Task 3, Verification of LTPP Virtual Weather Stations Phase I Report: Accuracy and Reliability of Virtual Weather Stations, FHWA-RD-03-092 - LTPP - Pavements

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

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:

Closest: Estimate climatic conditions based on data from the closest weather station.
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.
Weight 1/R: Similar to the previous method; however, weighting by the inverse distance.
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
Temp.	Period	Freq.	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
No.	AWS ID	Days of Data	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
No.	AWS ID	Days of Data	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

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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

Comparing Different Methods of Calculating VWS Estimates

Different Methods of Calculating VWS

Comparing Different Methods of Estimating

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