College Park, MD November 14, 2012JCSDA Seminar Developments in Radiative Transfer Modeling, Microwave Observing Systems, and Radiance Assimilation over

College Park, MDNovember 14, 2012JCSDA Seminar

Developments in Radiative Transfer Modeling, Microwave Observing Systems, and Radiance

Assimilation over Clouds

Professor Albin J. Gasiewski

NOAA-CU Center for Environmental TechnologyDepartment of Electrical and Computer Engineering

University of Colorado, Boulder, CO, USA

Thanks to: Bob Weber (DeTect, Inc.)Miao Tian (CU/ECEE)

Srikumar Sandeep (CU/ECEE)Brian Sanders (CU CoSGC)


Topics

High spatio-temporal resolution microwave observing system concepts:

- Geostationary (PATH: GEM and GeoSTAR)- LEO Cubesat fleet

Prospects for microwave radiance assimilation over clouds by “precipitation locking”

Polarimetric microwave atmospheric and surface emission models

- Extension of DOTLRT- Mie look-up libraries


Microwave Imaging and Sounding from Geostationary Orbit


NRC Decadal Survey & PATH

• NRC = U.S. National Research Council, which conducted a decadal survey of Earth satellite missions in 2006-07:Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond Committee on Earth Science and Applications from Space: A Community Assessment and Strategy for the Future (2007)*

• PATH = Precipitation, Atmospheric Temperature and Humidity mission

– One of ten approved new Earth science missions to be conducted by NASA

– Tier 3 mission to be launched 2016-2020 ($450M)

• Based on implementation of an “Array Spectrometer”

* http://www.nap.edu/catalog.php?record_id=11281


PATH Capabilities

• All-weather AMSU-class temperature and humidity sounding at ~15-30 minute intervals over a large fraction (up to ~25%) of Earth’s surface– Mesoscale weather forecasting

• Imaging of precipitation and convective thermodynamics beneath cloud tops and at time scales relevant for precipitation– Quantitative precipitation forecasting (QPF)– Hurricane intensification– Global water and energy cycling

• Cross-calibration and temporal interpolation of low-earth orbiting sensors (GMI, JPSS, …)


GEM Spatial Resolution

3-dB best resolution degrades by ~1.3x to ~21 km at 50o latitude. Oversampling by ~2x above Nyquist expected to recover ~30-40% of this lost resolution for high SNR cases.


GEM Concept SummaryGEosynchronous Microwave (GEM) Sensor*

* Geosynchronous Microwave Sounder Working Group, Chair: D.H. Staelin (MIT)

Azimuth Motor& Compensator

Elevation Motor& Compensator

Nodding / MorphingSubreflector

Space Calibration Tube

BackupStructure

3” Thick Composite Reflector

54GHz Feeds &

Receivers

Estimated Mass ~65 kg

• Baseline system using 54, 118, 183, 380, and 424 GHz with ~2 m diameter Cassegrain antenna.

• ~16 km subsatellite resolution (~12 km using oversampling) above 2-5 km altitude at highest frequency channels.

• The 380 and 424 GHz channels selected to map precipitation through most optically opaque clouds at sub-hourly intervals. (Gasiewski, TGARS, 1992)

• Temperature and humidity sounding channels penetrate clouds sufficiently to drive NWP models with ~hourly data.

• Estimated 2010 costs: ~US$50M non-recurring plus ~US$45M/unit.


GEM Geo-Microwave Bands

5 principal bands being considered


GEM Vertical Response- Clear Air -

Klein & Gasiewski, JGR-ATM, July 2000

Clear-air incemental weighting functions

O2 118.750 GHz424.763 GHz

H2O 183.310 GHz380.197/340


Effects of Hydrometeors on Microwave Signatures

Scattering and absorption by hydrometeors needs to be considered in all-weather microwave radiance assimilation both to extend soundings into cloudy regions and “lock” NWP models to raincell occurrence.

