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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An Improved Convection Parameterization with Detailed Aerosol–Cloud Microphysics for a Global Model

Abstract A new microphysical treatment that includes aerosol–cloud interactions and secondary ice production (SIP) mechanisms is implemented in the convection scheme of the Community Atmosphere Model, version 6 (CAM6). The approach is to embed a 1D Lagrangian parcel model in the bulk convective plume of the existing deep convection parameterization. Aerosol activation, growth processes including collision/coalescence, and three processes of SIP mechanisms, two of which are normally overlooked in atmospheric models, are represented in this embedded parcel model. These microphysical processes are treated with a hybrid bin/bulk scheme and a high spatial and temporal resolution for the integration of the embedded parcel in 1D, allowing vertical velocity to determine the microphysical evolution following the in-cloud motion during ascent. Simulations of an observed case (Midlatitude Continental Convective Clouds Experiment) of a mesoscale convective system in Oklahoma, United States, with a single-column model (SCAM) version of CAM, are compared with aircraft in situ and ground-based observations of microphysical properties from the convection and precipitation. Results from the validation show the new microphysical scheme has a good representation of the ice initiation in the bulk convective plume, including the known and empirically quantified pathways of primary and secondary initiation, with benefits for the accuracy of properties of its supercooled cloud liquid. The sensitivity simulations and use of tagging tracers for the validated simulation confirm that the newly included SIP mechanisms are of paramount importance for convective microphysics and can be successfully treated in the global model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Parameter Tuning and Calibration of RegCM3 with MIT-Emanuel Cumulus Parameterization Scheme over CORDEX East Asian Domain

In this study, we calibrated the performance of regional climate model RegCM3 with Massachusetts Institute of Technology (MIT)-Emanuel cumulus parameterization scheme over CORDEX East Asia domain by tuning the selected seven parameters through multiple very fast simulated annealing (MVFSA) sampling method. The seven parameters were selected based on previous studies, which customized the RegCM3 with MIT-Emanuel scheme through three different ways by using the sensitivity experiments. The responses of model results to the seven parameters were investigated. Since the monthly total rainfall is constrained, the simulated spatial pattern of rainfall and the probability density function (PDF) distribution of daily rainfall rates are significantly improved in the optimal simulation. Sensitivity analysis suggest that the parameter “relative humidity criteria” (RH), which has not been considered in the default simulation, has the largest effect on the model results. The responses of total rainfall over different regions to RH were examined. Positive responses of total rainfall to RH are found over northern equatorial western Pacific, which are contributed by the positive responses of explicit rainfall. Followed by an increase of RH, the increases of the low-level convergence and the associated increases in cloud water favor the increase of the explicit rainfall. The identified optimal parameters constrained by the total rainfall have positive effects on the low-level circulation and the surface air temperature. Furthermore, the optimized parameters based on the extreme case are suitable for a normal case and the model’s new version with mixed convection scheme.

emanual cumulus parameterization↗
DOE OSTI2018

An Evaluation of Marine Boundary Layer Cloud Property Simulations in the Community Atmosphere Model Using Satellite Observations: Conventional Subgrid Parameterization versus CLUBB

