Forecasting weather radar propagation conditions - Springer Link

Meteorol Atmos Phys 96, 229–243 (2007) DOI 10.1007/s00703-006-0211-x Printed in The Netherlands

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Catalan Meteorological Service, Barcelona, Spain Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain

Forecasting weather radar propagation conditions J. Bech1;2 , B. Codina2 , and J. Lorente2 With 12 Figures Received July 12, 2005; revised May 9, 2006; accepted July 18, 2006 Published online: October 25, 2006 # Springer-Verlag 2006

Summary The increasing use of weather radar quantitative precipitation estimates, particularly in automatic applications such as operational hydrometeorological modelling or assimilation in numerical weather prediction (N W P) models, has promoted the development of quality control procedures on radar data. Anomalous propagation (AP) of the radar beam due to deviation from the standard refractivity vertical profile, is one of the factors that may affect seriously the quality of radar observations because of the increase in quantity and intensity of non-precipitating clutter echoes and consequent contamination of the estimated rainfall field. Another undesired effect of AP is the change in the expected radar echo height, which may be relevant when correcting for beam blockage in radar rainfall estimation in complex terrain. The aim of this paper is to study the use of N W P mesoscale forecasts to predict and monitor AP events. A nested 15-km grid resolution version of the M A S S model has been used to retrieve refractivity profiles in the coastal area of Barcelona, near a weather radar and a radiosonde station. Using the refractivity profiles two different magnitudes were computed: the vertical refractivity profile of the lowest 1000 m layer and a ducting index which describes the existence and intensity of the most superrefractive layer contained in the lowest 3-km layer. A comparison between model forecasts and radiosonde diagnostics during a six-month period showed that the model tended to underestimate the degree of super-refraction, with a bias of 4 km1 and R M S E of 11 km1 in the 1-km vertical refractivity gradient. Further analysis of the data showed that a combination of previous observations and forecasts allowed to produce modified forecasts improving the original direct model output, decreasing substantially the bias, reducing the

R MS E by 20% and improving the skill by 40%, beating also

radiosonde observations persistence.

1. Introduction Quantitative applications of weather radar observations, such as precipitation estimates used in hydrological models or assimilation in numerical weather prediction (NWP) systems, require an exhaustive quality control (see, for example, Joss and Waldvogel, 1990). In the recent European Concerted action COST 717 (Rossa, 2000), the importance of quality control on radar observations and derived products was stressed both in the area of hydrological forecast systems (Bruen, 2000) and NWP assimilation and validation activities (Macpherson, 2000; Fr€uhwald, 2000) and specific reviews and proposals about quality control were reported (Alberoni et al, 2003; Michelson et al, 2004). Radio propagation conditions in the troposphere may lead the radar beam to follow a different trajectory – essentially higher or lower – compared to its normal path. Therefore, the deviation from normal propagation is a factor that can affect seriously the quality of radar observations. In particular, when the atmospheric thermodynamic conditions are such that electromagnetic

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waves refract much more than usual, part of the radar energy may be directed downwards, to the ground, increasing the intensity and quantity of spurious non-precipitating ground (or sea) clutter echoes (Collier, 1996; 1998). This phenomenon, associated to super-refraction, is usually known as anomalous propagation (AP or anaprop) and the associated echoes are designated as AP echoes. Another undesired effect of AP is the intrinsic change in the expected radar echo height, which may be relevant when correcting for topographic beam blockage in radar rainfall estimation in complex terrain (Gjertsen and Dahl, 2002; Bech et al, 2003; Fornasiero et al, 2004). The opposite case of super-refraction, i.e., when the beam refracts less than usual diminishing the radio horizon, is known as sub-refraction and is also a form of anomalous propagation though its effects are less evident and it occurs less frequently. In the last decades a number of techniques have been developed to detect and correct ground clutter and AP echoes. In non-coherent radars, statistical techniques dealing with pulse-to-pulse data are typically used, mainly based in the autocorrelation properties of the non-precipitating echoes which are usually much more variable than real precipitation (Wessels and Beekhuis, 1994; Sugier et al, 2002; Nicol et al, 2003). Doppler radar systems offer advantages (see, for example, Keeler and Passarelli, 1990; Koistinnen, 1997) though do not solve the problem completely because they have difficulties eliminating ground clutter without removing some real precipitation. Moreover they are of limited use to deal with sea clutter due to wave motion. Therefore, post-processing of radar observations in hydrometeorological – oriented applications requires specific treatment of AP or clutter echoes as implemented operationally in a number of cases. This is done usually taking into account the two or three-dimensional structure of the reflectivity field (see, among others, Kitchen et al, 1994; Joss and Lee, 1995; da Silveira and Holt, 1997; Pamment and Conway, 1998; Fulton et al, 1998; Archibald, 2000; Alberoni et al, 2001; Sańchez-Diezma et al, 2001; Steiner and Smith, 2002) or combining information of radar data with other type of observations or forecasts (Pankiewicz et al, 2001; Michelson and Sunhede, 2004). On the other hand, a different approach to improve clutter and anaprop detection and

