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DOE OSTI2023

Advanced Turbulence Models for Large-Scale Atmospheric Boundary Layer Flows

We present high-fidelity large-eddy-simulation (LES) modeling approaches for the turbulent atmospheric boundary layer (ABL) flows. Wind energy is a prime example of an application driven by ABL. Generation of electrical energy from farms of wind turbines at night in the stable ABL is a particularly interesting situation. In this report, we consider the well-known GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) stably stratified benchmark LES case. We use a high-order spectral element code Nek5000/RS, which is supported under the DOE's Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms. In our earlier ANL report, we demonstrated our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. In this report, we extend the range of our SGS modeling approaches in the context of the mean-field eddy viscosity (MFEV), to include the solution of an SGS turbulent kinetic energy equation (TKE). We demonstrate the model fidelity of Nek5000/RS in comparison to that of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, with which we studied scaling performance for both codes in comparison on DOE's leadership computing platforms.

17 WIND ENERGY↗

DOE OSTI2025

Bayesian Calibration of Nuclear Graphite Property Models Accounting for Model Inadequacy and Impacts on Component Performance

Nuclear-grade structural graphite is extensively utilized in the core designs of various advanced nuclear reactors. In the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, including nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity requires accurate models of graphite's thermomechanical response. This report documents the Bayesian calibration of thermomechanical properties for nuclear-grade graphite and their application to graphite component modeling and simulation using the Grizzly code. As part of this work, uncertainty-quantified models were developed for the elastic modulus, coefficient of thermal expansion, irradiation-induced dimensional change, and irradiation-induced creep for graphite grades IG-110, NBG-18, NBG-17, PCEA, and 2114. Using a hierarchical Bayesian approach, multiple experimental data sources were combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due to inadequacies in the model and the inherent spread in the experimental data were quantified for three different models. These uncertainty-quantified models, with a model-form correction, were subsequently applied to a coupled-physics simulation of representative graphite components, revealing that the uncertainties have a large impact on the components' deformation.

36 - MATERIALS SCIENCE↗

NASA NTRS2015

Why Is Improvement of Earth System Models so Elusive? Challenges and Strategies from Dust Aerosol Modeling

Past decades have seen an accelerating increase in computing efficiency, while climate models are representing a rapidly widening set of physical processes. Yet simulations of some fundamental aspects of climate like precipitation or aerosol forcing remain highly uncertain and resistant to progress. Dust aerosol modeling of soil particles lofted by wind erosion has seen a similar conflict between increasing model sophistication and remaining uncertainty. Dust aerosols perturb the energy and water cycles by scattering radiation and acting as ice nuclei, while mediating atmospheric chemistry and marine photosynthesis (and thus the carbon cycle). These effects take place across scales from the dimensions of an ice crystal to the planetary-scale circulation that disperses dust far downwind of its parent soil. Representing this range leads to several modeling challenges. Should we limit complexity in our model, which consumes computer resources and inhibits interpretation? How do we decide if a process involving dust is worthy of inclusion within our model? Can we identify a minimal representation of a complex process that is efficient yet retains the physics relevant to climate? Answering these questions about the appropriate degree of representation is guided by model evaluation, which presents several more challenges. How do we proceed if the available observations do not directly constrain our process of interest? (This could result from competing processes that influence the observed variable and obscure the signature of our process of interest.) Examples will be presented from dust modeling, with lessons that might be more broadly applicable. The end result will either be clinical depression or there assuring promise of continued gainful employment as the community confronts these challenges.

Climate models↗

NASA NTRS2016

Recent Progresses in Incorporating Human Land-Water Management into Global Land Surface Models Toward Their Integration into Earth System Models

The global water cycle has been profoundly affected by human land-water management. As the changes in the water cycle on land can affect the functioning of a wide range of biophysical and biogeochemical processes of the Earth system, it is essential to represent human land-water management in Earth system models (ESMs). During the recent past, noteworthy progress has been made in large-scale modeling of human impacts on the water cycle but sufficient advancements have not yet been made in integrating the newly developed schemes into ESMs. This study reviews the progresses made in incorporating human factors in large-scale hydrological models and their integration into ESMs. The study focuses primarily on the recent advancements and existing challenges in incorporating human impacts in global land surface models (LSMs) as a way forward to the development of ESMs with humans as integral components, but a brief review of global hydrological models (GHMs) is also provided. The study begins with the general overview of human impacts on the water cycle. Then, the algorithms currently employed to represent irrigation, reservoir operation, and groundwater pumping are discussed. Next, methodological deficiencies in current modeling approaches and existing challenges are identified. Furthermore, light is shed on the sources of uncertainties associated with model parameterizations, grid resolution, and datasets used for forcing and validation. Finally, representing human land-water management in LSMs is highlighted as an important research direction toward developing integrated models using ESM frameworks for the holistic study of human-water interactions within the Earths system.

