R.K. Monson
A Bayesian model-data fusion analysis of net ecosystem CO2 exchange in a high-elevation,
subalpine forest
Russell K. Monson1, William J. Sacks2, Andrew A. Turnipseed3, Sean Burns1, David S. Schimel2
1
Department of Ecology and Evolutionary Biology, University of Colorado, Boulder, Colorado,
80309, U.S.A.
2
Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder,
Colorado, 80305, U.S.A.
3 Atmospheric Chemistry Division, National Center for Atmospheric Research, Boulder, CO,
80305, U.S.A.
Corresponding author: Dr. Russell Monson, Department of Ecology and Evolutionary Biology,
University of Colorado, Boulder, Colorado, 80309, U.S.A.
Phone = (303) 492-6319
Fax = (303) 492-8699
e-mail = Russell.Monson@colorado.edu
Running head: Bayesian modeling of NEE
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R.K. Monson
Summary
Quantifying environmental and biological controls over net ecosystem CO2 exchange
(NEE) from flux data remains a challenge. The problem is especially challenging in seasonally
snow-covered ecosystems where access to the soil system and concomitant characterization of
wintertime respiratory processes is even more restricted. We used a Bayesian parameter
optimization along with the Simple Photosynthesis and Evapotranspiration (SIPNET) model to
analyze seasonal and cumulative annual patterns of NEE over five continuous years at the Niwot
Ridge Ameriflux site in the Rocky Mountains of Colorado, USA. The subalpine forest
ecosystem at this site exhibits a high degree of interannual variation in cumulative annual NEE
(with the total range in annual NEE being 83% the maximum observed annual NEE within the
five-year study period), with much of the variation being dependent on variation in the
wintertime hydrologic cycle. Wintertime respiration from the forest results in the loss of 65-89%
of the carbon sequestered during the growing season, with the range of this amount being
dependent on the depth of late winter snows; higher snow depths are correlated with higher
respiratory losses, presumably due to higher soil temperatures. Interannual variation in summer
NEE is mostly due to the extent of mid-summer drought, and variation in autumn NEE is
correlated with prevailing air temperature.
The Bayesian model analysis involved the assimilation of half-daily rates of NEE over all
five years, which allowed for broad constraint of the parameter optimization. After optimization,
we were able to diagnose those components of the model structure that caused the greatest
mismatch between model predictions and assimilated data. Three components of the model were
found to be especially problematic: (1) The model consistently underestimated ecosystem
respiration rates during both the winter and summer; (2) The model consistently underestimated
the rate of springtime CO2 uptake; (3) The model consistently overestimated summer and
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R.K. Monson
autumn CO2 uptake. Our study demonstrates a powerful approach to diagnosing the structure of
ecosystem processes by (1) combining significant amounts of data for strong constraint of
processes, and (2) combining those data with a model to allow evaluation of complex hypotheses
about ecosystem regulation. The residual mismatch between model predictions and observations
after accomplishing these two steps allows the identification of gaps in knowledge and
inadequacies in model structure.
Key words: Ameriflux, biogeochemistry, carbon sequestration, coniferous, ecosystem,
evergreen, NEE, needle-leaf, Niwot Ridge, parameter estimation, simulation, snow, winter
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R.K. Monson
Introduction
The extraction of insight about ecosystem processes from large data sets has become a
priority in recent years, encouraged in large part by the availability of continuous data records
from tower flux sites (Baldocchi et al. 2001, Wilson et al. 2002, Falge et al. 2002, Law et al.
2002). Observational studies of ecosystem processes are often difficult due to complexities of
factor interactions and limited access to the various ecosystem components that drive material
and energy fluxes. This is especially true in ecosystems where dynamics in soil respiration exert
dominant controls over dynamics in overall NEE. In an effort to understand the primary controls
over ecosystem carbon, water and energy fluxes, we have been analyzing NEE data collected
continuously over a five-year period from a high elevation, subalpine forest site. This ecosystem
offers particularly difficult challenges because of its complex mountain topography and longlasting seasonal snow cover.
