Abstract

Radar-observed vertical structure of precipitation as defined by contoured frequency by altitude diagrams (CFADs) is related to dynamic and thermodynamic environmental parameters. CFADs from 559 storms occurring over the years 2004–11 in the vicinity of Locarno, Switzerland, combined with Interim ECMWF Re-Analysis (ERA-Interim) data show that the radar-observed vertical structure of precipitation correlates with synoptic pattern (as defined by 1000- and 500-hPa geopotential heights), integrated water vapor flux, atmospheric stability, and vertical profiles of temperature, moisture, and wind. Following the analysis of vertical structure and environmental parameters, a generalized linear model (GLM) is developed for radar-observed vertical structure as a function of data from ERA-Interim. The GLM provides expected values for the vertical extent and magnitude of radar reflectivity and predicts storm vertical structure type with 79% overall accuracy. The relationships found between environmental parameters and storm vertical structure underscore the importance of including both dynamic and thermodynamic variables when evaluating climate change effects on precipitation. In addition, the ability of the GLM to reproduce storm types shows the potential for using GLMs as a link between lower-resolution global model data and high-resolution precipitation observations.

1. Introduction

The mismatch in spatial resolution between global climate models (GCMs, typically having spatial resolution of 0.5°–2.5° latitude × longitude) and spatial scales relevant to complex terrain (<10 km; Smith et al. 2003; Gutmann et al. 2012) combined with the challenge of representing microphysical processes in GCMs (Pincus and Klein 2000; Larson and Griffin 2013) reduces the credibility of precipitation data obtained directly from GCM output, especially for mountainous areas. Therefore, methods of downscaling GCM output are necessary in order to meaningfully evaluate climate change impacts on the hydrologic cycle. Consequently, many studies have examined downscaling precipitation from GCMs, and these are generally categorized in two ways: 1) dynamical models in which GCM output is fed to regional climate models (RCMs) and 2) statistical models that rely on empirical or physically based dependencies established between lower-resolution GCM output and higher-resolution observations (i.e., Abatzoglou and Brown 2012; Beuchat et al. 2012, hereafter B12; Gutmann et al. 2012; Hidalgo et al. 2008; Stoner et al. 2012; Wilby 1998; Wood et al. 2004).

Since accurate prediction of precipitation in complex terrain is limited by the accuracy and resolution of numerical models and observations and the high temporal and spatial variability of precipitation, this paper presents a simplified model that correlates vertical structure of precipitation to environmental parameters, which can be evaluated or tracked in regional or global climate models more easily than precipitation itself. In this paper we explore dynamic and thermodynamic effects on precipitation in southern Switzerland, an area where regional precipitation is influenced by complex topography. As such, the objectives are 1) to analyze output variables from global reanalysis to identify potential relationships between environmental parameters and radar-observed vertical structure of precipitation systems and 2) to utilize these relationships to develop a predictive model for precipitation vertical structure as a function of environmental conditions in an area of complex terrain. The vertical structure of individual precipitation systems provides insight concerning the underlying microphysics responsible for the type, quantity, duration, and intensity of precipitation. Therefore, a model capable of predicting high-resolution features of precipitation vertical structure of precipitation provides information concerning not only future precipitation characteristics, but also physical reasons for the results. Our study is limited to the identification of relationships between environmental parameters and precipitation vertical structure. When combined with predicted precipitation occurrence, the models developed herein have the potential to downscale lower-resolution GCM output in order to provide high-resolution surface precipitation characteristics.

Our objectives are motivated by the societal importance of understanding the effects of climate change on future precipitation. Climate change is expected to alter dynamic and thermodynamic atmospheric attributes that influence surface precipitation quantity, duration, and intensity (Held and Soden 2006; Seager at al. 2010; Chang et al. 2012; Chou and Lan 2012, and references therein). Hence, assessment of future precipitation under a changing climate must include the effects of relevant dynamic and thermodynamic parameters. Our first objective addresses this through analysis of observed relationships between dynamic and thermodynamic environmental conditions and radar-observed precipitation vertical structure. Dynamic effects on precipitation include wind speed and direction and are generally related to synoptic and mesoscale weather patterns, as well as diurnal and terrain-induced effects. Thermodynamic effects on precipitation consist of changes in atmospheric temperature, moisture content, and atmospheric stability. Analysis of observed relationships between precipitation and dynamic and thermodynamic parameters allows the development of physical as well as empirical models for predicting future precipitation.

The second objective of this paper is the development of a generalized linear model (GLM) for linking the vertical structure of radar-observed precipitation to parameters that represent dynamic and thermodynamic effects on precipitation. As described in Rudolph and Friedrich (2013, hereafter RF13), precipitation vertical structure as observed by the operational radar near Locarno, Switzerland, is related to surface precipitation characteristics such as quantity, duration, and intensity as well as environmental parameters such as atmospheric stability and surface temperature. We extend the results from RF13 by developing a model to predict the vertical structure of precipitation that includes an expanded set of dynamic and thermodynamic parameters.

Previous work demonstrates the utility of GLMs for modeling precipitation. One example is the development of GLMs for daily precipitation at 27 locations in Switzerland as a function of reanalysis data (B12). The GLMs developed in B12 use reanalysis output to accurately reproduce observed historical daily precipitation statistics. The parameters included in B12’s GLMs are surface temperature and relative humidity, mean sea level pressure, and winds at 500 hPa. In addition, B12 coupled their GLMs with GCM data to assess future precipitation trends under climate change.

As in B12, our GLM for radar-observed vertical structure is based on environmental parameters taken from reanalysis output. However, our study is unique because we have vertical structure of precipitation every 30 min, rather than daily precipitation, as the dependent variable. Our use of vertical structure as the model output has the advantage that the resulting GLM provides information concerning the underlying microphysics, or the degree to which individual storms are stratiform or convective. In addition, our GLM utilizes an expanded set of environmental parameters that include atmospheric attributes such as stability, temperature, moisture, and wind at a variety of vertical levels. Unlike B12, however, the GLMs presented here are models of precipitation vertical structure, rather than daily precipitation statistics, and require additional identification of precipitation occurrence in order to arrive at daily quantities of precipitation.

The environmental parameters included in our GLM are also typically available from GCMs. The reason for this is to demonstrate a method for using lower-resolution global model output to predict higher-resolution radar-based precipitation observations. As in B12, observed changes in important environmental parameters from GCMs or reanalyses may then be used to generate a high-resolution precipitation outlook over multiple decades. Another example that combines GCM output with observations is previous work that links synoptic patterns and radar-estimated surface precipitation in the European Alps to predict a reduction in precipitation for Swiss river basins by ~10% over the twenty-first century due to dynamic effects (Rudolph et al. 2012). Furthermore, RF13 find that radar-observed vertical structure of reflectivity is related to surface temperature, so expected future increases in surface temperature from RCMs are used to predict the increasing probability of storms with convective characteristics.

