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**Earth System Dynamics**
An interactive open-access journal of the European Geosciences Union

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- Abstract
- Introduction
- Implementation of the moisture tagging capability
- Moisture tracer validation
- Application example: lake evaporation as moisture source in the Great Lakes snowstorm of 2014
- Summary and conclusions
- Data availability
- Author contributions
- Competing interests
- Special issue statement
- Acknowledgements
- References

ESD | Articles | Volume 9, issue 1

Earth Syst. Dynam., 9, 167–185, 2018

https://doi.org/10.5194/esd-9-167-2018

© Author(s) 2018. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/esd-9-167-2018

© Author(s) 2018. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: The 8th EGU Leonardo Conference: From evaporation to precipitation:...

**Research article**
26 Feb 2018

**Research article** | 26 Feb 2018

A new moisture tagging capability in the Weather Research and Forecasting model: formulation, validation and application to the 2014 Great Lake-effect snowstorm

A new moisture tagging capability in the Weather Research and Forecasting model: formulation, validation and application to the 2014 Great Lake-effect snowstorm
A new moisture tagging capability in the Weather Research and Forecasting model: formulation,...
Damián Insua-Costa and Gonzalo Miguez-Macho

- Non-Linear Physics Group, Universidade de Santiago de Compostela, Galicia, Spain

- Non-Linear Physics Group, Universidade de Santiago de Compostela, Galicia, Spain

**Correspondence**: Damián Insua-Costa (damian.insua@usc.es)
and Gonzalo Miguez-Macho (gonzalo.miguez@usc.es)

**Correspondence**: Damián Insua-Costa (damian.insua@usc.es)
and Gonzalo Miguez-Macho (gonzalo.miguez@usc.es)

Abstract

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A new moisture tagging tool, usually known as water vapor tracer (WVT) method or online Eulerian method, has been implemented into the Weather Research and Forecasting (WRF) regional meteorological model, enabling it for precise studies on atmospheric moisture sources and pathways. We present here the method and its formulation, along with details of the implementation into WRF. We perform an in-depth validation with a 1-month long simulation over North America at 20 km resolution, tagging all possible moisture sources: lateral boundaries, continental, maritime or lake surfaces and initial atmospheric conditions. We estimate errors as the moisture or precipitation amounts that cannot be traced back to any source. Validation results indicate that the method exhibits high precision, with errors considerably lower than 1 % during the entire simulation period, for both precipitation and total precipitable water. We apply the method to the Great Lake-effect snowstorm of November 2014, aiming at quantifying the contribution of lake evaporation to the large snow accumulations observed in the event. We perform simulations in a nested domain at 5 km resolution with the tagging technique, demonstrating that about 30–50 % of precipitation in the regions immediately downwind, originated from evaporated moisture in the Great Lakes. This contribution increases to between 50 and 60 % of the snow water equivalent in the most severely affected areas, which suggests that evaporative fluxes from the lakes have a fundamental role in producing the most extreme accumulations in these episodes, resulting in the highest socioeconomic impacts.

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Insua-Costa, D. and Miguez-Macho, G.: A new moisture tagging capability in the Weather Research and Forecasting model: formulation, validation and application to the 2014 Great Lake-effect snowstorm, Earth Syst. Dynam., 9, 167–185, https://doi.org/10.5194/esd-9-167-2018, 2018.

1 Introduction

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Water is the most important natural resource on the planet, and without its presence, no form of life would be possible. Small changes in Earth's water transport and redistribution, as well as in sources and sinks of atmospheric moisture, can therefore result in enormous socioeconomic impacts (Oki and Kanae, 2006). Detailed knowledge of the hydrologic cycle and its potential future alterations is thus of great relevance, and in particular of extreme hydrometeorological events, such as droughts and high precipitation episodes, which can cause catastrophic consequences in the very short term (Easterling et al., 2000). Among the many uncertainties around the water cycle, researchers have tried to respond to two questions of special interest: what the moisture source regions are for precipitation and what the consequences are for precipitation of possible future changes in source regions due to anthropogenic influences or natural variability. To answer these fundamental questions, different numerical methods have been applied in the last decades, namely analytical, Lagrangian and Eulerian models (Gimeno et al., 2012).

Analytical models derived from the conservation equation of atmospheric water mass (Peixoto and Oort, 1992) have been widely used in calculations of the recycling ratio, which quantifies the contribution of local evapotranspiration to precipitation (Brubaker et al., 1993; Eltahir and Bras, 1996; Rios-Entenza and Miguez-Macho, 2014; Trenberth, 1999). A great advantage of these methods is their simplicity and low computational cost, at the expense, however, of strong assumptions, such as that water vapor of all origins is well mixed in the column (Budyko, 1974), that limit their applicability. For this reason, analytical models can only provide a first order estimation of the recycling ratio. In more recent years, these models have been refined, and some of the former initial assumptions have been relaxed. Some newer analytical models can quantify the contribution of remote moisture sources to local precipitation, while improving recycling ratio calculations (Dominguez et al., 2006). Nevertheless, most models still assume that moisture of all origins is well-mixed in the atmospheric column, notwithstanding some attempts to relax the hypothesis (Burde et al., 2006), and this can significantly compromise their results (Bosilovich, 2002).

Offline Eulerian methods, the so-called 2-D moisture tracking models (Goessling and Reick, 2011; Van Der Ent et al., 2010; Yoshimura et al., 2004), are an alternative to traditional analytical models especially useful for calculations of continental moisture recycling ratios on a global scale. This method uses vertically integrated variables for calculations, and hence still assumes the well-mixed atmosphere hypothesis, which leads to errors particularly in regions of significant vertical shear (Goessling and Reick, 2013). However, in recent years, this hypothesis has been relaxed by adding an additional vertical level to some offline Eulerian models (i.e., moving from a single column to two layers), which has considerably improved the results provided by this method (van Der Ent et al., 2013).

