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Marcus van Lier-Walqui, Tomislava Vukicevic, and Derek J. Posselt

Abstract

Uncertainty in cloud microphysical parameterization—a leading order contribution to numerical weather prediction error—is estimated using a Markov chain Monte Carlo (MCMC) algorithm. An inversion is performed on 10 microphysical parameters using radar reflectivity observations with vertically covarying error as the likelihood constraint. An idealized 1D atmospheric column model with prescribed forcing is used to simulate the microphysical behavior of a midlatitude squall line. Novel diagnostics are employed for the probabilistic investigation of individual microphysical process behavior vis-à-vis parameter uncertainty. Uncertainty in the microphysical parameterization is presented via posterior probability density functions (PDFs) of parameters, observations, and microphysical processes. The results of this study show that radar reflectivity observations, as expected, provide a much stronger constraint on microphysical parameters than column-integral observations, in most cases reducing both the variance and bias in the maximum likelihood estimate of parameter values. This highlights the enhanced potential of radar reflectivity observations to provide information about microphysical processes within convective storm systems despite the presence of strongly nonlinear relationships within the microphysics model. The probabilistic analysis of parameterization uncertainty in terms of both parameter and process activity PDFs suggest the prospect of a stochastic representation of microphysical parameterization uncertainty—specifically the results indicate that error may be more easily represented and estimated by microphysical process uncertainty rather than microphysical parameter uncertainty. In addition, these new methods of analysis allow for a detailed investigation of the full nonlinear and multivariate relationships between microphysical parameters, microphysical processes, and radar observations.

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Marcus van Lier-Walqui, Tomislava Vukicevic, and Derek J. Posselt

Abstract

Recent studies have shown the importance of accounting for model physics uncertainty within probabilistic forecasts. Attempts have been made at quantifying this uncertainty in terms of microphysical parameters such as fall speed coefficients, moments of hydrometeor particle size distributions, and hydrometeor densities. It has been found that uncertainty in terms of these “traditional” microphysical parameters is highly non-Gaussian, calling into question the possibility of estimating and propagating this error using Gaussian statistical techniques such as ensemble Kalman methods. Here, a new choice of uncertain control variables is proposed that instead considers uncertainty in individual modeled microphysical processes. These “process parameters” are multiplicative perturbations on contributions of individual modeled microphysical processes to hydrometeor time tendency. The new process parameters provide a natural and appealing choice for the quantification of aleatory microphysical parameterization uncertainty. Results of a nonlinear Monte Carlo parameter estimation experiment for these new process parameters are presented and compared with the results using traditional microphysical parameters as uncertain control variables. Both experiments occur within the context of an idealized one-dimensional simulation of moist convection, under the observational constraint of simulated radar reflectivity. Results indicate that the new process parameters have a more Gaussian character compared with traditional microphysical parameters, likely due to a more linear control on observable model evolution. In addition, posterior forecast distributions using the new control variables (process parameters) are shown to have less bias and variance. These results strongly recommend the use of the new process parameters for an ensemble Kalman-based estimation of microphysical parameterization uncertainty.

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Gregory S. Elsaesser, Anthony D. Del Genio, Jonathan H. Jiang, and Marcus van Lier-Walqui

Abstract

Partitioning of convective ice into precipitating and detrained condensate presents a challenge for GCMs since partitioning depends on the strength and microphysics of the convective updraft. It is an important issue because detrainment of ice from updrafts influences the development of stratiform anvils, impacts radiation, and can affect GCM climate sensitivity. Recent studies have shown that the CMIP5 configurations of the Goddard Institute for Space Studies (GISS) GCM simulated upper-tropospheric ice water content (IWC) that exceeded an estimated upper bound by a factor of 2. Partly in response to this bias, a new GCM parameterization of convective cloud ice has been developed that incorporates new ice particle fall speeds and convective outflow particle size distributions (PSDs) from the NASA African Monsoon Multidisciplinary Analyses (NAMMA), NASA Tropical Composition, Cloud and Climate Coupling (TC4), DOE ARM–NASA Midlatitude Continental Convective Clouds Experiment (MC3E), and DOE ARM Small Particles in Cirrus (SPARTICUS) field campaigns. The new parameterization assumes a normalized gamma PSD with two novel developments: no explicit assumption for particle habit in the calculation of mass distributions, and a formulation for translating ice particle fall speeds as a function of maximum diameter into fall speeds as a function of melted-equivalent diameter. Two parameters (particle volume– and projected area–weighted equivalent diameter) are diagnosed as a function of temperature and IWC in the convective plume, and these parameters constrain the shape and scale of the normalized gamma PSD. The diagnosed fall speeds and PSDs are combined with the GCM’s parameterized convective updraft vertical velocity to partition convective updraft condensate into precipitating and detrained components. A 5-yr prescribed sea surface temperature GCM simulation shows a 30%–50% decrease in upper-tropospheric deep convective IWC, bringing the tropical and global mean ice water path into closer agreement with CloudSat best estimates.

