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Development of a two-dimensional zonally averaged statistical-dynamical model. I - The parameterization of moist convection and its role in the general circulation

The moist convection parameterization used in the GISS 3-D GCM is adapted for use in a two-dimensional (2-D) zonally averaged statistical-dynamical model. Experiments with different versions of the parameterization show that its impact on the general circulation in the 2-D model does not parallel its impact in the 3-D model unless the effect of zonal variations is parameterized in the moist convection calculations. A parameterization of the variations in moist static energy is introduced in which the temperature variations are calculated from baroclinic stability theory, and the relative humidity is assumed to be constant. Inclusion of the zonal variations of moist static energy in the 2-D moist convection parameterization allows just a fraction of a latitude circle to be unstable and enhances the amount of deep convection. This leads to a 2-D simulation of the general circulation very similar to that in the 3-D model. The experiments show that the general circulation is sensitive to the parameterized amount of deep convection in the subsident branch of the Hadley cell. The more there is, the weaker are the Hadley cell circulations and the westerly jets. The experiments also confirm the effects of momentum mixing associated with moist convection found by earlier investigators and, in addition, show that the momentum mixing weakens the Ferrel cell. An experiment in which the moist convection was removed while the hydrological cycle was retained and the eddy forcing was held fixed shows that moist convection by itself stabilizes the tropics, reduces the Hadley circulation, and reduces the maximum speeds in the westerly jets.

Yao, Mao-Sung

Development of a two-dimensional zonally averaged statistical-dynamical model. III - The parameterization of the eddy fluxes of heat and moisture

A number of perpetual January simulations are carried out with a two-dimensional zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional general circulation model with zonally symmetric forcing. The three-dimensional model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations. Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the two-dimensional model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the three-dimensional model, and only underestimate the magnitude of the fluxes by 10 to 20 percent.

Stone, Peter H.

The Influence of Microphysical Cloud Parameterization on Microwave Brightness Temperatures

The microphysical parameterization of clouds and rain-cells plays a central role in atmospheric forward radiative transfer models used in calculating passive microwave brightness temperatures. The absorption and scattering properties of a hydrometeor-laden atmosphere are governed by particle phase, size distribution, aggregate density., shape, and dielectric constant. This study identifies the sensitivity of brightness temperatures with respect to the microphysical cloud parameterization. Cloud parameterizations for wideband (6-410 GHz observations of baseline brightness temperatures were studied for four evolutionary stages of an oceanic convective storm using a five-phase hydrometeor model in a planar-stratified scattering-based radiative transfer model. Five other microphysical cloud parameterizations were compared to the baseline calculations to evaluate brightness temperature sensitivity to gross changes in the hydrometeor size distributions and the ice-air-water ratios in the frozen or partly frozen phase. The comparison shows that, enlarging the rain drop size or adding water to the partly Frozen hydrometeor mix warms brightness temperatures by up to .55 K at 6 GHz. The cooling signature caused by ice scattering intensifies with increasing ice concentrations and at higher frequencies. An additional comparison to measured Convection and Moisture LA Experiment (CAMEX 3) brightness temperatures shows that in general all but, two parameterizations produce calculated T(sub B)'s that fall within the observed clear-air minima and maxima. The exceptions are for parameterizations that, enhance the scattering characteristics of frozen hydrometeors.

Skofronick-Jackson, Gail M.

Parameterization of Cloud Droplet Formation in Global Climate Models

An aerosol activation parameterization has been developed based on a generalized representation of aerosol size and composition within the framework of an ascending adiabatic parcel; this allows for parameterizing the activation of chemically complex aerosol with an arbitrary size distribution and mixing state. The new parameterization introduces the concept of"population splitting", in which the cloud condensation nuclei (CCN) that form droplets are treated as two separate populations; those that have a size close to their critical diameter and those that do not.Explicit consideration of kinetic limitations of droplet growth is introduced. Our treatment of the activation process unravels much of its complexity. As a result of this, a substantial number of conditions of droplet formation can be treated completely free of empirical information or correlations; there are, however, some conditions of droplet activation for which an empirically derived correlation is utilized. Predictions of the parameterization are compared against extensive cloud parcel model simu;lations for a variety of aerosol activation conditions that cover a wide range of chemical variability and CCN concentrations. The parameterization tracks the parcel model simulations closely and robustly. The parameterization presented here is intended to allow for a comprehensive assessment of the aerosol indirect effect in general circulation models.

