Interpolation Of Spatial Data Research Articles

A Novel Interpolation Method for Soil Parameters Combining RBF Neural Network and IDW in the Pearl River Delta

Soil fertility is a critical factor in agricultural production, directly impacting crop growth, yield, and quality. To achieve precise agricultural management, accurate spatial interpolation of soil parameters is essential. This study developed a new interpolation prediction framework that combines Radial Basis Function (RBF) neural networks with Inverse Distance Weighting (IDW), termed the IDW-RBFNN. This framework initially uses the IDW method to apply preliminary weights based on distance to the data points, which are then used as input for the RBF neural network to form a training dataset. Subsequently, the RBF neural network further trains on these data to refine the interpolation results, achieving more precise spatial data interpolation. We compared the interpolation prediction accuracy of the IDW-RBFNN framework with ordinary Kriging (OK) and RBF methods under three different parameter settings. Ultimately, the IDW-RBFNN demonstrated lower error rates in terms of RMSE and MRE compared to direct RBF interpolation methods when adjusting settings based on different power values, even with a fixed number of data samples. As the sample size decreases, the interpolation accuracy of OK and RBF methods is significantly affected, while the error of IDW-RBFNN remains relatively low. Considering both interpolation accuracy and resource limitations, we recommend using the IDW-RBFNN method (p = 2) with at least 60 samples as the minimum sampling density to ensure high interpolation accuracy under resource constraints. Our method overcomes limitations of existing approaches that use fixed steady-state distance decay parameters, providing an effective tool for soil fertility monitoring in delta regions.

Machine Learning-Based Soil Moisture Retrieval Using CYGNSS and Interpolated SMAP Data

Abstract. Soil moisture is a crucial component of the global terrestrial ecosystem water vapor cycle, and higher spatial-temporal soil moisture product has significant impacts on research in agriculture, hydrology, and ecology. Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) is a new remote sensing technology which can be used to retrieve soil moisture. Cyclone Global Navigation Satellite System (CYGNSS), launched by NASA in 2016 to observe ocean surface hurricanes, has also collected a substantial amount of data of GNSS signals reflected over the land. This paper focuses on soil moisture retrieval using CYGNSS and SMAP dataset. In this study, three machine learning methods (GSVM, BP and RF) are used for spatial interpolation of SMAP soil moisture data. Result shows RF interpolation is the best with the RMSE of 0.044 cm3/cm3 and the CC of 0.959 compared with SMAP truly SM. Then soil moisture data after RF interpolation and conventional linear interpolation are respectively used as response variables to train the retrieval model by ELM, BP and RF machine learning methods respectively. Results show that, among the six regression models, the RF-RF regression model performs the best with the RMSE of 0.012 cm3/cm3 and the CC of 0.986. Using this model, we get a global soil moisture product and have higher temporal and spatial resolution.

Empirical Bayesian Kriging, a Robust Method for Spatial Data Interpolation of a Large Groundwater Quality Dataset from the Western Netherlands

No single spatial interpolation method reigns supreme for modelling the precise spatial distribution of groundwater quality data. This study addresses this challenge by evaluating and comparing several commonly used geostatistical methods: Local Polynomial Interpolation (LPI), Ordinary Kriging (OK), Simple Kriging (SK), Universal Kriging (UK), and Empirical Bayesian Kriging (EBK). We applied these methods to a vast dataset of 3033 groundwater records encompassing a substantial area (11,100 km2) in the coastal lowlands of the western Netherlands. To our knowledge, no prior research has investigated these interpolation methods in this specific hydrogeological setting, exhibiting a range of groundwater qualities, from fresh to saline, often anoxic, with high natural concentrations of PO4 and NH4. The prediction performance of the interpolation methods was assessed through statistical indicators such as root means square error. The findings indicated that EBK outperforms the other geostatistical methods in forecasting groundwater quality for the five variables considered: Cl, SO4, Fe, PO4, and NH4. In contrast, SK performed worst for the species except for SO4. We recommend not using SK to interpolate groundwater quality species unless the data exhibit low spatial variation, high sample density, or evenly distributed sampling.