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Hugh Morrison, Matthew R. Kumjian, Charlotte P. Martinkus, Olivier P. Prat, and Marcus van Lier-Walqui

Abstract

A general drop size distribution (DSD) normalization method is formulated in terms of generalized power series relating any DSD moment to any number and combination of reference moments. This provides a consistent framework for comparing the variability of normalized DSD moments using different sets of reference moments, with no explicit assumptions about the DSD functional form (e.g., gamma). It also provides a method to derive any unknown moment plus an estimate of its uncertainty from one or more known moments, which is relevant to remote sensing retrievals and bulk microphysics schemes in weather and climate models. The approach is applied to a large dataset of disdrometer-observed and bin microphysics-modeled DSDs. As expected, the spread of normalized moments decreases as the number of reference moments is increased, quantified by the logarithmic standard deviation of the normalized moments, σ. Averaging σ for all combinations of reference moments and normalized moments of integer order 0–10, 42.9%, 81.3%, 93.7%, and 96.9% of spread are accounted for applying one-, two-, three-, and four-moment normalizations, respectively. Thus, DSDs can be well characterized overall using three reference moments, whereas adding a fourth reference moment contributes little independent information. The spread of disdrometer-observed DSD moments from uncertainty associated with drop count statistics generally lies between values of σ using two- and three-moment normalizations. However, this uncertainty has little impact on the derived DSD scaling relationships or σ when considered.

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Hugh Morrison, Marcus van Lier-Walqui, Matthew R. Kumjian, and Olivier P. Prat

Abstract

A new framework is proposed for the bulk parameterization of rain microphysics: the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS). It is designed to facilitate direct constraint by observations using Bayesian inference. BOSS combines existing process-level microphysical knowledge with flexible process rate formulations and parameters constrained by observations within a Bayesian framework. Using a raindrop size distribution (DSD) normalization method that relates DSD moments to one another via generalized power series, generalized multivariate power expressions are derived for the microphysical process rates as functions of a set of prognostic DSD moments. The scheme is flexible and can utilize any number and combination of prognostic moments and any number of terms in the process rate formulations. This means that both uncertainty in parameter values and structural uncertainty associated with the process rate formulations can be investigated systematically, which is not possible using traditional schemes. In this paper, BOSS is compared to two- and three-moment versions of a traditional bulk rain microphysics scheme (denoted as MORR). It is shown that some process formulations in MORR are analytically equivalent to the generalized power expressions in BOSS using one or two terms, while others are not. BOSS is able to replicate the behavior of MORR in idealized one-dimensional rainshaft tests, but with a much more flexible and systematic design. Part II of this study describes the application of BOSS to derive rain microphysical process rates and posterior parameter distributions in Bayesian experiments using Markov chain Monte Carlo sampling constrained by synthetic observations.

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Matthew R. Kumjian, Charlotte P. Martinkus, Olivier P. Prat, Scott Collis, Marcus van Lier-Walqui, and Hugh C. Morrison

Abstract

There is growing interest in combining microphysical models and polarimetric radar observations to improve our understanding of storms and precipitation. Mapping model-predicted variables into the radar observational space necessitates a forward operator, which requires assumptions that introduce uncertainties into model–observation comparisons. These include uncertainties arising from the microphysics scheme a priori assumptions of a fixed drop size distribution (DSD) functional form, whereas natural DSDs display far greater variability. To address this concern, this study presents a moment-based polarimetric radar forward operator with no fundamental restrictions on the DSD form by linking radar observables to integrated DSD moments. The forward operator is built upon a dataset of >200 million realistic DSDs from one-dimensional bin microphysical rain-shaft simulations, and surface disdrometer measurements from around the world. This allows for a robust statistical assessment of forward operator uncertainty and quantification of the relationship between polarimetric radar observables and DSD moments. Comparison of “truth” and forward-simulated vertical profiles of the polarimetric radar variables are shown for bin simulations using a variety of moment combinations. Higher-order moments (especially those optimized for use with the polarimetric radar variables: the sixth and ninth) perform better than the lower-order moments (zeroth and third) typically predicted by many bulk microphysics schemes.

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Robert S. Schrom, Marcus van Lier-Walqui, Matthew R. Kumjian, Jerry Y. Harrington, Anders A. Jensen, and Yao-Sheng Chen

Abstract

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. The combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

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Marcus van Lier-Walqui, Hugh Morrison, Matthew R. Kumjian, Karly J. Reimel, Olivier P. Prat, Spencer Lunderman, and Matthias Morzfeld

Abstract

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is presented using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the additional benefit of rigorously quantified uncertainty of these estimates.

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Marcus van Lier-Walqui, Ann M. Fridlind, Andrew S. Ackerman, Scott Collis, Jonathan Helmus, Donald R. MacGorman, Kirk North, Pavlos Kollias, and Derek J. Posselt

Abstract

The representation of deep convection in general circulation models is in part informed by cloud-resolving models (CRMs) that function at higher spatial and temporal resolution; however, recent studies have shown that CRMs often fail at capturing the details of deep convection updrafts. With the goal of providing constraint on CRM simulation of deep convection updrafts, ground-based remote sensing observations are analyzed and statistically correlated for four deep convection events observed during the Midlatitude Continental Convective Clouds Experiment (MC3E). Since positive values of specific differential phase observed above the melting level are associated with deep convection updraft cells, so-called columns are analyzed using two scanning polarimetric radars in Oklahoma: the National Weather Service Vance WSR-88D (KVNX) and the Department of Energy C-band Scanning Atmospheric Radiation Measurement (ARM) Precipitation Radar (C-SAPR). KVNX and C-SAPR volumes and columns are then statistically correlated with vertical winds retrieved via multi-Doppler wind analysis, lightning flash activity derived from the Oklahoma Lightning Mapping Array, and KVNX differential reflectivity . Results indicate strong correlations of volume above the melting level with updraft mass flux, lightning flash activity, and intense rainfall. Analysis of columns reveals signatures of changing updraft properties from one storm event to another as well as during event evolution. Comparison of to shows commonalities in information content of each, as well as potential problems with associated with observational artifacts.

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