This paper presents a satellite-observation-based evaluation of the marine boundary layer (MBL) cloud properties from two Community Atmosphere Model, version 5 (CAM5), simulations, one with the standard parameterization schemes (CAM5–Base) and the other with the Cloud Layers Unified by Binormals scheme (CAM5–CLUBB). When comparing the direct model outputs, the authors find that CAM5–CLUBB produces more MBL clouds, a smoother transition from stratocumulus to cumulus, and a tighter correlation between in-cloud water and cloud fraction than CAM5–Base. In the model-to-observation comparison using the COSP satellite simulators, the authors find that both simulations capture the main features and spatial patterns of the observed cloud fraction from MODIS and shortwave cloud radiative forcing (SWCF) from CERES. However, CAM5–CLUBB suffers more than CAM5–Base from a problem that can be best summarized as “undetectable” clouds (i.e., a significant fraction of simulated MBL clouds are thinner than the MODIS detection threshold). This issue leads to a smaller COSP–MODIS cloud fraction and a weaker SWCF in CAM5–CLUBB than the observations and also CAM5–Base in the tropical descending regions. Finally, the authors compare modeled radar reflectivity with CloudSat observations and find that both simulations, especially CAM5–CLUBB, suffer from an excessive drizzle problem. Further analysis reveals that the subgrid precipitation enhancement factors in CAM5–CLUBB are unrealistically large, which makes MBL clouds precipitate too excessively, and in turn results in too many undetectable thin clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The Impact of Parameterized Lateral Mixing on the Antarctic Circumpolar Current in a Coupled Climate Model

This study examines the impact of changing the lateral diffusion coefficient ARedi on the transport of the Antarctic Circumpolar Current (ACC). The lateral diffusion coefficient ARedi is poorly constrained, with values ranging across an order of magnitude in climate models. The ACC is difficult to accurately simulate, and there is a large spread in eastward transport in the Southern Ocean (SO) in these models. This paper examines how much of that spread can be attributed to different eddy parameterization coefficients. A coarse-resolution, fully coupled model suite was run with A Redi = 400, 800, 1200, and 2400 m 2 s -1 . Additionally, two simulations were run with two-dimensional representations of the mixing coefficient based on satellite altimetry. Relative to the 400 m 2 s -1 case, the 2400 m 2 s -1 case exhibits 1) an 11% decrease in average wind stress from 50° to 65°S, 2) a 20% decrease in zonally averaged eastward transport in the SO, and 3) a 14% weaker transport through the Drake Passage. The decrease in transport is well explained by changes in the thermal current shear, largely due to increases in ocean density occurring on the northern side of the ACC. In intermediate waters these increases are associated with changes in the formation of intermediate waters in the North Pacific. We hypothesize that the deep increases are associated with changes in the wind stress curl allowing Antarctic Bottom Water to escape and flow northward.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Simulation of the Summer Monsoon Rainfall over East Asia using the NCEP GFS Cumulus Parameterization at Different Horizontal Resolutions

The most recent version of Simplified Arakawa-Schubert (SAS) cumulus scheme in National Center for Environmental Prediction (NCEP) Global Forecast System (GFS) (GFS SAS) has been implemented into the Weather and Research Forecasting (WRF) model with a modification of triggering condition and convective mass flux to become depending on model’s horizontal grid spacing. East Asian Summer Monsoon of 2006 from June to August is selected to evaluate the performance of the modified GFS SAS scheme. Simulated monsoon rainfall with the modified GFS SAS scheme shows better agreement with observation compared to the original GFS SAS scheme. The original GFS SAS scheme simulates the similar ratio of subgrid-scale precipitation, which is calculated from a cumulus scheme, against total precipitation regardless of model’s horizontal grid spacing. This is counter-intuitive because the portion of resolved clouds in a grid box should be increased as the model grid spacing decreases. This counter-intuitive behavior of the original GFS SAS scheme is alleviated by the modified GFS SAS scheme. Further, three different cumulus schemes (Grell and Freitas, Kain and Fritsch, and Betts-Miller-Janjic) are chosen to investigate the role of a horizontal resolution on simulated monsoon rainfall. The performance of high-resolution modeling is not always enhanced as the spatial resolution becomes higher. Even though improvement of probability density function of rain rate and long wave fluxes by the higher-resolution simulation is robust regardless of a choice of cumulus parameterization scheme, the overall skill score of surface rainfall is not monotonically increasing with spatial resolution.

