Introduction
Processes acting during the short travel of rain through the atmosphere from
the cloud base to the surface have a maybe surprisingly large relevance for
several atmospheric phenomena. The two-phase system of rain and vapour is in
constant molecular exchange. In addition, in unsaturated conditions, rain
partially evaporates, leading to latent cooling of the air and moistening of
the boundary layer. Surface rainfall totals may be substantially reduced in
cases of strong evaporation , and in the case of
convection in the Sahel, large evaporation-driven cold pools can trigger
extensive dust storms known as haboobs . In
mid-latitudes, cold pool formation influences low-level moisture convergence
and thereby the progression and organization of convective systems
.
Measurements of these so-called below-cloud processes
are challenging. Radiosonde profiles provide instantaneous snapshots of a
vertical profile of humidity and temperature, but do not capture
precipitation rates, and are expensive when deployed at high frequency.
Precipitation radar can continuously provide vertically resolved spectra of
raindrops, but does not provide information about relative humidity and
temperature, which are necessary to reasonably quantify precipitation
evaporation . Other remote-sensing systems, such as Raman
water vapour lidar , Fourier transform infrared radiometers
and passive microwave radiometers
provide vertical profiles of humidity, but are strongly
attenuated during precipitation.
As a consequence of the lack of sufficient observations, model parameters
that represent the interaction of falling raindrops with the air column below
the cloud base are poorly constrained. Errors in the representation of this
process diminish the model forecast quality due to its impact on the rainfall
amount and the dynamics of weather systems. This issue becomes even more
relevant as common weather prediction models, such as COSMO
, WRF , or AROME
progress to resolution beyond the grey zone. At horizontal resolutions below
about 10 km precipitation is commonly implemented as a prognostic variable,
and convective updrafts, downdrafts, and the formation of cold pools are
partly resolved at the grid scale. These modelling challenges provide an
additional motivation to better understand below-cloud processes.
In this context, stable isotopes of water vapour and rain are useful to
investigate below-cloud processes. Stable water isotopes are natural, passive
tracers that reflect the phase-change history of water. The stable isotope
composition is quantified using isotope ratios, defined as the concentration
of the rare (heavy 2H1H16O or
1H218O) over the abundant (light
1H216O) isotope, e.g.
2R=[2H1H16O][1H216O].
Most studies use the more intuitive δ notation
, which expresses the heavy isotope
composition of a reservoir in terms of relative deviation of R from an
internationally accepted standard:
δ=Rsample-RstandardRstandard⋅1000‰.
A δ-value is defined for both heavy over light isotope concentrations
(δ2H and δ18O) and generally indicated in
per mil (‰) relative to Vienna Standard Mean Ocean Water
VSMOW2;. As heavy isotopes preferentially condense
due to their larger mass, air subject to rainout subsequently loses heavy
isotopes. The increasing depletion with increasing rainout along the
trajectory of an air parcel can be approximated by the Rayleigh distillation
model . Air at higher altitudes and
latitudes has on average experienced more cooling and rainout and is thus
increasingly depleted of heavy isotopes, reflected in more negative
δ-values. As precipitation forms from this vapour depleted
in heavy isotopes, temperature-dependent fractionation will lead to a
relative enrichment of heavy isotopes in the hydrometeors. Typically, though,
precipitation δ-values will still be depleted relative to the standard
ocean water VSMOV2, as expressed in negative δ-values. As raindrops
fall through the air column, they continuously exchange water molecules with
the surrounding vapour. This exchange is particularly relevant if the air
column is at or near saturation. Thermodynamics will direct this exchange
towards isotopic equilibrium according to ambient temperature. This process
is termed equilibration and only occurs when the precipitation is
liquid.
In unsaturated conditions, a net transfer of water molecules from the drops
to the surrounding air occurs. In addition to the equilibrium fractionation
that happens during this transfer, the slower diffusion of the heavy
molecules 2H1H16O and 1H218O causes
non-equilibrium or kinetic fractionation. Thereby, lower relative humidity
leads to more intense non-equilibrium fractionation. The second-order
parameter d-excess
(d=δ2H-8⋅δ18O) is sensitive to such
non-equilibrium conditions, since 2H1H16O reaches
isotopic equilibrium faster than 1H218O
. The d-excess quantifies the difference in
2H1H16O and 1H218O from their ratio
expected during equilibrium conditions as a measure of non-equilibrium
. Evaporation of rain in unsaturated conditions causes a
decrease in d-excess in rain and consequently an increase in d-excess in
the surrounding air. Further parameters critically influence this process,
such as the drop size distribution , below-cloud relative
humidity , the height of the melting layer, the height of
the cloud base , and vertical wind velocity. Thus, isotopes
reflect the conditions that raindrops experience below the cloud, but in a
convoluted way that often renders interpretation cumbersome.
If stable isotopes are to be used
for constraining below-cloud processes, such factors need to be disentangled.
Previous studies often investigated only the condensed part of the two-phase
system
e.g..
These studies sampled rain in high temporal resolution and gave sometimes
contrasting explanations for the observed short-term isotopic variations. For
example, and investigated an
atmospheric river event in California and disagreed on whether below-cloud
processes or changes in the formation height caused the variations they
observed. Since vapour and rain are in continuous exchange, measuring one
without the other makes meaningful interpretation difficult. This is
especially the case in situations dominated by advection, for example
cold-frontal rain. There, the isotopic evolution of rain is a combined signal
of a changing air mass and in-cloud processes, below-cloud equilibration with
progressively depleted vapour as the front progresses, and rain evaporation
. Simultaneous observations of vapour and precipitation
are necessary to distinguish these processes and quantify below-cloud
processes. showed for a mid-latitude rain event that
combined observations of stable isotopes in vapour and rain more clearly
reveal the influence of below-cloud processes and the structure of the
precipitation system.
Thus, joint observations of the stable isotope composition of vapour and
precipitation at ground level are valuable recorders of the convoluted
influence of several factors and processes. However, extracting the
contribution of individual factors is challenging. Here we propose a new set
of measures to quantify the influences of equilibration and evaporation on
the isotope composition of near-surface vapour and rainfall. To this end, a
new interpretative framework is introduced, which allows us to determine the
leading below-cloud processes during a precipitation event. This framework is
used here to interpret both high-resolution isotope measurements from cold
fronts in central Europe and results from idealized simulations with a
below-cloud interaction model. Section 2 provides information about the
measurements and the below-cloud model. The stable water isotope measurements
during a cold frontal passage are presented in Sect. 3. Section 4 introduces
the new interpretative framework with an idealized model, before the
observations are discussed in the new interpretative framework in Sect. 5.