biogeochemistry↗

NASA NTRS2019

Modeling Quiet Solar Luminosity Variability from TSI Satellite Measurements and Proxy Models during 1980-2018

A continuous record of direct total solar irradiance (TSI) observations began with a series of satellite experiments in 1978. This record requires comparisons of overlapping satellite observations with adequate relative precisions to provide useful long term TSI trend information. Herein we briefly review the active cavity radiometer irradiance monitor physikalisch-meteorologisches observatorium davos (ACRIM-PMOD) TSI composite controversy regarding how the total solar irradiance (TSI) has evolved since 1978 and about whether TSI significantly increased or slightly decreased from 1980 to 2000. The main question is whether TSI increased or decreased during the so-called ACRIM-gap period from 1989 to 1992. There is significant discrepancy between TSI proxy models and observations before and after the gap, which requires a careful revisit of the data analysis and modeling performed during the ACRIM-gap period. In this study, we use three recently proposed TSI proxy models that do not present any TSI increase during the ACRIM-gap, and show that they agree with the TSI data only from 1996 to 2016. However, these same models significantly diverge from the observations from 1981 and 1996. Thus, the scaling errors must be different between the two periods, which suggests errors in these models. By adjusting the TSI proxy models to agree with the data patterns before and after the ACRIM-gap, we found that these models miss a slowly varying TSI component. The adjusted models suggest that the quiet solar luminosity increased from the 1986 to the 1996 TSI minimum by about 0.45 W/m2 reaching a peak near 2000 and decreased by about 0.15 W/m2 from the 1996 to the 2008 TSI cycle minimum. This pattern is found to be compatible with the ACRIM TSI composite and confirms the ACRIM TSI increasing trend from 1980 to 2000, followed by a long-term decreasing trend since.

total solar irradiance↗

NASA NTRSDate not supplied

Predictive Modeling of Carbon Ablators Using Micro and Macro-Scale Modeling

Efforts to build a Predictive Material Modeling (PMM) framework from the micro-scale to the macro-scale are presented in this abstract. To reduce the need for extensive testing, accelerate the design cycle process, and reduce uncertainty margins applied to final designs, NASA is developing simulation and modeling tools that enable characterization of material properties and response to high-enthalpy environments. The Porous Microstructure Analysis (PuMA) code has been developed for computing macroscale (volume averaged) properties of porous materials using microscale images from micro-computed tomography (micro-CT). Microscale modeling requires a realistic representation of a material microstructure; these are obtained either synthetically during the design of the material or through X-ray micro-CT. Volume averaged properties are then used to inform macroscale material response models, such as those implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO) software, also actively developed by NASA. The computational model in PATO is a generic heat and mass transfer model for porous reactive materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale assuming local thermal equilibrium. These tools were developed to efficiently interface with other pre-existing codes such as SPARTA (direct simulation Monte Carlo), DPLR (hypersonic CFD), NEQAIR (radiative transport) and DAKOTA (uncertainty quantification and optimization). Detailed flight data (Mars Science Laboratory [MSL] Entry Descent and Landing Instrument [MEDLI]) is critical for validating these computational tools for NASA applications. Examples of modeling ablative material response using these codes will be presented including 3D simulations of the full-scale heatshield of the MSL capsule. The simulations demonstrate the ability of the modern material response code, PATO, to handle the material response of geometrically complex and large domains, through the use of massively parallel computations.

Thermal Protection Systems↗

NASA NTRSDate not supplied

Assessment of Numerical and Modeling Errors of RANS based Transition Models for Low-Reynolds Numbers 2-D Flows

