Impact of clouds and solar radiation on downwelling longwave radiation in Gothenburg, Sweden

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2 UNIVERSITY OF GOTHENBURG Department of Earth Sciences Geovetarcentrum/Earth Science Centre Impact of clouds and solar radiation on downwelling longwave radiation in Gothenburg, Sweden Bengt Myrberg ISSN B896 Bachelor of Science thesis Göteborg 2015 Mailing address Address Telephone Telefax Geovetarcentrum Geovetarcentrum Geovetarcentrum Göteborg University S Göteborg Guldhedsgatan 5A S Göteborg SWEDEN

3 Abstract Atmospheric conditions influence the amounts of downwelling longwave radiation, which is the least studied of all radiation flux components at the Earth s surface. Correctly representing cloudiness and the longwave radiation being emitted by clouds is still a challenge. Clouds are a constituent factor in altering the surface radiation budget, which has great potential impact on the whole Earth- Atmosphere system. The ability to accurately calculate the surface radiation budget is as important as ever. The present study, based on fish-eye photography of the sky in Gothenburg, Sweden over the course of the month of April 2015, attempts to answer what roles cloudiness and clearness might have for downwelling longwave radiation fluxes. 76 images of the sky are selected for calulations of cloud ratios. Measurements of longwave radiation are taken from the top of an adjacent building and a correlation test run with cloud ratios gives a correlation of The longwave dataset is adjusted with a clear-sky formula for bias reduction. Testing cloud ratio versus a clearness index, a ratio of diffuse and global shortwave radiation, gives a similar result in Clear-sky adjusted longwave radiation values are found to be better correlated with cloud ratio during instances of high clouds than low clouds. The clear-sky formula is evaluated as functioning best during instances of small downwelling longwave fluxes, low cloud ratio and high clouds. A correlation of 0.74 is found for clearness index and adjusted longwave radiation, indicating that shortwave radiation levels are more influential in changes of downwelling longwave fluxes than cloud ratio is. This stresses the uncertainties involved in measuring longwave radiation without a suntracking device which secures uninterrupted shading of the instrument. However, several sources of error are thoroughly explored, including setup of photo sessions, sampling differences, skewness in image selection, various aspects of data analysis, and pyrgeometer window heating.

4 Table of contents Abstract... Introduction... 1 Background... 1 Radiation... 1 The Earth-Atmosphere system... 3 Emissivity of clear and cloudy skies... 4 Aim of study... 5 Methods and material... 5 Fish-eye camera and data analysis... 5 Pyrgeometer and detection of instrument heating... 8 The Prata formula for clear-sky emissivity... 9 Results... 9 Longwave radiation... 9 Cloud ratio Clearness index Cloud types Pyrgeometer window heating Discussion Sources of error Window heating of pyrgeometer The impact of cloud ratio and solar radiation Conclusions Acknowledgments References... 26

5 Introduction Background The Earth bathes in solar radiation, also called shortwave radiation. This input is causes heating of the planet and its surrounding atmosphere, as this high frequency radiation is transformed into longwave radiation and emitted from the Earth and the sky. Clouds influence incoming longwave radiation levels due to its emissivity being higher than the surrounding sky. Clouds trap outgoing radiation from the Earth and re-emits it, both upwards and out of the atmosphere, and back down towards the ground. The sky itself emits longwave radiation, clouds notwithstanding. In this study, downward longwave radiation from the clouds and the skies over Gothenburg will be explored. Average diurnal April values for both radiation types are displayed in Figure 1, with all solar radiation being shown along its scattered, diffuse component. Measurements of longwave radiation is wrought with problems, including accuracy issues. Instruments, called pyrgeometers, are heated by solar radiation which causes offsets in measured values. But direct measurements of longwave radiation are not always feasible, resulting in a need for estimation, on empirical basis or on basis of radiative transfer theory. Many emissivity formulas, which calculate a major variable in longwave radiation estimations, were proposed in the 1900s (Brunt, 1932; Swinbank, 1963; Aase & Idso, 1978; Hatfield et al., 1983). The formulas were often designed for clear-sky conditions. Eventually, all-sky formulas were also attempted (Crawford & Duchon, 1999; Iziomon et al., 2003), with inclusions of cloud correction techniques (Deardorff, 1978). Downwelling longwave radiation is an important phenomenon for overall energy exchanges between the Earth and the Atmosphere. Its spatial and temporal distribution thus needs to be understood and monitored. But before these issues are presented here, the foundation for all things of relevance in this context needs to be addressed, i.e. radiation itself. Figure 1. Hourly Gothenburg averages for global and diffuse radiation and incoming longwave radiation. The graph is based on data from the first 21 days of April Shortwave radiation has a distinct diurnal pattern. A similar variation is found in longwave radiation, but on a much smaller scale. Radiation The basis for radiation is rapid oscillations of electromagnetic fields, which can be signified as moving waves with the wavelength λ (Oke, 1987). All bodies with a temperature above absolute zero emit radiation. The emittance of energy is formulated in the Stefan-Boltzmann Law as E = σt 4, which states a direct proportionality between emitted radiation and the surface temperature of the emitting object, and is applicable for blackbody radiators. σ is the Stefan-Boltzmann constant (5.67*10-8 Wm -2 K -4 ), and T 4 is the absolute temperature to the power of four. A blackbody emits the maximum amount of radiation per unit of surface area in unit time. For less efficient radiators (grey body radiators), the variable ɛ (0< ɛ<1) for emissivity is added, resulting in ɛσt 4. Emittance is the radiant flux density emitted by a surface, that is, the rate of flow of radiation per unit area. Conversely, irradiance is the radiant flux density incident on a surface (Oke, 1987). 1

6 According to Wien s Displacement Law, an increase in body temperature also results in a higher fraction of shorter wavelengths being emitted. This is illustrated by the difference in radiation emitted by the sun, which has a mean surface temperature of 6000 K, and the Earth which has a mean surface temperature of 288 K. The sun emits shortwave radiation, i.e. radiation with λ between 0.15 and 3 µm, while the Earth s radiation has λ between 3 and 100 µm, often called longwave radiation. The total energy emitted from a blackbody can be illustrated graphically by a Planck curve (a term derived from Planck s Law), in which the spectral distribution of radiation at a particular temperature is shown (Figure 2). Comparing this distribution of the sun and the Earth, the Planck curves are similarly shaped but at different locations on the spectral axis. Also, the amount of energy emitted differs vastly. Figure 2. Spectral distribution and energy emitted from a blackbody with a temperature typical of the Sun (left and lower axes) and the Earth (upper and right axes). From Oke, Bodies which are effective emitters are also effective absorbers of incident radiation, i.e. they neither reflect nor transmit a large portion of this radiation. This is stated in Kirchhoff s Law. The main atmospheric components emitting longwave radiation are clouds, water vapor, CO 2 and O 3 (Sedlar & Hock, 2009). This means that those entities are also good absorbers of longwave radiation. Due to the prevalence of these so-called greenhouse gases, the atmosphere absorbs much of the outgoing longwave radiation, resulting in the greenhouse effect (Figure 3). Figure 3. Global annual mean energy budget for the Earth, March 2000 to May Of the 396 Wm -2 of longwave radiation emanating from the surface, 40 Wm -2 passes through the atmospheric window. There is a downwelling back radiation of 333 Wm -2. From Trenberth et al.,

