LWC estimation using radar-microwave radiometer synergy 

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Earth’s radiative balance and clouds

The sun is the primary energy source for most processes in the earth’s system. Although the sun emits electromagnetic radiation at various wavelengths, most of the incoming solar radiations consist of visible and parts of ultraviolet and short infrared radiations. The electromagnetic (EM) radiations are characterized by their wavelength , or by its frequency . The two variables are related as × = , where is the speed of light ( = 3 × 108 −1 in vacuum). The wavelength of peak radiation emitted by an object is inversely related to its temperature (Wien’s law). Due to the high surface temperature of the sun (average 5500 ), the wavelength of peak radiation has high intensity and shorter wavelengths, hence called shortwave(SW). The earth’s surface and the atmosphere reflects as well as absorb these solar radiations (SW). A part of the radiation (around 30%) is reflected, and the fraction absorbed by the earth ( ∼ 300 ) is re-radiated at the longer wavelengths in the infrared region (about ∼ 10 ) called longwave (LW) with relatively less intensity. Figure 2.2 presents the radiation intensity and range of wavelengths of incoming solar radiations and the emitted radiations from the earth. Notice that the radiation intensity on the y-axis is relative.
Several factors influence the amount of solar radiation reaching the earth’s surface and the amount of radiation leaving the atmosphere. The interaction of radiation with atmospheric gases, water vapour, aerosols, and clouds includes absorption, emission, and scattering processes. These processes play a vital role in the thermodynamic conditions of the atmosphere.

Scattering, absorption and extinction processes

When radiation interacts with a particle, a part of the incident energy is absorbed, whereas the other is spatially redistributed in a non-isotropic direction. These processes are known as the absorption and scattering processes, respectively. The absorbed part  of the radiation is converted into molecular kinetic and potential energies whereas, scattered radiation is simply redirected without any loss of energy. The extinction or attenuation of radiation by a particle represents the sum of absorption and scattering processes. An electromagnetic wave of intensity propagates along an optical path in an atmospheric layer gets attenuated by a factor which is given by: 0= − (2.1) where is the extinction coefficients and has unit −1. The contributions of scattering and absorption to the extinction of the incident beam of radiation defines the scattering and absorption coefficient, such as: =+ (2.2).
Scattering is a process, which conserves the total amount of energy, but the direction in which the radiation propagates may be altered. The amount of scattering depends on several factors, including the wavelength of the radiation, the size of particles (or gas molecules), the amount of particles, and the incident and scattering angles. If we assume a spherical particle of radius , we define a dimensionless size parameter to be the ratio of the circumference of the particle to the wavelength of radiation:0 = 2 (2.3).

Cloud feedback on climate

Reflection of solar radiations by clouds serves as a key feedback mechanism for climate change. A reduction in reflection of SW radiations due to low cloud induce positive feedback, while increase in cloud water content with warming induce negative feedback on climate [Stephens et al., 2015]. Clouds and aerosols contribute to climate change in a variety of ways. As shown in figure 2.7, the global radiative balance is affected by anthropogenic forcing agents such as greenhouse gases and aerosols. When a forcing agent alters internal energy flows in the earth system, it affects cloud cover and other climate system components, which in turn affects the global energy budget. In contrast to changes in the global mean surface temperature, which are slowed by the huge heat capacity of the oceans, these adjustments often occur within a shorter time span (generally a few weeks). These rapid adjustments are associated with changes in climate variables that are mediated by a change in global mean surface temperature. These variables further contribute to the amplification or dampening in global temperatures through their effect on the radiative budget [Change, 2014].
The representation of clouds is widely regarded as the largest source of uncertainty in estimates of climate sensitivity obtained by global climate models (GCMs) [Schneider et al., 2017]. Among all the uncertainties in climate sensitivity estimates, represen-tation of boundary layer clouds such as stratus and stratocumulus have a significant contribution, specifically in the sensitivity of boundary layer clouds to changing surface and PBL (planetary boundary layer, the lowermost part of atmosphere which is directly influenced by surface) properties [Bony and Dufresne, 2005]. Various climate sensitivity studies indicate that climate models often underestimate the low-cloud cover and over-estimate the occurrence of mid- and high-clouds above low-clouds furthermore, these biases can be caused due to inaccurate representation of cloud microphysical parameters [Nam et al., 2012]. Investigation of cloud processes leads to a better understanding of boundary layer clouds behaviour under changing atmospheric conditions have the potential to reduce the uncertainty in model predictions and climate sensitivity significantly [Bony and Dufresne, 2005].
In order to advance our knowledge about clouds-climate interactions, observations at multiple scales are required to verify the theories and hypotheses about clouds. Essentially, observations are the acquisition of information from a primary source or a snapshot of reality, which is analysed to validate or modify the concepts. The next chapter introduces general measurements techniques used for cloud observations.

