Statistical Study and Prediction of Variability of Erythemal Ultraviolet Irradiance Solar Values in Valencia,Spain

The goal of this study was to statistically analyse the variability of global irradiance and ultraviolet erythemal (UVER) irradiance and their interrelationships with global and UVER irradiance, global clearness indices and ozone. A prediction of short-term UVER solar irradiance values was also obtained. Extreme values of UVER irradiance were included in the data set, as well as a time series of ultraviolet irradiance variability (UIV). The study period was from 2005 to 2014 and approximately 250,000 readings were taken at 5-min intervals. The effect of the clearness indices on global irradiance variability (GIV) and UIV was also recorded and bi-dimensional distributions were used to gather information on the two measured variables. With regard to daily GIV and UIV, it is also shown that for global clearness index (k_t) values lower than 0.6 both global and UVER irradiance had greater variability and that UIV on cloud-free days (k_t higher than 0.65) exceeds GIV. To study the dependence between UIV and GIV the χ² statistical method was used. It can be concluded that there is a 95% probability of a clear dependency between the variabilities. A connection between high k_t (corresponding to cloudless days) and low variabilities was found in the analysis of bi-dimensional distributions. Extreme values of UVER irradiance were also analyzed and it was possible to calculate the probable future values of UVER irradiance by extrapolating the values of the adjustment curve obtained from the Gumbel distribution.     

Solar Forcing of Global Climate Change Since The Mid-17th Century

Spacecraft measurements of the sun's total irradiance since 1980 have revealed a long-term variation that is roughly in phase with the 11-year solar cycle. Its origin is uncertain, but may be related to the overall level of solar magnetic activity as well as to the concurrent activity on the visible disk. A low-pass Gaussian filtered time series of the annual sunspot number has been developed as a suitable proxy for solar magnetic activity that contains a long-term component related to the average level of activity as well as a short-term component related to the current phase of the 11-year cycle. This time series is also assumed to be a proxy for solar total irradiance, and the irradiance is reconstructed for the period since 1617 based on the estimate from climatic evidence that global temperatures during the Maunder Minimum of solar activity, which coincided with one of the coldest periods of the Little Ice Age, were about 1 °C colder than modern temperatures. This irradiance variation is used as the variable radiative forcing function in a one-dimensional ocean–climate model, leading to a reconstruction of global temperatures over the same period, and to a suggestion that solar forcing and anthropogenic greenhouse-gas forcing made roughly equal contributions to the rise in global temperature that took place between 1900 and 1955. The importance of solar variability as a factor in climate change over the last few decades may have been underestimated in recent studies.     

Possibilities to detect trends in spectral UV irradiance

Summary It is investigated how long-term UV trends can be assessed by analysing the longest time series of measured spectral UV irradiance in Europe, which have been started in the early 1990s in Thessaloniki, Greece and Sodankylä, Finland. It can be concluded that both time series do not yet show an unambiguous yearly trend in UV irradiance. The regression lines show no uniform behaviour and vary irregularly in strength and from one solar zenith angle to the next if all sky conditions are analysed. It is emphasised that these findings do not disagree with previous studies, that significant changes in UV irradiance have been observed over Europe especially in spring.Our study introduces a new method to estimate the required time series length for trend detection using the measured time series in combination with model calculations. At Sodankylä, a reduction of the total ozone column of –5.7% per decade has been observed from 1979 to 1998. A positive UV trend due to such conditions may be detected after 12 years at the earliest. For Thessalonki, a decrease in total ozone of –4.5% per decade has been observed. A corresponding increase of UV irradiance should be detectable after 15 years. It should be noted that a constant ozone trend over the whole period had to be assumed for this analysis.Since 1990 there has been a considerable variability of total ozone, but no steady decrease could be observed. Consequently, no general UV increase could be expected due to ozone changes. Even if there was a constant ozone trend over that period it is shown that even the longest European time series of UV irradiance are still too short to show distinct trends. However, this does not imply that no changes have occurred, it only shows that the large natural variability of UV irradiance has so far hindered the identification of unambiguous trends. The only way to find significant and consistent UV trends is the continuation of high-quality long-term measurements of spectral UV irradiance.     

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.     

