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\begin{document}

\title{Assessing the significance of wet-canopy evaporation from forests during
extreme rainfall events for flood mitigation in mountainous regions of
the UK}



\author[1]{Trevor Page}%
\author[1]{Keith Beven}%
\author[1]{Nick Chappell}%
\author[1]{Ann kretzschmar}%
\author[2]{Barry Hankin}%
\affil[1]{Lancaster University}%
\affil[2]{JBA Consulting}%


\vspace{-1em}



  
  \date{June 09, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
There is increased interest in the potential of tree planting to help
mitigate flooding using nature-based solutions or natural flood
management. However, many publications based upon catchment studies
conclude that, as flood magnitude increases, benefit from forest cover
declines and is insignificant for extreme flood events. These
conclusions conflict with estimates of evaporation loss from forest plot
observations of gross rainfall, throughfall and stem flow. This study
explores data from existing studies to assess the magnitudes of
evaporation and attempts to identify the meteorological conditions under
which they would be supported. This is achieved using rainfall event
data collated from publications and data archives from studies
undertaken in temperate environments around the world. The
meteorological conditions required to drive the observed evaporation
losses are explored theoretically using the Penman-Monteith equation.
The results of this theoretical analysis are compared with the
prevailing meteorological conditions during large and extreme rainfall
events in mountainous regions of the UK to assess the likely
significance of wet canopy evaporation loss. The collated dataset showed
that Ewc losses between approximately 2 and 38\% of gross rainfall (1.5
to 39.4 mm d-1) have been observed during large rainfall events (up to
118 mm d-1) and limited data for extreme events (\textgreater{} 150 mm
d-1). Event data greater than 150 mm, where duration was not reported,
showed similarly high percentage evaporation losses. Theoretical
estimates of wet-canopy evaporation indicated that, to reproduce these
high losses, relative humidity and the aerodynamic resistance for vapour
transport needed to be within an envelope of approximately 90 to 97.5\%
and 0.5 to 2 s m-1 respectively. Surface meteorological data during
large and extreme rainfall events in the UK suggest that conditions
favourable for high wet-canopy evaporation are not uncommon and indicate
that significant evaporation losses during large and extreme events are
possible but not for all events and not at all locations. Thus the
disparity with the results from catchment studies remains.%
\end{abstract}%



\sloppy


\textbf{Keywords}

Wet-canopy evaporation; interception loss; extreme events; Natural Flood
Management; meteorological controls; complex terrain; upland UK

\textbf{1. Introduction}

Recently in the UK, and elsewhere, there is increased interest in
`natural flood management' (NFM) or `nature-based solutions' for flood
peak mitigation (Dadson \emph{et al} ., 2017; Environment Agency, 2018;
Jongman, Winsemius, Fraser, Muis, \& Ward, 2018; Lane, 2017;
Wingfield\emph{, et al} ., 2019; World Bank, 2017). Tree planting may be
one intervention that has the potential for flood peak reduction
through: 1. increased soil infiltration capacity; 2. enhanced soil
drying resulting from transpiration; 3. increased ground-surface
roughness and 4. enhanced wet-canopy evaporation (\emph{Ewc} ). However,
some studies suggest that the positive effects of tree cover on flood
peaks declines as event magnitude increases, such that it is likely to
be insignificant for large and extreme flood events (e.g.
Bathurst\emph{et al} ., 2018; Dadson \emph{et al} ., 2017; Robinson \&
Newson, 1986; Stratford \emph{et al} ., 2017). These results suggest,
implicitly, that \emph{Ewc} is insignificant during large and extreme
events.

For paired grassland and forest catchments on the Plynlimon massif (UK),
Kirby, Newson, \& Gillman (1991, p60) observed, using flood frequency
analysis, that mature conifer cover had little or no effect on the
magnitude of peak flows. They showed, using \emph{chronological
pairing}of flood peaks, that very small hydrograph peaks were
consistently greater from the grassland catchment compared to the
forested catchment and that moderately sized event hydrographs showed no
significant difference. At another paired forest and grassland study at
Coalburn, Northern England, Bathurst \emph{et al} . (2018) reported that
forests can reduce flood peaks for small to moderate events but that
hydrograph responses tend to converge at extreme events. Bathurst
\emph{et al.}(2011) explicitly tested the hypothesis: \emph{as the size
of the hydrological event increases, the effect of forest cover becomes
less important} ; they concluded, for a number of study sites across
Latin America, that forests do not eliminate floods and are unlikely to
reduce significantly peak flows generated by extreme rainfall.
Bathurst\emph{et al.} (2011) however acknowledged that their analyses
were based on relatively short periods with few extreme events such that
conclusive support for the test hypothesis is still lacking.

Recent NFM-related literature reviews of forest effects on flood peaks
support the idea of a diminishing effect with event magnitude.
Stratford\emph{et al.} (2017) carried out a systematic review of studies
to answer the question: \emph{Do trees in UK-relevant river catchments
influence fluvial flood peaks?} Their review focussed directly on the
magnitudes of flood peaks rather than on individual hydrological
processes and they concluded that the evidence is uncertain for the
impact of increasing tree cover on large floods but it is consistent in
showing increasing tree cover reduces small floods. Dadson \emph{et al}
. (2018) also reviewed evidence of the effects of forest cover and
reported the findings of a number of studies; they recognised that
forest management practices complicate determination of forest effects
but that under sustained winter rainfall, soil saturation will occur and
little mitigation of high flood flows would be expected.

