^{*}

Reproduction is permitted for noncommercial purposes.

A simulation study to understand the influence of topography on the surface emissivity observed by a satellite microwave radiometer is carried out. We analyze the effects due to changes in observation angle, including the rotation of the polarization plane. A mountainous area in the Alps (Northern Italy) is considered and the information on the relief extracted from a digital elevation model is exploited. The numerical simulation refers to a radiometric image, acquired by a conically-scanning radiometer similar to AMSR-E, i.e., flying at 705 km of altitude with an observation angle of 55°. To single out the impact on surface emissivity, scattering of the radiation due to the atmosphere or neighboring elevated surfaces is not considered. C and X bands, for which atmospheric effects are negligible, and Ka band are analyzed. The results indicate that the changes in the local observation angle tend to lower the apparent emissivity of a radiometric pixel with respect to the corresponding flat surface characteristics. The effect of the rotation of the polarization plane enlarges (vertical polarization), or attenuates (horizontal polarization) this decrease. By doing some simplifying assumptions for the radiometer antenna, the conclusion is that the microwave emissivity at vertical polarization is underestimated, whilst the opposite occurs for horizontal polarization, except for Ka band, for which both under- and overprediction may occur. A quantification of the differences with respect to a flat soil and an approximate evaluation of their impact on soil moisture retrieval are yielded.

Spaceborne microwave radiometric observations of land are mainly determined by surface emissivity and temperature, especially at frequencies where the atmosphere is more transparent. If bare soil is considered, its emissivity at a given frequency depends on moisture, which influences the dielectric permittivity of a smooth surface [

Large-scale relief effects on the upwelling brightness temperature (_{B}

The topography effects for microwave radiometry over land have been analyzed in a past investigation carried out by Mätzler and Standley [_{B}

The main objective of this study is the quantification of the effects of changes in local observation angle on the emitted component of the radiation measured by a satellite microwave radiometer observing a mountainous scene. In addition, we also aim at yielding an approximate evaluation of the impact of these effects on soil moisture retrieval. The interest in pursuing these goals is due to the fact that most of the algorithms developed to retrieve bio-geophysical parameters (such as soil moisture) assume that the Earth surface is flat, so that their applicability to mountainous areas may be questioned. A quantification of the relief effects on microwave radiometry is therefore useful for preliminary correcting radiometric data before applying retrieval algorithms tuned for flat terrains.

Here we focus on the modification of the local observation angle and the rotation of the plane of linear polarization, thus complementing the investigation accomplished in [_{B}_{B}

The work is organized as follows. Section 2 describes the simulation methodology, i.e., the procedure that we have adopted to compute the emissivity of each DEM point at the three AMSR-E frequency bands considered here and to simulate the radiometric observation. In section 3, the comparison between the synthetic _{B}

To simulate the radiometric observation of a mountainous area, we have firstly computed the local observation angle of each surface element of the DEM. Then, we have estimated the emissivity toward the satellite radiometer of a DEM element. To do this, we have selected two semi-empirical models that allow calculating the microwave surface emissivity as a function of the local observation angle and of the soil roughness parameters. Finally, the observation of the satellite radiometer has been simulated by assuming specific measurement geometry. For this purpose, we have evaluated the elements of the DEM comprised in the instantaneous field of view of the radiometer antenna and then we have estimated the antenna temperature. Hereafter, a description of the simulation methodology is given in detail.

We have focused our analysis on a mountainous area in the Alps (Northern Italy) and we have derived the topography from a DEM with a spatial resolution of 250×250 m. A matrix of 512×512 points, i.e., an area of 128×128 km has been considered. For each DEM element, the aspect and the slope angles have been extracted and the local surface normal has been determined. Then, the angle between the local surface normal and the radiometer pointing direction, i.e., the local observation angle _{l}

The electromagnetic models of the complex dielectric permittivity ^{3}) and soil temperature (296 K). The fractions of sand and clay have been assumed equal to 48.5% and 18.5%, respectively.

To calculate the surface emissivity, we have selected the model developed by Wegmüller and Mätzler [

According to [_{p}_{0H}) denotes specular reflectivity (one minus emissivity) at _{l}

The INRA model expresses the soil emissivity as [

The emissivity of each element of the DEM, as a function the local observation angle, has been firstly calculated by applying

We have simulated the radiometric image for three frequency bands: 6.925, 10.65 and 36.5 GHz. A conically-scanning sensor observing the Earth at

We have determined the elements of the DEM comprised in every radiometric pixel, i.e., in the instantaneous field of view (IFOV) of the radiometer antenna, in a fairly approximate way. Denoting by _{x}_{y}_{x}_{y}

Once the number _{ml}_{i}_{i}_{li}_{Bi}_{A}_{i} is the solid angle under which the _{li}^{2}cos_{i}

The histogram of the normalized occurrences (NO) of the local observation angle in the considered Alpine region is shown in the upper panel of _{l}_{B}

The histograms of the emissivity at 6.925 GHz for a bare soil with

The analysis of the results of our simulation is based on the comparison between the antenna temperature expressed by _{l}