Liquid Ice


GEM Simulated SMMW ImagerySpectral Response

Opaque

Transparent+/-0.6 GHz

+/-1.0 GHz

+/-1.5 GHz

424.763+/-4.0 GHz

Hurricane Opal1995

MM5/MRTReisner 5-phase


~6.5 kmNodding subreflector scans ~200-km swath,1 second per scan with0.1 sec retrace, ~6.5 km swath spacing for Nyquist sampling

200-km swaths are assembled into regional precipitation maps; antenna slews between regions in ~20 seconds

GEM/GOMAS Micro-Scan Concept

Nodding subreflector and slow steady scanning has

minimal momentum impact; primarily images rainy areas

200 km

Example ofscanning

16 km/sec

6.5 km/sec


GEM Sensitivity & Scan Times

Assumptions: - Midlatitude (30o-60o annual averaged atmosphere)- Nyquist sampling at 424 beamwidth- Averaging of beams to fundamental deconvolved resolution for each band

* Further reductions in TRMS achievable via additional spatial averaging.

• CONUS imaging time (3000 x 5000 km2) : 90 minutes

• Regional (1500 x 1500 km2) : ~15 minutesBand(GHz)

3-dB IFOV

(km, SSP)

Deconvolved Resolution(km, SSP)

TRMS

(K)TRMS

Required(K,SNR=100)

Probing Height

(km)

50-56 138.6 ~104 0.03-0.07 0.1-0.6 Surf

118.705 60.2 ~45 0.03-0.6 ~ 0.1-0.6 Surf

183.310 41.9 ~31 0.04-0.15 0.3-0.6 Surf

380.153 20.5 ~16 0.2-2.1 * 0.3-0.5 ~2.5

424.763 16.4 ~12 0.5-5.3 * 0.4-0.6 ~4

Downlink rate ~45 kb/sec at ~17 msec sample period


Filled Aperture (GEM) vs.

Synthetic Aperture (GeoSTAR)Considerations


Interferometric Imaging

Principle: Measure the complex field corelation function REa

(ρx, ρy,0) in an aperture plane, then apply a 2-D spatial

Fourier transform to obtain the angular distribution of radiation intensity. Practical issues include:

• Sampling (density, range, angular sensitivity)• Integration noise and bandwidth (fringe washing)• Absolute calibration (magnitude and phase)• Data corelation techniques

College Park, MDNovember 14, 2012JCSDA Seminar 16

SMOS – Soil Moisture and Ocean SalinityESA Project: L-band, Polar low-Earth orbit, Launched November 2, 2009

L-band: 1400-1427 MHz69 total elements in Y-array (21 elements per arm X three arms)

6.75-m maximum baselineDual polarimetric (Tx,Ty)

Surface resolution: ~50 km at 775 km altitude

Instantaneous (non-aliased) FOV :

17

SMOS Imagery over Scandinavia


GeoSTAR Concept2-D Geostationary Sounder/Imager

Y-Array of ~hundreds (N) of receiver elements and ~tens to hundreds of thousand (N2) one-bit corelators in AMSU A/B bands of 50-56 and 183 GHz.

GeoSTAR spatial response pattern for 298 elements with 2.8lspacing • ~50/25 km spatial resolution (55/183 GHz)• ~60% disk image every one hour• No moving parts or momentum transfer• ~2.5m maximum baseline• NASA/JPL concept (B. Lambrigtsen, PI)


Major Aperture Synthesis Issues

• Receiver power, weight, reliability, and cost

Approximately 1000 receivers and antennas are required in the 50-120 and 50-190 GHz bands for ~18 km resolution for precipitation, impacting power, weight, reliability, and cost.

• Corelator complexity and power

1000 receivers in a Y-array would require ~500,000 digital corelators per band that measure magnitude and phase. Additional bands and channels have large to moderate cost.

• Suitability to observational needs for rapidly evolving weather

Is full-disk imaging desirable over “random access” imaging using a scanned filled aperture system?


GEO vs LEO Considerationsfor High Spatio-temporal Resolution


LEO Fleet Concept

CU RadSat 118-GHz 8-channel CubeSat imager/Sounder on CU All-STAR 3-U bus

• Microwave imaging/sounding from altitude can provide ~15 km (or better) spatial resolution from ~350 km altitude using 3-U CubeSat envelope for all frequencies above ~90 GHz

• Fleet concept requires ~48 units in staggered orbital planes for GEO-equivalent temporal resolution

• Low altitude limits lifetimes on orbit to less than 2 years

• Economy of scale and simplicity of launch provide competitive cost model with regular tech- nology updates

• Challenges include power management & communications.


