Climate indices are also affected by the order of oper- ations, especially when thresholds are involved. Figure 2 (right) presents the Q–Q plots for the number of wet days defined as days with at least 1 mm day 21 of precipitation (RR1mm) during JJAS, remapped using the conservative method. As for the temporal std dev, the last-step re- mapped RR1mm indices best preserve the spatial distri- bution of the original-grid values, while the first-step remapped RR1mm indices have higher values for almost all quantiles for all destination grids. There are locations where the differences in the RR1mm indices computed with the two procedures are larger than 15 days when the remapping is done on the CORDEX-Africa grid, 20 days for the ERA-Interim grid, and 30 days for the NCEP grid. Other climate indices are affected as well. Figure 3 presents how the two procedures of remapping affect the longest period of consecutive wet days (CWD) in JJAS (where wet days are defined as for the RR1mm index); the highest amount of dailyprecipitation (RX1day); the RR1mm index; and the total amount of seasonal precipitation exceeding the dailyprecipitation 99th percentile, computed from the TRMM dataset. The comparison is done in terms of spatial mean and stan- dard deviation over the CWA region, with each panel presenting the values for the nonremapped original field (black solid line) and for the last- (solid lines) and first- step (dotted lines) remapped fields, using conservative, bilinear, and distance-weighted remapping methods. Whatever the remapping method and the four pre- cipitation indices, the last-step remapped fields have spatial means and std dev values over the domain, closer to the original-grid fields than the first-step procedure. The first-step procedure tends to smooth the original field by increasing the minima and decreasing the max- ima of the field on which it is applied. When the re- mapping is applied initially on the dailyprecipitation field, the average operation increases the number of days with low intensity and diminishes the number of
RX5day Maximum 5-day precipitation amount (annual
maximum of 5-day accumulated precipitation) mm/day 3 mm/day
Precipitation due to very wet days (annual total precipitation from days with dailyprecipitation > 95 th percentile of wet-day precipitation over the reference period)
with very different precipitation regimes (like in mountain- ous areas). This paper presents several significant extensions of the Wilks precipitation model, referred to as GWEX ver- sions, which will be used to generate long scenarios. These extensions aim to fit the most extreme precipitation amounts at different temporal (1- and 3-day amounts) and spatial scales. Novel components are thus introduced in GWEX, in- cluding robust estimation methods (regionalization methods) for critical parameters impacting directly on the behavior of extreme precipitation at each station. Recent advances in the choice of the marginal distributions for dailyprecipitation amounts are also included. Using 15 029 long daily precipi- tation records ( > 50 years) from around the world, Papalex- iou et al. (2013) conclude that heavy-tailed distributions are generally in better agreement with observed precipitation ex- tremes. Follow-up studies (Papalexiou and Koutsoyiannis, 2013; Serinaldi and Kilsby, 2014a) apply extreme value the- ory to annual maxima and “peaks over threshold” (POTs) of a large subset of these records and confirm that extreme dailyprecipitation is not adequately represented by light-tailed dis- tributions. Based on statistical tests on 90 000 station records of dailyprecipitation, Cavanaugh et al. (2015) also come to the same conclusion. These findings have important implica- tions for precipitation models.