2. Data

a. Vertical structure of precipitation

This study uses storm types identified by radar-observed vertical structure as described in RF13. RF13 analyzed the vertical structure of reflectivity with contoured frequency by altitude diagrams (CFADs) based on operational radar data from the Swiss Weather Service (MeteoSwiss). CFADs were developed in RF13 for 559 precipitation events that occurred between March 2004 and February 2011. The storms were identified by the occurrence of ≥1 mm of precipitation within 24 h as measured by rain gauge stations located near Locarno, Switzerland (Fig. 1; RF13). The CFADs were generated using radar data contained within 2–12 km above mean sea level (MSL) in the vertical dimension and a horizontal range of approximately 60 km as allowed by visibility due to the surrounding terrain. Centroids for the x and y dimensions of the CFAD, Cx and Cy, representing magnitude of reflectivity and vertical extent of reflectivity, respectively, were calculated for each individual storm. Seasonal average CFAD centroids for winter [December–February(DJF)], spring [March–May (MAM)], summer [June–August (JJA)], and fall [September–November (SON)] were then used to classify individual storms as DJF-type, MAM/SON-type (MAM and SON were grouped together because there was no significant difference between the MAM and SON seasonal average centroids), or JJA-type storms (Fig. 2; Table 1). The storm classification assigned to individual storms results from nearest neighbor comparison between the individual storm and seasonal CFAD centroids (RF13). Furthermore, RF13 found that surface precipitation characteristics such as precipitation total, duration, and intensity differ between storm types (Table 1). Based on comparison between the surface precipitation characteristics related to storm types and case studies from the Mesoscale Alpine Programme (MAP; Houze et al. 2001; Medina and Houze 2003; Yuter and Houze 2003; Rotunno and Houze 2007), RF13 conclude that DJF- type storms are more stratiform in nature; that is, they have less vertical extent of reflectivity, lower precipitation intensity as evidenced by reduced reflectivity magnitude and gauge-measured precipitation rate, longer duration, and less total precipitation. In contrast, JJA-type storms are associated with convective precipitation, contain embedded convection, exhibit greater vertical extent, are shorter in duration, and have higher reflectivity due to greater intensity. Further details concerning the radar data, development of CFADs, and vertical structure classification of individual storms are found in RF13.

Fig. 1.

Location of Locarno (red star), Monte Lema radar (ML, red box), and horizontal range of radar visibility used for CFADs in RF13 (yellow boxes). The radar data used to generate CFADs in RF13 have spatial resolution of 2 km × 2 km (shown for reference as black box in lower right). Locations of rain gauge stations used for storm identification, precipitation total, intensity, and duration are indicated by blue boxes (CIM: Cimetta; COM: Acquarossa/Comprovasco; LUG: Lugano; MAG: Magadino/Cadenazzo; OTL: Locarno/Monti; SBO: Stabio). Location of ERAi data used for this study is indicated by black circle (45.75°N, 9°E). Topography contours are in 1000-m increments with white denoting elevation <1000 m MSL. The inset shows the 70 km × 70 km area around the radar (red box), location of the radar (X), location of the ERAi data point used for this study (red +), and surrounding locations of ERAi data (blue +).

Fig. 1.

Location of Locarno (red star), Monte Lema radar (ML, red box), and horizontal range of radar visibility used for CFADs in RF13 (yellow boxes). The radar data used to generate CFADs in RF13 have spatial resolution of 2 km × 2 km (shown for reference as black box in lower right). Locations of rain gauge stations used for storm identification, precipitation total, intensity, and duration are indicated by blue boxes (CIM: Cimetta; COM: Acquarossa/Comprovasco; LUG: Lugano; MAG: Magadino/Cadenazzo; OTL: Locarno/Monti; SBO: Stabio). Location of ERAi data used for this study is indicated by black circle (45.75°N, 9°E). Topography contours are in 1000-m increments with white denoting elevation <1000 m MSL. The inset shows the 70 km × 70 km area around the radar (red box), location of the radar (X), location of the ERAi data point used for this study (red +), and surrounding locations of ERAi data (blue +).

Fig. 2.

Examples of seasonal average CFADs for (a) JJA 2010, (b) MAM and SON 2010, and (c) DJF 2011. Contours indicate frequency of observed reflectivity (dBZ) by height above the radar footprint indicated in Fig. 1. The seasonal CFADs and their accompanying centroids (+) indicate seasonal differences in vertical extent and magnitude of radar reflectivity (RF13).

Fig. 2.

Examples of seasonal average CFADs for (a) JJA 2010, (b) MAM and SON 2010, and (c) DJF 2011. Contours indicate frequency of observed reflectivity (dBZ) by height above the radar footprint indicated in Fig. 1. The seasonal CFADs and their accompanying centroids (+) indicate seasonal differences in vertical extent and magnitude of radar reflectivity (RF13).

Table 1.

Summary of mean precipitation characteristics for each storm-type classification according to RF13. The data ranges are 95% confidence intervals for the mean values.

Summary of mean precipitation characteristics for each storm-type classification according to RF13. The data ranges are 95% confidence intervals for the mean values.
Summary of mean precipitation characteristics for each storm-type classification according to RF13. The data ranges are 95% confidence intervals for the mean values.

b. Environmental conditions

The atmospheric conditions accompanying each of the 559 storms identified in RF13 were obtained from the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim, herein ERAi) dataset. The ERAi data have 6-h temporal and 0.75° × 0.75° latitude/longitude spatial resolution. All ERAi data used in this analysis are for the point located at 46.75°N, 9°E, the closest ERAi data point to the Monte Lema radar (Fig. 1). Rain gauge measurements accumulated over 10 min are used to identify the beginning and end of individual events as described in RF13. Here, we point out that MeteoSwiss weather stations typically utilize heated tipping-bucket rain gauges, which have known inaccuracies in snowfall measurement (Rasmussen et al. 2012). The difficulty of snowfall measurement likely introduces an error into winter precipitation event start and end times used in this study. ERAi data for each storm were taken from the 6-h interval (0000, 0600, 1200, or 1800 UTC) nearest to the storm start time as identified from the rain gauge data. We have not investigated potential sensitivity of results to the choice of ERAi time interval associated with each storm. Specific humidity (q), temperature (T), and zonal and meridional components of the wind (u and υ) from pressure levels 950–700 hPa in 50-hPa increments and from pressure levels 700–100 hPa in 100-hPa increments were obtained for each storm from the ERAi data. In addition, ERAi provides data for vertical integral of zonal and meridional water vapor flux (IWVu and IWVυ), geopotential height at 1000 and 500 hPa (denoted as Z1000 and Z500 hereafter), and convective available potential energy (CAPE). Table 2 provides a summary of the data used in this study.

Table 2.

