Solar Flux Variations Research Articles

Improvements in the Determination of ISS Ca ii K Parameters

Measurements of the ionized Ca ii K line are one of the major resources for long-term studies of solar and stellar activity. They also play a critical role in many studies related to solar irradiance variability, particularly as a ground-based proxy to model the solar ultraviolet flux variation that may influence the Earth’s climate. Full disk images of the Sun in Ca ii K have been available from various observatories for more than 100 years and latter synoptic Sun-as-a-star observations in Ca ii K began in the early 1970s. One of these instruments, the Integrated Sunlight Spectrometer (ISS) has been in operation at Kitt Peak (Arizona) since late 2006. The ISS takes daily observations of solar spectra in nine spectra bands, including the Ca ii K and H lines. We describe recent improvements in data reduction of Ca ii K observations, and present time variations of nine parameters derived from the profile of this spectral line.

Solar eclipse-induced variations in solar flux, j(NO2) and surface ozone at Kannur, India

Surface ozone is mainly produced by the photodissociation of nitrogen dioxide (NO2) by solar UV radiation. Subsequently, solar eclipses provide one of the unique occasions to explore the variations in the photolysis rate of NO2 and their significant impact on the production of ozone at a location. This study aims to examine the diurnal variations in the photodissociation rate coefficient of NO2, (j(NO2*)), and mixing ratios of surface ozone and NO X * (NO + NO2*) during the solar eclipse that occurred on 15 January 2010 at Kannur (11.9°N, 75.4°E, 5 m amsl), a tropical coastal site on the Arabian Sea in South India. This investigation was carried out on the basis of the ground level observations of surface ozone and its prominent precursor NO2*. The j(NO2*) values were estimated from the observed solar UV-A flux data. A sharp decline in j(NO2*) and surface ozone was observed during the eclipse phase because of the decreased efficiency of the ozone formation from NO2. The NO2* levels were found to increase during this episode, whereas the NO levels remained unchanged. The surface ozone concentration was reduced by 57.5%, whereas, on the other hand, that of NO X * increased by 62.5% during the solar eclipse. Subsequently a reduction of *% in the magnitude of j(NO2*) was found here during the maximum obscuration. Reductions in solar insolation, air temperature and wind speed were also observed during the solar eclipse event. The relative humidity showed a 6.4% decrease during the eclipse phase, which was a unique observation at this site.

Observations of pre-midnight 5-m irregularities in the equatorial F region over São Luís, Brazil: Solar-flux dependence and seasonal variations

The statistics of pre-midnight 5-m irregularities in the equatorial F region over São Luís is presented. The data set ranges from October 2001 to December 2008 and covers maximum solar-flux-to-minimum solar flux epoch. The variabilities in irregularity parameters, namely, height and time of their appearance in the radar echoes, with solar-flux variation are presented. The seasonal variations (combined over all years, irrespective of solar-flux) of occurrence of irregularities, occurrence of bottom-type layer (or bottom-side irregularities without plume) and bottom-side/topside plume (or bottom-side irregularities with plume) are presented. The largest occurrences of bottom-side irregularities without plume and with plume are found on April (equinox) and December (summer) months respectively. The ambient ionospheric conditions namely prereversal evening vertical drift, bottom-side density gradient and off-equatorial E region conductivity are inferred using digisonde measurements during April 2002 and December 2002. Based on these conditions and recent studies on gravity wave climatology over Brazil, it is suggested that shear in zonal plasma drift and low gravity wave activity may account for less occurrence of plume during April as compared to December months. This suggestion is quantified using numerical simulation model of collisional-interchange instability (CII) and plasma bubble.

Solar flux variation of the electron temperature morning overshoot in the equatorialFregion

[1] Using 8 years of CHAMP satellite observations of the equatorial electron temperature, Te, we investigate its behavior during the morning overshoot and at ionospheric altitudes below 450 km including its variation with solar activity. The morning Te has a maximum at the dip equator and decreases gradually with increasing latitude, which is due to the increasing importance of heat conduction as the dip angle becomes larger. The amplitude of the equatorial morning overshoot Te decreases with increasing solar flux by about −10°K/solar flux unit depending on season and longitude. Trends of similar magnitude are predicted by the FLIP model. The model calculations confirm that the electron cooling due to enhanced electron‐ion collisions increases faster than the heating of thermal electrons through collision with photoelectrons for increasing solar EUV. Both data and model showed that elevated electron temperatures persist to later local times during low solar activity. Obviously, the decreased background plasma density, together with the slower rise of electron density after sunrise under such conditions are responsible for the longer persistence. First investigations of longitudinal aspects revealed that the strength of the anticorrelation between morning Te and solar flux and the seasonal difference of the Te amplitude varies with longitude. The positive correlation between the morning overshoot and solar flux at 600 km as was shown earlier in Hinotori data is consistent with FLIP predictions and radar observations. The solar flux variation of the morning Te reverses sign between 400 and 600 km.

