Presupuestos Marketing

Radar is an active form of remote sensing. Active systems provide their own energy source rather than relying on the sun, giving them much greater control over illumination than possible with passive instruments. This greatly simplifies some model inversions and, uniquely, allows range resolved measurements. For these, a very short burst of radiation is emitted and the time taken for reflected energy to return recorded. With knowledge of the speed of electro-magnetic radiation this time can be converted into a range.

3.4.1 Synthetic aperture

Radars operate in the microwave domain, between 1cm and 1m, far longer than optical instruments. Due to the relationship between the diffraction limit of resolution (the smallest angular separation that can be resolved before diffraction causes objects to merge) and wavelength, much larger apertures are required to get usable ground resolutions from space (Tipler 1999, page 1128). Rather than use long antennae (which may flex, causing artifacts (Brooks 2008)), returns are collected as the satellite moves through its orbit, giving the effect of a larger aperture and so increasing resolution. This process is known as synthetic aperture radar (SAR) and was first developed as part of project “wolverine” during the 1950s, on behalf of the American military (Cutrona et al. 1961).

Whilst the long wavelength means that the illumination beam cannot be focused by reasonable sized antennae, various properties can be used to split the returns up into sections, using the synthetic aperture to create an “imaging radar”.

All electromagnetic (EM) radiation incident on a surface with a component of motion normal to the beam’s direction will suffer from a Doppler shift (Tipler 1999, page 463). In addition, for a moving radar platform (such as a satellite or aircraft) the reflected frequency will be higher

for surfaces coming towards the detector and lower for those moving away, much like the pitch change of a passing siren. As the beam has a finite width, the surfaces within different parts of the footprint will be travelling at different velocities and so result in Doppler shifts of different sizes. For a radar beam at an angle to the ground, the range to a return is related to the distance along the ground of its origin.

Therefore if a radar beam is pointed to the side so that no part of the beam crosses the platform’s velocity vector it is possible to slice the footprint up along the direction of motion using the Doppler shift, known as “along track” or “azimuthal” resolution. If the beam is not pointing straight downward, it is possible to split the footprint up along the beam’s axis using the ranging information, known as “across track” or “range” resolution. This then splits the footprint up into a two dimensional image, giving the effect of many, much higher resolution, radar footprints. This requires the full EM waves to be recorded, which at radar frequencies is possible. Unfortunately current electronics cannot respond to frequencies higher than a few tens of giga-Hertz, so the same techniques cannot be used at optical or thermal wavelengths.

To maximise the difference in Doppler shifts the beam points at right angles to the platform’s motion, then at some zenith angle to trade off between the distance to the surface (and so energy required) and angle of incidence (and so across track resolution).

Generally the range resolution of an active sensor is limited by the width of the outgoing pulse, as all returns will be convolved with this (Zebker and Goldstein 1986). The across track resolution can be further improved by using a range of frequencies in the outgoing pulse by starting off at a high frequency and returning to low during emission. This is known as a “chirp pulse” (Davidson

et al. 1996). In addition more power can be transmitted in total without needing a higher peak

power (which could damage the system’s circuits).

Interactions with vegetation For optical instruments, where the wavelength is much smaller

than canopy elements, it is assumed that all interactions are in the geometric domain and can be described by structure and BRDFs. Due to the longer wavelength this is not true for radar. For objects and gaps smaller than the wavelength the Rayleigh domain is entered (Tipler 1999, page 1031) and energy will be scattered from gaps that shorter wavelength energy could pass through

unhindered. In the Rayleigh domain the strength of scattering is related to the ratio of the scattering object size to the wavelength. This means that for shorter wavelength radars (<50cm) little energy reaches the canopy floor and so signals suffer from saturation at only moderate LAI values (typically 3-4 (Waring et al. 1995b)). For this reason the reflected intensity of shorter wavelength SARs suffers exactly the same problems of saturation and bias as passive optical sensors over forests (Lovell et al. 2003).

The range information can still be used to measure forest properties. Balzter (2001) used returns from bare ground to estimate nearby tree heights. This first study used the edge of a sharply bounded forest in Britain, however such features are not common around the globe and nor are clear gaps within forests, limiting the usefulness of such a direct approach.

Kellndorfer et al. (2004) proposed using the range resolution of SAR data to produce a height map of the top of forest canopies, then subtracting an existing ground height dataset (in this case from the USGS) to give tree height. However, the weak interaction of radar with vegetation means that the height predicted by SAR would not be to the tree tops but at a point somewhere within the crowns and so height was underestimated. Comparison with more reliable data sources (lidar and ground surveys) have confirmed this (Kenyi et al. 2009).

