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Abstract and Figures

A physical full-scale experimental set-up was designed and implemented in the wind tunnel to reproduce and capture the trajectories of falling water drops when approaching the collector of catching type precipitation gauges, reproducing rainfall measurements in windy conditions. The experiment allowed to collect, for the first time, a large data set of high-resolution footages of the deviation of such trajectories, as induced by the bluff-body aerodynamics of the outer gauge shape. By processing the collected images, a consistent quantitative interpretation of each drop pattern was possible, based on a detailed Computational Fluid Dynamics simulation of the airflow updraft and acceleration features above the collector of the gauge. Numerical airflow simulations were extensively validated in the wind tunnel, using local flow measurements and Particle Image Velocimetry. Capturing the deviation of the drop trajectories in the wind tunnel allowed a clear visualization of the physical reason for the wind-induced undercatch of precipitation gauges, since drops were individually observed to fall outside instead of inside of the collector, contrary to what would be expected by extrapolating their undisturbed trajectory. The adopted Lagrangian Particle Tracking model and the formulation used for the drag coefficient were suitable to closely reproduce the observed drop trajectories when affected by the airflow deformation due to the bluff-body aerodynamics of two investigated gauge geometries. The wind tunnel experiment provided the basis for the validation of the particle tracking model in terms of the difference between simulated and observed trajectories, after initial conditions were suitably set to represent the experimental setup.
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1. Introduction
The wind-induced undercatch of precipitation gauges is defined as the reduced amount of precipitation
captured by the collector of the gauge with respect to the amount that would be captured if the gauge
were transparent to the wind. When the gauge is exposed to the wind, airflow deformations occur above
and upwind of the collector due to the bluff-body aerodynamics of the gauge outer geometry. Significant
acceleration and vertical velocity components are generated (see e.g., Jevons,1861; Warnik,1953), inducing
some deformation of the fall trajectories of the approaching hydrometeors and generally resulting in a lower
collection of precipitation than in the absence of wind.
Instrumental measurement biases for precipitation gauges, well described and addressed in the literature
(see e.g., La Barbera etal.,2002; Molini etal.,2005; Valík etal.,2021), propagate through the applications or
the modeling chain (Habib etal.,2008) and their awareness is often rapidly lost, yielding limited reliability
of the obtained results (Lanza & Stagi,2008). Similar implications to real-world hydrological applications
are expected for the wind-induced undercatch.
Adjustments for the wind-induced bias are traditionally derived from field experiments, where the ratio
between the precipitation amount measured by the gauge and a suitable reference configuration with lim-
ited exposure to the wind is used as a measure of the Collection Efficiency (CE). This is a function of the
wind speed at the collector's height and of further influencing variables, such as the microphysical charac-
teristics of the precipitation events at the field test site. The choice of the influencing variables adopted to
derive best-fit adjustment curves from the field-measured data affects the representativeness of the results
and their transferability to any different site climatology and gauge configuration. This also reflects into
Abstract A physical full-scale experimental set-up was designed and implemented in the wind tunnel
to reproduce and capture the trajectories of falling water drops when approaching the collector of catching
type precipitation gauges, reproducing rainfall measurements in windy conditions. The experiment
allowed to collect, for the first time, a large data set of high-resolution footages of the deviation of such
trajectories, as induced by the bluff-body aerodynamics of the outer gauge shape. By processing the
collected images, a consistent quantitative interpretation of each drop pattern was possible, based on a
detailed Computational Fluid Dynamics simulation of the airflow updraft and acceleration features above
the collector of the gauge. Numerical airflow simulations were extensively validated in the wind tunnel,
using local flow measurements and Particle Image Velocimetry. Capturing the deviation of the drop
trajectories in the wind tunnel allowed a clear visualization of the physical reason for the wind-induced
undercatch of precipitation gauges, since drops were individually observed to fall outside instead of
inside of the collector, contrary to what would be expected by extrapolating their undisturbed trajectory.
The adopted Lagrangian Particle Tracking model and the formulation used for the drag coefficient were
suitable to closely reproduce the observed drop trajectories when affected by the airflow deformation
due to the bluff-body aerodynamics of two investigated gauge geometries. The wind tunnel experiment
provided the basis for the validation of the particle tracking model in terms of the difference between
simulated and observed trajectories, after initial conditions were suitably set to represent the experimental
setup.
CAUTERUCCIO ET AL.
© 2021. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution-NonCommercial License,
which permits use, distribution and
reproduction in any medium, provided
the original work is properly cited and
is not used for commercial purposes.
Wind Tunnel Validation of a Particle Tracking Model
to Evaluate the Wind-Induced Bias of Precipitation
Measurements
A. Cauteruccio1 , E. Brambilla2, M. Stagnaro1 , L. G. Lanza1,3 , and D. Rocchi2
1Department of Civil, Chemical and Environmental Engineering, University of Genova, Genoa, Italy, 2Department of
Mechanical Engineering, Politecnico di Milano, Milan, Italy, 3WMO/CIMO Lead Centre “B. Castelli” on Precipitation
Intensity, Genoa, Italy
Key Points:
Water drops are released in a
wind tunnel to mimic rainfall and
tracked to observe the wind-induced
measurement bias of raingauges
Numerical simulation of the airflow
field and a lagrangian particle
tracking model are applied to
reproduce the drop trajectories
Wind tunnel tests validate airflow
simulation and particle tracking
results supporting their application
in studying the wind-induced bias
Correspondence to:
L. G. Lanza,
luca.lanza@unige.it
Citation:
Cauteruccio, A., Brambilla, E.,
Stagnaro, M., Lanza, L. G., & Rocchi,
D. (2021). Wind tunnel validation of
a particle tracking model to evaluate
the wind-induced bias of precipitation
measurements. Water Resources
Research, 57, e2020WR028766. https://
doi.org/10.1029/2020WR028766
Received 9 SEP 2020
Accepted 17 JUN 2021
10.1029/2020WR028766
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a generally large spread of the residuals around the derived adjustment curves because a comprehensive
parameterization based on all the influencing variables is difficult to achieve.
Most recent advances in the literature are concentrated on a physically based numerical approach to supple-
ment experimental studies. CE curves for both liquid (see Cauteruccio & Lanza,2020) and solid (Cauteruc-
cio, Chinchella, etal.,2021) precipitation are derived as a function of the precipitation intensity, particle size
distribution, and wind speed. The numerical approach, after proper validation, allows to investigate various
gauge shape/precipitation type combinations, subject to the desired wind and precipitation climatology.
The numerical approach is based on Computational Fluid Dynamics (CFD) simulations of the airflow field
surrounding the gauge body (see e.g., Colli etal., 2018) and a Lagrangian Particle Tracking (LPT) model
to evaluate the airflow induced deformation on the trajectory of the approaching hydrometeors (see e.g.,
Nešpor & Sevruk,1999).
