Dependence of Predictability of Precipitation in the Northwestern Mediterranean Coastal Region on the Strength of Synoptic Control

The weather regime dependent predictability of precipitation in the convection permitting kilometric scale AROMEEPS is examined for the entire HyMeX SOP1 employing the convective adjustment timescale. This diagnostic quantifies variations in synoptic forcing on precipitation and is associated with different precipitation characteristics, forecast skill and predictability. During strong synoptic control, which is dominating the weather on 80% of the days in the 2-months period, the domain integrated precipitation predictability assessed with the normalized ensemble standard deviation is above average, 5 the wet bias is smaller and the forecast quality is generally better. In contrast, the spatial forecast quality of most intense precipitation in the afternoon, as quantified with its 95th percentiles, is superior during weakly forced synoptic regimes. The study also considers a prominent heavy precipitation event that occurred during the NAWDEX field campaign in the same region, and the predictability during this event is compared with the events that occurred during HyMeX. It is shown that the unconditional evaluation of precipitation widely parallels the strongly forced weather type evaluation and obscures forecast 10 model characteristics typical for weak control.

to 45-h forecast range) for the Nawdex case. b) In the ensemble simulations, AROME is driven by the global short-range ARPEGE-EPS (Descamps et al., 2014), called hereafter PEARP. Firstly, a subset of 12 members of the PEARP is selected according to the Nuissier et al. (2012) technique. The PEARP 35-member ensemble forecasts are classified by a complete-linkage clustering technique (Molteni et al., 2001). c) The initial conditions are provided by adding downscaled forecast perturbations 95 of the selected PEARP members to the AROME operational analysis (Raynaud and Bouttier, 2017). d) Atmospheric model errors are represented through the so-called SPPT scheme (stochastic perturbation of physics tendencies) described in Bouttier et al. (2012), which simulates the effect of random errors due to the physical parametrizations. e) Finally, random perturbations are added to various parameters of the surface externalisée (SURFEX) surface scheme, including for instance sea-surface temperature, soil moisture and temperature perturbations (Bouttier et al., 2016).

Domain and observational data
The investigation domain extends across 300 km × 800 km and encompasses southeastern France and northwestern Italy including the coastal regions of Cote d'Azur and Riviera as well as adjacent mountainous regions of the Massif Central and the Alpes Maritimes (Fig. 1). This region, that is herein called the Northwestern Mediterranean, is prone to heavy precipitation generated by a wide variety of flow conditions including synoptic systems characteristic of Rossby wave breaking at the eastern 105 end of the North Atlantic storm track, modulated by orography and thermal contrasts of the Mediterranean basin as well as calm, conditionally unstable situations requiring trigger mechanisms to generate rainfall (e.g. Ducrocq et al., 2014;Nuissier et al., 2016, and references therein). The choice of the location and size of the investigation domain is carefully chosen and represents a compromise between being large enough to have numerous precipitation events giving good statistics, but small enough to comprise a specific and unambiguous meteorological situation in combination with the good coverage of rainfall The data is plotted using a 24-hourly moving average on the 3-hourly values to increase readability. The thin lines represent the 3-hourly data of precipitation (blue), the convective adjustment timescale (green) and the normalized spread of precipitation (Sn, gray) for reference.
Note that the dependent variables are given in logarithmic scale, CAPE is divided by a factor of 10, Sn multiplied by a factor of 10 and precipitation is labeled on the right hand side. the maximum domain averaged ensemble mean τ c exceeds a threshold criterion at least once a day, that day is classified to be weakly forced.

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In the present study a threshold value of 3 h is chosen to account for the smaller τ c values occurring in the autumn season of HyMeX SOP1 (see Fig. 3). This is in contrast to applications of τ c in the summer season when a threshold of 6 h is reasonable to separate mid-latitude precipitation regimes due to dynamic control (Kühnlein et al., 2014;Keil et al., 2019). However, Zimmer et al. (2011 argue that the τ c diagnostic results in a continuous distribution and conclude that a value somewhere between 3 and 12 h clearly distinguishes between different regimes. It turns out that a threshold of 3 h substantially reduces the sampling 150 error giving a distribution of 48 strongly vs 11 weakly forced days during HyMeX SOP1.

