Marco Institucional Inducortec S.A.

Sections 2.3 and 2.4 described the wide range of VPR classification and correction schemes available from over 20 years of theoretical literature. This section revisits in further detail three complete operational schemes as documented in the literature. The importance of operational reliability and resilience are emphasised, along with the need to pair classi- fication and correction schemes that operate on a similar local or global scale. The aim here is to highlight the very different approaches to correction followed by different cen- tres, and to place in perspective and highlight the unique nature of the UK operational VPR procedure, in which context the remainder of this thesis will be based.

2.5.1 M´et´eo France

Tabary (2007) propose a modified version of the ratio method of Andrieu and Creutin (1995a) for application to the French operational radar network. They formulate the VPR as a ratio of Cartesian-gridded rainfall rates, as:

R(h,x) =Rs(x)za(h) (2.19)

where R is the rain rate calculated from a reflectivity at height h, Rs the true surface

rain rate, and za(h) is therefore the apparent VPR (cf equation 2.6), modified by a

Marshall-Palmer equivalent ZR exponent (equation 1.14). As part of the determination process, “ratio curves” as a function of range are calculated using ratios of hourly rainfall accumulations from different elevation scans.

The method of Tabary (2007) relies upon the generation of a family of a priori linear VPRs. Their generalised stratiform profile consists of a symmetrical bright band peak

(as for Kitchen et al. (1994), figure 2.3), constant reflectivity below the melting layer, and a constant dBZ reflectivity gradient in the ice. The profile has four variable parameters, each of which has only a limited range of permitted values for computational efficiency:

• The bright band top htop can be located at the model freezing level heighthf l, or

at either ofhf l±200 m

• The bright band peak strength (as a rain rate ratio) can take any integer value from 1 to 5 (corresponding to a maximum reflectivity enhancement of around 11 dB (Tabary et al., 2007))

• The bright band depth (htop−hbottom) is 200 m, 400 m, 600 m or 800 m

• The gradient above htop can take any of five values between -1.5 and -6 dB km−1

(see annotated VPR sketches, figure 2.1). This gives a total of 240a priori linear profiles. The best of these linear profiles for each hourly time step is chosen via a least squares optimisation using the measured ratio curves, and is applied to Cartesian rain rate accu- mulations. The final surface rain rate is computed as a weighted linear combination of all values available from different elevation scans (Tabary et al., 2007).

The M´et´eo France operational scheme is global in nature, assuming no change in the background VPR over the radar domain and hourly timescales. This approach can be problematic in frontal situations, where the height of the freezing level changes during the event (Tabary et al., 2007), and the authors acknowledge other potential weaknesses in cases of low level growth due to orography (Tabary, 2007). No explicit attempt is made to identify or exclude convection at the local scale, although it is possible for the domain averaged VPR to be “non-bright band” to the extent that the bright band peak strength can take a value of 1 (no enhancement).

Tabary et al. (2007) perform a detailed evaluation of the VPR scheme described in their earlier paper. The implementation details are slightly different in this validation, with a larger number of permitted values for each of the four variable parameters, and in particularhtop is not constrained by the model-predicted freezing level. This evaluation

is also run over daily, rather than hourly accumulations, in order to facilitate processing of a large historical dataset. This thorough climataological validation showed significant skill in reducing systematic accumulation biases on the daily timescale. However, no evaluation of instantaneous QPEs or hourly accumulations at the local scale have been published at this time.

2.5.2 Finnish Meteorological Institute (FMI)

An operational approach to VPR correction in Finland has recently been developed by Koistinen and Pohjola (2014). Unlike most regions, in which the dominant VPR bias error is overestimation due to bright band, at FMI the purpose of VPR is largely to correct for the underestimation of precipitation rates from measurements significantly above the melting layer. The high latitudes covered by the Finnish radar network result in an observed pre-VPR reflectivity underestimation beyond 100 km of between 4 and 15 dB.

The method of Koistinen and Pohjola (2014) uses both parameterised climatological profiles and radar measurements to generate a weighted ensemble of possible VPR bias corrections at each point in the radar domain. This global approach does not explicitly classify VPRs as stratiform or convective, but moulds the applied profile shape to the observed data. First, a mean field apparent VPR is determined for each radar using multi-elevation reflectivity ratios at 2-40 km range. This VPR is used to estimate the bias correction that should be applied to longer range measurements, in a way that accounts for additional broadening of the radar beam beyond the 40 km determination limit. At any given point in the radar domain, the 0-24 member ensemble of measured VPR biases is made up of the bias ratio calculated at this grid point at 15 minute intervals over the previous 6 hours.

