Calculation of solar irradiances for inclined surfaces: Validation of selected hourly and daily models

Abstract

Irradiance data obtained over a long period at Vancouver and Toronto, Canada, and covering a range of slope orientations are used to validate four models that estimate either the direct or diffuse solar irradiances for inclined surfaces. Evaluations are initially performed for daily and hourly time integrals. A simple parametrization of the diffuse sky radiance dramatically improves estimates of the diffuse irradiance. Both of the direct irradiance models have difficulty accommodating the diurnal characteristics of the irradiance, and consequently modelling errors are substantial for slopes not directly facing the equator. For equator‐facing slopes a saving in data requirements and computational effort through the use of daily integrals can be achieved with little additional error. A substantial portion of the differences between the measured and estimated irradiances is non‐systematic in nature and is therefore reduced through temporal averaging.     

Empirical estimation of daily clear sky solar radiation in Thessaloniki,Greece

Summary In the present study a mathematical model is proposed for estimating daily clear sky solar radiation in Thessaloniki. The relation I = A*sin (h) + B was used for calculating the intensity I of solar radiation. The coefficientsA andB depend on the quantities of water vapour and aerosols in the atmosphere and the sunheight (h).A andB have been estimated separately for each month. The application of the proposed model is only possible when the values ofA andB and two other astronomical parameters (sun's declination and hour angleH) are known. A good agreement has been found between observed and computed values, a fact significantly reinforcing the accuracy of the proposed model.NotesWith 2 Figures     

Assessing the distribution of solar irradiation in Mbarara, Uganda

Summary Existing literature lacks information on formulation and performance assessment of diffuse solar radiation models in the Eastern African region yet this region has a high potential for the utilization of solar energy. The objective of this paper is to assess the performance of seventeen diffuse solar irradiation empirical correlations, at Kampala, Uganda. The best performing correlations were determined using the ranking method. The normalized absolute mean bias error and root mean square error were computed and utilized in the ranking process. The results indicated that the correlations relating diffuse transmittance with relative sunshine duration are more reliable for diffuse solar radiation predictions at least in the Uganda environment. These models are expressed in terms of first, second and third order polynomials of the relative sunshine duration and are particularly recommended for their simplicity and worldwide applicability.     

Estimation of Hourly Solar Radiation at the Surface under Cloudless Conditions on the Tibetan Plateau Using a Simple Radiation Model

In this study,the clear sky hourly global and net solar irradiances at the surface determined using SUNFLUX,a simple parameterization scheme,for three stations(Gaize,Naqu,and Lhasa) on the Tibetan Plateau were evaluated against observation data.Our modeled results agree well with observations.The correlation coefficients between modeled and observed values were > 0.99 for all three stations.The relative error of modeled results,in average was < 7%,and the root-mean-square variance was < 27 W m 2.The solar irradiances in the radiation model were slightly overestimated compared with observation data;there were at least two likely causes.First,the radiative effects of aerosols were not included in the radiation model.Second,solar irradiances determined by thermopile pyranometers include a thermal offset error that causes solar radiation to be slightly underestimated.The solar radiation absorbed by the ozone and water vapor was estimated.The results show that monthly mean solar radiation absorbed by the ozone is < 2% of the global solar radiation(< 14 W m 2).Solar radiation absorbed by water vapor is stronger in summer than in winter.The maximum amount of monthly mean solar radiation absorbed by water vapor can be up to 13% of the global solar radiation(95 W m 2).This indicates that water vapor measurements with high precision are very important for precise determination of solar radiation.     

