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RHESSys: Regional Hydro-Ecologic
Simulation System—An Object-
Oriented Approach to Spatially
Distributed Modeling of Carbon,
Water, and Nutrient Cycling
C.L. Tague*
Department of Geography, San Diego State University, San Diego, California
L.E. Band
Department of Geography, University of North Carolina at Chapel Hill, Chapel Hill,
North Carolina
Received 29 October 2003; accepted 3 February 2004
ABSTRACT: Process-based models that can represent multiple and
interacting processes provide a framework for combining field-based measure-
ments with evolving science-based models of specific hydroecological
processes. Use of these models, however, requires that the representation of
processes and key assumptions involved be understood by the user community.
This paper provides a full description of process implementation in the most
recent version of the Regional Hydro-Ecological Simulation System
(RHESSys), a model that has been applied in a wide variety of research
* Corresponding author address: C.L. Tague, Department of Geography, San Diego State
University, 5500 Campanile Drive, San Diego, CA 92182-4493.
E-mail address: ctague@mail.sdsu.edu
Earth Interactions Volume 8 (2004) Paper No. 19 Page 1
settings. An overview of the underlying (Geographic Information System) GIS-
based model framework is given followed by a description of the mathematical
models used to represent various biogeochemical cycling and hydrologic
processes including vertical and lateral hydrologic fluxes, microclimate
variability, canopy radiation transfer, vegetation and soil microbial carbon
and nitrogen cycling. An example application of RHESSys for a small forested
watershed as part of the Baltimore Long-Term Ecological Research site is
included to illustrate use of the model in exploring spatial-temporal dynamics
and the coupling between hydrology and biogeochemical cycling.
KEYWORDS: Hydrology, Modeling, Ecosystems
1. Introduction
The Regional Hydro-Ecological Simulation System (RHESSys) is a hydro-
ecological model designed to simulate integrated water, carbon, and nutrient
cycling and transport over spatially variable terrain at small (first-order streams) to
medium (fourth- and fifth-order streams) scales. The model is structured as a
spatially nested hierarchical representation of the landscape with a range of
hydrological, microclimate, and ecosystem processes associated with specific
landscape objects at different levels of the hierarchy. This approach is designed to
facilitate environmental analysis that requires an understanding of within-
watershed processes as well as aggregate fluxes of water, carbon, and nitrogen.
As a hydrologic model, RHESSys is intermediate in terms of complexity. Unlike
lumped parameter hydrologic models such as the Identification of unit Hydro-
graphs and Component flows from Rainfall, Evaporation, and Streamflow data
(IHACRES; Evans and Jakeman 1998) or empirical curve number approaches,
RHESSys explicitly models connectivity and lateral hydrologic fluxes between
landscape units within a watershed. The representation of the vertical soil profile,
however, is based on a fairly simple two-layer model with a single unsaturated and
saturated zone. Additional hydrologic stores include a litter layer, surface detention
store, multiple canopy interception layers, and a snowpack. Process-based
hydrologic models such as MIKE-SHE (Refsgaard and Storm 1995) are at the
more complex end of the continuum and provide a 1D Richard’s equation solution
to drainage through multiple soil layers down to the saturated zone. In addition to
hydrology, RHESSys is able to model feedbacks between hydrology and
ecosystem carbon and nutrient cycling, including the growth of vegetation. Other
process-based eco-hydrologic models such as Macaque (Watson et al. 1999) and
Topog (Vertessy et al. 1993) also provide this capability. In each of these models,
representation of specific processes may differ but these models are relatively
similar in terms of overall complexity.
The version of RHESSys described in this paper has evolved from the
integration of stand-level ecosystem models with methods to compute the
distribution and flux of soil water at the landscape level. These earlier versions
of RHESSys were designed to explicitly couple the Forest Biogeochemical Cycles
(FOREST-BGC) canopy model (Running and Coughlan 1988) with landscape-
level patterns of critical meteorological forcing (Running et al. 1987) and later with
hydrologic processes using the TOPMODEL (Beven and Kirkby 1979) hydrologic
model. The first approach to distribute ecosystem processes at the landscape level
Earth Interactions Volume 8 (2004) Paper No. 19 Page 2
involved gridding the ‘‘ topclimatic’’ logic of Mountain Climate Simulator (MTN-
CLIM) with FOREST-BGC for a 1200 km
2
watershed in western Montana
(Running et al. 1987). Later versions of RHESSys followed a generalization of
FOREST-BGC to multiple biomes as Biome biogeochemical cycles Model
(BIOME-BGC) (Running and Hunt 1993). Hydrologic modeling studies using
RHESSys have included analysis of model sensitivity to landscape representation
(Band 1993; Band et al. 1993) and using the model to explore the sensitivity of
hydrologic response to climate change (Baron et al. 1998).
This current version of RHESSys continues to follow the basic BIOME-BGC
framework. As discussed in this paper, however, many submodels used for specific
processes have been altered and/or extended, largely to improve the soil
biogeochemical process representation and expand canopy representation to consider
both understory and overstory layers. Representation of soil organic matter decom-
position in both RHESSys and BIOME-BGC is based largely on the CENTURY
model. RHESSys also uses the CENTURY
NGAS
(Parton et al. 1996) approach to
model (nitrogen) N-cycling processes such as nitrification and denitrification.
The current version of RHESSys has extended these hydrologic studies through
the incorporation of an explicit hydrologic routing model in place of TOPMODEL.
This current version has been used to explore the combined impact of roads and
forest harvesting for several catchments in the Pacific Northwest (Tague and Band
2001; Krezek 2001), as well as in the Canadian boreal plain (Creed et al. 2000).
Coupled hydrologic-ecosystem and biogeochemical cycling studies using
RHESSys include Mackay and Band (Mackay and Band 1997) who applied an
earlier version of RHESSys to estimate carbon cycling in a small forested
watershed. Mitchell and Csillag (Mitchell and Csillag 2000) are using the current
version of RHESSys to explore spatially varying soil moisture controls on
grassland productivity. Creed and Band (Creed and Band 1998) illustrate the use of
similarity indices, derived using an earlier version of RHESSys, to compute a
nitrate-flushing index based on saturation and a source index based on nitrate
availability and dynamics in the saturation zone for a set of forested catchments in
Ontario, Canada. By using these similarity indices, Creed and Band (Creed and
Band 1998) were able to explain a significant amount of the variation in nitrate
export between catchments and over time within the region. These indices,
however, did not explicitly model N cycling and transport dynamics. Explicit
modeling of N cycling and transport dynamics is included in the current version of
RHESSys and has been tested for a small forested watershed as part of the
Baltimore Ecosystem Study (BES; Band et al. 2001). The current version is also
being used to explore spatial variation in N cycling in the Rocky Mountains
(Laundrum et al. 2002), N saturation in the Smokey Mountains (Webster et al.
2001), and to examine the alteration of N sources and sinks along hydrologic
flowpaths along a gradient of urbanization as part of the BES (Tague et al. 2000).
2. Implementation and model structure
One of the unique features of RHESSys is its hierarchical landscape representation.
This approach allows different processes to be modeled at different scales and
allows basic modeling units to be of arbitrary shape rather than strictly grid based.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 3
RHESSys is also structured using an object-based design approach to facilitate
algorithmic substitution. Additional details on model hierarchical structure and
coding implementation can be found in Band et al. (Band et al. 2000).
RHESSys partitions the landscape such that each level of the spatial hierarchy
fully covers the spatial extent of the landscape. Spatial levels define a containment
hierarchy with progressively finer units. Each spatial level is associated with
different processes modeled by RHESSys and with a particular scale. At the finest
scale, patches are typically defined on the order of meters squared, while basins
(km
2
) define the largest scale.
Within RHESSys, a given spatial level is defined as a particular object type with
a set of state (storage) and flux variables, process representations (equation sets),
and an associated set of model parameters. For example, the estimation of
atmospheric flux variables such as radiation occurs at the zone level. Thus, in
deriving the set of spatial objects for a given simulation, zones are chosen to
represent areas of similar climate or atmospheric-forcing conditions. The advantage
of this hierarchical approach is that it allows different processes, that is, climate
versus canopy processes, to be modeled at different spatial and temporal scales. It
also allows modeling to occur on ecologically meaningful units as opposed to
arbitrarily defined grid cells.
The definition of modeling units is done by the user prior to running the
simulation. Although the user is given considerable flexibility in choosing a
partitioning strategy for the different levels, partitioning should be tailored to take
advantage of the patterns of relevant variability within the landscape and, in the case
of patches, to maintain a coherent and solvable flow network. This permits efficient
parameterization and reduces the error associated with landscape partitioning. Band
et al. (Band et al. 1991), Lammers et al. (Lammers et al. 1997), and Tague et al.
(Tague et al. 2000) provide further justification for and discussion of partitioning
strategies, although this is an area requiring additional development.
2.1. Basins
Basins are defined as hydrologically closed drainage areas and encompass a single
stream network. Basins typically serve as aggregating units to determine net fluxes
of carbon, water, and nitrogen over the entire study area.
At present, RHESSys accounts for routing (storage and flux) of water within
hillslopes to the stream. Once water reaches the stream, however, it is assumed to
exit the basin within a single (daily) time step. For larger basins or shorter time
steps, in-stream channel processes can be important. Future versions of RHESSys
will likely use basins to organize the combination of hillslopes and stream reaches
as separate object types and include a channel-routing model for stream reaches
within the basin stream network.
2.2. Hillslopes
Hillslopes define areas that drain into one side of a single stream reach. Explicit
routing between patches is organized at the hillslope level to produce streamflow.
Hillslopes will usually be derived based upon drainage patterns using (Geographic
Information System) GIS-based terrain-partitioning algorithms such as r.watershed
Earth Interactions Volume 8 (2004) Paper No. 19 Page 4
in GRASS (Geographic Resources Analysis Support System) GIS environment
and as described in Lammers and Band (Lammers and Band 1990). Like basins,
hillslopes can also be used to aggregate sublevel processes. The spatial
redistribution of patch soil moisture is organized at the hillslope level and, for
simulations that use TOPMODEL for lateral flow distribution, a hillslope-level
base flow is defined.
2.3. Zones
Zones denote areas of similar climate. Zone objects contain meteorological
variables and use topclimate extrapolation methods necessary to characterize spatial
variation in these variables. Each zone is linked to a particular set of climate input
files. Thus, a given landscape may use data from multiple meteorological stations or
atmospheric model grid cells if this information is available. Data from a particular
station are modified based on zone elevation, slope, and aspect relative to the input
climate station. Zone processing also estimates additional climate variables that
may not be available from base climate station information such as vapor pressure
deficit. Numerous strategies exist to partition areas of similar climate. Elevation
bands in a mountainous area, for example, are likely to denote areas of similar
climate and exposure as discussed in Lammers et al. (Lammers et al. 1997). The
distribution of climate stations can also be used to define zone partitioning, where
each zone defines the area associated with a particular climate station.