The work of Mueller and Kidder (1972) is among the earliest studies on the modeling of hydrometeor
trajectories using a LPT model; in that work, particle trajectories were numerically simulated based on
the flow field measured in the wind tunnel (WT) employing hot film anemometers. Folland(1988) later
developed two simplified trajectory models to estimate the catch losses due to the wind. They were based
on flow patterns (flow velocity and direction) obtained in the vertical section along the symmetry axis in
the streamwise direction partially published by Robinson and Rodda(1969), and the flow field close to the
windward edge as described in the work of Warnik(1953). In the first model, a two-dimensional solution
was obtained by simulating one by one drops of fixed diameter until the expected drop size distribution was
generated. Then the model was extended to a three-dimensional domain by considering the variation of
the gauge orifice width in the transversal direction. The second model, which the author terms “semi-an-
alytical”, uses geometrical considerations to calculate the number of particles which fall outside instead of
inside of the gauge collector.
In the work of Nešpor and Sevruk(1999), the airflow velocity field around three cylindrical gauges charac-
terized by different shapes of the collector rim was calculated by numerically solving the Reynolds Average
Navier-Stokes (RANS) equations based on the k-ε turbulence closure model where k is the turbulence kinet-
ic energy and ε the energy dissipation per unit mass. Then, liquid particle trajectories were modeled by em-
ploying a one-way coupled model where spherical particles are separately simulated for each diameter and
the CE is evaluated by computing the integral, over the particle size distribution, of the number of particles
collected by the gauge with respect to the total precipitation. This simulation scheme was also adopted by
Thériault etal.(2012) and Colli etal.(2015;2016a,2016b) for solid precipitation, by increasing the details of
the computational mesh to better capture the airflow features and using also Large Eddy Simulations (LES).
In the work of Thériault etal.(2012) different crystal types were modeled by using a power law parametri-
zation of the terminal velocity, volume, density, and cross section of the particles, while Colli etal.(2016b)
investigated two macro categories: wet and dry snow as suggested by Rasmussen etal. (1999). In these
works, a fixed drag coefficient for each crystal type was adopted. In the work of Colli etal.(2016b), the
obtained CE curves for the two macro categories act as upper and lower thresholds of the wide spreading
of experimental data.
Colli etal.(2015) obtained a better comparison with real-world data by introducing the dependence of the
aerodynamic Drag Coefficient (
D
C
) on the local Reynolds number of the simulated particle (Rep). The Rep is
function of the instantaneous particle-to-air magnitude of velocity and the particle trajectory is obtained by
updating its value and the associated
D
C
at each simulation time step.
In the present work the improved LPT model used by Colli etal.(2015) for solid precipitation was adapted
to simulate the trajectories of water drops when falling through the atmosphere and approaching the gauge
collector, using suitable
D
C
equations as a function of the Rep. Various equations were implemented for
different Rep ranges derived from literature formulations and data.
Due to the difficulties in reproducing hydrometeors trajectories under controlled WT conditions, or to ob-
serve their deflection when approaching the gauge in any real world configuration, the validation of trajec-
tory models is scarcely documented yet in the literature. Very few works in the literature, Warnik(1953) and
Green and Helliwell(1972), report some attempts to detect water drops in the WT.
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The WT experiment performed by Warnik(1953) was a pioneering work,
where the trajectories of solid particles under windy conditions and their
deviations when approaching the gauge were first visualized. However,
no attempt to quantitatively measure and model the deviation of parti-
cles in the presence of the gauge collector was made and just the overall
undercatch was quantitatively obtained. The main objective was to define
the air-flow behavior around the investigated gauges and to give definite
information about the inconsistencies observed in records of snow catch
in precipitation gauges. Results were used to design the geometry of two
windshields with better performance than the shields in use at that time.
Green and Helliwell(1972) measured wind velocity profiles and raindrop
trajectories above a cylindrical rain gauge in a WT. The flow field was
measured using a grid of hotwire anemometers and the trajectories of in-
jected drops using photographs from a still reflex camera. They simulated
the drop trajectories based on the streamlines obtained by visually inter-
preting the pattern of smoke injected in the WT. Little details are however
provided about the algorithms and procedures used in that work.
The original contribution of the present work consists of a dedicated WT experimental setup, where a physi-
cal full-scale model was designed and realized to release water drops in the flow field and to detect—at high
resolution—their deviated trajectories close to the gauge collector, where the airflow field is modified by the
presence of the gauge body. Various wind speed and fall height combinations were tested in a controlled WT
environment. Flow velocity measurements were obtained by employing a multi-hole probe and a Particle
Image Velocimetry (PIV) technique.
The objective of the present work is the validation in the WT of the modeling chain composed of CFD
simulations—to establish the airflow patterns (acceleration, velocity components and turbulence intensity)
produced by the aerodynamic response of the gauge geometry—and LPT algorithm—to assess the one-way
coupled airflow-raindrop interaction.
2. Methodology
The most popular outer shapes of catching type precipitation gauges, cylindrical (hereinafter CY) and chim-
ney (CH), were investigated. Although actually exploiting a weighing measurement principle, the Lam-
brecht Rain(e)H3© precipitation gauge has a cylindrical outer shape with collector diameter D=0.16m
and height h=0.307 m (see Figure 1 top-left) and is assumed here as representative of the majority of
tipping-bucket gauges, while the Geonor T200B© (with the same D and h=0.740m) has a chimney shape
(see Figure1 bottom-left), as is typical of many weighing-type gauges.
Within the PRIN 20154WX5NA project “Reconciling precipitation with runoff: the role of understated
measurement biases in the modeling of hydrological processes,” an extensive experimental campaign was
conducted in the WT of the DICCA department at the University of Genova and in the WT facility available
at Politecnico di Milano, hereafter GVPM. This includes flow velocity measurements obtained by using a
multi-hole probe (employed in the DICCA WT), as well as Particle Image Velocimetry (PIV) and a dedicated
technique designed to release and track water drops using a drop generator and a high-speed camera (em-
ployed in the GVPM).
Dedicated numerical simulations of the experimental setup were performed with suitable initial conditions
(drop velocity and position), as observed in the WT. The comparison between CFD airflow fields and ve-
locity measurements and between the simulated and observed drop trajectories led to the validation of the
whole numerical approach.
In both the simulations and the reported observations, the three Cartesian coordinates are set with the x axis
orientated along the streamwise direction, the y axis along the crosswise direction and the z axis along the
upward vertical direction, as shown in Figure1.
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Figure 1. Lambrecht Rain(e)H3© (top-left) and Geonor T200B© (bottom-
left) precipitation gauges and experimental setup used to release drops and
photograph their trajectories as installed in the GVPM (wind is along the x
direction).