Lagrangian models, based on the spatiotemporal tracking of individual fluid
particles, are possibly the most extended method to study sources and sinks
of moisture. There are currently two main classes of Lagrangian models: the
method of quasi-isentropic back trajectories (Dirmeyer and Brubaker, 1999) and the
method of dispersion of Lagrangian particles (Stohl et al., 2004). Lagrangian
models have been extensively used in climatic studies of atmospheric water
vapor sources (Gimeno et al., 2010; Stohl and James, 2005) and in the diagnosis of the origin
of moisture in extreme precipitation events (James et al., 2004; Stohl et al., 2008).
The advantages of the method include computational efficiency, the fact that source
regions to analyze do not need to be selected a priori, since particles can
be traced back in time, and furthermore, that when using reanalysis data for
calculations, it effectively introduces an observational constraint.
Lagrangian models include, nevertheless, some simplifications in their
formulation that can result in serious biases. For example, the method of
dispersion of Lagrangian particles does not allow for a clear separation
between evaporation (*E*) and precipitation (*P*), in addition to neglecting
liquid water and ice, which results in an overestimation of both *E* and *P*. For
its part, the method of quasi-isentropic back trajectories does not have this
limitation, since evaporation and precipitable water content are needed for
calculations; however, the well-mixed atmosphere hypothesis is still invoked,
since water from surface evaporation is assumed to contribute uniformly
throughout the column; moreover, phase changes along the path of the
parcels are not considered. Apart from errors derived from approximations in
the specific formulation of the hydrological part of each method, a common
drawback to all Lagrangian models is the growing uncertainty in air parcel
trajectories with time (Stohl, 1998). An important reason for this error
comes from the existence of subgrid vertical motions, related to convection
and turbulent transport, which are not resolved by the gridded atmospheric
analyses that Lagrangian models use for calculations. Estimations of the
effect of these processes must be made; however, the mere existence of
subgrid vertical mixing in the column inevitably leads to imprecision in
determining parcel trajectories, which is especially critical when studying
variations in the moisture content of the parcel, since atmospheric mixing
ratios can change abruptly with height. Some of the aforementioned
limitations of the Lagrangian method could be avoided considerably by using
the output of a climate model (Brioude et al., 2013), thereby obtaining
more detailed information about the meteorological variables needed for an
improved particle tracking. Notwithstanding, with this strategy, the
observational constraint disappears and the computational cost increases
substantially, effectively offsetting the main benefits of the Lagrangian
method.

Online Eulerian methods, generally known as water vapor tracers (WVTs), are based on coupling a moisture tagging technique with a global or regional meteorological model. This strategy enables WVTs to fully consider all physical processes affecting atmospheric moisture, such as advection, molecular and turbulent diffusion, convection and cloud microphysics, thereby avoiding errors associated with offline methods. For this reason, this is presently regarded as the most accurate technique for the study of atmospheric moisture sources for precipitation. It has, nevertheless, some shortcomings, which are mainly related to the fact that it implies running an atmospheric model and relying on results from the simulation, since the method cannot be applied a posteriori, i.e., based, for example, on atmospheric analyses. Biases in WVTs are therefore not so much linked to the strategy itself but to the model where they are coupled; hence, the method provides sound results only if the atmospheric model simulation is realistic. In addition, the associated computational cost is much higher than in any of the other techniques mentioned above.

WVTs were introduced in general circulation models in the early studies of Koster et al. (1986) and Joussaume et al. (1986). There were successive later implementations in different global models (Bosilovich and Schubert, 2002; Bosilovich et al., 2003; Goessling and Reick, 2013; Noone and Simmonds, 2002; Numaguti, 1999; Singh et al., 2016; Werner et al., 2001), all of them proving very useful in climatic studies of precipitation moisture sources. WVTs in global models allow for investigations at the planetary scale, covering all existing moisture source regions. However, given the coarse resolution common to most of these models, some processes such as surface hydrology or water vapor transport in complex topography areas, are subject to sizeable biases, which compromise conclusions drawn from the WVT method. WVTs in regional climate models, which employ a much finer resolution and significantly improve the representation of small-scale features of the hydrology cycle, are perhaps the best alternative for diagnosing precipitation moisture sources in events of reduced temporal and spatial scales, such as extreme precipitation episodes. They can also be useful in climatic studies at the regional scale. The first implementation of the moisture tagging capability in a regional atmospheric model was in the climate high-resolution model (CHRM) by Sodemann et al. (2009) and more have followed since in different models (Arnault et al., 2016; Knoche and Kunstmann, 2013; Miguez-Macho et al., 2013; Winschall et al., 2014).

Although the different implementations of WVTs in global or regional models have the theoretical approach in common, they can, nevertheless, be somewhat different in practice. These differences are not only due to the model or parameterizations used but also to the considerations and simplifications that authors assume in their own implementations, which can potentially lead to significant inaccuracies. It is therefore fundamental to validate the method's precision before it can be reliably applied in practical cases.

This paper presents a new moisture tagging tool recently added to the Weather Research and Forecasting (WRF v3.8.1) regional meteorological model (WRF-WVT hereafter). Even though a preliminary version of the tool has already been tested in an older version of the model (Dominguez et al., 2016; Eiras-Barca et al., 2017; Miguez-Macho et al., 2013), we discuss here the formulation and implementation details of the method, and perform a thorough validation, thus avoiding the reliability uncertainty from which many other implementations of the kind suffer. The study is structured as follows: Sect. 2 describes the formulation and implementation into WRF of the WVT method. Section 3 contains the validation strategy and results. Section 4 shows results from an example application, and finally Sect. 5 includes a summary and conclusions of the work.

2 Implementation of the moisture tagging capability

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The basis of the moisture tagging technique is to replicate for moisture tracers the prognostic equation for total moisture:

$$\begin{array}{ll}{\displaystyle \frac{\partial {q}_{n}}{\partial t}}& {\displaystyle}=-\mathit{v}\cdot \mathrm{\nabla}{q}_{n}+{\mathit{\nu}}_{q}\cdot {\mathrm{\nabla}}^{\mathrm{2}}{q}_{n}+{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{PBL}}\\ \text{(1)}& {\displaystyle}& {\displaystyle}+{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{microphysics}}+{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{convection}},\end{array}$$

where *q*_{n} refers to the different moisture species considered, namely water
vapor, cloud water, rain water, snow, ice and graupel. The first two terms on
the right-hand side of Eq. (1) represent the tendencies due to
advection and molecular diffusion, respectively, and the others correspond to
tendencies resulting from parameterized turbulent transport (planetary
boundary layer – PBL scheme), microphysics and convection. The latter three
terms account for subgrid physical processes affecting atmospheric moisture,
such as phase changes and precipitation, or redistribution by convection and
turbulent diffusion.

To replicate Eq. (1), six new variables tq_{n} are created
corresponding to the tracers of the different moisture species: tvapor,
tcloud, train, tsnow, tice and tgraupel. We note that in earlier studies, only
water vapor was tagged (tvapor); hence, the name is WVT method. Perhaps this
denomination is no longer accurate when tagging all six
moisture species, and more properly the technique should be referred to as
simply the moisture tracers (MTs) method; we will keep in the text, however, the
common WVT term, as it is already well established in the literature.