2.4. Patches
Patches represent the smallest-resolution spatial unit and define areas of similar soil
moisture and land-cover characteristics. Vertical soil moisture processing and soil
biogeochemistry are modeled at the patch level. Patch variables include fluxes such
as infiltration, saturation zone recharge, and soil nutrient cycling. Patches are often
derived using an overlay of several different maps, such as a wetness index,
vegetation cover, and stream and road network layers. Patch definition, however,
must also be designed to maintain the underlying topographic controls on drainage
patterns in the watershed. Patches can be defined that contain a stream channel and
parameterized to regulate land-channel drainage flux. In landscapes modified by
humans, patches may also be defined to contain a stream channel, road segments,
or storm sewers that provide specific drainage conditions. Human sources of water
and nutrients including irrigation, fertilization, and septic system input are also
defined at this level.
2.5. Canopy strata
Canopy strata are a separate object type but they define vertical, aboveground
layers rather than horizontal spatial layers. The spatial resolution of the canopy
stratum is defined by the patch partitioning. Processes such as photosynthesis and
transpiration are modeled at the canopy stratum level. Each stratum corresponds to
a different layer such as overstory or understory in the canopy structure. The user
defines the number of vertical layers. A height state variable is associated with each
layer and defines its processing relative to the other layers. Incoming radiation,
Earth Interactions Volume 8 (2004) Paper No. 19 Page 5
precipitation throughfall, and wind are extinguished through the multiple layers
according to the height and vegetation characteristics of each layer. RHESSys also
permits multiple strata at the same height. This allows mixed vegetation types
within the same spatial area to be represented. Finally, a litter layer is defined at the
patch level and receives input from the overlying canopy layers. This litter layer
acts as the interface between each patch and its associated canopy strata layers. For
nonvegetated patches, a dummy litter layer (with no attenuation or processing of
hydrologic, energy and carbon/nutrient fluxes) is used.
2.6. Interface
Parameterization and management of RHESSys is complex due to the multiple
levels of spatial partitioning and the associated parameter sets. Most of these
parameters are derived from topographic, land-cover, and soil map layers.
Associated with RHESSys are a number of interface programs, which organize
input data into the format required by the simulation model. These include standard
GIS-based terrain-partitioning programs and RHESSys-specific programs that
derive landscape representation from GIS images and establish connectivity
between spatial units. These various programs can be run in stand-alone mode or as
part of an integrated RHESSys interface, RAINMENT. Additional details about the
RHESSys interface can be found in Band et al. (Band et al. 2000).
Key inputs into RHESSys include (see Figure 1) the following.
1. A description (worldfile) of the landscape representation and initial-state
variables associated with each component of the spatial hierarchy (i.e.,
basins, hillslopes, zones, etc.) Because of the length and spatial complexity
incorporated in this description, GRASS and ARCVIEW GIS-based
programs (GRASS2WORLD, ARCVIEW2WORLD) were developed to
generate this file.
2. The flow table describes connectivity between patches within a hillslope
when the explicit routing approach is used to model distributed hydrology.
The flow table is also generated automatically prior to running the main
RHESSys simulation using a software program (CREATE-FLOWPATHS).
3. The temporal event control (TEC) file describes the timing and nature of
temporal events that will occur during the course of the simulation, that is,
disturbances such as forest harvesting, fire, or road construction. Temporal
events refer to events that initiate a change in landscape-state variables or
parameterization or new processes in the simulation sequence. A spinup
period is typically run prior to output to remove transient behavior due to
initialization.The TEC file is also used to control data assimilation for output.
4. Time series inputs include a range of climate variables as discussed in
section 3, along with descriptions of the station at which this information
was collected. Each zone in the spatial hierarchy is associated with a
particular climate station. Note that base station coverage can be defined at
any level of the hierarchy and need not be spatially contained by hillslopes,
zones, or patches. Input stations can also be assigned at the patch level to
organize fertilizer and irrigation inputs.
5. Parameter files are associated with each level of the spatial hierarchy. A
Earth Interactions Volume 8 (2004) Paper No. 19 Page 6
library of commonly used parameter files assigned to specific soil and
vegetation types is available. The current library of parameter files include
standard parameters for conifer, deciduous, grass, chaparral, tundra, as well
as a number of more refined files for specific species groups such maple,
pine, spruce, oak, aspen, or douglas fir. The current library of parameter
files include all major soil textures, such as clay, sandy loam, etc.
2.7. Implementation and future development
This current version of RHESSys is implemented in the C programming language
using an object-based approach to facilitate the substitution of different process
algorithms. All of the processes as well as input/output routines are contained in
separate procedures with appropriate names. This allows for relatively easy
modification of specific process algorithms. Data structures are similarly defined
and named to maintain clarity about the level of the spatial hierarchy associated
with a specific algorithm.
The object-based approach and hierarchical landscape representation are also
designed to facilitate future RHESSys development. Structures exist to allow for
the development of subdaily time step models for certain processes such as
infiltration. Object-based landscape representation also facilitates the implementa-
tion of different land covers such as those found in urban areas. Hillslope-level
organization of drainage and particularly the implementation of roads as
mechanisms by which flow can be redirected serve as a foundation for
implementation of other man-made controls on flowpaths such as sewers.
3. Atmospheric and environmental forcing
Atmospheric variables or external forcing variables drive RHESSys hydrology and
biogeochemical cycling. These include climate variables such as daily temperature
Figure 1. RHESSys model structure: Inputs, output, and preprocessing.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 7
and precipitation as well as material inputs such as atmospheric nitrogen
deposition. Climate input and processing in RHESSys is done at the zone level.
Each zone is assigned a particular base station that manages external time series
inputs to the model. Multiple zone objects can be assigned to the same base station;
however, each zone must have a unique base station associated with it. The
appendix lists current atmospheric variables that are used internally in the model.
For most of these variables, the user has the option of providing a daily time series
as input (associated with its base station) or allowing RHESSys to estimate the
daily value from user parameters. Daily temperature and precipitation, however,
must be input by the user. Input time series may be derived from field observation
or from coupling with external models. Internal estimation of most meteorological
variables, including incoming radiation, is based on algorithms from the MTN-
CLIM model (Running et al. 1987).
Currently, nitrogen and precipitation are the only material inputs into the model.
Atmospheric nitrogen deposition as nitrate and as ammonium are input as separate
time series in RHESSys. Wet and dry deposition, however, are not distinguished in
the current model. If a time series of nitrogen deposition is not provided, a constant
daily value for nitrate based on a zone parameter will be used. In this case,
deposition as ammonium is assumed to be zero.
3.1. Temperature
Daily minimum and maximum temperature time series must be included in the
base station assigned to each zone object. Note that these time series may be
derived from field observations or from an external mesoscale atmospheric model
such as the Regional Atmospheric Modeling System (RAMS; Walko et al. 2000)
or external climate interpolation schemes such as the Parameter-Elevation
Regressions on Independent Slopes Model (PRISM; Daly et al. 1994) or Daymet
(Thornton et al. 1997). For each zone, the base station temperatures are scaled by a
lapse rate with elevation (included as a zone parameter).
Dewpoint temperature, if it is included with base station data, is similarly
adjusted by a dewpoint lapse rate. If it is not input as a time series, it is assumed to
be the minimum temperature value, after the elevation adjustment. Rooting zone
soil temperature is computed as a running average of average air temperature
similar to Zheng et al. (Zheng et al. 1993):
TsoilðtÞ¼0:9Tsoilðt1Þ
þ0:1ðTavgÞ;ð1Þ
where T
soil
is rooting zone soil temperature and T
avg
is average daily temperature.
The buffering effect of snow cover is not taken into account.
3.2. Precipitation
A daily precipitation time series must also be included in each base station and can be
adjusted using an isohyetal multiplier assigned to each zone. Orographic patterns in
precipitation can be modeled using this isohyetal multiplier. Rainfall duration
defaults to the entire day, unless a rainfall duration time series is included as a base
station input. The user also has the option of providing hourly, rather than daily,
rainfall input and running the hydrologic portion of the model in an hourly mode.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 8
The user may input a snowfall time series directly. If a snowfall time series is not
included, precipitation is partitioned into rain and snow by assuming a linear
transition from snow to rain across a temperature range defined by Tminrain and
Tmaxsnow , which are zone parameters indicating the minimum temperature at which
rain can occur and the maximum temperature at which snow can occur,
respectively.
3.3. Vapor pressure deficit
Saturation vapor pressure and relative humidity can be input directly. If these
observations are not available from the base station climate file, saturation vapor
pressure and vapor pressure deficit are estimated from standard air temperature–
vapor pressure relationships (Jones 1992).
3.4. Incoming radiation
Canopy radiation interception (see section 5.2.) depends upon top of canopy
inputs of both diffuse (K
diffuse
0
) and direct (K
direct
0
) solar radiation as well as
longwave radiation. These radiation streams can be input by the user as part of
the climate base station or can be estimated internally in the model. Within
RHESSys, a solar geometric-based estimate of atmospheric radiation is computed
based on site latitude, zone slope, aspect, and east–west horizon values. Incoming
radiation is then adjusted to account for atmospheric transmissivity, estimated
based on daily temperature variation and precipitation. These equations are not
described here since they directly follow the MTN-CLIM approach (Running et
al. 1987).
3.5. Atmospheric CO
2
In the current version of RHESSys, atmospheric CO
2
concentration is held
constant at 370 ppm. (Note: CO
2
concentration is used in estimates of stomatal
conductance.) It is included as a state variable, however, such that it can be readily
modified in future versions.
4. Soil hydrologic processes and transport mechanisms
Vertical and lateral soil moisture and associated nutrient fluxes are modeled for
each patch object. Patch topology (i.e., connectivity between patches) is organized
by basin objects.
To model vertical soil moisture processes, a simple three-layer model is used,
which includes a surface detention store, an unsaturated store, and a saturated store.
Snowpack and litter stores are also included.
Water can also be stored in the vegetation and litter layers above each patch as
interception storage (see section 5.5.). The soil column consists of two variable
depth layers: an unsaturated zone and a saturated zone. The boundary between the
saturated and unsaturated zone is defined by the saturation deficit (sas a water
equivalent deficit and zas an actual depth to saturation). Vertical fluxes between
each soil compartment are modeled to preserve mass balances such that, for each
time step
Earth Interactions Volume 8 (2004) Paper No. 19 Page 9
s¼qdrain þqcap þETsat ð2Þ
sunsat ¼qinfil qdrain þqcap ETunsat ð3Þ
detS¼TF þqmelt qinfil E;ð4Þ
where q
drain
,q
cap
, and q
infil
are drainage from the unsaturated zone, capilliary rise,
and infiltration, respectively; ET
sat
and ET
unsat
are evapotranspiration from the
saturated and unsaturated zone, respectively; s
unsat
is the soil moisture content of the
unsatured zone and detSis the surface detention storage; TF is the net throughfall
from canopy layers; Eis the surface storage evaporation; and q
melt
is snowmelt. All
stores are maintained as meters of water and fluxes as meters per day.
