Common Software Library

Transcription

1 EUMETNET OPERA Programme 6 November 003 Common Software Library OPERA Project 1e Jacqueline Sugier Met Office

2 1. SCOPE Within Work Area 1 (i.e. Production of Radar Data), the objective of project 1e is To develop and maintain a platform independent common software library (e.g. algorithms) for processing weather radar data. The first step of the project was to define the content of the software library, and has been detailed in deliverable WG1_1e1 Definition of Software Library Content (WD 06/0). The second step was to collate modules/algorithms from all OPERA members, into a common software library (CSL). The objectives of this document are to provide the list of the modules/algorithms available in CSL.. MODULES AVAILABLE IN CSL Table below shows the modules submitted to CSL. Basic documentation is provided for each module. The content of the documentation is as shown below; in some cases not all sections are completed:- 1. Algorithm Configuration Information a. Algorithm Name: Full Name and ACRONYM b. Algorithm Identifier: based on WD 06/0 when applicable c. Algorithm Specification Version History: Upgrades, new versions, etc.. General information about the Algorithm a. Objective: Problem to solve or geophysical parameter estimated from radar observations. b. Physical principles and Assumptions: Rational, justification, and assumption of the algorithm selected. c. Use: Describes the potential applications of the product, and lists some of its intended operational use. d. Operational Considerations: Identified operational considerations; Report about performance; Results of validation campaigns. 3. Inputs: Describes all the input data required by the algorithm. 4. Outputs: Describes all the output data generated by the algorithm. 5. References: The relevant scientific publications related to the algorithm.

3 ID Modules, source code names, and owners AIP-04 AIP-05 AIP-06 AIP-09 CM-03 FC-0 FC-07 FC-10 FC-11 FC-1 PG-01 PG-06 PG-07 PG-08 PG-10 Error of reflectivity:- regre.for and erro.for (Portugal) Post-integration variance:- Intdig.for (Portugal) Software tools for specific tasks:- Sategrad.for (Portugal): Power to reflectivity Linear.for (Portugal): Logarithm receiver linearity Propag.for (Portugal): True height and range correction Generation of a dynamic clutter map:- AddCount.c (UK) Warning for missing data:- aviso radar.ksh and atrasados.ksh (Portugal) Convert NMS data into BUFR format:- Rainbuf.c (Ireland): convert rainbow format to BUFR format Data smoother:- Cumul.c (France) Convert GIF files into D interger matrix:- Gif_decode.c (Switzerland) Scale dbz:- dbz_scale.pro (Switzerland) Scale rainfall rate:- r_scale.pro (Switzerland) Precipitation rate integrator:- pac.c (Eire) Generation of VAD wind:- vad.py (Sueden) description without code (Austria) Generation of VVP horizontal windfield:- description without code (Austria) Radar rain-gauge adjustment:- Kalman.for (Portugal) Computation of area-time integral:- ATI.pas and Quinus.pas (Portugal)

4 ID Modules, source code names, and owners PG-1 PG-13 PG-14 PP-01 PP-08 PP-13N PP-16N Software test tools:- VSI.for (Portugal): conversion of reflectivity into rainfall rate Veloce.for (Portugal): conversion of unambiguous radial velocity from m/s into digital value (0 to 55). Largura.for (Portugal): evaluation of radial velocity, spectral width, and unit conversion from m/s into digital values. VIL.for (Portugal): Evaluation of the vertically integrated liquid water content using the vertical profile of reflectivity. Maximum intensity:- description without code (Austria). Constant altitude PPI:- description without code (Austria). Polar to Cartesian:- polarcart.pro (Switzerland): project polar data into Cartesian grid. Convor.for (Switzerland): compute Cartesian coordinates from spherical coordinates. Conversion from Z to R and vice-versa:- ZR.for (Portugal) Attenuation correction in precipitation:- Att_CORR.c (UK) Clutter filter:- Clut_CORR.c (UK)

5 A PRIORI STANDARD ERROR OF REFLECTIVITY Auhtor: Sérgio Barbosa, IM, Portugal 1. Algorithm Configuration Information a. Algorithm name A Priori Standard Error of Reflectivity Estimates. b. Algorithm Identifier AIP-4 c. Algorithm Specification History Developed in General Information about the Algorithm a. Objective Software for computing the a priori standard error of reflectivity estimates. b. Physical Principles and Assumptions The a priori standard error of reflectivity measurements is computed from the electrical calibration errors and from the uncertainties inherent to the statistical properties of the radar signals back-scattered from the weather targets, as well as those associated with the processing chain. Assuming that all random variables are considered statistically independent, the a priori standard deviation of the radar reflectivity estimates, σ t, is given by: t 1 ' ( σ ) c + σ 0 σ q σ = + (1), where σ c is the electrical calibration standard error, σ 0 is the post-integration variance of ' the precipitation echo power and σ q is the variance resulting from the quantization (or grouping) for the processing system outputs. (i) Electrical calibration uncertainty The computation of the standard error for a single and complete electrical calibration is performed from the values of the standard errors estimated in the measurement of all the factors in the radar constant, as well as from the ones of the standard errors in measuring the parameters that determine the receiver transfer function and also from the standard error associated to the distance factor of the radar equation. 5

