This work analyses three uncertainty sources affecting the observation‐based gridded data sets: station density, interpolation methodology and spatial resolution. For this purpose, we consider ...precipitation in two countries, Poland and Spain, three resolutions (0.11, 0.22 and 0.44°), three interpolation methods, both areal‐ and point‐representative implementations, and three different densities of the underlying station network (high/medium/low density). As a result, for each resolution and interpolation approach, nine different grids have been obtained for each country and inter‐compared using a variance decomposition methodology.
Results indicate larger differences among the data sets for Spain than for Poland, mainly due to the larger spatial variability and complex orography of the former region. The variance decomposition points out to station density as the most influential factor, independent of the season, the areal‐ or point‐representative implementation and the country considered, and slightly increasing with the spatial resolution. In contrast, the decomposition is stable when extreme precipitation indices are considered, in particular for the 50‐year return value.
Finally, the uncertainty due to station sub‐sampling inside a particular grid box decreases with the number of stations used in the averaging/interpolation. In the case of spatially homogeneous grid boxes, the interpolation approach obtains similar results for all the parameters, excepting the wet day frequency, independently of the number of stations. When there is a more significant internal variability in the grid box, the interpolation is more sensitive to the number of stations, pointing out to a minimum stations’ density for the target resolution (six to seven stations).
The uncertainty due to the stations density, interpolation method and resolution has been analysed for the precipitation in two countries, Poland and Spain, by means a variance decomposition analysis. The results reflect that the main factor in the development of gridded data sets is the underlying station's density for both mean and extreme precipitation. In addition, a minimum density of six to seven stations per grid box has been identified to reach an effective resolution of 0.44.
•Prediction accuracy of clay was more affected by sampling strategies.•Vis-NIR spectra had higher prediction performance compared to pXRF spectra.•Combined Vis-NIR and pXRF spectra had no improvement ...on prediction accuracy.
The recent technologies employed for rapid, cost-effective, and non-destructive prediction of soil particle size distribution (clay, sand, and silt) are becoming increasingly interesting among soil scientists. Our aims were to explore the effect of surface, profile wall, and surface + profile wall on prediction accuracy using individual and combined both soil spectra (Vis-NIR and pXRF) with machine learning algorithms for sand, silt, and clay. In total, 191 soil samples were collected from the soil surface (0–30 cm) and profile wall (1 m × 1 m) from cultivated fields in Eskisehir, Central Anatolia of Türkiye. The pXRF (0–45 keV) and Vis-NIR (350–2500 nm) spectroradiometers were used to obtain soil spectra from sieved soil samples. The prediction accuracy of each soil particle size was evaluated by 54 models to explore the predictive performance. The five machine learning algorithms (elastic net, lasso, random forest, ridge, and support vector machine-linear) were applied with calibration (70% soil samples) and validation (30% soil samples) data set for each soil particle size.Results showed the dominant clay mineral in the A and C horizons is chlorite. Moderate and high prediction accuracy for sand (R2 = 0.56–0.84) and clay (R2 = 0.61–0.80), whereas only moderate prediction accuracy for silt (R2 = 0.47–0.55) using both soil spectra in the surface, profile wall, and surface + profile wall. The highest prediction accuracy for each soil particle size was achieved in the soil profile wall using Vis-NIR spectra with elastic net, which outperformed other samplings such as individual pXRF, combined both soil spectra, and other machine learning algorithms. In addition, the prediction accuracy of clay was more affected by sampling strategies compared to sand and silt. We concluded that individual Vis-NIR spectroradiometer can be utilized to achieve the highest prediction accuracy for sand, silt, and clay ratio in semiarid ecosystems for soil surveys and land use studies.
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.