Finally, we provide our main conclusions in Sect. 6.
Data and methods
Isotope measurements
Stable water isotopes in ambient water vapour were measured on a tower
building at the Institute for Atmospheric and Climate Science of ETH Zurich
(47.38∘ N, 8.55∘ E; 510 m a.s.l) between 9 October and
27 November 2015 with a cavity ring down spectrometer (L1115-i, Picarro Inc,
USA). Ambient air was directed to the analyser through a 10 m PFA tubing
heated to 70 ∘C that was flushed by a bypass pump (HN022AN.18, KNF
Neuberger, Germany) with a flow rate of 9 L min-1
. The isotopic analyser was calibrated
twice a day at ambient humidity levels using a commercial setup (Standards
Delivery Module A0101 and Vaporizer V1102-i, Picarro Inc. USA). Two
laboratory standards bracketing the composition of typical ambient values in
ambient vapour (Standard 1: δ2H=-75‰,
δ18O=-10‰; Standard 2:
δ2H=-247‰,
δ18O=-43‰) were provided to the analyser for
10 min each. The first 5 min and last 30 s of the calibration, as well as
the 10 min ambient air measurements after each calibration were discarded to
avoid the influence of memory effect on calibration and the final isotope
data. Raw measurements were corrected with an average calibration function
from all calibration runs of the measurement period. Frequent gaps in the
calibration make this time-independent calibration function more robust
compared to the usual linear interpolation between subsequent calibration
runs. The thereby neglected shorter-term drift leads to an increased
uncertainty of the calibrated measurements. The 5 s measurements of the
instrument were transformed to 10 min average values, which have an average
uncertainty after calibration of 1.23 ‰ for δ2H,
0.42 ‰ for δ18O, and 3.6 ‰ for d-excess.
For more details about the vapour isotope measurements, see .
At the same location, rain was manually sampled during selected events with a
simple rainfall collector. The collector consists of a PTFE funnel of 15 cm
diameter, which points into a 20 mL glass vial. Each sample was collected in
a separate vial, which was immediately closed after retrieval from the
sampler to avoid evaporation after sampling. A default sampling interval of
10 min was applied, which was shortened to 5 min during intense rain, or
prolonged up to 30 min if the sampled amount was not sufficient for
analysis. The approximate sample amount was recorded but not used to
determine rain rates. The samples were analysed for their isotopic
composition in the laboratory with a cavity ring down spectrometer (L2130-i,
Picarro Inc., USA) operating for liquid sample analysis . The
average uncertainty of the calibrated liquid samples is 1.25 ‰ for
δ2H, 0.24 ‰ for
δ18O, and 1.43 ‰ for
d-excess. In this study, 86 continuous rainfall samples collected during a
cold frontal passage on 20 November 2015 are presented.
Also measured at the same location were temperature, humidity, wind speed and
direction, and precipitation amount and intensity. These parameters were
obtained at a 10 min interval from different meteorological sensors (Thygan
VTP37 and wind gauge WN37, meteolabor AG; tipping bucket rain gauge
7051.1000, Theodor Friedrichs & Co.) on the rooftop with a measurement
distance of less than 5 m to the ambient air inlet of the isotopic analyser.
Equilibrium vapour from precipitation
Falling rain and the vapour in the atmospheric column below cloud base
compose a two-phase system. The constant exchange of water molecules makes
the system evolve towards an equilibrium in the isotopic composition of both
phases. In isotopic equilibrium, there is no net exchange of isotopologues
between the phases. Temperature-dependent isotopic fractionation between
light and heavy isotopes however creates different isotopic compositions of
the liquid and vapour phases in equilibrium:
Rl=αv→lRv,
which can be equivalently expressed in δ-notation as
δl1000+1=αv→lδv1000+1.
Here, subscripts “l” and “v” denote the liquid and vapour phase,
respectively, and αv→l is the
temperature-dependent fractionation factor of the vapour to liquid phase
transition. At 20 ∘C, αv→l is
1.0850 for 2H1H16O/1H216O and
1.0098 for 1H218O/1H216O
.
We denote the difference due to fractionation between two phases in
equilibrium as equilibrium difference
Δl-v=δl-δv. Consider, for
example, the equilibrium difference for a vapour–liquid system, where the
liquid has a composition of δl=0 ‰ for both
δ2H and δ18O (A in Table ).
Δl-v for δ2H is 78.4 ‰ at
20 ∘C and 101.0 ‰ at 0 ∘C. Thus, equilibrium
fractionation for cold temperatures is stronger and leads to a larger
equilibrium difference of δ2H and δ18O. In
addition, these differences are smaller if the liquid is more depleted in
heavy isotopes. For a liquid with δ2H=-120‰,
Δl-v becomes 69.0 ‰ at 20 ∘C and
88.9 ‰ at 0 ∘C (B in Table ). The increase
in fractionation strength with decreasing temperature is stronger for
δ2H than for δ18O, which leads to a more
positive equilibrium difference for d towards colder temperatures. In
addition, d of vapour increases and hence the equilibrium difference
decreases if the liquid or solid is depleted in heavy isotopes. The
dependence of the equilibrium difference on temperature and isotopic
composition further complicates matters, in particular for the interpretation
of the d-excess .
The problem that the comparison of δ-values in precipitation and
ambient vapour is not straightforward can be overcome by comparing the
isotopic composition of ambient vapour with the equilibrium vapour from precipitation for δ-values and d, termed
δp,eq and dp,eq
. The equilibrium vapour from precipitation is
calculated as the isotopic composition of vapour that is in equilibrium with
rain at ambient air temperature. The direction of isotopic exchange then
becomes apparent directly from the difference between
δp,eq and δv for the
δ-values, and from comparing dp,eq and
dv for the d-excess. This substantially simplifies the
interpretation of the state of equilibrium in the liquid–vapour system. In
principle, it would also be possible to introduce in an analogous way an
equilibrium precipitation from vapour. We regard the concept of equilibrium
vapour as more intuitive below cloud base, and use it here.