6 The uncertainties (one standard deviation) are randomly combined (square root of the sum of the squares), although some authors prefer to derive the final estimate of the expected (3-σ) maximum possible uncertainty for the radar calibration by adding the maximum possible uncertainties for each of the factors. So, the electrical calibration standard error, σ c, is given by: c [ 4σ ( G) + 4σ ( θ ) + 4σ ( f ) + 4σ ( r) + σ ( WG) + σ ( SG) + σ ( P h) σ ( P)] 1 / σ = + () where: ( G) σ is the standard error in the measurement of the antenna gain including the dry radome losses; σ θ is the standard error in the measurement of the beam width; ( ) σ ( f ) is the standard error in the measurement of the frequency; σ () r is the standard error in the measurement of the distance; ( WG) ( SG) σ is the standard error in the measurement of the losses in the waveguide; σ is the standard error of the signal generator used in obtaining the receiver response curve; σ ( P t h) is approximately equal to the standard error in the measurement of the average power, since: t Pav h Pt h = τ PRF σ PRF. as ( ) 0 = Pav c PRF σ ( P h) = σ ( P ) + σ ( PRF) σ ( P h) σ ( ) t av t P av σ P, is the standard error associated with the linear regression used in obtaining the receiver response curve. The regression equation is given by P = a + bd, where P is the injected power (dbm), d is the output in digital units, a is the P value (dbm) in the origin and b is the slope of the regression line. In order to simplify the scheme of the regression analysis, this equation can be written as P = a 0 + ( d d ) b 0, where b = b0, The last term, ( ) a = a0 b0 d and d is the mean of the outputs in digital units for all injected power values used in the linear regression. It can be shown that a P σ P is given by: σ ( P) σ ( a ) + ( d d ) σ ( b) 0 0 =. So, ( ) = (3) where ( a 0 ) σ ( b) the one associated to the computation of the slope b. ( P) σ is the standard error associated to the computation of the parameter a 0 and σ is thus dependent on the intensity of the signal, being higher near the noise and receiver saturation levels. The standard error associated to the receiver calibration is the sum (square root of the sum of the squares) of σ ( P) with the standard error of the signal generator σ ( SG) and, as stated above, depends on the intensity of the signal. 6

7 The distance factor of the radar equation introduces an offset error due to the cable length and the electronic delays. To correct the offset error, a fixed target at a distance r, which is accurately known, is often used. When the digitised signal is used to measure the target delay time, the maximum error is of the order of, where is the digitalisation interval. Admitting that the distribution of the error in a quantization interval is uniform, the error variance is given by. 1 For a digitalisation interval of 15m, the standard error in the distance calibration (in r terms of r and expressed in db units), σ( r) = db is, therefore, db at a 50 Km 1 1 / reference distance, i.e., in general, negligible. So, the electrical calibration error depends on the distance and on the signal intensity, although, as a good approximation, it can be considered as constant. (ii) Variance due to digital processing Digital processing introduces variance and, in some instances, an error (bias) due to the uncertainty associated with the digital number. Here the estimated variance for the A/D conversion is determined, as well as the ones resulting from the quantization for the digital words performed at the output of the range and azimuth averaging loops and from the quantization (or grouping) performed at the output of the radar processing system. In the A/D conversion, or in any of the other processing steps, truncation would result in a systematic underestimate of the true value, the expected bias associated being one half of the class width. If, as it is assumed here, the quantization is by round off, the expected bias is zero. In any case, the associated variance (assuming a uniform distribution of probability across the class) is: ( ) ( PdB ) σ q = (4) 1 where σ ( q) is the variance in db and PdB is the class width in db. (iii) Post-integration variance of weather radar signals The post-integration variance of the precipitation echo power σ 0 can be computed from the parameters of the radar and its signal processor, from the variance due to digital processing and also from the meteorological parameters determining the precipitation velocity spectrum variance. The variance σ 0 is given by (Rosa Dias et al., 1988): σ 0 31 σ q σ q = σ q n n N N N ID IA D A A db (5) where n ID and n IA represent, respectively, the number of independent samples in range and azimuth (or time), N D and N A the total number of range and azimuth samples, 7

8 respectively, and σ q represents the variance due to quantization for the A/D conversion and for the digital processing in the integration loops. The second and third parcels are negligible when compared with the others. For more details, please see description for module AIP-5. (iv) A priori standard deviation of reflectivity estimates Concerning the above-mentioned, the a priori standard deviation of the radar reflectivity estimates, σ t, is given by: c. Use 31 σ ' q σ q σ t = σ q σ c σ q (6). nid nia N D N A N A This program uses a set of radar parameters to compute the a priori standard error of reflectivity estimates. d. Operational Considerations This software was developed for running offline. The package was developed under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs - Absolute error (%) in antenna gain; - Absolute error (%) in the measurement of beam width; - Absolute error (%) in the measurement of frequency; - Absolute error (%) in the measurement of distance; - Absolute error (%) in the measurement of waveguide losses; - Absolute error (%) of the test signal generator; - Absolute error (%) in the measurement of peak power; - Absolute error (%) in the measurement of pulse width; - Standard error in the computation of the regression equation parameters (a 0 and b); - Average value of the digital answer to the injected powers. - Number of independent samples for range and time-angle sampling (values taken from the output of the program Intdig.for, which is part of module AIP-5); - Quantization variance (db). The values for the parameters stated under items i and j, are computed by using the programme regre.for, which is also included here. 4. Outputs - Standard/Absolute error of reflectivity estimates. 1 8

9 5. Computer programs - regre.for; - erro.for; 6. References Rosa Dias, M. P., F. Sena da Silva, e S. Barbosa, 1988, Variância dos Ecos de Radar da Precipitação à Saída de um Integrador Digital, VI Conferência Nacional de Física - Física 88, GFM3, Sociedade Portuguesa de Física, Aveiro (in Portuguese). Rosa Dias, M. P., e S. Barbosa, 1990, Assignment of Intensity Class Intervals in the Digital Processing of Reflectivity Weather Radar Signals, COST 73 working document 73/wd/176 (included in the final report of the Management Committee of the COST 73 Action), 16 pp. Rosa Dias, M. P., P. Pinto, e S. Barbosa, 1997, Calibration of radar hardware. Error Estimation (included in the final report of the Management Committee of the COST 75 Action, under paragraph 5.), 8 pp. 9

10 POST-INTEGRATION VARIANCE Author: Sérgio Barbosa, IM, Portugal 1. Algorithm Configuration Information a. Algorithm name Post-integration variance b. Algorithm Identifier AIP-05 c. Algorithm Specification History Developed in First release to OPERA in March General Information about the Algorithm a. Objectives Software package for computing the number of independent samples for range and timeangle sampling. b. Physical Principles and Assumptions The post-integration variance of the precipitation echo power σ 0 can be computed from the parameters of the radar and its signal processor, from the variance due to digital processing and also from the meteorological parameters determining the precipitation velocity spectrum variance. The variance σ 0 is given by (Rosa Dias et al., 1988): σ 0 = 31 σ q σ q σ n n N N N ID IA D A A q in db (1) where n ID and n IA represent, respectively, the number of independent samples in range and azimuth (or time), N D and N A the total number of range and azimuth samples, respectively, and σ q represents the variance due to quantization for the A/D conversion and for the digital processing in the integration loops. σ q (db ) is given by: ( P ) db σ q = () 1 10

