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Publication Number: FHWA-RD-03-092
Date: May 2006

Verification of LTPP Virtual Weather Stations Phase I Report: Accuracy and Reliability of Virtual Weather Stations

Task 2: Compare Estimated and Onsite Climatic Data

During this task, climatic estimates in the LTPP database were compared to the measured data. The daily, monthly, and yearly VWS data estimates were compared to the onsite SMP and AWS measured data. The results of the comparisons were presented in various charts and graphs for numerical and visual verification of the accuracy of the VWS estimates. An explanation of the comparisons for each climatic parameter follows.

Minimum and Maximum Temperatures

Daily and monthly temperature estimates (minimum and maximum) were compared to AWS and SMP measured data for the same periods. The results are presented below.

Precision and Bias of Estimate

The VWS estimates in the database were compared to the daily measured data from the AWS and SMP sites. For every SMP and AWS site, the collected daily low (minimum) and high (maximum) air temperatures were compared to the current VWS estimates in table CLM_VWS_DATA_DAILY, which is based on up to five nearby weather stations. Figures through 5 show the estimated versus measured maximum daily temperature for three sample sites. Figure 3 shows a close relationship between the estimated and collected data, while the data shown in figure 4 show more variation between the two. Figure 5 is an example of a relationship that is close, but has a shift in the data.

The mean and standard deviation of the difference between the estimated and measured data (error of estimate) were used for the purpose of numerical comparison of the data. The mean of the error was used as an estimate bias and shows a shift in the data (e.g., figure 5). The standard deviation of the error was used as estimate variation, which relates to the precision of the estimated data (low precision for data in figure 3 and higher precision in figure 4).

Comparing Daily Minimum and Maximum Temperatures

Table 14 includes the mean and standard deviation of error (bias and precision of estimate) for minimum and maximum temperatures for AWS and SMP sites. There are data for 82 sites (24 AWS and 58 SMP sites) in this table. The mean error for the maximum temperature ranged from –1.2 to 6.3 degrees Celsius (°C), with an average of 0.57 °C. The overall mean error was 0.51 °C (for all days of data). The standard deviation of error for the maximum temperature ranged from 0.73 to 5.8 °C, with an average of 2.75 °C per section. The standard deviation for all days of data (overall) was 3.14 °C. The overall value is usually higher than the average per section since it includes the effect of bias, while this effect is removed by averaging standard deviations for the sections. The average mean error per section and the overall mean error, however, are usually comparable.

The mean error for the minimum temperature was between –2.6 and 2.8 °C, with an average of –0.13 °C per section (–0.14 °C overall), and the standard deviation of error was between 1.0 and 7.0 °C, with an average of 2.26 °C per section (2.55 °C overall).

More than one set of climatic instrumentation was installed at some LTPP project sites. For example, the first three sections in table 14 were in the same vicinity since they were all installed at the same SPS–1 site (typically within a 1.6-kilometer (km) stretch). Despite their proximity, some differences in the precision and bias of the estimated value were evident. For example, the mean error for the minimum temperature estimate was between 0 and 1.33 °C, and the standard deviation ranged from 2.06 to 2.41 °C.

Similarly, SMP section numbers 4–8, 15–16, 37–38, 41–42, 47–48, 56–57, and 71–73 are built within the same project site. Data for these sites may be used to determine the variation between onsite measurements and thus the precision and bias of the measured data within a site. This provides a useful reference for comparing onsite and estimated data, and for determining the required accuracy of the estimated data.

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Figure 3. Graph. Estimated versus measured maximum temperature for section 331001.

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Figure 4. Graph. Estimated versus measured maximum temperature for site 010100.

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Figure 5. Graph. Estimated versus measured maximum temperature for site 040100.

 