In the following, we make use of the isotopic composition of the
equilibrium vapour from precipitation and denote differences between
ambient vapour at the surface and precipitation at any level in the column as
Δδ=δ2Hp,eq-δ2Hv,sfcandΔd=dp,eq-dv,sfc.
Calculated difference in isotopic composition of liquid
(Δl-v) or solid (Δs-v) in equilibrium with
a vapour of different isotopic composition. The fractionation factors of
are used for the calculations.
composition
Δl-v
Δl-v
Δs-v
of vapour
@ 20 ∘C
@ 0 ∘C
@ 0 ∘C
δ2H
-80.0 ‰
78.2 ‰
103.3 ‰
121.3 ‰
δ18O
-10.0 ‰
9.7 ‰
11.6 ‰
15.1 ‰
d
0.0 ‰
0.7 ‰
10.5 ‰
0.6 ‰
δ2H
-200.0 ‰
68.0 ‰
89.9 ‰
105.4 ‰
δ18O
-25.0 ‰
9.5 ‰
11.4 ‰
14.9 ‰
d
0.0 ‰
-8.4 ‰
-1.6 ‰
-13.4 ‰
A Δδ could also be defined for δ18O, which would
require an additional index for Δδ to discriminate between
δ2H and δ18O. Since information about
δ18O is already included in d, the notation is confined to
Δδ for δ2H. Note that a value of Δd=0
does not indicate the absence of non-equilibrium fractionation. It rather is
an indication that the ambient vapour and the equilibrium vapour of the
precipitation have experienced a similar degree of kinetic effects.
In the analysis below, we will use Δδ and Δd as measures
of the deviation of the vapour-precipitation system from equilibrium. For
instance, a negative value of Δδ indicates that precipitation is
more depleted in δ2H than ambient vapour, based on the
equilibrium difference at ambient temperature discussed above. It will be
shown that this results in a powerful, intuitive interpretative framework
(referred to as the ΔδΔd-diagram) to quantify physical
processes between the cloud base and the surface from highly resolved stable
isotope measurements in water vapour and precipitation. The interpretation of
this new diagram will be further substantiated with results from idealized
simulations with a below-cloud interaction model, introduced in the next
subsection.
Below-cloud interaction model
In order to support the interpretation of isotope measurements with our new
framework and to quantify the role of different processes, we apply a
one-dimensional below-cloud interaction model. The model simulates the
microphysical and isotopic interactions of a falling hydrometeor with the
surrounding air, as described in detail in Appendix and
. In this section, we lay out its general setup and
initialization.
The model consists of a single vertical column that extends from the ground
to the height where a single hydrometeor is introduced. The hydrometeor falls
through the column with its terminal velocity, grows or evaporates, changes
its temperature, and isotopically equilibrates with the surrounding vapour.
Isotope processes are parameterized following with
separate mass balance equations for all three isotope species
(Appendix ). Interactions with other hydrometeors
(collision and breakup) are neglected. Horizontal and vertical air motion are
also neglected; i.e. there is no horizontal advection into or out of the
column, and no updraft or downdraft. As output, the model yields vertical
profiles of the hydrometeor size and its isotopic composition.
Profiles of temperature, humidity, and the isotopic composition of the
surrounding vapour have to be provided to the model as input prior to the
initialization with rain. These initial profiles can be specified in two
ways: (i) based on measurements or simulations with isotope-enabled
atmospheric models such as COSMOiso,, or (ii) calculated
from the idealized (moist) adiabatic ascent of an air parcel from the surface
to the top of the model column with a Rayleigh fractionation process after
reaching saturation (Appendix ). The profiles are assumed
to be unaffected by the falling hydrometeor throughout the simulation. This
assumption only holds if a single hydrometeor is considered. When simulating
rain events during which many hydrometeors fall and subsequently affect the
surrounding air, the assumption becomes invalid over time. A remedy to this
problem would be to reinitialize the model regularly with updated profiles of
the surrounding air.
The hydrometeor size is defined as the equivalent liquid diameter,
which corresponds to the diameter of a spherical liquid drop with the same
mass as the hydrometeor. The model can be initialized with a pre-defined
hydrometeor size at the height of initialization. Alternatively, as used in
this study, the terminal diameter at the surface can be provided as input. In
this case, the hydrometeor size at the height of initialization is varied
iteratively until the target diameter at the surface is reached. To simulate
bulk precipitation, the model can be run (i) for all bins of a drop size
distribution, which are then used to calculate a mass and number-weighted sum
or (ii) for just one hydrometeor size, which approximates the drop size
distribution with a single diameter. This is represented by the mass-weighted
mean diameter Dm, which is obtained in this study from the rain
rate by assuming a Marshall–Palmer distribution.
The initial isotopic composition of the hydrometeor is determined by the
surrounding vapour at its initialization height. By default, formation via
the Wegener–Bergeron–Findeisen mechanism is assumed between 0 and
-23 ∘C. Optionally, a fraction of mass can be added that is formed
by riming of supercooled cloud droplets on the hydrometeor
(Appendix ). The hydrometeor is solid at
temperatures below 0 ∘C and melts instantaneously when its
temperature exceeds 0 ∘C. Although melting happens over a ∼300 m deep layer in reality , this is a valid assumption
considering that hydrometeors start to melt from the outside
and therefore expose their liquid fraction to the
surrounding vapour from the beginning of the melting process.
Cold frontal passage on 20 November 2015
We now apply the framework outlined above to data from a prolonged rainfall
period in northern Switzerland. High-resolution rain and vapour isotope
measurements reveal variations in the below-cloud processes during the event.
Meteorological situation
The local meteorology of this event was characterized by an extended front
over central Europe, which was the remnant of a cold front associated with a
decaying cyclone over the Gulf of Finland. The nearly zonally oriented front
passed Switzerland from a northerly direction during 20 November 2015, before
leading to the genesis of a new cyclone over the Gulf of Genoa on the
following day. The rainband associated with the cold front extended zonally
over a distance of about 400 km from Burgundy (France) across Switzerland to
the Lake Constance, with a distinct band of high rain intensity
(Fig. a). This intense rainband was embedded in a broader zone
with stratiform rain. Near Zurich, the frontal passage led to a decrease in
equivalent potential temperature (θe) at 850 hPa of more
than 12 K and to a veering of the wind from south-west to north-west
(Fig. b).
