GNSS Remote Sensing

• GNSS Atmospheric Sounding (ground based)

• GNSS Radio Occultation (satellite based)

• GNSS Reflectometry (uses variety of receivers)

GNSS (Global Satellite Navigation System) is an umbrella term for GPS, GLONASS, Beidou, Galileo.

GNSS uses (artificial) satellites to determine positions on earth.

Measurements between the receiver and satellite allow for calculating the receiver's position.

GNSS requires at least four satellites to be visible for accurate positioning (line of position!)

GNSS consists of a space segment (satellites), a control segment (monitor stations, master control stations, data uploading stations), and a user segment (receivers and processing software).

Observables are:

• Doppler observables, used for velocity determination

• Code pseudo-ranges, derived from PRN code

• Carrier-phase measurements

• Signal-to-noise-ratio (SNR), indicated signal quality

Orbit velocity? Altitude? How many satellites?

GNSS-RS uses GNSS satellite signals to observe the earth. (…)

Satellite data isn’t constricted to land mass and can collect data even for remote areas that aren’t easily accessible or for areas that are politically unstable. Satellite data can get us a good overview on large scale structures from space and, additionally,

globally consistent data sets which can be broadly diversified.

The 2 observations equations, which give the true range between the satellite and the observer plus errors/biases in m, for code and carrier phase are very similar, but not identical. The upper one is the code obs. eq., the lower equation carrier observation eq.:

The only differences are that the phase ambiguity is included in the carrier phase obervation equation and that the ionospheric delay is negative for the carrier observations but positive for the code observations.

So, for code measurements the ionosphere delays the signal and for carrier phase measurements the signal is faster by the same amount.

Units:

• true range in m (or any other distance measurement)

• c in m/s (or any other velocity measurement)

• clock errors in s (or any other time measurement)

• error + bias in m

• wave length in m

• ambiguity no unit

• relativistic contr. + error in carrier phase in m

• refraction/bending: signal bends as it passes from a vacuum (space) to another medium (atmosphere) due to density. The bending occurs due to a change in the speed of the signal (denser medium = slower; bending effect increases with density). For the ionosphere, refraction occurs due to changes in electron density. For the atmosphere, bending occurs due to changes in air & water vapor densities, although they are small compared to electron density effects. Bending allows that the signal can be received even when the transmitter is slightly behind the earth.

• dispersion: different frequencies of the signal travel different ways in a dispersive medium (example: rainbow!) -> caused by the ionosphere which is a dispersive medium (refractivity depends on the frequency in the ionosphere!). Dispersion causes spatial separation in different wavelengths.

• degradation: signal becomes weaker over time due to atmospheric absorption; appears due to strong ionospheric disturbances but also due to water vapor content and air density

• (de-)focussing: caused by ionosphere. When travelling through irregularities, for example due to iones, the intensity of the signal changes due to focussing or defocussing (like for glasses)

• multipath: caused mostly by ground environment. Signal comes from several ways due to reflection, e.g. at surfaces of buildings -> what is the right signal?

Effect of rain: Rain and clouds usually don’t affect GNSS signals due to the diameter of raindrops (is too low). However, when it’s raining a lot, it could have an effect (like ~ 10cm/h).

During disturbed times, the ranging delay can increase to more than 100m.

Distrubances can be caused by space weather events such as

• solar flares (bursts of radiation from the sun)

• coronal mass ejections CME (clouds of solar plasma)

• geomagnetic storms (often following a CME)

GNSS Atmopsheric sounding is the technique of observing the earth with GNSS signals that travel from GNSS satellites to a ground station. For the IGS (International GNSS service), there are currently 525 stations worldwide. With the GNSS signal errors, there can be info derived about water vapor content, ionospheric delay and ionospheric disturbances. When locating the station with GNSS signals, additionally info about its location & displacement over time (due to continental drift, land slides, uplift etc.) can be derived.

Observations are:

• timing

• positioning (location of the station + displacement over time)

• tracking (time derivative of positioning)

• L1/L2 signal analysis (signal errors, collected info:

GNSS Radio Occultation is the technique which uses LEO satellites which receives GNSS signals and aalyzes them in order to observe the atmosphere. The observations are therefore also restricted to the atmosphere.

It’s the only technique with altitude resolution and can collect information about the neutral atompshere (temperature, water vapor content, pressure) and ionosphere (electron density, disturbances).

Observables are:

• profiles of temperature, pressure,water vapor content (neutral atmosphere)

• electron density profiles, SNR profiles (ionosphere)

The LEO satellite receives the signal of GNSS satellites while they rise/set (on the other side of earth). Because the signal travels through the atmosphere, it is disturbed depending on the altitude. Due to the signal being sent many times, the time differences between these signals can be observed which gives information about where exactly this signal is disturbed.