Water Resources Research
2.1. Wind Tunnel Experiments
The DICCA WT has a working chamber of length of 8.8m and cross area of 1.7
1.35m2 (width
height),
while the GVPM has a low turbulence-high speed chamber of 4
4
4m3. In both facilities the gauge
collectors were positioned at 1m from the floor and in the center of the cross section to avoid any interac-
tion with the surrounding walls. The boundary layer develops in about 0.10m from the floor and all tests
were conducted under low turbulence conditions (turbulence intensity Iturb0.5%) and uniform-constant
incoming wind.
The Lambrecht Rain(e)H3© precipitation gauge (hereinafter CY gauge) was tested in the DICCA WT. Meas-
urements of the wind speed were acquired using a fast-response multi-hole probe, the “Cobra” probe, char-
acterized by a measuring cone of
45
, mounted on a traversing system with three degrees of freedom. Each
measurement was sampled at 2kHz for 30 s. The measurement positions were selected above the gauge
along two longitudinal profiles at different elevations and along two vertical profiles at the center and the
upwind edge of the collector.
The Geonor T200B© precipitation gauge (hereinafter CH gauge) was tested in the GVPM using the PIV
technique. The test chamber was uniformly filled with castor oil smoke, used as a tracer. A laser emitter
was mounted on the ceiling of the test chamber to illuminate the measurement plane, while the surround-
ing environment was kept in the dark. The video camera was positioned with its central axis normal to
the streamwise direction (x) and centered on the gauge collector. Post processing of the acquired images
provided the flow velocity field discretized in a regular grid with cell size of 7.5×7.5mm. Part of the data,
acquired very close to the gauge surface and disturbed by the reflection of the laser beam on the gauge rim,
were masked out.
With the aim to validate the LPT model, water drops were injected in the GVPM and their trajectories were
captured with a high-speed camera in the vertical 2-D plane (x, z) along the main flow direction. The devi-
ation of the drop trajectories approaching and traveling above the gauge collector was measured. The WT
was equipped with a hydraulic system and a high-power lamp to generate and illuminate drops along their
trajectories. The experimental setup is illustrated in the right-hand panel of Figure1.
The hydraulic system consisted of a tank with a constant water head, feeding a volumetric pump (Ismatec
Reglo-CPF digital) connected to a calibrated nozzle; the drops releasing frequency could be adjusted by
varying the pump flow rate between 0.4 and 18.0ml/min. Tests were conducted using a fixed flow rate of
0.8ml/min and a nozzle orifice size of 0.008’’. The support for the nozzle was shaped to have a reduced im-
pact on the airflow close to the orifice and to minimize the oscillations at the edge where drops are released.
The releasing position was fixed at about five diameters upstream of the upwind edge of the collector along
the streamwise symmetry axis of the gauge (x direction).
The high-speed camera was placed in front of the gauge (as described above for the PIV measurements) and
its distance from the gauge collector was optimized to increase the resolution of the captured drop images
without affecting the airflow field near the target. The focus plane was set as the vertical section along the
streamwise symmetry axis of the gauge collector (x direction). Acquisition of video sequences was carried
out at both a high and a low frame rate (fps). In the first case, the recording speed was optimized to maintain
high quality of the images, in terms of resolution and luminosity, suitable for capturing the drop movement
with no streaks appearing due to an excessive exposure time with respect to the drop displacement. The re-
cording speed was set to 1,000 fps, with an image resolution of 1,600×900 pixels. During the low frame rate
acquisition, the recording speed was kept low, 10 fps with the same image resolution, in order to increase
the exposure time. In this way the trajectory of a bright moving object was imprinted in a single image in
the form of a streak.
The lighting was designed to increase the visibility of drops in the video: an incandescent lamp was used to
illuminate the volume near the gauge collector. Tests were conducted in a dark environment while back-
lighting the gauge from above using the lamp. The lamp lights are suitably directed to avoid the saturation
of the recorded videos.
The GVPM campaign was realized in subsequent time slots, in each of them the dimension of the image
was about 40×20cm with the pixel size equal to 0.2370mm for the CH gauge and 0.2424mm for the CY
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gauge. The wind speed range investigated was between 9 and 13m s−1 to appreciate the deformation of the
drop trajectories when the flow field is disturbed by the presence of the gauge.
The drop release position was determined a priori using the LPT model based on the flow field provided
by CFD simulations at a wind speed equal to 10m s−1. Simulations were run by setting the drop size equal
to the minimum dimension that the video camera is able to capture (1mm) following dedicated tests per-
formed in still air and the initial velocity of the drop was imposed equal to zero in all directions according to
the releasing system. This configuration allowed a significant deformation of the trajectories to be observed
when drops traveled in the region where the flow field is disturbed by the presence of the gauge.
During the experiment drops of diameter between 0.7 and 1.2 mm were generated. The drop size/
wind speed configuration was chosen since drops could not be generated with their terminal velocity,
otherwise—given the above-mentioned constraints on the drop size—the high inertia of such large drops
would have resulted into an imperceptible deflection of the drop trajectories above the gauge collector.
The videos recorded by the camera were imported and analyzed in the MATLAB® environment. The meth-
odology of detection of the drop position differs depending on the type of acquisition. At high frame rate,
the path of each drop is identified by many frames: in every frame the drop is in a different position. Due to
the reduced exposure time of each image, little light enters into the camera sensor and the image is dark. To
improve the drop position identification, each image was then converted to greyscale and a combination of
a Gaussian and Laplacian filter was applied. The image was binarized using a threshold level, with the ze-
roes indicating the background color while the ones indicate the drop. Finally, using a moving window over
the image, the center of the drop was identified and stored. Knowing the time interval between two subse-
quent images and the conversion rate from pixels to mm, it was also possible to calculate the drop speed in
the 2-D shooting plane. In low frame rate acquisition, due to the high exposure time, every frame appears
much brighter and contains a streak representing the trajectory of each single drop. The same filtering and
binarization operations were used, adapting the filter and threshold parameters. Finally, morphological
operations were carried out to extract the middle line streak from the image, directly corresponding to the
trajectory of the drop.
2.2. CFD Simulations
To obtain the disturbed airflow velocity fields (magnitude and components) around the two investigated
gauges, CFD simulations were performed under constant wind velocity and uniform incoming free-stream
conditions. First, an Unsteady Reynolds Average Navier-Stokes (URANS) model was applied to the simula-
tion of the flow field around the Geonor T200B© gauge geometry to check the occurrence of any variation
in time of the average velocity field. Results revealed that a steady state solution is reached in the region of
major interest for this work, that is, above the gauge collector, and only beyond the gauge, in the wake, a
time dependent solution persists. For this reason, to reduce the computational burden, a RANS model was
used in the simulation of the Lambrecht Rain(e)H3© gauge. In both cases, the SST (Shear Stress Transport)
k-ω turbulence model, based on the turbulence kinetic energy (k), the energy dissipation per unit mass (ε)
and the turbulent specific dissipation rate (ω) as defined in Wilcox(2006), was adopted.