Longer wavelength SAR penetrates further into the canopy, so it may be possible to use it to measure the ground position and a shorter wavelength SAR to measure the tree top position (Hyde

et al. 2007). However, the high frequency signal will always penetrate someway into the canopy

whilst the longer wavelength will interact with tree trunks and larger branches (unless it is very long wavelength, unsuitable for satellites due to antennae size and atmospheric effects (Hyde et al. 2007)), leading to an underestimate of tree height (Balzter et al. 2007). This can be accounted for by site specific empirical relationships, but this would limit their global usefulness (Sexton et al. 2009).

ESA’s proposed Biomass Earth explorer mission plans to make use of a 60cm radar (ESA 2010), which will pass through foliage virtually unhindered but react strongly with tree trunks (which are around the same size as the wavelength). Whilst tree height measurements would not be trivial (requiring canopy models to predict attenuation) and it would have very little sensitivity to LAI,

the strength of the return should be related to trunk size and density and so biomass (Drinkwater

et al. 2008).

This is an exciting prospect in the early stages of development and may be launched around 2015. However long wavelengths radars suffer from increased interactions with the ionosphere (Freeman and Saatchi 2004).

3.4.2 Interferometry

Even with the various methods for improving range accuracy described above, the range resolution from an echo return of EM wave cannot be shorter than the carrier wavelength; which can be up to a few tens of centimetres. The resolution can be improved beyond this using interferometric SAR (InSAR). The signal reflected from a target at two different antennae locations will be out of phase, the phase difference depending on the difference in path length.

Combining these two measured signals results in interference and if the path difference is known, the phase difference can be used to give a more accurate estimate of range. This was first used to measure the topography of Venus from the Earth (Rogers and Ingalls 1969) (cited in Zebker and Goldstein (1986)) and first used in an airborne platform by Graham (1974).

Whilst the range resolution can be dramatically improved, it can only be determined as an integer multiple of the wavelength. If the range difference between the target and the two antennas is more than a wavelength, the interference wraps around. Therefore the phase information must be “unwrapped” to remove all ambiguities. Reliable methods have been developed to achieve this (Goldstein et al. 1988).

The two antennae need not collect data at the same time, to date there has only been one single pass InSAR in space, the SRTM mission of 1999 (Werner 2000). All other satellite InSAR attempts have used separate passes, either from two overflights by the same satellite or from two satellites on different orbits. Using measurements from two different times introduces complications. Any change in the target surface between the two passes will confuse the interferometry, an effect known as “temporal decoherence”. Over forests, where light breezes can move branches, this effect can be significant (Wagner et al. 2003), preventing accurate range estimates. Changes in weather conditions between passes, particularly rain, can have the same effect (Santoro et al. 2002).

Interactions with vegetation Interferometry has been shown to give accurate results over hard targets (Elhuset et al. 2003). However over diffuse targets, such as forests, the two antennae will travel along slightly different paths and so be affected by different scattering elements. This effect is known as “volume decoherence” and prevents accurate height estimation using the method described for non-interferometric SAR in the previous section with InSAR. However the volume decoherence itself contains information about the diffuse nature of the surface.

Sarabandi (1997) showed that, in theory, tree height can be physically related to the magni- tude of volume decoherence. Studies have attempted to extract tree height from InSAR, however they found that the effect saturated at only moderate tree heights, 5-10m (Santoro et al. 2002, Wagner et al. 2003). This may be because temporal decoherence tends to dominate over volume decoherence, limiting the accuracy possible (Wagner et al. 2003) and partly due to the saturation of signals at moderate canopy covers (Waring et al. 1995a). Santoro et al. (2002) states that “tree height retrieval from InSAR has severe limitations”.

3.4.3 Radar conclusions

An important advantage of radar is that it is in the Rayleigh domain in clouds, and so can see through with only weak attenuation. This is a huge advantage in frequently cloud covered regions, such as tropical rain forests (which also happen to contain the majority of the Earth’s above ground biomass), where, despite regular passes, successful optical measurements can be rare (Waring et al. 1995b).

Studies have used radar derived metrics (such as the decorrelation of repeat measurements) to

classify ground cover, but quantitative studies seem to be less common (Wegm¨uller and Werner

1997). When attempting physically based inversions, due to its weak interaction with canopies it tends to underestimate canopy height (Santoro et al. 2002, Balzter et al. 2007) and due to the long wavelength saturates at only moderate canopy densities (Waring et al. 1995a). Direct comparisons of inverted biophysical parameter accuracy against other active remote sensing techniques have shown radar to be inferior (Sexton et al. 2009).

Despite its limitations, the accuracy possible with radar is still greater than the uncertainty that would result from extrapolating between infrequent (once every 40 year) ground surveys (Wagner

et al. 2003). Combined with radar’s all weather capability and spatial coverage it can still provide

valuable information for monitoring the environment (Sexton et al. 2009) . However due to the lack of available long wavelength SAR data and the saturation of shorter wavelengths the rest of this thesis will concentrate on optical wavelengths. Of course the fusion of radar and optical data presents many exciting possibilities for constraining inversions and there seems to be much interest in this direction (Hyde et al. 2006) but this is beyond the scope of the thesis.