Wenjun Wu, Ruijie Gan, Junli Li, Xiu Cao, Xinxin Ye, Jie Zhang, Hongjiao Qu, "A Spatial Interpolation of Meteorological Parameters considering Geographic Semantics", Advances in Meteorology, vol. 2020, Article ID 9185283, 14 pages, 2020. https://doi.org/10.1155/2020/9185283
A Spatial Interpolation of Meteorological Parameters considering Geographic Semantics
Wenjun Wu,^{1,2}Ruijie Gan,^{1,3}Junli Li,^{1,4}Xiu Cao,^{1}Xinxin Ye,^{4}Jie Zhang,^{1} and Hongjiao Qu^{1}
^{1}School of Resources and Environment, Anhui Agricultural University, Hefei 230036, China
^{2}Huangshan Meteorology Bureau, Huangshan, Anhui 245000, China
^{3}Nanchang Meteorological Administration, Nanchang, Jiangxi 330038, China
^{4}Anhui Province Key Lab of Farmland Ecological Conservation and Pollution Prevention, Hefei 230036, China
Academic Editor: Maria Ángeles García
Received27 Aug 2019
Revised26 Mar 2020
Accepted12 Aug 2020
Published02 Sep 2020
Abstract
Spatial interpolation of meteorological parameters, closely related to the earth surface, plays important roles in climatological study. However, most of traditional spatial interpolation methods ignore the geographic semantics of interpolation sample points in practical application. This paper attempts to propose an improved inverse-distance weighting interpolation algorithm considering geographic semantics (S-IDW), which adds geographic semantic similarity to the traditional IDW formula and adjusts weight coefficient. In the interpolation process, the geographic semantic differences between sample points and estimation points are considered comprehensively. In this study, 3 groups of land surface temperature data from 2 different areas were selected for experiments, and several commonly used spatial interpolation methods were compared. Experimental results indicated that S-IDW outperformed IDW and several existing spatial interpolation methods, but there were also some abnormal value and interpolation outliers. This method provides a new insight toward the estimation accuracy, data missing, and error correction of spatial attributes related to meteorological parameters.
1. Introduction
Spatial interpolation of meteorological parameters is to obtain relatively accurate descriptions of spatial attributes related to climatological dynamics and weather patterns by using some reasonably located samples [1]. Traditionally, sampling observation is the best way to obtain the regional mean conditions in order to ensure equal sampling opportunities for each location in the region. However, the observation sampling points are sparse and of random distribution in practical application [1]. For example, the location of the sample points is systematic and changes smoothly. Furthermore, most meteorological models are obtained by sampling from observation stations at present. Spatial interpolation method is widely used to transform discrete observation data into continuous surface so as to better measure the spatial distribution pattern of data elements [2]. Currently, familiar spatial interpolation methods, such as IDW, Kriging, Spline, and trend surface method, have been widely used in different fields. Most of them have some limitations in application, such as distance weighting method with some problems, which affects calculation results due to distance, being not suitable for a large range [3]. Kriging method can adopt different variogram forms and parameters for different sampling data points, with certain flexibility. However, it loses the high efficiency of the original inverse-distance weighting method by first determining the variogram form and fitting the parameters of variogram. Kriging variograms require artificial selection, and there exists the problem that computation increases sharply when there are too many combinations of variograms [4]. Spline method is not suitable for sparse and finite sampling points and is often used for high-density sample point interpolation [5]. The trend surface method relies more on the existing spatial distribution trend of interpolation elements [6]. Consequently, many authors have carried on the continuous exploration and improvement to the spatial interpolation method [7]. For instance, the complexity of terrain and elevation factor were introduced by some researchers into the inverse-distance weighting [8, 9], and Li et al. brought the harmonic weighting coefficient of azimuth into the distance weighting interpolation [2]. The natural neighborhood relationship was led into the distance weighting interpolation [10], and some authors introduced the fuzzy trigonometric function into the distance weighting interpolation [3]. Others took into account the spatiotemporal variation characteristics of geographical factors and introduced time-series data to remove some numerical fluctuations in time, such as spatiotemporal weighting Kriging and spatiotemporal inverse-distance weighting interpolation [9]. The succession of methods proposed by the above-mentioned authors had achieved remarkable academic impact and showed high spatial autocorrelation, but most of them were based on numerical interpolation methods, without considering geographic semantics.
