BALTRAD

1. Algorithm name

Quality-based PPI (Plan Position Indicator) product generation – Product2D: PPI

2. Basic description

a) Physical basis of the algorithm

The algorithm interpolates polar data into Cartesian coordinates employing quality information (quality index e.g. from QI_TOTAL processing). It can be applied e.g. to radar reflectivity Z after VPR-based extrapolation down to ground.

The product is the basis for generating other 2-D products.

b) Amount of validation performed so far

Not performed yet.

c) References (names and contact information of all developers during the evolutionary history, scientific papers)

IMGW, Department of Ground Based Remote Sensing.

3. ODIM metadata requirements for I/O

Input data: SCAN

General “what”: source(NOD).
Dataset-specific “where” for data and QI: nbins, nrays.
Data-specific “what” for data: gain, offset, nodata, undetect.
Data-specific “what” for QI: gain, offset, nodata, undetect.

Output data: Cartesian data

Top-level “where”: lon, lat, xsize, ysize, xscale, yscale.
Dataset-specific “what”: product.
Data-specific “what” for data: gain, offset, nodata, undetect.
Data-specific “what” for QI: gain, offset, nodata, undetect.

4. Input data

a) What kind of radar data (including the list of previous algorithms and quality flags applied)

Radar-based quantity, e.g. reflectivity data after corrections DBZH as SCAN object.
Optionally QI information QIND (generated e.g. by QI_TOTAL algorithm) included in the same SCAN object.

b) Other data (optional and mandatory, applying “universally” agreed formats, geometry)

Defined projection and domain of Cartesian output.

5. Logical steps, using any of: text, flow charts, graphics, equations (or references to equations), conditional branches in “all possible cases”.

The algorithm transforms values for measurement gates of polar coordinates (α’’, ‘‘l’’), where ‘‘α’’ is the azimuth, ‘‘l’’ is the distance from the radar site, into values interpolated for Cartesian pixels defined by coordinates: (‘‘x’’, ‘‘y).

Fig 1 PPI
Fig. 1. Scheme of interpolation of gate values into Cartesian pixel.

Algorithm parameters

Set of the algorithm parameters:

Description	Denotation	Available options	Default value
Interpolation method	Method	nearest / uniform / inverse1 / inverse2 / bilinear / cressman	bilinear
Input quantity identifier	Quantity	TH / DBZH / …	DBZH
If to employ quality information QI for interpolation	IncludeQuality	0 (no) / 1 (yes)	1
Input quality field name	QIField	pl.imgw.qi_total / se.smhi.detector.poo / …	pl.imgw.qi_total
If to interpolate values in mm^6^ m^-3^ (for Quantity = TH / TV/ DBZH / DBZV / ZDR)	dBZtoZ	0 (no) / 1 (yes)	1

Separation of pixels due to distance to radar

The algorithm interpolates data in different ways for pixels close to radar site, where there is dense pattern of gates, and farther from radar site (so called inside and outside method). The border in distance to radar (D’’) is defined by empirically determined function of measurement parameters: step in azimuth d’‘Az’’ (°), step in distance from radar d’‘bin (km), and Cartesian spatial resolution dx (km):

$D = \sqrt{ \frac{9500(\frac {1.3}{\text{d}Az} + \frac{2.3}{\text{d}bin} + 1.6 \text{d}x) - 39000} {\pi} }$

For instance, for d_Az’’ 1 km, and d’‘x_ 57,5 km.

Inside method

For the centre of Cartesian pixel its four corners are considered, which coordinates are transformed into polar coordinates defining investigation area in polar data. Then the number of gates inside this area is determined. If it is higher than 2 the inside method based on quality weighted interpolation is employed:

$Z(x,y) = \frac {\sum_{i=1}^{n}(Z_i QI_i)} {\sum_{i=1}^{n}QI_i}$

where n is the number of gates inside the investigation area.