4.1. Detention storage and infiltration
At each time step, net throughfall from canopy layers and snowmelt are added to
current surface detention storage and allowed to infiltrate into the soil following
Phillip’s infiltration equation (Phillip 1957):
qinfil ¼ItpþSpffiffiffiffiffiffiffiffiffiffiffiffiffi
tdtp
pþKsatsðtdtpÞfor td>tp;
qinfil ¼Itdfor td,tp;ð5Þ
where qinfil is infiltration; Iand tdare input intensity and duration; and Ksatsis
saturated hydraulic conductivity at the wetting front, defined by the saturation
depth z. [Equation (8) is used to compute Ksatsat depth z.] Estimation of sorptivity
S
p
is based on Manley (Manley 1977):
Sp¼ffiffiffi
2
pKsats0:76uae;ð6Þ
where u
ae
is air entry pressure, which is set as a soil specific input parameter.
Time to ponding is denoted as t
p
, which is computed using the Green and Ampt
approximations (Green and Ampt 1911) as follows:
tp¼Ksats0:76uae ð/h0Þ
IðIKsatsÞ;ð7Þ
where /is porosity and h
0
is initial soil moisture content.
If a daily time step is used, it is assumed that all inputs (precipitation and
snowmelt) are distributed evenly throughout the day. In regions characterized by
high-intensity, short-duration rainfall, this approach will overestimate infiltration
rates. In these cases, the user may choose to input a rainfall duration time series,
which will override the assumption of a daily duration.
Ponded water that is not infiltrated within the daily time step becomes detention
storage. Detention storage beyond a surface detention storage capacity parameter
will become overland flow.
4.2. Hydraulic conductivity and porosity profiles
The vertical hydraulic conductivity profile controls both vertical and lateral soil
moisture fluxes in RHESSys. In the current implementation an exponential profile is
the default; although alternative profiles may be substituted for specific field sites
where the soil conductivity profile does not fit this exponential mode (e.g.,
Earth Interactions Volume 8 (2004) Paper No. 19 Page 10
Ambroise et al. 1996). Thus, saturated hydraulic conductivity, K
sat
(z) is computed as
KsatðzÞ¼Ksat0expð z
mÞ;ð8Þ
where Ksat0is hydraulic conductivity at the surface and mdescribes the decay rate of
conductivity with depth. Both are set as soil-type-specific input parameters.
Hydraulic conductivity profiles are difficult to measure and may vary widely for a
given soil texture/type. Further, field evidence suggests that at scales greater than
centimeters, conductivity controls on hydrologic fluxes must consider both the
properties of the soil matrix and macropore/preferential flowpath distributions
(McDonnell 1990). To account for both uncertainty in conductivity profiles and
preferential flow, both mand Ksat0are typically calibrated against observed
streamflow values in RHESSys (see section 7).
Porosity is also permitted to vary with depth such that
/ðzÞ¼/0expz
p;ð9Þ
where /0and pare soil specific parameters defining surface porosity and the decay
of porosity with depth, respectively. Setting a large value of p(e.g., p.1000.0)
allows a constant porosity to be assumed. Saturated soil moisture storage for a given
profile section must be calculated by integrating porosity over the associated depth.
4.3. Vertical unsaturated zone drainage
As noted above, RHESSys maintains both an unsaturated and saturated zone.
Drainage from the unsaturated zone to the saturated zone, qdrain, is limited by field
capacity h
fc
of the unsaturated zone (computed by integrading a pressure gradient
of 1 over the unsaturated profile), and by the vertical unsaturated hydraulic
conductivity at the boundary [KunsatðzÞ] between the unsaturated and saturated zone
such that
qdrain ¼min½KunsatðzsÞdT;hunsat hfc;ð10Þ
where dT is the time step.
Here KunsatðzÞcan be estimated using either vanGenuchten and Nielsen
(vanGenuchten and Nielsen 1984) or Clapp and Hornberger (Clapp and
Hornberger 1978) models of soil characteristics.
In the Clapp and Hornberger (Clapp and Hornberger 1978) approach:
KunsatðzÞ¼Ksat ðzÞSð2bþ3Þ;ð11Þ
where bis the pore size index, a soil-specific parameter; Ksat0ðzÞis calculated using
Equation (8), and Sis relative saturation.
If the vanGenuchten approach is used:
KunsatðzÞ¼Ksat0 ðzÞS0:5½1ð1S1
cÞc2;ð12Þ
where cis a soil-specific parameter.
To compute a depth of unsaturated zone soil moisture at field capacity [h
fc
in
Equation (10)], the relative saturation at field capacity is integrated over the
porosity profile from the surface to the water table depth (z
s
).
Relative saturation at field capacity S
fc
is derived again based on either the Clapp
Earth Interactions Volume 8 (2004) Paper No. 19 Page 11
and Hornberger (Clapp and Hornberger 1978) or vanGenuchten and Nielsen
(vanGenuchten and Nielsen 1984) assumptions such that, respectively,
SfcðzÞ¼ uae
ðzszÞ
b
;ð13Þ
SfcðzÞ¼ 1ðzszÞ
uc
ae
b
"#
:ð14Þ
Note that band care the soil-specific parameters used in Equations (11)–(12)
above, uae is the air entry pressure, again assigned based on soil type.
4.4. Soil evaporation
Soil evaporation is limited both by energy and atmospheric drivers and by a
maximum exfiltration rate as a function of soil properties at a given soil moisture.
Soil moisture limits on soil evaporation are accounted for using a potential
exfiltration rate, potqexfil , based on a modification of Eagleson (Eagleson 1978) by
Wigmosta et al. (Wigmosta et al. 1994) such that
potqexfil ¼S1
2bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8
/
Ksatuae
3ð1þ3bÞð1þ4bÞ
s
"#
;ð15Þ
where bis the pore size index. Porosity (
/) and saturated hydraulic conductivity
(
Ksat) are averaged over depth to saturation (zs) using Equations (9) and (8),
respectively, and Sis the relative soil moisture content computed as (unsat/s) with
an added restriction of a maximum active soil depth over which the exfiltration
process applies. Thus, if the saturation deficit is greater than an active soil depth,
the relative soil moisture Sis computed as unsat/s
active.soil.depth
. Active soil depth is
included as a soil-specific parameter.
Energy and atmospheric drivers of soil evaporation are accounted for using the
Penman–Monteith equation (see section 5.6.). Surface conductance for soil is
based on empirical relationships between rooting zone soil water content hand
diffusive resistance C
surf
, as observed by Kelliher et al. (Kelliher et al. 1986) in a
douglas fir forest:
Csurf ¼0:001 429 for h>0:185;
Csurf ¼1
83 000hþ16 100 for 0 ,h,¼0:185;and
Csurf ¼9 999 999 for h¼0:ð16Þ
Clearly, generalization of this empirical model to other sites may require
adjustment. In arid or sparsely vegetated environments where soil evaporation
can be a significant component of the water balance, substitution of local empirical
relationships may be necessary.
Final soil evaporation is a minimum of rates based on the Penman potential
evaporation and soil exfiltration rates.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 12
4.5. Capillary rise
Potential capillary rise is based upon the approach used by Eagleson (1978) such that
qcap ¼Ksatzs1þ1:5
ð1þ3bÞ
uae
ðzsuaeÞ
ð2þ3bÞ;ð17Þ
where Ksatzsis the hydraulic conductivity at the water table depth (zs) [computed using
Equation (8)]; band uae are pore size index and air entry pressure, respectively, and
are set based on soil type.
Capillary rise is limited to filling unsaturated zone to field capacity. To correct
for subdaily plant responses, one-half of the potential capillary rise, computed
using Equation (17) is allocated to the unsaturated zone at the start of the day. The
remaining potential is available later in the day to satisfy plant transpiration
demands (see section 5.6.).
4.6. Snow accumulation and melt
Snow accumlation is based on incoming precipitation and is assumed to fall evenly
over each climate zone. Modeling case studies using previous versions of
RHESSys, however, have shown that in snow-dominated environments, the
redistribution of snow by wind, can have a significant impact on hydrology
(Hartman et al. 1999). In the current model, we do not account for this effect;
however, an adaptation of a more sophisticated snow accumulation and melt
approach will likely be included in future versions.
Snowmelt, q
melt
, is computed using a quasi–energy budget approach that takes
into account radiation (M
rad
), a combination of melt due to sensible and latent heat
flux (MT), and advective (MV) (from rain on snow) controls on snowmelt such that,
at the daily time step
qmelt ¼Mrad þMTþMV:ð18Þ
Melt from temperature and advection occur only when the snowpack is ripe.
Snowpack temperature is approximated using an air temperature accumulation of a
snowpack energy deficit (SED):
SEDt¼max SEDðt1ÞþTair;SEDmax
;ð19Þ
where SED
(t1)
is the previous day’s energy deficit, T
air
is mean daily temperature,
and SED
max
is a maximum energy deficit that is set as a climate-region-specific
input parameter. Melt due to radiation can occur as sublimation when the energy
deficit SED is less than 0.
Radiation melt is computed as
Mrad ¼ðKdirect þKdiffuse þLÞ
kfqwater
for ðSED >¼0Þ;
Mrad ¼ðKdirect þKdiffuse þLÞ
ðkfþkvÞqwater
for ðSED ,0Þ;ð20Þ
where kvand kfare the latent heat of vaporization and and fusion, respectively;
qwater is the density of water; Kdirect and Kdiffuse are direct and diffuse shortwave
Earth Interactions Volume 8 (2004) Paper No. 19 Page 13
radiation absorbed by the snowpack; and Lis longwave radiation. Direct and
diffuse shortwave radiation absorption by the snowpack is computed based on a
Beer’s law extinction model of available radiative fluxes (Kdirect0and Kdiffuse0) and
accounts for albedo-driven reflectance at the level of the snowpack. This approach
is used to maintain consistency with radiation attenuation through vertical canopy
layers as described in section 5.2. Thus,
Kdirect ¼ð1aÞKdirect0ð1expksnow Þ:ð21Þ
The extinction coefficient k
snow
is input as a climate-specific default. Setting kto an
arbitrary large value will ensure that all nonreflected radiation will be absorbed by
the snowpack. Snowpack reflectance or albedo ais estimated based upon a
snowpack surface age following Laramie and Schaake (Laramie and Schaake
1972):
a¼0:85 0:82Age0:46
for ðSED >¼0Þ;
a¼0:85 0:94Age0:58
for ðSED ,0Þ;ð22Þ
where ‘‘Age’’ is the number of days since last snowfall. A similar approach is used
to account for diffuse radiation fluxes.
Longwave radiation into the snowpack is estimated from air temperature
following Croley (Croley 1989):
L¼41:868 essatmrðTair þ272Þ4663
hi
for ðSED >¼0Þand ðTair >¼0Þ;
L¼41:868 ðessatm 1ÞrðTair þ272Þ4663
hi
for ðSED ,0Þand ðTair ,0Þ;ð23Þ
where ris the Stefan–Boltzmann constant. Atmospheric emissivity ess
atm
is
adjusted for overstory canopy (Dingman 1994) and cloud fraction (CF; Croley
1989):
essatm ¼ð1FÞ0:53 þ0:065 ea0:5
100 ð1þ4:0CFÞþF
;ð24Þ
where Fis the fractional canopy cover over the snowpack and eais the atmospheric
vapor pressure. If cloud fraction data are not available, the cloud fraction is
assumed to be 1.0 for days with precipitation and 0.0 for dry days.