Global photosynthetically active radiation and its relationship with global solar radiation in the Eastern Mediterranean basin

Summary ?The relationship between global photosynthetically active radiation (PAR) and global solar radiation is studied with a 2-year data archive of hourly values H_PAR and H_SW of these irradiances obtained at Athalassa, Cyprus. These data are used to determine the temporal variability of H_PAR and its dependence on sky conditions. The seasonal variation of the ratio H_PAR/H_SW obtained from daily data ranges from 0.456 (during summer) to 0.451 (during winter) with an annual mean value of 0.454. The ratio increases from 0.454 to 0.467 (daily values) or from 0.460 to 0.501 (hourly values), as sky conditions change from clear to overcast. Finally, the effect of aerosol content on the H_PAR/H_SW ratio is found to incur substantial changes in the PAR fraction. Received June 27, 2001; revised April 17, 2002; accepted May 18, 2002     

Observations and estimations of PAR and solar visible radiation in North China

Integrated observations were made of solar irradiance (including photosynthetically active radiation (PAR), visible radiation (VIS), global radiation (G), etc.), and meteorological parameters at 4 stations in North China between September, 2004 and October, 2006. The ratios of hourly sum of PAR to G (H _PAR/H), VIS to G (H _VIS/H), and PAR to VIS (H _PAR/H _VIS) varied smoothly but exhibited significant diurnal, daily, seasonal variations, and were influenced by several factors, such as water vapor, cloud, haze, etc. The objective of this paper is to develop empirical formulas for estimation of hourly and daily sums of PAR and VIS and their relationship under all sky conditions in North China. The calculated PAR and VIS were in agreement with measured values, the relative biases were 13.0?% and 12.4?% for hourly sums, 9.9?% and 9.0?% for daily values, respectively.     

Fractal aspects of integrated concentration fluctuations

Time series of vertically integrated concentrations (VIC) across neutrally buoyant plumes are used to study the fractal and multifractal characteristics of passive scalar fluctuations in turbulent flow fields. Here, the multifractal analysis is based on a novel definition of the singularity spectrum-F() of the time records. Approximations for quantities such as the fractal dimension and the spectral exponent are derived as functions ofF() and are compared with the experimental results. Among other things, we show that VIC records are characterized by two typical subdomains. One domain, which is related to integrated concentration fluctuations, is a subfractal process; whereas the second one, which is directly related to the concentration fluctuations, is a fractal process.     

Intercepted flux and the horizontal component of solar radiation

Summary For the first time a method is presented to actually measure the radiative flux intercepted by cylindrical and conical objects in radiation fields of any unknown angular distribution.The horizontal component of solar radiationH is a newly introduced parameter expressed in Wm^–2 and defined as specific radiative flux intercepted by the lateral surface of a vertical cylinder. The horizontal componentH can be measured and must be considered complementary to the vertical component of solar radiationG which is conventionally measured as Global radiation.Radiative fluxes intercepted by cylindrical and conical objects are expressed as simple analytic functions ofG andH in any irregular radiation field. Before the introduction of the H-concept, when onlyG was measured, intercepted fluxes had to be approximated on the basis of assumed angular distributions of the radiation field.The climatological characteristics ofH andG are different: under clear skies in the open field the H-climatology is more temperate than the G-climatology all over the world and in all seasons. In the radiative environment of elongate vertical bodies H is generally a more significant parameter thanG. With 4 Figures     

New approach to measure the stability of the solar radiative regime

This paper focuses on different ways of characterizing the solar radiative regime of a day and the stability of this regime. The days may be stratified in classes of cloud shade, observed total cloud cover amount, daily averaged clearness index, and fractal dimension of the solar global irradiance signal. A new Boolean parameter related to solar irradiance fluctuation is defined, namely the sunshine stability number. The time averaged value of the sunshine stability number is used for the characterization of the radiative regime stability during a given time interval. Ranking the days from the view-point of the stability of their radiative regime is performed by using the daily average value of the sunshine stability number and appropriately defined values of disorder and complexity, respectively. Measurements performed in the Romanian town of Timisoara (latitude 45°46?? N, longitude 21°25?? E and 85?m altitude above mean sea level) are used here. They refer to time series of global and diffuse solar irradiance recorded at 15-s time interval between sunrise and sunset during all the days in 2009.     

