Improving the accuracy of precipitation estimates in a typical inland arid area of China using a dynamic Bayesian model averaging approach

Xinjiang Uygur Autonomous Region is a typical inland arid area in China with a sparse and uneven distribution of meteorological stations,limited access to precipitation data,and significant water scarcity.Evaluating and integrating precipitation datasets from different sources to accurately characterize precipitation patterns has become a challenge to provide more accurate and alternative precipitation information for the region,which can even improve the performance of hydrological modelling.This study evaluated the applicability of widely used five satellite-based precipitation products(Climate Hazards Group InfraRed Precipitation with Station(CHIRPS),China Meteorological Forcing Dataset(CMFD),Climate Prediction Center morphing method(CMORPH),Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record(PERSIANN-CDR),and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis(TMPA))and a reanalysis precipitation dataset(ECMWF Reanalysis v5-Land Dataset(ERA5-Land))in Xinjiang using ground-based observational precipitation data from a limited number of meteorological stations.Based on this assessment,we proposed a framework that integrated different precipitation datasets with varying spatial resolutions using a dynamic Bayesian model averaging(DBMA)approach,the expectation-maximization method,and the ordinary Kriging interpolation method.The daily precipitation data merged using the DBMA approach exhibited distinct spatiotemporal variability,with an outstanding performance,as indicated by low root mean square error(RMSE=1.40 mm/d)and high Person's correlation coefficient(CC=0.67).Compared with the traditional simple model averaging(SMA)and individual product data,although the DBMA-fused precipitation data were slightly lower than the best precipitation product(CMFD),the overall performance of DBMA was more robust.The error analysis between DBMA-fused precipitation dataset and the more advanced Integrated Multi-satellite Retrievals for Global Precipitation Measurement Final(IMERG-F)precipitation product,as well as hydrological simulations in the Ebinur Lake Basin,further demonstrated the superior performance of DBMA-fused precipitation dataset in the entire Xinjiang region.The proposed framework for solving the fusion problem of multi-source precipitation data with different spatial resolutions is feasible for application in inland arid areas,and aids in obtaining more accurate regional hydrological information and improving regional water resources management capabilities and meteorological research in these regions.

Response of Growing Season Gross Primary Production to El Nino in Different Phases of the Pacific Decadal Oscillation over Eastern China Based on Bayesian Model Averaging

Gross primary production(GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems.A set of validated monthly GPP data from 1957 to 2010 in 0.5°× 0.5° grids of China was weighted from the Multi-scale Terrestrial Model Intercomparison Project using Bayesian model averaging(BMA).The spatial anomalies of detrended BMA GPP during the growing seasons of typical El Nino years indicated that GPP response to El Nino varies with Pacific Decadal Oscillation(PDO) phases: when the PDO was in the cool phase,it was likely that GPP was greater in northern China(32°–38°N,111°–122°E) and less in the Yangtze River valley(28°–32°N,111°–122°E);in contrast,when PDO was in the warm phase,the GPP anomalies were usually reversed in these two regions.The consistent spatiotemporal pattern and high partial correlation revealed that rainfall dominated this phenomenon.The previously published findings on how El Nino during different phases of PDO affecting rainfall in eastern China make the statistical relationship between GPP and El Nino in this study theoretically credible.This paper not only introduces an effective way to use BMA in grids that have mixed plant function types,but also makes it possible to evaluate the carbon cycle in eastern China based on the prediction of El Nino and PDO.