7 The Earth-Atmosphere system The Earth-Atmosphere (E-A) system is virtually closed to the exchange of mass with the surrounding space, but open to exchanges of energy. The dominant input to the system is the incoming, shortwave solar radiation, amounting to 342 Wm -2 on annual average at the top of the atmosphere (Oke, 1987). To avoid a net gain or loss of energy to the system, the energy has to be balanced. This is illustrated by a radiation budget. The Earth and the atmosphere (including clouds) reflect 28% of the incoming solar beam, the atmosphere absorbs 25% and the Earth s surface absorbs 47%. The radiation absorbed at the surface is transformed into thermal energy and emitted according to E = ɛσt 4. The atmosphere is a good absorber in the longwave band of the spectrum, so most of the upward longwave flux from the Earth is captured by the atmosphere and eventually re-emitted, both upwards and downwards. Overall, nearly as much energy is exiting the E-A system as is entering it. However, within the E-A system there is not this radiative equilibrium. The Earth has a positive net all-wave radiation budget, due to longwave absorption and backradiation from the atmosphere. As for the atmosphere, the budget is instead negative, as these losses of longwave radiation to space and back to the surface exceed any gains of absorbed shortwave and longwave radiation (Oke, 1987). Atmospheric longwave radiation is relevant for knowledge of the global radiation budget (Iziomon et al., 2003). The surface radiation budget is a crucial part of the E-A system and since two thirds of its energy transformation occur near the surface, more data is going to be required (Marty et al., 2002). There is a history of challenges regarding the measurement of longwave radiation, some cost-related (Diak et al., 2000) resulting in a lack of data (Garratt & Prata, 1996; Kessler & Jaeger, 1999). Other issues have had their origin in a lack of data for parameters of relevance to longwave radiation, e.g. information on cloud cover. Ground stations providing direct measurements of longwave radiation are scarce and unevenly distributed (Prata, 1996), and automated weather stations often does not measure it at all (Sedlar & Hock, 2009). Some studies have shown a negative bias in models, i.e. an underestimation of downwelling longwave radiation fluxes (L ) (Garratt & Prata, 1996). Bias would be more easily determined if not for this insufficient ground station coverage. Longwave radiation fluxes at the surface is relevant in connection to warming, e.g. in the case of melting of glaciers, where L is the main source of energy followed by absorbed shortwave radiation and sensible heat flux (Sedlar & Hock, 2009). Surface temperature change itself may be caused by changes in L, so a full explanation of the surface net radiation at a site hinges on the availability of data for longwave radiation (Stanhill & Cohen, 1997). Increased L is detectable before changes in parameters such as temperature and water vapour (Marty et al., 2002). However, due to the aforementioned issues, such parameters are often used as proxies. Most of the downwelling flux, particularly during clear-sky conditions, originates in the lower parts of the atmosphere. By using measurements of air temperature and humidity in this part of the atmosphere, its radiation of longwave fluxes can be estimated. Surface measurements at screen height (1.5-2 meters above the ground) of temperature and vapour pressure are often used for these longwave estimations (Diak et al., 2000; Iziomon et al., 2003). Surface measurements are the basis for empirical models, which are commonly used in the absence of more thorough information on the atmospheric properties on various levels above the ground. Such information regarding the air column, which is necessary for theoretical models, is hard to access due to difficulties in specifying the emissivity (ɛ atm) and the temperature (T atm) for a vertical air column (Crawford and Duchon, 1999). Without vertical profiles for temperature and water vapour, extensive physical models of L and other fluxes are not applicable (Sedlar & Hock, 2009). The reliance on other types of meteorological parameters leads to a limitation in locations where empirical models can be applied (Crawford & Duchon, 1999). 3

8 Emissivity of clear and cloudy skies Atmospheric downwelling longwave radiation at the surface can be described, using the Stefan- Boltzmann Law for a grey body, as L = ɛσt 4, with the units Wm -2. Apart from the constant σ, the constituents of this formula are the variables, emissivity and temperature. The most important factor for atmospheric emissivity is the moisture content of the lower atmosphere (Diak et al., 2000; Raddatz et al., 2013). Since the 1930s, there were several attempts at linking atmospheric longwave emittance to either vapor pressure or temperature at ground level, or both (Brunt, 1932; Swinbank, 1963; Aase & Idso, 1978; Hatfield et al., 1983). Most of these early parameterizations (i.e. simplified dependencies of singular parameters for the sake of modelling), for estimating incoming longwave radiation were adopted only for clear skies and daytime conditions (Crawford & Duchon, 1999). In a comparison of seven different parameterizations of clear-sky emissivity (ɛ cs), Sedlar & Hock (2009) found that parameterizations using vapour pressure performed better than those using air temperature, when testing for correlations between measured and calculated L. Cloudiness is a crucial element in determining longwave radiation, as clouds increase sky emissivity. A clear sky has approximately 0.7 in emissivity and clouds may increase this to close to unity (Sedlar & Hock, 2009). The presence of clouds is thus also an important key in altering the surface radiation budget, as a higher amount of upwelling longwave radiation from the ground is absorbed and reemitted back to the surface. The cloud fraction, temperature of emitting clouds, and the integrated water vapour content participates in determining the size of this longwave flux. During winter time in the Alps, Marty et al. (2002), found increases of up to 40 Wm -2 due to such cloud forcing. Traditionally, cloud cover has been measured manually, with estimations on how many eights of the sky that are cloudy. The last few decades, manual observers have largely been replaced by automated stations and satellite data. There have been reports of resulting breaks in continuity, due to differences in definition of cloud characteristics during the shift to automated stations (Boers et al., 2010). In other cases, the transition led to decidedly lower amounts of cloudiness being reported, all across the year (SMHI, 2014). One possible cause could be that the automated stations only measure straight above the instrument, while a manual observer can observe the whole sky. Among the various attempts to parameterize atmospheric emissivity ɛ, clear-sky (cloudless) conditions were the norm until more recent attempts to incorporate variable sky conditions, e.g. Crawford & Duchon (1999) and Iziomon et al. (2003). In the later part of the 20 th century, a correction for cloudiness was developed in the parameterizations for estimating ɛ (Deardorff, 1978), though it still depended on observations of fractional cloud cover. This model was further developed by use of the observed magnitude of shortwave radiation as a proxy for fractional cloudiness (Crawford & Duchon, 1999). As a recent example, Sedlar and Hock (2009) parameterizes cloud fraction, by making it a function of the ratio of observed downwelling shortwave radiation and modelled top of the atmosphere shortwave radiation. Some attempts have been made to parameterize downwelling irradiance based on cloud types (DIN-VDI, 1999), but this has its limitations due to rarity in such information, as compared to cloud cover fraction (Iziomon et al, 2003). Satellite data can also be used for estimations of downwelling longwave radiation. However, the crucial temperature at the base of clouds cannot be detected with this method (Diak et al., 2000), and as previously noted, the main emittance of longwave radiation takes place closer to the ground and is unrelated to top of the atmosphere fluxes (Garratt & Prata, 1996). Difficulties in using satellite data to determine the surface and top of the atmosphere fluxes have been discussed in Zhang et al. (1995) and Zhang et al. (2004). Overlapping clouds is also an issue which is yet to be fully resolved, in determining the effects of clouds on downwelling longwave radiation (Gupta, 1999). Challenges in projecting changes in cloud cover and the resulting impact on the radiation budget are also evident in 4