A simplified but accurate spectral solar irradiance model

Summary ¶The paper deals with the computation of solar energy available in a specific location. First, a new formula describing the relation between global solar irradiation and the duration of bright sunshine is established. The analysis of its use shows that global solar clear sky irradiance models are essential tools for daily computation of global irradiation. An integrated spectral atmospheric transmittance model is presented, it can be used to compute beam and diffuse clear sky irradiance for all applications where broadband solar energy input is needed. Since it is desirable to use simplified estimation methods for many applications, a parametric global solar irradiance model, derived from the spectral model, is also presented. This model needs only surface meteorological data as input. The influence of the averaging method used for the input parameters on the model accuracy is evaluated. Comparison of model results with the measurements shows an acceptable level of accuracy with the new model. Finally, an application of daily global solar energy computation is presented.Received May 17, 2002; revised October 14, 2002; accepted February 11, 2003 Published online September 10, 2003     

On the annual and monthly mean diurnal variations of diffuse solar radiation at a meteorological station in west Africa

Summary In addition to global solar radiationE ^g , the hourly diffuse componentE ^d incident on a horizontal surface has been measured from February 1993 to January 1995 at a meteorological station in tropical West Africa. The measured diffuse solar irradiance data was corrected for shadow band effects. The monthly mean diurnal variations of diffuse solar irradiance obtained for identical months in the two years have been compared and found to be generally consistent. The corresponding monthly mean hourly values ofE ^d for identical months in 1993 and 1994 agreed to within 9% while yielding correlation coefficients greater than 0.960. In addition, the monthly mean daily totals ofE ^d for identical months were found to agree mostly to within 6% and showed virtually the same annual variations in both years. The monthly mean daily total values of diffuse solar radiation for most months in the two years ranged between 7.94 MJm^–2d^–1 and 10.50 MJm^–2d^–1. The monthly mean of daily hourly maximum values ofE ^d obtained for identical months in the two years have been discussed in relation to the dominant atmospheric conditions during these months. The results been presented here have been compared with those of some investigators within and outside the Africa region.With 8 Figures     

The medieval solar activity maximum

Paleoclimatic studies of the Medieval Solar Maximum (c. A.D. 1100–1250, corresponding with the span of the Medieval Warm Epoch) may prove useful because it provides a better analog to the present solar forcing than the intervening era. The Medieval Solar Activity Maximum caused the cosmogenic isotope production minimum during the 12th and 13th Centuries A.D. reflected by ¹⁴C and¹⁰Be records stored in natural archives. These records suggest solar activity has returned to Medieval Solar Maximum highs after a prolonged period of reduced solar activity. Climate forcing by increased solar activity may explain some of this century's temperature rise without assuming unacceptably high climate sensitivity. By analogy with the Medieval Solar Activity Maximum, the contemporary solar activity maximum may be projected to last for 150 years. The maximum temperature increase forced by increased solar activity stays well below the predicted doubled atmospheric CO₂ greenhouse forcing.     

New results regarding the influence of solar activity on the stratospheric-tropospheric exchange

Summary The dependence of stratospheric intrusions on solar events is analyzed on the basis of 8-years' recordings of the concentration of stratospheric radionuclides and the ozone at 3 km altitude, as well as of the atmospheric profile of the ozone concentration and the total ozone.A significant, even though weak influence of solar magnetic sector structure boundary passages of type-/+ can be identified, a seasonal influence, however, is also observed. The strong 50 to 80% increase in the frequency of stratospheric intrusions after solarH -flares is significant and completely independent of the phase of the solar cycle and season. The total atmospheric ozone shows also a correlation with solar flares: A well defined maximum on the day preceding the flare. The neutron density clearly shows the Forbush decrease on theH -key day. Using key days with Forbush minimum for the superposed epoch analysis reveals a significant maximum of the Be 7-concentration on the day before the flare (rise by about 45 to 60%).Notable is the following sequence: Approximately 3 days before the solar flare the neutron density begins to decrease, 1 to 2 days before the flare the total atmospheric ozone maximizes, and 2 to 3 days after the flare one finds the maximum of the Be 7 in the troposphere as a consequence of the stratospheric intrusion.Around days with maximum Be 7-concentration the reliability of weather forecasts is clearly reduced — a fact, which at this point is obviously indicative of an acute activation of a labile atmospheric condition.We selected some characteristic individual cases to demonstrate by means of tables the time lapse of typical solar atmospheric and geophysical variables associated with solar flares. The attendant structures of the vertical ozone profile are discussed.Some preliminary reflections on a physical link are set forth.

