# AT737 Temperature Sounding Oct. 4, 2010. AT737 Temperature Sounding2 Sounding sounding n (15c) 1 a : measurement of depth esp. with a sounding line b.

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AT737 Temperature Sounding Oct. 4, 2010

AT737 Temperature Sounding2 Sounding sounding n (15c) 1 a : measurement of depth esp. with a sounding line b : the depth so ascertained c pl : a place or part of a body of water where a hand sounding line will reach bottom 2 : measurement of atmospheric conditions at various heights 3 : a probe, test, or sampling of opinion or intention Merriam Webster’s Collegiate Dictionary, tenth edition

AT737 Temperature Sounding3 Schwarzchild’s Equation Assume no scattering. Then the Radiative Transfer Eq. becomes: Solution: surface termatmospheric term

AT737 Temperature Sounding4 Weighting Function Vertical transmittance Weighting Function

AT737 Temperature Sounding5 Weighting Function If you know the mixing ratio of the absorbing gas, you can calculate the atmospheric temperature

AT737 Temperature Sounding6 Weighting Function Shape  x   W Transmittance to satellite For a well-mixed gas, the absorption coefficient is dominated by atmospheric density Product has a definite peak

AT737 Temperature Sounding7 Properties of the Weighting Function Weighting function weights the Planck radiance Measured radiance is a weighted average of Planck function plus a surface term Weighting function is unavoidably broad

AT737 Temperature Sounding8 Sampling the Atmosphere Create a family of weighting functions by changing the wavelength/spectral resolution (mass absorption coefficient) But…

AT737 Temperature Sounding9 The Real World is Messy 1 2 3 4 GOES Sounder Channels Transmittance above 40 km

AT737 Temperature Sounding10 GOES Sounder Weighting Functions Not as “regular” as one would like

AT737 Temperature Sounding11 AMSU Weighting Functions

AT737 Temperature Sounding12 Spectrometers IASI (Four Adjacent Spectra Red, black, blue, green) AIRS (1528 Retrieval Channels in Red) 10 5 (  m) 7 8 6 9412.5

AT737 Temperature Sounding13 AIRS Weighting Functions 2378 Channels!

AT737 Temperature Sounding14 Sounding Retrieval Lots of ways to do it. One way: 1.Make a first guess (the better the first guess, the better the result) 2.Calculate radiances 3.Compare with satellite-observed radiances 4.Adjust temperatures to better match radiances 5.Repeat until satisfactory convergence is achieved.

AT737 Temperature Sounding15 Sounding Retrieval Because weighting functions are broad, retrieved soundings are smooth.

AT737 Temperature Sounding16 Limb Sounding Great vertical resolution… …but poor horizontal resolution.

AT737 Temperature Sounding17 Soundings for NWP Direct Radiance Insertion Model ingests radiances Retrieval done inside model Big advantage: retrieved temps consistent with other model fields, so the results persist, rather than radiating away as gravity waves. Volume of satellite data much larger than volume of conventional data even though only a fraction of satellite data are used

AT737 Temperature Sounding18 CIRA 1DVAR Optimal Estimator (C1DOE) Data Flow C1DOE Retrieval AMSU-AAMSU-B SST / LST (GDAS) Dynamic Data Land Emissivity (MEM - AGRMET) Outputs Mixing ratio profile, temperature profile, cloud liquid water profile 6 Emissivity bands TPW Integrated CLW Many diagnostics! Errors and Correlations (S a and S y ) Instrument Properties (Capability for SSMIS) T(p), RH (p), T sfc (GDAS) Cloud mask (optional) First Guess and a priori data Near real-time system has been demonstrated

AT737 Temperature Sounding19 Bias Correction for RTM Vital Channel -4 -2 0 2 4 windows DTb Obs – Model (K) 26 level – 7 level RTM 1 2 3 4 5 6 7 8 16 17 18 19 20 Channel 0 -2 -4 2 4 1 2 3 4 5 6 7 8 16 17 18 19 20 Model Bias for 26 vertical RTM levels Minus 7 Levels CH 1 = 23.8 CH 2 = 31.4 CH 3 = 50.3 CH 4-8 = T(p) CH 16 = 89 CH 17 = 150CH 18-20 = 183 window windows window Simulated TB’s calculated from pristine, clear sky, island sonde matchups and compared to AMSU TB’s. Further refinement in progress All zenith angles

AT737 Temperature Sounding20 C1DOE Retrieval Methodology First guess atmosphere and surface Calculate weighting functions (sensitivity) Forward problem solved to yield estimates of the radiance in each channel Millimeter Wave Propagation (MPM92) Model (Liebe et al. 1993) Rayleigh cloud droplet absorption (Liebe et al. 1991) assuming a plane parallel, non-scattering atmosphere Match observed and modeled radiances Iterative process Additional details in Rodgers (2000)

AT737 Temperature Sounding21 Inverse problems Satellites provide measurements of radiation (i.e. brightness temperatures). The user must make use of models in order to extrapolate atmospheric parameters from these measurements. This is known as an inverse problem. The nature of inverse problems can be understood using the “footprint” analogy.

AT737 Temperature Sounding22 Inverse problems (cont.) The relationship between the measured radiances, and the state vector is given by: where x is the state vector, b contains the model parameters,  y is the measurement error, and f is the forward model.

AT737 Temperature Sounding23 Inverse problems (cont.) Linearizing about the real state vector and the real model parameters leads to: where x contains the estimated water vapor profiles, temperature profiles and 5 emissivities, and b is the estimated model parameter vector. The derivative terms are important for determining sensitivities of the radiances to both the model parameters and the water vapor profiles.

AT737 Temperature Sounding24 Optimal Estimation OE is a method used to introduce constraints to a system A cost function must be minimized in order to find the optimal solution for the atmospheric state

AT737 Temperature Sounding25 Cost function The cost function used in the C1DOE is given by: The first term is a penalty for deviating from the first guess (first guess and a priori are equivalent in this retrieval). This limits the outcome to only physical solutions. The second term is a penalty for deviations of the simulated radiances from the forward model output. This is a way to constrain the forward model and observational errors.

AT737 Temperature Sounding26 C1DOE cost function (Φ): *Error per channel (<= 3.5 K) NEDT (noise) Forward Model error Biases: sensor - model Minimize Differences between Observed and Simulated Tbs Minimize Differences between a priori and retrieved states *A priori errors q(p): 25-50% RH w(p): 0.15 mm T(p): 1.5 K, ε: 0.01 A priori ensures solution is physical and acts as a virtual measurement to further constrain the problem.

AT737 Temperature Sounding27 Data – The Advanced Microwave Sounding Unit (AMSU) Two modules: AMSU – A and AMSU – B (MHS) 20 channels: 23.8 to 183 GHz Spatial resolution from 16 – 48 km at nadir NEDT values ranging from 0.11 to 1.06 K (very low) On NOAA satellites and Aqua Microwave Transmittance Spectrum 183 GHz used for moisture sounding

AT737 Temperature Sounding28 AMSU Data came from the Advanced Microwave Sounding Unit (AMSU) 20 channel microwave radiometer Ch. 1-15 used for temperature (AMSU-A) Ch. 16-20 used for water vapor (AMSU-B)

AT737 Temperature Sounding29 AMSU-A Channelization Table 3.3.2.1-1. Channel Characteristics and Specifications of AMSU-A

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