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1 An Assessment of AMSU-A Moisture Retrievals over Land and Ocean Stan Kidder 20 June 2006

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2 Purpose of Study To determine how accurately atmospheric water vapor and liquid water can be retrieved from AMSU-A data using 1. A simplified forward model and 2. Rodger’s (2000) maximum a posteriori (MAP) solution

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3 In Other Words To use a simplified atmosphere (in which everything is known) to determine the best that one can hope for in moisture retrieval accuracy and how various factors (especially surface emittance) influence this accuracy. To use a simplified atmosphere (in which everything is known) to determine the best that one can hope for in moisture retrieval accuracy and how various factors (especially surface emittance) influence this accuracy.

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4 The Forward Model T B ( ) = T s surface emission + T A (1 - ) atmospheric emission + T A (1 - )(1 – ) surface reflection T B = brightness temperature (K) = frequency (GHz) = surface emittance (unitless) = atmospheric transmittance (unitless) T S = surface temperature (K) T A = constant atmospheric temp (K)

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5 The Forward Model (cont.) o oxygen exp[− L ( )L] cloud liquid water exp[− V ( )V] water vapor o ( ) = vertical transmittance of dry, cloud-free atmosphere L = vertically integrated cloud liquid water (kg m -2 or mm) V = vertically integrated water vapor (TPW, kg m -2 or mm) L ( ) = liquid water mass absorption coefficient (m 2 kg -1 ) V ( ) = water vapor mass absorption coefficient (m 2 kg -1 )

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6 Forward Model Constants* (GHz) (GHz) oooo L (m 2 kg -1 ) V (m 2 kg -1 ) 10 − 10 − 10 − 10 −3 *Determined using Liebe (1992).

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7 The Measurement Vector S = I 4 = 0.5 K (“noise”)

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8 The State Vector

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9 A Priori

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10 A Priori Covariance

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11 Surface Emittance Treated as a forward model parameter, that is, as a random variable which is not retrieved and thus adds error to the retrieved quantities Treated as a forward model parameter, that is, as a random variable which is not retrieved and thus adds error to the retrieved quantities The standard deviation of surface emittance is varied to evaluate the accuracy with which it must be known to achieve the desired accuracy of retrieval The standard deviation of surface emittance is varied to evaluate the accuracy with which it must be known to achieve the desired accuracy of retrieval

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12 Mean Emittance Channel Ocean* Land *From Kohn (1995). T S = 300 K, WS = 5 m s -1, salinity = 35 ppt, zenith angle = 0

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13 The Retrieval Scheme K = analytic Jacobian [K ij = ∂T B (ν i )/ ∂x j ] K = analytic Jacobian [K ij = ∂T B (ν i )/ ∂x j ] Rodgers’ iterative solution (eq. 5.8) with K being recalculated at every iteration: Rodgers’ iterative solution (eq. 5.8) with K being recalculated at every iteration: Convergence is achieved (eq. 5.29) when Convergence is achieved (eq. 5.29) when

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14 Retrieval Error Covariance At convergence (Rodgers eq. 5.30): At convergence (Rodgers eq. 5.30):

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15 Model Parameter-Caused Error Rodgers eq & 3.27: Rodgers eq & 3.27: Note that in the x equation, stands for surface emittance, whereas, in the G y equation, S is the measurement covariance matrix.

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16 Procedure 1. Choose a state vector, and an emissivity vector, approximating the values as Gaussian variables 2. Calculate the measurement vector with noise 3. Retrieve the state vector using 0 4. Repeat steps times 5. Calculate the retrieval statistics as functions of emittance noise

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17 Results Presented as a series of graphs showing the bias, standard deviation, and RMS error of retrieving T S, T A, L, and V. Presented as a series of graphs showing the bias, standard deviation, and RMS error of retrieving T S, T A, L, and V.

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18 T S Ocean

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19 T S Land

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20 T A Ocean

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21 T A Land

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22 L Ocean

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23 L Land

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24 V Ocean

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25 V Land

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26 Conclusions Atmospheric temperature (T A ) is accurately retrieved over land or ocean Atmospheric temperature (T A ) is accurately retrieved over land or ocean Surface temperature (T S ) is accurately retrieved over land, but poorly retrieved over ocean Surface temperature (T S ) is accurately retrieved over land, but poorly retrieved over ocean Liquid water (L, CLW) is marginally retrieved over ocean, but lost in the noise over land Liquid water (L, CLW) is marginally retrieved over ocean, but lost in the noise over land Water vapor (V, TPW) is accurately retrieved over ocean, but probably not retrievable over land with AMSU-A channels Water vapor (V, TPW) is accurately retrieved over ocean, but probably not retrievable over land with AMSU-A channels

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27 Conclusions (cont.) Retrieving surface emittances instead of treating them as model parameters is unlikely to help Retrieving surface emittances instead of treating them as model parameters is unlikely to help Adding AMSU-B channels would possibly help with land retrievals Adding AMSU-B channels would possibly help with land retrievals Experiments with C1DOE should be performed to see if they support these results Experiments with C1DOE should be performed to see if they support these results

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28 References Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. World Scientific, 238 pp. Kohn, D. J., 1995: Refinement of a semi-empirical model for the microwave emissivity of the sea surface as a function of wind speed, M.S. thesis, meteorology dept., Texas A&M University. Liebe, H. J., 1992: Atmospheric Attenuation and Delay Rates from 1 to 1000 GHz. Institute for Telecommunication Sciences, NTIA/ITS.S1, 325 BROADWAY, Boulder, CO 80303

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