Ensemble Simulation Method Research Articles

Using Baseflow Ensembles for Hydrologic Hysteresis Characterization in Humid Basins of Southeastern China

AbstractBaseflow plays a vital role in protecting the environment and ensuring a stable water supply for farming. There are still gaps in the current understanding of baseflow convergence rates in the humid region due to the abundance of rainfall and the high‐water table. Therefore, this study focused on the evolution and hysteresis characteristics of baseflow in humid basins of southeastern China. The baseflow ensemble simulation (BES) method was established to improve the reliability and applicability of baseflow simulation. We suggest a way of differentiating the wet and dry seasons based on the multi‐year average monthly baseflow index (BFI) to determine the intra‐annual distribution of water effectively and simply. The hydrological hysteresis effect of baseflow on precipitation is revealed by characterizing baseflow response to precipitation under precipitation events during wet and dry seasons. A methodology for assessing the performance of baseflow simulation was proposed from observations of streamflow and precipitation. We found that the BES method performed better in baseflow simulation than other single separation methods. Using the BES method, the lag time of baseflow to precipitation during the wet and dry seasons was found to be 3.09 and 4.04 days after utilizing the BFI to divide the hydrological situation into wet and dry seasons. Additionally, precipitation had nearly twice as much intensity influence on baseflow during the dry season compared to the wet season. These findings have significant ramifications for the use, management, and planning of water resources in humid areas of China.

Path Ensembles for Pin1-Catalyzed Cis-Trans Isomerization of a Substrate Calculated by Weighted Ensemble Simulations.

Pin1 enzyme protein recognizes specifically phosphorylated serine/threonine (pSer/pThr) and catalyzes the slow interconversion of the peptidyl-prolyl bond between cis and trans forms. Structural dynamics between the cis and trans forms are essential to reveal the underlying molecular mechanism of the catalysis. In this study, we apply the weighted ensemble (WE) simulation method to obtain comprehensive path ensembles for the Pin1-catalyzed isomerization process. Associated rate constants for both cis-to-trans and trans-to-cis isomerization are calculated to be submicroseconds time scales, which are in good agreement with the calculated free energy landscape where the cis form is slightly less favorable. The committor-like analysis indicates the shift of the transition state toward trans form (at the isomerization angle ω ∼ 110°) compared to the intrinsic position for the isolated substrate (ω ∼ 90°). The calculated structural ensemble clarifies a role of both the dual-histidine motif, His59/His157, and the basic residues, Lys63/Arg68/Arg69, to anchor both sides of the peptidyl-prolyl bond, the aromatic ring in Pro, and the phosphate in pSer, respectively. The rotation of the torsion angle is found to be facilitated by relaying the hydrogen-bond partner of the main-chain oxygen in pSer from Cys113 in the cis form to Arg68 in the trans form, through Ser154 at the transition state, which is really the cause of the shift in the transition state. The role of Ser154 as a driving force of the isomerization is confirmed by additional WE and free energy calculations for S154A mutant where the isomerization takes place slightly slower and the free energy barrier increases through the mutation. The present study shows the usefulness of the WE simulation for substantial path samplings between the reactant and product states, unraveling the molecular mechanism of the enzyme catalysis.

Helmholtz free-energy high-temperature perturbation expansion for square-well and square-shoulder potentials

ABSTRACT The Helmholtz free-energy high-temperature perturbation terms of the square-shoulder and the square-well potentials of variable range were calculated using the Microcanonical Ensemble simulation method up to the eight-order. The numerical evaluation of the coefficients can be useful to build improved equations of state for these systems. To our knowledge, this is the first work that reports values for the seventh and eighth expansion coefficients for these discrete potentials. The square-shoulder high temperature expansion coefficients are numerically compared with those of the square-well potential. We confirmed that there exists a simple relation among them: even terms are equal for both potentials and odd terms differ by a minus sign, for all the densities and ranges considered. This relation was first proposed in the work of Benavides and Gil-Villegas (Molecular Physics 97, 1225 (1999)) in the context of Discrete Perturbation theory but it was only analytically tested for the first and second-order perturbation terms, and, for the second-order term, it has only been analysed within the Barker and Henderson Local and Macroscopic Compressibility approximations.