Developing δ15N and δ13C isoscapes using whole blood from Magellanic penguins, Spheniscus magellanicus.

Understanding the migration of marine animals is hindered by the limitations of traditional tracking methods. It is therefore crucial to develop alternative methods. Stable isotope-based tracking has proven useful for this task, although it requires detailed isoscapes in the focal area. Here, we present predator-based isoscapes of the coastal zone of the Patagonian Shelf Large Marine Ecosystem (PSLME), which offers a novel tool for geolocation. Whole-blood samples from breeding Magellanic penguins nesting at 11 colonies were used to create δ15N and δ13C isoscapes. Isotopic values were assigned to random positions inside their corresponding foraging area. Spatial analysis and data interpolation resulted in δ15N and δ13C isoscapes for the coastal zone of the PSLME, which were validated through cross-validation. The isoscapes mean standard error ranged from 0.05 to 0.41 for δ15N and from 0.07 to 0.3 for δ13C, similar to the error range of the mass spectrometer used for measuring isotope ratios. Predictive surfaces reflected the latitudinal trends, with δ13C and δ15N values increasing northwards. δ13C values showed a strong latitudinal gradient, while δ15N values had two distinct domains, with higher values in the north. The error surface indicated the highest certainty within 130 km from the shore and within the reported Magellanic penguin foraging areas. Both isoscapes revealed strong spatial variation. The δ13C isoscape showed a latitudinal gradient, consistent with patterns in other oceans. The δ15N isoscape clearly separated northern and southern colonies, likely influenced by nitrogen sources. The error obtained fell within the measurement error ranges, adding credibility to the models.

Uncertainty analysis of Altantic salmon fish scale’s acoustic impedance using 30 MHz C-Scan measurements

Understanding the biomechanics of fish scales is crucial for their survival and adaptation. Ultrasonic C-scan measurements offer a promising tool for non-invasive characterization, however, existing literature lacks uncertainty analysis while evaluating acoustic impedance. This article presents an innovative integration of uncertainty into the analytical framework for estimating stochastic specific acoustic impedance of salmon fish scale through ultrasonic C-scans. In this study, the various types of uncertainties arising due to variation in biological structures and aging, measurement errors, and analytical noises are combined together in the form of uncertain reflectance. This uncertain reflectance possesses a distribution which is derived using a theory of waves by assuming suitable stochasticity in wavenumber. This distribution helps in development of a stochastic-specific acoustic impedance map of the scales which demonstrates the possible deviations of impedance from mean value depending on uncertainties. Furthermore, maximal overlap discrete wavelet transform is employed for efficient time–frequency deconvolution and Kriging for spatial data interpolation to enhance the robustness of the impedance map, especially in scenarios with limited data. The framework is validated by accurately estimating the specific acoustic impedance of well-known materials like a pair of target medium (polyvinylidene fluoride) and reference medium (polyimide), achieving over 90% accuracy. Moreover, the accuracy of the framework is found superior when compared with an established approach in the literature. Applying the framework to salmon fish scales, we obtain an average specific acoustic impedance of 3.1 MRayl along with a stochastic map visualizing the potential variations arising from uncertainties. Overall, this work paves the way for more accurate and robust studies in fish scale biomechanics by incorporating a comprehensive uncertainty analysis framework.

Hydrogeologic Framework Model‐Based Numerical Simulation of Groundwater Flow and Salt Transport and Analytic Hierarchy Process‐Based Multi‐Criteria Evaluation of Optimal Pumping Location and Rate for Mitigation of Seawater Intrusion in a Complex Coastal Aquifer System

