Data description and study methodology

a) Datasets

The observed rain dataset was provided by the Automatic System of Hydrological Information (SAIH) of the Catalan Water Agency (ACA). Records of precipitation in mm h-1 at 126 automatic rain gauges (Figure 7.1), every 5 minutes from 1130 UTC 9 to 1230 UTC on the 10th of June, are available. The rain gauge network is located in the internal basins of Catalonia (closed polygonal line area in figure 7.1) and is considered dense enough to perform a kriging analysis method using a linear model for the variogram fit to create rain rate fields for the calibration process and 3 hours rain accumulation fields for the verification phase, both at 2 by 2 km resolution. This minimal error variance interpolation method is recommended for spatially irregular grids with a relatively low number of observations (<250) and has been widely used to compute rainfall fields from rain gauges (Krajewski 1987; Seo 1998; Bhagarva and Danard 1994). These fine grid fields were then remapped to radar projection in order to implement the different techniques.

The lower radar CAPPI (Constant Altitude Plan Position Indicator) images at 1.2 km altitude in dBZ units from the C-band radar of Barcelona are supplied by the INM. The radar is located 20 km to the southwest of Barcelona city at 654 m above sea level and the main radar characteristics are 0.9º 3-dB beam width, λ=5.4 cm and 20 elevation angles. The lowest CAPPI fields, used by various meteorological centres to estimate precipitation, were computed using software provided by the INM and called STArPcw (Riosalido, 1994). Under this approach, ground echoes were detected and substituted by suitable radar measurements derived from horizontal and vertical analyses (Martín and De Esteban, 1994). CAPPI fields were selected every 10 minutes from 2100 UTC 9 to 1230 UTC June 10th, with 2 by 2 km pixel resolution and covering a circular area of around 480 km diameter as shown in figure 7.1. Significant attenuation problems occurred in radar images from 0250 to 0430 UTC caused, presumably, by the high precipitation rate over the radar zone, and no valid images were available for that period.

Figure 7.1 Area inside the polygonal line in Catalonia well covered by the 126 ACA rain gauges (little black dots) and affected by the heavies’ precipitations. The circle represents the radar area, which is located in Barcelona. The thick continuous line demarcates the Spanish and French provinces and the thin lines, the internal basins in the Catalonia region.

b) Study methodology

Radar reflectivies and interpolated rain rates from the ACA network were matched point to point during the hours of heaviest rainfalls in order to capture the main rainfall patterns of the Montserrat storm. The study domain is limited by the closed polygonal line shown in figure 7.1 and the radar-gauge association process was applied from 0020 to 0520 UTC on the 10th of June, every 30 minutes. The period between 0250 and 0430 UTC was avoided for calibration and verification because of the aforementioned radar problems. Table 7.1 shows the simultaneous radar-gauge fields and the number of matched radar-rain points taken into account in the calibration. A

total of 38010 points (Table 7.1) were employed to delineate Z-R relationships by the HMT and the DCM and, also, used to test the Marshall and Palmer coefficients.

The verification is performed for rain rates comparing gauge and radar estimations from 2100 UTC on 9 June to 0830 UTC on the 10th of June every 30 minutes. In this case radar rain rates are tested in two ways: firstly, radar estimations are verified with respect to rain gauge data used in calibration in order to analyze the benefits of adjusted methods with respect the standards. Secondly, radar estimations are tested using independent gauge data outside the calibration period. On the other hand three hours of rainfall accumulations from 2100 to 0900 UTC of the next day divided into four periods, are also verified. To obtain the radar and gauge rainfall accumulation maps all available data at the highest temporal resolutions has been used (10 minutes for radar and 5 minutes for gauges).

The statistical indices employed in the quantitative verification in the area well covered by the rain gauges (polygonal area in figure 7.1) are: mean, standard deviation (SD), BIAS, standard deviations difference (SDD), root mean square error (RMS), and correlation coefficient (CORR). Special care has been taken in the present work about the BIAS and SDD parameters because they are used to execute adjustments after the main calibration processes. The first one, as in chapter 5, is the difference between the estimated and the observed spatial averaged precipitation while the second is the difference between both standard deviations, from the estimated and observed fields. Positive values of both parameters, BIAS and SDD, mean radar over-estimation, and negative values, radar under-estimation.

The spatial accuracy of the estimated radar rain rates can be calculated with the help of certain indices. The probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) indices are based on equations 4.5, 4.6 and 4.7 and computed from a contingency table as shown in section 4.2c of this thesis and described also by Marzban (1998). Another interesting index that can be easily calculated from the contingency table is the fraction correct (FRC) defined as follows.

D C B A D A egatives correct n rms false ala misses hits egatives correct n hits FRC + + + + = + + + + = 7.1 where:

- hits (A), is the number of rain points from the rain gauges correctly estimated as rainy by the radar.

- misses (B), number of rain gauge points estimated as no rainy by the radar. - false alarms (C), number of no rain gauge points estimated rainy by the radar.

- correct negatives (D), number of no rain gauge points correctly estimated as non rainy by the radar.

The FRC, besides to the CSI, takes into account the correct negatives points giving new information that can be complemented by the CSI. However, the results given by the FRC has to be interpreted with caution. Under certain circumstances of little or weak rainfall (which is not our case), the number of correct negatives (D) might be much larger than the rest of the parameters (D >> A, B, C) and therefore, FRC might show a high score, with a value close to one, while the CSI might give a much lower result.

Sometimes the interpretation of the results is not clear when using only the POD or the FAR indices; in these cases we can employ a derived index called the product coefficient POD (1-FAR). It was proposed by Marzban (1998) in order to obtain a unified result based on the two coefficients. This can be applied for the CSI and FRC indices with the direct product of both indices.

Table 7.1. Radar-rain images used for the calibration file generation.

Day Hour (UTC) Number of collocated Z, R

pointsa in the domainb Comments

June-10-2000 0020 5430 Radar-Rain images present

“ 0050 5430 “

“ 0120 5430 “

“ 0150 5430 “

“ 0220 5430 “

“ 0250-0420 0 Radar error

“ 0450 5430 Radar-Rain images present

“ 0520 5430 “

38010 Total number of Z, R points in the

calibration file

a

Every point correspond to a radar-rain image pixel where each one has a spatial resolution of 2 by 2 km.

b

The domain is limited by the polygonal lines in figure 2 and correspond to the area well covered by the 126 ACA rain gauges.