From a process point of view, the benefits of increased infiltration
rates and drier antecedent soil moisture conditions are likely to
diminish with increasing event magnitude (Calder \& Aylward, 2006; Lull
and Reinhart 1972; Pereiea, 1989); it is also likely that that boundary
layer vapour pressure deficits, which exert a strong control
on\emph{Ewc} , are likely to decrease during large and extreme rainfall
events but the extent to which they decrease across large areas is not
well known. The studies cited above did not explicitly included evidence
from forest plot studies which estimate \emph{Ewc} in a more direct way
using a \emph{canopy water balance} (described below), perhaps because
only very few studies report \emph{Ewc} for large or extreme events;
they primarily considered the detection of hydrograph change from
catchment studies globally.

Worldwide, catchment studies taken as a whole provide conflicting
results regarding effects on large flood peaks; compare for example
Jones \& Grant (1996), Thomas and Megahan (1998) and Beschta \emph{et
al} ., 2000. Many studies have found that the magnitudes or frequencies
of large flood peaks are changed significantly by afforestation or
forest harvesting (e.g. Alila \emph{et al} ., 2009; Belmar \emph{et al}
., 2018; Fahey and Payne, 2017; Guillemette, Plamondon, Pr\selectlanguage{ngerman}évost \&
Lévesque, 2005; Jones \& Grant, 1996; López-Moreno et al., 2006); many
do, however, show decreasing effects on flood peak as event magnitude
increases or no significant change (Beschta \emph{et al} ., 2000,
Birkinshaw \emph{et al} ., 2014; Robinson \& Newson, 1986; Thomas and
Megahan, 1998; Whitehead and Robinson, 1993; Newson \& Calder, 1989).
Uncertainties associated with catchment studies of hydrograph change,
particularly for extreme events, can be very large (Bathurst \emph{et
al} ., 2018; Beschta \emph{et al} ., 2000; Carrick \emph{et al} ., 2018;
Dadson \emph{et al} ., 2017). Underlying signals of change associated
with specific processes (e.g. evaporation or infiltration) can also be
obscured by effects resulting from forestry practices, such as road
construction, drainage or harvesting method (Bathurst \emph{et al} .,
2018; Beschta \emph{et al} ., 2000; Jones \& Grant, 1996;
Guillemette\emph{et al} ., 2005; Robinson \& Newson, 1986; Thomas and
Megahan, 1998). These factors combined with limited observations for
extreme events (Lewis, Reid \& Thomas, 2010) mean that simple
conclusions regarding forest effects on large or extreme flood peaks
cannot be made (Andreassian, 2004; Carrick \emph{et al} . 2017).

\textbf{1.1 Forest plot studies of wet-canopy evaporation: losses during
large and extreme rainfall events}

Forest plot studies estimate \emph{Ewc} , using a canopy water balance
(CWB), as the difference between the gross rainfall (\selectlanguage{english}?\selectlanguage{english}?) incident upon a
vegetation canopy and the fraction of \selectlanguage{english}?\selectlanguage{english}? that reaches the ground
as\emph{net rainfall} (Pn). Net rainfall comprises
rainfall that bypasses or drips from the canopy (\emph{throughfall} :
\emph{TF} ) and that which flows via stems and trunks (\emph{stem flow}
: \emph{SF} ). As noted above, very few studies have focused on CWB
estimated\emph{Ewc} during large (\textgreater{} 50 mm
d\textsuperscript{-1} of \selectlanguage{english}?\selectlanguage{english}?) or extreme (\textgreater{} 150 mm
d\textsuperscript{-1} of \selectlanguage{english}?\selectlanguage{english}?: Collier, Fox \& Hand, 2002) rainfall
events. A notable exception is the work of Keim, Skaugset, Link and
Iroume (2004) who report Ewc losses above 30\% of \selectlanguage{english}?\selectlanguage{english}? at temperate sites
in Chile and Northwest USA. Equally high \emph{Ewc} losses during large
magnitude rainfall events at other locations with a temperate climate
have been reported (e.g. see Deguchi\emph{et al} ., 2006 and Hashino
\emph{et al} ., 2002)\emph{.} Taken at ``face value'', these \emph{Ewc}
losses appear to be potentially significant in the context of flooding:
removal of such large fractions of event rainfall from a catchment
system are likely to have a significant effect on a flood hydrograph
where tree planting covers a large proportion of a catchment (Hankin
\emph{et al} ., 2017). Consequently, there is an apparent disparity
between the publications which conclude that forest effects on flood
peaks are likely to be small or insignificant for large and extreme
events and the CWB observations from forest plot studies.

The significance of forest \emph{Ewc} for flood mitigation depends upon
the difference in \emph{Ewc} between a given forest canopy and another
land cover. For example, moorland vegetation species such as Heather
(\emph{Calluna vulgaris} ) tend to have
\emph{long-termevapotranspiration} losses approximately 30\% to 60\% of
that for tall forests and short semi-natural grasses lose around 10 to
40\% of that for forests (e.g. Calder, 1976, Calder \& Newson, 1979;
Calder\emph{et al} ., 1981). However, as most comparative studies derive
estimates from catchment or lysimeter water balances over relatively
long periods, and do not separate \emph{Ewc} and transpiration losses,
these estimates are of limited use when considering individual events.
Additionally, evaporation from a forest understorey or soil litter layer
can be significant (Bulcock \& Jewitt 2012; Carlisle \emph{et al} .,
1967; Gerrits \emph{et al} ., 2007, 2010) and effectively increase the
difference in \emph{Ewc} loss (e.g. between forest and grass). We
therefore assume that \emph{Ewc} losses from tall canopies are likely to
be significantly higher than for short vegetation under meteorological
conditions favourable for wet-canopy evaporation and, consequently, that
the absolute magnitude of \emph{Ewc} from tall forest canopies is of
primary relevance here. Thus it is important to determine the full
extent of evidence for significant \emph{Ewc} from forest canopies
during large and extreme rainfall events as well as an understanding of
the meteorological conditions under which significant losses might be
supported.

