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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.

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

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

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.

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

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

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

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 windspeed