Nenes, A.

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.

Sensitivity of CONUS Summer Rainfall to the Selection of Cumulus Parameterization Schemes in NU-WRF Seasonal Simulations

This study investigates the sensitivity of daily rainfall rates in regional seasonal simulations over the contiguous United States (CONUS) to different cumulus parameterization schemes. Daily rainfall fields were simulated at 24-km resolution using the NASA-Unified Weather Research and Forecasting (NU-WRF) Model for June-August 2000. Four cumulus parameterization schemes and two options for shallow cumulus components in a specific scheme were tested. The spread in the domain-mean rainfall rates across the parameterization schemes was generally consistent between the entire CONUS and most subregions. The selection of the shallow cumulus component in a specific scheme had more impact than that of the four cumulus parameterization schemes. Regional variability in the performance of each scheme was assessed by calculating optimally weighted ensembles that minimize full root-mean-square errors against reference datasets. The spatial pattern of the seasonally averaged rainfall was insensitive to the selection of cumulus parameterization over mountainous regions because of the topographical pattern constraint, so that the simulation errors were mostly attributed to the overall bias there. In contrast, the spatial patterns over the Great Plains regions as well as the temporal variation over most parts of the CONUS were relatively sensitive to cumulus parameterization selection. Overall, adopting a single simulation result was preferable to generating a better ensemble for the seasonally averaged daily rainfall simulation, as long as their overall biases had the same positive or negative sign. However, an ensemble of multiple simulation results was more effective in reducing errors in the case of also considering temporal variation.

Iguchi, Takamichi

Novel Parameterization of Ice Cloud Effective Diameter from Collocated CALIOP-IIR and CloudSat Retrievals

Satellite-based measurements of global ice cloud microphysical properties are sampled to develop a novel set of physical parameterizations, relating to cloud layer temperature and effective diameter D(e), that can be implemented for two separate applications: in numerical weather prediction models and lidar-based cloud radiative forcing studies. Ice cloud optical properties (i.e., spectral scattering and absorption) are estimated based on the effective size and habit mixture of the cloud particles. Historically, the ice cloud D(e) has been parameterized from aircraft in situ measurements. However, aircraft-based parameterizations are opportunistic in that they only represent specific types of clouds (e.g., convective anvil, tropopause-topped cirrus) in the regions in which they were sampled and, in some cases, are limited in fully resolving the entire vertical cloud layer. Breaking away from the aircraft-based parameterization paradigm, this study is the first of its kind to attempt a parameterization of D(e) as a function of temperature, ice water content (IWC), and lidar-derived extinction from satellite-based global oceanic measurements of ice clouds. Data from both active and passive remote sensing sensors from two of NASA’s A-Train satellites, CloudSat and CALIPSO, are collected to guide development of globally robust parameterizations of all ice cloud types and one exclusively for cirrus clouds.

Ice Cloud

Impacts of Light Use Efficiency and fPAR Parameterization on Gross Primary Production Modeling

