# Orographic Precipitation Extremes: An Application of LUME (Linear Upslope Model Extension) over the Alps and Apennines in Italy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. LUME Model Equations

**U**(x,y) with the microphysical variable q

_{c}(x,y) and q

_{s}(x,y) and the source term S(x,y). q

_{c}(x,y) represents the vertically integrated cloud water density and q

_{s}(x,y) is the hydrometeor density, expressed in kg m

^{−2}. All quantities are vertically integrated, so the “z” dependence is missed.

**WVF**) and the relief h(x,y). The

_{0}**WVF**, expressed in kg m

_{0}^{−1}s

^{−1}, represents the initial condition that is responsible for carrying the amount of water vapor that causes the precipitation. According to [57,66], it is directly related to the precipitable water PW that is estimated from the radiosonde. This quantity expresses the integral across the column height of the precipitation and is used as a proxy for evaluating the probability of extreme precipitation. Since the atmosphere column is not a static element but generally follows the airmasses that are blown from one location to another by the wind,

**WVF**is obtained as a product of PW and wind velocity vector

_{0}**U**(x,y).

**WVF**is related only to the state of the atmosphere, but it cannot transform into real precipitation if a triggering condition for water vapor condensation is matched. A mountain range represents a real obstacle to the incoming flow that is naturally forced to rise, condensate, and consequently produce rain. In Equations (3)–(6), the source term that defines the condensation triggered by the slope gradient is described. In Equation (3), the vertical component of the wind $\mathrm{w}\left(\mathrm{x},\mathrm{y}\right)$ is calculated from the gradient of the terrain slope $\nabla \mathrm{h}\left(\mathrm{x},\mathrm{y}\right)$. In Equation (4), the condensation ratio is defined as a product of ${\mathsf{\rho}}_{\mathrm{S}\mathrm{r}\mathrm{e}\mathrm{f}}$ that is the reference density of the atmosphere near the ground, the moist lapse rate ${\mathsf{\Gamma}}_{\mathrm{m}}$ (0.0065 °C/m), and the $\mathsf{\gamma}$ environmental lapse rate. In Equation (5), the water scale height (moist layer depth) ${\mathrm{H}}_{\mathrm{w}}$ is defined as a function of ${\mathrm{R}}_{\mathrm{v}}$ = 461 J kg

_{0}^{−1}K

^{−1}, ${\mathrm{T}}_{\mathrm{r}\mathrm{e}\mathrm{f}}^{}$ = reference temperature on the ground, ${\mathrm{L}}_{\mathrm{v}}=2.5\xb7{10}^{6}$ J kg

^{−1}and $\mathsf{\gamma}$. Equation (6) expresses the source term in integral form as a function of elevation z. The lower limit corresponds to z

_{1}= LCL (Lifted Condensation Level), while the upper limit corresponds to z

_{2}= EL (Equilibrium Level).

_{c}(x,y) and q

_{s}(x,y). These coefficients take into consideration the time of conversion from water vapor to a single water drop due to microphysical processing and the time taken for a raindrop to fall from the cloud to the soil surface.

_{c}(x,y) variable. Due to microphysical processes of nucleation, collision, and coalescence [95], the droplets start to form, increase their diameters, and convert a part of q

_{c}(x,y) into q

_{s}(x,y). This process takes time, as described by the ${\mathsf{\tau}}_{\mathrm{c}}$ parameter. Then, q

_{s}(x,y) density starts to increase even as the precipitation is starting to form and a part of the “cloud water” is removed from the “cloud system”. The precipitation process takes time, as described by the ${\mathsf{\tau}}_{\mathrm{f}}$ parameter, which defines the time taken by a droplet to fall from the cloud to the ground. The precipitation term P(x,y) is no longer identified with the source S(x,y) but is now described through Equation 7.

#### 2.2. Estimating Microphysical ${\mathsf{\tau}}_{\mathrm{c}}$ and Fallout ${\mathsf{\tau}}_{\mathrm{f}}$ Time-Delay Coefficients from Precipitation Efficiency

_{dynamic}, PE

_{cloud}, and PE

_{fallout}. The first term is related to the dynamic components of the incoming flux that are stored in the term ${\widehat{\mathrm{H}}}^{}$ that can be interpreted as the ratio of the moist layer depth ${\mathrm{H}}_{\mathrm{w}}$ to the penetration depth of the forced ascent $\mathrm{d}=\mathrm{U}/{\mathrm{N}}_{\mathrm{m}}$, where U is the wind module and N

_{m}is the moist Brunt–Väisälä frequency [16,57]. PE

_{dynamic}is valid for an ideal sinusoidal terrain type (exponent −0.5). PE

_{cloud}and PE

_{fallout}depend on ${\mathsf{\tau}}_{\mathrm{c}}$ and ${\mathsf{\tau}}_{\mathrm{f}}$ coefficients, respectively, from wind-velocity module U and the parameter $\mathrm{a}$ that is representative of the width of the simulated mountain range (50–100 km for our case studies).

_{cloud}and PE

_{fallout}assume values ≤ 1. The reference value for precipitation efficiency is around 0.3, comprising between 0.2 and 0.4, which can change sensibly in the function of the state of the atmosphere [96,97].

- From radiosonde data, PE was estimated through the empirical relation of Equation (12);
- Considering the quantities retrieved from radiosonde and local orography, the $\mathrm{P}{\mathrm{E}}_{\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{c}}$ was calculated from Equation (9);
- Then, two different assumptions were tested for calculating the coefficient, inverting Equation (8):
- The two coefficients are equal, so ${\mathsf{\tau}}_{\mathrm{c}}={\mathsf{\tau}}_{\mathrm{f}}$ This condition, which is plausible according to the range of compatible values proposed by the authors of the model in [57], permits one to invert and resolve Equation (8) coupled with (10) and (11) straightforwardly;
- The fallout term is estimated first, based on the time taken by the water drop to fall vertically from the central part of the cloud to the surface, with an average velocity (V
_{rain}) of 5 m s^{−1}[17,19,94,97]. In this case, knowing from the radiosonde the average heights of EL (Equilibrium Level) and LCL (Lifted Condensation Level) of the cloud, it is possible to estimate the average cloud height and the fallout coefficient using Equation (13). Then, using Equations (8)–(12), we retrieve the value of the conversion coefficient ${\mathsf{\tau}}_{\mathrm{c}}$.

$${\mathsf{\tau}}_{\mathrm{f}}=\frac{0.5\xb7\left(\mathrm{E}\mathrm{L}-\mathrm{L}\mathrm{C}\mathrm{L}\right)}{{\mathrm{V}}_{\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}}$$

#### 2.3. LUME Error Analysis

#### 2.4. Case Studied in the Central Alps and Northern Apennines

- ▪
- A rather irregular rainfall field distribution was recorded by local rain gauges, with the stations closer to the mountain peaks reporting extreme values;
- ▪
- Longitudinal distribution of the rainfall along the direction of the incoming airflow was shown by the rain gauges network and also by radar observations (where available);
- ▪
- The complete dissipation of the rainfall field was recorded far away from the mountain range along the downward flank, and no rainfall was recorded at the bottom of the range.

## 3. Results

**WVF**module, with PE, BL, and WD from the radiosonde of Linate Airport (Milan, IT) for the events located in northern Lombardy and the Ajaccio (Corse, FR) for the event located in the northern Apennines. As can be observed from the

_{0}**WVF0**graph (Figure 4A), this quantity shows a sinusoidal behavior that reaches a central peak within 12 h from the start of the event. During this phase, the magnitudes of

**WVF0**are situated above the threshold of 400 kg m

^{−1}s

^{−1}that, according to [51,111], was established as a significant indicator of extreme rainfall triggering across Europe. The selected case studies confirm that the highest rainfall intensities were recorded in correspondence with the highest

**WVF0**. The PE graph (Figure 4B) was obtained using Equation (12) and describes the fluctuation of precipitation efficiency as a function of wind shear (WS). In all cases, the PE is bounded between 0.6 and 0.2 with distribution around the mean values of 0.3–0.4, which are typical for this type of precipitation event [96,99]. Regarding the BL (Figure 4C), there is a higher heterogeneity with a fluctuation of between 500 m and 1500 m for the northern Lombardy events and values approximately equal to 100–200 m for the northern Apennines. For the Apennine areas, the influence of BL can be neglected, while for the Alps, it is necessary to exclude the part of the atmosphere that does not participate in the orographic rainfall intensification. The last picture (Figure 4D) represents the fluctuation of wind direction. The winds mainly blow from the south quadrant, precisely from the southwest, and this is a common pattern that has been shown by all the events. That situation justifies the application of LUME along the 1D digital elevation model (DEM) traces defined approximately by the incoming southerly flow direction. We considered the Hydroshed DEM [112] (resolution of 90 m at the equator) that was smoothed due to a 1 km “smoothing window” to reduce the sensitivity of the upslope model to the steep gradients [67]. This is shown in Figure 2, with blue arrows indicating the DEM traces. The latter were obtained by averaging 5 parallel DEM traces across the investigated areas. Their orientations were opportunely corrected according to the rainfall paths depicted by rain gauge amounts (Figure 3), considering the airflow incoming direction, and, where possible, using meteorological radar information.