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Instruments used in this study

In this thesis, a method to estimate the microphysical characteristics of low-level clouds and fog is presented (in chapter 5) using a cloud radar and microwave radiometer synergy. Observations from BASTA cloud radar colocated with the HATPRO (Humidity And Temperature PROfiler) microwave radiometer at SIRTA observatory and SOFOG-3D field experiment are utilized. The fundamental concept of these remote sensing instru-ments is already introduced in this chapter, and this section describes these instruments and their capabilities in further depth. While the SIRTA observatory and SOFOG-3D experiment observation sites are detailed in section 3.5. The retrievals of the cloud mi-crophysical parameter using the mentioned synergy are compared with measurements from an in-situ sensor called CDP. To ensure that this section covers all instrumentation utilized in this research, the in-situ sensor is also described here.

BASTA cloud radar

A 95 FMCW radar called BASTA [Delanoë et al., 2016] developed in LATMOS (Laboratoire Atmosphères, Observations Spatiales) is operational at SIRTA observatory since 2010 (shown in figure 3.5). In addition to its first prototype operational at SIRTA, several other BASTA radars are working over different locations around the globe.
This Doppler cloud radar uses the frequency-modulated continuous wave (FMCW) technique, rather than pulses, making it less expensive than standard cloud radars by reducing the emitted power. The principle of FMCW radar is same as the radar principle discussed in the previous section, except that the radar transmits the continuous wave of energy whose frequency varies between 0 +Δ and 0 −Δ with a constant time period with 0 as the central frequency and Δ is half of the frequency band. The wave, which is returned by a target situated at a range , is received after time Δ = 2 / where is the speed of wave propagation in the given medium. The radar returned signal is convolved (mixed) with the transmitted signal, and the beat frequency can be defined such that =2Δ × Δ (3.10).
The acquisition of the signal occurs only for half of the total time period to avoid echo from other chirp, which costs 3 loss in sensitivity in BASTA. The range resolution is calculated as = (3.11) 2×2Δ.

Table of contents :

1 Introduction and Motivation 
2 Clouds 
2.1 Cloud formation and classification
2.2 Earth’s radiative balance and clouds
2.2.1 Scattering, absorption and extinction processes
2.2.2 Earth’s radiative equilibrium
2.2.3 Cloud radiative forcing
2.2.4 Cloud feedback on climate
3 Instruments for cloud observation 
3.1 In-situ measurements
3.2 Remote Sensing
3.2.1 Passive sensors
3.2.2 Active sensors
3.3 Instruments used in this study
3.3.1 BASTA cloud radar
3.3.2 HATPRO microwave radiometer
3.3.3 Cloud Droplet Probe (CDP) on tethered balloon during SOFOG- 3D experiment
3.4 Observation platforms
3.5 Observation sites and field campaigns used in this study
3.5.1 SIRTA
3.5.2 SOFOG-3D
4 Prerequisites and overview of the literature for LWC retrieval 
4.1 Microphysical parameters of liquid phase clouds
4.2 Classification of hydrometeors
4.3 Atmospheric Attenuation
4.4 Cloud radar based techniques for LWC retrieval
4.4.1 Empirical relation
4.4.2 Spectral Analysis
4.4.3 Multi-sensor retrieval techniques
5 LWC estimation using radar-microwave radiometer synergy 
5.1 Introduction
5.2 Methodology of LWC retrieval
5.2.1 Optimal estimation formulation
5.2.2 Definition of the state and observation vectors
5.2.3 Description of the forward model and Jacobian matrix
5.2.4 Discussion of the retrieval uncertainty
5.2.5 Analysis of the method when microwave radiometer is available
5.3 Sensitivity analysis of retrieval algorithm using synthetic data
5.3.1 Description of synthetic data
5.3.2 Sensitivity analysis of impact of error in observation
5.3.3 Sensitivity analysis of impact of attenuation due to liquid droplets model
5.3.4 Sensitivity analysis of bias in Z and LWP
5.3.5 Sensitivity analysis of LWP assimilation
5.3.6 Sensitivity of parameter b
5.3.7 Analysis of the sensitivity exercise
5.4 Comparison of LWC retrieval with in-situ data
5.4.1 Presentation of the case study of 09 February 2020
5.4.2 Comparison between in-situ and radar measurements
5.5 Statistical analysis of retrievals to derive climatology
5.6 BASTA standalone LWC retrieval using climatology
5.6.1 BASTA standalone LWC retrieval approach
5.6.2 BASTA standalone LWC retrieval first assessment using LWP retrieved from MWR
6 Conclusion and outlook 
6.1 Conclusion
6.2 Outlook

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