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Neue Ergebnisse über den Einfluß der Sonnenaktivität auf den stratosphärisch-troposphärischen Austausch

Zusammenfassung Anhand 8jähriger Registrierungen der Konzentration stratosphärischer Radionuklide und des Ozon in 3 km Höhe sowie des atmosphärischen Profils der Ozon-Konzentration und des Gesamt-Ozon wird die Abhängigkeit stratosphärischer Lufteinbrüche in die Troposphäre von solaren Ereignissen analysiert.Ein signifikanter, wenn auch schwacher Einfluß von Sektordurchgängen des interplanetarischen Magnetfeldes beim Polaritätswechsel vom Typ-/+ läßt sich nachweisen, jedoch geht ein jahreszeitlicher Einfluß mit ein.Signifikant und völlig unabhängig von der Phase des solaren Zyklus und der Jahreszeit ist die starke Zunahme der Häufigkeit bzw. der Stärke von stratosphärischen Lufteinbrüchen 2 bis 3 Tage nachH -Eruptionen (Zunahme um 50 bis 80%). Das atmosphärische Gesamt-Ozon zeigt ebenfalls eine Korrelation mitH -Eruptionen: Ein gut ausgeprägtes Maximum am Tag vor der Eruption wird festgestellt. Die Neutronendichte zeigt amH -Stichtag deutlich den Forbush-Effekt. Verwendet man Stichtage mit einem Forbush-Effekt für die Überlagerungs-Analyse, so findet man am Tage vor dem Stichtag ein signifikantes Maximum der Be 7-Konzentration (Anstieg um 45–60%). Auffallend ist die folgende Zeitfolge: Etwa 3 Tage vor derH -Eruption beginnt die Neutronendichte abzusinken, 1 bis 2 Tage vor der Eruption erreicht das atmosphärische Gesamt-Ozon das Maximum, 2 bis 3 Tage nach derH -Eruption findet man das Maximum des Be 7 in der Troposphäre als Folge der stratosphärischen Lufteinbrüche.Um Tage mit maximaler Be 7-Konzentration ist die Treffsicherheit von Wetterprognosen eindeutig reduziert. Man hat es also zu diesem Zeitpunkt offensichtlich mit der akuten Aktivierung eines labilen atmosphärischen Zustandes zu tun.Anhand von Tabellen wird der zeitliche Ablauf von charakteristischen solaren atmosphärischen und geophysikalischen Größen im Zusammenhang mit solaren Ereignissen für einige charakteristische Einzelfälle dargelegt. Die zugehörigen Strukturen des vertikalen Ozon-Profiles werden besprochen.Einige vorläufige Gedanken über einen Kausalzusammenhang werden dargelegt.