11 where P db is the class width in db. In equation (1) the same value σ q was considered for the variances associated to the A/D conversion and to range and azimuth digital integrations, since it was assumed that the number of bits used at the A/D conversion was equal to the length of the digital words at the output of the range and azimuth averaging loops. However, it should be noted that, in modern radar systems, only the quantization variance for the A/D conversion and the variance resulting from the quantization (or grouping) for the signal processor outputs need to be considered. The number of independent samples is computed from the following set of equations. It is considered that the velocity variance of precipitation particles is given, with a good approximation for low elevations, by: ( 0 98KR ) v v 1 t σ =. θ + σ (3) where R (m) is the distance, θ 1 is the half-power beam width (radian), K v is the vertical shear of radial velocity and σ t is the variance due to turbulence, the values taken for K v and σ 1 t being, respectively, s and ms. The Doppler spectrum variance σ f is given, as a function of σ v, by: σ f σ v = 4 (4) λ where λ is the wavelength. Let ρ( D, τ ) be the correlation function of the inphase and quadrature components of the signal at the receiver input. As it is known, ρ( D τ) ρ( D) ρ( τ), = (5) ρτ are the autocorrelation functions computed, respectively, for the range and azimuth sampling at the logarithmic receiver input. where ρ( D ) and ( ) The latter is given by, ρτ ( ) = e τ ' ( σ τ ) (6) where, for low elevations, ' ( σ τ ) βα 1 = + θ σ 1 τ (7) with β = ( ln ) 1, α being the antenna speed (rad s -1 ) and σ τ being given by 11

12 σ τ 1 f = ( π) σ (8) The autocorrelation function for the range sampling at the logarithmic receiver input is given by: ρ( D) D 1 0 D D = D0 0 D D0 0 (9) The autocorrelation function at the logarithmic receiver output is given by: ρ log = 6 π m= 1 ρ m m (10) where ρ is replaceable by either ρ( D ) or ( ) autocorrelation function in range or azimuth. The number of independent samples in range or azimuth is given by: σ σ 1 N N 1 M = N K= ( N 1) N ρτ, as it is intended to compute the k ρ log ( kl) (11) where N is the number of samples taken (in range or azimuth), spaced l apart, and ρ log is the autocorrelation function at the logarithmic receiver output. So, by replacing (6) in (10) and, then, in (11), the number of independent samples in azimuth ( n IA ) is obtained; by replacing (9) in (10) and, then, in (11), the number of independent samples in range ( n ID ) is obtained. c. Use This program uses a set of radar parameters to compute the number of independent samples for range and time-angle sampling. d. Operational Considerations This software was developed for running offline. The package was developed under MS- DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs - Beam-width (degree); - PRF (Hz); 1

13 - Wave-length (m); - Antenna speed (degree/s); - 1/ Pulse length (m); - Distance between consecutive range samples (m); - Number of samples in the range integration. 4. Outputs - Number of independent samples for range and time-angle sampling. 5. Computer programs Intdig.for 6. References Rosa Dias, M. P., F. Sena da Silva, e S. Barbosa, 1988, Variância dos Ecos de Radar da Precipitação à Saída de um Integrador Digital, VI Conferência Nacional de Física - Física 88, GFM3, Sociedade Portuguesa de Física, Aveiro (in Portuguese). Rosa Dias, M. P., e S. Barbosa, 1990, Assignment of Intensity Class Intervals in the Digital Processing of Reflectivity Weather Radar Signals, COST 73 working document 73/wd/176 (included in the final report of the Management Committee of the COST 73 Action), 16 pp. 13

14 SOFTWARE TOOLS FOR SPECIFIC TASKS PART 1. CALIBRATION TOOL POWER TO REFLECTIVITY Author: Paulo Pinto, IM, Portugal 1. Software Configuration Information a. Software name Sateqrad. b. Software Identifier AIP-06 c. Software Specification History Developed in 1997 First release to OPERA in March General Information about the Software a. Objective Software tool using the radar equation for computing the reflectivity corresponding to RF power signals fed into the waveguide and vice-versa. The power signals are fed from a signal generator into several reference points of the waveguide. The system parameters and losses measured at a calibration run are taken into account. b. Physical Principles and Assumptions c. Use Not specified This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984, The programme also runs under Windows environment, at least up to version Windows 000 Professional. 14

15 3. Inputs - Losses between the Bidireccional Coupler (BDC) and the Antenna Coupler (in db); - Losses between the BDC and the Low Noise Amplifier (LNA) (in db); - Cabling losses between the BDC and the LNA (in db); - Two-way radome losses (in db); - Pulse length (in µs); - Peak power (in kw) or Mean power (in W); - Frequency (in MHz); - Range (in km); - Antenna Gain (in dbi); - Beam width (in degree); - Reflectivity (in dbz, mm6.m-3 or system digital units) or injected power (in dbm or W). 4. Outputs - Injected power (in dbm or W) or reflectivity (in dbz, mm6.m-3 or system digital units). 5. Computer programme Sateqrad.for 6. References Not specified 15

16 PART. CALIBRATION TOOL LOG RECEIVER LINEARITY Author: Sérgio Barbosa, IM, Portugal 1. Software Configuration Information a. Software name Log receiver linearity. b. Software Identifier AIP-06 c. Software Specification History Developed in 001. First release to OPERA in March General Information about the Software a. Objective Software tool for checking the linearity of the radar log receiver using its response to signals of known RF power fed into the waveguide through a coupler from a signal generator. b. Physical Principles and Assumptions c. Use Not specified This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984, The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs - Lowest injected power (dbm); - Step (db); - Highest injected power (dbm); - Digital values corresponding to the injected power values; - Power for ADU=0 (dbm); 16

17 - Slope (db/adu). 4. Outputs - Power deviations (db). 5. Computer programme Linear.for 6. References Not specified 17