removal is provided by polarimetric observations (Ryhzkov and Zrnic, 1998; Illingworth, 2003). Other studies developed specifically from the point of view of the hydrological application usually combine radar data with raingauge observations and make use of geostatistical techniques such as kriging to decontaminate radar data from ground clutter or AP echoes (see, for example, Todini, 2001; Wesson and Pegram, 2004). In this work, N W P mesoscale data are used to forecast the propagation environment in the Barcelona Mediterranean coastal area (NE Spain). Six months of numerical forecasts are compared with radiosonde observations in order to assess the potential use of the forecast data to monitor and anticipate anomalous propagation events. Other examples devoted to specific fieldcampaigns – and therefore restricted to shorter time periods than the present study – may also be found in the literature. For example Burk and Thompson (1997), focused in the coast of California, or Atkinson et al (2001), centered over the Persian Golf, also reported the use of N W P forecasts to examine in detail the propagation environment. On the other hand, von Engeln and Teixeira (2004) employed global analysis of the European Centre for Medium-Range Weather Forecasts to obtain a ducting climatology to be used in the analysis of radio occultation of GPS data signal. The two magnitudes used to monitor the propagation conditions are introduced in Sect. 2. Section 3 describes the data employed (radiosonde observations and N W P fields) to produce the forecasts and the verification data sets, and Sect. 4 presents the results and a discussion of an improved version of the original forecasts in relation to the persistence of the observations and the skill with respect to climatology. 2. Weather radar propagation conditions Variations of the air refractive index, n, control the propagation conditions of the radar beam. A related magnitude, the refractivity N, may be expressed in terms of meteorological variables (Bean and Dutton, 1968): 77:6 4810 e 6 pþ ; ð1Þ N ¼ ðn 1Þ10 ¼ T T

Forecasting weather radar propagation conditions

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Table 1. Effects upon propagation under different ranges of dN=dZ, dM=dZ and ID Characteristic

dN=dZ (1=km)

dM=dZ (1=km)

ID

Ducting Super-refraction Normal Sub-refraction

dN=dZ 157 157 < dN=dZ 79 79 < dN=dZ 0 0 > dN=dZ

dM=dZ 0 0 < dM=dZ 79 79 < dM=dZ 157 157 > dM=dZ

ID 78 78 > ID 1 1 > ID 79 79 > ID

where T is the air temperature (K), p is the atmospheric pressure (hPa) and e is the water vapour pressure (hPa). The constants in this equation were determined empirically and are valid for microwave frequencies; between 1 and 100 GHz the error of N computed from Eq. (1) is below 0.1. Therefore most results of this study are not only valid for weather radar frequencies but also for other transmitters such as micro-wave terrestrial or satellite links. A different magnitude, called the modified refractivity M, is also commonly used: M ¼ N þ 0:157 h; ð2Þ where h is the altitude (in m) of the level considered. Modified refractivity takes into account the height of each layer and is particularly convenient for ducting estimation as its vertical gradient becomes negative in that situation. The vertical variation of N determines the degree of refraction of the radar beam. Therefore, the value of the vertical refractivity gradient of the first kilometer of air (hereafter VR G), which may be calculated from radiosonde observations, is usually taken as reference. Standard conditions, which are dominant in mid-latitudes (V R G ¼ 40 N units=km) are commonly assumed by weather radar processing software. In general, normal conditions range between 0 and 80 N units=km. However, departures from this value are not unusual and, in some places, show significant seasonal variations or remarkable extremes. For example, according to the International Telecommunication Union (ITU, 2003), the areas with lowest VRG – i.e., super-refractive conditions – observed in August correspond on average to the Persian Gulf, the coastal area in front of California and the Western Mediterranean. This last region is consistent with a previous study which indicates that during this period of the year the lowest V R G median values are observed in the Barcelona area (Bech et al, 2000).