Table 14. Summary statistics for error of daily temperature estimates.
No. SHRP
ID
Source of
Measured
Data
Days of
Data
Error (Measured-Estimated), °C
Max. Temperature Min. Temperature
Mean Std. Dev. Mean Std. Dev.
1 10101 AWS 686 -0.08 3.03 -0.01 2.06
2 10101 SMP 313 0.35 3.34 -0.10 2.41
3 10102 SMP 442 0.47 3.17 1.33 2.09
4 40100 AWS 606 4.98 1.28 2.23 2.34
5 40113 SMP 253 5.47 1.93 -0.02 3.01
6 40114 SMP 330 6.28 1.28 -0.36 3.15
7 40200 AWS 892 1.25 1.61 -0.79 1.59
8 40215 SMP 310 2.00 1.45 -1.26 1.63
9 41024 SMP 286 1.85 1.26 -2.59 2.66
10 50113 AWS 601 -0.01 3.19 -0.49 2.02
11 63042 SMP 295 2.03 1.90 -0.40 1.03
12 80200 AWS 459 -0.39 5.83 -0.99 2.76
13 81053 SMP 600 0.65 3.50 0.59 2.52
14 91803 SMP 599 0.26 0.85 0.18 1.15
15 100100 AWS 410 -0.24 2.58 1.47 1.94
16 100102 SMP 335 0.38 2.47 1.09 1.83
17 120101 AWS 201 0.05 2.23 -0.26 1.20
18 131005 SMP 395 -0.26 2.74 -0.84 1.90
19 131031 SMP 342 -0.14 3.38 0.22 2.16
20 133019 SMP 353 0.27 3.31 1.87 2.28
21 161010 SMP 519 1.45 1.94 1.05 1.92
22 183002 SMP 287 1.38 3.56 -0.27 2.57
23 200100 AWS 147 -0.53 5.04 -1.35 2.96
24 200200 AWS 146 0.46 2.75 0.76 1.78
25 204054 SMP 302 1.40 3.25 0.43 2.04
26 231026 SMP 629 0.44 2.91 0.48 2.54
27 241634 SMP 502 1.28 1.58 0.19 1.32
28 251002 SMP 569 -0.21 3.29 -2.03 2.10
29 271018 SMP 898 1.44 3.17 1.12 1.99
30 271028 SMP 1057 0.89 2.50 0.11 2.27
31 274040 SMP 730 0.85 4.36 -0.05 3.42
32 276251 SMP 979 -0.61 4.33 -0.08 3.71
33 281016 SMP 457 0.13 3.23 -0.46 2.53
34 281802 SMP 410 -1.06 2.09 0.94 1.84
35 300800 AWS 763 1.37 2.51 -1.74 2.40
36 308129 SMP 692 0.94 2.88 -0.36 2.43
37 310100 AWS 143 -0.43 4.14 -0.50 2.41
38 310114 SMP 309 0.59 4.73 -1.08 2.99
39 313018 SMP 313 0.61 5.72 -1.49 2.90
40 320101 SMP 51 0.37 1.93 0.45 1.91
41 320200 AWS 571 0.84 1.51 -0.57 1.95
42 320204 SMP 52 0.22 1.92 0.01 1.89
43 331001 SMP 624 0.45 0.73 -1.15 1.21
44 350101 AWS 458 -0.11 2.46 -1.69 1.96
45 350801 AWS 142 0.34 1.37 -1.72 1.66
46 351112 SMP 356 0.92 1.57 -0.11 1.71
47 360800 AWS 403 0.56 2.31 -0.19 1.71
48 360801 SMP 355 1.15 2.46 0.06 1.79
49 364018 SMP 636 0.20 3.25 -0.83 2.92
50 370200 AWS 877 0 1.60 0.01 1.95
51 371028 SMP 464 0 1.78 1.02 1.68
52 380200 AWS 402 0.47 4.05 -0.28 2.75
53 390200 AWS 635 -0.41 4.31 -0.28 3.19
54 404165 SMP 495 0.86 3.79 0.51 2.58
55 421606 SMP 362 0.02 2.03 -0.26 1.27
56 460800 AWS 68 -0.24 1.64 0.51 2.14
57 460804 SMP 406 0.52 1.73 -0.34 1.81
58 469187 SMP 342 0.15 3.46 0.70 1.71
59 480801 AWS 90 0.69 2.07 -0.35 1.90
60 481060 SMP 577 0.86 1.44 0.92 1.53
61 481068 SMP 583 -0.39 4.04 -1.01 2.75
62 481077 SMP 605 -0.02 2.82 -0.09 1.85
63 481122 SMP 535 -0.01 3.05 -0.79 2.59
64 483739 SMP 601 -0.46 3.03 0.49 2.41
65 484142 SMP 611 -1.20 4.06 -0.27 3.18
66 484143 SMP 447 0.59 4.06 0.63 6.97
67 490800 AWS 43 2.25 2.29 2.76 2.86
68 491001 SMP 536 0.17 1.36 -1.71 1.66
69 493011 SMP 603 1.55 2.09 -0.07 1.98
70 501002 SMP 604 -0.43 2.97 -0.24 2.99
71 510100 AWS 362 -0.32 4.49 -0.86 3.06
72 510113 SMP 324 0.19 4.36 0.65 2.70
73 510114 SMP 266 0.75 4.27 -0.51 2.88
74 530200 AWS 631 -0.58 3.07 -0.89 1.82
75 530800 AWS 526 -0.35 3.66 -0.33 1.60
76 533813 SMP 356 0.80 2.97 -1.19 1.60
77 561007 SMP 588 0.48 3.96 -1.05 3.37
78 831801 SMP 973 0.02 1.29 -0.16 1.39
79 833802 SMP 575 -0.18 1.35 -0.12 2.61
80 871622 SMP 582 0.23 1.25 0.12 1.78
81 893015 SMP 782 0.19 1.60 0.33 2.09
82 906405 SMP 606 0.23 1.69 0.68 2.02
All Days   38,665 0.51 3.14 -0.14 2.55
Average Section   471.5 0.57 2.75 -0.13 2.26

The distribution of errors for maximum and minimum temperatures is shown in figures 6 and 7 for AWS sites. Figures 8 and 9 show the same distribution for SMP sites. It shows that errors in these figures are approximately normally distributed.

