Bayesian Maximum Entropy Research Articles

Assessing the impact of hard data patterns on Bayesian Maximum Entropy: a simulation study.

This study empirically tested the robustness of Bayesian Maximum Entropy (BME) in predicting spatiotemporal data, with an emphasis on skewness, sample size, and spatial dependency level. Simulated data, both Gaussian and non-Gaussian, were generated using the unconditional sequential simulation method, with sample sizes ranging from 100 to 500 at the interval length of 50 and varying skewness (0, 1, 3, 6 and 9) and spatial dependency levels (weak, moderate, and strong). Findings revealed sample size variations and spatial dependence levels did not significantly influence BME prediction's Mean Square Error (MSE) and bias. While skewness significantly impacted MSE (p-value < 0.001), bias remained unaffected. Moreover, skewness and spatial dependence interactions affected both MSE and bias. Despite this, BME proved robust to sample size and skewness, demonstrating a negligible MSE on the graphical plot (heatmap).

Enhancing insights in sexually transmitted infection mapping: Syphilis in Forsyth County, North Carolina, a case study.

In 2008-2011 Forsyth County, North Carolina experienced a four-fold increase in syphilis rising to over 35 cases per 100,000 mirroring the 2021 state syphilis rate. Our methodology extends current models with: 1) donut geomasking to enhance resolution while protecting patient privacy; 2) a moving window uniform grid to control the modifiable area unit problem, edge effect and remove kriging islands; and 3) mitigating the "small number problem" with Uniform Model Bayesian Maximum Entropy. Data is 2008-2011 early syphilis cases reported to the NC Department of Health and Human Services for Forsyth County. Results were assessed using latent rate theory cross validation. We show combining a moving window and a UMBME analysis with geomasked data effectively predicted the true or latent syphilis rate 5% to 26% more accurate than the traditional, geopolitical boundary method. It removed kriging islands, reduced background incidence rate to 0, relocated nine outbreak hotspots to more realistic locations, and elucidated hotspot connectivity producing more realistic geographical patterns for targeted insights. Using the Forsyth outbreak as a case study showed how the outbreak emerged from endemic areas spreading through sexual core transmitters and contextualizing the outbreak to current and past outbreaks. As the dynamics of sexually transmitted infections spread have changed to online partnership selection and demographically to include more women, partnership selection continues to remain highly localized. Furthermore, it is important to present methods to increase interpretability and accuracy of visual representations of data.

Improving heat transfer prediction across catalytic SiC interface through a multiscale framework leveraging machine learning and data fusion techniques

Accurate aerothermal prediction under hypersonic flow conditions is crucial for any thermal protection materials design and engineering. The surface catalytic effect, where dissociated atoms recombine into their molecular forms at the air-solid interface, is an exothermic reaction and plays an important role in high-enthalpy aerodynamic environment prediction. Taking SiC, a widely recognized high-temperature thermal protection material as an example, a multiscale fusion approach for aerothermal prediction is proposed. The approach utilizes reactive molecular dynamics method to construct an interface catalysis model, and the Bayesian maximum entropy to integrate experimental and simulational data into an optimized database. Subsequently, using the radial basis function neural network algorithm, a machine learning-based reaction kinetics model with precise analysis of surface catalysis is trained. The obtained catalytic recombination efficiency is used as a boundary input for computational fluid dynamics simulation, enabling rapid and accurate prediction of hypersonic thermal environment. The result shows that the predicted surface heat flux by this novel approach is consistent with the benchmark studies, but comes with significantly reduced computation time. The stagantion heat flux predictions based on the assumptions of full catalytic wall, finite rate catalytic wall (from the proposed multiscale fusion method), and non-catalytic wall are determined to be 8.65×106 W/m2, 7.51×106 W/m2, and 4.02×106 W/m2, respectively. Comparing these with the wind tunnel benchmark value of 7.48×106 W/m2, the error from the proposed multiscale fusion method is 0.30 %, indicating significant enhancement in prediction accuracy through the proposed upscaling method. The new approach could not only reveal complex exothermic reaction processes at the interface, but also enhance the prediction accuracy at much higher computational efficiency, providing an alternative for multiscale modeling of complex flow and heat transfer at the interface.

