Diffuse Components Of Solar Radiation Research Articles

Evaluating direct and diffuse solar radiation components through global radiation measurements from three fixed directions

Solar systems are deemed to play a pivotal role within the process which should lead to the reduction in the carbon intensity of the worldwide energy use. However, for the analysis of solar system performance, the availability of data regarding the various components (direct and diffuse) of solar radiation is crucial.Nevertheless, the measure of either direct or diffuse solar irradiance requires sun tracker apparatuses (pyrheliometers) or shadow devices (e.g. shadow-band pyranometers) which involve mechanical appliances needing constant maintenance and articulated measurement protocols; therefore, these data are usually derived from global solar radiation measured records, by using empirical functions.With a view to trying to address these issues, the article proposes a methodology for the assessment of the direct and diffuse components of solar radiation from both global solar irradiance and infrared radiation data, all measured on three planes differently tilted and oriented.Therefore, no tracking or moving devices are involved, whereas the real configuration and weather conditions of the site (Sky View Factor, clouds, climate conditions, presence of reflective surfaces, etc.) are taken into account. Therefore, the results should possibly characterize the site, so that its actual potential for solar system installation can be properly assessed.Comparisons with different correlation models demonstrate good agreement, showing correlation coefficients ranging from 0.75 to 0.89 for diffuse radiation and from 0.97 to 0.99 for direct radiation. Notably, the proposed method tends to produce lower values for diffuse radiation. These discrepancies may be due to the peculiar features of the site.

Capturing Building Fabric Thermal Performance and Solar Heat Gains Through a Whole House Heat Loss Test – an In-Situ Study in Poland

Determining a building’s “as built” heat loss coefficient (HLC) is one of the key starting points to understand the role of residents’ practices in heating or cooling-related energy consumption. It is also a starting point for white-box modelling of different behaviour scenarios within a given home environment. Co-heating test is a recognised experimental method to evaluate the building’s fabric thermal performance. It involves a quasi-stationary homogeneous heating experiment performed on an unoccupied dwelling. This paper discusses the results of a co-heating test carried out in a low-energy semi-detached house in Wrocław, Poland between 6th-12th December 2021. The periods of different types of solar operation are captured to evaluate HLC: night-time with no solar gains, daytime with direct solar gains, and daytime with only the diffuse component of solar radiation. Internal solar gains in the building are calculated using the TRNSYS simulation program, assuming detailed modelling of the radiation incident on the vertical partitions (including the anisotropy of the diffused radiation component and complex analyses of the sun path geometry inside the building). Based on the results, the HLC values excluding infiltration and ventilation corresponding to different solar operation types are calculated and compared. This contributes to a more nuanced understanding of HLC under different external conditions.

Performance analysis of a Silicon PV module (100W) in outdoor conditions: Experimental and Simulation study

In this paper, the incident solar radiation on horizontal and tilting surfaces was measured of a year using a pyranometer on the roof of Tanta University's Faculty of Science in Tanta city which is locating at Latitude (30° 41`). The average of daily global hourly solar radiation values on horizontal surfaces (H) and the global hourly solar radiation values on inclined surfaces (Ht) had been measured in the south direction of the sun for the meteorological variables. Miguel et al. correlation was used to determine hourly values of the beam and diffuse components of solar radiation (SR) from global solar irradiance. In order to attain best solar module performance throughout the year, the solar energy devices must be tilted south with a tilting angle equal to Tanta city latitude. The maximum value of Ht was 1174.15 Wm-2 in April and the minimum value of Ht was 816.11Wm-2 in October. The performance of 100 W solar silicon photovoltaic (PV) module in outdoor condition can be studied by depending on the incident values of H and Ht. The obtained results showed that the efficiencies of the 100 W solar PV module in winter, spring, summer and autumn were 4.29, 3.78, 7.56 and 4.58 %, respectively. The Maximum power point (Pmax) was calculated in July and its value was 45.98 W at solar noon and the minimum power point (Pmin) was calculated in October with value equal to 18.56 W at solar noon.