So with this we know the altitude - but how do we know the latitude/longitude?

In GNSS-RO, we assume that the atmosphere and ionosphere is spherically symmetric around the earth so that the atmospheric conditions only depend on altitude.

• Geosphere:

  • continental drift, land uplift, vulcano monitoring, landslides (Ground stations)

• Biosphere:

  • bee flight tracking, lynx monitoring (Ground stations)

  • vegeation observation (Reflectometry)

• Hydrosphere:

  • water level monitoring (Reflectometry/Ground stations)

  • flooding prediction

  • tsunami early warning (ground stations)

  • soil moisture (Reflectometry)

• Atmosphere:

  • weather forecast (Radio Occulation)

  • temperature in troposphere/stratosphere (Radio Occultation)

  • Gravity wave detection

  • footprints of quakes, volcanos, tsunamis (ground stations)

• Cryosphere:

  • glacier motion (Ground stations)

  • snow depth (Reflectometry)

GNSS reflectometry works by receivers analyzing GNSS signals that have been reflected by the earth’s surface. These receivers can be satellites, ground stations, or even ships and aircrafts.

The reflected GNSS signal is weaker and also can change its polarization. With this, info about

• altimetry (water level)

• soil moisture, snow depth, vegeation info (surface)

can be derived - mainly surface parameters.

The Global Positioning System is a satellitebased navigation system owned by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provide geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites.

NOT equal to GNSS, because GNSS is an umbrella term for many systems including GPS.

With the launch of the Soviet Sputnik satelllite in 1957, it was discovered that the signal the satellite sent are Doppler shifted which meant that the signals could be used to determine its position. This discoverey led to the idea that maybe, by turning this around, with the satellites position known the position of the receiver could be tracked.

In the 1960s, the Transit system (also known as NAVSAT or NNSS) of the US was launched, which was the first operational satellite navigation system. These satellites were quite small, about 1m in diameter, relatively light weight, and had a low polar orbit.

The GPS project began in 1973. After in 1983, a plane was shot down due to it being in a prohibited zone because its system had a navigation error, US President Reagan announced that when GPS is completed it would be avaiable for civilian use. Since 1995 GPS is fully operational and with that the first GNSS.

Today, we have Multi-GNSS - 4 GNSS systems (GPS, GLONASS, Beidou and Galileo) and 2 regional satellite systems (QZSS and IRNSS).

Additionally:

GPS: project started in 1973, fully operational since 1995

Galileo: limited services since 2016, fully op. since 2020; first sat. launched in 2005 -> independence from U.S. civil service

BeiDou: geostationary sat. since 2000, extended to pacific region in 2012, fully op. since 2020

GLONASS: construction from 1982-1996, almost down in 2001 but was recompleted: recently 27 satellites! New “K1” satellites with only one frequency

GNSS satellites transmit continuous electromagnetic waves; the phase of the carrier wave which has a high frequency is tracked by the receiver. The receiver then measures the phase difference between the transmitted and the received signal - this difference allows for the calculation of the distance between the satellite and the receiver.

With Carrier-phase measurements, there is an ambiguity in the number of complete wavelengths between satellite & receiver which needs to be resolved to determine the true distance accurately.

This can be achieved by combining pseudoranges and phase observations but needs a (more expensive) receiver which is able to do so! (Most smartphones, for example, can’t)

Once that is resolved, carrier-phase measurements can achieve millimeter-level precision.

Augmentation systems are designed to improve the performance of existing GNSS signals, for example to improve accuracy, reliability and avaiability.

They do this by providing additional information like correction data (e.g. for clocks) and atmospheric delay corrections to users by broadcastng differential signals.

There are satellite-based augmentation systems (SBAS) and ground-based augmentation systems (GBAS).

Examples are:

• WAAS (North America)

• EGNOS (Europe)

• GAGAN (India)

• QZSS-SBAS (Japan)

A GEO (geosynchronos equatorial orbit) is just a dot because they rotate with earth in the same time (alt. ~ 36000 km); they all have an inclination of 0° and are therefore always on the equator.

A IGSO (inclined geosynchronous orbit) is geosynchronous (same altitude!) but with an inclination, which produces 8-shaped groundplots which stay on the longitude and are in between the latitude of their incliantion. With no eccentricity, the loops cross at the equator. They are often eccentrical as well, making one of the “ribbons” of the 8 larger than the other (where it’s larger: farther away) and makes it so that they are not crossing directly at the equator.