For instance, under super-refractive conditions (VRG 0 N units=km) and the radio horizon is decreased; it occurs seldom and is less obvious in radar data because implies a decrease of clutter echoes. In this study two different magnitudes have been considered to monitor the radar propagation environment: a standard definition of the vertical refractivity gradient (VRG) of the first 1000 m above ground level, and an index to measure the degree of ducting, denoted as ID. A summary of the different propagation characteristics under different ranges of dN=dZ, dM=dZ and the ducting index ID, which will be explained in the following section, is given in Table 1. 2.1 Vertical refractivity gradient The Vertical refractivity gradient (V R G) is calculated as the difference between refractivity values at surface Ns and at 1000 m above ground level N1000, according to the International Telecommunication Union recommendations (ITU, 2003): V R G ¼ Ns N1000 : ð3Þ This definition allows simple calculation from refractivity profiles obtained with radiosonde observations or model forecasts. The surface refractivity Ns is calculated from the lowest ground level and N1000 is interpolated from the vertical profile of refractivity.

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The V R G defined in these terms, though it ignores the existence of possible sub-refractive or ducting layers between the ground and the 1000 m level, has been used extensively in the past. For example Steiner and Smith (2002) estimated the potential of weather radar AP occurrence in the US employing this approach and examining 16 years of radiosonde observations. 2.2 Ducting index A different magnitude, the ducting index ID, considers the degree of departure from the threshold of the super-refractive gradient (78 M units=km) in a given layer of depth z and modified refractivity variation M: ð4Þ ID ¼ 78 z M: The height increment z is in km and M is in modified refractivity M units. This magnitude is computed in all layers contained in the 3 first km of air, examining both surface and surface based microwave ducts and selecting the highest ID. Positive ID values indicate super-refraction. Johnson et al (1999) found a high positive correlation between this index and anomalous propagation echoes observed in the UK weather radar network. 3. Radiosonde observations and N W P forecasts A description of the data used in this study is provided in this section. Two different types of operational data were considered to retrieve refractivity profiles in order to calculate propagation conditions in the Barcelona coastal area: radiosonde observations and NWP mesoscale forecasts obtained with the M A SS model (Koch et al, 1985; Codina et al, 1997a, b). The temporal period considered ranged from 12th November 2002 to 25th April 2003, approximately six months. During this period the MASS model configuration and settings remained constant, a crucial requirement to perform a consistent analysis. This fact excluded warm season periods – more favorable to anomalous propagation events –, though previous studies have shown that AP may take place any time of the year, as in fact happened during the period examined. The total number of couples forecast-observation was 303 (92% of the period covered).

3.1 Radiosonde observations Since 1997, radiosonde observations have been made in Barcelona (41 230 N, 2 70 E and 98 m above sea level) to support the operations of the regional administration’s Subdirectorate of Air Quality and Meteorology. Observations are performed operationally twice a day at 00 and 12 UTC (00 and 12 LST) using Vaisala RS-80 sondes. Radiosonde observations used in this study were sampled every 10 s allowing a vertical resolution (approximately 50 m) better than the standard radiosonde data TEMP format. After applying a quality control procedure based on GTS data processing to eliminate erroneous or suspect data to available observations (MeteoFrance, 1997), 322 profiles were considered valid (98% of the possible observations during the period studied).

3.2 The M A S S model The M A S S model was used to obtain vertical refractivity profiles from operational runs initialised at 00 UTC and 12 UTC. The refractivity profiles were built from 24-h forecasts of temperature, pressure and humidity profiles over the same location of the radiosonde station. The limited area model M A S S (which stands for Mesoscale Atmospheric Simulation System), is a proprietary numerical weather prediction model that has been in constant development over the past 20 years, both as a research tool and to provide commercial weather forecast services. As a dynamical model, M A S S embodies the fundamental physics of the atmosphere including conservation of mass, momentum, and energy, as well as the moisture phases. It can be run both hydrostatically and non-hydrostatically, and several grid and subgrid-scale parameterizations can be chosen. In the operational environment in which M A S S was run in this occasion, the options used have been the most conservative in order to achieve a reasonable performance in a broad range of weather phenomena. Therefore, in this work the configuration used was the hydrostatic version of M A S S at 15 km grid-point resolution, 30 sigma levels, Grell convective parameterization, diagnostic microphysics approach, and turbulent kinetic energy scheme in the boundary layer. To initialise


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Fig. 1. Nested domain of the M A S S simulation indicating the location of the radiosonde station and the Vallirana weather radar

the model, both global model simulation output and surface and upper air observations were used, blended with an optimal interpolation technique. The region over which M A S S solves the set of primitive equations, and the radar and rawindsonde locations are displayed in Fig. 1. During the period of study 95% of the possible forecasts of vertical refractivity profiles were available.