Solar greenhouses: Climates, glass selection, and plant well-being

Solar greenhouses are currently the most energy-intensive agricultural sector. In literature, there is no worldwide mapping of solar greenhouse performance under different climate scenarios. This study analyzes the performance of a Venlo solar greenhouse for 48 localities around the world. Solar greenhouses are mainly made of a transparent envelope and the effect of the direct and diffuse component of solar radiation impacts the internal plant well-being. This study aims to identify the best solution of a transparent envelope on locations with different latitudes and evenly distributed around the globe. The simulations are carried out using TRNsys, considering different thermal phenomena three-dimensional shortwave and longwave radiative exchange, airflow exchanges, presence of lamps with their exact 3D position, ground, plant evapotranspiration, and convective heat transfer coefficients. A total of 336 simulations are performed in the free-floating regime. A new index for the identification of the best glass solutions based on annual average deviation is defined. For all climates, the best glass solutions work better in winter than in summer. The optimal choice of the glass must be combined with effective scheduling of openings for natural ventilation to avoid internal overheating phenomena.

Long term performance analysis of low concentrating photovoltaic (LCPV) systems for building retrofit

Low concentrating photovoltaic (LCPV) systems offer viable solution for generating higher energy output per unit cell area compared to a typical flat PV panel, making them potential candidates for building retrofit. However, the best LCPV geometry for a given location is yet to be identified. The current study investigates the technical, economic and environmental feasibility of three geometrically equivalent LCPV designs installed at a building within Brunel University London (UK). The studied LCPV systems comprised of Asymmetric Compound Parabolic Concentrating (ACPC), Compound Parabolic Concentrating (CPC) and V-Trough optical concentrators with the post-truncation geometric concentration ratios of 1.53, 1.46, 1.40 respectively. The performances of the prototypes have been monitored every 15 min over 10 months and analyzed on hourly, daily, and monthly basis. Performance parameters such as reference yield, array yield, performance ratio, electrical conversion efficiency and the generated energy output per unit area have been derived and presented. Payback periods have been estimated in two separate scenarios. Measurements have showed that the ACPC integrated LCPV achieved the highest annual optical efficiency generating the highest amount of electrical energy per unit cell area of 246.2 kWh/m2 compared to CPC-LCPV, V-Trough-LCPV and conventional flat modules which produced 224.6 kWh/m2, 196.1 kWh/m2 and 185.4 kWh/m2 respectively. One particular conclusion of the study is that the ACPC based LCPVs perform better in locations where diffuse component of solar radiation is predominant as in the case of the UK. Consequently, ACPC based LCPV modules are recommended for the building retrofit in such locations.

Spectrally Selective Transformations of Solar Radiation by Retinal Photoreceptors in the Control of the Circadian Rhythm of the Human Body throughout an 11-Year Cycle of Solar Activity

Abstract—The round-the-day effect of solar radiation on photoreceptors of the retina of the eye and its role in the control of the circadian rhythm of the human body within an arbitrary 11-year cycle of solar activity are considered. Processed data describing the variation of the spectral and energy characteristics of solar radiation that reach the Earth’s surface over a solar activity cycle are given. On this basis, a generalized analytical expression has been obtained that models the spectrally selective processing of the sum of the direct and diffuse components of solar radiation by retinal rods and blue-sensitive (S type) cones. The obtained expression allows consideration of separate spectrally selective processing of the direct and diffuse components of solar radiation by rods and S cones of retina, including the case of a catastrophic lesion of one of the neuronal paths that connect rods or S cones with suprachiasmatic hypothalamus nuclei. It is shown that the effective spectrum obtained as a result of spectral selection of the components of solar radiation that is used to control the circadian activity of the human body is determined solely by the spectral sensitivity of rods and S cones. The effective spectrum does not depend on daily variations in the spectrum of solar radiation as the angular elevation of the Sun varies; the daily energy characteristics of the effective spectrum, which vary within each solar activity cycle, retain their dependence on the Sun’s elevation in the daytime and on the current phase of the solar activity cycle. Significant changes in the characteristics of solar radiation within the cycle of solar activity infer that it is necessary to take them into account in studying and modeling the control processes of human circadian activity driven by solar radiation.