Model-data fusion approaches offer unique opportunities for the study of processes in
complex ecosystems. In a recent study of NEE in the Harvard Forest, Braswell et al. (2004)
demonstrated reasonable compatibility between an ecosystem process model and data, allowing
good constraint of model parameters when diagnosed at the daily and seasonal time scales.
Using this approach of model-data synthesis, these workers were able diagnose the relevant time
scales for control over NEE by ecosystem processes, as well as estimate optimized parameter
values and prioritize the most limiting processes controlling dynamics in NEE. In the current
study, we used the same Bayesian approach to optimize parameter estimation for the Simple
Photosynthesis Evapotranspiration (SIPNET) model across five years of NEE data at the Niwot
Ridge Ameriflux site in Colorado. We then used the optimized parameter field to probe the
match between model predictions and data during extreme climate periods. In ecosystem
modeling it is often assumed that model structure is accurate in its reflection of fundamental
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processes, and adjustments to the parameter field are used to 'tune' the model to match validating
data (e.g., Luo et al. 2001, Vukicevic et al. 2001).. We reversed this process by first defining all
parameters through a highly iterative model-data synthesis. Assuming that the parameter field
was as constrained and well-defined as is possible given the observed data set, we asked the
question: to what degree does model structure fail to adequately reflect assimilated data, despite
being constrained by the optimized parameter field?
The high-elevation, subalpine forest ecosystem at the Niwot Ridge Ameriflux site is
dominated by coniferous trees that must survive relatively dry, short growing seasons alternating
with cold, snow-covered winters. Thus, in this ecosystem the climate variables that drive
ecosystem processes can exhibit extremes that are potentially hard to capture accurately in
models that focus on predictions for the 'average' year. In the current study, we begin our
analysis with a description of the seasonal and interannual variance in NEE over a five-year
period, accompanied by an explanation of the causes of extremes in the variance. We then apply
the model-data fusion approach to evaluate how effectively predictions of the SIPNET model
match observed data in the face of the highly-constrained parameter field.
Materials and Methods
Study site
The Niwot Ridge Ameriflux Site is located approximately 50 miles west of Boulder,
Colorado (40o 1'58'' N: 105o 32'47''W) at 3050m elevation above sea level. The site is situated in
the subalpine forest ecosystem with the dominant species being Abies lasiocarpa (subalpine fir),
Picea engelmannii (Engelmann spruce) and Pinus contorta (lodgepole pine). The canopy at the
site is relatively open with an average gap fraction of 17%. The average canopy height is 11.4 m
and the average mid-summer leaf-area index is 4.2 m2 m-2 (Monson et al. 2002, Turnipseed et al.
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2002). The site has a sparse, heterogeneous ground cover, mostly composed of Vaccinium sp.,
lichens and occasional moss. Soils are sandy and derived from granitic moraine with a distinct,
thin (< 6 cm) organic horizon. Mean annual precipitation at the site averages 800 mm and the
mean annual temperature is 4 ºC.
Measurements of NEE and associated parameters
The eddy covariance method was used to measure CO2 and H2O fluxes. General details of
the eddy covariance approach are provided in Baldocchi (2003), and specific details for
measurements at the Niwot Ridge Ameriflux site are provided in several previous papers
(Monson et al. 2002, Turnipseed et al. 2002, Turnipseed et al. 2003, Turnipseed et al. 2004).
Briefly, turbulent fluxes were measured using a triaxial sonic anemometer (SWS-211/3K,
Applied Technologies, Inc., Boulder CO, USA) and a closed-path infrared gas analyzer (Li-Cor
6262, Li-Cor Inc, Lincoln NE, USA). Measurements were aligned with the mean wind
streamlines (Kaimal and Finnigan 1994), and standard density corrections (Webb et al. 1980)
were applied. Beneath-canopy CO2 storage was determined by vertical integration of six profile
stations located on the tower, and added to the eddy-flux measurement to compute the overall
NEE as described in Goulden et al. (1996). In the micrometeorological literature, CO2 fluxes are
assigned a mathematical sign, which by convention is referenced to the atmosphere; negative
CO2 fluxes (net photosynthesis) represent CO2 loss from the atmosphere and positive CO2 fluxes
(net respiration) represent CO2 gain by the atmosphere.