A MEO (medium earth orbit) is an orbit with an altitude of around 2000 - 30000 km. Most GNSS satellites are in this orbit. They need around 3 - 12 hours to orbit earth, meaning that they produce wide waves on a groundplot. A satellite with a 12h-orbit produces 24/12 = 2 waves on the groundplot. For a 3h orbit it would be 24/3 = 8. Most satellites fly eastwards, therefore the groundplot shifts westwards. The reach as high in latitude as their inclination allows.

A LEO (low earth orbit) is an orbit with an altitude of up to 2000km. Most GNSS RS satellites are in this orbit, as are most scientific satellites. They need around 90 minutes to orbit earth. Therefore, the groundplot has 24/1.5 = 16 waves. They reach as high in latitude as their inclination allows - a lot of them have polar orbits. Most satellites fly eastwards, therefore the groundplot shifts westwards.

GPS has 6 orbital planes, so while all satellites have the same inlcination, they are shifted in longitude to ensure maximum coverage. For GPS, this is a 60° shift in longitude. Even though the inclination is only at around 55°, the polar areas can still receive enough signals due to the high altitude of the GPS satellites.

Regional satellite systems provide independent positioning, navigation and timing but not globally. Instead they provide these services in a limited area.

Examples are:

• QZSS (Japan); Quasi-Zenith Satellite System, has 4 satellites from which one is geostationary and the other one is inclined geostationary

• IRNSS/NaviC (India); Indian Regional Navigation Satellite System, op. since 2018, has 7 satellites

Skyplot: Imagine you’re looking into the sky and project that half-sphere (up until the horizon!) onto a circular map. The satellites can be seen as dots. They show the elevation of satellites (how high they are above the horizon) and the azimuth (the direction where the satellite is).

For groundplots, one can see how the satellites move around earth (“what they see”).

The neutral atmosphere and the ionosphere blocks certain wavelengths for electromagnetic waves on the earth (Acoustic waves obviously can’t be used as they need a medium). There are some windows which wavelengths are let through: Visible light, infrared windows, some microwave windows and a big radio window. Long-wavelength radio waves are blocked by the ionosphere, so the wavelength can’t be too long (this is how old radios work: they send long-wavelength radio waves which get reflected by the ionosphere to be received somewhere else in the world!)

GNSS systems use different bands to broadcast their signals. For GPS, these are L1, L2 and L5. With the exception of L2, these bands are also similar for the other GNSS systems, but they are typically a bit wider so they can be received at a wider range of frequency.

They range from ~ 1100 - 1600 MHz, having a wavelength of ~ 0.27 - 0.18m.

A GNSS signal consists of several different things (GLONASS not included as they work a bit differently):

• carrier wave: radio frequency sinusoidal signal

• PRN code: sequences of randomly distributed 0s and 1s (binary, here: follows Gold Code), is repeated over and over, usually 1 ms long -> used to identify satellite as it’s unique for every satellite

• navigation data: binary coded message providing info about satellite’s position and velocity as well as clock bias, satellite health etc. -> necesary info for user to perform positioning service

Positioning is done with help of the carrier wave (carrier-phase measurements) and/or with the PRN code (Code-phase measurements).

PRN code can be the P- or the C/A-code. C/A code is for civilian use (L1 band) and P-Code (more precise) can be encrypted, preventing unauthorized access. P-Code works a bit different than C/A code:

The P-Code is a very long code which would take a week to repeat. Each satellite is assigned a portion of it, repeating it every 7 days. It’s broadcasted on L1 and L2 frequencies.

• Doppler observables, used for velocity determination

• Code pseudo-ranges, derived from PRN code with time delays (Pseudorange and not range due to e.g. clock errors (mainly from receiver)!)

• Carrier-phase measurements

• Signal-to-noise-ratio (SNR), indicated signal quality

However, the primary observable is of course the time delay.

Code-phased measurements use a known, repeating sequence of signals (pseudorandom noise PRN, series of binary numbers 0 or 1) which is transmitted by the satellite at a very high speed. For GPS, this is often the C/A (Coarse/Acquisition) code. The receiver generated an identical PRN code and shifts it until it matches the one it receives from the satellite.

The time delay between when the receiver's code matches the satellite's incoming code indicates the signal’s time of arrival (ToA).

The receiver calculates how long it took for the signal to travel from the satellite to the receiver by determining the shift required to synchronize the codes. This shift is always half of the width of tau (basically half of the 1 or 0s that make up the code). To know which satellites code has been received, the receiver needs to “know” all the codes emitted by the GNSS satellites. This time is called Time of Flight.

Code-phase measurements from C/A Code have an accuracy of 5 -10 meters without augmentation.

They are used for the initial estimation of the receivers position.

Spoofing & Jamming can lead to being unable to do positioning. Other than that, ionospheric delays can cause a location error up to 100m.

