## No full-text available

To read the full-text of this research,

you can request a copy directly from the author.

Since programmable electronic calculators were first employed in marine navigation, a variety of formulae has been used for calculating astronomical refraction. As the choice is wide, some formulae have been selected from commonly used reference sources and their accuracy and suitability examined. No attempt has been made to assess the validity of the selected formulae to represent astronomical refraction in practical circumstances. Accuracy comparisons have been made using the refraction algorithm proposed by Garfinkel – the standard adopted by the British and American Nautical Almanac Offices. New formulae are given that are simple and accurate, even over a wide range of temperature and pressure, and which for all practical purposes may be considered equivalent to the tables of refraction given in the Nautical Almanac.

To read the full-text of this research,

you can request a copy directly from the author.

... which is given on the first page of [2]. It is not recommended when app is smaller than 15 degrees. ...

... It is not recommended when app is smaller than 15 degrees. Bennett [2] compares many analytic approximations for the refraction angle ( app ). We apply his method H, a more complicated formula than (19), which is widely used, notably in the U. S. Naval Observatory's Vector Astrometry software. ...

... Different observers will see different elevation angles. 2 The close-Polaris hypothesis allows the computation of D star , the distance to Polaris, by triangularization as described in the next section. ...

For millenia, sailors have used the empirical rule that the elevation angle of Polaris, the North Star, as measured by sextant, quadrant or astrolabe, is approximately equal to latitude. Here, we show using elementary trigonometry that Empirical Law 1 can be converted from a heuristic to a theorem. A second ancient empirical law is that the distance in kilometers from the observer to the North Pole, the geodesic distance measured along the spherical surface of the planet, is the number of degrees of colatitude multiplied by 111.1 kilometers. Can Empirical Law 2 be similarly rendered rigorous? No; whereas as the shape of the planet is controlled by trigonometry, the size of our world is an accident of cosmological history. However, Empirical Law 2, can be rigorously verified by measurements. The association of 111 km of north-south distance to one degree of latitude trivially yields the circumference of the globe as 40,000 km. We also extend these ideas and the parallel ray approximation to three different ways of modeling a Flat Earth. We show that photographs from orbit, taken by a very expensive satellite, are unnecessary to render the Flat Earth untenable; simple mathematics proves Earth a sphere just as well.

... Bennett [2] developed an empirical formula, which allows us to calculate refraction from the apparent altitude h in arcminutes: ...

... For horizon alignment, we used the spirit level of the theodolite ("ALHIDADEN LIBELLE"; see fig. 2. 1. ...

... when that happened, they verbally signalled it to another member which then read off the UTC at that moment from the USNO Master Clock 3 using their smartphone, and yet another member took a note of that;4. one member read off the values from the theodolite's gauges as described in section 2.1, and two other members each took a note of those on paper and, as a backup, electronically with a smartphone online app, respectively.2 Previously we made sure that the theodolite's gauge uses units of degrees; in the training session we were given a device with a scale in gradians instead. ...

We obtained the horizontal coordinates of three unnamed celestial objects using a theodolite and converted them to equatorial coordinates using astronomical software (considering necessary corrections for atmospheric conditions). Using their equatorial coordinates, we find the observed objects to be the stars Capella (α Aur), Aldebaran (α Tau), and the planet Mars (Sol IV). We find the calculated coordinates to be differing from the catalogue values only by at most +4.44 −4.22 arcseconds for right ascension, and only by at most +1.394 −0.091 arcminutes for declination.

... In a follow-on paper using a test site at Spring Bay, Australia, Santamaría-Gómez and Watson [2016] found a consistent elevation-dependent error for angles below 12°. They attributed this to the bending effect of the incident angle and used local atmospheric pressure and temperature to calculate the change in elevation angle [Bennett, 1982], which is then applied to the vacuum elevation angles before calculating the estimated heights. The bias was generally reduced when this correction was applied. ...

... In a vertically stratified atmosphere, the refracted or apparent elevation will always be larger than the vacuum or geometric elevation. Santamaría-Gómez and Watson [2016] assumed that the predominant tropospheric effect is this bending δε of the radio wave elevations [Bennett, 1982], particularly at low-elevation angles [Anderson, 2000]. Consequently, they input the bent elevation angle in the geometric delay formula equation (3), so that the tropospheric delay is the difference with respect to the vacuum specular delay: ...

... In order to test the appropriateness of mapping functions for our purpose, we compared it to [Bennett, 1982] bending model as used by Santamaría-Gómez and Watson [2016]. There is a small offset between the two (around 3 cm at high-elevation angles), but the elevation-dependent trend is well represented in both ( Figure 2, bottom right). ...

Recent studies have demonstrated the utility of ground based GNSS Multipath Reflectometry (GNSS-MR) for sea level studies. Typical root-mean-square (RMS) differences of GNSS-MR derived sea level time series with respect to nearby tide gauges are on the order of 6 – 40 cm, sufficiently accurate to estimate tidal and secular sea level variations but are possibly biased due to delay of the signal through the troposphere. In this study we investigate the tropospheric effect from more than 20 GNSS coastal sites located from several meters up to 280 m above sea level. We find a bias in the estimated heights that is elevation and height dependent and can reach orders of 1 m for a 90 m site. Without correcting for tropospheric delay we find that GNSS-MR estimated tidal coefficients will be smaller than their true amplitudes by around 2% while phases seem unaffected. Correcting for the tropospheric delay also improves levelling results as a function of reflector height. Correcting for the tropospheric delay in GNSS-MR for sea level studies is therefore highly recommended for all sites no matter the height of the antenna above the sea surface as it manifests as a scale error.

... After decades of development in the principles of atmospheric refraction, many refraction correction models have been proposed [20]. Considering the computational complexity and correction effect, we chose the Bennett model to correct the signal bending error in elevations [20]. ...

... After decades of development in the principles of atmospheric refraction, many refraction correction models have been proposed [20]. Considering the computational complexity and correction effect, we chose the Bennett model to correct the signal bending error in elevations [20]. Under standard meteorological parameters, with a temperature of 10 °C and a pressure of 1010 mb, the elevation correction (units of minutes) is ...

Sea-level monitoring is important for the safety of coastal cities and analysis of ocean and climate. Sea levels can be estimated based using the global navigation satellite system–interferometry reflectometry (GNSS–IR). The frequency in a signal-to-noise ratio (SNR) arc has been found to be related to the height between the GNSS antenna and reflecting surface, which is called reflector height (RH, h). The height variation of the reflecting surface causes an error, and this error is the most significant error in the GNSS–IR sea-level retrieval. The key to the correction of height variation error lies in the determination of the RH variation rate ḣ. The classical correction method determines ḣ based on tide analysis of a coarse RH series over a longer time period. Therefore, ḣ inherits errors in coarse RH series, which contains significant bias during a storm surge, and correcting this requires data accumulation. This study proposes a correction method of height variation error based on just one SNR arc based on wavelet analysis and least-square estimation. First, using wavelet analysis, instantaneous frequencies are extracted in one SNR arc; these frequencies are then converted to RH series. Second, using least-square estimation, h and ḣ are conjointly solved based on the RH series from wavelet analysis. Data of GNSS site HKQT located in Hong Kong, China, during a period of time that includes Typhoon Hato were used. The root-mean-square errors (RMSEs) of retrievals were 21.5 cm for L1, 9.5 cm for L2P, 9.3 cm for L2C, and 7.6 cm for L5 of GPS; 16.8 cm for L1C, 14.1 cm for L1P, 12.6 cm for L2C, and 10.7 cm for L2P of GLONASS; 15.7 cm for L1, 11.2 cm for L5, 12.2 cm for L7, and 9.6 cm for L8 of Galileo. Results showed this method can correct the height variation error based on just one SNR arc, can avoid the inheritance of errors, and can be used during periods of storm surge.

