Evaluation of Time Series Tandem-x Digital Elevation Models

Digital Elevation Model (DEM) is an important input for geo-spatial analysis. For various applications like flood management, ortho rectification of remote sensing images, navigation, architectural works, defence, etc., high resolution DEM is required. TanDEM-X mission was launched in 2010 to obtain high resolution global DEM with HTRI-3 standard. SAR interferometry (InSAR) technique is used for DEM generation from TanDEM-X SAR data. The accuracy of DEM depends on many parameters like height ambiguity, incidence angle, polarization, etc. In this study, time series TanDEM-X data spanning over 3 years, had processed for generating DEM at the spatial resolution of 6 m and their accuracy had studied using DGPS elevation data and SRTM 90 m DEM. The products generated during DEM generation process are DEM, precision (or height error), coherence, layover and shadow images. Using weighted average fusion technique, ascending and descending DEMs are fused for improving the quality of DEM and to reduce invalid pixels corresponding to layover and shadow areas. Results from time series data were analysed and found RMSE error of fused DEMs is in the range of 2 m to 4 m, while individual DEM has accuracy of 3 m to 6 m with respect to DGPS elevation data. Fused DEMs are having high accuracy as well as less voids. The reduction of voids by fusion, ranges from 40 to 85% in different combinations of data.


INTRODUCTION
DEM is an important input for geo-spatial analysis, particularly in flood management, ortho-rectification of remote sensing images, navigation, architectural works, defence, etc.At present, freely available global DEMs are from SRTM and ASTER at spatial resolution of 90 m and 30 m respectively.For many applications, high resolution DEMs are required.In 2010, TanDEM-X mission was launched to obtain high resolution global DEM at the spatial resolution of 12 m with an absolute vertical accuracy of 10 m and relative accuracy of 2 m (Moreira et al., 2004(Moreira et al., , 2008;;Krieger et al., 2005;Toutin and Gray, 2000).According to Weber et al. (2006), there is a global need of HRTI-3 standard DEM having better vertical accuracy, consistency and global access.It is also important to know the quality and accuracy of DEMs because DEM quality can affects the quality of applications in which they are used.The quality of the DEM can be improved by fusing ascending and descending DEMs (Sansosti et al., 2000).
In this study, DEMs are generated from time series TanDEM-X data over three years period i e., 2011 to 2013 over Mumbai area, later these DEMs were fused and analysed.Weighted average fusion technique is used for fusion of DEMs.The accuracy of this fused DEMs depend on the parameters of input DEM like incidence angle, polarization, baseline, etc., which are considered for the selection of DEMs to be fused.All generated DEM's accuracy were studied using DGPS elevation data and SRTM DEM.

STUDY AREA AND DATA SETS
Mumbai is chosen as test area for this study.Mumbai covers varying land features such as reserved forest, mangroves, grass lands, wetlands, agriculture lands, and built-up area from high rise buildings to slums.Mumbai lies on the western coast of India * Corresponding author.and has total area of 603.4 km 2 .Elevation in this area vary from 15 m average in south Mumbai to 450 m in hilly region of north Mumbai above the mean sea level.The hilly terrain has thick to sparse vegetation cover and affects the DEM accuracy.The test area gives an opportunity to analyse and evaluate DEM with various land features.
For high resolution DEM generation and evaluation, TanDEM-X SAR Coregistered Single Look Slant Range Complex (CoSSC) data over Mumbai was acquired during 2011 to 2013.As the Mumbai area is selected for our research, DLR has been acquiring data under A.O. programme.11 data sets have been received for our application and they are listed in Table 1 with their sensor parameters like incidence angle, direction of system pass, baseline and Height of Ambiguity (HoA).

Date of
Inc. Coherence is a function of systemic spatial de-correlation and scene de-correlation that takes place between master and slave acquisitions.It's value ranges from 0 to 1.It is a ratio between coherent and incoherent summations.It is used to determine the quality of measurement.For 2 coregistered complex SAR images S1 and S2, interferometric coherence(γ) is given as: Precision is derived from parameters such as coherence, baseline and wavelength.Precision is an estimate of the measurement precision.Lower the precision value, the higher the measurement precision.Formula used for precision calculation is: where, p = precision value γ = coherence value As both ascending and descending DEMs have different HoA, their height error value (precision) is taken as reference along with layover shadow image, for the selection of fused DEM pixel value.The precision value at 90% cumulative frequency for both input DEMs is found using statistical tool and maximum of input DEM's HoA value is considered as Precision Threshold (PTH) for fusing the DEMs.(Deo et al., 2014) • NAN : If both DEM's n th pixel has layover shadow or if one has layover shadow and other has precision greater than threshold or in case of none has layover shadow but both have precision value greater than PTH, then fused DEM has NAN value for that pixel.
• Ascending or descending DEM value : If any input DEM's n th pixel has no layover shadow and it's precision value is less than PTH while other DEM has layover shadow or precision value greater than PTH value, then fused DEM has first DEM's pixel value.
• Weighted Sum : If both DEM's n th pixel has no layover shadow and also precision value is less than PTH, then fused DEM has weighted sum of both input DEM's pixel value.
The weighted average height value ĥ is then calculated using the maximum likelihood estimation as below: where, wi = Weight w assigned to i th DEM pixel, hi = Height value h of i th DEM pixel.
The weights for both DEMs have been derived from the precision map as where, σ h,i = Standard deviation of i th DEM at any pixel.
Water mask is created using ArcGIS online base map and one of precision images from TanDEM-X data for masking out water areas in accuracy assessment.Both raw DEMs and fused DEMs are analysed for their accuracy.The precision value and fused DEM elevation at DGPS locations are extracted for comparison.Validation of ascending, descending, and fused DEMs have been done using DGPS elevation data and also SRTM 90 m DEM.
In the fusion, if input ascending DEM has x% invalid pixels and descending DEM has y% invalid pixels and the fused DEM has f% invalid pixel, then Invalid Pixel Reduced (IPR) ratio is given by the ratio of minimum of input DEM invalids (x and y) and fused DEM invalids (f), as shown below: IPR shows improvement factor in fused DEM, higher the ratio more the improvement.The percentage improvement after fusion is given by: In this way, IPR shows degree of improvement for any ascending and descending DEM.

