Introduction
Land surface models (LSMs) are based upon fundamental mathematical laws and
physics applied within a theoretical framework. Certain processes are modeled
explicitly while others use more conceptual approaches. They are designed to
work across a large range of spatial scales, so that unresolved
scale-dependent processes represented as a function of some grid-averaged
state variable using empirical or statistical relationships. LSMs were
originally implemented in numerical weather prediction (NWP) and global
climate models (GCMs) in order to provide interactive lower boundary
conditions for the atmospheric radiation and turbulence parameterization
schemes over continental land surfaces. In the past 2 decades, LSMs have
evolved considerably to include more biogeochemical and biogeophysical
processes in order to meet the growing demands of both the research and the
user communities . A growing number
of state-of-the-art LSMs, which are used in coupled atmospheric models for
operational numerical weather prediction ,
climate modeling , or both
, represent most or all of the following processes:
photosynthesis and the associated carbon fluxes, multi-layer soil water and
heat transfer, vegetation phenology and dynamics (biomass evolution, net
primary production), sub-grid lateral water transfer, river routing,
atmosphere–lake exchanges, snowpack dynamics, and near-surface urban
meteorology. Some LSMs also include processes describing the nitrogen cycle
, groundwater exchanges , aerosol
surface emissions , isotopes , and the
representation of human impacts on the hydrological cycle in terms of
irrigation and ground water extraction
, to name a few.
As a part of the trend in LSM development, there have been ongoing efforts to
improve the representation of the land surface processes in the Interactions
between the soil–biosphere–atmosphere (ISBA) LSM within the EXternalized
SURFace (SURFEX; ,) model platform.
The original two-layer ISBA force–restore model consists in
a single bulk soil layer (generally having a thickness on the order of 50 cm
to several meters) coupled to a superficially thin surface composite
soil–vegetation–snow layer. Thus, the model simulates fast
processes that occur at sub-diurnal timescales, which are pertinent to short-term
numerical weather prediction, and it provides a longer-term water
storage reservoir, which provides a source for transpiration, a time filter
for water reaching a hydro-graphic network, and a certain degree of soil
moisture memory in the ground amenable to longer-term forecasts and climate
modeling. Additional modifications were made to this scheme over the last
decade to include soil freezing , which improved
hydrological processes .
This scheme was based on the pioneering work of and it
has proven its value for coupled land–atmosphere research and applications
since its inception. For example, it is currently used for research within
the mesoscale non-hydrostatic research model (Meso-NH)
. It is also used within the operational high-resolution
short-term numerical weather prediction at Météo-France within
the limited area model AROME and by HIRLAM countries
within the ALADIN–HIRLAM system as the HARMONIE–AROME model configuration
. Finally, it is used for climate research within the
global climate model (GCM) Action de Researche Petite Echelle Grande Echelle
(ARPEGE-climat; , ) and by
HIRLAM countries within the ALADIN–HIRLAM system as HARMONIE–AROME and
HARMONIE–ALARO Climate configurations .
Rationale for improved vegetation processes
Currently, many LSMs are pushing towards improved realism owing to an
increasing number of observations at the local scale, constantly improving
satellite data sets and the associated methodologies to best exploit such
data, improved computing resources, and in response to the user community via
climate services (and seasonal forecasts, drought indexes, etc…). In the
SURFEX context, the force–restore approach has been replaced in recent years
by multi-layer explicit physically based options for sub-surface heat
transfer , soil hydrological processes
, and the composite snowpack
. These new schemes have recently been
implemented in the operational distributed hydro-meteorological hindcast
system SAFRAN–ISBA–MODCOU , Meso-NH, and
ARPEGE-climat and ALADIN–HIRLAM HARMONIE–AROME and HARMONIE–ALARO Climate
configurations. The representation of vegetation processes in SURFEX has also
become much more sophisticated in recent years, including photosynthesis and
respiration , carbon allocation to biomass pools
, and soil carbon cycling
. However, for a number of reasons it has also
become clear that we have reached the conceptual limits of using of a
composite soil–vegetation scheme within ISBA and there is a need to
explicitly separate the canopy vegetation from the soil surface:
in order to distinguish the soil, snow, and vegetation surface temperatures
since they can have very
different amplitudes and phases in terms of the diurnal cycle, and therefore
accounting for this
distinction facilitates (at least conceptually)
incorporating remote sensing data, such as satellite-based thermal
infrared temperatures
e.g.,, into such models;
as it has become evident that the only way to simulate the
snowpack beneath forests in a robust and a physically consistent manner
(i.e.,
reducing the dependence of forest snow cover on highly empirical and poorly
constrained snow fractional cover parameterizations) and
including certain key processes (i.e., canopy interception and unloading of
snow) is to include a forest canopy above or buried by the ground-based
snowpack e.g.,;
for accurately modeling canopy radiative transfer, within or
below canopy turbulent fluxes and soil heat fluxes;
to make a more consistent photosynthesis and carbon allocation
model (including explicit carbon stores for the vegetation, litter, and
soil in a consistent manner);
to allow the explicit treatment of a ground litter layer, which has a significant
impact on ground heat fluxes and soil temperatures (and freezing)
and, by extension, the turbulent heat fluxes.
In response to this issue, a collaboration began in 2008 between the
high-resolution limited area model (HIRLAM) consortium and Météo-France
with the intention to develop an explicit representation of the vegetation in
ISBA under the SURFEX platform. A new parameterization has been developed
called the ISBA multi-energy balance (MEB) in order to account for all of the
above issues.
MEB is based on the classic two-source model for snow-free conditions, which
considers explicit energy budgets (for computing fluxes) for the soil and the
vegetation, and it has been extended to a three-source model in order to
include an explicit representation of snowpack processes and their
interactions with the ground and the vegetation. The vegetation canopy is
represented using the big-leaf method, which lumps the entire
vegetation canopy into a single effective leaf for computing energy budgets
and the associated fluxes of heat, moisture, and momentum. One of the first
examples of a two-source model designed for atmospheric model studies is
, and further refinements to the vegetation canopy
processes were added in the years that followed leading to fairly
sophisticated schemes, which are similar to those used today
e.g.,. The two-source big-leaf approach has been used
extensively within coupled regional and global scale land–atmosphere models
. In
addition, more recently multi-layer vegetation schemes have also been
developed for application in GCMs .
ISBA-MEB has been developed taking the same strategy that has been used
historically for ISBA: inclusion of the key first-order processes while
maintaining a system that has minimal input data requirements and
computational cost while being consistent with other aspects of ISBA (with
the ultimate goal of being used in coupled operational numerical weather
forecast and climate models, and spatially distributed monitoring and
hydrological modeling systems). In 2008, one of the HIRLAM partners, the
Swedish Meteorological and Hydrological Institute (SMHI), had already
developed and applied an explicit representation of the vegetation in the
Rossby Centre Regional Climate Model (RCA3) used at SMHI
. This representation was introduced into
the operational NWP HIRLAMv7.3 system, which became operational in 2010. In
parallel, the dynamic vegetation model LJP-GUESS was coupled to RCA3 as
RCA–GUESS , making it possible to simulate complex
biogeophysical feedback mechanisms in climate scenarios. Since then RCA–GUESS
has been applied over Europe , Africa , and
the Arctic . The basic principles developed by SMHI have been
the foundation since the explicit representation of the vegetation was
introduced in ISBA and SURFEX, but now in a more general and consistent way.