AbstractA series of hydrogeologic framework model (HFM)‐based steady‐ and transient‐state numerical simulations is performed first using a coupled subsurface flow‐transport numerical model to analyze groundwater flow and salt transport in an actual three‐dimensional complex coastal aquifer system before and during groundwater pumping. A series of analytic hierarchy process (AHP)‐based multi‐criteria evaluations is then performed applying a multi‐criteria decision‐making approach to determine optimal pumping location and rate for a new pumping well in the complex coastal aquifer system during groundwater pumping. The complex coastal aquifer system is composed of six anisotropic fractured porous geologic media (five rock formations and one fault) and three isotropic porous geologic media (three soil formations) and shows high geometric irregularity and significant heterogeneity and anisotropy of the nine geologic media. Results of the steady‐state numerical simulations show successful model calibration with 26 measured groundwater levels and two observed seawater intrusion front lines. The latter two are determined by spatial interpolation and extrapolation of electrical conductivity logging data and electrical resistivity survey data, respectively. Based on the status and prospect of necessary water uses and available groundwater resources, the field observations of groundwater and seawater intrusion, and the analyses of the steady‐state numerical simulation after the model calibration, six candidate pumping locations are selected for the new pumping well. In addition, from six preliminary individual transient‐state numerical simulations, maximum pumping rates at the six candidate pumping locations are calculated first, and a set of six incremental candidate pumping rates is then assigned at each of the six candidate pumping locations. Results of the transients‐state numerical simulations show that groundwater flow and salt transport are spatially and temporally changed, and seawater intrusion is further intensified by groundwater pumping. In addition, the magnitudes of such spatial and temporal changes and intensification are significantly different depending on the candidate pumping locations and rates. Results of the steady‐ and transient‐state numerical simulations also show that both complexity (geometric irregularity, heterogeneity, and anisotropy including the fault) and topography have significant effects on the spatial distributions and temporal changes of groundwater flow and salt transport in the coastal aquifer system before and during groundwater pumping. In addition, results of statistical estimations of the mesh Peclet and Courant numbers confirm acceptabilities of minimizing numerical dispersion in the steady‐ and transient‐state numerical simulations. Based on the analyses of the transient‐state numerical simulations, eight multiple criteria are chosen to judge, prioritize, and rank the six candidate pumping locations and six candidate pumping rates for optimal pumping. Results of the multi‐criteria evaluations determine the optimal pumping location and rate for the new pumping well among the six candidate pumping locations and six candidate pumping rates. In addition, results of consistency checks confirm consistencies of judgments in the multi‐criteria evaluations.

The last remnants of the Italian Apennine glaciers: 3-D modeling of the Lower Calderone Glacieret by the IDW spatial interpolation of GPR data

Abstract We present a quantitative ground-penetrating radar (GPR) analysis of the Lower Calderone Glacieret to highlight the recent evolution of one of the southernmost glacial systems in Europe. The Upper and Lower Calderone Glacierets are the last two perennial ice bodies in the Apennine Mountains (Italy), and their continuous monitoring is important for glaciology, hydrology and climate science. We applied a proprietary auto-picking algorithm to track reflections accurately and objectively within three pseudo-3-D GPR data sets that were acquired over the Lower Glacieret in different years. After the time-to-depth conversion, the basal reflections were projected onto the normal versors of a 3-D topographic model of the survey area, at the different GPR trace positions. We then applied an Adjusted Inverse-Distance Weighted Spatial Interpolation method to extrapolate the ice-bedrock interface within the areas not directly covered by the GPR profiles and compare it with the topographic surface to recover the glacieret volume. In this paper, we critically examine the accuracy of the reconstructed models, including possible issues related to the challenging survey areas, such as local artifacts in the interpolated interface caused by irregular GPR coverage. We further discuss the various advantages of the implemented procedure with respect to more traditional glacier monitoring techniques.

Spatial and temporal groundwater dynamics in extreme arid basins

AbstractTo accurately obtain the spatial distribution characteristics of groundwater level in an extremely arid zone and its dynamic change patterns under the influence of human activities, based on the data of 55 groundwater observation wells in the middle and lower reaches of the Kriya River, spatial interpolation of regional groundwater level data were performed using the inverse distance weight, spline function, trend surface, and the ordinary kriging methods. The optimal interpolation method was selected by its accuracy to spatially interpolate the groundwater level data in the study area from 2019 to 2021. The results show that: (1) the ordinary kriging method has the highest interpolation accuracy (MAE = 7.1393, MRE = 0.0058, RMSE = 9.4314) and reflects the spatial and temporal variability and distribution characteristics of groundwater levels with great accuracy. (2)The relationship between surface water–groundwater recharge and discharge in different areas of the river channel in the desert section varies depending on geological structure, surface water seepage, and other elements. (3) Groundwater in the Taklamakan Desert has little effect on groundwater recharge in the Dariyabui Oasis, and changes in groundwater dynamics in the oasis are predominantly influenced by surface runoff. (4) Monthly changes in groundwater levels in the Yutian Oasis are continuous, with ‘V’ shaped fluctuations, a declining trend in the southern part, no significant change in the central part, and a slight increase in the northern part. These results contribute to the sustainable management of water resources in the Kriya River Basin, provide a basis for groundwater prediction, and offer a reference for studies of other, similar extreme desert area basins.