9 research on climate change, in which the longer perspectives are at the helm (Marty & Philipona, 2000). The World Meteorological Organization has deemed the continued observation of cloudiness as one of the priorities for tracking changes in the climate (WMO, 2007). Distinct definitions of clear-sky and cloudy-sky situations are important for climate research, e.g. in determining the impact of cloud forcing. The first climate model runs are often done with clear-sky data, as different atmospheric parameters are more easily compared for correlations using this data (Marty et al., 2002). A clear-sky index, using atmospheric longwave radiation together with air temperature and humidity measurements, is proposed by Marty & Philipona (2000) and used in Marty et al. (2002). Cloud forcing is then calculated by subtracting clear-sky (conditions with no clouds) from all-sky radiation (all atmospheric conditions at a station). Sedlar & Hock (2009) uses the formula L = ɛ csfσt 4, where ɛ cs indicate clear-sky emissivity and F is the cloud factor (always >1). Aim of study The purpose of this thesis is to investigate causes for variations in downwelling longwave radiation in Gothenburg, as measured by instruments at the top of Geovetarcentrum (GVC). Two possible causes for fluctuations will be considered: on the one hand, shortwave induced heating of the instrument at GVC and, on the other hand, additions of longwave radiation due to the presence of clouds. Among the tools aiding the outcome of this attempt will be a correlation test between observed cloud ratio in images taken close to GVC, and the difference between observed downwelling longwave radiation from the GVC pyrgeometer and values calculated with a formula for clear-sky emissivity. Also, a clearness index based on diffuse and global shortwave radiation will be utilized. Methods and material Fish-eye camera and data analysis To capture the cloud fraction of the sky, a Nikon Coolpix 4500 camera was mounted with a Nikon FC- E8 Fisheye Converter. Photographs were taken during various conditions of cloudiness. In fully overcast situations, there is no direct beam solar radiation heating the window of the pyrgeometer, and for clear skies a clear-sky index has been used for calculation of downwelling longwave fluxes. First day of photography was April 2, 2015, the final day of these original sessions was April 28, In total, nine days were chosen and an average of 12 photos were taken on each of these days. During photo sessions, an image was taken every ten minutes at a fixed spot and pointing to the north, at a height of 1.8 meters above the ground. The location was the tram station Wavrinskys plats in Guldheden, Gothenburg, located at 63 meters above sea level. For some days there were unbroken sequences of images, in other cases two different sessions were undertaken the same day. The amount, distribution and type of clouds varied between photo shoots, from almost clear skies to nearly overcast conditions; from conditions with chiefly low Cumulus or Stratocumulus clouds, to situations with high Cirrus clouds and contrails across the sky. In some images there is direct sunlight, in other images the sun is wholly or partially clouded. Images were adjusted with the image viewer software IrfanView, to ensure the fish-eye motif was clearly centered in the images. They were then transferred to MATLAB, version R2014b, and attributed with the 8-bit unsigned integer (uint8) numeric class (Figure 4a). Thus, images were converted into matrices representing the red, green and blue spectral bands. Each cell in these matrices was thereby assigned a number between 0 and 255, going from dark to light (Figure 4b). The final outcome of the image analysis was to reach an estimation of cloud ratio, i.e. a ratio between cloudy areas and blue sky areas. In order to reach that outcome, it was important not only to distinguish clouds from the sky but also from other elements in the image, including the sun and the surrounding areas. Different approaches were taken to address each of these issues. As for 5

10 differentiating the sky from the clouds, pixel-for-pixel comparisons were made between the blue and the red matrices, as the blue sky tend to be much more differentiated in this regard. The resulting matrix, based on this differential and illustrated in Figure 5a, shows a positive difference of units for the sky and a range of +10 to -10 units for clouds. The differential for the sun is zero, as the sun disc has maximum pixel values for all three colours. Pixels with low values in either blue or red were exempt and valued as N-a-N. Some parts of the surrounding area, whose values elude this criteria, reach as low as the -50s. Figure 5b shows a logical matrix, extracted from the previous one, in which all excluded pixels have been separated as a single category, with all other pixels collected in another. Figure 4. An image taken with fish-eye objective at Wavrinskys plats in Gothenburg, adjusted with IrfanView, and imported to MATLAB (4a). The image consists of three matrices, one for the colour red, one for green, and one for blue, each containing over 4 million pixels. Prominent onsite objects include the sun, the sky, clouds, houses, trees, and street lamps. The large building at the bottom of the image is located to the north. Figure 4b is a red colour matrix. The sun and some clouds have the highest values, while some parts of the sky reach values as low as 60. All values below 50 have been excluded from further analysis, including pixels for the frame and for some of the surrounding ground areas. Axis numbers represent number of pixel rows and pixel columns. Figure 5. The ratio between blue and red colours in the imported photo is shown in 5a. The biggest positive ratio belongs to the sky, while parts of the surroundings have a large negative ratio. Most of the sun lacks this colour difference, and it is mostly small in cloudy parts of the sky. Dark blue elements are excluded from calculation of cloud ratio. These excluded pixels are highlighted (in yellow) in Figure 5b, where pixels are being valued as either 1 (non-sky) or 0 (sky), in a logical matrix extracted from the one in 5a. The new logical matrix contains only two types of value, distinguishing the ground from the sky. Yet another logical matrix was created from Figure 5a, with the purpose of separating the blue sky from the clouds. A close-up of the rendering of this new matrix is shown in Figure 6, along with a close-up of the original photography, to illustrate the issue of terrestrial elements being interpreted as skies or clouds. Some of these objects persisted throughout the process, but most were excluded. Subtracting 6