... These ADCP measurements of the SWH were used for an additional validation of the SWH predictions resulting from supervised machine learning. IGS precise orbits from the Center for Orbit Determination in Europe (CODE) [32] were applied for computation of elevation angles, which were corrected for tropospheric refraction with a standard method [33] by using atmospheric pressure and air temperature data from FINO2. We used the reflectometry preprocessing tool [34] for preparing the SNR and elevation data, based on the aforementioned IGS orbit data and RINEX observation files containing the SNR values as transformed, dimensionless quantity S = 20 · log 10 (SNR). ...

Estimating reflector heights at stationary GNSS sites with interferometric reflectometry (IR) is a well-established technique in ocean remote sensing. Additionally, IR offers the possibility to estimate the significant wave height (SWH) with a linear model using the damping coefficient from an inverse modelling applied to GNSS signal-to-noise ratio (SNR) observations. Such a linear model serves as a benchmark in the present study, where an alternative approach for the estimation of both SWH and reflector height is presented that is based on kernel regression and clustering techniques. In this alternative approach, the reflector height is estimated by analyzing local extrema occurring in the interference pattern that is present in GNSS SNR observations. Various predictors are derived from clustering statistics and the estimated reflector heights. These predictors are used for the SWH determination with supervised machine learning. Linear models, bagged regression trees, and artificial neural networks are applied and respective results are compared for various predictor sets. In a second step, damping coefficients obtained from the inverse modelling mentioned above are additionally taken into account as predictors. The usability of the alternative approach is demonstrated. Compared to the benchmark, a significant improvement in terms of accuracy is found for an artificial neural network with predictors from both the alternative and the inverse modelling approach.

... Raytracing might be performed over the complete interferometric procedure (reflection and direct paths) or only in the direct path for faster evaluation, in which case eq.(12) would be approximated as ℓ ≈ ant . Alternatively, in case raytracing software is not available, blind atmospheric models such as the Global Pressure and Temperature (GPT) [19], [20] can be used to obtain refractivity at the station ℓ and models such as those of [21], [22] can approximate the elevation bending . ...

p> Radio wave propagation involved in Global Navigation Satellite System Reflectometry (GNSS-R) is subject to atmospheric refraction. Even for ground-based tracking stations, in applications such as coastal sea-level altimetry, the interferometric or reflection-minus-direct effect might be significant. Although atmospheric propagation delays are best investigated numerically via raytracing, including reflections, such a procedure is not trivial. We have developed simpler closed formulas to account for atmospheric refraction in ground-based GNSS-R, validated against independent raytracing. We provide specific expressions for the two components of the atmospheric interferometric delay and corresponding altimetry correction components, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for both components. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites.</p

... Raytracing might be performed over the complete interferometric procedure (reflection and direct paths) or only in the direct path for faster evaluation, in which case eq.(12) would be approximated as ℓ ≈ ant . Alternatively, in case raytracing software is not available, blind atmospheric models can be used, such as the Global Pressure and Temperature (GPT) [19], [20] to obtain refractivity at the station and models such as those of [21], [22] to approximate the elevation bending. In that case, the discrepancy between closed formulas and raytracing will also include errors in the atmospheric parameters ( ℓ and ). ...

p>Radio wave propagation involved in Global Navigation Satellite System Reflectometry (GNSS-R) is subject to atmospheric refraction. Even for ground-based tracking stations, in applications such as coastal sea-level altimetry, the interferometric or reflection-minus-direct effect might be significant. Although atmospheric propagation delays are best investigated numerically via raytracing, including reflections, such a procedure is not trivial. We have developed simpler closed formulas to account for atmospheric refraction in ground-based GNSS-R, validated against independent raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction components, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. For the conditions analyzed, about half of the delay was found to originate above the receiving antenna, for satellites at low elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and station height. For example, for a station five meters above sea level, observations for satellites below 20° elevation angle are subject to more than one centimeter of atmospheric altimetry error.</p

... Raytracing might be performed over the complete interferometric procedure (reflection and direct paths) or only in the direct path for faster evaluation, in which case eq.(12) would be approximated as ℓ ≈ ant . Alternatively, in case raytracing software is not available, blind atmospheric models can be used, such as the Global Pressure and Temperature (GPT) [19], [20] to obtain refractivity at the station and models such as those of [21], [22] to approximate the elevation bending. In that case, the discrepancy between closed formulas and raytracing will also include errors in the atmospheric parameters ( ℓ and ). ...

p> Radio wave propagation involved in Global Navigation Satellite System Reflectometry (GNSS-R) is subject to atmospheric refraction. Even for ground-based tracking stations, in applications such as coastal sea-level altimetry, the interferometric or reflection-minus-direct effect might be significant. Although atmospheric propagation delays are best investigated numerically via raytracing, including reflections, such a procedure is not trivial. We have developed simpler closed formulas to account for atmospheric refraction in ground-based GNSS-R, validated against independent raytracing. We provide specific expressions for the two components of the atmospheric interferometric delay and corresponding altimetry correction components, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for both components. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. </p

... ̃=̃+̃= 2 (sin ′ + ℓ sin ′ ⁄ ) (20) It should be emphasized that the ancillary atmospheric parameters (average refractivity ℓ and elevation bending ) will be taken from a previous direct rigorous raytracing, as our goal is to validate the mathematical formulation of the closed expressions. Alternatively, in case raytracing software is not available, empirical models such as the Global Pressure and Temperature (GPT) [19], [20] can be used to obtain the refractivity at the station and models such as those of [21], [22] can be used to approximate the elevation bending. In this case, the discrepancy between closed formulas and raytracing will include also errors in the atmospheric proxies ( ℓ and ). ...

Radio waves used in Global Navigation Satellite System Reflectometry (GNSS-R) are subject to atmospheric refraction, even for ground-based tracking stations in applications such as coastal sea-level altimetry. Although atmospheric delays are best investigated via ray-tracing, its modification for reflections is not trivial. We have developed closed-form expressions for atmospheric refraction in ground-based GNSS-R and validated them against raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. About half of the delay was found to originate above the receiving antenna at low satellite elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and reflector height. For example, for 5-meter reflector height, observations below 20° elevation angle have more than 1-centimeter atmospheric altimetry error.

... To obtain airless star vectors on Earth, s S i , , atmospheric refraction corrections are calculated according to Bennett (2009) and applied to the ′ s S i , vectors using the method outlined in Enright et al. (2012). The airless star vectors still contain measurement errors not associated with refraction effects. ...

... The inverse of this formula, Equation (27) [16], allows for the correction of observations: ...

Simulation plays a critical role in the development of UAV navigation systems. In the context of celestial navigation, the ability to simulate celestial imagery is particularly important, due to the logistical and legal constraints of conducting UAV flight trials after dusk. We present a method for simulating night-sky star field imagery captured from a rigidly mounted ‘strapdown’ UAV camera system, with reference to a single static reference image captured on the ground. Using fast attitude updates and spherical linear interpolation, images are superimposed to produce a finite-exposure image that accurately captures motion blur due to aircraft actuation and aerodynamic turbulence. The simulation images are validated against a real data set, showing similarity in both star trail path and magnitude. The outcomes of this work provide a simulation test environment for the development of celestial navigation algorithms.