Summary of data used in this study. Specific humidity (qp), temperature (Tp), and zonal and meridional components of the wind (up and υp) are taken from isobaric levels 950–700 hPa in 50-hPa increments and from isobaric levels 700–100 hPa in 100-hPa increments.

Summary of data used in this study. Specific humidity (qp), temperature (Tp), and zonal and meridional components of the wind (up and υp) are taken from isobaric levels 950–700 hPa in 50-hPa increments and from isobaric levels 700–100 hPa in 100-hPa increments.
Summary of data used in this study. Specific humidity (qp), temperature (Tp), and zonal and meridional components of the wind (up and υp) are taken from isobaric levels 950–700 hPa in 50-hPa increments and from isobaric levels 700–100 hPa in 100-hPa increments.

3. Relationships between environmental conditions and storm structure

a. Synoptic weather patterns

Previous work indicates that precipitation rate and quantity are related to the synoptic weather situation (Lin et al. 2001; Rudari et al. 2004; Rudolph et al. 2011). A relationship has also been found between the vertical structure of radar-observed precipitation and surface precipitation characteristics (RF13). But does a relationship exist between synoptic weather patterns and the vertical structure of precipitation systems? Figure 3 shows 1000- and 500-hPa geopotential heights, Z1000 and Z500, averaged over all storms of each vertical reflectivity structure classification that occurred in southern Switzerland during March 2004–February 2011. DJF- and MAM/SON-type storms generally occur during an advective synoptic pattern associated with frontal passage. An advective pattern occurs when a strong surface pressure gradient is present over Switzerland (Wanner et al. 1998). The synoptic pattern associated with DJF-type storms exhibits a surface trough to the west of the Alps that extends southward to the Mediterranean Sea. The average synoptic pattern for MAM/SON-type storms also indicates the presence of a surface trough; however, it does not extend as far south as for DJF-type storms and also indicates the presence of an isolated area of lower Z1000 over the Ligurian Sea. Troughs located to the west of the Alps, extending southward from Great Britain to the Mediterranean Sea, are associated with large daily precipitation totals for the southern Swiss Alps (Doswell et al. 1998; Massacand et al. 1998; Lin et al. 2001; Martius et al. 2006; Grazzini 2007; Rudolph et al. 2011). The large total amount of precipitation received during advective synoptic patterns is due to longer duration and lower intensity precipitation (Rudolph et al. 2011). DJF- and MAM/SON-type storms are also associated with larger quantity, longer duration, and lower intensity precipitation (RF13). Therefore, the apparent association between advective synoptic patterns and DJF- and MAM/SON-type storms is consistent with previous findings.

Fig. 3.

Geopotential height at 1000 hPa (Z1000, in m, color contours) and 500 hPa (Z500, in m, dashed lines) for each storm type: (a) DJF-type, (b) MAM/SON-type, and (c) JJA-type. Differences in geopotential height at 500 and 1000 hPa are used to classify the synoptic weather type in RF13.

Fig. 3.

Geopotential height at 1000 hPa (Z1000, in m, color contours) and 500 hPa (Z500, in m, dashed lines) for each storm type: (a) DJF-type, (b) MAM/SON-type, and (c) JJA-type. Differences in geopotential height at 500 and 1000 hPa are used to classify the synoptic weather type in RF13.

In contrast, the average synoptic pattern associated with JJA-type storms indicates an isolated area of higher geopotential heights in Z1000 over southern Switzerland. A convective synoptic pattern is characterized by lack of a strong surface pressure gradient over Switzerland, similar to the pattern found for JJA-type storms (Fig. 3; Wanner et al. 1998). Precipitation that occurs during a convective situation is generally more intense, but shorter in duration, and results in lower total quantity (Rudolph et al. 2011). RF13 found that JJA-type storms are associated with precipitation characteristics similar to those of convective synoptic patterns. Again, we find consistency in the relationships among synoptic patterns, precipitation characteristics, and vertical structure of precipitation whereby the convective synoptic pattern with intense and short duration precipitation and JJA-type storms are related.

b. Integrated water vapor flux

Based on the ERAi annual mean integrated water vapor (IWV) fluxes, an anomaly is directed to the northeast for all three classes of storm type between March 2004 and February 2011 (Fig. 4). The northward component of IWV flux provides upslope flow on the southern side of the Alps and indicates that orographic lift is the main mechanism that generates precipitation throughout the year, regardless of storm type. Comparison of IWVu and IWVυ for DJF-, MAM/SON-, and JJA-type storms shows that JJA-type storms have the largest northward and eastward components of IWV (not shown). The mean values of IWVυ and IWVu for MAM/SON-type and DJF-type storms are not significantly different at 95% confidence (not shown). Differences in the magnitude of the IWV flux between the different storm types may be attributed to the temperature dependence of atmospheric moisture via the Clausius–Clapeyron equation. JJA-type storms become more likely as surface temperature increases (RF13) and, therefore, have the largest values of IWV.

Fig. 4.

(a) Annual mean water vapor flux over March 2004 through February 2011, and water vapor anomaly as compared to annual mean for each storm type: (b) DJF, (c) MAM/SON, and (d) JJA. Magnitude of water vapor flux is depicted by color scale and direction is indicated by vectors. Note that magnitude scales are different for the annual mean and for the anomalies.

Fig. 4.

(a) Annual mean water vapor flux over March 2004 through February 2011, and water vapor anomaly as compared to annual mean for each storm type: (b) DJF, (c) MAM/SON, and (d) JJA. Magnitude of water vapor flux is depicted by color scale and direction is indicated by vectors. Note that magnitude scales are different for the annual mean and for the anomalies.

Northeastward moisture flux observed for each storm type is associated with the synoptic weather pattern (Figs. 2 and 3). All of the synoptic patterns shown in Fig. 3 indicate northeast geostrophic flow over southern Switzerland. For DJF- and MAM/SON-type storms moisture flux is directed by an approaching trough that extends to the surface. The synoptic pattern shown for MAM/SON-type storms additionally indicates that moisture transport is influenced by a surface low located to the south of the Alps. For JJA-type storms, northeastward geostrophic flow appears at 500 hPa, but is not as apparent at the surface.

c. Wind and specific humidity

The synoptic patterns and water vapor flux anomalies described in sections 3a and 3b provide a view of moisture transport across the entire depth of the troposphere for each type of storm. However, variations in wind and moisture content at various heights may also affect the vertical structure of precipitation. For example, the Froude number [Fr, Eq. (1)] is often used to quantify the tendency for flow to pass over or around terrain and is defined as

 
formula

with the low-level wind velocity perpendicular to the barrier (V) as well as Brunt–Väisälä frequency (N) and the mountain height (h). Case studies from MAP include observations of precipitation systems on the south side of the Alps that occurred under blocked and unblocked flow conditions. Those characterized by blocked flow (Fr ≪ 1) resulted in stratiform precipitation while unblocked flow (Fr ≫ 1) was associated with embedded convection (Medina and Houze 2003; Yuter and Houze 2003; Rotunno and Houze 2007). Therefore, since Fr is related to the development of stratiform versus convective precipitation, it follows that winds advecting moisture at various levels throughout the troposphere, especially at low levels, affect precipitation characteristics.