\textbf{1.2 Aim and objectives of this study}

This study focuses on \emph{Ewc} from forest canopies during large and
extreme rainfall events. We use the Cumbrian Mountains, UK, as a focus
for some of our analyses as large catchment-scale hydrological
simulations of broad-scale tree planting are required. These simulations
are designed to inform UK policy on the most effective methods of NFM.
To inform these simulations, pertinent event-scale \emph{Ewc} data from
temperate sites around the world are collated and are contextualised
using UK meteorological conditions via theoretical analyses. In the UK,
large and extreme rainfall events primarily occur as long-duration
autumn and winter storms when forest canopies can be continually wet,
solar radiation is low and Ewc will dominate evaporative losses (Calder,
1990); these events are the focus of this study rather than extreme
summer convective storms.

Our specific objectives are:

\textbf{Objective 1} - to collate all available \emph{Ewc} data from
UK-relevant event-scale forest plot studies to quantify the magnitude
and range of observed losses, particularly during large (\textgreater{}
50 mm d\textsuperscript{-1}) and extreme (\textgreater{} 150 mm
d\textsuperscript{-1}) rainfall events;\textbf{Objective 2} - to explore
the meteorological conditions consistent with the magnitudes of
\emph{Ewc} losses from Objective 1 using the Penman-Monteith
equation;\textbf{Objective 3} - to examine meteorological data from
Cumbria and other mountainous regions of the UK during large and extreme
rainfall events and to compare with the findings of Objective
2;\textbf{Objective 4} - to discuss the implications of the findings
from objectives 1 to 3 for estimating \emph{Ewc} across large catchments
in complex terrain.

\textbf{2. Methods}

\textbf{Study area}

The primary area of interest for this study, Cumbria, Northwest England
(Figure 1) where the Q-NFM project
(http://www.lancaster.ac.uk/lec/sites/qnfm) is tasked with simulating
the effects of broad-scale tree planting scenarios on flood hydrographs
using a catchment hydrological model. The study catchments are within a
mountainous area where there have been 4 major flood events in the last
15 years. Cumbria, as for many mountainous regions of the UK, is
situated towards the west coast and hence strongly influenced by
temperate maritime airflows from the Atlantic Ocean. Mountainous regions
of the UK are areas of extremely complex topography which, in
combination with the predominant airflow, gives rise to
orographically-influenced and spatially heterogeneous meteorological
patterns (Blackie and Simpson, 1993; Ferranti, Whyatt, \& Timmis, 2009,
Mayes, 2013). Annual rainfall is generally high; for example, across
Cumbria the long-term annual average rainfall ranges from below 1000 mm
yr\textsuperscript{-1} on the coast and in areas of rain shadow to
greater than 3500 mm yr\textsuperscript{-1} across the highest
mountains. Given there are no CWB \emph{Ewc} data for this study area we
consider other mountainous sites in the UK (Figure 1) and other
temperate locations around the world.

\textbf{2.2 Observed event \emph{Ewc} estimates from forest plot studies
in temperate locations}

Studies relevant to UK conditions with forest plot CWB
\emph{Ewc}observations were identified. Relevant studies were defined
climatologically using the revised Koppen climate classification (Chen
\& Chen, 2013) with the recognition that the classification provides
general climatic classes within which there is a large degree of
variability. Although this variability exists, Koppen climate
classifications were used with the rationale that hydrometerological
conditions will have similarities to those of UK mountainous regions
during large and extreme rainfall events. The specific classifications
deemed acceptable for the purposes of this study were: Cfa (mild
temperate; fully humid; hot summer), Cfb (mild temperate; fully humid;
warm summer), Cfc (mild temperate; fully humid; cool summer), Csb (mild
temperate; dry summer; warm summer), Dfb (snow; fully humid; warm
summer), Dfc (snow; fully humid; cool summer), Dfd (snow; fully humid;
cold summer): the classifications Cfb and Cfc encompass all mountainous
regions of the UK. For the climate classes where snow can form a
significant part of winter precipitation (i.e. Dfb, Dfc and Dfd), care
was taken not to include data affected by snow falls: in most cases this
was already carried out in the original study.

From the studies identified as relevant (Table Supp. 1), only
CWB\emph{Ewc} observations reported on a rainfall event basis or as a
daily total were collated for analyses. For consistency, events reported
to be over 24 hours (but no more than 48 hours) duration were
standardised by calculating a \emph{normalised 24-hour rainfall}
(i.e.\(Pg=\ 24\left(\frac{\text{Pe}}{\text{De}}\right)\)) wherePe is the total event
precipitation and De is event duration in hours): note
that, in the text below, \selectlanguage{english}?\selectlanguage{english}? relates to a daily or normalised daily total
rainfall unless otherwise stated. It is accepted that using daily
observations is somewhat artificial in as much as the duration of
rainfall events may be truncated where they span multiple days; it is
also recognised that both daily and event data may include periods
without rain. Event-based data where event duration was not reported
were also collated and are presented separately.

Data were gathered using values provided in tables or by digitising data
presented as figures in published material and by abstracting data from
field log sheets; in the case of Aussenac (1968) and Reynolds and
Henderson (1967) Pg-\emph{Ewc} relationships were
digitised. Where observations were obtained from digitised figures, and
where there were many data points, obscured or overlapping data will
have resulted in some values not being included; these data were,
however, invariably for relatively low \selectlanguage{english}?\selectlanguage{english}? magnitudes. In some cases, the
dates associated with individual rainfall events were not provided in
the published material, which does not allow separation by season (or by
leafed or leafless period for deciduous species). Furthermore, as event
data were limited and data for deciduous forest plots were very few, all
events irrespective whether they were evergreen or deciduous were
combined for the comparison with theoretical estimates, but are
identified separately in figures.