This study examines the impact of parameterization of two variables, light use efficiency (LUE) and the fraction of absorbed photosynthetically active radiation (fPAR or fAPAR), on gross primary production(GPP) modeling. Carbon sequestration by terrestrial plants is a key factor to a comprehensive under-standing of the carbon budget at global scale. In this context, accurate measurements and estimates of GPP will allow us to achieve improved carbon monitoring and to quantitatively assess impacts from cli-mate changes and human activities. Spaceborne remote sensing observations can provide a variety of land surface parameterizations for modeling photosynthetic activities at various spatial and temporal scales. This study utilizes a simple GPP model based on LUE concept and different land surface parameterizations to evaluate the model and monitor GPP. Two maize-soybean rotation fields in Nebraska, USA and the Bartlett Experimental Forest in New Hampshire, USA were selected for study. Tower-based eddy-covariance carbon exchange and PAR measurements were collected from the FLUXNET Synthesis Dataset. For the model parameterization, we utilized different values of LUE and the fPAR derived from various algorithms. We adapted the approach and parameters from the MODIS MOD17 Biome Properties Look-Up Table (BPLUT) to derive LUE. We also used a site-specific analytic approach with tower-based Net Ecosystem Exchange (NEE) and PAR to estimate maximum potential LUE (LUEmax) to derive LUE. For the fPAR parameter, the MODIS MOD15A2 fPAR product was used. We also utilized fAPAR chl, a parameter accounting for the fAPAR linked to the chlorophyll-containing canopy fraction. fAPAR chl was obtained by inversion of a radiative transfer model, which used the MODIS-based reflectances in bands 1-7 produced by Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm. fAPAR chl exhibited seasonal dynamics more similar with the flux tower based GPP than MOD15A2 fPAR, especially in the spring and fall at the agricultural sites. When using the MODIS MOD17-based parameters to estimate LUE, fAPAR chl generated better agreements with GPP (r2= 0.79-0.91) than MOD15A2 fPAR (r2= 0.57-0.84).However, underestimations of GPP were also observed, especially for the crop fields. When applying the site-specific LUE max value to estimate in situ LUE, the magnitude of estimated GPP was closer to in situ GPP; this method produced a slight overestimation for the MOD15A2 fPAR at the Bartlett forest. This study highlights the importance of accurate land surface parameterizations to achieve reliable carbon monitoring capabilities from remote sensing information.

grossprimary

A New Theoretical Framework for Parameterizing Nonequilibrium Fractionation During Evaporation From the Ocean

The evaporation model for water isotopes proposed by Craig and Gordon (1965, https://books.google.co.in/books?id=6wIKAQAAIAAJ) is used in most isotope-enabled atmospheric models for the parameterization of nonequilibrium fractionation during evaporation from the ocean. In this model, one of the most uncertain parameters is the nonequilibrium fractionation factor 𝛼 𝑘 . Many isotope models use the formulation of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029), which parameterizes 𝛼 𝑘 as a function of wind speed and distinguishes between a smooth and a rough regime to account for the effect of ocean waves. The resulting discontinuity in 𝛼 𝑘 between smooth and rough regimes has been disputed by several empirical studies. Here, we present a new approach to parameterizing 𝛼𝑘 by explicitly accounting for the influence of wave drag on the momentum flux near the surface. Following Cifuentes-Lorenzen et al. (2018, https://doi.org/10.1007/s10546-018-0376-0), we add a third wave-induced component to the total momentum flux, in addition to the viscous and turbulent components, and extend the definition of the eddy viscosity to account for the momentum flux due to waves and turbulent dissipation near the surface. The new scheme predicts a slight decrease of 𝛼 𝑘 with wind speed, similar to the smooth-regime parameterization of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029). This new parameterization is incorporated into the isotope-enabled Community Atmosphere Model, where it improves the correlation of simulated and measured vapor deuterium excess relative to the default version and a version with constant 𝛼 𝑘 , suggesting that it may be used as a valid representation of fractionation during evaporation from the ocean in future isotope models.

54 ENVIRONMENTAL SCIENCES

A Fortran–Python interface for integrating machine learning parameterization into earth system models

Abstract. Parameterizations in earth system models (ESMs) are subject to biases and uncertainties arising from subjective empirical assumptions and incomplete understanding of the underlying physical processes. Recently, the growing representational capability of machine learning (ML) in solving complex problems has spawned immense interests in climate science applications. Specifically, ML-based parameterizations have been developed to represent convection, radiation, and microphysics processes in ESMs by learning from observations or high-resolution simulations, which have the potential to improve the accuracies and alleviate the uncertainties. Previous works have developed some surrogate models for these processes using ML. These surrogate models need to be coupled with the dynamical core of ESMs to investigate the effectiveness and their performance in a coupled system. In this study, we present a novel Fortran–Python interface designed to seamlessly integrate ML parameterizations into ESMs. This interface showcases high versatility by supporting popular ML frameworks like PyTorch, TensorFlow, and scikit-learn. We demonstrate the interface's modularity and reusability through two cases: an ML trigger function for convection parameterization and an ML wildfire model. We conduct a comprehensive evaluation of memory usage and computational overhead resulting from the integration of Python codes into the Fortran ESMs. By leveraging this flexible interface, ML parameterizations can be effectively developed, tested, and integrated into ESMs.

