GAMMA Interferometric Point Target Analysis Software (IPTA): Reference Manual

temp_mod_pt

NAME
temp_mod_pt - Calculate linear regression of differential interferometric phase with respect to temperature difference between SLCs and the related model for the temperature dependent phase

SYNOPSIS
temp_mod_pt <plist> <pmask> <SLC_tab_temp> <itab> <pres> [mode] [pdph_dtemp] [pph_offset] [pph_model] [pph_sigma] [dttab] [temp_max]

<plist>	(input) point list (int)
<pmask>	(input) point data stack of mask values (uchar, set to - to accept all points)
<SLC_tab_temp>	(input) table of SLC filenames, SLC parameter filenames, and temperature values (C) (text) SLC SLC_par Temperature C
<itab>	(input) table associating interferogram stack records with pairs of SLC stack records (text) pSLC_rec1 pSLC_rec2 itab_rec_num switch_flag
<pres>	(input) unwrapped phase data stack for each interferogram containing the temperature dependent phase (float)
<mode>	phase model processing mode: 0: a1temp[i] phase model has slope only, without temperature difference correction for each interferogram layer 1: a0 + a1temp[i] phase model has slope and intercept, without temperature difference correction for each interferogram layer 2: a1temp[i] phase model has slope only, with temperature difference correction for each interferogram layer 3: a0 + a1temp[i] phase model has slope and intercept, with temperature difference correction for each interferogram layer (default)
[pdph_dtemp]	(output) derivative of phase w.r.t. temperature for each point (radians/degree C, float) (enter - for none)
[pph_offset]	(output) phase offset of linear regression of phase w.r.t. temperature (radians, float) (enter - for none)
[pph_model]	(output) linear model for the phase due to temperature difference for each interferogram layer (radians, float) (enter - for none)
[pph_sigma]	(output) standard deviation of the linear regression residual phase for each point (radians, float) (enter - for none)
[dttab]	(output) table of delta temperature corrections for each interferogram layer (text) (enter - for none)
temp_max	maximum temperature difference for an SLC pair such that the interferometric phase is included in the regression (default: unlimited)

EXAMPLE

`temp_mod_pt pt - SLC_tab_temp itab pres1 3 pdh_dtemp - pph_mod pph_sigma dttab -`

This command uses a specially formatted list of the SLC_tab_temp file containing the average scene temperatures to calculate a model for temperature dependent phase for differential interferograms.

DESCRIPTION

It is known that structures expand and contract due to changes in the local temperature and solar illumination. These changes in the structure dimensions lead to changes in the distance of point targets to the radar. This manifests as changes in the absolute propagation phase along the line of sight. Since SLC data in IPTA analysis is from single point targets, we can observe a thermal contribution to interferometric phase proportional to the difference in temperatures when the image data were acquired. The program temp_mod_pt performs a linear regression on the residual interferometric phase with respect to the difference in scene temperatures for the days when the two SLC images were acquired. The slope of the linear regression is the derivative of the phase with respect to temperature difference.

The SLC_tab_temp has an additional third column with the average scene temperature in degrees C near to the time when the SLC data were acquired. An example of the SLC_tab_temp used in an example is shown below:

20071230.rslc 20071230.rslc.par 8.0 20080110.rslc 20080110.rslc.par 13.0 20080121.rslc 20080121.rslc.par 9.0 20080212.rslc 20080212.rslc.par 8.0 20080223.rslc 20080223.rslc.par 11.0 20080305.rslc 20080305.rslc.par 8.0