\textbf{2.3 Theoretical Ewc estimates}

\textbf{2.3.1 Exploring the drivers of observed \emph{Ewc} losses using
the Penman-Monteith equation}

To explore the meteorological conditions required for consistency with
observed \emph{Ewc} losses, a broad range of Ewc estimates were made
using the Penman-Monteith equation (Monteith, 1965 ;Eqn. 1); estimates
were made using stratified samples from ranges of relative humidity
(85\% to 100\%; expressed via\(\text{\ e}_{z}\) where Tz
is assumed to be 10\textsuperscript{o}C) and aerodynamic resistances
(0.5 s m\textsuperscript{-1} to 12 s m\textsuperscript{-1}). This
analysis creates a response surface where different combinations of
meteorological variables that lead to similar \emph{Ewc} losses can
easily be visualised. The Penman-Monteith equation takes the form:

\(\lambda E_{\text{PM}}=\ \frac{\Delta_{e}H{\ +\ \rho}_{a}c_{p}\ (e_{s}\left(\text{Tz}\right)-e_{z})/r_{a}\_s\ }{\Delta_{e}+\ \Upsilon\left(1+r_{g}/r_{a}\_s\right)}\)(1)

where \(\lambda\) is the latent heat of vaporisation (J
kg\textsuperscript{-1}), \(E_{\text{PM}}\ \)is the evapotranspiration
rate (kg m\textsuperscript{-2} s\textsuperscript{-1}),
\(\Delta_{e}\)is the slope of the saturation vapour pressure curve
versus temperature relationship (Pa K\textsuperscript{-1}) at
temperature,\(\left.\ \text{Tz}\right.\ ,\) where \emph{z} is the observation height
in metres, \(H\) is the total energy available for
evaporation (J m\textsuperscript{-2}), \(\rho_{a}\) is the density
of air at Tz (kg m\textsuperscript{-3}),
\(c_{p}\ \)is the specific heat capacity of air (J
kg\textsuperscript{-1} K\textsuperscript{-1}),\(e_{s}\left(\text{Tz}\right)\) is the
saturation vapour pressure at Tz, \(e_{z}\ \)is
the actual vapour pressure at \emph{z} ,\(\gamma\) is the
psychrometric constant (\(\approx\) 66 x 10\textsuperscript{-3}
Pa K\textsuperscript{-1}) and \(r_{a}\_s\) and\(r_{g}\)
are the resistance to the aerodynamic exchange for scalars (sensible
heat and vapour) and surface resistances respectively (s
m\textsuperscript{-1}). Note that in all calculations made here, the
canopy is assumed to be wet and \(r_{g}\) is assumed to be
zero such that the term \(\left(1+r_{g}/r_{a}\_s\ \right)\) disappears (Stewart, 1977;
VanDijk et al., 2015). The total energy available (\(H\))
was assumed to be the approximate net radiation (\(R_{n}\))
for a cloudy day during winter in Northern England: nominally 2.5 MJ
m\textsuperscript{-2} d\textsuperscript{-1}.

\textbf{2.3.2 Estimates of aerodynamic exchange and}\(\mathbf{E}_{\mathbf{\text{PM}}}\)
\textbf{using meteorological observations}

To explore the potential for Ewc across mountainous regions of the UK
during large and extreme rainfall events, \(E_{\text{PM}}\) was
calculated using meteorological data for 17 sites (Figure 1a and Table
Supp. 2) using Eqn. 1. The aerodynamic resistance for momentum
(\(r_{a}\_m\)) was estimated using Eqn. 2:

\(r_{a}\_m=\frac{\ln\left(\frac{z-d}{z0\_m}\right)^{2}}{\kappa^{2}U_{\text{z\ }}}\)(2)

where \(z\) is the wind speed observation height,
\(d\) is the zero-plane displacement, \(z0\_m\)
is the roughness length for momentum (all in metres),
\(U_{\text{z\ }}\)is the wind speed (m s\textsuperscript{-1}) at
\(z\) and \(\kappa\) is the dimensionless von
Karman constant (\(\approx\ \)0.41). The canopy height
(Zc) was arbitrarily assumed to be 20 m,
\(d\) to be 0.75(Zc)
and\(z0\_m\) as 0.1(Zc) in accordance with
Szeicz, Endrodi and Tajhman (1969) and Rutter, Robins, Morton and
Kershaw (1972). However, studies have shown an enhancement of exchange
compared to estimates assuming these approximations for
\(z0\_m\) (e.g. Holwerda \emph{et al} ., 2012). Enhancement of
momentum exchange has been observed both for tall canopies and in
complex terrain owing to breakdown of theoretical vertical logarithmic
wind profiles (Cellier and Brunet, 1992; Raupach, 1979; Simpson,
Thurtell, Neumann, Den Hartog, \& Edwards, 1998). For the indicative
calculations made here, where z \textless{} Zc, wind
speed was extrapolated to Zc using a logarithmic wind
profile relationship. Wind speed observations used here are taken over
short grass surfaces and extrapolated to hypothetical canopy height as
if the logarithmic profile assumption is valid. It is recognised that
this may not be the case in complex terrain but, as the degree of
enhancement of momentum exchange is not easily estimated and because the
calculations made here are purely indicative no enhancements have been
made for \(r_{a}\_m\).