Inspired by the gradient theory in the field of image processing, the gradient is the first-order differential of gray value, reflecting the change rate between adjacent pixels in the direction of X and Y [11]. Where the gradient change rate of image is larger in the region, the types of land cover tend to change, such as the boundary between land and water in the image. Existing research based on remote sensing image inversion, such as land surface temperature (LST), vegetation index, and moisture index, is to some extent a model to describe the relationship between remote sensing signals or remote sensing data and surface applications [12]. For example, the temperature nearby residential buildings is quite different from forest land or water body. The air temperature of some exposed land surfaces, like build roofs and pavement, is hotter than that of the shades of forests. Therefore, geographic semantics are indispensable to exploring geospatial description of surface remote sensing pixel information. Currently, some authors have put forward semantic Kriging method, which has achieved excellent research results, but there are still some problems such as the complexity of calculating the variogram imported by the semantic similarity [13–15]. In addition, the prediction of multivariable meteorological factors by embedding geographic semantics into Bayesian networks weakens the influence of parameter uncertainty but lacks the knowledge of meteorological modeling [16]. Although the aforementioned spatial interpolation methods show performance in different applications, there still exists scope of improvements by introducing geographic semantics into spatial interpolation process. Furthermore, information semantics are growing in the field of spatial statistics and environmental modeling [17, 18].
This paper attempts to introduce the geographic semantics into inverse weighting spatial interpolation by embedding hierarchical geographic semantics into spatial interpolation model and using semantic similarity to measure factor weight. The following analyses were carried out in this study: (1) the S-IDW methods used in this study are explained in the next section; (2) the findings are discussed in the Experimental Results and Comparison section; (3) finally, our conclusions and subsequent research are drawn in the Conclusions section.
2. Methodology
The S-IDW integrates the geographic semantic knowledge into the inverse-distance weighting interpolation method. Considering the effect of distance on interpolation results, the influence of land-use type on land surface temperature interpolation is added. The S-IDW reconsiders the interpolation weight, increases the weight of the same land-use type, and reduces the weight of different land-use types on the basis of distance, constructing the S-IDW method [19].
In the S-IDW, the first step is to calculate the semantic similarity of geographic entities. The formula is as follows:
In equations (1)–(4), is the estimated value of the th point to be interpolated; is the measured value of the th discrete point; is the distance between the th discrete point and the th point to be interpolated; is the latitude of the point to be interpolated; is latitude of discrete points; is the longitude of the point to be interpolated; is the longitude of the discrete point; is the number of measured sample points participating in the interpolation; is the power exponent, which controls the degree to which the weight coefficient decreases with the increase of the distance between the point to be interpolated and the sample point. When is larger, the closer sample point is endowed with higher weight; when is smaller, the weight is more evenly distributed to all sample points. When , it is called inverse-distance weighting method, which is a common and simple spatial interpolation method. When , it is called inverse-distance squared method, which is often used in practical application. In this study, is taken.
is the semantic similarity between the th point to be interpolated and the th discrete point, and the value range is . Semantic similarity refers to the degree to which two concepts can replace each other in the same context without changing the semantic structure of the text [19]. The larger the change of semantic structure, the smaller the similarity; the smaller the change of semantic structure, the greater the similarity. In this study, a comprehensive semantic similarity algorithm for geographic ontology is adopted. On the basis of analyzing the influencing factors of semantic distance similarity, the weighted sum method is used to calculate semantic distance similarity, concept attribute similarity, and information similarity. The calculation formula is as follows [20]:
The semantic similarity is calculated by referring to the hierarchical structure of geographical entities in Table 1 and Figure 1. In formulas (5)–(8), is the semantic distance, which refers to the shortest path between any two concept nodes and b in the ontology hierarchy, and is the regulating factor. In this paper, = 8. represents the similarity of concept attributes between concept nodes and b. The function is the set of entity attributes, and is the number of attributes. In addition, , is a real number, and its value is controlled at [0, 2max (IC (a, b))], where . The information quantity is defined as the function of the occurrence probability of concept a. In equation (5), when the land-use types of the th point to be interpolated and the th discrete point are equivalent,; when the land-use types of the th point to be interpolated and the th discrete point are not equivalent, .
Geographic entities
Parent class
Parent use
Specific uses
Cover (or location)
Operational characteristics
01 Farmland
Land
Agricultural production
Planting crops
Crops
02 Garden plot
Land
Agricultural production
Planting and collecting fruit, leaf, and root crops
Perennial woody plants and herbs
Intensive management
03 Woodland
Land
Agricultural production
Growing trees, bamboos, shrubs, and coastal mangroves
Woody plants
Production management, ecological management
04 Grassland
Land
Agricultural production
Growing herbs
Herbs
05 Commercial land
Land
Building construction
Constructing business and service industry
Houses, buildings
06 Industrial mining warehouse land
Land
Building construction
Constructing industrial production and material storage sites
Houses, buildings
07 Residential land
Land
Building construction
Constructing living places
Houses, buildings
08 Public management and service land
Land
Building construction
Constructing public management and public service places
Houses, buildings
09 Special land
Land
Building construction
Building construction
Houses, buildings
10 Transport land
Land
Building construction
Constructing ground routes and stations for transport
State-owned
11 Waters and water conservancy facility land
Land
Hydraulic structures of land waters, shallows, ditches, and marshes
12 Other lands
Land
In equation (5), ,, and ;, and are the adjustment coefficients of semantic distance similarity, concept attribute similarity, and information similarity, respectively; . and are geographical entities. For the convenience of calculation, GB/T21010-2017 classification of land use in China and its meaning are used to extract geographical entities. The semantic attributes of geographical entities are shown in Table 1, and the ontological hierarchical network structure of land-use status classification is shown in Figure 1. Based on equation (5), the semantic similarity for some geographical entities of land-use type ontology is calculated as shown in Table 2.