For C and X bands, only the WM emissivity model has been used. _{A}_{m}_{li}_{H}_{V}^{3} for the sake of representation clarity). The values obtained for a flat terrain are also shown (red solid lines: _{Hflat}_{Vflat}_{flat}_{A}_{H}_{H}_{Hflat}_{V}_{Vflat}_{flat}

_{V}_{H}_{V}_{H}_{A}_{Bi}_{li}_{i}_{li}_{i}

The modification of the local observation angle tends to lower the emissivity, especially at _{H}_{V}_{li}

Regarding the impact of the beam weighting, due to the presence of the term (cos_{li}_{i}_{li}_{i}_{Bi}_{A}_{li}_{li}_{i}_{i}_{Bi}_{A}_{H}_{V}_{H}_{V}

We can now explain the results of _{A}_{V}_{H}

The differences (bias as well as standard deviation) quantified in _{H}_{H}_{0}_{H}_{H}

The results for X band,

By observing left and central panels of _{A}_{H}_{V}

_{H}_{V}_{A}_{m}_{m}_{A}_{H}_{m}_{V}_{Vflat}

_{V}_{H}_{H}_{V}_{H}_{H}_{m}_{H}_{Hflat}

It must be considered that the results that we have obtained so far depend on the sensitivity of the emissivity to the observation angle as predicted by the WM model. It is interesting to verify whether the use of another model, characterized by a different trend emissivity-observation angle, leads to different results. We have applied our procedure, for the 36 GHz band, by adopting the INRA model too, whose behavior, especially for

The general overprediction of _{H}_{V}_{A}_{li}_{H}_{V}_{li}_{i}_{H}_{Hflat}_{V}^{-3}, respectively). With respect to _{V}_{m}

The mean values of Δ_{H}_{V}_{H}_{li}_{li}_{i}

_{H}_{H}_{V}

A simulation study aiming at quantifying the effects of changes in local observation angle on satellite microwave radiometric observations of a mountainous scene has been presented. A conically-scanning spaceborne radiometer similar to AMSR-E has been assumed. C and X bands, not affected by the atmosphere, as well as Ka band have been analyzed. Only the surface emissivity has been considered in this study that complements the investigation carried out in [

We have found that the changes tend to decrease the upward emissivity towards the sensor. This decrease is contrasted, for horizontal polarization and amplified, for vertical polarization, by the rotation of the plane of linear polarization. Accounting for the beam weighting performed by the radiometer antenna too, we have found that the brightness temperature at vertical polarization and the polarization index are underestimated with respect to the measurements over a flat terrain. The opposite generally occurs for horizontal polarization, although, at Ka band, we have found some situations in which the average observation angle within a radiometric pixel _{m}

Emissivity versus observation angle for a bare soil according to the WM model (left panel:

Measurement geometry assumed in the simulation. Upper panel shows the conical scan at 36 GHz. The green ellipses represent the radiometric pixels, _{i} (_{i}_{li}

Histograms (Normalized Occurrences: NO) of the local observation angle (upper panel) and of the emissivities at 6 GHz (WM model) for

Trend of _{H}_{V}^{3} (right panel) versus average observation angle (_{m}

Histograms (Normalized Occurences: NO) of the retrieved SMC computed by inverting the forward model assuming a constant observation angle of 55°.

Trend of _{H}_{V}^{3} (right panel) versus average observation angle (_{m}

Same of

Comparison between the values of Δ_{H}

Statistics of Δ_{H}_{V}

Δ_{H} |
Δ_{V} |
Δ^{3} | |
---|---|---|---|

mean | 4.16 | -3.31 | -15.20 |

std. dev. | 0.39 | 0.24 | 0.81 |

max | 5.10 | -2.70 | -13.58 |

min | 3.49 | -3.79 | -16.77 |

Statistics of Δ_{H}_{V}

Δ_{H} |
Δ_{V} |
Δ^{3} | |
---|---|---|---|

mean | 3.65 | -2.79 | -12.79 |

std. dev. | 0.56 | 0.37 | 0.97 |

max | 5.06 | -1.76 | -10.48 |

min | 2.68 | -3.59 | -14.98 |

Mean values of Δ_{H}_{V}

Δ_{H} |
Δ_{V} |
Δ^{3} | |
---|---|---|---|

6 GHz | 3.29 | -2.54 | -11.42 |

10 GHz | 2.77 | -2.09 | -9.31 |

Statistics of Δ_{H}_{V}

Δ_{H} |
Δ_{V} |
Δ^{3} | |

mean | 1.84 | -1.59 | -6.38 |

std. dev. | 2.11 | 1.21 | 2.74 |

max | 5.83 | 0.77 | 1.32 |

min | -6.71 | -7.70 | -11.48 |

Same of

Δ_{H} |
Δ_{V} |
Δ^{3} | |
---|---|---|---|

mean | 4.38 | -8.20 | -29.54 |

std. dev. | 2.52 | 2.38 | 10.97 |

max | 9.28 | -1.14 | 1.67 |

min | -2.21 | -12.51 | -50.23 |

Mean values of Δ_{H}_{V}

Δ_{H} |
Δ_{V} |
Δ^{3} | |
---|---|---|---|

36 GHz - WM | 1.02 | -1.23 | -4.06 |

36 GHZ - INRA | 0.07 | -2.42 | -5.29 |