Dual- or even triple-frequency receivers can compensate ionospheric delay: they remove up to 99.9% of ionospheric effects. Single-frequency receivers work best when the ionosphere is undistrurbed and can correct up to 75% of the delay when the ionosphere is calm.

• tunnels: solution could be a series of antennas aboveground. A software could simulate satellite’s signals and GNSS receivers could then use the “GNSS” signals transmitted by the antennas

• underwater: GNSS signals can’t penetrate water (this is why GNSS Reflectometry works in the first place); acoustic waves could be used instead

Refractivity depends on different parts of the atmosphere:

• dry: depends on atmospheric pressure & temperature

• wet: depends on water vaopr partial pressure and temperature

• Ionosphere: depends on electron density in the ionosphere and the carrier frequency

The main challenge for calculating refractivity models is the spatial & temporal change of the refractivity

Less than a second. If we assume the signal travels with the speed of light at 300000 km/s and the satellite is ~ 20000 km away, the signal needs 20000/300000 = 0.066 s, so around 70 ms.

The C/A code as well as the p code are ranging codes used by GPS.

C/A-Code, also Clear/Aquisition code, is code that can be used for measurements by the general public. It is usually less accurate (~ 5-10 m) and is broadcasted on a single frequency (L1). It’s also around a ms long.

The P-Code, also Precision Code, is code that is much more precise (~ 30-40cm) and broadcasted onto two frequencies (L1 and L2). It’s different for each satellite and much (!) longer.

The lower the elevation of the satellite is, the more atmosphere the signal has to cross which results in larger delays. For example in the polar regions, there are no GNSS satellites which are in zenith. The delay is exponential:

5° -> 25m

10° -> 13m

20° -> 7m

90° (zenith) -> 2.3m

The troposphere is the lowest atmosphere layer from the ground up to 10km.

The ionosphere is located in the thermosphere from 60-300km above the earth’s surface.

Up to 3h

GPS has a higher error in the ionosphere than GLONASS.

The ionospheric delay depends on the signal frequency, and is lower for higher frequencies (dispersion of signals is higher at lower frequencies). Because GLONASS signals have a higher frequency than GPS signals, they experience less delays in the ionosphere.

The electron density in the ionosphere changes with time and also depending on location.

The temporal variability of the electron density is correlated with the solar activity, which produces an 11-year cycle. At the maximum of a solar cycle, more sunspots appear at the sun, which causes more UV radiation and causes more ionization = higher electron density. Also, during a maximum geomagnetic storms occur more often.

The electron denisty also changes with local time. In the daytime, the electron density is higher due to the sun (solar ionization). Therefore, the electron density is also higher in summer.

The electron density also varies with location. For example, in the equatiorial regions and the polar regions the electron density is highest. In the polar (“auroral”) regions this is due to external influence (= the sun), in the equatorial regions this is caused by magnetism (equatorial ionization anomaly).

In GNSS, what is measured by code phase measurements is the time delay between the sent and received signal. If there were no errors, for example due to clock biases, multiplying the time delay with the speed of light would result in the (true) range. But because there are biases and errors, it’s called a pseudorange that has to be corrected first.

The refractive index describes how much the speed of light is reduced in a medium compared to a vacuum, which leads to a “bending” of the path. It can be calculated with the Smith Weintraub formula. The refractivity then is a scaled version of the refractive index:

N = (n-1)*10^6, which makes it easier to work with. For the Earth’s atmosphere at the surface, the refractivity is 360.

Integrated water vapor is a measurement of how much water vapor is in a vertical column above the ground station. This is important because water vapor is a greenhouse gas and measuring the water vapor content can be beneficial for climate change modelling. It’s also used for weather forecasts because water vapor fuels cloud formation. There is more water vapor in summer & less in winter; the water vapor content is also increasing (climate change!).

IWV is derived by measuring the Zenith Path Delay of GNSS signals from the GNSS satellites to the ground station. This delay has a wet and a dry component, and beacuse the dry part can be calculated, there is a direct link to the Zenith wet delay, which partly consists of the IWV. Then, with the Zenith Path Delay and mapping functions the IWV can be derived.

To derive the Zenith Path delay, the satellite must theoretically not be flying directly overhead, but there are also mapping functions that estimate the zenith delay from many slant delays. This is how IWV measurements are possible even for polar regions. Still, the models are not as good for polar regions simply because there are less stations & possibly also due to a very dry atmosphere (wet delay is low, therefore small errors can lead to great errors in IWV).

With slant delays 3D water vapor measurements acan be performed.

The Ionosphere is part of Earth’s upper atmosphere, between 80 and about 600 km (Mesosphere & Thermosphere) where Extreme Ultra Violet (EUV) and X-ray solar radiation ionizes the atoms and molecules thus creating a layer of electrons.

