Journal articles on the topic 'Parameterizations'
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Kuznetsova, Alexandra, Georgy Baydakov, Vladislav Papko, Alexander Kandaurov, Maxim Vdovin, Daniil Sergeev, and Yuliya Troitskaya. "Adjusting of Wind Input Source Term in WAVEWATCH III Model for the Middle-Sized Water Body on the Basis of the Field Experiment." Advances in Meteorology 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/8539127.
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Adjusting of wind input source term in numerical model WAVEWATCH III for the middle-sized water body is reported. For this purpose, the field experiment on Gorky Reservoir is carried out. Surface waves are measured along with the parameters of the airflow. The measurement of wind speed in close proximity to the water surface is performed. On the basis of the experimental results, the parameterization of the drag coefficient depending on the 10 m wind speed is proposed. This parameterization is used in WAVEWATCH III for the adjusting of the wind input source term within WAM 3 and Tolman and Chalikov parameterizations. The simulation of the surface wind waves within tuned to the conditions of the middle-sized water body WAVEWATCH III is performed using three built-in parameterizations (WAM 3, Tolman and Chalikov, and WAM 4) and adjusted wind input source term parameterizations. Verification of the applicability of the model to the middle-sized reservoir is performed by comparing the simulated data with the results of the field experiment. It is shown that the use of the proposed parameterizationCD(U10)improves the agreement in the significant wave heightHSfrom the field experiment and from the numerical simulation.
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Jin, Han-Gyul, Hyunho Lee, and Jong-Jin Baik. "A New Parameterization of the Accretion of Cloud Water by Graupel and Its Evaluation through Cloud and Precipitation Simulations." Journal of the Atmospheric Sciences 76, no. 2 (January 21, 2019): 381–400. http://dx.doi.org/10.1175/jas-d-18-0245.1.
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Abstract A new parameterization of the accretion of cloud water by graupel for use in bulk microphysics schemes is derived by analytically integrating the stochastic collection equation (SCE). In this parameterization, the collection efficiency between graupel particles and cloud droplets is expressed in a functional form using the data obtained from a particle trajectory model by a previous study. The new accretion parameterization is evaluated through box model simulations in comparison with a bin-based direct SCE solver and two previously developed accretion parameterizations that employ the continuous collection equation and a simplified SCE, respectively. Changes in cloud water and graupel mass contents via the accretion process predicted by the new parameterization are closest to those predicted by the direct SCE solver. Furthermore, the new parameterization predicts a decrease in the cloud droplet number concentration that is smaller than the decreases predicted by the other accretion parameterizations, consistent with the direct SCE solver. The new and the other accretion parameterizations are implemented into a cloud-resolving model. Idealized deep convective cloud simulations show that among the accretion parameterizations, the new parameterization predicts the largest rate of accretion by graupel and the smallest rate of accretion by snow, which overall enhances rainfall through the largest rate of melting of graupel. Real-case simulations for a precipitation event over the southern Korean Peninsula show that among the examined accretion parameterizations, the new parameterization simulates precipitation closest to observations. Compared to the other accretion parameterizations, the new parameterization decreases the fractions of light and moderate precipitation amounts and increases the fraction of heavy precipitation amount.
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Liu, Yangang, Peter H. Daum, R. McGraw, and R. Wood. "Parameterization of the Autoconversion Process. Part II: Generalization of Sundqvist-Type Parameterizations." Journal of the Atmospheric Sciences 63, no. 3 (March 1, 2006): 1103–9. http://dx.doi.org/10.1175/jas3675.1.
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Abstract Existing Sundqvist-type parameterizations, which only consider dependence of the autoconversion rate on cloud liquid water content, are generalized to explicitly account for the droplet concentration and relative dispersion of the cloud droplet size distribution as well. The generalized Sundqvist-type parameterization includes the more commonly used Kessler-type parameterization as a special case, unifying the two different types of parameterizations for the autoconversion rate. The generalized Sundqvist-type parameterization is identical with the Kessler-type parameterization presented in Part I beyond the autoconversion threshold, but exhibits a more realistic, smooth transition in the vicinity of the autoconversion threshold (threshold behavior) in contrast to the discontinuously abrupt transition embodied in the Kessler-type parameterization. A new Sundqvist-type parameterization is further derived by applying the expression for the critical radius derived from the kinetic potential theory to the generalized Sundqvist-type parameterization. The new parameterization eliminates the need for defining the driving radius and for prescribing the critical radius associated with Kessler-type parameterizations. The two-part structure of the autoconversion process raises questions regarding model-based empirical parameterizations obtained by fitting simulation results from detailed collection models with a single function.
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BAJAJ, CHANDRAJIT L., and ANDREW V. ROYAPPA. "FINITE REPRESENTATIONS OF REAL PARAMETRIC CURVES AND SURFACES." International Journal of Computational Geometry & Applications 05, no. 03 (September 1995): 313–26. http://dx.doi.org/10.1142/s0218195995000180.
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Global parameterizations of parametric algebraic curves or surfaces are defined over infinite parameter domains. Considering parameterizations in terms of rational functions that have real coefficients and vary over real parameter values, we show how to replace one global parameterization with a finite number of alternate bounded parameterizations, each defined over a fixed, bounded part of the real parameter domain space. The new bounded parameterizations together generate all real points of the old one and in particular the points corresponding to infinite parameter values in the old domain. We term such an alternate finite set of bounded parameterizations a finite representation of a real parametric curve or surface. Two solutions are presented for real parametric varieties of arbitrary dimension n. In the first method, a real parametric variety of dimension n is finitely represented in a piecewise fashion by 2n bounded parameterizations with individual pieces meeting with C∞ continuity; each bounded parameterization is a map from a unit simplex of the real parameter domain space. In the second method, only a single bounded parameterization is used; it is a map from the unit hypersphere centered at the origin of the real parameter domain space. Both methods start with an arbitrary real parameterization of a real parametric variety and apply projective domain transformations of different types to yield the new bounded parameterizations. Both these methods are implementable in a straightforward fashion. Applications of these results include displaying entire real parametric curves and surfaces (except those real points generated by complex parameter values), computing normal parameterizations of curves and surfaces (settling an open problem for quadric surfaces).
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Wang, Wenping, Barry Joe, and Ronald Goldman. "Rational Quadratic Parameterizations of Quadrics." International Journal of Computational Geometry & Applications 07, no. 06 (December 1997): 599–619. http://dx.doi.org/10.1142/s0218195997000375.
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Every irreducible quadric in E3 has infinitely many different rational quadratic parameterizations. These parameterizations and the relationships between them are investigated. It is shown that every faithful rational quadratic parameterization of a quadric can be generated by a stereographic projection from a point on the quadric, called the center of projection (COP). Two such parameterizations for the same quadric are related by a rational linear reparameterization if they have the same COP; otherwise they are related by a rational quadratic reparameterization. We also consider unfaithful parameterizations for which, in general, a one-to-one correspondence between points on the surface and parameters in the plane does not exist. It is shown that all unfaithful rational quadratic parameterizations of a properly degenerate quadric can be characterized by a simple canonical form, and there exist no unfaithful rational quadratic parameterizations for a nondegenerate quadric. In addition, given a faithful rational quadratic parameterization of a quadric, a new technique is presented to compute its base points and inversion formula. These results are applied to solve the problems of parameterizing the intersection of two quadrics and reparameterizing a given quadric parameterization with respect to a different COP without implicitization.
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Lee, Hyunho, and Jong-Jin Baik. "A Physically Based Autoconversion Parameterization." Journal of the Atmospheric Sciences 74, no. 5 (May 1, 2017): 1599–616. http://dx.doi.org/10.1175/jas-d-16-0207.1.
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Abstract A physically based parameterization for the autoconversion is derived by solving the stochastic collection equation (SCE) with an approximated collection kernel. The collection kernel is constructed using the terminal velocity of cloud droplets and the collision efficiency between cloud droplets that is obtained using a particle trajectory model. The new parameterization proposed in this study is validated through comparison with results obtained by a bin-based direct SCE solver and other autoconversion parameterizations using a box model. The autoconversion-related time scale and drop number concentration are employed for the validation. The results of the new parameterization are shown to most closely match those of the direct SCE solver. It is also shown that the dependency of the autoconversion rate on drop number concentration in the new parameterization is similar to that in the direct SCE solver, which is partially caused by the shape of drop size distribution. The new parameterization and other parameterizations are implemented into a cloud-resolving model, and idealized shallow warm clouds are simulated. The autoconversion parameterizations that yield the small (large) autoconversion rate tend to predict large (small) cloud optical thickness, small (large) cloud fraction, and small (large) surface precipitation amount. Cloud optical thickness and cloud fraction are changed by up to ~45% and ~20% by autoconversion parameterizations, respectively. The new parameterization tends to yield the moderate autoconversion rate among the autoconversion parameterizations. Moreover, it predicts cloud optical thickness, cloud fraction, and surface precipitation amount that are generally the closest to those of the bin microphysics scheme.
