Horizontal scales of ice-supersaturated regions

Figures & data

Fig. 1 Different resolution. Top panel: original (high) resolution, bottom panel: coarse resolution (running mean, leading to a resolution of Δx~100 km).

Table 1. Definition of pressure levels for vertical distribution of ISSRs and distances between them

Number	1	2	3	4	5	6
p (hPa)	340–290	290–270	270–250	250–230	230–210	210–190

Fig. 2 Pdfs of pathlengths of ISSRs as obtained from data with different resolution (blue: original resolution, red: coarse resolution). (a) Linear binning; (b) logarithmic binning.

Fig. 3 Weibull plot of pathlengths of ISSRs as obtained from data with different resolution and additional fits. (a) Original resolution; (b) coarse resolution.

Fig. 4 Pdfs of pathlengths of ISSRs for different regions (blue: extratropics, red: tropics).

Fig. 5 Cumulative distributions of pathlengths of ISSRs for different seasons as obtained for extratropical data in coarse resolution.

Fig. 6 Median values of pathlengths for different regions, seasons and resolutions. The values can be found in Table 2.

Table 2. Numbers, mean values, standard deviations and median values of pathlengths for different regions and seasons

Season	Resolution	N		σ L	med(L)
Total data
Total	Coarse	16 767	235	270	142
MAM	Coarse	3455	219	258	131
JJA	Coarse	5725	214	233	137
SON	Coarse	4575	258	297	154
DJF	Coarse	3012	256	300	150
Extratropical data
Total	Coarse	12 503	247	282	149
MAM	Coarse	2381	229	263	137
JJA	Coarse	4742	218	240	138
SON	Coarse	3580	277	317	164
DJF	Coarse	1800	284	324	165
Tropical data
Total	Coarse	4264	199	226	124
MAM	Coarse	1074	199	246	116
JJA	Coarse	983	192	194	131
SON	Coarse	995	188	197	117
DJF	Coarse	1212	215	253	133

Fig. 7 Cumulative distributions of pathlengths of ISSRs for different dynamic regimes, i.e. total data separated into troposphere/in between/stratosphere.

Fig. 8 Seasonal cycle of number of ISSRs as obtained for different dynamic regimes.

Table 3. Numbers, mean values, standard deviations and median values of pathlengths for different atmospheric levels (troposphere/in between/stratosphere)

Season	Resolution	N		σ L	med(L)
Troposphere
Total	Coarse	11 209	235	267	143
MAM	Coarse	2283	216	253	130
JJA	Coarse	2548	202	211	134
SON	Coarse	3791	254	286	154
DJF	Coarse	2587	257	297	151
In between
Total	Coarse	4965	236	273	143
MAM	Coarse	1015	229	262	138
JJA	Coarse	2866	226	249	142
SON	Coarse	741	283	352	157
DJF	Coarse	343	242	291	137
Stratosphere
Total	Coarse	593	213	287	124
MAM	Coarse	157	201	303	120
JJA	Coarse	311	200	239	123
SON	Coarse	43	184	215	131
DJF	Coarse	82	302	411	155

Table 4. Numbers, mean values, standard deviations and median values of pathlengths for different vertical pressure levels in both resolutions

Level (hPa)	Resolution	N		σ L	med(L)
1 (340–290)	Original	1492	81	107	44
2 (290–270)	Original	3728	97	145	48
3 (270–250)	Original	11 448	109	164	54
4 (250–230)	Original	11 591	114	186	52
5 (230–210)	Original	9788	129	212	55
6 (210–190)	Original	2521	112	177	52
1 (340–290)	Coarse	547	164	174	115
2 (290–270)	Coarse	1476	199	218	127
3 (270–250)	Coarse	4676	225	248	141
4 (250–230)	Coarse	4778	241	284	143
5 (230–210)	Coarse	4163	264	302	155
6 (210–190)	Coarse	1039	230	258	139

Fig. 9 Median values of pathlengths in different dynamic regions, total and seasonal. The values can be found in Table 3.

Fig. 10 Pdfs of distances between ISSRs as obtained from data with different resolution (blue: original resolution, red: coarse resolution). (a) Linear binning; (b) logarithmic binning.

