FORWADY Forest Hydrology Model – UBC Modelling Webpage 5/3/2023

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

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CanopyTranspiration

Canopy Interception

Rain

Humus layer

Outflow

Soil B

Soil A

Forest floorpercolation

Soil A percolation

Soil B percolation

Runoff

SnowpackThroughfall

ForWaDy

UnderstoryTranspiration

Transpiration DeficitIndex

Litter layer

Infiltration

Evaporation

Interflow

CanopyTranspiration

Demand

Snowthroughfall

Snow

Air tempmelt

Radiationmelt

Sublimation

Subsoil

drainage

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

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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

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radiation as it passes through the canopy and subsequently through the understorey is

calculated as a 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).

Rn Rad * (1 a) (1)

0

20

40

60

80

100

0 2 4 6 8

Inte

rcep

ted

Ligh

t (%

)

LAIFigure 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):

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PET s

s (Rn G M)

1L

(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

s RnCan

1L

(3)

PETUS s

s RnUS

1L

(4)

PETFF s

s (RnFF G)

1L

(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 * RnFF (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

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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

RCan = 1- ( / 1.26) References

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)

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

(VAI), where a maximum canopy storage term is calculated based on the assumption

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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 CWat < CMax TF CWat - CMax CWat CMax

(8)

ECan = min(CMax,CWat, PETCan) (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.

Soil-limited evapotranspiration

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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.

0

0.25

0.5

0.75

1

0 25 50 75 100

Pro

port

ion

of P

ET

Available soil water (%)

PET

Energy limitedtranspiration

Figure 3. The relative rate of transpiration determined as a function of available soil water and energy-

limited evapotranspiration (PET). The function curve shifts to the right as PET increases.

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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.

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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.

TDI CanT (total)i CanT (actual)i

CanT (total)ii0

i t

(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

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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.

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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.

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Kelliher, F.M., D. Whitehead, K.J. McAneney, M.J. Judd (1990). Partitioning

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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

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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

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Meyers, B.J. (1988). Water stress integral—a link between short-term stress and long-

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Monteith, J.L. (1973). Principles of Environmental Physics. Edward Arnold, London.

Munro, D.S. (1979). Daytime energy exchange and evaporation from a wooded swamp.

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