Geographic entities
01 Farmland
02 Garden plot
03 Woodland
04 Grassland
07 Residential land
10 Transport land
11 Waters and water conservancy facility land
01 Farmland
1
0.4198
0.4218
0.4198
0.2576
0.2628
0.2632
02 Garden plot
0.4198
1
0.4229
0.4207
0.2585
0.264
0.2645
03 Woodland
0.4218
0.4229
1
0.4229
0.2597
0.2667
0.2665
04 Grassland
0.4198
0.4207
0.4229
1
0.2585
0.264
0.2645
07 Residential land
0.2576
0.2585
0.2597
0.2585
1
0.4212
0.2616
10 Transport land
0.2628
0.264
0.2667
0.264
0.4212
1
0.2685
11 Waters and water conservancy facility land
0.2632
0.2645
0.2665
0.2645
0.2616
0.2685
1
3. Experimental Results and Comparison
3.1. Experimental Design and Error Metric
The experimental study has been carried out using land surface temperature (LST) data from Landsat 8 OLI-TIRS satellite. Due to the complex and changeable surface environment, LST shows different characteristics in different surface environments. In order to explore the spatial interpolation accuracy in different areas and different land surface temperatures, LST at diverse time intervals were selected in the 2 study areas, and 3 distinct LST conditions of high temperature, low temperature, and normal temperature were used to carry out experiments. The interpolation accuracy of traditional numerical interpolation methods is often closely related to the density and sparsity of the discrete points. In this paper, the discrete points and the points to be valued are selected randomly and distributed evenly. 15 points to be valued and 60 discrete points were randomly selected in the experiment. Assuming that the LST values of the 15 points are missing or abnormal, we use 60 discrete points of known LST values to interpolate the 15 points in order to compensate for and correct the missing or abnormal values. The popular approaches for spatial interpolation include Kriging, IDW, Natural, Spline, and S-IDW. On this basis, we compared and analyzed the results of 5 interpolation methods with the original LST values of 15 points to be valued. As shown in Figure 2, the experimental flow chart of semantic inverse-distance weighting interpolation is shown.
In the experiment, the accuracy of the estimated value is evaluated by means of root mean squared of errors (RMSE) [21], mean absolute error (MAE), mean absolute percentage error (MAPE) [16], and the ratio of variance of the estimated values to variance of the observed values (RVAR) [22, 23]. The formal definition of each indicator is given as follows:
In formulas (10)–(13), is the total number of measured values; is the measured value of the th discrete point; is the estimated value of the th point to be interpolated; is the average value of measured value at discrete point; is the average value of the estimated value of the point to be evaluated; is the variance of the estimated value of the point to be interpolated; is the variance of measured value at discrete point. The best fitting between measured value and estimated value under ideal conditions can be obtained as follows: RMSE≈0, MAE≈0, MAPE≈0, and RVAR≈1.
3.2. Analysis and Discussion of the Interpolation Results in Study Area-1
In order to verify the interpolation effect of S-IDW under three temperature environments, the imaging dates of the remote sensing images in study area-1 are January 11, 2018, April 17, 2018, and August 9, 2013. The corresponding image clouds are 0.54%, 0.05%, and 4.76%, respectively. Under these conditions, LST inversion is carried out and the inversion data are extracted and processed. The distribution of 60 discrete points and 15 points to be valued in study area-1 is shown in Figure 3.
Interpolation data results and interpolation accuracy of five methods under low-temperature conditions in study area-1 can be seen in Tables 3–5. As shown in Table 3, the interpolation results of S-IDW for 8 of the 15 points to be valued are closer to the land surface temperature than those of the other 4 interpolation methods. Generally, through the mathematical statistics analysis and Pearson correlation analysis of the five interpolation methods, it is indicated that the MAE, MAPE, and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than the other 4 interpolation methods. As far as RVAR is concerned, Natural and Spline are better than S-IDW, but S-IDW is better than Kriging and IDW. In terms of Pearson correlation, the results of S-IDW, Kriging, IDW, and Natural interpolation are significantly correlated with LST at 0.01 level (two-tailed), of which the correlation coefficient r between S-IDW interpolation results and LST is 0.959, with the strongest correlation, and the significant correlation coefficient r between Spline interpolation results and LST was 0.616 at 0.05 level (two-tailed), with the weakest correlation.
