Experimental Transmission Functions for the Pure Rotation Band of Water Vapor*

C. Harvey Palmer

doi:10.1364/JOSA.50.001232

Journal of the Optical Society of America
Vol. 50,
Issue 12,
pp. 1232-1242
(1960)
•https://doi.org/10.1364/JOSA.50.001232

Experimental Transmission Functions for the Pure Rotation Band of Water Vapor

C. Harvey Palmer

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C. Harvey Palmer, "Experimental Transmission Functions for the Pure Rotation Band of Water Vapor*," J. Opt. Soc. Am. 50, 1232-1242 (1960)

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Abstract

Experimental transmission data are given for mixtures of water vapor and nitrogen for the 20- to 50-μ region of the pure rotation band of water vapor. These data yield a set of transmission functions for 50 cm⁻¹ intervals in agreement with a theoretical curve of Benedict. Average transmission is plotted as a function of the parameter U=WP*, in which W is the vapor optical path in precipitable centimeters and P* an effective pressure. This effective pressure is the sum of the total pressure and the water vapor partial pressure multiplied by a variable self-broadening factor. For meteorological purposes the self-broadening may be omitted. The set of transmission functions in turn yields a generalized absorption coefficient for the region.

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Series X 20μ–30μ
Spectrum		W g/cm²	p_w atm	P_t atm	log U₀	log U₆	Temp. °C
S6	— 0	0.0041	0.000279	0.000279	$\bar{6}$ .058	$\bar{6}$ .902	19
	— 2	0.0041	0.000279	0.0280	$\bar{4}$ .060	$\bar{4}$ .086	20
	— 6	0.0043	0.000283	0.0784	$\bar{4}$ .527	$\bar{4}$ .538	13
	—20	0.0045	0.000296	0.260	$\bar{3}$ .069	$\bar{3}$ .071	13
	—60	0.0050	0.000334	0.797	$\bar{3}$ .601	$\bar{3}$ .602	17
S12	— 0	0.0080	0.000539	0.000539	$\bar{6}$ .635	$\bar{5}$ .479	18
	— 2	0.0080	0.000539	0.0309	$\bar{4}$ .393	$\bar{4}$ .437	18
	— 6	0.0075	0.000500	0.081	$\bar{4}$ .781	$\bar{4}$ .797	17
	—20	0.0077	0.000517	0.264	$\bar{3}$ .310	$\bar{3}$ .314	18
	—60	0.0077	0.000516	0.784	$\bar{3}$ .781	$\bar{3}$ .783	17
S25	— 0	0.015	0.00101	0.00101	$\bar{5}$ .182	$\bar{4}$ .026	21
	— 2	0.015	0.00101	0.0284	$\bar{4}$ .630	$\bar{4}$ .714	20
	— 6	0.015	0.00101	0.0814	$\bar{3}$ .087	$\bar{3}$ .117	21
	—20	0.0135	0.00091	0.258	$\bar{3}$ .541	$\bar{3}$ .551	16
	—60	0.014	0.00094	0.789	$\bar{2}$ .043	$\bar{2}$ .046	17
S50	— 0	0.032	0.00215	0.00215	$\bar{5}$ .837	$\bar{4}$ .682	19
	— 2	0.032	0.00215	0.0314	$\bar{3}$ .003	$\bar{3}$ .153	19
	— 6	0.032	0.00216	0.0803	$\bar{3}$ .411	$\bar{3}$ .475	20
	—20	0.033	0.00221	0.262	$\bar{3}$ .937	$\bar{3}$ .958	16
	—60	0.0325	0.00218	0.789	$\bar{2}$ .409	$\bar{2}$ .417	17
S100	— 0	0.076	0.00515	0.00515	$\bar{4}$ .592	$\bar{3}$ .437	21
	— 2	0.076	0.00516	0.0280	$\bar{3}$ .329	$\bar{3}$ .652	22
	— 6	0.076	0.00511	0.0797	$\bar{3}$ .783	$\bar{3}$ .924	19
	—20	0.075	0.00507	0.262	$\bar{2}$ .292	$\bar{2}$ .341	19
	—60	0.074	0.00500	0.783	$\bar{2}$ .763	$\bar{2}$ .780	17
S200	— 0	0.133	0.00900	0.00900	$\bar{3}$ .078	$\bar{3}$ .923	18
	— 2	0.133	0.00903	0.0287	$\bar{3}$ .582	$\bar{2}$ .042	19
	— 6	0.133	0.00903	0.0805	$\bar{2}$ .029	$\bar{2}$ .253	20
	—20	0.134	0.00909	0.263	$\bar{2}$ .548	$\bar{2}$ .630	20
	—60	0.143	0.00971	0.788	$\bar{1}$ .052	$\bar{1}$ .083	22