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Figure 6. Bar chart. Error distribution of maximum temperature estimates for AWS sites.

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Figure 7. Bar chart. Error distribution of minimum temperature estimates for AWS sites.

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Figure 8. Bar chart. Error distribution of maximum temperature estimates for SMP sites.

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Figure 9. Bar Chart. Error distribution of minimum temperature estimates for SMP sites.

Comparing Monthly Minimum and Maximum Temperatures

The monthly average maximum and minimum daily temperatures were calculated for all SMP and AWS sites and were compared with the monthly estimates in LTPP database table CLM_VWS_TEMP_MONTH. Table 15 shows the mean and standard deviation of error (estimated minus measured) for all AWS and SMP sites and contains 1120 months of measured and estimated data. Some sections had as few as 1 month of data and some had as many as 32 months.

The mean error for the maximum temperature ranged from –1.2 to 6.26 °C, with an average of 0.58 °C. The overall mean error was 0.51 °C. The highest mean error (bias) belongs to site 040100 (section numbers 4–6). The bias is mainly caused by the high elevation difference between the site and the five closest weather stations and can be somewhat improved.

The standard deviation of error for the maximum temperature for the sections ranged from 0.19 to 1.11 °C, with an average of 0.47 °C. The overall standard deviation for all 1120 months of data was 1.2 °C. The standard deviation for the majority of the sites was less than 0.5 °C.

The mean error (bias) for the minimum temperature ranged from –2.5 to 2.55 °C, with an average mean error of –0.14 °C. The standard deviation of error for the sections ranged from 0.11 to 2.22 °C, with an average of 0.53 °C. The overall standard deviation for all months of data was almost twice as much (1.04 °C).

The average estimated bias (mean error) for the daily and monthly maximum temperatures is very close (0.57 and 0.58 °C, respectively). This was also the case for the minimum temperature (–0.13 and –0.14 °C, respectively). The average standard deviation (used as an estimate of precision) for the monthly maximum temperature estimate was substantially less than the daily estimates (0.47 versus 2.75 °C, respectively). The same is true for the minimum temperature (0.53 versus 2.26 °C, respectively).

 