Melt due to latent and sensible heat flux is based on an empirical relationship
with air temperature (Coughlan and Running 1997) that is adjusted for the effects
of variation in wind speed due to the fractional forest cover Fover a snowpack
(Dunne and Leopold 1979)
MT¼bMTTair ð10:8FÞ;ð25Þ
where b
MT
is an empirical temperature melt coefficient that is input as a climate-
region-specific parameter.
Advection melt contributions due to warming by incoming precipitation are
computed as
MV¼qwaterTair TFcpwater
ðÞ=kf;ð26Þ
Earth Interactions Volume 8 (2004) Paper No. 19 Page 14
where TF is net throughfall entering the snowpack, and cp
water
and q
water
are the
heat capacity and density of water, respectively.
4.7. Lateral redistribution
Soil moisture redistribution through saturated throughflow and associated runoff
production can be modeled using either a quasi-spatially distributed model,
TOPMODEL (Beven and Kirkby 1979) or via an explicit routing model, which is a
modification of the Distributed Hydrology Soil Vegetation Model (DHSVM;
Wigmosta et al. 1994).
TOPMODEL is applied at the hillslope level. DHSVM is applied at the basin
level, since it can include some limited streamflow routing. Both approaches are
executed at the end of the day, following vertical soil moisture updates.
4.7.1. TOPMODEL
TOPMODEL is a statistically based approach that redistributes saturation zone
water based on an index of hydrologic similarity. As a statistically based approach,
TOPMODEL represents a simplified approach that has been applied and tested in
numerous catchments. TOPMODEL relationships are based on the assumption that
saturated hydraulic conductivity varies exponentially with depth, that water table
gradients can be approximated by local topographic slope, and that steady-state
flux is achieved within the modeling time step. TOPMODEL distributes a mean
soil moisture deficit,
sbased on a local wetness index wi:
wi¼ln arTe
Totanb;ð27Þ
where Teand Toare the mean and local hillslope saturated transmissivity,
respectively, tanbis the local slope, and ar is the upslope contributing area.
Local saturation deficit sifor each patch, is computed as
si¼
sþmsð
wwiÞ;ð28Þ
where
wis mean hillslope wetness index value,
sis the mean hillslope saturation
deficit, and msdescribes a decay rate of hydraulic conductivity with saturation
deficit. Transmissivity TR is computed as
Tr ¼Zzsat
‘
Ksat0exps
msdz;ð29Þ
where Ksat0is saturated hydraulic conductivity at surface.
Alternatively, a constant or user-defined profile of hydraulic conductivity can
replace the assumption of an exponential decay.
Saturation overland flow (return flow) is produced for patches if ðsi,0Þ.
Baseflow q
base
for the hillslope is calculated as
qbase ¼expð
wÞexpð
s0Þ;ð30Þ
where
s0is the areally weighted mean of the saturation deficit of all hillslope
patches adjusted to include a portion of the capillary fringe as follows:
Earth Interactions Volume 8 (2004) Paper No. 19 Page 15
s0¼X
n
i¼1
si0:5ðuaeiÞai=sumn
i¼1ai/0a
;ð31Þ
where uae is the air entry pressure, /0is the porosity at the surface, siis the
saturation deficit, and aiis the area for patch i.
4.7.2. Explicit routing
Alternatively, the explicit routing model is based on the DHSVM (Wigmosta et al.
1994) routing approach that has been modified to account for nongrid-based
patches and nonexponential transmissivity profiles. Similar to TOPMODEL,
DHSVM assumes that hydraulic gradients follow surface topography. Flow
topology is generated by a GIS-based preprocessing routine, CREATE-
FLOWPATHS. Multiple flow directions, from any given patch, are permitted.
In the explicit routing approach, three distinct patch types are considered:
streams, roads, and land surface. In the current implementation, stream patches
include the riparian area adjacent to the stream. Thus vertical processes such as
infiltration are modeled using the same algorithms applied for land surface patches.
Lateral flow from the stream patch, however, is assumed be channelized. In the
current implementation, all channelized flow is assumed to exit the basin in a single
time step. Future implementation, however, will include an in-stream routing
model between stream patches. Unique characteristics of lateral flow from road
patches are discussed below.
Within the model time step, explicit routing is computed for a user-specified
time step to achieve stability. This can be useful to maintain a Couret number less
than 1 and reduce errors due to over/underestimation of downslope flood wave
propagation. All vertical fluxes and storage adjustments including rainfall
infiltration are done before the routing of lateral subsurface throughflow. If,
however, hourly precipitation data are available, the vertical hydrologic flux
portion of the model can be run at a corresponding hourly time step.
The DHVSM routing scheme assumes that saturated throughflow qðtÞa;bfrom
patch ato patch bcan be estimated as
qðtÞa;b¼TrðtÞa;btanba;bxa;b;ð32Þ
where xa;bis the flow width between patches aand b, tanbis local slope, and Tr is
transmissivity as defined in Equation (29).
For grids, flow widths are assumed to be 0.5 times the grid size for cardinal
directions and 0.354 times the grid size for diagonal directions after Quinn et al.
(Quinn et al. 1991). For irregular elements, flow widths are summed along the
shared boundary between patches aand b.
Surface flow (i.e., saturation overland flow or Hortonian overland flow)
produced is routed following the same patch topology used from routing saturated
subsurface throughflow. All surface flow produced by a patch is assumed to exit
from the patch within a single time step. If the receiving patch is not saturated,
surface flow is allowed to infiltrate based on Equation (5) and is added to
unsaturated soil moisture storage. Patch routing is sequenced to occur from the
uppermost patches first.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 16
Within the explicit routing model, patches that contain roads are treated as
special cases.
4.7.3. Road patches
Roads have been shown to alter the routing of both overland and subsurface
throughflow (Wemple et al. 1996; Luce and Cundy 1994). Road culverts produce
channelized flow that in some cases can connect directly to the stream and
effectively extend the stream drainage network. Flow in road culverts is produced
from two sources: 1) runoff from the road surface and 2) interception of subsurface
routing by the road cut bank. At present, patches can be parameterized using an
areally weighted conductivity. If resolution is such that the road covers a
significant portion of patch surface, then the infiltration capacity parameter
assigned to that patch should reflect low infiltration capacities associated with
roads.
The amount of saturated subsurface flow intercepted by the road is a function of
the road cut depth and the current saturation deficit. If the road cut bank depth is
less than depth to saturation, none of the saturated throughflow is intercepted by
the road. If road cut depth is greater than depth to saturation, all subsurface
throughflow produced above the road cut depth is captured by the road culvert.
Use of an alternative receiving patch allows flow intercepted by a road to be
routed either to an adjacent patch or to a stream/storm network. The former
represents the situation in which culverts serve to concentrate flow but allow this
flow to be redistributed and reinfiltrated in down-slope patches. The latter models
the case in which culverts form part of an extended drainage network. The location
of patches to receive flow intercepted by culverts are specified as part of the routing
topology in the CREATE-FLOWPATHS preprocessing routine prior to RHESSys
execution. A new routing topology can be read in during execution, however, so
that disturbances can be modeled.
4.7.4. Vertical and lateral redistribution of nitrate
In the current model, nitrate enters the soil from infiltrated rain or surface detention
storage, using a mean concentration such that
soilNO3t¼soilNO3t1þqinfil
Sdet þPsurfNO3;ð33Þ
where soilNO3t1and soilNO3tare total soil nitrate at the previous and current time
step, respectively; q
i
nfil is infiltration; S
det
is surface detention storage; Pis
precipitation; and surf
NO3
is the total mass of nitrate in surface detention storage
and precipitation.
Vertical drainage of soluble nitrogen downward through the soil profile is not
explicitly modeled in RHESSys. A simplified vertical redistribution is assumed
based on a specified nitrate profile with depth. The current implementation assumes
an exponential distribution such that
soilNO3 ¼Zzsoil
z0
NO3surface expNdecayz;ð34Þ
Earth Interactions Volume 8 (2004) Paper No. 19 Page 17
soil
NO3
is total mass of nitrate N in the soil profile, which is maintained as a state
variable throughout the simulation. Here N
decay
is a soil-specific parameter that
defines the rate of decay of nitrate with depth and z
soil
is soil depth. Equation (35)
can be rearranged to determine N
surface
and used to compute available nitrate N at
any soil depth as
soilNO3z¼NO3surface expNdecayz:ð35Þ
Available nitrate N from Equation (35) is coupled with estimates of lateral
saturated subsurface throughflow, Equation (32), to determine the total export of
nitrate N from a given patch as
NO3out ¼Zzszsoil
‘
qz
Sz
soilNO3zNO3mobile;ð36Þ
where Szis soil moisture (in meters of water) at depth z;zsis saturation zone depth;
qzis net lateral transport of water from the patch at depth z; and NO3
mobile
is the
portion of nitrate that is mobile (set as a soil-type parameter).
This approach to modeling nitrate export follows the flushing hypothesis. Use of
an exponential profile distribution of nitrate, results in greater supplies of mobile N
as saturation throughflow levels rise in the soil, and begin tapping more nutrient-
rich near-surface soils. Field investigation of N-transport mechanisms (e.g.,
McDonnell 1990; Peters et al. 1995) suggests that this may be a reasonable
assumption in areas, such as humid forests, where much of the infiltrating water
rapidly moves through the unsaturated layer through preferential flowpaths,
without significant matric contact. Further model development will investigate the
marginal gains made by adopting a more rigorous vertical transport representation.
When using the TOPMODEL approach for soil moisture redistribution, the
spatial variation in nitrate export is ignored. For model applications that focus on
nutrient export in spatially heterogeneous terrain, the explicit routing option is
therefore recommended. When TOPMODEL is used, a basin-scale-lumped
approach is used to estimate mobile N transport. A mean hillslope soil nitrate
storage is computed and used to determine a hillslope-scale nitrate export based on
a mean basin saturation deficit following Equation (36) above. To account for
losses due to lateral N export, all patches are assigned the updated mean basin soil
nitrate value.
5. Canopy radiative and moisture fluxes
RHESSys models surface radiation and rainfall attenuation through a series of
canopy layers.
In vegetated catchments, these layers correspond to overstory and understory
vegetation. In urbanizing catchments, nonphotosynthesizing layers, such as
buildings, can be represented to model the evaporation of intercepted water. For
vegetated canopy, absorbed radiation also controls carbon/nitrogen cycling through
photosynthesis and respiration. Carbon and nitrogen cycling are discussed in
section 6.
Canopy layers are processed sequentially according to height. Radiation, wind,
and rain or snow throughfall are attenuated as they are absorbed/intercepted by
Earth Interactions Volume 8 (2004) Paper No. 19 Page 18
each successive layer. Layers at equal height share the same environment. Canopy
layers at the same height must have combined fractional coverage less than or
equal to 1.
5.1. Leaf area and plant area index
Canopy layer leaf area index (LAI) reflects current leaf carbon storage cs.leaf,
scaled by LAI
sp
, specific leaf area index that varies with vegetation type.