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With 12 Figures     

Estimates of effective aerosol optical depths from spectral solar radiation measurements

Summary This study reports a 37-year long record of direct beam spectral irradiance measurements made in Athens, Greece. An analysis of aerosol effects on the spectral distribution of solar radiation through effective optical depths, are presented. Thus, spectrally resolved aerosol optical depths were calculated and analyzed for the period 1954–1990. Summertime aerosol optical depths were found to be larger than winter values, while their seasonal variations were related to varying weather conditions throughout the year. The interrelationships between effective optical depths were found to be linear and were related strongly to microphysics of aerosol loading in the atmosphere. For the period 1962–1983 as wavelength exponent ₀ values ranged between 0.76–1.14 the spectrally resolved optical depths were found to increase markedly with respect to remaining periods 1954–1961 and 1984–1990 in which ₀ values ranged between 1.16–1.39. A minimum in aerosol optical depths, believed to be near background levels, was reached during period 1954–1957, while there was some indication that both optical depths continued to decrease reaching background levels at the end of the study period. From the long-term variation of aerosol effective optical depths some interesting information on the time evolution of air quality in Athens was gained. In addition, their frequency distribution, temporal daily variations and some remarks on photosynthetically active radiation for plant development, are presented and discussed.With 7 Figures     

Retrospective cloud determinations from surface solar radiation measurements

Surface solar radiation measurements have been made at many meteorological sites for long periods. These data potentially provide higher temporal resolution cloud amount information than traditional estimations of cloud amount recorded in eighths of the sky obscured (oktas). To utilise existing solar radiation datasets for this, two quantities are derived from the surface measurements of global (G) and diffuse (D) solar irradiance, and top of atmosphere solar irradiance (E) — the Diffuse Fraction (DF = D/G) and the Opaqueness (Op = 1 - G/E). These are compared with subjective cloud observations made at Reading daily during 1997 to 2006. This shows that DF measurements are sensitive to cloud amount, particularly for low and moderate cloud coverage. Complimentary information is available in Op, which is particularly sensitive to cloud amount in moderate to overcast cloud coverage. In overcast conditions, DF = 1, during which Op provides a measure of overcast cloud thickness. As well as cloud amount, the variability in DF and Op provides a basis for discriminating between cumuliform and stratiform cloud: large variability indicates convective cloud whereas only small variability occurs under stratiform cloud.     

Effects of tropospheric aerosols on the solar radiative heating in a clear atmosphere

Summary The broadband solar absorptivity concept is employed to parameterize the aerosol absorption effect. The solar radiation model developed by Liou and his associates was modified to incorporate the parameterization of solar radiative transfer in an aerosol layer. Comparison of the results from this method with other schemes exhibits close agreement. A Sahara dust storm case was also chosen to test the performance of the present model, and the computed heating rate profiles agree well with calculations based on optical properties derived from observations for both clear and dust cases. In general, enhanced heating due to aerosol absorption of solar flux occurs particularly in the lower troposphere (below 5 km). The heating rate is independent of the scattering partition factor (), but the planetary albedo increases with . Further study shows that the aerosol heating is sensitive to the surface albedo (r _s ) and to the cosine of the solar zenith angle (µ ₀). The decrease inr _s and/or increase inµ ₀ lower the solar heating rate, the planetary albedo and the atmospheric absorptivity, but raise the surface absorptivity due to reduced multiple reflection between the atmosphere and surface.With 9 Figures     

Aerosol modulation of atmospheric and surface solar heating over the tropical Indian Ocean

The major finding of this study is that aerosols over the tropical Indian Ocean enhance clear sky atmospheric solar heating significantly and decrease the surface solar heating by even a larger amount. The results presented here are based on aerosol chemical, microphysical, and optical and radiometric data collected at the island of Kaashidhoo (4.97°N, 73.47°E) during February and March of 1998, as part of the first field phase of the Indian Ocean experiment (INDOEX). The aerosol optical properties were integrated with a multiple scattering Monte Carlo radiative transfer model which was validated at the surface with broadband flux measurements and at the top of the atmosphere (TOA) with the clouds and earth's radiant energy system (CERES) radiation budget measurements. We consider both externally and internally mixed aerosol models with very little difference between the two models in the estimated forcing. For the February–March period, the aerosols increase the monthly mean clear sky atmospheric solar heating by about 12 W/m²(about 15% of the total atmospheric solar heating) and decrease the sea surface clear sky solar heating by about 16 W/m² with a daily range from 5 to 23 W/m². The net aerosol forcing at the top of the atmosphere is about −4 W/m² with a daily range from −2 to −6 W/m². Although the soot contributes only about 10% to the aerosol optical thickness, it contributes more than 50% to the aerosol induced atmospheric solar heating. The fundamental conclusion of this study is that anthropogenic aerosols over the tropical Indian Ocean are altering the clear sky radiation budget of the atmosphere and surface in a major manner.     