Table 15. Summary statistics for error of monthly temperature estimates.
No. SHRPID Source of
Measured
Data
Months of
Data
Error (Virtual-Measured), °C
Max. Temperature Min. Temperature
Mean Std. Dev. Mean Std. Dev.
1 10101 AWS 22 -0.05 0.41 0.02 0.38
2 ? SMP 8 0.35 0.35 -0.21 0.56
3 10102 SMP 14 0.46 0.33 1.34 0.40
4 40100 AWS 19 4.96 0.45 2.18 0.56
5 40113 SMP 6 5.61 0.32 0.04 1.07
6 40114 SMP 9 6.26 0.57 -0.36 0.80
7 40200 AWS 29 1.25 0.26 -0.79 0.58
8 40215 SMP 9 1.97 0.24 -1.26 0.71
9 41024 SMP 7 1.97 0.45 -2.50 1.31
10 50113 AWS 19 -0.02 0.41 -0.48 0.35
11 63042 SMP 8 1.95 0.98 -0.50 0.34
12 80200 AWS 14 -0.42 0.58 -1.01 0.33
13 81053 SMP 17 0.71 1.03 0.67 1.11
14 91803 SMP 18 0.26 0.49 0.19 0.42
15 100100 AWS 13 -0.25 0.31 1.47 0.38
16 100102 SMP 10 0.34 0.51 1.09 0.44
17 120101 AWS 6 0.08 0.51 -0.30 0.18
18 131005 SMP 11 -0.24 0.36 -0.91 0.29
19 131031 SMP 10 -0.15 0.30 0.20 0.23
20 133019 SMP 10 0.27 0.31 1.87 0.32
21 161010 SMP 13 1.46 0.58 1.07 0.72
22 183002 SMP 8 1.41 0.50 -0.23 0.42
23 200100 AWS 4 -0.67 0.28 -1.51 0.27
24 200200 AWS 4 0.64 0.43 0.73 0.19
25 204054 SMP 8 1.48 0.51 0.54 0.33
26 231026 SMP 19 0.43 0.38 0.44 0.56
27 241634 SMP 15 1.25 0.47 0.16 0.25
28 251002 SMP 16 -0.24 0.52 -2.03 0.57
29 271018 SMP 22 1.68 0.78 1.26 0.44
30 271028 SMP 32 0.88 0.42 0.11 0.55
31 274040 SMP 22 0.98 0.49 -0.09 0.54
32 276251 SMP 29 -0.61 0.43 -0.15 0.82
33 281016 SMP 14 0.15 0.61 -0.46 0.65
34 281802 SMP 12 -1.08 0.56 0.99 0.42
35 300800 AWS 25 1.39 0.61 -1.74 1.02
36 308129 SMP 21 0.98 0.60 -0.33 0.85
37 310100 AWS 3 -0.43 0.24 -0.65 0.11
38 310114 SMP 7 0.66 0.36 -0.99 0.40
39 313018 SMP 8 0.62 0.40 -1.57 0.62
40 320101 SMP 1 0.30 ? 0.54 ?
41 320200 AWS 17 0.84 0.39 -0.57 0.73
42 320204 SMP 1 0.03 ? 0.20 ?
43 331001 SMP 18 0.49 0.41 -1.08 0.36
44 350101 AWS 15 -0.13 0.58 -1.71 0.54
45 350801 AWS 4 0.45 0.59 -1.72 0.27
46 351112 SMP 9 0.91 0.58 -0.13 0.30
47 360800 AWS 13 0.57 0.94 -0.19 0.63
48 360801 SMP 11 1.13 1.11 0.05 0.77
49 364018 SMP 20 0.20 0.24 -0.83 0.30
50 370200 AWS 28 0.02 0.47 0.01 0.46
51 371028 SMP 12 -0.01 0.36 1.05 0.62
52 380200 AWS 12 0.45 0.40 -0.33 0.27
53 390200 AWS 19 -0.38 0.38 -0.29 0.39
54 404165 SMP 14 0.93 0.45 0.55 0.34
55 421606 SMP 11 0.03 0.20 -0.23 0.20
56 460800 AWS 2 -0.32 0.27 0.45 0.44
57 460804 SMP 10 0.51 0.57 -0.41 0.42
58 469187 SMP 8 0.15 0.28 0.63 0.35
59 480801 AWS 3 0.70 0.50 -0.34 0.71
60 481060 SMP 18 0.89 0.32 0.90 0.36
61 481068 SMP 16 -0.33 0.58 -0.91 0.66
62 481077 SMP 17 -0.03 0.30 -0.15 0.38
63 481122 SMP 16 -0.03 0.44 -0.85 0.63
64 483739 SMP 18 -0.49 0.43 0.49 0.40
65 484142 SMP 17 -1.20 0.93 -0.28 0.48
66 484143 SMP 11 0.63 0.40 -0.01 2.22
67 490800 AWS 1 1.95 ? 2.55 ?
68 491001 SMP 12 0.13 0.66 -1.75 0.80
69 493011 SMP 16 1.58 0.58 -0.16 0.72
70 501002 SMP 18 -0.45 0.48 -0.25 0.80
71 510100 AWS 11 -0.29 0.33 -0.87 0.49
72 510113 SMP 8 0.09 0.35 0.65 0.24
73 510114 SMP 8 0.76 0.41 -0.49 0.41
74 530200 AWS 20 -0.58 0.80 -0.90 0.41
75 530800 AWS 17 -0.34 0.40 -0.32 0.37
76 533813 SMP 10 0.80 0.49 -1.08 0.52
77 561007 SMP 17 0.47 1.01 -1.10 1.15
78 831801 SMP 28 0.02 0.31 -0.16 0.29
79 833802 SMP 16 -0.18 0.28 -0.13 0.53
80 871622 SMP 17 0.27 0.19 0.16 0.40
81 893015 SMP 22 0.17 0.40 0.34 0.49
82 906405 SMP 17 0.23 0.30 0.64 0.31
All Days   1120 0.51 1.21 -0.15 1.04
Average Section   13.7 0.58 0.47 -0.14 0.53

Precipitation and Freezing Index

The monthly and yearly precipitation estimates in the LTPP database were compared with the monthly SMP and AWS measured values, and the results are presented below.

Comparing Monthly Precipitation and Freezing Index

Table 16 includes the mean and standard deviation of error for the monthly precipitation and the freezing index (FI) estimates for 82 SMP and AWS sections. There were between 1 and 28 months of data for each section and a total of 1120 months of data. The overall values (mean and standard deviation for all months of data) and the average values per section are highlighted at the end of table 16.