... Raytracing might be performed over the complete interferometric procedure (reflection and direct paths) or only in the direct path for faster evaluation, in which case eq.(12) would be approximated as ℓ ≈ ant . Alternatively, in case raytracing software is not available, empirical or blind atmospheric models can be used, such as the Global Pressure and Temperature (GPT) [19], [20] to obtain refractivity at the station and models such as those of [21], [22] to approximate the elevation bending. In that case, the discrepancy between closed formulas and raytracing will also include errors in the atmospheric proxies ( ℓ and ). ...

Radio waves employed in Global Navigation Satellite System Reflectometry (GNSS-R) are subject to atmospheric refraction, even for ground-based tracking stations in applications such as coastal sea-level altimetry. Although radio propagation atmospheric delays are best investigated via raytracing, including reflections, such a procedure is not trivial. We have developed simpler closed formulas to account for atmospheric refraction in ground-based GNSS-R and validated them against raytracing. We provide specific expressions for the linear and angular components of the atmospheric interferometric delay and corresponding altimetry correction components, parameterized in terms of refractivity and bending angle. Assessment results showed excellent agreement for the angular component and good for the linear one. For the conditions analyzed, about half of the delay was found to originate above the receiving antenna, for satellites at low elevation angles. We define the interferometric slant factor used to map interferometric zenithal delays to individual satellites. We also provide an equivalent correction for the effective satellite elevation angle such that the refraction effect is nullified. Lastly, we present the limiting conditions for negligible atmospheric altimetry correction (sub-cm), over domain of satellite elevation angle and reflector height. For example, for 5-meter reflector height, observations below 20° elevation angle have more than 1-centimeter atmospheric altimetry error.

... In Fig. 3 we have also overplotted the results obtained from using the formula for refraction as a function of apparent solar altitude, equation 3.283-2, of the ESAA (It is also published in the Astronomical Almanac.). This formula, apparently based on empirical sources (see Wilson), is usually attributed to Sinclair (for small view angles, β < 15 o ) and to Bennett (1982) 6 (for larger view angles β ≥ 15 o ). It will be referred to from now on simply as SB. ...

In a previous paper we compared observations to calculated values of the sunrise times for one place in Jerusalem. It was shown that the sunrise over the actual physical horizon could be modelled to an accuracy of about ±15 seconds for most of the year. Success of those calculations suggested that terrain modeling was the most important factor in obtaining this result. To investigate this point, we repeated our calculations using the ray tracing method and simplified atmosphere developed by Siebren Van der Werf, whose atmospheric model is easily applied to other places in the world. Our results show that the new calculation method maintained our requirement of ±15 sec. accuracy (required for publication of sunrise time tables, critical for daily Jewish observances worldwide). Standard formulas for atmospheric refraction produce approximately the same results even for near horizon zenith angles. For portions of the year where low altitude inversions are especially important, e.g., during those days associated with maximum radiative cooling, these additional atmospheric effects can be effectively modeled in a very simple way.

... Applying ; cos 1; sin T T T z z z is the geometric zenith distance (without refraction), and 0 z is the apparent zenith distance (with refraction), R R is measured in arc minutes. Bennett (1982) (Meeus, 1991, p. 102) obtained an empirical formula that gives with a very good approximation the angle of refraction for all the values of the apparent altitude of a star above the horizon ...

Schaefer (1991) determined the Danjon limit or minimum angle between the Sun and the Moon from which the Moon can be seen shortly after the conjunction. Schaefer's method uses Hapke's (1984) lunar photometric theory and considers a fixed value for the threshold illuminance. We show Schaefer's method and its shortcomings, and we expose a modified theory, where the threshold illuminance to see the lunar crescent depends on several factors, mainly atmospheric absorption. We consider that vision is a probabilistic phenomenon; that is, when we use the experimental data of Blackwell (1946), we cannot be sure whether or not the Moon will be seen. Finally, we conclude that «perhaps» Hapke's theory overestimates the shielding of the sun's rays by the irregularities of the lunar surface at large phase angles.

... The monument can be regarded as stable with respect to the permafrost and barely has any impact on the GPS-IR-measured surface elevation changes. Regarding the tropospheric delays, we use the in situ air temperature and pressure measurements to quantify them, using the refraction correction model of Bennett (1982). The tropospheric biases are ∼ 1.3 cm and relatively steady (Fig. 10). ...

Ground surface elevation changes, soil moisture, and snow depth are all essential variables for studying the dynamics of the active layer and permafrost. GPS interferometric reflectometry (GPS-IR) has been used to measure surface elevation changes and snow depth in permafrost areas. However, its applicability to estimating soil moisture in permafrost regions has not been assessed. Moreover, these variables were usually measured separately at different sites. Integrating their estimates at one site facilitates the comprehensive utilization of GPS-IR in permafrost studies. In this study, we run simulations to elucidate that the commonly used GPS-IR algorithm for estimating soil moisture content cannot be directly used in permafrost areas, because it does not consider the bias introduced by the seasonal surface elevation changes due to active layer thawing. We propose a solution to improve this default method by introducing modeled surface elevation changes. We validate this modified method using the GPS data and in situ observations at a permafrost site in the northeastern Qinghai–Tibet Plateau (QTP). The root-mean-square error and correlation coefficient between the GPS-IR estimates of soil moisture content and the in situ ones improve from 1.85 % to 1.51 % and 0.71 to 0.82, respectively. We also propose a framework to integrate the GPS-IR estimates of these three variables at one site and illustrate it using the same site in the QTP as an example. This study highlights the improvement to the default algorithm, which makes the GPS-IR valid in estimating soil moisture content in permafrost areas. The three-in-one framework is able to fully utilize the GPS-IR in permafrost areas and can be extended to other sites such as those in the Arctic. This study is also the first to use GPS-IR to estimate environmental variables in the QTP, which fills a spatial gap and provides complementary measurements to ground temperature and active layer thickness.

... donde H es la altura observada y r es el ángulo de refracción. Para obtener el valor de r hay que calcular el factor de refracción R. En nuestros cálculos empleamos la fórmula 3, en la que la altura H se expresa en grados y el resultado R es en minutos de arco (Bennett 1982 (3) Los valores exactos de refracción dependen no sólo de la altura H del punto observado, sino también de las condiciones atmosféricas concretas (temperatura, presión del aire); en alturas cerca del horizonte matemático (plano horizontal) manifiestan variaciones impredecibles (cf. Young 2004). ...

Las múltiples hipótesis propuestas sobre la función astronómica de los grupos E en la arquitectura maya van desde las que les atribuyen un papel primordial en las observaciones astronómicas hasta las que los consideran meras alusiones alegóricas a ciclos celestes. Basándome en los análisis cuantitativos de los datos sobre los alineamientos medidos en diversos sitios, así como en evidencias contextuales, argumento que los grupos E eran astronómicamente funcionales, pero no tenían un papel específico o particularmente prominente en observaciones astronómicas. También muestro que las orientaciones plasmadas inicialmente en los grupos E –que representan la forma estandarizada más antigua de la arquitectura monumental maya y cuya presencia en prácticamente todas las ciudades tempranas en la parte central de la península de Yucatán atestigua su significado sociopolítico– fueron posteriormente transferidas a edificios y conjuntos de otro tipo. Por lo tanto, es precisamente la importancia de las direcciones astronómica y cosmológicamente significativas, primero incorporadas en los grupos E, la que nos permite comprender algunos aspectos sobresalientes de la arquitectura y el urbanismo de los mayas.