Series Y 30μ–40μ

S6	— 0	0.00243	0.000158	0.000158	$\bar{6}$ .584	$\bar{6}$ .429	7
	— 2	0.00243	0.000158	0.0268	$\bar{5}$ .815	$\bar{5}$ .829	7
	— 6	0.00284	0.000184	0.0779	$\bar{4}$ .344	$\bar{4}$ .352	7
	—20	0.00278	0.000182	0.263	$\bar{4}$ .864	$\bar{4}$ .867	8
	—60	0.00318	0.000208	0.793	$\bar{3}$ .402	$\bar{3}$ .402	10
S12	— 0	0.00604	0.000395	0.000395	$\bar{6}$ .377	$\bar{5}$ .223	10
	— 2	0.00604	0.000396	0.0276	$\bar{4}$ .223	$\bar{4}$ .259	11
	— 6	0.00706	0.000461	0.0791	$\bar{4}$ .746	$\bar{4}$ .761	9
	—20	0.00710	0.000463	0.250	$\bar{3}$ .249	$\bar{3}$ .253	9
	—60	0.00641	0.000418	0.784	$\bar{3}$ .701	$\bar{3}$ .703	9
S25	— 0	0.0124	0.000813	0.000813	$\bar{5}$ .004	$\bar{5}$ .850	10
	— 2	0.0124	0.000818	0.0275	$\bar{4}$ .532	$\bar{4}$ .604	11
	— 6	0.0144	0.000933	0.0793	$\bar{3}$ .058	$\bar{3}$ .088	7
	—20	0.0147	0.000958	0.263	$\bar{3}$ .587	$\bar{3}$ .596	8
	—60	0.0151	0.000983	0.786	$\bar{2}$ .074	$\bar{2}$ .077	8
S50	— 0	0.0253	0.00165	0.00165	$\bar{5}$ .619	$\bar{4}$ .463	8
	— 2	0.0253	0.00166	0.0286	$\bar{4}$ .858	$\bar{4}$ .989	10
	— 6	0.0294	0.00193	0.0795	$\bar{3}$ .369	$\bar{3}$ .427	12
	—20	0.0272	0.00176	0.258	$\bar{3}$ .846	$\bar{3}$ .863	7
	—60	0.0264	0.00171	0.784	$\bar{2}$ .315	$\bar{2}$ .320	7
S100	— 0	0.0627	0.00416	0.00416	$\bar{4}$ .416	$\bar{3}$ .262	13
	— 2	0.0627	0.00418	0.0279	$\bar{3}$ .243	$\bar{3}$ .522	15
	— 6	0.0658	0.00440	0.0792	$\bar{3}$ .717	$\bar{3}$ .842	15
	—20	0.0680	0.00455	0.258	$\bar{2}$ .243	$\bar{2}$ .288	16
	—60	0.0632	0.00416	0.774	$\bar{2}$ .690	$\bar{2}$ .702	11
S200	— 0	0.117	0.00772	0.00772	$\bar{4}$ .956	$\bar{3}$ .801	13
	— 2	0.117	0.00778	0.0301	$\bar{3}$ .547	$\bar{3}$ .953	15
	— 6	0.125	0.00832	0.0800	$\bar{2}$ .000	$\bar{2}$ .209	14
	—20	0.132	0.00882	0.271	$\bar{2}$ .554	$\bar{2}$ .631	16