The mean error of the precipitation estimate was between –5.8 and 38 millimeters (mm), with an average of 9.1 mm per section. The overall mean error for all months of data was 8.58 mm, which is not significantly different. The standard deviation of error was between 1.3 and 84.3 mm, and the average standard deviation per section was 18.6 mm. The overall standard deviation (22.3 mm) was higher.

The FI was calculated as the sum of all the mean daily temperatures less than 0 °C and is reported as °C-days. The mean error of the FI ranged from –8.6 to 55.8 °C-days, and the average mean error per section was 1.7 °C-days (overall average was 0.97 °C-days). The standard deviation of error was between zero and 26.8 °C-days, and the average standard deviation per section was 4.7 °C-days (overall standard deviation was 8.4 °C-days).

Comparing Yearly Precipitation and Freezing Index

Table 17 includes the mean and standard deviation of error for yearly total precipitation and the FI estimates for SMP and AWS sites. Only 37 sites had 1 or 2 years of measured and estimated (VWS) data, and 7 sites had 2 years of data.

As shown in table 17, the average of the mean error of the yearly precipitation estimates per section was 99.8 mm (overall mean was 97.5 mm), and the average standard deviation per section was 31.5 mm (overall standard deviation was 78.7 mm).

The average mean error of the FI estimate was about 9.4 °C-days (8.1 °C-days overall), and the average standard deviation per section was 9.5 °C-days. This value was substantially less than the overall standard deviation (around 50 °C-days).

Since precipitation and FI are accumulated values (rather than monthly mean values in the case of temperature), their variation is higher for yearly estimates (since yearly values accumulate the error). For this reason, both the average per section and the overall yearly statistics are significantly higher than the monthly estimates.

 

