Irradiance on a Flat Object Underwater

John E. Tyler; Alma Shaules

doi:10.1364/AO.3.000105

Applied Optics
Vol. 3,
Issue 1,
pp. 105-110
(1964)
•https://doi.org/10.1364/AO.3.000105

Irradiance on a Flat Object Underwater

John E. Tyler and Alma Shaules

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John E. Tyler and Alma Shaules, "Irradiance on a Flat Object Underwater," Appl. Opt. 3, 105-110 (1964)

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Abstract

Relative irradiance as a function of the orientation of a flat object underwater has been calculated for clear-sunny and overcast lighting conditions from experimental radiance data. Tables give the relative irradiance on an object whose normal is oriented every 10° of tilt angle from the zenith and every 20° of azimuth. From theoretical considerations the computed irradiances should apply to other waters for which the ratio σ/α is the same as in the original experiment.

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Tilt angle γ	Depth 29.0 m					Sun altitude 56.6°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	13,200	13,200	13,200	13,200	13,200	13,200	13,200	13,200	13,200	13,200
10	13,500	13,500	13,400	13,200	13,000	12,800	12,600	12,500	12,400	12,400
20	13,600	13,500	13,300	13,000	12,600	12,200	11,800	11,500	11,300	11,300
30	13,200	13,100	12,800	12,300	11,800	11,100	10,600	10,200	9,890	9,950
40	12,400	12,200	11,800	11,300	10,700	9,930	9,320	8,730	8,410	8,430
50	11,400	11,200	10,700	10,100	9,320	8,480	7,750	7,130	6,780	6,750
60	10,000	9,780	9,300	8,700	7,880	6,960	6,160	5,520	5,170	5,110
70	8,510	8,250	7,790	7,140	6,290	5,430	4,660	4,120	3,800	3,710
80	6,900	6,640	6,170	5,560	4,760	3,990	3,360	2,940	2,700	2,620
90	5,310	5,040	4,650	4,090	3,410	2,830	2,390	2,090	1,900	1,830
100	3,780	3,580	3,280	2,820	2,340	1,960	1,670	1,460	1,320	1,280
110	2,560	2,430	2,180	1,870	1,580	1,350	1,160	1,020	936	904
120	1,600	1,520	1,400	1,230	1,070	933	820	733	677	657
130	1,030	990	926	837	722	665	597	544	510	525
140	675	661	632	587	539	491	452	422	403	396
150	492	485	469	445	418	392	369	351	340	336
160	385	381	374	362	348	333	321	311	305	302
170	324	323	320	315	310	303	298	294	291	290
180	291	291	291	291	291	291	291	291	291	291

Tilt angle γ	Depth 41.3 m					Sun altitude 56.6°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	1670	1670	1670	1670	1670	1670	1670	1670	1670	1670
10	1690	1680	1680	1660	1650	1630	1620	1600	1590	1600
20	1660	1650	1640	1610	1590	1560	1530	1500	1490	1490
30	1590	1570	1550	1520	1480	1440	1390	1360	1330	1340
40	1470	1450	1430	1390	1330	1280	1230	1190	1160	1160
50	1320	1300	1270	1220	1160	1100	1040	1000	971	970
60	1140	1120	1090	1040	974	911	850	802	773	771
70	942	927	894	844	780	718	661	620	589	586
80	742	730	699	653	595	540	491	454	430	427
90	559	548	521	481	435	392	353	325	305	303
100	399	389	368	338	304	273	246	226	212	209
110	272	265	250	229	207	187	169	156	147	144
120	179	175	166	153	140	128	117	109	104	101
130	120	117	112	104	94.0	89.7	83.3	78.5	75.6	79.4
140	81.8	80.4	77.6	73.5	69.3	65.3	61.8	59.2	57.5	56.7
150	60.3	59.5	58.1	56.0	53.8	51.6	49.7	48.2	47.2	46.8
160	47.7	47.4	46.8	45.9	44.8	43.6	42.6	41.8	41.3	41.2
170	41.2	41.1	40.9	40.5	40.1	39.6	39.2	38.8	38.6	38.6
180	37.9	37.9	37.9	37.9	37.9	37.9	37.9	37.9	37.9	37.9