Application of solar max ACRIM data to analysis of solar-driven climatic variability on Earth

Climatic change caused by solar variability has been proposed for at least a century, but could not be assessed reliably in the past because the uncertainty in solar irradiance measured from the Earth's surface is too large. Now satellite measurements by such instruments as the Active Cavity Radiometer Irradiance Monitor (ACRIM) permit a preliminary assessment. The satellite data exhibit irradiance variations over a spectrum of shorter timescales, but the first 5-yr overall trend indicates slightly decreasing luminosity. The global temperature response to monthly-mean ACRIM-measured fluctuations from 1980–1984 was computed from the NYU 1D transient climate model - which includes thermal inertia effects of the world oceans - starting from an assumed pre-existing steady state, and the results compared with observations of recent global temperature trends. The modeled surface temperature evolution exhibited a complex history-dependent behavior whose fluctuations were an order of magnitude smaller than observed, primarily owing to oceanic thermal damping. Thus solar variability appears unlikely to have been an important factor in global-scale climate change over this period. The possibility of using the measurements to develop simple correlations for irradiance with longer term solar activity observable from the surface, and therefore to analyze historical effects, was considered, but is not supported by the satellite data. However, we have used a model of solar irradiance variation with time (Schatten, 1988), covering the period 1976–1997 in order to assess our model's response to forcing whose fluctuation timescale is comparable to the thermal relaxation time of the upper ocean. Continuous monitoring of solar flux by space-based instruments over timescales of 20 yr or more, comparable to timescales for thermal relaxation of the oceans, and of the solar cycle itself, is probably needed to resolve issues of long-term solar variation effects on climate.Presently at Lamont-Doherty Geological Observatory of Columbia University, Palisades, NY 10964.     

Are Natural Climate Forcings Able to Counteract the Projected Anthropogenic Global Warming?

A two-dimensional global climate model is used to assessthe climatic changes associated with the new IPCC SRES emissions scenarios and to determine which kind of changes in total solar irradiance and volcanic perturbations could mask the projected anthropogenic global warming associated to the SRES scenarios. Our results suggest that only extremely unlikely changes in total solar irradiance and/or volcanic eruptions would be able to overcome the simulated anthropogenic global warming over the century. Nevertheless, in the critical interval of the next two decades the externally-driven natural climate variability might possibly confuse the debate about temperature trends and impede detection of the anthropogenic climate change signal.     

Trends in solar radiation over Germany and an assessment of the role of aerosols and sunshine duration

Summary ¶Global, diffuse, and horizontal direct (beam) irradiances have been evaluated for 13 stations in Germany where the time series vary between 11 and 48 years. Global irradiance has decreased significantly at two stations and increased at four stations. The mean trend in global is an increase of 1.94Wm^–2 or 1.83% per decade. Diffuse irradiance has decreased at five stations, with a mean reduction of 2.44Wm^–2 or 3.46% per decade, while horizontal direct irradiance has increased an average of 4.86Wm^–2 or 10.40% per decade at five stations. Increases in global and direct are most common at stations in the southwest region of Germany, decreases in global were observed in the southeast, and there was an absence of spatial homogeneity in the diffuse trends. Spatial variability in irradiance over Germany is higher in the direct component compared to variability in global and diffuse.Trend analyses of concomitant time series of radiation, bright sunshine duration, and modeled estimates of Ångströms turbidity coefficient suggest that long-term decreases in aerosols are the most likely cause of increases in global irradiance observed at Mannheim, Norderney, and Trier; decreases in diffuse at Hohenpeissenberg, Kassel, Mannheim, and Trier; and increases in direct irradiance at Bocholt, Kassel, Mannheim, and Trier. An increase in sunshine duration at Freiburg likely contributed to an increase in global and direct irradiance observed at that station.     

