Aerosols, solar long wave radiation and scattering by clouds are not included in the CIRC calculations. The temperature, pressure, gas concentration profiles and cloud properties used in the proposed radiative model are obtained from the input files provided on the CIRC website for validation purposes. The summarized model parameters and results of surface downwelling flux for Case 6 and Case 7 are presented in Table 3.5. Scenario 1 recovers the CIRC model parameters except that six out of ten gases are included to be consistent with Ref.. Compared with Scenario 1, Scenario 2 further includes the scatteringby cloud droplets. Scenario 3 adds aerosols where the aerosol profile is adapted from Ref.. Scenario 4 adds the ∼ 13 W m−2 extraterrestrial long wave irradiance. Scenario 5 uses the Gamma cloud droplet size distribution presented before, while also keeping the liquid water path unchanged. The results of the proposed radiative model are within 3% of the CIRC measurements for all scenarios. Since the measurements have uncertainties of 3%, the proposed model produces reliable results that are within the uncertainties of the measurements. The comparisons of different scenarios are presented in Fig. 3.9 and Fig. 3.10 for Case 6 and Case 7, respectively. The difference between S2 and S1 indicates the contribution of cloud scattering, which reduces the downwelling flux of the cloud layers and the layers below the clouds because part of the long wave radiation is scattered to outer space. The contribution of aerosols is quantified by the difference between S3 and S2, ebb and flow tray which increases the downwelling flux above the cloud layers while the surface downwelling flux is nearly unchanged. In the cloud layers and the layers below the clouds, the contribution of aerosols is diminished by the presence of clouds.
By comparing Figs. 3.10 and 3.9, the aerosol contribution is more distinct when optically thin clouds are present . The contribution of long wave irradiance from the Sun increases the downwelling flux above the cloud layers as shown by the difference between S4 and S3.The downwelling flux remains nearly unchanged in or below the cloud layers since the clouds ‘shield’ the long wave radiation from the layers above, so that layers below the clouds ‘see’ only the clouds. The difference between S5 and S4 shows the contribution of cloud droplet size distribution. The proposed size distribution has ∼ 30% lower COD when compared with the one used in CIRC , which increases the downwelling flux in and below the cloud layers. The difference is more distinct for optically thick clouds when comparing Figs. 3.9 and 3.10. The spectral differences between scenarios show up only in the atmospheric windowing bands . The surface downwelling flux for the five scenarios are presented in Table 3.5, where the differences between scenarios are smaller than 5 W m−2 , indicating that the surface downwelling flux is insensitive to the cloud scattering, aerosols, extraterrestrial long wave radiation and cloud droplet size distributions under cloudy skies.The primary goal of this Chapter is to develop an effective minimal model that incorporates the main physical mechanisms needed for calculation of the atmospheric downwelling long wave radiation at the ground level for widely different geographical sites. The operative word effective here means a complete model that is capable of discerning the effects of the main contributors to DLW while allowing for fast computations that can be performed by mini computers within time frames compatible with both the time scale of variations in the atmosphere, but also with time scales of engineering systems . All main features of the model and its implementation are described within the body of this work. A secondary goal is to examine the effects of water vapor, carbon dioxide and aerosols content on the surface DLW at high spectral resolutions. A spectrally resolved, multi-layer radiative model is developed to calculate surface downwelling long wave irradiance under clear-sky conditions.
The wave number spectral resolution of the model is 0.01 cm−1 and the atmosphere is represented by 18 non-uniform plane-parallel layers with the pressure of each layer determined by a constant σ coordinate system. Standard AFGL profiles for temperature and atmospheric gas concentrations have been adopted with the correction for current surface atmospheric gas concentrations. The model incorporates the most up-to-date HITRAN molecular spectral data for 7 atmospheric gases: H2O, CO2, O3, CH4, N2O, O2 and N2. The MT CKD model is used to calculate water vapor and CO2 continuum absorption coefficients.For a scattering atmosphere , the aerosol size distribution is assumed to follow a bimodal distribution. The size and refractive index of aerosols change as they absorb water, therefore the size distribution and refractive index are corrected for different values of local water vapor concentrations . The absorption coefficients, scattering coefficients and asymmetry factors for aerosols are calculated from the refractive indices for different size distributions by Mie theory. The radiosity and irradiance of each layer are calculated by energy balance equations using transfer factors with the assumption of isotropic aerosol scattering . The monochromatic downwelling and upwelling fluxes with scattering for each layer are further calculated using a recursive plating algorithm. Broadband fluxes are integrated over the spectrum for both non-scattering and scattering atmospheres. A model with 18 vertical layers is found to achieve grid independence for DLW. For a non-scattering atmosphere , the calculated surface DLW irradiance agrees within 2.91% with the mean values from InterComparison of Radiation Codes in Climate Models program, and the spectral density difference is smaller than 0.035 W cm m−2 . For a scattering atmosphere, the modeled DLW irradiance agrees within 3.08% relative error when compared to measured values from 7 climatologically diverse SURFRAD stations. This relative error is smaller than the error from a calibrated empirical model regressed from aggregate data for those same 7 stations, i.e., the proposed model captures the climatological differences between stations. We also note that these deviation values are within the uncertainty range of pyrgeometers . In summary, the proposed model is capable of capturing climatological and meteorological differences between locations when compared to extensive surface telemetry, which justifies its use for calculating DLW at other locations across the contiguous United States where measurements are not readily available. The proposed model also serves as a powerful and robust tool to study high spectral resolution interactions between atmospheric constituents within the critical long wave region of the electromagnetic spectrum.The LBL model proposed in Chapter 3 employs the two-flux approximation , reusable transfer factors and a recursive plating algorithm for aerosol scattering with the objective of improving overall computational performance for calculation of atmospheric DLW radiation using high-resolution spectral data. The complete model is easily coded in Python within a few hundred lines of code. Wave numbers are vectorized so that CPU time is only weakly dependent on spectral resolution when adapting the plating algorithm. As a comparison with a radiation model that can also be easily coded in Python, the speed of computation of a standard Monte Carlo simulation is linearly proportional to spectral resolution. A single run of the complete model described in this work requires 100s of Intel Xeon E5-2640 CPU time, where each run corresponds to one data point in Fig. 4.1. The use of the recursive plating algorithm alone reduces the total computational time by 30% when compared to direct matrix reduction. By contrast, an efficient Monte Carlo simulation for the same single case using 50,000 representative photon bundles emitted from each layer requires 90 minutes in the same CPU with 100 times smaller spectral resolution .