11 the matrix in Figure 5b from 5a resulted in the image in Figure 7a. Here, there are three separate categories: sky, clouds, and surroundings. However, the issues apparent in Figure 5b and Figure 6 are still not solved. To address most of this problem, a mask was constructed from parts of code from the radiation model SOLWEIG (Lindberg et al., 2008). This allowed for the selection of outer limit to the working area of the images, executed with a cursor marking three radius points. The resulting mask, which would be used on all 76 images, ended up circumventing almost 1.6 million pixels, or 71% of the original fish-eye section of images. Figure 6. Close-up of the bottom part of the original image (6a), and the corresponding section in the logical matrix (6b). Yellow colour signify cloud, blue non-cloud. Areas of the terrestrial surroundings, eg. light colour advertisement boards and windows in buildings, are still interpreted as clouds at this stage of the process and need to be masked out. The masked image can be seen in Figure 7b. For each image, the mask determined whether constituent pixels breached a set limit. Pixels outside of this preset radius were discarded from further analysis. As a result, most of the surroundings in images were excluded from calculation of cloud ratio. But even with this, some non-sky features were still within the radius of the mask and treated as either clouds or sky. Then again, some parts of the sky were excluded from being outside of the mask radius. The influence of those features on cloud ratio can be estimated to be at most 1%. Figure 7a. To the left, an image of a logical matrix giving basis for cloud ratio for the original picture in Figure 4a. Dark blue pixels are excluded from the sum of sky and cloud pixels. Notice how some surrounding objects are still falsely treated as either sky (turquoise) or clouds (yellow). Figure 7b. The hemispheric part in Figure 7a being masked to 71% of its original extension, excluding much of the surrounding terrestrial area. The outer circle was added for clarification. The sun has been masked out as well and given a value of its own. From this new matrix, cloud ratio can be calculated. Sun pixels were distinguished from non-sun pixels with a similar masking method. Due to the sun s shifting position and appearance throughout the image set, masking was done individually for each image. Sun pixels were given an index of their own and excluded from calculation. The reasons for this, 7

12 as well as problems associated with it, will be elaborated on in the discussion section. Figure 7b expresses the final step in the process, in which cloud ratio is determined. Cloud ratio was calculated by division of the amount of cloud pixels with all mask pixels, with the exception of sun pixels and excluded surrounding areas which were subtracted from the mask. For images with no sun, cloud pixels were simply divided by all mask pixels minus surrounding areas. For the image chosen as an example in this walkthrough, cloud ratio ended up being Images were also analysed manually for the purpose of calculating correlations for specific cloud conditions. A distinction was drawn between high and low clouds, roughly covering various Cirrus genera and Cumulus genera, respectively. The presence of midlevel clouds (Alto genera) was treated as high clouds. For most of the sampling days, there was a clear dominance of either category of clouds, but on some occasions both types (including combinations of Cumulus and Alto) co-existed. For those images a main cloud type was simply determined by eye test. Pyrgeometer and detection of instrument heating A Kipp & Zonen CGR3 pyrgeometer is mounted among other instruments at the roof of GVC in Gothenburg, at 75 meters above sea level. This pyrgeometer is measuring downwelling longwave radiation (Figure 8). The instrument has a 10 second sampling rate and is connected to a Campbell Scientific CR1000 logger, which collects 10 minute averages. The same applies for the pyranometer at the roof, of Delta-T SPN1 model, which measures incoming shortwave radiation (Delta-T Devices, 2015). Radiation values taken 5 minutes after photo occasions were used, as these values are averages for the whole previous 10 minutes and each photo was thus taken squarely within the sampling period. Figure 8. The CGR3 net radiometer from Kipp & Zonen, which is used at the roof of Geovetarcentrum in Gothenburg for measurements of downwelling longwave radiation (Kipp & Zonen, 2003). The dark silicon window gets heated by solar radiation, which can cause an offset in longwave radiation measurements of up to 15 Wm -2. The CGR3 has a silicon window with a 150 o field of view, which has been calibrated outdoors with a similar device with a 180 o field of view, making the more limited CGR3 model representative for this range. A filter inside the window blocks all solar radiation. Window heating is a major source of error for pyrgeometer measurements. The CGR3 conducts most of the solar radiation, but a smaller amount still affects the instrument. Absorption of shortwave radiation with wavelengths below 1.1 µm, results in heating of the window and radiative or convective heat transfer to the sensor. This leads to the thermopile registering higher amounts of longwave radiation than is present in the surrounding atmosphere. Ventilation is often insufficient to eliminate the effect, so corrective calculations must be made (Kipp & Zonen, 2003). Under clear skies, a moving shading device called a sun tracker is needed to avoid a window heating offset which can be as high as 15 Wm -2 (Kipp & Zonen, 2003). The added effect on recorded longwave radiation can be inferred by a simple test, performed during a clear day. The tester first takes position 8

13 close to the instrument without shading it, for a certain amount of time. In this first step, the pyrgeometer starts taking up the body heat of the tester, adjusting the overall amount of longwave radiation recorded. Once the new level is reached, the pyrgeometer should be shaded for the amount of time needed for noticeable effect. This can be done with the body or a suitable item for a few sampling cycles, to differentiate the effect of solar radiation on the instrument from longwave fluxes from the sky and then body. As the pyrgeometer at GVC lacks a moving shading device, it was relevant to conduct a test of this kind on a clear-sky day. The Prata formula for clear-sky emissivity L -data for sampling occasions were gathered from the GVC pyrgeometer. However, images were only taken during more or less cloudy conditions, though a clear sky also emits incoming longwave radiation. An historical summary of attempts to calculate clear-sky emissivity was given in the introduction. As mentioned earlier, clear-sky emissivity is about 0.7 and thus results in a drop of L to as little as 70%, in accordance with L = ɛσt 4 0. For this assignment, a formula developed by Prata (1996) was used to calculate longwave fluxes during clear-sky conditions, as compared to the conditions prevalent during photography. Prata (1996) compares previous formulations of downwelling longwave radiation from clear skies, and introduces a new formula. Prata does not propose a formula for cloudysky irradiation, only for clear skies. Most of the formulas tested in Prata (1996) are empirical, i.e. based on screen-level temperature and, in some cases, screen level vapour pressure, which is derived from dew-point measurements. The Prata formula for clear-sky emissivity: This formula, which can be inserted into Stefan-Boltzmann s Law so that L can be gathered from ɛσt 4, contains a number of variables, including screen level temperature T 0 and vapour pressure e 0. M w is the molecular weight of water vapour, R is the universal gas constant, and k is water vapour scale height. ψ expresses the ratio between the molecular weights of water vapour and dry air, times the average ratio of vapour pressure and air pressure. Data for temperature and relative humidity, on which longwave radiation depends, was gathered from Femman station at the city center (Göteborgs stad, 2015). This station is located at 35 meters above sea level, and approximately 2.3 km from GVC in Guldheden. Data from this station solved the problem created by some randomly missing GVC April data for various meteorological parameters, including temperature. Emissivity was calculated and inserted into the Stefan-Boltzmann Law, resulting in clear-sky values for downwelling longwave radiation. The difference between observed longwave data from GVC and the calculated clear-sky longwave data was then run in a correlation test with observed cloud ratio as the independent variable. The outcome of this test would be a testament to the amount of influence that clouds exert on longwave radiation fluxes in Gothenburg. Results Longwave radiation The 76 occurrences of measured longwave data (L obs) ranged from to Wm -2, with a median of Longwave data calculated with Femman temperature and humidity (L cs) generated a corresponding series ranging from to Wm -2 and a median of (Figure 9). The Prata formula clear-sky L is related to the observed GVC L in a way reminiscent of the clear-sky index approach discussed in Marty & Philipona (2000) and Marty et al. (2002). But Marty et al. (2002) breaks 9

