geostatistical analysis of spatial...

Geostatistical Analysis of Spatial Data Spatial Statistics

2014

Tianya Zhang Niagara College

3/21/2014

Tianya Zhang

174 Highland Ave St. Catharines

ON L2R4J8

March 21, 2014

GISC9308 Assignment 4b

Ian Smith, M.Sc., OLS, OLIP

GIS-GM Program Facilitator

Niagara College 135 Taylor Road

Niagara-On-the-Lake, ON L0S 1J0

Dear Mr. Smith,

Subject: Submission of GISC9308 Assignment 4b

Please accept this letter as my formal submission of GISC9308

Assignment 4b: Geostatistical Analysis of Spatial Data.

Attached is a report detailing the methodology of creating two prediction

maps of average annual precipitation in southeast China by IDW and

Kriging based on sample data points collected. All the processing work

has been done with Geostatistical Analyst tool in ArcGIS. The conclusion is that both the two models are able to give accurate predictions

mathematically, while the prediction result performed by Kriging is closer

to the reality.

Should you have any questions please contact me at your convenience by

e-mail at [email protected]. Thank you for your time and attention. I look forward to your comments and suggestions.

Sincerely,

Tianya Zhang, B.Sc. (GIS)

T.Z./

Enclosure: Geostatistical Analysis of Spatial Data

21 March 2014

Geostatistical Analysis of Spatial Data Page i

Executive summary

In this report two predicted surfaces with values of average annual

precipitation in southeast China has been created by Inverse Distance

Weighted (IDW) and Kriging, based on 151 sample data points collected

previously. The result is both the IDW and Kriging model are giving

accurate predictions of precipitation mathematically. The prediction result

performed by Kriging, however, is closer to the reality.

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Geostatistical Analysis of Spatial Data Page ii

Table of Contents

Executive summery ..........................................................................i

1. Introduction ........................................................................... 1

2. Exploratory data analysis ......................................................... 1

3. Inverse distance weighted (IDW) .............................................. 7

4. Kriging ................................................................................ 12

5. Evaluation of the two methods ................................................ 17

5.1 Cross-validation .................................................................... 17

5.2 Comparison with reality ......................................................... 17

6. Evaluation of sample data ...................................................... 18

5.1 Sample coverage .................................................................. 18

5.2 better data collection coverage ............................................... 18

7. Conclusion ........................................................................... 19

8. Bibliography......................................................................... 19

Appendix A – Cross-validation ......................................................... 20

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Geostatistical Analysis of Spatial Data Page iii

List of Figures

Figure 1: Study area and sample data points ....................................... 2

Figure 2: Histogram of data points ..................................................... 3

Figure 3: Q-Q Plot of sample data ...................................................... 4

Figure 4: Trend Analysis .................................................................. 5

Figure 5: Semivariogram .................................................................. 6

Figure 6: Inverse distance weighted ................................................... 7

Figure 7: Search neighborhood ......................................................... 8

Figure 8: Scatter plot of IDW ............................................................ 9

Figure 9: Prediction result by IDW ................................................... 11

Figure 10: Select method to kriging ................................................. 12

Figure 11: Select kriging type ......................................................... 12

Figure 12: Semivariogram modeling................................................. 13

Figure 13: Searching neighborhood of kriging .................................... 14

Figure 14: Scatter plot of krigng ...................................................... 15

Figure 15: Predicted precipitation by kriging ...................................... 16

Figure 16: Mean annual precipitation of China ................................... 18

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Geostatistical Analysis of Spatial Data Page 1

1. Introduction

IDW interpolation determines cell values using a linearly weighted

combination of a set of sample points. This method assumes that the

variable being mapped decreases in influence with distance from its

sampled location (ESRI, How IDW works). Kriging is an interpolation

technique in which the surrounding measured values are weighted to

derive a predicted value for an unmeasured location. Kriging is unique

among the interpolation methods in that it provides an easy method for

characterizing the variance, or the precision, of predictions (ESRI, GIS

Dictionary).

In this report both IDW and Kriging will be used to create the prediction,

based on 151 sample data points collected previously in Deliverable 4a.

Each data point represents a city in southeast China, with the average

annual precipitation value of the city.

2. Exploratory data analysis

Study area and sample data points are as displayed in Figure 1. The

sample data points are in good distribution, covering the study area

properly.