The third column of the SLC_tab_temp file is read by temp_mod_pt to determine the scene temperature. The SLC images used in the stack of interferograms is specified in the itab file and the residual unwrapped interferometric phase after removal of height related phase and tropospheric phase is stored in the pres file. Each layer in the pres file is the differential interferometric phase for interferogram using SLCs in the SLC_tab. The program temp_mod_pt prints out the temperature and date data for each interferogram. A section of the table for the first 6 interferograms in the stack of a test example is shown below:

interf #SLC-1 #SLC-2 Date-1 Date-2 Temp-1 Temp-2 Diff-Temp ************************************************************************** 1 40 1 2010 6 8 2007 12 3 21.000 8.000 -13.000 2 40 2 2010 6 8 2008 1 10 21.000 13.000 -8.000 3 40 3 2010 6 8 2008 1 21 21.000 9.000 -12.000 4 40 4 2010 6 8 2008 2 12 21.000 8.000 -13.000 5 40 5 2010 6 8 2008 2 23 21.000 11.000 -10.000 6 40 6 2010 6 8 2008 3 5 21.000 8.000 -13.000

Notice that this is a single reference stack with SLC 40 as the reference scene. Note that the reference scene in June is quite a bit warmer than the scenes acquired early in the year. The model for the temperature dependence of the interferometric phase can be calculated either with or without a constant offset. The value of the model phase for each point is given by the equation:

where is a phase constant and is the derivative of phase with respect to temperature difference for each point with index i. The slope and phase constant are obtained by least-squares fit of the residual phase with respect to difference temperature of each interferogram with index k. The standard deviation of the differences between the model and the phase values is stored in an array. The physical basis for this model is that thermal expansion is a linear function of temperature. The degree of expansion is dependent on the material properties, dimension of the structure, and the temperature difference.

For single-reference stacks the phase constant should be included in the phase model because the indicated temperature will not exact for many points causing a phase offset. In the case of multi-reference stacks the constant should rather be set to 0. Below is a part of the screen output for different points in the stack shown the phase offset, phase slope, and standard-deviation of the phase relative to the regression.

point: 0 offset (rad): -0.112 rad/deg.: -0.017 std.dev.(rad): 0.993 point: 9535 offset (rad): -0.024 rad/deg.: -0.005 std.dev.(rad): 0.572 point: 19070 offset (rad): -0.154 rad/deg.: -0.026 std.dev.(rad): 0.703 point: 28605 offset (rad): -0.018 rad/deg.: -0.002 std.dev.(rad): 0.329 point: 38140 offset (rad): -0.187 rad/deg.: -0.032 std.dev.(rad): 0.960 point: 47675 offset (rad): -0.205 rad/deg.: -0.034 std.dev.(rad): 0.778 point: 57210 offset (rad): 0.003 rad/deg.: 0.003 std.dev.(rad): 0.612 point: 66745 offset (rad): 0.108 rad/deg.: 0.018 std.dev.(rad): 0.654

If there is an offset in the average temperature difference of a single interferogram layer, there will be a bias in the phase constant values away from zero. Averaging over all the points in the layer an average temperature offset can be estimated by averaging the weighted values over all the points:

where the weights w_i for each point derived from the sensitivity and standard deviation of the phase relative to the point phase model:

Sample offsets calculated for the first 6 layers of the interferogram stack from the screen output is shown below.

The values for the first 6 interferograms in the stack are shown below:

itab tdiff tdiff1 delta std_dev ******************************************************* 1 -13.0000 -18.0009 -5.0009 6.761e-02 2 -8.0000 -1.8846 6.1154 5.588e-02 3 -12.0000 -4.6286 7.3714 4.955e-02 4 -13.0000 -14.2420 -1.2420 4.903e-02 5 -10.0000 -1.3900 8.6100 4.997e-02 6 -13.0000 -4.7219 8.2781 4.936e-02

The standard deviation of the weighted temperature corrections estimated for the interferometric phases of each point can be calculated using:

The standard deviation of the average of the all the individual offsets of the offset scales as if all the offsets have the same average. However the since the temperature correction for a layer is most likely not a constant over the scene, this assumption is not correct and there the actual standard deviation can be an order of magnitude greater than the value that is printed in the table. The value in the table is average weighted value divided by the number of points where the slope is greater than .02 radians/deg.

In the case where the average temperature correction is estimated for each interferogram (modes 2,3), the phase model is recalculated using the updated average temperature difference tdiff1.