A simplified calibrated model for estimating daily global solar radiation in Madinah, Saudi Arabia

Solar radiation is the most important parameter in defining the energy budget at the surface thereby influencing the hydroclimate. Several empirical models based on air temperature are developed and used in several decision-making needs such as agriculture and energy sector. However, a calibration against direct observations is a priori for implementing such models. A calibrated model is developed for Saudi Arabia (Madinah) based on observations during 2007–2011. The model $ \left( {\mathrm{Rs}=A+B\cdot \mathrm{R}{{\mathrm{s}}_0}{{{\left( {{T_{\max }}-{T_{\min }}} \right)}}^C}} \right) $ is used to estimate daily solar radiation and results show a correlation coefficient of 0.94. The calibrated model outperforms the uncalibrated model available for this location. To increase the confidence, the calibrated model is also compared with a simple artificial neural network.     

Spectral distribution of solar radiation in Athens

Summary A 25-year (1966–1990) record of measurements of the broadband direct solar irradiances performed in Athens, has been utilized to determine the radiant energy distribution in several spectral bands. Using these data the year-to-year trend of the time sequences of the mean values of the irradiation ratios in the various spectral intervals, viz. blue, green/orange, red, and photosynthetically active radiation (PAR) and the total direct irradiance for the whole spectrum, are evaluated.From this trend the following can be concluded: the blue spectral band (0.380–0.525 m) decreased from the beginning of the examined period until the mid-seventies and then increased gradually; the red band (0.630–0.710 m) shows similar trend but opposite in sense. The PAR band (0.380–0.710 m) decreased slightly until 1985 and then increases. In the green/orange band (0.525–0.630 m) the trend can be considered as nearly constant throughout the examined period. This trend of the irradiation ratios is related to the aerosol and gaseous pollutant content of the atmosphere, which probably reflects the urbanization, industrialization and heavy traffic conditions of the Athens area, during the last three decades.With 2 Figures     

Short term variability of atmospheric turbidity and optical turbulence in a desert environment

Summary Variability of atmospheric turbidity calculated from direct beam solar radiation measurements and the transverse coherence length,r ₀, derived from differential image motion of stellar sources show pronounced fluctuations on the order of a few minutes under convectively unstable conditions in a desert environment. The quiescent periods, neutral events, when local near surface adiabatic conditions occur show substantial reductions in the fluctuations of the same quantities. Image motion results for nighttime (stable) conditions display slowing varying patterns with reduced short term (few minutes) variations.The measurements were taken using a suite of instrumentation probing the same volume of atmosphere. The instrumentation used includes a pyrheliometer, Atmospheric Turbulence Measurement and Observation System (ATMOS), a sodar, a scintillometer, and tower- mounted sensors. A time-height display of sodar data calibrated for the refractive index structure parameter,C _n ² , coupled with scintillometer measurements show the diurnal evolution of the boundary layer responding to the local heating-cooling cycle and drainage flows from the surrounding mountains. Several atmospheric features are seen and discussed in these results as they affect the nature of the patterns of turbidity andr ₀. Of particular interests are the development of convection, changes in the capping inversion, thermal plume structures, neutral events, and wave-turbulence interactions. Sinusoidal oscillations, identified as internal gravity waves, are seen in the nighttime laminated structures.With 10 Figures