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Figure 1: Study area and sample data points

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From Geostatistical Analyst, a histogram, Q-Q Plot, Trend Analysis, and

Semivariogram/Covariance Cloud have been created for sample data

analysis.

The Histogram is showing the frequency distribution of the sample data

points (Figure 2). Most of the data points are located within the value

range from 760mm to 1910mm.

Figure 2: Histogram of data points

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On the Q-Q Plot, most data points are close to the line which represents

the expected values for a normal distribution. This means the distribution

of the sample data points is similar to a standard normal distribution

(Figure 3).

Figure 3: Q-Q Plot of sample data

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In the Trend Analysis, the green line is relatively flat, which indicates

there is no obvious trend of in east-west direction. However, the blue line

is rising from north to south, which means data points in the south are

likely to have higher values (Figure 4).

Figure 4: Trend Analysis

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In the Semivariogram, points which are close to each other have small

semivariogram value. Thus the data points values are overall accurate

(Figure 5).

Figure 5: Semivariogram

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3. Inverse distance weighted (IDW)

Import the data points collected into ArcMap.

From Geostatistical Analyst select Geostatistical Wizard, and choose

Inverse Distance Weighting as method. Select Data Point as source

dataset, and Precipitation as Data Field (Figure 6).

Figure 6: Inverse distance weighted

As China faces the Pacific in south-east, along an extensive shoreline in

southeast, the country’s climate is heavily influenced by the seasonal

movement of large air masses between the Pacific and the Chinese

mainland (Britannica Online Encyclopedia). Thus there is directional

influence on the distribution of precipitation, where the rainfall is the

heaviest in southeast part of China, and gradually decreases from

southeast to northwest. As for the data points, locations from southwest

or northeast to a prediction location tend to be more similar at farther

distance than locations that are from northwest or southeast but located

closer to the prediction location. Thus an ellipse with its major axis going

21 March 2014


from southwest to northeast direction was chosen as the search

neighborhood (Figure 7).

Click optimize power value button as shown in the red circle in Figure 7 to

generate a suitable power value for the IDW. Select to divide search

neighborhood into eight sectors.

Figure 7: Search neighborhood

In next step, a scatterplot of predicted values versus true values has been

given (Figure 8). These predicted values should have scattered around the

1:1 line—the black dashed line in the plot. However, the slope of the blue

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line, which represents the predicted values, is actually less than 1. It is a

property of Kriging that tends to underpredict large values and overpredict

small values (ESRI, Performing cross-validation and validation). As a

good model, the blue line should be closer to the black dashed line. In

this case, as shown in the regression function just below the plot, the

slope of the blue line is around 0.76, which is a fair result for prediction.

The cross-validation done by the software is giving the error value

between each pair of predicted value and the true value. The root-mean-

square of the error calculated is approximate 231, indicating the model is

giving good prediction mathematically.

Click export result table to export the cross-validation result table.

Figure 8: Scatter plot of IDW

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Then click Finish to generate the IDW. Export the IDW result to raster

dataset and assign suitable colour ramp. The final result of predicted

precipitation in southeast China by IDW is as displayed in Figure 9.

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Figure 9: Prediction result by IDW

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4. Kriging

From Geostatistical Wizard select Kriging/CoKriging as method. Then

select data point as source dataset and precipitation as data field (Figure

10).

Figure 10: Select method to kriging

Select ordinary kriging type, which is used for creating maps of kriging

predicted values. For output surface type, select prediction (Figure 11).

Figure 11: Select kriging type

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Next step is semivariogram modeling. Click Optimize model button as

shown in the red circle in Figure 12 to generate a suitable model for the

prediction. In the plot, the blue line indicates that each pair of data points

with shorter distance tends to have smaller semivariogram value in the

model.

Figure 12: Semivariogram modeling

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For the searching neighborhood, modify it to an ellipse same with the one

in IDW. Also divide the searching neighborhood into eight sectors (Figure

13).

Figure 13: Searching neighborhood of kriging

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Then in the cross-validation, a scatterplot is given which displays the

predicted values versus true values (Figure 14). The regression function

below the plot shows the slope of the blue line is approximate 0.84, which

is larger than the one in IDW, and closer to the 1:1 black line. The root-

mean-square is approximate 232, indicating a good model.

Click Export Result Table button to export the cross-validation table.