The SST k-ω closure model was developed by Menter(1993) and concentrates the advantages of the more
classic k-ε and k-ω models because it can switch to a k-ε behaviour in the free stream far from the object and
to the k-ω model near the walls. Indeed, the k-ε model formulated by Jones and Launder(1972), is robust
and reliable in the free flow region but it proved to be unreliable near the boundary layer, while the k-ω
model formulated by Wilcox(1988) is capable of correctly modeling turbulence near the boundary layer,
though presenting a strong dependency on arbitrary values in the free flow. Concerning the topic of this
work, Constantinescu etal.(2007) tested different numerical methods to investigate the shielding problem
between two contiguous precipitation gauges and concluded that the SST k-ω model is more consistent with
the time-dependent LES results on the upstream gauge, in conditions that are similar to the present work.
Although it was demonstrated (Cauteruccio etal.,2020) that the free-stream turbulence intensity inherent
to the natural wind has a significant role in attenuating the aerodynamic effect of precipitation gauges,
due to the energy dissipation induced by turbulent fluctuations, in this work a low free-stream turbulence
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condition was used to suitably reproduce the WT environment where the particle tracking experiment was
carried out.
To prepare the simulation setup, first the numerical models of the gauge geometries were realized in the
Standard Triangulation Language (STL) format using a 3D CAD software. The three-dimensional compu-
tational spatial domains were discretized using an unstructured hybrid hexahedral/prismatic finite volume
mesh. The number of cells of the computational mesh is 1.5×106 for the Geonor T200B© and doubled for
the Lambrecht Rain(e)H3© due to the sharp edge that characterized the rim geometry, which requires an
accurate discretization. In both cases, mesh refinement boxes and thin layers were realized close to the
gauge and on its surface to increase the accuracy of the numerical solution in the region affected by large
gradients of velocity and pressure. The quality of the mesh was checked by using the geometry parameters
of orthogonality, skewness, and aspect ratio.
The open-source OpenFOAM software was employed to solve the URANS and RANS equations. The fluid
air was modeled as a Newtonian incompressible fluid with kinematic viscosity νa=1.5×10−5 m2 s−1 and
density ρa=1.25kg m−3 at a reference environmental temperature Ta=20°C. For each configuration, at
the inlet of the computational domain (y-z plane) the undisturbed wind speed, Uref, equal to 10m s−1 was
imposed parallel to the x axis and it was maintained uniform and constant in time, while a null gradient
condition was set for pressure. At the outlet, y-z plane opposite to the inlet, the atmospheric pressure and a
null gradient condition for the velocity were imposed. The lateral surfaces of the domain were set as sym-
metry planes, while the ground and the gauge surface were assumed impermeable with a no-slip condition.
In all computational cells, initial conditions were imposed equal to Uref for the velocity and equal to zero for
the relative pressure.
This model was applied to the simulation of the airflow field generated in the WT. The aerodynamic be-
havior of the two precipitation gauges investigated was simulated and compared with the PIV and probe
velocity measurements for validation purposes.
2.3. The Lagrangian Particle Tracking Model
The LPT model used by Colli etal. (2015) for solid precipitation was modified by introducing drag coef-
ficient equations suitable for liquid precipitation. Drop trajectories were computed with a forward step
procedure by calculating at short time intervals the particle position, velocity and acceleration. The relative
particle-to-air velocity was updated at every time step by interpolating the CFD airflow field to obtain the
flow velocity in the exact position of the drop. This model is one-way coupled since the potential influence
of the particles on the airflow field is neglected. This simplification is acceptable since the particles concen-
tration in the air is very low as observed by Cauteruccio(2020). A spherical shape was assumed for the water
drops, with the associated equivalent diameter d, and the particle density was set equal to 1,000kg m−3
at the air temperature of 20°C. The drag coefficient equations were implemented for various ranges of par-
ticle Reynolds number established a priori among those proposed in the literature by Folland(1988) and
formulated starting from data published by Khvorostyanov and Curry(2005), hereinafter KC05.
The motion of particles when falling in the atmosphere is described by:
 
  
 
1
2
ppp D pa p a p a p p a
V CA V
a vvvv g
(1)
where
is the particle acceleration,
a
v
and
p
are the velocity vectors of the air and the particle,
g
is the
gravity acceleration,
D
C
is the drag coefficient,
p
A
is the particle cross section area and
a
and
p
are the den-
sity of the air and the particle. Equation1 assumes an upward positive orientation of the z axis, while the
velocity and acceleration components are positive in the positive direction of the related axes. The quantity
pa
vv
is the relative particle-to-air velocity.
The drag coefficient

D
C
is a dimensionless quantity used to represent the aerodynamic resistance of an
object in motion in a fluid, such as air or water, and depends on the cross-sectional area of the object

p
A
.
The estimation of the drag coefficient is not easy. In the literature, different experiments were carried
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out with hydrometeors falling through the atmosphere with the objective
of identifying suitable relationships between the drag coefficient and the
particle dimension and/or its terminal velocity. Beard(1976) derived
D
C
by performing experiments in stagnant air and measuring the dimension
d (mm) of the drops and their fall velocity
T
w
(m s−1).
When a particle falls in a stagnant air its Reynolds number is expressed
as:
T
p
a
wd
Re
(2)
where
a
is the air viscosity in m2 s−1. The drag coefficient is directly re-
lated to the Reynolds number of the particle in motion. When a particle
is immersed in a flow field the Equation 2 becomes a function of the
particle-to-air velocity as follows:
pa
p
a
d
Re
vv
(3)
Folland(1988) proposed different relationships between
p
Re
and
,
D
C
for various ranges of
p
Re
(see Equa-
tions47) and assumed that the minimum value for
D
C
must be fixed at 0.55.

0.01 2547
pD
Re C
(4)


 
1 0.045
0.01 2 1.06 24 2.400
pD p p
Re C Re Re
(5)


 
1 0.190
2 21 1.06 24 2.6 40
pD p p
Re C Re Re
(6)


 
1 0.368
21 1.06 24 4.536
pD p p
Re C Re Re
(7)
The equations proposed by Folland(1988) provide terminal velocities of raindrops in still air at the temper-
ature of 7.5°C and atmospheric pressure that agree to within 2% with those of Mason(1971) over the range
of terminal velocities 0.1<
T
w
<8.3m s−1.
In the work of KC05, different formulations of
,
D
C
as a function of
p
Re
obtained from experimental studies
and analytical models, were summarized. Some of the curves proposed by KC05 are derived for spherical
particles and other for crystals. The authors also introduce a correction, when the particle Reynolds number
exceeds the value of 103, to account for the turbulence effect due to the flow.
The
D
C
values proposed by KC05 as a function of
p
Re
, for spherical particles in turbulent conditions, were
fitted here for
60
p
Re
(approximately corresponding to a spherical drop of d=1mm falling in air, with
a
= 1.5 10−5 m2 s−1, at an indicative fall velocity of 1m s−1) with an inverse first-order equation (Equa-
tion8). The values of the three parameters are
00.442y
,
3.402a
,
21.383b
and the correlation factor
(R2) is equal to 0.996.