4. Results and discussion In this section a description of the comparison between the model forecasts and the radiosondebased AP diagnostics is given. Moreover, further discussion is provided examining several properties of the persistence of the observations. Finally, based on the previous results, a new

Fig. 2. Time series of Vertical Refractivity Gradient [V R G] (top) and Ducting Index ID (bottom) NWP – derived forecasts (dashed line) and radiosonde – based diagnostics (solid line)

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method to improve the original forecasts is proposed and discussed. 4.1 Direct model output Figure 2 shows the temporal evolution of model forecasts and radiosonde diagnosis of the vertical

Fig. 3. Temporal evolution at 12-h intervals of 0.7 PPI uncorrected equivalent reflectivity factor observations recorded with the Vallirana weather radar showing clutter variations: (a) 10th March 2003 00 Z, (b) 10th March 2003 12 Z, (c) 11th March 2003 00 Z, (d) 11th March 2003 12 Z, (e) 12th March 2003 00 Z, (f) 12th March 2003 12 Z, (g) 13th March 2003 00 Z, and (h) 13th March 2003 12 Z. Darker echoes indicate more intense reflectivity values, ranging from 10 to above 60 dBZ

refractivity gradient (VRG) and the ducting index (ID) during the period considered. One of the most remarkable anomalous propagation events in the period considered occurred in the first half of March. In particular, in the 12th of March 00 UTC a minimum in the VRG was observed (a decrease of 77 N units in the first km). The increase of amount and intensity of clutter echoes may be noted in Fig. 3 which shows a sequence of PPI radar images of the Vallirana weather radar; the time of the minimum VR G is coincident with the maximum clutter observed. Clear clutter patterns (both ground and sea clutter) appeared in the area between 40 and 41 latitude and 0 and 2 longitude and also in the northern mountains of the Majorca Island (39 latitude and 2 to 4 longitude). After normal VR G values were restored, the additional ground clutter also disappeared. During the whole period considered it may be appreciated that model forecasts tend to underestimate super-refraction; both VRG and ID are biased in this direction (a bias or average difference of 4 N units=km and 10 ID units, respectively). Differences between V R G forecasts and observations are usually caused because the surface super-refractive layer – typically associated to a

Fig. 4. Vertical profile of modified refractivity on 13th November 2002 at 12 Z over Barcelona: model forecast (dotted line), radiosonde observation (solid line) and radiosonde observation interpolated to model forecast levels (dashed line). Detail of the first 350 m are zoomed on the right


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Fig. 5. Relative frequency distributions and cumulative probabilities plots of forecast (left) and observed (right) Vertical refractivity gradient: midnight (top), noon (middle) and combined (bottom)

thermal inversion which appears frequently – is not usually simulated correctly by the model. This fact is illustrated in Fig. 4, which shows that in the lower layers the average profile observed and forecasted are very similar. However, as the surface refractivity inversion is not reproduced by the model, VRG values observed (34 N units=km) and forecasted (25 N units= km) are substantially different (9 N units=km). The mean absolute errors of the whole period tested were 9 N units=km and 12 ID units for VRG and the ducting index, respectively. Histograms of VRG observations and forecasts of the data set examined are shown in Fig. 5. It may be noted that both midday (12 Z) and midnight (00 Z) radiosonde-based VRG distributions

present a slightly bimodal pattern with a clear peak around 40 N units=km – corresponding to the normal propagation mode value as indicated by the 50% position of cumulative probability curve – and also a weaker secondary peak at 70 N units=km, associated to super-refractive events. This pattern is correctly reproduced by midnight forecasts, but not by 12 Z forecasted data, whose distribution is simply unimodal, thus missing the super-refractive events represented by the secondary peak in the distribution of the V R G observations. The whole data set (00 and 12 Z) smooths this effect and hides the limitations of 12 Z forecasts. A similar behaviour is observed in the ID histograms (Fig. 6), but with a much greater sub-

