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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.

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.

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.

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.

Representing microphysics within weather and climate models is challenging because we lack fundamental understanding of microphysical processes and are limited by the computational inability to track each hydrometeor within a cloud system. Microphysics schemes parameterize rates for specific processes such as drop evaporation, collision-coalescence, or collisional-breakup, but their inherent assumptions lead to uncertainty in model solutions which are often difficult to understand and quantify. Observations such as those from polarimetric radar provide insight into the microphysical evolution of clouds, but alone they are unable to provide quantitative information about the process rates that lead to this evolution. The Bayesian Observationally Constrained Statistical-Physical Scheme (BOSS) is a recently-developed bulk microphysics scheme designed to bridge the gap between observations and the processes acting on individual drops, such that process rate information can be directly learned from polarimetric radar observations. BOSS operates with no predefined drop size distribution (DSD) shape and makes few assumptions about the process rate formulations. Because there is no prescribed DSD shape, a new moment-based polarimetric forward operator is used to relate model prognostic moment output to polarimetric radar variables. Process rates are written as generalized power functions of the prognostic DSD moments (related to bulk quantities such as mass concentrations), with flexibility to choose the number and order of the prognostic DSD moments and number of power terms in the process rate formulations. The corresponding process rate parameters are constrained directly with observation using Markov chain Monte Carlo in a Bayesian inference framework, allowing BOSS to learn microphysical information directly from observations while simultaneously quantifying parametric uncertainty. The process rate formulations in BOSS can be made systematically more complex by adding more terms and/or more prognostic DSD moments, which allows us also to track down sources of structural uncertainty. In this study, we use a detailed bin microphysics scheme as “truth” to generate the constraining observations synthetically, which include profiles of polarimetric radar variables (ZH, ZDR, KDP) and vertical fluxes of prognostic DSD moments at the surface. An error analysis shows that BOSS produces process rate profiles similar to those of a bin scheme when only provided polarimetric rain profiles and surface prognostic moment fluxes. We also display initial results where BOSS is used to estimate microphysical process rate information from real polarimetric radar observations.

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.

Advancing understanding of deep convection microphysics via mesoscale modeling studies of well-observed case studies requires observation-based aerosol inputs. Here, we derive hygroscopic aerosol size distribution input profiles from ground-based and airborne measurements for six convection case studies observed during the Midlatitude Continental Convective Cloud Experiment (MC3E) over Oklahoma. We demonstrate use of an input profile in simulations of the only well-observed case study that produced extensive stratiform outflow on 20 May 2011. At well-sampled elevations between −11 and −23 °C over widespread stratiform rain, ice crystal number concentrations are consistently dominated by a single mode near ∼ 400 µm in randomly oriented maximum dimension (Dmax). The ice mass at −23 °C is primarily in a closely collocated mode, whereas a mass mode near Dmax ∼ 1000 µm becomes dominant with decreasing elevation to the −11 °C level, consistent with possible aggregation during sedimentation. However, simulations with and without observation-based aerosol inputs systematically overpredict mass peak Dmax by a factor of 3–5 and underpredict ice number concentration by a factor of 4–10. Previously reported simulations with both two-moment and size-resolved microphysics have shown biases of a similar nature. The observed ice properties are notably similar to those reported from recent tropical measurements. Based on several lines of evidence, we speculate that updraft microphysical pathways determining outflow properties in the 20 May case are similar to a tropical regime, likely associated with warm-temperature ice multiplication that is not well understood or well represented in models.

To probe the potential value of a radar-driven field campaign to constrain simulation of isolated convection subject to a strong aerosol perturbation, convective cells observed by the operational KHGX weather radar in the vicinity of Houston, Texas, are examined individually and statistically. Cells observed in a single case study of onshore flow conditions during July 2013 are first examined and compared with cells in a regional model simulation. Observed and simulated cells are objectively identified and tracked from observed or calculated positive specific differential phase (KDP) above the melting level, which is related to the presence of supercooled liquid water. Several observed and simulated cells are subjectively selected for further examination. Below the melting level, we compare sequential cross sections of retrieved and simulated raindrop size distribution parameters. Above the melting level, we examine time series of KDP and radar differential reflectivity (ZDR) statistics from observations and calculated from simulated supercooled rain properties, alongside simulated vertical wind and supercooled rain mixing ratio statistics. Results indicate that the operational weather radar measurements offer multiple constraints on the properties of simulated convective cells, with substantial value added from derived KDP and retrieved rain properties. The value of collocated three-dimensional lightning mapping array measurements, which are relatively rare in the continental US, supports the choice of Houston as a suitable location for future field studies to improve the simulation and understanding of convective updraft physics. However, rapid evolution of cells between routine volume scans motivates consideration of adaptive scan strategies or radar imaging technologies to amend operational weather radar capabilities. A 3-year climatology of isolated cell tracks, prepared using a more efficient algorithm, yields additional relevant information. Isolated cells are found within the KHGX domain on roughly 40 % of days year-round, with greatest concentration in the northwest quadrant, but roughly 5-fold more cells occur during June through September. During this enhanced occurrence period, the cells initiate following a strong diurnal cycle that peaks in the early afternoon, typically follow a south-to-north flow, and dissipate within 1 h, consistent with the case study examples. Statistics indicate that ∼ 150 isolated cells initiate and dissipate within 70 km of the KHGX radar during the enhanced occurrence period annually, and roughly 10 times as many within 200 km, suitable for multi-instrument Lagrangian observation strategies. In addition to ancillary meteorological and aerosol measurements, robust vertical wind speed retrievals would add substantial value to a radar-driven field campaign.

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.

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.

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.

Advancing understanding of deep convection microphysics via mesoscale modeling studies of well-observed case studies requires observation-based aerosol inputs. Here we derive hygroscopic aerosol size distribution input profiles from ground- based and airborne measurements for six convection case studies observed during the Midlatitude Continental Convective Cloud Experiment (MC3E) over Oklahoma. We demonstrate use of the aerosol inputs in mesoscale model simulations of the only well-observed case study that produced extensive stratiform outflow, on 20 May 2011. At well-sampled elevations between −10 and −23 °C over widespread stratiform rain, ice crystal number concentrations are consistently dominated by a single mode near ∼ 400 μm in randomly oriented maximum dimension (Dmax). The ice mass at −23 °C is primarily in a closely collocated mode, whereas a mass mode near Dmax ∼ 1000 μm becomes dominant with decreasing elevation to the −10 °C level, consistent with possible aggregation during sedimentation. However, simulations with and without observation-based aerosol inputs systematically overpredict mass peak Dmax by a factor of 3–5 and underpredict ice number concentration by a factor of 4–10. Previously reported simulations with both two-moment and size-resolved microphysics have shown biases of a similar nature. The observed ice properties are notably similar to those reported from recent tropical measurements. Based on several lines of evidence, we speculate that the microphysics pathways associated with deep tropical convection outflow also occurred in the 20 May MC3E case, likely associated with warm-temperature ice multiplication that is not well understood or well represented in models.

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.