BALTRAD

1. Algorithm name

Quality-based vertically integrated liquid water (VIL) product generation – Product2D: VIL

2. Basic description

a) Physical basis of the algorithm

The algorithm generates vertically integrated liquid water (VIL) 2-D product from radar reflectivity volume with quality information using product2D_PPI algorithm.

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: VOL

General “what”: source(NOD).
For particular SCANs:
- 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)

object=PVOL:

quantity=DBZH, otherwise TH,
quantity=QIND (generated e.g. by QI_TOTAL algorithm).

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 generates vertically integrated liquid water (VIL) 2-D products in Cartesian coordinates from radar reflectivity volume and based on the data quality information.

Algorithm parameters

Set of the algorithm parameters:

Description	Denotation	Unit	Default value
Lower height limit for VIL product generation (a.s.l.)	VIL_hMin	km	1
Upper height limit for VIL product generation (a.s.l.)	VIL_hMax	km	10
Coefficient c’’ in ‘‘Z-M formula	VIL_ZMc	-	24000
Coefficient d’’ in ‘‘Z-M formula	VIL_ZMd	-	1.82

Algorithm description

Vertically integrated liquid water (VIL) product represents Cartesian image of the water content residing in a user-defined layer in the atmosphere (in dBA) (Fig. 1). Generally, in the first step a vertical profile of liquid water content M (based on Z-M relationship) is determined by interpolation between all pairs of neighbouring measurements. Then the VIL in a preset range of height (between h_min and h_max) is calculated by integration of the profile. In order to find the vertical profile of M(h), values between two measurements M’ and M” detected at heights h’ and h” respectively, the linear interpolation is applied:

$M(h) = \frac {(h-h'')(M'-M'')} {h'-h''} + M''$

Fig 1 VIL
Fig. 1. Scheme of generation of vertically integrated liquid water product (VIL).

Radar reflectivity Z is related to liquid water content M (in cm^3^ m^-3^) according to so called Z-M relationship:

$M(h) = \frac {(h-h'')(M'-M'')} {h'-h''} + M''$

where constants: c 1.82 (as proposed by Selex, 2010).

The VIL (vertically integrated liquid water content) is defined as:

$VIL(\text{dBA}) = 10 \cdot \text{log}_{10} \int_{h_{min}}^{h_{max}} M(h) \text{d}h$

In the VIL algorithm there are considered only measurements (Cartesian pixels on PPIs) between h_min and h_max, and two closest ones (below h_min and above h_max).

The following ranges of integration are considered:

If the highest measurement is higher than h_max, then the two measurements above and below h_max are interpolated and values of M below h_max are taken for integration, else the integration is performed up to height of the highest measurement.
If the lowest measurement is lower than h_min, then the two measurements above and below h_min are interpolated and values of M above h_min are taken for integration, else the integration is performed with the assumption that the lowest measurement was also at h_min.

Data quality characterization

Quality of the VIL depends on the two factors:

quality of reflectivity data from which VIL was determined, QI_source,
how large fraction of investigated heights (between h_min and h_max) was scanned, QI_scope,

and the final quality index QI is taken as a product of the both factors:

$QI = QI_{source} \cdot QI_{scope}$

The value of the first component QI_source is taken as an average quality of all measurements defining VIL. If VIL “nodata”, and if VIL 1.

Fig 2 VIL
Fig. 2. Quality characterization for vertically integrated liquid water product in terms of scope.

The second component QI_scope is determined based on heights of the lowest and highest scans for considered Cartesian pixel (h_lowest and h_highest respectively) in relation to h_min and h_max (Fig. 2):

if h_highest < h_min then

QI_scope “nodata”.
if h_highest ≥ h_min and h_lowest <= h_max then QI_scope depends on what part of height range between h_min and h_max was scanned:

$QI_{scope} = \frac {min(h_{highest},h_{max}) - max(h_{lowest},h_{min})} {h_{max} - h_{min}}$

if h_lowest > h_max then

QI_scope “nodata”.

6. Output

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

Input quantity as IMAGE object (in Cartesian coordinates) with:

“how”: task - “pl.imgw.product2d.vil”,
“how”: task_args
- parameters inherited from PPI algorithm (interpolation method and selected quality field name),
- parameters of VIL algorithm,

b) Quality index (QI) field

Quality index field QIND as IMAGE object with:

“how”: task - “pl.imgw.product2d.vil”,
“how”: task_args - parameters inherited from PPI algorithm (interpolation method and selected quality field name).

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

TBD