Changes in Irradiance and Illuminance on Earth Surface during 11-Year Solar Activity Cycle

The article formulates the analytic expression approximating the sequence of Gregorian 11-year solar cycles and the expression of solar activity within one cycle. The dependences of effective thermodynamic temperature of the Sun photosphere and the solar constant, and the solar illuminance constant at the upper border of Earth atmosphere on the year number within one solar cycle were obtained. The generalised analytic expression for integral transmittance of atmosphere (within its spectral window) on the Earth surface for the direct and diffuse components of solar radiation and their sums at different solar altitude angles is presented. The analytic expressions of dependences of irradiance and illuminance on the Earth surface within spectral window of atmosphere and within the visible region of solar radiation spectrum on the year number within a certain solar cycle at different solar altitude angles are obtained. The results of calculation of direct and diffuse components of irradiance and illuminance and their sums in the case of clear sky are presented for example. The proposed approach allows similar calculations to conduct for different types of sky cover.

Models for the Calculation of Diffuse Radiation on Solar Collectors

For the design and exploitation of solar energy systems, information of both direct and diffuse component of solar radiation is necessary. However, the measurement data that are available are usually restricted to total horizontal irradiance. Therefore, many models have been developed to determine the diffuse component of the irradiance on solar collectors. This paper discusses the most well-known isotropic and anisotropic models for the calculation of the diffuse component of the solar irradiance. A modification of the isotropic clear day model for determining the diffuse component of solar radiation on a horizontal surface has been presented. The presented model has the same form as a simple clear day model, with the parameters determined using the least squares method and measurement data on horizontal irradiance in the region of Belgrade, Serbia. The applicability of isotropic clear day models was examined. The paper also discusses the applicability of the models for determining the diffuse irradiance on tilted collectors in real weather conditions during the year. The basic expressions are given and the characteristics of individual models are highlighted. Based on the measurement data on horizontal irradiance, the possibilities of applying different models for the calculation of the diffuse component of irradiance on solar collectors located in the region of Belgrade were examined.

Performance Evaluation of Models Established for the Estimation of Diffused Solar Radiation: Case Study Lahore, Pakistan

A suitable design of solar power project requires accurate measurements of solar radiation for the site ofinvestigation. Such measurements play a pivotal role in the installation of PV systems. While conducting such studies,in general, global solar radiation (GSR) is recorded, whereas diffuse component of solar radiation on a horizontalsurface is seldom recorded. The objective of the present study is to assess diffuse solar radiation (DSR) on horizontalsurfaces by using polynomial models for Lahore, Pakistan (27.89 N, 78.08 E) and by correlating clearness index withdiffuse fraction. The established models are compared with some of the existing models from the literature.Performance of models is evaluated by employing five goodness-of-fit (GoF) tests that are, mean bias error (MBE),root mean square (RMSE), Coefficient of Determination (R2), Mean Absolute Percentage Error (MAPE) and Akaike’sInformation Criterion (AIC). The comparison of the results of goodness-of-fit tests with those of existing modelsindicate that the models established in the present study are performed better as compared to the existing models. Thevalues of statistical error analysis further suggested that a cubic model with a good accuracy of 97.5% and AIC of -22.8is relatively more suitable for this climatic region for estimating diffuse solar radiation. The study shows that the modeldeveloped is in good agreement with Elhadidy and Nabi model with an accuracy of 96.1% and AIC of 4.4 andsatisfactory results are obtained for Lahore. The findings can help to give a generous understanding of solar radiation inorder to optimize the solar energy conversion systems. The results of this study provide a better understanding of theassociations between global solar radiation, clearness index and diffused fraction for the region under study.

