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Meteorological observations are essential for climate modelling, prediction, early warning systems, decision-making processes, and disaster management. These observations are critical to societal development and the safeguarding of human activities and livelihoods. Spatial interpolation techniques play a pivotal role in addressing gaps between observation sites, enabling the generation of continuous meteorological datasets. However, due to the inherent complexity of atmosphere–surface interactions, no single interpolation technique has proven universally effective in achieving consistently accurate results for meteorological variables. This study proposes a novel interpolation model based on Fuzzy Adaptive Optimal Fusion (FAOF). The FAOF model integrates fuzzy theory by constructing station-specific fuzzy sets and sub-method element pools, employing a nonlinear membership function with error as the independent variable. An iterative accuracy index is used to identify the optimal parameter combination, facilitating adaptive data fusion and interpolation optimisation. The model’s performance is evaluated against 10 individual methods from the method pool. Experimental results demonstrate that FAOF effectively combines the strengths of multiple methods, achieving significantly enhanced interpolation accuracy. Additionally, the model consistently performs well across diverse regions and meteorological variables, underscoring its robustness and strong generalisation capability.

With the rapid advancement of information technology, the Internet, as the core infrastructure for global information exchange, faces increasingly severe security challenges. However, traditional network traffic detection methods typically focus solely on the local features of traffic, failing to comprehensively consider the global relationships between traffic flows. This limitation results in poor detection performance against multi-flow coordinated attacks. Additionally, the inherent imbalance in real-world network traffic data significantly hampers the performance of most models in practical scenarios. To address these issues, this paper proposes a network traffic detection method based on data interpolation and contrastive learning (TICL). The method employs data interpolation techniques to generate negative samples, effectively mitigating the data imbalance problem in real-world scenarios. Furthermore, to enhance the model’s generalization capability, contrastive learning is introduced to capture the differences between positive and negative samples, thereby improving detection performance. Experimental results on two publicly available real-world datasets demonstrate that TICL significantly outperforms existing intrusion detection methods in large-scale data scenarios, showcasing its strong potential for practical applications.

Episodes of mass coral bleaching have been reported in recent decades and have raised concerns about the future of coral reefs on a warming planet. Despite the efforts to enhance and coordinate coral reef monitoring within and across countries, our knowledge of the geographic extent of mass coral bleaching over the past few decades is incomplete. Existing databases, like ReefBase, are limited by the voluntary nature of contributions, geographical biases in data collection, and the variations in the spatial scale of bleaching reports. In this study, we have developed the first-ever gridded, global-scale historical coral bleaching database. First, we conducted a targeted search for bleaching reports not included in ReefBase by personally contacting scientists and divers conducting monitoring in under-reported locations and by extracting data from the literature. This search increased the number of observed bleaching reports by 79%, from 4146 to 7429. Second, we employed spatial interpolation techniques to develop annual 0.04° × 0.04° latitude-longitude global maps of the probability that bleaching occurred for 1985 through 2010. Initial results indicate that the area of coral reefs with a more likely than not (>50%) or likely (>66%) probability of bleaching was eight times higher in the second half of the assessed time period, after the 1997/1998 El Niño. The results also indicate that annual maximum Degree Heating Weeks, a measure of thermal stress, for coral reefs with a high probability of bleaching increased over time. The database will help the scientific community more accurately assess the change in the frequency of mass coral bleaching events, validate methods of predicting mass coral bleaching, and test whether coral reefs are adjusting to rising ocean temperatures.

Initial assessment of landslide susceptible areas is important in designing landslide mitigation measures. This study, a part of our study on the developing a landslide spatial model, aims to identify landslide susceptible areas using hard soil depth. In here, hard soil depth, defined as the depth interpreted from cone penetration test where the tip resistance reaches up to 250 kg/cm2, was used to identify landslide susceptible areas in a relatively small mountainous region in the middle western Central Java where landslides frequently occur. To this end, hard soil depth was interpolated using two different methods: inverse distance weighting and ordinary kriging (OK). The method producing the least errors and the most similar data distribution was selected. The result shows that OK is the best fitting model and exhibits clear pattern related to the recorded landslide sites. From interpolated hard soil depth in the landslide sites, it can be surmised that landslide susceptible areas are places possessing hard soil depth of 2.6–13.4 m. This finding is advantageous for policy makers in planning and designing efforts for landslide mitigation in middle western Central Java and should be applicable for other regions.

