Development and application of a method for the objective differentiation of fog life cycle phases

Figures & data

Table 1. Applied instruments on the Marburg Ground Truth and Profiling Station

Instrument	Measured parameter	Time interval	Manufacturer
94 GHz FMCW Radar	Altitude of cloud top	10 sec	Rutherford Appleton Laboratory, UK
Ceilometer (CL31)	Altitude of cloud base	20 sec	Vaisala, Finland
Optical particle counter (CDP with PbP)	Drop size spectrum^a	1 sec	Droplet Measurement Technologies, USA
Climatological station	Temperature^b Precipitation^a Pressure^a Relative humidity^b Wind direction^a Wind speed^c	5 min	Campbell Scientific, USA
Present weather sensor (HSS VPF-730)	Horizontal visibility^b	20 sec	Biral, UK

^aMeasured at 2 m height.

^bMeasured at 2 m and 10 m height.

^cMeasured at 10 m height.

Fig. 1 Synoptic weather regimes during the three fog events referring to Hess and Brezowsky (1977) and James (2007) (DWD, 2011): (a) first fog event: 26–27 October 2011; (b) second fog event: 31 October 2011–1 November 2011; (c) third fog event: 13–14 November 2011. Left column: 500 hPa level, right column: surface pressure level.

Fig. 2 Flowchart of the statistical approach for the detection and statistical proof of change point (CP) in double sum curves of measurement series.

Table 2. Found potential change points (CP) of the three fog events from the homogeneity test of Mann–Whitney for the cumulative sum of VIS, LWC, N _t, r _c and r _mean

				Phase 1		Phase 2		Phase 3
Fog event	Duration	CP1	CP2	Period	n	Period	n	Period	n
1	10/26, 19:21–10/27, 08:05	10/27, 01:50	10/27, 06:00	10/26, 19:21–10/27, 01:50	390	10/27, 01:51–10/27, 06:00	250	10/27, 06:01–10/27, 08:05	125
2	10/31, 17:38–11/01, 07:55	10/31, 19:17	11/01, 01:57	10/31, 17:38–10/31, 19:17	100	10/31, 19:18–11/01, 01:57	400	11/01, 01:58–11/01, 07:55	358
3	11/13, 18:48–11/14, 08:15	11/13, 23:47	11/14, 06:27	11/13, 18:48–11/13, 23:47	300	11/13, 23:48–11/14, 06:27	400	11/14, 06:28–11/14, 08:15	108

Table 3. Two-sided t-test on the slopes of the phases regarding the microphysical parameters and VIS from the three measured fog events

		VIS		LWC		N t		r mean		r c
Fog event	Change point		p (%)		p (%)		p (%)		p (%)		p (%)
1	1	23.57	99.99	37.83	99.99	49.59	99.99	29.27	99.99	34.54	99.99
	2	19.59	99.99	20.09	99.99	10.96	99.99	46.61	99.99	43.72	99.99
2	1	35.94	99.99	12.00	99.99	13.20	99.99	8.71	99.99	11.40	99.99
	2	64.30	99.99	54.54	99.99	33.11	99.99	101.12	99.99	96.74	99.99
3	1	123.77	99.99	7.56	75	1.14	99.99	47.13	99.99	36.62	99.99
	2	40.09	99.99	14.33	99.99	15.15	99.99	19.09	99.99	20.21	99.99

Fig. 3 Measured data during third fog event: 13–14 November 2011. (a) Horizontal visibility (VIS); (b) microphysical properties: liquid water content (LWC), total number of droplets per cm³ (N _t), mean droplet radius (r _mean), modal droplet radius (r _c); (c) meteorological properties: temperature (T), relative humidity (RH), wind speed; (d) cloud ceilings. The first and last vertical line represent the time when VIS is the first and last time below 1 km during the fog event. The other two vertical lines signify the break points determined by the statistical approach.

Table 4. Overview of the microphysical properties of the three fog measurements differentiated by evolutionary stages liquid water content (LWC), total amount of droplets N _t, arithmetic mean of radius r _mean, modal value of radius r _c, minimum value of radius r _min, maximum value of radius r _max, range between minimum and maximum value within a drop size spectrum