Solar irradiance during the last 1200 years based on cosmogenic nuclides

Based on a quantitative study of the common fluctuations of ¹⁴C and ¹⁰Be production rates, we have derived a time series of the solar magnetic variability over the last 1200 years. This record is converted into irradiance variations by linear scaling based on previous studies of sun‐like stars and of the sun's behavior over the last few centuries. The new solar irradiance record exhibits low values during the well‐known solar minima centered at about 1900, 1810 (Dalton) and 1690 ad (Maunder). Further back in time, a rather long period between 1450 and 1750 ad is characterized by low irradiance values. A shorter period is centered at about 1200 ad , with irradiance slightly higher or similar to present day values. It is tempting to correlate these periods with the so‐called "little ice age" and "medieval warm period", respectively. An accurate quantification of the climatic impact of this new irradiance record requires the use of coupled atmosphere–ocean general circulation models (GCMs). Nevertheless, our record is already compatible with a global cooling of about 0.5‐1°C during the "little ice age", and with a general cooling trend during the past millenium followed by global warming during the 20th century (Mann et al., 1999).     

1/f noise in the UV solar spectral irradiance

The investigation of the intrinsic properties of the solar spectral irradiance as a function of the ultraviolet (UV) wavelength is attempted by exploiting rare observations performed at the Villard St. Pancrace station of the Lille University of Sciences and Technology ranging from 278 to 400 nm with a step of 0.05 nm every half an hour from nearly sunrise to sunset. To achieve this goal, the modern method of the detrended fluctuation analysis was applied on the solar spectral irradiance values versus wavelength. This analysis revealed that the solar incident flux at the top of the atmosphere and the solar spectral irradiance at the ground during two overcast sky days fluctuate with the UV wavelength exhibiting persistent long-range power-law behavior. More interestingly, the exponent of the power-law relationship between the fluctuations of the solar spectral irradiance versus UV wavelength at both the top of the atmosphere and the ground is consistently close to unity (of 1/f-type) throughout the day. This 1/f behavior has been detected in many complex dynamical systems, but despite much effort to derive a theory for its widespread occurrence in nature, it remains unexplained so far. According to the above-mentioned findings we speculate that the 1/f property of the incident solar UV flux at the top of the atmosphere could probably drive both the 1/f behavior depicted in the atmospheric components and the solar UV irradiance at the Earth's surface. The latter could influence the UV-sensitive biological ecosystems, giving rise to a 1/f-type variability in the biosphere, which has already been proven by recent observational data. We finally propose that Wien approximation could be multiplied by a 1/f function of wavelength (e.g., of the type of the fractional Brownian motion) in order to reproduce the aforementioned 1/f feature of the solar UV flux.     

Long-Term Trend in Ozone and Erythemal UV at Indian Latitudes

The role of atmospheric ozone to protect the living organisms and vegetation from the harmful effects of ultraviolet irradiation is well known. Depletion of the ozone layer is a great threat to the human society. In this paper we have discussed the lethal effects of ozone depletion and have presented the ozone and UV-B scenarios from 1979 to 2005 at different Indian latitudes using satellite data. The erythemal UV irradiance data obtained from Nimbus-7 and Earth probe total ozone mapping spectrometer (TOMS) and the tropospheric and stratospheric ozone data obtained from the convective cloud differential (CCD) method have been used to study the variability of erythemal UV irradiance and the stratospheric and tropospheric column ozone, respectively, over a period from 1979 to 2005. The observed results along with the expected upper and lower tolerance limits for tropospheric and stratospheric ozone, respectively, for different Indian latitudes, which have been estimated statistically using monthly mean CCD ozone data from 1979 to 2005 have been discussed in detail.     

Solar irradiance forcing of centennial climate variability during the Holocene

Centennial climate variability during the Holocene has been simulated in two 10,000 year experiments using the intermediate-complexity ECBilt model. ECBilt contains a dynamic atmosphere, a global 3-D ocean model and a thermodynamic sea-ice model. One experiment uses orbital forcing and solar irradiance forcing, which is based on the Stuiver et al. residual ¹⁴C record spliced into the Lean et al. reconstruction. The other experiment uses orbital forcing alone. A glacier model is coupled off-line to the climate model. A time scale analysis shows that the response in atmospheric parameters to the irradiance forcing can be characterised as the direct response of a system with a large thermal inertia. This is evident in parameters like surface air temperature, monsoon precipitation and glacier length, which show a stronger response for longer time scales. The oceanic response, on the other hand, is strongly modified by internal feedback processes. The solar irradiance forcing excites a (damped) mode of the thermohaline circulation (THC) in the North Atlantic Ocean, similar to the loop-oscillator modes associated with random-noise freshwater forcing. This results in a significant peak (at time scales 200–250 year) in the THC spectrum which is absent in the reference run. The THC response diminishes the sea surface temperature response at high latitudes, while it gives rise to a signal in the sea surface salinity. A comparison of the model results with observations shows a number of encouraging similarities.     