... Briefly, for the churches of interest, the angular height of the horizon, γ, has been calculated from the digital terrain model of HeyWhatsThat (Kosowsky 2012). Refraction is introduced as a function of γ using Bennett's (1982) formula to calculate the corrected value of the angular height γ * . Standard astronomical computations, supported by software tools (e.g., Stellarium 2020), allow the estimation of the solar declination, δ S , at meaningful dates in the Julian calendar. ...

Most of the earliest new churches built in Andalusia (southern Spain) following the thirteenth-century Christian Reconquista occupied the sites of former mosques. In some cases, these churches incorporated pre-existing architectonic elements – particularly minarets, which were converted into bell towers – or took some inspiration from Islamic architecture, creating a
combination of Gothic style and elements from Muslim architecture known as Gothic-Mudéjar. This paper analyses the orientation pattern of a group of 68 Gothic-Mudéjar churches built in the cities of re-conquered Andalusia up to the early fifteenth century, and the normalised frequency distribution of azimuths is compared with published data for the qibla (the direction toward which Muslims turn to pray) observed at a group of 82 Andalusian mosques. Results confirm that a large number of churches were oriented via a 90° anticlockwise rotation from orientation to the qibla after placing the apse in the former eastern wall of the mosque. It is further argued, based on the histogram and a distinctive peak around 84°, that the architects aligned these churches to sunrise over the local horizon for 25th March according to the Julian calendar, the date of the canonical equinox. This practice reflects Church teaching and a medieval foundation-stone rite involving a dawn vigil, and the built structures reflect the limited technical capacity of the church builders. The method of orientation would also have created a precedent for the alignment of some later churches in southern Spain dedicated to the Virgin of the Assumption to sunrise on 15th August, the Feast of the Assumption.

... Therefore, the magnitude of the tropospheric uncertainty is small. Zhang et al. (2020a) calculated the tropospheric uncertainties at RESO by using the data in 2004 and the tropospheric refraction correction model of Bennett (1982). They found that the uncertainties were ~1.6 cm and relatively steady during the summer. ...

Ground surface elevation changes are closely linked to the dynamics of the active layer and near-surface permafrost. GNSS interferometric reflectometry (GNSS-IR), a technique utilizing reflected signals regarded as noise in the GNSS applications, such as positioning and navigation, can measure surface elevation changes in permafrost areas. In this study, we screen seven major open-data GNSS networks to identify the sites which are suitable for using GNSS-IR to study the permafrost areas in the Arctic. We identify 23 usable sites and obtain their surface elevation changes. As for the unusable sites in the permafrost areas, 68% and 25% of them are due to the undulated reflecting surface and obstructions (e.g., buildings and trees), respectively. And 7% of the unsuitable sites are due to insufficient usable observations, though open and relatively smooth areas can be found in their surroundings. This study provides usable sites in the Arctic permafrost areas, which can fill some spatial gaps of the existing permafrost monitoring programs and provide complementary measurements to active layer thickness and permafrost temperature. The GNSS-IR measurements can provide new perspectives into permafrost studies and contribute to assessing the potential hazards of permafrost degradation to the infrastructures and residential communities.

... For a numeric evaluation we again use the setting from Section 2 and assume that the bending angle esp could possibly be replaced by e. We used Bennett's formula (Bennett 1982) and calculated the bending angle for a temperature of 23° C and a pressure of 1013 hPa as 0.1596° for an elevation angle of 5°. With these values, the bent ray interferometric delay from eq. (9) will become 1.743129 m. ...

The application of signal-to-noise ratio (SNR) observations from ground-based GNSS Reflectometry is becoming an operational tool for coastal sea-level altimetry. As in all data analyses, systematic influences must be reduced here too, to achieve reliable results. A prominent influence results from atmospheric refraction. Different approaches exist to describe or to correct for this influence. In our contribution we will revise the latest developments and suggest a simple atmospheric interferometric delay model that takes into account ray bending as well as along-path propagation delay. The model takes into account a spherical reflector and can therefore be applied for data from very low elevation angles, too. The findings are double-checked by numerical experiments based on a step-by-step raytracing procedure.

... For a numeric evaluation we again use the setting from Section 2 and assume that the bending angle esp could possibly be replaced by e. We used Bennett's formula [20] and calculated the bending angle for a temperature of 23° C and a pressure of 1013 hPa as 0.1596° for an elevation angle of 5°. With these values, the bent ray interferometric delay from eq. (9) will become 1.743129 m. ...

The application of signal-to-noise (SNR) observations from ground-based GNSS Reflectometry is becoming an operational tool for coastal sea-level altimetry. As in all data analyses, systematic influences must be reduced here too, to achieve reliable results. A prominent influence results from atmospheric refraction. Different approaches exist to describe or to correct for this influence. In our contribution we will revise the latest developments and suggest a simple atmospheric interferometric delay model that takes into account ray bending as well as along-path propagation delay. The findings are double-checked by numerical experiments based on a step-by-step raytracing procedure.

... It is pointed out that the main influences are the troposphere delay and the dynamic sea surface in the inverse modeling. Thus, Biased reflector heights caused by tropospheric delay can be corrected using the Vienna Mapping Function and the Global Pressure and Temperature 2 Wet delay model (GPT2w), especially at SC02 and other sites where the height between the antenna and the sea surface is large (Williams and Nievinski, 2017;Bennett, 1982;Bö hm et al., 2014). For the dynamic surface, the height rate is determined using tidal analysis and this part is then removed from the original sequence to obtain the final time sequence using the cubic spline (Larson et al., 2017a). ...

This paper presents an improved new method with differential evolution and the cubic spline approach is proposed to retrieve sea level height based on GNSS SNR observations from a single geodetic receiver. Considering the B-spline function is unstable at the beginning or end, and the feature that B-spline functions do not pass through nodes may introduce errors. Thus, the cubic spline is applied to the retrieval process and accounts for a continuous and smooth in sea level retrieval time series. Besides, the biases caused by tropospheric delay and dynamic sea level are considered and corrected. Testing data from two stations with different tidal range and the final solution agrees well with measurements from co-located tide gauges, reaching the RMSE of 3.67 cm at Friday Harbor, Washington, and 1.36 cm at Onsala, Sweden. Comparison of the nonlinear least squares, this method leads to a clear increase in precision of the sea level retrievals within 50%. Additionally, referring to the result of Purnell et al. (2020) and the IAG inter-comparison campaign, the results of this paper show more potential.

... In our study, because (1) all sites are located in the Canadian Arctic, characterized by a dry and cold climate, and (2) their antenna heights are ∼ 2 m (Table 1), the tropospheric biases at these sites are expected to be limited. More quantitatively, we calculate the tropospheric biases at RESO in the thaw season in 2014 by using the astronomical refraction model of Bennett (1982) and present them in Fig. S3. The magnitudes of tropospheric biases are ∼ 1.6 cm and stay relatively steady during the thaw season. ...