14 out the emissivity from measured L for direct comparison with calculated clear-sky emissivity, to create a clear-sky index from the ratio of these emissivities, whereas here L is calculated from clearsky emissivity and subtracted from observed L. Data corresponding with all 76 photo occasions resulted in 13 instances of positive difference and 63 cases of negative difference (Figure 10). The largest discrepancies were and Wm -2, respectively. The large negative numbers will be addressed later, in the discussion section. There were relatively few values in-between those extremes. For nearly all high values (>270 Wm -2 ) of calculated L, there were negative differentials. Figure 9. Cumulative distribution function plot of downwelling longwave radiation, with measured values in yellow (L obs) and calculated values in green (L cs). Data taken from the CGR3 pyrgeometer at GVC includes both higher and lower values than data calculated with clear-sky formula. However, over 90% is below calculated values, often by a rather large margin. The median is and Wm -2, respectively. It is notable that the lowest calculated value equals the median value in the GVC series. Lobs -Lcs (Wm-2) Lobs-Lcs Lobs Lcs Day of photography (April) Wm-2 Figure 10. Distribution of the 76 samples of observed and calculated L and difference in Wm -2 between those two variables, displayed according to sampling day in the month of April. 13 instances show a positive difference, 63 are being negative. Most of the calculated values are in the realm of the very highest observed values of L. Placed directly against each other, calculated clear-sky L and measured L would not be expected to be highly correlated, as the clear-sky formula is geared toward cloudless conditions. Indeed, the correlation of these variables for the 76 samples is virtually non-existent (R 2 = 0.04). Based on the fact that cloudy skies increase emissivity, as introduced earlier, and thus also L, an exclusion of all high GVC values from the dataset would likely generate a better correlation. Removing 19 samples with a value over 265 Wm -2 from the correlation test, resulted in a strong increase of correlation (R 2 = 0.52). 10

15 Lgvc-Lcs (Wm-2) In other words, the Prata formula fits the GVC data better for relatively clear conditions, as could be expected from a clear-sky formula for emissivity. Cloud ratio Cloud ratios, which were calculated from all 76 images, ranged in value from 0.05 to 1.00 with a median of There were 63 instances of a cloud ratio below 0.50 (Figure 11). This was partly due to the weather conditions during April, but also because 31 images were left out of the process of image analysis at an early stage due to inadequate quality. Many of those images conveyed more cloudiness. Figure 11. Cumulative distribution function plot for calculated cloud ratio, for the month of April (Figure 11a). Figure 11b displays daily distribution of cloud ratio for days of photo shoots. Only in 13 of the 76 instances does the ratio exceed Figure 12 is a close-up of the last sampling day, when cloud ratio values were stable and low throughout the session. Plotted along the index showing difference in L during all-sky conditions, there is a clear concordance with cloud ratio. It is notable how low the clear-sky adjusted L -values are indexed during these hours. This will be problematized in the discussion section ,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 Cloud ratio Figure 12. Data from the final day of photography, when 18 pictures were taken in sequence during the afternoon. Cloud ratio (dotted line) showed little variation during these hours, as did the difference in observed and calculated L (bars). This relation reveals consequence in data produced through the Prata formula. But the large L discrepancy suggests a bias in the formula, as low cloud ratio should generate an equally homogenuous but much smaller difference in L. Some images with an apparently cloudy sky scored relatively low values, eg One common factor seemed to be which type of clouds were involved. High ice clouds (Cirrus), did not generate as high a ratio as did lower Cumulus clouds due to their more transparent features, as observed from the ground. This will be further analysed in the discussion part. As for the distinction in observed and calculated L, positive values were typically associated with cloudy conditions in corresponding images, while negative index values mostly but not always occurred during clearer skies (Figure 13). 11

16 Figure 13. Examples of positive and negative difference in L obs- L cs. 13a: image taken April 2, at Difference: Wm b: image taken April 4, at Difference: Wm -2. Figures 13c and 13d illustrate the respective cloud ratios, of 0.80 and These are among the clear-cut examples. More divergent cases will be explored in the discussion section. Plotting cloud ratio as the independent variable against the L index shown in Figure 10, resulted in an R 2 correlation of 0.36 (Figure 14). Primarily, most of the values from the first day of shooting, April 2, led to decreased correlation. On this day, L was positively indexed despite cloud ratio not being very high. However, as the sky got cloudier during the day, with L obs-l cs persistingly being positive, there were additions to the positive correlation in Figure 14. For the most part, negative differences were connected to low cloud ratio in the data. None of the occurrences with a cloud ratio over 0.50, yielded large negative difference in L obs-l cs L obs -L cs (Wm -2 ) R² = 0, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Cloud ratio Figure 14. Difference between observed (GVC) and calculated clear-sky L (with Prata formula), as a function of calculated cloud ratio. Large negative L -indexing coincides with low cloud amounts, indicating few clouds reduce the excess L. All instances of high cloud ratio (>0.50) have a higher difference in L than does over 85% of low cloud ratio values. All of the least correlated samples (top left) came from the same day, April 2. 12

17 Shortwave Radiation (Wm-2) Clearness index Solar radiation has two components, direct beam radiation and diffuse radiation. Together, they constitute global radiation. Direct beam radiation reaches the Earth s surface unscathed, while parts of the solar beam which have been scattered across the sky is labelled diffuse radiation. The ratio between these two variables can be classified as a clearness index. Figure 15 displays the relation between diffuse and global radiation for all sampling days, in Wm Day (April) diffuse global sdiff/sglob 1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 Sdiff/Sglob Figure 15. Global and diffuse shortwave radiation as well as clearness index for all 76 samples. Averages are and Wm -2, for global and diffuse radiation. Median values are and 83.5 Wm -2. The gradual drop in global SW during one single day, eg. the 28 th, is due to solar angle reduction. More drastic drops may be caused by breaks in photo sessions. As for clearness index, note how the largest numbers corresponds with very low and equal numbers in shortwave diffuse and global radiation. Overall, diffuse radiation is mostly small in relation to global radiation and it is often in the range of Wm -2. The average value is 126.1, and the median is a much lower 83.5, due to many instances of low diffuse radiation. For global radiation, there is naturally a larger span of values, with many exceeding 500 Wm -2. Average global radiation among those samples is and the median value is Wm -2. Typical measured solar radiation values are Wm -2 for clear and sunny conditions, Wm -2 for sunny and partly cloudy, and Wm -2 for fully clouded conditions (Kipp & Zonen, 2014). Global radiation levels depend on the sun s position in the sky, while diffuse radiation is always lower and follows suit. A given amount and type of clouds in the sky may give approximately the same clearness index at noon and four hours later, but the actual amount of Wm -2 will be lower for both global radiation and its constituent, diffuse radiation. Global radiation levels as measured on the ground depend on cloud ratio, as clouds reflect incoming shortwave radiation. As incoming longwave radiation also depends on cloud ratio, it is relevant to compare both of these variables. Global radiation alone will not correctly describe these relations. The diffuse shortwave radiation, whose scattered character is a testament to effects of the clouds and the rest of the atmosphere, is more suitable in its relation to global radiation. During cloudy conditions, it would be expected that the total amount of solar radiation decreases due to absorption and reflection at the top of the clouds, and also that the amount of diffuse radiation increases. A lower index means a clearer sky, whereas cloudy conditions reduce global radiation and increase diffuse radiation, giving higher index values. There is less ambiguity with this variable than the longwave radiation index. A rapid increase in clearness index suggests that the pyranometer has been shaded by clouds. Clouds 13

