3.4.5. Scattering from Ice-Covered Seas

There have been many oceanographic applications of HF radar but with a sole exception, they share the attribute that the dispersion relation assumed to govern the sea surface dynamics is that corresponding to a free water surface. In almost all applications, the general form of the dispersion relation,

$$
\omega^2 = \left(\text{g}\,\text{\textkappa} + \frac{\tau}{\rho}\,\text{\textkappa}^3\right) \text{tanh}\,\text{\textkappa}\,\text{H} \tag{16}
$$

is approximated by the inviscid, deep-water limit, τ → 0, *H* → ∞

$$
\alpha r^2 = \text{g\chi} \tag{17}
$$

though several studies have considered the shallow water case [29,41,42].

In the polar regions, the sea surface freezes and a complex ice structure forms over millions of square kilometers, varying dramatically with the season. This 'skin' is not completely rigid; it possesses mechanical properties that allow waves from the open sea to penetrate the ice zone, causing the surface to undulate as they propagate. In order to measure the surface motions and, from the Doppler signature, infer the structural and mechanical properties of the ice, the free surface dispersion relation has to be replaced by a new model that takes flexural and viscoelastic characteristics into account. Moreover, the HF scattering theory that is the basis of radar echo interpretation has to be reformulated with the appropriate ice dispersion relation. Different forms of ice have different dispersion relations, so a prerequisite to ice field mapping is a computational scattering theory that can handle any situation. Such a theory has been developed and reported in [11,37]; it solves the forward problem for HF radar, treating the most general case of bistatic geometry and polarimetric dependence. Figure 20 compares the Doppler spectra for a particular sea state and radar configuration, with and without ice present.

**Figure 20.** Doppler spectra computed for two situations: (**a**) A free ocean surface, and (**b**) a sea covered with small ice floes ('pancake' ice). Results for three radar frequencies are superimposed.

There are two key features of waves in the ice field that immediately draw our attention to bistatic HF radar geometries. First, the short waves tend to be attenuated far more quickly than long waves, in line with physical intuition. To give an idea of scale, waves in the swell frequency band can penetrate well over 100 km into the ice zone. Second, the most accessible properties of the ice that we seek to measure are encoded in the first-order Bragg scatter components. Together these imply is that we need to be able to sample the first-order Bragg scatter from the longer waves with our radars. As we noted earlier, bistatic scattering gives us greater access to the long waves.

Of course, the radar signal needs to propagate to areas of interest within the ice field, and this is another component of the remote sensing problem, but the local properties of the ice are reflected in the local ice dynamics and hence the local intrinsic Doppler spectrum.

#### 3.4.6. Scattering from the Ionosphere

In addition to providing the propagation channel for HF skywave radar, the ionosphere is relevant to a wide range of human activities, so its physical properties are of keen interest. To HFSWR users, it poses a hazard in the form of field-aligned irregularities that result in ionospheric clutter, a potent source of obscuration of desired echoes. Techniques aimed at mitigating ionospheric clutter are employed in some systems but seldom achieve the goal of peeling away the elevated clutter to reveal the echoes from the sea. The most successful methods exploit detailed knowledge of the physics

involved, and this applies to other technologies that rely on the ionosphere, such as communication with spacecraft, and to climate studies.

To determine the properties of the ionosphere, various sounding systems are used. Vertical incidence sounders provide useful point information but to sample a wide area, we need to employ oblique illumination. Line-of-sight HF radars, included in the table of Figure 1, support some types of observation, but to obtain some more subtle properties, a bistatic sounding technique is required; that is, a form of bistatic radar. There is a vast literature on this, but for now it suffices to point out that the demands of modern HF radar systems go far beyond the 'traditional' channel transfer function parameterization—the distribution of energy over group range and Doppler [23]. More advanced applications of HF skywave radar and HF communications demand information on the structure and dynamics of the ionospheric plasma as manifested in wavefront geometry [14], repolarization and depolarization [15], wideband phase path modulation [13], nonlinear effects [25], and a variety of higher-order parameters. Bistatic skywave radar is a powerful tool for exploring these phenomena, as well as being a beneficiary of the derived knowledge.