**WVF0**, PE, BL, and WD) and the orographic boundaries (1D DEM traces), the other parameters necessary for LUME application were calculated. Table 3 lists, among others, the τ

_{c}and τ

_{f}time-delay coefficients that have been obtained primarily from the PE estimations, applying Equations (8)–(12). The methodologies presented in Section 2.1 and depicted in Figure 5 were implemented automatically for obtaining a range of possible realistic values of those coefficients. Then, to address the specific event variability of PE (Figure 4B), a brief Monte Carlo iterative procedure was applied for retrieving the best time-delay coefficients that minimize the multiplicative root mean square errors (RMSE) of the simulated rainfall with respect to the referenced rain gauge observations.

_{c}values are generally higher than τ

_{f}for the Alps cases than for the Apennine cases. Furthermore, to take into account the non-orographic effects [57] that could originate across the Valpadana, for events in 1983, 1997, 2008, and 2019, background precipitation was included in the model. These data were equal to the mean of the rainfall amounts recorded by the surrounding rain gauge stations for the trace’s starting point. Regarding the duration of the events simulated, we considered the values reported in Table 4. Since 1983 and 1997 lasted more than one day (60 h and 96 h), the

**WVF0**vector has been averaged considering the data in Figure 4A, respectively 300 kg m

^{−1}s

^{−1}and 600 kg m

^{−1}s

^{−1}. For other events, the duration (~12 h) was almost comparable to the central phase where the higher

**WVF0**was recorded by radiosonde, so that the highest values were considered for the computation.

## 4. Discussion

#### 4.1. Comments on Cases Studied in the Central Alps and Northern Apennines

#### 4.2. Orographic Precipitation Linear Regression with Elevation

^{2}index are reported. According to the previous results, not surprisingly, the performances of the simple linear regressions are rather low since the R

^{2}values are always below 0.5. In particular, for Bellano 1997, it seems that there is no correlation with topographic elevation, while for Tresenda 1983, Talamona 2008, and Piacenza 2015, the scores are noticeably higher, around 0.4. The other two cases are settled intermediately, with R

^{2}comprising between 0.2 and 0.3.

^{2}< 0.5, especially for event-based analysis. However, using LUME, it was possible to add further information to the mechanism of orographic precipitation. Figure 6 shows that rainfall redistribution is different considering upslope and downslope mountain flanks. The rainfall advection operated by time-delay coefficients is crucial for interpreting correctly why a certain amount of rainfall has occurred at a particular location. In addition, with respect to the previous version, LUM, a smoothing function for resulting precipitation is not strictly necessary since the produced rainfall field is much more uniform, and unphysical oscillations are not detected in the ultimate solution. Moreover, with LUME, it was possible to confirm those events that have experienced a much stronger orographic uplift (Tresenda 1983, Parma 2014, and Piacenza 2015) than others (especially Bellano 1997).

#### 4.3. Comments on LUME

_{c}≥ τ

_{f}. The τ

_{f}coefficient which is a measure of the falling velocity of the droplet has exhibited a lower variability concerning the τ

_{c}.

**WVF**and

_{0}**U**) [16,67]. Since for northern Lombardy, the radiosonde station of Linate was quite near to the trace’s starting points, shown in Figure 2 and Figure 3, whereas for the Emilia case studies, the parameters were considered from Ajaccio station, which is rather far (300 km) from the investigated area. A first run was carried out using Ajaccio

**WVF**but the resultant rainfall field appeared rather underestimated (BIAS around −20% for 2014 and around −40% for 2015 events) with respect to the one recorded in the area. A possible explanation is the presence of the warmer Ligurian Sea, which has probably contributed to an increase in the

_{0}**WVF**of the incoming southern flow [36,43]. This fact is plausible since the sea path of the wind is about 300 km long before reaching the Apennines. Another hypothesis could be related to the airflow convergence mechanism, typical of the Ligurian region, that has intensified wind velocities locally, increasing the

_{0}**U**term and consequently

**WVF**[90,124,125,126]. To cope with these issues, the Cuneo Levaldigi and Linate radiosonde were also analyzed because, with respect to Ajaccio, they could realistically depict the atmospheric state on the downslope flank of the Apennine mountain range. Looking at Table 3, we can see that:

_{0}- ▪
- For the 2014 event, Cuneo and Linate
**WVF**were in accordance (around 600 kg m_{0}^{−1}s^{−1}), while Ajaccio was higher (832 kg m^{−1}s^{−1}) but uncertain. LUME was run iteratively, modifying the input**WVF**from Ajaccio at the starting point of the trace until the Cuneo and Linate_{0}**WVF**values were matched at the ending point of the trace. As a result, the initial condition for LUME was estimated indirectly from surrounding radiosonde stations. The best performances were obtained by slightly increasing the Ajaccio value up to 900 kg m_{0}^{−1}s^{−1}. Changing the initial condition required a model recalibration that was obtained for τ_{c}= 1000 s and τ_{f}= 750 s. For simplicity, other initial parameters were kept the same for Ajaccio stations. - ▪
- For the 2015 event, the same procedure was adopted considering Linate and Cuneo
**WVF**, respectively equal to 815 and 640 kg m_{0}^{−1}s^{−1}. The best performance was obtained considering the Linate radiosonde as a boundary condition, while when using Cuneo data, rainfall fields were underestimated. Moreover, with respect to the 2015 event, Linate is about 100 km northward, so it is more representative than Cuneo, which is located 150 km westward (Figure 2). The input**WVF**was increased by about 55% up to 1160 kg m_{0}^{−1}s^{−1}and LUME was recalibrated, giving τ_{c}= 1300 s and τ_{f}= 1000 s.

**WVF**value is modified and not other radiosonde parameters) but, for the two cases analyzed, the model performance has improved a lot, reducing rainfall field underestimation. Another alternative strategy consists of taking into account newly available reanalysis data [82,127,128] that could provide in some cases a reasonable reconstruction 3D state of the atmosphere at any location and for several atmospheric layers. Considering these data, not investigated in this work, the applicability of LUME could be significantly extended, not only for well-monitored places but also for those remote locations too distant from the radiosonde data stations. Moreover, high-resolution satellite data [79] are now starting to become available worldwide and to be included inside LAMs. These data are generally adopted for tracking water vapor fluxes, especially in atmospheric rivers and extratropical cyclonic structures [17,89,91,129,130]. Further explorations in this field could be helpful for LUME to reduce such uncertainties in

_{0}**WVF**estimation. In fact, by integrating satellite measurements with radiosonde data, a more complete description of the local 3D structure of the atmosphere could be in principle acquired.

_{0}## 5. Conclusions

_{c}and τ

_{f}coefficients are no longer calibration parameters of LUME but could be correlated with the real state of the atmosphere recorded during the rainfall event.

^{2}< 0.5), confirming the inapplicability of regression models for observing the orographic effect at a single-event scale.