Global Positioning System interferometric reflectometry (GPS-IR) is a relatively new technique which uses reflected GPS signals to measure surface elevation changes to study frozen-ground dynamics. At present, more than 200 GPS stations are operating continuously in the Northern Hemisphere permafrost areas, which were originally designed and maintained for tectonic and ionospheric studies. However, only one site in Utqiaġvik, Alaska (formerly Barrow), was assessed to be usable for studying permafrost by GPS-IR. Moreover, GPS-IR has high requirements on the ground surface condition, which needs to be open, flat, and homogeneous. In this study, we screen three major GPS networks in Canada and identify 12 out of 38 stations located in permafrost areas as useful ones where reliable GPS-IR measurements can be obtained. We focus on the five Canadian Active Control System stations and obtain their daily GPS-IR surface elevation changes. We find that the ground surface subsided in Alert, Resolute Bay, and Repulse Bay respectively by 0.61±0.04 cm yr−1 (2012–2018), 0.70±0.02 cm yr−1 (2003–2014), and 0.26±0.05 cm yr−1 (2014–2019). At the other two sites of Baker Lake and Iqaluit, the trends are not statistically significant. The linear trends of deformation were negatively correlated with those of thaw indices in Alert, Resolute Bay, and Repulse Bay. Furthermore, in Resolute Bay, we also find that the end-of-thaw elevations during 2003–2012 were highly negatively correlated with the square root of thaw indices. This study is the first one using multiple GPS stations to study permafrost by GPS-IR. It highlights the multiple useful GPS stations in northern Canada, offering multi-year, continuous, and daily GPS-IR surface deformation, which provides new insights into frozen-ground dynamics at various temporal scales and across a broad region.

... The complementary angle of the incidence angle ε defers from the elevation angle of the satellite due to the curvature of the reflecting surface and can be calculated according to [15,6]. The tropospheric refraction can be considered by a correction of ε derived from an astronomic refraction model [16][17][18][19]. ...

The signal-to-noise ratio (SNR) data are part of the global navigation satellite systems (GNSS) observables. In a marine environment, the oscillation of the SNR data can be used to derive reflector heights. Since the attenuation of the SNR oscillation is related to the roughness of the sea surface, the significant wave height (SWH) of the water surface can be calculated from the analysis of the attenuation. The attenuation depends additionally on the relation between the coherent and the incoherent part of the scattered power. The latter is a function of the correlation length of the surface waves. Since the correlation length changes with respect to the direction of the line of sight relative to the wave direction, the attenuation must show an anisotropic characteristic. In this work, we present a method to derive the wave direction from the anisotropy of the attenuation of the SNR data. The method is investigated based on simulated data, as well by the analysis of experimental data from a GNSS station in the North Sea.

... Under the assumption of a locally flat and horizontal reflector, the SNR as a function of elevation can be expressed as a monotonically increasing trend superimposed by a high-frequency oscillation pattern (Bilich and Larson 2007), as presented in Fig. 1. After removing the trend with a low-order polynomial, the high-frequency residual oscillations behave like a damped sinusoid (Strandberg et al. 2016), which can be described by where is the elevation to the GNSS satellite corrected for atmospheric refraction (Bennett 1982), k the wave number of the signal, and h the vertical distance between the antenna and the horizontal reflector. The remaining parameters, A , , and , are aggregate variables depending on several properties, including, for example, antenna gain patterns of the receiver installation and the satellite, and electromagnetic properties of the reflector (Nievinski and Larson 2014a). ...

Current GNSS-R (GNSS reflectometry) techniques for sea surface measurements require data collection over longer periods, limiting their usability for real-time applications. In this work, we present a new, alternative GNSS-R approach based on the unscented Kalman filter and the so-called inverse modeling approach. The new method makes use of a mathematical description that relates SNR (signal-to-noise ratio) variations to multipath effects and uses a B-spline formalism to obtain time series of reflector height. The presented algorithm can provide results in real time with a precision that is significantly better than spectral inversion methods and almost comparable to results from inverse modeling in post-processing mode. To verify the performance, the method has been tested at station GTGU at the Onsala Space Observatory, Sweden, and at the station SPBY in Spring Bay, Australia. The RMS (root mean square) error with respect to nearby tide gauge data was found to be 2.0 cm at GTGU and 4.8 cm at SPBY when evaluating the output corresponding to real-time analysis. The method can also be applied in post-processing, resulting in RMS errors of 1.5 cm and 3.3 cm for GTGU and SPBY, respectively. Finally, based on SNR data from GTGU, it is also shown that the Kalman filter approach is able to detect the presence of sea ice with a higher temporal resolution than the previous methods and traditional remote sensing techniques which monitor ice in coastal regions.

... (2) d = 2H + 2Ḣ tan ∕̇, refraction (Bennett 1982) and the Global Pressure and Temperature 2 (GPT2) Wet model (Böhm et al. 2015) to correct tropospheric delay. The expression for the elevation angle correction Δ is described as where Θ = + 7.31 � ∕( + 4.4 • ) , in units of degree, in units of minute, T the temperature in units of Celsius degree, and P is the pressure in a unit of hPa. ...

A single geodetic GNSS station placed at the coast has the capability of a traditional tide gauge for sea-level measurements, with the additional advantage of simultaneously obtaining vertical land motions. The sea-level measurements are obtained using GNSS signals that have reflected off the water, using analysis of the signal-to-noise ratio (SNR) data. For the first time, we apply this technique to detect extreme weather-induced sea-level fluctuations, i.e., storm surges. We first derive 1-year sea-level measurements under normal weather conditions, for a GNSS station located in Hong Kong, and compare them with traditional tide-gauge data to validate its performance. Our results show that the RMS difference between the individual GNSS sea-level measurements and tide-gauge records is about 12.6 cm. Second, we focus on the two recent extreme events, Typhoon Hato of 2017 and Typhoon Mangkhut of 2018, that are ranked the third and second most powerful typhoons hitting Hong Kong since 1954 in terms of maximum sea level. We use GNSS SNR data from two coastal stations to produce sea-level measurements during the two typhoon events. Referenced to predicted astronomical tides, the storm surges caused by the two events are evident in the sea-level time series generated from the SNR data, and the results also agree with tide-gauge records. Our results demonstrate that this technique has the potential to provide a new approach to monitor storm surges that complement existing tide-gauge networks.

... The higher elevation limit was chosen due to the antenna gain pattern in the case of the static antenna, while in the case of the ship's measurement, the specular point had to lay outside of the ship's wave system [16]. The elevation angles were corrected for tropospheric refraction using the refraction model of [22]. The required pressure and temperature data were taken from DWD weather stations at Alte Weser Lighthouse and on Heligoland. ...

Currently, GNSS reflectometry based on the signal-to-noise ratio (SNR) has become an established tool in ocean remote sensing. Here, the distance between an antenna and the water surface is measured by analyzing the oscillation of the SNR observation. Due to the antenna gain pattern, this oscillation is more pronounced for satellite signals coming from low elevation angles. Additionally, the sea surface roughness is related to the attenuation of the SNR oscillation. Hence, the significant wave height (SWH) can be estimated by analyzing the SNR signal. In this work, a method is presented with which the SWH can be calculated from the attenuation’s damping coefficient of the SNR observations measured with surface-based receivers. The method’s usability is demonstrated using data from a static antenna operated in the German Bight and with data from a ship-based antenna. The estimated SWH values were validated against numerical wave model data. For both experiments, a high correlation was found.