18 PART 3. TRUE HEIGHT AND RANGE CORRECTION Author: Sérgio Barbosa, IM, Portugal 1. Software Configuration Information a. Software name Propag. b. Software Identifier AIP-06 c. Software Specification History Developed in First release to OPERA in March General Information about the Software a. Objective Software tool for computing the true height above mean sea level, the corrected range along the surface of the Earth and the true elevation angle of the radar beam for standard refraction. b. Physical Principles and Assumptions c. Use Not specified This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984, The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs - Radar station height above mean sea level (m); - Range (Km); - Height above mean sea level (m); - Elevation angle; - Slant range (Km). 18

19 4. Outputs - Elevation angle (degree); - Height above mean sea level (m); - Range along the Earth surface (Km). 5. Computer programme Propag.for 6. References Not specified 19

20 PART 4. CONVERT DECIBELS INTO PERCENTAGE Author: Sérgio Barbosa, IM, Portugal 1. Software Configuration Information a. Software name Deciper. b. Software Identifier AIP-06 c. Software Specification History Developed in First release to OPERA in March General Information about the Software a. Objective Software tool for converting deviations (db) into percentages and vice-versa. b. Physical Principles and Assumptions c. Use Not specified This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs - Deviation (db) or Percentage. 4. Outputs 0

21 - Percentage or Deviation (db). 5. Computer programme Deciper.for 6. References Not specified 1

22 GENERATION OF A DYNAMIC CLUTTER MAP Author: Robert Scovell, Met Office, UK 1. Algorithm Configuration Information a. Algorithm name Generation of a dynamic clutter map b. Algorithm Identifier AIP-09 c. Algorithm Specification History Developed in 00. First release to OPERA in March General Information about the Algorithm a. Objectives Software tool for generation of a dynamic clutter map, using statistical frequency of detection of each polar pixels, over a pre-defined period. b. Physical Principles and Assumptions c. Use Not specified This program uses operational radar data to count the number of time each polar pixel is detected with a reflectivity value greater than a pre-defined noise threshold. This program maybe be run over a short (e.g. 1 day) or long (e.g. 3 month) period, depending on the application. d. Operational Considerations 3. Inputs The programme is written in C, and requires input data in Met Office polar format. - Number of azimuth gate; - Number of range gate; - Noise threshold coefficients; - Input data (new data); - Accumulation count data;

23 4. Outputs - Number of time each polar pixel was detected. - Total number of scan analysed 5. Computer programs dyn_map.c Also included: polar_format_spec.doc documentation of Met Office polar data format. 6. References Not specified 3

24 WARNINGS FOR MISSING DATA Author: Rosário Ribeiro, IM, Portugal 1. Algorithm Information a. Algorithm name Warnings for Missing Data. b. Algorithm Identifier CM-3 c. Algorithm Specification History Developed in 00.. General Information about the Script a. Objective b. Use The scripts routinely check the system for missing data at a predefined periodicity. When it runs, the script looks into the directory of reflectivity products, identify the last file, compare its time stamp with the computer system time stamp and if there is a significant difference, the script generates and sends an to the system supervisor indicating the most recent file in the directory. At the same time, the script copies to the archive all raw data and products that were not yet copied. c. Operational Considerations These scripts were developed for running online. The package of these scripts was developed in Korn Shell under Digital Unix operating system. 3. Inputs File name of the reflectivity products directory. 4. Outputs Log of the script running; to the system supervisor. 4

25 5. Computer scripts aviso radar.ksh; atrasados.ksh. 5

26 RAINBOW DATA FOR BUFR ENCODING Author: Kieran Commins, Met Éireann, Ireland 1. Algorithm Configuration Information a. Algorithm name Rainbow to BUFR b. Algorithm Identifier FC-0 c. Algorithm Specification History Developed in Latest update made in 00 First release to OPERA in March General Information about the Algorithm a. Objectives Software tool for converting Rainbow generated radar data files into raw data and header for BUFR encoding. b. Physical Principles and Assumptions c. Use Not specified. Not specified. d. Operational Considerations The programme is written in C, and requires input data in Rainbow format. 3. Inputs Rainbow source file. 4. Outputs 4-bit data file. 6

27 Descriptor file. GTS header file. 5. Computer programs rainbuf.c 6. References Not specified. 7

28 DATA SMOOTHER Author: Patrick Roquain, Météo-France, France 1. Algorithm Configuration Information a. Algorithm name Data smoother b. Algorithm Identifier FC-07 c. Algorithm Specification History Developed in 00. First released to OPERA in March General Information about the Algorithm a. Objectives Software tool to smooth rainfall rate data for accumulation products, using advection technique. b. Physical Principles and Assumptions Figure 1 illustrates the different step of the algorithm, which comprises 3 majors stage: And the determination of a field of advection. The elimination of ground clutter for the reflectivity image; The in-filling of removed clutter pixels, through horizontal extrapolation; The advection field is built using radar Cartesian images collect at time t and t + 5 mins. The movement of each pixel in 5 minutes (i.e. between each scans), is determined by searching for correlation between pixels reflectivity at time t (Im t i,j) and time t + 5 (Im t+5 i+di, j+dj), in a limited area of 80 x 80 km. The correlation coefficient is calculated as follows: Correlation( di, dj) = i, j t Imi, j Im Im t+ 5 t i+ di, j+ dj + Imi di, j dj i, j t+ 5 i, j 8

29 Clutter map image Z image at time t: Advection field at time t - 5 mins: Infilled Z image at time t - 5 mins: J(t) V(t-5) J inf (t-5) Apply clutter map to Z image Extrapolation of the infilled Z image at time t-5 mins to time t Z image without clutter echoes at time t - 5: J wce (t-5) Z image without clutter echoes at time t: J wce (t) Infilled Z image at time t: J ext (t-5) Determination of advection field at time t Determination of the infilled Z image at time t Advection field at time t: V(t) Infilled Z image at time t: J inf (t) Determination of smoothed Z image at time t Smooth Z image at time t-10mins Smooth Z image at time t-5mins Smooth Z image at time t Determination of the 15 mins accumulation image at time t 15 mins accumulation image at time t Figure 1: Algorithm to produce 15 mins accumulation product with smoothing of the data 9