All-STAR Development Bus


Geomicrowave Pathway Study:

An Extended Kalman Filter System Demonstration


Geomicrowave Pathway Study

• Goal: Provide an independent assessment of GEM, GeoSTAR, and LEO fleet systems based on NOAA NWS forecasting needs.

• Basis: System tradeoff studies and OSSEs using optimal precipitation and sounding retrieval and radiance assimilation techniques

• Strategy: Develop concept of hydrometric tracking (“precipitation locking”). Concept pushes state of the art in extended Kalman filtering for highly nonlinear and multidimensional processes.


MM5 RT Hurricane Simulations

Hurricane Bonnie, August 26, 1998, 0000-2430 UTC

24-Hr simulation, 6-km innermost nested grid, 15-minute archived frames

MM5/MRT Reisner 5-phase simulations, statistically validated*

DOTLRTv1.0c Fast DO scattering-based Radiative Jacobian with 6 streams and 60 vertical levels**

* Skofronik-Jackson, G.M., A.J. Gasiewski, and J.R. Wang, "The Influence of Microphysical Parameterizations on Microwave Brightness Temperatures," IEEE Trans. Geosci. Remote Sensing, vol. 40, No. 1, pp. 187-196, February 2002.

** Voronovich, A.G., A.J. Gasiewski, and B.L. Weber, "A Fast Multistream Scattering-Based Jacobian for Microwave Radiance Assimilation," IEEE Trans. Geosci. Remote Sensing, vol. 42, no. 8, pp. 1749-1761, August 2004.


420.7631 GHz (O2 Transparent)- Full Resolution TB Imagery -


420.7631 GHz (O2 Transparent)- GEM 2-m TA Imagery -


113.7503 GHz (O2 Transparent)- Full Resolution TB Imagery -


113.7503 GHz (O2 Transparent)- GEM 2-m TA Imagery -


TB

S

TB

A

TB

T

S

TB

g

a

TB


Jacobian Components

H=HI HR HG

H = Total Jacobian

HI = Instrument Jacobian

HR = Radiation JacobianHG = Geophysical

Jacobian



NWP Precipitation “Locking”

• To realize “locking” of an NWP model onto precipitation, observations are needed at time and space scales of order ~5-15 km and ~15 minutes.

• Locking is analogous to phase-locked loop in electrical engineering wherein linear phase differencing is achieved only when oscillator and signal remain within same phase cycle.

• Similarly, linear NWP model updates can be achieved provided that the cloud and precipitation state does not decorrelate between satellite observations.


TB

S

TB

A

TB

T

424+/-4 GHz - 15 min time steps


TB

S

TB

A

TB

T

424+/-4 GHz – 3 hour time steps


Hurricane Bonnie, August 26, 1998, 0900 UTC

GEM Response to Precipitation Jacobian Cross-sections at 183±17 GHz

MM5/MRT Reisner 5-phase with DO RT model at 183.310 ± 17 GHz

33o

TB

S

TB

A

TB

T


Hurricane Bonnie, August 26, 1998, 0900 UTC

GEM Response to Precipitation Jacobian Cross-sections at 424±4 GHz

MM5/MRT Reisner 5-phase with DO RT model at 424.763 ± 4 GHz

33o

TB

S

TB

A

TB

T


Sampling Requirements for NWP Precipitation Locking

The sampling requirements for all-weather microwave assimilation using near-term NWP models (especially regional models) are well satisfied by a large-aperture geosynchronous microwave imaging sounder or fleet of low cost microwave imaging sounders


Hydrometric Tracking Simulator

DOTLRTv1.0cSOSFilled ApertureSynthetic Aperture

NWP (MM5)Assimilation StepError Covariance Model

DOTLRTv1.0cSOSFilled ApertureSynthetic Aperture

+

n

…

Σ

…

+

-

XKF(Nonlinear IterativeD-matrix)State Vector Update

ECU

Observed GEO Data (future)

…

Truth Radiances

Innovations

…

Initial State

……

Iterate State

Corrected State

…

Forecast State

Simulated Truth State Sequence

NWP Model Radiances

…

…

Error Covariance

Jacobian

Gasiewski and Weber

Radiative Transfer and Sensor Model

Radiative Transfer and Sensor Model (truth)

Corrector:

Predictor:

Kalman gain (D-matrix):

Error covariance update:

Initial conditions:

Extended Kalman Filter (XKF)