Field evidence has shown that sunlit and shaded leaves respond differently in
terms of photosynthetic efficiency, leaf nitrogen content, and specific leaf area
(Thornton 1998). To account for this, we partition the canopy into sunlit and
shaded components, following Chen et al. (Chen et al. 1999) such that
LAIprojsunlit ¼2:0 cosðnoonÞ1:0exp0:5ð1GFÞLAIproj =cosðnoon Þ
hi
;
LAIprojshade ¼LAIproj LAIprojsunlit ;ð37Þ
where
noon
is the solar angle at noon and GF is the gap fraction. In addition to
LAI, a total plant area index PAI is also required to account for the role played by
stem wood in interception:
PAI ¼LAIproj þðcs:live:stem þcs:dead:stemÞswa;ð38Þ
where cs.live.stem and cs.dead.stem are sapwood and heartwood stem carbon
stores, respectively, and swa is a vegetation-specific parameter that defines stem
wood equivalent area per unit of carbon. For grasses, PAI ¼LAI.
5.2. Radiation attenuation
Incoming direct and diffuse radiation at the top of the canopy is input directly or
estimated as described in section 3.4. Canopy radiation attenuation and absorption
by each canopy layer is modeled separately for diffuse, direct, and photosyntheti-
cally active radiation (PAR) radiative fluxes.
5.2.1. Direct radiation
Direct radiation interception is based on a modification of Beer’s law with a
correction for the effect of low sun angles in sparse canopies (Chen et al. 1997)
such that
Kdirect ¼ð1adirectÞKdirect0ð1expextcoef Þ;ð39Þ
where a
direct
is the vegetation-specific reflectance (albedo); K
direct
is the absorbed
direct radiation by the entire vegetation layer, including both leaves and stem
wood; and Kdirect0is the incoming direct radiation at the top of that canopy layer.
The extinction coefficient ext
coef
is computed as
extcoef ¼1:1kð1GFÞPAI
cosðnoonÞ;ð40Þ
where kis the vegetation-specific Beer’s law extinction coefficient. For low values
of the extinction coefficient a correction factor (Chen et al. 1997) is applied to
Earth Interactions Volume 8 (2004) Paper No. 19 Page 19
account for the effect of low sun angles in sparse canopies such that
Kdirect ¼ð1adirectÞKdirect0ð1corr expextcoef Þ;
corr ¼ð1abackgroundÞðnoon
2ÞsinðnoonÞþcosðnoon Þ
ð
2noonÞ1sinðnoon Þ½
;ð41Þ
where a
background
is background (litter) reflectance and currently assumed to be
equal to canopy reflectance.
5.2.2. Diffuse radiation
Total diffuse radiation absorption is computed based on the approach developed by
Norman (1981) such that:
Kdiffuse ¼ð1adiffuseÞKdiffuse0f1expð1GFÞPAI½
0:7þScg;ð42Þ
where adiffuse is the vegetation-specific reflectance (albedo); GF is the gap
fraction; Kdiffuse is the direct radiation absorbed by the entire vegetation layer,
including both leaves and stem wood; and Kdiffuse0is the incoming diffuse
radiation at the top of that canopy layer. The scattering coefficient Scis com-
puted as
Sc¼0:07 Kdirect0
Kdiffuse0
1:10:1ð1GFÞPAI½expcosðnoonÞ:ð43Þ
5.2.3. PAR radiation
Absorbed PAR (APAR
direct
; APAR
diffuse
) are calculated using Equations (41) and
(42) above where reflectance coefficients, aand direct radiation extinction
coefficients kare replaced by PAR-specific coefficients and LAI replaces PAI.
Radiation inputs per LAI, which are used to drive leaf conductance and
photosynthesis submodels, are computed separately for sunlit (ppdf
sunlit
) and
shaded leaves (ppfd
shade
).
5.3. Aerodynamic resistance
Aerodynamic resistance is computed separately for the top (overstory) canopy and
understory layers following the model developed by Heddeland and Lettenmaier
(Heddeland and Lettenmaier 1995). This model assumes a logarithmic wind speed
decay profile to the top of the canopy and an exponential decay profile within the
canopy. A patch-level stability correction is included based upon Oke (Oke 1987).
Overstory resistance ra
o
is computed as
rao¼
log ðzscd0Þ
zo0
hi
=0:41
2
u;ð44Þ
where zsc is the screen height; d
0
is the zero plane displacement of the overstory
estimated as 0:7zo, where zois the overstory canopy height and zo
0
is the roughness
length estimated as 0:1zoand uis the friction velocity. To compute resistance of
Earth Interactions Volume 8 (2004) Paper No. 19 Page 20
understory layers, the wind speed profile must be estimated. Friction velocity is
computed as
uo¼ulogðzod0
zo0Þ
logðzsd0
zo0Þ;ð45Þ
and then allowed to decay exponentially through canopy layers, until within
0.1zo
0
, after which a logarithmic profile is assumed. Resulting estimates of
understory resistance becomes
rau¼raoþlog ðzsd0Þ
zo0
zoexpcn ðexp 1cnðÞ
ðduþzouÞ
zo
hi
exp 1cnðÞ
ðd0þzo0Þ
zo
hi
Þ
u0:412cnðzod0Þ
for zu.0:1zo;ð46Þ
where cn is a vegetation-specific wind attenuation coefficient and duis the zero
plane displacement of the understory. For understory layers less than 0:1zo,an
additional term is added to Equation (46) so that
rau0¼rauþlogð0:1zoÞ
zou
2
0:412u:ð47Þ
For additional understory layers, Equation (46) is repeated using successive values
of canopy-layer heights for overstory and understory height (zoand zu) and wind
speed, ufollowing Equation (45).
5.4. Canopy conductance
Canopy conductance is computed separately for vascular and nonvascular layers.
Vascular stratum conductance represents the inverse of additional resistance
provided by stomatal control. Vascular stratum conductance is based upon the
Jarvis multiplicative model of stratum conductance (Jarvis 1976) where maximum
(plant specific) conductance is scaled by the environmental factors. To account for
differences in radiative forcing, stomatal conductance is computed separately for
sunlit (gs
sunlit
) and shaded leaves (gs
shade
):
gssunlit ¼fðppfdsunlitÞfðCO2ÞfðLWPÞfðvpdÞgsmax LAIprojsunlit
;
gsshade ¼fðppfdshadeÞfðCO2ÞfðLWPÞfðvpdÞgsmax LAIprojshade
;ð48Þ
where gs
max
is the vegetation-type-specific maximum conductance. Functional
relationships for environmental controls on stomatal conductance can be readily
substituted in RHESSys. Current implementation of a 0–1 multipliers to reflect the
influence of each environmental control—light [f(ppfd)], CO
2
[f(CO
2
)], leaf water
potential [f(LWP)], and vapor pressure deficit [f(vpd)]—are based on relationships
developed by Running and Coughlan (Running and Coughlan 1988) for BIOME-
BGC and are not shown here (with the exception of [f(LWP)]), which has been
modified to reflect RHESSys approach to computing soil moisture conditions.
Leaf water potential is assumed to be a direct function of soil water tension ,
which is estimated based on soil moisture using either the Clapp and Hornberger
Earth Interactions Volume 8 (2004) Paper No. 19 Page 21
(Clapp and Hornberger 1978) approach where
LWPpredawn ¼min LWPmin:spring;0:01uae ðSbÞ
ð49Þ
or the vanGenuchten and Nielsen (vanGenuchten and Nielsen 1984) approach where
LWPpredawn ¼min LWPmin:spring;0:01uae S
1
11
b1!
1
b
2
6
43
7
5:ð50Þ
Air entry pressure uae and pore size index bare parameters associated with a specific
soil type. Here LWP
min.spring
is a vegetation-specific parameter, giving the leaf water
potential when stomata are fully open. Here Sis the rooting zone percent saturation.
Leaf water potential control on stomatal conductance follows the approach used in
BIOME-BGC.
Finally, the effect of CO
2
augmentation on stomatal conductance has not yet
been implemented. Many field experiements have shown that increasing
atmospheric CO
2
concentration may improve plant water use efficiency by
reducing stomatal conductance (Medlyn et al. 2001). These relationships will be
included in RHESSys in a subsequent version.
Nonvascular conductance
Nonvascular stratum conductance represents the inverse of additional resistance to
surface vapor flux beyond aerodynamic conductance provided by a nonvascular
layer. Note that this refers to nonvascular layers, such as mosses, rather than
conductance from surface soil, which is discussed in section 4.4. The nonvascular
conductance term is also used in the calculation of evaporation of intercepted water
as discussed in section 5.6. below. Following Williams and Flanagan (1997)
nonvascular conductance is based on an empirical linear relationship with water
storage for boreal forest mosses:
gsnonvas ¼maxðagsurf I0þbgsurf ;0:0Þ:ð51Þ
Typical values for empirical parameters, agsurf and bgsurf , for mosses can be found in
Williams and Flanagan (Williams and Flanagan 1997). Here I0is the relative
interception storage by the layer, adjusted for potential evaporative losses during
the day as follows:
I0¼max 0;ð2I0:001Þ
2Imax
;ð52Þ
where
I
is the current time step interception storage, and Imax is a specific rain
capacity scaled by PAI.
5.5. Interception
Canopy interception is a function of the water-holding capacity of the vegetation
such that canopy interception CI is computed as
CI ¼max 0:0;min ð1GFÞRT;PAIcprain I
½
fg
;ð53Þ
Earth Interactions Volume 8 (2004) Paper No. 19 Page 22
where Iis the current time step interception storage; GF is the gap fraction; and
cp
rain
is the specific rain capacity (based on vegetation type). Here RT is rain
throughfall from preceding canopy layers or incoming rainfall for the highest
canopy layer. Snow interception is also computed using Equation (53) by
substituting a specific snow interception capacity cp
snow
and snow throughfall ST.
5.6. Evapotranspiration
Total evaporative fluxes from each canopy layer may include the evaporation of
water intercepted by the canopy, sublimation of intercepted snow, and transpiration
by vascular layers. Both evaporation and transpiration rates are computed using the
standard Penman–Monteith equation (Monteith 1965).
For transpiration from sunlit and shaded portions of the canopy, canopy
conductance gs is computed using Equation (48). For evaporation of surface water
and nonvascular strata, such as mosses, gs
nonvas
is computed using Equation (51).
Here R
net
is net radiation computed as
Rnet ¼Kdirect þKdiffuse þL;ð54Þ
where Kdirect andKdiffuse are computed for each layer using Equations (41) and (42),
respectively; and Lis the net longwave radiation. Note that transpiration for sunlit
and shaded components of the canopy are computed separately, and R
net
is adjusted
to account for radiation intercepted by sunlit and shaded LAI.
Evapotranspiration rates are computed for rainy and dry periods of each day and
the vapor pressure deficit is adjusted accordingly. Thus, if rainfall durations for
each day are input into the model, total daily evaporation is computed as
E¼min I;Epotðvpd ¼0;gs ¼gsnonvas ÞðDrainÞþ
Epotðvpd ¼vpd;gs ¼gsnonvas ÞðDday DrainÞ;ð55Þ
where Iis the current time step interception storage; D
rain
is the daytime rain
duration; D
day
is the day length; and vpd is the daily average vapor pressure deficit.