Air temperatures were determined from the temperature signal of the sonic anemometer at
the same height as the turbulent flux measurements. Precipitation values were obtained from the
University of Colorado Long-term Ecological Research web site (http://culter.colorado.edu),
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R.K. Monson
which in turn were obtained from standard precipitation gauge measurements. The site used for
the precipitation measurements is located 500 m to the north of the tower flux site.
The SIPNET ecosystem model
Our approach to the modeling was to develop a relatively simple model as a first iteration.
Using insight gained from the Bayesian parameter optimization, we could then add greater model
complexity when needed to improve the match between model output and data. The initial
model was developed for an eastern deciduous forest ecosystem, the Harvard Forest (Braswell et
al. 2004). In the current study, we applied a modified version of the Harvard Forest model to the
Niwot Ridge coniferous forest.
The model we used is, for the most part, a simplified version of the PnET (PhotosynthesisEvapoTranspiration) model originally developed by Aber and co-workers (e.g., Aber and Federer
1992, Aber et al. 1995, Aber et al. 1996); acknowledging the contributions of the PnET model,
we refer to our version as SIPNET (for Simplified PnET). The structure of SIPNET has been
described previously (Braswell et el. 2004). Briefly, SIPNET describes carbon flux dynamics
among two vegetation carbon pools and an aggregated soil carbon pool. To accomplish biomass
partitioning and respiration, the vegetation is split into leaves and wood, where 'wood' refers to
the combined pool of boles, branches and roots. We used SIPNET with half-daily daytime and
nighttime time steps. The length of each time step depended on day of year. In each step, we
used eight climate variables to drive the flux dynamics: (1) average air temperature, (2) average
soil temperature, (3) precipitation, (4) flux density of photosynthetically-active radiation, (5)
atmospheric vapor pressure, (6) atmospheric vapor pressure deficit, (7) vapor pressure deficit
between the soil and the atmosphere and (8) wind speed. In practice, vapor pressure and vapor
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R.K. Monson
pressure deficits are computed from the relative humidity, air temperature and soil temperature.
The model’s dynamics are governed by the values of thirty-eight parameters (Table 1).
There are six carbon fluxes in SIPNET: (1) gross photosynthetic CO2 assimilation, (2)
autotrophic respiration, (3) heterotrophic respiration, (4) new leaf growth, (5) formation of leaf
litter, and (6) formation of wood litter (this last flux was simply modeled using a constant
turnover rate). We used the same model structure for calculating gross photosynthesis rate as is
used in PnET (Aber and Federer 1992). Basically, a maximum gross photosynthetic rate was
multiplied by four factors, each carrying a value between 0 and 1: an air temperature factor, an
atmospheric vapor pressure deficit factor, a photon flux density factor, and a soil water deficit
factor. The relationship between air temperature and photosynthesis is modeled by a quadratic
function, falling to zero above and below threshold temperatures. Photosynthesis is also
assumed to decrease quadratically with increasing atmospheric vapor pressure deficits. The
attenuation of the photon flux density through the canopy is modeled according to an exponential
decay function scaled to the leaf area index, and canopy-level photosynthesis is modified based
on the amount of light falling on the top of the canopy and this exponential decay. Finally,
photosynthesis is further decreased if there is not enough available soil water to satisfy the
transpiration demand; this transpiration demand increases both with increasing levels of potential
(i.e. without water stress) photosynthesis and with increasing atmospheric vapor pressure
deficits.
Autotrophic respiration in SIPNET is represented as the sum of two respiratory terms:
foliar and wood maintenance respiration. (In an effort to keep the initial model as simple as
possible, we aggregated growth and maintenance respiration.) The temperature dependence of
both foliar and wood respiration was represented as a Q10 function, with a single parameterized
Q10 value represented for the entire year. Wood maintenance respiration was calculated as a
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R.K. Monson
function of the total volume of wood and temperature. We recognize that this simplifying
assumption carries the unrealistic corollary that all of the wood respires, rather than only the
outer, live wood. However, as long as the ratio of live wood to total plant biomass does not
change significantly over the course of a model run, the model will give reasonable results as
long as the base respiration rate is expressed in terms of g C respired per g biomass rather than g
C respired per g live wood. This method of determining maintenance respiration has been used
in some other models, such as the Terrestrial Ecosystem Model (Raich et al. 1991).
