molecular number density N(z), which is the N2 molecule number density. The N(z) profile is calculated from radiosonde observations, or in case of water, derived from the ratio of the N2and H2O Raman signals (see Sec. 5.1.6). Taking the logarithm of Eq. 3.22 and differentiating it with respect toz yields the total extinction coefficient:
α(z,λ0) +α(z,λram) = d
dzln N(z)
z2Pram(z,λ0,λram)+ d
dzlnO(z). (5.10)
Table 5.1: Considered Raman wavelengths in the KARL system.
λ0 molecule λram
532 nm N2 607 nm
532 nm H2O 660 nm
355 nm N2 387 nm
355 nm H2O 407 nm
In the following, the overlap term is considered to be O(z)= 1, e.g., the analysis is concentrated on the optimum measurement range. Again, extinction coefficients are split up into the molecular (αray) and aerosol (αaer) contribution:
αaer(z,λ0) =
d
dzln N(z)
z2Pram(z,λ0,λram) −αray(z,λ0)−αray(z,λram) 1+ αaer(z,λram)
αaer(z,λ0)
. (5.11)
The wavelength dependence of the particle extinction coefficient is described by the Ångström exponent a˚:
αaer(z,λ0) αaer(z,λram) =
λram λ0
a˚(z)
, (5.12)
⇒αaer(z,λ0) =
d
dzln N(z)
z2Pram(z,λ0,λram) −αray(z,λ0)−αray(z,λram) 1+λram
λ0
a˚(z) . (5.13)
Photometer measurements in Ny-Ålesund show an Ångström exponent of a˚≈-1.2. Over-or underestimation ofa˚by 0.5 leads to relative errors of the order of 5 % [Weitkamp, 2005].
The aerosol backscatter coefficient βaer at an elastic wavelength λ can be calculated from the ratio of the elastic signal and the respective N2 Raman signal. Furthermore, as
in the Klett algorithm, a reference value for particle backscattering at a reference range zref must be estimated. With
BSR(z,λ) = P
ram(zref,λram)Pel(z,λ)
Pel(zref,λ),Pram(z,λram) (5.14) follows
βaer(z,λ) = −βray(z,λ) + [βaer(zref,λ) +βray(zref,λ)]
· P
ram(zref,λram)Pel(z,λ) Pel(zref,λ),Pram(z,λram)
N(z) N(zref)
·exp −Rz
zref[αray(z,λram) +αaer(z,λram)]dz exp
−Rz
zref[αray(z,λ) +αaer(z,λ)]dz . (5.15) Air density and molecular backscatter terms are again calculated from radiosonde profiles, the particle transmission ratio is estimated as in Eq. 5.12. Finally, LR can be calculated directly using Eq. 5.4.
5.1.3. Depolarization
The VDR is defined as the quotient of the backscattered light in perpendicular and parallel polarization direction to the emitted beam (Eq. 3.23):
VDR(z,λ) =C·P⊥(z,λ)
Pk(z,λ). (5.16)
The constantCis determined within the aerosol free stratosphere, where VDR approaches the molecular background value of 1.4 % due to Rayleigh scattering [Bridge and Buck-ingham, 1966] (cf. Sec. 3.4). As multiple scattering influences VDR [Hu et al., 2006], the considered aerosol layers need to be optically relatively thin (AOD<0.3–0.5). Some remarks on error analysis can be found in Appendix B.
5.1.4. Color Ratio
The backscatter coefficient βaer(z,λ) depends on the effective scattering cross section, which is primarily a function of particle size [Sassen, 1978] but which is amongst others also influenced by the particle shape and the refractive index. Hence, the color ratio (CR), defined as the quotient of the backscatter ratio BSR at different wavelengths λ1
and s:lambda2, is a rough measure of particle size, and can be written as:
CR(z,λ1,λ2) = BSR(z,λ1)−1
BSR(z,λ2)−1 with λ1> λ2 (5.17a)
= β
aer(z,λ1)·βray(z,λ2)
βaer(z,λ2)·βray(z,λ1). (5.17b) Defined this way [Liu and Mishchenko, 2001], a color ratio close to unity indicates particles much smaller than the wavelength (Rayleigh limit), while large CR values (up to 5 forλ1= 532 nm and λ2= 355 nm) indicate large particles compared to the wavelength.