(a) Radar composite of surface rain intensity
from MeteoSwiss at 19:00 UTC 20 November 2015, when the surface front passed
over the measurement site. (b) Equivalent potential temperature (θe in K,
colour)
and horizontal wind (arrows) at 850 hPa from COSMO-2 analysis data at 19:00 UTC 20 November 2015.
The location of the measurement site at Zurich is indicated by a red and
green
cross, respectively.
Meteorological surface observations
An overview of selected surface measurements between 06:00 UTC 20 November
and 01:00 UTC 21 November 2015 is shown in Fig. . The local
2 m temperature (T; red line in Fig. a) remained roughly
constant during the first part of the event, with a slight increase before
14:00 UTC. At 19:00 UTC, when the surface front arrived at the measurement
location, a rapid drop of about 2.5 ∘C in 30 min was recorded. The
temperature gradually decreased further by about 3.5 ∘C between
20:00 and 22:00 UTC and remained constant thereafter, resulting in an
overall decrease in T of ∼6 K. Local relative humidity at 2 m (h;
blue line in Fig. a) varied between 75 and 85 % before the
frontal passage, and increased to values around 85–90 % thereafter.
The rain associated with this frontal event started in Zurich at 06:00 UTC
20 November and lasted until 03:00 UTC 21 November 2015. Most of the
precipitation appeared to be of stratiform nature. The total rain measured by
a rain gauge on the rooftop was 30.9 mm, whereof 27.5 mm fell during the
part of the event investigated here (07:00–23:30 UTC). The intensity varied
between 0 and 3 mm h-1, before increasing briefly to 10 mm h-1
as the surface front passed at 19:00 UTC (Fig. b). Thereafter,
the intensity remained relatively high compared to the period prior to the
frontal passage with an average of 3 mm h-1 until approximately
23:00 UTC, when it decreased to low values for the remainder of the event.
Between 12:00 and 18:00 UTC, sustained wind speeds occurred with values
between 5 and 10 m s-1, and therefore the rain intensity is likely
underestimated during this period due to the exposed location of the rain
gauge. A less exposed meteorological station (MeteoSwiss Station Zurich
Fluntern, at a distance of 1.3 km) recorded a total amount of rain of
38.3 mm at 1 m above ground level. For further analysis, we split the event
into a pre-frontal period until about 18:45 UTC (purple shading,
precipitation samples 1–54) and a post-frontal period thereafter (green
shading, precipitation samples 55–86).
According to two balloon soundings launched from the measurement site in
Zurich during the event, the height of the 0 ∘C isotherm decreased
from 2700 m a.s.l. at 16:30 UTC to 1500 m a.s.l. at 22:30 UTC during
the frontal passage (not shown).
Time series of observations in Zurich between 06:00 UTC 20 November and
01:00 UTC 21 November 2015. (a) Local temperature (T; red) and relative
humidity (h; blue) measured by the meteorological station. (b) Rain intensity
from the rain gauge (black). Blue bars indicate the average values for each rain
sample period. (c) δ2H of near-surface vapour (10 min averaged
δ2Hv; black line) and of the equilibrium vapour from
precipitation (δ2Hp,eq; blue bars). The width of
the blue bars denotes the period over which the rain samples were collected. (d) Same
as in (c), but for d. The calibrated uncertainties are
indicated by the shaded areas (hardly or not visible for δ2Hv
and δ2Hp,eq). Pre- and post-frontal periods are indicated
with purple and green bars, respectively.
Isotopic composition of vapour and rain
The 10 min averaged isotope values in surface vapour in Zurich were between
-265 ‰ and -105 ‰ for
δ2Hv (Fig. c, black line), and
between -35 ‰ and -14 ‰ for
δ18Ov (not shown). The vapour isotope
measurements exhibit an overall decrease of more than 160 ‰ for
δ2Hv during the entire event. A weak decrease
in δ2Hv around 08:00 UTC was followed by a
steady increase until 14:00 UTC. δ2Hv
decreased thereafter, and the decrease became steeper after 18:00 UTC,
before reaching a roughly constant minimum value at 23:00 UTC of about
-265 ‰. For dv, values increased from 5 ‰
to 20 ‰ during the event (Fig. d, black line). A
gradual increase by about 5 ‰ before the arrival of the surface
front was followed by a more rapid 10 ‰ increase in the 4 h after
the frontal passage at about 19:00 UTC, marked by a distinct spike of
5 ‰ in dv. Other short-term variations of
dv were within the uncertainty range (grey shading).
To identify the possible influence of below-cloud processes we now compare
the vapour isotope measurements with the precipitation, using the
above-defined metric of equilibrium vapour. The isotopic signals of vapour
(δ2Hv; black line in Fig. c) and
equilibrium vapour from the 86 rain samples
(δ2Hp,eq; blue bars in
Fig. c) exhibit a similar evolution during the whole event.
Differences are overall less than 23 ‰.
δ2Hp,eq is more variable and its
evolution is less smooth than for δ2Hv. After
an initial decrease with a subsequent increase similar to
δ2Hv,
δ2Hp,eq reaches two maxima at around
14:00 and 16:00 UTC, which coincide with low relative humidity and weak rain
intensity. It decreases afterwards until the end of the sampling period. The
decrease is particularly strong during the passage of the surface front and
during the second distinct temperature drop (after 20:30 UTC). The overall
evolution corresponds to a flat W-shape in the first part of the event until
16:00 UTC, and a strong decrease in the second part. This is similar to what
found for a cold front in an idealized extratropical
cyclone, but in our case without the increasing branch at the end, which may
have occurred during weak rain at the end of the event (not sampled).
The dp,eq varies around 0 ‰ before
19:00 UTC, and then increases markedly during the passage of the front with
values of more than 10 ‰ (Fig. d). Notably, negative
values of dp,eq occur during periods with weak rain
(e.g. around 08:30, 13:30, and 16:00 UTC). dv also increases
during the event, but less abruptly and with less variations than for
dp,eq, which exhibits a positive correlation with h
(Spearman ρ=0.88) and rain intensity (ρ=0.63). Smaller drops during
phases with weak rain and low relative humidity experience enhanced
evaporation, which decreases dp,eq.
