^{1}

^{*}

^{2}

^{2}

^{1}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

This paper presents a theoretical study of microwave remote sensing of vegetated surfaces. The purpose of this study is to find out if satellite bistatic radar systems can provide a performance, in terms of sensitivity to vegetation geophysical parameters, equal to or greater than the performance of monostatic systems. Up to now, no suitable bistatic data collected over land surfaces are available from satellite, so that the electromagnetic model developed at Tor Vergata University has been used to perform simulations of the scattering coefficient of corn, over a wide range of observation angles at L- and C-band. According to the electromagnetic model, the most promising configuration is the one which measures the VV or HH bistatic scattering coefficient on the plane that lies at the azimuth angle orthogonal with respect to the incidence plane. At this scattering angle, the soil contribution is minimized, and the effects of vegetation growth are highlighted.

A bistatic radar system is defined when antennas for reception and transmission are physically separated [

The effect of soil moisture (

As for vegetation, some airborne bistatic measurement campaigns at P-band have been carried out to find bistatic configurations allowing for the minimization of double bounce scattering from vertical trees in order to detect vehicles in forest concealment [

Extending the well-established TOV model to bistatic configurations different from the specular one, this paper investigates the bistatic radar potential in view of vegetation parameter estimation. The bistatic scattering simulations, provided herewith, focus on the identification of the configuration, which provides the most accurate crop height retrieval; in particular, corn plants are considered for this purpose. The sensitivity yielded by the selected bistatic configurations is compared with that of standard monostatic radar. Moreover, the potential of combining both measurements, considering that backscatter is expected to be measured by conventional SAR missions (multistatic case) is assessed. We have used the Cramér–Rao Lower Bound to quantify and compare the retrieval performances of the different configurations.

In Section 2, a summary of the electromagnetic model used to perform the bistatic simulations will be given, together with a description of the parameters used for the sensitivity analysis of the bistatic configurations carried out in the following Section 3. The directional properties of vegetation are deeply investigated and, in particular, it will be shown that co-polar bistatic measurements, acquired on a plane orthogonal with respect to the incidence one, show an interesting sensitivity to biomass. Finally, a bistatic configuration will be selected on the basis of the sensitivity analysis, and its performance will be compared against the one of a monostatic system.

Bistatic configurations are defined in terms of frequency, polarization and transmitter-target-receiver relative geometry. This geometry is shown in _{i}_{s}_{s}_{i}_{i}_{s}_{s}_{n}

In order to identify the set of bistatic system parameters (especially geometric parameters, but also polarization and frequency), which optimize the sensitivity to the crop height, the adopted methodology is based on a set of simulations of ^{0} carried out by running the TOV model in correspondence of a range of system and target parameters. For the purpose of identifying the best configurations in terms of polarizations, incidence and scattering angles, the retrieval accuracy is quantified by using the Cramér–Rao Lower Bound (CRLB), already used in [

The selected electromagnetic model is described in the next section, with additional details reported in the

The TOV model is fully polarimetric, since it can simulate the backscattering coefficient corresponding to any polarization of the incident and scattered power. However, in this work, simulations related to linear polarization only are discussed.

This section ends by describing the parameters chosen to identify the best configurations for crop status monitoring.

The TOV model, which has been selected to predict the bistatic scattering coefficient of crops, is based on the radiative transfer theory. It adopts a discrete approach [

The incoherent bistatic scattering coefficient of soil is computed through the Integral Equation Model (IEM) [^{0}_{HV}^{0}_{VV}^{0}_{VV}

In order to combine vegetation and soil contributions, the TOV model adopts the Matrix Doubling algorithm [

We recall here that model simulations showed a good fitting with polarimetric backscattering signatures measured over sunflower fields at L-band and two angles [

The reliability and accuracy of a theoretical model depends on its capacity to reproduce real measurements and, as just mentioned, the Tor Vergata model has been tested and validated against data collected under different conditions. Furthermore, a reliable model can also be used to predict measurements in order to evaluate the potential of a novel system. The model must then ensure the correct electromagnetic representation of the processes under study, but also a correct representation of the environmental scenario to be observed. To this end, the TOV model is made up of an electromagnetic module and of a growth module.

Indeed, the TOV model takes plant height as an input parameter, and it includes equations that, for a given height, calculate all other vegetation parameters, which are used to model corn bistatic scattering,

The sensitivity study carried out here is focused on the capability to retrieve plant height, from which it is possible to get information about the vegetation biomass. Height is related to plant water content in a way that depends on geographical characteristics and on working procedures of the agricultural site. As an example, in ^{2}, respectively.