The general form of the prognostic equation for WVTs is totally analogous to
Eq. (1), just replacing *q*_{n} by tq_{n}. The Eulerian form of this
equation and the fact that it is solved simultaneously with Eq. (1) are
the reasons for the method to be classified as “online”
Eulerian. One could think that since the prognostic equations for WVTs and
total moisture have the same form, it would suffice with repeating the
calculations performed for total moisture species for the tracer species,
just changing initial or boundary conditions. However, this is not the case,
since the behavior of the tagged moisture is not independent from that of
total moisture. In other words, the tagged moisture does not evolve as if it
was completely on its own. A very simple example of this is saturation
conditions and phase changes, which would hardly occur if only tagged
moisture were considered. When an air parcel saturates, it does so in regards
to its total moisture content, independently of whether its tracer moisture
content is high or low. Similarly, since it is total moisture that determines
the thermodynamical setting for turbulence and convection, primary and
derived variables in the basis of the parameterizations of those processes,
such as virtual temperature, dew point, profile instability, convective
available potential energy (CAPE), level of free convection, eddy
diffusivity and many more, must be computed using total moisture, even when
calculations are performed for tagged moisture tendencies. Therefore, the
prognostic equations for tracer moisture must be solved coupled to the
governing equations of the model, i.e., “online”, although tracer variables
do not appear elsewhere and hence do not have an effect on the model's
dynamics in any way.

Thus, for the implementation of WVTs into WRF, three fundamental parameterizations of the model, such as the turbulence (PBL) scheme, microphysics and convection, must be modified for calculating the associated tracer moisture tendencies, as discussed above. Conversely, advection and diffusion routines can be simply called for tracers in the same way as for total moisture or any other scalar, since in these processes tracer moisture can indeed be treated independently from total moisture. We note that it is important to use an advection numerical scheme that is positive definite, conserves mass and minimizes numerical diffusion, in order to limit numerical errors in WVT calculations. Both total moisture and tagged moisture must use the same scheme. All other components of the model remain unchanged, since they do not affect moisture dynamics directly.

Of the several scheme options available, we have altered for moisture tagging the Yonsei University (Hong et al., 2006) PBL scheme, the WRF Single-Moment 6-class (Hong and Lim, 2006) microphysics scheme and the Kain–Fritsch (Kain, 2004) convective parameterization. These schemes have been selected because they are some of the most commonly used and show a reliable performance in numerous situations.

The equation of turbulent diffusion for moisture (Hong et al., 2006),

$$\begin{array}{}\text{(2)}& {\displaystyle}{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{PBL}}={\displaystyle \frac{\partial}{\partial z}}\left[{K}_{q}\left({\displaystyle \frac{\partial {q}_{n}}{\partial z}}-{\mathit{\gamma}}_{q}\right)-{\stackrel{\mathrm{\u203e}}{\left({w}^{\prime}{q}_{n}^{\prime}\right)}}_{h}{\left({\displaystyle \frac{z}{h}}\right)}^{\mathrm{3}}\right],\end{array}$$

is solved in this parameterization for *q*_{n} of water vapor, cloud water and
ice, with boundary conditions

$$\begin{array}{}\text{(3)}& {\displaystyle}\left\{\begin{array}{l}\mathit{\eta}=\mathrm{1}\Rightarrow {K}_{q}\left({\displaystyle \frac{\partial {q}_{n}}{\partial z}}\right)=-{\displaystyle \frac{{Q}_{\mathrm{E}}}{{\mathit{\rho}}_{\mathrm{air}}}}\\ \mathit{\eta}={\mathit{\eta}}_{\mathrm{end}}\Rightarrow {K}_{q}\left({\displaystyle \frac{\partial {q}_{n}}{\partial z}}\right)=\mathrm{0}\end{array}\right.,\end{array}$$

where *Q*_{E} represents the water vapor flux at the surface.

To compute turbulent diffusion for tracer species, we replicate Eq. (2), keeping the same eddy diffusivity coefficients *K*_{q},
turbulent vertical velocity *w*^{′} and boundary layer height *h* as in the
total moisture calculation:

$$\begin{array}{}\text{(4)}& {\displaystyle}{\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial t}}\right)}_{\mathrm{PBL}}={\displaystyle \frac{\partial}{\partial z}}\left[{K}_{q}\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial z}}-{\mathit{\gamma}}_{\mathrm{tq}}\right)-{\stackrel{\mathrm{\u203e}}{\left({w}^{\prime}{\mathrm{tq}}_{n}^{\prime}\right)}}_{h}{\left({\displaystyle \frac{z}{h}}\right)}^{\mathrm{3}}\right].\end{array}$$

Boundary conditions are analogous to Eq. (3):

$$\begin{array}{}\text{(5)}& {\displaystyle}\left\{\begin{array}{l}\mathit{\eta}=\mathrm{1}\Rightarrow {K}_{q}\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial z}}\right)=-{\displaystyle \frac{{\mathrm{TQ}}_{\mathrm{E}}}{{\mathit{\rho}}_{\mathrm{air}}}}\\ \mathit{\eta}={\mathit{\eta}}_{\mathrm{end}}\Rightarrow {K}_{q}\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial z}}\right)=\mathrm{0}\end{array}\right.,\end{array}$$

considering that now TQ_{E} is the tracer water vapor flux at the
surface, which, when upward, is equal to that of total water vapor in the
areas that are selected for tagging and zero in the rest.

The tendencies computed in the WSM6 microphysics parameterization account for grid-scale precipitation and for the different phase changes among the several species considered (water vapor, cloud water, rain water, ice, snow and graupel):

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{microphysics}}=\\ \text{(6)}& {\displaystyle}& {\displaystyle}\phantom{\rule{2em}{0ex}}\sum _{x}{\displaystyle \frac{\partial {Q}_{{q}_{x}\to {q}_{n}}}{\partial t}}-\sum _{x}{\displaystyle \frac{\partial {Q}_{{q}_{n}\to {q}_{x}}}{\partial t}}-{\displaystyle \frac{{q}_{n}}{{\mathit{\rho}}_{\mathrm{air}}}}{\displaystyle \frac{\partial}{\partial z}}({\mathit{\rho}}_{\mathrm{air}}\cdot {V}_{{q}_{n}}),\end{array}$$

where ${Q}_{{q}_{x}\to {q}_{n}}$ and ${Q}_{{q}_{n}\to {q}_{x}}$ refer to the amount of moisture
species *q*_{x} transformed via phase change into moisture species *q*_{n}, and
vice versa, respectively (Hong and Lim, 2006). The last term on
the right-hand side of Eq. (6) represents the tendency due to
hydrometeor *q*_{n} fallout, with an associated mass-weighted mean terminal
velocity ${V}_{{q}_{n}}$. In the latter case, *q*_{n} refers only to rain water,
snow, ice or graupel.

We consider that phase changes among the different tracer species occur in amounts proportional to their total moisture counterparts:

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{TQ}}_{{\mathrm{tq}}_{x}\to {\mathrm{tq}}_{n}}={\displaystyle \frac{{\mathrm{tq}}_{x}}{{q}_{x}}}\cdot {Q}_{{q}_{x}\to {q}_{n}}\\ \text{(7)}& {\displaystyle}& {\displaystyle}{\mathrm{TQ}}_{{\mathrm{tq}}_{n}\to {\mathrm{tq}}_{x}}={\displaystyle \frac{{\mathrm{tq}}_{n}}{{q}_{n}}}\cdot {Q}_{{q}_{n}\to {q}_{x}},\end{array}$$

where the proportionality coefficients in Eq. (7) correspond to
the tracer fraction in the species undergoing the change (tq_{x}/*q*_{x} when
tq_{x} changes phase and tq_{n}∕*q*_{n} when tq_{n} does).