Ionospheric heating due to solar flares as measured by SROSS-C2 satellite

The data on thermal fluctuations of the topside ionosphere have been measured by Retarding Potential Analyser (RPA) payload aboard the SROSS-C2 satellite over the Indian region for half of the solar cycle (1995–2000). The data on solar flare has been obtained from National Geophysical Data Center (NGDC) Boulder, Colorado (USA) and other solar indices (solar radio flux and sunspot number) were download from NGDC website. The ionospheric electron and ion temperatures show a consistent enhancement during the solar flares. The enhancement in the electron temperature is 28–92% and for ion temperature it is 18–39% compared to the normal day’s average temperature. The enhancement of ionospheric temperatures due to solar flares is correlated with the variation of sunspot and solar radio flux (F10.7cm). All the events studied in the present paper fall in the category of subflare with almost same intensity. The ionospheric electron and ion temperatures enhancement have been compared with the IRI model values.

Effect of Cameralike Aperture in Quest for Maintaining Quasi-Constant Radiation Inside a Solar Reactor

Solar reactors can convert intermittent solar radiation into storable chemical energy in the form of fuels that are transportable. In order to use solar energy as a source of high temperature process heat in a solar reactor, incident radiation needs to be concentrated over a small surface area, the inlet of which is called the aperture. The image of the incoming solar radiation over the aperture can be approximated by a Gaussian distribution where the solar radiation inside the reactor varies by the peak value and aperture size. Due to the transient nature of solar energy, there is a critical need for proper control to maximize system efficiency under field conditions. The objective of this paper is to present numerically proven advantages of having a camera-like variable aperture, one that is sensitive to natural variations in solar flux, and having the ability to shrink or enlarge accordingly in order to maintain quasi-constant radiation inside the reactor. Since the internal temperature has a major impact on reactant to product conversion efficiency, by maintaining the temperature constant, process efficiency is kept high. By maintaining the internal temperature despite transient operating conditions, the system can maintain peak performance through a wider insolation range than fixed aperture systems. Our numerical results from optical, thermodynamic, and flow dynamic simulations led us to develop a computational two dimensional heat transfer distribution model inside the reactor in order to validate our optical results. The combined simulation results show that correctly varying the aperture diameter with respect to transient incoming solar flux densities facilitates the maintenance of quasi-constant temperature distributions inside the reactor.

Correlative Study between UV Irradiance and TOC Using AURA OMI at Kannur (12.3N, 75.4E)

The solar UV radiation has prominent impacts on human life, animals and plants with positive and negative effects. Atmospheric ozone, which is formed from the photodissociation of molecular oxygen mainly in the stratosphere, absorbs a significant factor of solar UV radiation. The ozone in the stratosphere acts as a protective layer to prevent UV radiation reaching on the surface of the earth. Hence the intensity of solar UV radiation on the surface has a strong dependence on the Total Ozone Column (TOC). The UV irradiance on earth surface depends on geometrical factors such as solar zenith angle, altitude, latitude and other atmospheric parameters as well. This is an attempt to study the variation of solar UV flux at its four discrete wavelengths ranging from 305 - 380 nm at Kannur, which is located in the north of Kerala in India. Hence such a correlation of TOC and UV irradiance is relevant to realize the radiation budget at this location (12.3N, 75.4E) using AURA OMI data. This paper reveals the correlation of day to day, month to month temporal variation of total ozone column (in DU) and UV irradiance (w/m2). From the analysis, the anti-correlation between UV and TOC is revealed and its impact in the solar radiation budget is established.

Numerical Simulation of Solar Absorption Machine

Abstract An analytical study is to performed on solar energy utilization in space cooling using a solar lithium bromide absorption system. The introduction presents the importance, the availability and the applications of solar energy, followed by a description for solar absorption machine [1] , [2] . Matlab numerical simulation of this system illustrates the change of the temperatures in the main parts starting from the collector since the temperatures change with the variation of the heat flux density provided from the sun. The temperature changes only in the part of heat exchanger collector and the idle heat exchanger where as in all other part. An electric source is required to ensure the necessary heat that when the solar heat flux does not supply the total air conditioning load. Finally the paper is concluded by studying the variation of solar flux in three cities, the collector length and the auxiliary source required in each city.