Figure 14: Scatter plot of krigng

Finish the geostatistical wizard and a kriging result is created. Convert

the kriging to raster dataset and assign a suitable colour ramp for

symbology. The layout of predicted precipitation in southeast China by

kriging is as displayed in Figure 15.

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Figure 15: Predicted precipitation by kriging

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5. Evaluation of the two methods

5.1 Cross-validation

The cross-validation results have been exported to tables which have been

displayed in Appendix A. To find out how big the error is between the

predicted values and the true values, one good way is to compare the

root-mean-square of the error values of each model. It turned out that

the root-mean-square value of error is 231 in IDW model and 232 in

Kriging model. This proves both models are good from mathematical

aspect.

5.2 Comparison with reality

In reality, annual precipitation in China is decreasing from southeast to

northwest. From the map of mean annual precipitation of China created

by others (Figure 16), this trend is even more typical just in the southeast

part of China. As there are no large mountain ranges or inner lakes in

this area, the amount of rains of a location are basically based on the

distance from the sea. From this aspect, the prediction result by Kriging

is closer to the reality, because the raster created is giving a smoother

surface which corresponds to the precipitation distribution.

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Figure 16: Mean annual precipitation of China (Source: http://course.bnu.edu.cn/course/cgeography/en/html/7ziyuan/2ditu/)

6. Evaluation of sample data

5.1 Sample coverage

The 151 sample data points are in good distribution, covering the study

area properly.

5.2 better data collection coverage

These data points were collected by selecting some cities randomly in

each province. As the provinces are usually small in southeast China,

those randomly chosen cities just formed a good coverage in the study

area. To make the distribution of sample points better, cities should have

been chosen according to location, which means to select a city every

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certain distance. This is helping to make sure the density of data points in

each location are approximately the same.

7. Conclusion

Both the IDW and Kriging model are giving accurate predictions of

precipitation values in the case discussed in this report. Thus both of

them are good models mathematically. However, the prediction result

performed by Kriging is closer to the reality.

8. Bibliography

(n.d.). Retrieved from Britannica Online Encyclopedia:

http://www.britannica.com/EBchecked/topic/111803/China/70982/

Precipitation

ESRI. (n.d.). Retrieved from GIS Dictionary:

http://support.esri.com/en/knowledgebase/GISDictionary/term/krig

ing

ESRI. (n.d.). How IDW works. Retrieved from ArcGIS Resource Center,

ArcGIS Help 10.1:

http://resources.arcgis.com/en/help/main/10.1/index.html#//009z

00000075000000

ESRI. (n.d.). How inverse distance weighted interpolation works.

Retrieved from ArcGIS Resource Center, ArcGIS Help 10.1:

http://resources.arcgis.com/en/help/main/10.1/index.html#//0031

0000002m000000

ESRI. (n.d.). Performing cross-validation and validation. Retrieved from

ArcGIS Resource Center Desktop 10:

http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Per

forming_cross_validation_and_validation/003100000059000000/

21 March 2014


Smith, I. (2014). GISC9308 Spatial Statistics Deliverable D4 Terms of

Reference.

Appendix A – Cross-validation

Cross validation result of IDW

Measured (mm) Predicted (mm) Error (mm)

