U.S. Department of Transportation
1200 New Jersey Avenue, SE
Washington, DC 20590
202-366-4000

Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

 This report is an archived publication and may contain dated technical, contact, and link information
 Federal Highway Administration > Publications > Research Publications > Infrastructures > Pavements > LTPP Publications > 03092 > Verification of LTPP Virtual Weather Stations Phase I Report: Accuracy and Reliability of Virtual Weather Stations
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 Different Methods of Calculating VWS Estimates

Climatic data from five weather stations (OWS) near SMP and AWS sites were compared to the collected SMP and AWS data. The daily data for the five closest weather stations (OWS data) were averaged using three different methods: (1) without using a weight, (2) by using the inverse distance square (1/R2) weight, and (3) by using the inverse distance (1/R) weight. Also, estimates were made based on the data from the closest weather station. The resulting estimates were then compared with the LTPP VWS estimates and SMP and AWS measured data.

#### Different Methods of Calculating VWS

Four different methods of calculating VWS were compared with the LTPP VWS estimates currently available in the IMS database to investigate the possibility of improving the current LTPP methodology. The four methods of estimating climatic conditions at a site using data from nearby weather stations were:

1. Closest: Estimate climatic conditions based on data from the closest weather station.
2. Weight 1/R2: Estimate the climatic parameter based on averaging the data for up to five of the closest weather stations weighted by the inverse squared distance.
3. Weight 1/R: Similar to the previous method; however, weighting by the inverse distance.
4. No Weight: Calculate estimates based on a simple average without using any weight, as shown in figure 31.

Figure 31. Equation. Average temperature calculation.

where:

Vm = Calculated data element for day m for the VWS.
k = Number of weather stations associated with the project site (up to five).
Vmi = Value of a data element on day m for weather station i.

Figure 32 shows the distribution of the percent contribution of the closest weather station to the estimated value for all 880 LTPP sites when using the 1/R2 rule. The percent contribution is the ratio of the weight (1/R2) of the closest weather station to the sum of the weights for all of the weather stations. It shows that the closest weather station contributed more than 70 percent to the VWS estimate for half of the LTPP sites. For this reason, the LTPP VWS estimates are closer to data from the closest weather station. Figure 33 shows results for the 1/R rule. It shows that the contribution of the closest weather station to the estimate is significantly less (less than 50 percent half of the time) with this method. This method provides results that are close to using a simple average.

Figure 32. Bar chart. Percent contribution of closest weather stations to VWS using the 1/R2 rule.

Figure 33. Bar chart. Percent contribution of closest weather stations to VWS using the 1/R rule.

The overall daily and monthly summaries for the AWS and SMP sections combined are shown in table 27.

Table 27. Summary statistics for error of daily and monthly estimates of AWS and SMP maximum temperature using five different calculation methods.
Temp. Period Freq. Mean Error (Estimated-Measured), °C Standard Deviation Error, °C
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
Max. Daily 30601 0.41 0.47 0.45 0.41 0.34 3.13 3.41 3.03 2.81 2.69
Min. Daily 30601 -0.14 -0.11 -0.03 -0.06 -0.12 2.58 3.05 2.65 2.43 2.33
Max. Monthly 1170 0.41 0.48 0.44 0.4 0.33 1.14 1.44 1.26 1.12 0.99
Min. Monthly 1170 -0.14 -0.11 -0.03 -0.06 -0.11 1.44 1.85 1.59 1.45 1.40

The following observations were made from table 27:

• The simple average method (No Weight column) provided the lowest standard deviation of all the methods for the daily and monthly estimates.
• The next lowest standard deviation was provided by the inverse distance method (Weight 1/R column), which provided more precise estimates (lower standard error) than the inverse distance squared method (Weight 1/R2 column).
• The estimate based on the closest weather station (Closest column) gave the highest standard error and the highest mean error. This method provided the poorest climatic estimates.
• All methods gave a similar mean error of the estimate for the daily and monthly estimates.
• The overall standard deviation of error of the simple average method was at least 10 percent lower than the inverse squared distance method (Weight 1/R2 column).