Implementation of canopy turbulence scheme, longwave radiation transmission
function, and snow interception formulations in MEB largely follows the
implementation used in RCA3 . In addition,
we have taken this opportunity to incorporate several new features into
ISBA-MEB compared to the original SMHI scheme:
a snow fraction that can gradually bury the vegetation
vertically thereby transitioning the turbulence coupling from the
canopy air space directly to the atmosphere (using a fully
implicit numerical scheme);
the use of the detailed solar radiation transfer scheme
that is a multi-layer model that considers two spectral bands, direct and
diffuse flux components, and the concept of sunlit and shaded leaves, which was
primarily developed to improve the modeling of photosynthesis within ISBA
(Carrer et al., 2013);
a more detailed treatment of canopy snow interception and
unloading processes and a coupling
with the ISBA physically based multi-layer snow scheme;
a reformulation of the turbulent exchange coefficients within the
canopy air space for stable conditions, such as over a snowpack;
a fully implicit Jacobean matrix for the longwave fluxes from
multiple surfaces (snow, below-canopy snow-free ground surface,
vegetation canopy);
all of the energy budgets are
numerically implicitly coupled with each other and with the atmosphere
using the coupling method adapted from , which was
first proposed by ;
an explicit forest litter layer model (which also acts as the
below-canopy surface energy budget when litter covers the soil).
This paper is the first of two parts: in part one, the ISBA-MEB model
equations, numerical schemes, and theoretical background are presented. In
part two, a local-scale evaluation of the new scheme is presented along with
a detailed description of the new forest litter scheme
. An overview of the model is given in the next
section, followed by conclusions.
Model description
Description of the patches for the natural land surface
sub-grid tile. The values for the 19-class option are shown in the
leftmost three columns, and those for the 12-class option are shown
in the rightmost three columns (the name and description are only
given if they differ from the 19-class values). MEB can currently be
activated for the forest classes:
4–6 (for both the 12- and 19-class options), and 13–17.
Index
Name
Description
Index
Name
Description
1
NO
Bare soil
1
2
ROCK
Rock
2
3
SNOW
Permanent snow or ice
3
4
TEBD
Temperate broad leaf
4
TREE
Broad leaf
5
BONE
Boreal evergreen needle leaf
5
CONI
Evergreen needle leaf
6
TRBE
Tropical evergreen broad leaf
6
EVER
Evergreen broad leaf
7
C3
C3 crops
7
8
C4
C4 crops
8
9
IRR
Irrigated crops
9
10
GRAS
Temperate grassland
10
11
TROG
Tropical grassland
11
12
PARK
Bog, park, garden
12
13
TRBD
Tropical broad leaf
14
TEBE
Temperate evergreen broad leaf
15
TENE
Temperate evergreen needle leaf
16
BOBD
Boreal broad leaf
17
BOND
Boreal needle leaf
18
BOGR
Boreal grassland
19
SHRB
Shrubs
SURFEX uses the tile approach for the surface, and separate physics modules
are used to compute surface–atmosphere exchange for oceans or seas, lakes,
urbanized areas, and the natural land surface . The ISBA LSM
is used for the latter tile, and the land surface is further split into
upwards of 12 or 19 patches (refer to
Table ), which represent the various land
cover and plant functional types. Currently, forests make up eight patches for
the 19-class option, and three for the 12-class option. The ISBA-MEB
(referred to hereafter simply as MEB) option can be activated for any number
of the forest patches. By default, MEB is coupled to the multi-layer soil
(ISBA-DF: explicit DiFfusion equation for heat and Richard's equation for
soil water flow; ,;
, ) and snow (ISBA-ES:
multi-layer Explicit Snow processes with 12 layers by default;
, ,
, ) schemes. These schemes have
been recently updated to include improved physics and
increased layering (14 soil layers by default). MEB can also be coupled to
the simple three-layer soil force–restore (3-L) option in
order to be compatible with certain applications, which have historically used
3-L, but by default, it is coupled with ISBA-DF since the objective is to
move towards a less conceptual LSM.
A schematic representation of
the turbulent aerodynamic resistance, Ra, pathways for ISBA-MEB.
The prognostic temperature, liquid water, and liquid water equivalent
variables are shown. The canopy air diagnostic variables are enclosed by the
red-dashed circle. The ground-based snowpack is indicated using turquoise,
the vegetation canopy is shaded green, and ground layers are colored dark
brown at the surface, fading to white with depth. Atmospheric variables
(lowest atmospheric model or observed reference level) are indicated using
the a subscript. The ground snow fraction, png, and
canopy-snow-cover fraction, pnα, are indicated.
A schematic diagram illustrating the various resistance pathways
corresponding to the turbulent fluxes for the three fully (implicitly)
coupled surface energy budgets is shown in Fig. . The
water budget prognostic variables are also indicated. Note that the
subscripts, which are used to represent the different prognostic and
diagnostic variables and the aerodynamic resistance pathways, are summarized
in Table . The canopy bulk vegetation layer is
represented using green, the canopy-intercepted snow and ground-based
snowpack are shaded using turquoise, and the ground layers are indicated
using dark brown at the surface, which fade to white with increasing depth.
There are six aerodynamic resistance, Ra (s-1), pathways
defined as being between (i) the non-snow-buried vegetation canopy and the
canopy air, Ravg-c, (ii) the non-snow-buried ground surface (soil
or litter) and the canopy air, Rag-c, (iii) the snow surface and
the canopy air, Ran-c, (iv) the ground-based snow-covered part of
the canopy and the canopy air, Ravn-c, (v) the canopy air with
the overlying atmosphere, Rac-a), and (vi) the ground-based snow
surface (directly) with the overlying atmosphere, Ran-a. Previous
papers describing ISBA expressed heat
fluxes using a dimensionless heat and mass exchange coefficient,
CH;
however, for the new MEB option, it is more convenient to express the
different fluxes using resistances (s m-1), which are related to the
exchange coefficient as Ra=1/VaCH,
where Va represents the wind speed at the atmospheric forcing
level (indicated by using the subscript a) in m s-1.
The surface energy budgets are formulated in terms of prognostic equations
governing the evolutions of the bulk vegetation canopy, Tv, the
snow-free ground surface (soil or litter), Tg, and the
ground-based snowpack, Tn (K). The prognostic hydrological
variables consist of the liquid soil water content, Wg,
equivalent water content of ice, Wgf, snow water equivalent (SWE),
Wn, vegetation canopy-intercepted liquid water, Wr,
and intercepted snow, Wrn (kg m-2). The diagnosed canopy air
variables, which are determined implicitly during the simultaneous solution of
the energy budgets, are enclosed within the red-dashed circle and represent
the canopy air specific humidity, qc (kg kg-1), air
temperature Tc, and wind speed Vc. The ground
surface specific humidity is represented by qg. The surface snow
cover fraction area is represented by png while the fraction of
the canopy buried by the ground-based snowpack is defined as pαn. The snowpack has Nn layers, while the number of soil
layers is defined as Ng where k is the vertical index
(increasing from 1 at the surface downward). The ground and snowpack
uppermost layer temperatures correspond to those used for the surface energy
budget (i.e., k=1).
Snow fractions
Subscripts used to represent the prognostic and diagnostic
variables. In addition, the symbols used to represent the
aerodynamic resistance pathways (between the two elements separated by the
dash) are also shown (refer also to Fig. ). These
symbols are used throughout the text.