The similar evolution of δ2Hv and
δ2Hp,eq in Fig. c
indicates that equilibration of rain with the surrounding vapour plays an
important role for the evolution of the time series. Alternatively, part of
the vapour sampled at the surface could have been transported downwards from
cloud formation levels by convective downdrafts. In the case analysed here,
this influence may be limited due to the mainly stratiform character of the
event. Nonetheless, it remains a principal challenge to identifying the
influence of below-cloud processes in joint observations of vapour and
precipitation. One example are signals from meso-scale meteorological
processes, such as the transition between air masses at the weather front. In
order to facilitate the interpretation of these measurements in terms of
below-cloud processes, we introduce in the next sections a new framework that
makes the involved physical processes more explicit.
One can also consider the effect of below-cloud processes on ambient vapour.
However, on short enough timescales (a hydrometeor falling from the cloud to
the ground), the effect on vapour can be neglected, since the amount of
vapour in a given air volume exceeds the amount of liquid or solid by far,
especially for the rain rates we measured (for the calculation, see
). The effect on vapour would only appear over a longer
time period. In the event we present here, a part of the gradual depletion of
vapour after 16:00 UTC could be caused by interaction with falling
precipitation or downward motion of the air, which introduces depleted
moisture.
Time series of (a) Δδ and (b) Δd of the
precipitation samples collected on 20 November 2015. The width of the blue
bars denotes the period over which the rain samples were collected. The calibrated
uncertainties are indicated by the shaded areas. Pre- and post-frontal periods are
indicated with purple and green bars, respectively.
It is apparent from Fig. c, d that the difference between
vapour isotope measurements and the equilibrium vapour for precipitation
varies systematically throughout the precipitation event. Their difference is
conveniently quantified by Δδ for δ2H
(Eq. ), and correspondingly by Δd for
δd (Eq. ). The time series of
Δδ for all precipitation samples from the frontal event varies
between -20 permil and 12 ‰ (Fig. a). For Δd, the time series shows negative values, except for the passage of the
front (Fig. b). Some rain samples are in equilibrium with
vapour for δ2H (Δδ≃0‰; e.g. at
15:00 UTC), for d (Δd≃0‰; at about 19:00 and
21:00 UTC), or for both (Δδ and Δd≃0‰; at
10:00 UTC). Other samples indicate the influence of below-cloud evaporation
with a positive Δδ and a strongly negative Δd (at about
14:00 and 16:00 UTC). Most post-frontal samples have a strongly negative
Δδ and a Δd close to zero, which indicates the
conservation of depleted δ2Hp,eq from
the cloud and incomplete equilibration with near-surface vapour. The
influence of rain evaporation also results in a negative correlation of
Δδ with h (ρ=-0.65) and rain intensity (ρ=-0.44). The
correlation with h is also strong for Δd (ρ=0.83).
Idealized simulations with a below-cloud interaction model
The systematic variation of Δδ and Δd throughout the
precipitation event motivates us to investigate the influence of
meteorological driving factors on these parameters using an idealized model
of below-cloud effects (Sect. ). To illustrate the
representation of below-cloud processes in this model, we in detail consider
the isotopic fractionation of falling precipitation in a set of reference
simulations and sensitivity experiments, before transferring the findings to
the measurements of the precipitation during 20–21 November 2015.
Results of the reference simulation of the single-column model. (a) Vertical
profiles of air temperature (green line) and relative humidity
over
liquid (solid blue line), obtained from the (moist) adiabatic ascent of an air
parcel from the surface with initial T0=12 ∘C and h0=75 %. The
relative humidity of the surrounding air with respect to the temperature of the
1 mm hydrometeor, denoted as effective relative humidity heff, is
shown as dotted blue line. (b) Hydrometeor mass relative to the initial mass at the formation height. The
coloured lines correspond to three hydrometeors that arrive at the surface
with an equivalent liquid diameter of 0.5, 1, and 2 mm,
respectively. (c) Isotopic
composition of hydrometeors and the surrounding vapour. Coloured lines show the
isotopic composition of the hydrometeors (δ2Hp, solid) and
the equilibrium vapour from the hydrometeors (δ2Hp,eq,
dashed). The black line indicates the composition of the ambient vapour (δ2Hv).
The letters mark locations that are referenced in the text. (d) Same as (c) but
for dp and dp,eq. Horizontal dashed and dotted black
lines in all plots mark the height of the 0 ∘C isotherm
and the height of the cloud base (CB), respectively.
Reference simulations
The model configuration consists here of a single-column model domain with a
surface pressure of 950 hPa, and extending from 500 m at the surface to
3500 m a.s.l. Time-constant vertical background profiles of temperature
T, relative humidity h, δ2Hv, and
dv are obtained from the moist adiabatic ascent of an air
parcel that is lifted from the surface with initial values of T0=12 ∘C, h0=0.75 (Fig. a, green and blue lines).
The background isotope profiles are obtained correspondingly from Rayleigh
fractionation during a moist-adiabatic ascent with a surface composition of
δ2Hv=-150 ‰ and
dv=10 ‰ (Fig. c, d, solid black
lines). Below cloud base (lifting condensation level) at 1030 m a.s.l.
(dotted horizontal lines), specific humidity and isotopic composition of the
vapour are constant, while h increases. Above cloud base, the air parcel
follows a Rayleigh fractionation process. Fractionation increases with
decreasing temperature and hence the rate of decrease in
δ2Hv becomes more negative with height. The
effect of condensation on the profile of dv (black line in
Fig. d) is small at low altitudes and only becomes apparent
in the uppermost 500 m of the domain, where dv starts to
increase. Note that this background state of the model is not affected by
evaporating droplets or other processes during the simulation.
Now, three hydrometeors representing typical drop sizes for mid-latitude rain
are introduced at the formation height at 3500 m a.s.l. The initial
diameters (0.56, 1.02, and 2.00 mm) have been calculated iteratively such
that the hydrometeors reach target diameters of 0.5, 1, and 2 mm when
arriving at the surface. The hydrometeors fall with an average terminal
velocity of 2.4, 4.2, and 7.0 m s-1, respectively, while growing in
supersaturated and shrinking in unsaturated conditions, as expressed by their
mass relative to the mass at formation height m/minit
(Fig. b). The saturation of the environment with respect to
the hydrometeor depends on the phase and the temperature of the hydrometeor,
quantified by the effective relative humidity heff of a 1 mm
hydrometeor (Fig. a, dotted blue line). The air layer between
formation height (3500 m) and the 0 ∘C isotherm (∼2250 m) is
saturated with respect to liquid water and supersaturated with respect to
ice. Therefore, solid hydrometeors grow due to heff>100 %.