0D
p
ab
Cy
b Re
(8)
As shown in Figure2, also the relationships proposed by Folland(1988) (black line) were compared with the
raw data provided by KC05 (diamond). Based on this comparison the best-fit curve reported in Equation8
(gray line in Figure2) was implemented in the LPT model to calculate the drag coefficient for
400
p
Re
,
while the equations proposed by Folland(1988) were adopted for
400
p
Re
.
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Figure 2. Comparison between the raw data proposed by KC05
(diamond), the best-fit curve of Equation8 (gray line) and the formulation
proposed by Folland(1988) (black line).
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The LPT model was applied to the simulated airflow field to reproduce
the trajectories of water drops as released in the WT. These were com-
pared to the trajectories of the real drops detected by means of the video
tracking system installed in the WT.
3. Results
3.1. CFD Simulation Results and Validation
CFD results are shown below in terms of normalized velocity profiles
(continuous line) sampled in (x/D, z/D) planes at different crosswise co-
ordinates (y/D). CFD profiles are compared with PIV and Cobra meas-
urements indicated with markers for CH and CY gauges, respectively.
In the first case their absolute difference (
ΔU
) is also reported, while
for the Cobra measurements the uncertainty bars are depicted. For both
simulation and WT results the term Uref indicates the freestream velocity,
while Umag and Uz indicate the magnitude and vertical component of flow
velocity, respectively. In the figures, a photograph of each gauge collector
is inserted, colored black for the CH gauge and gray for CY gauge and the
projection of the edges and the center of the collector are indicated with
dashed and dash-dot lines, respectively.
Validation of the performed simulations was obtained in the WT us-
ing PIV and Cobra probe measurements for the CH and CY gauges,
respectively.
A comparison between PIV measurements and CFD longitudinal profiles of the normalized magnitude of
the flow velocity at Uref=10m s−1, for the CH gauge, is reported in Figure3 and Figure4. The plots refer
to different elevations (z/D) and vertical sections, at y/D=0 and y/D=0.25, respectively, and the absolute
difference (
ΔU
) between the measured and calculated values is also reported. The maximum differences
occur at the minimum elevation where PIV measurements are available (z/D =0.23 and 0.33) and range
between 0.2 and 0.3. Close to the gauge collector, indeed, the effect of the
locally generated turbulence is more relevant, and the CFD model is less
accurate in simulating turbulence fluctuations.
For the CY gauge, four velocity profiles were sampled by employing a Co-
bra probe above the collector, along the longitudinal symmetry plane of
the gauge, in the (x/D, z/D) section at y/D=0. A comparison between the
Cobra probe velocity measurements (circles) and numerical results (solid
lines) is shown in Figure5. The longitudinal profiles were measured at
z/D=0.125 and z/D=0.25, while the vertical profiles at the upwind edge
and the center of the collector (x/D=−0.5 and x/D=0, respectively). In
all cases, the numerical profiles fall within the uncertainty of the probe
measurements, depicted with bars.
3.2. Observation of the Deflected Trajectories
For the two investigated gauges, a few sets of drops captured in the GVPM
when traveling above the gauge collector are shown in this section, and
the observed trajectories are commented according to the aerodynamic
response of the gauge body. Drop trajectories are depicted in the dimen-
sionless plane (x/D, z/D), where the gauge collector is centered in (0, 0)
and the longitudinal coordinate, x/D, of the drop releasing position is
fixed, while its elevation, z/D (assumed positive downward), varies with
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Figure 3. Comparison between simulated velocity profiles (continuous
lines) and Particle Image Velocimetry measurements (markers) of the
normalized magnitude of flow velocity (Umag/Uref ) at Uref=10m s−1 and at
different elevations along the central plane (y/D=0) (top panel) and their
absolute difference
ΔU
(bottom panel) for the chimney gauge.
Figure 4. Comparison between simulated velocity profiles (continuous
lines) and Particle Image Velocimetry measurements (markers) of the
normalized magnitude of flow velocity (Umag/Uref ) at Uref=10m s−1 and
at different elevations along the plane y/D=0.25 (top panel) and their
absolute difference
ΔU
(bottom panel) for the chimney gauge.
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the wind speed. In the legend, the prefix in the coding of each trajectory indicates the name of the gauge
under test (G for GeonorT200B© and L for Lambrecht Rain(e)H3©).
Overall, the experimental campaign in the WT resulted in the capturing of 82 trajectories of drops released
between z/D=−0.05 and z /D=−0.7 above the CH gauge, at Uref=8.86–13.6m s−1, and 106 trajectories of
drops released between z/D=−0.18 and z /D=−0.7 above the CY gauge at Uref=8.9–13.1m s−1. For both
gauges, drop trajectories were shot at 10 and 1,000 fps.
Nineteen pairs of observed drop trajectories, for the two investigat-
ed gauge geometries, allowed to verify the repeatability of the exper-
imental setup as demonstrated in the work of Cauteruccio, Brambilla,
etal.(2021).
Two sample sets of drop trajectories shot at 1,000 and 10 fps are shown
in Figure6 (left and right panel, respectively), as observed above the col-
lector of the CY and CH gauges at Uref=12.5m s−1 and Uref=11.4m s−1,
respectively. The particle-fluid interaction above the collector of the
gauges is responsible for a significant deviation of the trajectories, and
this can be observed here for all trajectories when traveling beyond the
upwind edge of the collector (x/D = −0.5). In both cases, a few undis-
turbed trajectories aiming at entering the collector close to the downwind
edge (x/D=0.5) overtake its rim and fall outside of the gauge.
The estimated undisturbed trajectory is added in the top panel of Fig-
ure7 (dashed line) for one sample drop traveling above the CY gauge
at Uref = 12.5 m s−1. In this case, the observed trajectory starts detach-
ing from the undisturbed one when its longitudinal coordinate reaches
the upwind edge of the collector (at about x/D = −0.5), where the air-
flow updraft is most significant (as shown by Cauteruccio, Brambilla,
etal.,2021).
The observed drop trajectory was elaborated by linearly interpolating the
positions associated with the undisturbed part of the trajectory, while the
disturbed part was fitted with a third order polynomial. In Figure7 (top
panel), the undisturbed part of the observed trajectory is painted in dark
gray while the disturbed part is painted in light gray and the interpolation
curves are marked with dots. The threshold between the undisturbed and
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Figure 5. Comparison between simulated velocity profiles (continuous lines) and Cobra probe velocity measurements
(circles with uncertainty bars) of the normalized magnitude of flow velocity (Umag/Uref ) at Uref=10m s−1 in the central
plane (y/D=0). Two longitudinal profiles at different elevations z/D (left-hand panel) and two vertical profiles at the
upwind edge (x/D=- 0.5) and at the center (x/D=0) of the collector (right-hand panel) are shown for the cylindrical
gauge.