Heterotrophic respiration represents the respiration of microbes in the model’s single
aggregated soil pool. Respiration rate was assumed to be proportional to the total amount of
carbon in the soil, and the temperature dependence was modeled with an exponential temperature
function (similar to autotrophic respiration, but using soil temperature rather than air
temperature) as well as a soil moisture function (Aber et al. 1997, Raich et al. 1991). As in
PnET-CN (Aber et al. 1997), we assumed that soil respiration rate increased linearly with soil
moisture content.
There were three major changes between the version of the model used in this study and
that described by Braswell et al. (2004), applied to the Harvard Forest. First, a more complex
soil moisture sub-model was used, incorporating evaporation and the modeling of a snow pack.
Second, the model was modified to allow an evergreen phenology. Third, photosynthesis was
shut down when the soil was frozen. These three changes are described briefly below, and will
be discussed in more detail in a future publication (Sacks et al., manuscript in preparation).
The most significant change to the model was in the soil moisture sub-model. The
vegetation at Harvard Forest experiences little water stress (Aber et al. 1995); at Niwot Ridge, in
contrast, water stress is one of the largest determinants of NEE (Monson et al. 2002).
Consequently, we added complexity to the soil moisture sub-model to better capture the
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influence of water availability at this site. First, we added a snow pack; when air temperatures
are below freezing, the model assumes that precipitation falls as snow, and when air
temperatures are above freezing, the model assumes that the snow melts at a rate proportional to
air temperature. Second, not all liquid precipitation enters the soil water reservoir that is
available to plants; a constant fraction is either intercepted and immediately evaporated, or goes
immediately to drainage, as in Aber et al. (1995). Third, water is lost from the snow pack
through sublimation and from the soil through evaporation. The modeling of
evaporation/sublimation is based on equations in the SiB2 model (Sellers et al. 1996).
Evaporation from the soil is based on the vapor pressure deficit between the soil and the
atmosphere, an aerodynamic resistance term that depends on the wind speed, and a soil
resistance term that depends on the relative soil moisture content. Sublimation from the snow
surface is based on the vapor pressure deficit between the snow and the atmosphere and the same
aerodynamic resistance term. The addition of a soil evaporation term required that we split the
soil moisture pool into two layers. Precipitation enters the upper layer, and water drains down
into the lower layer at a rate proportional to the fractional wetness of the upper layer.
Evaporation removes water from the upper layer, and transpiration, which is dependent on the
amount of water available to vegetation and on the potential (i.e. without water stress) level of
photosynthesis, removes water from the lower layer. The particular equations used in SIPNET
are given by Braswell et al. (2004) and will be provided in a future publication (Sacks et al.,
manuscript in preparation).
Seasonal phenology patterns were modeled as a weighted combination of an evergreen-like
phenology scheme and a deciduous-like phenology scheme. Under the evergreen-like scheme, in
each time step leaf carbon was added at a rate proportional to the mean NPP over the previous
five days, and carbon was lost from the leaves (and added to the soil) based on a constant
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turnover rate. Under the deciduous-like scheme, a fixed amount of carbon was added to the leaf
pool on a given day in the spring, and a fixed fraction of leaf carbon was lost (and added to the
soil) on a given day in the fall. The parameters governing the amount of leaf growth and loss
through these two different schemes, as well as the parameters governing the timing of the
deciduous-like scheme, were determined through the Bayesian parameter optimization.
Finally, it has been found that photosynthesis in cold climates is drastically reduced when
the soil is frozen; a suggested mechanism involves the shutdown of water flow in frozen soils
(Hollinger et al. 1999; Monson et al. 2002). We incorporated this control into the modified
version of SIPNET by shutting down photosynthesis entirely when the soil temperature was
below freezing.
The Bayesian parameter estimation
The parameters governing the initial state and time evolution of SIPNET (Table 1) were
optimized through a Bayesian model-data synthesis. The procedure used for this optimization
was essentially the same as that described by Braswell et al. (2004). Initial values and
boundaries for the parameters were defined through a combination of literature values, best
guesses and actual measurements. We did not try to find the ‘right’ values for the parameters;
rather, we tried to start with reasonable initial guesses, assuming that the optimization would find
the ‘best-fit’ value.