Input to the program consists of the following data and parameters

plist IPTA point list with the range and azimuth coordinates of the points, see plist file format
pmask IPTA pmask file. This file is an unsigned byte file set to 1 where a point is to be considered and 0 where not. Entering a "-" assumes all points are accepted in the input point list
SLC_tab SLC_tab with the addition of a third column with nominal temperature in the area of the scene preferably close to the time of the data acquisition.
itab interferogram table. This is a text file with 4 columns that specifies the interferograms. The first two columns are references to entries in the SLC_tab, see itab file format
pres unwrapped residual phase for each point based interferogram in the stack
pmode This parameter determines if the phase mode: with or without phase constant, and if a temperature correction will be calculated and applied to the phase model.
temp_max Maximum magnitude of the temperature change to consider for consideration in the linear regression (degrees). By default all temperature differences are accepted

Output from the temp_mod_pt are IPTA data sets and optionally a text file with the temperature correction information for each interferogram layer. Entering a "-" character for a command line argument will cause that file not to be produced.

pdh_dtemp This is estimate of the derivative of the interferometric phase with respect to temperature difference (radians/degree) assuming a linear dependence. The linear regression is performed for each accepted point in the stack.
pph_offset This is the intercept of the linear regression of phase with respect to temperature difference (radians). In the case where the phase model does not include an offset, all values are set to 0.0.
pph_model Temperature dependent phase model values (radians). Evaluated for each point and each interferogram.
pph_sigma Standard deviation of the linear regression (radians).
ddtab Text file with 5 columns. 1: Interferogram number referring to entries in the itab. 2: Temperature difference calculated from the values in the SLC_tab. 3: Updated temperature value (degrees). 4: Difference between initial and updated value (degrees). 5: Standard deviation of the temperature correction (deg.). An example of the output in the dttab is shown below:

    1 -13.0000 -18.0009   -5.0009    6.761e-02
    2   -8.0000   -1.8846    6.1154    5.588e-02
    3 -12.0000   -4.6286    7.3714    4.955e-02
    4 -13.0000 -14.2420   -1.2420    4.903e-02
    5 -10.0000   -1.3900    8.6100    4.997e-02
    6 -13.0000   -4.7219    8.2781    4.936e-02

OPTIONS

The program temp_mod_pt can be used late in the processing to give a physical explanation to a part of the residual phase, or it can be done very early in the processing to support expansion of the spatial coverage of the solution, especially in the presence of very tall buildings.

When using temp_mod_pt very late in the processing it is typically done on a single-reference interferogram stack. At this stage reasonable solutions for most point heights, linear deformation rates, and atmospheric path delay phases already exist from having run several iterations of def_mod_pt. Displaying the residual phases shows, at least for some layers, a clear correlation with the building height. temp_mod_pt determines for each point the linear regression between the residual phases and the temperature difference of the corresponding pairs. The output from temp_mod_pt is the phase to temperature sensitivity, the phase offset (optional) and the temperature dependet phase model. Subtracting this model phase reduces the residual phase resulting in a higher quality solution. In an initial application of temp_mod_pt, the spatial coverage corresponds to the coverage already achieved. To extend the phase model to include taller buildings the following steps are followed:

Spatially expand the modeled phase to adjacent points (expand_data_pt)
Subtract the expanded temperature dependent phase model from the point differential phase stack (pres)
Run the phase regression again (def_mod_pt)
Run temp_mod_pt

To apply temp_mod_pt very early in the processing, a multi-reference stack is used typically that includes pairs with relatively short baselines and possibly also small changes in temperature (but not 0). When using a multi-reference stack with temp_mod_pt, it is reasonable to set the phase offset to 0.0 (modes 0, 2). With a multi-reference stack it is also possible to estimate the height corrections for each point. The temperature sensitivities as well as the height corrections from the multi-reference stack can be applied to model the temperature and height dependent phase in the single-reference interferogram stack. This facilitates keeping points on tall buildings within the solution.