FORWADY Forest Hydrology Model – UBC Modelling Webpage
2/13/2016
A forest hydrology model for simulating the effect of stand management and climate
change on forest water dynamics.
B. Seely, and J. P. Kimmins.
Introduction
With the expanding use of alternative silviculture systems in Canada and other
timber producing countries and the growing threat of climate change, the need for
ecosystem models that can cope with the changing ecosystem dynamics produced by such
management and climate conditions has increased. One aspect of forest ecosystems
particularly sensitive to these types of changes is the effect of soil moisture conditions on
tree growth and other ecosystem processes. Several models of forest growth have
included soil moisture or rainfall data as a parameter in the calculation of forest
production, but few consider the effects of stand management on the dynamics of forest
hydrology. Alterations in forest hydrology, whether induced by management or climate
change, can have a significant impact on the partitioning of limited water resources
among trees and understory species and ultimately on tree water stress and stand
development.
Here we describe a two-dimensional forest hydrology model designed for
simulating the hydrologic dynamics of a forest stand under a given set of climatic and
vegatation conditions. The primary goal in model development was to produce a forest
hydrology model which could be integrated with the forest ecosystem models FORCEE
and FORECAST (Kimmins et al. 1997) for the purpose of simulating the effects of forest
water dynamics on stand growth and development. In order to facilitate the use of the
forest hydrology model in management applications the data requirements and calibrated
parameters were kept to a minimum.
Model Description
The model described here called ForWaDy (Forest Water Dynamics) was
constructed around the foundation of FORHYM, a general water balance model designed
by Arp and Yin (1992) for the simulation of water fluxes through temperate forest
ecosystems. The major difference between the two models lies in the nature of the central
potential evapotranspiration (PET) algorithms. While FORHYM uses a PET equation
based on relationships with air temperature, ForWaDy drives PET using an empirically
based energy budget approach. The energy budget approach employed in ForWaDy
allows the model to partition evapotranspiration into its primary components, thereby
facilitating the capacity to simulate water competition. The daily energy available for
evapotranspiraton is divided among canopy trees, understory plants and the forest floor
based on the proportional interception of incoming solar radiation by each layer adjusted
for reflection depending on surface albedos. Subsequently, a passive competition for
available soil moisture is simulated through the use of an algorithm that combines
species-specific root occupancy information with energy-limited transpiration and
evaporation demands. Canopy
2
Rain
Snow
Evaporation
Sublimation
Canopy Interception
ForWaDy
Air temp
melt
Throughfall
Snow
throughfall
Snowpack
Radiation
melt
Litter lay er
Transpiration Def icit
Index
Runoff
Infiltration
Humus lay er
Canopy
Transpiration
Demand
Forest floor
percolation
Canopy
Transpiration
Soil A
Understory
Transpiration
Soil A percolation
Soil B
Soil B percolation
Subsoil
Interflow
drainage
Outf low
Figure 1. Schematic of the forest hydrology model indicating the various flow pathways and storage
compartments in the model. Compartments with bold borders indicate areas of the model which will
facilitate a future integration with FORECAST and FORCEE.
water stress is determined as a function of energy-limited canopy transpiration demand
and soil-limited actual canopy transpiration through the calculation of a cumulative water
stress index. This index represents a dynamic measure of tree water stress over a given
time period and may be used as a parameter to limit tree growth rates based on light and
3
nutrient availability in models such as FORECAST and FORCEE. The simulation of
snowfall and snowpack dynamics in ForWaDy is based on the RHYSSys Snow Model
(RSM) (Coughlan and Running 1997).
All equations describing water flow within the model are solved using a
simulation dt of 0.25 days. The use of a dt less than one day enables the model to divide
the flux of water from a particular soil reservoir among competing outflows.
Data Requirements
One of the goals in model development was to produce a model that is portable
and suitable for use in forest management; thus, climate and site-specific soil and
vegetation data requirements were kept to a minimum (Table 1). The use of parameters
that must be calibrated for each site was also avoided when possible.