Seasonal dynamics of dissolved inorganic nitrogen in groundwater: Tracing environmental controls and land use impact

High levels of dissolved inorganic nitrogen (DIN) in groundwater pose challenges for regions like northern Anhui Province, China, where groundwater is a crucial domestic resource. This study utilized modern geostatistics to explore the spatial and temporal dynamics of DIN in groundwater. Significant seasonal influences on DIN concentrations were identified: ammonium peaks during wet season driven by agricultural activities, while nitrate peaks during the dry season primarily influenced by municipal inputs. This study established a Bayesian Maximum Entropy - Random Forest (BME-RF) model based on Land Use/Land Cover data to infer the spatio-temporal performance of DIN, achieving an interpretation rate above 90 %. It also highlighted the role of hydrogeological conditions and aquifer types in the evolution of DIN. By employing a DIN environmental interaction model, it further analyzed the eco-hydrological drivers and seasonal trends affecting DIN variability, enhancing the understanding of groundwater nitrogen dynamics and their link to environmental factors with low consumption. SynopsisThis study reveals seasonal shifts in groundwater DIN, links them to human activity, and uses the BME model to guide targeted nitrogen fluctuation.

Mapping reservoir water quality from Sentinel-2 satellite data based on a new approach of weighted averaging: Application of Bayesian maximum entropy

In regions like Oman, which are characterized by aridity, enhancing the water quality discharged from reservoirs poses considerable challenges. This predicament is notably pronounced at Wadi Dayqah Dam (WDD), where meeting the demand for ample, superior water downstream proves to be a formidable task. Thus, accurately estimating and mapping water quality indicators (WQIs) is paramount for sustainable planning of inland in the study area. Since traditional procedures to collect water quality data are time-consuming, labor-intensive, and costly, water resources management has shifted from gathering field measurement data to utilizing remote sensing (RS) data. WDD has been threatened by various driving forces in recent years, such as contamination from different sources, sedimentation, nutrient runoff, salinity intrusion, temperature fluctuations, and microbial contamination. Therefore, this study aimed to retrieve and map WQIs, namely dissolved oxygen (DO) and chlorophyll-a (Chl-a) of the Wadi Dayqah Dam (WDD) reservoir from Sentinel-2 (S2) satellite data using a new procedure of weighted averaging, namely Bayesian Maximum Entropy-based Fusion (BMEF). To do so, the outputs of four Machine Learning (ML) algorithms, namely Multilayer Regression (MLR), Random Forest Regression (RFR), Support Vector Regression (SVRs), and XGBoost, were combined using this approach together, considering uncertainty. Water samples from 254 systematic plots were obtained for temperature (T), electrical conductivity (EC), chlorophyll-a (Chl-a), pH, oxidation–reduction potential (ORP), and dissolved oxygen (DO) in WDD. The findings indicated that, throughout both the training and testing phases, the BMEF model outperformed individual machine learning models. Considering Chl-a, as WQI, and R-squared, as evaluation indices, BMEF outperformed MLR, SVR, RFR, and XGBoost by 6%, 9%, 2%, and 7%, respectively. Furthermore, the results were significantly enhanced when the best combination of various spectral bands was considered to estimate specific WQIs instead of using all S2 bands as input variables of the ML algorithms.

Detection of soil salinity distribution and its change in the Yellow River Delta comparing 2006 and 2022

AbstractThe Yellow River Delta (YRD) has the world's highest land formation rate. However, soil salinization has caused severe land degradation in the region. Understanding the distribution of soil salinity and its variation is essential for saline soil management. This study combined soil salinity sampling data, remote sensing imagery, and layers of geographic environmental factors. Three different models, including Ordinary Kriging (OK), Geographically Weighted Regression (GWR), and Bayesian Maximum Entropy (BME), were used and compared to predict the soil salinity of two soil layers in 2006 and 2022. Then the spatial distribution characteristics and development trends of soil salinity in the YRD were analyzed. The results indicated that (1) The BME model is an optimal salinity prediction model that integrates soft data from multiple sources to perform nonlinear estimates. Compared to the OK and GWR models, the RMSE was reduced by up to 25% and 13%, respectively, and the greatest improvement in R2 was increased from 0.0534 and 0.2718 to 0.5569, respectively. (2) Soil salinity in the YRD shows a spatially increasing trend from the southwestern inland to the northeastern coast. Over the past 16 years, the salinization pattern has become more complex: soil salinization has been mitigated in the central and southern regions, with the average salinity decreasing from 1.03% to 0.86% and the salinization rate decreasing from 99% to 88%; and it has significantly intensified in the northern part of the study area near the old Yellow River channel and the Gubei Reservoir, and in some scattered inland areas. Continuous water and sediment regulation in the Yellow River basin and ecological management of natural reserves can generally alleviate soil salinization, but the risk of soil salinization can be increased by seawater erosion, inappropriate land use, and resource exploitation.