CPS↗
DOE OSTI2020

Evaluating and Improving Convective Parameterization for GCMs Using ARM Observations. Final report

This technical report summarizes the achievements during the project period funded by the Atmospheric System Research (ASR) program. The general goal of the project is to improve the representation of atmospheric deep convection in global climate models. By using DOE Atmospheric Radiation Measurement (ARM) program observations and a hierarchy of models from cloud-resolving to global climate models, we evaluated and improved many aspects of convection parameterization schemes, such as the trigger function for convection and closure condition to determine the amount of convection. We also incorporated the stochasticity of convection into a convection scheme. These improvements, when implemented into the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM) and the DOE Exascale Energy Earth System Model (E3SM), led to improved simulation of precipitation characteristics, including precipitation intensity, Intertropical Convergence Zone, and Madden-Julian oscillation. The project also improved the representation of microphysical processes in convective clouds. It enables the interaction of cloud microphysics with aerosols in weather and climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation (Rev.1)

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model’s predictions with reference circuits from Sim et al. and IBM Qiskit’s hardwareefficient ansatz sets to further evaluate our model’s performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model’s efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Evaluation of the wind farm parameterization in the Weather Research and Forecasting model (version 3.8.1) with meteorological and turbine power data

Forecasts of wind-power production are necessary to facilitate the integration of wind energy into power grids, and these forecasts should incorporate the impact of wind-turbine wakes. Our paper focuses on a case study of four diurnal cycles with significant power production, and assesses the skill of the wind farm parameterization (WFP) distributed with the Weather Research and Forecasting (WRF) model version 3.8.1, as well as its sensitivity to model configuration. After validating the simulated ambient flow with observations, we quantify the value of the WFP as it accounts for wake impacts on power production of downwind turbines. We also illustrate with statistical significance that a vertical grid with approximately 12 m vertical resolution is necessary for reproducing the observed power production. Further, the WFP overestimates wake effects and hence underestimates downwind power production during high wind speed, highly stable, and low turbulence conditions. We also find the WFP performance is independent of the number of wind turbines per model grid cell and the upwind–downwind position of turbines. Rather, the ability of the WFP to predict power production is most dependent on the skill of the WRF model in simulating the ambient wind speed.

17 WIND ENERGY↗
DOE OSTI2026

Slow Wake Recovery and Low Turbulence Behind Wind Farms Parameterized in Mesoscale Simulations

Numerical weather prediction (NWP) and climate models equipped with wind-farm parameterizations (WFPs) can simulate cluster wake effects affecting downstream wind farms in both onshore and offshore environments. This study evaluates wake recovery behind a wind farm represented by the NWP-WFP approach in the Weather Research and Forecasting (WRF) model using either the Fitch et al. (2012) or Ma et al. (2022a, b) WFPs. Results are benchmarked against large-eddy simulations (LES) of an idealized offshore wind farm with aligned and staggered layouts under neutral atmospheric stability. Near-farm wake recovery is underestimated in NWP-WFP simulations due to its representation on a coarse mesoscale grid. This limitation leads to slow wake recovery through two interconnected mechanisms: (i) spatial gradients in the wind velocity field are weaker compared to LES and (ii) turbulence kinetic energy (TKE) remains low not because of excessive dissipation but due to insufficient shear production caused by these weakened gradients. For the scenario considered here, a wind-speed bias develops in the near-farm wake and persists into the far wake. Differences between the NWP-WFP simulations and LES emerge within a short distance downstream of the farm exit, where the mesoscale simulations recover too slowly. This reduced recovery contributes approximately 0.15-0.50 m s-1 to the near-farm wind-speed bias. The bias established in this region is not subsequently compensated for downstream but instead propagates into the far wake, where wind-speed differences of approximately 0.4-0.6 m s-1 remain up to 50 km downstream. Higher-resolution mesoscale simulations partially reduce this bias. Increasing turbine-added TKE or including subgrid wake effects provides additional improvement, but neither fully addresses the underlying cause. The slow wake recovery is not caused by limitations of the WFPs themselves, as it also occurs outside their region of influence, and adding subgrid wake effects does not significantly impact recovery. Rather, the slow wake recovery is a consequence of mesoscale flow representation. This behavior is not limited to regions downstream of the wind farm but is less visible within the farm, where wake recovery occurs simultaneously with turbine-induced momentum extraction. These results highlight the need for improved representations of wake recovery both within and downstream of wind farms. While enhanced subgrid modeling, shear-driven TKE production, and refined WFP formulations may improve intra-farm dynamics, accurately capturing near-farm wake recovery downstream remains challenging, as WFPs do not act in this region.