Table 1. Data requirements for ForWaDy
Data Requirements
Climate data (daily)
Vegetation data
Forest floor & soil data
• Mean, Max and Min
air temperature
• Percent cover by conifers &
hardwoods
• LF layer mass (kg/ha)
• Solar radiation
• Seasonal conifer and hardwood LAI
• Humus depth and bulk density
• Total precipitation
• Seasonal understorey % cover
• Depth of soil layers (rooting zone)
• Snow fraction
• Rooting depths for trees
• Soil texture class of each soil layer
• Rooting depths for understorey
• Coarse fragment content of layers
• Root occupancy in each layer
• Canopy resistance
Radiation interception
The energy available for driving evapotranspiration is estimated separately for the
canopy, understorey, and forest floor based upon the proportion of adjusted total daily
solar radiation intercepted by each layer. The interception and extinction of radiation as
it passes through the canopy and subsequently through the understorey is calculated as a
4
function of LAI using a simple formulation of Beer’s Law with an extinction coefficient
of 0.4 (Figure 2). Forest floor radiation is calculated as the total remaining radiation
following simulated canopy and understorey interception. For simplification purposes,
the transmittance of net radiation (Rn) is assumed to be equal to that of shortwave
radiation (Kelliher et al. 1990) following the reflection of a portion of total incident
shortwave radiation according to a surface albedo (a) (Eq. 1). Albedo (a) for the canopy
and understory is set at 0.12 which is representative of typical values reported for forests
(Spittlehouse and Black, 1981a; Jarvis et al., 1976) and should be used as a reasonable
approximation in the absence of a measured value. The forest floor albedo is determined
as a function of solar zenith angle and moisture content according to Yin and Arp (1994).
Intercepted Light (%)
Rn  Rad * (1  a)
(1)
100
80
60
40
20
0
0
2
4
LAI
6
8
Figure 2. The relationship between leaf area index (LAI) and intercepted light as a percent of total above
canopy light according to Beer’s Law with an extinction coefficient of 0.4.
Energy-limited evapotranspiration
Energy-limited or potential evapotranspiration (PET) is calculated for each layer
represented in the model based on the following simplification of the Penman-Monteith
equation proposed by Priestly and Taylor (1972):
5
PET  
 
s
1 
(Rn  G  M) 
s
L 
(2)
where  is an experimentally determined coefficient, s, y, and L are respectively, the
slope of the saturation vapor pressure curve, the psychrometric constant, and the latent
heat of vaporization of water each evaluated at the daily average air temperature and Rn,
G and M represent the daily (24-hour) values of net radiation, soil heat flux and energy
storage in the canopy. The daily value of M is ignored in this model as it generally
represents less than 5% of RN in coniferous forests (Monteith, 1973). Thus, using the
Rn values calculated for each layer according to the radiation interception submodel,
PET is calculated separately for the canopy, understory and forest floor using equations
(3-5), respectively.
PETCan  
 
s
1 
RnCan  
s 
L 
(3)
 
s
 1 
PETUS  
RnUS  
s
 L 
PETFF  
(4)
 
s
 1 
(Rn FF  G) 
s
 L 
(5)
In (Eq. 5) soil heat flux is estimated as a function of RnFF (Eq. 6) (Flint and Childs,
1991)
G  43.1  0.335 * Rn FF
(6)
Typically, the use of (Eq. 2) has been limited by the fact that, for dry canopy
conditions,  must be calibrated against actual evapotranspiration rates for a particular
site using Bowen ratio / energy balance techniques (Spittlehouse and Black, 1981b)
which can be prohibitively expensive. For a range of dry forest conditions,  has been
shown to vary from 0.6 to 1.1 (Flint and Childs, 1991). However, for a wide range of
6
relatively smooth, freely evaporating (wet) surfaces  is generally equal to 1.26 (Priestly
and Taylor, 1972; Stewart and Rouse, 1977; Davies and Allen, 1973). Values of  less
than 1.26, typical in most forests with dry canopies, are thought to be the result of surface
control of evaporation through stomatal resistance (McNaughton et al., 1979). In an
effort to eliminate the need for  to be experimentally determined for each new site, we
suggest the use of a canopy resistance term (RCan) based on mean literature values of 
for dry canopies of various forest types (Table 2). Using this method  is set at 1.26 for
wet canopy conditions and adjusted under dry canopy conditions (where evaporated
water must pass through stomata) through the use of RCan.