The growth slows down as heff becomes smaller towards the
0 ∘C isotherm, but continues between the 0 ∘C isotherm and
the cloud base as hydrometeors fall into warmer air and retain a slightly
lower temperature than the environment. Finally, the hydrometeors fall into
sub-saturated air below the cloud base and start to evaporate. The decrease
in m/minit is fastest for the small hydrometeor
(Fig. b, blue line). Evaporation decreases the droplet
temperature, which leads to a higher heff than h below the
cloud base. This effect dampens evaporation by more than 50 % compared to a
case where the droplet takes on ambient air temperatures.
The initial isotopic composition of the hydrometeors (Fig. c,
solid coloured lines, symbol A) is enriched by about 100 ‰ in
δ2H compared to the composition of the surrounding vapour
(black line). Above the 0 ∘C isotherm, the hydrometeors are frozen
and thus hardly change their isotopic composition (Fig. c, d;
A to B). Simulated hydrometeors melt instantaneously when their temperature
exceeds 0 ∘C and equilibration sets in, which rapidly changes their
isotopic composition towards equilibrium with the surrounding vapour.
Comparison between the isotopic composition of the droplets
(Fig. c, d, solid coloured lines, symbols A, B, C) and the
background vapour is facilitated here by using the equilibrium variables
δp,eq and dp,eq (dashed
coloured lines, symbols A', B', C'). A drawback of these variables is the
discontinuity at the height of the 0 ∘C isotherm
(Fig. c, d, symbol B'). When the hydrometeor changes its
state from solid to liquid, the fractionation coefficients change and
consequently δp,eq and
dp,eq jump.
Hydrometeors equilibrate more quickly the smaller they are, while the 2 mm
hydrometeor never reaches equilibrium. Below cloud base, evaporation leads to
an enrichment of the small hydrometeors with respect to equilibrium with the
surrounding vapour (symbol C' in Fig. c). The hydrometeors'
d-excess is smaller than dv (Fig. d, solid
lines at symbol A, black line). Non-equilibrium fractionation due to
supersaturation with respect to ice increases dp compared to
dv (symbol C in Fig. d). The smaller
dp-values found here are due to the fact that for strongly
depleted vapour, the equilibrium fractionation of δ2H is
less than 8 times stronger than that of δ18O, as discussed
in detail by .
Isotopic composition of the hydrometeors and the surrounding vapour
of a reference simulation (see Sect. ). (a) Difference
between the surface vapour and the equilibrium vapour from a falling liquid
hydrometeor (Δδ, coloured lines). The composition of the ambient
vapour at different altitudes relative to surface vapour
(δ2Hv-δ2Hv,0) is shown as black lines. The curves are
similar to the coloured lines in Fig. c, but
instead of the absolute value showing the deviation from the surface vapour composition. The
horizontal dashed and dotted black lines mark the height of the 0 ∘C
isotherm and the height of the cloud base (CB),
respectively. (b) Same as (a), but for dp and
dp,eq and rotated to match the y axis
of (c). (c) ΔδΔd-diagram:
Δδ from (a) vs. Δd from (b). In all plots, the isotopic composition at
every full 500 m is highlighted with a small dot. The compositions at the following altitudes
are also highlighted: diamond: altitude of release; triangle: altitude of Td=0 ∘C;
cross: altitude of the cloud base; large filled circle: surface. For simplicity, the equilibrium
vapour from a liquid hydrometeor is shown above the 0 ∘C
isotherm.
Reference simulations in the Δδ and Δd diagram
We will now cast the results from the idealized model using the variables
Δδ and Δd that have been introduced above to measure the
deviation of the precipitation from equilibrium with ambient vapour at the
surface. To this end, we consider first the Δδ in the reference
simulations above for three different raindrops that fall through the
atmospheric column (Fig. a). After formation at a height
of z=3500 km (coloured diamonds), the hydrometeors are depleted by
63 ‰ in δ2H (i.e. Δδ is
-63 ‰) compared to surface vapour. This is both a contribution
from the depletion of the background vapour profile (-75 ‰). For
simplicity, we only show vapour above liquid, which results in a
Δδ of -63 ‰. As the droplets fall, the Δδ
changes little until it reaches the melting level (coloured triangles).
Equilibration above cloud base (coloured crosses) moves them progressively
closer to the ambient vapour (black line) and its surface value (black
circle). Below cloud base, evaporation in addition introduces fractionation
that leads to positive Δδ for the smallest droplet (blue line),
whereas the largest droplet has a negative Δδ at the surface,
indicating incomplete equilibration that was not overprinted entirely by the
evaporation-induced fractionation.
ΔδΔd-diagram for the precipitation samples collected
on 20 November 2015. (a) Samples coloured according to their sequential sample
number (see legend) to highlight the temporal evolution of Δδ and
Δd. (b) Same samples as in (a), but with pre-frontal samples coloured
in purple and post-frontal ones in green. The size of the circle corresponds to the
average rain intensity of the sample. The solid black line represents a linear
fit through all samples with the 95 % confidence band in shading. Dashed
red lines correspond to the linear fits through the samples of three other
events (cf. text). Data points from reference simulations shown as large
yellow, red, and blue dots.
The initial Δd of -7.5 ‰ at formation height evolves due
to both equilibrium and kinetic fractionation as the droplets fall through
the atmospheric column (Fig. b). This leads initially to
Δd becoming less negative, reaching equilibrium with the ambient
vapour for the smallest droplets at cloud base. As the droplets continue to
fall through an unsaturated atmosphere below, kinetic fractionation sharply
increases Δd, again most markedly for the small droplets, which
experience the strongest relative loss of their mass.
When using Δδ and Δd as the axes of a new diagram, the
evolution of the droplets in the three reference simulations yield inverted
U-shaped curves (Fig. c). In the examples provided here,
these curves depend entirely on the size of the raindrops at the surface
(large filled dots), placing them either in the lower left quadrant of the
diagram (large drop, comparatively weak below-cloud interaction) or in the
lower right quadrant (small drop, with at first complete equilibration
followed by strong below-cloud evaporation). Hence, the location of a
precipitation sample in this ΔδΔd-diagram is determined by
several processes that occur along the trajectories of the raindrops from
their formation until they are measured at the surface. The origin of the
diagram (Δδ=0 ‰, Δd=0 ‰) indicates full
equilibrium between vapour and precipitation. Note that this does not
indicate that the involved vapour and raindrops did not experience
non-equilibrium fractionation processes; it merely indicates that at the time
of simultaneously measuring water isotopes in vapour and rain, the two values
correspond to the local equilibrium conditions.