Ensemble flood simulation for the typical catchment in humid climatic zone by using multiple hydrological models

Abstract. A good performance of hydrological model for flood simulation is of critical importance for flood forecasting. Taking Yandu River catchment, as the study area, three hydrological models (i.e. Xin'anjiang model, TOPMODEL, artificial neural network model) and a multi-model ensemble simulation method (i.e. entropy-based method) were applied to simulate the hydrological processes of 30 flood events occurring in 1981–1987. The performance of the ensemble members and multi-model ensemble simulation method was evaluated by comparing indicators of Nash-Efficiency coefficient, errors in root mean square, peak occurrence time, and relative errors of flood peak discharge, event runoff depth. Results show that the three hydrological models perform well for hydrological simulation of all 30 storm floods with Nash and Sutcliffe Efficiency coefficient of above 0.75 and relative error of less than 10 %. However, different model exhibits a difference in simulation errors of peak discharge and peak occurrence time. For example, BP model has the smallest error of 3.78 % for peak discharge simulation while that of Xin'anjiang model and TOPMODEL are 20.9 % and 24.7 % respectively. The entropy-based ensemble simulation method improved flood simulation accuracy to some extent for all evaluation criteria comparing to the three hydrological models. It is feasible to apply entropy-based ensemble approach for improving accuracy of flood forecasting in humid regions of China.

Vapor–Liquid Equilibria of Mixtures of Molecular Fluids Using the Activity Fraction Expanded Ensemble Simulation Method

The activity fraction expanded ensemble (AFEE) simulation technique has been extended to predict the vapor–liquid coexistence behavior of binary mixtures of molecular fluids. The systems of molecular mixtures studied are thiophene–n-hexane (a mixture of an aromatic compound with a n-alkane) and methane–n-hexane (mixture of n-alkanes with significant difference in size). Comparison with results from the grand canonical transition matrix Monte Carlo method and experimental data available in the literature has also been provided. Further, we have investigated the computational efficiency of the AFEE technique at temperatures where both compounds exhibit subcritical behavior (thiophene–n-hexane at 338.15 K) and where one of the components shows supercritical behavior (methane–n-hexane at 373 K). Canonical Monte Carlo simulations are also performed to obtain the radial distribution functions which have been used to study the structure of the coexisting liquid phases to gain insights into the molecular origins ...

Rice yield development and the shrinking yield gaps in China, 1981–2008

Increasing population, limited land resources, and the demand for environmental protection highlight the urgency of improving crop yield on the limited cultivated land. To identify a possible food supply under a sustainable intensification of agricultural production, it is necessary to accurately estimate yield potentials and yield gaps. Here, we used a well-validated, large-scale process-based crop model, Model to capture the Crop-weather relationship over a Large Area for rice, and an ensemble model simulation method to estimate the yield potential across the rice planting area of China. We further evaluated the spatiotemporal patterns of actual yield, yield potential, and yield gap over the past three decades. Rice yield showed an increasing trend in more than 95% of the studied counties. However, 48.3% of the counties were already experiencing yield stagnation. The yield potential in northeast China had increased over the past three decades by 20–40 kg/ha per year because of the increase in temperature, while the increased temperature and decreased solar radiation reduced the yield potentials in other regions by 10–30 kg/ha per year. Because of changes in the actual yield and yield potential, the yield gap decreased in 93.4% of the counties by an average of 0.5–2% per year, resulting in less room for yield improvement. Additionally, 65.9% of the counties had nearly approached their yield ceilings (>70% of the yield potential). Our study highlights that popularizing advanced management technologies to close yield gaps and breeding climate-resilient cultivars to expand yield potentials should be of equal importance for the sustainable development of agricultural production and food security.