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Xu, Shibo, and Alexey Stovas. "A new parameterization for acoustic orthorhombic media." GEOPHYSICS 82, no. 6 (November 1, 2017): C229—C240. http://dx.doi.org/10.1190/geo2017-0215.1.
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We have defined a group of new parameterizations for P-wave in acoustic orthorhombic (ORT) media with three cross-term normal moveout velocities and three cross-term anellipticity parameters. The corresponding perturbation-based approximations for traveltime in ORT model are developed using the new parameterizations. The perturbation coefficients are computed by solving the eikonal equation in corresponding parameterization. Eight types of parameterization are defined based on the different elliptical background model and selection of anellipticity parameters. As the traveltime can be converted from the group velocity inverse, the sensitivity of the group velocity inverse to anellipticity parameters is analyzed for different parameterizations and different range of offsets. To stabilize the perturbation series and improve the accuracy, the Shanks transform is applied. From the comparison of traveltime after the Shanks transform using different parameterizations, we have concluded that the parameterization with vertical, two horizontal velocities, and three cross-term anellipticity parameters results in the best accuracy of traveltime function for P-wave in acoustic ORT medium.
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Song, Yong, Christopher K. Wikle, Christopher J. Anderson, and Steven A. Lack. "Bayesian Estimation of Stochastic Parameterizations in a Numerical Weather Forecasting Model." Monthly Weather Review 135, no. 12 (December 1, 2007): 4045–59. http://dx.doi.org/10.1175/2007mwr1928.1.
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Abstract Parameterizations in numerical models account for unresolved processes. These parameterizations are inherently difficult to construct and as such typically have notable imperfections. One approach to account for this uncertainty is through stochastic parameterizations. This paper describes a methodological approach whereby existing parameterizations provide the basis for a simple stochastic approach. More importantly, this paper describes systematically how one can “train” such parameterizations with observations. In particular, a stochastic trigger function has been implemented for convective initiation in the Kain–Fritsch (KF) convective parameterization scheme within the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5). In this approach, convective initiation within MM5 is modeled by a binary random process. The probability of initiation is then modeled through a transformation in terms of the standard KF trigger variables, but with random parameters. The distribution of these random parameters is obtained through a Bayesian Monte Carlo procedure informed by radar reflectivities. Estimates of these distributions are then incorporated into the KF trigger function, giving a meaningful stochastic (distributional) parameterization. The approach is applied to cases from the International H2O project (IHOP). The results suggest the stochastic parameterization/Bayesian learning approach has potential to improve forecasts of convective precipitation in mesoscale models.
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Pan, Wenyong, Kristopher A. Innanen, Yu Geng, and Junxiao Li. "Interparameter trade-off quantification for isotropic-elastic full-waveform inversion with various model parameterizations." GEOPHYSICS 84, no. 2 (March 1, 2019): R185—R206. http://dx.doi.org/10.1190/geo2017-0832.1.
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Simultaneous determination of multiple physical parameters using full-waveform inversion (FWI) suffers from interparameter trade-off difficulties. Analyzing the interparameter trade-offs in different model parameterizations of isotropic-elastic FWI, and thus determining the appropriate model parameterization, are critical for efficient inversion and obtaining reliable inverted models. Five different model parameterizations are considered and compared including velocity-density, modulus-density, impedance-density, and two velocity-impedance parameterizations. The scattering radiation patterns are first used for interparameter trade-off analysis. Furthermore, a new framework is developed to evaluate the interparameter trade-off based upon multiparameter Hessian-vector products: Multiparameter point spread functions (MPSFs) and interparameter contamination sensitivity kernels (ICSKs), which provide quantitative, second-order measurements of the interparameter contaminations. In the numerical experiments, the interparameter trade-offs in various model parameterizations are evaluated using the MPSFs and ICSKs. Inversion experiments are carried out with simple Gaussian-anomaly models and a complex Marmousi model. Overall, the parameterization of the P-wave velocity, S-wave velocity, and density, and the parameterization of the P-wave velocity, S-wave velocity, and S-wave impedance perform best for reconstructing all of the physical parameters. Isotropic-elastic FWI of the Hussar low-frequency data set with various model parameterizations verifies our conclusions.
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De la Sen, M., and A. Ibeas. "Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control." Discrete Dynamics in Nature and Society 2009 (2009): 1–28. http://dx.doi.org/10.1155/2009/315713.
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This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.
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Liang, Chang-Rong, Xiao-Dong Shang, Yong-Feng Qi, Gui-Ying Chen, and Ling-Hui Yu. "A Modified Finescale Parameterization for Turbulent Mixing in the Western Equatorial Pacific." Journal of Physical Oceanography 51, no. 4 (April 2021): 1133–43. http://dx.doi.org/10.1175/jpo-d-20-0205.1.
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AbstractFinescale parameterizations are of great importance to explore the turbulent mixing in the open ocean due to the difficulty of microstructure measurements. Studies based on finescale parameterizations have greatly aided our knowledge of the turbulent mixing in the open ocean. In this study, we introduce a modified finescale parameterization (MMG) based on shear/strain variance ratio Rω and compare it with three existing parameterizations, namely, the MacKinnon–Gregg (MG) parameterization, the Gregg–Henyey–Polzin (GHP) parameterization based on shear and strain variances, and the GHP parameterization based on strain variance. The result indicates that the prediction of MG parameterization is the best, followed by the MMG parameterization, then the shear-and-strain-based GHP parameterization, and finally the strain-based GHP parameterization. The strain-based GHP parameterization is less effective than the shear-and-strain-based GHP parameterization, which is mainly due to its excessive dependence on stratification. The predictions of the strain-based MMG parameterization can be comparable to that of the MG parameterization and better than that of the shear-and-strain-based GHP parameterization. Most importantly, MMG parameterization is even effective over rough topography where the GHP parameterization fails. This modified MMG parameterization with prescribed Rω can be applied to extensive CTD data. It would be a useful tool for researchers to explore the turbulent mixing in the open ocean.
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Kim, Ah-Hyun, Seong Soo Yum, Dong Yeong Chang, and Minsu Park. "Optimization of the sulfate aerosol hygroscopicity parameter in WRF-Chem." Geoscientific Model Development 14, no. 1 (January 15, 2021): 259–73. http://dx.doi.org/10.5194/gmd-14-259-2021.
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Abstract. A new sulfate aerosol hygroscopicity parameter (κSO4) parameterization is suggested that is capable of considering the two major sulfate aerosols, H2SO4 and (NH4)2SO4, using the molar ratio of ammonium to sulfate (R). An alternative κSO4 parameterization method is also suggested that utilizes typical geographical distribution patterns of sulfate and ammonium, which can be used when ammonium data are not available for model calculation. Using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem), the impacts of different κSO4 parameterizations on cloud microphysical properties and cloud radiative effects in East Asia are examined. Comparisons with the observational data obtained from an aircraft field campaign suggest that the new κSO4 parameterizations simulate more reliable aerosol and cloud condensation nuclei concentrations, especially over the sea in East Asia, than the original κSO4 parameterization in WRF-Chem that assumes sulfate aerosols as (NH4)2SO4 only. With the new κSO4 parameterizations, the simulated cloud microphysical properties and precipitation became significantly different, resulting in a greater cloud albedo effect of about −1.5 W m−2 in East Asia than that with the original κSO4 parameterization. The new κSO4 parameterizations are simple and readily applicable to numerical studies investigating the impact of sulfate aerosols in aerosol–cloud interactions without additional computational expense.
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Kok, J. F., N. M. Mahowald, S. Albani, G. Fratini, J. A. Gillies, M. Ishizuka, J. F. Leys, et al. "An improved dust emission model with insights into the global dust cycle's climate sensitivity." Atmospheric Chemistry and Physics Discussions 14, no. 5 (March 11, 2014): 6361–425. http://dx.doi.org/10.5194/acpd-14-6361-2014.
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Abstract. Simulations of the global dust cycle and its interactions with a changing Earth system are hindered by the empirical nature of dust emission parameterizations in climate models. Here we take a step towards improving global dust cycle simulations by presenting a physically-based dust emission model. The resulting dust flux parameterization depends only on the wind friction speed and the soil's threshold friction speed, and can therefore be readily implemented into climate models. We show that our parameterization's functional form is supported by a compilation of quality-controlled vertical dust flux measurements, and that it better reproduces these measurements than existing parameterizations. Both our theory and measurements indicate that many climate models underestimate the dust flux's sensitivity to soil erodibility. This finding can explain why dust cycle simulations in many models are improved by using an empirical preferential sources function that shifts dust emissions towards the most erodible regions. In fact, implementing our parameterization in a climate model produces even better agreement against aerosol optical depth measurements than simulations that use such a source function. These results indicate that the need to use a source function is at least partially eliminated by the additional physics accounted for by our parameterization. Since soil erodibility is affected by climate changes, our results further suggest that many models have underestimated the climate sensitivity of the global dust cycle.