Table 16. Summary statistics for error of monthly precipitation and FI estimates.
No. SHRP
ID
Source of
Measured
Data
Months of
Data
Error (Virtual-Measured)
Precipitation, mm Freezing Index, °C
Mean Std. Dev. Mean Std. Dev.
1 10101 AWS 22 8.68 26.91 -0.15 1.40
2 ? SMP 8 26.85 20.22 -0.19 1.81
3 10102 SMP 14 23.14 19.65 0.35 1.88
4 40100 AWS 19 -3.27 4.88 0 0
5 40113 SMP 6 -3.62 6.26 0 0
6 40114 SMP 9 -3.88 7.53 0.01 0.02
7 40200 AWS 29 0.08 7.95 0 0
8 40215 SMP 9 -0.41 8.20 0 0
9 41024 SMP 7 2.40 8.29 2.01 5.03
10 50113 AWS 19 -2.58 21.42 -0.38 1.98
11 63042 SMP 8 3.02 13.18 0 0
12 80200 AWS 14 8.80 8.12 -3.93 5.68
13 81053 SMP 17 2.49 8.14 -0.29 12.13
14 91803 SMP 18 4.94 34.97 1.18 1.71
15 100100 AWS 13 9.95 23.13 4.53 6.00
16 100102 SMP 10 29.91 48.86 4.56 6.19
17 120101 AWS 6 10.63 49.70 0 0
18 131005 SMP 11 10.37 17.66 -0.73 1.85
19 131031 SMP 10 19.97 25.88 -0.07 0.22
20 133019 SMP 10 12.91 21.41 1.19 2.27
21 161010 SMP 13 10.52 9.37 9.90 15.62
22 183002 SMP 8 7.77 13.17 8.32 9.33
23 200100 AWS 4 -4.25 11.30 -4.68 7.51
24 200200 AWS 4 7.30 7.70 6.52 9.66
25 204054 SMP 8 9.39 7.56 13.54 16.21
26 231026 SMP 19 12.84 23.73 3.27 6.20
27 241634 SMP 15 9.08 31.70 1.32 2.41
28 251002 SMP 16 4.56 16.62 -4.99 11.65
29 271018 SMP 22 8.13 18.71 16.43 16.97
30 271028 SMP 32 11.68 14.81 6.70 7.45
31 274040 SMP 22 12.23 12.96 3.61 7.43
32 276251 SMP 29 9.90 15.45 -8.55 14.14
33 281016 SMP 14 6.11 26.35 0.49 2.35
34 281802 SMP 12 15.78 37.61 0.32 1.08
35 300800 AWS 25 4.74 7.00 2.62 7.48
36 308129 SMP 21 1.67 10.39 10.19 12.25
37 310100 AWS 3 -3.40 4.43 -0.67 1.15
38 310114 SMP 7 12.29 22.19 -1.13 5.33
39 313018 SMP 8 1.80 14.97 -5.62 5.83
40 320101 SMP 1 23.50 ? 8.20 ?
41 320200 AWS 17 3.85 13.18 1.18 3.25
42 320204 SMP 1 20.60 ? 4.70 ?
43 331001 SMP 18 0.72 15.40 -2.77 3.87
44 350101 AWS 15 5.04 16.12 -0.24 0.58
45 350801 AWS 4 3.25 2.49 0.01 0.02
46 351112 SMP 9 -1.70 20.41 0.32 0.64
47 360800 AWS 13 2.58 27.33 -4.82 7.70
48 360801 SMP 11 12.21 28.39 -3.71 6.15
49 364018 SMP 20 24.38 36.83 -1.84 5.02
50 370200 AWS 28 6.48 12.97 0.23 1.05
51 371028 SMP 12 4.83 19.69 1.55 2.61
52 380200 AWS 12 14.43 24.04 0.15 3.56
53 390200 AWS 19 13.51 23.69 -1.18 6.01
54 404165 SMP 14 7.22 18.31 1.60 3.24
55 421606 SMP 11 4.48 16.91 1.82 2.41
56 460800 AWS 2 26.10 1.27 2.55 3.39
57 460804 SMP 10 7.08 10.34 -2.73 5.66
58 469187 SMP 8 12.59 13.52 4.12 7.76
59 480801 AWS 3 2.30 4.37 -0.08 0.14
60 481060 SMP 18 6.47 32.21 0 0
61 481068 SMP 16 4.62 27.95 -0.62 1.63
62 481077 SMP 17 1.36 13.64 0.31 2.29
63 481122 SMP 16 4.29 18.08 0 0
64 483739 SMP 18 8.41 14.18 0 0
65 484142 SMP 17 15.11 37.33 -0.13 0.52
66 484143 SMP 11 3.52 24.17 -0.09 0.30
67 490800 AWS 1 28.10 ? 55.80 ?
68 491001 SMP 12 0.57 3.74 -2.61 5.22
69 493011 SMP 16 6.81 6.65 8.79 10.08
70 501002 SMP 18 21.46 25.32 -0.59 6.77
71 510100 AWS 11 16.68 25.38 -1.07 1.93
72 510113 SMP 8 12.84 15.52 -0.13 0.33
73 510114 SMP 8 3.34 22.41 -0.21 0.73
74 530200 AWS 20 -5.83 14.56 -4.43 8.85
75 530800 AWS 17 9.11 14.18 0.87 5.90
76 533813 SMP 10 38.04 84.33 -0.15 2.29
77 561007 SMP 17 5.71 5.79 -2.43 26.76
78 831801 SMP 28 12.32 14.84 -0.27 4.15
79 833802 SMP 16 18.96 24.27 -1.10 3.46
80 871622 SMP 17 23.46 25.70 1.87 5.30
81 893015 SMP 22 6.61 18.61 0.29 7.05
82 906405 SMP 17 13.24 10.03 7.29 9.15
All Months   1120 8.58 22.31 0.97 8.4
Average Section   13.7 9.10 18.60 1.7 4.7

 

Table 17. Summary statistics for error of yearly precipitation and FI estimates.
No. SHRP
ID
Source of
Measured
Data
Years of
Data
Error (Virtual-Measured)
Precipitation, mm Freezing Index, °C
Mean Std. Dev. Mean Std. Dev.
1 10101 AWS 2 84.65 36.98 -1.03 6.61
2 40100 AWS 1 -69.10 ? 0 ?
3 40200 AWS 2 4.50 8.63 0 0
4 50113 AWS 1 -2.60 ? -3.95 ?
5 80200 AWS 1 109.40 ? -26.30 ?
6 91803 SMP 1 138.50 ? 7.75 ?
7 100100 AWS 1 139.40 ? 44.60 ?
8 161010 SMP 1 91.60 ? 142.45 ?
9 231026 SMP 1 184.10 ? 13.00 ?
10 251002 SMP 1 15.50 ? -97.65 ?
11 271018 SMP 1 28.70 ? 144.95 ?
12 271028 SMP 2 113.75 14.50 56.27 5.55
13 274040 SMP 1 118.20 ? 37.65 ?
14 276251 SMP 2 117.55 43.91 -72.10 28.71
15 300800 AWS 2 53.85 26.38 32.27 5.62
16 308129 SMP 1 -2.00 ? 108.65 ?
17 320200 AWS 1 44.20 ? 22.45 ?
18 331001 SMP 1 35.70 ? -39.10 ?
19 350101 AWS 1 74.70 ? -2.50 ?
20 360800 AWS 1 11.60 ? -44.95 ?
21 364018 SMP 1 160.30 ? -13.15 ?
22 370200 AWS 2 86.90 1.41 3.20 1.41
23 380200 AWS 1 106.60 ? 14.10 ?
24 481060 SMP 1 117.30 ? 0 ?
25 481068 SMP 1 33.80 ? -9.65 ?
26 481077 SMP 1 3.10 ? 13.60 ?
27 481122 SMP 1 102.10 ? 0 ?
28 483739 SMP 1 147.70 ? 0 ?
29 484142 SMP 1 153.90 ? -0.40 ?
30 501002 SMP 1 323.90 ? -45.80 ?
31 530200 AWS 1 226.30 ? -79.30 ?
32 530800 AWS 1 125.70 ? 12.95 ?
33 561007 SMP 1 49.70 ? 57.60 ?
34 831801 SMP 2 135.50 88.67 -11.65 17.82
35 833802 SMP 1 269.10 ? -15.40 ?
36 871622 SMP 1 236.10 ? 14.85 ?
37 906405 SMP 1 124.00 ? 84.85 ?
All Years   44 97.50 78.70 8.10 50.30
Average Section   1.2 99.80 31.50 9.40 9.40