In order to take into account different plant developments with respect to that of the Central Plain (like in the Belgian site reported in

The bistatic TOV model has been run in order to simulate the bistatic scattering of corn fields, and the results are outputted as a matrix whose rows represent the scattering azimuth angles and whose columns represent the scattering look angles. In order to represent the bi-dimensional scattering properties of this vegetation medium, a color map has been used, as that reported in _{s}_{s}_{s}_{s}_{s}_{i}_{s}_{s}_{i}

In _{z}_{s}_{s}_{i}_{s}_{s}_{s}

The increase of plant height (compare right and left column of

The effects of increasing soil roughness or moisture content are to increase bistatic scattering in most of the scattering directions, due to a higher soil contribution, which is visible due the incomplete coverage of crop (60%) and to higher interactions between soil and vegetation. However, it has been found (not shown in this paper) that, around the specular direction, an increase of roughness causes a decrease of coherent scattering, while an increase of moisture content causes an increase in all directions.

Changing incidence angle does not change the considerations previously drawn for _{i}^{0} values (except, of course, for the specular direction, where an increase of attenuation produces a decrease of scattering), the angular trends are in general analogous to those at L-band (as it can be deduced by comparing ^{0} maps is unique, so their color can be directly compared).

The retrieval accuracy of a given relevant target parameter (here, the crop height) obviously depends on the sensitivity of the measurement (the bistatic scattering coefficient, in this case) to the parameter itself. In order to evaluate the sensitivity to plant height, the soil parameters have been kept constant, and the following incremental ratio has been calculated from the model output:
_{z}

Besides the sensitivity, the Cramér–Rao Lower Bound (^{0}_{1},^{0}_{2},…,^{0}_{n}^{0} to estimate a given target parameter _{i}_{i}_{j}_{n}^{2}, the minimum variance of the estimate, _{i}, is defined by the following inequality [^{0}_{1} and ^{0}_{2,} and two parameters, _{1} (the target parameter) and _{2} (the nuisance parameter), the _{ij}^{0}_{i}_{j}

_{2}, so that the greater the numerator, the larger the variance of the estimator. As for the denominator, it is equal to the determinant of [^{T}[_{1} parameter. In fact, if the term (_{11}_{12} + _{21}_{22})^{2} compensates for the term
^{T}[_{1}, the sensitivity to _{1} must be high, and the various measurements must provide non-redundant information. The _{1} and _{2}.

Note that introducing in

As previously stated, the sensitivity analysis for the vegetated target has been carried out by considering corn, which is one of the world most common agricultural crops. In order to explore a wide range of bistatic configurations (polarizations and geometry) with a reasonable number of model runs, the system parameters reported in

Furthermore, two frequencies,

The following sensitivity analysis will be performed on single configuration data, that is, assuming that the measurement is acquired along a single observation direction.

The sensitivity to plant height is defined by ^{0}/Δ

The above plots (_{z}^{0} are shown at different directions, depending on the polarization: at horizontal polarization, it occurs on the scattering plane orthogonal to the incidence one, that is, for directions with _{s}_{s}_{s}_{s}_{s}_{i}_{s}^{0} in the specular direction.

As mentioned in Section 2, a plant cover fraction of approximately 60% has been assumed for the tallest plant, whereas for _{s}_{s}

Indeed, the sensitivity in the specular configuration is connected to the attenuation by the plant canopy, which makes it very suitable to vegetation biomass monitoring. The scattering phenomena, which take place in this direction, were theoretically analyzed in [

In order to understand this behavior, we singled out the contributions originating from the various scattering sources along the directions, which presented the maximum variability of sensitivity, _{s}_{s}^{0}_{HH}_{s}_{s}

We can conclude that the maximum sensitivity to plant height is displayed when the soil contribution is very low and the plant growth can appear with the maximum contrast.

The effects of changing incidence direction (_{i}_{s}_{s}_{i}_{s}_{s}_{i}_{s}_{s}

The sensitivity to plant height has been evaluated at C-band too. Although it is reduced with respect to L-band, it is still significant at vertical polarization at the same angles of the lower frequency. At C-band, the two co-polar linear polarizations show similar values (around 0.5 dB/(10 cm)), with horizontal polarization showing the best sensitivity on the “orthogonal” scattering plane.