30 The determination of the advection field becomes more complicated over areas contaminated by ground clutter. Therefore clutter are removed using a clutter map collected during period of dry weather. However, the holes generated after having applied the clutter map may also deteriorate de evaluation of the advection field and thus, those pixels are in-filled by extrapolating the reflectivity of the surrounding pixels. c. Use Not specified. d. Operational Considerations The software is required a time resolution between scan of 5 minutes, and produce an accumulation product every 15 minutes. 3. Inputs Reflectivity image at time t and t-5. Clutter map. Advection field at time t 5. Reflectivity image after clutter removal at time t-5. In-filled image at time t-5. Smoothed image at time t-5 and t Outputs Advection field at time t. Reflectivity image after clutter removal at time t. In-filled image at time t. Smoothed image at time t. 15-mins accumulation at time t. 5. Computer programs cumul.c 6. References Not specified. 30

31 DECODE GIF FILES Author: Gianmario Galli, MeteoSvizzera, Switzerland 1. Algorithm Configuration Information a. Algorithm name Decoding GIF files for the Swiss radar products b. Algorithm Identifier FC-10 c. Algorithm Specification History First released to OPERA in March General Information about the Algorithm a. Objectives Software tool to convert GIF files from the Swiss weather radar Network into binary formatted files. A 3-bytes header prefixes the binary output file. b. Physical Principles and Assumptions c. Use Not specified. Not specified. d. Operational Considerations The software was developed under Unix and tested under Solaris 5. The conventions of the Unix file system are assumed (/ as separator). The length of the input file must be less then 13. The combined length of the name and the type part must be greater than 4 characters. The output file is located in the working directory, and has the same name as the input file with the 4 th character before last set to U. 3. Inputs GIF file. xvv.h header.h 31

32 4. Outputs binary file. 5. Computer programs gif_decode.c Also included: xvv.h header.h xvgif_gga.c Makefile gif_decode decoded.dat coded.dat GIF reader routine Build procedure for Solaris Executable program for Solaris Sample data file decoded Sample data file coded in GIF 6. References Not specified. 3

33 SCALE dbz Author: Gianmario Galli, MeteoSvizzera, Switzerland 1. Algorithm Configuration Information a. Algorithm name dbz_scale b. Algorithm Identifier FC-11 c. Algorithm Specification History Developed in June 1999 First released to OPERA in March General Information about the Algorithm a. Objectives Software tool to define the class values given a range of precipitation intensities by using a linear scale in dbz. b. Physical Principles and Assumptions A linear scale in dbz for purposes of quantization is defined: dbz = mindbz + k * stepdbz with k = 0, 1, etc. where k is the class index, dbz is the lower bound value of the class interval, mindbz is the lowest dbz value of the scale, and stepdbz is the class width in dbz. It is possible also to specify following quantities: mindbr (lowest dbr value of the scale), minr (lowest R value of the scale), and stepdbr (class width in dbr), resulting from the formula: c. Use Z = A * R ^ b CALLING SEQUENCE: dbz = DBZ_SCALE(Class_index) EXAMPLE: IDL> print, DBZ_SCALE(k=1, A=316.0, b=1.5, mindbz=13, stepdbz=0.3) Or IDL> for k=1,15 do $ 33

34 print,dbz_scale(k, A=316.0, b=1.5, mindbz=13, stepdbz=3) d. Operational Considerations Not specified 3. Inputs k. A and b mindbz stepdbz 4. Outputs quantized dbz. 5. Computer programs dbz_scale.c 6. References Not specified 34

35 SCALE RAINFALL RATE Author: Gianmario Galli, MeteoSvizzera, Switzerland 1. Algorithm Configuration Information a. Algorithm name R_SCALE b. Algorithm Identifier FC-1 c. Algorithm Specification History Developed in June 1999 First released to OPERA in March General Information about the Algorithm a. Objectives Software tool to define the class values given a range of precipitation intensities by using a linear scale in rainfall rate. b. Physical Principles and Assumptions A linear scale in dbz for purposes of quantization is defined: dbz = mindbz + k * stepdbz with k = 0, 1, etc. where k is the class index, dbz is the lower bound value of the class interval, mindbz is the lowest dbz value of the scale, and stepdbz is the class width in dbz. It is possible also to specify following quantities: mindbr (lowest dbr value of the scale), minr (lowest R value of the scale), and stepdbr (class width in dbr), resulting from the formula: c. Use Z = A * R ^ b CALLING SEQUENCE: R = R_SCALE(Class_index) EXAMPLE: IDL> print, R_SCALE(k=1, A=316.0, b=1.5, minr=0.017, stepdbz=0.3) Or IDL> for k=1,15 do print, SQRT(R_SCALE(k, A=316.0, b=1.5, $ 35

36 mindbz=13, stepdbz=3)*r_scale(k+1, A=316.0, b=1.5, $ mindbz=13, stepdbz=3)) d. Operational Considerations Only scalar values (0-55) for the Class_index are accepted 3. Inputs k. A and b mindbz stepdbz 4. Outputs quantized R. 5. Computer programs r_scale.c 6. References Not specified 36

37 PRECIPITATION RATE INTEGRATOR Author: Kieran Commins, Met Éireann, Ireland 1. Algorithm Configuration Information a. Algorithm name pac b. Algorithm Identifier PG-01 c. Algorithm Specification History Developed in First release to OPERA in March General Information about the Algorithm a. Objectives Software tool for calculating precipitation accumulations from instantaneous rainfall amount or from Rainbow 1-hour accumulation files. Output is ASCII files of rainfall accumulation. b. Physical Principles and Assumptions c. Use Not specified. Not specified. d. Operational Considerations 3. Inputs The programme is written in C, and requires input data in Rainbow format. Rainbow input data file. Output file name. Output data path. ftp path. Time resolution of the accumulation (default 4-hours). Star data. End hour. 37

38 4. Outputs Accumulation file. 5. Computer programs pac.c 6. References Not specified. 38