In this paper we report the outcome of selected workshops organized as part of the NATO Applied Vehicle Technology (AVT)-313 activity Incompressible Laminar-to-Turbulent Flow Transition Study that focused on assessing the numerical and modeling accuracy of the γ−Reθ and γ transition models coupled to the k−ω Shear-Stress Transport (SST) two-equation eddy-viscosity model. Three different test cases involving nominally 2D flow configurations were selected: flow over a flat plate with two different levels of turbulence intensity at the inlet; flow around the Eppler 387 foil at a Reynolds number of 3×10^5 and angles of attack of 1 deg. and 7 deg. flow around the NACA 0015 foil at a Reynolds number of 1.8×10^5 and angles of attack of 5 deg. and10 deg. The flat plate flow conditions correspond to natural and by-pass transition, whereas the other two test cases include laminar separation bubbles that lead to separation-induced transition. For each test case, the selected quantities of interest include both integral and local flow quantities. Geometrically similar grids with a wide range of grid refinement ratios were generated for each of the test cases to allow the estimation of numerical uncertainties for all quantities of interest selected for this study. Several RANS flow solvers were used, employing common grids with the same boundary conditions and mathematical models. Therefore, it is possible to analyze the consistency of the results, i.e., to check if the intervals defined by the different numerical solutions with their respective uncertainties overlap with each other. Modeling errors can also be addressed for the selected flow quantities that have experimental data available. However, the experimental information available in these cases is not sufficient to guarantee that experiments and simulations are performed with the same settings. Nonetheless, the available experimental data is sufficient to guarantee that modeling errors are significantly reduced with the use of the transition models when compared to simulations performed using only the k−ω SST model.

CFD Modeling↗

DOE OSTI2017

Modeling of Hydraulic Fracture Propagation at the kISMET Site Using a Fully Coupled 3D Network-Flow and Quasi- Static Discrete Element Model

Aimed at supporting the design of hydraulic fracturing experiments at the kISMET site, ~1500 m below ground in a deep mine, we performed pre-experimental hydraulic fracturing simulations in order to estimate the breakdown pressure, propagation pressure, fracture geometry, and the magnitude of induced seismicity using a newly developed fully coupled three-dimensional (3D) network flow and quasi-static discrete element model (DEM). The quasi-static DEM model, which is constructed by Delaunay tessellation of the rock volume, considers rock fabric heterogeneities by using the “disordered” DEM mesh and adding random perturbations to the stiffness and tensile/shear strengths of individual DEM elements and the elastic beams between them. A conjugate 3D flow network based on the DEM lattice is constructed to calculate the fluid flow in both the fracture and porous matrix. One distinctive advantage of the model is that fracturing is naturally described by the breakage of elastic beams between DEM elements. It is also extremely convenient to introduce mechanical anisotropy into the model by simply assigning orientation-dependent tensile/shear strengths to the elastic beams. In this paper, the 3D hydraulic fracturing model was verified against the analytic solution for a penny-shaped crack model. We applied the model to simulate fracture propagation from a vertical open borehole based on initial estimates of rock mechanical properties and in-situ stress conditions. The breakdown pressure and propagation pressure are directly obtained from the simulation. In addition, the released elastic strain energies of individual fracturing events were calculated and used as a conservative estimate for the magnitudes of the potential induced seismic activities associated with fracturing. The comparisons between model predictions and experimental results are still ongoing.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Quantifying Turbine-Level Risk to Golden Eagles Using a High-Fidelity Updraft Model and a Stochastic Behavioral Model

To minimize the effects of wind farms on Golden Eagle (Aquila chrysaetos) populations while enabling sustainable development of renewable energy resources, it is important to understand how eagles interact with atmospheric flows, terrain features, and anthropogenic structures. Models that predict migratory flight paths provide one tool that helps us grasp how the location of wind farms may influence interactions and impacts on migrating Golden Eagles. The current state-of-the-art in predicting migratory flight paths uses a deterministic fluid-flow analogy to predict eagle trajectory using only an orographic updraft potential computed from topographical features. This model does not take into account variables, such as thermal updrafts and time varying atmospheric conditions that are known to influence migratory behavior. In this work, we improve on the model with the objective of developing tools that advance our understanding of how atmospheric flows and terrain features affect migratory eagle behavior and their interactions with wind farms. Specifically, we 1) incorporate both orographic and thermal updraft information in simulating eagle flight paths; 2) incorporate stochasticity into eagle travel patterns to better capture the influence of exogenous factors on, and the inherent stochasticity of eagle behavior; 3) consider spatio-temporal atmospheric data at wind-farm-scale when computing updraft potential; and 4) account for how atmospheric conditions and the direction of migration change seasonally and how these changes affect eagle migratory flight behavior. We tested the model using a 50km by 50km region with 50 m resolution in the western United States. We simulated 900 independent, probabilistic eagle tracks during southerly and northerly migration, assuming eagles solely rely on orographic updrafts. The preliminary results indicate that the inclusion of finer resolution atmospheric data allows for the inclusion of realistic conditions that an eagle experiences. The stochasticity in eagle tracks provides a platform to include uncertainty in eagle decision making and help produce robust eagle presence maps. We will deploy updraft and downdraft velocities computed using a high-fidelity, wind farm scale, computational fluid dynamics solver under development at National Renewable Energy Laboratory. This work is a first step in the development of a predictive and generalizable eagle behavior model at the wind farm scale that does not rely on empirical data collection. Although the current model is intended for migratory eagles, we will extend and refine this model to inform the development of additional behavioral modes, including resident eagle behavior. This modeling approach improves our ability to understand eagle use of the landscape at a fine scale, and it is our hope that this work will ultimately help advance strategies that minimize the impact of wind development on Golden Eagle populations.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2025