Classification based on the strength of synoptic control
At first glance the timeseries spanning the entire 2-months period shows the variability of weather on daily timescales in autumn 2012 (Fig. 2). The precipitation curve highlights some of the 'golden cases' observed during HyMeX SOP1 (e.g. IOP6 During these episodes convective instability is created by, for instance, solar insolation but cannot be removed by precipitation because of inhibiting factors like capping inversions atop the boundary layer prevent convection initiation. The rank correlation of CAPE and 3-hourly precipitation (and its normalized standard deviation S n ) amounts to 0.44 (and 0.28, respectively) and confirms the limited predictive power of CAPE alone.
Here the convective adjustment timescale τ c provides a better suitable measure to distinguish and to classify weather situations with different synoptic control. Using a categorical threshold of 3 h for the daily maximum area averaged convective adjustment timescale results in 48 strongly and 11 weakly forced days in the Northwestern Mediterranean domain during 165 HyMeX SOP1. Many of the weakly forced cases occur in the first week of the SOP1 (8 to 11 Sept, Fig. 2). After mid-October there are no weakly forced cases anymore suggesting the influence of the seasonal cycle, as decreased solar insolation limits diurnally-driven precipitation. However it is the interplay between the creation of convective instability and its removal by precipitation (both variables make τ c ) that shows the overall decrease in autumn that is strongly modulated by the occurrence of mid-latitude weather systems. During SOP1 τ c exceeds the threshold value ultimately on 13 October, while area averaged 170 CAPE maxima exceeding 100 J/kg still occur in late October (e.g. on 26 October, IOP16a). A comparison of the timeseries of τ c and of the normalized standard deviation S n in Fig. 2 gives a first indication of a connection between both, that is between the weather regime and the forecast uncertainty. Large values of τ c indicating weakly forced weather conditions correspond with above average values of S n suggesting below average precipitation predictability.
This relationship and clear dependence of the convective adjustment timescale τ c and the normalized standard deviation S n 175 of precipitation is further illustrated in Fig. 3. Large values of τ c correspond with large S n of precipitation being a sign of    Cevennes region the ensemble overestimates the 6 h precipitation (exceeding 20mm/6h) and there is a considerable ensemble spread. There, forecasts of single members diverge (Fig. 7c-f) and show a displacement of heaviest precipitation (e.g. shifted eastward in member 7, very intense and southward in member 8). In the eastern Rhone valley, an area where the ensemble mean indicates more than 5 mm, the intra-ensemble variability is large and individual members fail to predict any precipitation (e.g. member 12).

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A second hotspot of strong precipitation occurs in the Var region where maximum rainfall accumulations are observed (larger 50mm/6h). There, larger values of S n point towards a higher intra-ensemble variability that becomes apparent when looking at the rainfall sums of individual members (e.g. Fig. 7e,f). A third heavy precipitation region is forecast close to Genova in Italy.
Observations indicate a considerable overprediction in this region with filled circles depicting rain-gauge observations being clearly recognizable (Fig. 7a). However, the hidden circles across large regions of the Massif Central and the Alpes Maritimes

Weakly forced case on 11 September 2012
Weather on 11 September represents a characteristic case of a weakly forced situation during HyMeX. Before noon single 230 convective cells are triggered with very different intensity and location in the individual members (not shown) resulting in very small area averaged rainfall accumulations (Fig. 6). Subsequently, convection intensifies leading to more than 50mm/6h in individual members at different locations (Fig. 8c,d,f). The differences in terms of exact location of heaviest precipitation result in maximum ensemble mean values of less than 20 mm (Fig. 8a). Overall, precipitation is strongest across mountainous regions (a more or less distinct precipitation band extends from southwest to northeast across the Massif Central in all members) 235 with correctly forecast dry conditions south of 44°N in the Var region. Whereas the accumulated precipitation distribution in members 1 and 3 resembles the ensemble mean pattern, other members exhibit big deviations: member 4 forecasts hardly any rainfall, while member 9 forecasts a lot of precipitation in the western part of the domain only. Large S n values west of 6°E demonstrate this considerable intra-ensemble variability. Overall, the comparison with rainfall observations suggests a notable overestimation (Fig. 8a) and a clear connection to orography during weak control.