Further evidence of the importance of airflow at different levels on precipitation location and intensity on the south side of the Alps is provided in Panziera and Germann (2010, hereafter PG10). They used wind direction and speed at various levels to predict the onset and end of orographic precipitation around Locarno, Switzerland (Fig. 1). PG10 divide atmospheric flow into layers relative to the terrain height (Table 3). Radar-estimated wind velocity and direction within each layer are shown to impact rainfall frequency and location (PG10). Variation in flow layers is also found between different classes of precipitation system vertical structure (Fig. 5). Following PG10, we also divide the ERAi atmospheric flow into low-level flow (LLF), midlevel flow (MLF), cross-barrier flow (CBF), and upper-level flow (ULF). Since the ERAi wind data are available at isobaric atmospheric levels, the flow level boundaries defined in PG10 are converted from height to pressure levels via the hypsometric equation and result in the level definitions used for this paper (Table 3).

Table 3.

Height ranges of tropospheric flow layers (from PG10) and converted to pressure ranges for this study.

Height ranges of tropospheric flow layers (from PG10) and converted to pressure ranges for this study.
Height ranges of tropospheric flow layers (from PG10) and converted to pressure ranges for this study.
Fig. 5.

Hodographs (m s−1) for DJF- (blue), MAM/SON- (green), and JJA-type (red) storms (a) at all levels [950–100 hPa; lowest vertical level (900 hPa) is point nearest origin for all classes] and for (b) low-level flow (LLF, 950–700 hPa), (c) midlevel flow (MLF; 700–650 hPa), (d) cross-barrier flow (CBF; 650–600 hPa), and (e) upper-level flow (ULF; 500–100 hPa). Note scale differences in panels.

Fig. 5.

Hodographs (m s−1) for DJF- (blue), MAM/SON- (green), and JJA-type (red) storms (a) at all levels [950–100 hPa; lowest vertical level (900 hPa) is point nearest origin for all classes] and for (b) low-level flow (LLF, 950–700 hPa), (c) midlevel flow (MLF; 700–650 hPa), (d) cross-barrier flow (CBF; 650–600 hPa), and (e) upper-level flow (ULF; 500–100 hPa). Note scale differences in panels.

Hodographs depicting average winds over the duration of each storm type are shown in Fig. 5. Wind velocity increases in magnitude and veers with height throughout the levels of LLF, MLF, and CBF until reaching the level of ULF. Veering with height indicates warm air advection and is consistent with southerly flow depicted by synoptic patterns and water vapor flux anomalies (Figs. 2 and 3). The higher velocity of the LLF for DJF-type storms may imply increased Fr and greater probability of embedded convection. DJF-type storms, on the other hand, demonstrate stratiform precipitation characteristics, indicating that the increased velocity of the LLF is accompanied by increased Brunt–Väisälä frequency in order for Fr to remain low [Eq. (1)]. Similarly, JJA-type storms exhibit convective qualities and therefore must have reduced atmospheric stability (lower Brunt–Väisälä frequency) to enable the development of convection since wind velocities during JJA-type storms are generally less than in DJF-type storms. Velocities during MAM/SON- and JJA-type storms are nearly identical. This implies different atmospheric stabilities between the MAM/SON- and JJA-type storms, with the JJA-type being less stable since they are found to be more convective. This, in fact, is the case, as shown by the moist Brunt–Väisälä frequency and CAPE: JJA is least stable, MAM/SON is more stable than JJA, and DJF is most stable (see section 3d).

The combination of specific humidity, q, and wind at each isobaric level allows a moisture transport hodograph, or Q hodograph, to be plotted (Fig. 5). The Q hodograph indicates water vapor flux magnitude and direction at various isobaric levels. The direction of moisture transport, Q, (Fig. 6) is identical to wind direction (Fig. 5). The magnitude of Q (kg m−2 s−1) is calculated as

 
formula

where V is the magnitude of the wind velocity (m s−1, as in Fig. 5) and w is the mixing ratio (kg water vapor per kg dry air, assumed equivalent to specific humidity). Air density, ρ (kg m−3), in Eq. (2) is calculated from the pressure at each isobaric level (P) as

 
formula

with virtual temperature (Tυ) based on the temperature at each level (T),

 
formula

and the gas constant for dry air (Rd). All storm types exhibit positive northward and eastward components to moisture transport at all but the lowest levels, again indicating the importance of moist southerly flow on development of precipitation on the south side of the Alps (Fig. 6). The Q hodograph also shows greater magnitude of moisture transport for JJA-type storms in LLF, MLF, and CBF (Fig. 6). The increased moisture content associated with JJA-type storms probably results from the greater moisture carrying capacity of warmer air during summer months when JJA-type storms are most likely to occur (RF13). This results in more moisture transport during JJA-type storms than DJF-type precipitation systems despite weaker winds in LLF and MLF during JJA-type storms. The upper portion of the LLF and the entire MLF and CBF are responsible for the majority of moisture transport during JJA-type storms (Fig. 5). In contrast, the quantity of moisture transported in LLF, MLF, and CBF is more uniform during DJF-type precipitation systems. Water vapor flux at pressure levels between 850 and 600 hPa, corresponding to LLF, MLF, and CBF, is the major contributor to the differences in total integrated water vapor flux between the storm types characterized in Table 1.

Fig. 6.

Water vapor hodographs (units are kg H2O m−2 s−1) for DJF- (blue), MAM/SON- (green), and JJA-type (red) storms (a) at all levels [950–100 hPa; lowest vertical level (900 hPa) is point nearest origin for all classes], and for (b) LLF (950–700 hPa), (c) MLF (700–650 hPa), (d) CBF (650–600 hPa), and (e) ULF (500–100 hPa).

Fig. 6.

Water vapor hodographs (units are kg H2O m−2 s−1) for DJF- (blue), MAM/SON- (green), and JJA-type (red) storms (a) at all levels [950–100 hPa; lowest vertical level (900 hPa) is point nearest origin for all classes], and for (b) LLF (950–700 hPa), (c) MLF (700–650 hPa), (d) CBF (650–600 hPa), and (e) ULF (500–100 hPa).

d. Atmospheric stability

We compare the atmospheric stability in the boundary layer for the different storm types in terms of squared moist Brunt–Väisälä frequency (Nm2) and CAPE. As in PG10, we evaluate Nm2 using ground station data from the vicinity of Locarno following Eq. (26) of Durran and Klemp (1982). Temperature (T), potential temperature (Θ), mixing ratio (w), and relative humidity (rh) from Locarno-Monti (366 m) and Cimetta (1661 m) are used to calculate Nm2 for each storm. We use the Locarno-Monti and Cimetta stations for this paper instead of Stabio (353 m) and Monte Generoso (1608 m) as used in PG10 because this study uses rain gauge data from the Locarno-Monti and Cimetta stations to identify precipitation events, and both stations lie to the north of the Monte Lema radar and within the radar volume utilized to generate the CFAD centroids (Fig. 1). Also, Locarno-Monti and Cimetta represent a layer with a top to bottom elevation difference (~1.3 km) similar to that of Stabio/Monte Generoso while lying extremely close to each other (<4 km apart).