39 VAD PROFILE GENERATOR Author: Daniel Michelson, SMHI, Sweden 1. Algorithm Configuration Information a. Algorithm name Velocity Azimuth Display b. Algorithm Identifier PG-06 c. Algorithm Specification History First release to OPERA in March General Information about the Algorithm a. Objectives To generate a vertical profile of horizontal wind information from a polar volume of data. Fundamental observables are wind speed and direction along a vertical profile. Supporting variables are provided as well. b. Physical Principles and Assumptions The method is a traditional VAD algorithm, which analyse individual circles of data at given ranges from the radar. It assumes a linear wind field and that the polar data are not aliased. A technical assumption is that it assumes that all rays of data are aligned clockwise starting from due north, with no missing rays. Another, big, technical assumption is that the Radar Analysis and Visualization Environment is available, since the VAD module is integrated with this system. RAVE is not presently contributed to the OPERA CSL. Data from all azimuth gates at a given range are subject to a least squares fit to a sin wave. Rudimentary quality control is included such that the variance of the radial winds along the wave is not allowed to be larger than 0.1. Circles that pass this QC test are used to generate VAD output (see Outputs, below). If a reflectivity volume is available, then a corresponding vertical reflectivity profile is also generated. c. Use The VAD generator can either be called from memory, i.e. a polar volume of data is already available in memory and the VAD is also generated and returned in memory. Alternatively, the 39

40 software can be called on the command line to read from and write to file. Or a polar volume in memory can be used with the VAD generator and written to file. This program uses a set of radar parameters to compute the number of independent samples for range and time-angle sampling. A basic knowledge of radar radial wind data and VAD is assumed. The code using the very high level programming language used to implement this VAD generator (Python) is in many ways easier to read than most pseudocode languages designed to facilitate code generation. So the reader should refer to the code, and its commentary, for exact details. d. Operational Considerations This software is a small module in a larger system with a number of external dependencies, which must be installed and working in order for this product generator to work. The software system is that which has been used routinely at the BALTEX Radar Data Centre since 1999, and it is robust and provides a high product availability. The quality of VAD profiles is high, but this is dependent on the quality of the input data available. This software is designed and built for ease of use, flexibility and reliability, but not for speed. 3. Inputs Required input is polar volume data containing radial wind velocity data, and optionally corresponding radar reflectivity factor data as well. The polar data either must be completely selfdescribing or look-up tables containing a description of the polar configuration must be available. The VAD module cannot read data itself; it is dependent on other modules for reading data in various file formats. The VAD module is known to work well with files in EWIS (Ericsson) format, and other formats are supported as well. Work is ongoing to enable the management of HDF5 files written according to COST 717 specification. Required attributes are: number of scans elevation angles for each scan (degrees) number of azimuth gates per scan number of range bins per ray range bin size (km) halfpower beamwidth (degrees) height (meters a s l) of the radar linear scaling factors (y = Ax + B) for transforming raw data to physical quantity. These are required both for radial winds and reflectivity. Arguments used by the VAD generator are: optional input file string for volume containing radial winds optional input file string for volume containing reflectivity optional output file string for output VAD profile optional thickness of profile layers, default is 00 m optional maximum range bin index to use, default is 5 40

41 4. Outputs VAD profiles can either be returned in memory or written to file. A VAD profile contains the following variables: mean height (m a s l) maximum height (m a s l) minimum height (m a s l) wind direction (degrees) wind speed (m/s) standard deviation of wind direction (degrees) standard deviation of wind speed (m/s) sample size (n) mean radar reflectivity value (dbz) Depending on which file format (used to write the VAD profile) is used, it may not be possible to store all of this information. The provided software includes a simple support module for writing to simple ASCII. The user can easily add modules for managing different file formats. 5. Computer programs vad.py wpascii.py - Python module for VAD generation. - Python module for simple ASCII output. Also included: Kkr - Output WRWP product as a BALTRAD ASCII file wdp_kkr_0111t Polar volume of radial winds in Ericsson EWIS format zdp_kkr_0111t Polar volume of reflectivities in Ericsson EWIS format 6. References Michelson D.B., Andersson T., Collier C.G., Riedl J., Szturc J., Gjertsen U., Nielsen A., and Overgaard S., 000: BALTEX Radar Data Centre Products and their Methodologies. Reports Meteorology and Climatology RMK 90. SMHI SE Norrköping, Sweden. 76 pp. Michelson D.B., 1999: RAVE User's Guide. SMHI SE Norrköping Sweden. 51 pp. 41

42 VAD VERTICAL WIND PROFILE Author: Helmut Paulitsch, University of Technology, Graz / Austria 1. Algorithm Configuration Information a. Algorithm name VAD vertical wind profile b. Algorithm Identifier PG-06 c. Algorithm Specification History First release to OPERA in March General Information about the Algorithm a. Objectives To generate a vertical profile of horizontal wind information from radial wind velocities. Fundamental observables are wind speed and direction along a vertical profile. Supporting variables are provided as well. b. Physical Principles and Assumptions Unlike traditional VAD algorithms which analyze individual circles of data at given ranges from the radar, this method is optimised to work well on a cartesian volume even with inaccurate, missing and aliased velocities. A linear wind field is assumed. 4

43 The VAD algorithm analyses a series of velocity measurements made at all available CAPPI levels to estimate the horizontal wind at the height represented by that level. In principle the radial velocities are sampled along a circle and under the assumption of a linear windfield, the sampled data will be a simple sinusoid in azimuth. Since the volume contains missing and aliased data, the sampled velocities are filtered and dealiased, before the resulting curve is fitted to a sine. For each CAPPI level, the following actions are repeated: sample velocities along a circle filter sampled data interpolate missing values remove spikes unfold data (dealias) fit to sine c. Use The VAD algorithm is an integral part of the Weather Image Information System (WIIS) and is not adapted for standalone use. WIIS is not contributed to the OPERA CSL. 3. Inputs The input is a three dimensional cartesian volume containing radial wind velocity data. This volume is coded in a proprietary format and consists actually of a number of CAPPI levels. The velocity data is stored with lookup-tables. Typical attributes are: 16 CAPPI levels 1km resolution in all dimensions 43

44 range of velocity from -8 to +8 m/s (aliased!) accuracy of velocity ~ 1m/s 4. Outputs The VAD profiles contain the following information: height wind direction (degrees) wind speed (m/s) quality factor 5. Computer programs and test files None 6. References Doviak, R., Zrnic, D. (1984), Doppler Radar and Weather Observations, Academic Press Inc., San Diego 44

