Appendix A: Calibration Results for Speed-Density Relation and WAF

Highway	Milemark	Station ID	Weather condition	k_bp (vpmpl)	u_f (mph)	v_f (mph)	α	v₀ (mph)	k_jam (vpmpl)>	RMSE¹ (reg.1)	R-sqrd²(reg.2)	# of obs.		Weather Adjustment Factor (WAF)³
Highway	Milemark	Station ID	Weather condition	k_bp (vpmpl)	u_f (mph)	v_f (mph)	α	v₀ (mph)	k_jam (vpmpl)>	RMSE¹ (reg.1)	R-sqrd²(reg.2)	reg.1	reg.2	F_k_bp	F_u_f	F_v_f	F_f_max
I-64	284.2	6	Normal	16	61.5	83.4	4.2	2	225	4.2	0.72	296	1,950	1	1	1	1
			Light Rain	16	63	80.4	3.4	2	225	5.22	0.51	84	241	1	1.02	0.96	0.91
			Moderate Rain	15	67	85.3	3.6	2	225	4.04	0.66	13	59	0.94	1.09	1.02	0.92
			Heavy Rain	16	67.4	85	3.2	2	225	3.88	0.53	7	28	1	1.1	1.02	0.82
I-64	284.2	8	Normal	15	63.1	85.1	4.5	2	225	4.09	0.8	21,710	21,968	1	1	1	1
			Light Rain	10	62.9	77	4.6	2	225	6.6	0.79	1,066	4,043	0.67	1	0.91	0.91
			Moderate Rain	12	51.9	63.7	3.9	2	225	13.02	0.74	105	299	0.8	0.82	0.75	0.74
			Heavy Rain	10	57.5	70.8	4.7	2	225	7.98	0.89	21	85	0.67	0.91	0.83	0.71
			Light Snow	10	59.9	72.4	4.3	2	225	7.73	0.75	107	183	0.67	0.95	0.85	0.69
I-64	286.1	23	Normal	20	50.4	64.2	2.7	2	225	8.19	0.62	7,160	8,704	1	1	1	1
			Light Rain	15	47.8	56.6	2.5	2	225	7.92	0.7	372	1,756	0.75	0.95	0.88	0.91
			Moderate Rain	10	44	48.5	2.3	2	225	5.48	0.65	7	103	0.5	0.87	0.76	0.63
			Heavy Rain	21	46.8	64.2	3.4	2	225	9.28	0.94	7	13	1.05	0.93	1	0.49
I-64	286.1	24	Normal	12	53.2	63.6	3.4	2	225	9.31	0.59	7,159	17,859	1	1	1	1
			Light Rain	12	47.5	55.9	3.1	2	225	11.85	0.53	850	1,871	1	0.89	0.88	0.89
			Light Snow	12	47.8	58	3.7	2	225	15.85	0.61	53	107	1	0.9	0.91	0.45
I-64	286.6	27	Normal	23	33.5	41.9	2.2	2	225	4.12	0.53	4,058	10,215	1	1	1	1
I-64	286.6	27	Light Rain	28	31.6	45.4	2.9	2	225	4.75	0.49	523	567	1.22	0.94	1.08	0.82
I-64	286.4	28	Normal	10	52.7	58.9	2.5	2	225	5.93	0.85	5,536	8,162	1	1	1	1
			Light Rain	11	50.8	59.2	3.2	2	225	6	0.44	483	513	1.1	0.96	1.01	0.59
			Moderate Rain	12	51.6	72.4	6.4	2	225	9.02	0.66	35	9	1.2	0.98	1.23	0.43
I-64	282.5	37	Normal	26	65.3	195.2	9.1	2	225	0.94	0.71	22,113	307	1	1	1	1
I-64	282.5	37	Light Rain	24	65	118.8	5.5	2	225	0.75	0.61	1,533	83	0.92	0.99	0.61	0.99
I-64	283.5	48	Normal	25	61.2	205.4	10.5	2	225	7.18	0.8	23,611	660	1	1	1	1
			Moderate Rain	14	54.1	72.1	4.6	2	225	9.86	0.52	315	64	0.56	0.88	0.35	0.74