Table 2. Estimated canopy resistance (RCan) for three forest types based on reported
literature values of .
Forest
Type

Dry Pine
0.7*
0.45
* Estimation based on reported range Spittlehouse
and Black (1981b)
Conifer
0.84
0.33
Black (1979);Giles et al. (1984); Spittlehouse and
Black (1981b)
Broadleaf /
understory
1.1*
0.13
Munro (1979); * Estimation based on reported range
Spittlehouse and Black (1981b)
RCan = 1- (  / 1.26)
References
The use of an approximated RCan will undoubtedly lead to some error in the calculation
of canopy PET, but it should provide a reasonable estimate suitable for the intended use
of the model.
Canopy water, throughfall and canopy evaporation
The amount of water held in the canopy at time t (CWat(t)) is calculated as the
difference between incoming rainfall (P) and the sum of throughfall (TF) and canopy
evaporation (ECan) evaluated at each time step (dt) (Eq. 7). The fraction of rainfall
intercepted by the canopy is determined as a function of canopy vegetation area index
7
(VAI), where a maximum canopy storage term is calculated based on the assumption
that at saturation the upper surface of leaves and branches can hold a film of water 0.2
mm in depth (Rutter, 1975), thus CMax = 0.2 * VAI.
CWat(t + dt)  CWat(t)  (P(t)  TF(t)  ECan(t)) * dt
(7)
Throughfall and canopy evaporation are calculated as follows:
TF  0
TF  CWat - CMax
CWat < CMax
CWat  CMax
ECan = min(CMax,CWat, PETCan)
(8)
(9)
Stemflow is assumed to be included as part of throughfall.
Soil water storage and drainage
Hydrologic dynamics in the forest floor and rooting zone are simulated using a
multi-layered approach in which inflows and outflows are estimated sequentially for each
soil layer (Figure 1). Water storage in and vertical movement through the mineral soil
layers are simulated using a “tipping bucket” type algorithm based on total porosity
adjusted for coarse fragment content, field capacity and permanent wilting point
boundaries determined as functions of soil texture (Arp and Yin, 1992). Water stored in
the humus and soil layers between field capacity and permanent wilting point boundaries
is considered to be available for plant uptake. Water storage in the litter layer is
calculated as a function of fine litter mass (i.e. not including coarse woody debris) per
area and is assumed to be unavailable for plant uptake. Lateral flow or interflow of water
from soil layers into stream channels is only allowed to occur when the water content of a
given soil layer is greater than its estimated field capacity and is based on a coefficient
related to slope.
8
Soil-limited evapotranspiration
As the forest floor and soil layers begin to dry, evapotranspiration rates are
limited by the availability of soil water. Transpiration loss is calculated separately from
each layer for both the canopy and understory. Rooting depths of canopy and understory
species are used to determine the layers from which water may be extracted. In order to
represent the limited capacity of a drying soil to supply water to roots, particularly during
periods of high PET, the daily, energy-limited transpiration rate is scaled back through
the use of a relative transpiration rate (RTR) term. RTR is estimated as an empirical
function of the percent of available water in each layer and PET (Denmead and Marsh,
1962) (Fig. 3). A root fraction term is also introduced for both the canopy (RFCan) and
understory (RFUS) as a scalar to account for the fraction of each layer occupied by roots.
Proportion of PET
1
Energy limited
transpiration
0.75
PET
0.5
0.25
0
0
25
50
75
Available soil water (%)
Figure 3. The relative rate of transpiration determined as a function of available soil water and energylimited evapotranspiration (PET). The function curve shifts to the right as PET increases.
9
100
This term is calculated from root depth occupancy data as well as soil layer depths
provided by the user.