Climate change in the Tianshan and northern Kunlun Mountains based on GCM simulation ensemble with Bayesian model averaging

Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan and northern Kunlun Mountains（TKM） based on the general circulation model（GCM） simulation ensemble from the coupled model intercomparison project phase 5（CMIP5） under the representative concentration pathway（RCP） lower emission scenario RCP4.5 and higher emission scenario RCP8.5 using the Bayesian model averaging（BMA） technique. Results show that（1） BMA significantly outperformed the simple ensemble analysis and BMA mean matches all the three observed climate variables;（2） at the end of the 21^（st） century（2070–2099） under RCP8.5, compared to the control period（1976–2005）, annual mean temperature and mean annual precipitation will rise considerably by 4.8°C and 5.2%, respectively, while mean annual snowfall will dramatically decrease by 26.5%;（3） precipitation will increase in the northern Tianshan region while decrease in the Amu Darya Basin. Snowfall will significantly decrease in the western TKM. Mean annual snowfall fraction will also decrease from 0.56 of 1976–2005 to 0.42 of 2070–2099 under RCP8.5; and（4） snowfall shows a high sensitivity to temperature in autumn and spring while a low sensitivity in winter, with the highest sensitivity values occurring at the edge areas of TKM. The projections mean that flood risk will increase and solid water storage will decrease.

Improving the simulation of terrestrial water storage anomalies over China using a Bayesian model averaging ensemble approach

The ability to estimate terrestrial water storage(TWS)is essential for monitoring hydrological extremes(e.g.,droughts and floods)and predicting future changes in the hydrological cycle.However,inadequacies in model physics and parameters,as well as uncertainties in meteorological forcing data,commonly limit the ability of land surface models(LSMs)to accurately simulate TWS.In this study,the authors show how simulations of TWS anomalies(TWSAs)from multiple meteorological forcings and multiple LSMs can be combined in a Bayesian model averaging(BMA)ensemble approach to improve monitoring and predictions.Simulations using three forcing datasets and two LSMs were conducted over China's Mainland for the period 1979–2008.All the simulations showed good temporal correlations with satellite observations from the Gravity Recovery and Climate Experiment during 2004–08.The correlation coefficient ranged between 0.5 and 0.8 in the humid regions(e.g.,the Yangtze river basin,Huaihe basin,and Zhujiang basin),but was much lower in the arid regions(e.g.,the Heihe basin and Tarim river basin).The BMA ensemble approach performed better than all individual member simulations.It captured the spatial distribution and temporal variations of TWSAs over China's Mainland and the eight major river basins very well;plus,it showed the highest R value(>0.5)over most basins and the lowest root-mean-square error value(<40 mm)in all basins of China.The good performance of the BMA ensemble approach shows that it is a promising way to reproduce long-term,high-resolution spatial and temporal TWSA data.

Improving microwave brightness temperature predictions based on Bayesian model averaging ensemble approach

The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature （Tb） sim- ulation. How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging （BMA） ensemble approach. The simulations by the community microwave emission model （CMEM） cou- pled with the community land model version 4.5 （CLM4.5） over China's Mainland are con- ducted by the 24 configurations from four vegetation opacity parameterizations （VOPs）, three soil dielectric constant parameterizations （SDCPs）, and two soil roughness param- eterizations （SRPs）. Compared with the simple arithmetical averaging （SAA） method, the BMA reconstructions have a higher spatial correlation coefficient （larger than 0.99） than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system （AMSR-E） at the vertical polarization. Moreover, the BMA product performs the best among the ensemble members for all vegetation classes, with a mean root-mean-square difference （RMSD） of 4 K and a temporal correlation coefficient of 0.64.

Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach

It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The proposed method, using Bayesian decision theory, is based on the well known Bayesian model averaging (BMA)’s machinery;and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.

A Mixture-Based Bayesian Model Averaging Method

Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.

Influences of Mixed Traffic Flow and Time Pressure on Mistake-Prone Driving Behaviors among Bus Drivers