652 739.42 87.42

730 692.67 -37.33

622 699.35 77.35

615 726.16 111.16

685 684.45 -0.55

737 769.13 32.13

849 861.02 12.02

1900 1684.60 -215.40

1900 1719.55 -180.45

1550 1684.52 134.52

1750 1794.04 44.04

2200 1853.47 -346.53

1650 1778.90 128.90

2000 1850.21 -149.79

1924 2026.50 102.50

2035 1681.20 -353.80

2040 1725.35 -314.65

1650 1725.75 75.75

1610 1724.29 114.29

2214 1897.10 -316.90

2405 2331.39 -73.61

1570 1823.34 253.34

1785 1703.25 -81.75

2157 2000.40 -156.60

1642 2075.29 433.29

2828 2103.73 -724.27

1845 1799.89 -45.11

1466 1998.82 532.82

1237 1238.80 1.80

1684 1850.18 166.18

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1815 1816.47 1.47

2072 2078.42 6.42

1348 2126.01 778.01

2400 1855.45 -544.55

1292 1233.77 -58.23

1250 1423.92 173.92

1122 1328.96 206.96

1130 1363.73 233.73

1243 1399.75 156.75

1350 1244.47 -105.53

1431 1279.84 -151.16

1360 1266.38 -93.62

1532 1349.03 -182.97

1950 1506.01 -443.99

1400 1495.51 95.51

1413 1464.15 51.15

1504 1689.89 185.89

1643 1583.74 -59.26

1600 1625.49 25.49

1304 1560.11 256.11

1650 1661.05 11.05

2363 1602.17 -760.83

1670 1854.66 184.66

1584 1585.79 1.79

1200 1554.37 354.37

606 665.74 59.74

672 657.49 -14.51

650 647.06 -2.94

550 725.98 175.98

589 987.74 398.74

1150 607.02 -542.98

528 750.76 222.76

630 781.05 151.05

641 756.11 115.11

623 828.97 205.97

950 800.13 -149.87

656 1054.28 398.28

822 831.01 9.01

835 915.63 80.63

881 955.20 74.20

885 950.92 65.92

893 970.02 77.02

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1036 1083.97 47.97

1000 1132.29 132.29

1250 1087.62 -162.38

1060 1134.72 74.72

1200 1141.62 -58.38

1150 1234.49 84.49

1549 1468.96 -80.04

920 906.91 -13.09

865 870.24 5.24

910 931.14 21.14

957 1006.99 49.99

1047 1037.25 -9.75

1038 1071.73 33.73

1020 1083.32 63.32

1088 1058.10 -29.90

1106 1082.26 -23.74

1040 1160.63 120.63

1122 1154.17 32.17

1100 1210.23 110.23

1271 1233.42 -37.58

1169 1307.67 138.67

1454 1337.34 -116.66

1274 1464.64 190.64

1443 1398.59 -44.41

1480 1358.94 -121.06

1350 1477.61 127.61

1424 1479.85 55.85

1843 1491.79 -351.21

1632 1605.88 -26.12

1838 1574.87 -263.13

1800 1643.26 -156.74

1450 1541.66 91.66

1614 1425.57 -188.43

1805 1466.63 -338.37

1329 1465.32 136.32

1650 1485.27 -164.73

1552 1509.52 -42.48

1720 1527.51 -192.49

960 1590.00 630.00

1680 1381.82 -298.18

1603 1502.66 -100.34

1856 1515.72 -340.28

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1700 1467.01 -232.99

1960 1680.76 -279.24

1742 1762.05 20.05

1770 1743.27 -26.73

2350 1529.36 -820.64

1500 1513.46 13.46

1382 1534.46 152.46

1200 1610.24 410.24

1071 1445.77 374.77

1350 1595.54 245.54

1200 1536.01 336.01

1686 1312.44 -373.56

1172 1552.63 380.63

1423 1375.42 -47.58

1400 1317.00 -83.00

1550 1358.25 -191.75

1465 1403.25 -61.75

1456 1365.95 -90.05

1358 1378.86 20.86

1300 1416.22 116.22

1350 1388.41 38.41

1600 1341.16 -258.84

1337 1493.53 156.53

1218 1471.13 253.13

1550 1491.18 -58.82

828 938.81 110.81

878 1017.23 139.23

1100 1119.28 19.28

949 1145.65 196.65

1135 1175.33 40.33

1198 1094.77 -103.23

1205 1264.46 59.46

1350 1350.36 0.36

1211 1236.99 25.99

1200 1202.90 2.90

1383 1364.39 -18.61

1577 1330.15 -246.85

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Cross validation result of Kriging