	Min	Max	Mean	Standard deviation	Median	Min	Max	Mean	Standard deviation	Median	Min	Max	Mean	Standard deviation	Median
	Formation stage of 26 October–27 October 2011					Formation stage of 31 October–1 November 2011					Formation stage of 13 November–14 November 2011
LWC (g m^−3)	0.00	0.09	0.01	0.02	0.00	0.00	0.06	0.02	0.02	0.01	0.00	0.02	0.00	0.00	0.00
N t (cm^−3)	0.02	115.69	11.04	17.83	2.79	0.05	50.72	12.23	11.53	7.85	0.00	16.11	1.24	2.65	0.14
r mean (µm)	3.15	9.50	4.94	1.25	4.54	3.02	7.61	5.36	0.91	5.27	2.50	12.45	5.44	2.06	4.95
r c (µm)	2.50	7.08	3.82	0.97	3.52	2.50	4.70	3.37	0.59	3.31	2.50	7.13	3.45	1.10	2.93
r min (µm)	2.50	5.21	3.08	0.58	2.89	2.50	4.20	2.75	0.31	2.63	2.50	10.95	4.00	1.38	3.75
r max (µm)	3.38	22.47	10.98	5.71	11.15	3.43	22.70	16.12	4.35	16.69	2.50	16.56	7.93	4.01	7.18
dr (µm)	0.00	19.97	7.90	6.11	8.15	0.44	20.20	13.38	4.58	13.99	0.00	13.18	3.93	3.86	3.12
	Mature fog of 26 October–27 October 2011					Mature fog of 10/31–1 November 2011					Mature fog of 13 November–14 November 2011
LWC (g m^−3)	0.00	0.05	0.01	0.01	0.01	0.00	0.06	0.01	0.01	0.01	0.00	0.03	0.01	0.00	0.01
N t (cm^−3)	0.20	38.28	2.15	3.25	1.47	0.01	41.43	4.58	6.98	1.90	0.00	9.66	2.73	1.71	2.42
r mean (µm)	4.03	11.22	8.63	1.62	8.97	3.20	13.13	6.54	1.88	6.40	2.50	11.50	6.82	0.79	6.89
r c (µm)	2.58	10.25	5.99	1.56	5.93	2.50	7.24	3.71	0.91	3.53	2.50	6.31	4.80	0.65	4.86
r min (µm)	2.50	7.46	3.58	0.99	3.25	2.50	12.25	3.45	1.40	2.91	2.50	11.50	3.25	0.89	3.00
r max (µm)	6.34	23.07	17.10	2.61	17.25	3.38	22.05	14.25	3.99	14.81	2.50	18.72	13.88	2.44	14.16
dr (µm)	3.46	20.57	13.52	3.12	13.69	0.33	19.55	10.80	4.50	11.56	0.00	16.17	10.63	2.96	11.06
	Dissipation stage of 26 October–27 October 2011					Dissipation stage of 31 October–1 November 2011					Dissipation stage of 13 November–14 November 2011
LWC (g m^−3)	0.00	0.03	0.01	0.01	0.00	0.00	0.03	0.00	0.00	0.00	0.00	0.01	0.00	0.00	0.00
N t (cm^−3)	0.14	5.66	1.57	1.33	1.07	0.00	33.78	0.75	3.58	0.05	0.00	5.43	0.89	1.41	0.02
r mean (µm)	4.85	9.63	7.56	0.98	7.50	2.50	5.97	3.88	0.69	3.75	2.75	8.14	5.10	1.04	5.10
r c (µm)	2.72	7.30	4.98	0.92	4.96	2.50	3.95	2.89	0.30	2.78	2.52	5.74	3.34	0.79	2.91
r min (µm)	2.50	5.14	3.45	0.74	3.29	2.50	5.62	3.50	0.59	3.44	2.53	8.14	4.33	1.21	4.22
r max (µm)	5.96	21.13	14.61	3.64	14.49	2.50	17.18	4.73	2.27	4.04	2.75	13.76	6.58	2.80	5.42
dr (µm)	1.91	18.57	11.16	4.22	10.96	0.00	14.68	1.22	2.38	0.47	0.00	11.14	2.24	3.36	0.18

Fig. 4 Measured data during first fog event: 26–27 October 2011. (a) Horizontal visibility (VIS); (b) microphysical properties: liquid water content (LWC), total number of droplets per cm³ (N _t), mean droplet radius (r _mean), modal droplet radius (r _c); (c) meteorological properties: temperature (T), relative humidity (RH), wind speed; (d) cloud ceilings. The first and last vertical line represent the time when VIS is the first and last time below 1 km during the fog event. The other two vertical lines signify the change point (CP) determined by the statistical approach.

Fig. 5 Measured data during second fog event: 31 October 2011–1 November 2011. (a) Horizontal visibility (VIS); (b) microphysical properties: liquid water content (LWC), total number of droplets per cm³ (N _t), mean droplet radius (r _mean), modal droplet radius (r _c); (c) meteorological properties: temperature (T), relative humidity (RH), wind speed, wind direction; (d) cloud ceilings. The first and last vertical line represent the time when VIS is the first and last time below 1 km during the fog event. The other two vertical lines signify the break points determined by the statistical approach.

Fig. 6 Horizontal visibility (VIS) as a function of (a) liquid water content (LWC) and (b) total number of droplets per cm³ for all three fog events.

Table 5. Comparison of the measured microphysical parameters (LWC, N _t, r _c) with values from literature compiled in Maier et al. (2012)

	LWC (g m^−3)				N t (cm^−3)				r c (µm)
	Measurements		Maier et al. 2012		Measurements		Maier et al. 2012		Measurements		Maier et al. 2012
	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max
Whole dataset of measured radiation fog events	0.00	0.09	0.02	0.21	0.00	115.69	15.90	249.93	2.50	10.25	2.13	12.22
Formation stage	0.00	0.06	0.08	0.17	0.05	50.72	21.73	138.04	2.50	4.70	3.49	10.82
Mature fog	0.00	0.06	0.12	0.16	0.00	41.43	28.00	59.02	2.50	10.25	4.99	9.00
Dissipation stage	0.00	0.03	0.17	0.16	0.00	33.78	24.14	32.51	2.50	7.30	6.92	10.10

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