Pr ( Z ≤ zi | X =x i ) = F Γ (μ i , γ i ; x i )
Dailyprecipitation distribution is represented by a two-parameter Gamma distribution (μ, γ), [position and shape]
VGLM models allow the dailyprecipitation parameters at sites to be functions
region, with quite similar mean values over the Sahel (172, 173 and 178 Julian days for ARC2, GPCP and TRMM, respectively, corresponding to 21 June, 22 June and 27 June respectively). As for the large-scale onset, the TRMM local onset is later than in ARC2 and GPCP datasets. The com- parison between the observation large-scale mean onset and the mean local onset shows also that only GPCP mean local onset (22 June) is falling within the large-scale pentad (20– 24 June). For ARC2, the mean local onset (21 June) is fall- ing slightly after the mean large-scale onset (15–19 June) while for TRMM, the mean local onset (27 June) is falling before its mean large-scale onset (30 June–4 July). It must be mentioned that the Sahel mean for the local onset is com- puted only over the points where the local onset is defined, and it does not consider the white points in the Northern Sahel shown in Fig. 15 . On the other hand, the large-scale onset is computed considering all points in the two regions implicated in the computation. The local onset in observa- tions is characterised by a smaller interval of uncertainty than the large-scale onset that is based on pentads. For the local onset, the largest differences are observed in the South Sahel, where ARC2 dataset shows in general an earlier mean onset than TRMM and GPCP, in particular over North of Burkina Faso and North of Nigeria. Both CanRCM4 simulations display an earlier mean onset (i.e. end of March and beginning of April) than in observations, for a large part of the domain. As mentioned previously, the CanRCM4 simulations show the presence of dailyprecipitation values between 2 and 4 mm/day over Sahel by the end of March, while the maximum is still over the Guinea Gulf Coast dur- ing that time (Fig. 14 ). However, the CanRCM4 local onset is closer to observations over the West Senegal and the East Mali (domain SW: 15°W–9.7°W; 12°N–14°N). The CRCM5 simulation displays a similar overall picture, with an earlier (20–40 days) onset over North Burkina Faso and North Nigeria and local onsets similar to observations over
function of both CAPE and the amount of moisture available ( Lepore
et al., 2015 , 2016 ; Dong et al., 2018 ). The CAPE-precipitation in-
tensity relationship saturates even more quickly for AMP 24 hr , for
which atmospheric instability plays only a secondary role. These results have multiple implications. As reported in previous works, the intermittent nature of precipitation is masked out in daily data, especially in the less precipitation-prone regions. For instance ( Pendergrass and Knutti (2018) ), have recently shown that half of total annual precipitation falls in only a few days across many regions of the world. This unevenness is expected to be stronger in hourly data given that precipitation is intermittent from one day to another but also within a day. Sub-daily data also enables a better characterization of the true precipitation intensity as well as a better understanding of processes driving extremes. Given the growing interest in sub-dailyprecipitation extremes in the literature, the hourly precipitation dataset used here can provide the hydroclimate community with better information on in- tensities initiating flash floods.
Fewer studies have targeted the ability of RCMs to reproduce the monsoon intraseasonal events such as rain- fall onset and retreat, AEW intermittency, or the precipita- tion diurnal cycle. Druyan et al. ( 2010 ) have shown that reanalysis-driven RCMs are much more realistic (relatively to GCM-driven) in representing the African monsoon dynamics, such as the structure of the African Easterly Jet (AEJ), the low-level circulation and, hence, the humidity and heat transport. Sylla et al. ( 2010 ) have investigated the intraseasonal variability of the WAM using RegCM3 2 (Regional Climate Model version 3). They demonstrated the model’s ability to represent the WAM dynamics and, more specifically, the AEWs and their related AEJ. Even though this study showed the high potential of RegCM3 to handle very subtle interactions between the AEWs and the AEJ, it was quite limited in terms of quantitative evidence, such as the extent to which this synoptic-scale activity determines the monsoon precipitation. The recent studies by Gbobaniyi et al. ( 2013 ), Diallo et al. ( 2014 ) and Mounkaila et al. ( 2015 ) broadly show a good representa- tion of the WAM onset by RCMs participating in COR- DEX. Mariotti et al. ( 2014 ) have shown better performance of RCMs in comparison with GCMs in reproducing the AEW activity, but their analysis is qualitative. Crétat et al. ( 2015 ) conducted a more detailed analysis on the relation- ship between AEWs and daily rainfall, using various regional simulations, and revealed the fairly good perfor- mance of RCM in terms of spatial and temporal phases. Although a set of arguments tends to confirm the real added value of RCMs, Flaounas et al. ( 2011 ) have shown a deci- sive impact of physical parameterizations on the monsoon onset and precipitation intraseasonal variability, implying