Performance Evaluation of Models Established for the Estimation of Diffused Solar Radiation: Case Study Lahore, Pakistan

A suitable design of solar power project requires accurate measurements of solar radiation for the site ofinvestigation. Such measurements play a pivotal role in the installation of PV systems. While conducting such studies,in general, global solar radiation (GSR) is recorded, whereas diffuse component of solar radiation on a horizontalsurface is seldom recorded. The objective of the present study is to assess diffuse solar radiation (DSR) on horizontalsurfaces by using polynomial models for Lahore, Pakistan (27.89 N, 78.08 E) and by correlating clearness index withdiffuse fraction. The established models are compared with some of the existing models from the literature.Performance of models is evaluated by employing five goodness-of-fit (GoF) tests that are, mean bias error (MBE),root mean square (RMSE), Coefficient of Determination (R2), Mean Absolute Percentage Error (MAPE) and Akaike’sInformation Criterion (AIC). The comparison of the results of goodness-of-fit tests with those of existing modelsindicate that the models established in the present study are performed better as compared to the existing models. Thevalues of statistical error analysis further suggested that a cubic model with a good accuracy of 97.5% and AIC of -22.8is relatively more suitable for this climatic region for estimating diffuse solar radiation. The study shows that the modeldeveloped is in good agreement with Elhadidy and Nabi model with an accuracy of 96.1% and AIC of 4.4 andsatisfactory results are obtained for Lahore. The findings can help to give a generous understanding of solar radiation inorder to optimize the solar energy conversion systems. The results of this study provide a better understanding of theassociations between global solar radiation, clearness index and diffused fraction for the region under study.

Algoritmo teórico para la estimación de la radiación solar global para una atmósfera despejada

En este trabajo se desarrolló un algoritmo para la estimación de la radiación solar global, para una atmósfera despejada, mediante el modelamiento de las ecuaciones teóricas de transferencia radiativa de onda corta (0,3 µm - 2,8 µm). Se determinaron las transmitancias espectrales de la radiación solar directa, debidas a la dispersión de Rayleigh y Mie. Mediante el software Propiedades Ópticas de Aerosoles y Nubes (Optical Properties of Aerosols and Clouds, OPAC) se calculó la Profundidad Óptica de los Aerosoles (Aerosol Optical Depth, AOD) para cuatro diferentes tipos de atmósferas, indispensable para la determinación del índice de turbidez de Ångström. Así mismo, se calcularon la transmitancias espectrales por absorción de la radiación solar directa, incluyendo aerosoles, vapor de agua, ozono y aire seco (mezcla de gases). El contenido de O3 se obtuvo de los datos diarios existentes en base de datos de la NASA. Para la componente difusa de la radiación solar, se dedujo una nueva expresión para el cálculo de la fracción de la radiación solar dispersada por los aerosoles hacia la superficie terrestre. La comparación estadística entre los resultados obtenidos con el algoritmo desarrollado, los datos medidos de la radiación global (estación Potsdam - Alemania) y los resultados de otros tres modelos radiativos, entre 2012 y 2014, muestra que el nuevo modelo permite calcular los valores horarios de la radiación solar global con suficiente precisión. © 2018. Acad. Colomb. Cienc. Ex. Fis. Nat.

Improving the separation of direct and diffuse solar radiation components using machine learning by gradient boosting

Based on a large and recently developed database of 1-min irradiance and ancillary data observations at 54 world stations, this study uses the gradient boosting Machine Learning (ML) technique to improve the process of components separation, through which the direct and diffuse solar radiation components are estimated from 1-min global horizontal irradiance data. Here, the XGBoost implementation of gradient boosting is used both with ensembles of linear and ensembles of non-linear weak prediction models. The predictions of 140 separation models of the literature are combined using XGBoost to overall improve the random errors of the predictions of the individual separation models at any of the validation sites. The minimum prediction error is essentially achieved by a combination of 26 out of the original 140 models, with no meaningful reduction in error by combining more models. Most of these 26 models use at least three inputs in addition to clearness index. In parallel, XGBoost is also used to separate the components directly from the inputs to the separation models. From the 24 possible inputs used in the original 140 separation models, only 14 are found relevant. These 14 inputs could be used with appropriate formalism to subsequently develop a better separation model. It is found that when the training and validation datasets are not collocated, the RMSD of the predictions increases, on average, 2% with respect to the case of collocated datasets. Overall, the present results indicate that a data-driven ML approach combining a limited number of existing models can be used to considerably decrease the currently large random errors associated with such models when used separately at high temporal frequency.