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The weather situation on 11 September is characteristic for the first week of the HyMeX SOP1 period (see Fig. 2) when solar insolation in early autumn is still strong enough to generate convective instability by surface heating resulting in large 11 https://doi.org/10.5194/acp-2020-508 Preprint. Discussion started: 10 June 2020 c Author(s) 2020. CC BY 4.0 License. CAPE and large τ c values indicating a need for local triggering mechanisms to overcome convective inhibition and to form precipitation (see Fig. 6).

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The detailed examination of individual heavy precipitation events in the Western Mediterranean region is complemented with one of the most prominent cases in that region that developed downstream of the cyclone Sanchez during the NAWDEX field campaign in autumn 2016 (Schäfler et al., 2018). Fig. 9 shows a good match of forecast and observed 24 h precipitation peaking in the Cevennes region with more than 200 mm. This event is clearly classified as strongly forced regime with an area averaged maximum τ c of less than 30 min (see Fig. 3 and Fig. 6).  13 https://doi.org/10.5194/acp-2020-508 Preprint. Discussion started: 10 June 2020 c Author(s) 2020. CC BY 4.0 License. Figure 11. Aggregated time series of the spread (standard deviation) and skill (RMSE) averaged over the full SOP1 period (black) and over weakly (blue) and strongly forced weather regimes (red). The RMSE is the ensemble mean of the member RMS forecast error. members 5 and 6, Fig. 10d,e). Within the heaviest precipitation region all members agree well resulting in small S n values.

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Above average precipitation variability occurs northward (across the Massif Central) and across the Mediterranean Sea.
In summary, the three selected cases indicate that the heaviest precipitation is co-located with orography during both regimes, that the spatial predictability of precipitation can considerably vary from case-to-case even within one forcing type, and that the precipitation intensity is overestimated during weak control.

Systematic verification conditional to the strength of synoptic control 260
Finally, we examine the question how precipitation forecasts during the different weather regimes compare with observations using a hierarchy of measures applied on the full 2-months period. Firstly, we show the mean diurnal evolution of the gridpoint based root-mean-square error (RMSE) of 3-hourly precipitation forecasts and rain-gauge observations conditionally averaged on both weather regimes.
During strong control the RMSE exhibits less diurnal variations than during weak control when a typical diurnal cycle is 265 recognizable attaining the highest error during the convective most active period in the afternoon between 12 and 18 UTC (Fig. 11). The magnitude of the error reaches values up to 1.2mm(3h) −1 in the Northwestern Mediterranean, which is roughly 50% less than found by Bouttier et al. (2016) looking at large parts of Western Europe. Given that rainfall rates during weak forcing amount to only about 60% of the rates during strong forcing (Fig. 5b), the relative error is higher in the weak regime.
Likewise, the ensemble spread shows a diurnal cycle and is highest during the convective most active period in the afternoon 270 under weak synoptic control. Since 80% of the days during HyMeX SOP1 are classified as strongly forced weather regime it is not surprising that the regime independent curve follows the strongly forced curve closely thus obscuring the forecast model characteristic during weak control.
Secondly, the regime dependent probabilistic performance of the ensemble is investigated using the ROC and reliability diagrams for 3-hourly (Fig. 12a,b) and daily accumulations (Fig. 12c,d). Both probabilistic scores highlight the superior per-275 formance during strongly forced weather regimes. A ROC curve closer to the left and upper boundaries displays a greater event discrimination in this weather situation. The larger distance of the ROC curve points during strong control indicates the higher absolute spread when 3-hourly (and daily) precipitation accumulations are averaged over the entire SOP1. In this weather regime the AROME-EPS forecasts are generally more reliable, in particular when averaged over 24 hours (Fig. 12d).
The calibration functions in the reliability diagrams show that the forecast probabilities are consistently too large relative to 280 the conditional observed relative frequencies. This is an indication of overforecasting equivalent to a wet bias. The general wet bias is strongest during weak synoptic control for short (3-hourly) time windows (Fig. 12b). Moreover, the flatness of the calibration function for this weather regime reveals a poor resolution and an overconfidence. Observed relative frequencies depend only slightly on the forecast probabilities and always amount to less than 20% for all forecast probabilities of moderate 3mm(3h) −1 precipitation rates. Relaxing the temporal exactness and extending the window to daily accumulations improves 285 the reliability, in particular during strong control (Fig. 12d).
Finally, the Fractions Skill Score (Roberts and Lean, 2008;Faggian et al., 2014) is employed to address the double penalty problem inherent in convective scale precipitation forecasts. In Fig. 13 the ensemble mean FSS is shown as a function of neighborhood size for absolute rainfall rates (0.3mm(3h) −1 , a threshold frequently used to separate rain versus no-rain areas, and 10mm(24h) −1 accumulation) splitted into weather regimes aggregated for the 2-months period. During strong forcing 290 the spatial forecast quality of the low rainfall threshold is superior for all neighborhood sizes (Fig. 13a) (Roberts and Lean, 2008). Thus, 25% of the time (3-hourly intervals on 48 strongly forced days, i.e. for 96 time windows within SOP1) the forecasts are skillful at a scale of O(100 km), which is of the same order as found in previous studies (Clark et al., 2010;Mittermaier et al., 2011;Schwartz and Sobash, 2019;Bachmann et al., 2020), based on FSS and other neighborhood methods. Useful precipitation forecasts are hardly encountered during weak forcing using absolute rainfall rates.

