Application of AIRS v5.0 Averaging Kernels Eric Maddy, Chris - - PowerPoint PPT Presentation
Application of AIRS v5.0 Averaging Kernels Eric Maddy, Chris Barnet, Murty Divakarla, Jennifer Wei, Antonia Gambacorta, Mitch Goldberg 10/6/06 AIRS Science Team Meeting Greenbelt, MD 1 Outline Provide an overview of v5.0 averaging
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90hPa 151hPa 250hPa 350hPa 670hPa
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– Related to the amount of information determined from the radiances and how much is due to the first guess [Rodgers, 1976].
measurements vs. retrievals due to incorrect first guesses.
– Related to the vertical resolution of retrievals [Backus and Gilbert, 1969; Conrath, 1972; Rodgers, 1976; Purser and Huang, 1993] – Required by modelers to properly use AIRS trace gas products. – Enables assessment of retrieval skill on a case by case basis.
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correlation of products because the startup regression solution (T/H2O/O3) has it’s own averaging kernel.
– This becomes important only when our products are overdamped. – We (NOAA) have the ability to calculate this averaging kernel for case studies if necessary.
interpretation
– There is a cross-talk between averaging kernels that is not addressed properly.
averaging kernel for products does not exactly relate to the amount of the radiances believed.
intelligent selection of channels minimizes this effect.
– Non-linearity (I won’t go into this too much here) is not properly handled by the linear averaging kernel analysis.
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adequately with respect to channel temperature and gaseous kernel functions.
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– Define a reduced measurement space on which finite difference derivatives are calculated. – Ensure a smooth product (interpolation).
j j L L
,
Coarse layer retrieved quantities Fine level/layer retrieved quantities interpolated onto RTA grid.
j L,
' , ' ' , ' 1 ' , , ' ' ' , L L T L j j L T L j L L L j j
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[Rodgers and Connor 2003] form of the equation assumes linearity in changes in state. For temperature this is true and we have: For minor constituents (H2O, O3, CO, CH4, etc.) the averaging kernels act in logarithmic or %changes in state:
For small perturbations/low information content we can write in terms of % changes relative to the first guess:
First Guess Averaging Kernel Truth Unit vector
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The retrieval calculates coarse layer derivatives and assigns retrieved changes to fine layers using slb2fin (trapezoids denoted ). We can handle the trapezoidal retrieval functions in much the same way that the retrieval handles them by:
and use the functions to interpolate to the RTA grid.
' , ' ' , ' 1 ' , , ' ' ' , L L T L j j L T L j L L L j j
' ' , , ,
j j j j j j L L L L
j L,
Minor gases: Let: x = log(x)
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' ' , 1 , , ' ' , ,
L T L j j L T L j j j j L L
Averaging Kernel Smoothing
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assuming averaging kernel = identity matrix
– Ideal case -- what we would do in the absence of damping.
case dependent averaging kernel. Retrieval and Convolved Sonde Compare very well.
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RTA grid.
dependent on the trapezoid spacing, variability in the truth and variability in the first guess).
' ' , ' , ,
L L j j L L L L
L L j j L L j j L L L L j j L L
+
, ' ' , ' ' , ' ' , ' ' ,
Components of the trapezoidal smoothing error are zero if the difference between the first guess and “truth” can be written as a superposition
Slab avg. F+ 5%-10% 5%-10% 0.25K-0.5K 10%-20% O3(p) 10%-20% H2O(p) 0.5K-1.0K T(p)
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– Backus-Gilbert, 1969 – Conrath, 1972
i i i j i j i j i
,
Retrieved value at RTA grid index, i Truth value at RTA grid index, i
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(e.g. clear vs. cloudy, tropical vs. polar, ocean vs. land, etc. ). Therefore, the vertical resolution and accuracy of any given retrieval is a function of scene.
(e.g. those due to the first guess/trapezoidal smoothing) are beyond the physical retrieval capability.
case-by-case basis for comparisons of retrievals to correlative measurements.
– Use the averaging kernel/trapezoids to convolve the correlative measurement such the this profile is more comparable to what the retrieval would “see” given that profile.
– Weighted toward polar cases – Water from matched operational radiosonde
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– smoothing due to trapezoids – smoothing due to damping (averaging kernel)
– MAX 0.5 K for T – MAX 10% for H2O and O3
– averaging kernels for the physical temperature and moisture retrievals are good representations of retrieval vertical weighting
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' , , ' , j n n j j j
T j k k k j j j T j k k k j T j k k k k j j j j n n n T n j T j k k k k j j j ' , , ' , ' , , ' , , ' , ' , ' ' , , ' ' , , ' ,