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In this paper, we are interested in the data gathering for Wireless Sensor Networks (WSNs). In this context, we assume that only some nodes are active in the network, and that these nodes are not transmitting all the time. On the other side, the inactive nodes are considered to be inexistent or idle for a long time period. Henceforth, the sink should be able to recover the entire data matrix whie using the few received measurements. To this end, we propose a novel technique that is based on the Matrix Completion (MC) methodology. Indeed, the considered compression pattern, which is composed of structured and random losses, cannot be solved by existing MC techniques. When the received reading matrix contains several missing rows, corresponding to the inactive nodes, MC techniques are unable to recover the missing data. Thus, we propose a clustering technique that takes the inter-nodes correlation into account, and we present a complementary minimization problem based-interpolation technique that guarantees the recovery of the inactive nodes’ readings. The proposed reconstruction pattern, combined with the sampling one, is evaluated under extensive simulations. The results confirm the validity of each building block and the efficiency of the whole structured approach, and prove that it outperforms the closest scheme.

Geotechnical investigation is an important aspect of construction engineering. In order to optimize this link, this paper analyzes the current status of the application of geotechnical investigation in construction engineering through the fusion of multidimensional spatial data interpolation of geotechnical geology as well as the structural design of geotechnical profiles by combining with triangular mesh search algorithm. On this basis, the parameter prediction of the fusion of multi-source parameter data in geotechnicals was carried out by determining the estimated variance and weight coefficients. In addition, the optimal interpolation algorithm was selected through the indoor test and in-situ test, and the accuracy of the modeling of the soil and the prediction of the geotechnical parameters were analyzed. The results show that the modeling width error is between [0.04,0.20], the length error is between [0.7,0.23], the planar accuracy error is around 0.2cm, the depth error is within 0.02cm, and the errors of the actual and predicted values of the rock and map parameters are within 0.1 and 0.09, respectively. Geotechnical investigation measures and techniques in construction engineering based on multi-source data fusion can optimize construction engineering.

In the Jizera Mountains (Czech Republic) the density of climate station network was tested in relation to spatial data interpolation, and watershed management targets. Point weather data (precipitation, air temperature, humidity and wind velocity) were interpolated by the nearest neighbourhood (NN), inverse distance weighting (IDW), spline (SPL), hypsometric (HYP) and kriging (KRI) methods. The results were assessed by the root mean square error (RMSE). The interpolation effectiveness showed the following order: HYP, IDW, KRI, NN and SPL. The advantage of the hypsometric method was recognised, particularly, by providing reasonable outputs in marginal catchments of the region and outside of the main instrumented area. However, in case of a higher density of observation points (11 hectares per station), all interpolation methods manifested comparable and realistic outputs in the focused mountain watersheds.

High-spatial-resolution and long-term climate data are highly desirable for understanding climate-related natural processes. China covers a large area with a low density of weather stations in some (e.g., mountainous) regions. This study describes a 0.5′ (∼ 1 km) dataset of monthly air temperatures at 2 m (minimum, maximum, and mean proxy monthly temperatures, TMPs) and precipitation (PRE) for China in the period of 1901–2017. The dataset was spatially downscaled from the 30′ Climatic Research Unit (CRU) time series dataset with the climatology dataset of WorldClim using delta spatial downscaling and evaluated using observations collected in 1951–2016 by 496 weather stations across China. Prior to downscaling, we evaluated the performances of the WorldClim data with different spatial resolutions and the 30′ original CRU dataset using the observations, revealing that their qualities were overall satisfactory. Specifically, WorldClim data exhibited better performance at higher spatial resolution, while the 30′ original CRU dataset had low biases and high performances. Bicubic, bilinear, and nearest-neighbor interpolation methods employed in downscaling processes were compared, and bilinear interpolation was found to exhibit the best performance to generate the downscaled dataset. Compared with the evaluations of the 30′ original CRU dataset, the mean absolute error of the new dataset (i.e., of the 0.5′ dataset downscaled by bilinear interpolation) decreased by 35.4 %–48.7 % for TMPs and by 25.7 % for PRE. The root-mean-square error decreased by 32.4 %–44.9 % for TMPs and by 25.8 % for PRE. The Nash–Sutcliffe efficiency coefficients increased by 9.6 %–13.8 % for TMPs and by 31.6 % for PRE, and correlation coefficients increased by 0.2 %–0.4 % for TMPs and by 5.0 % for PRE. The new dataset could provide detailed climatology data and annual trends of all climatic variables across China, and the results could be evaluated well using observations at the station. Although the new dataset was not evaluated before 1950 owing to data unavailability, the quality of the new dataset in the period of 1901–2017 depended on the quality of the original CRU and WorldClim datasets. Therefore, the new dataset was reliable, as the downscaling procedure further improved the quality and spatial resolution of the CRU dataset and was concluded to be useful for investigations related to climate change across China. The dataset presented in this article has been published in the Network Common Data Form (NetCDF) at https://doi.org/10.5281/zenodo.3114194 for precipitation (Peng, 2019a) and https://doi.org/10.5281/zenodo.3185722 for air temperatures at 2 m (Peng, 2019b) and includes 156 NetCDF files compressed in zip format and one user guidance text file.

For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.