アンサンブルシミュレーションと擬似温暖化手法による特定の気象イベントの将来変化の推定

In a flood-control planning in Japan, a high-water level is estimated from selected target rainfall events. To draw up adaptive flood control measures for future climate change, information about possible maximum rainfall are indispensable. Climatological or statistical information about precipitation are not enough for that purpose. In this study, a method to evaluate future variations of a particular extreme weather event is developed by combining ensemble simulation and pseudo global warming method. Perturbations for ensemble members are generated from simulation results by Lagged Average Forecasting method. The perturbations are scaled up/down and added to the original conditions, and ensemble members are prepared. Ensemble technique enables to examine whether differences between the present and future simulations are caused by global warming or chaotic behaviors from perturbation. Probability density curves from ensemble results give clearer view of future variations of a weather event.

Microcanonical ensemble simulation method applied to discrete potential fluids.

In this work we extend the applicability of the microcanonical ensemble simulation method, originally proposed to study the Ising model [A. Hüller and M. Pleimling, Int. J. Mod. Phys. C 13, 947 (2002)0129-183110.1142/S0129183102003693], to the case of simple fluids. An algorithm is developed by measuring the transition rates probabilities between macroscopic states, that has as advantage with respect to conventional Monte Carlo NVT (MC-NVT) simulations that a continuous range of temperatures are covered in a single run. For a given density, this new algorithm provides the inverse temperature, that can be parametrized as a function of the internal energy, and the isochoric heat capacity is then evaluated through a numerical derivative. As an illustrative example we consider a fluid composed of particles interacting via a square-well (SW) pair potential of variable range. Equilibrium internal energies and isochoric heat capacities are obtained with very high accuracy compared with data obtained from MC-NVT simulations. These results are important in the context of the application of the Hüller-Pleimling method to discrete-potential systems, that are based on a generalization of the SW and square-shoulder fluids properties.

An automated multiscale ensemble simulation approach for vascular blood flow

Cerebrovascular diseases such as brain aneurysms are a primary cause of adult disability. The flow dynamics in brain arteries, both during periods of rest and increased activity, are known to be a major factor in the risk of aneurysm formation and rupture. The precise relation is however still an open field of investigation. We present an automated ensemble simulation method for modelling cerebrovascular blood flow under a range of flow regimes. By automatically constructing and performing an ensemble of multiscale simulations, where we unidirectionally couple a 1D solver with a 3D lattice-Boltzmann code, we are able to model the blood flow in a patient artery over a range of flow regimes. We apply the method to a model of a middle cerebral artery, and find that this approach helps us to fine-tune our modelling techniques, and opens up new ways to investigate cerebrovascular flow properties.

Uncertainty analysis of bias from satellite rainfall estimates using copula method

The aim of this study is to develop a copula-based ensemble simulation method for analyzing the uncertainty and adjusting the bias of two high resolution satellite precipitation products (PERSIANN and TMPA-3B42). First, a set of sixty daily rainfall events that each of them occurs concurrently over twenty 0.25°×0.25° pixels (corresponding to both PERSIANN and TMPA spatial resolution) is determined to perform the simulations and validations. Next, for a number of fifty-four out of sixty (90%) selected events, the differences between rain gauge measurements as reference surface rainfall data and satellite rainfall estimates (SREs) are considered and termed as observed biases. Then, a multivariate Gaussian copula constructed from the multivariate normal distribution is fitted to the observed biases. Afterward, the copula is employed to generate multiple bias fields randomly based on the observed biases. In fact, copula is invariant to monotonic transformations of random variables and thus the generated bias fields have the same spatial dependence structure as that of the observed biases. Finally, the simulated biases are imposed over the original satellite rainfall estimates in order to obtain an ensemble of bias-adjusted rainfall realizations of satellite estimates. The study area selected for the implementation of the proposed methodology is a region in the southwestern part of Iran. The reliability and performance of the developed model in regard to bias correction of SREs are examined for a number of six out of those sixty (10%) daily rainfall events. Note that these six selected events have not participated in the steps of bias generation. In addition, three statistical indices including bias, root mean square error (RMSE), and correlation coefficient (CC) are used to evaluate the model. The results indicate that RMSE is improved by 35.42% and 36.66%, CC by 17.24% and 14.89%, and bias by 88.41% and 64.10% for bias-adjusted PERSIANN and TMPA-3B42 estimates, respectively.

