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E-mail deze pagina. Uitgever: Springer International Publishing Ag. Co-auteur: Xiao-Fan Li. Samenvatting This is an updated and revised second edition of the book presenting new developments in the field of cloud-resolving modeling. The first edition of the book introduces the framework of cloud-resolving model, methodologies for analysis of modeling outputs, and validation of simulations with observations. It details important scientific findings in the aspects of surface rainfall processes, precipitation efficiency, dynamic and thermodynamic processes associated with tropical convection, diurnal variations, radiative and cloud microphysical processes associated with development of cloud clusters, air-sea coupling on convective scales, climate equilibrium states, and remote sensing applications.

In additional to the content from the first edition of the book, the second edition of the book contains the new scientific results in the development of convective-stratiform rainfall separation scheme, the analysis of structures of precipitation systems, the thermal effects of doubled carbon dioxide on rainfall, precipitation predictability, and modeling depositional growth of ice crystal. The book will be beneficial both to graduate students and to researchers who do cloud, mesoscale and global modeling.

Toon meer Toon minder. Recensie s From the reviews: The book focuses on clouds and precipitation and their interaction with larger scales of motion and the Earths surface in e. The book comprises 13 well-written chapters, all of which include a chapter-specific list of references. A large number of figures The book is densely written and addresses graduate students and researches with interest in cloud-, precipitation-, atmospheric-, and general modeling.

Reviews Schrijf een review. For each of the four subperiods, we define a peak convection instantaneous snapshot listed in Table 1 , defined as the time of maximum rain and snow water paths. Table 1. Model configuration and selected periods from three m benchmark simulations. The three simulations are conducted using the same set of physics parameterizations and model configuration Table 1 with a horizontal grid spacing of m and a vertical grid spacing of 25 m near the surface varying up to m over model levels.

All simulations are driven by horizontally homogeneous large-scale forcing derived from the objective variational analysis of Zhang et al. Surface latent and sensible heat fluxes are prescribed. The single-column input to the proposed scheme is diagnosed using instantaneous 3D model fields at min intervals. The output from the scheme is then compared with results computed explicitly using the three-dimensional output.

Figure 1 shows the time evolutions of the domain-mean profiles of cloud condensate liquid and ice mixing ratios with superimposed isolines of the vertical velocity variances for the three simulated cases. Our simulations indicate that the cloud condensates reach higher altitudes up to approximately 18 km in the tropical environment case than for the continental cases approximately 15 km. These higher cloud tops are also evident in radar echo-top observations that were found to extend up to 17 km for the most intense deep convective cells during the TWP-ICE field campaign May et al.

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Red contour lines show domain-averaged vertical velocity variance at 0. Shaded regions mark the time periods of the deep convective cases. CLUBB was originally developed to handle subgrid-scale interactions between turbulence and shallow boundary layer clouds Golaz et al. Guo et al. We therefore do not apply our scheme to cloud liquid water mixing ratio. Sedimentation processes are not considered here as they are handled by the microphysics scheme during each call by the subsampler.

Subgrid-scale vertical turbulent fluxes of hydrometeor mass and number mixing ratios are modeled using an eddy-diffusion approximation in CLUBB. This formulation of eddy diffusivity increases K by a factor of for cumulus layers while remaining small for stratocumulus layers, as vindicated by high-resolution numerical studies Storer et al. This modified formulation for K was designed to use prognostic variables in CLUBB, namely the variance of the hydrometeor mixing ratios and skewness of vertical velocity Sk w , which are linked to physical attributes of deep convection.

The existing parameterization is based on a downgradient formulation and is aimed at parameterizing the covariance. Let us now describe the covariance from a PDF perspective. CLUBB assumes that the vertical velocity w marginal distribution has a double-Gaussian shape, and mass mixing ratios for all hydrometeors q x have marginal distributions of a delta-double-lognormal shape.

The delta function is placed at zero to account for hydrometeor-free fraction in the grid cell Griffin and Larson ; Larson and Griffin ; Griffin and Larson The width of each of the double-lognormal hydrometeor distributions depends on its variance, which is approximated as being proportional to the squared mean of the distribution Storer et al. The width of each vertical velocity distribution is defined to be proportional to the square root of the vertical velocity variance a prognostic variable in CLUBB.

The covariance flux is the integral where P w , q x is the joint distribution of w and q x.

This book examines cloud-resolving modeling of tropical convective processes and summarizes modeling results during TOGA COARE since The book. This is an updated and revised second edition of the book presenting new developments in the field of cloud-resolving modeling. The first edition of the book.

Instead of defining P w , q x , it is possible to compute the covariance directly from the variances and the correlation coefficient between w and q x. The variances may be provided by a PDF-based scheme e.