18 Sdiff/Sglob Lobs-Lcs (Wm-2) which are not in the way of solar irradiation are less relevant. Clear-sky adjusted longwave radiation, expressed as L obs-l cs and previously shown in Figure 10, can be plotted against this clearness index based on shortwave radiation. The relation is examined in Figure ,0 40,0 R² = 0,74 20,0 0,0-20,0-40,0-60,0 0 0,2 0,4 0,6 0,8 1 Sdiff/Sglob Figure 16. Clear-sky adjusted L as a function of clearness index. Correlation is high (R 2 = 0.74), with most points following a rather straight line. This is particularly true for instances of relatively clear skies with low observed values of L, but it is also evident that a low difference in Sdiff/Sglob is followed by an advantage for observed L. The two indexes in Figure 16 turned out to be closely correlated (R 2 = 0.74). This was particularly true for instances of highly negative relation between observed and calculated L, i.e. during relatively clear skies, but the correlation applied to most of the other samples as well. As mentioned earlier, cloud ratio has naturally a role in how much shortwave radiation reaches the ground. Figure 17 illustrates a positive correlation (R 2 = 0.34) between shortwave radiation and cloud ratio, though it is decidedly weaker than the one for L. 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 R² = 0, ,2 0,4 0,6 0,8 1 Cloud ratio Figure 17. Clearness index as a function of cloud ratio. With an R 2 correlation of 0.34, there is a positive correlation between clearness index and cloud ratio, but it is no stronger than the one between cloud ratio and L obs,-l cs. Only for very low percentages of diffuse radiation and low cloud amount is there an unequivocal correlation. 14

19 Cloud types As was mentioned in the introduction, different approaches have been taken by researchers to parameterize L, including basing it on cloud ratio and cloud types. One important distinction between these choices is the availability of data, which is scarce for cloud types. In this study, cloud ratio has been the prime tool for gathering information on the behaviour of longwave fluxes, but some attempts will also be made at distinguishing patterns related to cloud types. Judging by images which have undergone data analysis, low lying clouds (eg. Cumulus, Stratus, Stratocumulus) have generally been better recognized as cloud pixels, mainly due to lower transparency than higher clouds (eg. Cirrus). With this modification in mind, apparently high cloud ratio to an observer is generally accompanied by higher longwave radiation levels. Sedlar & Hock (2009) addresses the bias in these kinds of sky observations, with different cloud types resulting in different cloud ratios and also regarding efficiency of emittance being dependent on cloud phase and optical depth. Ranking the images according to L gives a somewhat inconclusive answer. Indeed, the top seven images are all taken during Cu conditions, but among the following eight, six are taken under Ci skies. As for the bottom of the dataset, almost all images comes from two days, the second day (April 4) and the final day of shooting (April 28). On April 4, there are Cu and Sc clouds, while on April 28 there is just the occasional Sc cloud along with bands of Ci or at least Alto genera (mid-level clouds). This mix indicates that cloud ratio is more important than which type of clouds appeared. If all images in the photo series are ranked according to cloud ratio, some notable discrepancies are found. The image with the seventh highest cloud ratio out of all 76, at 0.77, only has the 33 rd highest L, at Wm -2. And, incidentally, the seventh highest ranked image in L, at Wm -2, is ranked as number 38 for cloud ratio at In both of these somewhat contradictory cases, there were Cu-type clouds (Cu, Sc) (Figure 18). Figure 18. Two images with similar cloud type conditions, but opposite rank in L and cloud ratio, respectively. 18a rendered a cloud ratio of 0.77, the 7th highest of all images, but its L was only the 33rd in order. 18b exhibits the 7th highest L, but a cloud ratio of 0.27 ranked it as a middle-of-thepack 38th out of 76 images. Revisiting the relation examined in Figure 14 can also provide some information. This time, the dataset is divided into Cu/Sc and Ci genera, respectively, which are analysed separately. The result was decent correlations for both limited datasets, but it was stronger for high clouds (Figure 19). Skies with predominantly Ci and Alto genera, showed a correlation of There were a few slightly deviating samples which were taken during the same day, the 20 th of April, when the high clouds became exceedingly covered by mid-level Alto type clouds. This underlines that any presence of lower clouds than Ci reduces the correlation. 15

20 Figure 19. The relation between adjusted L and cloud ratio, for lower (Cu, Sc) (19a) and higher (Alto, Ci) (19b) atmospheric cloud types. R 2 correlation for low clouds is 0.44 and for high clouds This means that observed L adjusted with clear-sky formula gives a relatively strong overall correlation to cloud ratio, particularly for high clouds. Note the difference in scale for the L axis in the two images. Pyrgeometer window heating The average downwelling longwave radiation observed at GVC, during the 76 sampling instances in April, was Wm -2. The maximum window heating offset of the Kipp & Zonen CGR3 pyrgeometer, which is used at the roof at GVC, is 15 Wm -2, or 6% of mean measured L. For comparison, the more advanced K&Z CGR4, which has a spheric window dome, has a window heating offset of max 4 Wm -2. This precondition called for a pyrgeometer test of the CGR3 for window heating offset. A few attempts were made, however methodological missteps made the results flawed. Correction for body heat notwithstanding, the sensor actually recorded higher L during sequential shading. Weather conditions were unchanged before and during tests, so the only explanation for this increase was an influence from the shading device on the sensor. A previous attempt had revealed an effect of body heat on the instrument of about 12 Wm -2, but the solar effects were not possible to determine due to an overall incoherent methodology. Discussion Sources of error Formula bias Results presented here were conditioned on a number of sources of error and issues of methodology. Judging by the results from calculations with the Prata emissivity formula, there is a noticeable and consequent difference in relation to observed Gothenburg data. For relatively clear conditions, calculated values often exceed observed values by more than 30 Wm -2, as was shown in Figure 12. For some occurences of relative cloudiness, observed values are just barely higher, which can also be argued to depend on this bias. A correct description of L for clear skies would come close to observed numbers in relatively clear conditions, while the difference for cloudier conditions would be unanimous. However, as similar conditions - eg. photos taken during days with few shifts in cloudiness results in a predictable shift, the issue was more likely to be a constant bias than some other problem with the formula. There was a methodological lapse involved here. The opportunity to photograph fully clear skies, pick out the corresponding observed data and compare this to the data calculated with Prata, was never taken. This would have given a clearer view of the purported bias. Suspicion of bias grew stronger, in light of a report from Jonsson et al. (2006) of recorded overestimation of emissivity by 0.04 in the Prata formula for urban daytime values. Nighttime values instead showed an underestimation by The Prata formula was therefore run with this correction 16

