The modeling results enable direct calculation of the equilibrium temperature and cooling efficiency of passive cooling devices in terms of meteorological conditions observed at the surface level.The solar irradiance is emitted by the Sun while atmospheric lonwave irradiance is emitted by gases and surfaces at a temperature of 200 to 320 K. Figure 1.1 plots the monochromatic emissive power of a black surface at various temperatures according to Planck’s law. For the solar irradiance, 2000 ASTM Standard Extraterrestrial Spectrum is used. As shown in Fig. 1.1, atmospheric long wave irradiance is mostly in the spectral range from 0 to 2,500 cm−1 while solar shortwave irradiance is from 2,500 to 40,000 cm−1 . Therefore, the long wave irradiance referred in this work is the emitted radiation from atmosphere constituents and the Earth’s surface, in the spectral range of 0 to 2,500 cm−1 . The solar shortwave irradiance is the emitted radiation from the Sun that in the spectral range of 2,500 to 40,000 cm−1 . The emission by the atmosphere and Earth is assumed to be diffuse while the solar irradiance is highly directional. The LW transfer in the atmosphere includes processes of emission, absorption, scattering/reflection. While for SW, botanicare rolling benches the processes involves only absorption and scattering/reflection.
The downward atmospheric long wave irradiance flux is an essential component of radiative balance for solar power plants and is of great importance in meteorological and climatic studies, including the forecast of nocturnal temperature variation and cloudiness. It also plays a critical role in the design of radiant cooling systems, as well as in the modeling of weather and climate variability, and on the determination of selective optical properties for photovoltaic panels, photovoltaic-thermal collectors, solar thermoelectricity parabolic disks, etc.. The downward long wave atmospheric irradiance can be measured directly by pyrgeometers. However, pyrgeometers are not standard irradiance equipment in most weather stations because pyrgeometers are relatively expensive and require extensive calibration and adjustments to exclude the LW radiation emitted by surrounding obstacles, buildings and vegetation. Spectral calculations considering the interactions of LW irradiance with atmospheric molecules , aerosols and clouds yield reasonable estimates of DLW for global calculations, but line-by-line calculations are generally too complex for meteorological or engineering use. A simple approach to estimate DLW relies on parametric modeling of meteorological variables measured routinely at the surface level, such as screening level air temperature and relative humidity. The parametric models imply specific assumptions regarding the vertical structure of the atmosphere.
These assumptions are either explicit, or implicitly included in the parametric models by locally fitting coefficients.Even though the parametric models described above have different functional forms and different coefficients as shown in Table 2.5, most models have nearly identical accuracies after the calibration of their coefficients as shown in Table 2.6. Further examination of the modeling results show that most of the examined parametric models correspond to only a few independent model families. As shown in Fig.2.3, DLWc calculated by calibrated Brunt, Brutsaert, Berdahl and Fromberg, Berdahl and Martin, Prata, Dilley and O’Brien, Niemela, Iziomon, and Dai and Fang models correspond to the same model family. The models ¨ proposed by Idso, Satterlund and Carmona also yield identical values of DLWc after the calibration and they collapse to another model family. The different functional forms relate only to the use of different variables that are not independent from each other. In other words, each model family represents the same model expressed in terms of either mutually dependent or redundant variables. In these cases, the increased complexity of the functional relationships does not yield higher accuracy. Since the calibrated Brunt model has the simplest functional form and remains the most accurate, we recommend its use as the baseline model for further developments.By comparing the effective clear sky emissivity during the nighttime and the daytime, a positive difference is observed, indicating that the clear sky is more emissive during the night. Fig.2.4 shows that on average, the nighttime emissivity is around 0.035 higher than the daytime values under the same ground-level partial pressure of water vapor.
This behavior is related to the formation of inversion layers during clear nights where the surface temperature is reduced compared with the temperature aloft. The day and night difference is observed by other studies as well. For energy balance applications in solar engineering, the effective emissivity during the daytime is more favorable while for nighttime passive cooling applications, the effective emissivity during the nighttime is more favorable. Therefore, the parametric clear-sky Brunt models for both daytime and nighttime are proposed as,highest accuracy during the daytime and nighttime Brunt model has the highest accuracy during nighttime. For applications that require both daytime and nighttime DLWc information, the all-sky Brunt model is the most accurate model to use.Under all-sky conditions, the downward long wave irradiance is increased by the radiation emission from clouds . Therefore, the all-sky parametric models need to include cloud information such as cloud cover fraction or cloud modification factor .Using the calibrated clear-sky Brunt model to calculate the clear-sky DLWc, the MBE, RMSE, rMBE and rRMSE of all-sky models in modeling LW are presented in Table 2.8. The accuracies of Carwford and Duchon, Bilbao and Aldos model increase after the calibration of coefficients. During the daytime periods, the proposed all-sky model outperforms the three other models and has 15.3% ∼ 31.8% lower RMSE. If GHI irradiance measurements are available, using CMF has 7.5% lower RMSE than using CF. During the nighttime, the proposed model has 1.3% lower RMSE than the calibrated Crawford and Duchon model. During all day periods, the proposed model has 3.8% lower RMSE than the calibrated Carwford and Duchon model. For different applications that require daytime and/or nighttime DLW information, specific values of c1 ∼ c5 of proposed model can be selected from Table 2.8.Under clear-sky conditions, fifteen parametric models proposed in the bibliography to estimate downward atmospheric long wave irradiance are compared and recalibrated using data collected from 7 climatologically diverse SURFRAD stations over the contiguous United States. All fifteen models achieve 2.8% ∼ 58.9% smaller errors when their coefficients are recalibrated. After the recalibration, we identify several models as yielding identical values of DLWc, which indicate that they are different expression of the same model, and that the increased complexities of the proposed formulas does not result in higher accuracies. Models that correspond to the recalibrated Brunt model include the ones proposed by Refs.. Another group of models correspond to recalibrated Carmona model, and includes the ones proposed by Refs.. Since the expression of effective sky emissivity in the Brunt model has only two coefficients and one variable and it achieves high accuracy , the use of recalibrated clear-sky Brunt models is recommended. Clear night skies has higher effective emissivity than clear days at the same level of surface partial pressure of water vapor, which is observed in this work. The clear nighttime emissivity is larger than the daytime value by 0.035. Therefore, both daytime and nighttime calibrated Brunt-type models are proposed and validated in this study. Under all sky conditions, the parametric models for calculating DLW should consider the radiation emitted from clouds. Three parametric models proposed in the literature are compared and recalibrated, and a new model is proposed to account for the alternation of vertical atmosphere profiles by clouds. During the daytime, commercial plant racks the proposed all-sky model has 15.3% ∼ 31.8% lower RMSE than the other three calibrated models. If GHI irradiance measurements are available, using CMF has 7.5% lower RMSE than using CF. During the nighttime and all day periods, the proposed model yields 1.3% ∼ 3.8% lower RMSE than the recalibrated Crawford and Duchon model. For different applications that require LW information during daytime and/or nighttime, coefficients of the proposed model can be selected for use.