Important features of P w , q x i. We refer to this step as conditional sampling. The remaining correlation that exists within these quadrants can then be further represented by scaling the means of the quadrant PDFs. Wong et al. Implementing the quadrant-based decomposition as described in Wong et al. Here, we reformulate the Wong et al. Using the product of only the marginals inherently sets the correlation within each section to zero. To parameterize the effect of , a similar conditional sampling method, but with a different set of criteria, followed by power-law scaling are applied.

The conditional sampling sections the two univariate distributions into groups of pairs of values with similar correlations.

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The power-law scaling approximates the correlation effect in each section. The advantages of this approach are that the estimated subgrid-scale vertical fluxes will be able to utilize the PDFs of vertical velocity and hydrometeor mass mixing ratios made available for example by CLUBB, and using the conditional sampling method with a scaling factor, subplume spatial correlations are incorporated and can in principle vary effectively with time, height, and by the type of convective element.

Here, for simplicity, we set the scaling factor to be a constant for each convective element type—that is, effectively setting the subplume spatial correlations to be invariant with time and height. If the covariance is given, the PDF component correlations can be backsolved and can potentially be used to diagnose the correlations among hydrometeors, such as in Larson et al. The transport scheme is intended to compute vertical fluxes assuming that only marginal PDFs of subgrid-scale vertical velocity and hydrometeor mass mixing ratios are known.

In CLUBB, a double-Gaussian marginal PDF of vertical velocity is selected based on prognostic variance and the third-order moment, and a delta-double-lognormal marginal PDF for each mixing ratio is constructed using the predicted mean and diagnosed variance. These marginal PDFs are different at each time step and grid cell.

The 3D fields of vertical velocity and hydrometeor mass mixing ratios are explicitly binned to generate discrete marginal PDFs. For hydrometeor mass mixing ratios, only grid cells with nonzero mixing ratios are used grid cells with no hydrometeor present are assumed to be represented by the delta function in the assumed PDF. An example of a joint two-dimensional PDF of vertical velocity and rain mass mixing ratio together with their respective marginal PDFs is shown in Fig.

Also plotted are the marginal distributions. Horizontal dotted line and center vertical dotted line show the mean mass mixing ratio and mean vertical velocity, respectively. The overbar in the scaled means denotes the average over each flux type and the prime notations denote the corresponding deviations from the CRM domain-mean or gridcell mean values in CLUBB. The net subgrid-scale vertical flux in Eq.

Compared to the Wong et al. Updraft and downdraft regions so defined approximate Wong et al. As shown, strong updrafts and downdrafts are typically associated with greater-than-mean mixing ratios. All four hydrometeor types show similar behavior, perhaps except for rain above approximately 5 km. At the lower model levels, the blue regions indicate that the stronger positive vertical velocities are associated with below-mean hydrometeor mixing ratios. As will be shown later, this is consistent with negative correlations found in updrafts at these model levels and will be accounted for in the parameterization using a lower model-level adjustment described later in this section.

We also varied the vertical velocity thresholds from 1 to 2. The products of the scaled means in the heavily precipitating updraft and downdraft regions were found to give a more accurate representation of the vertical hydrometeor fluxes than simply the product of the means as it accounts for subplume intraquadrant correlations Wong et al.

The subplume correlations indicate that greater mass mixing ratios are typically associated with stronger updrafts and downdrafts e. We now discuss how we obtain the scaled means for each flux type within a probability context. The overbars, as before, denote the average over each flux type, except in the case of , which denotes the mean over the entire CRM domain. The prime notations denote the corresponding deviations from the CRM domain mean. The heavier weights represent the greater contribution from these larger absolute values to the total flux.

The normalization factor [denominator in Eq. If the PDFs provided vary in space and time, such as those provided by CLUBB, the vertical fluxes will reflect the prognostic subgrid-scale variability. The mean of vertical velocity in each section is defined using the same set of w 1 and w 2 thresholds as for the fractional areas i.

For the hydrometeor mixing ratios in the convective updraft and downdraft components, the scaled means are computed based on the distribution of mixing ratios greater than the domain mean. Based on the benchmark simulations, the scaled means of the mixing ratios in convective updrafts are comparable to those in convective downdrafts, but the former are typically greater than the latter Fig.

Using the definitions from Wong et al. A slight difference between the two is that the latter typically has a value equal or greater than 0. We will show in the next section that the assumption that the updraft scaled mean mixing ratios are greater than those in downdrafts requires some adjustment at the lower model levels.