Tilt angle γ	Depth 53.7 m					Sun altitude 56.6°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	223	223	223	223	223	223	223	223	223	223
10	223	223	222	221	220	218	217	216	215	215
20	217	217	216	214	211	209	206	204	203	202
30	205	205	203	200	196	193	189	186	185	184
40	188	187	185	181	177	173	169	165	163	162
50	167	166	163	159	154	149	144	140	138	137
60	142	141	138	134	129	123	118	114	111	110
70	115	115	112	108	103	97.6	92.5	88.7	86.0	85.0
80	89.5	88.7	86.3	82.7	78.2	73.6	69.1	65.7	63.3	62.5
90	66.3	65.7	63.6	60.7	57.1	53.4	49.9	47.1	45.3	44.6
100	46.4	46.0	44.5	42.4	39.8	37.2	34.7	32.7	31.4	31.0
110	31.5	31.2	30.2	28.8	27.1	25.4	23.8	22.5	21.7	21.4
120	21.0	20.8	20.2	19.4	18.4	17.3	16.4	15.6	15.1	14.9
130	14.3	14.2	13.9	13.4	12.8	12.2	11.6	11.2	10.9	11.4
140	10.0	9.97	9.80	9.55	9.23	8.89	8.59	8.35	8.20	8.15
150	7.62	7.59	7.50	7.36	7.19	7.01	6.84	6.72	6.64	6.61
160	6.20	6.19	6.14	6.08	5.99	5.90	5.82	5.76	5.72	5.70
170	5.45	5.44	5.42	5.40	5.36	5.33	5.29	5.27	5.25	5.24
180	5.08	5.08	5.08	5.08	5.08	5.08	5.08	5.08	5.08	5.08

Tilt angle γ	Depth 66.1 m					Sun altitude 56.6°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	33.2	33.2	33.2	33.2	33.2	33.2	33.2	33.2	33.2	33.2
10	33.0	33.0	32.9	32.8	32.7	32.6	32.4	32.3	32.3	32.3
20	32.0	31.9	31.8	31.6	31.4	31.1	30.9	30.7	30.6	30.5
30	30.0	30.0	29.8	29.5	29.2	28.8	28.5	28.2	28.0	28.0
40	27.3	27.2	27.0	26.7	26.3	25.8	25.4	25.1	24.8	24.8
50	24.0	23.9	23.7	23.3	22.8	22.3	21.8	21.5	21.2	21.1
60	20.3	20.2	19.9	19.0	19.0	18.5	18.0	17.6	17.3	17.2
70	16.4	16.3	16.0	15.7	15.2	14.6	14.1	13.8	13.5	13.4
80	12.6	12.5	12.3	12.0	11.5	11.1	10.6	10.3	10.1	9.97
90	9.29	9.22	9.03	8.74	8.39	8.02	7.68	7.40	7.22	7.14
100	6.50	6.44	6.29	6.08	5.82	5.56	5.31	5.11	4.98	4.93
110	4.38	4.34	4.24	4.10	3.93	3.76	3.60	3.46	3.37	3.33
120	2.88	2.86	2.80	2.72	2.62	2.51	2.41	2.33	2.28	2.25
130	1.93	1.91	1.88	1.83	1.78	1.72	1.66	1.61	1.58	1.56
140	1.32	1.31	1.30	1.27	1.24	1.21	1.17	1.15	1.13	1.12
150	0.975	0.972	0.963	0.950	0.933	0.914	0.896	0.881	0.872	0.868
160	0.773	0.772	0.767	0.760	0.751	0.742	0.732	0.724	0.719	0.717
170	0.665	0.665	0.663	0.660	0.656	0.652	0.648	0.645	0.643	0.642
180	0.614	0.614	0.614	0.614	0.614	0.614	0.614	0.614	0.614	0.614