Otherwise (if the number of gates inside the investigation area is not higher than 2) the outside method is applied.

Outside method

In outside method the closest gates are determined in the following way. The coordinates of the Cartesian pixel centre are transformed into polar coordinates and four surrounding gates are taken into account. In case when difference between the considered pixel centre and one or two the investigated gates is lower than the preset limit (5% of “rscale” or azimuth step in terms of distance to radar or azimuth respectively) then only the closest gates are taken into calculations.

Then quantity in given pixel of coordinates (x’’, ‘‘y’’) is estimated as weighing average value ‘‘Z’’(‘‘x’’, ‘‘y’’) from the ‘‘n’’ selected gates ‘‘Z_i, taking both distances to the gates and data quality information in the gates into account:

$Z(x,y) = \frac{\sum_{i=1}^{n} (Z_i W_{Di} W_{QIi})}{\sum_{i=1}^{n} (W_{Di} W_{QIi})}$

where: W_Di’’ is the weight related to distance of ‘‘i’‘-gate to pixel (‘‘x’’, ‘‘y’’); ‘‘W_QIi’’ is the quality index ‘‘QI’’ of the ‘‘i’‘-gate; ‘‘n is the number of the closest gates taken into account.

Determination of weigths in outside method

The polar coordinates of selected i’‘-gate are transformed into Cartesian coordinates (‘‘x,,i,,’’, ‘‘y,,i,,’’) in order to determine its distance to the considered pixel (‘‘x’’, ‘‘y):

$D_i = \sqrt{ (x - x_i)^2 + (y - y_i)^2 }$

Weights due to distances to gates D_i are determined by means of the following methods:

nearest:
$\quad\quad W_{Di} = \begin{cases} 1\qquad\qquad\text{}D_i = min(D_j, j=1,..., n) \\ 0\qquad\qquad\text{otherwise:\ }D_i > min(D_j, j=1,..., n) \end{cases}$

uniform:
$\quad \quad W_{Di} = 1$

inverse1:
$\quad \quad W_{Di} = \frac{1}{D_i}$

inverse2:
$\quad \quad W_{Di} = \frac{1}{D_i^2}$

bilinear:

Fig 2 PPI
Fig. 2. Scheme of bilinerar interpolation.

$\quad \quad W_{Di} = \frac{1}{A_i}$

where A_i is the area of annulus sector.

cressman:
$\quad \quad W_{Di} = \frac{a^2-D_i^2}{a^2+D_i^2}$

where a’’ is the influence radius, ‘‘a 0. If for the considered pixel there are no gates with D_i’’ < ‘‘a’’ then the calculation is repeated with longer ‘‘a = 20 km.

Weights due to data quality for 1, .., n pixels are determined as:

$W_{QIi} = QI_i$

Data quality characterization

Quality index for interpolated pixel (x’’, ‘‘y) is calculated in dependence on method applied to data interpolation:

for inside method
$QI(x,y) = \frac {\sum_{i=1}^{n}QI_i} {n}$

for outside method
$QI(x,y) = \frac{\sum_{i=1}^{n} (QI_i W_{Di})}{\sum_{i=1}^{n} W_{Di}}$

where: W_Di’’ are the distance-related weights for ‘‘n selected gates.

6. Output

a) Data type using ODIM notation where possible, e.g. DBZH

Input quantity as IMAGE or COMP objects (in Cartesian coordinates) with
- “pl.imgw.product2d.ppi” in quality-specific “how”: task,
- interpolation method, selected quality field name, and whether values were interpolated in mm^6^ m^-3^, listed in “how”: task_args.

b) Quality index (QI) field

Quality index field QIND as IMAGE or COMP objects with:
- “pl.imgw.product2d.ppi” in quality-specific “how”: task,
- interpolation method and selected quality field name listed in “how”: task_args.

7. Outline of a test concept exemplifying the algorithm, as a suggestion for checking that an implementation has been successful.

TBD