Study area-1
Forecast date: January 11, 2018
Forecasting methods (unit of temperature: °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
31.743
115.91
1.428
1.76
1.552
1.572
1.577
1.356
2
Farmland 2
31.688
115.974
3.624
2.569
2.641
2.695
2.604
2.234
3
Farmland 3
31.682
115.876
2.394
1.924
1.909
2.305
2.294
2.028
4
Farmland 4
31.671
115.924
2.429
2.43
2.852
2.97
2.741
2.003
5
Woodland 1
31.745
115.947
2.186
1.840
1.729
1.544
1.507
1.306
6
Woodland 2
31.741
115.792
1.163
1.116
0.914
0.933
0.897
0.953
7
Woodland 3
31.731
115.848
1.226
1.533
1.483
1.323
1.296
0.573
8
Woodland 4
31.685
115.722
1.282
1.231
0.962
0.714
0.359
0.405
9
Residential land 1
31.77
115.931
1.703
1.168
1.143
1.095
1.049
0.774
10
Residential land 2
31.724
115.942
1.631
2.083
2.075
2.067
2.07
1.807
11
Residential land 3
31.702
115.803
2.113
2.108
1.515
1.365
1.475
0.299
12
Transport land 1
31.669
115.951
2.364
2.348
2.26
2.348
2.095
1.923
13
Transport land 2
31.59
115.917
2.324
2.366
2.232
1.555
5.592
5.458
14
Waters and water conservancy facility land 1
31.625
115.86
5.125
5.431
4.373
4.054
3.927
-0.376
15
Waters and water conservancy facility land 2
31.623
115.999
7.96
6.284
5.524
5.617
5.753
7.651
Study area
Forecasting methods
Forecast date
January 11, 2018
RMSE
MAE
MAPE (%)
RVAR
Study area-1
S-IDW
0.581
0.376
7.091
0.674
IDW
0.784
0.552
14.859
0.492
Kriging
0.830
0.615
17.447
0.512
Natural
1.173
0.813
9.544
0.788
Spline
1.804
1.145
27.103
1.326
Study area-1
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Pearson correlation
1
0.959
0.954
0.944
0.763
0.616
Significance (two-tailed)
0.000
0.000
0.000
0.001
0.015
N
15
15
15
15
15
15
Significant correlation at 0.01 level (two-tailed). ∗Significant correlation at 0.05 level (two-tailed).
Interpolation data results and accuracy of five methods under normal temperature conditions in study area-1 can be seen in Tables 6–8. As shown in Table 6, the interpolation results of S-IDW for 8 of the 15 points to be estimated are closer to the land surface temperature than those of the other 4 interpolation methods. Generally, through the mathematical statistics analysis and Pearson correlation analysis of the 5 interpolation methods, it is found that the MAE, MAPE, and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than the other 4 interpolation methods. In terms of MAPE, Natural is better than S-IDW, but S-IDW is better than Kriging, IDW, and Spline. In terms of RVAR, Spline is better than S-IDW, but S-IDW is better than Kriging. In terms of Pearson correlation, the results of S-IDW, Kriging, IDW, Natural, and Spline are significantly correlated with LST at 0.01 level (two-tailed), of which the correlation coefficient r between S-IDW interpolation results and LST is 0.930, with the strongest correlation.