Table 5. Numbers, mean values, standard deviations and median values of distances between ISSRs for different regions and seasons

Season	Resolution	N		σ D	med(D)
Total data
Total	Coarse	7741	514	753	217
MAM	Coarse	1527	504	754	218
JJA	Coarse	2750	525	754	218
SON	Coarse	2128	514	772	217
DJF	Coarse	1336	503	715	215
Extratropical data
Total	Coarse	5427	506	742	211
MAM	Coarse	957	474	723	200
JJA	Coarse	2223	536	763	218
SON	Coarse	1580	495	741	212
DJF	Coarse	667	478	692	199
Tropical data
Total	Coarse	2314	534	777	234
MAM	Coarse	570	554	801	251
JJA	Coarse	527	479	712	218
SON	Coarse	548	572	854	240
DJF	Coarse	669	528	736	229

Fig. 11 Pdfs of distances between ISSRs for different dynamic regimes, i.e. total data separated into troposphere/in between/stratosphere.

Table 6. Numbers, mean values, standard deviations and median values of distances between ISSRs for different atmospheric levels (troposphere/in between/stratosphere)

Season	Resolution	N		σ D	med(D)
Troposphere
Total	Coarse	4758	407	623	179
MAM	Coarse	965	419	616	182
JJA	Coarse	1091	367	601	164
SON	Coarse	1578	406	635	177
DJF	Coarse	1124	435	631	194
In between
Total	Coarse	2125	462	691	224
MAM	Coarse	411	468	756	227
JJA	Coarse	1168	400	612	193
SON	Coarse	400	571	746	326
DJF	Coarse	146	647	852	293
Stratosphere
Total	Coarse	858	1240	1085	1014
MAM	Coarse	151	1150	1139	794
JJA	Coarse	491	1173	990	952
SON	Coarse	150	1504	1273	1256
DJF	Coarse	66	1344	1069	1147

Fig. 12 Pathlengths of relative humidity as obtained from the original data for different thresholds RHi _t =95/90/80/70 %. (a) Linear binning of the data; (b) logarithmic binning.

Table 7. Numbers, mean values and standard deviations for pathlengths of RHi until the threshold RHi _t is reached. Here, all data in original resolution are used without separation into horizontal or vertical regions

Season	RHi t	N			med(L RHi )
Total	95	60 631	14	16	9
MAM	95	12 963	15	18	9
JJA	95	21 702	12	14	8
SON	95	15 598	14	17	9
DJF	95	10 368	15	18	9
Total	90	50 189	29	35	17
MAM	90	10 645	31	38	18
JJA	90	18 050	26	31	16
SON	90	12 985	29	35	17
DJF	90	8509	31	39	18
Total	80	38 409	63	80	37
MAM	80	8153	68	87	39
JJA	80	13 909	57	70	34
SON	80	9882	64	78	38
DJF	80	6465	70	90	40
Total	70	31 404	104	126	62
MAM	70	6756	112	139	65
JJA	70	11 364	93	113	55
SON	70	8027	106	124	65
DJF	70	5257	115	138	69

Table 8. Numbers, mean values and standard deviations for pathlengths of RHi until the threshold RHi _t is reached. All data in original resolution here are used with separation into different pressure levels

Level (hPa)	RHi t	N			med(L RHi )
1 (340–290)	95	2292	9	11	6
2 (290–270)	95	5637	11	13	7
3 (270–250)	95	17 354	13	15	8
4 (250–230)	95	16 966	14	17	9
5 (230–210)	95	14 220	16	18	10
6 (210–190)	95	3659	16	18	10
1 (340–290)	90	1933	19	24	12
2 (290–270)	90	4739	21	26	13
3 (270–250)	90	14 372	26	30	16
4 (250–230)	90	14 032	30	37	18
5 (230–210)	90	11 664	33	41	20
6 (210–190)	90	3057	36	40	21
1 (340–290)	80	1487	37	45	22
2 (290–270)	80	3665	45	55	27
3 (270–250)	80	10 937	56	67	34
4 (250–230)	80	10 676	68	84	40
5 (230–210)	80	8980	75	93	44
6 (210–190)	80	2404	82	94	49
1 (340–290)	70	1256	59	75	34
2 (290–270)	70	2980	72	88	43
3 (270–250)	70	8918	92	105	57
4 (250–230)	70	8720	111	132	67
5 (230–210)	70	7363	124	149	73
6 (210–190)	70	1963	133	149	84

Fig. 13 Example of relative humidity along a simulated flight track. Shown are high-resolution data (red), running mean (blue) and coarse resolution as obtained from running mean data (green) in the interval 50 ≤ x≤300 km.