In performing the optimization, each parameter was restricted to specified boundaries
(using a uniform prior distribution for all parameters). We did not use a systematic method to
determine boundary widths. In general, we tried to specify relatively broad parameter
boundaries. Use of a broad boundary increases the likelihood that the range will include the
optimal parameter value. If the boundaries are too wide, however, the optimization may spend
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more time exploring unrealistic regions of the parameter space, and unrealistic estimates for one
parameter can force other parameters to take on less realistic values. Thus the ranges used in the
optimization represent an attempt at a compromise: wide enough that the optimum value for each
parameter falls within the specified range, but narrow enough that the ranges exclude parameter
values that are grossly unrealistic. Most of the ranges, though, were based on a combination of
intuition, examination of the results of initial tests of the optimization, and consideration of the
range of values used in a few different ecosystem models.
We conducted the parameter optimization according to Metropolis et al. (1953). Briefly,
we performed a quasi-random walk through the multi-dimensional parameter space to find the
parameter set that causes the model to generate the best match of predicted NEE with observed
NEE. Here, “best match” is defined as the model output that maximizes likelihood (L):
n
L
i 1
1
 ( x   ) 2 / 2 2
e i i
2
where n is the number of data points and  is the standard deviation on each data point. We
only used data points for which at least 50% of the half-hourly values making up a given halfdaily time step were measured – that is, not gap-filled. This criterion meant that we used 77% of
the half-daily data points in the optimization. In practice, log likelihood is used in place of
likelihood because it is easier to compute.
Note that we assume that each data point has the same uncertainty and that the deviations
from the model predictions are independent over time. Because we did not have measured
values of  , we treated  as a parameter to be estimated at each step of the optimization. For a
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R.K. Monson
given model output (that is, a given set of i values), the value of  that maximizes L (which we
denote e) is given by:
e 
1
n
n
 x i   i 
2
i 1
We then used e in place of  in the calculation of L.
At each step in the optimization, a parameter is chosen at random and its value changed.
The optimization then evaluates the likelihood at the new point (by running the model using the
newly-generated parameter set) and compares it to the likelihood of the old point. If L(new) >
L(old), then the algorithm accepts the new parameter value. If L(new) ≤ L(old), then the
algorithm accepts the new parameter value with probability equal to the ratio of the likelihoods.
If the new value is rejected, then the algorithm takes another random step using the old value.
The occasional acceptance of worse points in the parameter space helps prevent the optimization
from getting stuck on local optima.
Results
Net ecosystem CO2 exchange
Measurements of NEE over five continuous years revealed considerable interannual
variation (Fig. 1). Four of the five years (2000-2004) were drier than the long-term average, and
one of the four years (2001-2002) was the driest ever recorded for the Rocky Mountain Front
Range (in over 100 years of climate records). Only one of the five years (1998-1999) exhibited
near-normal precipitation in both the winter and summer. The winter period in all five years was
characterized by a respiratory phase in which the forest exhibited persistent CO2 emissions to the
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atmosphere. The magnitude of winter respiration varied from year to year, with this variation
becoming especially obvious during the late winter and early spring. For example, from January
1 to the time of initial forest CO2 uptake in the late spring in 2000, the forest emitted 8.34 mol m2
of respired CO2, but for the same period in 2002 the forest only emitted 5.99 mol m-2 of
respired CO2. The spring and summer period in all five years was characterized by a persistent
phase of net CO2 uptake, although in midsummer during the driest years (e.g., 2001 and 2002) a
short period of net respiration was observed. Once again, considerable interannual variation was
observed in the magnitude of the photosynthetic phase, with CO2 uptake during the three month
period of June-August varying from 11.33 mol m-2 in the wettest summer (1999) to 3.76 mol m-2
in the driest summer (2002). The timing of the transition between the respiratory and
photosynthetic phases varied from early-April (2002) to mid-May (1999).