54 ENVIRONMENTAL SCIENCES

A Fortran-Python Interface for Integrating Machine Learning Parameterization into Earth System Models

Parameterizations in Earth System Models (ESMs) are subject to biases and uncertainties arising from subjective empirical assumptions and incomplete understanding of the underlying physical processes. Recently, the growing representational capability of machine learning (ML) in solving complex problems has spawned immense interests in climate science applications. Specifically, ML-based parameterizations have been developed to represent convection, radiation and microphysics processes in ESMs by learning from observations or high-resolution simulations, which have the potential to improve the accuracies and alleviate the uncertainties. Previous works have developed some surrogate models for these processes using ML. These surrogate models need to be coupled with the dynamical core of ESMs to investigate the effectiveness and their performance in a coupled system. In this study, we present a novel Fortran-Python interface designed to seamlessly integrate ML parameterizations into ESMs. This interface showcases high versatility by supporting popular ML frameworks like PyTorch, TensorFlow, and Scikit-learn. We demonstrate the interface's modularity and reusability through two cases: a ML trigger function for convection parameterization and a ML wildfire model. We conduct a comprehensive evaluation of memory usage and computational overhead resulting from the integration of Python codes into the Fortran ESMs. By leveraging this flexible interface, ML parameterizations can be effectively developed, tested, and integrated into ESMs.

54 ENVIRONMENTAL SCIENCES

The rainout parameterization in a photochemical model

Photochemical models of tropospheric trace species typically simulate the effects of wet removal of soluble species from the atmosphere through a first-order rainout parameterization, which is independent of the species solubility and constant in time. In this work a modified first-order rainout parameterization is proposed that is a function of the species' solubility and takes into account the intermittent nature of atmospheric wet removal. In the case of a highly soluble species, such as HNO3, the inclusion of the effects of intermittent rainout in the parameterization leads to averaged rainout lifetimes considerably higher than ones used in most photochemical models. For illustrative purposes this parameterization is applied to a one-dimensional steady state model with parameterized eddy diffusion, although in principle it can be used in more sophisticated multidimensional models. The model results are compared to analagous calculations obtained with a 3-D tracer transport model.

Giorgi, F.

Parameterization of sub-grid scale convection

The following topics are discussed: an overview of the cumulus parameterization problem; interactions between explicit and implicit processes in mesoscale models; effects of model grid size on the cumulus parameterization problem; parameterizing convective effects on momentum fields in mesoscale models; differences between slantwise and vertical cumulus parameterization; experiments with different closure hypotheses; and coupling cumulus parameterizations to boundary layer, stable cloud, and radiation schemes.

Frank, William

Toward a Unified Parameterization of the Boundary Layer and Moist Convection: A New Type of Mass-Flux Model - Part 1

Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.

Lappen, Cara-Lyn

Evaluation of a New Cloud Droplet Activation Parameterization wtih in Situ Data from CRYSTAL-FACE and CSTRIPE

The accuracy of the 2003 prognostic, physically based aerosol activation parameterization of A. Nenes and J. H. Seinfeld (NS) with modification introduced by C. Fountoukis and A. Nenes in 2005 (modified NS) is evaluated against extensive microphysical data sets collected on board the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS) Twin Otter aircraft for cumuliform and stratiform clouds of marine and continental origin. The cumuliform cloud data were collected during NASA's Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE, Key West, Florida, July 2002), while the stratiform cloud data were gathered during Coastal Stratocumulus Imposed Perturbation Experiment (CSTRIPE, Monterey, California, July 2003). In situ data sets of aerosol size distribution, chemical composition, and updraft velocities are used as input for the NS parameterization, and the evaluation is carried out by comparing predicted cloud droplet number concentrations (CDNC) with observations. This is the first known study in which a prognostic cloud droplet activation parameterization has been evaluated against a wide range of observations. On average, predicted droplet concentration in adiabatic regions is within -20% of observations at the base of cumuliform clouds and -30% of observations at different altitudes throughout the stratiform clouds, all within experimental uncertainty. Furthermore, CDNC is well parameterized using either a single mean updraft velocity w or by weighting droplet nucleation rates with a Gaussian probability density function of w. This study suggests that for nonprecipitating warm clouds of variable microphysics, aerosol composition, and size distribution the modified NS parameterization can accurately predict cloud droplet activation and can be successfully implemented for describing the aerosol activation process in global climate models.