Study area-1
Forecast date: January 11, 2018
Forecasting methods (unit of temperature: °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
31.743
115.91
28.266
26.247
27.014
26.981
25.915
28.132
2
Farmland 2
31.688
115.974
24.056
25.687
26.022
25.977
26.251
27.399
3
Farmland 3
31.682
115.876
27.657
26.708
27.342
24.66
26.983
28.251
4
Farmland 4
31.671
115.924
25.586
25.069
24.758
24.761
24.903
27.626
5
Woodland 1
31.745
115.947
27.254
27.542
28.959
28.502
28.852
28.134
6
Woodland 2
31.741
115.792
24.079
24.049
24.341
23.972
24.74
24.979
7
Woodland 3
31.731
115.848
22.263
23.859
24.202
24.382
23.472
23.559
8
Woodland 4
31.685
115.722
21.083
22.450
22.473
22.447
23.386
19.394
9
Residential land 1
31.77
115.931
30.309
29.533
29.472
28.717
29.137
28.786
10
Residential land 2
31.724
115.942
28.418
28.909
28.882
28.341
29.631
30.642
11
Residential land 3
31.702
115.803
26.475
24.428
23.534
23.277
23.506
26.003
12
Transport land 1
31.669
115.951
26.794
26.034
26.471
25.365
26.551
26.961
13
Transport land 2
31.59
115.917
26.191
24.145
23.216
23.356
21.925
22.816
14
Waters and water conservancy facility land 1
31.625
115.86
20.925
21.042
21.693
21.937
21.731
24.497
15
Waters and water conservancy facility land 2
31.623
115.999
17.673
19.391
20.451
20.954
18.998
17.321
Study area
Forecasting methods
Forecast time
Apr. 17, 2018
RMSE
MAE
MAPE (%)
RVAR
Study area-1
S-IDW
1.295
1.090
0.514
0.640
IDW
1.668
1.383
3.329
0.651
Kriging
1.959
1.686
0.901
0.497
Natural
1.886
1.578
0.278
0.763
Spline
1.891
1.504
1.981
1.127
Study area-1
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Person correlation
1
0.930
0.867
0.817
0.824
0.859
Significance (two-tailed)
0.000
0.000
0.000
0.000
0.000
N
15
15
15
15
15
15
Significant correlation at 0.01 level (two-tailed).
The interpolation data results and accuracy of five methods under high-temperature conditions in study area-1 can be seen in Tables 9–11. As shown in Table 9, the interpolation results of the S-IDW for 4 of the 15 points to be valued are closer to the land surface temperature than those of the other 4 interpolation methods. Generally, through the mathematical statistics analysis and Person correlation analysis of the 5 interpolation methods, it is indicated that the MAE and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than the other 4 interpolation methods. As far as MAPE is concerned, 1.252% of S-IDW is higher than 0.781% of IDW and 0.057% of Spline but lower than 1.818% of Kriging and 1.253% of Natural. In terms of RVAR, 0.983 of Natural is better than 0.827 of S-IDW, but S-IDW is better than Kriging and Natural. In terms of Person correlation, the interpolation results of S-IDW, Kriging, IDW, Natural, and Spline are significantly correlated with LST at 0.01 level (two-tailed), of which the correlation coefficient r between S-IDW and LST was 0.914, stronger than 0.843 of IDW, 0.794 of Kriging, 0.791 of Natural, and 0.669 of Spline.
Study area-1
Forecast date: Aug. 9, 2013
Forecasting methods (unit of temperature: °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
31.743
115.910
44.086
44.572
45.299
44.968
43.377
41.169
2
Farmland 2
31.688
115.974
45.801
44.902
45.305
45.549
45.355
45.859
3
Farmland 3
31.682
115.876
44.473
45.434
45.592
42.255
45.385
46.336
4
Farmland 4
31.671
115.924
45.277
44.080
43.174
43.515
42.791
45.183
5
Woodland 1
31.745
115.947
44.369
45.916
47.383
46.870
47.569
48.472
6
Woodland 2
31.741
115.792
43.869
41.352
41.862
41.053
42.568
43.502
7
Woodland 3
31.731
115.848
39.674
41.126
40.758
41.101
40.362
40.240
8
Woodland 4
31.685
115.722
39.962
39.635
39.509
39.795
39.722
36.678
9
Residential land 1
31.770
115.931
49.092
48.774
48.794
47.180
48.849
49.691
10
Residential land 2
31.724
115.942
48.106
47.027
47.066
46.580
47.482
48.167
11
Residential land 3
31.702
115.803
44.395
42.426
41.770
41.326
42.269
43.038
12
Transport land 1
31.669
115.951
46.802
45.416
46.645
44.797
46.878
47.756
13
Transport land 2
31.590
115.917
45.973
42.301
41.063
40.912
38.718
39.513
14
Waters and water conservancy facility land 1
31.625
115.860
37.502
37.878
38.794
39.143
39.568
45.812
15
Waters and water conservancy facility land 2
31.623
115.999
36.887
37.213
38.130
39.294
37.152
35.224
Study area
Forecasting methods
Forecast time
Aug. 9, 2013
RMSE
MAE
MAPE (%)
RVAR
Study area-1
S-IDW
1.531
1.234
1.252
0.827
IDW
1.955
1.537
0.781
0.870
Kriging
2.290
1.977
1.818
0.605
Natural
2.340
1.509
1.253
0.983
Spline
3.233
2.177
0.057
1.450
Study area-1
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Pearson correlation
1
0.914
0.843
0.794
0.791
0.669
Significance (two-tailed)
0.000
0.000
0.000
0.000
0.006
N
15
15
15
15
15
15
Significant correlation at 0.01 level (two-tailed).