Bayesian maximum entropy interpolation analysis for rapid assessment of seismic intensity using station and ground motion prediction equations

In this paper, we explored the combination of seismic station data and ground motion prediction equations (GMPE) to predict seismic intensity results by using Bayesian Maximum Entropy (BME) method. The results indicate that: 1) In earthquake analysis in Japan, soft data has predicted higher values of intensity in disaster areas. BME corrected this phenomenon, especially near the epicenter. Meanwhile, for earthquakes in the United States, BME corrected the erroneous prediction of rupture direction using soft data. 2) Compared with other spatial interpolation methods, the profile results of Japan earthquake and Turkey earthquake show that BME is more consistent with ShakeMap results than IDW and Kriging. Moreover, IDW has a low intensity anomaly zone. 3) The BME method overcomes the phenomenon that the strength evaluation results do not match the actual failure situation when the moment magnitude is small. It more accurately delineates the scope of the disaster area and enriches the post-earthquake processing of disaster area information and data. BME has a wide range of applicability, and it can still be effectively used for interpolation analysis when there is only soft data or few sites with data available.

Coking exhaust contributes to airborne particulate matter in the Beijing–Tianjin–Hebei region

Coking was regarded as a predominant source of air pollution. Despite the adoption of more environmentally friendly equipment, whether the coking enterprises in the Beijing–Tianjin–Hebei (BTH) region are still causing regional air pollution is worthy of study, which is essential for the control of coking enterprises in this area. To improve the prediction accuracy of large-scale air pollutant distribution, the air particle distribution in the BTH region was simulated via land use regression (LUR) combined with Bayesian maximum entropy (BME); then, the distribution was correlated with the exhaust gas emitted from coking enterprises. Results indicated that the R2 of the “LUR + BME” method reached 0.95, higher than 0.82 using LUR alone. The air quality distribution presented a pattern of “low in the northern mountains and high in the southern plains”, similar to the distribution of coking enterprises in BTH region. A significant correlation was found between exhaust emissions from coking enterprises and air quality in the BTH region, confirming the contribution of coking emissions to air pollution in this region, and the necessity to continue the strict control on coking enterprises in BTH area.

Spatial heterogeneity of long-range dependence and self-similarity of global sea surface chlorophyll concentration with their environmental impact factors analysis

Understanding the long-range dependence and self-similarity of global sea surface chlorophyll concentration (SSCC) will enrich its characteristics description and analysis with global change patterns. The satellite SSCC products were collected from the European Space Agency during the period from 29 July 1998 to 31 December2020. After resampling the SSCC products into the spatial resolution of 1°, the missing values were interpolated by Bayesian maximum entropy with mean absolute error of cross validation equaling to 0.1295 mg/m3. Generalized Cauchy model was employed to quantitatively determine the long-range dependence and self-similarity of SSCC at a global scale by using the Hurst parameter and fractal dimension. Good fitted results were achieved with an averaged R2 of 0.9141 and a standard deviation of 0.0518 across the 32,281 spatial locations of the entire ocean; the averaged values of Hurst parameter and fractal dimension were 0.8667 and 1.2506, respectively, suggesting strong long-range dependence and weak self-similarity of SSCC in the entire oceans. Univariate and multivariate generalized addictive models (GAM) were introduced to depict the influence of sea surface height anomaly, sea surface salinity, sea surface temperature and sea surface wind on the Hurst parameter and fractal dimension of SSCC; and smaller mean absolute error were achieved for the GAM of Hurst parameter than that of fractal dimension. Sea surface height anomaly showed the strongest influence for the Hurst parameter than the other three factors, and sea surface wind depicted similar influence; the sea surface temperature owned opposite influence on Hurst parameter compared to sea surface salinity.