Bearing the latter consideration in mind, we replicate Eq. (6) to calculate moisture tracers' tendencies:

$$\begin{array}{ll}\text{(8)}& {\displaystyle}& {\displaystyle}{\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial t}}\right)}_{\mathrm{microphysics}}={\displaystyle}& {\displaystyle}\phantom{\rule{2em}{0ex}}\sum _{x}{\displaystyle \frac{\partial {\mathrm{TQ}}_{{\mathrm{tq}}_{x}\to {\mathrm{tq}}_{n}}}{\partial t}}-\sum _{x}{\displaystyle \frac{\partial {\mathrm{TQ}}_{{\mathrm{tq}}_{n}\to {\mathrm{tq}}_{x}}}{\partial t}}-{\displaystyle \frac{{\mathrm{tq}}_{n}}{{\mathit{\rho}}_{\mathrm{air}}}}{\displaystyle \frac{\partial}{\partial z}}({\mathit{\rho}}_{\mathrm{air}}\cdot {V}_{{q}_{n}}).\end{array}$$

Sedimentation processes yielding precipitation rates are computed in this WSM6 parameterization with a forward semi-Lagrangian advection scheme with mass conservation and positive definition (Henry Juang and Hong, 2010), from which total accumulated grid-scale rain, snow and graupel are obtained. Applying the same strategy, we obtain the corresponding precipitation amounts for tracers. The ratio of tracer rain, snow and graupel to their total counterparts provides information about the contribution of the selected moisture sources to precipitation.

Following the formalism in Bechtold et al. (2001), the effect of convection in moisture can be generally described as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\left({\displaystyle \frac{\partial {q}_{n}}{\partial t}}\right)}_{\mathrm{convection}}={\displaystyle \frac{\mathrm{1}}{{\mathit{\rho}}_{\mathrm{air}}\cdot A}}\left[{\displaystyle \frac{\partial}{\partial z}}\right({M}^{\mathrm{u}}+{M}^{\mathrm{d}}){q}_{n}-({\mathit{\u03f5}}^{\mathrm{u}}+{\mathit{\u03f5}}^{\mathrm{d}}){q}_{n}\\ \text{(9)}& {\displaystyle}& {\displaystyle}\phantom{\rule{2em}{0ex}}+{\mathit{\delta}}^{\mathrm{u}}{q}_{n}^{\mathrm{u}}+{\mathit{\delta}}^{\mathrm{d}}{q}_{n}^{\mathrm{d}}]+{S}_{{q}_{n}},\end{array}$$

where *A* is the grid cell area; *M*^{u} and *M*^{d} are the
mass fluxes in updraft and downdraft;
*ϵ*^{u}−*ϵ*^{d} and
*δ*^{u}−*δ*^{d} represent mass exchanges between
the convective cloud and environment in the updraft
and downdraft due to entrainment and detrainment processes, respectively;
${q}_{n}^{\mathrm{u}}$ and ${q}_{n}^{\mathrm{d}}$ refer to the moisture amounts present
in updraft and downdraft; and finally ${S}_{{q}_{n}}$ corresponds to sources and
sinks of moisture species *q*_{n} in the convective cloud, linked to phase
changes and precipitation. The Kain–Fritsch parameterization considers up to
five moisture species (*q*_{n} of water vapor, cloud water, rain water, snow
and ice), but not all are equally treated, and simplified forms of
Eq. (9) are used for some of them (Kain, 2004; Kain and Fritsch, 1990; Kain et al., 2003).

Similarly to the previously discussed parameterizations, we replicate the general equation for convective moisture tendencies (Eq. 9) for the case of tracers:

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\left({\displaystyle \frac{\partial {\mathrm{tq}}_{n}}{\partial t}}\right)}_{\mathrm{convection}}={\displaystyle \frac{\mathrm{1}}{{\mathit{\rho}}_{\mathrm{air}}\cdot A}}\left[{\displaystyle \frac{\partial}{\partial z}}\right({M}^{\mathrm{u}}+{M}^{\mathrm{d}}){\mathrm{tq}}_{n}\\ \text{(10)}& {\displaystyle}& {\displaystyle}\phantom{\rule{2em}{0ex}}-({\mathit{\u03f5}}^{\mathrm{u}}+{\mathit{\u03f5}}^{\mathrm{d}}){\mathrm{tq}}_{n}+{\mathit{\delta}}^{\mathrm{u}}{\mathrm{tq}}_{n}^{\mathrm{u}}+{\mathit{\delta}}^{\mathrm{d}}{\mathrm{tq}}_{n}^{\mathrm{d}}]+{S}_{{\mathrm{tq}}_{n}},\end{array}$$

where the proportionality assumption of Eq. (7) is applied again to calculate amounts in tracer phase changes.

In the Kain–Fritsch parameterization, a large fraction of the liquid water or ice that forms in the updraft is converted to precipitation (Kain et al., 2003), which can evaporate or sublimate on the way to the ground, resulting finally in total accumulated cumulus precipitation. The replication of these processes for tracers yields cumulus tracer precipitation. As in the case of the microphysics scheme, the ratio of tracer to total precipitation quantifies the existing contribution from the selected moisture sources.

Tracer initial and lateral boundary conditions are usually set to zero, even though this does not always have to be the case, as we show when we perform the validation of the method in Sect. 3 and in the nested simulation discussed in Sect. 4. Lower boundary conditions depend largely on the moisture source to analyze. The implementation that we present here of the WVT method allows for the tracking of moisture from two- and three-dimensional sources.

Working with a two-dimensional source
commonly refers to tagging surface evapotranspiration fluxes (*Q*_{E}) from a
certain region or interest *A*_{2-D}. The flux of tracer water vapor
at the surface TQ_{E} can be written as

$$\begin{array}{}\text{(11)}& {\displaystyle}\left\{\begin{array}{l}{Q}_{\mathrm{E}}(x,y,t)>\mathrm{0}\Rightarrow {\mathrm{TQ}}_{\mathrm{E}}(x,y,t)\\ ={Q}_{\mathrm{E}}(x,y,t)\phantom{\rule{1em}{0ex}}\forall (x,y,t)\in {A}_{\text{2-D}}\\ {Q}_{\mathrm{E}}(x,y,t)<\mathrm{0}\Rightarrow {\mathrm{TQ}}_{\mathrm{E}}(x,y,t)\\ ={\displaystyle \frac{\mathrm{tvapor}(x,y,\mathit{\eta}=\mathrm{1},t)}{\mathrm{vapor}(x,y,\mathit{\eta}=\mathrm{1},t)}}\cdot {Q}_{\mathrm{E}}(x,y,t)\phantom{\rule{1em}{0ex}}\forall (x,y,t)\end{array}\right.\end{array}$$

Negative fluxes indicate dew (or frost) deposition, and in this case, we use
again the proportionality assumption for phase changes, as elsewhere in the
atmosphere (Eq. 7). The tracer deposition flux is simply the total
deposition flux times the tracer fraction in the water vapor of the first
atmospheric level. The resulting flux TQ_{E} is used in
Eq. (5) as a lower boundary condition for moisture turbulent
diffusion in the PBL parameterization.