3.3. Analysis and Discussion of Interpolation Results in Study Area-2
In order to verify the interpolation effect of S-IDW under three temperature environments, the imaging dates of the remote sensing images in study area-1 are February 11, 2017, April 19, 2018, and July 10, 2013. The corresponding image clouds are 0.54%, 0.05%, and 4.76%, respectively. Under these conditions, LST inversion is carried out and the inversion data are extracted and processed. The distribution of 60 discrete points and 15 points to be valued in study area-2 is shown in Figure 4.
Interpolation data results and accuracy of 5 methods under low temperature conditions in study area-2 can be seen in Tables 12–14. As shown in Table 12, the interpolation results of S-IDW for 9 of the 15 points to be valued are closer to the land surface temperature than those of the other 4 interpolation methods. The interpolation result of S-IDW at point 11 to be valued is 9.052°C, which deviates from the LST value more than the interpolation results of other 4 interpolation methods. Generally, through the mathematical statistics analysis and Pearson correlation analysis of the 5 interpolation methods, it is known that the MAE, MAPE, RVAR, and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than those of the other 4 interpolation methods. In terms of Pearson correlation, the results of S-IDW, Kriging, IDW, Natural, and Spline are significantly correlated with LST at 0.01 level (two-tailed), of which the correlation coefficient r between S-IDW interpolation results and LST is 0.890.
Study area-2
Forecast date: Feb. 11, 2017
Forecasting methods (unit of temperature °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
29.835
118.266
7.900
8.205
8.517
9.019
8.971
9.778
2
Farmland 2
29.697
118.228
6.902
8.867
8.106
8.125
8.254
8.812
3
Woodland 1
29.914
118.139
1.939
1.316
1.192
−0.869
−0.065
−1.176
4
Woodland 2
29.900
118.330
6.939
7.658
8.842
8.670
8.651
8.373
5
Woodland 3
29.894
118.524
7.147
7.798
8.637
8.982
9.025
10.682
6
Woodland 4
29.842
118.524
6.948
6.234
7.139
6.788
6.390
7.234
7
Woodland 5
29.750
118.525
3.188
2.662
2.873
1.054
2.014
0.001
8
Woodland 6
29.698
118.108
9.340
7.255
8.854
8.921
8.679
9.470
9
Woodland 7
29.677
118.353
5.960
5.508
7.421
5.451
4.136
2.635
10
Residential land 1
29.832
118.337
8.289
8.814
8.903
8.842
8.876
9.143
11
Residential land 2
29.756
118.264
7.201
9.052
8.589
8.172
8.283
8.133
12
Transport land 1
29.758
118.091
7.087
7.776
7.798
9.194
8.698
9.734
13
Transport land 2
29.727
118.204
8.000
8.102
8.697
8.538
8.509
9.173
14
Waters and water conservancy facility land 1
29.903
118.241
7.431
6.969
6.593
6.785
7.002
7.174
15
Waters and water conservancy facility land 2
29.816
118.425
7.803
7.933
8.714
8.676
8.636
8.850
Study area
Forecasting methods
Forecast time
Feb. 11, 2017
RMSE
MAE
MAPE (%)
RVAR
Study area-2
S-IDW
1.00
0.786
2.033
1.389
IDW
1.019
0.905
8.621
1.473
Kriging
1.395
1.175
4.187
2.576
Natural
1.267
1.152
3.904
2.205
Spline
2.064
1.714
5.820
3.73
Study area-2
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Pearson correlation
1
0.890
0.934
0.942
0.925
0.909
Significance (two-tailed)
0.000
0.000
0.000
0.000
0.000
N
15
15
15
15
15
15
Significant correlation at 0.01 level (two-tailed).
The interpolation data results and accuracy of 5 methods under normal temperature conditions in study area-2 can be seen in Tables 15–17. As shown in Table 15, the interpolation results of S-IDW for 6 of the 15 points to be valued are closer to the land surface temperature than those of the other 4 interpolation methods. The LST value of point 11 to be valued is 25.245°C, and the S-IDW interpolation result of this point to be valued is 30.266°C, which deviates from the LST value more than the interpolation results of the other 4 interpolation methods. Generally, through the mathematical statistics analysis and Pearson correlation analysis of the 5 interpolation methods, it is known that the MAE and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than those of the other 4 interpolation methods. In terms of MAPE, 1.856% of S-IDW is higher than 1.723% of Natural but lower than Kriging, IDW, and Spline. As far as RVAR is concerned, 1.051 of Natural and 0.844 of IDW are closer to the best fitting values between measured values and estimated values under ideal conditions than 0.806 of S-IDW. In terms of Pearson correlation, the results of S-IDW and Natural interpolation are significantly correlated with LST at 0.05 level (two-tailed), of which the correlation coefficient r between S-IDW interpolation results and LST is 0.620, with the strongest correlation.