In other words, rolling greenhouse benches the proposed model is 3000 to 5400 times faster than an equivalent Monte Carlo simulation. Although other radiative models used in commercial codes also far outperform Monte Carlo simulations in terms of CPU time consumption, there are fewer options for doing so while retaining the level of accuracy and model robustness presented here, and not requiring either thousands of lines of FORTRAN/C coding, and/or expensive yearly fees for the use of optimized commercial products. The model proposed in this work is readily and efficiently implementable in high-level, open-source interpreted computer languages like Python, can easily accommodate different pressure-temperature and aerosol profiles, is only weakly dependent on spectral resolution, and is fast enough to be computed in real-time using low-cost mini-computers.For long wave radiative transfer in the atmosphere , a two – flux spectral multilayer model was developed by the authors to calculate the downwelling and upwelling flux densities in the atmosphere at a spectral resolution of 0.01 cm−1 . The two – flux model is sufficiently accurate for long wave radiative transfer because the radiation sources from the system are diffused. However, for shortwave transfer , the radiation source is highly directional so a two – flux model would be inappropriate. Therefore, a Monte Carlo radiative model is developed to calculate the shortwave radiative transfer in the atmosphere – Earth system. The atmosphere here is again modeled as N plane parallel layers extending from the ground to the top of atmosphere . The layers are divided using a pressure coordinates as detailed in Ref.. The temperature and atmospheric gas profiles are assumed to follow Air Force Geophysics Lab midlatitude summer profiles, with gas profiles corrected for current surface concentrations. The continuum absorption coefficients of water vapor and carbon dioxide are calcualted using MT CKD continuum model. In the long wave spectrum, the gas molecules are treated as non-scattering because the particle size is much smaller than the wavelength. The absorption, scattering coefficients and asymmetry parameters of aerosols and clouds are calculated via Mie theory by assuming proper size distributions. In the shortwave spectrum, the scattering of gas molecules are modeled as Rayleigh scattering. Ozone and oxygen continuum absorption are added because it is more significant in the shortwave than in the long wave spectrum. The following sections present the methodologies of calculating scattering coefficients of molecules, continuum absorption coefficients of ozone and oxygen and the Monte Carlo method.Large-scale deployment of renewable energy technologies as replacement for fossil fuel generation aims at mitigating global warming rates by reducing the emission of greenhouse gases . The scale of this offset is critical to validate societal investments in technologies that may be at the brink of achieving power grid parity. Two major solar technologies arose from market competition in the past decade for utility scale central power plants: photovoltaic and concentrated solar power . Of the several CSP technologies, those based on central towers with large heliostat fields appear to be the most efficient. These large scale solar farms also interact with the atmosphere and with the ground though surface albedo replacement in addition to the direct GHG emission offset. Solar PV farms are highly absorbing while CSP farms are highly reflective when compared to the ground that they cover. On one hand, PV generation is economically viable for distributed generation and can be scaled down to kilowatts . On the other hand, CSP plants offer a number of advantages for larger-scale power production, including higher efficiency , lower cost of thermal storage, higher capacity factors, etc. Photovoltaic systems supply usable solar power by means of direct photoelectric conversion. A typical PV system consists of fixed or sun tracking arrays of semiconductor solar panels that absorb and convert broad wavelength solar irradiance into DC power. Inverters transform electric current from direct to alternating current locally, and transformers elevate the voltage for transmission. Concentrated solar power systems generate solar power by using mirrored surfaces to concentrate the beam solar irradiance in order to elevate the temperature of pressurized steam. The energized steam then drives one or more turbines that are coupled to AC generators. Direct steam CSP tower plants use tens to hundreds of thousands of mirrors to concentrate radiative power on a boiler that transfer the heat to high-energy steam for operation of vapor turbines. Dry cooling fans that dispense the use of additional cooling water close the low-temperature Rankine cycle and return the vapor to the liquid state for pumping. A modern tower CSP plant operates with very low consumption of water and is thus suitable for arid and semi-arid climates. Widely recognized advantages of CSP technologies for central power plant generation are: higher thermodynamic conversion efficiency ; reliance on the direct normal component of the solar irradiance, which allows for a flatter generation profile throughout the day; and the lower cost of long-term thermal storage as compared to long-term electrical storage.