Measured Predicted Error StdError Stdd_Error NormValue

652 697.73 45.73 232.45 0.20 0.29

730 670.79 -59.21 257.13 -0.23 -0.43

622 644.09 22.09 219.23 0.10 0.07

615 710.30 95.30 212.72 0.45 0.56

685 595.97 -89.03 218.77 -0.41 -0.66

737 756.40 19.40 215.00 0.09 0.03

849 784.51 -64.49 203.73 -0.32 -0.52

1900 1713.84 -186.16 207.72 -0.90 -0.96

1900 1812.16 -87.84 200.88 -0.44 -0.68

1550 1587.07 37.07 207.14 0.18 0.25

1750 1847.68 97.68 198.34 0.49 0.60

2200 1827.94 -372.06 199.46 -1.87 -1.72

1650 1853.18 203.18 198.85 1.02 1.16

2000 1743.47 -256.53 207.36 -1.24 -1.30

1924 1943.88 19.88 201.05 0.10 0.05

2035 1929.01 -105.99 200.95 -0.53 -0.74

2040 1807.73 -232.27 201.95 -1.15 -1.20

1650 1820.18 170.18 200.98 0.85 0.96

1610 1810.25 200.25 201.53 0.99 1.07

2214 1941.48 -272.52 204.64 -1.33 -1.43

2405 2086.26 -318.74 211.73 -1.51 -1.65

1570 1722.52 152.52 211.24 0.72 0.88

1785 1756.01 -28.99 222.25 -0.13 -0.23

2157 2128.07 -28.93 211.04 -0.14 -0.25

1642 1889.37 247.37 201.50 1.23 1.30

2828 2006.21 -821.79 215.65 -3.81 -2.33

1845 2002.90 157.90 222.01 0.71 0.86

1466 1961.22 495.22 200.43 2.47 1.99

1237 1166.12 -70.88 207.68 -0.34 -0.54

1684 1928.89 244.89 203.92 1.20 1.23

1815 1847.50 32.50 207.78 0.16 0.23

2072 1857.85 -214.15 210.49 -1.02 -1.04

1348 2077.54 729.54 239.77 3.04 2.33

2400 1725.35 -674.65 217.08 -3.11 -1.99

1292 1152.56 -139.44 261.03 -0.53 -0.77

1250 1381.74 131.74 208.60 0.63 0.72

1122 1313.86 191.86 214.83 0.89 0.99

1130 1351.37 221.37 203.78 1.09 1.20

1243 1371.23 128.23 205.05 0.63 0.70

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1350 1303.65 -46.35 219.76 -0.21 -0.39

1431 1314.05 -116.95 204.34 -0.57 -0.83

1360 1299.51 -60.49 204.38 -0.30 -0.48

1532 1290.68 -241.32 235.78 -1.02 -1.10

1950 1395.74 -554.26 205.23 -2.70 -1.88

1400 1429.65 29.65 204.53 0.14 0.20

1413 1451.83 38.83 215.81 0.18 0.27

1504 1760.18 256.18 200.79 1.28 1.39

1643 1592.72 -50.28 199.89 -0.25 -0.45

1600 1602.94 2.94 199.58 0.01 -0.05

1304 1596.61 292.61 201.90 1.45 1.48

1650 1647.71 -2.29 199.48 -0.01 -0.08

2363 1460.95 -902.05 209.86 -4.30 -2.72

1670 1691.58 21.58 203.22 0.11 0.10

1584 1557.94 -26.06 202.01 -0.13 -0.22

1200 1659.56 459.56 217.24 2.12 1.79

606 657.42 51.42 206.30 0.25 0.36

672 651.74 -20.26 209.08 -0.10 -0.15

650 660.79 10.79 203.24 0.05 -0.02

550 686.80 136.80 200.85 0.68 0.83

589 699.16 110.16 200.53 0.55 0.62

1150 634.86 -515.14 199.58 -2.58 -1.79

528 727.40 199.40 199.55 1.00 1.13

630 794.94 164.94 256.32 0.64 0.79

641 719.88 78.88 200.71 0.39 0.50

623 750.71 127.71 201.52 0.63 0.74

950 724.19 -225.81 205.99 -1.10 -1.13

656 962.45 306.45 202.12 1.52 1.53

822 782.64 -39.36 201.35 -0.20 -0.37

835 858.90 23.90 199.22 0.12 0.13

881 950.79 69.79 197.54 0.35 0.45

885 875.35 -9.65 200.65 -0.05 -0.10

893 980.72 87.72 198.45 0.44 0.54

1036 1048.81 12.81 196.62 0.07 0.00

1000 1114.87 114.87 198.34 0.58 0.66

1250 1095.15 -154.85 199.41 -0.78 -0.93

1060 1135.70 75.70 197.34 0.38 0.48

1200 1220.65 20.65 198.27 0.10 0.08

1150 1276.55 126.55 198.92 0.64 0.77

1549 1515.59 -33.41 199.72 -0.17 -0.29

920 861.01 -58.99 206.09 -0.29 -0.46

865 792.93 -72.07 200.46 -0.36 -0.56

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910 886.68 -23.32 199.87 -0.12 -0.18