			Heavy Rain	19	56.6	118.7	8.6	2	225	8.82	0.73	84	13	0.76	0.93	0.58	0.72
			Light Snow	11	58.1	68.1	3.3	2	225	8.86	0.43	116	88	0.44	0.95	0.33	0.79
I-64	282.2	50	Normal	30	65.7	87.2	2	2	225	5.85	0.34	11,257	601	1	1	1	1
			Light Rain	28	63.1	99.3	3.5	2	225	7.51	0.84	1,349	207	0.93	0.96	1.14	0.82
			Moderate Rain	21	61.9	98.2	4.8	2	225	5.07	0.65	224	19	0.7	0.94	1.13	0.77
			Heavy Rain	11	57.6	64.8	2.4	2	225	12.45	0.27	36	12	0.37	0.88	0.74	0.59
I-64	282.2	51	Normal	19	62.5	89.7	4.2	2	225	4.65	0.75	23,153	10,234	1	1	1	1
			Light Rain	15	61	81.8	4.4	2	225	6.74	0.8	1,347	1,968	0.79	0.98	0.91	0.87
			Moderate Rain	10	57.1	71.2	5	2	225	9.27	0.84	48	252	0.53	0.91	0.79	0.89
			Heavy Rain	16	61.6	85.5	4.6	2	225	6.11	0.91	36	49	0.84	0.99	0.95	0.72
			Light Snow	14	58.5	83.2	5.6	2	225	6.14	0.82	127	104	0.74	0.94	0.93	0.59
I-64	282.1	52	Normal	24	38.3	47	1.9	2	225	4.75	0.55	12,660	9,920	1	1	1	1
I-64	282.1	52	Moderate Rain	11	38.3	47	4.3	2	225	4.1	0.31	20	59	0.46	1	1	0.41
I-64	280.7	65	Normal	22	62.2	87.6	3.4	2	225	5.47	0.59	19,123	21,707	1	1	1	1
I-64	280.7	65	Light Snow	27	56.7	101.9	4.7	2	225	9.16	0.73	250	60	1.23	0.91	1.16	0.83
I-64	280.8	66	Normal	14	65.5	112.8	8.7	2	225	1.37	0.75	18,478	1,468	1	1	1	1
			Light Rain	16	65.1	126.5	9.2	2	225	1.69	0.67	1,318	151	1.14	0.99	1.12	1
			Moderate Rain	14	64.5	104.1	7.6	2	225	0.74	0.98	71	17	1	0.98	0.92	0.49
I-64	279	85	Normal	30	65.7	123.1	4.5	2	225	2.87	0.73	27,950	1,277	1	1	1	1
			Light Rain	28	63.6	110	4.2	2	225	4.44	0.83	2,284	260	0.93	0.97	0.89	0.89
			Moderate Rain	28	65.3	122.8	4.9	2	225	9.78	0.96	79	31	0.93	0.99	1	0.82
I-64	279	86	Normal	12	61.1	72.6	3.2	2	225	4.69	0.52	17,578	10,478	1	1	1	1
			Light Rain	13	57.7	102.7	10	2	225	7.38	0.27	1,705	567	1.08	0.94	1.42	0.67
			Moderate Rain	10	42.4	65.5	10	2	225	16.32	0.3	94	55	0.83	0.69	0.9	0.43
			Light Snow	14	54	102.7	10.3	2	225	8.51	0.28	84	11	1.17	0.88	1.41	0.52
I-264	13.8	148	Normal	30	68.3	147.3	5.5	2	225	3.91	0.65	5,538	744	1	1	1	1
			Light Rain	24	64.9	94.3	3.4	2	225	1.29	0.56	379	246	0.8	0.95	0.64	0.85
			Moderate Rain	20	64.4	100.4	4.9	2	225	0.75	0.55	16	19	0.67	0.94	0.68	0.59
			Light Snow	16	62.5	82.4	3.9	2	225	1.34	0.91	14	14	0.53	0.91	0.56	0.45
I-264	14	153	Normal	14	64.9	84	4.1	2	225	1.13	0.56	5,471	1,366	1	1	1	1