Smart solar reactor for co-production of hydrogen and industrial grade carbon under any weather conditions

Abstract The impending shortage of fossil fuels and environmental consequences of fossil fuel consumption are two of the most imperative problems in the world. This presentation is about a novel design of a solar reactor cavity system composed of a camera-like aperture and moving-wall system to house a unique thermo-fluid-chemical process known as ‘solar cracking’. Differing from typical solar powered Rankine cycles, solar cracking uses concentrated solar energy as a heat source for direct decomposition of natural gas into gaseous H2 and particulate carbon. This process offers a CO2 emission free hydrogen production method, as the carbon is collected in a high-grade and/or nanotube form. However, solar cracking reactors have two implicit major problems: The intrinsic losses in energy conversion efficiency as a result of the high internal temperatures and corresponding re-radiation losses as well as the inherently transient nature of the solar energy. Literature on solar reactors reveals a distinct focus on optimal reactor design for steady state efficiency, but little regarding transient inefficiencies. This presentation provides an advanced perception to solar cracking reactors by presenting you the latest results of our research at Sustainable Energy Research Lab on the design of a ‘smart solar reactor’ that is sensitive to variations in solar flux, and can adjust itself accordingly to maintain quasi-equilibrium internal conditions. A unique system design is presented featuring a solar-flux intensity sensitive aperture that can enlarge the aperture diameter when the flux is low and reduce the diameter when the flux is high. Carbon particle deposition on the reactor window, walls, and at the exit. Carbon deposition. particularly at the exit, causes reactor clogging. There have been many innovative reactor designs aimed to achieve increased conversion efficiencies through novel flows developed at ETH-Zurich, CNRS-France, WIS-Israel, Colorado-USA, Florida-USA, and DLR-Germany. From vortex-flow to tornado, and from fluidized bed to rotating cavity, the designs of these reactors have moved toward the goal of seeking enhanced flow conditions that result in improved overall efficiencies, but have not solved the carbon deposition problem. Our latest research results at Sustainable Energy Research Lab shows that our ‘aero-shielded cyclone solar reactor’ concept provides a laminar flow shield covering the walls as a thin layer flow with a velocity that is strong enough to sweep carbon particles away. This presentation will show you the results of our research on this concept with a 3D animation of the reactor.

Possible ozone influence on the quasi-biennial oscillation in the equatorial stratosphere

Crossspectral analysis between the time series of zonal wind velocity in the equatorial stratosphere and the flux of solar UV radiation revealed high coherence between the variations of these two parameters on a quasibiennial scale (24-30 months) in the atmo� spheric layer 500-1 hPa (~6-48.5 km). A lag of the quasibiennial variations in wind velocity behind the quasibiennial variations in the solar radiation flux, the maximum (~ 24 months) of which is located at a level of 100 hPa (16.5 km), decreases with height, and in the stratopause region (~1 hPa), the wind velocity variations are approximately in phase with the varia� tions in the solar radiation flux. This points at the pos� sibility of the influence of quasibiennial variations in the shortwave solar radiation on the quasibiennial oscillation of the zonal wind in the neighborhood of the equatorial stratopause. It has been shown that the meridional gradient and the curvature degree of the meridional profile of ozone concentration in this layer undergo quasibiennial variations such that could be a cause of synchronization between the quasibiennial variations in the wind velocity and thermal variations according to the solar wind equation. 1. The quasibiennial oscillation (QBO) manifests itself most clearly in the change of the direction of the

No evidence for antineutrinos significantly influencing exponential β+ decay

High-precision measurements were conducted on the time evolution of gamma-ray count rates during reactor-on and reactor-off periods to investigate the possible influence of antineutrinos on nuclear decay. This experiment was triggered by a recent analysis (Jenkins et al., 2009) of long-term measurements suggesting a possible link to variations in nuclear decay rate and solar neutrino flux. The antineutrino flux during reactor-off periods is mainly due to geoneutrinos and four orders of magnitude lower than during reactor-on periods. No effects have been observed for the two branches in the decay of (152)Eu and the decay of (137)Cs, (54)Mn and (22)Na. The upper limit determined of the ratio Δλ/λ for (22)Na is (-1±2)×10(-4), and (54)Mn is (-1±4)×10(-4). In comparison to the interpretation of Jenkins et al. our measurements do not show any such effect to at least two orders of magnitude less. Hence either the hypothesis of Jenkins et al. is not true or else one of two rather unlikely possibilities must also be true: either the effect of neutrinos on β(-) decay differs considerably from the effect of antineutrinos on β(+) decay, or the effect of antineutrinos on β(+) decay must be identical to their effect on β(-) and electron-capture decay.