Study area-2
Forecast date: Apr. 19, 2018
Forecasting methods (unit of temperature: °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
29.835
118.266
28.319
29.329
30.205
28.295
31.402
33.163
2
Farmland 2
29.697
118.228
27.913
28.669
27.289
27.577
27.147
26.398
3
Woodland 1
29.914
118.139
26.573
25.333
25.081
25.916
24.636
24.906
4
Woodland 2
29.900
118.330
26.710
28.893
29.930
30.326
29.204
28.371
5
Woodland 3
29.894
118.524
27.722
28.717
29.123
28.665
29.350
32.286
6
Woodland 4
29.842
118.524
26.715
27.145
27.100
27.199
27.442
30.523
7
Woodland 5
29.750
118.525
26.039
25.032
24.704
26.027
24.679
25.179
8
Woodland 6
29.698
118.108
29.600
27.468
27.927
28.226
27.658
30.677
9
Woodland 7
29.677
118.353
26.205
27.298
29.026
28.417
26.651
18.758
10
Residential land 1
29.832
118.337
32.115
30.855
30.579
30.712
30.154
30.312
11
Residential land 2
29.756
118.264
25.245
30.204
29.724
29.506
29.511
28.246
12
Transport land 1
29.758
118.091
28.044
28.270
27.958
26.828
29.346
35.263
13
Transport land 2
29.727
118.204
28.170
28.289
28.016
28.063
28.075
30.576
14
Waters and water conservancy facility land 1
29.903
118.241
23.053
24.556
25.234
27.370
25.125
24.395
15
Waters and water conservancy facility land 2
29.816
118.425
26.727
26.616
27.856
28.520
25.823
24.521
Study area
Forecasting methods
Forecast time
Apr. 19, 2018
RMSE
MAE
MAPE (%)
RVAR
Study area-2
S-IDW
1.719
1.268
1.839
0.805
IDW
1.995
1.627
2.591
0.844
Kriging
2.081
1.512
3.054
0.461
Natural
1.965
1.666
1.723
1.051
Spline
3.659
3.018
3.525
4.369
Study area-2
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Pearson correlation
1
0.617
0.514
0.382
0.541
0.513
Significance (two-tailed)
0.014
0.050
0.159
0.037
0.051
N
15
15
15
15
15
15
Significant correlation at 0.05 level (two-tailed).
The interpolation data results and accuracy of the 5 methods under high-temperature conditions in study area-2 can be seen in Tables 18–20. As shown in Table 18, the interpolation results of S-IDW for 5 of the 15 points to be valued are closer to the land surface temperature than those of the other 4 interpolation methods. The LST value of point 2 to be valued is 37.981°C and the interpolation result of S-IDW at point 2 is 35.398°C, which deviates from the LST value more than Spline interpolation but is better than Kriging, IDW, and Natural interpolation, similar to that of point 10. Generally, through the mathematical statistics analysis and Pearson correlation analysis of the 5 interpolation methods, it is found that the MAE, MAPE, and RMSE of S-IDW are closer to the best fitting values between measured and estimated values under ideal conditions than those of the other 4 interpolation methods. As far as RVAR is concerned, 0.870 of Kriging and 0.813 of Natural are closer to the best fitting values between measured values and estimated values under ideal conditions than 0.695 of S-IDW. In terms of Pearson correlation, the results of S-IDW, Kriging, IDW, Natural, and Spline interpolation are significantly correlated with LST at 0.01 level (two-tailed), of which the correlation coefficient r between S-IDW interpolation results and LST is 0.906, with the strongest correlation.