Comparative Study of Enhanced Geothermal System Supply Curves Across CONUS from Two Temperature Models Using the Renewable Energy Potential Model (reV)

Enhanced geothermal systems (EGS) have had recent breakthroughs within the geothermal sector. These breakthroughs are reflected in the National Renewable Energy Laboratory (NREL) 2024 Annual Technology Baseline and will result in updated EGS supply curves (i.e., the available resource capacity relative to cost). Our research uses NREL's Renewable Energy Potential (reV) model to compare EGS supply curves across the conterminous United States (CONUS) for two different temperature models: the Stanford temperature model (STM) and the Southern Methodist University temperature model (SMU). The reV model provides the levelized cost of energy (LCOE) at a consistent resolution across CONUS, taking into consideration transmission costs and constraints as well as technical exclusions pertaining to sensitive cultural, ecological, or infrastructure locations. In addition to a countrywide analysis of both models, we also conducted a regional analysis of Texas. We observed the STM had, on average, lower temperatures across different depths, resulting in slightly higher mean and median LCOEs as compared to the SMU temperature model at the same depths. In the regional analysis for Texas, however, when we compared only the common points between the two temperature models, the STM had lower median and mean LCOEs compared to SMU due to higher temperatures at depths greater than 5 km.

enhanced geothermal systems↗

DOE OSTI2024

Quantification of modeling uncertainty in the Rayleigh damping model

Understanding and accurately characterizing energy dissipation mechanisms in civil structures during earthquakes is an important element of seismic assessment and design. The most commonly used model is attributed to Rayleigh. This paper proposes a systematic approach to quantify the uncertainty associated with Rayleigh's damping model. Bayesian calibration with embedded model error is employed to treat the coefficients of the Rayleigh model as random variables using modal damping ratios. Through a numerical example, we illustrate how this approach works and how the calibrated model can address modeling uncertainty associated with the Rayleigh damping model.

42 ENGINEERING↗

DOE OSTI2025

Automatic building energy model development and debugging using large language models agentic workflow

Building energy modeling (BEM) is a complex process that demands significant time and expertise, limiting its broader application in building design and operations. While Large Language Models (LLMs) agentic workflow have facilitated complex engineering processes, their application in BEM has not been specifically explored. This paper investigates the feasibility of automating BEM using LLM agentic workflow. Here, we developed a generic LLM-planning-based workflow that takes a building description as input and generates an error-free EnergyPlus building energy model. Our robust workflow includes four core agents: 1) Building Description Pre-Processing, 2) IDF Object Information Extraction, 3) Single IDF Object Generator Suite, and 4) IDF Debugging Agent. These agents divide the complex tasks into manageable sub-steps, enabling LLMs to generate accurate and reliable results at each stage. The case study demonstrates the successful translation of a building description into an error-free EnergyPlus model for the iUnit modular building at the National Renewable Energy Laboratory. The effectiveness of our workflow surpasses: 1) naive prompt engineering, 2) other LLM-based workflows, and 3) manual modeling, in terms of accuracy, reliability, and time efficiency. The paper concludes with a discussion on the interplay between foundational models and LLM agent planning design, advocating for the use of fine-tuned, specialized models to advance this field.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

One-dimensional biomass fast pyrolysis model with reaction kinetics integrated in an Aspen Plus Biorefinery Process Model

A biomass fast pyrolysis reactor model with detailed reaction kinetics and one-dimensional fluid dynamics was implemented in an equation-oriented modeling environment (Aspen Custom Modeler). Portions of this work were detailed in previous publications; further modifications have been made here to improve stability and reduce execution time of the model to make it compatible for use in large process flowsheets. The detailed reactor model was integrated into a larger process simulation in Aspen Plus and was stable for different feedstocks over a range of reactor temperatures. Sample results are presented that indicate general agreement with experimental results, but with higher gas losses caused by stripping of the bio-oil by the fluidizing gas in the simulated absorber/condenser. Lastly, this integrated modeling approach can be extended to other well-defined, predictive reactor models for fast pyrolysis, catalytic fast pyrolysis, as well as other processes.