**WVF**for the whole duration), LUME scores at the event-based level achieved an effective level of performance that is comparable to the LAM’s results. Depending on the specific event, RMSE multiplicative errors are generally below 50 mm, giving the best scores for the Premana 2019 event (20 mm). The hypothesis of stationarity has been revealed as not always suitable for interpreting dynamic events such as extreme rainfall where convective behaviours may dominate, enhancing rainfall scattering. Furthermore, the 1D hypothesis, even if it is considered sufficient for these cases, is no more practicable if broader widespread events must be studied. These model limitations are exacerbated by lack of data and the uncertainties adopted for model initialization that in some cases is not realistic since other processes are involved in their definition (

_{0}**WVF**for Parma 2014 and Piacenza 2015). In this regard, the problem has been resolved estimating indirectly the unknown initial conditions (

_{0}**WVF**) for LUME, considering the data coming from surrounding radiosonde stations. However, since radar data, satellite data, and reanalysis data are starting to become available, we are confident that future improvements of LUME will reach a better integration among these data sources, reducing model initialization uncertainties.

_{0}## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Abbate, A.; Papini, M.; Longoni, L. Analysis of Meteorological Parameters Triggering Rainfall-Induced Landslide: A Review of 70 Years in Valtellina. Nat. Hazards Earth Syst. Sci.
**2021**, 21, 2041–2058. [Google Scholar] [CrossRef] - Longoni, L.; Ivanov, V.I.; Brambilla, D.; Radice, A.; Papini, M. Analysis of the Temporal and Spatial Scales of Soil Erosion and Transport in a Mountain Basin. Ital. J. Eng. Geol. Environ.
**2016**, 16, 17–30. [Google Scholar] [CrossRef] - Longoni, L.; Papini, M.; Arosio, D.; Zanzi, L. On the Definition of Rainfall Thresholds for Diffuse Landslides. Trans. State Art Sci. Eng.
**2011**, 53, 27–41. [Google Scholar] [CrossRef] [Green Version] - Ciccarese, G.; Mulas, M.; Alberoni, P.P.; Truffelli, G.; Corsini, A. Debris Flows Rainfall Thresholds in the Apennines of Emilia-Romagna (Italy) Derived by the Analysis of Recent Severe Rainstorms Events and Regional Meteorological Data. Geomorphology
**2020**, 358, 107097. [Google Scholar] [CrossRef] - Longoni, L.; Papini, M.; Brambilla, D.; Barazzetti, L.; Roncoroni, F.; Scaioni, M.; Ivanov, V.I. Monitoring Riverbank Erosion in Mountain Catchments Using Terrestrial Laser Scanning. Remote Sens.
**2016**, 8, 241. [Google Scholar] [CrossRef] [Green Version] - Guzzetti, F.; Reichenbach, P.; Cardinali, M.; Galli, M.; Ardizzone, F. Probabilistic Landslide Hazard Assessment at the Basin Scale. Geomorphology
**2005**, 72, 272–299. [Google Scholar] [CrossRef] - Crosta, G.; Frattini, P. Rainfall Thresholds for Triggering Soil Slips and Debris Flow. In Proceedings of the 2nd EGS Plinius Conference on Mediterranean Storms, Siena, Italy, 16–18 October 2001; pp. 463–487. [Google Scholar]
- Coe, J.; Michael, J.; Crovelli, R.; Savage, W.; Laprade, W.; Nashem, W. Probabilistic Assessment of Precipitation-Triggered Landslides Using Historical Records of Landslide Occurrence, Seattle, Washington. Environ. Eng. Geosci.
**2004**, 10, 103–122. [Google Scholar] [CrossRef] - Corominas, J.; van Westen, C.; Frattini, P.; Cascini, L.; Malet, J.-P.; Fotopoulou, S.; Catani, F.; Van Den Eeckhaut, M.; Mavrouli, O.; Agliardi, F.; et al. Recommendations for the Quantitative Analysis of Landslide Risk. Bull. Eng. Geol. Environ.
**2014**, 73, 209–263. [Google Scholar] [CrossRef] - Albano, R.; Mancusi, L.; Abbate, A. Improving Flood Risk Analysis for Effectively Supporting the Implementation of Flood Risk Management Plans: The Case Study of “Serio” Valley. Environ. Sci. Policy
**2017**, 75, 158–172. [Google Scholar] [CrossRef] - Brambilla, D.; Papini, M.; Ivanov, V.I.; Bonaventura, L.; Abbate, A.; Longoni, L. Sediment Yield in Mountain Basins, Analysis, and Management: The SMART-SED Project. In Applied Geology: Approaches to Future Resource Management; De Maio, M., Tiwari, A.K., Eds.; Springer International Publishing: Cham, Switzerland, 2020; pp. 43–59. ISBN 978-3-030-43953-8. [Google Scholar]
- Molinari, D.; Ballio, F.; Menoni, S. Modelling the Benefits of Flood Emergency Management Measures in Reducing Damages: A Case Study on Sondrio, Italy. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 1913–1927. [Google Scholar] [CrossRef] - Baartman, J.; Jetten, V.G.; Ritsema, C.; de Vente, J. Exploring Effects of Rainfall Intensity and Duration on Soil Erosion at the Catchment Scale Using OpenLISEM: Prado Catchment, SE Spain. Hydrol. Processes
**2012**, 26, 1034–1049. [Google Scholar] [CrossRef] - Guzzetti, F.; Peruccacci, S.; Rossi, M.; Stark, C.P. The Rainfall Intensity–Duration Control of Shallow Landslides and Debris Flows: An Update. Landslides
**2008**, 5, 3–17. [Google Scholar] [CrossRef] - Ceriani, M.; Lauzi, S.; Padovan, M. Rainfall Thresholds Triggering Debris-Flow in the Alpine Area of Lombardia Region, Central Alps—Italy. In Proceedings of the Man and Mountain’94, Ponte di Legno (BS), Italy, 20 June 1994. [Google Scholar]
- Abbate, A.; Longoni, L.; Papini, M. Extreme Rainfall over Complex Terrain: An Application of the Linear Model of Orographic Precipitation to a Case Study in the Italian Pre-Alps. Geosciences
**2021**, 2021, 18. [Google Scholar] [CrossRef] - Stull, R.B. Practical Meteorology: An Algebra-Based Survey of Atmospheric Science; University of British Columbia: Vancouver, BC, Canada, 2017. [Google Scholar]
- De Michele, C.; Rosso, R.; Rulli, M.C. Il Regime Delle Precipitazioni Intense Sul Territorio Della Lombardia: Modello Di Previsione Statistica Delle Precipitazioni Di Forte Intensità e Breve Durata; ARPA Lombardia: Milan, Italy, 2005. [Google Scholar]
- Wallace, J.M.; Hobbs, P.V. Atmospheric Science: An Introductory Survey; Elsevier: Oxford, UK, 2006. [Google Scholar]
- Rotunno, R.; Houze, R. Lessons on Orographic Precipitation for the Mesoscale Alpine Programme. Q. J. R. Meteorol. Soc.
**2007**, 133, 811–830. [Google Scholar] [CrossRef] - Kirshbaum, D.; Adler, B.; Kalthoff, N.; Barthlott, C.; Serafin, S. Moist Orographic Convection: Physical Mechanisms and Links to Surface-Exchange Processes. Atmosphere
**2018**, 9, 80. [Google Scholar] [CrossRef] [Green Version] - Marra, F.; Armon, M.; Borga, M.; Morin, E. Orographic Effect on Extreme Precipitation Statistics Peaks at Hourly Time Scales. Geophys. Res. Lett.
**2021**, 48, e2020GL091498. [Google Scholar] [CrossRef] - Gocho, Y. Numerical Experiment of Orographic Heavy Rainfall Due to a Stratif Orm Cloud. J. Meteorol. Soc. Jpn. Ser. II
**1978**, 56, 405–423. [Google Scholar] [CrossRef] [Green Version] - Formetta, G.; Marra, F.; Dallan, E.; Zaramella, M.; Borga, M. Differential Orographic Impact on Sub-Hourly, Hourly, and Daily Extreme Precipitation. Adv. Water Resour.
**2021**, 159, 104085. [Google Scholar] [CrossRef] - Bongioannini Cerlini, P.; Emanuel, K.A.; Todini, E. Orographic Effects on Convective Precipitation and Space-Time Rainfall Variability: Preliminary Results. Hydrol. Earth Syst. Sci.
**2005**, 9, 285–299. [Google Scholar] [CrossRef] - Pujol, O.; Georgis, J.-F.; Chong, M.; Roux, F. Dynamics and Microphysics of Orographic Precipitation during MAP IOP3. Q. J. R. Meteorol. Soc.
**2005**, 131, 2795–2819. [Google Scholar] [CrossRef] - Davolio, S.; Buzzi, A.; Malguzzi, P. Orographic Triggering of Long Lived Convection in Three Dimensions. Meteorol. Atmos. Phys.
**2009**, 103, 35–44. [Google Scholar] [CrossRef] [Green Version] - Smith, R.B. The Influence of Mountains on the Atmosphere. In Advances in Geophysics; Saltzman, B., Ed.; Elsevier: Cham, Switzerland, 1979; Volume 21, pp. 87–230. ISBN 0065-2687. [Google Scholar]
- Rontu, L. Studies on Orographic Effects in a Numerical Weather Prediction Model. Master’s Thesis, University of Helsinki, Helsinki, Finland, 2013. [Google Scholar]