Bus safety is a matter of great importance in many developing countries, with driving behaviors among bus drivers identified as a primary factor contributing to accidents. This concern is particularly amplified in mixed traffic flow (MTF) environments with time pressure (TP). However, there is a lack of sufficient research exploring the relationships among these factors. This study consists of two papers that aim to investigate the impact of MTF environments with TP on the driving behaviors of bus drivers. While the first paper focuses on violated driving behaviors, this particular paper delves into mistake-prone driving behaviors (MDB). To collect data on MDB, as well as perceptions of MTF and TP, a questionnaire survey was implemented among bus drivers. Factor analyses were employed to create new measurements for validating MDB in MTF environments. The study utilized partial correlation and linear regression analyses with the Bayesian Model Averaging (BMA) method to explore the relationships between MDB and MTF/TP. The results revealed a modified scale for MDB. Two MTF factors and two TP factors were found to be significantly associated with MDB. A high presence of motorcycles and dangerous interactions among vehicles were not found to be associated with MDB among bus drivers. However, bus drivers who perceived motorcyclists as aggressive, considered road users’ traffic habits as unsafe, and perceived bus routes’ punctuality and organization as very strict were more likely to exhibit MDB. Moreover, the results from the three MDB predictive models demonstrated a positive impact of bus route organization on MDB among bus drivers. The study also examined various relationships between the socio-demographic characteristics of bus drivers and MDB. These findings are of practical significance in developing interventions aimed at reducing MDB among bus drivers operating in MTF environments with TP.

Bayesian ensemble methods for predicting ground deformation due to tunnelling with sparse monitoring data

Numerous analytical models have been developed to predict ground deformations induced by tunneling,which is a critical issue in tunnel engineering.However,the accuracy of these predictions is often limited by errors and uncertainties resulting from model selection and parameter fittings,given the paucity of monitoring data in field settings.This paper proposes a novel approach to estimate tunnelling-induced ground deformations by applying Bayesian model averaging to several representative prediction models.By accounting for both model and parameter uncertainties,this approach enables more realistic predictions of ground deformations than individual models.Specifically,our results indicate that the Gonzalez-Sagaseta model outperforms other models in predicting ground surface settlements,while the Loganathan-Poulos model is most suitable for predicting subsurface vertical and horizontal deformations.Importantly,our analysis reveals that when monitoring data are sparse,model uncertainties may contribute up to 78.7%of the total uncertainties.Thus,obtaining sufficient data for parameter fitting is crucial for accurate predictions.The proposed method in this study offers a more realistic and efficient prediction of tunnelling-induced ground deformations.

Probabilistic Precipitation Forecasting Based on Ensemble Output Using Generalized Additive Models and Bayesian Model Averaging

A probabilistic precipitation forecasting model using generalized additive models （GAMs） and Bayesian model averaging （BMA） was proposed in this paper. GAMs were used to fit the spatial-temporal precipitation models to individual ensemble member forecasts. The distributions of the precipitation occurrence and the cumulative precipitation amount were represented simultaneously by a single Tweedie distribution. BMA was then used as a post-processing method to combine the individual models to form a more skillful probabilistic forecasting model. The mixing weights were estimated using the expectation-maximization algorithm. The residual diagnostics was used to examine if the fitted BMA forecasting model had fully captured the spatial and temporal variations of precipitation. The proposed method was applied to daily observations at the Yishusi River basin for July 2007 using the National Centers for Environmental Prediction ensemble forecasts. By applying scoring rules, the BMA forecasts were verified and showed better performances compared with the empirical probabilistic ensemble forecasts, particularly for extreme precipitation. Finally, possible improvements and a^plication of this method to the downscaling of climate change scenarios were discussed.

A new approach for Bayesian model averaging

Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.

Clinical characteristics and mortality risk prediction model in children with acute myocarditis