Figure 6. Sample sets of drop trajectories shot at 1,000 (left) and 10 (right)
fps, as observed above the collector of the cylindrical and chimney gauges
at Uref=12.5m s−1 and Uref=11.4m s−1, respectively.
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disturbed part of the trajectory was obtained by adopting a trial-and-error procedure with the objective to
ensure the continuity of the slope curve (dz /dx) obtained as the first derivative of the fitted trajectory (Fig-
ure7, bottom panel).
Two drop trajectories, identified with the names G8 and G9, traveling above the collector of the CH gauge at
Uref=10.2m s−1 are depicted in Figure8. The initial elevation (z/D) of the two drops is not much different.
The initial, undisturbed part of the slope curve reveals that the two drops have a similar size, while the drop
starting at a higher elevation is deviated a bit later following the airflow pattern. The difference between the
observed and undisturbed trajectories, red markers with scale on the right-hand axis, is larger in the second
half part of the collector where the two drops are dragged beyond the gauge, resulting in some undercatch.
3.3. Validation of the Lagrangian Particle Tracking Model
The validation of the LPT model was obtained by comparison between observed and simulated trajectories.
In the numerical model the initial conditions, normalized position (x/D and z/D) and velocity components
(u and w [m s−1], the latter assumed positive downward), of the simulated trajectories were set consistently
with the WT observations. CFD airflow velocity fields were rescaled according to the free-stream velocity
value used in the WT. The initial velocity components were set equal to the mean values of the three to five
initial positions of each drop as shot by the camera, to avoid the noise due to the uncertainty in the initial
positions. The drop diameter, d, which has a major role in the calculation of the drop trajectory by affecting
p
Re
and therefore
D
C
, is obtained here as a calibration parameter for each trajectory, since the drop releasing
mechanism and the acquisition system cannot provide sufficient accura-
cy in the assessment of the drop size, while the use of other non-invasive
drop size detectors was made difficult by the operating conditions in the
WT.
A subset of about 25 observed drop trajectories is compared with the sim-
ulated ones in this section to support the validation phase. They were
chosen in order to cover a variety of wind speed, drop size, initial drop
velocity and position for each gauge geometry. The initial conditions of
the nine drop trajectories visualised in this section and their estimated
drop diameter are listed in Table1.
The observed (circles) and simulated (solid line) patterns of the drop tra-
jectory identified with the name G2, are compared in Figure9. The max-
imum difference between the vertical positions (z in mm), computed at
each normalized longitudinal coordinate (x/D) of the observed trajectory,
arises at the upwind edge of the collector and is about 1.2mm. This dif-
ference is comparable with the drop size (see Table1), therefore with the
uncertainty in the assessment of the drop position, identified as a bright
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Figure 7. Observed (circles) and undisturbed (dashed line) drop trajectory above the collector of the cylindrical gauge (top panel) at Uref=12.5m s−1, and the
associated slope curves for both trajectories (bottom panel).
Figure 8. Comparison of two drop trajectories (circles) having similar size,
traveling above the collector of the chimney gauge at Uref=10.2m s−1,
together with the associated undisturbed trajectories (dashed lines).
The associated slope curves (scale on the right-hand axis) are shown
with colored solid and dashed lines for the disturbed and undisturbed
trajectories, respectively. Red markers represent the difference between
the observed and undisturbed trajectories in terms of normalized vertical
coordinates (scale on the right-hand axis).
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moving object in each frame. The calculated horizontal acceleration of
the drop, normalized with the one experienced in the initial undisturbed
part of the trajectory, is also shown (scale on the right-hand axis). Con-
sistently with the PIV airflow velocity fields, the drop significantly accel-
erates when traveling above the upwind part of the collector, where the
airflow is indeed accelerated, until crossing the separation layer between
the airflow recirculation and accelerated zones, when it starts decelerat-
ing abruptly toward the downwind edge of the collector.
The good repeatability of the trajectories of very similar drops in the WT
(see their estimated size in Table1) is shown in Figure 10. By injecting
drops of the same size in the WT, the observed trajectories are indeed very
close to each other, and they experience very similar deviations above the
collector. Moreover, simulated trajectories show that the LPT model is
able to replicate even the small variations due to slight differences in the
initial conditions about the drop velocity.
The observed drop trajectories G8 and G9, already shown in Figure8, are
compared with the simulated trajectories in Figure11. As already noted,
the two drops have the same size; this assumption is confirmed by the obtained numerical trajectories
because the optimal agreement between the observed and simulated trajectories is reached by setting the
drop diameter equal to one millimeter. Again, the difference between observed and simulated trajectories
is comparable with the uncertainty in the assessment of the drop position, given the dimension of the drop
(see Table1) and the image resolution. The vertical acceleration of the drops (az) obtained from the sim-
ulation, normalized with the one experienced in the initial undisturbed part of the trajectory, is depicted
with dashed lines: the two drops accelerate when reaching the upwind edge of the collector, due to the
updraft, and then decelerate. This behavior is in line with the measured PIV velocity field where, beyond
x/D= −0.25, the updraft zone is always located above the normalized elevation |z/D|= 0.2 and the two
drops are fully immersed in the recirculation zone.
Observed and simulated patterns are depicted in Figure12 for a pair of drop trajectories (named L97 and
L100) having different drop size (d=0.7 and 0.9mm) but being released at the same initial position. As
reported in Table1, also the values of the initial velocity components are very similar. The smaller drop has
a lower slope and is maintained at a higher elevation along the entire trajectory. As revealed by the PIV ve-
locity field, this is due to the persistence of updraft velocity components
above |z/D| = 0.25 within the limits of the collector, while below this
vertical coordinate the separation layer occurs, and downward vertical
velocity components arise.
Validation of the coupled CFD and LPT approach was obtained after nu-
merically simulating about 25 trajectories of drops released in the WT
experiment. A synthesis of the validation performance is reported in Ta-
ble2. The maximum, mean and median difference, dz, between the verti-
cal coordinates along each observed and simulated trajectory, normalized
with the estimated drop diameter, d, were calculated as suitable perfor-
mance parameters. For each of them, the maximum, minimum, mean
and standard deviation values obtained over the set of all trajectories
used in the validation exercise are listed in Table 2. The same statistics
are included for the root mean square difference between the observed
and simulated vertical coordinates along each trajectory.
The validation was satisfactory since the mean of the maximum normalized
differences between the simulation and the observed trajectory is about uni-
ty, with a low standard deviation (the coefficient of variation is about 0.4).