957 947.25 -9.75 199.76 -0.05 -0.12

1047 982.47 -64.53 208.33 -0.31 -0.50

1038 1047.40 9.40 198.70 0.05 -0.03

1020 1047.13 27.13 196.55 0.14 0.15

1088 1052.85 -35.15 196.38 -0.18 -0.34

1106 1072.60 -33.40 196.24 -0.17 -0.30

1040 1091.37 51.37 204.60 0.25 0.37

1122 1150.12 28.12 196.76 0.14 0.18

1100 1183.17 83.17 197.73 0.42 0.52

1271 1247.65 -23.35 196.37 -0.12 -0.20

1169 1261.46 92.46 197.50 0.47 0.58

1454 1343.08 -110.92 196.90 -0.56 -0.81

1274 1420.94 146.94 220.08 0.67 0.81

1443 1421.24 -21.76 197.05 -0.11 -0.17

1480 1379.88 -100.12 204.61 -0.49 -0.72

1350 1605.81 255.81 198.03 1.29 1.43

1424 1665.83 241.83 198.31 1.22 1.27

1843 1613.74 -229.26 198.89 -1.15 -1.23

1632 1690.28 58.28 212.04 0.27 0.41

1838 1703.90 -134.10 199.63 -0.67 -0.91

1800 1822.44 22.44 205.61 0.11 0.12

1450 1467.58 17.58 198.69 0.09 0.02

1614 1433.26 -180.74 198.06 -0.91 -0.99

1805 1557.40 -247.60 199.43 -1.24 -1.34

1329 1512.15 183.15 196.38 0.93 1.04

1650 1578.20 -71.80 197.78 -0.36 -0.58

1552 1599.90 47.90 198.10 0.24 0.32

1720 1645.69 -74.31 199.50 -0.37 -0.60

960 1608.85 648.85 198.72 3.27 2.72

1680 1487.34 -192.66 197.91 -0.97 -1.01

1603 1488.55 -114.45 197.62 -0.58 -0.86

1856 1573.70 -282.30 204.32 -1.38 -1.53

1700 1464.97 -235.03 199.27 -1.18 -1.27

1960 1660.11 -299.89 199.66 -1.50 -1.59

1742 1667.33 -74.67 200.10 -0.37 -0.62

1770 1662.17 -107.83 200.51 -0.54 -0.79

2350 1662.06 -687.94 201.20 -3.42 -2.13

1500 1684.17 184.17 199.28 0.92 1.01

1382 1743.81 361.81 199.80 1.81 1.65

1200 1575.72 375.72 202.56 1.85 1.72

1071 1528.18 457.18 198.73 2.30 1.88

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1350 1474.97 124.97 200.69 0.62 0.68

1200 1449.77 249.77 200.46 1.25 1.34

1686 1414.78 -271.22 200.61 -1.35 -1.48

1172 1748.18 576.18 200.08 2.88 2.13

1423 1388.56 -34.44 196.75 -0.18 -0.32

1400 1271.56 -128.44 209.48 -0.61 -0.88

1550 1345.88 -204.12 199.73 -1.02 -1.07

1465 1369.17 -95.83 197.84 -0.48 -0.70

1456 1419.82 -36.18 196.67 -0.18 -0.36

1358 1433.43 75.43 197.15 0.38 0.46

1300 1456.59 156.59 197.07 0.79 0.93

1350 1461.43 111.43 197.65 0.56 0.64

1600 1343.90 -256.10 203.90 -1.26 -1.39

1337 1536.02 199.02 199.85 1.00 1.10

1218 1552.29 334.29 202.18 1.65 1.59

1550 1547.98 -2.02 203.33 -0.01 -0.07

828 887.04 59.04 234.55 0.25 0.39

878 936.57 58.57 206.38 0.28 0.43

1100 1089.15 -10.85 198.94 -0.05 -0.13

949 1108.41 159.41 201.46 0.79 0.91

1135 1165.52 30.52 197.83 0.15 0.22

1198 1117.76 -80.24 208.53 -0.38 -0.64

1205 1251.26 46.26 197.61 0.23 0.30

1350 1305.94 -44.06 197.61 -0.22 -0.41

1211 1260.04 49.04 196.96 0.25 0.34

1200 1228.45 28.45 199.50 0.14 0.17

1383 1351.80 -31.20 197.52 -0.16 -0.27

1577 1357.64 -219.36 196.86 -1.11 -1.16

geostatistical analysis of spatial...

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