Note that the measured data points of Δδ and Δd shown in
Fig. c can be compared with the values from our idealized
simulations at the final (surface) location shown in Fig. .
Therefore, we now display the measurement data points in the ΔδΔd-diagram to investigate the influence of different below-cloud
processes on the surface measurements during the frontal passage. By means of
additional model sensitivity experiments, we then apply this framework to
interpret and quantify the influence of below-cloud effects on the vapour and
precipitation isotope composition observed at the surface during the frontal
passage in November 2015.
Observed below-cloud effects in the ΔδΔd-diagram
Rain samples during the cold frontal passage
The 86 rain samples cover a much larger range in the ΔδΔd-diagram than the three idealized simulations (Fig. a). Some
data points are located in the lower right quadrant, associated with
intermediate rain rates (cf. Fig. b) during the pre-frontal
phase of the event (blue to green shading). Compared to the idealized
simulations, these data points match with intermediate to small droplets that
experienced evaporation (blue and red dot). Data points located to the left
of the origin indicate that precipitation is more depleted than ambient
vapour, and reflect that more of the initial signal after formation (“cloud
signal”) is retained in precipitation. In the idealized experiments, this
corresponds to the largest drop size (yellow dot). Most of the post-frontal
data points with the most intense rain rates (cf. Fig. b) are
located to the left of the origin (orange to red shading).
Drop size and thus rain rate appear as important driving factors of the
below-cloud processes. Figure b shows another variant of the
ΔδΔd-diagram where the dot size indicates rain rate. It
appears that samples with the highest rain rates are located in the upper
left corner, as they are least affected by below-cloud processes and retain
more of their initial strongly negative Δδ. Samples from periods
with weak rain rates are located in the bottom right corner of the diagram,
reflecting a stronger evaporation influence. Overall, complete equilibration
with ambient vapour seems to be rather limited because only a few data points
are close to the origin of the diagram. The regions in Fig. a
that are covered by pre-frontal (purple) and post-frontal (green) samples are
fairly well separated. Pre-frontal samples, which are on average higher in
Δδ and lower in Δd, seem to be more strongly affected by
below-cloud processes than post-frontal samples. From the idealized model
experiments, such a difference can be explained by an on average lower rain
intensity and a lower relative humidity during the pre-frontal phase, and
therefore by enhanced below-cloud equilibration and evaporation.
Additionally, the melting layer was clearly lower after the passage of the
front, and thus both vertical distance and time for equilibration were
reduced. Post-frontal samples therefore carry more of their depleted initial
δ2Hp,eq from the cloud base to the
surface.
The data points in Fig. roughly fall along a line with a
negative slope. A linear fit through the samples yields a regression line
with a slope of ΔdΔδ=-0.31 (Fig. b,
solid black line). It is noteworthy that similar slopes (-0.30±0.02;
dashed black lines in Fig. b) were found for three other cold
fronts in Switzerland . This indicates that the slope could
represent a general characteristic of below-cloud evaporation and
equilibration of rainfall, at least for continental mid-latitude cold front
passages. It will be insightful to explore the slope in the ΔδΔd-diagram for other climatic regions in future studies.
It is important to recall that the isotopic evolution of sedimenting
raindrops is strongly influenced by ambient meteorological conditions, in
particular the detailed relative humidity profile, the formation height of
precipitation, the isotope profile of vapour, and potential updrafts and
downdrafts, and turbulent motions below the cloud base. The effect of some of
these processes is now investigated with the aid of the idealized below-cloud
interaction model, providing further insight into the interpretation of our
measurements in the ΔδΔd-diagram.
Sensitivity experiments in the ΔδΔd-diagram
We now use the below-cloud interaction model to assess the relevance of
different ambient conditions for the raindrop trajectories and surface
arrival points in the ΔδΔd-diagram. Explored parameters
include the sensitivity to surface relative humidity, surface temperature,
formation height, riming, and the background isotope profiles in terms of
δ2H and d (as described in detail in ).
For each parameter, several simulations were performed for a range of drop
sizes from 0.6 to 1.8 mm. Assuming a standard Marshall–Palmer drop-size
distribution, these diameters correspond to the mass-weighted mean diameter
for rain intensities in the range from 0.1 to 20 mm h-1.
For a particular setup of the ambient parameters, the different
Δδ and Δd when the drops arrive at the surface are
connected by dashed lines in Fig. . The black line shows
the reference experiment (REF, cf. Sect. ), where the filled circle
corresponds to the highest rain intensity, and the triangle to the lowest.
The label of the experiments points to the input parameter that is modified.
RH50 and RH100 correspond to sensitivity experiments with different surface
relative humidity h0=50 % and h0=100 %, respectively. T7 and T17
denote experiments with different surface temperatures T0=7 ∘C
and T0=17 ∘C, FH2.5 and FH5.0 refer to experiments with formation
heights of 2.5 km and 5.0 km a.s.l., respectively, and RIM corresponds to
formation by riming. Experiments with altered background profiles of stable
water isotopes are denoted as δ±50
(δ2Hv profile changed by ±50‰
above the cloud base) and d±10 (dv profile changed by
±10‰ above the cloud base).
ΔδΔd-diagram for the results of
sensitivity experiments with the idealized below-cloud interaction model.
The black line shows results from the reference setup, and coloured lines
reveal the results from experiments with altered input parameters (see text for
explanation). For each setup, a line is shown that connects results of simulations
with different drop sizes (corresponding to surface precipitation intensities from
0.1 to 20 mm h-1). The triangles correspond to the lowest rain intensity
(0.1 mm h-1). Empty circles correspond to an intensity of 2 mm h-1
and filled circles correspond to an intensity of 20 mm h-1. Grey dots show
precipitation samples collected on 20 November 2015.