This paper describes the construction of a 0.25° × 0.25° daily soil temperature (TS) data set at six soil depths (i.e., 0, 5, 10, 15, 20, and 40 cm) based on a homogenized TS at more than 2,000 ...meteorological stations across mainland of China for 1960–2017. First, at each station, the observed TS is split into a daily climatology of 1981–2010 and a daily anomaly for 1960–2017. Then, they are respectively interpolated to 0.25° × 0.25° horizontal resolution by using the thin‐plain spline and the angular distance weight interpolation methods. Finally, a gridded multilayer TS data set is constructed from the sum of the above two gridded products. Latitude, longitude, and high‐resolution digital elevation models are explicitly incorporated into the interpolation processes. Selectivity tests indicate that the optimal interpolation distance for the TS anomaly field is 500 km, where the gridded data set may have maximum coverage of the entire Chinese mainland. The results show that the gridded TS climatology is slightly lower than the station observations. The differences between gridded and the station‐based TS varies ±3°C, with relatively large in SW and TIBET. For the gridded anomaly fields, the cross‐validation shows that the mean absolute errors between gridded and station‐based TS are generally less than 0.6°C in the YZ, SW, and SC, but they are above 1.0°C in the NW and TIBET due to the sparse station distribution and large topographic relief. From 1961 to 2016, the seasonal variability of the gridded TS is generally consistent with that of the surface air temperature. The gridded TS over the majority of land displays significantly positive trends in both summer and winter (p > 95%), indicating an overall warming land surface in China. The long‐term gridded TS data not only preserves the spatial features represented in the station observations, but also provides a spatio‐temporal continuous long‐term product of mainland China. Thus, it may be used in future studies, for example, evaluation of land surface model simulations, validation of satellite retrievals, land‐atmosphere interactions, and climate change.
The construction process of a 0.25° × 0.25° daily soil temperature data set at six soil depths (i.e., 0, 5, 10, 15, 20, and 40 cm) across mainland China for the period of 1960–2017. The data sets are based entirely on the in‐situ measurements at meteorological stations, and have been strictly homogenized. The thin‐plate spline interpolation and angular distance weight interpolation methods are respectively used to interpolate the daily climatology and its anomaly of observation from station locations to the rectangle grids.
Abstract
Most massive stars are members of a binary or a higher-order stellar system, where the presence of a binary companion can decisively alter their evolution via binary interactions. ...Interacting binaries are also important astrophysical laboratories for the study of compact objects. Binary population synthesis studies have been used extensively over the last two decades to interpret observations of compact-object binaries and to decipher the physical processes that lead to their formation. Here, we present
POSYDON
, a novel, publicly available, binary population synthesis code that incorporates full stellar structure and binary-evolution modeling, using the
MESA
code, throughout the whole evolution of the binaries. The use of
POSYDON
enables the self-consistent treatment of physical processes in stellar and binary evolution, including: realistic mass-transfer calculations and assessment of stability, internal angular-momentum transport and tides, stellar core sizes, mass-transfer rates, and orbital periods. This paper describes the detailed methodology and implementation of
POSYDON
, including the assumed physics of stellar and binary evolution, the extensive grids of detailed single- and binary-star models, the postprocessing, classification, and interpolation methods we developed for use with the grids, and the treatment of evolutionary phases that are not based on precalculated grids. The first version of
POSYDON
targets binaries with massive primary stars (potential progenitors of neutron stars or black holes) at solar metallicity.
A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) ...method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs). In the presence of a general nonlinearity, the standard POD-Galerkin technique reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. The original empirical interpolation method (EIM) is a modification of POD that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD. We propose a discrete empirical interpolation method (DEIM), a variant that is suitable for reducing the dimension of systems of ordinary differential equations (ODEs) of a certain type. As presented here, it is applicable to ODEs arising from finite difference discretization of time dependent PDEs and/or parametrically dependent steady state problems. However, the approach extends to arbitrary systems of nonlinear ODEs with minor modification. Our contribution is a greatly simplified description of the EIM in a finite-dimensional setting that possesses an error bound on the quality of approximation. An application of DEIM to a finite difference discretization of the one-dimensional FitzHugh-Nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long-time integration that fully captures nonlinear limit cycle behavior. We also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results. PUBLICATION ABSTRACT
Precipitation data availability plays a crucial role in many climatic, hydrological and agricultural-related applications. In this study, the use of alternative data sources (i.e. interpolation ...methods and ERA5-Land reanalysis data) was combined for improving the spatially distributed precipitation estimates at the Simeto river basin, located in Eastern Sicily (Italy). A total of 51 rain gauges were used to generate a monthly precipitation dataset for the reference period 2002–2019. Among the 6 tested interpolation methods, Natural Neighbour was the method that predicted precipitation the best at monthly level with a Distance between Indices of Simulation and Observation (DISO) of 0.51. Radial Basis Functions and Inverse Distance Weighting provided the highest precipitation accuracies, respectively, for winter and autumn (with DISO values of 0.44 and 0.50, respectively), and for spring and summer seasons (with DISO values of 0.50 and 0.63, respectively). Underestimations on the ERA5-Land precipitation estimates were observed when compared to the most accurate interpolation methods both at monthly (25%) and seasonal temporal scales (21% in winter and summer, 36% in autumn), with the exception for spring. The performance was significantly improved when the interpolation estimates were corrected with local observations (with RMSD values ranging from 35.29 mm to 26.46 mm at monthly scale, and from 23.33–55.34 mm to 23.15–37.88 mm at seasonal level). The spatial distribution of the estimation errors associated to precipitation obtained from ERA5-Land reanalysis revealed a significant positive correlation (p value <0.05) with the altitude variation in each ERA5-Land cell within the basin under study. These results confirm the good performance on the combined use of alternative precipitation data sources, while adjustments are required to reduce site-specific uncertainties due to local microclimatic conditions occurring at the basin scale.