Also, the mean and median values of dz are very similar, showing a sym-
metrical spread of these differences around the perfect agreement, which
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ID Wind (m s−1)x/D z/D u (m s−1) w (m s−1)d (mm)
G2 10.2 −1.259 −0.690 4.286 0.952 1.2
G4 10.2 −1.257 −0.523 4.140 1.104 1.0
G5 10.2 −1.257 −0.523 4.122 1.122 1.0
G8 10.2 −1.247 −0.455 4.048 1.190 1.0
G9 10.2 −1.256 −0.477 3.968 1.190 1.0
L84 13.1 −1.280 −0.349 5.571 0.667 0.7
L86 13.1 −1.293 −0.343 5.801 0.602 0.7
L97 13.1 −1.392 −0.389 5.855 0.482 0.7
L100 13.1 −1.379 −0.393 5.667 0.524 0.9
Table 1
WT Flow Velocity, Initial Coordinates and Velocity Components for the
Simulated Drop Trajectories and the Resulting Drop Diameter
Figure 9. Observed (circles) and simulated (solid line) drop trajectories
above the collector of the chimney gauge at Uref=10.2m s−1. The
difference dz (mm) between the observed and simulated vertical
coordinates of the drop trajectories (red crosses) at each normalized
observed longitudinal coordinate (x/D) is reported (scale on the right-hand
axis), together with the numerical longitudinal acceleration (ax) of the
drop (dashed line).
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suggests quite a random nature of the error. Finally, the RMSD is very low, always below 10−3, indicating an
overall good agreement for all pairs of simulated and observed trajectories.
4. Discussion
Although the experimental conditions implemented in the WT tests were forcedly different from reality
(constant and low turbulence airflow), and the initial conditions of the drops at their releasing position were
different from those expected in the natural environment (null horizontal and vertical velocity instead of
the free-stream and terminal velocity, respectively), the performed validation of the coupled CFD and LPT
approach on a physical full-scale model in the WT supports its application in realistic simulation scenarios.
The diameter of drops generated in this work ranges between 0.7 and 1.2mm. Although they do not span
over the entire range of the typical rain drop size in nature, such drops account for about 27%–33% of the
total number of drops and 37% to 20% of the total water volume, in the observed Drop Size Distribution
(DSD) of real rainfall events for rain intensity classes from light (<1mm/h) to intense (>20mm/h) events
(see Caracciolo etal.,2008). Most of the remaining drop would have a smaller diameter.
The generated drops are also assumed to be spherical, and the associated drag coefficient used in the sim-
ulation is that typical of spherical drops, although large drops are oblate in nature due to the resistance of
air to the falling movement of the drop. Drops start to be significantly oblate at a diameter slightly larger
than 2mm (axis ratio b/a=0.90 according to Beard & Chuang,1987). Drops smaller than 2mm account for
about 99%–97% of the total number of drops and for 85%–62% of the total water volume, depending on the
same rainfall intensity classes reported by Caracciolo etal.(2008). Therefore, the performed experiments
are representative of most part of the DSD of real rainfall events and, most importantly, precisely of that
portion of the DSD that is strongly influenced by the aerodynamic behavior of the gauge (large drops are
more inertial and do not change their trajectory significantly in windy
conditions).
The performed CFD simulations confirmed previous literature results
(e.g., Cauteruccio,2020; Colli etal.,2018): the airflow accelerates above
the collector of the investigated gauges and significant updraft is obtained
just in front of the gauge collector and above it. The region of maximum
acceleration for the CH gauge shows higher values and is larger and more
dispersed upward if compared with the aerodynamic response of the
CY gauge. The maximum normalized updraft Uz/Uref occurs above the
upwind edge of the collector and, for example, at z /D=0.125 it equals
0.65 and 0.50 (against the expected null value) for the CH and CY gauge,
respectively. These airflow features are the most influential on the hy-
drometeor trajectories, which are deflected upward due to the updraft
and tend to be dragged beyond the collector when falling through the
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Figure 10. Pairs of drops having approximately the same size traveling above the collector of the chimney gauge at Uref=10.2m s−1 (left-hand panel) and
cylindrical gauge at Uref=13.1m s−1 (right-hand panel). Observed (circles) and simulated (lines) trajectories are depicted for the two pairs of drops.
Figure 11. Comparison of two simulated and observed trajectories for two
drops traveling above the collector of the chimney gauge at Uref=10.2m s−1,
together with the simulated profiles of their normalized vertical
acceleration (scale on the right-hand axis).
Water Resources Research
accelerated zone, where the horizontal velocity is larger than the undis-
turbed wind speed.
For the CH gauge the validation of CFD simulation results was obtained
by comparison with PIV measurements. An overall good agreement
of the simulated profiles with measurements was obtained. The maxi-
mum absolute differences (
ΔU
) obtained at the minimum elevation
(z/D=0.23) are due to the coarse discretization of the measured spatial
domain, which introduces a smoothing effect on the measured flow field.
Moreover, close to the gauge, measurements are still slightly affected by
the reflection of the laser beam on the gauge rim, partially concealing the
passive tracer from detection despite a mask was implemented to reduce
such effect.
For the CY gauge the numerical profiles were compared with Cobra
measurements. In all cases the velocity profiles fall within the uncertain-
ty of the probe measurements confirming the good quality of the adopted
CFD setup. The adoption of two different WT approaches to validate the
CFD setup can be considered as a strong point of the present work.
The video shooting of the deviated trajectories in the WT allowed clear visualization of the wind-induced
undercatch by showing that some drops actually fall outside instead of inside of the collector, contrary
to what would be expected by following their undisturbed trajectory. Validation of the coupled CFD and
LPT approach was obtained by comparing simulated and observed drop trajectories under the same initial
and boundary conditions as demonstrated by the statistics of the performance parameters summarized in
Table2.
Note that the LPT model is fully deterministic, therefore there would be limited added value in validating
the model with a large number of very similar trajectories. The chosen trajectories are on the contrary
representative of different drop dynamics due to the varied initial, microphysical and boundary conditions.
5. Conclusions
Previous works on wind-induced errors mostly concentrated on field studies (see e.g., Buisán etal.,2017
and Kochendorfer etal.,2017 for both liquid and solid precipitation) based on the comparison of measure-
ments obtained from shielded and unshielded gauges. Adjustment curves (also termed transfer functions)
are usually derived from field data alone, assuming some gauge/windshield configuration as a reference.
Limitations of the empirical approach include the high variability of the hydrometeor microphysical char-
acteristics in precipitation events (Thériault etal.,2012), as well as the possible wind-induced biases associ-
ated with the reference configuration (Thériault etal.,2015). The resulting large spread of field data around
the interpolating curves suggests that important driving factors are understated, such as precipitation inten-
sity and/or the particle size distribution, as recently shown by Colli etal.(2020).
The present work overcomes these existing gaps, shedding additional light on the wind exposure problem,
with results that can be used operationally to adjust precipitation measurements obtained in windy condi-
tions. Indeed, the WT validation of the numerical approach based on CFD and LPT simulations supports
its use as the theoretical basis for the interpretation of the wind-induced
bias of field measurements obtained from shielded and unshielded pre-
cipitation gauges. Field measurements from suitable test sites, equipped
with reference gauges in the appropriate configuration, remains essential
to provide the real-world test bench and calibration basis needed to con-
firm the parameterization adopted (e.g., for the drag coefficient) in the
theoretical approach.