Fig. 14 Variations of different variables (RHi, w, q and T) relevant for the small structure of ISSRs.

Fig. 15 Vertical temperature profile and adiabatic ascents for the lowest and highest levels occurring in the simulation.

Table 9. Range of variables for start conditions (vertical velocity w and start level z _start ) and obtained at flight level z=10000 m (temperature T, relative humidity RHi and specific humidity q) during the simulation

w (cm s^−1)	Start level z (m)	T (K)	RHi (%)	q (mg/kg)
2.60 ≤ w≤7.67	8896.5 ≤ z start ≤9624.4	206.126 ≤ T≤206.509	68.6 ≤ RHi≤157.5	6.38 ≤ q≤13.88

Fig. 16 Correlation between specific humidity and relative humidity for the high-resolution simulation data.

Fig. 17 Pdf of pathlengths of ISSRs as obtained from the high-resolution simulation data (red), running means on coarse binning (blue) and coarse resolution (green).

Fig. 18 Pdfs of RHi as obtained from the high-resolution simulation data (red), running means on coarse binning (blue) and coarse resolution (green).

Table 10. Numbers, mean values, standard deviations and median values of pathlengths for different regions and seasons, original resolution

Season	Resolution	N		σ L	med(L)
Total data
Total	Original	40 951	113	180	52
MAM	Original	8891	103	167	48
JJA	Original	14 232	102	153	50
SON	Original	10 543	128	207	57
DJF	Original	7285	123	200	54
Extratropical data
Total	Original	29 702	122	194	55
MAM	Original	5927	111	177	51
JJA	Original	11 491	106	160	52
SON	Original	7952	142	225	64
DJF	Original	4332	142	230	60
Tropical data
Total	Original	11 249	88	134	44
MAM	Original	2964	87	141	44
JJA	Original	2741	84	120	43
SON	Original	2591	87	128	43
DJF	Original	2953	95	142	46

Table 11. Numbers, mean values, standard deviations and median values of pathlengths for different atmospheric levels (troposphere/in between/stratosphere), original resolution

Season	Resolution	N		σ L	med(L)
Troposphere
Total	Original	27 988	111	177	51
MAM	Original	5994	100	160	47
JJA	Original	6792	93	136	46
SON	Original	8831	126	198	57
DJF	Original	6371	121	194	53
In between
Total	Original	11 514	117	188	55
MAM	Original	2486	111	176	52
JJA	Original	6695	111	168	54
SON	Original	1593	145	252	62
DJF	Original	740	136	232	57
Stratosphere
Total	Original	1449	102	186	46
MAM	Original	411	96	200	46
JJA	Original	745	99	160	47
SON	Original	119	83	146	39
DJF	Original	174	144	259	48

Table 12. Numbers, mean values, standard deviations and median values of distances between ISSRs for different regions and seasons, original data

Season	Resolution	N		σ D	med(D)
Total data
Total	Original	28 571	253	543	66
MAM	Original	6145	252	540	65
JJA	Original	10 125	261	551	69
SON	Original	7272	257	555	67
DJF	Original	5029	234	511	61
Extratropical data
Total	Original	19 932	254	550	66
MAM	Original	3885	247	543	65
JJA	Original	8015	269	563	70
SON	Original	5274	252	551	67
DJF	Original	2758	228	516	57
Tropical data
Total	Original	8639	251	526	66
MAM	Original	2260	261	536	64
JJA	Original	2110	234	501	65
SON	Original	1998	270	562	69
DJF	Original	2271	241	504	68

Table 13. Numbers, mean values, standard deviations and median values of distances between ISSRs for different atmospheric levels (troposphere/in between/stratosphere), original data

Season	Resolution	N		σ D	med(D)
Troposphere
Total	Original	18 906	187	414	58
MAM	Original	4102	193	410	58
JJA	Original	4594	175	416	55
SON	Original	5840	194	426	59
DJF	Original	4370	184	401	57
In between
Total	Original	7503	239	495	71
MAM	Original	1601	239	488	72
JJA	Original	4325	205	448	65
SON	Original	1131	332	601	101
DJF	Original	446	339	599	79
Stratosphere
Total	Original	2162	885	1050	433
MAM	Original	442	845	1120	319
JJA	Original	1206	796	916	406
SON	Original	301	1198	1251	877
DJF	Original	213	1032	1183	475