CAPE and Nm2 both indicate differences in stability between the storm-type classifications (Figs. 6 and 7). In terms of Nm2, DJF-type storms occur during more stable conditions (higher Nm2) with JJA-type storms under the least stable conditions (lower Nm2), and MAM/SON-type storms are associated with intermediate values of Nm2 (Fig. 7). Similarly, JJA-type storms are accompanied by the highest CAPE, followed by MAM/SON, and DJF has the least CAPE among the storm classes (Fig. 8). The reduced Nm2 and increased CAPE associated with JJA-type storms coincides with the convective nature of JJA-type storms as evidenced by higher precipitation intensity and shorter duration (RF13). Furthermore, higher Nm2 and lower CAPE support the stratiform nature of DJF-type storms that are associated with precipitation of lower intensity and longer duration.

Fig. 7.

Squared moist Brunt–Väisälä Frequency (Nm2) for each storm type. Boxes indicate median and interquartile range (IQR, 25th to 75th quantile) with extended hash marks at 1.5 × IQR. The value of Nm2 was determined from weather stations at Locarno-Monti (366 m) and Cimetta (1661 m); Nm2 shown above is limited to the years 2008–11 due to data availability.

Fig. 7.

Squared moist Brunt–Väisälä Frequency (Nm2) for each storm type. Boxes indicate median and interquartile range (IQR, 25th to 75th quantile) with extended hash marks at 1.5 × IQR. The value of Nm2 was determined from weather stations at Locarno-Monti (366 m) and Cimetta (1661 m); Nm2 shown above is limited to the years 2008–11 due to data availability.

Fig. 8.

CAPE from ERA-i for each storm type. Box plots as in Fig. 7.

Fig. 8.

CAPE from ERA-i for each storm type. Box plots as in Fig. 7.

4. Generalized linear model for storm types

a. Development

In the previous sections and in RF13 we have demonstrated that vertical reflectivity structure (i.e., storm type) is related to temperature, wind speed and direction (synoptic pattern), atmospheric moisture flux, and atmospheric stability. This suggests that environmental parameters may be used to predict storm type and related precipitation characteristics. Which combination of these parameters provides the best model for predicting the storm type? We developed generalized linear models for the vertical structure of precipitation as a function of environmental conditions using the following relationships (McCullagh and Nelder 1989):

 
formula
 
formula

GLMs provide expected values of Cx and Cy, the x- and y- CFAD centroids (see RF13), as a function of environmental parameters observed during each storm (pij or pik, where i is the storm number and j or k is the number of parameters) and the coefficient associated with each variable (βj and βk). The expected values of Cx and Cy [Eqs. (5) and (6)] provide a predicted location of the CFAD centroid for each set of environmental conditions. The predicted CFAD centroid is then used to classify the vertical structure by identifying the nearest neighbor among seasonal CFAD centroids (as described in RF13).

We begin our development of GLMs for Cx and Cy [Eqs. (5) and (6)] by including all environmental parameters listed in Table 2 for the years 2004 through 2009. The t values and associated significance for several coefficients (βj and βk) in our initial GLMs indicate the potential to reduce the number of included parameters without affecting model accuracy (not shown). Therefore, we perform a stepwise selection of model parameters to optimize the GLMs and choose the GLMs that produce the best accuracy with the least number of parameters. The stepAIC function in R statistical software selects the best GLM by evaluating the Akaike information criterion (AIC) for each combination of model parameters, defined as (Venables and Ripley 1997)

 
formula

The GLMs for Cx and Cy that result in minimum AIC values are selected and together comprise our best model for the storm type. AIC rewards models (decreases AIC values) with greater accuracy and penalizes models (increases AIC values) for increasing the number of parameters. Selection of the best GLMs for Cx and Cy on the basis of AIC results in improved accuracy (reduction of model deviance) and reduction of included parameters from 61 (Table 2) to 25 and 23 parameters for Cx and Cy, respectively (Tables 4 and 5).

Table 4.

Parameter coefficients (βj), standard error of parameter estimates, t values, and significance for best model of ln(Cx) [Eq. (5)]. Significance of coefficients noted as confidence levels >99.9% (***), >99% (**), >95% (*), and >90% (.).

Parameter coefficients (βj), standard error of parameter estimates, t values, and significance for best model of ln(Cx) [Eq. (5)]. Significance of coefficients noted as confidence levels >99.9% (***), >99% (**), >95% (*), and >90% (.).
Parameter coefficients (βj), standard error of parameter estimates, t values, and significance for best model of ln(Cx) [Eq. (5)]. Significance of coefficients noted as confidence levels >99.9% (***), >99% (**), >95% (*), and >90% (.).
Table 5.

Parameter coefficients (βk), standard error of parameter estimates, t values, and significance for best model of ln(Cy) [Eq. (6)]. Significance of coefficients noted as in Table 4.

Parameter coefficients (βk), standard error of parameter estimates, t values, and significance for best model of ln(Cy) [Eq. (6)]. Significance of coefficients noted as in Table 4.
Parameter coefficients (βk), standard error of parameter estimates, t values, and significance for best model of ln(Cy) [Eq. (6)]. Significance of coefficients noted as in Table 4.

We note here that the GLM for Cy includes ln(Cx) as a parameter. It was decided to include ln(Cx) in the GLM for Cy because of the apparent dependence of Cy on Cx (RF13). We developed log-GLMs that provide expected values of ln(Cx) and ln(Cy) because we found the log-log function provides a better fit (R2 = 0.37) than a linear fit (R2 = 0.33) to the CFAD data. As part of our analysis we also developed standard GLMs (not containing log terms); however, the overall accuracy of the standard GLMs was less than the log-GLMs reported here. The GLMs for storm type, comprised of two GLMs, one for Cx and one for Cy, are summarized in Tables 4 and 5. The GLMs are based on precipitation systems occurring in all seasons. GLMs specific to the summer and winter seasons were also investigated and found to have reduced accuracy in predicting vertical structure of the storm type. It is likely that the accuracy of the seasonal model is adversely affected by the reduced range of observed CFAD centroid values represented individually in the winter and summer seasons and results in a model that has more difficulty in discriminating between storm types.