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Moon, Il-Ju, Isaac Ginis, and Tetsu Hara. "Impact of the Reduced Drag Coefficient on Ocean Wave Modeling under Hurricane Conditions." Monthly Weather Review 136, no. 3 (March 1, 2008): 1217–23. http://dx.doi.org/10.1175/2007mwr2131.1.
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Abstract Effects of new drag coefficient (Cd) parameterizations on WAVEWATCH III (WW3) model surface wave simulations are investigated. The new parameterizations are based on a coupled wind–wave model (CWW) and a wave tank experiment, and yields reduced Cd at high wind speeds. Numerical experiments for uniform winds and Hurricane Katrina (2005) indicate that the original Cd parameterization used in WW3 overestimates drag at high wind speeds compared to recent observational, theoretical, and numerical modeling results. Comparisons with buoy measurements during Hurricane Katrina demonstrate that WW3 simulations with the new Cd parameterizations yield more accurate significant wave heights compared to simulations with the original Cd parameterization, provided that accurate high-resolution wind forcing fields are used.
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da Silva, Nuno V., Andrew Ratcliffe, Vetle Vinje, and Graham Conroy. "A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set." GEOPHYSICS 81, no. 4 (July 2016): U25—U38. http://dx.doi.org/10.1190/geo2015-0349.1.
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Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.
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Burlingame, Bryan M., Clark Evans, and Paul J. Roebber. "The Influence of PBL Parameterization on the Practical Predictability of Convection Initiation during the Mesoscale Predictability Experiment (MPEX)." Weather and Forecasting 32, no. 3 (May 19, 2017): 1161–83. http://dx.doi.org/10.1175/waf-d-16-0174.1.
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Abstract This study evaluates the influence of planetary boundary layer parameterization on short-range (0–15 h) convection initiation (CI) forecasts within convection-allowing ensembles that utilize subsynoptic-scale observations collected during the Mesoscale Predictability Experiment. Three cases, 19–20 May, 31 May–1 June, and 8–9 June 2013, are considered, each characterized by a different large-scale flow pattern. An object-based method is used to verify and analyze CI forecasts. Local mixing parameterizations have, relative to nonlocal mixing parameterizations, higher probabilities of detection but also higher false alarm ratios, such that the ensemble mean forecast skill only subtly varied between parameterizations considered. Temporal error distributions associated with matched events are approximately normal around a zero mean, suggesting little systematic timing bias. Spatial error distributions are skewed, with average mean (median) distance errors of approximately 44 km (28 km). Matched event cumulative distribution functions suggest limited forecast skill increases beyond temporal and spatial thresholds of 1 h and 100 km, respectively. Forecast skill variation is greatest between cases with smaller variation between PBL parameterizations or between individual ensemble members for a given case, implying greatest control on CI forecast skill by larger-scale features than PBL parameterization. In agreement with previous studies, local mixing parameterizations tend to produce simulated boundary layers that are too shallow, cool, and moist, while nonlocal mixing parameterizations tend to be deeper, warmer, and drier. Forecasts poorly resolve strong capping inversions across all parameterizations, which is hypothesized to result primarily from implicit numerical diffusion associated with the default finite-differencing formulation for vertical advection used herein.
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Huang, Hsin-Yuan, Alex Hall, and Joao Teixeira. "Evaluation of the WRF PBL Parameterizations for Marine Boundary Layer Clouds: Cumulus and Stratocumulus." Monthly Weather Review 141, no. 7 (July 1, 2013): 2265–71. http://dx.doi.org/10.1175/mwr-d-12-00292.1.
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Abstract The performance of five boundary layer parameterizations in the Weather Research and Forecasting Model is examined for marine boundary layer cloud regions running in single-column mode. Most parameterizations show a poor agreement of the vertical boundary layer structure when compared with large-eddy simulation models. These comparisons against large-eddy simulation show that a parameterization based on the eddy-diffusivity/mass-flux approach provides a better performance. The results also illustrate the key role of boundary layer parameterizations in model performance.
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Richter, Jadwiga H., Fabrizio Sassi, and Rolando R. Garcia. "Toward a Physically Based Gravity Wave Source Parameterization in a General Circulation Model." Journal of the Atmospheric Sciences 67, no. 1 (January 1, 2010): 136–56. http://dx.doi.org/10.1175/2009jas3112.1.
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Abstract Middle atmospheric general circulation models (GCMs) must employ a parameterization for small-scale gravity waves (GWs). Such parameterizations typically make very simple assumptions about gravity wave sources, such as uniform distribution in space and time or an arbitrarily specified GW source function. The authors present a configuration of the Whole Atmosphere Community Climate Model (WACCM) that replaces the arbitrarily specified GW source spectrum with GW source parameterizations. For the nonorographic wave sources, a frontal system and convective GW source parameterization are used. These parameterizations link GW generation to tropospheric quantities calculated by the GCM and provide a model-consistent GW representation. With the new GW source parameterization, a reasonable middle atmospheric circulation can be obtained and the middle atmospheric circulation is better in several respects than that generated by a typical GW source specification. In particular, the interannual NH stratospheric variability is significantly improved as a result of the source-oriented GW parameterization. It is also shown that the addition of a parameterization to estimate mountain stress due to unresolved orography has a large effect on the frequency of stratospheric sudden warmings in the NH stratosphere by changing the propagation of stationary planetary waves into the polar vortex.
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Hendricks, Eric A., Jason C. Knievel, and Yi Wang. "Addition of Multilayer Urban Canopy Models to a Nonlocal Planetary Boundary Layer Parameterization and Evaluation Using Ideal and Real Cases." Journal of Applied Meteorology and Climatology 59, no. 8 (August 1, 2020): 1369–92. http://dx.doi.org/10.1175/jamc-d-19-0142.1.
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AbstractThe multilayer urban canopy models (UCMs) building effect parameterization (BEP) and BEP + building energy model (BEM; a building energy model integrated in BEP) are added to the Yonsei University (YSU) planetary boundary layer (PBL) parameterization in the Weather Research and Forecasting (WRF) Model. The additions allow for the first analysis of the detailed effects of buildings on the urban boundary layer in a nonlocal closure scheme. The modified YSU PBL parameterization is compared with the other 1.5-order local PBL parameterizations that predict turbulent kinetic energy (TKE), Mellor–Yamada–Janjić and Bougeault–Lacarerre, using both ideal and real cases. The ideal-case evaluation confirms that BEP and BEP+BEM produce the expected results in the YSU PBL parameterization because the simulations are qualitatively similar to the TKE-based PBL parameterizations in which the multilayer UCMs have long existed. The modified YSU PBL parameterization is further evaluated for a real case. Similar to the ideal case, there are larger differences among the different UCMs (simple bulk scheme, BEP, and BEP+BEM) than across the PBL parameterizations when the UCM is held fixed. Based on evaluation against urban near-surface wind and temperature observations for this case, the BEP and BEP+BEM simulations are superior to the simple bulk scheme for each PBL parameterization.
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Sikma, M., and H. G. Ouwersloot. "Parameterizations for convective transport in various cloud-topped boundary layers." Atmospheric Chemistry and Physics 15, no. 18 (September 23, 2015): 10399–410. http://dx.doi.org/10.5194/acp-15-10399-2015.
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Abstract. We investigate the representation of convective transport of atmospheric compounds by boundary layer clouds. We focus on three key parameterizations that, when combined, express this transport: the area fraction of transporting clouds, the upward velocity in the cloud cores and the chemical concentrations at cloud base. The first two parameterizations combined represent the kinematic mass flux by clouds. To investigate the key parameterizations under a wide range of conditions, we use large-eddy simulation model data for 10 meteorological situations, characterized by either shallow cumulus or stratocumulus clouds. The parameterizations have not been previously tested with such large data sets. In the analysis, we show that the parameterization of the area fraction of clouds currently used in mixed-layer models is affected by boundary layer dynamics. Therefore, we (i) simplify the independent variable used for this parameterization, Q1, by considering the variability in moisture rather than in the saturation deficit and update the parameters in the parameterization to account for this simplification. We (ii) next demonstrate that the independent variable has to be evaluated locally to capture cloud presence. Furthermore, we (iii) show that the area fraction of transporting clouds is not represented by the parameterization for the total cloud area fraction, as is currently assumed in literature. To capture cloud transport, a novel active cloud area fraction parameterization is proposed. Subsequently, the scaling of the upward velocity in cloud cores by the Deardorff convective velocity scale and the parameterization for the concentration of atmospheric reactants at cloud base from literature are verified and improved by analysing six shallow cumulus cases. For the latter, we additionally discuss how the parameterization is affected by wind conditions. This study contributes to a more accurate estimation of convective transport, which occurs at sub-grid scales.
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Resseguier, Valentin, Wei Pan, and Baylor Fox-Kemper. "Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty." Nonlinear Processes in Geophysics 27, no. 2 (April 16, 2020): 209–34. http://dx.doi.org/10.5194/npg-27-209-2020.