Identification of multi-mineral-species geochemical anomalies using Bayesian maximum entropy and the spectrum separable module-constrained convolutional autoencoder

In this paper, we present a dual-drive multi-mineral-species anomaly detection system which involves the combined use of Bayesian maximum entropy, a spectral separable module, high-order factor analysis, a geologically constrained loss function, as well as a mixed Gaussian distribution-based thresholding algorithm, attaching to a deep convolutional autoencoder. We have achieved several firsts rarely considered in the existing literature, for example: previous works focus mainly on separating single-mineral-species rather than multi-elemental anomalies, while we have attempted to recognize multi-mineral-species anomalies; previous works pay more attention to data, while we suggest how to discover the ore-related correlations hidden within the input data; previous works fail to integrate soft data in a quantitative fashion, while we have achieved that by capitalizing on Bayesian maximum entropy and the stratigraphic combination entropy. A series of comparative experiments have demonstrated the advantages over other state-of-the-art approaches. Finally, we obtained a mineral-occurrence identification rate ( δ ) ranging from 36.87 to 61.46% v. the anomaly area ranging from 33.75 to 55.38% for each metalliferous anomaly division.

Predicting rock mass rating ahead of the tunnel face with Bayesian estimation

The rock mass rating (RMR) system plays a crucial role in geomechanics assessments for tunnel projects. However, conventional methods combining empirical and geostatistical approaches often yield inaccuracies, particularly in areas with weak strata such as faults and karst caves. To address these uncertainties and errors inherent in empirical techniques, we propose a progressive RMR prediction strategy based on the Bayesian framework. This strategy incorporates three key components: 1) Variogram modeling: utilizing observational data from the excavation face, we construct and update a variogram model to capture the spatial variability of RMR. 2) TSP-RMR statistic model: we integrate a TSP-RMR statistical model into the Bayesian sequential update process. 3) Bayesian maximum entropy (BME) integration: the BME method combines geological information obtained from tunnel surface excavation with tunnel seismic prediction (TSP) data, ultimately enhancing the RMR prediction accuracy. Our methodology is applied to the Laoying rock tunneling project in Yunnan Province, China. Our findings demonstrate that the fusion of soft data and geological interpretation significantly improves the accuracy of RMR predictions. At selected prediction points, the relative error of our method is less than 15% when compared to the traditional Kriging method. This approach holds substantial potential for advancing RMR estimation ahead of tunnel excavation, particularly when advanced geological forecast data are available.

Quantitative heterogeneous source apportionment of toxic metals through a hybrid method in spatial random fields

Toxic metals in soils pose hazards to food security and human health. Accurate source apportionment provides foundation for pollution prevention. In this study, a novel hybrid method that combines positive matrix factorization, Bayesian maximum entropy and integrative predictability criterion is proposed to provide a new perspective for exploring the heterogeneity of pollution sources in spatial random fields. The results suggest that Cd, As and Cu are the predominant pollutants, with exceedance rates of 27%, 12% and 11%, respectively. The new method demonstrates superiority in predicting toxic metals when combined major and all sources as auxiliary information., with the improvements of 44% and 46%, respectively, Although the major sources identified with the hybrid method are the primary contributors to the accumulation of toxic metals (e.g. coal combustion for Hg, traffic emission for Pb and Zn, industrial activities for As, agricultural activities for Cd and Cu and natural sources for Cr and Ni), the impact of nonmajor sources on toxic metal sin specific regions should not be ignored (e.g. industrial activities on Ni, Pb and Zn in the north and natural sources on Cd, Cu, As, Pb and Zn in the south). For better pollution control, specific local sources should be considered.

