Cloud Detection Method Based on All-Sky Polarization Imaging.

Sky cloud detection has a significant application value in the meteorological field. The existing cloud detection methods mainly rely on the color difference between the sky background and the cloud layer in the sky image and are not reliable due to the variable and irregular characteristics of the cloud layer and different weather conditions. This paper proposes a cloud detection method based on all-sky polarization imaging. The core of the algorithm is the "normalized polarization degree difference index" (NPDDI). Instead of relying on the color difference information, this index identifies the difference between degree of polarization (DoPs) of the cloud sky and the clear sky radiation to achieve cloud recognition. The method is not only fast and straightforward in the algorithm, but also can detect the optical thickness of the cloud layer in a qualitative sense. The experimental results show a good cloud detection performance.

Foraging trip duration of honeybee increases during a poor air quality episode and the increase persists thereafter.

Increased concentration of airborne particulate matter (PM) in the atmosphere alters the degree of polarization of skylight which is used by honeybees for navigation during their foraging trips. However, little has empirically shown whether poor air quality indeed affects foraging performance (foraging trip duration) of honeybee. Here, we show apparent increases in the average duration of honeybee foraging during and after a heavy air pollution event compared with that of the pre-event period. The average foraging duration of honeybees during the event increased by 32 min compared with the pre-event conditions, indicating that 71% more time was spent on foraging. Moreover, the average foraging duration measured after the event did not recover to its pre-event level. We further investigated whether an optical property (Depolarization Ratio, DR) of dominant PM in the atmosphere and level of air pollution (fine PM mass concentration) affect foraging trip duration. The result demonstrates the DR and fine PM mass concentration have significant effects on honeybee foraging trip duration. Foraging trip duration increases with decreasing DR while it increases with increasing fine PM mass concentration. In addition, the effects of fine PM mass concentration are synergistic with overcast skies. Our study implies that poor air quality could pose a new threat to bee foraging.

Success of sky-polarimetric Viking navigation: revealing the chance Viking sailors could reach Greenland from Norway.

According to a famous hypothesis, Viking sailors could navigate along the latitude between Norway and Greenland by means of sky polarization in cloudy weather using a sun compass and sunstone crystals. Using data measured in earlier atmospheric optical and psychophysical experiments, here we determine the success rate of this sky-polarimetric Viking navigation. Simulating 1000 voyages between Norway and Greenland with varying cloudiness at summer solstice and spring equinox, we revealed the chance with which Viking sailors could reach Greenland under the varying weather conditions of a 3-week-long journey as a function of the navigation periodicity Δt if they analysed sky polarization with calcite, cordierite or tourmaline sunstones. Examples of voyage routes are also presented. Our results show that the sky-polarimetric navigation is surprisingly successful on both days of the spring equinox and summer solstice even under cloudy conditions if the navigator determined the north direction periodically at least once in every 3 h, independently of the type of sunstone used for the analysis of sky polarization. This explains why the Vikings could rule the Atlantic Ocean for 300 years and could reach North America without a magnetic compass. Our findings suggest that it is not only the navigation periodicity in itself that is important for higher navigation success rates, but also the distribution of times when the navigation procedure carried out is as symmetrical as possible with respect to the time point of real noon.

Accuracy of the hypothetical sky-polarimetric Viking navigation versus sky conditions: revealing solar elevations and cloudinesses favourable for this navigation method.

According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers. It has frequently been claimed that this method might have been suitable for navigation even in cloudy weather. This hypothesis has been accepted and frequently cited for decades without any experimental support. In this work, we determined the accuracy of this hypothetical sky-polarimetric Viking navigation for 1080 different sky situations characterized by solar elevation θ and cloudiness ρ, the sky polarization patterns of which were measured by full-sky imaging polarimetry. We used the earlier measured uncertainty functions of the navigation steps 1, 2 and 3 for calcite, cordierite and tourmaline sunstone crystals, respectively, and the newly measured uncertainty function of step 4 presented here. As a result, we revealed the meteorological conditions under which Vikings could have used this hypothetical navigation method. We determined the solar elevations at which the navigation uncertainties are minimal at summer solstice and spring equinox for all three sunstone types. On average, calcite sunstone ensures a more accurate sky-polarimetric navigation than tourmaline and cordierite. However, in some special cases (generally at 35° ≤ θ ≤ 40°, 1 okta ≤ ρ ≤ 6 oktas for summer solstice, and at 20° ≤ θ ≤ 25°, 0 okta ≤ ρ ≤ 4 oktas for spring equinox), the use of tourmaline and cordierite results in smaller navigation uncertainties than that of calcite. Generally, under clear or less cloudy skies, the sky-polarimetric navigation is more accurate, but at low solar elevations its accuracy remains relatively large even at high cloudiness. For a given ρ, the absolute value of averaged peak North uncertainties dramatically decreases with increasing θ until the sign (±) change of these uncertainties. For a given θ, this absolute value can either decrease or increase with increasing ρ. The most advantageous sky situations for this navigation method are at summer solstice when the solar elevation and cloudiness are 35° ≤ θ ≤ 40° and 2 oktas ≤ ρ ≤ 3 oktas.

Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions.

If a human looks at the clear blue sky from which light with high enough degree of polarization d originates, an 8-shaped bowtie-like figure, the yellow Haidinger's brush can be perceived, the long axis of which points towards the sun. A band of high d arcs across the sky at 90° from the sun. A person can pick two points on that band, observe the yellow brushes and triangulate the position of the sun based on the orientation of the two observed brushes. This method has been suggested to have been used on the open sea by Viking navigators to determine the position of the invisible sun occluded by cloud or fog. Furthermore, Haidinger's brushes can also be used to locate the sun when it is below the horizon or occluded by objects on the horizon. To determine the position of the sun using the celestial polarization pattern, the d of the portion of the sky used must be greater than the viewer's degree of polarization threshold d* for perception of Haidinger's brushes. We studied under which sky conditions the prerequisite d > d* is satisfied. Using full-sky imaging polarimetry, we measured the d-pattern of skylight in the blue (450 nm) spectral range for 1296 different meteorological conditions with different solar elevation angles θ and per cent cloud cover ρ. From the measured d-patterns of a given sky we determined the proportion P of the sky for which d > d*. We obtained that P is the largest at low solar elevations θ ≈ 0° and under totally or nearly clear skies with cloud coverage ρ = 0%, when the sun's position is already easily determined. If the sun is below the horizon (-5° ≤ θ < 0°) during twilight, P = 76.17 ± 4.18% for [Formula: see text] under clear sky conditions. Consequently, the sky-polarimetric Viking navigation based on Haidinger's brushes is most useful after sunset and prior to sunrise, when the sun is not visible and large sky regions are bright, clear and polarized enough for perception of Haidinger's brushes.

North error estimation based on solar elevation errors in the third step of sky-polarimetric Viking navigation.

The theory of sky-polarimetric Viking navigation has been widely accepted for decades without any information about the accuracy of this method. Previously, we have measured the accuracy of the first and second steps of this navigation method in psychophysical laboratory and planetarium experiments. Now, we have tested the accuracy of the third step in a planetarium experiment, assuming that the first and second steps are errorless. Using the fists of their outstretched arms, 10 test persons had to estimate the elevation angles (measured in numbers of fists and fingers) of black dots (representing the position of the occluded Sun) projected onto the planetarium dome. The test persons performed 2400 elevation estimations, 48% of which were more accurate than ±1°. We selected three test persons with the (i) largest and (ii) smallest elevation errors and (iii) highest standard deviation of the elevation error. From the errors of these three persons, we calculated their error function, from which the North errors (the angles with which they deviated from the geographical North) were determined for summer solstice and spring equinox, two specific dates of the Viking sailing period. The range of possible North errors ΔωN was the lowest and highest at low and high solar elevations, respectively. At high elevations, the maximal ΔωN was 35.6° and 73.7° at summer solstice and 23.8° and 43.9° at spring equinox for the best and worst test person (navigator), respectively. Thus, the best navigator was twice as good as the worst one. At solstice and equinox, high elevations occur the most frequently during the day, thus high North errors could occur more frequently than expected before. According to our findings, the ideal periods for sky-polarimetric Viking navigation are immediately after sunrise and before sunset, because the North errors are the lowest at low solar elevations.

Adjustment errors of sunstones in the first step of sky-polarimetric Viking navigation: studies with dichroic cordierite/ tourmaline and birefringent calcite crystals.

