COMPUTATION OF MIXED LAYER HEIGHT AND COMPARISON WITH LIDAR MEASURED VALUES
Under the guidance of:
ABSTRACT
Keywords: Atmospheric Boundary Layer, Planetary Boundary Layer, LIDAR, analytical methods, wavelet covariance method
ABBREVIATIONS
EBL  Elastic Backscatter LIDAR 
PBL  Planetary Boundary Layer 
ABL  Atmospheric Boundary Layer 
MLH  Mixed Layer Height 
BLH  Boundary Layer Height 
INTRODUCTION
The left panel in Fig 3 shows potential temperature which is unstable near the ground and is stable at the boundary layer. It is also clear from the right panel that the concentration of aerosol particles in the boundary layer is significantly higher when compared to the concentration in other regions.
There are several ways to measure ABL/PBL height (ABLH/PBLH). Many groundbased (LIDAR, Ceilometer), flightbased remote sensing instruments (radiosonde balloonborne instrument and CALIPSO satellite (https://wwwcalipso.larc.nasa.gov/tools/read_sw/index.php) can be used to determine PBLH. PBLH is generally derived from data measured with radiosondes, which give thermodynamic measurement variables including, temperature and pressure (Hennemuth and Lammert 2006). Nevertheless, there is always a lack of resolution if one tries to find ABLH/PBLH as the temporal estimates derived from radiosonde are restricted to the launchtime of the radiosondes, which are typically between 2 and 4 times per day. On the other hand, LIDAR measurements dependent on aerosol (tiny particles that hand in the atmosphere in solid and liquid forms) concentration in the atmosphere as its concentration is high compared to the free atmosphere above and this contrast is the basis for PBLH detection from LIDAR measurements (Cohn and Angevine 2000).
LIDAR technique is utilized to study the altitude profiles of aerosols, clouds, winds, temperature and humidity layers in the atmosphere (Nagamuni et al 2017). It is true that a large variety of instruments are available to measure the PBL height and there is also a large variety of algorithms used to determine the PBL depth. In this study, we have made an attempt to estimate PBL height using the Elastic Backscatter LIDAR (EBL) which is located at NARL. We acquired the raw data from EBL and converted it into readable ASCII format. Then, we applied several analytical methods including the gradient method (GM), double gradient method (DGM), logarithmic gradient method (LGM), variance method (VM) and a signal processing method which is Wavelet Covariance Transform (WCT) to study the EBL data.
METHODOLOGY
Theoretical PBLH Computation
$z_i\;=\;\sqrt{\left\{\frac{Q_{AK}}{\left[0.5\ast\left({\displaystyle\frac{\triangle\theta}{\triangle z}}\right)\right]}\right\}}$ 1
where, ‘z_{i}’ is the height of the mixed layer,
‘Q_{AK}’ is the cumulative daytime heating and
'∆θ/∆z' is the lapse rate in the layer.
This equation, hence, requires cumulative daytime heating and lapse in the layer as input parameters.
Cumulative daytime heating
Cumulative daytime heating can be calculated using the following equation
$Q\_AK=\;\;(F\_Hmax.D)/\pi\;\lbrack1\cos((\pi.t)/D)\rbrack$ 2
where, ‘F_{Hmax}’ is the maximum heat flux,
‘t’ is the arbitrary time and
‘D’ is the day duration.
Therefore, for calculating cumulative daytime heating, we require heat flux and day duration. The heat flux data has been acquired from the Baseline Surface Radiation Networking (BSRN) of World Radiation Monitoring Center (WRMC). BSRN of WRMC is developed to provide regular and frequent surface radiation fluxes measured by accurate operational and calibration techniques. It provides surface radiation values at regular intervals of time at different BSRN stations. Hence, the radiation flux data, measured at the nearest BSRN station, Tiruvallur (13.25^{0} N, 80.00^{0} E), India has been used in the calculation of cumulative daytime heating.
As the data contains different values including, shortwave downward radiation, direct radiation, diffuse radiation and longwave downward radiation, the required heat flux values have been extracted and are substituted in the above expression. In order to verify the monthly variations of cumulative daytime heating, we have plotted various months’ (Jan, Feb and March 2014) diurnal trends in Fig 4. The trend of cumulative daytime heating during Jan, Feb and March 2014 has been observed and those results are presented in Fig 4. It is obvious from this figure that diurnal variations of cumulative heating shows a Gaussian shape.
The same procedure is applied for the months January, February and March of 2014 to observe the variations in cumulative daytime heating and a nomogram has been developed.