In order to understand the oceans role as a global carbon sink, we must accurately quantify the amount of carbon exchanged at the air‐sea interface. A widely used machine learning neural network product, the SOM‐FFN, uses observations to reconstruct a monthly, 1° × 1° global CO2 flux estimate. However, uncertainties in neural network and interpolation techniques can be large, especially in seldom‐sampled regions. Here, we present a three‐dimensional (latitude, longitude, time) gridded product for our SOM‐FFN observational data set consisting of uncertainties (pCO2 mapping, transfer velocity, wind) and biases (pCO2 mapping). We find that polar regions are dominated by uncertainty from gas exchange transfer velocity, with an average 48.7% contribution. In contrast, for subtropical regions, wind product choice contributes an average 50.0%. Regions with fewer observations correlate with higher uncertainty and biases, illustrating the importance of maintaining and expanding existing measurements. Plain Language Summary The ocean plays an important role in regulating climate and the carbon cycle by absorbing and releasing carbon through the air‐sea interface. In order to better understand these dynamics, we need to accurately quantify the amount of carbon exchanged between the ocean and atmosphere reservoirs, known as our air‐sea carbon flux. Since the data can't be retrieved by satellites, it is challenging to get a global scale monthly product, so interpolation techniques such as neural networks are used. While these techniques have proven to provide robust observation‐based estimates, uncertainties can be high, especially in regions where few observations are available. We calculate the uncertainty and bias created while using a two‐step neural network machine learning method, the SOM‐FFN. We find the sources of flux uncertainty vary regionally, with subtropical uncertainty dominated by choice of wind product but polar uncertainty influenced most by the coefficient chosen for the air‐sea gas exchange transfer. Areas with fewer observations correlate with higher uncertainty and bias. This analysis provides important motivation for maintaining and increasing global ocean carbon observations, and is an important step toward closing the carbon budget through accurate quantification of the fluxes at the air‐sea interface. Key Points We analyze a new explicit spatial quantification of bias and uncertainty in the air‐sea CO2 exchange from observation‐based SOM‐FFN method We find variations in seasonal uncertainty with higher magnitude in boreal wintertime and larger uncertainty in less‐observed regions Flux uncertainty is dominated by the exchange transfer velocity in polar regions and wind reanalysis estimates in the subtropics

Spatial interpolation methods usually differ in their underlying mathematical concepts. Each has inherent advantages and disadvantages, and choosing a method should be based on the type of data to be analyzed. This paper, therefore, compares and evaluates the performances of well-established interpolation techniques that can be used to estimate monthly rainfall in Thailand. The approaches analyzed include inverse distance weighting (IDW), inverse exponential weighting (IEW), multiple linear regression (MLR), artificial neural networks (ANN), and ordinary kriging (OK) methods. In addition, a search of the nearest stations has also been conducted for some of the aforementioned schemes. A k-fold cross-validation is exploited to assess the efficiency of each method. Results show that ANN might be the least desirable choice as it underperformed, with the remaining methods being roughly comparable. Considering both accuracy and computational flexibility, the IEW approach with a restricted number of neighboring stations is recommended in this study.

The growing recognition within the water industry that cyclic loading from pressure transients could accelerate pipe failures has motivated the development and application of the Cumulative Pressure‐Induced Stress (CPIS) metric. This metric incorporates both mean pressures, derived from extended period simulation hydraulic models, and the more challenging dynamic pressures (DP). Estimating DP requires high‐temporal‐resolution data to count pressure cycles, yet sparse pressure monitoring locations and the computational complexity of transient modeling hinder network‐wide DP estimation. To overcome these limitations, this study investigates various methods to estimate DP across an entire water distribution network using spatial interpolation techniques and simplified transient modeling, which use pressure monitoring data from a limited number of locations. Applying these approaches to an operational system, we found that inverse distance weighting reliably approximates DP for pipes without direct measurements. The estimation accuracy depends on factors such as the magnitude and proximity of transient sources and the density of sensors throughout the network. By integrating the interpolated DP values with mean pressures to calculate CPIS for each pipe, models predicting pipe failures can more accurately assess causality and forecast future breaks. The resulting insights offer a better understanding of how to estimate benefits associated with hydraulically calming water distribution networks.