Humidity

The daily estimates of maximum and minimum humidity in the LTPP database were compared with the AWS measured humidity to assess the accuracy of the estimated humidity values. Only 10 AWS sections had both measured and estimated humidity data. These data were combined into a database that had data for about 4100 days.

Comparing Daily Maximum and Minimum Humidity

Table 18 includes the mean error and standard deviation for daily maximum and minimum humidity estimates. The average mean error of the maximum humidity per section was –4.8 percent (–4.2 percent overall), and the standard deviation (Std. Dev. column) was 6.1 percent (7.3 percent overall).

The average mean error of the minimum humidity was 2.1 percent (2.5 percent overall), and the standard error was 7.8 percent (8.6 percent overall). The results indicated that the maximum humidity estimates were made slightly more accurately than the minimum humidity estimates. Generally, daily humidity estimates were within 10 percent of the measured data.

 

Table 18. Summary statistics for error of daily maximum and minimum humidity estimates.
AWS ID Error (Virtual-Measured), percent
Maximum Humidity Minimum Humidity
Mean Std. Dev. Days Mean Std. Dev. Days
010100 -5.5 6.8 674 4.2 7.3 674
120100 -9.3 7.5 201 6.0 7.5 201
200100 -2.6 4.6 147 1.4 7.7 147
200200 -2.4 5.6 146 5.4 6.6 146
310100 -2.1 3.9 146 2.8 6.1 146
360800 1.6 5.3 405 1.9 10.4 405
370200 -6.6 7.6 859 4.2 7.1 869
380200 -3.0 3.9 408 0.6 7.0 408
390200 -5.8 6.7 567 -3.6 8.2 635
530800 -6.3 9.1 526 1.8 10.5 526
Days -4.8 7.3 4079 2.1 8.6 4157
Average Section -4.2 6.1 407.9 2.5 7.8 415.7

Comparing Monthly Maximum and Minimum Humidity

The mean error and standard deviation of the monthly humidity estimates (minimum and maximum) are shown in table 19. This table includes 142 months of data (from 5 to 29 months per site).

The average mean error per section was similar to the daily estimates (–4 percent and 2.6 percent for maximum and minimum humidity, respectively); however, the average standard deviation was less than half of the daily estimates (2.1 percent and 3.4 percent for maximum and minimum humidity, respectively).

 

AWS ID Error (Virtual-Measured), percent
Maximum Humidity Minimum Humidity
Mean Std. Dev. Months Mean Std. Dev. Months
010100 -5.5 3.1 23 4.5 3.2 23
120100 -9.1 3.0 7 6.1 3.3 7
200100 -2.5 1.0 5 1.6 4.3 5
200200 -2.3 1.0 5 5.5 1.8 5
310100 -2.0 1.0 5 2.9 2.2 5
360800 1.9 2.1 14 2.2 4.1 14
370200 -6.5 3.0 29 4.3 2.8 29
380200 -2.9 1.7 14 0.7 3.2 14
390200 -5.2 2.8 22 -3.5 4.9 22
530800 -6.3 2.2 18 2.1 3.9 18
All Months -4.6 3.7 142 2.3 4.5 142
Average Section -4.0 2.1 14.2 2.6 3.4 14.2

Windspeed

The daily and monthly windspeed estimates were compared to the measured AWS data. As with humidity, only 10 AWS sites had both average windspeed estimates (VWS) and measured data. However, only four sites had maximum windspeed estimates and measured data. This is mainly a result of the lack of data for maximum windspeed in the VWS monthly table.

Comparing Daily Average and Maximum Windspeeds

Table 20 includes the mean error and standard deviation for the daily average and maximum windspeeds. There were 4183 days with estimated and measured average windspeed data, but only 1365 days for maximum windspeed (because of lack of estimates).