TanDEM-X DEM generated from various datasets
For all datasets mention in Table 1, DEMs were generated using SAR Interferometric DEM generation procedure with the help of SARscape 5.0 tool.All generated DEMs are having spatial resolution of 6 meters.Ascending and descending DEM precision maps are shown in Figure 2.

TanDEM-X DEM Fusion Analysis
Figure 5 shows common area for all datasets for fusing ascending and descending DEM which are indicated by * symbol in Table 1.
For fusion, 3 ascending and 3 descending DEMs as mentioned in methodology are selected and all possible combinations are examined and as a result, nine fused DEMs are generated.All fused DEMs are analysed.The RMSE error of fused DEMs with reference to DGPS data, Invalid Pixel Reduced (IPR) ratio, invalid pixels percentage in all DEMs w.r.t.fusion threshold are shown in Table 4.
Input DEMs and fused DEMs invalid pixel percentage, RMSE in fused DEM elevation and respective IPR ratio are plotted in Figure 6.Here fused DEM invalid pixels percentage ranges from 0.13 to 2.1%, whereas input DEM has invalid pixels in the range of 0.3% to 14.6%.Since, all ascending DEMs and descending DEMs have same target area and incidence angle of 46.2 o and 33.7 o , so it can be assumed that in this study, the fusion procedure is independent of incidence angle and depends on HoA mainly.In Table 5 and Figure    Ascending, descending and fused DEM for F. N. 7 is shown in Figure 8 as colour shaded map with pixels having layover shadow and precision greater than threshold as invalid voids.Considerable reduction of voids are seen in fused DEM (84%).

CONCLUSION
From the time series analysis within the span of 3 years, it has been observed that TanDEM-X DEMs generated in this study have better accuracy than the specified values for TanDEM-X global DEM with HRTI-3 standard and have similar accuracy as TanDEM-X proposed regional DEMs with HTRI-4 standard.RMS errors in ascending and descending DEM varies from 3 to 6 m while by fusing ascending and descending DEM, the error reduces by 2 to 4 m and invalid pixel count reduced upto 80% with respect to input DEM values.As the HoA and RMSE follows same trend, HoA can assist in preliminary analysis for dataset selection in DEM generation as well as for DEM fusion.It is also observed that HoA's difference lying between 35 to 50 m range had shown a better reduction in void's count.Fusion of datasets with different incidence angles and different PTH for each input can be extension of this study.

Figure 4 :
Figure 4: Normalized RMSE for various raw DEMs with their precision and HoA.

Figure 5 :
Figure 5: Precision image of common area for DEM fusion.
7, invalid pixels % and the RMSE in fused DEMs are plotted against the difference of input's HoAs of each fusion.It has been observed that increase in HoA's difference in between the input DEMs, reduces the RMSE and invalid pixels % values in fused DEM.Six out of nine fused DEM follows this trend, while Fusion No. (F.N.) 6, 9 and 2 shows quite high

Figure 7 :
Figure 7: Fused DEM invalid pixels count with respect to difference in HoA of input DEMs

Figure 8 :
Figure 8: ArcScene view of Ascending DEM subset with voids.
and shadow images.SRTM DEM is used for flat terrain removal in processing of TanDEM-X SAR data.The detailed flow chart of the InSAR procedure is shown in Figure1.
Deo et al. (2014) HoA.In fusion, pixel value is selected from ascending and descending DEM pixel values.Ascending DEM pixel value, descending DEM pixel value, weighted average of both DEM's pixel values and NAN are possible values for fused DEM pixel in different scenarios.The DEM accuracy with respect to their characteristics like HoA and incidence angle are throughly checked.Deo et al. (2014)has given the description of the fusion technique.

Table 2 :
Data sets characteristics and DEM RMSE w.r.t.DGPS data and SRTM data.
Baseline for these datasets vary and hence HoA.Although it has different HoA, RMSE deviation is not much different for the generated DEMs.Mean of the difference between TanDEM-X DEM and DGPS elevation data is also given in Table2.Elevation difference between DGPS and generated DEM elevation varies from 0 m to 17 m for flat to hilly terrain.The data acquired on 08-05-11 and 03-12-11 in ascending pass gives lower RMSE.The elevation difference for this data sets are 0 m to 8 m with respect to DGPS elevation data.From Table2, it can be concluded that higher the HoA, larger the error in generated raw DEM.Therefore, HoA can assist in dataset selection for DEM generation.For DEM fusion, input with lower RMSE are preferred for generating more accurate DEM.

Table 3 :
Mean and RMSE of precision (Height error) value at DGPS locations for different data sets.

Table 4 :
Fusion of various combination of date sets and RMSE error of fused DEMs with reference to DGPS data.

Table 5 :
HoA of input, RMSE and HoA difference of fused DEMs.