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Fig. 6. Relative frequency distributions and cumulative probabilities plots of forecast (left) and observed (right) ducting index ID: midnight (top), noon (middle) and combined (bottom)

refractive bias of the model and also more spread distributions in the ID forecasts. Differences in the observed and modelled ducting index ID may have two main distinct origins. One of them is that the model and the observation had a different surface refractivity value (for example, due to the limitations of the model to simulate an existing surface thermal inversion, which would imply a different surface refractivity value). The other one may be explained by the fact that the index is defined as the maximum value computed over the 3 km vertical column. Radiosonde observations have much more vertical resolution allowing to depict sharp refractivity gradients of thinner air layers. For example, in Fig. 4, between 2000 m and

2500 m, an intense refractivity gradient is observed; this level of detail may not be handled by the coarser vertical resolution of the mesoscale model and, therefore, the corresponding ID forecast is smoothed. However, this effect is largely compensated when the radiosonde observations are interpolated to the levels of the forecasted profile. The V R G 12 h tendency was generally in good agreement with the observations, particularly its sign. The sign of the tendency is related to the change or intensification of the propagation character (super refraction and sub refraction). For example, a negative sign in the V R G tendency implies a change (or intensification) towards super refraction. In the case of the ducting index,


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Fig. 7. Two and seven days time averaged plots of V R G (top) and its 12 h tendency (bottom) of observations (solid line) and N W P forecasts (dashed line)

Fig. 8. Two and seven days time averaged plots of ID (top) and its 12 h tendency (bottom) of observations (dashed line) and N W P forecasts (solid line)

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Fig. 9. Scatter plots of NWPforecasts vs radiosonde-diagnostics of Vertical refractivity gradient (left) and ducting index (right). Top images are forecasts and bottom images are referred to 12-h tendencies

tendencies were systematically greater than those observed. Time averaging with moving windows of 2 and 7 days indicated that average conditions and tendencies were reasonably well simulated by the model for V R G (Fig. 7) and, to a lesser extent, for ID (Fig. 8), which presented more variability. Time averaged plots show clearly that differences in the tendencies converge faster than VRG or ID values. Scatter plots of VRG and ID observations and their corresponding forecasts and 12 h tendencies (Fig. 9) confirm that 12 h tendencies are much less biased than forecasts. Examining the sign of the tendency, which indicates if there is a change or intensification in the propagation character (sub or super refraction), it was found that 57% of the VRG and 48% of the ID tendency signs were correctly forecasted by the direct model output. Therefore, though the NW P model has limitations in forecasting the actual observed values (for both VRG and ID), it performs a better job regarding the tendency of the forecasted magnitude though still the dispersion was high, as shown by the scatter plots of Fig. 9.

4.2 Persistence To assess the goodness of the forecasts, an analysis of the persistence of the observations is given in this section. The persistence is considered here as the temporal continuity of the local value of a magnitude. In particular, it was examined the temporal autocorrelation function (obtained with the Pearson correlation coefficient R), bias or mean error (ME), mean absolute error (M A E) and root mean squared error (R M SE) comparing the most recent observations with the previous ones up to 108 h at 12 h intervals (Fig. 10 and Tables 2 and 3 for 12 and 24 h persistence). As expected, these magnitudes score worse results as the time lag increases. In the case of the bias, however, there was a local minimum at 72 h where the mean error was slightly lower than at 48 h, probably due to particular characteristics of the observation data set rather than to a specific physical process. The correlation of the direct forecast (0.516) was slightly higher than the persistence at 12 h (0.482). However the rest of the scores yielded better results for the 12 h persistence. The mean error or bias


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Fig. 10. Autocorrelation function, bias, root mean squared error and mean absolute error of the persistence of the observations of the vertical refractivity gradient considering a temporal lag up to 108 h at 12 h intervals Table 2. Verification statistics of V R G forecasts Predictand