17 WIND ENERGY↗
DOE OSTI2014

Statistical characteristics of cloud variability. Part 2: Implication for parameterizations of microphysical and radiative transfer processes in climate models

The effects of subgrid cloud variability on grid-average microphysical rates and radiative fluxes are examined by use of long-term retrieval products at the Tropical West Pacific, Southern Great Plains, and North Slope of Alaska sites of the Department of Energy's Atmospheric Radiation Measurement program. Four commonly used distribution functions, the truncated Gaussian, Gamma, lognormal, and Weibull distributions, are constrained to have the same mean and standard deviation as observed cloud liquid water content. The probability density functions are then used to upscale relevant physical processes to obtain grid-average process rates. It is found that the truncated Gaussian representation results in up to 30% mean bias in autoconversion rate, whereas the mean bias for the lognormal representation is about 10%. The Gamma and Weibull distribution function performs the best for the grid-average autoconversion rate with the mean relative bias less than 5%. For radiative fluxes, the lognormal and truncated Gaussian representations perform better than the Gamma and Weibull representations. The results show that the optimal choice of subgrid cloud distribution function depends on the nonlinearity of the process of interest, and thus, there is no single distribution function that works best for all parameterizations. Examination of the scale (window size) dependence of the mean bias indicates that the bias in grid-average process rates monotonically increases with increasing window sizes, suggesting the increasing importance of subgrid variability with increasing grid sizes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Sensitivity of a global climate model to the critical Richardson number in the boundary layer parameterization

The critical bulk Richardson number (Ri cr ) is an important parameter in planetary boundary layer (PBL) parameterization schemes used in many climate models. This paper examines the sensitivity of a Global Climate Model, the Beijing Climate Center Atmospheric General Circulation Model, BCC_AGCM to Ri cr . The results show that the simulated global average of PBL height increases nearly linearly with Ri cr , with a change of about 114 m for a change of 0.5 in Ri cr . The surface sensible (latent) heat flux decreases (increases) as Ri cr increases. The influence of Ri cr on surface air temperature and specific humidity is not significant. The increasing Ri cr may affect the location of the Westerly Belt in the Southern Hemisphere. Further diagnosis reveals that changes in Ri cr affect stratiform and convective precipitations differently. Increasing Ri cr leads to an increase in the stratiform precipitation but a decrease in the convective precipitation. Significant changes of convective precipitation occur over the inter-tropical convergence zone, while changes of stratiform precipitation mostly appear over arid land such as North Africa and Middle East.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

An analysis of the operational GFS simplified Arakawa Schubert parameterization within a WRF framework: A Hurricane Sandy (2012) long‐term track forecast perspective

Abstract Hurricane Sandy (2012) is known as an incredibly destructive storm and one defined meteorologically by its large size, and its significant forecast track spreads among various operational models roughly 1 week before landfall. While the operational European Centre for Medium‐Range Weather Forecasts model accurately depicted a northeastern United States landfall, the Global Forecasting System (GFS) model consistently forecast a track toward the North Atlantic Ocean. Using a Weather Research and Forecasting (WRF) model framework, Bassill ( ) suggested that these differences were primarily a function of differences between the two models' cumulus parameterization (CP). This study also uses a WRF model framework to examine the simplified Arakawa Schubert CP used in the GFS model. It is found that increasing the deep convective entrainment coefficient produces more realistic forecast tracks for forecasts initialized roughly 1 week before landfall. This occurs through a reorientation of the precipitation (and associated latent heating) around Sandy during a critical time period in which it was interacting with a series of upper troughs to its west and northwest. Reorienting the latent heating reshapes the upper tropospheric steering pattern toward the one that is more negatively tilted and consistent with observations.