Theoretical modelling of X-ray fluorescence signals for different lunar compositions and dependence on solar activity

We present a forward modelling technique for calculating the surface X-ray spectra for a variety of lunar terrains. Our calculations considered variations in solar fluxes from solar quiescent condition to large flare activity (M1 flare), and expected elemental concentrations in the target, as well as yield, instrumental, and viewing geometry parameters for X-ray induced fluorescence from the lunar surface. Additionally, we present estimates of anticipated XRF signals from prominent K α lines observable by a collimated 14 cm 2 X-ray detector from a 100 km lunar orbit with ∼20 km spatial resolution. Our results show that Mg, Al and Si characteristic K α lines can be observed for all solar conditions. The Ca K α lines line can be differentiated from a fixed background during more energetic solar conditions such as C1 and M1 flares, whereas Ti and Fe lines are identifiable only during C1 and M1 solar flare conditions for Apollo 12 site composition. Both the K α X-ray intensity ratios of Mg/Si and Al/Si correlate well with concentration ratios of Mg/Si and Al/Si, respectively, for B1 and M1 solar conditions. The K α X-ray intensity ratios of Fe/Si and Ca/Si correlates with concentration ratios of Fe/Si and Ca/Si, respectively, for M1 solar condition. In principle, the modelling technique outlined here can be used to determine absolute elemental abundances (Mg, Al, Si, Ca, Ti and Fe) from X-ray spectra measured during recent and future lunar missions.

Quasi-biennial variations of the total solar flux: Their manifestation in variations of the stratospheric wind and the Earth’s rotation velocity

A detailed representation of variations of the total solar flux I has been obtained by analyzing the regular measurements of this flux by the Nimbus-7 and other spacecrafts. In particular, quasi-biennial variations (QBVs) of the monthly average value 〈I〉 and standard deviation sI within a month interval have been revealed. It is remarkable that the QBVs of sI almost coincide in shape with the QBVs of many solar activity and ionospheric indices, and the QBVs of 〈I〉 are almost in antiphase with the variations of sI. The manifestation of the QBVs of 〈I〉 in some processes on the Earth has been already revealed. A relation between the QBVs of 〈I〉 for solar radiation (according to the Nimbus-7 and ACRIM-2 data) and the QBVs of the zonal stratospheric wind near the equator, as well as the QBVs of the Earth’s rotation velocity, has been found. Many of the considered QBV-processes on the Earth are seemingly attributed to the variations of the total solar flux.

Structure of Titan's ionosphere: Model comparisons with Cassini data

Solar extreme ultraviolet and X-ray radiation and energetic plasma from Saturn's magnetosphere interact with the upper atmosphere producing an ionosphere at Titan. The highly coupled ionosphere and upper atmosphere system mediates the interaction between Titan and the external environment. New insights into Titan's ionosphere are being facilitated by data from several instruments onboard the Cassini Orbiter, although the Ion and Neutral Mass Spectrometer (INMS) measurements will be emphasized here. We present dayside ionosphere models and compare the results with both Radio and Plasma Wave–Langmuir Probe (RPWS/LP) and INMS data, exploring the sensitivity of models to ionospheric chemistry schemes and solar flux variations. Modeled electron densities for the dayside leg of T18 and all of T17 (dayside) had reasonable agreement with the measured RPWS electron densities and INMS total ion densities. Magnetospheric inputs make at best minor contributions to the ionosphere for these flybys, at least for altitudes above about 1000 km. At lower (<1100 km) altitudes, the total ion densities measured by the INMS are less than the electron densities measured by the RPWS/LP which could be due to heavy (>100 daltons) ions, which the INMS is not able to detect. Qualitatively, INMS spectra exhibit the same ion species and 12 amu family separations for the dayside ionospheres of T17 and T18 as were seen in the mass spectra measured during T5 (nightside). However, the relative abundance of high-mass ( m>50) ion species is about 10 times less for the dayside T17 and T18 passes than it was for the polar nightside T5 flyby, which can perhaps be explained in several ways including differences in neutral composition, less dissociative recombination on the nightside than on the dayside (due to lower electron densities and affecting heavier ion species more than lighter ones), and transport of longer-lived high-mass species from day-to-night.