... grad/solcalc/index.html, last access: 12 December 2018) that implements Meeus (1998) algorithms and are subsequently corrected for atmospheric refraction effects according to Bennett (1982). AMFs are calculated using the Kasten and Young algorithm (Kasten and Young, 1989). ...

The near-infrared (NIR) part of the solar spectrum is of prime importance for solar physics and climatology, directly intervening in the Earth's radiation budget. Despite its major role, available solar spectral irradiance (SSI) NIR datasets, space-borne or ground-based, present discrepancies caused by instrumental or methodological reasons. We present new results obtained from the PYR-ILIOS SSI NIR ground-based campaign, which is a replication of the previous IRSPERAD campaign which took place in 2011 at the Izaña Atmospheric Observatory (IZO). We used the same instrument and primary calibration source of spectral irradiance. A new site was chosen for PYR-ILIOS: the Mauna Loa Observatory (MLO) in Hawaii (3397ma.s.l.), approximately 1000m higher than IZO. Relatively to IRSPERAD, the methodology of monitoring the traceability to the primary calibration source was improved. The results as well as a detailed error budget are presented. We demonstrate that the most recent results, from PYR-ILIOS and other space-borne and ground-based experiments, show an NIR SSI lower than the previous reference spectrum, ATLAS3, for wavelengths above 1.6 µm.

... Refraction reduces the masking effect of the Earth curvature by approximately 1/7. However, this coefficient drastically decreases with the (turbine) height 21,22 . As a consequence, for turbines far enough beyond the horizon distance l hor , the hidden part of the tower is high enough to reduce this refraction coefficient to a value such that the unmasking effect is not noticeable. ...

The following study describes a method to quantify the visual impact of an offshore wind farm, as seen from the coast. In brief, the method involves distinguishing between the visual impact due to the intrusion in the observer's vision field and the un-aesthetic effect of the arrangement unevenness. Both parameters, visual intrusion
and unevenness, can be quantifiable; therefore, a final indicator for the visual impact of the wind farm can be calculated for a specific wind farm layout. Two approaches are presented to calculate the visual intrusion, which give rise to similar results. The method has been programmed and included in an application that has been tested
with two known wind farm layouts, showing a complete coherence of the results given by the method. This method provides the designer with a tool that allows him to take into account the estimated visual impact of a wind farm under study. If an algorithm is used to look for the optimum location/layout for an offshore wind farm, its programmer can include this method in order to obtain a trade-off between maximum profitability, and minimum visual impact.

... Атмосферная рефракция рассчитывалась нами по эмпирической формуле Беннета (Bennett, 1982): ...

This article describes the method and results of archaeoastronomical analysis of Maeotian burial assemblage from the necropolis of Kobyakovo hillfort (Rostov-on-Don, Russia). Research of burial assemblage with ditches and jumpers from Kobyakovo necropolis was made to clarify the religious beliefs of Meotians and ascertain possible relationships their rituals with celestial cults. From the written evidence about Meotians only to message of Maximus of Tyre (VIII, 8) was known that Maeotians considered Meotian Lake (Meotida) as a god. The article presents the results of archaeoastronomical analyze of burial assemblage, surrounded by a rectangular small ditch with joining bank, dating back to the first centuries AD. For the study of this assemblage was designed by a more accurate method archaeoastronomical analysis, comprising carrying out iteration on the calculation of azimuths with considering the visible horizon, obtained by HeyWhatsThat program, and given the atmospheric refraction at low altitudes, which is calculated by means empirical formula Bennett. Results archaeoastronomical analysis using the developed method showed that planigraphy burial assemblage with the burial 21 and in the location of pottery fragments and stones in the small ditch there are some astronomical regularities, indicating possible availability of a basic understanding of the features of the visible movement of the Sun and the Moon at inhabitants of Kobyakov settlement – Maeotians. Also, with the help the developed method, it was found that in a narrow sector to the east of the necropolis and hillfort there is an abnormal visibility. Due to it, residents of Kobyakov hillfort could theoretically be observed in this regard the phenomenon of visible small "jump" the Sun rising in the equinox over the riverbed, or the Moon, rising in the same direction. Choosing a place for the hillfort and necropolis with such anomalous visibility range can be regarded as an indication high religious significance for Maeotians not only Meotida, but also the Sun, Moon and the river Don.

... Manual tracking of a special flight and long exposures at night were used in[44].3 Higher than 20 • above the horizon[11], errors caused by atmospheric refraction are smaller than 0.05 • , much less than the angular size of each of our pixels, 0.18 • . ...

Light-field imaging can be scaled up to a very large area, to map the Earth’s atmosphere in 3D. Multiview spaceborne instruments suffer low spatio-temporal-angular resolution, and are very expensive and unscalable. We develop sky light-field imaging, by a wide, scalable network of wide-angle cameras looking upwards, which upload their data to the cloud. This new type of imaging-system poses new computational vision and photography problems, some of which generalize prior monocular tasks. These include radiometric self-calibration across a network, overcoming flare by a network, and background estimation. On the other hand, network redundancy offers solutions to these problems, which we derive. Based on such solutions, the light-field network enables unprecedented ways to measure nature. We demonstrate this experimentally by 3D recovery of clouds, in high spatio-temporal resolution. It is achieved by space carving of the volumetric distribution of semi-transparent clouds. Such sensing can complement satellite imagery, be useful to meteorology, make aerosol tomography realizable, and give new, powerful tools to atmospheric and avian wildlife scientists.

... El Anuario del Observatorio Astronómico [5] ofrece el modelo desarrollado por Bennet [4]. El modelo viene en función de la altura observada aparente (h ) del astro y tiene la expresión 12. ...

... Therefore, in a second processing of the SNR series, we applied the same strategy but, before running the EKF, the elevation angles [sine(e)] in the SNR series were corrected for the bending effect of the tropospheric refraction. The bending effect was estimated using atmospheric pressure and temperature recorded at the TG following (Bennett 1982): ...

We further developed a new approach using GNSS reflectometry to determine the leveling connection between a tide gauge and a GNSS antenna. This approach includes the optimization of the unknown receiver bandwidth and the estimation of frequency changes in the signal-to-noise ratio (SNR) oscillation through an extended Kalman filter/smoother algorithm. We also corrected the geometric bending of the GNSS signals due to tropospheric refraction using local meteorological observations. Using 3 weeks of SNR data in Spring Bay, Australia, from a GNSS antenna placed sideways (i.e., ground plane orientated vertically and directed in azimuth toward the sea surface) to improve the SNR interference near the horizon, we obtained mean leveling differences of approximately 5 mm, with an RMS of approximately 3 cm level with respect to the nominal leveling from classical surveying techniques. SNR data from three different receiver manufacturers, coupled to the same antenna, provided similar leveling results. With a second antenna in the usual upright configuration, we obtained mean leveling differences of 1–2 cm and a RMS of about 10 cm. In the upright configuration, the leveling differences may include errors in the GNSS antenna phase center calibration, which are avoided in our technique but not in the classical surveying techniques. These results demonstrate the usefulness of the reflectometry technique to obtain precisely and remotely the leveling between a GNSS antenna and a tide gauge. In addition, this technique can be applied continuously, providing an independent and economical means to monitor the stability of the tide gauge zero.