基于EC细网格数值预报产品的太阳辐照度订正技术

太阳辐照度与光伏电站发电功率密切相关,其预报的准确性直接影响发电功率预报的准确性。根据光伏电站太阳辐照度实况、气象站实况、WRF(Weather Research and Forecast Model)模式辐照度预报、EC细网格数值预报以及太阳理论辐照度,利用逐步回归法开展太阳辐照度预报订正研究,得到以下结论:①太阳辐照度实况与太阳理论辐照度的比值与EC细网格数值预报中气象要素的相关性优于太阳辐照度实况与气象要素的相关性;②不同时刻影响太阳辐照度的气象因子存在差异,通过逐步回归法建立不同时刻太阳辐照度预报模型;③在非晴天情况下,回归预报辐照度相对均方根误差比WRF模式预报辐照度降低10%左右,减小了辐照度预报误差。该研究成果在光伏电站的新能源数值预报服务中有一定的应用价值。     

Potential Role of Solar Variability as an Agent for Climate Change

Numerical experiments have been carried out with a two-dimensional sector averaged global climate model in order to assess the potential impact of solar variability on the Earth's surface temperature from 1700 to 1992. This was done by investigating the model response to the variations in solar radiation caused by the changes in the Earth's orbital elements, as well as by the changes intrinsic to the Sun. In the absence of a full physical theory able to explain the origin of the observed total solar irradiance variations, three different total solar irradiance reconstructions have been used. A total solar irradiance change due to the photospheric effects incorporated in the Willson and Hudson (1988) parameterization, and the newly reconstructed solar total irradiance variations from the solar models of Hoyt and Schatten (1993) and Lean et al. (1995). Our results indicate that while the influence of the orbital forcing on the annual and global mean surface temperature is negligible at the century time scale, the monthly mean response to this forcing can be quite different from one month to another. The modelled global warming due to the three investigated total solar irradiance reconstructions is insufficient to reproduce the observed 20th century warming. Nevertheless, our simulated surface temperature response to the changes in the Sun's radiant energy output suggests that the Gleissberg cycle (88 years) solar forcing should not be neglected in explaining the century-scale climate variations. Finally, spectral analysis seems to point out that the 10- to 12-year oscillations found in the recorded Northern Hemisphere temperature variations from 1700 to 1992 could be unrelated to the solar forcing. Such a result could indicate that the eleven-year period which is frequently found in climate data might be related to oscillations in the atmosphere or oceans, internal to the climate system.     

Naturally forced multidecadal variability of the Atlantic meridional overturning circulation

The mechanisms by which natural forcing factors alone could drive simulated multidecadal variability in the Atlantic meridional overturning circulation (AMOC) are assessed in an ensemble of climate model simulations. It is shown for a new state-of-the-art general circulation model, HadGEM2-ES, that the most important of these natural forcings, in terms of the multidecadal response of the AMOC, is solar rather than volcanic forcing. AMOC strengthening occurs through a densification of the North Atlantic, driven by anomalous surface freshwater fluxes due to increased evaporation. These are related to persistent North Atlantic atmospheric circulation anomalies, driven by forced changes in the stratosphere, associated with anomalously weak solar irradiance during the late nineteenth and early twentieth centuries. Within a period of approximately 100 years the 11-year smoothed ensemble mean AMOC strengthens by 1.5 Sv and subsequently weakens by 1.9 Sv, representing respectively approximately 3 and 4 standard deviations of the 11-year smoothed control simulation. The solar-induced variability of the AMOC has various relevant climate impacts, such as a northward shift of the intertropical convergence zone, anomalous Amazonian rainfall, and a sustained increase in European temperatures. While this model has only a partial representation of the atmospheric response to solar variability, these results demonstrate the potential for solar variability to have a multidecadal impact on North Atlantic climate.     