Sorption and diffusion of carbon dioxide and nitrogen in poly(methyl methacrylate)

Molecular dynamics simulations are performed to determine the solubility and diffusion coefficient of carbon dioxide and nitrogen in poly(methyl methacrylate) (PMMA). The solubilities of CO2 in the polymer are calculated employing our grand canonical ensemble simulation method, fixing the target excess chemical potential of CO2 in the polymer and varying the number of CO2 molecules in the polymer matrix till establishing equilibrium. It is shown that the calculated sorption isotherms of CO2 in PMMA, employing this method well agrees with experiment. Our results on the diffusion coefficients of CO2 and N2 in PMMA are shown to obey a common hopping mechanism. It is shown that the higher solubility of CO2 than that of N2 is a consequence of more attractive interactions between the carbonyl group of polymer and the sorbent. While the residence time of CO2 beside the carbonyl group of polymer is about three times higher than that of N2, the diffusion coefficient of CO2 in PMMA is higher than that of N2. The higher diffusion coefficient of CO2, compared to N2, in PMMA is shown to be due to the higher (≈3 times) swelling of polymer upon CO2 uptake.

Study on Resistance Characteristics of Marine Moisture Filter

Based on the periodic features of structure and flow field, two periodic boundaries are used to study the combined filter. The three stages filters are taken as integration for numerical simulation to acquire the resistance characteristics, which provide a reasonable foundation for performance analysis and optimized design of the filter. The resistance characteristics under different operating conditions acquired by experiment are compared with numerical simulation results of two periodic boundaries. The comparison validates the high precision of the ensemble simulation method.

Potential outcomes of glider data assimilation in the Solomon Sea: Control of the water mass properties and parameter estimation

Steerable underwater gliders are a recent addition to ocean observing systems. Gliders were deployed in the Solomon Sea to improve our knowledge of this potentially important region for Pacific climate. In this study, we explore the potential use of glider data assimilation to control some properties of the ocean state estimation, chosen here to be Solomon Sea thermohaline misfits due to an erroneous tidal-mixing parameterization. Ocean observing system simulation experiments involving several scenarios of glider deployment show that the fleet design can strongly impact the control efficiency. A fairly good control of the Solomon Sea mass field can be achieved with a somewhat unrealistic fleet of 50 gliders. With a more realistic configuration of 10 gliders, the performance depends on the space and time distribution of the vehicles. Substantial control is achieved when glider trajectories are coordinated to collect information-rich data. As a complement, glider data assimilation was used to directly correct the model: the uncertain tidal mixing parameter is estimated through assimilation of data provided by the 10 coordinated gliders using an ensemble simulation method. This promising strategy allows an accurate estimation of the parameter and therefore yields an efficient correction of the errors in Solomon Sea thermohaline properties.

Computation of Surface Tensions Using Expanded Ensemble Simulations

A method for the direct simulation of the surface tension is examined. The technique is based on the thermodynamic route to the interfacial tension and makes use of the expanded ensemble simulation method for the calculation of the free energy difference between two inhomogeneous systems with the same number of particles, temperature, and volume, but different interfacial area. The method is completely general and suitable for systems with either continuous or discontinuous interactions. The adequacy of the expanded ensemble method is assessed by computing the interfacial tension of the planar vapor-liquid interface of Lennard-Jones, Lennard-Jones dimers, Gay-Berne, and square-well model fluids; in the latter, the interactions are discontinuous and the present method does not exhibit the asymmetry of other related methods, such as the test area. The expanded ensemble simulation results are compared with simulation data obtained from other techniques (mechanical and test area) with overall good agreement.

Simulating replica exchange simulations of protein folding with a kinetic network model.