The mean error of the average daily windspeed estimate was 1.4 kilometers per hour (km/h), and the standard deviation was 1.1 km/h. The mean error of the maximum daily windspeed was 1.5 km/h, and the standard deviation was 2.2 km/h. The average per section values was similar to the overall values.

These data indicate that the daily windspeed estimates were estimated within 1 to 2 km/h of the measured values.

 

Table 20. Summary statistics for error of daily average and maximum windspeed estimates.
SHRP ID Error (Virtual-Measured), km/h
Average Windspeed Maximum Windspeed
Mean Std. Dev. Days Mean Std. Dev. Days
010100 1.3 0.7 691 ? ? 0
120100 2.0 1.1 201 ? ? 0
200100 2.0 0.8 146 ? ? 0
200200 1.6 0.9 146 ? ? 0
310100 0.8 0.7 146 ? ? 0
360800 2.4 1.1 404 3.3 2.4 219
370200 2.0 0.9 875 2.3 1.7 420
380200 1.3 0.8 408 1.4 1.9 287
390200 0.3 0.7 634 0.1 1.8 439
530800 0.6 0.9 532 ? ? 0
All Days 1.4 1.1 4183 1.5 2.2 1365
Average Section 1.4 0.9 418.3 1.8 2.0 136.5

Comparing Monthly Average and Maximum Windspeeds

Table 21 includes the mean error and standard deviation for the monthly average and maximum windspeeds. There are 142 months of estimated and average windspeed data and only 47 months of data for the maximum windspeed.

The mean error of the average and maximum monthly windspeeds was similar to the daily data (1.3 and 1.5 km/h). However, the standard deviations were lower for the monthly data (0.8 and 1.3 km/h). The average per section mean error was similar to the overall error; however, the average standard deviation was less than half of the overall value.

In general, the monthly windspeed estimates were estimated within 1 km/h of the measured values.

 

Table 21. Summary statistics for error of monthly average and maximum windspeed estimates.
SHRP ID Error (Virtual-Measured), km/h
Average Windspeed Maximum Windspeed
Mean Std. Dev. Months Mean Std. Dev. Months
010100 1.3 0.3 23 ? ? 0
120100 2.0 0.4 7 ? ? 0
200100 1.9 0.3 5 ? ? 0
200200 1.6 0.3 5 ? ? 0
310100 0.8 0.2 5 ? ? 0
360800 2.4 0.4 14 3.2 0.5 8
370200 2.0 0.3 29 2.3 0.5 14
380200 1.2 0.2 14 1.4 0.3 10
390200 0.3 0.5 22 0.1 0.6 15
530800 0.6 0.2 18 ? ? 0
All Months 1.3 0.8 142 1.5 1.3 47
Average Section 1.4 0.3 14.2 1.8 0.5 4.7

Summary of Comparisons

A summary of all of the comparisons performed between the estimated (VWS) and measured (AWS and SMP) LTPP climatic data is presented in table 22. This table includes the per section average for the mean and standard deviation of the error. Depending on the parameter, the results are shown either for daily and monthly or monthly and yearly estimates. The following are some general observations drawn from the comparisons:

  • Daily and monthly temperatures were estimated within 2.5 and 0.5 °C, respectively.
  • Monthly and yearly precipitation were estimated within 19 and 32 mm, respectively.
  • Monthly and yearly FI were estimated within 5 and 10 °C-days.
  • Daily and monthly humidity were estimated within 7 and 3 percent.
  • Daily and monthly windspeeds were estimated within 2 and 0.5 km/h.

 

Table 22. Summary statistics for error of various LTPP VWS estimates for AWS and SMP sites.
Parameter Unit Period Number Error (Measured-Estimated)
Mean Std. Dev.
Maximum Temperature °C Daily 38665 0.57 2.75
°C Monthly 1120 0.58 0.47
Minimum Temperature °C Daily 38665 -0.13 2.26
°C Monthly 1120 -0.14 0.53
Precipitation mm Monthly 1120 9.10 18.60
mm Yearly 44 99.80 31.50
Freezing Index °C Monthly 1120 1.70 4.70
°C Yearly 44 9.40 9.40
Maximum Humidity % Daily 4079 -4.20 6.10
% Monthly 142 -4.00 2.10
Minimum Humidity % Daily 4157 2.50 7.80
% Monthly 142 2.60 3.40
Average Windspeed km/h Daily 4183 1.40 0.90
km/h Monthly 142 1.40 0.30
Maximum Windspeed km/h Daily 1365 1.80 2.00
km/h Monthly 47 1.80 0.50
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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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