Any three-dimensional volume *V*_{3-D} can be set as a 3-D source for moisture
tagging. This can refer to the entire atmosphere over a region of interest
or to only a part of it (for example, the stratosphere). Setting the lateral
boundaries plus the adjacent relaxation zone as 3-D wall-like source regions
is also the most convenient strategy for tagging incoming moisture fluxes
from the exterior of the regional model domain.

To turn any given set of model domain points *V*_{3-D} into a 3-D source for
moisture tracers, we simply impose

$$\begin{array}{}\text{(12)}& {\displaystyle}{\mathrm{tq}}_{n}(x,y,\mathit{\eta},t)\phantom{\rule{0.125em}{0ex}}=\phantom{\rule{0.125em}{0ex}}{q}_{n}(x,y,\mathit{\eta},t)\forall (x,y,\mathit{\eta},t)\in {V}_{\text{3-D}}.\end{array}$$

3 Moisture tracer validation

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The validation simulation for the newly implemented moisture tagging tool is
performed with the WRF model version 3.8.1 (Skamarock et al., 2008) for the
duration of 1 month (November 2014) and with a domain D1 of 20 km horizontal
resolution and 35 vertical levels (Fig. 2). Initial and boundary
conditions, updated every 6 h, were obtained from the National Centers
for Environmental Prediction (NCEP) Final (FNL) Operational Model Global
Tropospheric Analyses, available at 1^{∘} resolution (National Centers for Environmental Prediction, National Weather Service, NOAA, 2000). In addition
to the YSU PBL, WSM6 microphysics and Kain–Fritsch convective
parameterizations that we adapted to calculate the corresponding tracer
tendencies (as described in Sect. 2), in the simulations, we also use the
Noah land surface model (Chen and Dudhia, 2001) and the Rapid Radiative
Transfer Model (Mlawer et al., 1997) and Dudhia (Dudhia, 1989)
schemes for long and short wave radiation, respectively. Moisture and tracer
advection are calculated with the fifth-order weighted essentially
non-oscillatory (Liu et al., 1994) scheme with a positive definite
limiter. Spectral nudging of waves longer than around 1000 km is activated to
avoid distortion of the large-scale circulation within the regional model
domain due to the interaction between the model's solution and the lateral
boundary conditions (Miguez-Macho et al., 2004).

The methodology followed to validate WVTs is analogous to that used
previously by Bosilovich and Schubert (2002) and Sodemann et al. (2009), and it is
based on tagging moisture from all possible sources, so that if the method
were exact, the difference between tracer and total moisture should be zero.
In other words, let *S*_{n} (with $n=\mathrm{1},\mathrm{2},\mathrm{3}\mathrm{\dots}$) be a set of moisture sources
covering all possible atmospheric moisture sources, ${\mathrm{tq}}_{{S}_{n}}$ the total
moisture (the sum of all moisture species) from each source *S*_{n}, and *q*
the total moisture; then, the absolute error (*ε*_{a}) of the method
can be written as

$$\begin{array}{}\text{(13)}& {\displaystyle}{\mathit{\epsilon}}_{{\mathrm{a}}_{\mathrm{tq}}}(x,y,\mathit{\eta},t)=\sum _{n}{\mathrm{tq}}_{{S}_{n}}(x,y,\mathit{\eta},t)-q(x,y,\mathit{\eta},t),\end{array}$$

or in terms of precipitable water, integrating Eq. (13) in the vertical yields

$$\begin{array}{}\text{(14)}& {\displaystyle}{\mathit{\epsilon}}_{{\mathrm{a}}_{\mathrm{TTPW}}}(x,y,t)=\sum _{n}{\mathrm{TTPW}}_{{S}_{n}}(x,y,t)-\mathrm{TPW}(x,y,t),\end{array}$$

where TTPW${}_{{S}_{n}}$ refers to the total precipitable water coming from source
*S*_{n} and TPW is the total precipitable water simulated by the model.
Similarly, for precipitation,

$$\begin{array}{}\text{(15)}& {\displaystyle}{\mathit{\epsilon}}_{{\mathrm{a}}_{\mathrm{TP}}}(x,y,t)=\sum _{n}{\mathrm{TP}}_{{S}_{n}}(x,y,t)-P(x,y,t),\end{array}$$

where TP${}_{{S}_{n}}$ corresponds to the precipitation from source *S*_{n} and *P*
is the total precipitation produced by the model. Equation (15)
can also be applied to any particular type of precipitation, such as rain,
snow or graupel, individually.

Here, we have divided the possible moisture sources into five (${S}_{\mathrm{1}},\mathrm{\dots},{S}_{\mathrm{5}}$) sources, three of them two-dimensional (Fig. 3a) and two three-dimensional (Fig. 3b). The two-dimensional source regions cover all evaporative sources within the domain, namely sea, land and lakes, whereas the three-dimensional sources tag incoming moisture from the lateral boundaries and the moisture contained in the full atmospheric volume of the domain at initial time. For the latter purpose, the three-dimensional source “INITIAL” (Fig. 3b) is activated only at the first time step of the simulation. The “BOUNDARY” source (Fig. 3b) is a wall-like volume encompassing the relaxation zone where lateral boundary conditions are applied, along the domain's outer edges. To prevent moisture from evaporative or initial condition sources to be counted twice, this boundary volume becomes a sink for tracers of these other origins; that is, tagged moisture species from other sources are set to zero when they enter BOUNDARY. All possible atmospheric moisture sources are covered by the aforementioned five sources, and therefore Eqs. (13), (14) and (15) should be fulfilled at all times with zero error if the method were perfectly accurate.

To provide insights on the temporal evolution of the error, we follow the statistical treatment of Bosilovich and Schubert (2002), based on the calculation of the mean (ME) and standard deviation (SD) of the error at each point in time, that can be written as (following the notation used previously)

$$\begin{array}{}\text{(16)}& {\displaystyle}\left\{\begin{array}{l}\mathrm{ME}={\displaystyle \frac{\mathrm{1}}{N}}\sum _{i=\mathrm{1}}^{N}{\mathit{\epsilon}}_{{\mathrm{a}}_{\mathit{\alpha}}}^{i}\\ \\ \mathrm{SD}=\sqrt{{\displaystyle \frac{{\sum}_{i=\mathrm{1}}^{N}({\mathit{\epsilon}}_{{\mathrm{a}}_{\mathit{\alpha}}}^{i}-\mathrm{ME}{)}^{\mathrm{2}}}{N}}}\end{array}\right.,\end{array}$$

where *N* is the number of grid cells in the domain and *α* can
correspond to TP (total tracer precipitation or rain, snow or graupel
separately) or TTPW (tracer total precipitable water).