The atmosphere represents an anisotropic inhomogenous media.

Starting from the Earth’s surface:

• Troposphere (up to ~ 10km): Heated by warm ground, temp decreases with altitude. min. -53°C.

• Stratosphere (~15-50km): contains ozone layer which absorbs UV radiation, temp therefore increases with altitude (-50 to -5°C)

• Mesosphere (~50-80km): The coldest atmosphere layer, down to -90°C due to no gases that absorb sunlight. There is CO2 in the mesosphere, which releases heat in infrared, cooling the mesosphere down. Is especially cool in summer due to mesospheric circulation. Ionosphere is part of mesopshere.

• Thermosphere (~85km up to 500-1000km): solar UV and X-ray radiation is absorbed, ionizing molecules (here is the ionosphere!) -> heating, temp increases with altitude! (You wouldn’t feel the heat though because the density is so low).

• Plasmasphere (2000-20200km): also called inner magnetosphere; consists of low-energy (relatively cool) plasma, particle motion dominated entirely by the geomagnetic field & co-rotating with the earth

• neutral atmosphere (Troposphere & Stratosphere): neutral particles; ozone layer (O3) and greenhouse gases like CO2, SO2

• Mesosphere & Thermosphere: mixture of neutral and charged particles like O and O+, N2 and N2+; additionally metallic ions (coming from meteors!)

• Exosphere: mainly charged particles like H+, He+.

In general, with increasing altitude the weight of particles decrease.

Plasma is the state of matter after gas.

It’s a hot, (partially) ionized gas (so hot that electrons are freed from the atoms). The free electrons & ions allow electric currents to flow through the plasma, which enables plasma to react to electric and magnetic fields.

Lightning is an example of plasma. Also, stars are made out of plasma.

TECU (TEC Unit), where 1 TECU = 10^16 electrons/m²

TEC = total electron content, which describes the number of electrons in a column stretching between the Earth’s surface and the upper observation boundary.

Particles become ionized due to the photoelectric effect (= the sun). The radiation from the sun (UV, EUV, X-ray) has enough energy to ionize atoms and molecules.

This means that during the day a certain amount of air particles become ionized; after sunset, there is a high recombination rate which leads to a loss of ionization.

The ionosphere consists of 4 layers:

• D-layer (50-80km): Only present during day, consists mostly of H3O+ and NO3+ ions

• E-layer (100-150km): present during day & night, but stronger at day; consists mainly of O2+ and NO+ ions

• F-layer: splits up to 2 layers during day, consists mostly of O+ ions:

  • F1-layer (150-250km)

  • F2-layer (from 250km), highest electron density

The highest electron denisty is in the F layer (daytime: F2-layer) at daytime at ~ 15° N/S (magnetic equator!).

During the day, the sun ionizes the atmopshere due to the photoelectric effect. The 2 maxima at ~ 15°N/S are due to the equatorial anomaly/equatoral fountain effect.

This effect leads to an upward motion of electrons at the equator and distributes them at 15° North and south similar to a water fountain. This is because of Earth’s magnetic & electric field and due to the shape of the field lines; at the equator, the magnetic field lines are nearly horizontal, and charged particles move perpendicular to that, driving them up. then they come down again along the curved magnetic field lines.

• meteors: Burn up in the atmosphere due to increased air density & thermal friction. They leave behind ionized trails at around 80-110km altitude.

• aurora: result from disturbances in the magnetosphere caused by solar winds; charged particles precipitate in upper atmosphere & “light up” the atmosphere

• airglow: caused by recombination of ions

• noctilucent clouds: ice crystal clouds at 50-70°N/S (mesopshere must be cold enough, but at more than 70°N/S, sun doesn’t get low enough) in summer (when mesosphere is coldest), are only visible in astronomical twilight. Seen in 2024 due to the Hunga Tonga vulcano eruption (underwater vulacone) which brought a lot of water in the atmosphere!)

1 ‰ (per mille)

• rockets (in-situ): can measure chemical composition, ion concentration, winds & temperature as well as 3D accelerations

• radars

  • incoherent scatter radar (ISR), 5 sites worldwide, observe electron density, ion & electron temperatures as well as ion composition & plasma velocity

  • ionosondes: vertical sounding technique, observeselectron density profiles & E- and F-layer parameters as well as plasma drift measurements. Produce ionograms

• GNSS atmospheric sounding: TEC maps

• GNSS radio occultation: electron density profiles

• in situ measurements of satellites, for example with accelerometer or magnetometers

During a solar maximum:

• higher ioniztion level in ionosphere -> greater disturbances for signals, reducing accuracy

• layers of ionosphere are higher -> changes max electron density altitudes which impact ionospheric models

• higher chance of severe space weather events -> can damage satellites & disrupt power grids, but also more auroral activity

• higher neutral density of the atmosphere -> increases atmospheric drag for satellites

Space Weather refers to a collection of physical processes, beginning at the Sun and ultimately affecting human activities on Earth and in space. It defines the electromagnetic conditions near-earth.

