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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 3: Determine Accuracy of Vws Estimates and Verify The Vws Algorithm (Cont.)

Comparing Measured Daily Temperatures to Estimates from a Simple Average

The same approach used for SMP and AWS sites was used here to determine the precision and bias of estimates for 5347 locations throughout the United States. For this purpose, the climatic data for all cooperative weather stations from the NCDC between 1994 and 1996 (1096 days) were used. For every weather station, the five closest weather stations were determined and the estimated daily weather data were calculated by simply averaging data for the five closest weather stations, without using distance as a weight or eliminating weather stations with a high elevation difference. The estimated data were then compared with the measured data at the site.

Table 32 shows the mean and standard deviation error for minimum and maximum temperatures by elevation. The results in table 32 indicate that the mean error (estimate bias) increases with elevation. This is because elevation differences between the weather stations are more probable at higher elevations. The lowest mean error was for elevations of less than 250 m; however, the standard deviation did not significantly differ. Below this elevation, the overall standard deviation was 2.1 °C for maximum and 1.9 °C for minimum temperatures. Almost 40 percent of the weather stations in the United States are located below a 250-m elevation. Figures 34 through 37 show the distribution of the mean and standard deviation of the errors for maximum and minimum temperatures.

The overall precision and bias of maximum (2.2 and 0.2 °C, respectively) and minimum (2.0 and 0.1 °C, respectively) temperatures are comparable to the results from the AWS and SMP sections. Since the estimated bias increases with the elevation difference, the bias can be remedied by correcting the temperature for the elevation difference.

 

Table 32. Summary statistics of mean error for maximum and minimum temperatures versus weather station elevation.
Elevation Number of Sites Number of Days Error (Estimated-Measured), °C
Maximum Temperature Minimum Temperature
Mean Std. Dev. Mean Std. Dev.
0-250 2168 2,214,330 -0.1 2.1 -0.1 1.9
250-500 1231 1,258,811 0 2.3 0 2.1
500-750 470 473,303 0.2 2.4 0.2 2.1
750-1000 316 326,772 0.2 2.3 0.2 2.0
1000-1250 267 276,052 0.4 2.3 0.3 2.0
1250-1500 312 325,627 0.2 2.3 0.1 2.1
1500-1750 213 219,487 0.6 2.4 0.6 2.3
1750-2000 162 166,121 0.9 2.3 0.5 2.4
2000-2250 107 106,261 1.4 2.2 0.9 2.4
All Days 5347 5,471,796 0.2 2.2 0.1 2.0

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Figure 34. Bar chart. Distribution of mean error for maximum temperature (NCDC data).

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Figure 35. Bar chart. Distribution of mean error for minimum temperature (NCDC data).

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Figure 36. Bar chart. Distribution of standard deviation of error for maximum temperature (NCDC data).

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Figure 37. Bar chart. Distribution of standard deviation of error for minimum temperature (NCDC data).

Correcting Temperature for Elevation Difference

In this part of the study, maximum temperatures were corrected for elevation differences and the results of the corrected and uncorrected errors were compared. The LTPP AWS and SMP databases were used for the study and the maximum temperature was corrected using the following algorithm derived from the analysis of the elevation differences in table 26:

  • Temperature correction was applied to elevation differences between 250 and 1000 m (higher and lower elevation differences).
  • For every 100-m increase in elevation, 0.75 °C was subtracted from the temperature (0.75 °C was added for elevation decrease) as Corrected Maximum Temperature = Maximum Temperature – Elevation Difference (km) * 7.5 °C.

Table 33 includes the mean and standard deviation of error for maximum temperature estimates using a simple average (corrected and uncorrected). Table 34 includes the same data for SMP sections. In both cases, correcting the maximum temperature dramatically reduced the bias, while the standard deviation did not change significantly.