Bassill, Nick P.↗
DOE OSTI2015

Evaluating convective parameterization closures using cloud‐resolving model simulation of tropical deep convection

Abstract Closure is an important component of a mass flux‐based convective parameterization scheme, and it determines the amount of convection with the aid of a large‐scale variable (closure variable) that is sensitive to convection. In this study, we have evaluated and quantified the relationship between commonly used closure variables and convection for a range of global climate model (GCM) horizontal resolutions, taking convective precipitation and mass flux at 600 hPa as measures for deep convection. We have used cloud‐resolving model simulation data to create domain averages representing GCM horizontal resolutions of 128 km, 64 km, 32 km, 16 km, 8 km, and 4 km. Lead‐lag correlation analysis shows that except moisture convergence and turbulent kinetic energy, none of the other closure variables evaluated in this study show any relationship with convection for the six subdomain sizes. It is found that the correlation between moisture convergence and convective precipitation is largest when moisture convergence leads convection. This correlation weakens as the subdomain size decreases to 8 km or smaller. Although convective precipitation and mass flux increase with moisture convergence at a given subdomain size, as the subdomain size increases, the rate at which they increase becomes smaller. This suggests that moisture convergence‐based closure should scale down the predicted mass flux for a given moisture convergence as GCM resolution increases.

Suhas, E.↗
DOE OSTI2015

Quantifying sensitivities of ice crystal number and sources of ice crystal number variability in CAM 5.1 using the adjoint of a physically based cirrus formation parameterization

Abstract We present the adjoint of a cirrus formation parameterization that computes the sensitivity of ice crystal number concentration to updraft velocity, aerosol, and ice deposition coefficient. The adjoint is driven by simulations from the National Center for Atmospheric Research Community Atmosphere Model version 5.1 CAM 5.1 to understand the sensitivity of formed ice crystal number concentration to 13 variables and quantify which contribute to its variability. Sensitivities of formed ice crystal number concentration to updraft velocity, sulfate number, and is sufficient but sulfate number concentration is low, indicating a sulfate‐limited regime. Outside of the tropics, competition between homogeneous and heterogeneous nucleation may shift annually averaged sensitivities to higher magnitudes, when infrequent strong updrafts shift crystal production away from purely heterogeneous nucleation. Outside the tropics, updraft velocity is responsible for approximately 52.70% of the ice crystal number variability. In the tropics, sulfate number concentration and updraft jointly control variability in formed crystal number concentration. Insoluble aerosol species play a secondary, but still important, role in influencing the variability in crystal concentrations, with coarse‐mode dust being the largest contributor at nearly 50% in certain regions. On a global scale, more than 95% of the temporal variability in crystal number concentration can be described by temperature, updraft velocity, sulfate number, and coarse‐mode dust number concentration.

Sheyko, B. A.↗
DOE OSTI2015

RACORO continental boundary layer cloud investigations. 3. Separation of parameterization biases in single-column model CAM5 simulations of shallow cumulus