According to an old but still unproven theory, Viking navigators analysed the skylight polarization with dichroic cordierite or tourmaline, or birefringent calcite sunstones in cloudy/foggy weather. Combining these sunstones with their sun-dial, they could determine the position of the occluded sun, from which the geographical northern direction could be guessed. In psychophysical laboratory experiments, we studied the accuracy of the first step of this sky-polarimetric Viking navigation. We measured the adjustment error e of rotatable cordierite, tourmaline and calcite crystals when the task was to determine the direction of polarization of white light as a function of the degree of linear polarization p. From the obtained error functions e(p), the thresholds p* above which the first step can still function (i.e. when the intensity change seen through the rotating analyser can be sensed) were derived. Cordierite is about twice as reliable as tourmaline. Calcite sunstones have smaller adjustment errors if the navigator looks for that orientation of the crystal where the intensity difference between the two spots seen in the crystal is maximal, rather than minimal. For higher p (greater than p crit) of incident light, the adjustment errors of calcite are larger than those of the dichroic cordierite (p crit=20%) and tourmaline (p crit=45%), while for lower p (less than p crit) calcite usually has lower adjustment errors than dichroic sunstones. We showed that real calcite crystals are not as ideal sunstones as it was believed earlier, because they usually contain scratches, impurities and crystal defects which increase considerably their adjustment errors. Thus, cordierite and tourmaline can also be at least as good sunstones as calcite. Using the psychophysical e(p) functions and the patterns of the degree of skylight polarization measured by full-sky imaging polarimetry, we computed how accurately the northern direction can be determined with the use of the Viking sun-dial under 10 different sky conditions at 61° latitude, which was one of the main Viking sailing routes. According to our expermiments, under clear skies, using calcite or cordierite or tourmaline sunstones, Viking sailors could navigate with net orientation errors [Formula: see text]. Under overcast conditions, their net navigation error depends on the sunstone type: [Formula: see text], [Formula: see text] and [Formula: see text].

How could the Viking Sun compass be used with sunstones before and after sunset? Twilight board as a new interpretation of the Uunartoq artefact fragment.

Vikings routinely crossed the North Atlantic without a magnetic compass and left their mark on lands as far away as Greenland, Newfoundland and Baffin Island. Based on an eleventh-century dial fragment artefact, found at Uunartoq in Greenland, it is widely accepted that they sailed along chosen latitudes using primitive Sun compasses. Such instruments were tested on sea and proved to be efficient hand-held navigation tools, but the dimensions and incisions of the Uunartoq find are far from optimal in this role. On the basis of the sagas mentioning sunstones, incompatible hypotheses were formed for Viking solar navigation procedures and primitive skylight polarimetry with dichroic or birefringent crystals. We describe here a previously unconceived method of navigation based on the Uunartoq artefact functioning as a 'twilight board', which is a combination of a horizon board and a Sun compass optimized for use when the Sun is close to the horizon. We deduced an appropriate solar navigation procedure using a twilight board, a shadow-stick and birefringent crystals, which bring together earlier suggested methods in harmony and provide a true skylight compass function. This could have allowed Vikings to navigate around the clock, to use the artefact dial as a Sun compass during long parts of the day and to use skylight polarization patterns in the twilight period. In field tests, we found that true north could be appointed with such a medieval skylight compass with an error of about ±4° when the artificially occluded Sun had elevation angles between +10° and -8° relative to the horizon. Our interpretation allows us to assign exact dates to the gnomonic lines on the artefact and outlines the schedule of the merchant ships that sustained the Viking colony in Greenland a millennium ago.

Celestial orientation with the sun not in view: lizards use a time-compensated sky polarization compass.

The present investigation was aimed at testing whether the lizard sky polarization compass is time compensated. For this purpose, ruin lizards, Podarcis sicula, were both trained and tested for orientation inside a Morris water maze under clear skies with the sun not in view. During training, lizards showed a striking bimodal orientation along the training axis, demonstrating their capability of determining the symmetry plane of the sky polarization pattern and thus the use of polarization information in orientation. After reaching criteria, lizards were kept 7 days in a 6-h fast clock-shift treatment and then released with the sun not in view. Six-hour clock-shifted lizards showed a bimodal distribution of directional choices, which was oriented perpendicularly to the training axis, as it was expected on the basis of the clock-shift. The results show that the only celestial diurnal compass mechanism that does not need a direct vision of the sun disk (i.e., the sky polarization compass) is a time-compensated compass.