			Light Rain	12	64.2	77.5	3.5	2	225	2.34	0.85	457	249	0.86	0.99	0.92	0.98
			Moderate Rain	10	61.1	66.5	1.9	2	225	3.82	0.98	14	14	0.71	0.94	0.79	0.64
			Heavy Rain	12	64.1	94.4	7.3	2	225	1.07	0.76	18	19	0.86	0.99	1.12	0.68
I-264	14	154	Normal	21	64.4	85	2.9	2	225	0.64	0.82	3,497	1,677	1	1	1	1
I-264	14	154	Light Rain	20	63.6	85.4	3.3	2	225	1.26	0.94	295	148	0.95	0.99	1	0.88
I-264	14.9	158	Normal	12	54	61.9	2.6	2	225	4.64	0.62	2,177	28,203	1	1	1	1
			Light Rain	10	53.5	61.3	3.1	2	225	4.76	0.86	137	2,164	0.83	0.99	0.99	0.71
			Moderate Rain	11	49.3	59.1	3.7	2	225	3.42	0.82	10	1	0.92	0.91	0.95	0.59
			Heavy Rain	17	47.2	72.6	5.7	2	225	4.52	0.45	17	24	1.42	0.87	1.17	0.53
I-264	16.3	168	Normal	18	51.3	61.5	2.3	2	225	4.08	0.82	8,566	19,564	1	1	1	1
			Light Rain	12	51.4	57.8	2.2	2	225	6.66	0.85	172	1,998	0.67	1	0.94	0.93
			Moderate Rain	12	46.4	52.1	2.2	2	225	8.53	0.82	10	109	0.67	0.9	0.85	0.8
I-264	16.3	169	Normal	10	62.3	76.5	4.7	2	225	2.16	0.92	19,488	9,717	1	1	1	1
			Light Rain	10	59.8	74.6	5	2	225	3.73	0.91	1,555	645	1	0.96	0.97	0.89
			Moderate Rain	10	54.6	65.1	4	2	225	7.54	0.95	79	18	1	0.88	0.85	0.78
			Light Snow	16	46.2	62.2	4.2	2	225	11.19	0.78	89	15	1.6	0.74	0.81	0.79
I-564	50	135	Normal	16	63.4	90.8	5	2	225	7.06	0.75	38,675	5,125	1	1	1	1
			Moderate Rain	10	51.7	67.1	5.9	2	225	13.76	0.64	253	86	0.63	0.81	0.74	0.82
			Heavy Rain	11	57.9	77.3	5.9	2	225	9.99	0.74	53	53	0.69	0.91	0.85	0.81
			Light Snow	10	59.8	77	5.8	2	225	12.14	0.79	156	65	0.63	0.94	0.85	0.89
I-564	50	136	Normal	12	63.3	72.6	2.6	2	225	3.49	0.67	26,067	2,961	1	1	1	1
I-564	50	136	Heavy Rain	10	52.2	84	10.8	2	225	9.6	0.64	29	13	0.83	0.83	1.16	0.57
I-564	50	137	Normal	13	38.7	44.4	2.4	2	225	4.3	0.49	10,193	7,431	1	1	1	1
I-564	50	137	Light Rain	10	35.1	38.8	2.3	2	225	8.94	0.25	623	1,053	0.77	0.91	0.87	0.8
¹ Root mean squared error of free-flow speed (uf) for the 1st regime. ² R-squared value of the speed-density curve for the 2nd regime from the linear regression. ³ WAF for selected parameters for each location and each weather condition. For normal weather, WAF has the value of 1. These WAF results are used as dependent variables in the linear regression of the WAF calibration process.

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