Subscript
Name
Description
v
Vegetation
Bulk canopy layer
g
Ground
Temperature or liquid water (for Ng layers)
gf
Ground
Frozen water (for Ng layers)
a
Atmosphere
At the lowest atmospheric or forcing level
c
Canopy air space
Diagnosed variables
n
Ground-based snowpack
For Nn layers
ng
Ground-based snowpack
Fractional ground snow coverage
α n
Ground-based snowpack
Fractional vegetation snow coverage
r
Interception reservoir
Intercepted rain and snow meltwater
rn
Interception reservoir
Intercepted snow and frozen meltwater or rain
vg-c
Aerodynamic resistance
Non-snow-buried vegetation canopy and canopy air
g-c
Aerodynamic resistance
Non-snow-buried ground surface and canopy air
n-c
Aerodynamic resistance
Snow surface and canopy air
vn-c
Aerodynamic resistance
Ground-based snow-covered canopy and canopy air
c-a
Aerodynamic resistance
Canopy air with overlying atmosphere
n-a
Aerodynamic resistance
Ground-based snow surface and overlying atmosphere
Snow is known to have a significant impact on heat conduction fluxes, owing to
its relatively high insulating properties. In addition, it can significantly
reduce turbulent transfer owing to reduced surface roughness, and it has a
relatively large surface albedo thereby impacting the surface net radiation
budget. Thus, the parameterization of its areal coverage turns out to be a
critical aspect of LSM modeling of snowpack–atmosphere interactions and
sub-surface soil and hydrological processes. The fractional ground coverage
by the snowpack is defined as
png=Wn/Wn,crit0≤png≤1,
where currently the default value is Wn,crit=1 (kg m-2). Note
that this is considerably lower than the previous value of 10 kg m-2
used in ISBA , but this value has been shown to
improve the ground soil temperatures, using an explicit snow scheme within
ISBA .
The fraction of the vegetation canopy, which is buried by ground-based snow, is
defined as
pnα=Dn-zhv,b/zhv-zhv,b0≤pnα≤1,
where Dn is the total ground-based snowpack depth (m) and
zhvb represents the base of the vegetation canopy (m) (see
Fig. ), which is currently defined as
zhvb=ahvzhv-zhv,minzhvb≥0,
where ahv=0.2 and the effective canopy base height is set to
zhv,min=2 (m) for forests. The foliage distribution should be
reconsidered in further development since literature suggests, e.g.,
, that the foliage is not symmetrically distributed in the
crown but skewed upward.
Energy budget
The coupled energy budget equations for a three-source model can be expressed
for a single bulk canopy, a ground-based snowpack, and a underlying ground
surface as
Cv∂Tv∂t=Rnv-Hv-LEv+LfΦv,Cg,1∂Tg,1∂t=1-pngRng-Hg-LEg+pngGgn+τn,NnSWnet,n-Gg,1+LfΦg,1,Cn,1∂Tn,1∂t=Rnn-Hn-LEn-τn,1SWnet,n+ξn,1-Gn,1+LfΦn,1,
where Tg,1 is the uppermost ground (surface soil or litter layer)
temperature, Tn,1 is the surface snow temperature, and
Tv is the bulk canopy temperature (K). Note that the subscript 1
indicates the uppermost layer or the base of the layer (for fluxes) for the
soil and snowpack. All of the following flux terms are expressed in
W m-2. The sensible heat fluxes are defined between the canopy air
space and the vegetation Hv, the snow-free ground
Hg, and the ground-based snowpack Hn. In an
analogous fashion to the sensible heat flux, the latent heat fluxes are
defined for the vegetation canopy Ev, the snow-free ground
Eg, and the ground-based snowpack En. The net
radiation fluxes are defined for the vegetation canopy, ground, and snowpack
as Rnv, Rng, and Rnn, respectively. Note
that part of the incoming shortwave radiation is transmitted through the
uppermost snow layer, and this energy loss is expressed as
τn,1SWnet,n, where τ is
the dimensionless transmission coefficient. The conduction fluxes between the
uppermost ground layer and the underlying soil and the analogue for the
snowpack are defined as Gg,1 and Gn,1, respectively. The
conduction flux between the base of the snowpack and the ground surface is
defined as Ggn. The last term on the right-hand side (RHS) of
Eq. (), ξn,1, represents the effective
heating or cooling of a snowpack layer caused by exchanges in enthalpy
between the surface and sub-surface model layers when the vertical grid is
reset (the snow model grid-layer thicknesses vary in time).
The ground-based snow fraction is defined as png. Note that certain
terms of Eq. () are multiplied by png to make
them patch relative (or grid box relative in the case of single-patch mode)
since the snow can potentially cover only part of the patch. Within the snow
module itself, the notion of png is not used (the computations are
snow relative). But note that when simultaneously solving the coupled
equations Eqs. ()–(),
Eq. () must be multiplied by png since again,
snow only covers a fraction of the area: further details are given in
Appendices and . The
formulation for png is described in Sect. .
A schematic sketch illustrating the role of pnα,
the fraction of the vegetation canopy, which is buried by ground-based snow.
In panel (a), the snow is well below the canopy base, zhvb,
resulting in pnα=0, and the snow has no direct energy
exchange with the atmosphere. In panel (b), the canopy is partly buried by
snow (0<pnα<1) and the snow has energy exchanges with both
the canopy air and the atmosphere. In panel (c), the canopy is fully buried by
snow (pnα=1) and the snow has energy exchange only with
the atmosphere, whereas the soil and canopy only exchange with the canopy air
space (png<1). Finally, in panel (d), both png=1 and
pnα=1 so that the only exchanges are between the snow and
the atmosphere.
The phase change terms (freezing less melting: expressed in
kg m-2 s-1) for the snow water equivalent intercepted by
the vegetation canopy, the uppermost ground layer, and the uppermost snowpack
layer are represented by Φv, Φg,1, and
Φn,1, respectively, and Lf represents the latent
heat of fusion (J kg-1).
The computation of Φg,1 uses the Gibbs free-energy method
, Φn,1 is based on available liquid for
freezing or cold content for freezing , and
Φv is described herein (see Eq. ). Note that all
of the phase change terms are computed as adjustments to the surface
temperatures (after the fluxes have been computed); therefore, only the energy
storage terms are modified directly by phase changes for each model time
step.
The surface ground, snow, and vegetation effective heat capacities,
Cg,1, Cv, and
Cn,1 (J m-2 K-1) are defined, respectively,
as
Cg,1=Δzg,1cg,1Cv=Cvb+CiWr,n+CwWr,Cn,1=Dn,1cn,1,
where Ci and Cw are the specific heat capacities for solid
(2.106×103 J kg-1 K-1) and liquid water (4.218×103 J kg-1 K-1), respectively. The uppermost ground-layer
thickness is Δzg,1 (m), and the corresponding heat capacity
of this layer is defined as cg 1 (J m-3 K-1). The
uppermost soil layer ranges between 0.01 and 0.03 m for most applications
so that the interactions between surface fluxes and fast temperature changes
in the surface soil layer can be represented. There are two options for
modeling the thermal properties of the uppermost ground layer. First, they
can be defined using the default ISBA configuration for a soil layer with
parameters based on soil texture properties, which can also incorporate the
thermal effects of soil organics . The second option, which
is the default when using MEB, is to model the uppermost ground layer as
forest litter. The ground surface in forest regions is generally covered by a
litter layer consisting of dead leaves and or needles, branches, fruit, and
other organic material. Some LSMs have introduced parameterizations for
litter , but the
approach can be very different from one case to another depending on their
complexity. The main goal of this parameterization within MEB is to account
for the generally accepted first-order energetic and hydrological effects of
litter; this layer is generally accepted to have a strong insulating effect
owing to its particular thermal properties (leading to a relatively low
thermal diffusivity), it causes a significant reduction of ground evaporation
(capillary rise into this layer is negligible), and it constitutes an
interception reservoir for liquid water, which can also lose water by
evaporation. See for a detailed description of this
scheme and its impact on the surface energy budget.