A Bayesian maximum entropy model for predicting tsetse ecological distributions

BackgroundAfrican trypanosomiasis is a tsetse-borne parasitic infection that affects humans, wildlife, and domesticated animals. Tsetse flies are endemic to much of Sub-Saharan Africa and a spatial and temporal understanding of tsetse habitat can aid surveillance and support disease risk management. Problematically, current fine spatial resolution remote sensing data are delivered with a temporal lag and are relatively coarse temporal resolution (e.g., 16 days), which results in disease control models often targeting incorrect places. The goal of this study was to devise a heuristic for identifying tsetse habitat (at a fine spatial resolution) into the future and in the temporal gaps where remote sensing and proximal data fail to supply information.MethodsThis paper introduces a generalizable and scalable open-access version of the tsetse ecological distribution (TED) model used to predict tsetse distributions across space and time, and contributes a geospatial Bayesian Maximum Entropy (BME) prediction model trained by TED output data to forecast where, herein the Morsitans group of tsetse, persist in Kenya, a method that mitigates the temporal lag problem. This model facilitates identification of tsetse habitat and provides critical information to control tsetse, mitigate the impact of trypanosomiasis on vulnerable human and animal populations, and guide disease minimization in places with ephemeral tsetse. Moreover, this BME analysis is one of the first to utilize cluster and parallel computing along with a Monte Carlo analysis to optimize BME computations. This allows for the analysis of an exceptionally large dataset (over 2 billion data points) at a finer resolution and larger spatiotemporal scale than what had previously been possible.ResultsUnder the most conservative assessment for Kenya, the BME kriging analysis showed an overall prediction accuracy of 74.8% (limited to the maximum suitability extent). In predicting tsetse distribution outcomes for the entire country the BME kriging analysis was 97% accurate in its forecasts.ConclusionsThis work offers a solution to the persistent temporal data gap in accurate and spatially precise rainfall predictions and the delayed processing of remotely sensed data collectively in the − 45 days past to + 180 days future temporal window. As is shown here, the BME model is a reliable alternative for forecasting future tsetse distributions to allow preplanning for tsetse control. Furthermore, this model provides guidance on disease control that would otherwise not be available. These ‘big data’ BME methods are particularly useful for large domain studies. Considering that past BME studies required reduction of the spatiotemporal grid to facilitate analysis. Both the GEE-TED and the BME libraries have been made open source to enable reproducibility and offer continual updates into the future as new remotely sensed data become available.

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy data fusion to map global surface ozone concentration

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m−3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Uncovering PM2.5 transport trajectories and sources at district within city scale

To continuously improve air quality, it is necessary to carry out fine management of air pollution prevention and control. However, research into regional transport of PM2.5 at a smaller spatial scale such as district is limited. In this study, a novel combined method was constructed to simulate and identify the regional transport trajectories and potential sources of PM2.5 concentrations at district scale, based on a hybrid model that integrates the Bayesian maximum entropy (BME) model, Weather Research and Forecast (WRF) and backward trajectory model. Take Tianjin as an example, an analysis of the transport trajectories showed that the air masses from northwest and southwest were the dominant atmospheric transport pathway in all seasons except summer. The number of transport trajectories from northwest and southwest accounted for 42.41% and 40.75% of the total number of transport trajectories. Despite the dominant wind direction in winter was northwest, it can be beneficial to atmospheric transport. This was because northwest trajectories were the long-range pathways, corresponding to fast-moving air masses that facilitate the dispersion of pollutants. On contrast, it is noteworthy that the southwest trajectories were the short-range pathways, resulting in limited diffusion and unfavorable conditions. The major potential cities that were likely contributors of PM2.5 (Weighted Concentration-Weighted Trajectory (WCWT) values greater than 40 μg m−3) were situated in the southwest. Furthermore, the inter-district transport results indicated that the primary direction of PM2.5 transport in Tianjin was also from south to north. It is critical that the current layout of Tianjin is adjusted in a timely manner through relocating or phasing out, as the majority of industrial enterprises with severe air pollution in Tianjin are located in the southern districts. This method of combining BME, WRF and backward trajectory can be used for atmospheric environment planning in other similar city and district-scale around the world. It also provides useful insights to policy makers when they formulate pollutants prevention control policies.

Linking Satellite, Land Capability, and Socio-Economic Data for Local-Level Climate-Change-Adaptive Capacity Assessments and Decision Support