45 VVP Horizontal Windfield Author: Helmut Paulitsch, University of Technology, Graz / Austria. 1. Algorithm Configuration Information a. Algorithm name VVP Horizontal windfield b. Algorithm Identifier PG-07 c. Algorithm Specification History First release to OPERA in March General Information about the Algorithm a. Objectives To generate a low altitude horizontal wind field from radial wind velocities. Fundamental observables are wind speed and direction along a horizontal profile. Supporting variables are provided as well. b. Physical Principles and Assumptions The VVP method is an analysis technique of linear wind fields over a three-dimensional volume. To provide reliable results, all values in the volume have to be dealiased. Since the polar velocity volumes are not dealiased, dealiasing is part of this VVP implementation. After dealiasing the polar velocity volume, it is divided into smaller analysis volumes. The size of this volumes is chosen with 30 in azimuthal width, 30km radial range and the first three elevations (for low altitude wind). For each volume a least square fit of the wind field is performed and a mean wind speed and direction is calculated for this volume. 45

46 c. Use The VVP algorithm is an integral part of the Weather Image Information System (WIIS) and is not adapted for standalone use. WIIS is not contributed to the OPERA CSL. 3. Inputs The input is a polar volume containing radial wind velocity data. Typical attributes are: 16 elevations 1 degree azimuthal resolution 1km radial resolution range of velocity from -8 to +8 m/s (aliased!) 4. Outputs The VAD profiles contain the following information: azimuth distance from radar wind direction (degrees) wind speed (m/s) 5. Computer programs and test files None 46

47 6. References Doviak, R., Zrnic, D. (1984), Doppler Radar and Weather Observations, Academic Press Inc., San Diego. Waldteufel, P., Corbin, H. (1979), On the analysis of single Doppler data, J. Appl. Meteorol. 18,

48 RADAR-RAINGAUGE ADJUSTMENT Author: Sérgio Barbosa, IM, Portugal 1. Algorithm Configuration Information a. Algorithm name Radar-Raingauge Adjustment b. Algorithm Identifier PG-08. c. Algorithm Specification History Developed in Some improvements have been introduced in First release to OPERA in March General Information about the Algorithm a. Objective Software package for radar-raingauge adjustment using the Kalman filter and an interpolation scheme based on multiquadric interpolation. The Kalman filter parameters computation is based on the method of the moments. b. Physical Principles and Assumptions The great space and time variability, both of the raingauge observations and of the radar rainfall estimates, as well as of the relation between the respective values, suggests that the adjustment factors should be modelled by stochastic processes. On the other hand, as both sensors are prone to errors, a state-space representation seems to be a good way of combining the two measurements. The Kalman filter is an important general method of handling state-space models, providing optimal estimates of the adjustment factors, as well as the variances of these estimates. The Kalman filter performs a continuous updating of the adjustments, being very efficient for computer processing. c. Use This program uses the precipitation data recorded by means of the raingauge network and the precipitation estimates using weather radar. The Radar-Raingauge Adjustment is performed in three steps: 1) The processing begins with the use of a pre-processing procedure that applies an exponential function to the radar estimates of precipitation, whose aim is to 48

49 reduce somehow their great space and time variability (this is performed only for non-frontal or mixed time series); ) Afterwards, the use of a state space model and the Kalman filter allows the computation of adjustment factors in selected sites where adjustment raingauges are located; 3) Finally, adjustment factors are computed in a grid of n n cells, by means of multiquadric interpolation. For this purpose, the adjustment factors computed under item ) above are used. 4) The program also allows the adjustment factors forecasting for the next time period (typically one-hour). For the validation process, the mean hourly precipitation is computed for the abovementioned grid, before and after the adjustment, and compared with the corresponding ground-truth value, computed using the several raingauges available in the same area. Several statistics are used in this process. c. Use This software was developed for running offline. The assessment of the adjustment model was assessed over a region of hydrometeorological interest where a fairly dense raingauge network is available. d. Operational Considerations The package was developed under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs Hourly radar rainfall estimates at each radar grid cell; Hourly precipitation amounts at each adjustment raingauge; Initial value for the adjustment factor at each raingauge location; Initial value for the mean square error; Values for the variance/covariance matrix of the observations; Values for the variance/covariance matrix of the deviations; Values for the matrix G (time correlation of the adjustment factors). 4. Outputs Hourly adjustment factors at each radar grid cell; Hourly adjusted estimates of precipitation at each radar grid cell; 5. Computer programs and test files 49

50 kalman.for Also included: radar - (8 8 radar grid cells, for a 63 h time series, with hourly radar rainfall estimates); gauge - (hourly radar estimates of precipitation at each radar cell where a raingauge is located (5), hourly precipitation amounts at each raingauge (5) and ground-truth (1), for the same 63 h time series) 6. References Barbosa, S., 1996, "Kalman Filters in the Optimisation of Precipitation Estimates using Radar and Raingauge Observations", MSc. Thesis, Faculdade de Ciências da Universidade de Lisboa, 198 pp (in Portuguese). Alpuim, T, 1997: "Moments Estimators for the Noise Variances in the Kalman Filter", CAUL/CMAF, Faculdade de Ciências da Universidade de Lisboa, Lisboa, 17 pp. Alpuim, T., e S. Barbosa, 1999, "The Kalman Filter in the Estimation of Area Precipitation", Environmetrics, the official journal of the International Environmetrics Society, John Wiley & Sons, Ltd., 10,

51 ATI Author: Paulo Pinto, IM, Portugal 1. Algorithm Configuration Information a. Algorithm name ATI b. Algorithm Identifier PG-10 c. Algorithm Specification History Developed in 1993/1994. First release to OPERA in March General Information about the Algorithm a. Objective Software package for computing Area-Time Integrals. b. Physical Principles and Assumptions The ATI technique for radar rainfall measurement has received important inputs (Atlas et al., 1990) in connection with the development of new spaceborn radar systems under the scope of the Tropical Rain Measurement Mission (TRMM). The results already obtained with this technique are fairly promising and so its interest for hydrometeorological purposes and other is growing. However, a number of questions remain unsolved, needing further investigation before the method can be employed in an operational context. The important ones include the applicability to stratiform precipitation, the magnitude of the smallest fixed area and time interval for which the methods are applicable, and the requirements regarding seasonal or geographic calibration of the relationships. The basic area-time integral (ATI) concept was first described by Doneaud et. al. (1984). The volumetric rainfall V from a rainstorm over an area A and a time interval T may be expressed by: ( ATI ) R V = Rdadt = R dadt = R A t (1) T A T A being R the average rainfall rate over the space-time domain with rain, A i the area over which rainfall rate in excess of a specified threshold was detected during the i th observing period i i i 51