Impact of ocean optical properties on seasonal SST: results with a surface ocean model coupled to the LMD AGCM

As the accuracy of ocean models improves, determination of the solar irradiance within the ocean may become important to simulate precisely the seasonal evolution of the SST. As ocean optical properties are not well documented in space and time, we have undertaken a sensitivity study to measure the corresponding SST uncertainties at a global scale using a model coupling the LMD AGCM with an integral mixed layer model and a thermodynamic sea ice representation. The downwelling irradiance formulation is that of Paulson and Simpson which has been tuned for the five water types of the Jerlov classification. Two sensitivity, and academic, experiments corresponding to a uniformly clear ocean or turbid ocean are carried out. Turbid waters exhibit, in general, a stronger seasonal cycle of the SST of about 2°C. The sensitivity is far from uniform, with a maximum in the subtropics and the mid-latitudes of the summer hemisphere. It corresponds precisely to the area in which the observed optical properties present a large temporal variability which is therefore likely to have an action on the seasonal cycle of the ocean surface temperatures. We perform a decomposition of the model sensitivity in four terms, corresponding to the direct impact of the water type change, feedback due to the mixed layer change, feedback due to the surface solar irradiance change, and feedback due to the non solar heat fluxes change. The first two terms dominate the SST change. The direct effect tends to increase the warming of the mixed layer. In addition, the mixed layer depth diminishes because of a higher stabilizing effect of solar radiation on the TKE budget. This tends to increase further summer warming of the SST as well as their winter cooling.     

Exciting natural modes of variability by solar and volcanic forcing: idealized and realistic experiments

Using multi-millenium simulations performed with the three-dimensional climate model ECBILT-CLIO, we analyze how variations in the external forcing can excite low-frequency modes of climate variability. We find that prescribing an idealized, abrupt decrease in solar irradiance can trigger a large perturbation of the oceanic thermohaline circulation (THC) associated with a cooling of more than 5 °C in the North Atlantic over decades to centuries. Using more realistic scenarios that include the variations of solar irradiance and the influence of volcanic eruptions, such large perturbations of the THC are not triggered. Nevertheless, modifications of the forcing can strongly modify the probability of very cold years in the North Atlantic. During those cold years, sea-ice covers a large part of the Nordic Seas and the inflow of warm Atlantic waters at high latitudes is strongly reduced. Those processes induce a temporarily, strong local amplification of the forcing and generate modifications of the atmospheric conditions. Simulations of the last millenium climate using realistic forcing reveal that the probability to have such very cold years in the model is higher during the period AD 1300–1850 than during the first centuries of the second millenium or during the twentieth century. This might explain the higher variability observed during this period in some climate records in the Nordic Seas.     

The influence of clouds on surface UV erythemal irradiance

The purpose of this study is to examine the effect of clouds on the ultraviolet erythemal irradiance. The study was developed at three stations in the Iberian Peninsula: Madrid and Murcia, using data recorded in the period 2000–2001, and Zaragoza, using data recorded in 2001. In order to determine the cloud effect on ultraviolet erythemal irradiance, we considered a cloud modification factor defined as the ratio between the measured values of ultraviolet erythemal irradiance and the corresponding clear-sky ultraviolet erythemal irradiance, which would be expected for the same time period and atmospheric conditions. The dependence of this cloud modification factor on total cloud amount, cloud type and solar elevation angle was investigated. The results suggest that the effect of cloud on ultraviolet erythemal irradiance can be parameterized in a simple way in terms of the cloud amount. Our results suggest that the same cloud modification factor model can be used at the three analysed locations estimating the ultraviolet erythemal irradiance with mean bias deviation (MBD) in the range of the expected experimental errors. This cloud modification factor is lower than that associated to the whole solar spectral range, indicating that the attenuation for the ultraviolet erythemal irradiance is lower than that associated to other solar spectral ranges. The cloud modification factor for ultraviolet erythemal irradiance presents dependence with solar elevation, with opposite dependencies with solar elevation for overcast and partial cloud cover conditions, a fact that can be explained in terms of the influence of reflection-enhancement of the ultraviolet irradiance in the last case. Concerning the influence of cloud type, a limited study of two cloud categories, low and medium level and high level, indicated that for overcast conditions, lower clouds presents an attenuation of ultraviolet erythemal irradiance 20% greater than that associated to high level clouds.     