Series Z 40μ–50μ

S6	— 0	0.00302	0.000204	0.000204	$\bar{6}$ .790	$\bar{6}$ .635	19
	— 2	0.00302	0.000204	0.0261	$\bar{5}$ .896	$\bar{5}$ .916	19
	— 6	0.00452	0.000305	0.0788	$\bar{4}$ .552	$\bar{4}$ .563	19
	—20	0.0049	0.000332	0.261	$\bar{3}$ .106	$\bar{3}$ .111	19
	—60	0.0049	0.000332	0.786	$\bar{3}$ .585	$\bar{3}$ .587	19
S12	— 0	0.0114	0.000770	0.000770	$\bar{6}$ .943	$\bar{5}$ .790	19
	— 2	0.0114	0.000770	0.0278	$\bar{4}$ .501	4.568	19
	— 6	0.0135	0.000917	0.0809	$\bar{3}$ .039	$\bar{3}$ .067	19
	—20	0.0141	0.000957	0.263	$\bar{3}$ .570	$\bar{3}$ .579	19
S25	— 0	0.0129	0.000876	0.000876	$\bar{5}$ .053	$\bar{5}$ .898	19
	— 2	0.0129	0.000876	0.0297	4.585	$\bar{4}$ .655	19
	— 6	0.0149	0.00101	0.0820	$\bar{3}$ .087	$\bar{3}$ .119	19
	—20	0.0145	0.000982	0.262	$\bar{3}$ .579	$\bar{3}$ .588	19
	—60	0.0151	0.00102	0.789	$\bar{2}$ .076	$\bar{2}$ .080	19
S50	— 0	0.0327	0.00221	0.00221	$\bar{5}$ .861	$\bar{4}$ .705	19
	— 2	0.0327	0.00221	0.0270	$\bar{4}$ .946	$\bar{3}$ .119	19
	— 6	0.0343	0.00233	0.0799	$\bar{3}$ .437	$\bar{3}$ .509	19
	—20	0.0349	0.00237	0.262	$\bar{3}$ .961	$\bar{3}$ .984	19
S100	— 0	0.0644	0.00437	0.00437	$\bar{4}$ .450	$\bar{3}$ .294	19
	— 2	0.0644	0.00437	0.0278	$\bar{3}$ .253	$\bar{3}$ .541	19
	— 6	0.0632	0.00428	0.0789	$\bar{3}$ .698	$\bar{3}$ .820	19
	—20	0.0690	0.00467	0.262	$\bar{2}$ .256	$\bar{2}$ .301	19
S200	— 0	0.125	0.00850	0.00850	$\bar{3}$ .026	$\bar{3}$ .873	19
	— 2	0.125	0.00850	0.0287	$\bar{3}$ .555	$\bar{3}$ .998	19
	— 6	0.125	0.00850	0.0795	$\bar{3}$ .997	$\bar{2}$ .213	19

Series X 20μ–30μ
Spectrum		500–490	490–480	480–470	470–460	460–450	450–440	440–430	430–420	420–410
S6	— 0	1000	1000	985	989	973	981	988	981	981
	— 2	990	989	960	969	930	948	971	912	936
	— 6	977	973	925	956	910	924	964	869	909
	—20	964	952	881	931	864	880	937	795	861
	—60	934	918	824	876	771	798	882	648	800
S12	— 0	994	995	976	988	966	979	994	970	977
	— 2	989	987	947	971	919	943	973	896	927
	— 6	977	970	916	944	885	909	952	834	887
	—20	952	947	877	920	817	849	926	749	817
	—60	941	922	798	873	725	762	865	632	767
S25	— 0	992	988	968	970	951	961	985	946	964
	— 2	967	961	906	932	885	902	946	843	904
	— 6	943	935	857	897	831	858	916	754	861
	—20	929	908	809	862	759	787	875	655	810
	—60	910	884	759	831	689	713	825	550	756
S50	— 0	962	963	912	924	901	911	941	844	903
	— 2	919	915	836	879	814	835	890	734	826
	— 6	879	874	773	835	741	771	841	627	777
	—20	854	839	708	779	646	674	780	519	709
	—60	783	722	573	663	495	521	645	345	597
S100	— 0	904	897	809	849	780	801	861	672	789
	— 2	882	868	761	807	724	749	826	603	751
	— 6	857	837	706	765	658	689	785	496	717
	—20	774	739	580	645	521	535	642	328	623
	—60	669	596	418	501	336	363	455	179	446
S200	— 0	824	790	676	721	619	641	715	496	632
	— 2	788	758	637	686	579	606	678	424	612
	— 6	755	716	579	631	507	533	619	369	553
	—20	642	582	416	471	335	367	470	208	427
	—60	441	350	200	248	131	158	226	70	225

Spectrum		410–400	400–390	390–380	380–370	370–360	360–350	350–340	340–330	330–320