- Rädler, A.T.; Groenemeijer, P.H.; Faust, E.; Sausen, R.; Púčik, T. Frequency of Severe Thunderstorms across Europe Expected to Increase in the 21st Century Due to Rising Instability. NPJ Clim. Atmos. Sci.
**2019**, 2, 30. [Google Scholar] [CrossRef] - Kahraman, A.; Kendon, E.J.; Chan, S.C.; Fowler, H.J. Quasi-Stationary Intense Rainstorms Spread across Europe under Climate Change. Geophys. Res. Lett.
**2021**, 48, e2020GL092361. [Google Scholar] [CrossRef] - Jean-Luc, M.; Brissette François, P.; Lucas-Picher, P.; Magali, T. Arsenault Richard Climate Change and Rainfall Intensity–Duration–Frequency Curves: Overview of Science and Guidelines for Adaptation. J. Hydrol. Eng.
**2021**, 26, 03121001. [Google Scholar] [CrossRef] - Caroletti, G.; Barstad, I. An Assessment of Future Extreme Precipitation in Western Norway Using a Linear Model. Hydrol. Earth Syst. Sci.
**2010**, 14, 2329–2341. [Google Scholar] [CrossRef] [Green Version] - Kirchmeier-Young, M.C.; Zhang, X. Human Influence Has Intensified Extreme Precipitation in North America. Proc. Natl. Acad. Sci. USA
**2020**, 117, 13308. [Google Scholar] [CrossRef] - Tabari, H. Climate Change Impact on Flood and Extreme Precipitation Increases with Water Availability. Sci. Rep.
**2020**, 10, 13768. [Google Scholar] [CrossRef] - Volosciuk, C.; Maraun, D.; Semenov, V.A.; Tilinina, N.; Gulev, S.K.; Latif, M. Rising Mediterranean Sea Surface Temperatures Amplify Extreme Summer Precipitation in Central Europe. Sci. Rep.
**2016**, 6, 32450. [Google Scholar] [CrossRef] [Green Version] - Muller, C.; Takayabu, Y. Response of Precipitation Extremes to Warming: What Have We Learned from Theory and Idealized Cloud-Resolving Simulations, and What Remains to Be Learned? Environ. Res. Lett.
**2020**, 15, 035001. [Google Scholar] [CrossRef] - Myhre, G.; Alterskjær, K.; Stjern, C.W.; Hodnebrog, Ø.; Marelle, L.; Samset, B.H.; Sillmann, J.; Schaller, N.; Fischer, E.; Schulz, M.; et al. Frequency of Extreme Precipitation Increases Extensively with Event Rareness under Global Warming. Sci. Rep.
**2019**, 9, 16063. [Google Scholar] [CrossRef] [Green Version] - IPCC; Allen, M.; Babiker, M.; Chen, Y.; de Coninck, H.; Connors, S.; van Diemen, R.; Dube, O.; Ebi, K.; Engelbrecht, F.; et al. Summary for Policymakers. In Global Warming of 1.5 °C; An IPCC Special Report; IPCC: Geneva, Switzerland, 2018. [Google Scholar]
- Abram, N.; Adler, C.; Bindoff, N.; Cheng, L.; Cheong, S.-M.; Cheung, W.; Derksen, C.; Ekaykin, A.; Frölicher, T.; Garschagen, M.; et al. Summary for Policymakers. In IPCC Special Report on the Ocean and Cryosphere in a Changing Climate; IPCC: Geneva, Switzerland, 2019. [Google Scholar]
- Arias, P.; Bellouin, N.; Coppola, E.; Jones, R.; Krinner, G.; Marotzke, J.; Naik, V.; Palmer, M.; Plattner, G.-K.; Rogelj, J.; et al. IPCC AR6 WGI Technical Summary; IPCC: Geneva, Switzerland, 2021. [Google Scholar]
- Tuel, A.; Eltahir, E.A.B. Why Is the Mediterranean a Climate Change Hot Spot? J. Clim.
**2020**, 33, 5829–5843. [Google Scholar] [CrossRef] - Spano, D.; Mereu, V.; Bacciu, V.; Serena, M.; Trabucco, A.; Adinolfi, M.; Giuliana, B.; Bosello, F.; Breil, M.; Coppini, G.; et al. Analisi del Rischio. I Cambiamenti Climatici in Italia; Centro Euro-Mediterraneo sui Cambiamenti Climatici: Lecce, Italy, 2020. [Google Scholar]
- Barredo, J.; Mauri, A.; Caudullo, G.; Dosio, A. Assessing Shifts of Mediterranean and Arid Climates under RCP4.5 and RCP8.5 Climate Projections in Europe. Pure Appl. Geophys.
**2018**, 175, 3955–3971. [Google Scholar] [CrossRef] - Ozturk, T.; Ceber, Z.P.; Türkeş, M.; Kurnaz, M.L. Projections of Climate Change in the Mediterranean Basin by Using Downscaled Global Climate Model Outputs. Int. J. Climatol.
**2015**, 35, 4276–4292. [Google Scholar] [CrossRef] - Scoccimarro, E.; Gualdi, S.; Bellucci, A.; Zampieri, M.; Navarra, A. Heavy Precipitation Events over the Euro-Mediterranean Region in a Warmer Climate: Results from CMIP5 Models. Reg. Environ. Chang.
**2014**, 16, 595–602. [Google Scholar] [CrossRef] - Faggian, P. Future Precipitation Scenarios over Italy. Water
**2021**, 13, 1335. [Google Scholar] [CrossRef] - Peres, D.J.; Senatore, A.; Nanni, P.; Cancelliere, A.; Mendicino, G.; Bonaccorso, B. Evaluation of EURO-CORDEX (Coordinated Regional Climate Downscaling Experiment for the Euro-Mediterranean Area) Historical Simulations by High-Quality Observational Datasets in Southern Italy: Insights on Drought Assessment. Nat. Hazards Earth Syst. Sci.
**2020**, 20, 3057–3082. [Google Scholar] [CrossRef] - Jacob, D.; Petersen, J.; Eggert, B.; Alias, A.; Christensen, O.B.; Bouwer, L.M.; Braun, A.; Colette, A.; Déqué, M.; Georgievski, G.; et al. EURO-CORDEX: New High-Resolution Climate Change Projections for European Impact Research. Reg. Environ. Change
**2014**, 14, 563–578. [Google Scholar] [CrossRef] - Faggian, P. Climate Change Projection for Mediterranean Region with Focus over Alpine Region and Italy. J. Environ. Sci. Eng.
**2015**, 4, 482–500. [Google Scholar] [CrossRef] - Taszarek, M.; Allen, J.; Púčik, T.; Groenemeijer, P.; Czernecki, B.; Kolendowicz, L.; Lagouvardos, K.; Kotroni, V.; Schulz, W. A Climatology of Thunderstorms across Europe from a Synthesis of Multiple Data Sources. J. Clim.
**2019**, 32, 1813–1837. [Google Scholar] [CrossRef] - Daly, C.; Taylor, G.; Gibson, W. The PRISM Approach to Mapping Precipitation and Temperature. In Proceedings of the 10th AMS Conference on Applied Climatology, Reno, NV, USA, 20–24 October 1997. [Google Scholar]
- Napoli, A.; Crespi, A.; Ragone, F.; Maugeri, M.; Pasquero, C. Variability of Orographic Enhancement of Precipitation in the Alpine Region. Sci. Rep.
**2019**, 9, 13352. [Google Scholar] [CrossRef] [Green Version] - Mazzoglio, P.; Butera, I.; Alvioli, M.; Claps, P. The Role of Morphology in the Spatial Distribution of Short-Duration Rainfall Extremes in Italy. Hydrol. Earth Syst. Sci.
**2022**, 26, 1659–1672. [Google Scholar] [CrossRef] - Singer, M.B.; Michaelides, K.; Hobley, D.E.J. STORM 1.0: A Simple, Flexible, and Parsimonious Stochastic Rainfall Generator for Simulating Climate and Climate Change. Geosci. Model Dev.
**2018**, 11, 3713–3726. [Google Scholar] [CrossRef] [Green Version] - Terzago, S.; Palazzi, E.; von Hardenberg, J. Stochastic Downscaling of Precipitation in Complex Orography: A Simple Method to Reproduce a Realistic Fine-Scale Climatology. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 2825–2840. [Google Scholar] [CrossRef] [Green Version] - Smith, R.B.; Barstad, I. A Linear Theory of Orographic Precipitation. J. Atmos. Sci.
**2004**, 61, 1377–1391. [Google Scholar] [CrossRef] - Daly, C.; Slater, M.E.; Roberti, J.A.; Laseter, S.H.; Swift, L.W., Jr. High-Resolution Precipitation Mapping in a Mountainous Watershed: Ground Truth for Evaluating Uncertainty in a National Precipitation Dataset. Int. J. Climatol.
**2017**, 37, 124–137. [Google Scholar] [CrossRef] [Green Version] - Osborn Herbert, B. Estimating Precipitation in Mountainous Regions. J. Hydraul. Eng.
**1984**, 110, 1859–1863. [Google Scholar] [CrossRef] - Dinka, M.O.; Hromadka, T.V., II. Prasada Rao Development and Application of Conceptual Rainfall-Altitude Regression Model: The Case of Matahara Area (Ethiopia). In Topics in Hydrometerology; IntechOpen: Rijeka, Croatia, 2019; Chapter 3; ISBN 978-1-83880-561-6. [Google Scholar]
- Srivastava, A.; Yetemen, O.; Saco, P.M.; Rodriguez, J.F.; Kumari, N.; Chun, K.P. Influence of Orographic Precipitation on Coevolving Landforms and Vegetation in Semi-Arid Ecosystems. Earth Surf. Processes Landf.