Replica exchange (RE) is a generalized ensemble simulation method for accelerating the exploration of free-energy landscapes, which define many challenging problems in computational biophysics, including protein folding and binding. Although temperature RE (T-RE) is a parallel simulation technique whose implementation is relatively straightforward, kinetics and the approach to equilibrium in the T-RE ensemble are very complicated; there is much to learn about how to best employ T-RE to protein folding and binding problems. We have constructed a kinetic network model for RE studies of protein folding and used this reduced model to carry out "simulations of simulations" to analyze how the underlying temperature dependence of the conformational kinetics and the basic parameters of RE (e.g., the number of replicas, the RE rate, and the temperature spacing) all interact to affect the number of folding transitions observed. When protein folding follows anti-Arrhenius kinetics, we observe a speed limit for the number of folding transitions observed at the low temperature of interest, which depends on the maximum of the harmonic mean of the folding and unfolding transition rates at high temperature. The results shown here for the network RE model suggest ways to improve atomic-level RE simulations such as the use of "training" simulations to explore some aspects of the temperature dependence for folding of the atomic-level models before performing RE studies.

Gibbs ensemble simulation of water in spherical cavities

Chemical equilibration with a bulk reservoir is the crucial problem in computer simulations of liquids in confined geometries. The Gibbs ensemble simulation method is used in the present paper to solve this problem for water in pores. MC simulations of TIP4P water in spherical cavities with smooth surfaces and radii from 6 to 15 Å were done in equilibrium with bulk water at T=300 and 350 K. Chemical equilibration between confined and bulk water was obtained by an essential number of molecular transfers. To our knowledge this is the first application of the Gibbs ensemble simulation method for the equilibration of two dense liquid water systems. As most important result we find that liquid water exists in a cavity only if the water–substrate interaction exceeds some critical value. An increase of the average water density by about 20% with the strengthening of the interaction is observed. For all systems there are two prominent water layers near the cavity surface which exhibit strong orientational ordering. The pair correlation functions evidence a strong distortion of the tetrahedral water structure in the first, outer layer towards a square lattice arrangement. The diffusivity of the water in the cavity always decreases with respect to the bulk.

Multiphase equilibria using the Gibbs ensemble Monte Carlo method

The Gibbs ensemble simulation method is extended to multiphase equilibria by increasing the number of boxes that can be used concurrently in the simulation. Atoms are moved within each box and pairs of boxes are selected at random for the volume and particle exchange moves. The equivalence between the Gibbs ensemble with an arbitrary number of boxes and the corresponding canonical ensemble is established. Simulations of two-component, three-phase equilibria and three-component, four-phase and three-phase equilibria are demonstrated for simple model systems, and the model phase diagrams are determined.

On the phase diagrams of fluids of linearly fused Lennard-Jones sites

Computational methods which are used to obtain the liquid–gas phase diagram have been compared for the particular case of fluids of linearly fused Lennard-Jones sites, and for aspect ratios ranging from 1 to 3. Gibbs ensemble Monte Carlo results for the liquid–gas coexistence line are compared with those obtained by fitting the van der Waals isotherms directly obtained by Monte Carlo simulations. The combination of Gibbs ensemble simulation method together with Wegner-type fits, as obtained from scaling arguments, is found to give reliable coexistence data. In particular, the Wegner-type fit is shown to be applicable even quite far from the critical point. The relevance of the isotherm fitting method is discussed mainly in view of results thus obtained, which are quite fair for short aspect ratios but worsen significantly for the larger ones.

Theoretical Calculation of the Liquid—Vapor Coexistence Curve of Water, Chloroform and Methanol with the Cavity-Biased Monte Carlo Method in the Gibbs Ensemble

Abstract The Gibbs ensemble computer simulation method of Panagiotopoulos is combined by the cavity-biased sampling technique used previously in the grand-canonical ensemble. The combined technique is applied to the determination of the liquid—vapor coexistence curve of the Lennard—Jones fluid as a test case, two water models (SPC and TIP4P) as well as methanol and chloroform, both described with the OPLS model. The application of the virial-based sampling technique, used earlier in the isobaric ensemble is also discussed.