... Refraction reduces the masking effect of the Earth curvature by approximately 1/7. However, this coefficient drastically decreases with the (turbine) height 21,22 . As a consequence, for turbines far enough beyond the horizon distance l hor , the hidden part of the tower is high enough to reduce this refraction coefficient to a value such that the unmasking effect is not noticeable. ...

This study describes a method to quantify the visual impact of an offshore wind farm, as seen from the coast. In brief, the method involves distinguishing between the visual impact due to the intrusion in the observer's vision field and the un-aesthetic effect of the arrangement unevenness. Both parameters, visual intrusion and unevenness, can be quantifiable; therefore, a final indicator for the visual impact of the wind farm can be calculated for a specific wind farm layout. Two approaches are presented to calculate the visual intrusion, which give rise to similar results. The method has been programmed and included in an application that has been tested with two known wind farm layouts, showing a complete coherence of the results given by the method. This method provides the designer with a tool that allows him to take into account the estimated visual impact of a wind farm under study. If an algorithm is used to look for the optimum location/layout for an offshore wind farm, its programmer can include this method in order to obtain a trade-off between maximum profitability and minimum visual impact.

... is shown in the top part of the figure, with latitude φ, declination δ and hour angle ω (Woolf 1968) and a small heuristic correction R of at most 34 arc minutes due to the refraction in the atmosphere (Bennett 1982). Over that measurement time where weather and building geometry permitted to collect data, the elevation angle α covers a range from about 70 • around noon to 20 • in the evening, making the length of the air column s = h0/ sin α the light has to pass through to range from 1.06h0 to 2.92h0, where h0 is the effective height of the atmosphere. ...

Conventional ground-based astronomical observations suffer from image distortion due to atmospheric turbulence. This can be
minimized by choosing suitable geographic locations or adaptive optical techniques, and avoided altogether by using orbital
platforms outside the atmosphere. One of the promises of optical intensity interferometry is its independence from atmospherically
induced phase fluctuations. By performing narrowband spectral filtering on sunlight and conducting temporal intensity interferometry
using actively quenched avalanche photon detectors (APDs), the Solar g(2)(τ) signature was directly measured. We observe an averaged photon bunching signal of g(2)(τ) = 1.693 ± 0.003 from the Sun, consistently throughout the day despite fluctuating weather conditions, cloud cover and
elevation angle. This demonstrates the robustness of the intensity interferometry technique against atmospheric turbulence
and opto-mechanical instabilities, and the feasibility to implement measurement schemes with both large baselines and long
integration times.

Archaeoastronomical studies have demonstrated that the important civic and ceremonial buildings in Mesoamerica were largely oriented to sunrises or sunsets on specific dates, but the origin and spread of orientation practices were not clear. Using aerial laser scanning (lidar) data, we analyzed orientations of a large number of ceremonial complexes in the area along the southern Gulf Coast, including many recently identified Formative sites dating to 1100 BCE to 250 CE. The distribution pattern of dates marked by solar alignments indicates their subsistence-related ritual significance. The orientations of complexes built between 1100 and 750 BCE, in particular, represent the earliest evidence of the use of the 260-day calendar, centuries earlier than its previously known use in textual records.

The Global Meteor Network (GMN) utilizes highly sensitive low-cost CMOS video cameras which run open-source meteor detection software on Raspberry Pi computers. Currently, over 450 GMN cameras in 30 countries are deployed. The main goal of the network is to provide long-term characterization of the radiants, flux, and size distribution of annual meteor showers and outbursts in the optical meteor mass range. The rapid 24-h publication cycle the orbital data will enhance the public situational awareness of the near-Earth meteoroid environment. The GMN also aims to increase the number of instrumentally observed meteorite falls and the transparency of data reduction methods. A novel astrometry calibration method is presented which allows decoupling of the camera pointing from the distortion, and is used for frequent pointing calibrations through the night. Using wide-field cameras (88° × 48°) with a limiting stellar magnitude of +6.0 ± 0.5 at 25 frames per second, over 220 000 precise meteoroid orbits were collected since 2018 December until 2021 June. The median radiant precision of all computed trajectories is 0.47°, 0.32° for $\sim 20{{\ \rm per\ cent}}$ of meteors which were observed from 4 + stations, a precision sufficient to measure physical dispersions of meteor showers. All non-daytime annual established meteor showers were observed during that time, including five outbursts. An analysis of a meteorite-dropping fireball is presented which showed visible wake, fragmentation details, and several discernible fragments. It had spatial trajectory fit errors of only ∼40 m, which translated into the estimated radiant and velocity errors of 3 arcmin and tens of meters per second.

The near-infrared sky is a very dynamic entity. It varies across all timescales spatially, temporarily, and thermally. Unavoidably, the near-infrared sky dictates how instruments need to be built to optimize the scientific return, dictates how astronomers need to prepare their observations, and dominates the various strategies they require to reduce the resulting data. In this chapter first some fundamental quantities such as airmass, atmospheric refraction, and extinction are introduced. This is followed by a discussion on turbulence and its consequences like seeing, Airy pattern, and Strehl ratio. In the second part of this chapter, the sky brightness and variability are described and the emission and absorption spectrum of the near-infrared sky be introduced. The chapter ends with a brief description of how observations from space are affected by the near-infrared sky and contributions off the atmosphere.

In the scope of archaeoastronomy, the analysis of a large number of structures through the frequency histograms for their azimuths and declinations can identify singular patterns of orientation. Conclusions often rely on qualitative assessments. Quantitative assessments have been proposed by using as null hypothesis a pure random distribution of azimuths over the 360º horizon. In some cases, such as orientation of Christian churches, the histograms or spectra are composite, with peaks overlapping a continuous and not uniform background. This paper presents a methodology for assessing the statistical significance of the net area of a peak in the histogram in relation to the local background level. The spectra use Normal kernel functions. The background contribution is estimated from the area of the trapezoidal polygon under the peak, and it is interpreted as the probability parameter for a Binomial distribution. The methodology is illustrated with a real case study which includes the azimuth and declination histograms for a set of churches from southern Spain dedicated to the Virgin of the Assumption. The method is more restrictive than previous approaches.

Bruin (1977) devised a procedure to find out the visibility of the first crescent Moon. He applied various simplifications to his theory, not all of them acceptable. We rethink Bruin's method by making some corrections: we take into account the variation of the luminance of the Moon with the phase, we use the experimental results of Knoll et al. (1946) on threshold contrast, we apply Riccò's law, and we consider the atmospheric extinction coefficient to be variable. We use the theory to derive the Danjon limit.

This work studies the alignment of the Assumption churches in Soria (N = 73). The group from the Romanesque of repopulation (N = 45, twelfth-thirteenth centuries) shows solar patterns of orien-tation: 47% of the churches were aligned to the sun of the equinox (80% of them to the ortho at the canonical equinox, March 25th), 26% were oriented to the solar ortho on the feast of the Assump-tion, while 7% opposed their apses to the sunset on that date. These patterns also appear in some medieval churches in the Cordoba countryside.
Estudiamos la orientación de las iglesias de la Asunción en Soria (N=73). El grupo del románico de repoblación (N=45, siglos XII-XIII) muestra patrones de orientación solar: 47% de las iglesias se alinean con el sol del equinoccio (80% de ellas al orto en el equinoccio canónico, 25 de marzo), 26% se orientan al orto solar en la festividad de la Asunción, mientras que un 7% oponen su ábside al ocaso en esa fecha. Reencontramos estos patrones en algunas iglesias medievales de la campiña de Córdoba.

