IEEE Geoscience and Remote Sensing Magazine - March 2020 - 52

temperature, pressure, and humidity) at two imaging moments can cause different propagation delays, and there
exists an atmospheric phase component, usually called the
atmospheric phase screen (APS), in the interferometry phase
[70], [71]. The atmospheric phase contribution can be neglected for short-range, short-term applications (indicatively when the distance radar target is fewer than 100-200
m and the time between the acquisitions is shorter than
1-2 h) [4], [66].
The refractive-index change function N of the atmospheric phase component z(t)atm at time t between the radar sensor and the target is obtained by integrating along
path L:

	

z(t)atm =

4rfc < # N (R, t) dLF
L

c

, (24)

where n represents the change in the refractive index (which
varies with time t and space c), L represents a transmission
path of the signal, and fc is the system's center frequency.
Current InSAR atmospheric phase-correction algorithms
are mainly divided into two categories. The processing flow
for these two groups of atmospheric phase-compensation
methods is presented in Figure 13. One is based on the
distance-function model, which mainly includes stable PSs

DIn Phase

APS Phase Estimation
MultipleRegression
Model

DistanceFunction
Model

Based on Stable Targets
(PSs or High-Coherence
Points)

Based on Meteorological
Observations
(Temperature, Humidity,
and Pressure)
APS Compensation

Differential Phase
After APS Compensation
FIGURE 13. The processing flowchart of atmospheric phase
compensation.

52

or high-coherence points [76], [77]. When this assumption
of atmosphere spatial homogeneity is fulfilled, the projection of the high-coherence phase differences onto the range
direction exhibits a polynomial function relationship. The
other kind of atmospheric phase-correction algorithm is
based on a multiple-regression model [78], [79]. Multipleregression models may be more effective where large variations in temperature, pressure, and humidity linked to
height differences may be appreciated along the scene.
DISTANCE-FUNCTION MODEL
In general, the APS effect is strongly correlated spatially; that
is, it varies smoothly in space. Luzi and Pieraccini assume
that the APS is modeled as a linear function of distance, and
it is estimated using just one ground control point [70]. Other authors have used a similar approach by slightly changing
the model, for example, from linear to quadratic, or by varying the number of the stable PSs or high-coherence points
[72], [76], [77]. In the case of inhomogeneity refractiveindex distribution along the range direction, the piecewise
multiple-regression approach can be adopted [73]. These approaches are easy to implement and, considering that they
do not require extra data, quite effective.
For smooth terrain, the refractive-index N of the entire
measurement area should be constant. When spatial uniformity is satisfied, the phase difference of the high-coherence
point in the range direction has a linear relationship. Therefore, considering the atmospheric conditions at different times
t 1 and t 2, the atmospheric phase delay is calculated by estimating a simple phase slope, which is theoretically described
by the slope coefficient [76]. At the same time, assuming that
the refractive-index N depends only on the measured time,
the atmospheric phase difference between the sensor and the
target at different times has the following expression:
	

Tz(t 1, t 2)atm =

4rfc R $ 6N (t 2) - N (t 1)@
, (25)
c

where R is the distance from the radar sensor to the target.
MULTIPLE-REGRESSION MODEL
In steep-terrain areas, distance model-based solutions have
large errors [79]. In these areas, atmospheric disturbances
are closely related to terrain elevation, and spatial uniformity cannot be achievable [78]. Changes in atmospheric
conditions (temperature, pressure, and humidity) at the
time of radar imaging are important factors affecting the
APS [74], [75], [80]. An approach based on the refinement
of the meteorological delay model by means of a humidity calibration has been proposed. Under low-turbulence
atmospheric conditions, the proposed technique, based
on the model's refinement through a humidity-calibration
step, leads to significant improvements in compensation
performance [78]. In addition, in some areas, there are atmospheric disturbances that are closely related to the terrain elevation. In [79], several meteorological observatories at different elevation locations were set up to obtain
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2020
IEEE Geoscience and Remote Sensing Magazine - March 2020

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