5.1. KARL DATA PREPARATION
5.1.5. Mie-Code Calculations
Mie-code calculations allow the determination of microphysical aerosol particle properties by an inversion algorithm that uses optical data. The inversion problem is ill-posed and requires the application of mathematical regularization techniques. The optical and physical particle parameters are related to each other via a Fredholm system of at least five integral equations of the first kind for the backscatter (three) and extinction (two) coefficients [Böckmann, 2001]:
βaer(z,λ) = where r denotes the particle radius, m is the complex index of refraction, and rmin and rmax are the lower and upper limits (in our case: rmin= 0.001 µm andrmax= 1.25 µm) of realistic particle radii. n(r) is the unknown aerosol size distribution,kπ is the backscatter and kext the extinction kernel. The kernel functions generally contain information on size and material information of particles. For the Mie inversion code used (based on Böckmann et al.[2006]), Mie particles, e.g., homogeneous particles of spherical shape are assumed. The algorithm was developed for LIDAR systems measuring two extinction coefficients and three backscatter coefficients (βaer355/532/1064, αaer355/532). First, the index of refractionm for all three elastic wavelengths is iteratively estimated. Second, a numerical inversion is performed to estimate the particle size distribution. Usually, the size distribution is approximated by a logarithmic-normal distribution. The code which was used allows the retrieval of monomodal distributions:
dn(r) = √ nt nt is the total number concentration, rmod,N is the mode radius with respect to the number concentration and σr is the mode width. The mean properties of the particle ensemble are given by: One has to be aware that these calculations suffer from a lot of uncertainties. First, there are several a priori assumptions such as the ideal sphericity of the particles. Second, solving an ill-posed problem can be described as finding the cause of a given effect.
However, distinct causes can account for the same effect and small changes in the effect can be induced by very large changes in a given cause. To judge the stability of the retrieved solution, one can perform several inversions of one aerosol layer at different intervals in space and time. For instance, the inversion is stable, if inversions performed at the backscatter maximum of an aerosol layer as well as slightly below or above the maximum, retrieve a similar refractive index and particle size with maximum number concentrations at βaermax (see Sec. 8.3.1).
5.1.6. Relative Humidity
For the lowermost kilometers of the atmosphere, the estimation of RH from LIDAR data is possible with the Raman method for gas-concentration measurements. Two Raman LIDAR signals are necessary, one of which is the return signal from the gas of interest, e.g., water vapor and the other one is the Raman signal of a reference gas, usually N2. By dividing and rearranging the two Raman equations (Eq. 3.22) the volume mixing ratio of water vapor relative to dry airw(z) is obtained:
w(z) =C This method assumes identical overlap factors of the two Raman signals and range independent Raman backscatter cross sections. The difference between atmospheric transmission at the two wavelengths is mainly due to Rayleigh scattering and is corrected by using temperature and pressure profiles from the radiosonde. Differences caused by wavelength dependent particle extinction can almost be neglected as the two wavelengths are close to each other. The calibration constant C can be determined by calibration against the mixing ratio profile of the co-located radiosonde [Sherlock et al., 1999].
However, the results then depend on the accuracy of the radiosonde data. Furthermore, the signal intensity distribution in the Raman bands is temperature dependent [Whiteman, 2003], which induces a temperature dependence of the calibration constant if the spectral width of the interference filter is too narrow. For significant analysis, the SNR of the water vapor signal should exceed values of 15. The volume mixing ratio can then be transformed into RH using Eq. 2.3. Additional error sources are the assumption of the ideal gas law and the calculation of the saturation water vapor pressure.