09 BIOMASS FUELS↗

DOE OSTI2015

How does increasing horizontal resolution in a global climate model improve the simulation of aerosol-cloud interactions?

The Community Atmosphere Model Version 5 is run at horizontal grid spacing of 2, 1, 0.5, and 0.25 degrees, with the meteorology nudged towards the Year Of Tropical Convection analysis, and cloud simulators and the collocated A-Train satellite observations are used to explore the resolution dependence of aerosol-cloud interactions. The higher-resolution model produces results that agree better with observations, showing an increase of susceptibility of cloud droplet size, indicating a stronger first aerosol indirect forcing (AIF), and a decrease of susceptibility of precipitation probability, suggesting a weaker second AIF. The resolution sensitivities of AIF are attributed to those of droplet nucleation and precipitation parameterizations. The annual average AIF in the northern hemisphere mid-latitudes (where most anthropogenic emissions occur) in the 0.25° model is reduced by about 1 W m⁻² (-30%) compared to the 2° model, leading to a 0.26 W m⁻² reduction (-15%) in the global annual average AIF.

Ma, Po -Lun↗

DOE OSTI2016

Model representations of aerosol layers transported from North America over the Atlantic Ocean during the Two-Column Aerosol Project

The ability of the Weather Research and Forecasting model with chemistry (WRF-Chem) version 3.7 and the Community Atmosphere Model version 5.3 (CAM5) in simulating profiles of aerosol properties is quantified using extensive in situ and remote sensing measurements from the Two Column Aerosol Project (TCAP) conducted during July of 2012. TCAP was supported by the U.S. Department of Energy’s Atmospheric Radiation Measurement program and was designed to obtain observations within two atmospheric columns; one fixed over Cape Cod, Massachusetts and the other several hundred kilometers over the ocean. The performance is quantified using most of the available aircraft and surface measurements during July, and two days are examined in more detail to identify the processes responsible for the observed aerosol layers. The higher resolution WRF-Chem model produced more aerosol mass in the free troposphere than the coarser resolution CAM5 model so that the fraction of aerosol optical thickness above the residual layer from WRF-Chem was more consistent with lidar measurements. We found that the free troposphere layers are likely due to mean vertical motions associated with synoptic-scale convergence that lifts aerosols from the boundary layer. The vertical displacement and the time period associated with upward transport in the troposphere depend on the strength of the synoptic system and whether relatively high boundary layer aerosol concentrations are present where convergence occurs. While a parameterization of subgrid scale convective clouds applied in WRF-Chem modulated the concentrations of aerosols aloft, it did not significantly change the overall altitude and depth of the layers.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2016

Select strengths and biases of models in representing the Arctic winter boundary layer over sea ice: the Larcform 1 single column model intercomparison

We struggle to represent lower tropospheric temperature and moisture profiles and surface fluxes in Artic winter using weather and climate models, partly because they lack or misrepresent physical processes that are specific to high latitudes. Observations have revealed two preferred states of the Arctic winter boundary layer. In the cloudy state, cloud liquid water limits surface radiative cooling, and temperature inversions are weak and elevated. In the radiatively clear state, strong surface radiative cooling leads to the build-up of surface-based temperature inversions. Many large-scale models lack the cloudy state, and some substantially underestimate inversion strength in the clear state. The transformation from a moist to a cold dry air mass is modeled using an idealized Lagrangian perspective. The trajectory includes both boundary layer states, and the single-column experiment is the first Lagrangian Arctic air formation experiment (Larcform 1) organized within GEWEX GASS (Global atmospheric system studies). The intercomparison reproduces the typical biases of large-scale models: some models lack the cloudy state of the boundary layer due to the representation of mixed-phase microphysics or to the interaction between micro- and macrophysics. In some models, high emissivities of ice clouds or the lack of an insulating snow layer prevent the build-up of surface-based inversions in the radiatively clear state. Models substantially disagree on the amount of cloud liquid water in the cloudy state and on turbulent heat fluxes under clear skies. Finally, observations of air mass transformations including both boundary layer states would allow for a tighter constraint of model behavior.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

The GFDL Global Atmosphere and Land Model AM4.0/LM4.0: 2. Model Description, Sensitivity Studies, and Tuning Strategies

Here, in Part 2 of this two–part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part 1. Part 2 provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the model's clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

Abstract Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

Zhang, Jiangjiang↗