Tilt angle γ		Depth 6.1 m				Sun altitude 40.0°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	447,000	447,000	447,000	447,000	447,000	447,000	447,000	447,000	447,000	447,000
10	448,000	448,000	447,000	446,000	444,000	442,000	440,000	439,000	438,000	437,000
20	434,000	434,000	432,000	429,000	426,000	422,000	418,000	415,000	414,000	413,000
30	408,000	407,000	405,000	400,000	395,000	390,000	385,000	381,000	378,000	377,000
40	372,000	371,000	367,000	362,000	356,000	349,000	343,000	338,000	335,000	333,000
50	327,000	325,000	321,000	316,000	308,000	301,000	294,000	288,000	284,000	283,000
60	276,000	275,000	271,000	265,000	257,000	249,000	242,000	236,000	232,000	231,000
70	224,000	223,000	219,000	213,000	206,000	198,000	191,000	185,000	181,000	180,000
80	173,000	172,000	169,000	163,000	157,000	150,000	144,000	138,000	135,000	134,000
90	128,000	127,000	124,000	120,000	114,000	109,000	104,000	99,400	96,600	95,700
100	90,400	89,600	87,300	83,900	79,700	75,400	71,400	68,200	66,100	65,400
110	61,300	60,700	59,100	56,700	53,800	50,700	47,900	45,700	44,200	43,700
120	40,300	39,900	38,900	37,400	35,500	33,500	31,700	30,200	29,300	29,000
130	27,300	27,100	26,500	25,500	23,800	23,100	22,000	21,100	20,500	21,200
140	19,300	19,200	18,800	18,300	17,500	16,800	16,100	15,500	15,100	15,000
150	14,900	14,800	14,500	14,200	13,700	13,300	12,800	12,500	12,300	12,200
160	12,100	12,100	12,000	11,700	11,500	11,200	11,000	10,700	10,600	10,600
170	10,600	10,500	10,500	10,400	10,300	10,100	10,000	9,920	9,860	9,840
180	9,690	9,690	9,690	9,690	9,690	9,690	9,690	9,690	9,690	9,690

Tilt angle γ		Depth 18.3 m				Sun altitude 40.0°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	32,300	32,300	32,300	32,300	32,300	32,300	32,300	32,300	32,300	32,300
10	32,000	32,000	32,000	31,900	31,700	31,600	31,500	31,400	31,300	31,300
20	31,100	31,100	30,900	30,700	30,500	30,200	30,000	29,800	29,700	29,600
30	29,300	29,200	29,000	28,700	28,400	28,000	27,600	27,300	27,200	27,100
40	26,700	26,600	26,400	26,000	25,600	25,100	24,700	24,300	24,100	24,000
50	23,600	23,500	23,200	22,800	22,300	21,800	21,300	20,900	20,600	20,600
60	20,000	19,900	19,600	19,200	18,700	18,200	17,600	17,200	16,900	16,800
70	16,200	16,200	15,900	15,500	15,000	14,500	14,000	13,600	13,300	13,200
80	12,600	12,600	12,300	12,000	11,500	11,100	10,600	10,200	9,960	9,860
90	9,430	9,370	9,190	8,900	8,540	8,150	7,760	7,430	7,210	7,130
100	6,740	6,700	6,560	6,340	6,060	5,760	5,460	5,200	5,030	4,970
110	4,690	4,660	4,560	4,410	4,210	3,980	3,770	3,590	3,470	3,420
120	3,220	3,190	3,130	3,030	2,890	2,740	2,600	2,480	2,410	2,370
130	2,240	2,230	2,180	2,120	1,930	1,940	1,850	1,770	1,720	1,780
140	1,600	1,590	1,560	1,520	1,470	1,410	1,360	1,310	1,280	1,270
150	1,220	1,210	1,190	1,170	1,140	1,100	1,070	1,040	1,030	1,020
160	982	978	969	955	938	918	901	887	879	875
170	851	850	846	840	832	824	816	810	806	805
180	785	785	785	785	785	785	785	785	785	785

Tilt angle γ		Depth 30.5 m				Sun altitude 40.0°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	2940	2940	2940	2940	2940	2940	2940	2940	2940	2940
10	2930	2920	2920	2910	2890	2880	2870	2860	2850	2850
20	2840	2840	2830	2810	2780	2750	2730	2710	2700	2690
30	2680	2670	2650	2630	2590	2550	2520	2490	2470	2460
40	2450	2440	2420	2380	2340	2290	2250	2210	2190	2180
50	2160	2160	2130	2090	2040	1990	1940	1900	1870	1860
60	1840	1830	1810	1770	1710	1660	1600	1560	1530	1520
70	1500	1490	1470	1430	1380	1330	1270	1230	1200	1190
80	1170	1160	1140	1110	1060	1020	968	927	898	888
90	873	868	852	826	792	752	712	677	652	643
100	623	620	608	590	565	535	505	477	459	451
110	433	430	423	410	393	373	352	333	319	314
120	297	295	290	282	271	258	244	232	224	221
130	208	206	203	198	191	183	175	167	162	160
140	149	149	147	143	139	134	129	125	122	121
150	115	115	113	111	109	106	103	100	98.6	97.9
160	94.2	93.9	93.1	91.9	90.4	88.7	87.1	85.7	84.8	84.5
170	82.4	82.3	81.9	81.4	80.7	79.9	79.2	78.7	78.3	78.2
180	76.3	76.3	76.3	76.3	76.3	76.3	76.3	76.3	76.3	76.3