In this section, it will be assumed that measurements at two polarizations, with the same bistatic observation direction, are available. It is understood that this analysis includes the special case of the observation of backscattered waves. Three different possible combinations of polarization are considered: bistatic measurements at VV and VH polarizations, bistatic measurements at HH and HV polarizations and bistatic measurements at VV and HH polarizations. To evaluate the performance of these multipolarized bistatic systems, the _{1}) is the corn plant height, _{2}) has been supposed to be the soil moisture content, while the soil roughness has been assumed to be constant (_{z}_{n}

In the maps presented in

We remind that ^{0}_{HV}_{s}_{i}

In general, horizontal and vertical polarizations are highly correlated on a wide range of bistatic angles, which results in high values of ^{0}_{VV}^{0}_{HV}^{0}_{HH}^{0}_{VH}_{s}^{0}_{VV}^{0}_{HV}^{0}_{HV}

A bistatic system requires the implementation of a suitable receiver, but the monostatic data are expected to be available through the active SAR missions, which provide the signal. Then, we can assume that the monostatic measurement (_{s}_{i}_{s}

Like in the previous section, the ^{0}_{VV}^{0}_{VV}^{0}_{HV}^{0}_{HV}^{0}_{HH}^{0}_{HH}^{0}_{VV}^{0}_{HV}^{0}_{HV}^{0}_{VV}^{0}_{HH}^{0}_{HV}^{0}_{HV}^{0}_{VV}^{0}_{HV}^{0}_{HH}

Note that when monostatic ^{0}_{HV}_{1} is the corn plant height, _{2}, has been supposed to be the soil moisture content and the soil roughness has been fixed to _{z} = 1.5 cm. ^{0}_{1}^{0}_{2}^{0}_{3}^{0}_{HV}^{0}_{VV}^{0}_{HV}^{0}_{HH}

The maps in ^{0}_{HV}^{0}_{VV}^{0}_{HH}

At HH and VV polarizations (top and bottom plots), bistatic scattering behaves similarly to backscattering, as long as the azimuth scattering angle _{s}_{s}_{s}_{i}

The maps concerning HV polarization (on the 2nd row) always display large values of ^{0}_{HV}

If the incidence angle is shifted to higher values, the maps show analogous correlations between measurements, but with slightly higher values of _{s}_{s}

The simulations performed at C-band (_{s}

The simulation results presented in the previous sections indicate that the specular configuration (especially at L-band), with a tolerance of about ±5° both in aspect and azimuth, is by far the most sensitive to vegetation biomass. The specular configuration, however, presents some problems in terms of achievable geometrical resolution of a radar imaging system, as discussed in [

If the receiver of the bistatic system is foreseen to operate at single polarization (see _{i}_{s} = 80°, _{s}_{i}_{VV}_{s} = 90° (where Δ_{HH}

^{0}_{VV}_{s}_{s}_{i}

The performance maps developed for the bistatic multipolarization configurations and for the multistatic configurations have shown that several bistatic configurations can provide measurements that are expected to yield good performances. In order to select the most significant ones, we take as a reference the multipolarized measurements performed in monostatic configuration,

At L-band, the monostatic couples are very much correlated (their ^{0}_{VV}^{0}_{HV}^{0}_{HH}^{0}_{VH}_{i}

^{0}_{VV}_{s}_{s}^{0}_{VV}^{0}_{HV}

^{0}_{HH}_{s}_{s}^{0}_{HH}^{0}_{VH}

At C-band, the error standard deviation is between 50 and 60 cm for the three monostatic couples. Lower values are shown by:

^{0}_{VV}_{s}_{s}^{0}_{VV}^{0}_{HV}

^{0}_{HH}_{s}_{s}^{0}_{HH}^{0}_{VH}

To summarize, the configurations in

In this paper, we have performed an investigation, based on theoretical simulations, on the potential of bistatic and multistatic radar measurements for retrieving crop parameters. To our knowledge, this is the first attempt to analyze this topic. The investigation has taken into account a single crop type (a corn field) and the bistatic configurations, which could be implemented having as master a SAR satellite system operating at one or two polarizations. The results show that, besides the observations around the specular direction, which are implemented, for instance, by the GNSS-R technique, bistatic imaging systems could provide a significant performance in retrieving corn height when looking at about 90° in azimuth with respect to the plane of incidence. The simulations yield a corn height retrieval error standard deviation reduced at least by a factor of three with respect to a monostatic system.

The sensitivity analysis indicates that the most useful responses show up when the soil contribution is at a minimum, so that the vegetation signature shows off with its maximum contrast. Although simulations reported in this paper refer to corn plants, this conclusion may apply to other vegetation types also.

A preliminary analysis of the feasibility of this bistatic geometry, which has been carried out, has shown that the image resolution is still adequate in this geometry, and a limited, but still significant coverage can be ensured using an Envisat type satellite as a master [

The work has been funded by the European Space Agency under contract ESTEC 19173/05/NL/GLC.