Study area-2
Forecast date: Jul. 10, 2013
Forecasting methods (unit of temperature: °C)
Point to be valued
Land-use types
Lat
Lon
LST
S-IDW
IDW
Kriging
Natural
Spline
1
Farmland 1
29.835
118.266
35.071
36.730
38.018
38.408
40.071
43.826
2
Farmland 2
29.697
118.228
37.981
35.398
34.928
34.230
34.662
35.745
3
Woodland 1
29.914
118.139
30.012
29.221
28.643
27.689
27.914
28.126
4
Woodland 2
29.900
118.330
34.162
35.963
37.472
36.833
36.132
34.809
5
Woodland 3
29.894
118.524
35.395
36.822
37.653
37.505
38.331
40.496
6
Woodland 4
29.842
118.524
36.442
35.110
35.729
35.586
35.827
39.280
7
Woodland 5
29.750
118.525
31.775
32.236
32.297
31.740
32.968
32.647
8
Woodland 6
29.698
118.108
33.573
34.817
34.728
35.205
35.340
32.472
9
Woodland 7
29.677
118.353
34.980
36.399
39.335
39.142
35.644
29.332
10
Residential land 1
29.832
118.337
41.655
39.583
39.386
39.255
39.308
39.936
11
Residential land 2
29.756
118.264
40.206
39.690
38.307
38.235
37.247
33.101
12
Transport land 1
29.758
118.091
36.348
35.363
34.768
36.077
36.815
40.110
13
Transport land 2
29.727
118.204
37.221
35.640
35.083
35.242
35.438
38.313
14
Waters and water conservancy facility land 1
29.903
118.241
28.349
29.977
30.234
30.705
30.449
30.414
15
Waters and water conservancy facility land 2
29.816
118.425
35.644
35.757
37.428
36.487
35.722
34.758
Study area
Forecasting methods
Forecast time
Jul. 10, 2013
RMSE
MAE
MAPE (%)
RVAR
Study area-2
S-IDW
1.451
1.307
0.021
0.695
IDW
2.303
2.083
0.982
0.835
Kriging
2.345
2.047
0.667
0.870
Natural
2.315
1.953
0.577
0.813
Spline
3.894
3.048
0.861
1.753
Study area-2
LST
S-IDW
IDW
Kriging
Natural
Spline
LST
Pearson correlation
1
0.906
0.755
0.746
0.747
0.541
Significance (two-tailed)
0.000
0.001
0.001
0.001
0.037
N
15
15
15
15
15
15
Significant correlation at 0.01 level (two-tailed).
4. Conclusions
In this paper, S-IDW considering geographic semantics is proposed, which is a novel spatial interpolation algorithm of meteorological parameters. The geographical semantic similarity and weight between known observation points and estimated points are considered comprehensively, which makes the interpolation result of IDW more reasonable. We selected 2 research areas with abundant land-use types to analyze the interpolation under different temperature conditions and used 4 different statistical methods to evaluate the interpolation accuracy. At the same time, the interpolation results of 5 interpolation methods were analyzed and compared by Pearson correlation analysis. The experimental results show that the accuracy of S-IDW is generally higher than the inverse-distance weighting method, Kriging, natural neighbor interpolation, and spline function interpolation, but there are also some abnormal value and interpolation outliers. Comparing the interpolation results of five methods, it is found that the interpolation results of S-IDW are closer to the measured value of LST than those of four other interpolation methods. The MAE, MAPE, RVAR, and RMSE of S-IDW are closer to the best fitting value between the measured and estimated values under ideal conditions than those of the other 4 interpolation methods, and the correlation between the interpolation results of S-IDW and LST is also the strongest. Under the above experimental conditions, the interpolation results of S-IDW are more accurate and stable.
Note that we check the sample points involved in the calculation and find that the semantic interpolation is a little less effective than the traditional numerical interpolation when there are many surface types of the same kind. When there are more homogeneous interpolation points, there is similarity to numerical interpolation. Other interpolation methods have obvious advantages in numerical interpolation. For example, Kriging interpolation method has a wide range of applicability, which can better reflect a variety of terrain changes. Spline interpolation method is suitable for gradually changing surfaces, such as temperature, elevation, groundwater level height, or pollution level. IDW interpolation is suitable for the data with large density and uniform distribution. In our experiment, when the type of interpolation point is single, the advantage of semantic interpolation is not obvious, even less than numerical interpolation. Meanwhile, when there are more types, the semantic interpolation method is obviously better.
However, there are still defects in our study, which need to be improved in further researches. First, for the future development framework of semantic interpolation, we hope to consider the continuity of time to make up for some missing data and combine the time factor [9, 16] with semantic interpolation method to study spatiotemporal semantic interpolation. In addition, we also attempt to integrate the density, direction, elevation, and other influencing factors [6–10] of interpolation points into semantic interpolation and develop multifactor semantic interpolation methods. Moreover, in order to handle the complexity and uncertainty of predicting spatial attributes in most real-world problems, deep learning and artificial intelligence technology [16, 24] including logical and statistical learning algorithms can be considered as future extension of the work in the age of Big Data.
Data Availability
The S-IDW data used to support the findings of this study are available from the corresponding author upon request via email.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Junli Li and Ruijie Gan conceived and designed the new analytical approach. Wenjun Wu, Ruijie Gan, Junli Li, and Xiu Cao wrote the paper. Xinxin Ye, Jie Zhang, and Hongjiao Qu advised on the methods applied in the study. Ruijie Gan performed the experimental analyses. All authors read and approved the final manuscript.
Acknowledgments
This research was financially supported by the National Natural Science Foundation of China (Grant no. 41571400) and supported in part by the Open Research Fund Program of Anhui Province Key Lab of Farmland Ecological Conservation and Pollution Prevention.
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