Of particular importance to the annual rate of CO2 sequestration at this site is the
wintertime loss of respiratory carbon (Table 2). Cumulative wintertime respiration resulted in
the loss of 65-89 % of the carbon gained during the growing season. Most of this respiratory
loss was due to heterotrophic respiration in the soil since there was no significant autotrophic
activity, and thus no fresh photosynthate, to support autotrophic respiration during the winter.
In order to get a more detailed look at seasonal interactions between climate and NEE, we
partitioned the data into four bins; the winter and summer bins (December-April and JulySeptember, respectively) and the spring and autumn transition bins (May-June and OctoberNovember, respectively) (Fig. 2). For each of these binned sets of data, we plotted monthly NEE
against monthly mean air temperature or monthly total precipitation for the five-year data set.
We eliminated five months from the data set (April of 2000-2004 and May of 1999) because
these months contained strong transitions in mid-month from respiration to photosynthesis, with
the highest fluxes of the annual cycle swinging from positive to negative within a matter of days.
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R.K. Monson
This made it difficult to fit these months into our mean monthly-based analysis. The autumnal
transitions seemed to occur regularly within the last few days of October or the first few days of
November each year, and the swing from photosynthesis to respiration was fairly muted because
the fluxes were so low at this time of the year due to soil moisture limitations; thus, we left the
autumnal transition months in the analysis. During the winter, higher temperatures were
correlated with higher ecosystem respiration rates. During the summer, higher temperatures
were correlated with lower net CO2 uptake rates, presumably because ecosystem respiration rates
were also stimulated by higher temperatures during this season. These results are consistent with
those obtained through formal path analysis in a previous study (Huxman et al. 2003). Monthly
NEE was positively related to precipitation during the winter and summer (i.e., more snow
caused higher wintertime respiration rates and more rain caused higher summertime CO2 uptake
rates). During the transitory spring and autumn months, precipitation did not appear to influence
NEE as much as temperature. Springtime NEE exhibited a temperature optimum between 8-10
C, and during the autumn warmer temperatures stimulated net CO2 uptake.
When taken as a whole, the five-year record of NEE at the Niwot Ridge Ameriflux site
provides a broad range of variability in both magnitude and temporal pattern with which to test
the SIPNET model. The record includes strong negative and positive relationships with
temperature and strong to no relationship with precipitation. There are strong transitions
between respiratory and photosynthetic phases in the annual carbon cycle, and these transitions
vary significantly in magnitude and timing.
Bayesian modeling
The match between modeled annual cumulative NEE predictions and measurements was
relatively close for the first of five successive years, but degenerated progressively for each
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subsequent year (Fig. 3). In general, the model predicted higher annual cumulative rates of
carbon sequestration compared to observations. We examined the match between model and
measurements for the half-daily NEE data to get a better idea as to where in the seasonal record
the model had the greatest difficulty matching the data (Fig. 4). There appeared to be three
domains where the model was in need of improvement. (1) The model consistently
underestimated nighttime respiration rate during both the winter and summer. (2) The model
consistently overestimated rates of carbon sequestration during the mid-summer and autumn,
especially during the periods of greatest summer drought. (3) The model consistently
underestimated rates of carbon sequestration during the early spring months of May and June.
The combined effect of these three deficiencies was to cause the model to predict lower
estimates of cumulative ecosystem CO2 loss at the end of each winter, allow the predictions of
cumulative NEE to move closer to observations during the subsequent spring periods, then
diverge again during the mid-summer and autumn periods.
Discussion
The SIPNET model, accompanied with a Bayesian parameter optimization, has been tested
previously with NEE data from the Harvard Forest (Braswell et al. 2004). There is tremendous
diagnostic power in the Bayesian approach as we have demonstrated in this study. By
optimizing all relevant parameters, and constraining their values beyond what has been possible
with traditional parameterization approaches, we were able to probe the causes of mismatched
domains of the model-data comparison, and identify regions of the model structure in need of
revision (Fig. 5).
In the current study, we aimed to expand the test of the SIPNET model by applying it to an
ecosystem with a very different set of controls over NEE. In the subalpine forest ecosystem, our
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observations revealed that temperature and moisture combined in complex ways to determine
seasonal dynamics in NEE. The spring and autumn transition periods reflected strong control by
temperature. A distinct temperature optimum was observed for springtime net CO2 uptake (Fig.