Total transpiration Trp is computed as
Trp ¼Epotðvpd ¼0;gs ¼gssunlit Þþ Epotðvpd ¼0;gs ¼gsshadeÞ
3ðDrainÞþEpot ðvpd ¼vpd;gs ¼gssunlitÞ
þEpotðvpd ¼vpd;gs ¼gsshade ÞðDday DrainÞ:ð56Þ
5.7. Litter interception and evaporation
Litter interception of net canopy rain throughfall RT is limited by a per-PAI
maximum litter interception capacity (litterraincap ). The amount of interception per
storm event can also be limited by a litter gap fraction GF in sparse canopies where
litter does not cover the ground surface. Interception is computed as
CIlitter ¼min RTð1:0GFÞ;PAI litterraincap Slitter
;ð57Þ
where S
litter
is the current water content in litter.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 23
In the current version, litter PAI is set to 1.0 if litter carbon storage is greater
than 0 and 0 otherwise.
Evaporation from the litter is computed based on radiation available following
attenuation through canopy layers. Evaporation is computed using the Penman
approach, where gs is set to an arbitrarily large value (10 000) and ga is based on a
reduction of wind speed through the canopy to the litter layer as discussed in
section 5.3.
Note that in cases where detention storage capacity is greater than 0, water in
excess of litter interception capacity may be collected at the surface and
evaporated.
6. Carbon and nitrogen cycling
The main structure of carbon cycling in RHESSys is based on BIOME-BGC
(Thornton 1998) although many of the specific algorithms have been extended and/
or modified.
Carbon and nitrogen cycling associated with live vegetation (e.g., photosyn-
thesis, respiration) is included in canopy strata object routines. Carbon and nitrogen
cycling associated with litter and soil layers (e.g., decomposition) occurs within
patch objects. Thus, all vegetation strata associated with a particular patch
contribute and extract material (carbon, water, and nitrogen) to and from the same
well-mixed soil and litter pools.
RHESSys carbon and nitrogen stores are partitioned into leaves, roots, stems,
and coarse roots. Stem and coarse-root stores also include both live and dead wood
components to account for differences in respiration and C:N ratios. For grasses,
stores are restricted to leaves and fine roots and include an additional store used to
account for dead biomass that remains standing. Vegetation nitrogen stores follow
carbon stores based on stoichiometric relationships discussed in more detail below.
6.1. Vegetation: Carbon cycling
6.1.1. Photosynthesis
Carbon enters the system through photosynthesis. The Farquhar model (Farquhar
and vonCaemmerer 1982) calculates photosynthesis based on limitations due to
enzymes (i.e., nitrogen), electron transport (i.e., light), and stomatal conductance
(i.e., light and water) such that the net assimilation rate per unit LAI, Ais
A¼fðlnc;irad;gs;pa;CO2;TdayÞ;ð58Þ
where gs is the stomatal conductance, p
a
is the atmospheric pressure, CO
2
is the
atmospheric carbon dioxide concentration, T
day
is the daytime average air
temperature, and lnc is leaf nitrogen concentration computed. Here irad is the net
incoming radiation per unit LAI, which is computed as
irad ¼ðAPARdirect þAPARdiffuseÞ=LAIproj =time step;ð59Þ
Note that the Farquhar model computes an assimilation rate per unit LAI. For the
daily time step, to determine total daily canopy photosynthesis, g
psn
, the mean
Earth Interactions Volume 8 (2004) Paper No. 19 Page 24
absorbed PAR, mean stomatal conductance, and daytime temperature are used to
compute a mean assimilation rate that is then scaled by day length and LAI to yield
total gross daily canopy photosynthesis. To account for nonlinearities in the
responses of sunlit and shaded leaves, assimilation rates are computed separately so
that total gross daily canopy photosynthesis, g
psn
, for the strata becomes
gpsn ¼ðAsunlitLAIsunlit þAshaded LAIshadedÞdayl:ð60Þ
Sunlit and shaded proportion of LAI are computed using (37). A summary of the
specific equations used in the Farquhar model can be found in Waring and Running
(Waring and Running 1998).
Finally, the Farquhar model takes into account the control exerted by the leaf
nitrogen content. Photosynthesis is also constrained by the amount of nitrogen in
the soil that is available for uptake by the plant. As computed, g
psn
is a potential
photosynthesis subject to the availability of nitrogen. The amount of nitrogen
required, however, depends upon the allocation strategy used by the plant since
different plant components (i.e., leaves versus stems) have different C:N ratios.
The allocation strategy is discussed in section 6.1.4. below. Total nitrogen required
from the soil, potential.plant.N.uptake, is determined based on g
psn
and the
allocation strategy. If sufficient mineralized nitrogen is available, g
psn
is used for
plant allocation. If, however, nitrogen is limiting, g
psn
is reduced until the nitrogen
requirements can be met. Section 6.3.1. discusses how soil nitrogen availability is
determined.
6.1.2. Respiration
As in BIOME-BGC total maintenance respiration total
mr
integrates respiration for
each live carbon store including leaves, roots, and stems. Respiration for each
component is computed as a function of nitrogen concentration and the current air
temperature using the model developed by Ryan (Ryan 1991).
Growth respiration is also computed and subtracted from the carbon allocated to
each vegetation component. Growth respiration is computed as a fixed percentage
gr
perc
of new carbon allocation, where gr
perc
is a strata-specific (i.e., vegetation
type) parameter. Ryan (Ryan 1991) suggests a growth respiration rate gr
perc
of 25%
for trees.
6.1.3. Phenology
In RHESSys, as in BIOME-BGC, net photosynthesis can be allocated on a daily or
annual basis. Each day, net
psn
is partitioned to the various tissues (leaves, roots,
and stems). Partitioning between these various tissues is discussed below. The
vegetation-type parameter alloc.prop.day.growth sets the percentage of newly
assimilated carbon, which is expressed on a daily basis. The remaining carbon is
stored and expressed during an annual leaf-out period. For deciduous trees and
grasses, alloc.prop.day.growth must be substantially less than 1 to ensure enough
stored carbon for spring leaf out. The timing and length of the annual leaf out
period is also set in the vegetation-type parameter file, using parameters day.leaf.on
Earth Interactions Volume 8 (2004) Paper No. 19 Page 25
and ndays.expand, respectively. Note that although this period is referred to as leaf
out, it also controls the assimilate allocated annually to roots. Carbon stored for
annual allocation from the previous year is expressed during the leaf-out period.
For each day during the leaf-out period, stored carbon is transferred to leaf and fine
root pools such that amounts transferred to each component decreases linearly over
each day of the leaf-out period.
In addition to annual leaf-out periods, leaf and fine root turnover periods are
defined, again using a fixed timing set by stratum-specific parameters (day.leaf.off
and ndays.litfal). The amount of leaf and fine root carbon transferred to the litter
pool during this period is a fixed percentage (leaf.turnover and froot.turnover,
respectively) of current leaf and fine root carbon pools. Parameters are set in a
stratum parameter file. For deciduous trees, however, the entire leaf carbon pool is
transferred to the litter pool. For grasses, the leaf carbon pool is first transferred to a
standing dead leaf carbon pool, which acts as an intermediate store. Transfer from
standing dead leaf carbon to the litter pool occurs at the rate defined by
deadleaf
turnover
(percentage of dead leaf turnover per year). For all vegetation types,
the amounts of leaf and fine root turnover during the fall turnover period follows a
linearly decreasing daily transfer schedule similar to that used for leaf out during
the spring.
Future versions of RHESSys will incorporate a variable phenology model (i.e.,
White et al. 1997) to account for environmental (i.e., temperature, radiation, etc.)
controls on the timing of spring leaf out and fall leaf drop. This will also allow the
model to account for plant responses to environmental stress through increases in
leaf fall.
Different vegetation types show different sensitivities to daily versus annual
allocation and the timing of phenology. Conifers, because they lose only a portion
of their leaves, are less sensitive. For deciduous trees and grasses, some portion of
photosynthesis must be reserved for annual allocation (i.e., alloc.prop.day.growth
must be less than 1) to restart photosynthesis during the spring and these vegetation
types are typically more sensitive to phenology timing.
For trees, the sapwood components of stem and coarse root pools must also be
transferred to heartwood stem and coarse root pools. The rate of sapwood to
heartwood turnover is also based on a fixed percentage (livewood
turnover
) of the
associated sapwood pools. Loss of carbon from heartwood pools can only occur
due to whole tree mortality (discussed below).
6.1.4. Allocation
New net photosynthesis must be partitioned between roots, stems, and leaves or in
the case of grasses, between roots and leaves. BIOME-BGC (Thornton 1998)
maintains a fixed partitioning strategy such that the ratio of carbon allocated to
each store is constant and set by species-specific parameters.
In RHESSys, a variable partitioning strategy based on Landsberg and Waring
(Landsberg and Waring 1997) has been included to reflect the impact of soil
moisture and nutrient stress on plant leaf to root allocation ratios. The fraction of
the new assimilate that is allocated to roots depends on the ratio of actual to
potential photosynthesis such that more carbon is allocated to roots when water or
Earth Interactions Volume 8 (2004) Paper No. 19 Page 26
nutrient limitations reduce actual photosynthesis. The fraction allocated to roots
f
root
, is computed as
froot ¼0:8=1þ2:5ðpsnpot=psnactual Þ
hino
;ð61Þ
where psn
pot
and psn
actual
are computed using Equation (58) such that for psn
pot
,
stomatal conductance and leaf nitrogen concentration values are set to the
maximum given by species-specific parameters. For psn
actual
, actual stomatal
conductance [see Equation (48)] and the actual lnc are used.
Once the fraction allocated to roots has been determined, the remaining assimilate
is allocated to leaves and, in the case of trees, stem wood based on a fixed ratio
(alloc
stemc.leafc
). For trees, carbon allocated to stem wood is further partitioned into
coarse-root and stem components and further into live and dead wood components
based on fixed ratios (alloc
crootc.stemc
and alloc
livewood.woodc
, respectively).
Finally once fractions to be allocated to each plant component have been
determined, the total amount of carbon allocated to leaves is then given as
cpool:to:leafc¼nlc plant:calloc
ðÞfleaf ð62Þ
and
cpool:to:leafc:store ¼ð1:0nlcÞplant:calloc
ðÞfleaf ;ð63Þ
where plant.c
alloc
is the total carbon available for allocation, nlc is the percentage to
be allocated daily, c
pool
.to.leaf
c
is carbon allocated to leaves on that day, and
c
pool
.to.leaf
cstore
is additional carbon to be allocated to leaves during the next leaf-
out period.
Allocations to fine and coarse roots and stems follow a similar approach.
6.1.5. Alternative allocation strategy
Finally, there is considerable uncertainty in current models of plant carbon
allocation strategies. To explore the implications of uncertainty, we have included
an alternative approach to carbon allocation, which can be substituted by the user.
Dickenson et al. (Dickenson et al. 1998) developed an allocation approach that
reflects changes in allocation strategy in response to changing average canopy light
levels as vegetation develops. This approach computes the fraction of assimilate
allocated to leaves as follows:
fleaf ¼expð2:5LAIÞ:ð64Þ
For trees, partitioning between roots and wood (coarse root and stem) is calculated
such that the ratio of root to wood carbon (C
root
/C
wood
) approaches a constant:
froot ¼1=bexpðrwbCroot=Cwood Þ;ð65Þ
where rwand bare species-specific empirical constants.