The parameters included in the best models for Cx and Cy indicate that a combination of environmental factors differentiate the storm types (Tables 4 and 5). The number of days before or after the summer solstice (ds) is included in the best model for Cx. The inclusion of ds indicates the role of solar radiation and associated surface heating on storm type classification. The positive coefficient associated with ds (βi; Table 4) means that days farther from the summer solstice tend toward increased magnitude of reflectivity, Cx. This is a nonintuitive result as a negative correlation is expected, whereby reflectivity magnitude increases near the summer solstice as convective structure becomes more common. However, the negative correlation that is found is likely influenced by the observed increase in occurrence of convective-type storms in late summer and fall (RF13). Possibly, further insight may be gained concerning the impact of solar radiation on vertical structure by incorporating various heat balance parameters from ERAi into the GLMs.

Meridional and zonal water vapor flux (IWVυ and IWVu) are also included as a component of our vertical structure GLM. Northward moisture transport (positive values of IWVυ) increases the magnitude of reflectivity, Cx, as a result of the orographic effect induced by the primarily south-facing terrain around Locarno. This corresponds to the previously described increase in the northward IWVυ anomaly associated with JJA-type vertical structure (Fig. 4). An eastward anomaly in IWVu accompanies all three types of vertical structure, and similar to IWVu, the anomaly is greatest for JJA-type vertical structure (Fig. 4). The differences in IWVu between the three types of vertical structure likely lead to the inclusion of IWVu in the GLM. Water vapor flux does not explicitly appear in our GLM for Cy, representing the height of observed reflectivity. Nonetheless, it implicitly affects the height of reflectivity because of the dependence of Cx on IWVυ and IWVu and the inclusion of ln(Cx) in the model for Cy.

Temperature (T), specific humidity (q), and zonal and meridional wind velocity (u and υ) at multiple levels also are significant components of the GLM. The coefficients of T, q, u, and υ at vertical pressure levels that range from near the surface through upper levels of the troposphere (950–200 hPa) exhibit both positive and negative relationships with Cx and Cy (Tables 4 and 5). As previously reported in RF13, increased surface temperature increases the probability of JJA-type storms, which are characterized by larger values of both Cx and Cy. Here, the coefficients included in our GLM reveal more complexity in the relationship between temperature at various heights (isobaric pressure levels) and vertical structure of precipitation. The alternating patterns of positive and negative coefficients for T, as well as q, u, and υ, suggest that layers of instability may be a factor in the relative stratiform versus convective structure. The absence of CAPE from the models for Cx and Cy further indicates that the effect of stability on precipitation vertical structure is accounted for by the included temperature and moisture variables. One exception is q in the model for Cx (Table 4), which shows a positive relationship for moisture at 800 hPa and a negative relationship aloft (600, 300, 100 hPa). The positive relationship at the lower vertical level and negative relationship at higher vertical levels corresponds to differences in wind direction and magnitude (Fig. 5). Therefore, as low-level moisture increases and upper-level moisture decreases, reflectivity tends toward convective storm types with greater magnitude of reflectivity (Cx) and increased vertical extent (Cy). Also of note are the prevalence of υ terms and lesser role of u in the GLMs for both Cx and Cy. This indicates the relative importance to storm vertical structure of meridional flow perpendicular to the alpine barrier.

b. Evaluation

We evaluate the GLM over two time periods: 1) March 2004–December 2009, the time period from which data were selected for development of the model, and 2) January 2010–March 2011 to provide observations occurring outside the time period of the model basis. The CFAD centroids predicted by our GLM compare favorably with observations over the years 2004–09 (Fig. 9). With the exception of a few outliers, the population of observed CFAD centroids qualitatively appears well represented by the predicted CFAD centroids in all seasons since the populations of predicted and observed values show considerable overlap. The combined root-mean-square error (RMSE) is evaluated individually for each season of the years 2004–09 and ranges from 0.52 to 0.86 (Table 6). The precision of predicted CFAD centroids is similar during the winter, spring, and fall with combined RMSEs of 0.53, 0.52, and 0.57, respectively (Table 6). Conversely, the predicted CFAD centroid values are least precise in summer, which has the highest combined RMSE of 0.86. However, CFAD centroids predicted for the summer season have the lowest combined normalized RMSE (NRMSE; 0.17), which takes into account summer’s larger range of CFAD centroid values. Therefore, the GLM appears to adequately model the increased range of CFAD centroids observed in summer.

Fig. 9.

Observed (red plus signs) and predicted (black squares) CFAD centroid locations for storms occurring in each season during the years 2004–09: (a) winter, (b) spring, (c) summer, and (d) fall.

Fig. 9.

Observed (red plus signs) and predicted (black squares) CFAD centroid locations for storms occurring in each season during the years 2004–09: (a) winter, (b) spring, (c) summer, and (d) fall.

Table 6.

Model performance for precipitation events over the years 2004–09, root-mean-square error (RMSE) of Cx and Cy, singly and combined, and normalized RMSE (NRMSE); ClassP = ClassO (%) is the percentage of storms where storm type resulting from GLM predicted Cx and Cy matches observed storm type. Combined RMSE and NRMSE are calculated by Euclidean distance. RMSE divided by the range of observed data to obtain NRMSE.

Model performance for precipitation events over the years 2004–09, root-mean-square error (RMSE) of Cx and Cy, singly and combined, and normalized RMSE (NRMSE); ClassP = ClassO (%) is the percentage of storms where storm type resulting from GLM predicted Cx and Cy matches observed storm type. Combined RMSE and NRMSE are calculated by Euclidean distance. RMSE divided by the range of observed data to obtain NRMSE.
Model performance for precipitation events over the years 2004–09, root-mean-square error (RMSE) of Cx and Cy, singly and combined, and normalized RMSE (NRMSE); ClassP = ClassO (%) is the percentage of storms where storm type resulting from GLM predicted Cx and Cy matches observed storm type. Combined RMSE and NRMSE are calculated by Euclidean distance. RMSE divided by the range of observed data to obtain NRMSE.

Storm type is determined by nearest neighbor comparison of Cx and Cy for individual storms (Fig. 9) to seasonal averages of Cx and Cy (as described in RF13; Table 1). The GLM-predicted CFAD centroids result in storm types having 72% accuracy over all seasons (Table 6). We define the accuracy of predicted storm type as the percentage of cases where predicted vertical structure agrees with observed storm type. In terms of accuracy, the model performs better in the winter months (81% accuracy) than in the other seasons (accuracy ranges from 66% to 77%). Comparison of Table 1 and Fig. 9 reveals a possible explanation for the increased accuracy of predicted storm types in winter over other seasons. Model accuracy in the winter season likely benefits from reduced dispersion of observed CFAD centroids that culminates in DJF-type storms dominating during the winter season. Outside of winter, the CFAD centroids are more disperse as all storm types (DJF, MAM/SON, and JJA) have been observed in spring, summer, and fall (RF13). Therefore, in spring, summer, and fall the precision of the model in predicting CFAD centroids is more critical to the accuracy of predicted storm types since the centroids in these seasons lie within three possible vertical structure classifications (DJF, MAM/SON, and JJA) rather than two (DJF or MAM/SON) as in winter.