Long-term variability in mesopause region temperatures over Fort Collins, Colorado (41°N, 105°W) based on lidar observations from 1990 through 2007

During 1990–2007, there were 894 lidar observations of nocturnal mesopause region temperatures over Fort Collins, Colorado. In an earlier analysis with data to April 1997, an unexpected episodic warming, peaking in 1993 with a maximum value over 10 K, was reported and attributed to the Mount Pinatubo eruption in June 1991. With all data, long-term temperature trends from a 7-parameter linear regression analysis including solar cycle effect and long-term trends leads to a cooling of as much as 6.8 K/decade at ∼100 km, consistent with some reported observations but larger than model predictions. Including the observed episodic warming response in an 11-parameter nonlinear regression analysis reduces the maximum long-term cooling trends to ∼1.5 K/decade at 91 km, with magnitude and altitude dependences consistent with the prediction of two models, Spectral Mesosphere/Lower Thermosphere Model (SMLTM) and Hamburg Model of the Neutral and Ionized Atmosphere (HAMMONIA). In addition, the mid-latitude middle-atmospheric response to solar flux variability in Thermosphere–Ionosphere-Energetics and Dynamics (TIMED)/Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperatures is presented.

A Century of Solar Ca ii Measurements and Their Implication for Solar UV Driving of Climate

Spectroheliograms and disk-integrated flux monitoring in the strong resonance line of Ca ii (K line) provide the longest record of chromospheric magnetic plages. We compare recent reductions of the Ca ii K spectroheliograms obtained since 1907 at the Kodaikanal, Mt. Wilson, and US National Solar Observatories. Certain differences between the individual plage indices appear to be caused mainly by differences in the spectral passbands used. Our main finding is that the indices show remarkably consistent behavior on the multidecadal time scales of greatest interest to global warming studies. The reconstruction of solar ultraviolet flux variation from these indices differs significantly from the 20th-century global temperature record. This difference is consistent with other findings that, although solar UV irradiance variation may affect climate through influence on precipitation and storm tracks, its significance in global temperature remains elusive.

Cumulative solar irradiance and potential large-scale sea ice algae distribution off East Antarctica (30°E–150°E)

We present a computational model of the large-scale cumulative light exposure of sea ice in the Southern Ocean off East Antarctica (30°E–150°E). The model uses remotely sensed or modelled sea ice concentration, snow depth over sea ice, and solar irradiance data, and tracks sea ice motion over the season of interest in order to calculate the cumulative exposure of the ice field to photosynthetically active radiation (PAR). Light is the limiting factor to sea ice algal growth over winter and early spring, and so the results have implications for the estimation of algal biomass in East Antarctica. The model results indicate that highly light-exposed ice is restricted to within a few degrees of the coast in the eastern part of the study region, but extends much further north in the 30°E–100°E sector. The relative influences of sea ice motion, solar flux, and snow depth variations on interannual variations in model predictions were evaluated. The model estimates of cumulative PAR were found to correlate with satellite estimates of subsequent open-water chlorophyll-a concentration, consistent with the notion that sea ice algae can provide inocula for phytoplankton blooms.