Meskhidze, Nicholas

Cloud Simulations in Response to Turbulence Parameterizations in the GISS Model E GCM

The response of cloud simulations to turbulence parameterizations is studied systematically using the GISS general circulation model (GCM) E2 employed in the Intergovernmental Panel on Climate Change's (IPCC) Fifth Assessment Report (AR5).Without the turbulence parameterization, the relative humidity (RH) and the low cloud cover peak unrealistically close to the surface; with the dry convection or with only the local turbulence parameterization, these two quantities improve their vertical structures, but the vertical transport of water vapor is still weak in the planetary boundary layers (PBLs); with both local and nonlocal turbulence parameterizations, the RH and low cloud cover have better vertical structures in all latitudes due to more significant vertical transport of water vapor in the PBL. The study also compares the cloud and radiation climatologies obtained from an experiment using a newer version of turbulence parameterization being developed at GISS with those obtained from the AR5 version. This newer scheme differs from the AR5 version in computing nonlocal transports, turbulent length scale, and PBL height and shows significant improvements in cloud and radiation simulations, especially over the subtropical eastern oceans and the southern oceans. The diagnosed PBL heights appear to correlate well with the low cloud distribution over oceans. This suggests that a cloud-producing scheme needs to be constructed in a framework that also takes the turbulence into consideration.

Yao, Mao-Sung

A Two-Habit Ice Cloud Optical Property Parameterization for GCM Application

We present a novel ice cloud optical property parameterization based on a two-habit ice cloud model that has been proved to be optimal for remote sensing applications. The two-habit ice model is developed with state-of-the-art numerical methods for light scattering property calculations involving individual columns and column aggregates with the habit fractions constrained by in-situ measurements from various field campaigns. Band-averaged bulk ice cloud optical properties including the single-scattering albedo, the mass extinction/absorption coefficients, and the asymmetry factor are parameterized as functions of the effective particle diameter for the spectral bands involved in the broadband radiative transfer models. Compared with other parameterization schemes, the two-habit scheme generally has lower asymmetry factor values (around 0.75 at the visible wavelengths). The two-habit parameterization scheme was widely tested with the broadband radiative transfer models (i.e. Rapid Radiative Transfer Model, GCM version) and global circulation models (GCMs, i.e. Community Atmosphere Model, version 5). Global ice cloud radiative effects at the top of the atmosphere are also analyzed from the GCM simulation using the two-habit parameterization scheme in comparison with CERES satellite observations.

Yi, Bingqi

Radiative Flux and Forcing Parameterization Error in Aerosol-Free Clear Skies

This article reports on the accuracy in aerosol- and cloud-free conditions of the radiation parameterizations used in climate models. Accuracy is assessed relative to observationally validated reference models for fluxes under present-day conditions and forcing (flux changes) from quadrupled concentrations of carbon dioxide. Agreement among reference models is typically within 1 W/m2, while parameterized calculations are roughly half as accurate in the longwave and even less accurate, and more variable, in the shortwave. Absorption of shortwave radiation is underestimated by most parameterizations in the present day and has relatively large errors in forcing. Error in present-day conditions is essentially unrelated to error in forcing calculations. Recent revisions to parameterizations have reduced error in most cases. A dependence on atmospheric conditions, including integrated water vapor, means that global estimates of parameterization error relevant for the radiative forcing of climate change will require much more ambitious calculations.

Climate