In summary, the SMP and AWS data showed that the simple average method was the best method, while weighting by 1/R was the next best. Estimates from the closest weather station were the poorest. This validates the use of multiple weather stations in estimates.

#### Comparing Different Methods of Estimating

The four different methods of estimating daily climatic data explained in the previous section and the VWS estimates currently in the IMS were compared with the climatic data for the AWS sections. Table 28 includes the mean and standard deviation of error (difference between the AWS measured and estimated temperatures) for the maximum air temperature for the five different methods of estimating the daily temperature. Table 29 includes the same data for minimum temperature. Similar data for SMP sites are included in tables 30 and 31.

Table 28. Summary statistics for error of daily estimates of AWS maximum temperature using three different calculation methods.
No. AWS
ID
Days
of
Data
Mean Error (AWS-Estimate), °C Standard Deviation Error, °C
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
1 10101 673 -0.05 -0.39 -0.05 -0.02 0 3.03 3.58 3.05 2.97 2.90
2 40100 604 4.98 7.02 6.56 5.63 4.14 1.28 2.18 2.03 1.80 1.52
3 40200 643 1.29 1.49 1.29 1.16 1.04 1.62 1.66 1.62 1.57 1.52
4 50113 579 0.05 0.29 -0.02 -0.08 -0.14 3.20 4.26 3.46 3.27 3.13
5 80200 443 -0.45 -0.48 -0.44 -0.31 -0.07 5.82 6.37 5.84 4.44 2.74
6 100100 395 -0.26 -0.43 -0.26 -0.21 -0.17 2.59 2.04 2.55 2.49 2.29
7 120101 201 0.05 0.23 0.04 -0.13 -0.33 2.23 2.43 2.23 2.03 1.82
8 200100 144 -0.58 -0.12 -0.12 -0.12 0.46 5.09 1.45 1.44 1.31 2.69
9 200200 141 0.45 1.20 0.50 0.18 -0.14 2.75 2.11 2.78 3.08 3.28
10 300800 706 1.40 1.47 1.41 1.14 0.65 2.48 2.51 2.48 2.44 2.69
11 310100 139 -0.38 -0.55 -0.37 -0.17 0.05 4.14 5.16 4.17 3.29 2.45
12 320200 547 0.82 1.06 0.83 0.61 0.35 1.51 1.45 1.50 1.67 1.98
13 350101 150 0.40 0.96 0.40 0.14 -0.08 2.69 3.13 2.71 2.55 2.45
14 350801 141 0.33 2.11 1.68 0.98 0.03 1.37 2.21 1.96 1.73 1.63
15 360800 391 0.58 0.67 0.59 0.57 0.56 2.33 2.46 2.35 2.46 2.67
16 370200 863 0 0 0 -0.03 -0.17 1.60 1.60 1.60 1.63 1.81
17 380200 389 0.48 0.50 0.48 0.46 0.44 4.06 4.40 4.09 3.03 1.59
18 390200 611 -0.42 -0.53 -0.42 -0.20 0.10 4.33 4.59 4.33 3.84 3.20
19 460800 66 -0.25 -0.60 -0.26 -0.15 -0.14 1.66 1.91 1.65 1.60 1.64
20 480801 69 0.89 1.45 0.90 0.72 0.55 1.36 0.71 1.35 1.93 2.57
21 490800 40 2.39 1.86 2.35 2.43 2.49 2.25 2.17 2.28 2.35 2.42
22 510100 358 -0.30 -0.05 -0.29 -0.45 -0.54 4.47 4.62 4.48 4.17 3.70
23 530200 597 -0.55 -0.90 -0.47 -0.14 0.21 3.07 3.65 2.95 2.48 2.07
24 530800 497 -0.35 -0.20 -0.21 -0.25 -0.40 3.61 2.10 2.08 2.12 2.77
All Days 9387 0.5 0.69 0.64 0.55 0.40 3.36 3.74 3.43 3.04 2.69
Avg. Section 391.1 0.44 0.67 0.59 0.49 0.37 2.86 2.86 2.71 2.51 2.40