The canopy is characterized by low heat capacity, which means that its
temperature responds fast to changes in fluxes. Thus, to realistically
simulate diurnal variations in 2 m temperature this effect must be accounted
for. defined the value as being the heat capacity of
0.2 kg m-2 of water per unit leaf area index (m2 m-2). This
results in values on the order of 1×104 J m-2 K-1 for
forest canopies in general. For local-scale simulations, Cvb can be
defined based on observational data. In spatially distributed simulations (or
when observational data is insufficient), Cvb=0.2/CV where the
vegetation thermal inertia CV is defined as a function of
vegetation class by the SURFEX default physiographic database ECOCLIMAP
. Note that CV has been determined for the
composite soil–vegetation scheme, and the factor 0.2 is used to reduce this
value to be more representative of vegetation and on the order of the value
discussed by . Numerical tests have shown that using this
value, the canopy heat storage is on the order of 10 W m-2 at mid-day
for a typical mid-latitude summer day for a forest. The minimum vegetation
heat capacity value is limited at 1×104 (J m-2 K-1) in
order to model, in a rather simple fashion, the thermal inertia of stems,
branches, trunks, etc. The contributions from intercepted snow and rain are
incorporated, where Wr,n and Wr (kg m-2)
represent the equivalent liquid water content of intercepted canopy snow and
liquid water, respectively.
The uppermost snow-layer thickness is Dn,1 (m), and the
corresponding heat capacity is represented by cn,1
. Note that Dn,1 is limited to values no
larger than several centimeters in order to model a reasonable thermal
inertia (i.e., in order to represent the diurnal cycle) in a fashion analogous
to the soil. For more details, see .
The numerical solution of the surface energy budget,
sub-surface soil and snow temperatures, and the implicit numerical
coupling with the atmosphere is described in Appendix .
Turbulent fluxes
In this section, the turbulent heat and water vapor fluxes in
Eqs. ()–() are described.
Sensible heat fluxes
The MEB sensible heat fluxes are defined as
Hv=ρaTv-TcRav-c,Hg=ρaTg-TcRag-c,Hn=ρa1-pnαTn-TcRan-c+pnαTn-TaRan-a,Hc=ρaTc-TaRac-a,H=ρa1-pnαpngTc-TaRac-a+pnαpngTn-TaRan-a,
where ρa represents the lowest atmospheric layer average air
density (kg m-3). The sensible heat fluxes appear in the surface energy
budget equations (Eqs. –). The
sensible heat flux from the ground-based snowpack (Eq. ) is
partitioned by the fraction of the vegetation, which is buried by the
ground-based snowpack pnα, between an exchange between
the canopy air space, and the overlying atmosphere (Eq. ).
The heat flux between the overlaying atmosphere and the canopy air space is
represented by Hc, and it is equivalent to the sum of the fluxes
between the different energy budgets and the canopy air space. The total flux
exchange between the overlying atmosphere and the surface (as seen by the
atmosphere) is defined by H. It is comprised of two components: the heat
exchange between the overlying atmosphere and the canopy air space and the
part of the ground-based snowpack that is burying the vegetation. This
method has been developed to model the covering of low vegetation canopies by
a ground-based snowpack. Finally, the final fluxes for the given patch are
aggregated using png and pnα: the full
expressions are given in Appendix .
The thermodynamic variable (T: J kg-1) is linearly related
to temperature as
Tx=Bx+AxTx,
where x corresponds to one of the three surface temperatures
(Tg, Tv, or Tn), canopy air temperature,
Tc, or the overlying atmospheric temperature, Ta. The
definitions of Ax and Bx depend on the
atmospheric variable in the turbulent diffusion scheme and are usually
defined to cast T in the form of dry static energy, or potential
temperature and are determined by the atmospheric model in coupled mode (see
Appendix ). The total canopy aerodynamic resistance is
comprised of snow buried, Ravn-c, and non-snow buried,
Ravg-c, resistances from
Rav-c=1-pnαpngRavn-c+1-pngRavg-c-1.
The separation of the resistances is done to mainly account for differences
in the roughness length between the buried and non-covered parts of the
vegetation canopy; therefore, the primary effect of snow cover is to increase the
resistance relative to a snow-free surface assuming the same temperature
gradient owing to a lower surface roughness, and thus Ravn-c≥Ravg-c. The formulation also provides a continuous transition to
the case of vanishing canopy turbulent fluxes as the canopy becomes entirely
buried (as pnα→1). In this case, the energy
budget equations collapse into a simple coupling between the snow surface and
the overlying atmosphere, and the ground energy budget simply consists in
heat conduction between the ground surface and the snowpack base. The
formulations of the resistances between the different surfaces and the canopy
airspace and the overlying atmosphere are described in detail in
Sect. . The canopy air temperature, which is needed by
different physics routines, is diagnosed by combining
Eqs. ()–() and solving for
Tc and using Eq. () to determine
Tc (see Appendix for details).
Water vapor fluxes
The MEB water vapor fluxes are expressed as
Ev=ρahsvqsatv-qcRav-c,Eg=ρaqg-qcRag-c,En=ρahsn1-pnαqsatin-qcRan-c+pnαqsatin-qaRan-a,Ec=ρaqc-qaRac-a,E=ρa1-pnαpngqc-qaRac-a+pnαpnghsnqsatin-qaRan-a.
The vapor flux between the canopy air and the overlying atmosphere is
represented by Ec, and the total vapor flux exchanged with the
overlying atmosphere is defined as E. The specific humidity (kg kg-1)
of the overlying atmosphere is represented by qa, whereas
qsat and qsati represent the specific humidity at
saturation over liquid water and ice, respectively. For the surface specific
humidities at saturation, the convention qsatx=qsatTx is used. The same holds true for saturation
over ice so that qsatin=qsatiTn. The canopy air specific humidity
qc is diagnosed assuming that Ec is balanced by the
vapor fluxes between the canopy air and each of the three surfaces considered
(the methodology for diagnosing the canopy air thermal properties is
described in Appendix ,
Sect. ). The effective ground specific humidity is
defined as
qg=hsgqsatg+1+haqc,
where the humidity factors are defined as
hsg=δghug1-pgfLvL+δgfhugfpgfLsL,ha=δg1-pgfLvL+δgfpgfLsL.
The latent heats of fusion and vaporization are defined as Ls and
Lv (J kg-1), respectively. The fraction of the surface
layer that is frozen, pgf, is simply defined as the ratio of the
liquid water equivalent ice content to the total water content. The average
latent heat L is essentially a normalization factor that ranges
between Ls and Lv as a function of snow cover and
surface soil ice (see Appendix ). The
soil coefficient δg in
Eqs. ()–() is defined as
δg=Rag-cRag-c+Rgδgcor,
where the soil resistance Rg is defined by
Eq. (). Note that the composite version of ISBA did not
include an explicit soil resistance term, and therefore this also represents a new
addition to the model. This term was found to further improve results for
bare-soil evaporation within MEB, and its inclusion is consistent with other
similar multi-source models e.g.,. See
Sect. for further details. The delta function
δgcor is a numerical correction term that is required owing
to the linearization of qsatg and is unity unless both hugqsatg<qc and qsatg>qc, in which case it is set to zero. The surface ground humidity
factor is defined using the standard ISBA formulation from
as
hug=121-coswg,1wfc,1∗π0≤hug≤1.
In the case of condensation (qsatg<qa),
hug=1 (see ,
, for details).
The effective field capacity wfc,1∗ is computed relative to
the liquid water content of the uppermost soil layer (it is adjusted in the
presence of soil ice compared to the default field capacity). The analogous
form holds for the humidity factor over the frozen part of the surface soil
layer, hugf, with wg,1 and wfc,1∗ replaced
by wgf,1 and wfcf,1∗ (m3 m-3) in
Eq. (), respectively . Note that it
would be more accurate to use qsati in place of qsat for
the sublimation of the canopy-intercepted snow and the soil ice in
Eqs. ()–(), respectively, but this
complicates the linearization and this has been neglected for now. The snow
factor is defined as hsn=Ls/L. This factor can be
modified so that En includes both sublimation and evaporation
, but the impact of including a liquid water flux
has been found to be negligible; thus, for simplicity only sublimation is
accounted for currently.