Geotechnical investigation measures and techniques in construction engineering based on multi-source data fusion

Abstract 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.

Improvement of the multi-source weighted-ensemble precipitation dataset and application in the arid area of Tianshan Mountains, central Asia

With high resolution and wide coverage, satellite precipitation products like the Multi-Source Weighted Ensemble Precipitation (MSWEP) could support hydrological research in arid regions, where the spatial heterogeneity of precipitation is high, but rain gauges are sparse, but these products are inevitably subject to errors. In this study, we integrated measured precipitation and topographic data, and improved MSWEP by interpolation and an optimal regression model. The Tianshan Mountain area was taken as a typical arid area, and spatial stratified heterogeneity of precipitation was analyzed. The results show that: (1) The optimal regression model combined the advantages of site interpolation and MSWEP and improved the underestimation of precipitation in mountainous areas; (2) The precipitation decreased from West to East, and from North to South, and the precipitation in West and East subregions increased linearly with the elevation. The maximum precipitation height zone in the North is located at 4300 m. There are two maximum precipitation height zones in the South; (3) The accuracy of spatial interpolation of station data was limited by the uneven distribution of the stations in the East subregion, and the inaccuracy of MSWEP was due to the land cover and topography of the North and South subregions. The improved MSWEP (IMMSWEP) not only resolved the problem of lack of rainfall stations in arid area, but also resulted in an inversion of regional spatial precipitation differentiation with high resolution and high precision, providing a reference for meteorological researchers.

Analysis of Mixing Patterns of River Confluences through 3D Spatial Interpolation of Sensor Measurement Data

Aquatic environmental problems, such as algae, turbid water, and poor oxygen content, have become increasingly common. In river analysis, hydrological and water quality characteristics are used for evaluating aquatic ecological health, which necessitates continuous monitoring. In addition, because measurements are conducted using a fixed measurement method, the hydrological and water quality characteristics are not investigated for the entire river. Furthermore, obtaining high-resolution data is tedious, and the measurement area and time are limited. Hence, low-resolution data acquisition is generally preferred; however, this requires an appropriate interpolation method to obtain a wide range of data. Therefore, a 3D interpolation method for river data is proposed herein. The overall hydraulic and water quality information of a river is presented by visualizing the low-resolution measurements using spatial interpolation. The Kriging technique was applied to the river mapping to improve the mapping precision through data visualization and quantitative evaluation.

Cephy: Astand-alone, free and open-source toolkitfor hydrocarbon in place evaluation by ordinary kriging

Cephy is a software toolkit written inJava that enables the user to perform spatial interpolation of subsurface data by ordinary kriging. Key features of the software include data exploration by map plot with symbol dimension proportional to the magnitude of the property at a given location;variogram modeling and interpolation of petrophysical properties;as well as oil in placeestimationper area unit throughout the reservoir. Cephy enables the user to define the tolerance and the minimum number of pairs required to validate the experimental variogram of the corresponding lag distance when learning the relationship between geolocated data. The software is entirelymade of a graphical user interface for adjusting the variogram modeling parameters and visualizing the subsequent interpolationally-generated map.Cephy is applied on Kinkasi reservoir in Kinkasi field (Coastal basin of DR Congo) to demonstrate its functionalities. The result supports a better understanding of oil distribution throughout the reservoir and can be used as a baseline forthesuggestion of new infill drilling locations.