Climatically important low-level clouds are commonly misrepresented in climate models. The FAst-physics System TEstbed and Research (FASTER) project has constructed case studies from the Atmospheric Radiation Measurement (ARM) Climate Research Facility's Southern Great Plain site during the RACORO aircraft campaign to facilitate research on model representation of boundary-layer clouds. This paper focuses on using the single-column Community Atmosphere Model version 5 (SCAM5) simulations of a multi-day continental shallow cumulus case to identify specific parameterization causes of low-cloud biases. Consistent model biases among the simulations driven by a set of alternative forcings suggest that uncertainty in the forcing plays only a relatively minor role. In-depth analysis reveals that the model's shallow cumulus convection scheme tends to significantly under-produce clouds during the times when shallow cumuli exist in the observations, while the deep convective and stratiform cloud schemes significantly over-produce low-level clouds throughout the day. The links between model biases and the underlying assumptions of the shallow cumulus scheme are further diagnosed with the aid of large-eddy simulations and aircraft measurements, and by suppressing the triggering of the deep convection scheme. It is found that the weak boundary layer turbulence simulated is directly responsible for the weak cumulus activity and the simulated boundary layer stratiform clouds. Increased vertical and temporal resolutions are shown to lead to stronger boundary layer turbulence and reduction of low-cloud biases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Toward a new parameterization of hydraulic conductivity in climate models: Simulation of rapid groundwater fluctuations in N orthern C alifornia

Abstract Preferential flow through weathered bedrock leads to rapid rise of the water table after the first rainstorms and significant water storage (also known as “rock moisture”) in the fractures. We present a new parameterization of hydraulic conductivity that captures the preferential flow and is easy to implement in global climate models. To mimic the naturally varying heterogeneity with depth in the subsurface, the model represents the hydraulic conductivity as a product of the effective saturation and a background hydraulic conductivity K bkg , drawn from a lognormal distribution. The mean of the background K bkg decreases monotonically with depth, while its variance reduces with the effective saturation. Model parameters are derived by assimilating into Richards’ equation 6 years of 30 min observations of precipitation (mm) and water table depths (m), from seven wells along a steep hillslope in the Eel River watershed in Northern California. The results show that the observed rapid penetration of precipitation and the fast rise of the water table from the well locations, after the first winter rains, are well captured with the new stochastic approach in contrast to the standard van Genuchten model of hydraulic conductivity, which requires significantly higher levels of saturated soils to produce the same results. “Rock moisture,” the moisture between the soil mantle and the water table, comprises 30% of the moisture because of the great depth of the weathered bedrock layer and could be a potential source of moisture to sustain trees through extended dry periods. Furthermore, storage of moisture in the soil mantle is smaller, implying less surface runoff and less evaporation, with the proposed new model.

58 GEOSCIENCES↗
DOE OSTI2017

Closing the scale gap between land surface parameterizations and GCMs with a new scheme, SiB3-Bins: SOIL MOISTURE SCALE GAP

The interaction of land with the atmosphere is sensitive to soil moisture (W). Evapotranspiration (ET) reacts to soil moisture in a nonlinear way, f(W), as soils dry from saturation to wilt point. This nonlinear behavior and the fact that soil moisture varies on scales as small as 1–10 m in nature, while numerical general circulation models (GCMs) have grid cell sizes on the order of 1 to 100s of kilometers, makes the calculation of grid cell-average ET problematic. It is impractical to simulate the land in GCMs on the small scales seen in nature, so techniques have been developed to represent subgrid scale heterogeneity, including: (1) statistical-dynamical representations of grid subelements of varying wetness, (2) relaxation of f(W), (3) moderating f(W) with approximations of catchment hydrology, (4) “tiling” the landscape into vegetation types, and (5) hyperresolution. Here we present an alternative method for representing subgrid variability in W, one proven in a conceptual framework where landscape-scale W is represented as a series of “Bins” of increasing wetness from dry to saturated. The grid cell-level f(W) is defined by the integral of the fractional area of the wetness bins and the value of f(W) associated with each. This approach accounts for the spatiotemporal dynamics of W. We implemented this approach in the SiB3 land surface parameterization and then evaluated its performance against a control, which assumes a horizontally uniform field of W. We demonstrate that the Bins method, with a physical basis, attenuates unrealistic jumps in model state and ET seen in the control runs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.

97 MATHEMATICS AND COMPUTING↗