Validation of a method to estimate direct normal irradiance of UVA and PAR bands from global horizontal measurements for cloudless sky conditions in Valencia, Spain, by a measurement campaign

A method is proposed to provide measurement of direct normal solar irradiance of bands with wavelength ranges (315?C400?nm, 400?C700?nm) from measurements of global horizontal band irradiance for cloudless sky conditions in Valencia. Global and normal direct irradiance data for every air mass were obtained by applying the SMART2 model to the atmosphere of Valencia. The direct normal to global irradiance ratio was parameterized versus the relative optical air mass. A measurement campaign of global horizontal and diffuse irradiance of UVA and PAR bands was carried out in Valencia, after which, the inferred direct normal irradiance was compared with those provided by the method. The result of the comparison shows that the method is acceptably accurate. The proposed model tends to underestimate the direct normal irradiance of the UVA band by 6%, although for values below 25?W/m² the model overestimates the direct irradiance by 6%, while for values above 25?W/m² the model underestimates it by 10%. The other two error estimators used ranging from 11% to 15% are similar in the defined interval measurements in relation to the whole UVA band. Regarding the PAR band, the model overestimates the direct normal irradiance of the PAR band by only 2.2%. With this, the results of the PAR band are more conclusive, as it has been found that for direct normal irradiance values higher than 280?W/m² the MBE error is almost zero and the other two estimator errors are small, about 5%.     

Long-term patterns of solar irradiance forcing in model experiments and proxy based surface temperature reconstructions

Comparisons are made of long-term empirical and model-estimated patterns of solar irradiance forcing during a 200-year period (1650-1850), which precedes any apparent anthropogenic influence on climate. This interval encompasses a considerable range (approximately 4 W/m²) of estimated variation in solar output, including the "Maunder" and "Dalton" Minima of solar irradiance, and an intervening interval of relatively high values of irradiance, but does not encroach into the industrial era wherein it is difficult to separate solar and anthropogenic influences. Particular emphasis is placed on comparing empirical and modeled patterns of forced surface temperature variation. The empirical patterns bear a greater similarity to the pattern of forced response of a coupled ocean-atmosphere general circulation model (AOGCM) than with an independent model simulation result using an ocean with specified heat transport, both in terms of the spatial pattern of response and implied global mean sensitivity to forcing. Heightened sensitivity in the western Pacific warm pool apparent in the empirical response pattern, is not observed in the forced response of the coupled model. It is possible that this pattern is the result of feedback processes not currently reproduced in course-resolution coupled models. The greatest empirical response is found at the multidecadal-to-century (> 40 year period) time scale, for which the forcing is dominated by the roughly 90-year Gleissberg Cycle of irradiance. This indicates a global-mean sensitivity (approximately 0.3 K/W/m²), which is close to the coupled model result (approximately 0.4 K/W/m²). At decadal time scales (8-25 year period), for which the forcing is dominated by the 11-year and 22-year period solar cycles), the temperature sensitivity is moderately reduced, and its spatial pattern of response is dominated by an apparent resonance with known decadal modes of climate variability.     

Procedure of embedding biological action functions into the atmospheric transmittance

In order to perform calculations of biologically effective irradiance, the usual procedure is to modulate the ground-measured spectral solar irradiance with a specific biological action function. The inconvenience is that only a few meteorological stations worldwide are equipped to measure the spectral solar irradiance in the ultraviolet range. This motivates the search for a numerical substitute, which constitutes the subject of this report. An innovative approach based on generalized mean is used to infer the effective atmospheric transmittance. Its illustration resulted in a new parametric model for computing the biological dose under clear sky. The action spectrum for the growth response of plants, as a carrier of biological effects, is encapsulated into the atmospheric transmittance, leading to the calculation of the effective irradiance by simple algebra. The overall results indicate that the new parametric model performs accurately enough to be routinely used in practice. The procedure is general; therefore, it is described in detail to guide potential users in developing similar models incorporating other biological action spectra as needed. For speed-intensive applications, an executable file intended to run on any PC, which computes the effective irradiance with the proposed model, is provided.