Table 29. Summary statistics for error of daily estimates of AWS minimum temperature using three different calculation methods.
No. AWS ID Days
of
Data
Mean Error (AWS-Estimate), °C Standard Deviation Error, °C
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
IMS
VWS
Closest Weight
1/R^2
Weight
1/R
No
Weight
1 10101 673 -0.01 -0.75 -0.01 0.01 -0.01 2.07 2.60 2.07 2.01 1.98
2 40100 604 2.24 6.66 5.21 3.02 0.22 2.34 2.31 2.23 2.22 2.35
3 40200 643 -1.01 -1.46 -1.01 -0.55 0 1.54 1.83 1.54 1.39 1.34
4 50113 579 -0.47 -0.77 -0.82 -0.66 -0.45 2.03 3.01 2.23 2.02 1.83
5 80200 443 -1.05 -1.09 -1.06 -0.98 -0.93 2.70 2.97 2.70 2.06 1.51
6 100100 395 1.45 1.26 1.44 1.61 1.75 1.96 1.94 1.96 1.90 1.77
7 120101 201 -0.26 -0.35 -0.26 -0.15 0.05 1.20 1.35 1.20 1.12 1.20
8 200100 144 -1.36 -0.93 -0.93 -0.94 -0.61 2.98 1.31 1.30 1.24 1.61
9 200200 141 0.77 1.38 0.81 0.55 0.32 1.81 1.74 1.83 1.90 1.94
10 300800 706 -1.67 -1.58 -1.66 -1.98 -2.48 2.35 2.42 2.35 2.15 2.21
11 310100 139 -0.53 -0.81 -0.54 -0.29 -0.02 2.42 2.97 2.42 1.93 1.50
12 320200 547 -0.58 -0.62 -0.58 -0.57 -0.58 1.95 2.12 1.95 1.85 1.82
13 350101 150 -1.25 -0.88 -1.27 -1.47 -1.66 1.87 2.23 1.87 1.78 1.76
14 350801 141 -1.71 1.23 0.49 -0.52 -1.70 1.67 2.23 1.93 1.72 1.72
15 360800 391 -0.21 0.08 -0.19 -0.31 -0.44 1.71 1.89 1.72 1.74 1.83
16 370200 863 0.01 0.03 0.01 -0.15 -0.35 1.94 1.96 1.94 1.75 1.51
17 380200 389 -0.26 -0.33 -0.26 -0.05 0.24 2.76 2.97 2.77 2.13 1.42
18 390200 611 -0.27 -0.39 -0.27 -0.04 0.28 3.19 3.46 3.19 2.74 2.25
19 460800 66 0.49 0.38 0.50 0.54 0.57 2.17 2.44 2.17 2.06 1.98
20 480801 69 -0.04 0.96 -0.03 -0.43 -0.80 1.16 0.74 1.16 1.67 2.21
21 490800 40 2.88 2.69 2.82 2.88 2.97 2.92 2.97 2.96 3.01 3.09
22 510100 358 -0.86 -0.32 -0.84 -1.22 -1.51 3.06 3.19 3.06 2.80 2.41
23 530200 597 -0.89 -1.09 -0.71 -0.33 0.13 1.85 2.18 1.81 1.65 1.62
24 530800 497 -0.34 0.77 0.72 0.49 -0.36 1.62 1.76 1.70 1.50 1.45
All Days 9387 -0.30 0.01 -0.02 -0.15 -0.34 2.40 3.09 2.68 2.27 2.05
Avg. Section 391.1 -0.21 0.17 0.07 -0.06 -0.22 2.14 2.27 2.09 1.93 1.85