Typical applications include the numerical calculation of the collec-
tion efficiency of precipitation gauges having different outer geometries
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Figure 12. Observed (circles) and simulated (lines) drop trajectories
for two drops of different size, released at the same initial position and
traveling above the collector of the cylindrical gauge at Uref=13.1m s−1.
Max (dz/d) Mean (dz/d) Median (dz/d) RMSD
Max 2.1492 1.0444 1.2154 0.000812
Min 0.1871 −0.4230 −0.4946 0.000213
Mean 1.0968 0.0332 0.0337 0.000429
Std dev 0.4351 0.3514 0.3905 0.000168
Table 2
Validation Statistics for the Selected Performance Parameters
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(based on suitable assumptions and/or ancillary measurements about the hydrometeor characteristics, drag
coefficient and drop size distribution). Adjustment curves for the wind-induced bias of precipitation meas-
urements can be therefore derived to be used operationally for correcting the raw measurements (Cauter-
uccio & Lanza,2020).
Also, this work may help investigating the propagation of measurement biases into the modeling of hydro-
logical processes, especially in the field of water resources assessment, by validating a suitable simulation
framework. Fully validated simulations are indeed precious to quantify the impact of wind-induced errors on
the estimation of rain fields used as an input to hydrological models operating at the natural catchment scale.
Additionally, knowledge of the wind-induced biases of ground-based measurement instruments supports a
better understanding of the reliability of remotely sensed estimates of the rain field from satellite sensors,
which provide the necessary information about areal precipitation over large regions, and of the uncertain-
ty of radar-based rainfall retrieval.
Both such aspects were the focus of an Italian national project entitled “Reconciling precipitation with run-
off: the role of understated measurement biases in the modeling of hydrological processes,” which raised
the need for the present research.
Data Availability Statement
The coordinates of the observed drop trajectories used in this work are available online at: http://www.
precipitation-biases.it/Drop-Trajectories-WRR.php.
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... In the most recent works of Cauteruccio et al. ( , 2021b and Nešpor and Sevruk (1999), WT measurements of the flow velocity were obtained by employing multi-hole pressure probes located in selected positions above the investigated gauge geometries, at different wind speeds, with the objective to validate numerical CFD simulations. ...
... Water drops were released in the WT flow upstream the gauge and their trajectories were captured with a high-speed camera in the vertical 2-D plane centered on the longitudinal symmetry axis of the gauge collector. The experimental setup is described in detail in Cauteruccio (2020) and Cauteruccio et al. (2021b). ...
... The maps confirm previous literature works (Colli et al., 2016;Colli et al., 2018) about the scalability (low Reynolds dependency) of the airflow fields, except for the chimney-shaped gauge for undisturbed wind velocity, U ref , between 5 and 10 m s − 1 , as detailed below. In addition, local velocity flow measurements previously obtained at the University of Genova, and used to validate CFD airflow simulation results (Cauteruccio et al., 2021b), show that the normalized velocity components are fairly scalable, especially in the range between 10 and 20 m s − 1 . An example of the low Reynolds dependency of the profiles of the normalized vertical flow velocity, U z /U ref , along the central stream-wise symmetry plane above the gauge collector is reported in Fig. 1, for the three outer geometries investigated in this work. ...
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... The system uses a high-resolution camera (Sony with two flashes, which are triggered three times in a very short sequenc ond intervals) to capture three images of each drop in flight within a s Figure 5). The timing for the activation of the speedlights and the openi shutter are defined based on a numerical model of the drop vertical accel [13]. To verify the size and fall velocity of the generated drops just above the sensing area of the instrument under test, a photogrammetric device is included in the drop generator assembly (see Figure 4). ...
... The system uses a high-resolution camera (Sony a6100) equipped with two flashes, which are triggered three times in a very short sequence (at 4.2 millisecond intervals) to capture three images of each drop in flight within a single picture (see Figure 5). The timing for the activation of the speedlights and the opening of the camera shutter are defined based on a numerical model of the drop vertical acceleration in still air [13]. To verify the size and fall velocity of the generated drops just above of the instrument under test, a photogrammetric device is included in th assembly (see Figure 4). ...
... The system uses a high-resolution camera (Sony with two flashes, which are triggered three times in a very short sequenc ond intervals) to capture three images of each drop in flight within a si Figure 5). The timing for the activation of the speedlights and the openi shutter are defined based on a numerical model of the drop vertical accel [13]. tween 1.5 and 5 mm, respectively. ...
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... We started from the CFD Water 2020, 12, 3431 5 of 15 simulations (see Figure 1) partially published in the work of [13] for various wind speeds (U re f = 2, 5, 7, 10, and 18 m s −1 ). The Lagrangian Particle Tracking (LPT) model used by [9] for solid precipitation was modified by [24] to introduce drag coefficient equations suitable for liquid precipitation. These were derived for various ranges of the particle Reynolds number among those proposed in the literature by [7], and formulated starting from data published by [25,26]. ...
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The introduction of automatic instruments for precipitation measurements may have resulted in some differences in results from those taken by previous manual instruments. In the station network of the Czech Hydrometeorological Institute (CHMI) this replacement process began in the 1990s, when precipitation measurements taken by the METRA 886 rain gauge gave way to automatic tipping‐bucket rain gauges, the MR3H and later the MR3H‐FC. Continuous simultaneous measurement by both types of rain gauge at the Brno‐Žabovřesky and Ostrava‐Poruba stations in the 2000–2019 period enable differences in recorded daily precipitation totals to be compared. Only those days upon which at least one of the two types of rain gauge recorded precipitation are analysed herein. Although the highest proportion of differences in daily precipitation totals lies between −0.1 and 0.1 mm, there is a distinct tendency towards higher totals in positive deviations as measured by the manual METRA 886, that is, tipping‐bucket rain gauges generally record lower precipitation totals then the ‘standard’ manual rain gauge (the MR3H‐FC undervalues totals to a greater extent than the MR3H). The design and construction of tipping‐bucket rain gauges are reflected in overvaluation of precipitation days with smaller totals and undervaluation of days with high totals when compared with the METRA 886. Series combining measurements by METRA 886 and by tipping‐bucket rain gauges (as held in the CHMI database) and series measured by the METRA 886 alone were created, homogenized and analysed in terms of long‐term fluctuations and annual variations. Homogenisation of precipitation series based on combined measurements leads to generally undervalued totals compared with those measured only by the METRA 886. Results are discussed with respect to other similar articles, sources of errors in both types of precipitation measurement, and with regard to the homogenisation of precipitation series. Fluctuations in differences of daily precipitation totals measured simultaneously by METRA 886 and automatic rain gauges, MR3H (red) and MR3H‐FC (blue), at the Brno‐Žabovřesky and Ostrava‐Poruba stations in the January 1, 2000–December 31, 2019 period.
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