This paper summarises briefly and in English some of the results of the book Hoffmann: Hipparchs Himmelsglobus, Springer, 2017 that had to be written in German. The globe of Hipparchus is not preserved. For that reason, it has been a source of much speculation and scientific inquiry during the last few centuries. This study presents a new analysis of the data given in the commentary on Aratus' poem by Hipparchus, in comparison with other contemporary Babylonian and Greek astronomical data, as well as their predecessors in the first millennium and their successors up to Ptolemy. The result of all these studies are the following: i) although the data of Ptolemy and Hipparchus are undoubtedly correlated, it is certainly also wrong to accuse Ptolemy having simply copied and transformed it without correct citation; ii) although Hipparchus presumably observed most of his star catalogue with his own instruments, we cannot neglect Babylonian influences. Hipparchus was educated in Greek astronomy but, in his time, there are traces of Babylonian influences since at least two centuries. Since we are unable to definitely prove that Hipparchus used Babylonian data, we are not sure if there are direct Babylonian influences in his time or as a consequence of his education only. Finally, we present a virtual 3D-image showing what the globe of Hipparchus might have looked like.

Geometrical Optics is one of the oldest of the physical sciences, but still remains the most effective approach for explaining a good part of the most common optical phenomena. It is particularly useful for tracing the propagation of light in inhomogeneous media and for describing or designing optical instruments. The emphasis of this discipline is to find the path of light rays, imagined as geometric lines along which energy flows.

Ships create a wave system while moving. Changing pressure conditions lead to changes in draught an trim, the so called squat effect. Knowiing about this effect is crucial from the shipping industry and if sea surface height measurments shall be done from GNSS aboard ships.
The paper describes a methodology for estimating the squat via GNSS reflectometry. Results from a three month data set are presented.

Measurements of the sea surface height (SSH) can be carried out with GNSS aboard ships, but data about the static draft and the hydrodynamic squat effect are necessary. This information is often not available or has an insufficient accuracy. In this study, an alternative method based on the GNSS signal-to-noise ratio observations is presented. Using this method, the distance between the water surface and a GNSS antenna can be estimated directly, if corrections of the heave and the ship’s attitude are considered properly. Suitable segments of a 3-month dataset, gathered aboard a ferry ship operating in the German Bight, were analysed. A global optimization approach based on interval analysis was used and all available observations from a segment were analysed in a common adjustment calculation. The resulting SSH was validated with data from a tide gauge station at Heligoland. The mean difference is 4 mm and a standard deviation of the differences of 5.3 cm was found. The SSH for the same GNSS dataset was also derived from a well-established processing based on the comprehensive consideration of ship dynamics. The mean difference with respect to the tide gauge was 2 mm with a slightly smaller standard deviation of 4.0 cm.

Determination of sea ice extent is important both for climate modeling and transportation planning. Detection and monitoring of ice are often done by synthetic aperture radar imagery, but mostly without any ground truth. For the latter purpose, robust and continuously operating sensors are required. We demonstrate that signals recorded by ground-based Global Navigation Satellite System (GNSS) receivers can detect coastal ice coverage on nearby water surfaces. Beside a description of the retrieval approach, we discuss why GNSS reflectometry is sensitive to the presence of sea ice. It is shown that during winter seasons with freezing periods, the GNSS-R analysis of data recorded with a coastal GNSS installation clearly shows the occurrence of ice in the bay where this installation is located. Thus, coastal GNSS installations could be promising sources of ground truth for sea ice extent measurements.

The Next Generation Transit Survey (NGTS), operating in Paranal since 2016, is a wide-field survey to detect Neptunes and super-Earths transiting bright stars, which are suitable for precise radial velocity follow-up and characterisation. Thereby, its sub-mmag photometric precision and ability to identify false positives are crucial. Particularly, variable background objects blended in the photometric aperture frequently mimic Neptune-sized transits and are costly in follow-up time. These objects can best be identified with the centroiding technique: if the photometric flux is lost off-centre during an eclipse, the flux centroid shifts towards the centre of the target star. Although this method has successfully been employed by the Kepler mission, it has previously not been implemented from the ground. We present a fully-automated centroid vetting algorithm developed for NGTS, enabled by our high-precision auto-guiding. Our method allows detecting centroid shifts with an average precision of 0.75 milli-pixel, and down to 0.25 milli-pixel for specific targets, for a pixel size of 4.97 arcsec. The algorithm is now part of the NGTS candidate vetting pipeline and automatically employed for all detected signals. Further, we develop a joint Bayesian fitting model for all photometric and centroid data, allowing to disentangle which object (target or background) is causing the signal, and what its astrophysical parameters are. We demonstrate our method on two NGTS objects of interest. These achievements make NGTS the first ground-based wide-field transit survey ever to successfully apply the centroiding technique for automated candidate vetting, enabling the production of a robust candidate list before follow-up.

Time-lapse videos, still photos, visual observations, and theoretical studies were used to investigate the antitwilight, i.e., twilight opposite the Sun. Colors, brightnesses, and antitwilight features as a function of solar altitude were measured. Four roughly horizontal bands were identified and explained physically in terms of atmospheric geometry, the observer's line-of-sight, optical depth, refraction, and multiple scattering. Particular emphasis is placed on (1) the origin of the dark segment, (2) the rapid rising of the Belt of Venus with solar altitude, and (3) ray tracing light through the low atmosphere to understand refractive effects. New names are suggested for three of the four bands, and the new terminology is reconciled with earlier papers.

This chapter explains the functional requirements of a concentrator photovoltaic (CPV) sun tracker. It derives the design specifications of a CPV tracker. The chapter presents taxonomy of trackers describing the most common tracking architectures, based on the number of axes, their relative position, and the foundation and placing of tracking drives. It deals with the structural issues related to tracker design, mainly related to structural flexure and its impact on the system's acceptance angle. The chapter analyzes the auto-calibrated sun tracking control, by describing the state of the art and its development background. It explores the sun tracking accuracy measurement with a practical example. The chapter discusses tracker manufacturing and tracker field works. It reviews survey of different types of tracker designs obtained from different manufacturers. Finally, the chapter deals with IEC62817, the technical standard developed for CPV sun trackers.

Based on the idea of rational function approximation, this paper proposes a method to calculate atmosphere refraction as the solar in the low angle. By using on "2012 Almanac" observation data as the experimental data, and comparing with the simplified differential equation and Saemundsson formula, the experimental results showed that the rational fitting formula is better than those of Saemundsson formula, in the maximum deviation, minimum deviation, average deviation and standard deviation, and those of the simplified differential equation formula besides the minimum deviation. Among them, the maximum deviation can be controlled within 3". Comparing to other formulae for calculating the refraction, the rational function approximation method not only simplifies the calculation process, but also can be used in the application accuracy of GIS city planning and sunshine analysis, etc.

Printing Options Send high resolution image to Level 2 Postscript Printer Send low resolution image to Level 2 Postscript Printer Send low resolution image to Level 1 Postscript Printer Get high resolution PDF image Get low resolution PDF Send 300 dpi image to PCL Printer Send 150 dpi image to PCL Printer More Article Retrieval Options HELP for Article Retrieval Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints

HP 65 Navigation Pac

- Packard Hewlett