 

Table 33. Summary statistics of error for AWS sections (corrected for elevation).
No. AWS
ID
Days
of
Data
Mean Error (AWS-Estimate), °C Standard Deviation Error, °C
IMS
VWS
No
Weight
Corrected
No Weight
IMS
VWS
No
Weight
Corrected
No Weight
1 10101 686 -0.1 0 0 3.0 2.9 2.9
2 40100 606 5.0 4.1 3.2 1.3 1.5 1.6
3 40200 892 1.3 1.0 1.0 1.6 1.5 1.5
4 50113 601 0 -0.2 -0.2 3.2 3.1 3.1
5 80200 459 -0.4 -0.1 -0.1 5.8 2.7 2.7
6 100100 410 -0.2 -0.1 -0.1 2.6 2.3 2.3
7 120101 201 0.1 -0.3 -0.3 2.2 1.8 1.8
8 200100 147 -0.5 0.5 0.5 5.0 2.7 2.7
9 200200 146 0.5 -0.1 -0.1 2.8 3.3 3.3
10 300800 763 1.4 0.7 -1.5 2.5 2.7 2.7
11 310100 143 -0.4 0.1 0.1 4.1 2.4 2.4
12 320200 570 0.8 0.4 0.4 1.5 2.1 2.1
13 350101 458 -0.1 -0.3 -0.3 2.5 2.4 2.4
14 350801 142 0.3 0 -0.6 1.4 1.6 1.7
15 360800 403 0.6 0.5 0.2 2.3 2.7 2.7
16 370200 877 0 -0.2 -0.2 1.6 1.8 1.8
17 380200 402 0.5 0.4 0.4 4.1 1.6 1.6
18 390200 635 -0.4 0.1 0.1 4.3 3.2 3.2
19 460800 68 -0.2 -0.1 -0.1 1.6 1.6 1.6
20 480801 90 0.7 0.4 0.4 2.1 3.0 3.0
21 490800 43 2.3 2.3 2.3 2.3 2.4 2.4
22 510100 362 -0.3 -0.6 -0.6 4.5 3.7 3.7
23 530200 631 -0.6 0.2 0.2 3.1 2.1 2.1
24 530800 525 -0.4 -0.4 -0.4 3.7 2.9 2.9
All Days 10260 0.48 0.39 0.15 3.31 2.67 2.64
Average Section 427.5 0.41 0.35 0.18 2.88 2.42 2.43

 