We intentionally excluded data for January 2010–February 2011 from our GLM model development in order to perform an unbiased model evaluation using environmental parameters and radar observations taken from outside the model basis of 2004–09. As with our results for 2004–09, the CFAD centroids for the years 2010 and 2011 predicted by our GLM [Eqs. (5) and (6); Tables 4 and 5] appear qualitatively similar to, or clustered within similar ranges as, the observations (Fig. 10). Also similar to our 2004–09 results, the winter season has among the lowest seasonal combined RMSEs (0.36 for DJF; other seasons range from 0.51 to 1.01), indicating that the GLM provides the greatest precision in CFAD centroid locations for the winter season (Table 7). However, as previously, the expanded range of CFAD centroids during the summer season results in summer having the lowest combined NRMSE among the seasons (0.39 for JJA; other seasons range from 0.54 to 0.97; Table 7). Considering all seasons for the 2010–11 data, the predicted vertical structure classifications are 79% accurate (Table 7), similar to the accuracy reported above for the model basis years of 2004–09 (72%; Table 6). Among individual seasons, the greatest accuracy in predicted storm type for the years 2010–11 occurs for the winter (95%). The consistency between results for years 2004–09, included in the model basis, and years 2010–11, not included in GLM parameter development, provides some confidence in the robustness of the model. However, it is realized that our unbiased dataset is limited to approximately one year and extension of the unbiased time period is desirable for further model evaluation. Nonetheless, it appears that our GLM for CFAD centroids is potentially applicable for precipitation events in southern Switzerland that occur outside the basis years of 2004–09.

Fig. 10.

As Fig. 9, but for the years 2010 and 2011.

Fig. 10.

As Fig. 9, but for the years 2010 and 2011.

Table 7.

Model performance for prediction of 2010 and 2011 storms (data as described in Table 6).

Model performance for prediction of 2010 and 2011 storms (data as described in Table 6).
Model performance for prediction of 2010 and 2011 storms (data as described in Table 6).

5. Conclusions

Our analysis of precipitation systems occurring in the vicinity of Locarno, Switzerland, has shown that radar-observed vertical structure of reflectivity is related to both dynamic and thermodynamic atmospheric parameters. Dynamic effects that influence the vertical reflectivity structure include wind speed and direction at multiple vertical levels of the troposphere. Thermodynamic effects on vertical reflectivity structure include atmospheric stability and vertical profiles of temperature and specific humidity. Our analysis reinforces the importance of including dynamic as well as thermodynamic impacts of climate change when evaluating the potential influence of climate change on storm structure and precipitation characteristics.

In addition, we have developed a GLM for storm type that is related to the vertical structure of reflectivity and, therefore, surface precipitation characteristics. This GLM is based on relevant environmental parameters rather than on fundamental physical equations. The nonphysical GLM for storm types presented herein is dependent on a combination of parameters representing dynamic and thermodynamic forcing and predicts radar observed vertical reflectivity classifications with overall accuracy of 79%. For this study, the inclusion of parameters in the GLM is determined by AIC selection of the best model and results in 25 and 23 parameters for Cx and Cy, respectively. With such a relatively large number of included parameters, it may be interesting in future work to compare results obtained via optimization of GLMs with an artificial neural network based model (i.e., Coulibaly et al. 2005; Haylock et al. 2006).

The GLM for precipitation vertical structure may provide a bridge between atmospheric parameters from global climate models and the prediction of precipitation characteristics such as total, intensity, and duration. Our results indicate that generalized models may be useful for predicting high-resolution precipitation vertical structure from data available at spatial resolution similar to global reanalysis, such as GCMs. Therefore, GLMs may be useful for evaluating future trends in precipitation vertical structure and, subsequently, precipitation characteristics for specific regions based on climate model output. Since orographic forcing mechanisms are similar in other mountain ranges, the general idea of using vertical structure to link precipitation characteristics with atmospheric conditions is applicable to less studied areas of complex topography located elsewhere in the world. Each individual region of interest requires development of specific GLMs, and this study may be used as a guideline for finding the best combination of parameters. Overall, this study represents an alternative analysis technique for evaluation of future precipitation trends at spatial scales relevant to localized climates. Of course, the prediction of future precipitation based on empirical relationships between precipitation and environmental conditions assumes that the relationships remain unchanged under future climate, and furthermore, previously unobserved values of environmental parameters that lie outside the model space may arise.

Acknowledgments

The authors thank Dr. Urs Germann and Marco Boscacci of MeteoSwiss for providing operational radar data products. We also thank the European Centre for Medium-Range Weather Forecasts (ECMWF) for providing free internet access to ERA-Interim reanalysis data (http://data-portal.ecmwf.int/data/d/interim_full_daily/) and MeteoSwiss for weather station data from the IDAWEB portal (https://gate.meteoswiss.ch/idaweb). This research was supported by National Science Foundation Grant AGS-0937035 and the University of Colorado at Boulder, Department of Atmospheric and Oceanic Sciences. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors, partners, and contributors.