The Implications of Assumed Boundary Conditions for the Reliability of Indoor Illuminance Predictions: A Case Study

In order to model daylight availability and distribution in architectural spaces, simulation tools require reliable representations of boundary conditions – typically in terms of sky luminance distribution models. However, the impact of sky model errors on simulation-based indoor illuminance predictions is not well documented. There are different tools and methods to simulate indoor illuminance conditions and related daylight indicators. In the present study, we selected Radiance lighting simulation program. In order to generate sky scene description, Radiance contains two routines, namely, Gendaylit and Gensky. These routines require, as input, information on both direct and diffuse components of solar radiation. To explore the implications of the sky model selection on the fidelity of simulation results, we used Radiance to compute the indoor illuminance in an existing test space on the rooftop of a university building. Thereby, the aforementioned two sky models were considered. A third option (SC) was a sky model generated based on measured values obtained from a sky scanner. Simultaneously, the actual illuminance levels in this room were monitored under different outdoor conditions (clear, intermediate, overcast). The comparison of the measurement results with multiple model prediction results facilitates an empirically based evaluation of the reliability of indoor illuminance predictions in the face of different assumptions pertaining to the prevailing boundary conditions.

Quantification of energy savings from dynamic solar radiation regulation strategies in office buildings

Traditionally, glazing-specific technologies have been studied at a theoretical or experimental level with the goal of identifying the optimum thermo-optical parameters that the glazing should have in order to provide energy savings. In this work, we focus on quantifying the impact of the direct and diffuse solar radiation components on energy savings for office buildings following a technology-agnostic approach. More specifically, the question to be answered is: “How can independent management of the solar radiation components offset electric lighting, but on the other hand, possibly put additional load requirements on space-heating/cooling, and fans?” We use EnergyPlus to simulate an adiabatic perimeter office space, with typical zone characteristics, under various solar radiation levels. The solar radiation values are derived from an EnergyPlus weather file. We process that original weather file and create new weather files with reduced solar radiation by specific percentages and simulate the same adiabatic office. We only reduce the direct and diffuse solar radiation components of the original weather file in order to study the impact of regulated solar radiation on the zone’s lighting, heating, fans, and cooling primary energy requirement. Second, we perform a dynamic solar radiation regulation analysis on a monthly, daily, and hourly basis. We show that faster regulation response time of the solar radiation leads to higher energy savings. The reference scenarios for the North, East, South, and West-facing zones require a total of 71, 106, 87, and 99kWh/m2y respectively. An hourly solar radiation regulation can lead to maximum energy savings of 18%, 33%, 37% and 36% for each orientation. Finally, we perform a study that quantifies the impact of potential technological constraints, such as reduced dynamic range and resolution of the solar radiation admittance, on energy savings.

A New Methodology for Quantifying the Impact of Direct and Diffuse Solar Radiation on Energy Savings in Commercial Office Spaces