An alternative statistical treatment, which is very visual and can be used as
a second test of the reliability of the method, is that of
Sodemann et al. (2009), based on computing the relative contribution of each
moisture source to total precipitable water, total precipitation or to each
type of precipitation (rain, snow or graupel) separately. The calculation
returns the relative error of the mean values of those variables at each
instant in time. For example, let $\stackrel{\mathrm{\u203e}}{P}$ be the mean total
precipitation; then, the contribution (in %) of each source *S*_{n} is

$$\begin{array}{}\text{(17)}& {\displaystyle}{F}_{{\mathrm{TP}}_{{S}_{n}}}=\mathrm{100}\cdot {\displaystyle \frac{{\stackrel{\mathrm{\u203e}}{\mathrm{TP}}}_{{S}_{n}}}{\stackrel{\mathrm{\u203e}}{P}}},\end{array}$$

where ${\stackrel{\mathrm{\u203e}}{\mathrm{TP}}}_{{S}_{n}}$ represents the mean total precipitation from
source *S*_{n}. Then, if the method were perfectly accurate, the sum of all
contributions (${\sum}_{n}{F}_{{\mathrm{TP}}_{{S}_{n}}}$) should equal 100 %. The degree of
deviation of this sum with respect to the latter value yields the relative
error (*ε*_{r}) of the mean tracer precipitation:

$$\begin{array}{}\text{(18)}& {\displaystyle}{\mathit{\epsilon}}_{{r}_{\stackrel{\mathrm{\u203e}}{\mathrm{TP}}}}=\sum _{n}\mathrm{100}\cdot {\displaystyle \frac{{\stackrel{\mathrm{\u203e}}{\mathrm{TP}}}_{{S}_{n}}}{\stackrel{\mathrm{\u203e}}{P}}}-\mathrm{100}=\mathrm{100}\cdot {\displaystyle \frac{{\sum}_{n}{\stackrel{\mathrm{\u203e}}{\mathrm{TP}}}_{{S}_{n}}-\stackrel{\mathrm{\u203e}}{P}}{\stackrel{\mathrm{\u203e}}{P}}}.\end{array}$$

The above equation can be applied not only to total precipitation but also to any particular type of precipitation or to total precipitable water. Finally, we note that the concept of relative error of the mean variables should not be confused with the mean relative error, which would be expressed, following the notation used in the equation above, as

$$\begin{array}{}\text{(19)}& {\displaystyle}\stackrel{\mathrm{\u203e}}{{\mathit{\epsilon}}_{{r}_{\mathrm{TP}}}}={\displaystyle \frac{\mathrm{1}}{N}}\sum _{i=\mathrm{1}}^{N}{\left(\mathrm{100}\cdot {\displaystyle \frac{{\sum}_{n}{\mathrm{TP}}_{{S}_{n}}-P}{P}}\right)}_{i}.\end{array}$$

This last variable will also be used during the validation treatment shown below.

As mentioned earlier, the validation experiment is a month-long simulation
for November 2014 over North America. Figure 4 shows the results
obtained in this simulation for total precipitation from each of the five
analyzed sources (TP_{S1}, TP_{S2}, …) depicted in Fig. 3
and the total sum of precipitation from all sources (${\sum}_{n}{\mathrm{TP}}_{{S}_{n}}$).
The relaxation zone along the boundaries is excluded in these figures. The
largest contribution to total precipitation is from external advection into
the domain, and in the eastern half of it, also from sea evaporation. Lake
evaporation is locally important around the Great Lakes and in Canada, where
most smaller lakes in the grid are located. Evapotranspiration over land is not very
relevant in the month of November and neither is its contribution to
precipitation. Moisture present at initial time precipitates significantly
only toward the eastern boundary of the domain in the downwind direction of
the dominant westerly flow.

According to Eq. (15), for the absolute error to be zero at each point, the result in Fig. 4f should exactly match the total precipitation calculated by the model, shown in Fig. 5a. The values of this error (i.e., the differences between the results of Fig. 4f and Fig. 5a) are depicted in Fig. 5b. The maximum deviations between the sum of the precipitation coming from the five considered sources and the total precipitation calculated by the model occur over the sea, near the domain's edges, and hover around −3 mm. These values correspond to very low relative errors (Fig. 5c), since the cumulative precipitation in these areas during the month of November is very high, often exceeding 300 mm. In most regions, however, the absolute error is clearly less than 1 mm, close to zero for the most part and thus very small, even in the relative sense. Neglecting cells where the total monthly precipitation is less than 1 mm to avoid arithmetical problems, the area-averaged value of the relative error (Eq. 19) is −0.17 %, with a standard deviation of 0.20 %. The maximum relative error found at any point is only −3.73 % in areas of the US desert southwest with low accumulated precipitation during the simulated month of November.

Figure 6 shows, at 3 h intervals, the ME and SD for the three precipitation types, rain (Fig. 6a),
snow (Fig. 6c) and graupel (Fig. 6e), throughout the
monthly period of simulation. Values of the mean error are very close to zero
at all times, with small standard deviations of about 0.05 mm day^{−1} for rain,
0.01 mm day^{−1} for snow and 0.005 mm day^{−1} for graupel, indicating that the
compensations between positive and negative errors are not very relevant. As
expected, the error is larger for the domain-wide most abundant precipitation
types (rain and snow, in this order) and smaller for the most residual type
of precipitation (graupel). Bosilovich and Schubert (2002) found mean errors very
close to zero for precipitation, as in our case, but comparatively much
larger standard deviations of about 0.2 mm day^{−1} (∼5 *%*). In addition,
Fig. 6 shows the relative contribution of each considered moisture
source to area-averaged rain (Fig. 6b), snow (Fig. 6d) and
graupel (Fig. 6f). Moisture initially present in the domain's
atmospheric columns only contributes to any precipitation type during
approximately the first week of simulation. Rain is roughly about 40 % of sea
evaporation origin and 60 % from moisture influxes from the lateral
boundaries, with these values oscillating throughout the month. In comparison
with rain, snow and graupel have a stronger contribution from external
moisture advection and also from land evapotranspiration and lake
evaporation, and a much smaller fraction of sea evaporation input. As these
figures are cumulative diagrams, the upper line (which separates the white
zone from the color zone), indicates the combined contribution of all sources
to precipitation. The deviation of this line from 100 % represents the
relative error of mean domain precipitation (Eq. 18), which, as
it is apparent, is very small for all three precipitation types and at all
times. Further discussion will follow later in this section.

