A variety of spatial interpolation methods have been proposed to allow better understanding of the spatial distribution of an area covered by existing observed points. Basically, spatial interpolation becomes a standard tool for geographic information system (GIS) software and plays an important role in Digital Earth (DE) research [1
]. Due to the continuous accumulation of historical data and the societal need for the analysis of variables that vary in space and time, such as weather and air quality variables, the collection and processing of spatiotemporal data is rapidly increasing [2
]. Researchers have begun to pay attention to the space–time interpolation problem to estimate the spatial and temporal variation characteristics of various spatial elements after time dimension integration and to provide support for decision-making. In recent years, the theoretical aspects of spatiotemporal geostatistics have made great progress [3
], but there are still some application problems. Spatiotemporal models are more complex than pure spatial models, and the operations involved in spatiotemporal models are much more expensive.
For these reasons, many scholars have studied the space–time interpolation problem. With the help of existing methods, some scholars have tried to improve time and space interpolations. For example, the kriging method is used for the best, unbiased, optimal estimation of regionalized sampling point variables using the structural features of observations with known spatial distributions. Although originally developed for geostatistics, the kriging method is now widely used in geology [4
], hydrology [5
], meteorology [6
], environmental science [7
] and other disciplines. However, in the real world, many geographical phenomena have temporal and spatial evolution processes. As a spatial interpolation method, kriging often ignores the important information about the time dimension in the problem, which is not conducive to further improving the accuracy of the interpolation.
Through the evolution of regionalized variables into spatiotemporal regionalized variables, scholars established spatiotemporal variogram models [8
], which can achieve the spatial and temporal extension of kriging interpolation. To date, spatiotemporal kriging interpolation has been applied in many fields. Raja et al. [9
] used spatiotemporal kriging interpolation to research the trends of spatiotemporal variation in regional precipitation, which can be used to plan and manage water resources in areas that are heavily dependent on precipitation. Yang et al. [10
] assessed the sources and spatiotemporal trends of heavy metal accumulation in soil using the spatiotemporal kriging method and provided suggestions for the prevention and control of heavy metal pollution in soil. Jost et al. [12
] used an interpolation method to determine the distribution of a forest ecosystem and the water storage layer near the desert; their method can assist groundwater managers to make correct decisions. Park et al. [14
] used the spatiotemporal kriging method to more accurately estimate the spread of air pollutants and the distribution of infectious diseases, adding to omissions in the data collection process.
With the expansion of interpolation algorithms in the time dimension, it is necessary to acquire sample points at different times and to obtain the time trend of the study area. As a result, the number of sampling points increases linearly and interpolation algorithms require large computation and storage resources; the algorithms are slow and inefficient on traditional personal computers (PCs), which is not conducive to the use of applications.
With the development of computing technology, high-performance computing (HPC) technology has been gradually integrated into the field of geographic information, which has improved the application, promotion and development of the field. Multiple processors, parallel clustering, grid computing, graphic processing unit (GPU) incorporation and other high-performance computing technologies have attracted much research attention in the geosciences field [16
]. In recent years, parallel computing has mainly appeared in the form of multi-core processors [19
]. A GPU has a large number of cores, which makes up for the shortcomings of the traditional central processing unit (CPU) architecture.
High-performance GIS computing algorithms are a research hotspot that is mainly divided into two aspects. One aspect is the optimization of processing from the technical level, parallel to existing high-density computing, to improve operational efficiency. The second aspect is the exploration of a new spatiotemporal analysis model using modeling and algorithms to develop a more efficient and convenient spatiotemporal analysis model.
To represent the spatial interpolation model by the kriging interpolation method in the technical level of optimization and new space interpolation algorithm improvement, scholars have begun to use GPUs to reduce computing time and introduce mature parallelization schemes. Cheng [20
] accelerated the universal kriging algorithm on the NVIDIA Compute Unified Device Architecture (CUDA) platform and achieved a nearly 18-fold speed increase with respect to the sequential program. Liu [21
] used the computation power of modern programmable graphics hardware (GPU) for 3D visualization in a reservoir modeling system. In terms of algorithms and model improvements, Liu [22
] proposed an algorithm based on the k-d tree method to address the unevenly distributed spatial data. Hu et al. [23
] proposed an fast Fourier transform (FFT)-based parallel algorithm to accelerate regression kriging interpolation, which was computed on a GPU device. As far as we know, spatiotemporal kriging is an improved method for spatiotemporal interpolation; however, the model and the algorithm have changed, and the original parallel method cannot adapt.
Although many people pay attention to the general spatial analysis of GIS, the support of spatiotemporal interpolation and efficiency improvement calculations lack in-depth research. To solve the above problems, the spatiotemporal kriging algorithm was analyzed, data associations were decoupled and parallelized, and a parallel algorithm of spatiotemporal kriging interpolation was proposed. The parallel model of the space–time interpolation is tested with meteorological data in this paper. The purpose of this paper is to propose a new space–time interpolation algorithm and technology supported by HPC, which will provide new research ideas for GIS spatiotemporal analysis modeling and the enrichment of GIS research contents.
This article is arranged as follows: in the first and second parts of Section 2
, we introduce the spatiotemporal kriging algorithm and the space–time extension in detail. The third part of Section 2
focuses on the design of the parallel spatiotemporal kriging algorithm and implementation by the OpenCL framework. In Section 3
, the experimental results and analysis are given. Section 4
presents the conclusion.
In the study of large-scale spatiotemporal phenomena, there are often missing data. The application of spatiotemporal kriging interpolation to spatiotemporal data interpolation can complement the missing historical data. It is beneficial to obtain the evolution process of temporal and spatial phenomena, which can improve the cognitive level of scholars and establish a spatiotemporal database.
In this paper, to address the shortage of space–time interpolation computing resource consumption and slow speed, a parallel accelerated algorithm based on OpenCL for spatiotemporal kriging interpolation is proposed, which solves the problem. The time dimension of the data is added to rationally and realistically improve the original spatial interpolation.
The experiments described showed that the method proposed in this paper can greatly improve the interpolation speed, and it can achieve fast computation of spatiotemporal kriging interpolation on a standard PC when compared with some of the existing solutions. The proposed method has great improvement in usability, experience and universality.
In future research, we will expand to other spatiotemporal interpolation methods with the help of this research method and run the interpolation algorithm on different heterogeneous computing platforms. At the same time, we will also expand the type and quantity of the experimental data as well as further improving and promoting the results of this paper.