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Relaxing the temporal exactness of 3-hourly accumulations towards daily sums confirms previous results. Using a fixed precipitation amount of 10 mm per day reveals that the mean FSS during strong control always lies higher than during weak control, that is on average the spatial forecast accuracy is higher during strongly forced weather situations, as expected (Fig. 13b). The discrepancy between the mean and the median of FSSs during strong forcing suggests that the high threshold of 10mm(24h) −1 represents rare events with different intermittency characteristics in forecast and observation leading to a 305 skewed distribution.  The inspection of the spatial forecast accuracy of the prominent cases again highlights the large day-to-day variability. Both strongly forced prominent events (IOP16a and NAWDEX) exhibit a very good spatial forecast quality with the FSS reaching values larger 0.8 for window sizes larger 25 km tantamount with the highest whiskers (Fig. 13). The NAWDEX case (occurring in 2016) even shows FSS values higher than the highest whiskers found during HyMeX. The excellent forecast performance 310 is mainly caused by the low precipitation threshold (0.3mm(3h) −1 ) and the widespread precipitation occurring on both days.
Large parts of the domain receive such precipitation rates and the FSS attains high values. The prominent weakly forced case indicates an average forecast performance (FSS of 11 Sept matches the mean value of this regime) for low rainfall rates separating essentially rain and no-rain regions.
However, taking into account a varying model bias during different weather regimes changes the picture. The pure forecast 315 location accuracy neglecting a model bias can be estimated by using percentiles of forecast and observed precipitation amounts.
Whereas the 95th percentiles of forecast and observed precipitation agree well during strong forcing (at least until 18 UTC), there is a considerable overprediction during weak forcing (Fig. 14a). This overforecasting is strongest during the convective most active period in the afternoon between 12 and 18 UTC. Taking this bias into account by using precipitation percentiles results in a superior spatial forecast quality during weakly forced regimes (Fig. 14b). Thus forecasting the location of heaviest 320 precipitation in the afternoon (expressed by the 95th percentiles) is better during comparably quiescent synoptic-scale atmospheric conditions. This is at first sight an unexpected and surprising result. Given the favourable meteorological ingredients for generating heavy precipitation at this specific geographical region in the autumn season (Grazzini et al., 2020), we hypothesize that well represented steady land surface structures (like orography, particularly) in kilometric scale models provide sufficient