We propose a fundamental theorem for eco-environmental surface modelling (FTEEM) in order to apply it into the fields of ecology and environmental science more easily after the fundamental theorem for Earth’s surface system modeling (FTESM). The Beijing-Tianjin-Hebei (BTH) region is taken as a case area to conduct empirical studies of algorithms for spatial upscaling, spatial downscaling, spatial interpolation, data fusion and model-data assimilation, which are based on high accuracy surface modelling (HASM), corresponding with corollaries of FTEEM. The case studies demonstrate how eco-environmental surface modelling is substantially improved when both extrinsic and intrinsic information are used along with an appropriate method of HASM. Compared with classic algorithms, the HASM-based algorithm for spatial upscaling reduced the root-mean-square error of the BTH elevation surface by 9 m. The HASM-based algorithm for spatial downscaling reduced the relative error of future scenarios of annual mean temperature by 16%. The HASM-based algorithm for spatial interpolation reduced the relative error of change trend of annual mean precipitation by 0.2%. The HASM-based algorithm for data fusion reduced the relative error of change trend of annual mean temperature by 70%. The HASM-based algorithm for model-data assimilation reduced the relative error of carbon stocks by 40%. We propose five theoretical challenges and three application problems of HASM that need to be addressed to improve FTEEM.

While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \\[u\\] and \\[v\\] in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \\[u\\] and \\[v\\]. In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and ordinary kriging. Overall, explanatory variables improve the interpolation results.

Precipitation has a strong and constant impact on different economic sectors, environment and social activities all over the world. An increasing interest for monitoring and estimating the precipitation characteristics can be claimed in the last decades. However, in some areas, the ground-based network is still sparse and the spatial data coverage insufficiently addresses the needs. In the last decades, different interpolation methods provide an efficient response for describing the spatial distribution of precipitation. In this study, we compare the performance of seven interpolation methods used for retrieving the mean annual precipitation over the mainland Portugal, as follows: local polynomial interpolation (LPI), global polynomial interpolation (GPI), radial basis function (RBF), inverse distance weighted (IDW), ordinary cokriging (OCK), universal cokriging (UCK) and empirical Bayesian kriging regression (EBKR). We generate the mean annual precipitation distribution using data from 128 rain gauge stations covering the period 1991 to 2000. The interpolation results were evaluated using cross-validation techniques and the performance of each method was evaluated using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), Pearson’s correlation coefficient (R) and Taylor diagram. The results indicate that EBKR performs the best spatial distribution. In order to determine the accuracy of spatial distribution generated by the spatial interpolation methods, we calculate the prediction standard error (PSE). The PSE result of EBKR prediction over mainland Portugal increases from south to north.

The WFDE5 dataset has been generated using the WATCH Forcing Data (WFD) methodology applied to surface meteorological variables from the ERA5 reanalysis. The WFDEI dataset had previously been generated by applying the WFD methodology to ERA-Interim. The WFDE5 is provided at 0.5∘ spatial resolution but has higher temporal resolution (hourly) compared to WFDEI (3-hourly). It also has higher spatial variability since it was generated by aggregation of the higher-resolution ERA5 rather than by interpolation of the lower-resolution ERA-Interim data. Evaluation against meteorological observations at 13 globally distributed FLUXNET2015 sites shows that, on average, WFDE5 has lower mean absolute error and higher correlation than WFDEI for all variables. Bias-adjusted monthly precipitation totals of WFDE5 result in more plausible global hydrological water balance components when analysed in an uncalibrated hydrological model (WaterGAP) than with the use of raw ERA5 data for model forcing. The dataset, which can be downloaded from https://doi.org/10.24381/cds.20d54e34 (C3S, 2020b), is distributed by the Copernicus Climate Change Service (C3S) through its Climate Data Store (CDS, C3S, 2020a) and currently spans from the start of January 1979 to the end of 2018. The dataset has been produced using a number of CDS Toolbox applications, whose source code is available with the data – allowing users to regenerate part of the dataset or apply the same approach to other data. Future updates are expected spanning from 1950 to the most recent year. A sample of the complete dataset, which covers the whole of the year 2016, is accessible without registration to the CDS at https://doi.org/10.21957/935p-cj60 (Cucchi et al., 2020).

The monthly global 2° × 2° Extended Reconstructed Sea Surface Temperature (ERSST) has been revised and updated from version 4 to version 5. This update incorporates a new release of ICOADS release 3.0 (R3.0), a decade of near-surface data from Argo floats, and a new estimate of centennial sea ice from HadISST2. A number of choices in aspects of quality control, bias adjustment, and interpolation have been substantively revised. The resulting ERSST estimates have more realistic spatiotemporal variations, better representation of high-latitude SSTs, and ship SST biases are now calculated relative to more accurate buoy measurements, while the global long-term trend remains about the same. Progressive experiments have been undertaken to highlight the effects of each change in data source and analysis technique upon the final product. The reconstructed SST is systematically decreased by 0.077°C, as the reference data source is switched from ship SST in ERSSTv4 to modern buoy SST in ERSSTv5. Furthermore, high-latitude SSTs are decreased by 0.1°–0.2°C by using sea ice concentration from HadISST2 over HadISST1. Changes arising from remaining innovations are mostly important at small space and time scales, primarily having an impact where and when input observations are sparse. Cross validations and verifications with independent modern observations show that the updates incorporated in ERSSTv5 have improved the representation of spatial variability over the global oceans, the magnitude of El Niño and La Niña events, and the decadal nature of SST changes over 1930s–40s when observation instruments changed rapidly. Both long-(1900–2015) and short-term (2000–15) SST trends in ERSSTv5 remain significant as in ERSSTv4.