# Presentation: 691128

## RT Modelling for All-Weather Microwave Radiance Assimilation

- Albin J. Gasiewski
- Bob L. Weber
- Dean F. Smith

- Center for Environmental Technology – University of Colorado, Boulder, CO

- Collaborators: T. Meissner, J. Johnson, V. Irisov, A. Voronovich, B. Stankov, and J. Zelenak

## Objectives

**Develop a fast accurate forward RT model providing**
**   ****tangent linear capability and compatible with the**
**   ****JCSDA CRTM**
**Incorporate full-Stokes ocean surface emission**
**   ****model with Jacobian applicable for all microwave**
**   ****satellites**
**Demonstrate precipitation “locking” of regional-**
**   ****scale NWP models onto satellite microwave**
**   ****radiances. **
**Improve snow surface emission models over ~10-89**
**   ****GHz.**

## All-Weather Microwave Assimilation

**   ****Anticipated capabilities include:**
- Extended thermodynamic information 	(water vapor and temperature fields) within the  forecast-sensitive and economically important cloud-covered regions.
- Improved accuracy of cloud and radiation products.
- Short-term prediction of mesoscale convection for warnings with high specificity (precipitation “locking”).
- Tracking of latent heat exchange within precipitation for improved thermodynamic knowledge.

## DOTLRT Evolution

## DOTLRT* Attributes

**DOTLRTv1.0b (January 2005, August 2005)**
- Discrete ordinate layer adding solution
- Polydispersive with 5-hydrometeor phases (cloud, rain, graupel, snow, cloud ice)
- Henyey-Greenstein phase function with Mie absorption, scattering, and asymmetry
- Liebe 87 and 93 attenuation models
- Fast multistream radiation and geophysical Jacobian, compatible with satellite streams
- Selective incorporation of scattering in layer solution
- CTRM compatible
- Intercompared with RTTOVS v7 (Oct 2005)
**DOTLRTv2.1 (~October 2006)**
- Exact Mie phase matrix model with Mie library
- Full Stokes ocean surface model with Jacobian
- Full Stokes (surface-generated) radiance product

- 	*Voronovich et al., "A Fast Multistream Scattering-Based Jacobian for Microwave Radiance Assimilation," IEEE Trans. Geosci. Remote Sensing, August, 2004. *

## Jacobian Components

*H=H**I** H**R** H**G  *
*H **	****=**** **	*Total Jacobian
*H**I** *	***=***	Instrument Jacobian
*H**R*	***=******	***Radiation Jacobian
*H**G*	***=******	***Geophysical Jacobian

## Slide 7

## Slide 8

## Exact Mie Library (DOTLRTv2.1)

**Input Parametrization**
- Mean size parameter ***k<a> ***(with exponential polydisperson)
- Complex effective dielectric constant ***ε******eff ******= ******ε******r ******- j******ε******i***
- Complex effective dielectric constant temperature derivative ***d******ε******eff******/dT = d******ε******r******/dT - jd******ε******i******/dT***
- Total 5x real*8 input parameters with nonlinear indexing
**Output (Product) Parameterization**
- Absorption coefficient
- Multistream scattering matrix (6 streams, 2 polarizations = 72 numbers)
- Derivatives of above WRT temperature and ***k<a>***
- Total 3(1x+72x)=219x real*8 output parameters
**Library Size**
- 2.5 GB for 0.1K error over Hurricane Bonnie run
- Size parameters up to ***k<a> ***= 4
- Goal of 50 MB currently exceeded by ~50x *(needs work!)*

## Absorption Cross Section vs. Dielectric Constant (6 stream)

**Absorption Cross Section vs. Dielectric Constant (6 stream)**

**Real Part of *****ε***

**Imaginary Part of *****ε***

***(Note: color ranges vary)***

***k<a>=*****0.02**

***k<a>=*****0.1**

***k<a>=*****1.0**

***k<a>=*****9.0**

## Scattering Cross Section Matrix Element (1,1) vs. Diel. Const. (6 stream)

**Scattering Cross Section Matrix Element (1,1) vs. Diel. Const. (6 stream)**

**Real Part of *****ε***

**Imaginary Part of *****ε***

***k<a>=*****0.02**

***k<a>=*****0.1**

***k<a>=*****1.0**

***k<a>=*****9.0**

***(Note: color ranges vary)***

## Mie Library Forward Error - Hurricane Bonnie – Full Mie vs Mie Library

**Upwelling T****B**

## Full Stokes 

***Ocean Surface Emission Model***

## Goal

**Develop a standardized fast full-Stokes ocean surface emissivity module for a wind-driven ocean surface applicable at arbritrary microwave frequencies and incidence angles, and thus relevant to all existing and planned conically and cross-track scanned sensors (WindSat, AMSR-E, TMI, SSMI, SSMIS, and CMIS as well as AMSU-A, NPP ATMS, and NPOESS ATMS, and GPM).**
**   **