S6	— 0	993	973	992	978	999	966	984	981	954
	— 2	961	894	942	871	974	770	912	913	789
	— 6	939	851	914	809	955	660	855	859	701
	—20	899	746	850	696	925	475	749	756	550
	—60	838	613	753	529	848	219	567	565	325
S12	— 0	992	960	975	947	968	906	954	937	912
	— 2	956	859	924	818	940	684	848	859	720
	— 6	924	800	885	741	911	550	787	793	620
	—20	896	676	796	615	860	350	640	668	431
	—60	836	548	708	461	790	129	467	473	220
S25	— 0	976	940	970	913	972	860	944	943	884
	— 2	929	825	903	775	934	619	828	836	675
	— 6	885	726	846	655	895	436	710	730	515
	—20	828	599	761	508	822	201	532	563	279
	—60	797	490	674	363	739	89	344	349	139
S50	— 0	907	827	884	769	907	638	814	822	675
	— 2	852	694	794	625	850	419	677	699	482
	— 6	797	602	705	497	790	248	540	558	314
	—20	747	470	610	365	688	92	332	354	149
	—60	623	325	432	189	483	25	115	111	43
S100	— 0	807	633	738	536	799	334	598	614	391
	— 2	764	562	662	450	749	216	492	502	271
	— 6	723	484	587	349	675	110	361	358	163
	—20	610	351	426	188	496	30	152	135	54
	—60	463	196	234	63	253	13	22	18	12
S200	— 0	649	443	524	342	588	126	331	331	151
	— 2	603	402	480	285	533	85	264	255	115
	— 6	560	343	408	220	456	51	174	165	68
	—20	439	221	250	95	272	16	43	29	14
	—60	221	76	71	15	69	2	0	0	0

Series Y 30μ–40μ
Spectrum		340–335	335–330	330–325	325–320	320–315	315–310	310–305	305–300	300–295
S6	— 0	1000	999	979	984	1000	1000	999	962	996
	— 2	936	938	845	867	968	955	976	765	946
	— 6	857	878	731	802	926	914	931	628	904
	—20	785	814	578	708	885	865	866	448	833
	—60	637	669	352	508	765	743	724	251	665
S12	— 0	968	970	924	948	989	988	993	898	985
	— 2	848	873	705	799	902	905	907	609	885
	— 6	794	826	598	725	880	861	870	484	837
	—20	652	689	383	539	758	750	712	277	683
	—60	493	522	202	346	613	597	534	122	479
S25	— 0	935	951	864	900	971	968	969	807	961
	— 2	808	837	620	732	890	870	872	499	849
	— 6	720	748	472	594	826	801	804	350	752
	—20	528	547	235	368	652	628	579	141	518
	—60	299	307	96	185	411	382	318	61	262
S50	— 0	855	873	725	805	918	912	919	632	904
	— 2	724	758	493	625	826	811	798	380	765
	— 6	565	603	292	431	688	660	623	195	588
	—20	381	404	135	256	509	479	413	84	372
	—60	227	130	35	79	228	202	144	24	110
S100	— 0	642	659	410	528	727	706	682	283	636
	— 2	516	528	262	360	604	577	538	154	482
	— 6	380	386	164	228	483	439	397	87	327
	—20	139	118	22	67	208	171	127	12	99
	—60	0	0	0	5	38	29	21	3	0
S200	— 0	348	359	139	246	422	405	347	86	315
	— 2	249	247	75	149	323	301	255	49	208
	— 6	149	141	36	75	211	183	144	22	110
	—20	24	17	5	16	68	42	39	4	14

Spectrum		295–290	290–285	285–280	280–275	275–270	270–265	265–260	260–255	255–250

S6	— 0	996	983	964	954	999	991	992	999	947
	— 2	945	875	744	666	951	914	965	944	736
	— 6	878	794	585	516	916	839	935	860	567
	—20	792	662	374	298	861	731	879	743	344
	—60	624	435	180	114	691	545	720	516	102
S12	— 0	972	943	887	871	988	964	988	987	896
	— 2	859	769	567	490	897	819	918	850	556
	— 6	804	687	419	333	855	743	878	764	391
	—20	636	464	188	130	705	558	733	535	137
	—60	462	231	83	53	481	359	516	305	3
S25	— 0	943	895	781	761	964	920	977	952	788
	— 2	819	699	439	355	858	759	891	779	434
	— 6	723	547	264	188	765	642	812	624	212
	—20	513	283	94	62	529	419	567	362	13
	—60	275	79	25	28	252	203	280	140	4
S50	— 0	878	788	591	537	905	829	926	847	573
	— 2	726	573	293	227	778	645	814	642	245
	— 6	552	342	129	77	590	456	634	413	61
	—20	356	135	49	37	358	274	393	200	0
	—60	112	9	0	11	89	75	91	33	0
S100	— 0	618	446	207	152	646	516	673	509	172
	— 2	480	269	100	71	485	380	523	339	49
	— 6	350	131	50	38	328	255	358	202	3
	—20	101	9	0	6	82	62	88	24	0
	—60	0	0	0	0	0	0	11	3	0
S200	— 0	305	138	43	37	302	214	326	177	4
	— 2	221	62	18	17	188	149	209	99	0
	— 6	126	13	4	4	91	73	107	43	0
	—20	14	0	0	0	0	0	0	0	0