•Monthly precipitation was estimated most accurately by deterministic interpolators.•ERA5-Land underestimated precipitation obtained by deterministic interpolators.•BIAS correction procedure improved the accuracy of the precipitation estimates.•Topography heterogeneity worsened the accuracy of ERA5-Land precipitation estimates.
The problem of hydraulic fracturing is of great relevance to various areas and is characterised by the occurrence of complex crack patterns with bifurcations and branches. For this reason, an ...interesting approach is the modelling of hydraulic fracture using a phase-field model. In addition to the discretisation using the Finite Element Method (FEM), some works have already explored the discretisation of the phase-field model with meshfree methods, including the Smoothed Point Interpolation Methods (SPIM) family. Seeking to take advantage of the good convergence results of SPIM for phase-field modelling of brittle fractures, this paper proposes the use of SPIM for phase-field modelling of pressurised fractures. In order to limit the computational cost, a prescribed SPIM-FEM coupling is employed, with the purpose of concentrating the meshless discretisation only in the regions of expected crack propagation. The model is characterised by a constant internal pressure load along the fracture that is applied indirectly from the formulation of the phase-field model. A series of numerical simulations is presented. The aim is to evaluate the proposed model, verify the results and point out characteristics of the phase-field model with internal pressure.
•Smoothed point interpolation methods are extended to the phase-field modelling of pressurised fractures.•Coupling with the FEM is used to improve the computational efficiency.•Edge-based and cell-based smoothing domains are studied with different support node selection strategies.
Soil total phosphorus (TP) is an essential indicator to reflect the soil fertility in agricultural ecosystems. The accurate prediction of the spatial heterogeneity of TP is crucial to evaluate the ...soil productivity and quality. In this study, the interpolation methods of inverse distance weighted (IDW), radial basis functions (RBF), ordinary kriging (OK), co-kriging (COK), multiple linear regression (MLR), geographically weighted regression (GWR), regression kriging (RK), and geographically weighted regression kriging (GWRK) were used to estimate the spatial patterns of TP in four Mollisol areas with different kinds of landscapes at diverse scales. The calculation method, accuracy (mean error, mean absolute error, root mean square error and relative improvement), cost (money, labour and time), and process by which the models were established were also compared in order to ascertain the best interpolation methods to analyse and predict the spatial heterogeneity of TP in Mollisol areas. The results showed that i) generally, compared with OK, the RK and GWRK methods typically increased the simulative accuracy of the spatial distribution of TP, while IDW, COK and MLR decreased the accuracy, and RBF and GWR were not consistent at improving the accuracy in the Mollisol area; ii) the slope steepness and brightness index could be introduced to regression models as superior auxiliary variables to improve the interpolation precision (0.8%–1.9%) of TP by RK and GWRK when the study area is relatively flat; iii) the GWRK and RK methods with smaller root mean square error and higher relative improvement outperformed other methods in the region with suitable sampling evenness (>45%), while the RBF method is an optional approach when the sampling evenness is low. In summary, the GWRK and RK could be regarded as the optimal interpolation methods, despite the fact that their improvement was limited in this study. Meanwhile, when considering the cost, time and process by which the models were established, OK can also be deemed an optional interpolation method with relatively acceptable accuracy. Furthermore, the evenness and density of sample should be considered when mapping soil TP in Mollisol areas.
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•Eight interpolation methods were used to predict TP distribution in Mollisol area.•Both of GWRK and RK were the optimal methods to predict soil TP distribution.•Brightness index as auxiliary variable can improve the interpolation precision.•Slope steepness as the best auxiliary variable can improve interpolation precision.•Interpolation precision is influenced by the evenness and density of soil sampling.
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