In this paper, we describe a new methodology for quantifying how direct and diffuse solar radiation impact total energy consumption in a standard perimeter office room by optimizing the allowed daylight penetration for achieving overall energy reduction. Our methodology is different from standard studies that focus on modification of window glazing geometrical, optical and/or thermal parameters and their impact on energy consumption. In our study, we consistently use the same window glazing geometry, and modify the weather file by varying the direct and/or diffuse components of solar radiation. This combination emulates the effect of an advanced dynamic glazing on the incoming solar radiation and is independent of the technology used. Such a glazing would regulate the proportions of direct and diffuse solar radiation to achieve overall energy reduction. In other words, our approach does not try to qualify or evaluate a particular glazing technology, but rather to generate specifications for advanced dynamic glazings that can manage the incoming radiation and hence help drive the development of such advanced dynamic glazing technology.To achieve our goal, we use EnergyPlus to simulate a 6m×3m×3m (length×width×height) office space with a 40% WWR, at all four cardinal orientations. To eliminate any effects that could arise from heat transfer from adjacent rooms — e.g., through walls — we treat those surfaces as adiabatic. In addition, since the front façade wall is the host surface of the window and thus cannot be defined as adiabatic, we intentionally set the façade wall at very high R-value, thus minimizing any thermal impact from that surface too. As a result, the only element responsible for daylight and thermal impact in the office space is the glazing. We present the results by comparing the energy requirements under various solar radiation penetrations into the office, as they are managed by the glazing. We compare the results under non-dynamic and dynamic glazing operation and offer recommendations on the optimum glazing operation for achieving year around energy savings. By investigating the interplay between managed solar radiation, via the emulated advanced dynamic glazing, and energy consumption in the room, we identify and quantify opportunities for energy savings.

Is there a transition of solar radiation from dimming to brightening over India?

Recent observational studies show that solar radiation incident on ground has not been stable over the last several decades but underwent significant multi-decadal variations. From the 1950s, solar radiation has had a general decreasing trend, named dimming. Since the late 1980s, a trend reversal and partial recovery has been observed at many observations sites across the globe; it is the so-called brightening. The present study examined temporal and spatial trends in surface solar radiation (global and diffuse) and sunshine duration in India using a 40-year data set (1971–2010) of the twelve stations of solar radiation network of the India Meteorological Department. The research work examines the global solar radiation trends in all-sky and cloud-free sky conditions. The long-term variability in the diffuse components of solar radiation, bright sunshine duration, and cloud cover has also been studied over India.India is one of the few regions that showed a continuous and steady decline in global solar radiation from the 1970s to 2000. The declining trend of all-sky global irradiance over India as a whole was 0.6Wm−2 year−1 during 1971–2000 and 0.2Wm−2 year−1 during 2001–2010. A third-order polynomial fit to the data indicated a reversal in all-sky global irradiance around 2001 at some sites. Reversal or stabilization of global irradiance is also seen in seasonal mean values at some of the stations. The reversal in clear-sky global irradiance was clearly evident from 2001. Similar trend is also observed in bright sunshine duration. This confirms the well-known phenomenon of global dimming and global brightening over India. The analysis of global irradiance data highlights the fact that in general the dimming/brightening is station dependent because of regional sources and meteorology which contribute to the variation in solar irradiance.

Distribution of solar irradiance on inclined surfaces caused by moving clouds

The distribution of solar irradiance in shadows of discrete (broken) clouds differs from the distribution calculated for inclined surfaces on the basis of traditional transposition models and changes fast. This phenomenon is studied in this paper. For calculations of dynamic distributions of irradiance on inclined surfaces, a formal point source of direct radiation near the real position of the sun is defined as the source of the “imaginable radiation.” This notion is used to create a one-dimensional (1D) simulation model, which allows the fast-changing distribution of irradiance to be calculated. In general, the coincidence of calculated and measured irradiance on inclined surfaces is good. The paper also shows how the current value of the diffuse component of solar radiation can be derived from measurements of total radiation in four differently tilted planes.