## Strategy

**   **
**1. Analyze a sufficiently long sequence of WindSat data to derive the wind induced isotropic and anisotropic emissivity variations for all four Stokes parameters. This was done by T. Meissner and F. Wentz [1], and corroborated by this JCSDA study.**

## Strategy (cont’d)

**Strategy (cont’d)**

## Strategy (cont’d)

**Strategy (cont’d)**

## Strategy (cont’d)

**4. However, the Elfouhaily angular spreading function produced non-physical values for ****Ω**** in the Johnson model.** **No existing sea spectrum model was able to  reproduce the WindSat result [1] that the second harmonic of the 3****rd**** Stokes parameter U decreased for wind speeds greater than 12 m/s. The model sea spectrum was thus tuned in both the isotropic and angular spreading parts to  reproduce the WindSat first and second harmonic U results.**

**Strategy (cont’d)**

## Other Spectrum Modifications

**5. The high-frequency portion of the Elfouhaily spectrum was also multiplied by the Pierson-Moskowitz shape spectrum to correct an error in [6].**
**6. The generalized Phillips-Kitaigorodskii equilibrium range parameter for short waves was modeled as continuous function of the friction velocity at the water surface to eliminate a discontinuous jump in the [6] formulation.**
**The following results are for an increase in power of the isotropic Elfouhaily spectrum by 25% compared to the Durden-Vesecky spectrum and a multiplier of the exponential factor in the Durden-Vesecky angular spreading function...**

## Meissner-Wentz vs. Our Results

**M-W**
**WindSat**

**1****st**** Azimuthal Harmonic**

**2****nd**** Azimuthal Harmonic**

**T****V**** 18.7**

## Meissner-Wentz vs. Our Results

**Meissner-Wentz vs. Our Results**

**M-W**
**WindSat**

**1****st**** Azimuthal Harmonic**

**2****nd**** Azimuthal Harmonic**

**T****H**** 18.7**

## Meissner-Wentz vs. Our Results

**Meissner-Wentz vs. Our Results**

**M-W**
**WindSat**

**1****st**** Azimuthal Harmonic**

**2****nd**** Azimuthal Harmonic**

**T****U**** 18.7**

## Meissner-Wentz vs. Our Results

**Meissner-Wentz vs. Our Results**

**M-W**
**WindSat**

**1****st**** Azimuthal Harmonic**
**(-1x)**

**2****nd**** Azimuthal Harmonic**
**(-1x)**

**T****4**** 18.7**

- (Note EE vs physics
- sign conventions!)

## With the Johnson code modified and tuned to the Meissner Wentz WindSat results there are a few more model adjustments/optimizations needed: 
A small adjustment needed for total consistency – replacement of the present dielectric constant of sea water code by the Meissner Wentz dielectric constant [7]. With this change all of the emission values in the following table will be generated by July 2006.
Adjustment of slope pdf of the long-wave portion of the spectrum to converge closer to the WindSat 1st harmonic behavior
Use automated gradient search to jointly optimize model parameters (multiplier for D-V spreading function, amplitude of short- and long wave portions of Elfouhaily spectrum) based upon WindSat 2-look data. 
Tabularize model and derivatives over wind speed and incidence angle range to generate ocean surface emission library:

**A small adjustment needed for total consistency – replacement of the present dielectric constant of sea water code by the Meissner Wentz dielectric constant [7]. With this change all of the emission values in the following table will be generated by July 2006.**
**Adjustment of slope pdf of the long-wave portion of the spectrum to converge closer to the WindSat 1****st**** harmonic behavior**
**Use automated gradient search to jointly optimize model parameters (multiplier for D-V spreading function, amplitude of short- and long wave portions of Elfouhaily spectrum) based upon WindSat 2-look data. **
**Tabularize model and derivatives over wind speed and incidence angle range to generate ocean surface emission library:**