Scaled means of hydrometeor mass mixing ratio decomposed by quadrants as in Wong et al. For the stratiform component, the mean hydrometeor mixing ratio i. The larger the scaling parameter, the greater the correlation between the magnitudes of the vertical velocity and hydrometeor mixing ratios is assumed. Graphically, pairs of and , of which the product equals the benchmark flux, can be presented in a w — q x plot, as illustrated in Fig. Best estimates of the scaling parameter and correlation coefficients are computed based on the quadrant definitions used in Wong et al.

As in Fig. Vertical profiles of subplume correlation coefficients in convective updrafts and downdrafts as defined in the two approaches are shown in black in Figs. However, as shown in both Figs. The subplume correlations vary in height and time. As shown in Fig. The increase is found to be necessary to match the benchmark fluxes computed using the new decomposition of the flux based on marginal w PDF rather than the quadrant decomposition tested in Wong et al.

The increased scaling is likely needed because the correlation between the variables changes with the redefinition of the decomposition. As mentioned above, the scheme assumes that both strong updrafts and downdrafts are associated with the same part of the mass mixing ratio PDFs above the mean. Analysis of the CRM simulations demonstrates that at lower altitudes this assumption becomes invalid. Typically, lower levels of strong ascents correspond to early periods of formation of precipitating hydrometeors.

For example, rain may only begin to form in strong updrafts when cloud water content reaches sufficiently large values, and raindrops may begin to convert into graupel above the freezing level. In these cases, the initial hydrometeor mixing ratios are small. At the same time, neighboring downdrafts at similar altitudes are carrying larger loads of older hydrometeor species from aloft that have grown to larger sizes. The reduced correlation between positive vertical velocities and hydrometeor mass mixing ratios at lower levels can be seen in Figs.

Since the updraft and downdraft fluxes are both parameterized using scaled mean hydrometeor mixing ratios based on the distribution where , we must account for the difference in correlations between the two flux types at the lower model levels. For graupel and snow below the freezing level, we note that the benchmark net flux blue solid lines in Figs. Near-zero updraft fluxes at these levels are likely because either the hydrometeors have not had a chance to form yet or are in only small amounts.

We set the parameterized updraft fluxes of graupel and snow to zero below the freezing level Z 1 , such that the net flux is parameterized by the downdraft flux. The parameterized updraft fluxes are then linearly increased from zero at the freezing level to their full values at the level of maximum updraft flux Z 2. The linear increase is justified based on the profiles of the benchmark fluxes. Black solid, dashed, and dotted lines show parameterized updraft fluxes, downdraft fluxes, and fluxes in stratiform regions, respectively, using scaled marginal PDFs without any adjustment to the updraft fluxes at the lower model levels for the ARM97 case.

Blue solid lines show the benchmark net fluxes from the CRM. The adjustment to the parameterized updraft fluxes are done by setting them to zero below Z 1. Between Z 1 and Z 2 , parameterized updraft fluxes linearly increase from zero to their full values. Profiles are temporal averages over the deep convective period see Table 1 using min-interval output. Similarly, for rain, the net flux is dominated by the downdraft fluxes Fig. Consequently, we set Z 1 to be the cloud base level and assign the parameterized updraft fluxes to zero below Z 1.

The updraft fluxes are then linearly increased from zero at the cloud base to their full values at the level of maximum updraft flux Z 2. Finally, for ice Fig. The updraft fluxes are again linearly increased to their full values between Z 1 and Z 2. Parameterized vertical fluxes using the proposed PDF-based hydrometeor transport scheme with adjustment are shown in Fig. In the same figure, the parameterized vertical fluxes without the adjustment are shown in red dotted lines. Benchmark vertical fluxes are shown in black solid lines.

All vertical hydrometeor fluxes are time averaged over the selected period in each case Table 1. Adjustment of the updraft fluxes greatly improves the shapes of the profiles, especially for rain, snow, and graupel below the levels of their maximum fluxes. The limited impact of the adjustment on cloud ice fluxes is likely because of the weaker downdraft fluxes at the lower altitudes Fig.

This has led to an improved representation of the urban heat island in these models. Mechem , : A PDF-based formulation of microphysical variability in cumulus congestus clouds. The broad perspective on convective variability afforded by the multi-model approach outlined above is being used to develop convective parameterization schemes whose behavior in models and whose spatial correlation statistics more closely mimic the observations. Xiaofan Li: B. This may lead to speedups of up to 7X for dedicated parts of the code [e. In addition to microphysics, a 1.

We note that it is the flux divergences based on these flux profiles that govern the vertical advection tendencies. This implies that, for example, the positive vertical advection tendencies of rain from the surface to near the freezing level will not be captured in the scheme without adjustment and, similarly, those just below the freezing level for graupel and snow. As mentioned, the hydrometeors at these levels are associated with strong downdrafts, which may lead to important subsequent diabatic feedback.