The HelioMont method for assessing solar irradiance over complex terrain: Validation and improvements

This study evaluates the suitability of the method HelioMont, developed by MeteoSwiss, for estimating solar radiation from geostationary satellite data over the Alpine region. The algorithm accounts for the influence of topography, clouds, snow cover and the atmosphere on incoming solar radiation. The main error sources are investigated for both direct and diffuse solar radiation components by comparison with ground-based measurement taken at three sites, namely Bolzano (IT), Davos (CH) and Payerne (CH), encompassing different topographic conditions. The comparison shows that the method provides high accuracy of the yearly cycle: the Mean Absolute Bias (MAB) is below 5Wm−2 at the lowland station Payerne and below 12Wm−2 at the other two mountainous stations for the monthly averages of global and diffuse radiation. For diffuse radiation the MAB is in the range 11–15Wm−2 for daily means and 34–40Wm−2 for hourly means. It is found that the largest errors in diffuse and direct radiation components on shorter time scales occur during summer and for cloud-free days. In both Bolzano and Davos the errors for daily-mean diffuse radiation can exceed 50Wm−2 under such conditions. As HelioMont uses monthly climatological values of atmospheric aerosol characteristics, the effects of this approximation are investigated by simulating clear-sky solar radiation with the radiative transfer model (RTM) libRadtran using instantaneous aerosol measurements. Both ground-based and satellite-based data on aerosol optical properties and water vapor column amount are evaluated. When using daily atmospheric input the estimation of the hourly averages improves significantly and the mean error is reduced to 10–20Wm−2. These results suggest the need for a more detailed characterization of the local-scale clear-sky atmospheric conditions for modeling solar radiation on daily and hourly time scales.

New model for subsurface irradiance reflectance in clear and turbid waters.

Modeling of subsurface irradiance reflectance fields especially in turbid coastal, harbor and lagoon waters has important applications in ecology, engineering and optical remote sensing. The present study aims at exploring many possible causes of variation in the proportionality factor f and analyzing its effect on the subsurface irradiance reflectance in different waters. A new model is then developed to estimate this optical property as a function of the absorption coefficient (a), backscattering coefficient (bb), incident illumination condition, and other wavelength-depth dependent factors. Implementation of this new model is examined for five types of waters with varying turbidity and chlorophyll. Model results are verified with in situ measurements data and compared with the results from existing models. Formulas already proposed for estimating R in the previous studies and generally expressed by R = 0.33(bb/(a + bb)) or R = f (bb/(a + bb)) where f = 0.975-0.629 μ(0) (μ(0) is the incident photons just below the sea surface) work fairly well in clear oceanic waters, but yield large errors in turbid coastal and lagoon waters due to the use of a constant value ~0.33 or the dimensionless parameter f which does not account for certain processes in the model (e.g., multiple scattering, depth-dependent changes in the diffuse components of solar radiation, and spectral variation in f). By contrast, the new model estimates the reflectances having good agreement with in situ data from just below the water surface and throughout the water column. The improved performance of the present model is because it includes a parameterization of the proportionality factor f which varies with wavelength and depends on the sun angle, inherent optical properties, and diffuse attenuation coefficients. Knowledge related to interrelationships between inherent optical properties and apparent optical properties can be used to study the variability of the subsurface reflectance in homogeneous and stratified coastal waters with respect to many possible causes of its variations.

Preliminary Investigation of The Attenuation of Solar Radation in The Atmosphere Over Makurdi, Nigeria

The attenuation of solar radiation in the atmosphere over Makurdi (Latitude 7o 7’ N and longitude 8o 6’ E) was investigated by measurements of direct solar radiation (I) carried out using a digital sun photometer that measured in Wm- 2. The measurements were made at 9:00hrs, 12:00 hrs and 15: 00hrs daily for six months. Global solar radiation, (IG) was calculated for the six months using Gun Bellani measurements from Air Force Base, Makurdi. The diffuse component of solar radiation (ID) was evaluated and the extraterrestrial solar radiation (Io) was obtained by calculation using the equation of Duffie and Beckman (1983) and Liou (1980). The variation of attenuation with clearness index Ki was found. The attenuation in the atmosphere over Makurdi was found to be highest in the month of August with a value of 0.975 and lowest in December with a value of 0.427. There was good agreement in the pattern of variation of attenuation in Makurdi when compared with that of Ilorin that lies in the same geographic latitude.