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Abstract. Stochastic subgrid parameterizations enable ensemble forecasts of fluid dynamic systems and ultimately accurate data assimilation (DA). Stochastic advection by Lie transport (SALT) and models under location uncertainty (LU) are recent and similar physically based stochastic schemes. SALT dynamics conserve helicity, whereas LU models conserve kinetic energy (KE). After highlighting general similarities between LU and SALT frameworks, this paper focuses on their common challenge: the parameterization choice. We compare uncertainty quantification skills of a stationary heterogeneous data-driven parameterization and a non-stationary homogeneous self-similar parameterization. For stationary, homogeneous surface quasi-geostrophic (SQG; QG) turbulence, both parameterizations lead to high-quality ensemble forecasts. This paper also discusses a heterogeneous adaptation of the homogeneous parameterization targeted at a better simulation of strong straight buoyancy fronts.
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Yamada, Kou, Iwanori Murakami, Yoshinori Ando, Takaaki Hagiwara, Da Zhi Gong, Yuki Nakui, and Tatsuya Sakanushi. "The Parameterization of All Disturbance Observers for Discrete-Time Plants with Input Disturbance." Key Engineering Materials 497 (December 2011): 197–209. http://dx.doi.org/10.4028/www.scientific.net/kem.497.197.
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Disturbance observers have been used to estimate the disturbance in the plant. Several paperson design methods of disturbance observers have been published. Recently, the parameterizationof all disturbance observers for discrete-time plants with any output disturbance was clarified. However,no paper examines the parameterization of all disturbance observers for discrete-time plants withany input disturbance. In this paper, we clarify existance conditions of a disturbance observer and ofa linear functional disturbance observer for discrete-time plants with any input disturbance. Underthese conditions, we propose parameterizations of all disturbance observers and all linear functionaldisturbance observers for discrete-time plants with any input disturbance.
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Shi, Xiaoxu, Dirk Notz, Jiping Liu, Hu Yang, and Gerrit Lohmann. "Sensitivity of Northern Hemisphere climate to ice–ocean interface heat flux parameterizations." Geoscientific Model Development 14, no. 8 (August 5, 2021): 4891–908. http://dx.doi.org/10.5194/gmd-14-4891-2021.
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Abstract. We investigate the impact of three different parameterizations of ice–ocean heat exchange on modeled sea ice thickness, sea ice concentration, and water masses. These three parameterizations are (1) an ice bath assumption with the ocean temperature fixed at the freezing temperature; (2) a two-equation turbulent heat flux parameterization with ice–ocean heat exchange depending linearly on the temperature difference between the underlying ocean and the ice–ocean interface, whose temperature is kept at the freezing point of the seawater; and (3) a three-equation turbulent heat flux approach in which the ice–ocean heat flux depends on the temperature difference between the underlying ocean and the ice–ocean interface, whose temperature is calculated based on the local salinity set by the ice ablation rate. Based on model simulations with the stand-alone sea ice model CICE, the ice–ocean model MPIOM, and the climate model COSMOS, we find that compared to the most complex parameterization (3), the approaches (1) and (2) result in thinner Arctic sea ice, cooler water beneath high-concentration ice and warmer water towards the ice edge, and a lower salinity in the Arctic Ocean mixed layer. In particular, parameterization (1) results in the smallest sea ice thickness among the three parameterizations, as in this parameterization all potential heat in the underlying ocean is used for the melting of the sea ice above. For the same reason, the upper ocean layer of the central Arctic is cooler when using parameterization (1) compared to (2) and (3). Finally, in the fully coupled climate model COSMOS, parameterizations (1) and (2) result in a fairly similar oceanic or atmospheric circulation. In contrast, the most realistic parameterization (3) leads to an enhanced Atlantic meridional overturning circulation (AMOC), a more positive North Atlantic Oscillation (NAO) mode and a weakened Aleutian Low.
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de la Sen, M. "Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls." Mathematical Problems in Engineering 2010 (2010): 1–33. http://dx.doi.org/10.1155/2010/693958.
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This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.
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Thayer-Calder, K., A. Gettelman, C. Craig, S. Goldhaber, P. A. Bogenschutz, C. C. Chen, H. Morrison, et al. "A unified parameterization of clouds and turbulence using CLUBB and subcolumns in the Community Atmosphere Model." Geoscientific Model Development 8, no. 12 (December 1, 2015): 3801–21. http://dx.doi.org/10.5194/gmd-8-3801-2015.
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Abstract. Most global climate models parameterize separate cloud types using separate parameterizations. This approach has several disadvantages, including obscure interactions between parameterizations and inaccurate triggering of cumulus parameterizations. Alternatively, a unified cloud parameterization uses one equation set to represent all cloud types. Such cloud types include stratiform liquid and ice cloud, shallow convective cloud, and deep convective cloud. Vital to the success of a unified parameterization is a general interface between clouds and microphysics. One such interface involves drawing Monte Carlo samples of subgrid variability of temperature, water vapor, cloud liquid, and cloud ice, and feeding the sample points into a microphysics scheme. This study evaluates a unified cloud parameterization and a Monte Carlo microphysics interface that has been implemented in the Community Atmosphere Model (CAM) version 5.3. Model computational expense is estimated, and sensitivity to the number of subcolumns is investigated. Results describing the mean climate and tropical variability from global simulations are presented. The new model shows a degradation in precipitation skill but improvements in shortwave cloud forcing, liquid water path, long-wave cloud forcing, precipitable water, and tropical wave simulation.
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Madi, Raneem, Gerrit Huibert de Rooij, Henrike Mielenz, and Juliane Mai. "Parametric soil water retention models: a critical evaluation of expressions for the full moisture range." Hydrology and Earth System Sciences 22, no. 2 (February 12, 2018): 1193–219. http://dx.doi.org/10.5194/hess-22-1193-2018.
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Abstract. Few parametric expressions for the soil water retention curve are suitable for dry conditions. Furthermore, expressions for the soil hydraulic conductivity curves associated with parametric retention functions can behave unrealistically near saturation. We developed a general criterion for water retention parameterizations that ensures physically plausible conductivity curves. Only 3 of the 18 tested parameterizations met this criterion without restrictions on the parameters of a popular conductivity curve parameterization. A fourth required one parameter to be fixed. We estimated parameters by shuffled complex evolution (SCE) with the objective function tailored to various observation methods used to obtain retention curve data. We fitted the four parameterizations with physically plausible conductivities as well as the most widely used parameterization. The performance of the resulting 12 combinations of retention and conductivity curves was assessed in a numerical study with 751 days of semiarid atmospheric forcing applied to unvegetated, uniform, 1 m freely draining columns for four textures. Choosing different parameterizations had a minor effect on evaporation, but cumulative bottom fluxes varied by up to an order of magnitude between them. This highlights the need for a careful selection of the soil hydraulic parameterization that ideally does not only rely on goodness of fit to static soil water retention data but also on hydraulic conductivity measurements. Parameter fits for 21 soils showed that extrapolations into the dry range of the retention curve often became physically more realistic when the parameterization had a logarithmic dry branch, particularly in fine-textured soils where high residual water contents would otherwise be fitted.
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Ochoa, José, Julio Sheinbaum, and Aleph Jiménez. "Lateral Friction in Reduced-Gravity Models: Parameterizations Consistent with Energy Dissipation and Conservation of Angular Momentum." Journal of Physical Oceanography 41, no. 10 (October 1, 2011): 1894–901. http://dx.doi.org/10.1175/2011jpo4599.1.
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Abstract The f-plane reduced-gravity model has been extended with the parameterization of lateral friction in the momentum equations. The parameterization should preferably fulfill some requisites. One of them is that in the absence of external torques the change in angular momentum should be determined by boundary conditions alone. Internal torques should balance in the angular momentum budget. This requirement is fulfilled when the parameterization in the vertically integrated momentum equations is the divergence of a symmetric stress tensor. These equations solve for the mean transport, which includes implicitly the eddy-induced contribution. Another requirement on the parameterization of lateral stress follows from considering that it should imply kinetic energy dissipation. Both requirements fail with a commonly used parameterization and are fulfilled with the one proposed by C. Schär and R. B. Smith, which also is in near agreement with derivations of the shallow-water equations via vertical integrations of the Navier–Stokes equations. Here, the authors show two other parameterizations that are consistent with the angular momentum and energy requirements. One of the parameterizations follows from the symmetric component of a stress tensor in agreement with the parameterization shown by P. R. Gent to be energetically consistent. The other parameterization is related to the so-called biharmonic dissipation. In general, the difficulty for friction parameterizations is on the energy dissipation requirement, because the one on angular momentum is easily fulfilled.
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Thayer-Calder, K., A. Gettelman, C. Craig, S. Goldhaber, P. A. Bogenschutz, C. C. Chen, H. Morrison, et al. "A unified parameterization of clouds and turbulence using CLUBB and subcolumns in the Community Atmosphere Model." Geoscientific Model Development Discussions 8, no. 6 (June 30, 2015): 5041–88. http://dx.doi.org/10.5194/gmdd-8-5041-2015.