The leading coefficient for the canopy evapotranspiration is defined as
hsv=1-pnvhsvgLv/L+pnvhsvnLs/L,
where pnv is an evaporative efficiency factor that is used to
partition the canopy interception storage mass flux between evaporation of
liquid water and sublimation (see Eq. ). When part of
the vegetation canopy is buried (i.e., pnα>0), a different
roughness is felt by the canopy air space so that a new resistance is
computed over the pnα-covered part of the canopy as is done for
sensible heat flux. This is accounted for by defining
hsvg=png1-pnαRav-cRavn-chvn+1-pngRav-cRavg-chvg,hsvn=png1-pnαRav-cRavn-c+1-pngRav-cRavg-c.
The Halstead coefficients in Eq. () are defined
as
hvg=Ravg-cRavg-c+Rs1-δ+δ,,hvn=Ravn-cRavn-c+Rsn1-δ+δ.
The stomatal resistance Rs can be computed using either the
Jarvis method described by or a
more physically based method that includes a representation of
photosynthesis . The stomatal resistance for the
partially snow-buried portion defined as
Rsn=Rs/1-minpnα, 1-Rs/Rs,maxRsn≤Rs,max
so that the effect of coverage by the snowpack is to increase the canopy
resistance. Note that when the canopy is not partially or fully buried by
ground-based snowpack (pnα=0) and does not contain any intercepted
snow (pnv=0), the leading coefficient for the canopy
evapotranspiration simplifies to the Halstead coefficient from the composite
version of ISBA
hsv=Ravg-cRavg-c+Rs1-δ+δpnα=0andpnv=0.
The fraction of the vegetation covered by water is δ
and is described in Sect. .
The evapotranspiration from the vegetation canopy, Ev, is
comprised of three components:
Ev=Etr+Er+Ern,
where the transpiration, evaporation from the canopy liquid water
interception store, and sublimation from the canopy snow interception store
are represented by Etr, Er, and Ern,
respectively.
The expressions for these fluxes are given in Appendix .
Radiative fluxes
The Rn terms in
Eqs. ()–() represent the surface net
radiation terms (longwave and shortwave components)
Rnx=SWnet,x+LWnet,x,
where x = n, g, or v. The total net radiation of the surface is
Rn=Rnn+Rng+Rnv=SW↓-SW↑+LW↓-LW↑,
where the total down-welling solar (shortwave) and atmospheric (longwave)
radiative fluxes (W m-2) at the top of the canopy or snow surface (in
the case snow is burying the vegetation) are represented by
SW↓ and LW↓, respectively. The total
upwelling (towards the atmosphere) shortwave and longwave radiative fluxes
SW↑ and LW↑, respectively, are simply defined
as the downward components less the total surface net radiative fluxes
(summed over the three surfaces). The effective total surface albedo and
surface radiative temperature (and emissivity) can then be diagnosed (see the
Sect. ) for coupling with the host atmospheric model.
The τn is defined as the solar radiation transmission at the
base of a snowpack layer, so for a sufficiently thin snowpack, solar energy
penetrating the snow to the underlying ground surface is expressed as
τn,NnSWnetn, where
Nn represents the number of modeled snowpack layers (for a deep
snowpack, this term becomes negligible).
Shortwave radiative fluxes
The total land surface shortwave energy budget can be shown to satisfy
SW↓=SWnetg+SWnetv+SWnetn+SW↑,
where SWnetg, SWnetv, and
SWnetn represent the net shortwave terms for the ground,
vegetation canopy, and the ground-based snowpack. The effective surface albedo
(which may be required by the atmospheric radiation scheme or for comparison
with satellite-based data) is diagnosed as
α‾s=SW↑/SW↓.
The multi-level transmission computations
for direct and diffuse radiation are
from .
The distinction between the visible (VIS)
and near-infrared (NIR) radiation components is important
in terms of interactions with the vegetation canopy.
Here, we take into account two spectral bands for the soil and the
vegetation, where visible wavelengths range from approximately 0.3 to
0.7 ×10-6 m, and NIR wavelengths range from
approximately 0.7 to 1.4 ×10-6 m. The spectral values for the
soil and the vegetation are provided by ECOCLIMAP as a
function of vegetation type and climate.
The effective all-wavelength ground (below-canopy) albedo is defined as
α‾gn=pngαn+1-pngαg,
where αg represents the ground albedo.
The ground-based snow albedo, αn, is prognostic and depends
on the snow grain size. It currently includes up to three spectral bands
; however, when coupled to MEB, only the two aforementioned
spectral bands are currently considered for consistency with the vegetation
and soil.
The effective canopy albedo, α‾v, represents the
combined canopy vegetation, αv, and intercepted snow
albedos. Currently, however, we assume that
α‾v=αv, which is based on
recommendations by . They showed that multiple reflections
and scattering of light from patches of intercepted snow together with a high
probability of reflected light reaching the underside of an overlying branch
implied that trees actually act like light traps. Thus, they concluded that
intercepted snow had no significant influence on the shortwave albedo or the
net radiative exchange of boreal conifer canopies.
In addition to baseline albedo values required by the radiative transfer
model for each spectral band,
the model requires the
direct and diffusive downwelling solar
components. The diffuse fraction can be provided by observations
(offline mode) or a host atmospheric
model. For the
case when no diffuse information is
provided to the surface model, the diffuse fraction is computed using
the method proposed by
.
Longwave radiative fluxes
The longwave radiation scheme is based on a representation of the
vegetation canopy as a plane-parallel surface.
The model considers one reflection with three reflecting surfaces (ground,
ground-based snowpack, and the vegetation canopy; a schematic is shown
in Appendix ).
The total land surface longwave energy budget can be shown to satisfy
LW↓=LWnetg+LWnetv+LWnetn+LW↑,
where LWnetg, LWnetv, and
LWnetn represent the net longwave terms for the ground,
vegetation canopy, and the ground-based snowpack. The effective surface
radiative temperature (which may be required by the atmospheric radiation
scheme or for comparison with satellite-based data) is diagnosed as
Trad=LW↑-LW↓1-ϵ‾sϵ‾sσ1/4,
where σ is the Stefan–Boltzmann constant, and
ϵ‾s represents the effective surface emissivity.
In Eq. (), there are two that are known (LW
fluxes) and two that are unknown (Trad and
ϵ‾s). Here we opt to pre-define
ϵ‾s in a manner that is consistent with the
various surface contributions as
ϵ‾s=pngϵ‾sn+1-pngϵ‾sg.
The canopy-absorption-weighted effective snow and ground emissivities are
defined, respectively, as
ϵ‾sn=σ‾nLWϵv+1-σ‾nLWϵn,ϵ‾sg=σ‾gLWϵv+1-σ‾gLWϵg,
where ϵv, ϵg, and ϵn
represent the emissivities of the vegetation, snow-free ground, and the
ground-based snowpack, respectively. The ground and vegetation emissivities
are given by ECOCLIMAP are vary primarily as a function of vegetation class
for spatially distributed simulations, or they can be prescribed for local
scale studies. The snow emissivity is currently defined as
ϵn=0.99. The effect of longwave absorption through the
non-snow-buried part of the vegetation canopy is included as
σ‾nLW=1-png-pnα1-pngσLW+png+pnα1-pngσfLW,σ‾gLW=1-png1-pnασLW+png1-pnασfLW,
where the canopy absorption is defined as
σLW=1-exp-τLWLAI=1-χv
and τLW represents a longwave radiation transmission factor
that can be species (or land classification) dependent, χv is
defined as a vegetation view factor, and LAI represents the leaf area index
(m2 m-2). The absorption over the understory snow-covered
fraction of the grid box is modeled quite simply from Eq. ()
σfLW= 1-exp-τLWLAI1-pnα= 1-exp-τLWLAIn
so that transmission is unity (no absorption or reflection by the canopy:
σ‾LW=σfLW=0) when
pnα=1 (i.e., when the canopy has been buried by snow);
LAIn is used to represent the LAI, which has been reduced
owing to burial by the snowpack.
