Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions

Jens Reichardt; Michael Hess; Andreas Macke

doi:10.1364/AO.39.001895

Applied Optics
Vol. 39,
Issue 12,
pp. 1895-1910
(2000)
•https://doi.org/10.1364/AO.39.001895

Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions

Jens Reichardt, Michael Hess, and Andreas Macke

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Jens Reichardt, Michael Hess, and Andreas Macke, "Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions," Appl. Opt. 39, 1895-1910 (2000)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5–0.7 followed by a gradual and monotonic decrease to 0.1–0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

Full Article | PDF Article

More Like This

Error analysis of Raman differential absorption lidar ozone measurements in ice clouds

Jens Reichardt
Appl. Opt. 39(33) 6058-6071 (2000)

Determination of the cirrus particle single-scattering phase function from lidar and solar radiometric data

C. M. R. Platt and A. C. Dilley
Appl. Opt. 23(3) 380-386 (1984)

Effect of multiple scattering on depolarization measurements with spaceborne lidars

Susanne Reichardt and Jens Reichardt
Appl. Opt. 42(18) 3620-3633 (2003)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (10)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (26)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

D ^k	Temperature Range (°C)	$A_{1}^{k}$ (m^-3 µm^-1)	$B_{1}^{k}$	$A_{2}^{k}$ (m^-3 µm^-1)	$B_{2}^{k}$
D ¹	-20 … -25	1.40 × 10²	-2.56	3.25 × 10^-1	-3.74
D ²	-25 … -30	1.75 × 10²	-2.51	2.60 × 10^-1	-4.49
D ³	-30 … -35	1.30 × 10²	-2.21	2.40 × 10^-1	-3.94
D ⁴	-35 … -40	2.50 × 10²	-2.29	1.30 × 10^-1	-4.37
D ⁵	-40 … -45	2.55 × 10¹	-3.23	1.70 × 10^-2	-3.23
D ⁶	-45 … -50	1.40 × 10¹	-3.15	1.00 × 10^-2	-3.15
D ⁷	-50 … -55	7.00 × 10⁰	-3.83	1.55 × 10^-3	-3.83
D ⁸	-55 … -60	5.02 × 10⁰	-3.85	7.25 × 10^-3	-3.85

p _i,j	Convolved Columns and Plates, Complex Crystals			Truncated Columns and Plates, Imperfect Columns and Plates
p _i,j	d _c(j) (µm)	d _min(j) (µm)	d _max(j) (µm)	d _c(j) (µm)	d _min(j) (µm)	d _max(j) (µm)
p _i,1	10	6	15	10a	6a	20a
p _i,2	20	15	25	30	20	40
p _i,3	30	25	35	60	40	90
p _i,4	40	35	50	130	90	200
p _i,5	60	50	70	300	200	400
p _i,6	80	70	90	600	400	900
p _i,7	100	90	130	1300	900	2000
p _i,8	150	130	180	–	–	–
p _i,9	200	180	250	–	–	–
p _i,10	300	250	350	–	–	–
p _i,11	400	350	500	–	–	–
p _i,12	600	500	700	–	–	–
p _i,13	800	700	1100	–	–	–

Cirrus	e _i	Truncated		Convolved		Imperfect		Complex Crystals
Cirrus	e _i	Columns	Plates	Columns	Plates	Columns	Plates	Complex Crystals
Warm	e ₀	0.594	0.746	0.674	0.835	0.524	0.547	—
d _min = 100 µm	e ₁	-0.253	-0.310	-0.433	-0.342	-0.287	-0.340	—
d _max = 1000 µm	e ₂	0.014	0.067	0.114	0.063	0.072	0.152	—
Warm	e ₀	0.580	0.692	0.661	0.775	0.555	0.583	0.504
d _min = 20 µm	e ₁	-0.937	-1.384	-1.580	-1.545	-1.144	-1.487	-0.821
d _max = 200 µm	e ₂	0.707	1.357	1.735	1.571	1.236	1.873	0.754
	e ₃	-0.185	-0.496	-0.682	-0.600	-0.510	-0.856	-0.277
Cold	e ₀	0.590	0.676	0.650	0.750	0.561	0.585	0.508
d _min = 20 µm	e ₁	-1.534	-1.992	-2.214	-2.323	-1.636	-1.988	-1.356
d _max = 200 µm	e ₂	1.803	2.541	3.075	3.126	2.136	2.823	1.688
	e ₃	-0.753	-1.125	-1.442	-1.447	-0.976	-1.357	-0.745
Cold	e ₀	0.561	—	0.633	—	0.553	—	—
d _min = 10 µm	e ₁	-3.090	—	-3.974	—	-3.307	—	—
d _max = 80 µm	e ₂	7.578	—	10.224	—	8.566	—	—
	e ₃	-8.285	—	-11.379	—	-9.706	—	—
	e ₄	3.302	—	4.559	—	3.961	—	—

D ^k	Temperature Range (°C)	$A_{1}^{k}$ (m^-3 µm^-1)	$B_{1}^{k}$	$A_{2}^{k}$ (m^-3 µm^-1)	$B_{2}^{k}$
D ¹	-20 … -25	1.40 × 10²	-2.56	3.25 × 10^-1	-3.74
D ²	-25 … -30	1.75 × 10²	-2.51	2.60 × 10^-1	-4.49
D ³	-30 … -35	1.30 × 10²	-2.21	2.40 × 10^-1	-3.94
D ⁴	-35 … -40	2.50 × 10²	-2.29	1.30 × 10^-1	-4.37
D ⁵	-40 … -45	2.55 × 10¹	-3.23	1.70 × 10^-2	-3.23
D ⁶	-45 … -50	1.40 × 10¹	-3.15	1.00 × 10^-2	-3.15
D ⁷	-50 … -55	7.00 × 10⁰	-3.83	1.55 × 10^-3	-3.83
D ⁸	-55 … -60	5.02 × 10⁰	-3.85	7.25 × 10^-3	-3.85

p _i,j	Convolved Columns and Plates, Complex Crystals			Truncated Columns and Plates, Imperfect Columns and Plates
p _i,j	d _c(j) (µm)	d _min(j) (µm)	d _max(j) (µm)	d _c(j) (µm)	d _min(j) (µm)	d _max(j) (µm)
p _i,1	10	6	15	10a	6a	20a
p _i,2	20	15	25	30	20	40
p _i,3	30	25	35	60	40	90
p _i,4	40	35	50	130	90	200
p _i,5	60	50	70	300	200	400
p _i,6	80	70	90	600	400	900
p _i,7	100	90	130	1300	900	2000
p _i,8	150	130	180	–	–	–
p _i,9	200	180	250	–	–	–
p _i,10	300	250	350	–	–	–
p _i,11	400	350	500	–	–	–
p _i,12	600	500	700	–	–	–
p _i,13	800	700	1100	–	–	–

Abstract

Cited By

Figures (10)

Tables (3)

Equations (26)

Applied Optics