Changes in the model input parameters systematically affect the position and
orientation of the curves in the ΔδΔd-diagram. The results
for simulations where the initial composition of hydrometeors is modified
(T7, T17, FH2.5, FH5.0, RIM, δ±50, and d±10) diverge for
strong rain intensities. For small drops, i.e. weak precipitation
intensities, however, the results converge and are quite similar for all
simulations. This agrees with the finding from the reference simulations that
below-cloud interaction affects samples from weak rain more strongly and
overwrites initial differences. Simulations that alter the extent of
below-cloud interaction (RH50, RH100, and to a small degree also T7) show
large differences for small drops. For example, evaporation in RH50 shifts
isotope values in small drops to high Δδ and low Δd. In
contrast, the absence of evaporation in RH100 leads to an almost complete
equilibration with the ambient vapour and almost no change in d. Large
drops, representative of strong rain intensities, carry a stronger imprint of
the different initial composition of precipitation to the surface. Therefore,
the coloured dots from simulations with a low initial δ2H
(T7, FH5.0, δ-50) are located at lower Δδ than simulations
with a high initial δ2H (T17, FH2.5, δ+50). The same
is the case for Δd in simulations where the initial d differs.
The set of idealized simulations reveals that the closer a precipitation
sample is to the origin of the coordinate system, the more it has
equilibrated with ambient vapour until it reaches the ground, while remaining
unaffected by evaporation. Samples that encountered significant evaporation
during their fall are located towards the bottom right of the ΔδΔd-diagram. This is typically the case for samples from weak rain
intensities. Samples that were weakly influenced by equilibration or
evaporation during their fall, which is typically the case for intense
precipitation, are located towards the left side of the diagram. Assuming
constant ambient conditions, variations of the rain intensity cause
variations in the ΔδΔd-diagram along a curve as indicated
in Fig. . The location and orientation of this curve in
this diagram is determined by the meteorological conditions. Studying the
evolution of precipitation samples in the ΔδΔd-diagram
during a rain event can thus clearly reveal information about the prevailing
meteorological conditions and their temporal evolution.
Conclusions
The processes acting on precipitation as it falls from the cloud base to the
surface are complex and difficult to access from surface measurements only.
Using highly resolved measurements of stable isotopes in vapour and rain at
the surface, we show here that it is possible to identify an integrated
signal of these so-called below-cloud processes when comparing the isotopic
composition of equilibrium vapour from precipitation relative to near-surface
vapour simultaneously for both δ2H and d.
We combine this information in a new interpretation framework, the
ΔδΔd-diagram, where Δδ is shown along the x
axis and Δd along the y axis. This combines a view of
δ2Hv,
δ2Hp,eq, dv, and
dp,eq while tuning down the influence of first-order
advection processes during a frontal transition. To display data in the
ΔδΔd-diagram, the isotopic composition of surface vapour
and precipitation have to be known, as well as surface temperature.
A ΔδΔd-diagram shows the isotopic composition of
equilibrium vapour from precipitation samples relative to the ambient surface
vapour at the time when the samples were taken. By means of idealized
below-cloud interaction model simulations, we show that the location of a
precipitation sample in the ΔδΔd-space is determined by two
factors: (i) the initial composition of precipitation after formation in the
cloud and (ii) the modification of this composition below the cloud by
equilibration and evaporation. These below-cloud processes depend on the rain
intensity: larger drops during intense rain are typically less affected by
below-cloud processes because they spend less time in the air due to a faster
fall velocity and they are less affected by exchanges with the ambient vapour
due to a smaller surface-to-volume ratio. The isotopic composition of a rain
sample is a mass-weighted average of the composition of all drops contained
in a sample. The processes that act on a single drop are thus directly
relevant for bulk precipitation. The usefulness of this diagram is
demonstrated with measurements from a cold frontal rain event in Switzerland
in November 2015.
The main conclusions from this study are the following.
Equilibration between vapour and rain and evaporation of rain in unsaturated
air leave distinct imprints on the isotope signal of surface rain. Both aspects of
the exchange between the liquid and solid phase become more accessible by quantifying
the deviation from isotopic equilibrium with the surface vapour by studying the two
quantities Δδ and Δd.
The ΔδΔd-diagram facilitates the interpretation of the effects
of below-cloud processes on rain samples by jointly displaying the degree of
equilibration between rain and vapour and the influence of evaporation using
the newly defined variables Δδ and Δd. Equilibration and
evaporation have different pathways in the ΔδΔd-diagram, which
makes them more easily distinguishable than in a time series. Investigating rain
samples in the ΔδΔd-diagram can therefore complement a time-series perspective.
During the 20 November 2015 cold frontal rainfall event evaporation appears
as the dominant below-cloud process regarding the isotopic composition of
surface rain. The effect of evaporation on the isotope composition is
strongly modulated by the rain rate. The pre-frontal period with weaker
rainfall therefore experienced a stronger signal of evaporation below cloud
base, whereas the more intense post-frontal rainfall contained a stronger
signal from the cloud level. The cloud signal was also more preserved due to
higher below-cloud relative humidity, and a lower temperature and melting
layer after the frontal passage.
In the ΔδΔd-diagram, below-cloud processes caused
precipitation measurements to follow a line with a negative slope of
ΔdΔδ=-0.31. Similar slopes were obtained for several
other frontal rain events, suggesting that the characteristics of below-cloud processes,
as revealed by the ΔδΔd-diagram are similar for this type of cold frontal
rain events in continental mid-latitudes.
Using the ΔδΔd framework, it will be highly valuable to
investigate below-cloud effects for other precipitation events. For example,
a snowfall event, or a transition from rain to snow could show a stronger
cloud signal due to the absent exchange between vapour and solid. Cases of
drizzle could exhibit a large degree of equilibration between small drops and
ambient vapour. Cases of convective rainfall could show variations due to
more cloud-related signals in convective downdrafts.
Further constraints on observations from radiosondes, vertically resolved
isotope measurements using aircraft e.g.,
and related measurements at high resolution will provide possibilities to
validate and apply the idealized modelling framework presented here for
below-cloud processes.
We expect that the analysis of the isotopic composition during rain events at
other locations and further model studies will benefit from using the
parameters Δδ and Δd, and the ΔδΔd-diagram as an additional viewing device to obtain insight into below-cloud
processes. Thereby, further constraints on microphysical processes in models
can be obtained, and ultimately contribute to a more complete use of stable
water isotopes to build internally consistent water cycles into numerical
weather prediction and climate models.