**2022**, 28, 1125–1142. [Google Scholar] [CrossRef] - Mazzoglio, P.; Butera, I.; Claps, P. I2-RED: A Massive Update and Quality Control of the Italian Annual Extreme Rainfall Dataset. Water
**2020**, 12, 3308. [Google Scholar] [CrossRef] - Singer, M.B.; Michaelides, K. Deciphering the Expression of Climate Change within the Lower Colorado River Basin by Stochastic Simulation of Convective Rainfall. Environ. Res. Lett.
**2017**, 12, 104011. [Google Scholar] [CrossRef] [Green Version] - Jeong, H.-G.; Ahn, J.-B.; Lee, J.; Shim, K.-M.; Jung, M.-P. Improvement of Daily Precipitation Estimations Using PRISM with Inverse-Distance Weighting. Theor. Appl. Climatol.
**2020**, 139, 923–934. [Google Scholar] [CrossRef] [Green Version] - Barry, R.G. Mountain Weater and Climate, 3rd ed.; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Smith, R. A Linear Time-Delay Model of Orographic Precipitation. J. Hydrol.
**2003**, 282, 2–9. [Google Scholar] [CrossRef] - Smith, R.B. 100 Years of Progress on Mountain Meteorology Research. Meteorol. Monogr.
**2018**, 59, 1–73. [Google Scholar] [CrossRef] - Skamarock, C.; Klemp, B.; Dudhia, J.; Gill, O.; Barker, D.M.; Duda, G.; Huang, X.; Wang, W.; Powers, G. A Description of the Advanced Research WRF Version 3; NCAR: Boulder, CO, USA, 2008. [Google Scholar]
- Steppeler, J.; Doms, G.; Schättler, U.; Bitzer, H.W.; Gassmann, A.; Damrath, U.; Gregoric, G. Meso-Gamma Scale Forecasts Using the Nonhydrostatic Model LM. Meteorol. Atmos. Phys.
**2003**, 82, 75–96. [Google Scholar] [CrossRef] - Kreibich, H.; Di Baldassarre, G.; Vorogushyn, S.; Aerts, J.C.J.H.; Apel, H.; Aronica, G.T.; Arnbjerg-Nielsen, K.; Bouwer, L.M.; Bubeck, P.; Caloiero, T.; et al. Adaptation to Flood Risk: Results of International Paired Flood Event Studies. Earth’s Future
**2017**, 5, 953–965. [Google Scholar] [CrossRef] [Green Version] - Lee, J.; Shin, H.H.; Hong, S.-Y.; Jiménez, P.A.; Dudhia, J.; Hong, J. Impacts of Subgrid-Scale Orography Parameterization on Simulated Surface Layer Wind and Monsoonal Precipitation in the High-Resolution WRF Model. J. Geophys. Res. Atmos.
**2015**, 120, 644–653. [Google Scholar] [CrossRef] - Li, H.; Liu, J.; Zhang, H.; Ju, C.; Shi, J.; Zhang, J.; Mamtimin, A.; Fan, S. Performance Evaluation of Sub-Grid Orographic Parameterization in the WRF Model over Complex Terrain in Central Asia. Atmosphere
**2020**, 11, 1164. [Google Scholar] [CrossRef] - Merino, A.; García-Ortega, E.; Navarro, A.; Sánchez, J.L.; Tapiador, F.J. WRF Hourly Evaluation for Extreme Precipitation Events. Atmos. Res.
**2022**, 274, 106215. [Google Scholar] [CrossRef] - Klasa, C.; Arpagaus, M.; Walser, A.; Wernli, H. An Evaluation of the Convection-Permitting Ensemble COSMO-E for Three Contrasting Precipitation Events in Switzerland. Q. J. R. Meteorol. Soc.
**2018**, 144, 744–764. [Google Scholar] [CrossRef] - Gebhardt, C.; Theis, S.E.; Paulat, M.E.; Ben Bouallègue, Z. Uncertainties in COSMO-DE Precipitation Forecasts Introduced by Model Perturbation and Variations of Later Boundaries. Atmos. Res.
**2011**, 100, 168–177. [Google Scholar] [CrossRef] - Elvidge, A.D.; Sandu, I.; Wedi, N.; Vosper, S.B.; Zadra, A.; Boussetta, S.; Bouyssel, F.; van Niekerk, A.; Tolstykh, M.A.; Ujiie, M. Uncertainty in the Representation of Orography in Weather and Climate Models and Implications for Parameterized Drag. J. Adv. Model. Earth Syst.
**2019**, 11, 2567–2585. [Google Scholar] [CrossRef] [Green Version] - Heim, C.; Panosetti, D.; Schlemmer, L.; Leuenberger, D.; Schär, C. The Influence of the Resolution of Orography on the Simulation of Orographic Moist Convection. Mon. Weather Rev.
**2020**, 148, 2391–2410. [Google Scholar] [CrossRef] [Green Version] - Suhas, E.; Zhang, G. Evaluation of Trigger Functions for Convective Parameterization Schemes Using Observations. J. Clim.
**2014**, 27, 7647–7666. [Google Scholar] [CrossRef] [Green Version] - Tiesi, A.; Pucillo, A.; Bonaldo, D.; Ricchi, A.; Carniel, S.; Miglietta, M.M. Initialization of WRF Model Simulations with Sentinel-1 Wind Speed for Severe Weather Events. Front. Mar. Sci.
**2021**, 8, 573489. [Google Scholar] [CrossRef] - Meyer, D.; Riechert, M. Open Source QGIS Toolkit for the Advanced Research WRF Modelling System. Environ. Model. Softw.
**2019**, 112, 166–178. [Google Scholar] [CrossRef] [Green Version] - Yan, D.; Liu, T.; Dong, W.; Liao, X.; Luo, S.; Wu, K.; Zhu, X.; Zheng, Z.; Wen, X. Integrating Remote Sensing Data with WRF Model for Improved 2-m Temperature and Humidity Simulations in China. Dyn. Atmos. Oceans
**2020**, 89, 101127. [Google Scholar] [CrossRef] - Bonanno, R.; Lacavalla, M.; Sperati, S. A New High-Resolution Meteorological Reanalysis Italian Dataset: MERIDA. Q. J. R. Meteorol. Soc.
**2019**, 145, 1756–1779. [Google Scholar] [CrossRef] - Du, Y.; Xu, T.; Che, Y.; Yang, B.; Chen, S.; Su, Z.; Su, L.; Chen, Y.; Zheng, J. Uncertainty Quantification of WRF Model for Rainfall Prediction over the Sichuan Basin, China. Atmosphere
**2022**, 13, 838. [Google Scholar] [CrossRef] - Cánovas-García, F.; García-Galiano, S.; Alonso-Sarría, F. Assessment of Satellite and Radar Quantitative Precipitation Estimates for Real Time Monitoring of Meteorological Extremes over the Southeast of the Iberian Peninsula. Remote Sens.
**2018**, 10, 1023. [Google Scholar] [CrossRef] [Green Version] - Lebedev, V.; Ivashkin, V.; Rudenko, I.; Ganshin, A.; Molchanov, A.; Ovcharenko, S.; Grokhovetskiy, R.; Bushmarinov, I.; Solomentsev, D. Precipitation Nowcasting with Satellite Imagery. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining; Association for Computing Machinery: New York, NY, USA, 2019; pp. 2680–2688. [Google Scholar]
- Rientjes, T.H.M.; Haile, A.T.; Gieske, A.S.M.; Maathuis, B.H.P.; Habib, E. Satellite Based Cloud Detection and Rainfall Estimation in the Upper Blue Nile Basin. In Nile River Basin: Hydrology, Climate and Water Use; Melesse, A.M., Ed.; Springer: Dordrecht, The Netherlands, 2011; pp. 93–107. ISBN 978-94-007-0689-7. [Google Scholar]
- Foresti, L.; Pozdnoukhov, A. Exploration of Alpine Orographic Precipitation Patterns with Radar Image Processing and Clustering Techniques. Meteorol. Appl.
**2012**, 19, 407–419. [Google Scholar] [CrossRef] - Sene, K. Hydrometeorology: Forecasting and Applications; Springer: Berlin/Heidelberg, Germany, 2010; p. 355. ISBN 978-90-481-3402-1. [Google Scholar]
- Ralph, F.M.; Neiman, P.J.; Wick, G.A. Satellite and CALJET Aircraft Observations of Atmospheric Rivers over the Eastern North Pacific Ocean during the Winter of 1997/98. Mon. Weather Rev.