Benchmark fluxes computed explicitly using the m simulations, parameterized fluxes using scaled marginal PDFs with adjustment, and those without adjustment are shown in solid black, solid red, and dotted red lines, respectively. Parameterized fluxes using unscaled marginal PDFs i.

Parameterized fluxes based on the modified eddy-flux formulation are shown in dashed cyan lines. Short blue horizontal lines indicate the level at which the temporally averaged domain-mean hydrometeor mixing ratio is maximum. Without scaling orange lines in Fig. The effect of the updraft flux adjustment on the unscaled fluxes is comparable to its effect on the scaled fluxes discussed above. Also plotted in Fig.

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To obtain the parameterized downgradient eddy fluxes, we follow the procedure as outlined in Wong et al. In their study, a comparison was made between the eddy-diffusion fluxes and quadrant-based fluxes, although the latter were based on some a priori knowledge of the covariance between vertical velocity and hydrometeor mass mixing ratio e. Here, the comparison is more direct since both approaches are based on input assumed to be available within CLUBB, albeit diagnosed for the presented cases from the CRM.

For rain, the downgradient formulation is able to reproduce the general shape of the explicit benchmark fluxes, including the negative fluxes below the freezing level. These results are consistent with those found in Wong et al. For graupel and snow, the negative fluxes near the freezing level are well represented, but the positive flux divergence negative advection tendency extends too high up.

These levels coincide with the average maximum microphysical content blue lines in Fig. For cloud ice, the behavior of the downgradient approximation is most evident, where there is a tendency to advect hydrometeor mass from the peak-content altitude to above and below that level. The explicit fluxes indicate that this is not the case. The scaled-PDF fluxes are also unable to capture the magnitude of the ice vertical fluxes, although the profile shapes are in much closer agreement to the benchmark.

Although we show only the temporal averages of the flux profiles, we note that improvement in the temporal evolution of the vertical fluxes as parameterized by the scaled marginal PDF scheme, as compared to those parameterized using the downgradient formulation, is also evident. In this study, we have demonstrated a new three-step approach to conditionally sample and scale marginal PDFs of vertical velocity and hydrometeor mass mixing ratios in order to parameterize subgrid-scale vertical hydrometeor fluxes.

A power-law scaling of the mean variables helps to account for correlation within each region, which is needed for a better estimate of the flux magnitudes. Finally, a lower-level adjustment is applied to the updraft flux to correct for the assumption that strong updrafts and downdrafts carry comparable hydrometeor mass mixing ratios, which does not hold at those altitudes. The mean flux profiles for mass mixing ratios of four hydrometeor types rain, cloud ice, snow, and graupel are computed using marginal PDFs of vertical velocity and mass mixing ratios taken from the CRM simulations.

The general shape of the flux profiles and the magnitude of the fluxes in the new parameterization are significantly improved over those computed using the eddy-diffusion approximation used in a current parameterization.

This study presents an important extension of Wong et al. Here it is demonstrated that comparable improvement in parameterized fluxes can be achieved by conditionally sampling the marginal PDFs of these quantities, making the scheme appropriate for implementation in PDF-based schemes which do not explicitly predict joint distributions. The proposed parameterization relies on the power-law PDF scaling, which has been empirically introduced by Wong et al.

These features will need to be evaluated against high-resolution spatial and temporal observations e. This facilitates a more direct comparison among models and observations. On the contrary, updraft mass fluxes and core velocities, as are often used in traditional convection schemes, are more difficult to compare because of differing definitions.

Based on this study, the parameterization scheme has shown great potential as a way to couple the convective vertical velocities with microphysics in existing cumulus schemes, assuming that the schemes can provide reasonable marginal distributions of these variables. This research is based on work supported by the U. Next Article. Previous Article. May Wong x May Wong.

Search for articles by this author. Mikhail Ovchinnikov x Mikhail Ovchinnikov. Keywords: Cloud parameterizations ; Cloud resolving models ; Convective parameterization ; Parameterization ; Subgrid-scale processes. Corresponding author e-mail : May Wong, mwong ucar. Model and case descriptions. Image of typeset table. View larger version 52K Fig. Subgrid-scale hydrometeor transport. Scheme description. View larger version 38K Fig. Parameterization using scaled marginal PDFs.

View larger version 49K Fig. View larger version 23K Fig. View larger version 25K Fig. View larger version 24K Fig. View larger version 37K Fig. View larger version 39K Fig. View larger version 27K Fig. Comparisons of parameterized fluxes with benchmark fluxes.

View larger version 43K Fig. Acknowledgments This research is based on work supported by the U. April Share this Article Share.