. Here we propose a new approach to this problem which may enable the development of new solutions to the atmospheric profile retrieval problem. Specifically, the goal of this work is to measure the structure of the radiometric emission from the atmosphere using two antennas separated by a certain distance and pointing to the same point in the atmosphere.

4. Atmospheric Sounding I – Radiative Transfer Equation (RTE) Basis Assuming a stratified atmosphere and a pencil beam antenna TC Layer N (10 km) dz ds Atmosphere ds Layer 1 Atmospheric attenuation (from the layer to the ground) Ground level Atmospheric attenuation Physical Temperature DiscreteRTE RTE Absorption coefficient Cosmic Background

5. Atmospheric Sounding II – Retrieval Algorithm Linearization Linearizing the discrete problem for retrieving Weighting Function (MxN) (Jacobian or Kernel) Linearization point (Mx1) Linearization error Linearization point (measured using RAOBmeasurements) (Nx1) M radiometric measurements (Mx1) @ several frequency channels WVC profile to retrieve (Nx1) The linearization approximation applies only for a certain period of time. It requires the launch of ROAB periodically.

7. M is the number of uncorrelated channels that the radiometer measures Usually N >M -> ill posed problem An information content analysis of the measurement determines the quality of the retrieval , i.e. a trade-off between accuracy and spatial resolution 𝑥=𝜕𝐹𝜕𝑥−1 (𝑦−𝐹𝑥0)+𝑥0 𝑦−𝐹𝑥0=𝜕𝐹𝜕𝑥𝑥−𝑥0+𝜀 Various inversion methods can be used for retrieving WVC: Newtonian Iteration retrieval Regression retrieval Neural Network Bayesian Maximum likelihood

8. New Concept proposal Brightness temperature from different atmospheric volumes could be measured independently, without the cumulative effect of the RTE Measure Brightness temperature using a CROSS-BEAM Interferometer TCB Layer N (10 km) (x0, y0, z0) Atmosphere z y x Baseline Layer 1 Ground level Antenna #2 (x2, y2, 0) Antenna #1 (x1, y1, 0) LPF True time delay for measuring at points which have different distance with respect Ant1 and Ant2, and sub-overlapping measurements 𝑆1𝑝𝑡𝑆2𝑞∗𝑡−𝜏𝑑

10. Antenna beamwidth and overlapping volume effect Main challenge posed by this technique To retrieve the brightness temperature the cross-beam interferometric measurement must be multiplied by the inverse of χ=l=−∞∞m=−∞∞n=0∞Ω1xp𝑝Ω2xp𝑞Ω𝑎1𝑝Ω𝑎2𝑞->1 If the overlapping solid angle decreases in comparison to the solid angles of the beams , the radiometric resolution (standard deviation) of the measurement increases. Very narrow beams mitigate this effect, then same order of magnitude between the overlapping solid angle and the beams’ solid angles

11. Spatial Resolution 1/2 Horizontal Spatial Resolution (determined by hardware decorrelation time) The spatial resolution is determined by the bandwidth of both receivers (FWF) If H1f=H2f with rectangular shapes and B𝑤1=B𝑤2=B𝑤 r12t≜e−j2πf0tB𝑤1B𝑤20∞H1fH2∗(f)ej2πft𝑑f r12t=sinc(𝐵𝑤τ)

12. Spatial Resolution 2/2, Horizontal Spatial Resolution Moreover, it allows several measurements in the same beam-overlapping volume by changing the delay between both receivers 3 sub beam-overlapping volume measurements obtained changing the relative delay Outside overlapping volume (This volume does not contribute to the measured visibility function.) Beam-overlapping volume (This volume contributes to the measured visibility function.) The overlapped volume depends on the antennas beamwidth (B−3dB) size of both antennas and on their spacing

13. Simulation Assumptions and Considerations Assumptions and considerations for the simulation 2D atmosphere for simplicity Stratified atmosphere with dx=dz=33 meters Atmosphere dimensions 10x66 Km (303x2000 voxels) Van Vleck model for absorption coefficients, using RAOB measurements for the water vapor, pressure and temperature profile. F=22.12 and 24.50 GHz the same channels as the CMR-H radiometers CSU, channels suitable for WVC retrieval. Gaussian antenna patterns. Identical and perfectly rectangular response of both systems WVC profile used for the synthetic atmosphere, obtained using a RAOB WVC [gr/m3]

14. Simulation Results, Vertical Scans 1/3 Measured temperatures using the cross-beam interferometer: D=600 m Centers of the overlapping area, scanned sequentially #2 #1 B−3dB=0.5 degrees B𝑤=100 MHz, #2 #1 D=600 m

15. Simulation Results, Vertical Scans 3/3 Antenna spacing change Measured temperatures using the cross-beam interferometer: #2 #1 D=600 m #2 #1 D=6600 m

16. Simulation Results, Horizontal Scans 1/2 B−3dB=0.5 degrees B𝑤=100 MHz, Measured temperatures using the cross-beam interferometer: Height #1 #2 D=600 m X axis [m] Atmosphere attenuation effect Height #1 #2 D=600 m X axis [m]

17. Simulation Results, Horizontal Scans 2/2 Measured temperatures using the cross-beam interferometer: Height #1 #2 D=600 m X axis [m] Height #1 #2 D=6600 m X axis [m]

20. Estimate the radiometric resolution for ±10% error WVC retrieval depending on the altitude.

21. Determinate methods for calibrate different parts of the system

22. Phase

23. Amplitude

24. Offset

25. Radiometric calibration (hot and cold load)

26. Perform retrievals from simulated atmospheres (applying techniques such as “onion peeling” instead of a Weighting function approximation).