Tilt angle γ	Depth 42.8 m					Sun altitude 40.0°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	315	315	315	315	315	315	315	315	315	315
10	313	313	313	312	311	309	308	308	307	307
20	304	303	302	300	298	296	294	292	291	291
30	285	285	283	281	278	275	272	269	268	267
40	260	259	258	255	251	247	244	241	239	238
50	230	229	227	223	219	215	211	207	205	205
60	195	195	192	189	184	180	175	172	170	169
70	160	159	157	153	149	144	140	137	134	134
80	125	124	122	119	115	111	107	104	102	102
90	93.8	93.2	91.6	89.2	86.1	82.9	79.7	77.1	75.4	74.8
100	67.7	67.2	66.0	64.2	61.9	59.4	57.1	55.2	53.8	53.4
110	47.5	47.2	46.3	45.0	43.5	41.8	40.2	38.8	37.9	37.6
120	32.8	32.6	32.1	31.2	30.2	29.1	28.1	27.3	26.7	26.5
130	23.1	23.0	22.7	22.1	21.0	20.8	20.1	19.6	19.2	19.8
140	16.7	16.6	16.4	16.1	15.7	15.3	14.9	14.6	14.3	14.3
150	12.9	12.9	12.7	12.5	12.3	12.0	11.8	11.6	11.4	11.4
160	10.6	10.6	10.5	10.4	10.2	10.0	9.90	9.78	9.71	9.68
170	9.27	9.26	9.22	9.17	9.10	9.03	8.96	8.91	8.87	8.86
180	8.61	8.61	8.61	8.61	8.61	8.61	8.61	8.61	8.61	8.61

Tilt angle γ	Depth 55.0 m					Sun altitude 40.0°
				Azimuth angle β
	0	20	40	60	80	100	120	140	160	180
0	35.1	35.1	35.1	35.1	35.1	35.1	35.1	35.1	35.1	35.1
10	34.8	34.8	34.7	34.7	34.6	34.5	34.4	34.4	34.3	34.3
20	33.5	33.5	33.4	33.3	33.2	33.0	32.9	32.8	32.7	32.7
30	31.4	31.3	31.3	31.1	30.9	30.7	30.5	30.3	30.2	30.2
40	28.5	28.5	28.4	28.2	27.9	27.7	27.4	27.2	27.1	27.0
50	25.1	25.0	24.9	24.7	24.4	24.1	23.8	23.6	23.4	23.4
60	21.3	21.2	21.0	20.8	20.5	20.2	19.9	19.6	19.5	19.4
70	17.3	17.2	17.1	16.9	16.6	16.3	16.0	15.8	15.6	15.5
80	13.5	13.4	13.3	13.1	12.8	12.5	12.3	12.1	11.9	11.9
90	10.1	10.0	9.94	9.78	9.57	9.35	9.13	8.95	8.83	8.79
100	7.25	7.22	7.15	7.03	6.88	6.72	6.56	6.43	6.34	6.31
110	5.09	5.07	5.01	4.93	4.83	4.72	4.62	4.53	4.46	4.44
120	3.52	3.51	3.47	3.42	3.38	3.29	3.22	3.17	3.13	3.11
130	2.48	2.47	2.45	2.41	2.37	2.33	2.29	2.25	2.23	2.22
140	1.78	1.78	1.76	1.74	1.72	1.69	1.66	1.64	1.63	1.62
150	1.36	1.36	1.35	1.34	1.32	1.31	1.29	1.28	1.27	1.27
160	1.11	1.10	1.10	1.09	1.08	1.07	1.06	1.06	1.05	1.05
170	0.963	0.962	0.960	0.957	0.953	0.949	0.945	0.941	0.939	0.938
180	0.896	0.896	0.896	0.896	0.896	0.896	0.896	0.896	0.896	0.896

Abstract

Cited By

Figures (2)

Tables (9)

Equations (5)

Applied Optics