• Core: concentrates 75% of the suns’s mass in 5% of its volume, here’s where the nuclear fusion happens

• Radiative zone: energy is transported outwards by electromagnetic radiation

• convection zone: the energy is further transported outwards by convection in huge cells

• photosphere: surface of the sun, ca. 100km thick, emits visible light, here are the sunspots. Is composed of plasma convection cells (=granules) whose lifetime is ~20min, gives a boiling pattern

• chromosphere: sun’s atmosphere

• corona: sun’s outer atmopshere, can be seen during solar eclipse

Sunspots are cooler (therefore dark), temporary spots on the sun’s surface (photosphere) which indicate the sun’s activity (more sunspots = sun is more active). Therefore, their number varies in the solar cycle.

At the beginning of a solar cycle the magnetic field lines of the sun are almost parallel. Differential rotation (the sun rotates quicker at the poles than at the equator) leads to a torsion of the magnetic field lines, so much so that they build loops on the photosphere. Where the field lines loop out of the photosphere, the plasma of the convection cells can’t move to the surface (because magnetic fields trap gas & plasma reacts to magnetic fields), causing a cooler region -> sunspot!

Funfact: At a solar maximum, sunspots are closer to the equator while at a solar minimum, the sunspots form at midlatitudes.

A solar cycle lasts 11 years, but a total (Hale) cycle lasts 22 years because after 11 years, the magnetic field flips (this is the solar maximum).

This is due to the differential rotation on the sun, causing torsion on the magnetic field lines until the magnetic field becomes unstable and reorganizes to an opposite polarity field.

(Earth’s magnetic field also flips! Just not as frequently).

We’re currently at the maximum of cycle 25.

The sun’s magnetic field, which causes the cycles, protects us from cosmic rays, which is why in solar minima more cosmic rays reach the earth, affecting the amount of radiation people get, for example on flights.

• sunspots: cool regions caused by tilted magnetic field lines, indicator of solar activity

• solar flares: sudden increases of brightness on the photosphere -> release of electronmagnetic radiation

• Coronal mass ejections (CMEs): release of plasma & radiation from corona

Solar flares are explosions on the sun which lead to a release of electronmagnetic radiation.

It is caused by stored energy in twisted magnetic field lines, susually above sunspots, which accelerates charged particles in the surrounding plasma, leading to a burst of radiation across the electromagnetic spectrum. This radiation travels with the speed of light, therefore reaches Earth in ~8 minutes.

Solar flares are classified into:

• A-class: no effect on us

• B-class: no effect on us

• C-class: few noticable consequences

• M-class: cause brief radio blackouts & may cause minor radiation storms

• X-class: trigger radio blackouts around the whole world & cause long lasting radiation storms

Solar flares affect the dayside of earth more because this side is aligned with the sun.

Coronal Mass Ejections (also CME) refers to a release of tons of plasma from the sun’s corona into space. They occur more often during solar maxima.

It needs around 20 hours - 3 days to reach the earth and the particles are deflected by Earth’s atmosphere. They cause geomagnetic storms.

They are caused by the magnetic field of the sun like solar flares. The differential rotation leads to a torsion in the magnetic field lines, which increases magnetic tension, until a magnetic reconnection happens: The field lines suddenly rearrange into a simpler configuration (locally)-> releases energy.

Solar wind is a stream of ionized gas (plasma) released from the Sun which consists mainly of electrons, protons and He2+. The solar wind vafries in density, temp and speed over time, but is around 300-800km/s fast.

We can “see” the solar wind when a comet flies by the sun; its tail always points away from the sun’s surface!

The particles of the solar wind are deflected by the Earth’s magnetic field, causing them to travel around the planet. The part of the magnetosphere not facing the sun gets elongated (magnetotail). Solar wind and geomagnetic storms cause magnetic reconnection in the magnetotail (field lines snap and reconnect!). This releases energy & flings charged particles back towards earth, along the field lines which have their footprint at the poles. It allows particles from the solar wind to enter at the reconnection points as well. At the magnetic poles, where the footprint of the magnetic field lines are, auroras are caused (auroral oval).