Background Acute myocarditis(AMC)can cause poor outcomes or even death in children.We aimed to identify AMC risk factors and create a mortality prediction model for AMC in children at hospital admission.Methods This was a single-center retrospective cohort study of AMC children hospitalized between January 2016 and January 2020.The demographics,clinical examinations,types of AMC,and laboratory results were collected at hospital admission.In-hospital survival or death was documented.Clinical characteristics associated with death were evaluated.Results Among 67 children,51 survived,and 16 died.The most common symptom was digestive disorder(67.2%).Based on the Bayesian model averaging and Hosmer–Lemeshow test,we created a final best mortality prediction model(acute myocarditis death risk score,AMCDRS)that included ten variables(male sex,fever,congestive heart failure,left-ventricular ejection fraction<50%,pulmonary edema,ventricular tachycardia,lactic acid value>4,fulminant myocarditis,abnormal creatine kinase-MB,and hypotension).Despite differences in the characteristics of the validation cohort,the model discrimination was only marginally lower,with an AUC of 0.781(95%confidence interval=0.675–0.852)compared with the derivation cohort.Model calibration likewise indicated acceptable fit(Hosmer‒Lemeshow goodness-of-fit,P¼=0.10).Conclusions Multiple factors were associated with increased mortality in children with AMC.The prediction model AMCDRS might be used at hospital admission to accurately identify AMC in children who are at an increased risk of death.

Improving Multi-Model Ensemble Forecasts of Tropical Cyclone Intensity Using Bayesian Model Averaging

This paper proposes a method for multi-model ensemble forecasting based on Bayesian model averaging （BMA）, aiming to improve the accuracy of tropical cyclone （TC） intensity forecasts, especially forecasts of minimum surface pressure at the cyclone center （Pmin）＇ The multi-model ensemble comprises three operational forecast models： the Global Forecast System （GFS） of NCEP, the Hurricane Weather Research and Forecasting （HWRF） models of NCEP, and the Integrated Forecasting System （IFS） of ECMWF. The mean of a predictive distribution is taken as the BMA forecast. In this investigation, bias correction of the minimum surface pressure was applied at each forecast lead time, and the distribution （or probability density function, PDF） of emin was used and transformed. Based on summer season forecasts for three years, we found that the intensity errors in TC forecast from the three models var-ied significantly. The HWRF had a much smaller intensity error for short lead-time forecasts. To demonstrate the proposed methodology, cross validation was implemented to ensure more efficient use of the sample data and more reliable testing. Comparative analysis shows that BMA for this three-model ensemble, after bias correction and distri-bution transformation, provided more accurate forecasts than did the best of the ensemble members （HWRF）, with a 5%-7% decrease in root-mean-square error on average. BMA also outperformed the multi-model ensemble, and it produced ＂predictive variance＂ that represented the forecast uncertainty of the member models. In a word, the BMA method used in the multi-model ensemble forecasting was successful in TC intensity forecasts, and it has the poten-tial to be applied to routine operational forecasting.

Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty

The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.

Quantitative Analysis and Prediction of China's Natural Gas Consumption in Different Sectors Based on Bayesian Network

In view of the heterogeneity of natural gas consumption in different sectors in China,this paper utilizes Bayesian network(BN)to study the driving factors of natural gas consumption in power generation,chemical and industrial fuel sectors.Combined with Bayesian model averaging(BMA)and scenario analysis,the gas consumption of the three sectors is predicted.The results show that the expansion of urbanization will promote the gas consumption of power generation.The optimization of industrial structure and the increase of industrial gas consumption will enhance the gas consumption of chemical sector.The decrease of energy intensity and the increase of gas consumption for power generation will promote the gas consumption of industrial fuel.Moreover,the direct influencing factors of gas price are urbanization,energy structure and energy intensity.The direct influencing factors of environmental governance intensity are gas price,urbanization,industrial structure,energy intensity and energy structure.In 2025,under the high development scenario,China’s gas consumption for power generation,chemical and industrial fuel sectors will be 66.034,36.552 and 109.414 billion cubic meters respectively.From 2021 to 2025,the average annual growth rates of gas consumption of the three sectors will be 4.82%,2.18%and 4.43%respectively.