Once these initial allocation fractions are computed, the impact of soil nitrogen
limitations and finally allocation amounts are computed using the same approach
described above.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 27
6.1.6. Mortality
An annual plant mortality rate as a fixed percentage of current biomass is set in the
stratum parameter file (mortality). Total carbon and nitrogen to be lost due to plant
mortality is set each year. The same percentage is taken from each of the available
tissue stores (i.e., leaves, roots, stem). Carbon that is lost from leaves and fine roots
is transferred to the litter pool. Coarse stem and root material is transferred to a
coarse wood debris pool that decays at a species-specific fragmentation rate before
it is transferred to litter carbon and nitrogen pools. Fragmentation does not alter
wood C:N ratios.
Material transfers due to mortality occur on a daily basis such that the annual
plant mortality rate is maintained. The annual rate is reset each year (at the start of
leaf out) to respond to changes in available stores. Future versions of RHESSys
may incorporate a variable mortality rate as a function of environmental stressors
that increase susceptibility to disease, blow down, etc. In the current version,
episodic changes in vegetation such as forest harvesting or fire can be implemented
through a dynamic redefinition of the stratum-level carbon- and nitrogen-state
variables. An independent disturbance model can be used to determine size and
frequency of these events.
6.2. Vegetation: Nitrogen cycling
In general, the cycling of nitrogen within the vegetation is tied stoichiometrically to
that of carbon. In RHESSys, the C:N ratios of the various plant biomass
components are fixed based on species-specific input parameters. A number of
studies have shown that plants may vary biomass C:N ratios, particularly of leaves,
in response to environmental stress (Aber and Melillo 1991). Thornton (Thornton
1998), on the other hand, summarizes studies that suggest that plants respond to
nitrogen limitations through variations in total leaf area and leaf area per unit of
nitrogen. At present, we follow the BIOME-BGC approach and hold leaf and other
C:N ratios constant. Within the simulation, however, carbon and nitrogen stores
and fluxes are maintained separately to facilitate future implementation of
algorithms to account for differences in C:N ratios in response to stress.
One exception to the above implementation occurs during leaf fall. Retrans-
location of leaf nitrogen as leaves fall results in increased C:N ratios in litter fall
and excess nitrogen stored within the plant. This retranslocated stored nitrogen is
then available for plant use during subsequent growth (i.e., in addition to nitrogen
available through uptake from the soil). Separate parameters are therefore required
to set leaf litter and leaf C:N ratios.
6.3. Soil
6.3.1. Decomposition
Daily soil and litter decomposition models are based on an approach developed by
Thornton (Thornton 1998) for use in BIOME-BGC, which is similar to the
approach used by CENTURY (Parton et al. 1996). Decomposition is based on a
set of litter and soil pools, each of which includes both organic material and
microbial biomass. Each pool is associated with a specific C:N ratio and a
Earth Interactions Volume 8 (2004) Paper No. 19 Page 28
potential decay rate. This decay rate includes both carbon lost due to microbial
respiration and carbon transferred to the next soil/litter pool. Respiration is
computed as a percentage of decomposition rates and are specific to each soil/litter
pool (based on Thornton 1998).
The potential decay rate associated with each soil or litter pool may be reduced
as a function of soil moisture, temperature, and nitrogen limitations. Scalar
multipliers for temperature and moisture effects (w
scalar
and t
scalar
, respectively) are
computed as follows:
tscalar ¼exp308:56 1
71:021
ðTsoilþ273:15227:13Þ
hi
for Tsoil >10;
tscalar ¼0:0 for Tsoil 10:ð66Þ
The equation used for soil moisture effects differs from that used in BIOME-BGC
in order to account for the reduction of decomposition rates in saturated soils.
While Thornton’s (Thornton 1998) approach assumed a well-drained soil
environment, RHESSys adjusts decomposition rates following the modifier used
by Parton et al. (Parton et al. 1996) to model soil moisture controls on nitrification:
wscalar ¼ðhbÞ
ðabÞ
dðbaÞ
ðacÞ
hi
ðhcÞ
ðacÞ
d
;ð67Þ
where a, b, c, d are soil parameters and his soil moisture.
Availability of mineralized nitrogen may also impact decay rates. Once the
potential decomposition rates have been adjusted for each soil and litter pool, total
immobilization and mineralization fluxes (i.e., from all pools) are computed based
on relative C:N ratios associated with soil/litter pool transfers. If net immobiliza-
tion flux (i.e., total immobilization mineralization) is greater than currently
available mineralized nitrogen store, immobilizing decomposition fluxes are
proportionally reduced. Note that potential competition with plant nitrogen uptake
must also be taken into account here. Thus, in the case of nitrogen limitation, plant
uptake and immobilizing decomposition rates are reduced proportionally such that
sum:N:demand ¼potential:plant:N:uptake þpotential:soilN:immobilized;
actual:plant:N:uptake ¼potential:plant:N:uptake
sum:N:demand soil:N:availðÞ;
actual:soilN:immobilized ¼potential:soilN:immobilized
sum:N:demand soil:N:availðÞ:ð68Þ
Note that soil.N.avail includes both mineralized N from soil decomposition and
any additional soil.NH
4
or soil.NO
3
from fertilization, nitrogen deposition, or N
fixation.
6.3.2. Nitrification
Mineralized nitrogen soil.sminn that is made available through organic matter
decomposition is assumed to be ammonia, soil.NH
4
. Nitrification may transform
soil.NH
4
into soil.NO
3
. Potential nitrification rates are based on the approach
developed and tested by Parton et al. (Parton et al. 1996) as part of the
Earth Interactions Volume 8 (2004) Paper No. 19 Page 29
CENTURY
NGAS
model. The nitrification rate N
nitrif
, is a function of soil moisture
(f
H
2
O
), carbon substrate availability (soil.sminn), soil temperature (fT), and
available soil.NH
4
such that
Nnitrif ¼fH2OfTfNH4soil:sminn;ð69Þ
where f
H
2
O
is computed following the same approached used to calculate w
scalar
in
Equation (67) and temperature control fTis computed as
fT¼0:06 þ0:13 exp0:07Tsoil ;ð70Þ
where T
soil
is the soil temperature.
Concentration of ammonium controls the rate of nitrification such that
fNH4¼1:0exp 0:0105 NH4conc
ðÞ½
;ð71Þ
where NH
4conc
is soil ammonium concentration in the organic soil layer.
Only mineralized soil nitrogen (i.e., from the decomposition of soil organic
material; soil.sminn or fertilizer) is used for nitrification. This ensures the availability
of soil carbon for the microbial nitrification processes (Gold et al. 2001).
6.3.3. Denitrification
Nitrate can be lost from the soil through flushing and/or denitrification. Flushing of
nitrate through lateral subsurface throughflow is discussed in section 4.7.4.
Denitrification is also modeled using the approach used in the CENTURY
NGAS
model (Parton et al. 1996). Denitrification N
denitrif
is a function of a maximum
denitrification rate (RNO3) based on available soil nitrate. This maximum rate is
then modified by soil moisture and soil respiration such that
Ndenitrif ¼fH2OfhrCO2RNO3:ð72Þ
Maximum denitrification RNO3is computed as
RNO3¼0:0011 þarctan½0:002ðNO3:soilÞ
NsoilþCsoil 180
;ð73Þ
where (NO
3
.soil) is available nitrate in the soil and N
soil
and C
soil
are soil nitrogen
and carbon masses, respectively.
Soil moisture limitation fH2Ois computed as
fH2O¼a
b
c
bdh
;ð74Þ
where a, b, c, d are set as a function of soil texture as described in Parton et al.
(Parton et al. 1996).
The soil (heterotrophic) respiration rate (hrCO2) is used as an index of carbon
availability, which has been shown to limit microbial denitrification:
fhrCO2¼0:0024
1þ200
exp0:35hrCO20:0001;ð75Þ
where hr is total soil respiration rate, which is calculated as discussed in section
6.3.1.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 30
7. Application: Hydrologic controls on N cycling for a small
forested catchment
Specific applications of RHESSys highlight different components of model structure
and function. Hydrologic applications of this model focus on predictions of stream-
flow and spatial patterns of soil moisture under a variety of land-cover and climate
forcing conditions. Biogeochemical applications have used the model to examine the
mechanisms that control the cycling and transport of both carbon and nitrogen within
a watershed. As an example, a brief overview of a current RHESSys application is
presented here. Additional detail on this study can be found in Band et al. (Band et al.
2001).
Pond Branch is a 34-ha catchment used as the control forested catchment as part
of the Baltimore Long-Term Ecological Research program. As part of this project,
continuous streamflow and weekly stream chemistry have been monitored since
fall 1998. Watershed topography is characterized by a gently sloping upland area
with steep side slopes draining to a broad riparian area. Upland soils are silt loam
soil with underlying deep saprolite. Side slopes contain very shallow soils, while
the bottomland is characterized by a substantial organic soil layer. Vegetation is
dominated by a mature oak–hickory forest.
Because this is a relatively small watershed, patches were based on 5-m pixels.
Hillslope delineation is shown in Figure 2. Soil parameters appropriate for sandy
loam and vegetation parameters for an oak–hickory forest were used. When
RHESSys is run in dynamic mode (i.e., soil and vegetation are not prescribed but
are computed by the model), the model must be run for a period of spinup to
generate carbon and nitrogen pools. In this case, the model was spun up for 200
Figure 2. Hillslope delineation and 30-m DEM for Pond Branch.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 31
years, at which point both canopy cover and soil carbon pools had stabilized (i.e.,
reached equilibrium values). Once stable carbon and nitrogen pools were achieved,
United States Geological Survey (USGS) stream gauge records were used to
calibrate the model by varying Ksat0, hydraulic conductivity at the surface and m,
the decay of hydraulic conductivity with depth. Calibration used a Monte Carlo–
Figure 3. RHESSys and measured stream nitrate concentrations (mgN L
1
)for
Pond Branch during Jan 1999–Dec 2000.
Figure 4. RHESSys and measured streamflow (normalized by drainage area) for
Pond Branch.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 32
based approach to run the model over a range of values for mand K. The set of
values producing the optimal correspondence between observed and modeled
streamflow as measured by the highest Nash–Sutcliffe efficiency (Nash and
Sutcliffe 1970) were selected for future runs.
Correspondence between modeled and observed streamflow as well as modeled
and observed stream nitrate concentration illustrate both the strengths and weakness
of RHESSys application in this particular watershed (see Figures 3 and 4). As
discussed in an earlier paper (Band et al. 2001), RHESSys tends to overpredict nitrate
concentration in this watershed, although it captures the temporal pattern of nitrate
export. RHESSys does not model in-stream processes, thus overprediction of the
nitrate export may suggest that in this watershed in-stream losses are significant. Field
data collected as part of this project support this conclusion. One of the surprising
patterns in both field and modeled nitrate export is the increase in N concentration
during the summer when biologic activity and hence biologic uptake of nitrogen is
typically high. RHESSys output was used to help explain this pattern. Examining
spatial outputs show that this increase in nitrification occurs primarily in the riparian
region as it dries out during the summer period. The location of these processes within
the riparian zones, which maintain connectivity to the stream throughout the summer,
is important. Examining RHESSys spatial patterns of soil moisture illustrates
temporal and spatial variation in surface saturated areas in which riparian zone
processes occur (Figure 5). Modeled spatial patterns of soil moisture suggest that in
addition to the classically defined riparian zone, topographic hollows, which drain
into the riparian area, are also areas of significant saturation during parts of the year.