It is often assumed that \(r_{a}\_s\) is equal to
\(r_{a}\_m\), but this assumption can to lead to considerable
error (Brutstaert, 1982, p62) owing to so-called \emph{excess
resistance} for scalars. Excess resistance occurs because pressure
forces associated with \emph{form drag} increase momentum exchange, but
not scalar exchange and because of differences in source and sink
distributions for these entities (Brutstaert, 1982; Moors, 2012;
Simpson, \emph{et al} ., 1998; Stewart \& Thom, 1973). Although there
can be differences between the magnitude of exchange for different
scalars, we assume that the exchange of heat and vapour are equal for
the purposes of this study and hence only explore differences between
the magnitude of scalar exchange compared to the exchange of momentum.
Aerodynamic exchange estimated using Eqn. 2 is more sensitive to the
value of \(z0\) than it is to the value of
\(d\)(Gash, Wright \& Lloyd, 1980). The value of
\(z0\) has been shown to vary significantly with wind speed
for forest canopies, whilst \(d\)tends to remain
relatively constant (Bosvelt, 1999; Szeicz, \& Endrodi, 1969).
Consequently, \(d\) is fixed as specified above for all
calculations made here and it is assumed that the primary differences
between \(r_{a}\_s\) and \(r_{a}\_m\) are driven by
differences in\(z0\_m\) and \(z0\_s\). It is worth
noting that \(d\) may vary significantly for very sparse
canopies or for deciduous canopies during the leafless period
(Brutstaert, 1982, p116; Dolman, 1986).

The ratio of \(z0\_s\)/\(z0\_m\) used in previous
studies varies over approximately an order of magnitude as it is
influenced by canopy roughness, canopy density, atmospheric stability
and wind speed (Bosvelt, 1999; Brutstaert, 1982, p114; Lalic,
Mihailovic, Rajkovic, Arsenic, \& Radlovic, 2003; Raupach, 1979; Thom,
Stewart, Oliver \& Gash, 1975). The sensitivity of \(r_{a}\_s\)
and \(E_{\text{PM}}\) to the ratio
\(z0\_s\)/\(z0\_m\) is explored here using three
scenarios:

Scenario 1 - \(z0\_s/z0\_m\text{\ \ }=\ \ 1.0\ \); i.e. \(\ z0\_s=\)
\(0.1(\text{Zc})\);

Scenario 2 -\(\text{\ \ }z0\_s/z0\_m\text{\ \ }=\ \ 0.5\); i.e.
\(\ z0\_s=\)\(0.05(\text{Zc})\);

Scenario 3 - \(z0\_s/z0\_m\text{\ \ }=\ \ 0.1\); i.e. \(\ z0\_s=\)
\(0.01(\text{Zc})\).

It is likely that vapour pressure deficit (also expressed as relative
humidity, \emph{RH} ) observations over grassland meteorological
observation sites are likely to be lower than those over an adjacent
forested area (e.g. see Pearce, Gash, \& Stewart 1980). No attempt has
been made to correct \emph{RH} observations for this study owing to the
complexities associated with such a correction and the indicative nature
of our calculations; this is also the case for Tz which
is likely to be lower above a forest canopy (Rutter, 1967).
Additionally, Eqn. 2 is strictly only valid for neutral atmospheric
conditions (Szeicz, and Endrodi, 1969) but corrections for non-neutral
conditions are often assumed to be insignificant during rainfall (e.g.
Morton, 1984; van Dijk \emph{et al} ., 2015) and we assume they are
negligible here.

\textbf{3. Results and discussion}

\textbf{3.1 Objective 1: canopy water balance observations of wet-canopy
evaporation during large and extreme events}

The data search provided observations from 18 study sites that have CWB
observations of \emph{Ewc} for large storms associated with either daily
or normalised event \selectlanguage{english}?\selectlanguage{english}? (see Table Supp. 3): none of the events were
extreme events based upon the classification employed (\textgreater{}150
mm d\textsuperscript{-1}). From these sites 1387 \selectlanguage{english}?\selectlanguage{english}?-\emph{Ewc} pairs
were obtained with a maximum \selectlanguage{english}?\selectlanguage{english}? of approximately 118 mm. Only 35 of
these pairs were associated with \selectlanguage{english}?\selectlanguage{english}? observations over 50 mm
d\textsuperscript{-1} (Table Supp. 3). In absolute terms, the
\emph{Ewc}data include some high magnitudes; they include a maximum
\emph{Ewc}loss of 39.4 mm d\textsuperscript{-1} with 40 events where
\emph{Ewc}loss was over 10 mm d\textsuperscript{-1}. When \emph{Ewc} is
expressed as a percentage of \selectlanguage{english}?\selectlanguage{english}? (\%\emph{Ewc} ), there is a decreasing
trend in \%\emph{Ewc} as \selectlanguage{english}?\selectlanguage{english}? increases (Figure 2). This pattern of
declining relative loss has been shown previously in many studies (e.g.
Iroume \& Huber, 2002; Bulcock \& Jewitt, 2012), including the seminal
review by Horton (1919). From these 1387 data pairs, 58 gave a negative
\%\emph{Ewc} and 25 were over 100 \%\emph{Ewc} ; these data lie
predominantly at low \selectlanguage{english}?\selectlanguage{english}? magnitudes and are not presented in Figure 2 and
can be caused by error, sampling truncation of events and fog-drip and
will be incorporated into uncertainty analysis in future work. The
subset of the data from UK catchments are overlain by green
filled-circles in Figure 2; the individual numbered events where \selectlanguage{english}?\selectlanguage{english}?
\textgreater{} 50 mm are specified in Table Supp. 3. These UK data tend
to span the higher rates of \%\emph{Ewc} for higher \selectlanguage{english}?\selectlanguage{english}? magnitudes and
include absolute losses up to 26.3 mm d\textsuperscript{-1}. The few
data which are associated with plots under entirely deciduous species
are highlighted as orange-filled circles in Figure 2: only one data pair
was associated with \selectlanguage{english}?\selectlanguage{english}? greater than 50 mm per day of which approximately
11\% was lost to \emph{Ewc} . The degree to which \%\emph{Ewc} continues
to decrease with increasing \selectlanguage{english}?\selectlanguage{english}?, or whether it has reached a stable range
is unclear from Figure 2 given the few data available at higher \selectlanguage{english}?\selectlanguage{english}?
magnitudes. This is important as the highest \selectlanguage{english}?\selectlanguage{english}? from these data is
significantly lower than extreme daily rainfall totals recorded in the
Cumbrian Mountains which has been observed to be as high as 341~mm in a
24-hour period at Honister Pass, Cumbria (Met. Office 2018) which led to
widespread severe flooding.