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Abstract. Most global climate models parameterize separate cloud types using separate parameterizations. This approach has several disadvantages, including obscure interactions between parameterizations and inaccurate triggering of cumulus parameterizations. Alternatively, a unified cloud parameterization uses one equation set to represent all cloud types. Such cloud types include stratiform liquid and ice cloud, shallow convective cloud, and deep convective cloud. Vital to the success of a unified parameterization is a general interface between clouds and microphysics. One such interface involves drawing Monte Carlo samples of subgrid variability of temperature, water vapor, cloud liquid, and cloud ice, and feeding the sample points into a microphysics scheme. This study evaluates a unified cloud parameterization and a Monte Carlo microphysics interface that has been implemented in the Community Atmosphere Model (CAM) version 5.3. Results describing the mean climate and tropical variability from global simulations are presented. The new model shows a degradation in precipitation skill but improvements in short-wave cloud forcing, liquid water path, long-wave cloud forcing, precipitable water, and tropical wave simulation. Also presented are estimations of computational expense and investigation of sensitivity to number of subcolumns.
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Yamada, Kou, Iwanori Murakami, Yoshinori Ando, Takaaki Hagiwara, Yoichi Imai, Da Zhi Gong, and Satoshi Aoyama. "The Parameterization of all Disturbance Observers for Plants with State Disturbance." Applied Mechanics and Materials 36 (October 2010): 263–72. http://dx.doi.org/10.4028/www.scientific.net/amm.36.263.
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In this paper, we examine the parameterization of all disturbance observers for plants with any state disturbance. The disturbance observers have been used to estimate the disturbance in the plant. Several papers on design methods of disturbance observers have been published. Recently, the parameterizations of all disturbance observers for plants with any output disturbance and all disturbance observers for plants with any input disturbance were clarified. However, no paper examines the parameterization of all disturbance observers for plants with any state disturbance. In this paper, we propose parameterizations of all disturbance observers and all linear functional disturbance observers for plants with any state disturbance.
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Guo, Feng Hua. "A New Piecewise Rational Reparameterization Method." Advanced Materials Research 734-737 (August 2013): 3057–60. http://dx.doi.org/10.4028/www.scientific.net/amr.734-737.3057.
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A new piecewise rational re-parameterization of a polynomial curve is presented. The method relies on a parametric polygonal decomposition method. With the proposed piecewise rational re-parameterization method, the optimal parameterization can be reached, and the optimal parameterizations asymptotic convergence to the arc-length parameterization is analyzed. Computing instances demonstrates the efficiency of the proposed method.
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Valmassoi, Arianna, Jimy Dudhia, Silvana Di Sabatino, and Francesco Pilla. "Evaluation of three new surface irrigation parameterizations in the WRF-ARW v3.8.1 model: the Po Valley (Italy) case study." Geoscientific Model Development 13, no. 7 (July 14, 2020): 3179–201. http://dx.doi.org/10.5194/gmd-13-3179-2020.
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Abstract. Irrigation is a method of land management that can affect the local climate. Recent literature shows that it affects mostly the near-surface variables and it is associated with an irrigation cooling effect. However, there is no common parameterization that also accounts for a realistic water amount, and this factor could ascribe one cause to the different impacts found in previous studies. This work aims to introduce three new surface irrigation parameterizations within the WRF-ARW model (v3.8.1) that consider different evaporative processes. The parameterizations are tested on one of the regions where global studies disagree on the signal of irrigation: the Mediterranean area and in particular the Po Valley. Three sets of experiments are performed using the same irrigation water amount of 5.7 mm d−1, derived from Eurostat data. Two complementary validations are performed for July 2015: monthly mean, minimum, and maximum temperature with ground stations and potential evapotranspiration with the MODIS product. All tests show that for both mean and maximum temperature, as well as potential evapotranspiration simulated fields approximate observation-based values better when using the irrigation parameterizations. This study addresses the sensitivity of the results to human-decision assumptions of the parameterizations: start time, length, and frequency. The main impact of irrigation on surface variables such as soil moisture is due to the parameterization choice itself affecting evaporation, rather than the timing. Moreover, on average, the atmosphere and soil variables are not very sensitive to the parameterization assumptions for realistic timing and length.
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Zhu, Meilin, Tandong Yao, Wei Yang, Baiqing Xu, and Xiaojun Wang. "Evaluation of Parameterizations of Incoming Longwave Radiation in the High-Mountain Region of the Tibetan Plateau." Journal of Applied Meteorology and Climatology 56, no. 4 (April 2017): 833–48. http://dx.doi.org/10.1175/jamc-d-16-0189.1.
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AbstractAccurate evaluations of incoming longwave radiation (Lin) parameterization have practical implications for glacier and river runoff changes in high-mountain regions of the Tibetan Plateau (TP). To identify potential means of accurately predicting spatiotemporal variations in Lin, 13 clear-sky parameterizations combined with 10 cloud corrections for all-sky atmospheric emissivity were evaluated at five sites in high-mountain regions of the TP through temporal and spatial parameter transfer tests. Most locally calibrated parameterizations for clear-sky and all-sky conditions performed well when applied to the calibration site. The best parameterization at five sites is Dilley and O’Brien’s A model combined with Sicart et al.’s A for cloud-correction-incorporated relative humidity. The performance of parameter transferability in time is better than that in space for the same all-sky parameterizations. The performance of parameter transferability in space presents spatial discrepancies. In addition, all all-sky parameterizations show a decrease in performance with increasing altitude regardless of whether the parameters of all-sky parameterizations were recalibrated by local conditions or transferred from other study sites. This may be attributable to the difference between screen-level air temperature and the effective atmospheric boundary layer temperature and to different cloud-base heights. Nevertheless, such worse performance at higher altitudes is likely to change because of terrain, underlying surfaces, and wind systems, among other factors. The study also describes possible spatial characteristics of Lin and its driving factors by reviewing the few studies about Lin for the mountain regions of the TP.
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Khan, Tanvir R., and Judith A. Perlinger. "Evaluation of five dry particle deposition parameterizations for incorporation into atmospheric transport models." Geoscientific Model Development 10, no. 10 (October 25, 2017): 3861–88. http://dx.doi.org/10.5194/gmd-10-3861-2017.
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Abstract. Despite considerable effort to develop mechanistic dry particle deposition parameterizations for atmospheric transport models, current knowledge has been inadequate to propose quantitative measures of the relative performance of available parameterizations. In this study, we evaluated the performance of five dry particle deposition parameterizations developed by Zhang et al. (2001) (Z01), Petroff and Zhang (2010) (PZ10), Kouznetsov and Sofiev (2012) (KS12), Zhang and He (2014) (ZH14), and Zhang and Shao (2014) (ZS14), respectively. The evaluation was performed in three dimensions: model ability to reproduce observed deposition velocities, Vd (accuracy); the influence of imprecision in input parameter values on the modeled Vd (uncertainty); and identification of the most influential parameter(s) (sensitivity). The accuracy of the modeled Vd was evaluated using observations obtained from five land use categories (LUCs): grass, coniferous and deciduous forests, natural water, and ice/snow. To ascertain the uncertainty in modeled Vd, and quantify the influence of imprecision in key model input parameters, a Monte Carlo uncertainty analysis was performed. The Sobol' sensitivity analysis was conducted with the objective to determine the parameter ranking from the most to the least influential. Comparing the normalized mean bias factors (indicators of accuracy), we find that the ZH14 parameterization is the most accurate for all LUCs except for coniferous forest, for which it is second most accurate. From Monte Carlo simulations, the estimated mean normalized uncertainties in the modeled Vd obtained for seven particle sizes (ranging from 0.005 to 2.5 µm) for the five LUCs are 17, 12, 13, 16, and 27 % for the Z01, PZ10, KS12, ZH14, and ZS14 parameterizations, respectively. From the Sobol' sensitivity results, we suggest that the parameter rankings vary by particle size and LUC for a given parameterization. Overall, for dp = 0.001 to 1.0 µm, friction velocity was one of the three most influential parameters in all parameterizations. For giant particles (dp = 10 µm), relative humidity was the most influential parameter. Because it is the least complex of the five parameterizations, and it has the greatest accuracy and least uncertainty, we propose that the ZH14 parameterization is currently superior for incorporation into atmospheric transport models.
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Niemand, Monika, Ottmar Möhler, Bernhard Vogel, Heike Vogel, Corinna Hoose, Paul Connolly, Holger Klein, et al. "A Particle-Surface-Area-Based Parameterization of Immersion Freezing on Desert Dust Particles." Journal of the Atmospheric Sciences 69, no. 10 (April 30, 2012): 3077–92. http://dx.doi.org/10.1175/jas-d-11-0249.1.