21 Wm-2 of emissivity for temperature and humidity data from Femman station. The result was a unison drop of calculated L -values by Wm -2 (Figure 20) Lcs esky-0.04 Lcs Δ 17,0 Figure 20. Prata s 16,5 emissivity formula run with met data 16,0 from Femman and 15,5 with an emissivity corrected accordingly 15,0 with Jonsson et al. 14,5 (2006). The result is a drop in L by 14.1 to 14, Wm-2, which is 13,5 a reflection of the original overestimation 13,0 in the emissivity formula. Sampling day (April) ΔWm-2 This decrease in calculated L would affect some of the reported results, but only in the slightest as the changes involve all values to approximately the same degree. The overall uplift of L obs-l cs led to 22 values now being positive compared to 13 without the adjusted emissivity. Also, the highest positive difference is now well over 50 Wm -2, while the highest negative difference stays just above -30 Wm -2. Various other plotted relations have unchanged correlations. With the corrected L -relation, L obs-l cs yielded only a slight improvement in correlation with cloud ratio, to 0.37, and to clearness index there was no difference. Prata (1996) assures that the formula is working well in atmospheres of various climate zones, with the exception of polar regions. The Jonsson study was conducted in Africa, though it also refers to similar results being found in Spain and the U.S. The main explanation for the prevalence of this phenomenon of estimation bias, is found in differences in data used from direct measurements and those parameterized from meteorological variables, eg. temperature. In the first case, data is a reflection of the whole vertical air column. In the latter case, only surface data is used. This data will be susceptible to the effects of near-surface warming and cooling. The well-known strong diurnal pattern at the surface leads to formula overestimations for daytime data and understimations for nighttime data (Jonsson et al., 2006). The bias problem may additionally be related to the limited sampling in the present study. Prata (1996) explicitly declares that the formula performs worse against individual measurements as compared to statistical data. Data sources There is also the issue of using meteorological data from another site than that of the observations. This also affected the results from the Prata formula. Incoming longwave radiation data from the Geovetarcentrum roof had turned out to be fine, but there was temperature data missing for the month of April. The missing data was unevenly distributed throughout the month and often only involved one or a few consecutive missing observations, but it would still affect six of the 76 sampling occasions. The decision was made to find data elsewhere for the calculation of clear-sky emissivity, as has been described in the methods section. This could be considered as problematic from a methodological standpoint, though it was somewhat done out of necessity. 17

22 The choice of Femman station worked out, but it led to difficulties from temperature discrepancies. Femman station is not only located 2.3 kilometers from GVC, but the topography of the two areas differs. Instruments are mounted at 35 and 75 meters, respectively, resulting in generally cooler air around the GVC instrument. Consequentially, when using the formula with temperature and humidity data from GVC instead of Femman, there were often drops in calculated clear-sky L of 1-5 Wm -2 but when temperature margins widened between the sites, there could be as much of a difference as 15 Wm -2. All of this strengthens the observed values visavi calculated ones, so the relation between L obs- L cs gets an overall positive increase. This increase can then be added to the one caused by emissivity correction due to diurnal temperature variations. All in all, Table 1 illustrates, with a limited sample how these changes affect L cs. These issues are of relevance because they show the importance of site and formula selection. They are however less relevant when it comes to the main results of this thesis, as few correlations between variables would undergo significant changes with the insertion of adjusted GVC data as opposed to unadjusted Femman data. L obs GVC L cs (Femman data) L cs (Femman data, adjusted) L cs (GVC data) L cs (GVC data, adjusted) Sample 1 287,6 260,1 245,8 257,7 243,6 Sample 2 293,2 260,2 245,9 257,4 243,4 Sample 3 302,2 261,8 247,4 254,1 240,2 Sample 4 300,4 261,5 247,1 249,3 235,7 Sample 5 294,6 264,4 249,9 248,1 234,6 Sample 6 223,6 255,3 241,1 250,7 236,7 Sample 7 222,4 254,3 240,2 250,3 236,3 Sample 8 221,7 254,3 240,2 249,9 235,8 Sample 9 220,8 253,3 239,1 249,6 235,5 Sample10 219,6 252,7 238,6 249,3 235,2 Table 1. Five samples from April 2 followed by five samples from April 4, here used to distinguish differences in L when using meteorological data from GVC and Femman, respectively, and when adjusting emissivity numbers according to Jonsson et al. (2006). The first column shows observed L, from which clear-sky values are to be subtracted. L calculated with GVC data is lower than that using Femman data, and emissivity-adjusted values are even lower, resulting in a total difference among clear-sky values in the range of Wm -2. Photography sessions The scheduling of photo sessions could have been better planned. Global shortwave radiation peaks during a few hours, approximately 10 AM to 2 PM during April, resulting in a relatively unchanged clearness index for almost clear weather. Photo sessions could have been excluded to those hours in the day. But only five photos were taken before noon and 45 photos were taken after As for cloud ratio calculation, many challenges arose during its extraction process. Photos were taken every 10 minutes, however they were taken 5 minutes into the 10 minute sampling cycle of the instrument at GVC, of both solar and longwave radiation. The decision was made to take averages of these variables, i.e. the two nearest samples were divided. Especially in the case of shortwave radiation, this meant averaging and sometimes perhaps offsetting some rather drastic differences in the data. A reconsideration, in which succedingly measured data was prefered to beforementioned averages, resulted in new values for L, L obs-l cs, S glob, and so on. For L, changes in individual values were normally within 5 Wm -2 and reaching up to 10 Wm -2 in a few cases. For S glob, a dozen values differentiated by 50 Wm -2 or more with the new extraction process. Correlation dropped slightly for cloud ratio and L (R 2 = 0.32), L and clearness index (R 2 = 0.73), and cloud ratio and clearness index (R 2 = 0.30), as a result of these recalculations of the measured GVC variables. 18