Development of a ZTD Vertical Profile Model Considering the Spatiotemporal Variation of Height Scale Factor with Different Reanalysis Products in China

Tropospheric delay is one of the key factors that may affect high-precision satellite navigation and positioning and water vapor retrieval performance. Its variation in the vertical direction is much greater than that in the horizontal direction. Therefore, the vertical profile model of zenith total delay (ZTD) is important for the spatial interpolation of high-precision ZTD products and the development of ZTD models. However, in China, low spatial and temporal resolutions remain persistent in ZTD vertical profile models and limit their application. In this study, ZTD vertical profile grid models (CZTD-H model: CZTD-HM and CZTD-HE models) were developed by considering the time-varying height scale factor for China and employing ZTD layered profile information with high temporal-spatial resolution calculated using MERRA-2 data and ERA5 data based on the integration method during 2012–2016. The CZTD-H model accuracy was verified using the global navigation satellite system (GNSS) data acquired from the Crustal Movement Observation Network of China (CMONOC) and radiosonde data as reference and was compared with the canonical GPT3 model accuracy. The applicability of CZTD-HM and CZTD-HE models was discussed. The results showed that: (1) CZTD-HM and CZTD-HE models exhibited excellent performance for ZTD layered vertical interpolation in northwestern and southeastern China, respectively. Among ZTD layered profiles from 84 radiosonde stations, the RMSE of ZTD data interpolated using CZTD-HM and CZTD-HE models improved by 12.9/16.23% and 13.8/17.16% compared with GPT3-1 and GPT3-5 models, respectively. (2) The CZTD-H model maintained high performance for the spatial interpolation of GGOS grid ZTD data. Validation with ZTD data from 249 GNSS stations showed that the RMSEs of both CZTD-HM and CZTD-HE models improved by 2.8 mm (19.7%) and 2.6 mm (18.6%) compared with those of the GPT3-1 and GPT3-5 models, respectively. The CZTD-HE model showed excellent performance in summer among all the models. Only the location and day of the year were required for the application of the CZTD-H model, which showed excellent ZTD vertical correction performance in China. With the different performances of the CZTD-HE and CZTD-HM models in China, the ERA5 model can be recommended for practical applications. Therefore, these results can provide a reference for the data source selection of ZTD vertical profile model construction on the basis of high-precision reanalysis data, GNSS real-time high-precision positioning, and GNSS meteorology in China.

Conjugate sparse plus low rank models for efficient Bayesian interpolation of large spatial data

AbstractA key challenge in spatial data science is the analysis for massive spatially‐referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance matrices that lack computationally exploitable structures. Recent developments in spatial statistics offer a variety of massively scalable approaches. Bayesian inference and hierarchical models, in particular, have gained popularity due to their richness and flexibility in accommodating spatial processes. Our current contribution is to provide computationally efficient exact algorithms for spatial interpolation of massive data sets using scalable spatial processes. We combine low‐rank Gaussian processes with efficient sparse approximations. Following recent work by Zhang et al. (2019), we model the low‐rank process using a Gaussian predictive process (GPP) and the residual process as a sparsity‐inducing nearest‐neighbor Gaussian process (NNGP). A key contribution here is to implement these models using exact conjugate Bayesian modeling to avoid expensive iterative algorithms. Through the simulation studies, we evaluate performance of the proposed approach and the robustness of our models, especially for long range prediction. We implement our approaches for remotely sensed light detection and ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska.

A generalised severity number to predict liquefaction damage with lateral spreading

This study introduces a generalisation of the classical one-dimensional liquefaction severity indexes to extend their predictive capability for the occurrence of lateral spreading. After a critical overview of the most used indexes, the rationale for extension to bi-dimensional conditions determined by non-horizontal geomorphology is presented, together with the rule to achieve generalisation. The efficacy of the new index is demonstrated with a performance-based study on two cases, the earthquakes of 20 May 2012 (Mw 6·1) at Terre del Reno (Emilia-Romagna, Italy) and 11 February 2011 (Mw = 6·2) at Christchurch (New Zealand). Stratigraphic attributes including thickness, depth, composition and relative density of the liquefiable layers, obtained over the whole territories from rich datasets of cone penetration tests, are coupled with topographic information derived from the digital elevation model to provide the input for the analysis. Consistency assessment and spatial interpolation of data are carried out with geostatistical tools implemented in a geographic information system platform. Validation against a post-earthquake damage survey, quantified with a binary classification method, shows the paramount role of the bi-dimensional conditions.