Observations associated with studies where no event duration data were
available provided 1144 \selectlanguage{english}?\selectlanguage{english}?-\emph{Ewc} pairs including some high
\%\emph{Ewc} losses (ranging from approximately 7 to 35 \%) for very
large \selectlanguage{english}?\selectlanguage{english}? values (up to 435 mm: see Table Supp. 2). These data are
plotted as black filled-circles in Figure 3 with plots under entirely
deciduous species highlighted as orange-filled circles. Although these
data are difficult to compare to the daily or normalised daily data, the
high losses observed are significant given that these are potentially
extreme events, likely to be of maximum 3 or 4 days in duration and
hence serve as a useful reference. An exception to this rule are the
data from Deguchi, Hattori, \& Park (2006) where it is possible that
observations were made over a period of up to 2 weeks; however, the
largest event from their study (which was identified as taking place on
September 11-12\textsuperscript{th}, 2000) deposited 347 mm \selectlanguage{english}?\selectlanguage{english}?, with
14\% of this being lost to \emph{Ewc} . The magnitude of the losses from
these non-normalised events are qualitatively consistent with the
normalised events presented in Figure 2.

The data for large and extreme events presented in Figures 2 and 3 show
a large range of \emph{Ewc} loss: approximately 2-38 \% of \selectlanguage{english}?\selectlanguage{english}?. These
losses are apparently significant in the context of flood mitigation
with absolute losses of up to approximately 40 mm d\textsuperscript{-1}.
Unfortunately, concurrent meteorological observations were generally not
reported for events greater than 50 mm d\textsuperscript{-1}: concurrent
observations were only available for 4 events at one site (Dolydd,
mid-Wales; events 7-10, Table Supp. 3). This lack of meteorological data
means that it is, in general, not possible to link the
observed\emph{Ewc} losses with the magnitude of important meteorological
variables which would allow some form of model calibration. Model
calibration of this kind is problematic and also needs to include canopy
storage limitation of \emph{Ewc} (see Calder, 1977).

\textbf{3.2 Objective 2: estimation of meteorological conditions
consistent with observed Ewc losses}

\textbf{3.2.1 The likely magnitude of meteorological controls driving
observed Ewc losses}

Penman-Monteith potential evaporation estimates, \(E_{\text{PM}}\),
were made across the ranges described in section 2.3 above. A
representation of how \(E_{\text{PM}}\) varies with \(r_{a}\_s\)
and saturation vapour pressure deficit (expressed as \emph{RH} ) is
shown in Figure 4. With respect to Objective 2, given the
Penman-Monteith equation and the assumptions of the analysis, to achieve
the higher end of absolute\emph{Ewc} losses observed (\(\approx\)
20 to 40 mm d\textsuperscript{-1}) either fairly low \emph{RH} or very
low\(r_{a}\_s\) values are required, or an equivalent combination
of\emph{RH} and \(r_{a}\_s\). Relative humidity needs to be below
approximately 90\% where \(r_{a}\_s\) is around 2 s
m\textsuperscript{-1} or around 97.5\% as \(r_{a}\_s\) approaches
0.5 s m\textsuperscript{-1}. Figure 4 also highlights
how\(\ E_{\text{PM}}\)becomes increasingly sensitive to small changes
in\(r_{a}\_s\) at lower values: i.e. for higher wind speeds and
rougher canopies (as previously shown by Beven, 1979 \& Dolman, 1986).
At these low \(r_{a}\_s\) values, \(E_{\text{PM}}\) is also
considerably more sensitive to changes in \emph{RH} , and even at
relatively high\emph{RH} , the potential for significant evaporation
loss exists. Owing to this extreme sensitivity at low
\(r_{a}\_s\) values, uncertainties associated with estimating
\emph{effective} \(r_{a}\_s\) values and\emph{RH} become critical
in the interpretation of the results presented here and are discussed in
more detail below.

\textbf{3.3 Objective 3: Meteorological conditions and wet-canopy
evaporation estimates for mountainous regions of the UK}

\textbf{3.3.1 Penman-Monteith wet-canopy evaporation estimates for
mountainous regions of the UK}

Estimates of \(E_{\text{PM}}\) made using the meteorological data for
the 17 sites specified in section 2.3.2 show that, given the assumptions
of our analysis, within-storm conditions for potentially high
\emph{Ewc}loss are possible in mountainous regions of the UK. High wind
speeds and relatively low \emph{RH} can prevail during days with
significant rainfall. This is illustrated in Figure 5a where hourly
average\(r_{a}\_s\) versus \emph{RH} data are plotted for the
sites identified in Table Supp. 2. The points plotted in Figure 5a
relate to hourly periods within a 24-hour period with over 50 mm of
rainfall and where the hourly rainfall total was above zero. The
estimates of \(r_{a}\_s\), using the 3 scenarios for
\(z0\_s\) as described above, are represented by: black
filled-circles for\(\ z0\_s=\) \(0.1(\text{Zc})\), green
filled-circles for\(z0\_s=\) \(0.05(\text{Zc})\) and red
filled-circles for \(z0\_s=\)\(0.01(Zc)\). Figure 5a
demonstrates that very low \(r_{a}\_s\ \)values can occur within
24-hour periods where \selectlanguage{english}?\selectlanguage{english}? is greater than 50 mm and that the majority of
these periods were associated with \emph{RH} values predominantly in the
range 85\% to 98\% which shows significant overlap with the conditions
required for significant \(E_{\text{PM}}\) estimated for Objective 2.
Meteorological conditions during more extreme events (\textgreater{}150
mm in 24-hours and where the hourly rainfall \textgreater{} 0), also
shown in Figure 5a as diamonds; this figure suggests that, particularly
for RH, conditions can be even more favourable for high
\(E_{\text{PM}}\) but are associated with the caveat that there are
relatively few observations during very few events of this magnitude.
The potential for high \(E_{\text{PM}}\) is shown more explicitly in
Figure 5b (which uses the same data as Figure 5a). The difference
between the estimates made using the 3 \(z0\_s\) highlights
again how sensitive \(E_{\text{PM}}\) magnitude is
to\(\ z0\_s\). However, fairly high rates of \(E_{\text{PM}}\)
are estimated for all\(z0\_s\) scenarios although the
\(z0\_s=\ 0.01(\text{Zc})\)scenario is mainly limited to losses of below 12 mm
d\textsuperscript{-1}.