Series Z 40μ–50μ
Spectrum		250–245	245–240	240–235	235–230	230–225	225–220	220–215	215–210	210–205	205–200
S6	— 0	963	987	1000	997	967	1000	1000	1000	1000	1000
	— 2	691	953	1000	888	654	728	842	737	717	598
	— 6	433	838	942	714	418	558	761	561	518	401
	—20	153	720	874	464	135	265	555	248	179	152
	—60	29	449	673	228	29	94	288	44	2	19
S12	— 0	837	945	982	910	843	838	882	822	826	778
	— 2	453	843	975	739	436	522	730	529	480	406
	— 6	208	758	908	525	199	308	593	308	252	204
	—20	62	503	686	233	59	101	306	76	44	61
S25	— 0	823	952	987	910	807	832	890	815	861	795
	— 2	402	837	954	692	359	481	712	482	463	385
	— 6	195	698	857	468	156	266	553	266	230	177
	—20	41	456	635	223	7	69	279	38	49	26
	—60	16	181	293	67	0	18	87	2	0	0
S50	— 0	448	763	863	646	420	563	733	543	545	457
	— 2	200	648	797	458	201	299	540	282	248	234
	— 6	82	488	645	263	68	119	342	97	77	77
	—20	30	199	317	76	4	27	93	7	0	0
S100	— 0	106	525	657	300	90	162	388	133	103	87
	— 2	40	379	513	165	11	60	234	35	30	24
	— 6	5	223	354	71	0	15	95	0	0	0
	—20	0	37	83	8	0	0	0	0	0	0
S200	— 0	4	179	269	65	0	16	98	0	0	0
	— 2	0	113	181	31	0	7	40	0	0	0
	— 6	0	38	94	7	0	1	8	0	0	0

Spectrum		Series X				Series Y		Series Z
Spectrum		500–450	460–410	410–360	370–320	340–290	300–250	250–200
S6	— 0	989	981	987	977	992	982	991
	— 2	968	939	928	872	914	869	781
	— 6	948	915	894	806	845	779	614
	—20	918	867	823	691	757	652	375
	—60	865	780	716	505	594	459	186
S12	— 0	984	977	968	935	964	948	866
	— 2	963	932	899	810	829	761	611
	— 6	938	893	852	732	768	671	426
	—20	903	830	769	590	608	477	213
	—60	850	750	669	416	437	297	⋯
S25	— 0	974	961	954	921	927	894	867
	— 2	930	896	873	778	780	688	577
	— 6	893	844	801	657	679	553	387
	—20	853	777	704	479	471	336	182
	—60	815	707	613	332	260	155	66
S50	— 0	932	900	859	771	842	778	598
	— 2	873	820	763	625	691	571	391
	— 6	820	751	678	490	520	384	226
	—20	765	666	576	323	339	217	75
	—60	647	521	410	155	129	53	⋯
S100	— 0	848	781	701	547	589	458	255
	— 2	808	731	637	446	450	318	149
	— 6	765	669	564	333	324	204	76
	—20	652	530	414	173	106	47	13
	—60	504	356	242	64	10	1	⋯
S200	— 0	726	621	509	305	297	186	63
	— 2	690	580	461	250	208	117	37
	— 6	638	516	397	183	120	57	15
	—20	489	361	255	75	24	3	⋯
	—60	274	162	90	14	⋯	⋯	⋯

Region	Height	Approx. temp.	Saturated vapor pressure	Total pressure	log P₀	log P₆	log P₁₀
Troposphere	0 km	10°C	1.00 cm	76 cm	1.881	1.914	1.935
	5	−15	0.14	40	1.602	1.611	1.617
	10	−50	0.003	20	1.301	1.301	1.302
Lower stratosphere	20	−50	0.003	4	0.602	0.604	0.605
Lower stratosphere	30	−50	0.003	0.9	$\bar{1}$ .954	$\bar{1}$ .963	$\bar{1}$ .969

Abstract

Cited By

Figures (12)

Tables (4)

Journal of the Optical Society of America