Climate change is now one of the most formidable threats to the livelihoods of resource-poor communities in low-income developing countries world-wide. Addressing this challenge continues to be undermined by the conspicuous absence of actionable adaptation strategies that are potentially capable of enhancing our capacities to realize the Millennial Sustainable Development Goals that seek to securitize access to adequate food supplies for everybody. This paper attempts to address this limitation by providing an improvised geostatistical methodology that integrates multi-source data to map the adaptive capacities of vulnerable communities in a selected South African local municipality, whose livelihoods are largely dependent on rain-fed agriculture. The development of this methodology was based on the use scripts that were compiled in Python and used to test-try its usefulness through a case-study-based assessment of the climate-change-adaptive capacities of local communities in Raymond Mhlaba Local Municipality (RMLM), Eastern Cape Province, South Africa. A Bayesian maximum entropy framework-based technique was used to overcome the lack of missing soil moisture data, which we included because of its reliable usefulness as a surrogate indicator of climate-change-driven variations in this variable on the sustainability of rain-fed agriculture. Analysis of the results from a sampling universe of 124 communities revealed that 65 and 56 of them had high and medium adaptive capacities, respectively, with the remaining 3 having low adaptive capacities. This finding indicates that more than half of the communities in the municipality’s communities have limited capabilities to cope with climate change’s impacts on their livelihoods. Although our proposed methodology is premised on findings from a case-study-based investigation, it is still extremely useful because it demonstratively shows that there is tremendous scope for the scientific community to provide objectively informed insights that can be used to enhance the adaptive capacities of those in need of the badly needed but difficult-to-access information. Added to this is the fact that our proposed methodology is not only applicable for use under different environmental settings but also capable of allowing us to cost-effectively tap into the rich, wide-ranging, freely accessible datasets at our disposal. The aim of this submission is to show that although we have the information, we need to address these persevering challenges by exploring innovative approaches to translate the knowledge we have into actionable climate-change-adaptation strategies.

Health burden evaluation of industrial parks caused by PM2.5 pollution at city scale.

Industrial park is an important emission sector of PM2.5 pollution. Previous studies have provided valuable information on the impact of PM2.5 from industrial parks on human health, but relevant studies at city scale are limited. In this study, the health burden of industrial parks was evaluated based on PM2.5-related premature deaths and economic contributions. The premature deaths were calculated in terms of a novel research model by integrating the Bayesian maximum entropy (BME) model, weighted concentration-weighted trajectory (WCWT), and integrated exposure-response function (IER). Take Tianjin City for example, it was found that since the main diffusion direction of PM2.5 in Tianjin is from south to north, the industrial parks in the south of Tianjin and close to the central city with high population density have high health burden. These industrial parks need to be focused on or even relocated in the future. The research model can provide scientific basis for the health burden evaluation of industrial parks at city scale, so as to help local governments optimize the layout of industrial parks and formulate environmental responsibility management policies for industrial parks.

A monthly 1° resolution dataset of daytime cloud fraction over the Arctic during 2000–2020 based on multiple satellite products

Abstract. The low accuracy of satellite cloud fraction (CF) data over the Arctic seriously restricts the accurate assessment of the regional and global radiative energy balance under a changing climate. Previous studies have reported that no individual satellite CF product could satisfy the needs of accuracy and spatiotemporal coverage simultaneously for long-term applications over the Arctic. Merging multiple CF products with complementary properties can provide an effective way to produce a spatiotemporally complete CF data record with higher accuracy. This study proposed a spatiotemporal statistical data fusion framework based on cumulative distribution function (CDF) matching and the Bayesian maximum entropy (BME) method to produce a synthetic 1∘ × 1∘ CF dataset in the Arctic during 2000–2020. The CDF matching was employed to remove the systematic biases among multiple passive sensor datasets through the constraint of using CF from an active sensor. The BME method was employed to combine adjusted satellite CF products to produce a spatiotemporally complete and accurate CF product. The advantages of the presented fusing framework are that it not only uses the spatiotemporal autocorrelations but also explicitly incorporates the uncertainties of passive sensor products benchmarked with reference data, i.e., active sensor product and ground-based observations. The inconsistencies of Arctic CF between passive sensor products and the reference data were reduced by about 10 %–20 % after fusing, with particularly noticeable improvements in the vicinity of Greenland. Compared with ground-based observations, R2 increased by about 0.20–0.48, and the root mean square error (RMSE) and bias reductions averaged about 6.09 % and 4.04 % for land regions, respectively; these metrics for ocean regions were about 0.05–0.31, 2.85 %, and 3.15 %, respectively. Compared with active sensor data, R2 increased by nearly 0.16, and RMSE and bias declined by about 3.77 % and 4.31 %, respectively, in land; meanwhile, improvements in ocean regions were about 0.3 for R2, 4.46 % for RMSE, and 3.92 % for bias. The results of the comparison with ERA5 and the Meteorological Research Institute – Atmospheric General Circulation model version 3.2S (MRI-AGCM3-2-S) climate model suggest an obvious improvement in the consistency between the satellite-observed CF and the reanalysis and model data after fusion. This serves as a promising indication that the fused CF results hold the potential to deliver reliable satellite observations for modeling and reanalysis data. Moreover, the fused product effectively supplements the temporal gaps of Advanced Very High Resolution Radiometer (AVHRR)-based products caused by satellite faults and the data missing from MODIS-based products prior to the launch of Aqua, and it extends the temporal range better than the active product; it addresses the spatial insufficiency of the active sensor data and the AVHRR-based products acquired at latitudes greater than 82.5∘ N. A continuous monthly 1∘ CF product covering the entire Arctic during 2000–2020 was generated and is freely available to the public at https://doi.org/10.5281/zenodo.7624605 (Liu and He, 2022). This is of great importance for reducing the uncertainty in the estimation of surface radiation parameters and thus helps researchers to better understand the Earth's energy imbalance.