52 t i the time interval between observations. The double integral or the summation in (1) is the ATI. Experimental evidence of high correlation between the rainfall area coverage and duration and the rain volume has been reported in a number of studies. The interest in the use of this method for radar measurements was arisen by its extreme simplicity and the stated strong correlation observed (typically 0.98), which means that rainfall can be estimated by just determining the ATIs if the relationship to rain volume is previously established. This relationship may be expressed by a power law of the general form: V = K (ATI) b () where K and b may be obtained on a log-log scatter plot. since R V = (3) ATI substituting () into (3) one obtains: b ( ATI) 1 R = K (4) The ATI calculations can be performed either for fixed areas in the ground or moving storm systems, using radar, satellite or raingauge data. c. Use This program uses the radar precipitation data estimates to evaluate the hourly ATI values. This software was developed for running offline. The assessment of the ATI technique was performed over a region of hydrometeorological interest where radar data have passed a quality control filter. d. Operational Considerations The package was developed under MS-DOS Operating System using the Borland Turbo Pascal 6.0 Compiler, The programme also runs under Windows environment, at least up to version Windows Inputs Radar rainfall estimates at each radar grid cell, provided that the images are no more than 15 minutes apart; Rainfall threshold to be used to evaluate the ATI values; Classification as "winter" or "summer" of the period over which ATI values are to be calculated. 5

53 4. Outputs Hourly ATI values 5. Computer programs ATI.pas; Quinus.pas 6. References Doneaud, A. A., S. I. Niscov, D. L. Priegnitz, and P. L. Smith, 1984, The area-time integral as an indicator for convective rain volumes, J. Clim. Appl. Meteor.,3, Atlas, D., D. Rosenfeld and D.B. Wolff, 1990, Climatologically tuned reflectivity-rain rate relations and links to area-time integrals, J. Appl. Meteor., 9, Macedo, M. E., S. Barbosa, M. P. Rosa Dias, e P. Pinto, 1994, A Hydrological Application of Area-Time Integrals, nd European Conference on Advances in Water Resources Technology and Managment, A. A. Balkema Publishers for the European Water Resources Association, pp

54 SOFTWARE TEST TOOLS Author: Paulo Pinto, IM, Portugal 1. Software Configuration Information a. Software name VSI b. Software Identifier PG-1 c. Software Specification History Developed in First released to OPERA in March General Information about the Software a. Objective Software tool for conversion of reflectivity values (in digital units) into rainfall intensity (mm.h -1 ) assuming the Marshall-Palmer Z/R relationship. b. Physical Principles and Assumptions c. Use Not specified. This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs Reflectivity value (digital units). 4. Outputs 54

55 Rainfall intensity (mm.h -1 ) and reflectivity (mm 6.m -3 ). 5. Computer programme VSI.for 6. References Not specified. 55

56 SOFTWARE TEST TOOLS Author: Paulo Pinto, IM, Portugal 1. Software Configuration Information a. Software name Veloce. b. Software Identifier PG-1 c. Software Specification History Developed in First released to OPERA in March General Information about the Software a. Objective Software tool for conversion of the unambiguous radial velocity from "m.s -1 " into "digital values" (0/55). b. Physical Principles and Assumptions c. Use Not specified. This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs Radar wavelength (?); PRF (Hz); Staggering ratio. 56

57 4. Outputs Unambiguous radial velocity in m.s -1 or digital units. 5. Computer programme veloce.for 6. References Not specified. 57

58 SOFTWARE TEST TOOLS Author: Paulo Pinto, IM, Portugal 1. Software Configuration Information a. Software name Largura. b. Software Identifier PG-1 c. Software Specification History Developed in First released to OPERA in March General Information about the Software a. Objective Software tool for evaluation of the unambiguous radial velocity, spectral width and unit conversion from "m/s" into "digital values" (1/55). b. Physical Principles and Assumptions c. Use Not specified. This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs Radar wavelength; PRF (Hz); Staggering ratio. 4. Outputs 58

59 Unambiguous radial velocity in m.s -1 or digital units. 5. Computer programme Largura.for. 6. References Not specified. 59

60 SOFTWARE TEST TOOLS Author: Paulo Pinto, IM, Portugal 1. Software Configuration Information a. Software name VIL b. Software Identifier PG-1 c. Software Specification History Developed in First released to OPERA in March General Information about the Software a. Objective Software tool for evaluation of the VIL value using the vertical distribution of reflectivity values. b. Physical Principles and Assumptions c. Use Not specified. This programme was developed for running offline. d. Operational Considerations The programme was written under MS-DOS Operating System using the IBM Professional Fortran Compiler, Profort, 1984,1987. The programme also runs under Windows environment, at least up to version Windows 000 Professional. 3. Inputs Number of tropospheric levels to be considered; Empirical coefficients to convert reflectivity into VIL; Reflectivity values (in digital units) to be considered. 4. Outputs 60

61 VIL values. 5. Computer programme Vil.for 6. References Not specified. 61

62 MAXIMUM INTENSITY Author: Thomas Leitner, University of Technology, Graz / Austria. 1. Software Configuration Information a. Software name Maximum intensity or MAXR b. Software Identifier PG-13 c. Software Specification History First released to OPERA in March General Information about the Software a. Objective To generate horizontal and vertical profiles with maximum intensity values. Fundamental observables are intensity values in a top-down, north-south and east-west projection. Supporting variables are provided as well. b. Physical Principles and Assumptions The MAXR algorithm calculates three profiles (top-down, north-south, east-west) from a single reflectivity volume by projecting the volume cells to a profile and selecting the maximum cell value for each profile pixel. The maximum intensity is stored as a dbz level. 6