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Abstract In climate and weather models, the quantitative description of aerosol and cloud processes relies on simplified assumptions. This contributes major uncertainties to the prediction of global and regional climate change. Therefore, models need good parameterizations for heterogeneous ice nucleation by atmospheric aerosols. Here the authors present a new parameterization of immersion freezing on desert dust particles derived from a large number of experiments carried out at the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) cloud chamber facility. The parameterization is valid in the temperature range between −12° and −36°C at or above water saturation and can be used in atmospheric models that include information about the dust surface area. The new parameterization was applied to calculate distribution maps of ice nuclei during a Saharan dust event based on model results from the regional-scale model Consortium for Small-Scale Modelling–Aerosols and Reactive Trace Gases (COSMO-ART). The results were then compared to measurements at the Taunus Observatory on Mount Kleiner Feldberg, Germany, and to three other parameterizations applied to the dust outbreak. The aerosol number concentration and surface area from the COSMO-ART model simulation were taken as input to different parameterizations. Although the surface area from the model agreed well with aerosol measurements during the dust event at Kleiner Feldberg, the ice nuclei (IN) number concentration calculated from the new surface-area-based parameterization was about a factor of 13 less than IN measurements during the same event. Systematic differences of more than a factor of 10 in the IN number concentration were also found among the different parameterizations. Uncertainties in the modeled and measured parameters probably both contribute to this discrepancy and should be addressed in future studies.
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Lupascu, A., R. Easter, R. Zaveri, M. Shrivastava, M. Pekour, J. Tomlinson, Q. Yang, et al. "Modeling particle nucleation and growth over northern California during the 2010 CARES campaign." Atmospheric Chemistry and Physics 15, no. 21 (November 6, 2015): 12283–313. http://dx.doi.org/10.5194/acp-15-12283-2015.
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Abstract. Accurate representation of the aerosol lifecycle requires adequate modeling of the particle number concentration and size distribution in addition to their mass, which is often the focus of aerosol modeling studies. This paper compares particle number concentrations and size distributions as predicted by three empirical nucleation parameterizations in the Weather Research and Forecast coupled with chemistry (WRF-Chem) regional model using 20 discrete size bins ranging from 1 nm to 10 μm. Two of the parameterizations are based on H2SO4, while one is based on both H2SO4 and organic vapors. Budget diagnostic terms for transport, dry deposition, emissions, condensational growth, nucleation, and coagulation of aerosol particles have been added to the model and are used to analyze the differences in how the new particle formation parameterizations influence the evolving aerosol size distribution. The simulations are evaluated using measurements collected at surface sites and from a research aircraft during the Carbonaceous Aerosol and Radiative Effects Study (CARES) conducted in the vicinity of Sacramento, California. While all three parameterizations captured the temporal variation of the size distribution during observed nucleation events as well as the spatial variability in aerosol number, all overestimated by up to a factor of 2.5 the total particle number concentration for particle diameters greater than 10 nm. Using the budget diagnostic terms, we demonstrate that the combined H2SO4 and low-volatility organic vapor parameterization leads to a different diurnal variability of new particle formation and growth to larger sizes compared to the parameterizations based on only H2SO4. At the CARES urban ground site, peak nucleation rates are predicted to occur around 12:00 Pacific (local) standard time (PST) for the H2SO4 parameterizations, whereas the highest rates were predicted at 08:00 and 16:00 PST when low-volatility organic gases are included in the parameterization. This can be explained by higher anthropogenic emissions of organic vapors at these times as well as lower boundary-layer heights that reduce vertical mixing. The higher nucleation rates in the H2SO4-organic parameterization at these times were largely offset by losses due to coagulation. Despite the different budget terms for ultrafine particles, the 10–40 nm diameter particle number concentrations from all three parameterizations increased from 10:00 to 14:00 PST and then decreased later in the afternoon, consistent with changes in the observed size and number distribution. We found that newly formed particles could explain up to 20–30 % of predicted cloud condensation nuclei at 0.5 % supersaturation, depending on location and the specific nucleation parameterization. A sensitivity simulation using 12 discrete size bins ranging from 1 nm to 10 μm diameter gave a reasonable estimate of particle number and size distribution compared to the 20 size bin simulation, while reducing the associated computational cost by ~ 36 %.
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Cessi, Paola. "An Energy-Constrained Parameterization of Eddy Buoyancy Flux." Journal of Physical Oceanography 38, no. 8 (August 1, 2008): 1807–19. http://dx.doi.org/10.1175/2007jpo3812.1.
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Abstract A parameterization for eddy buoyancy fluxes for use in coarse-grid models is developed and tested against eddy-resolving simulations. The development is based on the assumption that the eddies are adiabatic (except near the surface) and the observation that the flux of buoyancy is affected by barotropic, depth-independent eddies. Like the previous parameterizations of Gent and McWilliams (GM) and Visbeck et al. (VMHS), the horizontal flux of a tracer is proportional to the local large-scale horizontal gradient of the tracer through a transfer coefficient assumed to be given by the product of a typical eddy velocity scale and a typical mixing length. The proposed parameterization differs from GM and VMHS in the selection of the eddy velocity scale, which is based on the kinetic energy balance of baroclinic eddies. The three parameterizations are compared to eddy-resolving computations in a variety of forcing configurations and for several sets of parameters. The VMHS and the energy balance parameterizations perform best in the tests considered here.
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Demaeyer, Jonathan, and Stéphane Vannitsem. "Comparison of stochastic parameterizations in the framework of a coupled ocean–atmosphere model." Nonlinear Processes in Geophysics 25, no. 3 (August 30, 2018): 605–31. http://dx.doi.org/10.5194/npg-25-605-2018.
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Abstract. A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), a coupled ocean–atmosphere model of intermediate complexity. Two physically based parameterizations are investigated – the first one based on the singular perturbation of Markov operators, also known as homogenization. The second one is a recently proposed parameterization based on Ruelle's response theory. The two parameterizations are implemented in a rigorous way, assuming however that the unresolved-scale relevant statistics are Gaussian. They are extensively tested for a low-order version known to exhibit low-frequency variability (LFV), and some preliminary results are obtained for an intermediate-order version. Several different configurations of the resolved–unresolved-scale separations are then considered. Both parameterizations show remarkable performances in correcting the impact of model errors, being even able to change the modality of the probability distributions. Their respective limitations are also discussed.
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Rennolls, Keith, and Mingliang Wang. "A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data." Canadian Journal of Forest Research 35, no. 3 (March 1, 2005): 575–79. http://dx.doi.org/10.1139/x05-006.
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The SB distributional model of Johnson's 1949 paper was introduced by a transformation to normality, that is, z ~ N(0, 1), consisting of a linear scaling to the range (0, 1), a logit transformation, and an affine transformation, z = γ + δu. The model, in its original parameterization, has often been used in forest diameter distribution modelling. In this paper, we define the SB distribution in terms of the inverse transformation from normality, including an initial linear scaling transformation, u = γ′ + δ′z (δ′ = 1/δ and γ′ = γ/δ). The SB model in terms of the new parameterization is derived, and maximum likelihood estimation schema are presented for both model parameterizations. The statistical properties of the two alternative parameterizations are compared empirically on 20 data sets of diameter distributions of Changbai larch (Larix olgensis Henry). The new parameterization is shown to be statistically better than Johnson's original parameterization for the data sets considered here.
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Toro, Tatiana. "parameterizations." Duke Mathematical Journal 77, no. 1 (January 1995): 193–227. http://dx.doi.org/10.1215/s0012-7094-95-07708-4.
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Wong, Anthony Y. H., Jeffrey A. Geddes, Amos P. K. Tai, and Sam J. Silva. "Importance of dry deposition parameterization choice in global simulations of surface ozone." Atmospheric Chemistry and Physics 19, no. 22 (November 28, 2019): 14365–85. http://dx.doi.org/10.5194/acp-19-14365-2019.