\textbf{3.3.2 Meteorological conditions during extreme events across
Cumbria}

Figures 6 and 7 (and Figures Supp. 1 \& 2) show time series of
meteorological variables during the 4 extreme Cumbrian rainfall events
that occurred since 2005. Each event was associated with a frontal
system, the 2005, 2009 and 2015 events being classified as atmospheric
rivers, where enhanced horizontal water vapour transport from the
Atlantic Ocean occurs (Lavers \emph{et al} ., 2011, 2013; Matthews,
Murphy, McCarthy, Broderick, \& Wilby, 2018). The meteorological time
series show that, at many of the locations, during the main periods of
rainfall (indicated by the grey shaded area in Figures 6b, 7b, Supp. 1b
\& 2b) relatively low \emph{RH} (in the context of the results presented
above) occurs along with high wind speeds (Figures 6a, 7a, Supp. 1a \&
2a) and an increase in air temperature (Figures 6, 7c, Supp. 1a \& 2a).
A notable exception to these general patterns are the differences
in\emph{RH} between sites for the 2009 event where Keswick and Walney
were at approximately 90-95\% \emph{RH} during the main rainfall period
but the Shap and Walney sites were at, or close to, saturation. This was
also the case at the higher elevation site of Great Dun Fell where the
wind speeds were very high but the \emph{RH} remained at 100\%
throughout the entire period of rainfall (Figures 7a and 7b
respectively). Similarly, but for the 2015 flood event, in a clearing in
Gisburn Forest, Lancashire the \emph{RH} remained very high or at
saturation for a large part of the storm (Figure 7b). There is also
consistency in that Keswick, which is a less exposed site at relatively
low elevation on the lee side of one of the highest regions of
mountains, tends to have lower wind speeds, higher temperatures and
lower \emph{RH} than the other locations during all extreme events
considered (Figures 6, 7 and Supp. 1 \& 2). It is worth highlighting the
caveat that the Keswick, Shap and Warcop sites are located on the
leeward side (relative to the dominant south westerly flows) of mountain
ridges such that the observed favourable conditions for \emph{Ewc} loss
shown are not necessarily representative across the region as a whole:
as shown by the less favourable conditions for \emph{Ewc} loss at
Gisburn Forest and Great Dun Fell. These results show that even during
the 4 most extreme events in Cumbria over the last 15 years, high
windspeeds and surprisingly low \emph{RH} provide favourable conditions
for significant \emph{Ewc} loss at some locations. Consequently the need
to estimate \emph{Ewc} losses across large catchments, particularly in
complex mountainous terrain, requires a representation of the spatial
variability of meteorological controls which will be challenging where
only sparse meteorological observations are available.

\textbf{3.4 Objective 4: implications for estimating the magnitude
of\emph{Ewc} across large catchments in complex terrain}

The results from objectives 1 to 3 show that \emph{Ewc} losses up to
approximately 40 mm d\textsuperscript{-1} have been observed at
temperate sites around the world and that meteorological conditions that
have the potential to give rise to such large losses can exist in
mountainous regions of the UK. However, these findings must be treated
with caution because concurrent meteorological observations are rarely
reported with CWB \emph{Ewc} data, particularly during extreme events,
and Penman-Monteith estimates are extremely sensitive to\emph{estimated}
aerodynamic exchange and small changes in \emph{RH} at the higher
windspeeds that often prevail during the large rainfall events
considered here. The analysis has also shown that both wind speed and
\emph{RH} varies significantly with spatial location. Given that Ewc
estimates are required for hydrological simulation of large catchments,
a representation of this spatially variable control of
\emph{Ewc}magnitude is required; it is not appropriate to sample a
statistical distribution of Ewc loss generated from the worldwide
observations of\emph{Ewc} data (for a given gross rainfall total) as the
autocorrelation of \emph{Ewc} , controlled by autocorrelated
meteorological variables, through sequences of \emph{real} events is
needed. With respect to this requirement, even a spatially sparse time
series of meteorological observations contains important information
describing temporal patterns of some of the primary controls
on\emph{Ewc} and this information must be retained. Spatial
interpolation and extrapolation from these sparse meteorological
observations will inevitably be inherently uncertain but is an important
prerequisite for appropriate estimation of \emph{Ewc} losses.

Although simple empirical models can be used to estimate Ewc where there
is a scarcity of adequate meteorological data and knowledge of
appropriate parameter values for more complex models (e.g. see Lu,
McNulty \& Amatya, 1995), their use is limited as they may not
explicitly include important meteorological controls. Consequently, the
Penman-Monteith equation is still used to simulate evaporation from
wetted surfaces in the majority of \emph{Ewc} models (Muzylo \emph{et
al} ., 2009). Thus, Penman-Monteith equation remains a useful method to
determine the potential for \emph{Ewc} loss but the magnitude of any
estimates made will be highly uncertain without meaningful calibration
of critical and sensitive parameters such as \(r_{a}\_s\).
However, as there are so few \emph{Ewc} data associated with concurrent
meteorological observations, particularly large rainfall events, it is
rarely possible to calibrate the parameters of the Penman-Monteith
equation and any calibration would need to include the joint-calibration
of parameters of an (e.g. Rutter-type) \emph{effective} canopy store
model (e.g. see Calder, 1977).