From Eqs. ()–(), it can
be seen that when there is no snowpack (i.e., png=0 and
pnα=0), then the effective surface emissivity is simply an
absorption-weighted soil–vegetation value defined as
ϵ‾s=σLWϵv+1-σLWϵg. See
Appendix for the derivation of the net
longwave radiation terms in Eq. ().
Heat conduction fluxes
The sub-surface snow and ground heat conduction fluxes are modeled using
Fourier's law (G=λ∂T/∂z). The heat conduction fluxes
in Eqs. ()–() are written in
discrete form as
Gg,1=2Tg,1-Tg,2Δzg,1/λg,1+Δzg,2/λg,2=Λg,1Tg,1-Tg,2,Gn,1=2Tn,1-Tn,2Dn,1/λn,1+Dn,2/λn,2=Λn,1Tn,1-Tn,2,Ggn=2Tn,Nn-Tg,1Dn,Nn/λn,Nn+Δzg,1/λg,1=Λg,nTn,Nn-Tg,1,
where Ggn represents the snow–ground inter-facial heat flux which
defines the snow scheme lower boundary condition. All of the internal heat
conduction fluxes (k=2,N-1) use the same form as in Eq. ()
for the snow and Eq. () for the
soil .
The heat capacities and thermal conductivities λg for the
ground depend on the soil texture, organic content , and
potentially on the thermal properties of the forest litter in the uppermost
layer ; all of the aforementioned properties depend on
the water content. The snow thermal property parameterization is described in
.
Aerodynamic resistances
The resistances between the surface and the overlying atmosphere,
Ran-a and Rac-a, are based on
modified by to account for different roughness length
values for heat and momentum as in ISBA: the full expressions are given in
.
Aerodynamic resistance between the bulk vegetation layer
and the canopy air
The aerodynamic resistance between the vegetation canopy and the surrounding
airspace can be defined as
Ravg-c=gav+gav∗-1.
The parameterization of the bulk canopy aerodynamic conductance
gav between the canopy and the canopy air is based on
. It is defined as
gav=2LAIaavϕv′uhvlw1/2[1-exp(-ϕv′/2)],
where uhv represents the wind speed at the top of the canopy
(m s-1),and lw represents the leaf width (m: see
Table ). The remaining parameters and their values are
defined in Table . The conductance accounting for the free
convection correction from is expressed as
gav∗=LAI890Tv-Tclw1/4Tv≥Tc.
Note that this correction is only used for unstable conditions. The effect of
snow burying the vegetation impacts the aerodynamic resistance of the canopy
is simply modeled by modifying the LAI using
LAIn=LAI1-pnα.
The LAIn is then used in Eq. ()
to compute Ravn-c, and this resistance is limited to
5000 s m-1 as LAIn→0.
Surface vegetation canopy turbulence parameters that are constant.
Symbol
Definition
Unit
Value
Reference
Comment
aav
Canopy conductance scale factor
m s-1/2
0.01
Eq. (26)
ϕv′
Attenuation coeff. for wind
–
3
p. 386
lw
Leaf width
m
0.02
ϕv
Attenuation coeff. for mom.
–
2
p. 386
z0g
Roughness of soil surface
m
0.007
χL
Ross–Goudriaan leaf angle dist.
–
0.12
p. 26
ul
Typical local wind speed
m s-1
1
Eq. (B7)
υ
Kinematic viscos. of air
m2 s-1
0.15×10-4
Aerodynamic resistance between the ground and the canopy air
The resistance between the ground and the canopy air space is defined as
Rag-c=Ragn/ψH,
where Ragn is the default resistance value for neutral
conditions.
The stability correction term ψH depends on the canopy
structural parameters, wind speed, and temperature gradient
between the surface and the canopy air.
The aerodynamic resistance is also based on
.
It is assumed that the eddy diffusivity K (m2 s-1)
in the vegetation layer
follows an exponential profile:
Kz=Kzhvexpϕv1-zzhv,
where zhv represents the canopy height. Integrating the reciprocal
of the diffusivity defined in Eq. () from z0g to d+z0v yields
Ragn=zhvϕvKzhv{expϕv1-z0gzhv-expϕv1-d+z0vzhv}.
The diffusivity at the canopy top is defined as
Kzhv=ku∗hvzhv-d.
The von Karman constant k has a value of 0.4.
The displacement height is defined as
d=1.1zhvln1+cdLAI1/4,
where the leaf drag coefficient cd,is defined from
cd=1.3282Re1/2+0.451π(1-χL)1.6,
where χL represents the Ross–Goudriaan leaf angle distribution function,
which has been estimated according to (see
Table ), and Re is the Reynolds number defined
as
Re=ullwυ.
The friction velocity at the top of the vegetation canopy is
defined as
u∗hv=kuhvlnzhv-d/z0v,
where the wind speed at the top of the canopy is
uhv=fhvVa
and Va represents the wind speed at the reference height
za above the canopy.
The canopy height is defined based on vegetation class and climate within
ECOCLIMAP as a primary parameter. It can also be defined using an external
dataset, such as from a satellite-derived product (as a function of space and
time). The vegetation roughness length for momentum is then computed as a
secondary parameter as a function of the vegetation canopy height. The factor
fhv (≤1) is a stability-dependent adjustment factor (see
Appendix ).
The dimensionless height scaling factor
is defined as
ϕz=zhv-dzrϕz≤1.
The reference height is defined as zr=za-d for
simulations where the reference height is sufficiently above the top of the
vegetation canopy. This is usually the case for local scale studies using
observation data. When MEB is coupled to an atmospheric model, however, the
lowest model level can be below the canopy height; therefore, for coupled model
simulations zr=maxza,zhv-d+zmin where
zmin=2 (m).
Finally, the stability correction factor from
Eq. () is defined as
ψH=1-ahvRi1/2Ri≤0,=11+bRi1+cRi1/21+RiRi,critfz0-1Ri>0andRi≤Ri,crit,=fz01+bRi1+cRi1/2Ri>Ri,crit,
where the Richardson number is defined as
Ri=-gzhvTs-TcTsuhv2.
Note that strictly speaking, the temperature factor in the denominator should
be defined as Ts+Tc/2, but this has only a
minor impact for our purposes.
The critical Richardson number, Ri,crit, is set to 0.2.
This parameter has been defined assuming that some turbulent exchange is
likely always present (even if intermittent), but it is recognized that
eventually a more robust approach should be developed for very stable surface
layers .
The expression for unstable conditions (Eq. ) is
from where the structural parameter is defined as
ahv=9.
It is generally accepted that there is a need to improve the parameterization
of the exchange coefficient for extremely stable conditions typically
encountered over snow . Since the goal
here is not to develop a new parameterization, we simply modify the
expression for stable conditions by using the standard function from ISBA.
The standard ISBA stability correction for stable conditions is given by
Eq. (), where b=15 and c=5
. The factor that takes into account differing
roughness lengths for heat and momentum is defined as
fz0=lnzhv/z0glnzhv/z0gh,
where z0gh is the ground roughness length for scalars. The
weighting function (i.e., ratio of Ri to Ri,crit) in
Eq. () is used in order to avoid a
discontinuity at Ri=0 (the roughness length factor effect
vanishes at Ri=0) in Eq. (). An
example of Eq. is shown in
Fig. using the z0g from
Table , and for z0gh/z0g of 0.1 and 1.0.
Finally, the resistance between the ground-based snowpack Ran-c
and the canopy air use the same expressions as for the aerodynamic resistance
between the ground and the canopy air outlined herein, but with the surface
properties of the snowpack (namely the roughness length and snow surface
temperature).
Stability correction term is shown using the Sellers formulation
for Ri≤0 while the function for stable conditions adapted
from ISBA (Ri>0) for two ratios of z0g/z0gh. The ground surface roughness length is
defined in Table .