Spatial particle size distribution at intact sample surfaces of a Dystric Cambisol under forest use

Abstract The idea of the present study is to describe the spatially varying particle size distribution (PSD) along intact aggregate surfaces with the laser diffraction method (LDM) of four silty-loamy and OC enriched horizons of a Dystric Cambisol from the Uhlířská catchment (Czech Republic) with the laser diffraction method (LDM). Besides, the comparability of the LDM with the sieve and pipette method (SPM), the reproducibility, and the effect of pretreatment on the particle size distribution derived by LDM were analysed. The laser diffraction method enables rapid and continuous particle size distribution measurements with required sample amounts of 0.1–0.2 g for each measurement compared to 5–20 g for SPM. The LDM-derived PSD’s can be directly compared with the standardised SPM-derived PSD’s by using regression analysis with coefficients of determination (r2) between 0.83 and 0.93. Sample pretreatment following standardised proceedings indicates a better comparability between the particle size distributions of both methods. Besides, the highest coefficients of variation of up to 78.6 and therefore the lowest reproducibility were found for the unpretreated PSD of the AE and Bs horizon. Thus, limited evaluability and reproducibility of soil material enriched in organic carbon (OC), used in the current study, needs further analysis. For spatial analysis of PSD’s along intact surfaces of soil aggregates and profiles, spatial data interpolation by inverse distance weighting (IDW), kriging, and triangulated irregular networks (TIN) can be used for detailed measuring, mapping, and spatial extension of the sand, silt, and clay fractions at unsampled locations using a set of samples of known locations. The information offers the possibility of comparing and verifying data obtained by non-invasive mid-infrared spectroscopy and Vis–NIR spectroscopy by spatial extension for given soil aggregates and profiles.

Weekly Monitoring and Forecasting of Hydropower Production Coupling Meteo-Hydrological Modeling with Ground and Satellite Data in the Italian Alps

This paper presents a system for supporting hydropower production on mountainous areas. The system couples the outputs of a numerical weather prediction model and a snow melting and accumulation temperature-based model. Several procedures are presented for interpolating meteorological variables and calibrating and validating model parameters that can be generalized to any other mountainous area where the estimation of current and forecasted snow water equivalent and melting amount is required. The system reliability has been assessed through the validation of three components: spatial interpolation of meteorological data, mathematical modeling, and quantitative meteorological forecast. The results show that good accuracy of meteorological data spatial interpolation can be achieved when the data from snow gauges are used for assessing the precipitation lapse rate at higher altitudes, and the temperature lapse rate is computed from data at each time step. The temperature-based hydrological model proved to be effective in simulating lake inflow water volume and energy production. No clear result has been found for snow melt forecast due to the difficulties in providing reliable quantitative weather forecast in complex alpine area.

Pengembangan Sistem Informasi Manajemen Persuratan di Badan Informasi Geospasial

<em><span>Interpolation is a method to predict new data from existing data. The interpolation method can be used in estimating rainfall because each interpolated point is influenced by the value of the surrounding points. Isohyets are imaginary lines that describe the same amount of rainfall in an area. This map is the result of spatial interpolation of rainfall data. In addition to calculating regional rainfall, an isohyet map can also be used to see the pattern of annual rainfall that occurs. The purpose of this study is to make a map of rainfall in West Java Province so that it can analyze its distribution. The research method used is Waterfall. research conducted at the Meteorology, Climatology and Geophysics Agency regarding the making of rainfall maps in the West Java region on average tenths of a day or based on a map layout using the IDW method that the resulting rainfall pattern is different every tenth of a day. For the level of rainfall (mm) an average of tenths of a day, it can be concluded that in October – March is the rainy season with high rainfall (mm). Meanwhile, April-May is the transition season, namely the escape between the rainy season and the dry season which is in the medium level of rainfall (mm). June – September is the dry season because the level of rainfall (mm) is at a low level</span></em>