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Abstract. Dry deposition is a major sink of tropospheric ozone. Increasing evidence has shown that ozone dry deposition actively links meteorology and hydrology with ozone air quality. However, there is little systematic investigation on the performance of different ozone dry deposition parameterizations at the global scale and how parameterization choice can impact surface ozone simulations. Here, we present the results of the first global, multidecadal modelling and evaluation of ozone dry deposition velocity (vd) using multiple ozone dry deposition parameterizations. We model ozone dry deposition velocities over 1982–2011 using four ozone dry deposition parameterizations that are representative of current approaches in global ozone dry deposition modelling. We use consistent assimilated meteorology, land cover, and satellite-derived leaf area index (LAI) across all four, such that the differences in simulated vd are entirely due to differences in deposition model structures or assumptions about how land types are treated in each. In addition, we use the surface ozone sensitivity to vd predicted by a chemical transport model to estimate the impact of mean and variability of ozone dry deposition velocity on surface ozone. Our estimated vd values from four different parameterizations are evaluated against field observations, and while performance varies considerably by land cover types, our results suggest that none of the parameterizations are universally better than the others. Discrepancy in simulated mean vd among the parameterizations is estimated to cause 2 to 5 ppbv of discrepancy in surface ozone in the Northern Hemisphere (NH) and up to 8 ppbv in tropical rainforests in July, and up to 8 ppbv in tropical rainforests and seasonally dry tropical forests in Indochina in December. Parameterization-specific biases based on individual land cover type and hydroclimate are found to be the two main drivers of such discrepancies. We find statistically significant trends in the multiannual time series of simulated July daytime vd in all parameterizations, driven by warming and drying (southern Amazonia, southern African savannah, and Mongolia) or greening (high latitudes). The trend in July daytime vd is estimated to be 1 % yr−1 and leads to up to 3 ppbv of surface ozone changes over 1982–2011. The interannual coefficient of variation (CV) of July daytime mean vd in NH is found to be 5 %–15 %, with spatial distribution that varies with the dry deposition parameterization. Our sensitivity simulations suggest this can contribute between 0.5 to 2 ppbv to interannual variability (IAV) in surface ozone, but all models tend to underestimate interannual CV when compared to long-term ozone flux observations. We also find that IAV in some dry deposition parameterizations is more sensitive to LAI, while in others it is more sensitive to climate. Comparisons with other published estimates of the IAV of background ozone confirm that ozone dry deposition can be an important part of natural surface ozone variability. Our results demonstrate the importance of ozone dry deposition parameterization choice on surface ozone modelling and the impact of IAV of vd on surface ozone, thus making a strong case for further measurement, evaluation, and model–data integration of ozone dry deposition on different spatiotemporal scales.
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Bonino, Giulia, Doroteaciro Iovino, Laurent Brodeau, and Simona Masina. "The bulk parameterizations of turbulent air–sea fluxes in NEMO4: the origin of sea surface temperature differences in a global model study." Geoscientific Model Development 15, no. 17 (September 9, 2022): 6873–89. http://dx.doi.org/10.5194/gmd-15-6873-2022.
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Abstract. Wind stress and turbulent heat fluxes are the major driving forces that modify the ocean dynamics and thermodynamics. In the Nucleus for European Modelling of the Ocean (NEMO) ocean general circulation model, these turbulent air–sea fluxes (TASFs) can critically impact the simulated ocean characteristics. This paper investigates how the various bulk parameterizations used to calculate turbulent air-sea fluxes in NEMOv4 can lead to substantial differences in the estimation of sea surface temperatures (SSTs). Specifically, we study the contributions of different aspects and assumptions of the bulk parameterizations in driving the SST differences in the NEMO global model configuration at 1/4∘ of horizontal resolution. These aspects include the use of the skin temperature instead of the bulk SST in the computation of turbulent heat flux components and the estimation of wind stress and turbulent heat flux components, which vary in each parameterization due to different bulk transfer coefficients. The analysis of a set of short-term sensitivity experiments where the only change is related to one of the aspects of the bulk parameterizations shows that parameterization-related SST differences are primarily sensitive to wind stress differences and to the implementation of skin temperature in the computation of turbulent heat flux components. In addition, in order to highlight the role of SST–turbulent heat flux negative feedback at play in ocean simulations, we compare the TASF differences obtained using the NEMO ocean model with the estimations by Brodeau et al. (2017), who compared the different bulk parameterizations using prescribed SSTs. Our estimations of turbulent heat flux differences between bulk parameterizations are weaker than those found by Brodeau et al. (2017).
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Baran, Anthony J., Peter Hill, David Walters, Steven C. Hardiman, Kalli Furtado, Paul R. Field, and James Manners. "The Impact of Two Coupled Cirrus Microphysics–Radiation Parameterizations on the Temperature and Specific Humidity Biases in the Tropical Tropopause Layer in a Climate Model." Journal of Climate 29, no. 14 (July 5, 2016): 5299–316. http://dx.doi.org/10.1175/jcli-d-15-0821.1.
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Abstract The impact of two different coupled cirrus microphysics–radiation parameterizations on the zonally averaged temperature and humidity biases in the tropical tropopause layer (TTL) of a Met Office climate model configuration is assessed. One parameterization is based on a linear coupling between a model prognostic variable, the ice mass mixing ratio qi, and the integral optical properties. The second is based on the integral optical properties being parameterized as functions of qi and temperature, Tc, where the mass coefficients (i.e., scattering and extinction) are parameterized as nonlinear functions of the ratio between qi and Tc. The cirrus microphysics parameterization is based on a moment estimation parameterization of the particle size distribution (PSD), which relates the mass moment (i.e., second moment if mass is proportional to size raised to the power of 2) of the PSD to all other PSD moments through the magnitude of the second moment and Tc. This same microphysics PSD parameterization is applied to calculate the integral optical properties used in both radiation parameterizations and, thus, ensures PSD and mass consistency between the cirrus microphysics and radiation schemes. In this paper, the temperature-non-dependent and temperature-dependent parameterizations are shown to increase and decrease the zonally averaged temperature biases in the TTL by about 1 K, respectively. The temperature-dependent radiation parameterization is further demonstrated to have a positive impact on the specific humidity biases in the TTL, as well as decreasing the shortwave and longwave biases in the cloudy radiative effect. The temperature-dependent radiation parameterization is shown to be more consistent with TTL and global radiation observations.
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Koppers, Gijs A. A., and Donal P. Murtagh. "Model studies of the influence of O2 photodissociation parameterizations in the Schumann-Runge bands on ozone related photolysis in the upper atmosphere." Annales Geophysicae 14, no. 1 (January 31, 1996): 68–79. http://dx.doi.org/10.1007/s00585-996-0068-9.
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Abstract. A new parameterization for atmospheric transmission and O2 photodissociation in the Schumann-Runge band region has been developed and tested with a 1D radiative-photochemical model. The parameterization is based on the O2-column along the line of sight to the Sun and the local temperature. Line-by-line calculations have served as a benchmark for testing this method and several other, commonly used, parameterizations. The comparisons suggest that differences between the line-by-line calculations and currently accepted parameterizations can be reduced significantly by using the new method, particularly at large solar zenith angles. The production rate of O-atoms computed with this method shows less than 6% deviation compared to the line-by-line calculations at any altitude, all solar zenith angles and in all seasons. The largest errors are found toward the shorter wavelengths in the Schumann-Runge region at low altitudes. Transmittance is approximated to better than 4% at any altitude and/or solar zenith angle. The total O-production rate above 20 km is approximated to better than 2%. The new parameterization is easily implemented in existing photochemical models and in many cases it may simply replace the existing algorithm. The computational effort exceeds that of other parameterizations but in view of the total computation time needed for the actual calculation of the parameterized Schumann-Runge bands this should not lead to significant performance degeneration. The first 14 coefficients of the parameterization are included in this study. Both the complete sets of coefficients and a simple algorithm can be obtained by contacting the authors. A photochemical model study shows the largest effect of the parameterization method is on odd hydrogen concentrations. Subsequent interaction with an odd oxygen family causes differences in the ozone concentrations between the different parameterizations of more than 10% at selected altitudes. Although it is already established that deficiencies in the treatment of Schumann-Runge band absorption are unlikely to explain the current underestimation of ozone concentration at the stratopause in a variety of photochemical models, this study does show that the choice of parameterization has a large impact on the accuracy of the results at large solar zenith angles and in different seasons.
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Sikma, M., and H. G. Ouwersloot. "Parameterizations for convective transport in various cloud-topped boundary layers." Atmospheric Chemistry and Physics Discussions 15, no. 7 (April 14, 2015): 10709–38. http://dx.doi.org/10.5194/acpd-15-10709-2015.
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Abstract. We investigate the representation of convective transport of atmospheric compounds that can be applied in large-scale models. We focus on three key parameterizations that, when combined, express this transport: the area fraction of transporting clouds, the upward velocity in the cloud cores and the chemical concentrations at the cloud base. The first two parameterizations combined represent the mass flux by clouds. To investigate the key parameterizations under a wide range of conditions, we use Large-Eddy Simulation model data for 10 meteorological situations, characterized by either shallow cumulus or stratocumulus clouds. In the analysis of the area fraction of clouds, we (i) simplify the independent variable used for the parameterization, Q1, by considering the variability in moisture rather than in the saturation deficit. We show that there is an unambiguous dependence of the area fraction of clouds on the simplified Q1, and update the parameters in the parameterization to account for this simplification. We (ii) further demonstrate that the independent variable has to be evaluated locally to capture cloud presence. Furthermore, we (iii) show that the area fraction of transporting clouds is not represented by the parameterization for the total cloud area fraction, as is currently applied in large-scale models. To capture cloud transport, a novel active cloud area fraction parameterization is proposed. Subsequently, the scaling of the upward velocity in the clouds' core by the Deardorff convective velocity scale and the parameterization for the concentration of atmospheric reactants at cloud base from literature are verified and improved by analyzing 6 SCu cases. For the latter, we additionally discuss how the parameterization is affected by wind conditions. This study contributes to a more accurate estimation of convective transport in large-scale models, which occurs there at sub-grid scale.
