Shortened version of the Umkehr method for observing the vertical distribution of ozone

John J. DeLuisi

doi:10.1364/AO.18.003190

Applied Optics
Vol. 18,
Issue 18,
pp. 3190-3197
(1979)
•https://doi.org/10.1364/AO.18.003190

Shortened version of the Umkehr method for observing the vertical distribution of ozone

John J. DeLuisi

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John J. DeLuisi, "Shortened version of the Umkehr method for observing the vertical distribution of ozone," Appl. Opt. 18, 3190-3197 (1979)

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Abstract

A theoretical study was performed to explore the possibility of shortening the 2–3-h time requirement for a Dobson Umkehr observation by incorporating more wavelength pairs into the measurement procedure. In essence, the measurement becomes one of using wavelength in place of solar zenith angle as the independent variable. Practical and physical limitations restrict the variable-wavelength method to solar zenith angles 75° < θ₀ < 90°. Solution residual variance and correlation criteria are used to judge the statistical information content of each method in order to establish a degree of equivalence between the two. As a check on the validity of the theoretical approach, a limited eigenvalue analysis is performed on the synthesized Umkehr observations, and this is compared with eigenanalyses on real Umkehr data reported by other investigators. The over-all results of the present investigation indicate that the variable-wavelength method possesses the potential for deducing vertical ozone profiles at least equivalent to, if not slightly better than, profiles deduced by the standard Umkehr method.

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Covariance of ozonesonde observations

1	2	3	4	5	6	7	8	9
0.130095	0.193271	0.052067	0.020581	−0.001819	−0.000377	−0.000158	−0.000322	−0.000116
	0.749585	0.264779	0.094766	−0.001797	−0.037731	−0.032335	−0.018098	−0.005774
		0.155650	0.048879	−0.000229	−0.021971	−0.016711	−0.009387	−0.003066
			0.030767	0.003956	−0.008226	−0.007245	−0.004087	−0.001352
				0.006771	0.005689	0.002965	0.001622	0.000534
					0.022555	0.019218	0.010556	0.003527
						0.023467	0.013398	0.004478
							0.020000	0.010000
								0.030000

Logarithm base e of the average ozone concentrations (atm-cm) for Boulder data and at standard pressure levels for the nine-layer Umkehr model.
Layer No.	1	2	3	4	5	6	7	8	9
p (mb)	(1000-250)	(250-125)	(125-62.5)	(62.5-31.3)	(31.3-15.6)	(15.6-7.81)	(7.81-3.91)	(3.91-1.95)	(1.95-0.98)
ηi	−3.99465	−3.98718	− 3.11571	−2.47532	−2.59179	−3.11033	−3.82880	−4.65837	−5.11440

	E₁	E₂	E₃	E₄
Umkehr (present study)	0.741	0.239	0.019	0.001
MW method (present study)	0.826	0.167	0.005	0.001
Umkehr12	0.656	0.293	0.030	0.009
Umkehr21	0.709	0.238	0.034	0.006

			MW combinations

			80,83
		σ	85,86.5	80,83	80,83				88,86.5	88,86.5
Layer	Umkehr	f	88	85,86.5	85	80,83	88	88.86.5	85	85,83
1	0.308	0.361	0.279	0.289	0.298	0.303	0.305	0.299	0.293	0.286
2	0.407	0.866	0.354	0.370	0.380	0.383	0.461	0.427	0.398	0.374
3	0.172	0.395	0.169	0.171	0.173	0.174	0.211	0.197	0.185	0.175
4	0.088	0.175	0.086	0.088	0.090	0.092	0.100	0.093	0.089	0.087
5	0.058	0.082	0.056	0.058	0.060	0.062	0.064	0.061	0.059	0.057
6	0.059	0.150	0.053	0.058	0.064	0.070	0.068	0.061	0.057	0.054
7	0.067	0.153	0.062	0.069	0.074	0.078	0.068	0.063	0.062	0.062
8	0.081	0.141	0.086	0.092	0.098	0.103	0.102	0.099	0.094	0.090
9	0.115	0.173	0.115	0.136	0.150	0.160	0.162	0.150	0.135	0.122
$Σ σ_{i i}^{2}$	0.329	1.169	0.269	0.296	0.317	0.329	0.410	0.329	0.324	0.293
Correlation ( $\hat{f}$ f)
1	0.52		0.63	0.60	0.57	0.54	0.53	0.56	0.58	0.61
2	0.88		0.91	0.90	0.90	0.90	0.85	0.87	0.89	0.90
3	0.90		0.90	0.90	0.90	0.90	0.84	0.87	0.88	0.90
4	0.86		0.87	0.87	0.86	0.85	0.82	0.85	0.86	0.87
5	0.71		0.73	0.71	0.68	0.66	0.63	0.67	0.69	0.71
6	0.92		0.93	0.92	0.90	0.88	0.89	0.92	0.93	0.93
7	0.90		0.91	0.89	0.88	0.86	0.90	0.91	0.91	0.91
8	0.82		0.79	0.76	0.72	0.68	0.69	0.71	0.74	0.77
9	0.75		0.75	0.62	0.50	0.38	0.36	0.51	0.63	0.71

Covariance of ozonesonde observations

1	2	3	4	5	6	7	8	9
0.130095	0.193271	0.052067	0.020581	−0.001819	−0.000377	−0.000158	−0.000322	−0.000116
	0.749585	0.264779	0.094766	−0.001797	−0.037731	−0.032335	−0.018098	−0.005774
		0.155650	0.048879	−0.000229	−0.021971	−0.016711	−0.009387	−0.003066
			0.030767	0.003956	−0.008226	−0.007245	−0.004087	−0.001352
				0.006771	0.005689	0.002965	0.001622	0.000534
					0.022555	0.019218	0.010556	0.003527
						0.023467	0.013398	0.004478
							0.020000	0.010000
								0.030000

Abstract

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Figures (4)

Tables (3)

Equations (9)

Applied Optics