Evaluation of alternative surface runoff accounting procedures using SWAT model

For surface runoff estimation in the Soil and Water Assessment Tool(SWAT)model,the curve number(CN)procedure is commonly adopted to calculate surface runoff by dynamically updating CN values based on antecedent soil moisture condition(SCSI)in field.From SWAT2005 and onward,an alternative approach has become available to apply the CN method by relating the runoff potential to daily evapotranspiration(SCSII).While improved runoff prediction with SCSII has been reported in several case studies,few investigations have been made on its influence to water quality output or on the model uncertainty associated with the SCSII method.The objectives of the research were:(1)to quantify the improvements in hydrologic and water quality predictions obtained through different surface runoff estimation techniques;and(2)to examine how model uncertainty is affected by combining different surface runoff estimation techniques within SWAT using Bayesian model averaging(BMA).Applications of BMA provide an alternative approach to investigate the nature of structural uncertainty associated with both CN methods.Results showed that SCSII and BMA associated approaches exhibit improved performance in both discharge and total NO3 predictions compared to SCSI.In addition,the application of BMA has a positive effect on finding well performed solutions in the multi-dimensional parameter space,but the predictive uncertainty is not evidently reduced or enhanced.Therefore,we recommend additional future SWAT calibration/validation research with an emphasis on the impact of SCSII on the prediction of other pollutants.

Near-Term Projections of Global and Regional Land Mean Temperature Changes Considering Both the Secular Trend and Multidecadal Variability

Near-term climate projections are needed by policymakers; however, these projections are difficult because internally generated climate variations need to be considered. In this study, temperature change scenarios in the near-term period 2017-35 are projected at global and regional scales based on a refined multi-model ensemble approach that considers both the secular trend(ST) and multidecadal variability(MDV) in the Coupled Model Intercomparison Project Phase 5(CMIP5) simulations. The ST and MDV components are adaptively extracted from each model simulation by using the ensemble empirical mode decomposition(EEMD) filter, reconstructed via the Bayesian model averaging(BMA) method for the historical period 1901-2005, and validated for 2006-16. In the simulations of the "medium" representative concentration pathways scenario during 2017-35, the MDV-modulated temperature change projected via the refined approach displays an increase of 0.44℃(90% uncertainty range from 0.30 to 0.58℃) for global land, 0.48℃(90% uncertainty range from 0.29 to 0.67℃) for the Northern Hemispheric land(NL), and 0.29℃(90% uncertainty range from 0.23 to 0.35℃) for the Southern Hemispheric land(SL). These increases are smaller than those projected by the conventional arithmetic mean approach. The MDV enhances the ST in 13 of 21 regions across the world. The largest MDV-modulated warming effect(46%) exists in central America. In contrast,the MDV counteracts the ST in NL, SL, and eight other regions, with the largest cooling effect(220%) in Alaska.

BMA probability quantitative precipitation forecasting of land-falling typhoons in south-east China

The probability of quantitative precipitation forecast(PQPF)of three Bayesian Model Averaging(BMA)models based on three raw super ensemble prediction schemes(i.e.,A,B,and C)are established,which through calibration of their parameters using 1-3 day precipitation ensemble prediction systems(EPSs)from the China Meteorological Administration(CMA),the European Centre for Medium-Range Weather Forecasts(ECMWF)and the National Centers for Environmental Prediction(NCEP)and observation during land-falling of three typhoons in south-east China in 2013.The comparison of PQPF shows that the performance is better in the BMA than that in raw ensemble forecasts.On average,the mean absolute error(MAE)of 1 day lead time forecast is reduced by 12.4%,and its continuous ranked probability score(CRPS)of 1-3 day lead time forecast is reduced by 26.2%,respectively.Although the amount of precipitation prediction by the BMA tends to be underestimated,but in view of the perspective of probability prediction,the probability of covering the observed precipitation by the effective forecast ranges of the BMA are increased,which is of great significance for the early warning of torrential rain and secondary disasters induced by it.

Learning Dynamic Causal Relationships Among Sugar Prices

In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market （ZC）, spot sugar price in Zhengzhou （ZS） and futures sugar closing price in New York futures exchange market（NC） and the other includes futures sugar opening price in Zhengzhou （ZO）, ZS and NC. For each quarter, we first use Bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use Bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.