Ground resistance
The soil resistance term is
defined based on as
Rg=expaRg-bRgw‾g/w‾sat.
The coefficients are aRg=8.206 and bRg=4.255, and the
vertically averaged volumetric water content and saturated volumetric water
content are given by w‾g and w‾sat, respectively. The averaging is done from one to several upper
layers. Indeed, the inclusion of an explicit ground surface energy budget
makes it more conceptually straightforward to include a ground resistance
compared to the original composite soil–vegetation surface. The ground
resistance is often used as a surrogate for an additional resistance arising
due to a forest litter layer, therefore the soil resistance is set to zero
when the litter-layer option is activated. Finally, the coefficients
aRg and bRg were determined from a case study for a
specific location, and could possibly be location dependent. But currently
these values are used, in part, since the litter formulation is the default
configuration for MEB for forests as it generally gives better surface fluxes
.
Water budget
The governing equations for (water) mass for the bulk canopy, and
surface snow and ground layers are written as
∂Wr∂t=Prv+max0,-Etr-Er-Drv-Φv,∂Wrn∂t=In-Un-Ern+Φvpng∂Wn,1∂t=Ps-In+Un+pngPr-Prv+Drv-Fnl,1-En+Φn,1+ξnl,1,ρwΔzg,1∂wg,1∂t=Pr-Prv+Drv-Eg1-png+pngFnl,Nn-R0-Fg,1-Φg,1,ρwΔzg,1∂wgf,1∂t=Φg,1-Egf1-png,
where Wr and Wrn represent the vegetation canopy
water stores (intercepted water) and the intercepted snow and frozen water
(all in kg m-2), respectively. Wn,1 represents the snow
liquid water equivalent (SWE) for the uppermost snow layer of the multi-layer
scheme. The soil liquid water content and water content equivalent of frozen
water are defined as wg and wgf, respectively
(m3 m-3).
The interception reservoir Wr is modeled as single-layer
bucket, with losses represented by evaporation Er, and canopy
drip Drv of liquid water that exceeds a maximum holding capacity
(see Sect. for details). Sources include
condensation (negative Er and Etr) and
Prv,
which represents the intercepted precipitation. The positive part of
Etr is extracted from the sub-surface soil layers as a function of
soil moisture and a prescribed vertical root zone distribution
. This equation is the same as that used in ISBA, except
for the addition of the phase change term, Φv (kg m-2
s-1). This term has been introduced owing to the introduction of an
explicit canopy snow interception reservoir Wrn; the canopy snow
and liquid water reservoirs can exchange mass via this term which is modeled
as melt less freezing. The remaining rainfall (Pr-Prv) is
partitioned between the snow-free and snow-covered ground surface, where
Pr represents the total grid cell rainfall rate. The canopy snow
interception is more complex, and represents certain baseline processes such
as snow interception In and unloading Un; see
Sect. for details.
The soil water and snow liquid water vertical fluxes at the base of the
surface ground and snow are represented, respectively, by Fg,1
using Darcy's Law and by Fnl,1 using a tipping-bucket scheme (kg
m-2 s-1). The liquid water flux at the base of the snowpack
Fnl,Nn is directed downward into the soil and
consists in the liquid water in excess of the lowest model liquid water-holding capacity.
A description of the snow and soil schemes are given in
and , respectively. R0 is
the surface runoff. It accounts for sub-grid heterogeneity of
precipitation, soil moisture, and for when potential infiltration exceeds a
maximum rate . The soil liquid water equivalent ice
content can have some losses owing to sublimation in the uppermost soil
layer Egf but it mainly evolves owing to phase changes from soil
water freeze–thaw Φg. The remaining symbols in
Eqs. ()–() are defined and described in
Sect. and .
Precipitation interception
Canopy snow interception
The intercepted snow mass budget is described by Eq. (),
while the energy budget is included as a part of the bulk canopy prognostic
equation (Eq. ). The positive mass contributions acting
to increase intercepted snow on canopy are snowfall interception
In, water on canopy that freezes Φv<0, and
sublimation of water vapor to ice Ern<0. Unloading
Un, sublimation Ern>0, and snowmelt
Φv>0, are the sinks. All of the terms are in
kg m-2 s-1. It is assumed that intercepted rain and snow can
co-exist on the canopy. The intercepted snow is assumed to have the same
temperature as the canopy Tv; thus, there is no advective heat
exchange with the atmosphere that simplifies the equations. For simplicity,
when intercepted water on the canopy freezes, it is assumed to become part of
the intercepted snow.
The parameterization of interception efficiency
is based upon . It determines how much
snow is intercepted during the time step and is defined as
In,v,0=Wrn∗-Wrn1-exp-kn,vPsΔt,
where Wrn∗ is the maximum snow load allowed, Ps
the frozen precipitation rate, and kn,v a proportionality factor.
kn,v is a function of Wrn∗ and the maximum plan
area of the snow–leaf contact area per unit area of ground Cn,vp:
kn,v=Cn,vpWrn∗.
For a closed canopy, Cn,vp would be equal to one, but for a partly
open canopy it is described by the relationship
Cn,vp=Cn,vc1-Ccuhvzhv/wnJn,
where Cn,vc is the canopy coverage per unit area of ground which
can be expressed as 1-χv where χv is the
sky-view factor (see Eq. ), and uhv represents the
mean horizontal wind speed at the canopy top (Eq. ), which
corresponds to the height zhv (m). The characteristic vertical
snow-flake velocity, wn, is set to 0.8 m s-1
. Jn is set to 103 m, which is assumed to
represent the typical size of the mean forested down wind distance.
For calm conditions and completely vertically falling snowflakes,
Cn,vp=Cc. For any existing wind, snow could be
intercepted by the surrounding trees so that high wind speed increases
interception efficiency. Generally for open boreal conifer canopies,
Cn,vc<Cn,vp<1. Under normal wind speed conditions
(i.e.,
wind speeds larger than 1 m s-1), Cn,vc (and
Cn,vp) values are usually close to unity.
The maximum allowed canopy snow load, Wrn∗, is a function
of the maximum snow load per unit branch area, Sn,v (kg m-2),
and the leaf area index:
Wrn∗=Sn,vLAI
where Sn,v is defined as
Sn,v=Sn,v‾0.27+46ρn,v.
Based on measurements, estimated average values for
Sn,v‾ of 6.6 for pine and 5.9 kg m-2 for spruce
trees. Because the average value for this parameter only varies by about
10 % across these two fairly common tree species, and ECOCLIMAP does not
currently make a clear distinction between these two forest classes, we
currently use 6.3 as the default value for all forest classes.
ρn,v is the canopy snow density (kg m-3) defined by the
relationship
ρn,v=67.92+51.25expTc-Tf/2.59Tc≤Tcmax,
where Tc is the canopy air temperature and Tcmax is the
temperature corresponding to the maximum snow density. Assuming a maximum
snow density of 750 kg m-3 and solving Eq. () for
canopy temperature yields Tcmax=279.854 K. This gives values of
Sn,v in the range 4–6 kg m-2.
The water vapor flux between the intercepted canopy snow and the canopy air
Ern (Eq. ), includes the evaporative efficiency
pnv. This effect was first described by . In the
ISBA-MEB parameterization, the formulation is slightly modified so that it
approaches zero when there is no intercepted snow load:
pnv=0.89Snv0.31+exp-4.7(Snv-0.45),
where Snv is the ratio of snow-covered area on the canopy to the
total canopy area
Snv=WrnWrn∗0≤Snv≤1.
A numerical test is performed to determine if the canopy snow becomes less
than zero within one time step due to sublimation. If this is true, then the
required mass is removed from the underlying snowpack so that the intercepted
snow becomes exactly zero during the time step to ensure a high degree of
mass conservation. Note that this adjustment is generally negligible.