BIAS

R

RMS E

SKIL L

P12 P24

0.092 0.125 4.167 1.976 1.731 1.586 1.470

0.482 0.479 0.516 0.599 0.615 0.544 0.455

9.775 10.336 10.693 8.303 8.118 8.797 9.563

0.097 0.010 0.081 0.348 0.377 0.269 0.136

MASS

H2b H4b H6b H8b

Table 3. Verification statistics of ID forecasts Predictand

BIAS

R

RMSE

SKILL

P12 P24

0.030 0.245 9.882 2.258 2.253 2.151 1.442 1.037

0.462 0.255 0.112 0.475 0.526 0.485 0.530 0.528

3.527 3.809 11.429 4.247 3.927 4.050 3.437 3.259

0.665 0.609 2.521 0.514 0.584 0.558 0.682 0.714

MASS

H2b H4b H6b H4b3 H4b4

fact, both the R M S E and the M A E of the direct forecast were lower than the 36 h persistence; after 36 h the persistence was beaten by the direct model output. Similar results were obtained for the persistence of ID observations: the R M S E and the M A E were much lower if considering the 12 h persistence as predictand; the bias had equivalent absolute value but different sign and the temporal autocorrelation was higher at 12 h persistence (0.462) than the direct model output (0.112). Therefore, the analysis of the persistence of observations – performed examining only radiosonde data – shows that it is generally more reliable using past observations as forecasts than the N W P direct model output described earlier. So, taking into account these results, new modified forecasts were considered using both forecasts and previous observations. 4.3 Modified forecasts

was much lower (0.1 vs 4.2 1=km); the R M S E also decreased slightly (9.8 vs 10.7 1=km) and the M A E was also lower (7.2 vs 9.8 1=km). In

In general, direct model output shows discrepancies with local observations because of the existence of biases in the models, lack of re-

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presentativeness of local effects or limited temporal and spatial (horizontal or vertical) resolution. There are a number of post-processing techniques to improve the direct output of NWP products to obtain better agreement with observations such as Kalman filtering (Petersen, 1968), PerfectProg (Klein et al, 1959) or Model Output Statistics (Glahn and Lowry, 1972). With the same objective but with a different approach, Carroll (1997) described a technique to modify interactively not only point observations but NWP fields such as surface level pressure or geopotential topographies. Taking into account the sub refractive bias observed in the original M A S S model forecasts of propagation conditions and the properties of the persistence of the observations, new modified forecasts were proposed. The modified forecasts valid at time i, denoted here as Pi 0 , were built as a function of the information available at the time of issuing the forecast, i.e., previous observations (Oi1 ; Oi2 . . .) and current and past direct model output forecasts (Pi ; Pi1 ; Pi2 . . .), so this scheme could be implemented for real-time operation: Pi 0 ¼ Pi 0 ðPi ; Pi1 ; Pi2 . . . ; Oi1 ; Oi2 . . .Þ:

ð5Þ

Several types of combinations of past observations and forecasts were tested. One of them, denoted here as Hpbi, followed the general expression: p p X 1X 1 Hp bi ¼ Oik þ Pik ð6Þ p k¼1 2ðp þ 1Þ k¼0 which averages the last p observations available and the last p þ 1 M A S S model forecasts divided by a factor 2. This approach of assigning the same weights to all forecasts and observations, though simple, was more effective in removing the model bias than other schemes that, for example, gave more weight to more recent observations and forecasts. As discussed later, variations of the factor 2 dividing the M A S S model forecasts Pi were also considered for ID forecasts with a generic factor f, denoting then the new predictand as H4bf. For example, H4b3 indicates a H4b using a factor of 3 instead of 2, H4b4 a factor of 4, etc. It should be noted that these new modified forecasts are not fitted statistically with a particular data set of observations and forecasts. They are proposed as a means to improve the original

direct model output, after examining it and comparing it with some properties of the persistence of the observations. Therefore, they can be considered independent from the observations and they can be used for verification. 4.4 Verification For each modified forecast or predictand of vertical refractivity gradient VRG and ducting index ID a number of statistics were calculated and compared with the persistence of the observations for verification purposes. In order to estimate the relative accuracy of each forecast, an skill score SS was calculated following the standard formulation of categorical forecasts of continuous predictands (Wilks, 1995): ð7Þ SS ¼ ðS Sref Þ=ðSperf Sref Þ; where S is an score measuring the correspondence between the forecast and the observations, Sref is a reference value used for comparison and Sperf is the perfect value of the score. In this case, the score selected was the mean standard error (M S E). The perfect value Sperf was taken as 0 and the Sref was obtained assuming a climatological value of standard refraction (40 1=km) for the 1 km vertical refractivity value and a value of 0 ID units for the ducting index, derived from the average 100 m vertical refractivity value (ca. 80 1=km) obtained in a previous study. Tables 2 and 3 list results for some selected modified forecasts of VR G and ID, respectively, the direct MASS model output (referred simply as M A SS) and the persistence of the observations at 12 and 24 h (P12 and P24). Moreover, the correspondence between observations and forecasts and their variability were summarized graphically in a Taylor diagram for each magnitude (Figs. 11 and 12). This diagram shows a polar plot where the radius is proportional to the normalized standard deviation of the radiosonde observations (here marked as R AO B) and the azimuth indicates the linear correlation between the observations and the different forecasts (Taylor, 2001). As noted before, the V R G MA S S original forecast was biased towards subrefraction. As expected, the persistence at 12 and 24 h removed largely this bias. They also improved the RM SE and the skill score, yielding P12 the best results