2). Extremely cold or warm spring periods tended to be correlated with lower rates of carbon
sequestration, though presumably because of different effects; extremely cold spring periods
probably slowed the recovery of photosynthetic processes from wintertime downregulation,
whereas extremely warm spring periods probably stimulated soil respiration rates. In the
autumn, NEE was controlled by the frequency of warm periods which extended the growing
season into the latest months of the year; i.e., warm autumn periods extended the period of net
CO2 uptake by 1-2 weeks from late-October into the early part of November. Finally,
precipitation was correlated positively with respiratory CO2 loss during the winter and
photosynthetic CO2 uptake during the summer. While the correlation between precipitation and
summer CO2 uptake can be explained by the sensitivity of photosynthesis to summer drought,
the basis for the wintertime correlation between precipitation (as snow) and the respiratory CO2
flux is less obvious. One possible explanation is that that snow depth affects soil respiration rate
through an influence on soil temperature, with deeper snow depth causing warmer soil
temperature and higher respiration rate.
We were able to diagnose three problematic domains of the SIPNET model when applied
to the Niwot Ridge data set. The tendency of the model to underestimate ecosystem CO2 uptake
rates during the spring snow-melt period and overestimate CO2 uptake rates during summer and
autumn droughts (which together represent two of the three problematic domains) may be due to
compromises that are made when the model tries to match predictions with observations at two
extreme physiological states. During the spring snow-melt period, ecosystem CO2 uptake rates
typically reach their observed seasonal maxima; this is principally due to warm air temperatures
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R.K. Monson
which foster near-maximum photosynthesis rates and cold soil temperatures which foster nearminimum respiration rates. During the summer and autumn droughts, ecosystem CO2 uptake
typically reached its observed seasonal minimum; this was presumably due to suppression of
photosynthesis. When forced to assimilate NEE data from the entire growing season, the model
must make compromises between matching the maximal CO2 uptake rates in the spring and the
minimal CO2 uptake rates in the mid-summer and autumn. It is likely that SIPNET possesses
deficiencies in its representation of the photosynthetic responses to high moisture availability in
the spring and low moisture availability in the summer and autumn. To date, we have not
derived an alternative version of the model to better simulate processes during these critical
periods. It is possible that the solution will be found in a better representation of the ratio of
actual transpiration to potential transpiration in the model, which in turn affects the scaling of
gross photosynthesis rate to soil moisture limitations. This possibility will be explored in future
analyses of model performance.
With regard to the third problematic domain in the model, the model’s failure to accurately
capture nighttime respiration rate during both the winter and summer, we have begun to address
possible solutions. As discussed above, during the winter and spring, snow depth explains much
of the variance in NEE which, at this time of the season, reflects a persistent respiratory phase.
The SIPNET model should be capable of capturing these relationships since half-daily soil
temperature is entered into the model as a climate driver. We hypothesized that one of the
difficulties in the current structure of the model involves the single parameterization that is
allowed for both the base soil respiration rate and the Q10 for soil respiration. A single
respiratory parameterization may force the model to compromise between distinct summer and
winter respiratory processes. The existence of two separate respiratory states might be explained
if two different soil microbial communities exist at this site, one specific to winter and one
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specific to summer, as has been shown in the alpine ecosystem just above the subalpine forest
used in our study (Lipson et al. 2002).
We revised the model in order to allow for independent seasonal values for the base
respiration rate and the Q10 for soil respiration. Our intention in conducting this exercise was not
to delve deeply into model revision, but rather to provide a straightforward illustration of how
the Bayesian approach can be used to diagnose model structure and improve the match between
observations and model output. With two sets of soil respiration parameters (i.e., one for winter
and one for summer, where the division between winter and summer, defined in terms of soil
temperature, was determined by another optimized parameter) the model is able to match the
data significantly better than with only one set of parameters. This observed improvement was
due to an increase in the modeled mean summertime respiration rate and a decrease in the mean
wintertime respiration rate. The ‘best’ log likelihood for the model predictions with a single set
of soil respiration parameters was calculated to be -2372.1; with two sets of parameters it was
calculated to be -2299.0 (in this case a less negative value indicates a closer match to the data).