To assess the accuracy of commonly used 3D reconstruction techniques for coal samples and provide a foundation for examining the coal’s internal microstructure, as well as its mechanical and seepage properties, this study focuses on samples from the Yuwu and Yuecheng Mines. X-ray CT scanning was employed to acquire CT slices of the coal samples, which were then subjected to 3D reconstruction using Avizo, Mimics, and Matlab. By comparing and analyzing the strengths and limitations of each reconstruction method in terms of image processing quality and reconstruction fidelity, the most effective method was identified. This selected method was further refined using layer interpolation techniques, and its validity was confirmed with mercury intrusion experimental data. The results indicate that the 3D reconstructions achieved with Avizo are the most accurate and closely reflect the actual coal structure. The further improvement revealed that appropriate interpolation could bring the reconstructed coal sample data closer to the mercury intrusion data, thereby enhancing the accuracy of the coal sample’s 3D reconstruction. The improved 3D reconstruction method presented in this study provides more reliable data support for subsequent analyses of the coal’s microstructure.

Precipitation is considered a crucial component in the hydrological cycle and changes in its spatial pattern directly influence the water resources. We compare different interpolation techniques in predicting the spatial distribution pattern of precipitation in Chongqing. Six interpolation methods, i.e., Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Diffusion Interpolation with Barrier (DIB), Kernel Interpolation with Barrier (KIB), Ordinary Kriging (OK) and Empirical Bayesian Kriging (EBK), were applied to estimate different rainfall patterns. Annual mean, rainy season and dry-season precipitation was calculated from the daily precipitation time series of 34 meteorological stations with a time span of 1991 to 2019, based on Leave-One-Out Cross-Validation (LOOCV), Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE) and Nash–Sutcliffe Efficiency coefficient (NSE) as validation indexes of the applied models for calculating the error degree and accuracy. Correlation test and Spearman coefficient was performed on the estimated and observed values. A method combining Entropy Weight and Technique for Order Preference by Similarity to Ideal Solution (Entropy-Weighted TOPSIS) was introduced to rank the performance of six interpolation methods. The results indicate that interpolation technique performs better in estimating during periods of low precipitation (i.e., dry season, relative to rainy season and mean annual). The performance priorities of the six methods under the combined multiple precipitation distribution patterns are KIB > EBK > OK > RBF > DIB > IDW. Among them, KIB method has the highest accuracy which maps more accurate precipitation surfaces, with the disadvantage that estimation error is prone to outliers. EBK method is the second highest, and IDW method has the lowest accuracy with a high degree of error. This paper provides information for the application of interpolation methods in estimating rainfall spatial pattern and for water resource management of concerned regions.

Commodities flow through trade networks across the world, with trajectories that can be effectively modelled using approaches similar to those used in human mobility studies. Yet, documenting these movements comprehensively is challenging due to data sparsity, cost, and privacy constraints. Origin-destination (OD) matrices provide a widely used framework for representing mobility, although they inherently omit locations not directly observed as either origins or destinations. This incompleteness creates gaps across different geographical scales, constraining our ability to characterise movement patterns in underrepresented areas. In this study, we introduce a vector-field-based method to address these persistent data challenges. By transforming OD data into continuous vector fields, we capture spatial flow patterns more comprehensively than traditional network approaches, while also enabling robust analysis of mobility directions. Our approach incorporates interpolation techniques that handle incomplete and sparse datasets effectively; when approximately 500 out of 853 areas are removed, 189 areas (36%) maintain degree deviations of less than 15 degrees, showing that the general direction of flow is preserved for over one-third of the impacted areas and enabling continuous spatial analysis. We apply this framework to cattle trade data from Minas Gerais, Brazil. Cattle movements are particularly significant as they directly impact disease transmission, including foot-and-mouth disease. Accurately modelling these flows supports effective disease surveillance and preparedness, with benefits for both animal health and economic stability. Our analysis reveals distinct spatial clusters of trade behaviour, temporal patterns in flow directions, and seasonally varying critical points likely associated with known periodicities in cattle trade driven by breeding cycles, slaughter schedules, and fluctuations in global demand. While previous vector-field studies focused on human mobility, our framework addresses the distinct challenges of commodity flows, where aggregated OD data, sparse observations, and lack of data are the norm. It enables inference in unobserved areas which is a critical capability for modelling scenarios such as disease spread. This approach enhances our capacity to infer flow patterns from incomplete datasets and advances understanding of large-scale commodity trade dynamics.