Fig. 11. Taylor diagram of vertical refractivity gradient [V R G] radiosonde observations (R AO B), original M A S S forecasts, persistence of the observations and modified forecasts

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three scores improve when considering 4 instead of 2 past observations and then get worse when the number of past observations is increased. This effect may be appreciated in Fig. 11 which also shows that the smoothness introduced in the modified forecasts reduces their standard deviation when compared to the observations. The behavior of the ducting index forecasts is slightly different. The original ID M A S S model forecasts performed worse than V R G forecasts compared to persistence. The correlation, for example, was poorer than the persistence of observations at 60 h (see Fig. 12). Besides, the standard deviation was somewhat higher than the observations, unlike in the VRG case where both original M AS S forecasts and observations were nearly located along the same radial in the Taylor diagram. In this case, the modified forecasts could improve the correlation (for example H2b and H4b) but not the skill score and the R M SE. To achieve this improvement it was necessary to consider a new form of the modified predictands, where the weight of the M A S S forecasts was slightly lower (1=3 and 1=4 instead of 1=2). Following this approach the predictands H4b3 and H4b4 had a skill score of 71% and 68% compared with the 66% of P12 while the correlation was also higher. 5. Conclusions N W P model data were used to derive refractivity

Fig. 12. Taylor diagram of ducting index ID radiosonde observations (R AO B), original M A S S forecasts, persistence of the observations and modified forecasts

though the correlation was slightly lower. The modified forecasts improved the skill score, being H4b – averaging the last four observations, i.e., two days – the one which performed best (38% of improvement respect to climatology) and also got better RM SE and correlation. These

profiles in order to estimate weather radar anomalous propagation conditions in the Barcelona area (NE Spain). In particular, the vertical refractivity gradient of the first 1000 m above ground level and a ducting index were calculated. Six months of model forecasts were verified with radiosonde observations. From a first analysis, after examining the persistence of the observations, modified forecasts were tested. The new forecasts were built as linear combinations of previous observations and forecasts to improve both the average value and the tendency of original forecasts. Substantial improvements were obtained with the new predictands, increasing the skill (with respect to climatology) of the forecasts of the vertical refractivity gradient from 1% of the 12 h persistence to 40% with new predictands and also regarding the correlation between forecasts and observations. Some improvement

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was also achieved with ducting index forecasts though they were more limited compared to the radiosonde observations persistence at 12 h. Future work should include a temporal extension of the data set period to cover all seasons and refining the modified forecasts by adjusting the average and tendency terms coefficients. This fine tuning, which could be achieved by crosscorrelation, was not adopted with this data set to avoid overfitting with a sample not representative of the conditions of the whole year. The results presented here may be used to flag radar data affected by anomalous propagation or in a more complex quality control system of radar echoes such as the fuzzy-logic based scheme applied by Domıńguez et al (2004) to radar observations recorded in Catalonia. Both possibilities would help to enhance the quality of the radar observations and to avoid miscorrections in beam-blockage processing schemes or to discriminate rainfall overestimation by sea clutter, a usual problem in the verification of NWP precipitation forecasts in this area. Acknowledgements Part of this research was funded by the EU project CARPEDIEM (Contract EVG1-2001-00031) and was done within the framework of the former EU COST-717 action ‘‘Use of weather radar observations in numerical weather prediction and hydrological models’’ and the current EU COST-731 ‘‘Propagation of uncertainty in advanced hydro-meteorological forecasting systems’’. We thank two anonymous reviewers whose constructive and exhaustive comments contributed to improve the clarity and final form of this paper.

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