**2004**, 132, 1721–1745. [Google Scholar] [CrossRef] [Green Version] - Davolio, S.; Della Fera, S.; Laviola, S.; Miglietta, M.M.; Levizzani, V. Heavy Precipitation over Italy from the Mediterranean Storm “Vaia” in October 2018: Assessing the Role of an Atmospheric River. Mon. Weather Rev.
**2020**, 148, 3571–3588. [Google Scholar] [CrossRef] - Gimeno, L.; Nieto, R.; Vázquez, M.; Lavers, D. Atmospheric Rivers: A Mini-Review. Front. Earth Sci.
**2014**, 2, 2. [Google Scholar] [CrossRef] - Jiang, Q.; Smith, R.B. Cloud Timescales and Orographic Precipitation. J. Atmos. Sci.
**2003**, 60, 1543–1559. [Google Scholar] [CrossRef] - Luino, F. Sequence of Instability Processes Triggered by Heavy Rainfall in the Northern Italy. Geomorphology
**2005**, 66, 13–39. [Google Scholar] [CrossRef] - Barstad, I.; Schüller, F. An Extension of Smith’s Linear Theory of Orographic Precipitation: Introduction of Vertical Layers. J. Atmos. Sci.
**2011**, 68, 2695–2709. [Google Scholar] [CrossRef] - Pruppacher, H.R.; Klett, J. Microphysics of Clouds and Precipitation; Taylor & Francis: Abingdon-on-Thames, UK, 2010; Volume 18, ISBN 978-0-7923-4211-3. [Google Scholar]
- Robinson, P.J.; Lutz, J.T. Precipitation Efficiency of Cyclonic Storms. Ann. Assoc. Am. Geogr.
**1978**, 68, 81–88. [Google Scholar] [CrossRef] - Sui, C.-H.; Li, X.; Yang, M.-J. On the Definition of Precipitation Efficiency. J. Atmos. Sci.
**2007**, 64, 4506–4513. [Google Scholar] [CrossRef] - Noel, J.; Dobur, J.C. A Pilot Study Examining Model-Derived Precipitation Efficiency for Use in Precipitation Forecasting in the Eastern United States. Natl. Weather Dig.
**2002**, 26, 1–6. [Google Scholar] - Marwitz, J.D. Precipitation Efficiency of Thunderstorms on the High Plains. J. Rech. Atmos.
**1972**, 6, 367–370. [Google Scholar] - Shen, S.; Somerville, R. Climate Mathematics: Theory and Applications; Cambridge University Press: Cambridge, UK, 2019; ISBN 978-1-108-47687-4. [Google Scholar]
- Brownlees, C.; Cipollini, F.; Gallo, G. Multiplicative Error Models. In Handbook of Volatility Models and Their Applications; Wiley: Firenze, Italy, 2011. [Google Scholar] [CrossRef] [Green Version]
- Tian, Y.; Huffman, G.J.; Adler, R.F.; Tang, L.; Sapiano, M.; Maggioni, V.; Wu, H. Modeling Errors in Daily Precipitation Measurements: Additive or Multiplicative? Geophys. Res. Lett.
**2013**, 40, 2060–2065. [Google Scholar] [CrossRef] [Green Version] - McMillan, H.; Jackson, B.; Clark, M.; Kavetski, D.; Woods, R. Rainfall Uncertainty in Hydrological Modelling: An Evaluation of Multiplicative Error Models. J. Hydrol.
**2011**, 400, 83–94. [Google Scholar] [CrossRef] - Ciccarese, G.; Mulas, M.; Corsini, A. Combining Spatial Modelling and Regionalization of Rainfall Thresholds for Debris Flows Hazard Mapping in the Emilia-Romagna Apennines (Italy). Landslides
**2021**, 18, 3513–3529. [Google Scholar] [CrossRef] - ISPRA. Dissesto Idrogeologico in Italia: Pericolosità e Indicatori Di Rischio; ISPRA: Ispra, Italy, 2018. [Google Scholar]
- Rappelli, F. Definizione delle Soglie Pluviometriche d’Innesco Frane Superficiali e Colate Torrentizie: Accorpamento per Aree Omogenee; IRER, Istituto Regionale di Ricerca della Lombardia: Milan, Italy, 2008. [Google Scholar]
- Serafin, S.; Zardi, D. Structure of the Atmospheric Boundary Layer in the Vicinity of a Developing Upslope Flow System: A Numerical Model Study. J. Atmos. Sci.
**2010**, 67, 1171–1185. [Google Scholar] [CrossRef] - Serafin, S.; Adler, B.; Cuxart, J.; De Wekker, S.; Gohm, A.; Grisogono, B.; Kalthoff, N.; Kirshbaum, D.; Rotach, M.; Schmidli, J.; et al. Exchange Processes in the Atmospheric Boundary Layer over Mountainous Terrain. Atmosphere
**2018**, 9, 102. [Google Scholar] [CrossRef] [Green Version] - ARPA Emilia Rete Monitoraggio ARPA Emilia. Available online: https://www.arpae.it/it/temi-ambientali/meteo (accessed on 20 May 2022).
- ARPA Lombardia Rete Monitoraggio ARPA Lombardia. Available online: www.arpalombardia.it/stiti/arpalombardia/meteo (accessed on 20 May 2022).
- Rädler, A.; Groenemeijer, P.; Pistotnik, G.; Sausen, R.; Faust, E. Identification of Favorable Environments for Thunderstorms in Reanalysis Data. Meteorol. Z.
**2015**, 26, 59–70. [Google Scholar] [CrossRef] - Lehner, B.; Verdin, K.; Jarvis, A. New Global Hydrography Derived From Spaceborne Elevation Data. EOS Trans. Am. Geophys. Union
**2008**, 89, 93–94. [Google Scholar] [CrossRef] - Quan Luna, B.; Blahůt, J.; Camera, C.; Westen, C.J.; Apuani, T.; Jetten, V.G.; Sterlacchini, S. Physically Based Dynamic Run-Out Modelling for Quantitative Debris Flow Risk Assessment: A Case Study in Tresenda, Northern Italy. Environ. Earth Sci.
**2013**, 72, 645–661. [Google Scholar] [CrossRef] - ARPA Piemonte. L’Evento Alluvionale del 28–29 Giugno 1997 in Piemonte; Settore per la Prevenzione del Rischio Geologico, Meteorologico e Sismico: Torino, Italy, 1997; p. 24. [Google Scholar]
- Ćurić, M. Numerical Modeling of Thunderstorm. Theor. Appl. Climatol.
**1989**, 40, 227–235. [Google Scholar] [CrossRef] - Luino, F.; De Graff, J.; Roccati, A.; Biddoccu, M.; Cirio, C.G.; Faccini, F.; Turconi, L. Eighty Years of Data Collected for the Determination of Rainfall Threshold Triggering Shallow Landslides and Mud-Debris Flows in the Alps. Water
**2020**, 12, 133. [Google Scholar] [CrossRef] [Green Version] - Cotton, W.R.; Bryan, G.H.; Van Den Heever, S.C. Cumulonimbus Clouds and Severe Convective Storms. In Storm and Cloud Dynamics; Elsevier: London, UK, 2011. [Google Scholar]
- Emanuel, K.A. Atmospheric Convection; Oxford University Press: New York, NY, USA, 1994. [Google Scholar]
- Kunz, M.; Kottmeier, C. Orographic Enhancement of Precipitation over Low Mountain Ranges. Part I: Model Formulation and Idealized Simulations. J. Appl. Meteor. Climatol.
**2006**, 45, 1025–1040. [Google Scholar] [CrossRef] - Chardon, M. Les Catastrophes Naturelles de l’été 1987 En Lombardie: Crues, Inondations, Écroulement de Val Pola. Rev. Géogr. Alp.
**1990**, 78, 59–87. [Google Scholar] [CrossRef] - Anip, M.; Market, P. Dominant Factors Influencing Precipitation Efficiency in a Continental Mid-Latitude Location. Tellus A
**2007**, 59, 122–126. [Google Scholar] [CrossRef] - Hodges, D.; Pu, Z. Characteristics and Variations of Low-Level Jets and Environmental Factors Associated with Summer Precipitation Extremes over the Great Plains. J. Clim.
**2019**, 32, 5123–5144. [Google Scholar] [CrossRef] - Herman, G.R.; Schumacher, R.S. Extreme Precipitation in Models: An Evaluation. Weather Forecast.
**2016**, 31, 1853–1879. [Google Scholar] [CrossRef] - Davolio, S.; Silvestro, F.; Gastaldo, T. Impact of Rainfall Assimilation on High-Resolution Hydrometeorological Forecasts over Liguria, Italy. J. Hydrometeorol.
**2017**, 18, 2659–2680. [Google Scholar] [CrossRef] - Gallus, W.; Parodi, A.; Maugeri, M. Possible Impacts of a Changing Climate on Intense Ligurian Sea Rainfall Events. Int. J. Climatol.
**2017**, 38, 323–329. [Google Scholar] [CrossRef] - Weller, E.; Shelton, K.; Reeder, M.J.; Jakob, C. Precipitation Associated with Convergence Lines. J. Clim.
**2017**, 30, 3169–3183. [Google Scholar] [CrossRef] - Hersbach, H.; Bell, B.; Berrisford, P.; Hirahara, S.; Horányi, A.; Muñoz-Sabater, J.; Nicolas, J.; Peubey, C.; Radu, R.; Schepers, D.; et al. The ERA5 Global Reanalysis. Q. J. R. Meteorol. Soc.
**2020**, 146, 1999–2049. [Google Scholar] [CrossRef] - Kalnay, E.; Kanamitsu, M.; Kistler, R.; Collins, W.; Deaven, D.; Gandin, L.; Iredell, M.; Saha, S.; White, G.; Woollen, J.; et al. The NCEP/NCAR 40-Year Reanalysis Project. Bull. Am. Meteorol. Soc.
**1996**, 77, 437–472. [Google Scholar] [CrossRef] [Green Version] - Ralph, F.; Waliser, D.; Dettinger, M.; Rutz, J.; Anderson, M.; Gorodetskaya, I.; Guan, B.; Neff, W. The Future of Atmospheric River Research and Applications. In Atmospheric Rivers; Springer: Cham, Switzerland, 2020; pp. 219–247. ISBN 978-3-030-28905-8. [Google Scholar]
- Lavers, D.; Villarini, G.; Allan, R.; Wood, E.; Wade, A. The Detection of Atmospheric Rivers in Atmospheric Reanalyses and Their Links to British Winter Floods and the Large-Scale Climatic Circulation. J. Geophys. Res. Atmos.
**2012**, 117, 20106. [Google Scholar] [CrossRef]