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Lupascu, A., R. Easter, R. Zaveri, M. Shrivastava, M. Pekour, J. Tomlinson, Q. Yang, et al. "Modeling particle nucleation and growth over northern California during the 2010 CARES campaign." Atmospheric Chemistry and Physics Discussions 15, no. 14 (July 20, 2015): 19729–801. http://dx.doi.org/10.5194/acpd-15-19729-2015.
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Abstract. Accurate representation of the aerosol lifecycle requires adequate modeling of the particle number concentration and size distribution in addition to their mass, which is often the focus of aerosol modeling studies. This paper compares particle number concentrations and size distributions as predicted by three empirical nucleation parameterizations in the Weather Research and Forecast coupled with chemistry (WRF-Chem) regional model using 20 discrete size bins ranging from 1 nm to 10 μm. Two of the parameterizations are based on H2SO4 while one is based on both H2SO4 and organic vapors. Budget diagnostic terms for transport, dry deposition, emissions, condensational growth, nucleation, and coagulation of aerosol particles have been added to the model and are used to analyze the differences in how the new particle formation parameterizations influence the evolving aerosol size distribution. The simulations are evaluated using measurements collected at surface sites and from a research aircraft during the Carbonaceous Aerosol and Radiative Effects Study (CARES) conducted in the vicinity of Sacramento, California. While all three parameterizations captured the temporal variation of the size distribution during observed nucleation events as well as the spatial variability in aerosol number, all overestimated by up to a factor of 2.5 the total particle number concentration for particle diameters greater than 10 nm. Using the budget diagnostic terms, we demonstrate that the combined H2SO4 and low-volatility organic vapors parameterization leads to a different diurnal variability of new particle formation and growth to larger sizes compared to the parameterizations based on only H2SO4. At the CARES urban ground site, peak nucleation rates were predicted to occur around 12:00 Pacific (local) standard time (PST) for the H2SO4 parameterizations, whereas the highest rates were predicted at 08:00 and 16:00 PST when low-volatility organic gases are included in the parameterization. This can be explained by higher anthropogenic emissions of organic vapors at these times as well as lower boundary layer heights that reduce vertical mixing. The higher nucleation rates in the H2SO4-organic parameterization at these times were largely offset by losses due to coagulation. Despite the different budget terms for ultrafine particles, the 10–40 nm diameter particle number concentrations from all three parameterizations increased from 10:00 to 14:00 PST and then decreased later in the afternoon, consistent with changes in the observed size and number distribution. Differences among the three simulations for the 40–100 nm particle diameter range are mostly associated with the timing of the peak total tendencies that shift the morning increase and afternoon decrease in particle number concentration by up to two hours. We found that newly formed particles could explain up to 20–30 % of predicted cloud condensation nuclei at 0.5 % supersaturation, depending on location and the specific nucleation parameterization. A sensitivity simulation using 12 discrete size bins ranging from 1 nm to 10 μm diameter gave a reasonable estimate of particle number and size distribution compared to the 20 size bin simulation, while reducing the associated computational cost by ∼ 36 %.
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Arakawa, Akio, and Chien-Ming Wu. "A Unified Representation of Deep Moist Convection in Numerical Modeling of the Atmosphere. Part I." Journal of the Atmospheric Sciences 70, no. 7 (July 1, 2013): 1977–92. http://dx.doi.org/10.1175/jas-d-12-0330.1.
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Abstract A generalized framework for cumulus parameterization applicable to any horizontal resolution between those typically used in general circulation and cloud-resolving models is presented. It is pointed out that the key parameter in the generalization is σ, which is the fractional area covered by convective updrafts in the grid cell. Practically all conventional cumulus parameterizations assume σ ≪ 1, at least implicitly, using the gridpoint values of the thermodynamic variables to define the thermal structure of the cloud environment. The proposed framework, called “unified parameterization,” eliminates this assumption from the beginning, allowing a smooth transition to an explicit simulation of cloud-scale processes as the resolution increases. If clouds and the environment are horizontally homogeneous with a top-hat profile, as is widely assumed in the conventional parameterizations, it is shown that the σ dependence of the eddy transport is through a simple quadratic function. Together with a properly chosen closure, the unified parameterization determines σ for each realization of grid-scale processes. The parameterization can also provide a framework for including stochastic parameterization. The remaining issues include parameterization of the in-cloud eddy transport because of the inhomogeneous structure of clouds.
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Plant, R. S. "A review of the theoretical basis for bulk mass flux convective parameterization." Atmospheric Chemistry and Physics Discussions 9, no. 6 (November 23, 2009): 24945–84. http://dx.doi.org/10.5194/acpd-9-24945-2009.
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Abstract. Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.
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Tagle, Felipe, Judith Berner, Mircea D. Grigoriu, Natalie M. Mahowald, and Gennady Samorodnitsky. "Temperature Extremes in the Community Atmosphere Model with Stochastic Parameterizations*." Journal of Climate 29, no. 1 (December 30, 2015): 241–58. http://dx.doi.org/10.1175/jcli-d-15-0314.1.
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AbstractThis paper evaluates the performance of the NCAR Community Atmosphere Model, version 4 (CAM4), in simulating observed annual extremes of near-surface temperature and provides the first assessment of the impact of stochastic parameterizations of subgrid-scale processes on such performance. Two stochastic parameterizations are examined: the stochastic kinetic energy backscatter scheme and the stochastically perturbed parameterization tendency scheme. Temperature extremes are described in terms of 20-yr return levels and compared to those estimated from ERA-Interim and the Hadley Centre Global Climate Extremes Index 2 (HadEX2) observational dataset. CAM4 overestimates warm and cold extremes over land regions, particularly over the Northern Hemisphere, when compared against reanalysis. Similar spatial patterns, though less spatially coherent, emerge relative to HadEX2. The addition of a stochastic parameterization generally produces a warming of both warm and cold extremes relative to the unperturbed configuration; however, neither of the proposed parameterizations meaningfully reduces the biases in the simulated temperature extremes of CAM4. Adjusting warm and cold extremes by mean conditions in the respective annual extremes leads to good agreement between the models and reanalysis; however, adjusting for the bias in mean temperature does not help to reduce the observed discrepancies. Based on the behavior of the annual extremes, this study concludes that the distribution of temperature in CAM4 exhibits too much variability relative to that of reanalysis, while the stochastic parameterizations introduce a systematic bias in its mean rather than alter its variability.
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FERNANDES, Felipe Augusto, Édipo Menezes SILVA, Kelly Pereira LIMA, Sérgio Alberto JANE, Tales Jesus FERNANDES, and Joel Augusto MUNIZ. "PARAMETERIZATIONS OF THE VON BERTALANFFY MODEL FOR DESCRIPTION OF GROWTH CURVES." REVISTA BRASILEIRA DE BIOMETRIA 38, no. 3 (September 29, 2020): 369. http://dx.doi.org/10.28951/rbb.v38i3.457.
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The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.
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Curry, J. A., and V. I. Khvorostyanov. "Assessment of parameterizations of heterogeneous ice nucleation in cloud and climate models." Atmospheric Chemistry and Physics Discussions 10, no. 2 (February 3, 2010): 2669–710. http://dx.doi.org/10.5194/acpd-10-2669-2010.
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Abstract. Several different types of parameterization of heterogeneous ice nucleation for cloud and climate models have been developed over the past decades, ranging from empirically-derived expressions to parameterizations of ice crystal nucleation rates derived from theory (including the parameterization developed by the authors, hereafter referred to as KC). Parameterizations schemes that address the deliquescence-freezing (DF), which combines the thermodynamically indistinguishable modes of condensation freezing and immersion freezing, are assessed here in the context of thermodynamic constraints, laboratory measurements, and recent field measurements. It is shown that empirical schemes depending only on the ice saturation ratio or only on temperature can produce reasonable crystal concentrations, but ice crystal nucleation is thermodynamically prohibited in certain regions of the temperature-saturation ratio phase space. Some recent empirical parameterizations are shown to have insufficient efficiency, yielding clouds that are almost entire liquid at temperatures as low as −35 °C. A reasonable performance of the KC ice nucleation scheme is demonstrated by comparison with data from several recent field campaigns, laboratory data, climatology of cloud phase-state, and GCM parameterizations. Several mis-applications of the KC parameterization that appeared recently in the literature are described and corrected, by emphasizing that a correct application of the KC scheme with simultaneous dependence on the temperature and saturation ratio requires integration of the individual nucleation rates over the measured size spectrum of the environmental aerosol, and not over the spectrum of ice nuclei equal to the crystal concentration at the exit of an experimental device. Simulation with a spectral bin model and correct application of KC scheme adequately describes ice nucleation via the DF mode and yields crystal concentrations and phase state close to those measured in the single-layer stratocumulus cloud observed in the Mixed Phase Arctic Cloud Experiment (MPACE). An assessment of some deficiencies in current parcel modeling methods and cloud chamber observations and their impact on parameterization development and evaluation is provided.