50.3 GHz Innovations (O2 Transparent)- First Frame Innovations Convergence -


378.6974 GHz Innovations (H2O Transparent)- First Frame Innovations Convergence -


Innovation Trends – 166.3 GHzFull-Frame Error Covariance


Prognostic Variable Errors – Temperature – Lower Troposphere- First Frame Innovations Convergence -


Prognostic Variable Errors – Water Vapor – Lower Troposphere- First Frame Innovations Convergence -


Prognostic Variable Errors – Rain – Columnar- First Frame Innovations Convergence -


Prognostic Variable Errors – Cloud Ice – Columnar- First Frame Innovations Convergence -


Unified Microwave Radiative Transfer Model

(UMRT)


Unified MRT Model (UMRT)

Attribute UMRT DOTLRT *Fast, Stable Analytic Matrix Inversion Yes Yes

Fast Jacobian Yes, extended Yes

Phase MatrixReduced Mie or DMRT

(4x4)Reduced HG (2x2)

Media Sparse and Dense Sparse

PolarizationTri-polarization

+ 4th StokesSingle-polarization

Interface Refraction / Internal Reflection Yes No

Radiation Stream Interpolation Yes, cubic spline No

Thermal Emission Approximation Linear dependence Constant

Level/Layer Centric Level Centric Layer Centric

* Voronovich, A.G., A.J. Gasiewski, and B.L. Weber, "A Fast Multistream Scattering Based Jacobian for Microwave Radiance Assimilation,“ IEEE Trans. Geosci. Remote Sensing, vol. 42, pp. 1749-1761, August 2004.

Goal: Develop a unified microwave radiative transfer (UMRT) model having polarimetric applicability to sparse and dense scattering layers


UMRT Layering

(modified from Golden et al., 1998)

Upper-half, Sparse Medium

Lower-half, Dense Medium

• Specular interface and Snell’s law are applied at each layer boundary.

• Linear temperature profile applied in each layer

Upper-half, Sparse medium:a) General atmosphereb) Weakly homogeneous and slightly dissipativec) Incoherent scattering: scattering intensity is the sum of scattering intensities from each particle.d) Particle size distribution functione) Sparse medium radiative transfer

Lower-half, Dense medium: a) Ice, snow, soil and etc., b) Inhomogeneous and strongly dissipative c) Quasi- coherent volume

scattering: scattering intensity considered effects of neighboring particles.

d) Pair distribution function (Percus-Yevick Approximation).

e) Dense medium radiative transfer (DMRT)

CET 2012 July, 2012 Boulder, USA

(2a)

h

(2b)

(2c)

L. 1

L. n

2a) A fast and stable solution to reflection and transmission of a single layer

UMRT Layer Solution


CLPX Intercomparisons (2003)

Cold Land Processes Field Experiment (CLPX): GBMR-7 measurements in Colorado, 02/20/2003

UMRT Model: step through

18.7 GHz

36.5 GHz


Mie Library Tabularization: Enabling Computational Speed


Compact Fast Mie Library*

• Problem: Full Mie series calculations – especially for the geophysical Jacobian – require integration over a size distribution of a recursive series of calculations. Each recursive term requires Bessel evaluation. This is often repeated, and time consuming!

• Solution: Code Mie calculations for absorption, scattering, and asymmetry (and all derivatives) for ice and liquid exponential spherical polydispersions into a compact (few hundred kB) package with better than

~10-3 precision.

• Strategy: B-spline look-up procedure for speed and Jacobian capability. Current model uses data cube interpolation over f=1 to 1000 GHz, T=-50 to 50C, <D>=0.03 to 30 mm.

* Sandeep, S., and A.J. Gasiewski, "Fast Jacobian Mie Library for Terrestrial Hydrometeors," IEEE Trans. Geosci. Remote Sensing, vol. 50, no. 3, March 2012.


Fast B-Spline Mie Absorption

0oC Exponential Polydispersion

Liquid Ice


Fast B-Spline Mie Scattering


Liquid Ice


Liquid Ice

Fast B-Spline Mie Absorption Jacobian



Fast B-Spline Mie Scattering Jacobian


Liquid Ice


Computation Savings

Size : 6 B- spline LUTs:

~ 8 MB

Significant time saving for calculation of parameters for large hydrometeors at high frequencies

Applicable to specific sensor channels


Summary• A large-aperture geosynchronous microwave sounder or

dense low-cost LEO fleet satisfies the sampling requirements necessary for “precipitation locking.” CubeSat imaging sounders may be cost-competitive with GEO imaging sounders.