A multi-model data fusion methodology for reservoir water quality based on machine learning algorithms and bayesian maximum entropy

A major concern in the management of reservoirs is water quality because of the negative consequences it has on both environment and human life. Artificial Intelligence (AI) concept produces a reliable framework to recognize complicated and non-linear correlations between input and output data. Although various machine learning (ML) algorithms in recent studies were employed to predict water quality variables, the existing literature lacks exploring the combination of these algorithms, which has the potential to significantly amplify the outcomes achieved by individual models. Thus, the current study aims to bridge this knowledge gap by evaluating the precision of Random Forest Regression (RFR), Support Vector Regression, Multilayer Perceptron (MLP), and Bayesian Maximum Entropy-based Fusion (BMEF) models to estimate such water quality variables as dissolved oxygen (DO) and chlorophyll-a (Chl-a). The comparisons were conducted in two primary stages: (1) a comparison of the outcomes of different ML algorithms with each other, and (2) comparing the ML algorithms' findings with that of the BMEF model, which considers uncertainty. These comparisons were evaluated using robust statistical measures, and, finally, to indicate the utility and efficacy of the newly introduced framework, it was efficiently utilized in Wadi Dayqah Dam, which is situated in Oman. The findings indicated that, throughout both training and testing phases, the BMEF model outperformed individual machine learning models, namely MLP, RFR, and SVR by 5%, 26%, and 10%, respectively, when R2 and Chl-a are considered as evaluation index and water quality variables, respectively. Additionally, as the individual ML models are not capable of predicting electrical conductivity and oxidation-reduction potential efficiently, the BMEF model leads to better results by R2=0.89, which outperforms MLP (R2=0.81), RFR (R2=0.79), and SVR (R2=0.62) for oxidation-reduction potential. Regarding the study limits of the present study, spatio-temporal data should be collected over a long time to increase the data frequency and reduce the uncertainty related to climate variability.

Entropy-based air quality monitoring network optimization using NINP and Bayesian maximum entropy.

Effectual air quality monitoring network (AQMN) design plays a prominent role in environmental engineering. An optimal AQMN design should consider stations' mutual information and system uncertainties for effectiveness. This study develops a novel optimization model using a non-dominated sorting genetic algorithm II (NSGA-II). The Bayesian maximum entropy (BME) method generates potential stations as the input of a framework based on the transinformation entropy (TE) method to maximize the coverage and minimize the probability of selecting stations. Also, the fuzzy degree of membership and the nonlinear interval number programming (NINP) approaches are used to survey the uncertainty of the joint information. To obtain the best Pareto optimal solution of the AQMN characterization, a robust ranking technique, called Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE) approach, is utilized to select the most appropriate AQMN properties. This methodology is applied to Los Angeles, Long Beach, and Anaheim in California, USA. Results suggest using 4, 4, and 5 stations to monitor CO, NO2, and ozone, respectively; however, implementing this recommendation reduces coverage by 3.75, 3.75, and 3 times for CO, NO2, and ozone, respectively. On the positive side, this substantially decreases TE for CO, NO2, and ozone concentrations by 8.25, 5.86, and 4.75 times, respectively.