Validation results in terms of total precipitable water are presented in the
diagrams of Fig. 7, which are similar to those in Fig. 6
for precipitation. In this case, the mean error (Fig. 7a) takes
values around −0.01 mm, whereas the standard deviation is about 0.1 mm, which
are very small numbers. To contextualize these results, we refer again to
Bosilovich and Schubert (2002), who show a mean error around −0.5 mm (∼2 *%*) and
standard deviation of about 0.5 mm.

Finally, Fig. 8 shows in more detail the time evolution of the
relative error of mean domain precipitation of all three types, as well as of
mean domain TPW. This corresponds to the deviation from 100 % in the
cumulative values in figures Figs. 6b, d, f and 7b, as
discussed previously. Numbers are similar for the three precipitation types
and do not exceed ±0.4 %. On average, about 0.2 *%* of precipitation is
not associated with any of the five considered moisture sources; i.e., the
mean domain relative error is around −0.2 *%*. For TPW, errors are even
smaller. In this case, the deviation of the sum of contributions from all
sources from 100 %, is roughly −0.1 % (Fig. 8), which means that
only 0.1 % of TPW is not traceable. Sodemann et al. (2009) found, at first,
errors that were around 10 % for TPW, and later this value was improved to
1–2 % (Sodemann and Stohl, 2013). Finally, we note that during the simulation
period (1 month) there is no increasing trend in these errors, which
attests to the method's stability.

Both the small absolute and relative values of the analyzed error measures in this section, together with the lack of trends in the errors, demonstrate the high accuracy and soundness of the method. Finally, with regard to the causes of these inaccuracies, most likely, they are largely caused by numerical errors derived from the very large moisture tracer gradients that occur in some regions of the domain, for example, in the separation region between the BOUNDARY source (Fig. 3b) and the interior of the domain. These sharp transitions can induce small errors in the advection scheme and also stronger numerical diffusion than for full moisture. In addition, other errors, such as rounding errors or small inaccuracies in the water budget, contribute secondarily.

4 Application example: lake evaporation as moisture source in the Great Lakes snowstorm of 2014

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Heavy snowstorms are common meteorological phenomena in the North American Great Lakes region during autumn and winter months, usually associated with the intrusion of a cold and dry polar air mass over the warmer lake waters (Eichenlaub, 1970; Hjelmfelt and Roscoe, 1983; Niziol et al., 1995; Wiggin, 1950; Wright et al., 2013). The resulting large water–atmosphere temperature contrast increases heat and moisture fluxes from the lakes, destabilizing the planetary boundary layer (Chang and Braham, 1991; Lenschow, 1973) and leading to an activation and/or intensification of precipitation downwind. On some occasions, snow bands formed during these events produce huge snow accumulations, with high socioeconomic impacts (Changnon, 1979; Eichenlaub, 1978; Schmidlin, 1993).

It is well established that heat and moisture fluxes from the lakes are fundamental in the development of these episodes, since they cease to occur once open waters freeze over. Given the low moisture content of polar air masses, it is also likely that without evaporative fluxes from the lakes, large accumulations of snow would not be possible. It is still not clear, however, what the actual input of lake water to snowfall is in these events. Studies about the contribution of evaporated moisture from the Great Lakes to precipitation in lake-effect snowstorms are scarce, based on the analysis of the isotopic composition of precipitation (the so-called physical moisture tracers) and do not correspond to particular extreme events but to climatic periods (Gat et al., 1994; Machavaram and Krishnamurthy, 1995). The WRF-WVT tool that we present here can contribute to clarify this question, and, as an application example, in this section, we quantify the role of the Great Lakes as moisture sources in the famous case of the November 2014 severe lake-effect snowstorm, the so-called “Snowvember” by local residents, which affected especially New York state (mainly cities bordering lakes Erie and Ontario and, in particular, the Buffalo area) between 17 and 21 November, causing at least 13 fatalities, widespread food and gas shortages due to blocked roads and, in general, many other traffic problems and material losses derived from the storm (National Weather Service, NOAA, 2014).

The example application experiment is run for 4.5 days (17:00–00:00 to 21:00–12:00 UTC November) in a D2 domain nested within the validation simulation and encompassing the Great Lakes region with a horizontal resolution of 5 km and the same 35 vertical levels as the parent domain D1 (Fig. 2). Tracer moisture from the parent domain can feed the nested domain through its lateral boundaries, which are not set to zero. The simulation serves also as an example of the versatility of the tagging tool. The physics settings in this experiment are identical to those in the validation simulation, except for spectral nudging and the convective parameterization, which are turned off.

Figure 9 shows the general synoptic situation for the selected case,
in terms of surface pressure and 850 hPa temperature (Fig. 9a)
along with 500 hPa geopotential height and temperature (Fig. 9b),
both at 12:00 UTC on 18 November 2014. The situation is that which
is typically associated with Great Lake-effect snowstorms: a deep
trough with low temperatures aloft over the region, causing intense
west–northwest winds at lower levels across the Great Lakes and very cold
air advection. The lakes were mostly ice free at this time, with temperatures
between 0 and 8 ^{∘}C, the warmest in Lake Erie (Fig. 10b),
contrasting markedly with the below −15 ^{∘}C values at 850 hPa. The
topography of the area is also shown in Fig. 10, with the highest
terrain east of Lake Erie.

Figure 11 shows the daily evolution, from 17 to 20 November 2014, of
the precipitable water originating from evaporation in the lakes and the
10 m wind at 12:00 UTC. Paired panels depict the percentage of total
precipitable water that those amounts represent, together with 850 hPa
temperature. At 12:00 UTC on 17 November, a short wave trough was pushing
past the region. Winds ahead of the associated front were still from the
south over lakes Erie and Ontario, with moderately low temperatures above
−6 ^{∘}C at 850 hPa; however, behind the trough, a very cold air
mass was already in place over lakes Superior, Michigan and Huron, where
winds had already veered and were at this time from the west–northwest
direction. The enhancement of evaporation from the lakes is already apparent
at this time, with precipitable water plumes from lakes Superior and Huron
with values around 2–3 mm, which represent a contribution of 20–30 %
of the total. After frontal passage, the next day, winds increase in
intensity and change direction to the west–northwest, and the cold air
settles in with temperatures around −16 ^{∘}C at 850 hPa. The
arrival of the cold and dry air mass, together with the wind intensity rise,
augment evaporation fluxes from the surface of the lakes, so that the
precipitable water with this origin practically doubles with respect to the
previous day, increasing the lake moisture contribution to about 30–60 %
of the total. The highest values are attained in plumes aligned with the main
wind direction that originate from open waters and extend leeward of the
lakes. The cold air stays in place for the next days and lake water
evaporation values remain high; however, the direction of the moisture plumes
from this source vary as wind changes due to the approach of another short
wave trough, turning more toward the north as the flow becomes southerly on
19 November and again westward of the lakes when winds turn in this direction
on 20 November. In the areas where the 850 hPa temperatures remain below
about −15 ^{∘}C during the short wave passage, plumes of moisture
from the lakes still develop, with an input of lake moisture above 30 %
of total content.