**Ocean Emission – Next Steps**

- Desired
- tabularized
- model
- characteristics

## Precipitation Locking

## All Wx Precipitation Locking Simulator

## All Wx Precipitation Locking Simulator

- Implemented

## All Wx Precipitation Locking Simulator

- Implemented
- In progress

**All Wx Precipitation Locking Simulator**

## Hydrometric Error Covariance Models

- Spatial gradient mapping
- Hydrometric variable error proportional to spatial variance of prognostic field.
- Error covariance proportional to joint spatial variance
- Temporal gradient operator
- Requires tangent linear NWP time-operator

## Snow Emission Modeling

## Gridded Corrected Emissivity Maps CLPX 37 GHz North Park

## CLPX  ISA – PSR Comparison

**CLPX  ISA – PSR Comparison**

## Slide 33

## Slide 34

## Future Plans

## Complete compact Mie library for DOTLRTv2.1
Compress in dielectric space by ~(3x)(3x)=9x
Compress in d/dT space by ~1.5x
Compress in product space by ~4x using integer log mapping
If necessary: Can compress in product space using Henyey-Greenstein phase function by ~73x
Complete comprehensive ocean surface emission model and integrate into DOTLRTv2.1
Minimize error over long wave spectrum and modulation function to fit WindSat first azimuthal harmonic
Develop harmonic coefficient table with Jacobian
Develop and demostrate precipitation locking testbed
Develop/test hydrometric error covariance estimator
Incorporate snow emission spectral model
Regress PSR aircraft emissivity data to dense media RT model

**Complete compact Mie library for DOTLRTv2.1**
- Compress in dielectric space by ~(3x)(3x)=9x
- Compress in ***d/dT*** space by ~1.5x
- Compress in product space by ~4x using integer log mapping
- If necessary: Can compress in product space using Henyey-Greenstein phase function by ~73x
**Complete comprehensive ocean surface emission model and integrate into DOTLRTv2.1**
- Minimize error over long wave spectrum and modulation function to fit WindSat first azimuthal harmonic
- Develop harmonic coefficient table with Jacobian
**Develop and demostrate precipitation locking testbed**
- Develop/test hydrometric error covariance estimator
**Incorporate snow emission spectral model**
- Regress PSR aircraft emissivity data to dense media RT model

## DOTLRTv2.1 will contain major improvements over v1.0b, and is being designed to be directly usable within or readily transferable to operational environments.

All-weather precipitation locking demonstration anticipated to provide insight into use of microwave data under arbitrary cloud/precipitation conditions.

RT modeling effort transferred to and ongoing within the CU Center for Environmental Technology.

**DOTLRTv2.1 will contain major improvements over v1.0b, and is being designed to be directly usable within or readily transferable to operational environments.**
**All-weather precipitation locking demonstration anticipated to provide insight into use of microwave data under arbitrary cloud/precipitation conditions.**
**RT modeling effort transferred to and ongoing within the CU Center for Environmental Technology.**

## References (Ocean Emission)

- [2] Yueh, S.H., “Modeling of Wind Direction Signals in Polarimetric Sea Surface Brightness Temperatures”, *IEEE Trans. Geosci. Remote Sens.*, vol. 35, pp. 1400-1418, 1997.
- [3] Johnson, J.T., “An Efficient Two-scale Model for the Computation of Thermal Emission and Atmospheric Reflection From the Sea surface”, *IEEE Trans. Geosci. Remote Sens.*, vol. 44, pp. 560-568, 2006.
- [4] Wentz, F.J., and T. Meissner, “Algorithm Theoretical Basis Document: AMSR Ocean Algorithm, version 2, report from Remote Sensing Systems, available at *www.remss.com.*
- [5] Durden, S.L., and J.F. Vesecky, “A Physical Radar Cross-Section Model for a Wind Driven Sea with Swell, *IEEE Trans. Geosci. Remote Sens.*, vol. OE-10, pp.445-451, 1985.
- [6] Elfouhaily, T., B. Charon, K. Katsaros, and D. Vandemark, “A Unified Directional Spectrum for Long and Short Wind-driven Waves”, *J. Geophys. Res.*, vol. 102, C7, pp. 15781-15796, 1997.
- [7] Meissner, T., and F. Wentz, “The Complex Dielectric constant of Pure and
- Sea Water from Micorwave Satellite Observations”, *IEEE Trans. Geosci. Remote Sens., *vol. 42, 1836-1849, 2004.

**References (Ocean Emission)**

## Slide 39