The particles of the solar wind are deflected by the Earth’s magnetic field, causing them to travel around the planet. The part of the magnetosphere not facing the sun gets elongated (magnetotail). Solar wind and geomagnetic storms cause magnetic reconnection in the magnetotail (field lines snap and reconnect!). This releases energy & flings charged particles back towards earth, along the field lines which have their footprint at the poles. It allows particles from the solar wind to enter at the reconnection points as well. At the magnetic poles, where the footprint of the magnetic field lines are, the charged particles meet oxygen and nitrogen atoms in the Earth’s atmosphere, exciting them. When the ionized particles in the Earth’s atmosphere fall back into their normal state, they emit light -> aurora! (auroral oval).

During geomagnetic storms the auroral oval can extend downwards into the midlatitudes.

The colors of an aurora depend on the altitude of the excited particles of the Earth’s atmosphere.

Above 250km, it’s mostly oxygen and energetic electrons -> orange-red, mostly seen at midlatitudes (because of the curve of the earth, you can only see the auroras higher up!). This is at the edge of what humans can see with their eyes, so it’s harder to see for us. Blue colors coming from this altitude (F-Layer) is associated with geomagnetic storms.

At around 100km, it’s mostly oxygen and electrons coming from N2 -> green (most commonly seen!)

At around 80km, it’s mostly ionized nitrogen molecules n2+ and energetic electrons -> deep blue - purple

• increase in electron density

• increase in neutral density

• spacecraft damage

• satellite problems: degradation of material, increased drag -> orbit altitude decrease (example: 2022 Starlink, 40 satellites reentered Earth’s atmosphere), problems with instruments, more noise -> orientation problems

• radio communication blackouts/delays due to higher plasma density and plasma instabilities; higher radiation, radio waves interacting with ionosphere lose energy, could be completely absorbed -> relevant for planes

• disturbance in GNSS signals

• power grid outages: induced current causes hot spots, melting the wires

For the GNSS frequencies, the refractive index is given by the refractivity (which in turn depends on pressure, temp and water vapor), frequency (of the signal), electron density, the Earth’s magnetic field vector and the wave normal vector.

The optical path length describes how the signal slows down in the atmosphere as if it took a longer path (even though geometrically it didn’t).

It can be written as O = r + T + L,

where r = geometric distance, T = tropospheric delay, L = ionospheric advance

The excess path length is then the difference between the geometric path and the optical path.

Fermat’s principle, or the principle of least time, is the principle that a signal travels the path that takes the least time (not necessarily the path with the shortest distance).

In a vacuum, light travels in a straight line, but in a medium, the signal’s speed gets changed due to refractivity in the atmosphere. To minimize travel time, the signal might curve - similar to how when you want to get from one side of the lake to the other, the fastest path might be to walk around it, not swim through.

The actual ray paths are calculated with ray-tracing-algorithms. Once that is done, the tropospheric delay & the ionospheric advance are computed.

The linear combination of optical path lengths (for two frequencies) is done to remove the (first-order) effect of the ionosphere. This does not work for the troposphere because the tropospheric delay does not depend on the frequency and does therefore not cancel out in linear combination.

Hoewever, for the ionosphere, what’s left is the ionospheric residual.

To model this ionospheric resiudal, Zernike polynomials are used to parameterize them over the sky - this is called higher order ionospheric corrections (HOIC) and improves the accuracy of the measurements, for example for precise point positioning.

• zenith hydrostatic & wet delay

• gradients

• mappng functions

Higher-Order Ionospheric Corrections (HOIC) can correct errors in orders of cm - mm.

If HOIC is applied to PPP,

1. Stations appear to move southward because before, small ionospheric biases caused systematic position shifts in the north-south direction (because PPP is a relatively long session method, biases accumulate) and HOIC sets them back -> applying HOIC cn change the apparent position of the station by mm to over a cm

2. the “tilting” of the troposphere changes, making the troposphere model cleaner

3. ZTD (zenith total delay) is affected: improves accuracy

How much HOIC affects the measurements depends on the ionosphere and its changes, especially with respect to the solar cycle (& sun activity).

Least Squares Adjustment

• GPS/MET, demonstrated the potential of radio occultation to sound Earth’s atmosphere (1995-1997)

• CHAMP (2000-2010)

• COSMIC-1 (2006-2018): 6 satellites

• GRACE-FO (since 2019)

• FORMOSAT-7/COSMIC-2 (since 2019)

• Metop-A/B/C (since 2006/2012/2018)

• TerraSAR/TanDEM-X (since 2007/2010)

• FY-3C/D/E (since 2013)

Phase measurements, because the precision is higher. The difference in refractivity over altitude may be small, therefore a very fine resolution is needed.

