MCMC-Based Assessment of the Error Characteristics of a Surface-Based Combined Radar - Passive Microwave Cloud Property Retrieval

Transcription

1 MCMC-Based Assessment of the Error Characteristics of a Surface-Based Combined Radar - Passive Microwave Cloud Property Retrieval Derek J. Posselt University of Michigan Jay G. Mace University of Utah DOE-ASR DE-SC

2 Introduction Goal: quantify uncertainties in ARM cloud retrievals using inverse methods Retrievals seek the most likely solution for a given set of observations (and prior knowledge) Bayesian inverse methods can be used to Formalize obs forward model retrieval relationship Determine the solution properties (for a given set of obs, forward model(s), and prior) Case 1: mixed phase, bimodal cloud PSD for orographic precipitation D. J. Posselt 2

3 StormVEX Observations 2000 UTC 04 Feb 0000 UTC 05 Feb 2011 Test profile observed 2115 UTC 04 Feb 2011 Observation Units Value Error σ dbz (top) mm 6 m dbz (middle) mm 6 m dbz (bottom) mm 6 m V d (top) cm s V d (middle) cm s V d (bottom) cm s T b (23 GHz) K T b (31 GHz) K D. J. Posselt 3

4 Retrievals: Quantifying Relationships The model maps from one set of state values to another (e.g., evolution of the system) and/or from state to obs space The inverse problem places constraint on the solution P(y x) P(x) x P(x y) All Possible Input Model F(x) All Possible Output P(y) y Inference of a previous set of states from a current set or a set of states from a set of observations D. J. Posselt 4

5 Cloud Retrievals via Bayesian Sampling (MCMC) Goal: estimate P(y x) or P(x y) Markov chain Monte Carlo: Construct a Markov chain that samples P(x y) A random walk guided by information from observations Application: Characterize cloud microphysics retrieval uncertainty Is there a unique solution? How does solution change when we relax assumptions? Posselt et al. (2008, JGR), Posselt and Mace (2013, JAMC) D. J. Posselt 5

6 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 6

7 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 7

8 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 8

9 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 9

10 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 10

11 MCMC and Cloud Retrievals Posselt et al. (2008, JGR) D. J. Posselt 11

12 Combined Radar + MW Retrieval Idealized, Simulated Observations Uniform profile, specified true cloud PSD, simulated observations Vary either liquid or ice PSD parameters Posselt and Mace (2013, JAMC) D. J. Posselt 12

13 Combined Radar + MW Retrieval Real Observations, Liquid PSD Fix width parameters and ice crystal shape Retrieve LWC, N liq, IWC, N ice Posselt and Mace (2013, JAMC) D. J. Posselt 13

14 Combined Radar + MW Retrieval Real Observations, Ice PSD Fix width parameters and ice crystal shape Retrieve LWC, N liq, IWC, N ice Posselt and Mace (2013, JAMC) D. J. Posselt 14

15 Combined Radar + MW Retrieval Real Observations, Liquid PSD Vary width parameters and ice crystal shape Retrieve LWC, N liq, IWC, N ice Where did this solution go? Posselt and Mace (2013, JAMC) D. J. Posselt 15

16 Combined Radar + MW Retrieval Real Observations, Ice PSD Vary width parameters and ice crystal shape Retrieve LWC, N liq, IWC, N ice Posselt and Mace (2013, JAMC) Where did this solution go? D. J. Posselt 16

17 Subtlety in the Retrieval Fixed gamma width and crystal shape: bi-mode solution Small number of large particles = large number of small particles Forward obs are identical, but only over a very small range of liquid and ice solutions Variable alpha, shape, or both allows a larger range of solutions, no localized mode! Posselt and Mace (2013, JAMC) D. J. Posselt 17

18 Summary and Conclusions Idealized retrieval Unique solution for ice PSD if dbz and Vd are observed. No unique liquid solution when particles are small. Real observations Observe dbz and/or Vd, fix PSD width and ice shape: no unique solution for liquid or ice PSD Observe dbz, Vd, and Tb, fix PSD width and ice shape: emergence of a preferred (non-unique) PSD solution Vary ice PSD width or shape: unique solution Vary both ice PSD and shape: non-unique solution D. J. Posselt 18

19 Next Steps Apply the MCMC analysis method to drizzling Sc (bimodal liquid-only cloud) Examine time series of profiles: How does solution change with environment? References: Posselt, D. J., and G. G. Mace, 2013: MCMC-Based Assessment of the Error Characteristics of a Combined Radar-Passive Microwave Cloud Property Retrieval. J. Appl. Meteor. Clim., Accepted. Posselt, D. J., T. S. L Ecuyer, and G. L. Stephens, 2008: Exploring the Error Characteristics of Thin Ice Cloud Property Retrievals Using a Markov Chain Monte Carlo Algorithm. J. Geophys. Res., 113, D24206, doi: /2008jd D. J. Posselt 19

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