REFERENCES

REFERENCES
Abatzoglou
,
J. T.
, and
T. J.
Brown
,
2012
:
A comparison of statistical downscaling methods suited for wildfire applications
.
Int. J. Climatol.
,
32
,
772
780
,
doi:10.1002/joc.2312
.
Beuchat
,
X.
,
B.
Schaefli
,
M.
Soutter
, and
A.
Mermoud
,
2012
:
A robust framework for probabilistic precipitations downscaling from an ensemble of climate predictions applied to Switzerland
.
J. Geophys. Res.
,
117
, D03115, doi:10.1029/2011JD016449.
Chang
,
E. K. M.
,
Y.
Guo
, and
X.
Xia
,
2012
:
CMIP5 multimodel ensemble projection of storm track change under global warming
.
J. Geophys. Res.
,
117
,
D23118
, doi:10.1029/2012JD018578.
Chou
,
C.
, and
C.-W.
Lan
,
2012
:
Changes in the annual range of precipitation under global warming
.
J. Climate
,
25
,
222
235
.
Coulibaly
,
P.
,
Y. B.
Dibike
, and
F.
Anctil
,
2005
:
Downscaling precipitation and temperature with temporal neural networks
.
J. Hydrometeor.
,
6
,
483
496
.
Doswell
,
C. A.
,
C.
Ramis
,
R.
Romero
, and
S.
Alonso
,
1998
:
A diagnostic study of three heavy precipitation episodes in the western Mediterranean region
.
Wea. Forecasting
,
13
,
102
124
.
Durran
,
D. R.
, and
J. B.
Klemp
,
1982
:
On the effects of moisture on the Brunt–Väisälä frequency
.
J. Atmos. Sci.
,
39
,
2152
2158
.
Grazzini
,
F.
,
2007
:
Predictability of a large-scale flow conducive to extreme precipitation over the western Alps
.
Meteor. Atmos. Phys.
,
95
,
123
138
.
Gutmann
,
E. D.
,
R. M.
Rasmussen
,
C.
Liu
,
K.
Ikeda
,
D. J.
Gochis
,
M. P.
Clark
,
J.
Dudhia
, and
G.
Thompson
,
2012
:
A comparison of statistical and dynamical downscaling of winter precipitation over complex terrain
.
J. Climate
,
25
,
262
281
.
Haylock
,
M. R.
,
G. C.
Cawley
,
C.
Harpham
,
R. L.
Wilby
, and
C. M.
Goodess
,
2006
:
Downscaling heavy precipitation over the United Kingdom: A comparison of dynamical and statistical methods and their future scenarios
.
Int. J. Climatol.
,
26
,
1397
1415
.
Held
,
I. M.
, and
B. J.
Soden
,
2006
:
Robust responses of the hydrological cycle to global warming
.
J. Climate
,
19
,
5686
5699
.
Hidalgo
,
H. G.
,
M. D.
Dettinger
, and
D. R.
Cayan
,
2008
: Downscaling with constructed analogues: Daily precipitation and temperature fields over the United States. California Energy Commission, PIER Project Rep. CEC-500-2007-123, 48 pp.
Houze
,
R. A.
, Jr.
,
C. N.
James
, and
S.
Medina
,
2001
:
Radar observations of precipitation and airflow on the Mediterranean side of the Alps: Autumn 1998 and 1999
.
Quart. J. Roy. Meteor. Soc.
,
127
,
2537
2558
.
Larson
,
V. E.
, and
B. M.
Griffin
,
2013
:
Analytic upscaling of a local microphysics scheme. Part I: Derivation
.
Quart. J. Roy. Meteor. Soc.
,
139
,
46
57
.
Lin
,
Y.-L.
,
S.
Chiao
,
T. A.
Wang
,
M. L.
Kaplan
, and
R. P.
Weglarz
,
2001
:
Some common ingredients for heavy orographic rainfall
.
Wea. Forecasting
,
16
,
633
660
.
Martius
,
O.
,
E.
Zenklusen
,
C.
Schwierz
, and
H.
Davies
,
2006
:
Episodes of Alpine heavy precipitation with an overlying elongated stratospheric intrusion: A climatology
.
Int. J. Climatol.
,
26
,
1149
1164
.
Massacand
,
A. C.
,
H.
Wernli
, and
H. C.
Davies
,
1998
:
Heavy precipitation on the Alpine south side: An upper-level precursor
.
Geophys. Res. Lett.
,
25
,
1435
1438
.
McCullagh
,
P.
, and
J. A.
Nelder
,
1989
: Generalized Linear Models. 2nd ed. Chapman and Hall, 511 pp.
Medina
,
S.
, and
R. A.
Houze
Jr.
,
2003
:
Air motions and precipitation growth in Alpine storms
.
Quart. J. Roy. Meteor. Soc.
,
129
,
345
371
.
Panziera
,
L.
, and
U.
Germann
,
2010
:
The relation between airflow and orographic precipitation on the southern side of the Alps as revealed by weather radar
.
Quart. J. Roy. Meteor. Soc.
,
136
,
222
238
.
Pincus
,
R.
, and
S. A.
Klein
,
2000
:
Unresolved spatial variability and microphysical process rates in large-scale models
.
J. Geophys. Res.
,
105
(
D22
),
27 059
27 065
.
Rasmussen
,
R.
, and
Coauthors
,
2012
:
How well are we measuring snow? The NOAA/FAA/NCAR winter precipitation test bed
.
Bull. Amer. Meteor. Soc.
,
93
,
811
829
.
Rotunno
,
R.
, and
R. A.
Houze
,
2007
:
Lessons on orographic precipitation from the Mesoscale Alpine Programme
.
Quart. J. Roy. Meteor. Soc.
,
133
,
811
830
.
Rudari
,
R.
,
D.
Entekhabi
, and
G.
Roth
,
2004
:
Terrain and multiple-scale interactions as factors in generating extreme precipitation events
.
J. Hydrometeor.
,
5
,
390
404
.
Rudolph
,
J. V.
, and
K.
Friedrich
,
2013
:
Seasonality of vertical structure in radar-observed precipitation over southern Switzerland
.
J. Hydrometeor.
,
14
,
318
330
.
Rudolph
,
J. V.
,
K.
Friedrich
, and
U.
Germann
,
2011
:
Relationship between radar-estimated precipitation and synoptic weather patterns in the European Alps
.
J. Appl. Meteor. Climatol.
,
50
,
944
957
.
Rudolph
,
J. V.
,
K.
Friedrich
, and
U.
Germann
,
2012
:
Model-based estimation of dynamic effect on twenty-first-century precipitation for Swiss river basins
.
J. Climate
,
25
,
2897
2913
.
Seager
,
R.
,
N.
Naik
, and
G. A.
Vecchi
,
2010
:
Thermodynamic and dynamic mechanisms for large-scale changes in the hydrological cycle in response to global warming
.
J. Climate
,
23
,
4651
4668
.
Smith
,
R. B.
,
Q.
Jiang
,
M. G.
Fearon
,
P.
Tabary
,
M.
Dorninger
,
J. D.
Doyle
, and
R.
Benoit
,
2003
:
Orographic precipitation and air mass transformation: An Alpine example
.
Quart. J. Roy. Meteor. Soc.
,
129
,
433
454
.
Stoner
,
A. M. K.
,
K.
Hayhoe
,
X.
Yang
, and
D. J.
Wuebbles
,
2012
:
An asynchronous regional regression model for statistical downscaling of daily climate variables
.
Int. J. Climatol.
,
33
,
2473
2494
,
doi:10.1002/joc.3603
.
Venables
,
W.
, and
B.
Ripley
,
1997
: Modern Applied Statistics with S-Plus. 2nd ed. Springer, 548 pp.
Wanner
,
H.
,
E.
Salvisberg
,
R.
Rickli
, and
M.
Schüepp
,
1998
:
50 years of Alpine weather statistics (AWS)
.
Meteor. Z.
,
7
,
99
111
.
Wilby
,
R. L.
,
1998
:
Statistical downscaling of daily precipitation using daily airflow and seasonal teleconnection indices
.
Climate Res.
,
10
,
163
178
,
doi:10.3354/cr010163
.
Wood
,
A. W.
,
L. R.
Leung
,
V.
Sridhar
, and
D. P.
Lettenmaier
,
2004
:
Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs
.
Climatic Change
,
62
,
189
216
.
Yuter
,
S. E.
, and
R. A.
Houze
Jr.
,
2003
:
Microphysical modes of precipitation growth determined by S-band vertically pointing radar in orographic precipitation during MAP
.
Quart. J. Roy. Meteor. Soc.
,
129
,
455
476
.