A detailed description of the active and passive version of the Tor Vergata model can be found in [

In the scattering models available in the literature, contributions of the various sources of scattering and absorption are combined by using, basically, the Radiative Transfer theory. Nevertheless, this theory can be implemented using different numerical procedures; the Tor Vergata model adopts the Matrix doubling method [

Predominant scatterers identified for the corn cover analyzed in this study.

Leaves, twigs | |

Stems | |

Soil |

To characterize the behavior of the vegetation medium, the vegetation layers are further subdivided into _{θ}_{i}_{s}

Scattering from each sublayer, for a downwards propagating wave at ^{−} and by a lower half-space scattering matrix S^{+}. In [_{ij}_{sk}^{−}_{pq}_{i}_{s}_{s}_{i}^{+}_{pq}_{i}_{s}_{s}_{i}_{s}_{I}

In order to correctly include both the scattering effects and the attenuation, a transmission matrix, T, is defined as the sum of the downward scattered specific intensity, S^{+}, and the fraction of forward propagating intensity affected by attenuation [^{+}_{pq}^{e}_{q}_{ij}^{e}_{q}_{ij}_{ij}

In order to achieve a considerable improvement in the fineness subdivision of the angular directions, without much increase in computation complexity [_{s}_{i}_{m}^{−}) and _{m}

The contributions of two adjacent thin sublayers are then combined through the Matrix doubling algorithm (Chapter 8 of [^{1}_{m}^{1}_{m}^{2}_{m}^{2}_{m}

By reiterating this procedure, the _{m}^{top}_{m}^{top}_{m}_{m}_{i}_{s}_{pqm}_{i}_{s}

The scattering properties of the soil are expressed by the dimensionless bistatic scattering coefficient ^{0}_{gpq}_{i}_{s}_{s}_{i}_{gpq}_{s}_{i}

Once the total matrices ^{t}_{m}_{s}_{s}_{s}_{i}

Geometric elements that identify the transmitter-target-receiver (Tx-TG-Rx) bistatic configuration.

Plant Water Content

Bistatic scattering coefficient ^{0} (dB) of corn plants with 50 cm and 150 cm height (left and right column, respectively), at L-band, _{i}_{z}

Bistatic scattering coefficient ^{0} (dB) of corn plants with 50 cm and 150 cm height (left and right column, respectively), at C-band, _{i}_{z}

Sensitivity to corn plant height [dB/(10 cm)] at L-band, _{i}_{z}

Sensitivity to corn plant height [dB/(10 cm)]. Same parameters as in

The scattering components along the scattering cone with _{s}_{i}_{z} = 1.5 cm, m_{g} = 25%. Corn height = 50 cm, vegetation cover = 40% (left column) and 150 cm, vegetation cover = 100% (right column). VV polarization (top row), HV polarization (middle row) and HH polarization (bottom row).

Square root of Cramér–Rao Lower Bound (_{i}_{z}^{0}_{VV}^{0}_{HV}^{0}_{HH}^{0}_{VH}^{0}_{HH}^{0}_{VV}

Square root of _{i}_{z}^{0}_{VV}^{0}_{VV}^{0}_{VV}^{0}_{HV}^{0}_{HV}^{0}_{HV}^{0}_{HV}^{0}_{VV}^{0}_{HH}^{0}_{HH}^{0}_{HH}^{0}_{HH}^{0}_{VH}

Square root of _{i}_{z}^{0}_{VV}^{0}_{VV}^{0}_{VV}^{0}_{HV}^{0}_{HV}^{0}_{HV}^{0}_{HV}^{0}_{VV}^{0}_{HH}^{0}_{HH}^{0}_{HH}^{0}_{HH}^{0}_{VH}

System parameters considered for the sensitivity analysis.

_{i} |
_{s} |
_{s} | |
---|---|---|---|

HH, VV, HV | 20, 35, 50 | 0 to 180, step 10 | 0 to 60 step 10 |

Parameters of underneath soil considered for the sensitivity analysis.

0.5, 1.5 | 5 (exponential autocorrelation function) | 10, 25 |

Suggested polarization combinations for _{I} = 20° considering a single bistatic polarization, a dual-polarized bistatic and a multistatic (active and passive systems at single polarization). The corresponding optimal bistatic geometries at L- and C-band (excluding the specular case) are also reported.

^{0} |
^{0} |
---|---|

in single configuration | in single configuration |

combined with bistatic ^{0} |
combined with bistatic ^{0} |

combined with monostatic ^{0}^{0} |
combined with monostatic ^{0}^{0} |

_{i} |
_{i} |

_{s} |
_{s} |

0 ≤ _{s} |
_{s} |