#### 3.4.7. Polarization Considerations in Bistatic Scattering Configurations

The scattering theories that are most widely employed to model HF radar scattering phenomena and hence to solve the associated inverse problems—the small perturbation method, the Born approximation, and physical optics—share the attribute that, at first order, they predict zero cross-polarized return for backscatter. If we wish to extract information from the cross-polarized components of the scattered field by applying the inverse scattering operator to the measurements, and staying with a monostatic radar configuration, we need to extend the theories to second order, thereby complicating the inversion procedures. Moreover, the cross-polarized elements of the monostatic polarization scattering matrix are frequently small, though this certainly may not be the case for the value of the information they contain. Not only can bistatic scattering geometries provide access to the cross-polarized echo information content at first order, it is often the case that cross-polarization becomes more significant as the bistatic angle increases. Thus, even at the quite fundamental level, there can be strong reasons for adopting a bistatic configuration even when a monostatic configuration is simpler to engineer and install.

That said, we need to bear in mind that the surface wave propagation mode heavily favours transverse magnetic field propagation (ie, approximately vertical, but with a forward tilt), the line-of-sight mode departs only slightly from being polarization-blind, and skywave propagation introduces complex field transformations, with both repolarization and depolarization [15] entering the picture. It follows that the practicalities of antenna design and installation are heavily dependent on the propagation modalities involved. Bistatic surface wave radars, like their monostatic counterparts, rely predominantly on relatively simple, vertically polarized antenna elements, though auxiliary horizontally polarized elements can be used to reduce external noise and interference very effectively. Purely line-of-sight radars in any configuration can measure the full scattering matrix, even through an intervening ionosphere [43], if they are equipped with appropriate dual-polarized elements. For skywave radars, it is not yet clear whether the cost and complexity of deploying a polarimetric capability can achieve, in practice, the benefits that theory suggests might be accessible. In particular, to design polarimetric antennas able to radiate a controlled polarization state over a substantial range of azimuths and elevations is a formidable challenge.

## **4. Bistatic Configurations that Are Currently of Particular Interest**

The great majority of HF radar systems in operation today employ a single propagation mechanism, be it the skywave or surface wave mode. Recently, though, there has been a surge of interest in 'hybrid-mode' mode radars, so here we shall remark very briefly on three of these special configurations.

First consider these two configurations:

• The Tx→[skywave]→target→[surface-wave]→Rx configuration,

• The Tx→[skywave]→target→[line-of-sight]→Rx configuration.

These configurations are not new: Designs for both types were proposed in the 1980s for land-based transmitters and shore-based or shipborne receivers. Associated experiments carried out, but several studies concluded that these configurations were optimum only for niche applications. Nevertheless, the concept of augmenting skywave radars with forward-based receiving facilities was resurrected by several groups in the mid-2000s [44,45] and by others more recently [46–51]. To date, the modelling studies reported in the open literature have ignored many of the complexities of the skywave leg of the propagation path, though we may anticipate improvements in this area. The other area where endless complications enter the picture is platform dynamics and the associated impact on the Doppler spectrum of received signals, as noted in some recent publications [35,36,52–54].

We should also note the emergence of another, potentially potent configuration:

• Tx→[surface-wave]→target→[line-of-sight]→Rx, where the reception takes place in space.

Of the many non-standard configurations listed in Figure 1, this one has only recently been explored in the form where the receiver is mounted on an orbiting spacecraft; this is illustrated in the schematic in Figure 21a. As there are hundreds of HFSWR systems in operation, a single satellite might be able to collect information from a large number of radars as it travels around the Earth. Bernhardt et al. [55] conducted an experiment to test the closely related concept Tx→[skywave]→target→[line-of-sight]→Rx using the Canadian ePOP/CASSIOPE satellite and were able to identify land and sea features in the received echoes.

**Figure 21.** (**a**) The bistatic configuration of the satellite-borne receiver acquiring sea clutter echoes produced by a shore-based HFSWR, and (**b**) the computed Doppler spectrum of the signal arriving at points along the satellite orbital path.

An independent investigation [56] modelled the second-order intrinsic Doppler spectrum of the upwards-propagating signals as they reach orbital heights and demonstrated the viability of the concept by measuring the Doppler spectra of sea clutter collected over a Tx→[skywave]→target→[surface-wave]→Rx path. As shown in Figure 21b, the Doppler spectrum from a fixed patch on the sea varies in a complex and potentially highly informative way along the satellite's orbital path, though of course it must be acquired and processed by the spacecraft. Figure 22 depicts the geometry of an experiment that confirmed the viability of a signal path that includes mode (iii) as a subset in a time-reversed sense, i.e., retracing the signal path from receiver to sea to ionosphere.

**Figure 22.** Experimental data from a nominal HF surface wave radar, which by happenstance recorded signals on Tx -> skywave -> sea scatter -> surface wave -> receiver. The magenta traces indicate the direct overhead reflection, the orange traces show the path of interest. Note that dual reflection points in the corrugated ionosphere provided a pair of echo traces in each case, slightly displaced in Doppler.