The daily extraction of water from the various layers via transpiration occurs
sequentially from the top downward, beginning with the humus layer and continuing
down through the soil B layer. The total amount of energy available for canopy
transpiration (CanT(total) ) is estimated after accounting for the canopy PET energy
consumed by canopy evaporation and canopy resistance (Eqs. 10-11). CanT(total) is then
used to drive transpiration loss from each of the soil layers using an energy budget
approach, moving from the humus layer downward as the amount of extractable soil
water is depleted in each soil layer (Eqs. 12-14). The daily extractable fraction of
available water in a given layer is largely a function of the estimated RTR value and is
generally less than the total plant available water in that layer. The transpiration
algorithm continues until either all layers have been depleted of extractable water or the
energy available for daily transpiration is depleted. Understorey transpiration is
calculated simultaneously using the same method.
GCanT  (PETCan  ECan)
(10)
where: GCanT = gross canopy transpiration (mm day -1)
CanT (total)  GCanT *(1 - RCan)
(11)
CanT (humus)  CanT (total) * RTR(humus) * RFCan(humus)
(12)
CanT (soilA)  (CanT (total)  CanT (humus)) * RTR(SoilA) * RFCan(soilA)
(13)
CanT (soilB)  (CanT (total)  (CanT (humus)  CanT (soilA))) * RTR(soilB) * RFCan(soilB)
(14)
Energy-limited surface evaporation from the LF layer and humus compartments is
also regulated as a function of water content through the use of a relative evaporation rate
term (RER) estimated using a simple empirical function of available soil moisture.
Drying proceeds from the top downwards (Eqs. 15 & 16) and evaporation from the
humus layer is only allowed to occur when the litter layer has dried out.
10
ELitter  PETFF * RER(litter)
(15)
EHumus  (PET FF  ELitter ) * RER(humus)
(16)
Canopy water stress
Typically, models of forest growth which include water stress as a feedback to
forest growth have quantified tree water stress using a summed measure of soil water
deficit. One of the problems in a using a summed water deficit for a measure of water
stress is that it frequently fails to capture the dynamic interactions between different
components of the hydrological cycle and net effect of such interactions on tree water
stress. For example, as part of the Biology of Forest Growth Study near Canberra,
Australia, Meyers (1988) demonstrated that cumulative soil water deficit may not be well
correlated with tree water stress as defined by pre-dawn xylem potential, a commonly
used physiological indicator of tree water stress. The weakness of the technique is even
greater when monthly summaries of climate data are used to calculate the water deficit.
In order to evaluate tree water stress more dynamically we propose the use of a
cumulative index termed the transpiration deficit index (TDI) (Eq. 17-18). TDI provides
a means of summarizing the net effect of several factors including canopy evaporation,
understory transpiration and surface evaporation on actual tree transpiration.
Furthermore the index is calculated on a daily timestep to better capture the cumulative
effect of short term water stress events.
CanT (total)i  CanT (actual)i
CanT (total)i
i 0
it
TDI  
(17)
CanT (actual)  CanT (humus)  CanT(soilA)  CanT (soilB)
(18)
In (Eq. 17) the difference between total canopy transpiration demand (CanT(total)) and
actual canopy transpiration (CanT(actual)) is divided by CanT(total) to normalize the
11
effect of leaf area index on the relative canopy transpiration deficit. This adjustment
effectively converts the total canopy water deficit to a per unit leaf area measure of water
deficit which should be more representative of the water stress of individual trees.
Linking ForWaDy with ecosystem models
Use of the model for simulating and exploring the effects of water competition
and climate change scenarios such as shifting rainfall patterns on stand development
through time requires the linkage with a stand-level forest ecosystem model such as
FORECAST or FORCEE. An integration of such models will be facilitated through a
series of feedback loops (see Figure 1) in which stand and individual tree characteristics
including canopy and understory LAI, rooting depth, percent cover, and forest floor
characteristics are evaluated at each yearly time step in the ecosystem model and used as
state variables in the forest hydrology submodel. Likewise, cumulative annual results
characterizing canopy or individual tree water stress (i.e. TDI) produced by the forest
hydrology submodel, operating on a daily basis, may be directed back to the ecosystem
for use in calculating the current year’s growth. Another pathway for integrating the two
models is through the use of simulated water content in the forest floor layers for the
calculation of litter decomposition rates in the ecosystem model. When combined with
litter quality parameters, such a relationship will allow the integrated model to have more
flexibility in predicting the effects of various silviculture systems on forest floor moisture
contents and thus, litter decomposition rates. Development of these and other pathways
for the complete integration of the two models are currently underway.
