college park, md november 14, 2012jcsda seminar developments in radiative transfer modeling,...
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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)
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
Microwave Imaging and Sounding from Geostationary Orbit
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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, …)
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
GEM Geo-Microwave Bands
5 principal bands being considered
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
~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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
Filled Aperture (GEM) vs.
Synthetic Aperture (GeoSTAR)Considerations
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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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 :
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17
SMOS Imagery over Scandinavia
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College Park, MDNovember 14, 2012JCSDA Seminar
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)
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College Park, MDNovember 14, 2012JCSDA Seminar
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?
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College Park, MDNovember 14, 2012JCSDA Seminar
GEO vs LEO Considerationsfor High Spatio-temporal Resolution
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
All-STAR Development Bus
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College Park, MDNovember 14, 2012JCSDA Seminar
Geomicrowave Pathway Study:
An Extended Kalman Filter System Demonstration
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
420.7631 GHz (O2 Transparent)- Full Resolution TB Imagery -
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College Park, MDNovember 14, 2012JCSDA Seminar
420.7631 GHz (O2 Transparent)- GEM 2-m TA Imagery -
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College Park, MDNovember 14, 2012JCSDA Seminar
113.7503 GHz (O2 Transparent)- Full Resolution TB Imagery -
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College Park, MDNovember 14, 2012JCSDA Seminar
113.7503 GHz (O2 Transparent)- GEM 2-m TA Imagery -
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College Park, MDNovember 14, 2012JCSDA Seminar
TB
S
TB
A
TB
T
S
TB
g
a
TB
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College Park, MDNovember 14, 2012JCSDA Seminar
Jacobian Components
H=HI HR HG
H = Total Jacobian
HI = Instrument Jacobian
HR = Radiation JacobianHG = Geophysical
Jacobian
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College Park, MDNovember 14, 2012JCSDA Seminar
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
TB
S
TB
A
TB
T
424+/-4 GHz - 15 min time steps
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College Park, MDNovember 14, 2012JCSDA Seminar
TB
S
TB
A
TB
T
424+/-4 GHz – 3 hour time steps
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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)
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Corrector:
Predictor:
Kalman gain (D-matrix):
Error covariance update:
Initial conditions:
Extended Kalman Filter (XKF)
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College Park, MDNovember 14, 2012JCSDA Seminar
50.3 GHz Innovations (O2 Transparent)- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
378.6974 GHz Innovations (H2O Transparent)- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
Innovation Trends – 166.3 GHzFull-Frame Error Covariance
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College Park, MDNovember 14, 2012JCSDA Seminar
Prognostic Variable Errors – Temperature – Lower Troposphere- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
Prognostic Variable Errors – Water Vapor – Lower Troposphere- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
Prognostic Variable Errors – Rain – Columnar- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
Prognostic Variable Errors – Cloud Ice – Columnar- First Frame Innovations Convergence -
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College Park, MDNovember 14, 2012JCSDA Seminar
Unified Microwave Radiative Transfer Model
(UMRT)
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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)
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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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
Mie Library Tabularization: Enabling Computational Speed
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
Fast B-Spline Mie Absorption
0oC Exponential Polydispersion
Liquid Ice
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College Park, MDNovember 14, 2012JCSDA Seminar
Fast B-Spline Mie Scattering
0oC Exponential Polydispersion
Liquid Ice
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College Park, MDNovember 14, 2012JCSDA Seminar
Liquid Ice
Fast B-Spline Mie Absorption Jacobian
0oC Exponential Polydispersion
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College Park, MDNovember 14, 2012JCSDA Seminar
Fast B-Spline Mie Scattering Jacobian
0oC Exponential Polydispersion
Liquid Ice
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
Backup Slides
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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.
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
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
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College Park, MDNovember 14, 2012JCSDA Seminar
56.325 GHz (O2 Opaque)- Full Resolution TB Imagery -
Link
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College Park, MDNovember 14, 2012JCSDA Seminar
56.325 GHz (O2 Opaque)- GEM 2-m TA Imagery -
Link