Variations on Sun’s role in climate change

In their Opinion piece “Is Climate Sensitive to Solar Variability?” (Physics Today, Physics Today 0031-9228 61 3 2008 50 https://doi.org/10.1063/1.2897951. March 2008, page 50 ), Nicola Scafetta and Bruce West draw attention to a “phenomenological solar signature” they find in preindustrial records of global temperature. Correlations between temperature proxies and solar activity have been reported since the 18th century; see, for example, reference 11. J. Eddy, Science 192, 1189 (1976). https://doi.org/10.1126/science.192.4245.1189 . However, their significance cannot be judged without considering volcanism, which may account for much of the apparent correlation with solar activity over the past millennium. 2 2. G. Hegerl et al. , J. Climate 20, 650 (2007). https://doi.org/10.1175/JCLI4011.1 Scafetta and West assume that the only secular influence on preindustrial climate is the Sun.Scafetta and West also state that anthropogenic influence on global warming is overestimated if climate is as sensitive to solar activity as their studies suggest. But in their referenced work, they admit that such a high sensitivity requires more powerful couplings between solar activity and climate than have been identified so far. That is hardly news; for more than a decade, the big question has been whether such powerful Sun–climate coupling mechanisms exist. For reasons we reviewed recently, 3 3. P. Foukal et al. , Nature 443, 161 (2006). https://doi.org/10.1038/nature05072 variation in total solar irradiance (TSI) seems to lack the required power, and the solar UV flux variation—another candidate mentioned by the authors—seems to account for less than 10% of the variance in the 20th-century global temperature. Solar modulation of cosmic rays and their possible effect on cloud cover is the most complex candidate and remains hardest to test.Additionally, Scafetta and West use solar flare statistics as a proxy for TSI variations to derive a similarity in the power law indices of solar fluctuations and Earth temperature variations. Their claim is puzzling since solar flares make a negligible contribution to TSI variation. Why not just analyze the widely available TSI record itself?In summary, a solar effect on global temperature may well exist, and incisive correlation studies can play a role in its investigation. However, it is increasingly clear that deployment of improved radiometric and photometric instruments will be required to discriminate between suggested Sun–climate coupling mechanisms.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. Eddy, Science 192, 1189 (1976). https://doi.org/10.1126/science.192.4245.1189 , Google ScholarCrossref, ISI2. G. Hegerl et al. , J. Climate 20, 650 (2007). https://doi.org/10.1175/JCLI4011.1 , Google ScholarCrossref, ISI3. P. Foukal et al. , Nature 443, 161 (2006). https://doi.org/10.1038/nature05072 , Google ScholarCrossref, ISI© 2008 American Institute of Physics.

Short‐period solar cycle signals in the ionosphere observed by FORMOSAT‐3/COSMIC

We analyze 2 years of the FORMOSAT‐3/COSMIC GPS radio occultation data to study the response of the Earth's ionosphere to the solar rotation (27‐day) induced solar flux variations. Here we report electron density variations in the ionosphere (∼100–500 km) associated with the 27‐day solar cycle. The peak‐to‐peak variation in electron density at low latitudes in the F2 region is about ∼104–105 electrons cm−3 or 20–40%, and can be as high as 60% depending on altitude, latitude, and season. The half and double periods of the 27‐day are also observed at an amplitude comparable to that of the 27‐day. The results place useful constraints for modeling chemical and dynamical processes in the ionosphere.

Slope, aspect and climate: Spatially explicit and implicit models of topographic microclimate in chalk grassland

The slope and aspect of a vegetated surface strongly affects the amount of solar radiation intercepted by that surface. Solar radiation is the dominant component of the surface energy balance and influences ecologically critical factors of microclimate, including near-surface temperatures, evaporative demand and soil moisture content. It also determines the exposure of vegetation to photosynthetically active and ultra-violet wavelengths. Spatial variation in slope and aspect is therefore a key determinant of vegetation pattern, species distribution and ecosystem processes in many environments. Slope and aspect angle may vary considerably over distances of a few metres, and fine-scale species’ distribution patterns frequently follow these topographic patterns. The availability of suitable microclimate at such scales may be critical for the response of species distributions to climatic change at much larger spatial scales. However, quantifying the relevant microclimatic gradients is not straightforward, as the potential variation in solar radiation flux under clear-sky conditions is modified by local and regional variations in cloud cover, and interacts with long-wave radiation exchange, local meteorology and surface characteristics. We tested simple models of near-surface temperature and potential evapotranspiration driven by meteorological data with the incoming solar radiation flux adjusted for topography against measurements of temperature and soil moisture at two chalk grassland field sites in contrasting regional climates of the United Kingdom. We then estimated the cumulative distribution function of three key ecological variables (monthly temperature sums above 5 and 30 °C, plus potential evapotranspiration) across areas of complex topography at each site using two separate approaches: a spatially explicit and a spatially implicit method. The spatially explicit method uses digital elevation models of the sites to calculate the solar radiation at each grid cell and hence determines the spatial distribution of environmental variables. The second, less computationally intensive, method uses estimated statistical distributions of slope and aspect within the field sites to calculate the proportion of the surface area of each site predicted to exceed a given threshold of temperature sum or potential evapotranspiration. The spatially implicit model reproduces the range of the explicit model reasonably well but is limited by the parameterisation of slope and aspect, underlining the importance of variation in topography in determining the microclimatic conditions of a site.