12
References
Arp, P.A. and X. Yin (1992). Predicting water fluxes through forests from monthly
precipitation and mean monthly air temperature records. Canadian Journal of Forest
Research 22: 864-877.
Black, T.A. (1979). Evaporation from Douglas-fir stands exposed to soil water deficits.
Water Resources Research 15: 164-170.
Coughlan, J.C. and S.W. Running (1997). Regional ecosystem simulation: A general
model for simulating snow accumulation and melt in mountainous terrain.
Landscape Ecology 12: 119-136.
Davies, J.A. and C.D. Allen (1973). Equilibrium, potential, and actual evaporation from
cropped surfaces in southern Ontario. Journal of Applied Meteorology 12: 649-657.
Denmead, O.T. and R.H. Shaw (1962). Availability of soil water to plants as affected by
soil moisture content and meteorological conditions. Agronomy Journal 385-390.
Flint, A.L. and S.W. Childs (1991). Use of the Priestly-Taylor evaporation equation for
soil water limited conditions in a small forest clearcut. Agricultural and Forest
Meteorology 56: 247-260.
Giles, D.G., T.A. Black, and D.L. Spittlehouse (1984). Determination of growing season
soil water deficits on a forested slope using water balance analysis. Canadian
Journal of Forest Research 15: 107-114.
Jarvis, P.G., G.B. James, and J.J. Landsberg (1976). Coniferous forest, in Vegetation and
the Atmosphere, Vol. 2, Case Studies. J.L. Monteith (ed). Pp. 171-240. Acedemic
Press, New York.
Kelliher, F.M., D. Whitehead, K.J. McAneney, M.J. Judd (1990). Partitioning
evaporation into tree and understorey components in two young Pinus Radiata D.
Don stands. Agricultural and Forest Meteorology 50: 211-227.
Kimmins, J.P. (Hamish), K. A. Scoullar, B. Seely, D. W. Andison, R. Bradley , D.
Mailly and K. M. Tsze (These Proceedings) FORCEEing and FORECASTing the
HORIZON: Hybrid Simulation Modeling of Forest Ecosystem Sustainability
13
McNaughton, K.G., B.E. Clothier, and J.P. Kerr (1979). Evaporation from land surfaces,
in Physical Hydrology: New Zealand Experience. D.L. Murray and P. Ackroyd
(eds.), pp. 97-119. New Zealand Hydrological Society. Wellington North, New
Zealand.
Meyers, B.J. (1988). Water stress integral—a link between short-term stress and longterm growth. Tree Physiology 4: 315-323.
Monteith, J.L. (1973). Principles of Environmental Physics. Edward Arnold, London.
Munro, D.S. (1979). Daytime energy exchange and evaporation from a wooded swamp.
Water Resources Research 15:1259-1265.
Priestly, C.H.B. and R.J. Taylor (1972). On the assessment of surface heat flux and
evaporation using large-scale parameters. Monthly Weather Review 100: 81-92.
Rutter, A.J. (1975). The hydrologic cycle in vegetation. In: Vegetation and the
Atmosphere. Vol.I. Principles. J.L. Monteith (ed.) Academic Press. London.
Spittlehouse, D.L. and T.A. Black (1981a). A growing season water balance model
applied to two Douglas-fir stands. Water Resources Research 17: 1651-1656.
Spittlehouse, D.L. and T.A. Black (1981b). Measuring and modelling forest
evapotranspiration. The Canadian Journal of Chemical Engineering 59: 173-180.
Stewart, R.B. and W.R. Rouse (1977). Substantiation of the Priestly and Taylor
parameter a = 1.26 for potential evaporation in high latitudes. Journal of Applied
Meteorology 16:649-650.
Yin, X. and P.A. Arp (1994). Predicting forest soil temperatures from monthly air
temperature and precipitation records. Canadian Journal of Forest Research 23:
2521-2536.
14