23 The choice of photo shooting site came with its problems too, as a number of irrelevant objects became depicted in the images. The original photography procedure had its faults. There was no use of tripod and no exact adherence to site, height or direction of camera, just ad hoc approximations. The resulting differences in depictions were relatively small but prompted various actions, eg. deleting some images for being tilted northwards and thus becoming decentered and, later in the process during data analysis, the exclusion of pixels associated with unwanted elements. However, some elements could not be discarded this way, due to time or knowledge constraints, but they might have been dealt with more easily if conditions for photography had been more rigorously managed. Image analysis Data analysis demanded some decisions, where neither alternative present was perfect. Due to the topographical variations of the surrounding area, along with a slight northward tilt during some instances of photography, the creation of the circular mask required exclusion of a small part of the southern sky near the horizon for the mask to have the desired effect. Also, hemispheric correction of images was left out due to time constraints. Consequentially, clouds passing by directly overhead would generate a larger cloud ratio than clouds near the horizon. The second masking process, the one concerning the sun, was done individually for the 76 images and presented many challenges (Figure 21). Sun beams enlarged the problematic area of the sky on many images, meaning a radius larger than the sun disc had to be set. This in turn influenced, though to a smaller degree, cloud ratio as all omitted sun pixels were subtracted from the area within the overall mask. If the sky around the sun disc was clear behind the sun beams, this could slightly but undeservedly favour cloud ratio (Figure 22). Then again, there were several cases with the solar beams in the foreground of clouds and clouds over the sun disc. Sometimes, the sun mask was made smaller to compensate for the loss of cloud pixels being omitted, i.e. some sun beams would be counted as clouds instead of actual clouds which were within the solar disc and omitted. In heavily clouded pictures, a solar mask with radius 0 could be set, and sometimes clearly lit up clouds in an otherwise overcast sky would be accepted as well. In other cases, where sun and cloud was difficult to distinguish from each other, symbolically a small sun mask would be set. Many of these cases had a degree of uncertainty, though the effects on cloud ratio were estimated to be in the range of 0.5-1%, at most. There were only 13 instances (17%) in which the difference in L was positive, as was shown in Figure 10. This was partly due to the formula bias described above, but it was also a consequence of the early scrapping of pictures which had been taken with a slight tilt. Thus, a number of relatively cloudy 19 Figure 21. Decision-making in setting sun radius. 21a: standalone sun with sizeable solar beams. 21b: sun with adjacent cloud. 21c and 21d: partially clouded sun. 21e: sun within larger cloud segment, sun radius=0. 21f: no visible sun, sun radius=0. Overall, different things were factored into sun radius setting, eg. homogeneity of cloud cover and distance to clouds. Cloud types in 21c and 21d generate low cloud ratio, so some radius needed to be set as compensation for the overly bright area.

24 situations never underwent further analysis. In some instances, the location of clouds can possibly have skewed the relation between cloud ratio and difference in L. For the first day of photography, cloud ratio was low while L difference was high. The few Cumulus clouds were mainly located in the left part of images (to the West), approximately over GVC and the pyrgeometer sensor. This could possibly differentiate the results from other similar conditions as cloud ratio is concerned. Figure 22. Effects on cloud ratio in choosing solar radius. In 22c, a scenario is pictured with low clouds and a sun without any cloud interference. 22a: a larger radius than the solar disc is set, to compensate for solar beams. 22d: a scenario with high clouds covering the sun. 22b: a small solar radius is set, as some of the area where the sun is positioned might otherwise have been considered as sky. Excluding the sun and the surroundings increases cloud ratio with 1.1% and 0.4%, respectively. If ΔRatio instead is calculated from a point where surroundings are already subtracted from the mask, ΔCloud ratio is even lower, 0.7% and 0.1%. The different correlations for high and low clouds, which was shown in Figure 19, would suggest that the Prata formula results in overall reasonable values of L for subtraction from measured all-sky values, and it is particularly helpful during instances of high clouds, typically during high pressure weather. For the casual observer, high clouds can be apparently more dominant on the sky due to their extension, but their contribution to L at the surface may be smaller and also their structure results in a lower calculated cloud ratio that is in accord with the often lower observed values of L. Sampling differences The use of cloud ratio is based on instantaneous snapshots of the sky, unlike radiation measurements which were averages from a 10-minute cycle. This might have lead to the occasional misleading result, as cloudiness was sometimes duly transformed from one photo to the next. There are a few standout 20

25 examples, eg. during the first day when photos were taken during one hour and 20 minutes and cloud ratio changed from 0.12 to 0.80 as most. The largest 10-minute cloud ratio shift within this photo session was a jump from 0.34 to 0.61, as Sc clouds approached en masse from northwest. Also, on the sixth day, there was a sequence of 40 minutes in which cloud ratio oscillated between 0.28 and This increase actually happened between two subsequent photos, that is, within a ten minute span. Once again, the sky was predominantly filled with Sc clouds. But the third day of photo sessions consisted of a one and a half hour sequence with Sc clouds and a backdrop of high clouds, during which cloud ratio only shifted between 0.33 and 0.43, with a maximum 10-minute shift of 0.34 to The final day of photography, which included almost three hours in sequence, varied between 0.07 and 0.18 with a maximum 10-minute variation of 0.15 to Clouds were mainly of Cirrus genera during these hours. For the whole dataset, shifts of over 0.2 only occurred four times, and merely 13 sequential cloud ratios were larger than 0.1. Normally, a 10-minute difference in cloud ratio was in the range of 0 to 0.1, i.e. below 10%. There is also another aspect which reduces the impact of this error source. If images had been taken in direct temporal parallel with measurements, it could be argued that cloud ratio values must be averaged to better reflect measured values. However, images were taken five minutes into the sampling cycle of radiation measurements. They display what happened in the middle of the sampling cycle of longwave radiation. This could serve as a decent equivalent of the average of the ten minute sampling cycle, for most if not all cases. Considering cloud ratio mostly changed by in a 10-minute span, data correlation should not have been too badly affected by this situation, with the occasional exception mentioned above. In order to better estimate changes in cloud ratio between photographies, an additional photo session was conducted at Wavrinsky s plats on June 16. This time, one image per minute was taken, for a span of 50 minutes (Figure 23). A tripod was used to improve coherence among images. Weather was fair, with few cumulus clouds over the shooting site. A larger cloud bank was present in the East, throughout the session, but it changed little and only took up a few percent worth of cloud ratio. The sun was largely uninhibited by clouds, with the occasional exception. These conditions were relatively typical of those during many of the original photo days. The chosen time of day also reflected the April sessions well, as 26% of all original photos were taken within this time span and 56% during this hour or an adjacent one. Figure 23. A typical sequence of the sky from the additional photo shoot in June. These photos were taken each minute between and Cloud ratio starts at 0.11 and ends at Maximum cloud ratio is reached in the top right image, reaching nearly Average cloud ratio for the sequence is almost This makes for a difference between the final image and the average, of After MATLAB analysis of the new images, cloud ratios were systematized and some graphs created. The snapshot value for cloud ratio was compared with an average value for the whole preceding 10 21