**Figure 1.**Relationship between precipitation efficiency and wind shear, modified by [99].

**Figure 2.**Case studies area over northern Lombardy (Central Alps) and Emilia (northern Apennines). Radiosondes of Milan Linate Airport, Ajaccio Corse Airport, and Cuneo Levaldigi Airport are considered for the initial conditions of LUME. The blue arrows show the traces considered for LUME computations, while the orange dots show the starting/ending points of each trace considered for sampling the digital elevation model (DEM).

**Figure 3.**Rain gauge map for the area investigated of Tresenda 1983 (green), Bellano 1997 (yellow), Talamona 2008 (gray), Premana 2019 (red), Parma 2014 (orange), and Piacenza 2015 (purple). The table inset lists the number of rain gauge stations considered in this study.For the specific case of Parma 2014, two stations were discarded due to uncertainties (Berceto and Musiara Superiore) about data recorded with respect to surrounding stations while for Campora di Sasso and Calestano stations, rainfall amount were averaged comparing them with LUME results..

**Figure 4.**Initial conditions retrieved from radiosonde data regarding (

**A**) the

**WVF0**, (

**B**) the PE, (

**C**) the BL, and (

**D**) the WD. As can be seen, there is a certain variability of

**WVF0**that, during the most intense phase, has values higher than 400 kg m

^{−1}s

^{−1}. PE is less dispersed and fluctuates around 0.3–0.4 values, typical for this type of precipitation. BL is much more dispersed and appears significant for Alps cases rather than Apennine cases, where its influence is negligible. WD comes from a southwest direction in all cases studied. The variable evolution was studied according to the radiosonde data 24 h in advance with respect to the critical phase of the event (as can be appreciated by

**WVF0**fluctuation). For 1983 and 1997 events, we have depicted only the most intense phase, even though the rainfall lasted for 60 h and 96 h, respectively.

**Figure 5.**Monte Carlo iterative procedure adopted for estimating deterministically time-delay coefficients through minimization of multiplicative RMSE due to constrained PE.

**Figure 6.**Graphical depiction of selected case studies area over northern Lombardy (Central Alps) from (

**A**) to (

**D**), and Emilia (northern Apennines) from (

**E**) to (

**F**). Graph (

**A**) depicts the Tresenda 1983 event, (

**B**) the Bellano 1997 event, (

**C**) the Talamona 2008 event, (

**D**) the Premana 2019 event, (

**E**) the Parma 2014 event and (

**F**) the Piacenza 2015 event. In each graph, the x-axis represents the progression of the orographic trace depicted by a black dotted line. The blue dots represent the rain gauge amount along the traces, while the green line represents the precipitation simulated by LUME. The dotted red line shows the model simulation caried out with the previous version of the upslope model LUM described in [16]. In the six pictures can be appreciated the difference between LUM and LUME simulations. In almost all cases, the former has improved the reconstruction of the rainfall distribution if compared to the ground-based rain gauges records. With respect to the LUM version, unphysical oscillation of precipitation distribution is reduced and smoothed by time-delay coefficients, especially for (

**B**,

**D**) events. In graph (

**E**), within the black circle, the suspected rain gauge outliers are highlighted, and they are also included in Figure 3. In the orange square, the “fictitious rainfall station” obtained is computed as an average between Calestano station (140 mm) and Campora di Sasso station (25 mm), which are located about 15 km from each other but on the same transversal section along the trace. Here can be appreciate the uncertainties still embedded in the LUME model in the reconstruction of the rainfall dynamics along the lee side of the mountain range where larger errors are committed also for other events studied, especially (

**A**,

**C**).

**Figure 7.**For each event examined, the linear regression between elevation and precipitation was calculated. Table 5 shows the parameters and the low scores of this regression through the R

^{2}index. However, the angular coefficients of the line follow approximately the reference line produced for the 1987 event recorded across the Southern Alps area in the Lombardy region.