Our theoretical analyses show that it is possible to get a very wide
range of \emph{Ewc} estimates depending upon, in particular, the way
that \(r_{a}\_s\) is estimated. These analyses used 3 scenarios
of\(r_{a}\_s\) which were based upon a range of published values
derived both directly from micrometeorological observations and via
model calibration. Ratios of \(z0\_s\)/\(z0\_m\) have
been reported to be: of the order 0.1-0.2 (Klingaman, Levia, \& Frost,
2007; Lankreijer, Hendriks, \& Klaassen, 1993); approximately 0.3-0.5
(Brutstaert, 1982, p114; Stewart \& Thom, 1973) and around 1 in some
cases (Bosvelt, 1999; Gash, Valente, \& David, 1999; Moors, 2012).
Significant uncertainties exist when estimating \(r_{a}\_m\) and
the relative magnitude of\(r_{a}\_s\) compared to
\(r_{a}\_m\). When only momentum is considered, representing the
degree of exchange is not simple as it has been shown to vary, and to be
enhanced compared to theoretical estimates, in complex terrain and over
tall canopies (Cellier \& Brunet,1992; Holwerda \emph{et al} ., 2012);
\(r_{a}\_m\) also varies with canopy roughness and canopy density
(Brutstaert, 1982, Fig. 5.1; Cellier \& Brunet,1992; Holwerda \emph{et
al} ., 2012) as well as atmospheric stability and wind speed (Bosvelt,
1999; Cellier \& Brunet,1992; Szeicz, \& Endrodi, 1969). The ratio
\(z0\_s\)/\(z0\_m\)also varies widely and with the
same factors as \(r_{a}\_m\) and current understanding of scalar
exchange for tall canopies in complex terrain remains rudimentary
(Belcher, Harman \& Finnigan, 2012). There are, however, a relatively
large number of published studies which report \(r_{a}\_m\) and
\(r_{a}\_s\) for various vegetation of differing roughness which
may help elucidate the relevant range of\(r_{a}\_s\) for use in
\emph{Ewc} estimation for a given application: a review of these studies
is, however, beyond the scope of this paper.

Given the need for interpolation and extrapolation from sparse
meteorological data to estimate meteorological controls on
\emph{Ewc}spatially, uncertainties will be very large such that a
scenario-based approach may be most appropriate. Any defined scenario
will be\emph{conditional} on the evidence base used in its development
and any additional modelling assumptions. The conditionality of each
scenario must be made explicit and each scenario can be associated with
a confidence-weighting which can be propagated to simulation results.
This will be the subject of future publications.

\textbf{4. Conclusions}

At temperate locations around the world, high wet-canopy evaporation
losses have been observed from forests using canopy water balance
methods during large and extreme rainfall events and are associated with
significant variability. Wet-canopy evaporation of up to approximately
40 mm d\textsuperscript{-1} have been recorded for large rainfall events
(\textgreater{}50 mm d\textsuperscript{-1}) and across all events range
between approximately 2 and 38\% of gross rainfall. Taken at ``face
value'' these evaporation losses are \emph{qualitatively} significant in
the context of flood mitigation resulting from tree planting.
Theoretical wet-canopy evaporation estimates made using the
Penman-Monteith model for large and extreme events in mountainous
regions of the UK suggest consistency with these high observed losses
but uncertainties associated with the estimation of, in particular,
aerodynamic exchange are so large that this test of consistency remains
weak. During 4 major flood events in the Cumbrian Mountains, UK,
meteorological conditions were favourable for high rates of wet-canopy
evaporation: high windspeeds prevailed and surprisingly low relative
humidity was observed at some locations. Thus the disparity regarding
the significance of wet-canopy evaporation for flood mitigation between
conclusions based upon results from catchments studies of forest cover
effects and results from forest plot studies remains.

Our results suggest that it is possible for high rates of \emph{Ewc}over
forest to occur during large flood events in mountainous regions of the
UK but not in all locations and not for all events. To be able to
determine the potential of tree planting scenarios on flood hydrographs
using hydrological models, estimates of the spatial and temporal
patterns of wet-canopy evaporation through sequences of rainfall events
are needed. Appropriate estimates require simulation of the control
imposed by meteorological variables on wet-canopy evaporation to be made
necessitating interpolation and extrapolation from (normally) sparse
meteorological observation sites. This is difficult to implement with
any accuracy and the uncertainties associated with this step are
compounded with the large uncertainties associated with the estimation
of aerodynamic exchange with forest canopies such that wet-canopy
evaporation estimates may be represented best as scenarios. Simulations
must also be able to represent the limitation on evaporation imposed by
storage on the surfaces of different vegetation canopies (e.g. between
foliated and unfoliated deciduous trees) meaning that scenarios of
parameterisations must be incorporated into the simulations. Simulation
scenarios must be associated with a confidence weighting that can be
propagated to simulation results as expressions of modelling
uncertainty.

If the considerable uncertainties associated with estimating
meteorological conditions and \emph{Ewc} across large areas such are to
be constrained, collection and analysis of a larger number of
well-placed and well-distributed meteorological observations is
required, combined with concurrent wet-canopy evaporation observations.

\textbf{Data Availability Statement}

For part of the data which are digitized from this work, data sharing is
not applicable new data were created or analyzed in this study. Other
data which has been newly gathered from historical archives requires the
permission of the data holder.

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