4. Pre-processing of orbital TPR data
4.3. Re-projection to a regular grid
Once the orbital TPR scans are filtered and the relevant variables extracted, these are re- projected from geographic coordinates (latitude/ longitude) to a metric projection (Universal Transverse Mercator Zone 18). Furthermore, the orbital scans need to be re-mapped from the variable flightpaths to a static, regular grid so that every measurement has the same spatial support and long-term statistics can be computed and mapped. While this is a general issue associated with both orbital satellite data and ground-based radars, Sharif and Ogden (2014) have demonstrated that the use of approximate methods as opposed to a precise re-mapping of the orbital scans onto a regular grid can induce relative errors exceeding 100%. Precise remapping consists of dividing the area of the target grid cell proportionally into polygonal tiles corresponding to the overlapping pixels of the radar scan (comparable to Delaunay triangula- tion/ Thiessen polygons). The mean areal estimate across the target grid cell is then computed by weighted averaging of the rainfall estimates within the tile proportional to the area of their respective polygons (Sharif and Ogden, 2014). On the other hand, approximate methods, typi- cally assign values based on the location of the centroid of the orbital pixel to that of the target grid cell. Common examples include:
nearest neighbour interpolation (NNB): the target grid cell is assigned the measurement value of the scan pixel whose centroid is closest to that of the target grid cell,
inverse-distance weighting (IDW): the measurement values of all pixels within or neigh- bouring the target grid cell are averged with weights proportional to the inverse of the squared distance of their centroid to the target grid cell centroid,
bilinear interpolation (BLN): the neighbouring four scan pixels are averaged based on the distance in two-deminsional space between their centroids and the centroid of the target grid cell (i.e. linear intrpolation along the x- and y-axis). Bookhagen and Strecker (2008) used bilinear interpolation to re-map the combined orbital TRMM Microwave Imager and Precipitation Radar (TRMM product 2B31) to a regular grid in order to construct a high-resolution climatology from this product.
However, all these methods are to some extent affected by factors associated with the repre- sentativeness of the satellite pixel(s) for the target grid cell, i.e. the distance between the pixel centroid and the grid cell centroid, the pixel size and orientation relative to the grid cell as well as potential precipitation gradients across the pixel (Sharif and Ogden, 2014).
In the present research, a number of approaches were assessed to re-map the orbital TPR data to a regular grid:
Precise Re-mapping (PRM): this approach acts as a benchmark reference, but is ex- tremely computationally demanding and therefore unsuitable for gridding of the entire TPR record,
nearest neighbour interpolation (NNB) inverse-distance weighting (IDW)
inverse-distance weighting with threshold (IDWT): The output of the IDW re-mapping is further processed by removing positive measurement values below a threshold of 0.1 mm hr-1 and replacing them by zero. This is intended to remove large areas of miniscule rainfall resulting from the spatial propagation of measurement values when these are IDW-interpolated across areas with pixels reporting no rain.
bilinear interpolation (BLN)
The orbital TPR scans are re-mapped to a 1 km grid across the spatial extent of a TMPA cell (approximately 27 km x 28 km) for 78 sites with automatic tipping-buckets across Colombia and Ecuador. For each site the interpolated spatial grids using the approximate methods (NNB, IDW, IDWT, BLN) are compared to the reference (PRM) across all 1 km grid cells within each TMPA cell and descriptive statistics of the rainfall distribution are computed: mean, rainfall occurrence frequency, mean of non-zero rainfall intensities, standard deviation of non- zero rainfall intensities. The results in fig. 4.2 show that in terms of the long-term mean there is very little difference between the approximate methods, which all over-estimate the reference (PRM). However, the occurrence frequencies estimated by NNB are much closer to those of
Figure 4.2.: Boxplots for mean intensity, occurrence frequency, non-zero mean intensity and non- zero standard deviation of the different re-mapping approaches across 78 TMPA tiles in the Tropical Andes.
PRM than the other approximate methods. This suggests that the interpolation methods IDW and BLN extend rainfall fields by estimating low rainfall intensities in areas that should be dry, according to PRM. This is supported by the slightly improved result for IDWT; however, IDWT does not entirely remove this effect. With respect to the non-zero rainfall intensity distribution, NNB overestimates the non-zero rainfall mean of PRM, whereas IDW and BLN under-estimate by approximately the same absolute error. The removal of low intensities mitigates this to some extent, causing IDWT to be the best-performing approximate method. On the other hand, IDW, IDWT and BLN all under-estimate the rainfall variability with NNB returning the best estimate of the PRM non-zero intensity standard deviation.
It needs to be considered that, as high-resolution (1 km) areal rainfall observations are not available to assess the accuracy of the pecise re-mapping, its suitability as a reference can only be assumed. Furthermore, there are a number of contributing factors, which cause the orbital TPR and re-mapping thereof to behave differently to that of a ground-based radar. Firstly, the trajectory of successive TPR overpasses changes over 46 days (48.5 days post-boost) until a cycle is complete. The satellite performs about 16 global orbits per day, resulting in 1900 - 2400 visits from different angles and orientations to any location in the tropical Andes over the entire TRMM era (fig. 2.5). This means that re-mapping errors are not consistent over time but
vary from one measurement to the next and random errors are likely to balance out over time to some extent. Secondly, a grid resolution (1 km) is chosen that is far smaller than the orbital TPR pixels (4.3 km pre-boost 08-2001 and 5.0 km thereafter). Hence, most of the time entire grid cells fall within single TPR pixels making NNB (and to a lesser extent IDW and BLN) yield the same result as PRM, unlike in the case study presented by Sharif and Ogden (2014) where the radar pixels were smaller than the grid cells. Furthermore, the fraction of the total domain affected by partial coverage is reduced at a finer grid resolution. This is particularly beneficial, since the TPR flight paths vary over time, as described above, resulting in unique, irregular time-series of instantaneous rainfall estimates at each 1 km node. Ultimately, the rainfall intensities estimated at the 1 km resolution still represent mean areal intensities at 5 km resolution. If using the quantitative estimates at 1 km resolution, these should be averaged using a spatial moving window of 5 km, so that the final 1 km estimates can be considered local best estimates of a 5 km spatial average. However, in themselves the 1 km fields can be used to reflect the relative differences in statistical properties and their spatial patterns.
For the remainder of this research, the orbital TPR pixels have been re-mapped to 1 km using nearest-neighbour interpolation. This approach was found to be the most computationally efficient, while showing superior performance in terms of occurrence frequency and comparable errors to other approximate methods with respect to the rainfall distribution. Furthermore, the use of NNB also permits mapping estimates for the TRMM 2A25 algorithm error and the rainfall type classifications. Further modifications of the data for specific applications are described in the respective chapters.