The top panel of Fig. 1 shows the scatterplot between dailyprecipitation data in mm/day recorded at two stations named St Alban and Perreux which are fairly far away from each other (about 300 km). In contrast, the bottom panel of Fig. 1 displays the same type of scatterplot but between two nearby stations, Perreux and Riorges (about 10 km). As expected, this figure indicates that nearby stations can provide strongly dependent recordings. In this example, this dependence still exists for large rainfall amounts. Consequently, the analysis of extremes should be improved if this dependence is taken into account. We have not yet tried to define the term “bi- variate extreme event”. To clarify this expression, we need to introduce a few notations. Let R 1 and R 2 be two positive, continuous and heavy tailed random variables that represent the rainfall recordings at two stations, say station 1 and 2. Here “heavy tailed” means that the upper tail distribution of
Evaluation of CRCM5-LE output was performed using different observed gridded datasets for both domains ( Leduc et al. 2019 ). Regarding mean dailyprecipitation, a wet bias was observed throughout the year for both the NNA and EU domains with a strong dominant compo- nent in winter for both domains. A dry bias was also observed in summer for southwestern NNA and eastern Europe. A comparison with a CRCM5 run driven by the ERA-Interim reanalysis (ERA-CRCM5) showed that a significant portion of the wet bias can be attributed to CanESM2-LE ( Leduc et al. 2019 ). The CRCM5 perfor- mance, notably in terms of extreme precipitation quan- tiles and annual and daily cycles, has also been evaluated in a study by Innocenti et al. (2019) . A comparison of the ERA-CRCM5 simulation against station records for NNA domain showed good agreement for 2-, 10-, and 25-yr short-duration extreme precipitation quantiles but overestimations for daily and longer-duration extreme precipitation in some regions. The ERA-CRCM5 run provided a good representation of both the annual and diurnal cycles.
[ 51 ] We assess dailyprecipitation in winter in Southern
France for the calibration period 1951 to 1985 and the veri- fication period 1986 to 1999. NCEP precipitation is used as large‐scale variable. The results are verified by means of the 95% quantile, q ‐q plots, and the continuous ranked proba- bility score. The verification extremes represent on aver- age over all stations the upper 15% of the data at days with precipitation. It shows that an acceptable representation of extreme precipitation of Marseille, Nî, and Mont‐Aigoual is obtained. Those stations are subject to very different geo- graphic conditions: Marseille is situated on the coastline, here the moisture supply of the sea is important. Nîmes is located on the foothills of the Massif Central, and Mont‐Aigoual on one of its hilltops. For the latter two stations, the interplay of specific synoptic‐scale conditions with the local topography is relevant for the creation of heavy precipitation events [cf. Berne et al., 2009; Boudevillain et al., 2009]. Thus it appears to be feasible, even under very different geographic condi- tions, to deduce the CDF of local‐scale precipitation extremes from the CDF of large‐scale extremes.
[ 80 ] The third QC step, i.e., the estimation of reasonably
correct values, could only be performed for the temperature data, but not for precipitation. For TX, TN and TMEAN separately, we estimated approximate values by using adjusted and weighted averages of data from stations with highly correlated series. These approximate reference values were calculated for the calendar day in question, in a fashion analogous to that used on a seasonal basis when creating reference series in homogeneity testing [see Alexandersson and Moberg, 1997], i.e., weighting the reference series temperature anomalies (with respect to the baseline period 1961 – 1990) with their squared correlation coefficient with the candidate series and then adding the climatological average for the candidate station to ensure that the absolute value is representative for this station. The reference stations selected were the six having the largest correlation coefficients (calculated using monthly mean series with the annual cycle removed) with the candidate series, with the additional requirement that the squared correlation must exceed 0.7. Because of this latter criterion, less than six reference stations had sometimes to be used. We also found, after some trials, that this kind of approach was not at all applicable for the dailyprecipitation data because of the weaker spatial correlations compared to temperatures.