The ensemble of parameterised climatological VPRs also has 24 members. The profile shape is similar to that of Kitchen et al. (1994), with a symmetrical bright band 800 m deep, whose top is located using a gridded NWP model freezing level. The bright band intensity ∆Z is fixed at 7 dB, and the profile has climatological reflectivity gradients below and above the bright band. The different ensemble members are determined by the height of the NWP model freezing level at each point, at 15 minute intervals over the previous 6 hours, with the climatological gradients also varying depending on whether precipitation at the ground is rain, wet or dry snow.

Once both sets of ensembles have been calculated, the bias correction for each point in the radar domain is established as a time- and quality-weighted mean of the two ensembles, with more recent ensemble members being given a greater weight. The correction applied to the composite is then a distance-weighted mean of the bias corrections from each radar within 300 km of the composite grid point, which is applied during compositing to the reflectivity measurement from the closest available radar. This means that although based on spatially averaged observations for each radar domain, the VPR correction is applied in a way that is tuned locally for each radar composite grid point. The authors find this scheme reduces the mean VPR underestimation bias to less than 2 dB for measurements within 200 km of the nearest radar.

Like many authors, Koistinen and Pohjola (2014) begin from the premise that mean ap- parent VPRs provide better information as to the true background VPR than convergence with an idealised profile. From this perspective, the use of short range radar-determined ratios is taken as read; but the authors explicitly justify the addition of climatological profiles and temporal smoothing in terms of reducing the random variability apparent in VPRs determined purely through observed reflectivity ratios. Koistinen and Pohjola (2014) go further than most in making no attempt to determine a separate VPR for convective precipitation, or to exclude convective regions from correction using a bright band profile. The authors justify this choice on the grounds that unlike bright band, the dominant underestimation bias at long range is equally a problem for both stratiform and convective rainfall. It is acknowledged in the paper that the inappropriate correction for bright band can cause problems in short to medium range convective QPEs.

2.5.3 Met Office (UK)

Figure 2.3: The idealised stratiform VPR shape, derived by Kitchen et al. (1994), which is used operationally in the Met Office centralised radar processing system (Radarnet). The wet bulb freezing level is derived from the 5 km gridded operational forecast model output.

The Met Office radar processing soft- ware (Radarnet) implements a pixel-by- pixel VPR scheme originally developed by Kitchen et al. (1994), and refined by Kitchen (1997). The mean stratiform pro- file shape (figure 2.3) was derived from a three year climatological sample of high resolution range height indicator scans (RHIs) observed with the 25 m S-band dish at Chilbolton. The profile has a fixed bright band depth of 700 m, and uses the Euro4 forecast model wet bulb freezing level (Brown et al., 2012) to define the top of the bright band. Mittermaier and Illing- worth (2003) compared the forecast freez- ing level height with observations of the melting layer top from a vertically pointing radar, and found an RMS error of less than 150 m, confirming that the model height is sufficiently accurate for use in VPR correc-

tion. A single variable parameter in reflectivity is used to scale the idealised profile to the measured reflectivity at each radar pixel, using a known beam power profile to simu- late the observed reflectivity measurement and adjusting the variable scaling parameter until the simulated reflectivity matches the observation. The surface reflectivity is then

extrapolated from the fitted profile.

A significant strength of the Met Office scheme is its ability to account for sub-kilometre- scale variability such as changes in bright band height and intensity and the presence of embedded convection, as it responds to local conditions at the radar radial resolution (600 m for the standard UK QPE) along each azimuth. This allows additional local information, such as a change in freezing level height with frontal passage or low level orographic precipitation growth, to be included in the correction (Kitchen, 1997). For the stratiform profile in its current form, Kitchen et al. (1994) demonstrate a 60% over- all reduction in QPE error for a number of light stratiform cases, and emphasise that greater gains would be expected in heavier frontal rain. The overall design of the iter- ative convergence scheme also provides a flexible framework for assimilating additional information, which could be used to adapt or update idealised parameterised profiles for further improvements to real time QPEs.

The Kitchen et al. (1994) idealised stratiform profile is not suited to cases without bright band, such as occurs for example in embedded convection with graupel. The underesti- mation in surface rainfall caused by erroneous bright band correction disproportionately affects estimates of the intense, often flood-producing rainfall associated with convective cores. It is therefore important to identify where these profiles occur, to avoid errors in high impact situations.

The current UK VPR scheme uses a high level reflectivity threshold to identify local profiles without bright band in radar data. If a reflectivity exceeding 30 dBZ is measured at a height exceeding 1 km above the wet bulb freezing level (criterion hereafter referred to as Z1), the pixel is classed as convective, and the VPR at that pixel is set to be

constant with height. This draws on the assumption that high reflectivities above the zero degree isotherm can proxy for the strong updrafts associated with convection and non-bright band VPRs (Smyth and Illingworth, 1998).