These spatial patterns suggest that these topographic hollows may play a role similar
to the riparian area in terms of both overall control on hydrology and nitrogen cycling,
at least during the wetter periods. These results further suggest areas where additional
Figure 5. RHESSys saturation deficit (mm of water) for Pond Branch in Aug 2000.
Earth Interactions Volume 8 (2004) Paper No. 19 Page 33
field study may be needed to collect data in these areas, which potentially act as
controls on water quality and quantity in this watershed.
Acknowledgments. The Baltimore Ecosystem Study project is supported by the NSF
Grant GRS 0095796 to L. Band and C. Tague, and National Science Foundation Long-Term
Ecological Research program Grant DEB 9714835. We thank the USDA Forest Service
Northeastern Research Station and BES for site management. In addition we thank the
University of Maryland, Baltimore County, for their contribution of office and laboratory space
at the Research Technology Center. We also thank the Baltimore Department of Parks and
Recreation and Department of Public Works, the Baltimore County Department of Parks, and
the Maryland Department of Natural Resources for their support.
APPENDIX: RHESSys Variables
This appendix lists the current atmospheric variables that are used internally in the
RHESSys model.
A1. Environmental time series inputs.
Variable Description
Rain Precipitation (rain þsnow), required
T
min
Minimum daily temperature, required
T
max
Maximum daily temperature, required
T
day
Mean daytime temperature
T
night
max
Night time temperature at sundown
T
soil
Soil temperature
dayl Day length
daytimerainduration Duration of rainfall
LAIscalar Zone and seasonal scaling of LAI
LIncoming longwave radiation
K
direct
Incoming direct shortwave radiation
K
diffuse
Incoming diffuse shortwave radiation
PAR
diffuse
Incoming direct PAR radiation
PAR
direct
Incoming diffuse PAR radiation
relHRelative humidity
vpd Vapor pressure deficit
u* Wind speed
ndep
NO
3
Nitrate deposition
ndep
NH
4
Ammonium deposition
A2. The RHESSys variable list.
Variable Description Units
aEmpirical soil parameter DIM
ANet assimilation rate lmol m
2
s
1
aSnowpack albedo 0–1
a
direct
Vegetation reflectance (direct radiation) 0–1
a
background
Background (litter) reflectance 0–1
a
diffuse
Vegetation reflectance (diffuse radiation) 0–1
Earth Interactions Volume 8 (2004) Paper No. 19 Page 34
A2. (Continued)
Variable Description Units
A
sunlit
Sunlit assimilation rate lmol m
2
s
1
A
shaded
Shaded assimilation rate lmol m
2
s
1
agsurf Empirical moss parameter DIM
a
i
Area for patch m
2
Age Age of snowpack surface Days
alloc
crootc.stemc
Ratio of carbon allocated to coarse root and stem Ratio
alloc
livewood.woodc
Ratio of carbon allocated to live and dead wood Ratio
APAR
direct
Absorbed photosynthetically active direct radiation lmol m
2
day
1
APAR
diffuse
Absorbed photosynthetically active diffuse radiation lmol m
2
day
1
ar Upslope contributing area m
2
bPore size index DIM
bEmpirical soil parameter DIM
b
MT
Empirical temperature melt coefficient DIM
bSpecies specific empirical constant DIM
cPore disconnectedness index DIM
cEmpirical soil parameter DIM
C
soil
Soil carbon mass kgC m
2
cpool:to:leafcTotal amount of carbon allocated to leaves kg m
2
day
1
cpool:to:leafcstore Carbon to be allocated to leaves during the next leaf out period kg m
2
C
surf
Surface conductance for soil m day
1
CF Cloud fraction %
CI Canopy interception m
CI
litter
Litter interception m
cn Vegetation specific wind attenuation coefficient 0 1
CO
2
Atmospheric carbon dioxide concentration ppm
cp
rain
Specific rain interception capacity m
cp
snow
Specific snow interception capacity m
cp
water
Heat capacity of water kJ kg K
1
cs.dead.stem Heartwood stem carbon store kg m
2
cs.live.stem Sapwood stem carbon store kg m
2
dEmpirical soil parameter DIM
d
0
Zero plane displacement m
D
day
Day length s
D
rain
Daytime rain duration s
d
u
Understory zero plane displacement m
dayl Daylength s
daytimerainduration Duration of rainfall s
detSSurface detention storage m
ETotal daily evaporation m day
1
EEvaporation m day
1
e
a
Atmospheric vapor pressure Pa
ess
atm
Atmospheric emissivity Pa
ET
sat
Evapotranspiration from the saturated zone m day
1
ET
unsat
Evapotranspiration from the unsaturated zone m day
1
ext
coef
Canopy radiation extinction coefficient 0 1
FFractional canopy cover over the snowpack %
f
leaf
Fraction of assimilate allocated to leaves %
f
root
Fraction of assimilate allocated to roots %
g
psn
Gross daily canopy photosynthesis kgC m
2
day
1
GF Gap fraction 0 1
gr
perc
Percentage of NPP to growth respiration %
gs Canopy conductance m s
1
Earth Interactions Volume 8 (2004) Paper No. 19 Page 35
A2. (Continued)
Variable Description Units
gs
max
Vegetation type specific maximum conductance m s
1
gs
nonvas
Nonvascular conductance m s
1
gs
sunlit
Sunlit stomatal conductance m s
1
gs
shade
Shaded stomatal conductance m s
1
hrCO2Soil (heterotrophic) respiration rate kgC m
2
day
1
IRainfall intensity m day
1
irad Net incoming radiation lmol m
2
s
1
kVegetation-specific Beer’s law extinction coefficient 0 1
K
diffuse
Absorbed diffuse shortwave radiation kJ m
2
day
1
K
diffuse
0
Incoming diffuse shortwave radiation kJ m
2
day
1
K
direct
Absorbed direct shortwave radiation kJ m
2
day
1
K
direct
0
Incoming direct shortwave radiation kJ m
2
day
1
Ksat0Saturated hydraulic conductivity at the surface m day
1
KsatsSaturated hydraulic conductivity m day
1
K
snow
Snowpack radiation extinction coeff 0 1
K
unsat
Vertical unsaturated hydraulic conductivity m day
1
LLongwave radiation kJ m
2
day
1
k
v
Latent heat of vaporization kJ kg
1
k
f
Latent heat of fusion kJ kg
1
LAIprojshade Shaded projected leaf area index DIM
LAIprojsunlit Sunlit projected leaf area index DIM
litterraincap Maximum litter interception capacity m
livewood
turnover
Rate of sapwood to heartwood turnover %
lnc Leaf nitrogen concentration kg(Nleaf/m
2
)
LWP Leaf water potential MPa
LWP
min.spring
Fully open stomata leaf water potential MPa
LWP
predawn
Predawn leaf water potential MPa
mDecay rate of hydraulic conductivity with depth DIM
M
rad
Radiation melt m day
1
M
T
Latent and sensible heat melt m day
1
M
V
Advective melt m day
1
mortality Annual plant mortality rate % yr
1
N
dentrif
Denitrification rate kgN m
2
day
1
N
nitrif
Nitrification rate kgN m
2
day
1
N
soil
Soil nitrogen mass kgN m
2
ndepNO3Atm NO
3
deposition kgN m
2
day
1
ndepNH4Atm NH
4
deposition kgN m
2
day
1
net
psn
Net daily photosynthesis kgN m
2
day
1
nlc Percentage of NPP to be allocated daily %
NH
4conc
Soil ammonium concentration kgN m
3
NO3
decay
Parameter: vertical distribution of N in rooting zone DIM
NO3
out
Total export of nitrate N from patch kgN m
2
day
1
NO3
mobile
Proportion of soil nitrate that is mobile %
NO3
surface
Nitrate at top of soil profile kg m
2
NO
3
.soil Available nitrate in the soil kgN m
2
x
a,b
Flow width between patch aand bm
pDecay of porosity with depth DIM
PPrecipitation m day
1
/Porosity %
/0Surface porosity %
p
a
Atmospheric pressure Pa
PAI Plant area index DIM
Earth Interactions Volume 8 (2004) Paper No. 19 Page 36
A2. (Continued)
Variable Description Units
PAR
direct
0
Incoming direct PAR radiation kJ m
2
day
1
PAR
diffuse
0
Incoming diffuse PAR radiation kJ m
2
day
1
potqexfil Potential exfiltration rate m day
1
ppfd
shade
Shaded leaf photon flux density lmol m
2
s
1
ppfd
sunlit
Sunlit leaf photon flux density lmol m
2
s
1
psn
actual
Photosynthesis (with water, N limitation) kgC m
2
day
1
psn
pot
Photosynthesis (no water, N limitation) kgC m
2
day
1
q
base
Baseflow for the hillslope m day
1
q
cap
Capillary rise m day
1
q
drain
Unsaturated zone drainage m day
1
q
infil
Infiltration m day
1
q
melt
Snowmelt m day
1
q
z
Net lateral transport of water from the patch m day
1
q(t)
a,b
Saturated throughflow m day
1
R
net
Net radiation kJ m
2
day
1
RNO3Maximum denitrification rate kgN m
2
day
1
q
water
Density of water kg m
3
r
w
Species specific empirical constant DIM
ra
o
Overstory resistance s m
1
ra
u
Understory resistance s m
1
rain Incoming precipitation m
RT Rain throughfall m
sSaturation deficit (water) m(water)
SRelative soil moisture content %
SRooting zone soil wetness %
sHillslope mean saturation deficit m
s
active.soil.depth
Soil hydrologic depth m
S
c
Scattering coefficient 0 1
S
fc
(z) Relative saturation at field capacity %
S
litter
Current water content m
S
p
Sorptivity m=ffiffiffiffiffiffiffi
day
p
s
unsat
Soil moisture content of the unsaturation zone m
SED Snowpack energy deficit 8C
SED
max
Maximum energy deficit 8C
s0Hillslope mean saturation deficit, w capillary fringe m
rStefan–Boltzmann constant cal cm
2
day
1
K
4
soil.N.avail Total mineral soil N kgN m
2
soil.NH
4
Soil ammonia kgN m
2
soil.NO
3
Soil nitrate kgN m
2
soil.sminn Mineralized soil nitrogen kgN m
2
surf
NO3
Nitrate in surface detention store kg m
2
swa Stem wood equivalent area DIM
Trp Total transpiration m day
1
T
air
Mean daily temperature 8C
T
avg
Average daily temperature 8C
t
d
Precipitation duration days
T
day
Mean daytime temperature 8C
T
e
Mean hillslope transmissivity m day
1
T
max
Maximum daily temperature 8C
Tmaxsnow Maximum temperature at which snow can occur 8C
T
min
Minimum daily temperature 8C
Earth Interactions Volume 8 (2004) Paper No. 19 Page 37
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