The previous results suggest that the lakes' contribution to atmospheric moisture in the region is very significant for this event, and we assess next whether this is also the case for precipitation. Observed snowfall totals for the period between 17 November at 06:00 UTC and 21 November at 06:00 UTC (Fig. 12a, from NOAA's National Snow Analyses data; Carroll et al., 2006) were very high, with peak values close to 100 mm in the Buffalo, NY, area, to the lee of Lake Erie, and with other pockets of over 60 mm of snow water equivalent accumulations on the leeward shores of lakes Huron and Ontario, where orographic lifting from the existing hills further enhances precipitation. Figure 12b shows model results for the same period, which are in very good agreement with the observations, in amounts and distribution. This is particularly true for the aforementioned areas of highest snowfall totals.

The part of precipitation originating from lake evaporation during the same 4-day period is shown in Fig. 13, in terms of absolute (Fig. 13a) and relative (Fig. 13b) values to total accumulations. The role of the lakes as moisture sources is very relevant. In general, in all regions immediately downwind of the Great Lakes, water vapor with this origin accounts for more than 30 % of precipitation. The areas where the contribution of lake water vapor fluxes to precipitation is largest coincide with the locations of maximum snowfall totals, to the lee of lakes Huron, Erie and Ontario. Here, more than 50 % percent of the snow water equivalent has its source in lake evaporation, which attests to the fundamental role of lake moisture in producing the observed localized extreme accumulations during these events. In regions further from the lakes, the pattern of total precipitation and that of precipitation originating from lake evaporation lose correlation.

5 Summary and conclusions

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We presented here a new moisture tagging tool, coupled to the WRF model v3.8.1, for the analysis of precipitation sources and atmospheric humidity pathways in general. The technique is framed within the online Eulerian methods usually known as WVTs. We first detailed the method's formulation and its implementation into WRF, which required the modification of the turbulent, microphysics and cumulus parameterizations for the calculation of the associated tracer tendencies. We then assessed the method's precision with a validation strategy consisting in tagging moisture from all possible sources and evaluating the difference between the sum of all these contributions and total moisture results, in terms of precipitable water and precipitation. We identified the method's error with these deviations. The sources considered were incoming fluxes from the model grid's lateral boundaries, the moisture initially present in the entire atmospheric volume of the domain and surface evaporation. We further divided evaporative sources into three, namely ocean, land and lakes, which made the validation somewhat more challenging. We performed a 1-month long (November 2014) continental-scale (North America), 20 km resolution model simulation for this purpose and found that the deviations of area-averaged variables are consistently about −0.1 % for precipitable water and −0.2 % for 3 h accumulated rain, snow or graupel. This means that there is a small amount of precipitable water and precipitation that the method cannot link to any source. There is no noticeable increasing trend in these errors during the month-long period of simulation. The mean relative error and the standard deviation for the monthly accumulated precipitation is −0.17 and 0.2 %, respectively, about the same as for the 3 h values throughout the same period. These results demonstrate the robustness of our WRF-WVT implementation as a sound and highly accurate tool to track atmospheric moisture pathways.

Finally, as an example application of the moisture tagging technique, we
simulated the Great Lake-effect snowstorm of 2014, aiming at quantifying the
contribution of evaporative fluxes from the lakes to total precipitable
water and especially to snowfall amounts in this event. We employed for this
purpose a nested grid within the validation domain, covering the Great Lakes
region at 5 km resolution and simulated the 4-day period from 17 November
at 06:00 UTC to 21 November at 06:00 UTC. Results show the activation of the lake effect upon
arrival of a cold and dry arctic air mass over the area, with the formation
of total precipitable water plumes originating from the lakes and extending
tens and even hundreds of kilometers in the downwind direction. As expected,
the model shows how the lake effect intensifies with colder and stronger west
or northwesterly surface winds and tapers off with warmer and weaker
southerly airflows. The contribution of lake-evaporated moisture to total
precipitable water within the plumes is generally above 30 % across the area
downwind of the lakes when temperatures at 850 hPa are below around
−15 ^{∘}C, and exceeds 60 % in plumes to the lee of lakes Huron, Ontario and Erie when
conditions are most favorable for lake effect on 18 November.

The model simulation reproduces faithfully observed snowfall accumulations during the 4-day period, with maximum amounts of close to 100 mm of snow water equivalent in the Buffalo, NY, area, to the lee of Lake Erie and other pockets with values above 60 mm on the leeward shores of lakes Huron and Ontario. It is in these locations of highest impact where the contribution of lake evaporation to precipitation is largest, between 50 and 60 % of the total. In general, for all regions immediately downwind of the lakes, the input of lake moisture to precipitation is about 30–50 % and diminishes gradually at further distances.

These results highlight the important contribution of evaporative moisture fluxes from the lake surfaces in the genesis of precipitation during Great Lake-effect snowstorms. They also suggest that this input is fundamental in producing the most extreme accumulations, with the highest socioeconomic impacts, in the Buffalo, NY, area and other locations to the lee of the lakes, especially Erie, Ontario and Huron. To draw a more robust general conclusion, an in-depth investigation with a sufficient number of cases and further diagnostics would be needed; however, this is beyond the scope of the present article and a matter of future work, since our intent here is to simply illustrate with a practical example the possibilities of WRF-WVT as a powerful tool for moisture tracking.

Data availability

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Data availability.

No public data are derived from this research. For further information on the WRF-WVT tool, please contact the corresponding author.

Author contributions

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Author contributions.

GMM developed the WRF-WVT code. DIC refined this code, designed the experiments and performed the calculations. Both authors contributed equally to the development of the article.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement

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Special issue statement.

This article is part of the special issue “The 8th EGU Leonardo Conference: From evaporation to precipitation: the atmospheric moisture transport”. It is a result of the 8th EGU Leonardo Conference, Ourense, Spain, 25–27 October 2016.

Acknowledgements

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Acknowledgements.

Funding for this work came from the European Commission FP7 (EartH2Observe) and
the Spanish Ministerio de Economía y Competitividad (CGL2017-89859-R and
CGL2013-45932-R), and from contributions by the CRETUS Strategic Partnership
(AGRUP2015/02). Computation took place at CESGA (Centro de Supercomputación de Galicia),
Santiago de Compostela, Galicia, Spain.

Edited by: Sergio Martín Vicente Serrano

Reviewed by: three anonymous referees

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Short summary

We present here a newly implemented water vapor tracer tool into the WRF meteorological model (WRF-WVT). A detailed validation shows high accuracy, with an error of much less than 1 % in moisture traceability. As an example application, we show that for the 2014 Great Lake-effect snowstorm, above 30 % of precipitation in the regions immediately downwind originated from lake evaporation, with contributions exceeding 50 % in the areas with highest snowfall accumulations.

We present here a newly implemented water vapor tracer tool into the WRF meteorological model...

Earth System Dynamics

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