The main contributions of this chapter are: We propose novel accurate parametric models to calculate 1-minute averaged downward atmospheric long wave irradiance under both clear-sky and all-sky conditions. The coefficients of the proposed models should be considered more universal, since data from seven climatologically diverse stations are used. We also determined that several clear-sky parametric models proposed recently are equivalent.Surface downwelling long wave irradiance plays a critical role on weather and climate variability modeling, as well as on the heat balance design of solar power plants, of radiant cooling systems, and of the built environment. Surface DLW can be measured directly by pyrgeometers, but pyrgeometers are not widely available in weather stations due to capital and calibration expenses. Furthermore, infrared radiation from the surroundings tend to complicate the installation of research-quality pyrgeometers. Because of the importance of surface DLW on the thermal balance of both agricultural and industrial environments, simplified models to estimate the so-called sky radiosity have been proposed . A simple-to-use parametric model with coefficients regressed from measurements can be used to calculate the ground level long wave irradiance with satisfactory accuracy. However, for locations without pyrgeometers, choosing a parametric model with regression coefficients estimated from the measurements of other locations may introduce bias errors because the surface level downwelling irradiance depends on local meteorological conditions. This work aims to develop a minimal model for calculating the atmospheric downwelling long wave radiation within the uncertainty of commonly used pyrgeometers. A spectrally resolved radiative model is developed to calculate the interactions of long wave irradiancewith atmospheric molecules, aerosols and clouds. When compared with other available radiative models, this model incorporates the most up-to-date HIgh Resoluton TRANsmission molecule spectral line data combined with the Mlawer-Tobin-Clough-Kneizys-Davies water vapor and CO2 continuum model. The proposed model incorporates Mie theory to calculate aerosol extinction coefficients and asymmetry factors, with modifications for aerosol size distribution and refraction index corrections for aerosol – water vapor interactions. The complete model is a robust and inexpensive tool to study long wave radiative heat transfer in the atmosphere. The robustness of the model is derived from the use of a standard atmosphere that can be readily adjusted for surface altitude. The model was designed to be applied to the Air Force Geophysics Laboratory midlatitude summer atmosphere by simple displacement of the local altitude above sea level . In building the complete model, a recognition that most of the complexity related to the mutual interactions between atmosphere layers, aerosols and participating gases cannot be resolved without a detailed spectral consideration of each component. Thus, the model adopts high-resolution line-by-line data for all main constituents. The monochromatic thermal exchange between layers is calculated by an isotropic two-stream model, where the piecewise monochromatic sections of the spectrum are first treated as perfect emitters before they are recursively corrected by the application of a reflective plating algorithm. This application of the plating algorithm originally proposed by Edwards for radiative enclosures allows for expedited incorporation of piecewise non-black portions of the spectrum, including aerosol scattering. To the best of our knowledge, this type of recursive plating algorithm has not been applied to atmospheric radiation problems before. The combination of reusable transfer factors, high-resolution line-by-line spectral data, and the recursive plating algorithm results in a fast computational method that can be performed in real-time by a mini computer , thus allowing for the development of smart instruments for DLW calculations as opposed to relying on sparse pyrgeometer data networks. Because the proposed model incorporates the main thermal radiation contributions in the atmosphere, it can also be used to study the sensitivity of DLW to greenhouse gases and aerosols by adjusting the parameters in the model without the need for local telemetry. The main components of the proposed spectral model are outlined in Table 3.1, and the detailed methodology used for evaluation is presented in Section 3.2 to 3.4, and the model is validated in Section 3.5.Water clouds are modeled in the spectral radiative model using the similar methods as aerosols. Each water droplet is assumed to have a spherical shape, thus the absorption and scattering efficiencies of droplets are calculated using Mie theory with the input of the refraction index of water retrieved from. The absorption and scattering coefficients as well as the asymmetry factors of clouds are further calculated by integrating the efficiencies over a droplet size distribution]. The modeling of clear skies are validated against ICRCCM results as well as SURFRAD measurements, as presented in [5]. In this section, the modeling of cloudy skies are validated against the results from cloudy Case 6 and Case 7 of the Continual Intercomparison of Radiation Codes program.