1. Single differencing to remove LEO clock error: A LEO satellite receives signals from 2 satellites: the occulting GPS satellite (GPS-O), which is the one whose signal is bent through the atmosphere, and the reference GPS satelltite (GPS-R), whose signal doesn’t go through the atmosphere/througha astable geometry. The difference between the two phase measurements of GPS-O and GPS-R cancels out the LEO receiver clock error.

2. Double differencing to remove LEO and GPS clock errors: For this, the single differencing in (1) is needed as well as single differencing to remove FID clock errors: This works by having a ground station which also receives signals from GPS-O and GPS-R; the difference between the two measurements cancels out the FID clock error (from the ground station) but still included the GPS clock error. By taking the difference from (1) and single differencing for FID clock errors the GPS clock difference is cancelled out because it’s present in both expressions

Some GNSS-RO satellites use double differencing, some don’t. GRACE has a stable LEO oscillator (stable atomic clock) and doesn’t to differencing at all, while older satellites like CHAMP hat a “bad” LEO oscillator and therefore did single differencing to remove the LEO clock error. Before 2000, double differencing needed to be done due to the activation of S/A (Selective Avaiability), which degraded the GPS signals in order to reduce the accuracy for civilian users.

The atmospheric doppler shift is a time derivative of the atmospheric phase delay. It describes the component of the Doppler shift that is caused by the atmosphere, and is a measurable consequence of the bending of the signal. It carries information about the curvature of the path -> the bending angle, which with the help of Abel inversion can be converted into the refractivity profile.

Alternatively, the total Doppler frequency shift can be measured. Then, the geometric Doppler is removed as well as other effects, and we end up with the armospheric Doppler shift.

Abel inversion is a mathematical technique that can compute a vertical profile, for example of the refractivity with the bending angle as an input value (derived from the atmospheric doppler frequency shift).

This works because the bending of a ray depends on the gradient of the refractive index (assumption needed for this: spherical symmetry -> the refractive index only depends on altitude). Abel inversion inverts this relationship.

• weather forecast

• climate modelling & observation, for example measurement of Global Temperature change

GNSS waves are right-handed circularily polarized. When they’re reflected however, they can switch to left handed!

• amplitude modulation: Varying the amplitude of a carrier wave to encode information. Often used for AM Radio & (old) analog TV signals

• frequency modulation: Varies the frequency of a carrier wave to encode information. Used for FM radio and weather radars

• phase modulation: modulate the carrier wave with binar codes. GNSS waves are phase modulated

GNSS Reflectometry is multistatic because the transitter (GNSS satellite) and receiver (LEO satellite) are spatially seperated & the receiver receives signals from multiple transmitters.

The specular point. The specular point is geometrically speaking the point where incident and reflected angle are equal.

In GNSS reflectometry, the glistening zone size increases when the surface is rough, meaning the reflection is (more) diffuse and therefore the received signal is weaker.

Permittivity is a material property that tells us how much a material resists/allows electric field propagation. It affects how strongly a wave reflects at a boundary (like for example the boundary between air and water) and how deeply it penetrates into the material. A high permittivity like for seawater or wet soil means that the surface reflection is strong and the penetration is shallow. Dry soil, for example, has a much lower permittivity.

The Rayleigh Parameter is a dimensionless number that describes how “rough” a surface appears to a wave of a certain wavelength and incidence angle. If the Rayleigh Parameter is = 1, the surface is smooth and the reflection is only the specular point (perfect relfection). For a Rayleigh parameter bigger than 1, the surface is rough(er).

Because GNSS signals are relatively long-wavelength (19cm for L1 band), even surfaces that look “rough” to the eye can be smooth to GNSS signals.

The sensitivity of the Rayleigh parameter to windspeed is higher for lower incidence angles, meaning that for high incidence angles (like over 50 degrees), wind speeds can’t be derived as clearly.

When a GNSS wave reflects off a smooth surface, it changes sense of rotation, going from right-handed to left-handed. Left handed circularily polarized signals are not received well by RHCP antennas, which is why a satellite/receiver doing GNSS Reflectometry needs either a dual-polarized antenna or specifically an LHCP antenna aimed at the reflection geometry (= nadir-looking when receiver is satellite).

The rougher the surface, the larger the distribution in path delays, forming a “wider” and dampened curve.

A Delay-Doppler Map is a (3D) representation of the reflected GNSS signal power as a function of the delay (x-axis), the doppler shift (y-axis, how much the frequency of the reflected signal is shifted due to the relative motion between the transmitter, reflecting surface and receiver) and the power/signal strength (z-axis).

From the DDM, surface roughness, delay spread and doppler spread can be derived.

Doppler shift is the frequency shift of the reflected signal relative to the direct signal.

From this, you can derive how fast the reflecting surface is moving forward/moving away. By combining both delay and Doppler, the reflection can be spatially resolved better than by delay alone.