Spatial agents for geological surface modelling

Abstract. Increased availability and use of 3D-rendered geological models have provided society with predictive capabilities, supporting natural resource assessments, hazard awareness, and infrastructure development. The Geological Survey of Canada, along with other such institutions, has been trying to standardize and operationalize this modelling practice. Knowing what is in the subsurface, however, is not an easy exercise, especially when it is difficult or impossible to sample at greater depths. Existing approaches for creating 3D geological models involve developing surface components that represent spatial geological features, horizons, faults, and folds, and then assembling them into a framework model as context for downstream property modelling applications (e.g. geophysical inversions, thermo-mechanical simulations, and fracture density models). The current challenge is to develop geologically reasonable starting framework models from regions with sparser data when we have more complicated geology. This study explores the problem of geological data sparsity and presents a new approach that may be useful to open up the logjam in modelling the more challenging terrains using an agent-based approach. Semi-autonomous software entities called spatial agents can be programmed to perform spatial and property interrogation functions, estimations and construction operations for simple graphical objects, that may be usable in building 3D geological surfaces. These surfaces form the building blocks from which full geological and topological models are built and may be useful in sparse-data environments, where ancillary or a priori information is available. Critical in developing natural domain models is the use of gradient information. Increasing the density of spatial gradient information (fabric dips, fold plunges, and local or regional trends) from geologic feature orientations (planar and linear) is the key to more accurate geologic modelling and is core to the functions of spatial agents presented herein. This study, for the first time, examines the potential use of spatial agents to increase gradient constraints in the context of the Loop project (https://loop3d.github.io/, last access: 1 October 2021​​​​​​​) in which new complementary methods are being developed for modelling complex geology for regional applications. The spatial agent codes presented may act to densify and supplement gradient as well as on-contact control points used in LoopStructural (https://www.github.com/Loop3d/LoopStructural, last access: 1 October 2021) and Map2Loop (https://doi.org/10.5281/zenodo.4288476, de Rose et al., 2020). Spatial agents are used to represent common geological data constraints, such as interface locations and gradient geometry, and simple but topologically consistent triangulated meshes. Spatial agents can potentially be used to develop surfaces that conform to reasonable geological patterns of interest, provided that they are embedded with behaviours that are reflective of the knowledge of their geological environment. Initially, this would involve detecting simple geological constraints: locations, trajectories, and trends of geological interfaces. Local and global eigenvectors enable spatial continuity estimates, which can reflect geological trends, with rotational bias, using a quaternion implementation. Spatial interpolation of structural geology orientation data with spatial agents employs a range of simple nearest-neighbour to inverse-distance-weighted (IDW) and quaternion-based spherical linear rotation interpolation (SLERP) schemes. This simulation environment implemented in NetLogo 3D is potentially useful for complex-geology–sparse-data environments where extension, projection, and propagation functions are needed to create more realistic geological forms.

Comparative Analysis of Different Spatial Interpolation Methods Applied to Monthly Rainfall as Support for Landscape Management

Landscape management requires spatially interpolated data, whose outcomes are strictly related to models and geostatistical parameters adopted. This paper aimed to implement and compare different spatial interpolation algorithms, both geostatistical and deterministic, of rainfall data in New Zealand. The spatial interpolation techniques used to produce finer-scale monthly rainfall maps were inverse distance weighting (IDW), ordinary kriging (OK), kriging with external drift (KED), and ordinary cokriging (COK). Their performance was assessed by the cross-validation and visual examination of the produced maps. The results of the cross-validation clearly evidenced the usefulness of kriging in the spatial interpolation of rainfall data, with geostatistical methods outperforming IDW. Results from the application of different algorithms provided some insights in terms of strengths and weaknesses and the applicability of the deterministic and geostatistical methods to monthly rainfall. Based on the RMSE values, the KED showed the highest values only in April, whereas COK was the most accurate interpolator for the other 11 months. By contrast, considering the MAE, the KED showed the highest values in April, May, June and July, while the highest values have been detected for the COK in the other months. According to these results, COK has been identified as the best method for interpolating rainfall distribution in New Zealand for almost all months. Moreover, the cross-validation highlights how the COK was the interpolator with the best least bias and scatter in the cross-validation test, with the smallest errors.