Lapse Rate
Lapse rate, the rate at which temperature decreases with height, plays a pivotal role in the determination of PBL height. Lapse rate is the rate of change of atmospheric temperature. In other words, it is the slope of temperature. So, in order to calculate lapse rate, we need temperature versus altitude profile. It can be calculated using the expression
$\frac{d\theta}{dz}\;=\;\frac{\theta_2\theta_1}{z_2z_1}$
where ‘ $\frac{d\theta}{dz}$’ is the lapse rate,
‘Ɵ’ is the temperature and
‘z’ is the altitude.
Height of Planetary Boundary Layer
By substituting all the parameters in equation (1), PBL height is calculated for every three hours in a day. Likewise, height of PBL has been calculated for all the days in March, 2014. A diurnal variation of MLH has been observed in the case of PBL height.
Later a nomogram is prepared for comparing PBL height values of January, February and March of 2014.
Estimation of PBL height using LIDAR data:
To apply any method to estimate PBL height, the foremost thing is to make the signal noise corrected and path corrected. Noise correcting a signal implies subtracting the mean of certain range (34 km to 35 km) in backscattered signal from the entire backscatter profile. After noise correction, the signal should be path corrected. Path correction involves the multiplication of the noise corrected signal with the square of the altitude.
After noise correction and path correction, different methods can be applied to estimate PBL height.
Gradient Method
In the gradient method, numerical gradient (derivative) is applied to the path corrected signal (PCS) of LIDAR data. The altitude at which the gradient is minimum is considered as the PBL height.
H_{GM }= min[gradient(PCS)]
DoubleGradient Method
In applying the double gradient to the path corrected LIDAR signal, the altitude at which the gradient is minimum is considered as the PBL height.
H_{DGM} = min{grad[grad(RCS)]}
Logarithmic Gradient Method
Logarithmic gradient method of PBL estimation involves applying gradient to the logarithm of the path corrected signal. The altitude at which the value is minimum is taken as the PBL height.
H_{LGM } = min{gradient[log(PCS)]}
Variance method
The variance method of PBL estimation is a statistical method in which variance is calculated for a set of path corrected LIDAR backscatter signals. The maximum variability determines the PBL height.
H_{VM} = max[variance(PCS)]
Wavelet Covariance Technique
Wavelet Covariance Technique is a wavelet based technique in which the Haar function is applied to the path corrected LIDAR signal.
Haar function is ,
$h\left(\frac{zd}{t}\right)=\left\{\begin{array}{l}1,fort\frac{d}{2}zt\\ 1,fortzt+\frac{d}{2}\\ 0,elsewhere\end{array}\right.$
Where, ‘d’ is dilation and
‘t’ is translation.
where ‘z_{l}’ is the lower limit and
‘z_{u}’ is the upper limit of the LIDAR backscatter profile.
RESULTS:
A comparison is made between the computed theoretical values and measured values. The measured values show a better agreement when compared to the theoretical values, which clearly imply that better theoretical models need to be developed.
SUMMARY
During the two months (01 May – 28 June 2018) of my summer fellowship tenure at NARL, I have learned how to apply various analytical methods on LIDAR data and successfully calculated theoretical values and made a comparative study between them. Some of the important results out of this project are summarized hereunder.
The different analytical methods including, gradient, double gradient, variance, logarithmic gradient and WCT show excellent agreement with each other in terms of diurnal variations, although there exists a moderate difference with theoretical values.
There exist moderate differences in theoretical values, particularly, during postsunrise and postsunset timings, which clearly indicate that there is a need to develop better and appropriate theoretical models.
A Gaussianshaped response has been detected in different datasets while presenting them in terms of diurnal variations, which implies that stable and convective boundary layers existed during night and daytime periods.
Further, a nearGaussianshaped response can easily be detected in different datasets while presenting them in terms of diurnal variations, which implies that stable and convective boundary layers have existed during night and daytime.
ACKNOWLEDGEMENTS
I am grateful to my parents who supported me morally in completing this fellowship. I am also thankful to the management of Shri Vishnu Engineering College for Women (SVECW), Bhimavaram, India, for allowing me to report to this project and thanks are also due to Dr. P S Brahmanandam (Professor of Physics) and Dr. G Uma (Associate Professor of Physics), Dept. of Basic Science, SVECW for their moral support and constant encouragement that enabled me to apply for this prestigious summer research fellowship. I am extremely thankful to Indian National Science Academy (INSA), Govt. of India, for selecting me for this research fellowship. Finally, I would like to thank Authorcafe for helping me in improving my writing skills and also for its authorfriendly writing environment.
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