Table 34. Summary statistics of error for SMP sections (corrected for elevation).
No. SMP
ID
Days
of
Data
Mean Error (Estimate-SMP), °C Standard Deviation Error, °C
IMS
VWS
No
Weight
Corrected
No Weight
IMS
VWS
No
Weight
Corrected
No Weight
1 100102 335 0.4 0.4 0.4 2.5 2.3 2.3
2 131005 395 -0.3 0 0 2.7 2.3 2.3
3 131031 342 -0.1 -0.4 -3.5 3.4 2.6 2.6
4 133019 353 0.3 0.2 0.2 3.3 2.6 2.6
5 161010 518 1.4 1.3 1.3 1.9 2.2 2.2
6 183002 287 1.4 1.4 1.4 3.6 3.3 3.3
7 204054 302 1.4 0.7 0.7 3.3 4 4
8 231026 627 0.4 0.5 0.5 2.9 3.1 3.1
9 241634 502 1.3 1.1 1.1 1.6 1.8 1.8
10 251002 569 -0.2 -0.3 -0.4 3.3 3.4 3.4
11 271018 898 1.4 0.3 0.3 3.2 2.8 2.8
12 271028 1057 0.9 0.8 0.8 2.5 2.8 2.8
13 274040 727 0.8 0.7 0.7 4.4 3.4 3.4
14 276251 979 -0.6 -0.5 -0.5 4.3 3.5 3.5
15 281016 457 0.1 0.1 0.1 3.2 2.3 2.3
16 281802 410 -1.1 -1 -1 2.1 2.6 2.6
17 308129 692 0.9 0.6 0.6 2.9 2.9 2.9
18 310114 309 0.6 1.2 1.2 4.7 2.8 2.8
19 313018 313 0.6 1.1 1.1 5.7 3.6 3.6
20 320204 52 0.2 0 0 1.9 2 2
21 331001 624 0.5 0.2 0.2 0.7 2.2 2.2
22 351112 356 0.9 1.4 1.4 1.6 1.4 1.4
23 360801 355 1.2 1.1 1.1 2.5 2.8 2.8
24 364018 636 0.2 0 -1.7 3.3 2.7 2.7
25 371028 464 0 -0.2 -0.2 1.8 2 2
26 404165 495 0.9 1.2 1.2 3.8 2.7 2.7
27 421606 362 0 0 0 2 3 3
28 460804 406 0.5 0.5 0.5 1.7 1.7 1.7
29 469187 342 0.2 0.4 0.4 3.5 3.5 3.5
30 481060 577 0.9 0.9 0.9 1.4 1.4 1.4
31 481068 583 -0.4 -0.3 -0.3 4 3.9 3.9
32 481077 605 0 0.2 0.2 2.8 2.8 2.8
33 481122 535 0 -0.2 -0.2 3.1 2.2 2.2
34 483739 601 -0.5 -0.6 -0.6 3 2.9 2.9
35 484142 611 -1.2 -0.5 -0.5 4.1 3.3 3.3
36 484143 447 0.6 0.5 0.5 4.1 3.5 3.5
37 491001 536 0.2 0 -0.9 1.4 1.6 1.6
38 493011 603 1.6 0.9 0.9 2.1 1.9 1.9
39 501002 597 -0.5 0 -0.8 3 2.2 2.2
40 510114 266 0.8 0.4 0.4 4.3 3.5 3.5
41 533813 356 0.8 0.2 0.2 3 2.2 2.2
42 561007 588 0.5 0.3 0.3 4 4.1 4.1
43 831801 973 0 0 0 1.3 1.2 1.2
44 833802 575 -0.2 0.1 0.1 1.4 1.3 1.3
45 871622 581 0.2 0.3 0.3 1.3 1.2 1.2
46 893015 782 0.2 0.5 0.5 1.6 1.4 1.4
47 906405 605 0.2 0.1 0.1 1.7 1.7 1.7
All Days 24585 0.35 0.3 0.17 3.02 2.7 2.76
Average Section 523.1 0.37 0.33 0.19 2.81 2.57 2.57

Comparing Climatic Estimates from NCDC Data

Estimated climatic data were developed for NCDC weather station sites and were then compared to the measured NCDC data. Climatic estimates were developed by averaging data for the five closest weather stations for each NCDC site without using a weight. Table 35 includes the overall average and standard deviation of error (measured minus estimated) for the daily, monthly, and yearly climatic estimates of 5347 NCDC sites throughout the United States. The data period covers 1994 through 1996 and included 1096 days of data for each site. The following are some observations from the results:

  • Using a simple average of data from the five closest weather stations, maximum and minimum daily temperatures can be estimated within 2.2 °C.
  • Monthly minimum and maximum temperatures can be estimated within 0.7 °C.
  • Yearly minimum and maximum temperatures can be estimated within 0.6 °C.
  • Monthly and yearly precipitation can be estimated within 29 mm and 147 mm, respectively.
  • Yearly FI can be estimated within 56 °C-days.

These statistics were calculated using all observations and are overall values. The overall values are generally higher than the average per section values, especially for accumulated data such as precipitation and FI. This is caused by the effect of bias on the standard deviation (locations with a high bias will contribute more to the standard deviation).

 

Table 35. Overall mean and standard deviation of error of daily, monthly, and yearly estimates for NCDC sites.
Parameter Period Frequency Error (Estimated-Measured)
Mean Std. Dev.
Maximum Temperature, °C Daily 5,471,796 0.1 2
Monthly 178,840 0 0.7
Yearly 15,631 0 0.6
Minimum Temperature, °C Daily 5,471,796 0.2 2.2
Monthly 175,411 0 0.7
Yearly 15,622 0 0.6
Precipitation, mm Monthly 235,286 -3.4 28.6
Yearly 22,929 -35 147.3
Yearly Freezing Index, °C Yearly 23,969 -17.5 55.8
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