• Fast forward scattering-based RT modeling algorithm development to provide full Jacobian for XKF-based radiance assimilation has progressed, thus facilitating simulations and (potentially) operational assimilation.

• First-frame Extended Kalman Filter locking using iterative LMMSE in 2D-Var scheme are encouraging. Tracking studies over successive frames and horizontal spatial stabilization is needed.


Backup Slides


SMMW Degrees of Freedom- Maritime Convective Precipitation -

Nonlinear Karhunen-Loeve(KL) mode decomposition:MIR 150, 220, & 325±9 GHz

channels

(Gasiewski 1996, unpublished)

~20

0 km

k1 k2 k3150 220 325±9


GEM Mass, Power, Slew, Data Rate2-meter System – MIT/LL Study

Total Mass ~66 kg

MovingMass

~53 kg(momentum

compensated)

Main ReflectorMax Slew Rate

~0.1o/sec

Power~125-150 W

Data~64 kbps

Component Number Weight (kg) Weight (lb)

Main reflector 1 15.00 33.07

Subreflector 1 0.07 0.15

Strut 3 0.97 2.14

Subreflector support structure 1 1.78 3.92

Subreflector nodding actuator 1 1.00 2.20

Antenna shape-sensing hardware 1 1.00 2.20

Back structure collar 1 3.53 7.78

Back structure vanes 3 4.75 10.47

Rotary calibration optic 1 0.25 0.55

Rotary optic drive motor 1 0.70 1.54

RF feedhorns 5 1.50 3.31

Calibration bodies 2 2.00 4.41

Instrument mounting structure 1 2.00 4.41

Space tube 1 0.60 1.32

Receivers 5 18.00 39.68

Dichroic 1 0.25 0.55

Subtotal 53.40 117.72

Elevation structure & mechanisms 1 6.35 14.00

Azimuth structure & mechanisms 1 6.40 14.11

Total 66.15 145.83


Fast Scattering-Based Jacobian Algorithm*

• Planar stratified atmosphere• Liebe MPM 87 & 93 gaseous absorption model• Polydispersive Mie solution for five phase of water: Cloud (liquid), Rain (liquid), Graupel (liquid + solid), Snow (solid), Cloud Ice (solid)• Discrete-ordinate layer-adding solution• Incremental response to changes in bulk absorption and scattering coefficients and temperature• Efficiency compatible with satellite data streams• Stable & applicable for arbitrary wavelengths• Henyey-Greenstein hydrometeor phase matrix (v1.0), extended to incorporate an “exact” Mie library (v2.1)* Voronovich, A., A.J. Gasiewski, and B.L. Weber, "A Fast Multistream

Scattering-Based Jacobian for Microwave Radiance Assimilation," IEEE Trans. Geosci. Remote Sensing, August, 2004.


Potential Capabilities of Precipitation Locking (LEO or GEO)

• Extended thermodynamic information (water vapor and temperature fields) within frontal regions - beyond that of IR sounders

• Short-term prediction of mesoscale convection for warnings with high specificity - initialization of explicit cloud models based on existing precipitation fields

• Tracking of latent heat exchange within precipitation - indirect improvements in thermodynamic knowledge within frontal zones

• Improved accuracy of cloud and radiation products as a result of more accurate characterization of cloud parameters


Basic Technique

Maximum a posteriori estimation minimizes the following cost function J :

1 1Tb bJ x x B x x h x y R h x y

The basic linear solution:

11 1 1a b T T bx x B H R H H R y h x

Hh

x

Tangent linear approximationH for non linear observation

operator h :

The state vector x can include precipitation distribution parameterse.g., up to 4 parameters per hydrometeor phase for a Gamma distribution,

At 5 phases => up to 20 hydrometeor parameters at each level


56.325 GHz (O2 Opaque)- Full Resolution TB Imagery -

Link


56.325 GHz (O2 Opaque)- GEM 2-m TA Imagery -

Link

Documents

College Park, MD November 14, 2012JCSDA Seminar Developments in Radiative Transfer Modeling, Microwave Observing Systems, and Radiance Assimilation over