2. Daily Seasonalities in the Returns: the Evidence
The weak form of the efficient market hypothesis assumes that current prices fully and instantaneously reflect all information from historical sequences of prices. According to this hypothesis the distribution of the returns should not exhibit a seasonal pattern. Concerning daily returns more specifically, the average daily returns should not vary across the days of the week. With respect to this, French (1980) pointed out that two attitudes can be considered according to whether the process that generates the returns is continuous on the whole calendar week or on the trading period of the week only. Under the calendar time hypothesis, the average Monday return should be three times the average return of the other days of the week if the trading period is five days. And under the trading time hypothesis, no difference should be observed between the daily average returns.
Visualizations are objects that lend themselves to be used for personal training when individuals read information that relies on their own traces. The right side of Figure 2 illustrates the personal design process of someone looking at their own visual representation. Four steps compose the self-design iteration: a) the individual reads the visualization that has been produced from their personal digital traces, b) a careful reading modifies the individual’s knowledge and influences their actions in society, c) datafication transforms these daily practices and d) the result consists of the digital traces employed by the visualization to be updated. Even though the iteration is different, the design process can be equally applied to individuals as well as objects.
This study objective is to develop a process of magnesium silicate synthesis made by precipitation. This is the first step in the synthesis of synthetic talc by a process that will be an alternative to the milling of natural talc. The resultant product will have properties that are not possible to obtain with the milling process, in particular particle size smaller than one micrometer. The influence of different process parameters (reactants’ addition mode and order, reactants’ concentrations and ultrasound) on product properties is studied. Reactants’ addition by the mixing system, with ultrasound and low reactants’ concentrations resulted in a product with the smallest particles.
[ 49 ] Figure 8 shows the ranges of melting and subfreezing
layer depths as well as the maximum and surface temper- ature associated with the various single precipitation types and combinations. It is evident that there are classes of winter precipitation in terms of their range of maximum temperature (Figure 8a). IP and ZR-IP are produced within a wide range of temperatures (1 – 6C); ZR is produced within a medium range (4 – 6C); ZR-IP-SL-RWS-S and IP-RWS-S are only produced within a narrow range (1C). However, all these categories are produced within a wide range of minimum temperature (Figure 8b) except for the combina- tion of liquid, semimelted and frozen particles where the temperature varies from 1C to 3C. These three classes arise because of differences in the production processes. A variety of situations can all lead to ZR, IP and ZR-IP. Figure 7. A comparison of the model results and observations [Zerr, 1997]. (a) Average depth of the
f k;k ð Þ ¼ 2 y k k ð y; m; S Þ k SS 1 2 ð y m Þ; 0; I k S 2
which will be denoted CSN* k (m, S, S) and is similar to the homotopic framework described by Allard and Naveau . On all climate series considered as part of the research project CLIMATOR (11 sites in France), and in particular on the Colmar series studied in this paper, we observed that mixtures of skew‐normal densities could adequately be fitted on (R, V, T n , T x ). This hypothesis is however not necessarily reasonable for precipitations. Daily rainfalls were properly fitted in most cases by a Gamma distribution, which does not belong to the class of CSN. The gamma distribution was chosen for its flexibility to model distributions of precipitation amount encountered the 11 locations in France. Other choices, like generalized Pareto distributions (GPDs) are of course possible and can easily be implemented. GPD was not chosen because it is
that the rate and extension of mixing is determining for the pro- cess outcome: because of their ability to achieve the high mixing efﬁciencies necessary in the precipitation process, passive micro- mixers are currently being investigated for this application. The term micro-device strictly refers to systems with characteristic length-scales that are in the range of micrometers. Small dimen- sions lead to behaviors strictly controlled by molecular phenomena  , allowing rapid diffusive mixing with time-scales ranging from tens to hundreds of milliseconds  . Very interesting is also the recent investigation of large micro-mixers (with characteristics length-scales ranging from hundreds of micrometers to a few mil- limeters) in which some ﬂow instability is allowed to develop resulting, under extreme operating conditions, in turbulent ﬂow and turbulent mixing  . These devices present the main advan- tages of passive micromixers, such as more controlled process con- ditions, better and faster homogenization of the feed streams, short mean residence time and narrow residence time distribution, com- bined with other additional advantages, such as limited power consumption (when compared with traditional micro-ﬂuidic sys- tems) and ease of scalability for process intensiﬁcation.