The intercepted snow unloading, due to processes such as wind and branch
bending, has to be estimated. suggested an experimentally
verified exponential decay in load over time t, which is used in the
parameterization:
Un,v=In,v,0exp(-UnLt)=In,v,0cnL,
where UnL is an unloading rate coefficient (s-1) and
cnL the dimensionless unloading coefficient.
found that cnL=0.678 was a good approximation that, with a time
step of 15 min, gives UnL=-4.498×10-6 s-1. A
tuned value for the RCA-LSM from the Snow Model Intercomparison Project phase
2 (SnowMIP2) experiments is UnL=-3.4254×10-6 s-1, which has been adopted for MEB for now. All unloaded snow
is assumed to fall to the ground where it is added to the snow storage on
forest ground. Further, corrections to compensate for changes in the original
LSM due to this new parameterization have been made for heat capacity, latent
heat of vaporization, evapotranspiration, snow storages, and fluxes of latent
heat.
Finally, canopy snow will partly melt if the temperature rises above the
melting point and become intercepted water, where the intercepted (liquid and
frozen) water phase change is simply proportional to the temperature:
Φv=CiWrnLfτΦTf-Tv=CiSnvWrn∗LfτΦTf-Tv,
where Φv<0 signifies melting. Tf represents the
melting point temperature (273.15 K) and the characteristic phase change
timescale is τΦ (s). If it is assumed that the available heating
during the time step for phase change is proportional to canopy biomass via
the LAI then Eq. () can be written (for both melt and
refreezing) as
Φv=SnvkΦvTf-Tv.
Note that if energy is available for melting, the phase change rate is
limited by the amount of intercepted snow, and likewise freezing is
limited by the amount of intercepted liquid water.
The melting of intercepted snow within the canopy can be quite complex, thus
currently the simple approach in Eq. () adopted herein. The
phase change coefficient was tuned to a value of kΦv=5.56×10-6 kg m-2 s-1 K-1 for the SNOWMIP2
experiments with the RCA-LSM. Currently, this value is the default for
ISBA-MEB.
Canopy rain interception
The rain intercepted by the vegetation is available for potential
evaporation,
which means that it has a strong influence on the fluxes of heat and
consequently also on the surface temperature. The rate of change of
intercepted water on vegetation canopy is described by Eq. ().
The rate that water is intercepted by the overstory (which is not buried by
the ground-based snow) is defined as
Prv=Pr1-χv1-pngpαn,
where χv is a view factor indicating how much of the
precipitation that should fall directly to the ground (see
Eq. ). The overstory canopy drip rate Drv is
defined simply as the value of water in the reservoir which exceeds the
maximum holding capacity:
Drv=max0,Wrv-Wrv,max/Δt,
where the maximum liquid water-holding capacity is defined simply as
Wrv,max=cwrvLAI.
Generally speaking, cwrv=0.2 , although it can
be modified slightly for certain vegetation cover. Note that
Eq. () is first evaluated with Drv=0, and then the
canopy drip is computed as a residual. Thus, the final water amount is
corrected by removing the canopy drip or throughfall. This water can then
become a liquid water source for the soil and the ground-based snowpack.
The fraction of the vegetation covered with water is defined as
δv=1-ωrvWrWr,max2/3+ωrvWr1+arvLAIWr,max-arvWr.
used the first term on the RHS of Eq. ()
for relatively low vegetation and the second term for
tall vegetation . Currently in ISBA, a weighting
function is used which introduces the vegetation height dependence using the
roughness length as a proxy from
ωrv=2z0v- 10≤ωrv≤1,
where the current value for the dimensionless coefficient is arv=2.
Halstead coefficient
In the case of wet vegetation, the total plant evapotranspiration is
partitioned between the evaporation of intercepted water, and transpiration
via stomata by the Halstead coefficient. In MEB, two such
coefficients are used for the non-snow-buried and buried parts of the
vegetation canopy, hvg and hvn
(Eqs. and , respectively). In MEB,
the general form of the Halstead coefficient, as defined in ,
is modified by introducing the factor kv to take into account the
fact that saturated vegetation can transpire, i.e., when δv=1
. Thus, for MEB we define
δ=kvδv. The intercepted water forms full
spheres just touching the vegetation surface when kv=0, which
allows for full transpiration from the whole leaf surface. In contrast,
kv=1 would represent a situation where a water film covers the
vegetation completely and no transpiration is allowed. To adhere to the
interception model as described above, where the intercepted water exists as
droplets, we set the value of kv to 0.25. Note that in the case
of condensation, i.e., E<0, hv=1.
Without a limitation of hvg and hvn, the evaporative
demand could exceed the available intercepted water during a time step,
especially for the canopy vegetation which experiences a relatively low
aerodynamic resistance. To avoid such a situation, a maximum value of the
Halstead coefficient is imposed by calculating a maximum value of the
δv. See Appendix for details.
Conclusions
This paper presents the description of a new multi-energy balance (MEB) scheme
for representing tall vegetation in the ISBA land surface model component of
the SURFEX land–atmosphere coupling and driving platform. This effort is part
of the ongoing effort within the international scientific community to
continually improve the representation of land surface processes for
hydrological and meteorological research and applications.
MEB consists in a fully implicit numerical coupling between a multi-layer
physically based snowpack model, a variable-layer soil scheme, an explicit
litter layer, a bulk vegetation scheme, and the atmosphere. It also includes
a feature that permits a coupling transition of the snowpack from the canopy
air to the free atmosphere as a function of snow depth and canopy height
using a fully implicit numerical scheme. MEB has been developed in order to
meet the criteria associated with computational efficiency, high coding
standards (especially in terms of modularity), conservation (of mass, energy,
and momentum), numerical stability for large (time step) scale applications,
and state-of-the-art representation of the key land surface processes
required for current hydrological and meteorological modeling research and
operational applications at Météo-France and within the international
community as a part of the HIRLAM consortium. This includes regional scale
real-time hindcast hydro-meteorological modeling, coupling within both
research and operational non-hydrostatic models, regional climate models, and
a global climate model, not to mention being used for ongoing offline
land surface reanalysis projects and fundamental research applications.
The simple composite soil–vegetation surface energy budget approach of
ISBA has proven its ability to provide solid scientific results and
realistic boundary conditions for hydrological and meteorological
models since its creation over 2 decades ago.
However, owing to the ever increasing demands of the user community,
it was decided to improve the representation of the vegetation
processes as a priority.
The key motivation of the MEB development was to move away from the
composite scheme in order to address certain
known issues (such as excessive bare-soil evaporation in forested areas, the
neglect of canopy snow interception processes), to improve consistency
in terms of the representation of the carbon cycle (by modeling
explicit vegetation energy and carbon exchanges),
to add new key explicit processes (forest litter, the gradual covering of
vegetation by ground-based snow cover),
and to open the door
to potential improvements in land data assimilation (by representing
distinct surface temperatures for soil and vegetation).
Finally, note that while some LSMs intended for GCMs now use
multiple-vegetation layers, a single bulk vegetation layer is
currently used in MEB since it has been considered as a reasonable
first increase in complexity level from the composite
soil–vegetation scheme. However, MEB has
been designed such that the addition of more canopy layers could be
added if deemed necessary in the future.
This is part one of two companion papers describing the model formulation of
ISBA-MEB. Part two describes the model evaluation at the local scale for
several contrasting well-instrumented sites in France, and for over 42 sites
encompassing a wide range of climate conditions for several different forest
classes over multiple annual cycles (Napoly et al., 2016).
This two-part series of papers will be followed by a series of papers
in upcoming years
that will present the evaluation and analysis of ISBA-MEB with a specific
focus (coupling with snow processes, regional to global scale
hydrology, and finally fully coupled runs in a climate model).