**Table 1.**Definition of errors in LUME based on their possible propagation in additive or multiplicative error models.

Additive | Multiplicative | |
---|---|---|

Functional Form | $\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)+\mathsf{\epsilon}$ | $\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)\xb7\mathsf{\epsilon}$ |

Bias [mm] | $\mathrm{B}\mathrm{I}\mathrm{A}{\mathrm{S}}_{\mathrm{a}}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{y}-{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$ | $\mathrm{B}\mathrm{I}\mathrm{A}{\mathrm{S}}_{\mathrm{b}}=\overline{{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}\xb7\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\left(\frac{\mathrm{y}-{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}{{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}\right)$ |

Root Mean Square Error [mm] | $\mathrm{R}\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{a}}=\sqrt{{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\mathrm{y}-{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^{2}}$ | $\mathrm{R}\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{b}}=\overline{{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}\xb7\sqrt{{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\frac{\mathrm{y}-{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}{{\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}\right)}^{2}}$ |

All Indicator Scores (AIS) [mm] | $\mathrm{A}\mathrm{I}\mathrm{S}=\left|\mathrm{B}\mathrm{I}\mathrm{A}{\mathrm{S}}_{\mathrm{a}}\right|+\mathrm{R}\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{a}}+\left|\mathrm{B}\mathrm{I}\mathrm{A}{\mathrm{S}}_{\mathrm{b}}\right|+\mathrm{R}\mathrm{M}\mathrm{S}{\mathrm{E}}_{\mathrm{b}}$ |

**Table 2.**Studied events of extreme precipitation. Dates, locations, and extreme precipitation parameters that describe the maximum amount, the duration, and the return period, and the hydrogeological effects recorded on the territory. For 2008, 2014, and 2015 events, (**) represents the duration of the most intense phase, while () is the duration of the entire event.

Event | Location | Station | Extreme Precipitation | Hydrogeological Effects | ||
---|---|---|---|---|---|---|

- | - | - | Max Amount (mm) | Duration (h) | Return Period (yr) | - |

21–23 May 1983 | Tresenda (SO) | Ponte di Ganda | 261 | 60 | ≈100 | Shallow landslides |

26–30 June 1997 | Bellano (LC) | Bellano | 283 | 96 | ≈50 | Flash floods |

12–13 July 2008 | Talamona (SO) | Morbegno | 60 (174) | 12 ** (72) | ≈2 (10) | Debris flows |

11–12 June 2019 | Premana (LC) | Premana | 209 | 13 | ≈200 | Flash floods |

12–13 October 2014 | Parma (PR) | Marra | 296.6 (298.8) | 8 ** (12) | ≈200 | Debris flows |

13–14 September 2015 | Piacenza (PC) | Salsominore | 307.4 (308.6) | 6 ** (12) | ≈200 | Debris flows |

**Table 3.**LUME parameters for extreme precipitation modelling. For 2014 and 2015, due to the greater distance of the Ajaccio radiosonde station from the location of events (300 km), we also considered the Cuneo () and Linate [] radiosonde stations (150 km and 100 km) located downstream.

Event | Location | LUME Parameters for Each Extreme Precipitation Event | |||||||
---|---|---|---|---|---|---|---|---|---|

- | - | U (m s^{-1}) | Dir (°) | H_{w} (m) | WVF_{0 max} (kg m^{−1} s^{−1}) | τ_{c} (s^{−}^{1}) | τ_{f} (s^{−}^{1}) | h_{BL} (m) | P_{background} (mm) |

21–23 May 1983 | Tresenda (SO) | 18.6 | 192.4 | 2600 | 482.4 | 3750 | 500 | ≈600 | 34 |

26–30 June 1997 | Bellano (LC) | 20.8 | 196.4 | 2600 | 731.3 | 3500 | 750 | ≈400 | 76 |

12–13 July 2008 | Talamona (SO) | 15.8 | 222.3 | 2600 | 545.6 | 2500 | 1000 | ≈250 | 60 |

11–12 June 2019 | Premana (LC) | 22.2 | 194.3 | 2600 | 607.5 | 1000 | 500 | ≈600 | 10 |

12–13 October 2014 | Parma (PR) | 15.4 | 205.1 | 2600 | 832 (610) [600] | 1000 | 750 | ≈100 | 0 |

13–14 September 2015 | Piacenza (PC) | 15.9 | 229.2 | 2600 | 720 (640) [815] | 1300 | 1000 | ≈100 | 0 |

**Table 4.**Error calculation in LUME for the event examined with the two error models. For the event of Parma 2014, two rain gauge stations (Berceto and Musiara Superiore) were excluded since they were suspected to be outliers or not representative of that event.

Event | Location | BIAS (mm) | RMSE (mm) | AIS (mm) | ||
---|---|---|---|---|---|---|

- | - | Additive | Multiplicative | Additive | Multiplicative | - |

21–23 May 1983 | Tresenda (SO) | 7.9 | 2.05 | 29.42 | 35.92 | 75.29 [5] |

26–30 June 1997 | Bellano (LC) | −16.80 | −19.81 | 39.80 | 41.76 | 118.17 [6] |

12–13 July 2008 | Talamona (SO) | 4.9 | 5.09 | 30.81 | 29.79 | 70.59 [2] |

11–12 June 2019 | Premana (LC) | 4.31 | 2.92 | 19.78 | 19.42 | 46.43 [1] |

12–13 October 2014 | Parma (PR) | −3.76 | −0.2 | 33.36 | 47.07 | 84.35 [4] |

13–14 September 2015 | Piacenza (PC) | −4.43 | −3.4 | 32.24 | 48.93 | 89.05 [5] |

**Table 5.**Linear regression coefficient and R

^{2}calculated for the event simulated by LUME. Note the poor score of the regression, especially for the Bellano 1997 event, while for the others, the R

^{2}is always somewhat below 0.5.

Event | Location | Linear Regression Precipitation–Elevation Coefficients | ||
---|---|---|---|---|

- | - | a [mm m^{-1}] | b [mm] | R^{2} |

21–23 May 1983 | Tresenda (SO) | 0.096 | 64.386 | 0.400 |

26–30 June 1997 | Bellano (LC) | 0.030 | 169.280 | 0.010 |

12–13 July 2008 | Talamona (SO) | 0.069 | 94.731 | 0.385 |

11–12 June 2019 | Premana (LC) | 0.057 | 61.786 | 0.322 |

12–13 October 2014 | Parma (PR) | 0.130 | 30.267 | 0.239 |

13–14 September 2015 | Piacenza (PC) | 0.167 | 115.240 | 0.410 |

16–19 July 1987 | Event 1987 | 0.125 | 150 | - |

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**MDPI and ACS Style**

Abbate, A.; Papini, M.; Longoni, L.
Orographic Precipitation Extremes: An Application of LUME (Linear Upslope Model Extension) over the Alps and Apennines in Italy. *Water* **2022**, *14*, 2218.
https://doi.org/10.3390/w14142218

**AMA Style**

Abbate A, Papini M, Longoni L.
Orographic Precipitation Extremes: An Application of LUME (Linear Upslope Model Extension) over the Alps and Apennines in Italy. *Water*. 2022; 14(14):2218.
https://doi.org/10.3390/w14142218

**Chicago/Turabian Style**

Abbate, Andrea, Monica Papini, and Laura Longoni.
2022. "Orographic Precipitation Extremes: An Application of LUME (Linear Upslope Model Extension) over the Alps and Apennines in Italy" *Water* 14, no. 14: 2218.
https://doi.org/10.3390/w14142218