There is some expectation that with three additional parameters, the revised model will
perform better simply because it has more degrees of freedom. Therefore, we conducted a
further analysis using the Bayesian Information Criterion (BIC) to select between two models
with different numbers of parameters (Kendall and Ord 1990). The BIC weights the log
likelihood with regard to the number of parameters and the number of data points used for
constraint. Even with a higher number of parameters, the BIC for the model using two sets of
soil respiration parameters (4901) was lower than the BIC for the model using a single set of soil
respiration parameters (5023). The model with the lower BIC is considered to be the better
model. This analysis indicates that the addition of a seasonally-varying component to soil
respiration significantly improves the model-data fit.
19
R.K. Monson
In this study, we were able to show that even with rigid constraint on parameter values, the
SIPNET model, which admittedly represents a relatively simple characterization of ecosystem
processes, was not adequate to accurately capture the complex interactions that control NEE in
the subalpine forest ecosystem. The Bayesian parameter optimization, however, offered us the
unique opportunity to improve the model by probing the causes of mismatched domains of the
model-data comparison, and identifying regions of the model structure in need of revision.
When combined with the extensive model-data fusion opportunities provided by the
unprecedented availability of NEE data from tower flux sites, the Bayesian approach should
allow not only for improved diagnosis of model performance, but also for the improved analysis
of ecosystem processes, the development of eddy flux gap-filling models and the development of
global change prognostic models aimed at predicting rates of, and controls over, ecosystem
carbon sequestration.
Acknowledgements
We are grateful to the organizers of the IUFRO Conference on Forest Modeling for inviting
us to present this work at the Vienna meeting in April 2004. Much of the impetus for the
SIPNET modeling was provided by Dr. Rob Braswell and we are grateful for his intellectual
contributions. This work was financially supported by a grant from the South Central Section of
the National Institute for Global Environmental Change (NIGEC) through the US Department of
Energy (Cooperative Agreement No. DE-FC03-90ER61010). Any opinions, findings and
conclusions or recommendations expressed in this publication are those of the authors and do not
necessarily reflect the views of the DOE.
20
R.K. Monson
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R.K. Monson
Table 1. Parameters and associated units used in the SIPNET model
Parameter
Units
Initial Pool Values:
Initial plant wood C content
Initial plant leaf C content
Initial soil C content
Initial soil moisture content, top layer
Initial soil moisture content, bottom layer
Initial snow pack
g C · m-2
g C · m-2
g C · m-2
(no units: fraction of water holding capacity)
(no units: fraction of water holding capacity)
cm water equivalent
Photosynthesis Parameters:
Maximum net CO2 assimilation rate
Avg. daily max photosynthesis as fraction of AMax
Foliar maintenance respiration as fraction of AMax
Minimum temperature for photosynthesis
Optimum temperature for photosynthesis
Slope of VPD-photosynthesis relationship
Half saturation point of PPFD-photosynthesis relationship
Canopy PPFD extinction coefficient
nmol CO2 · g-1 (leaf biomass) · s-1
(no units)
(no units)
°C
°C
kPa-1
mol · m-2 · day-1
(no units)
Phenology Parameters:
Day of year for leaf out
Day of year for leaf drop
Leaf growth at day of leaf out
Fraction of leaf C lost at day of leaf drop
Fraction of NPP allocated to leaf growth
Turnover rate of leaf C
day of year
day of year
g C · m-2
(no units)
(no units)
g C · g-1 C · day-1
Respiration Parameters:
Wood respiration rate at 0°C
Vegetation respiration Q10
Soil respiration rate at 0°C and moisture-saturated soil
Soil respiration Q10
g C · g-1 C · day-1
(no units)
g C · g-1 C · day-1
(no units)
Moisture Parameters:
Fraction of soil water removable in one day
VPD-water use efficiency relationship
Soil water holding capacity, top layer
Soil water holding capacity, bottom layer
Fraction of rain immediately intercepted and evaporated
Fraction of water entering soil that goes directly to drainage
Snow melt rate
Rate of water drainage from upper to lower soil water layer for
fully-saturated upper layer
Scalar relating aerodynamic resistance to wind speed
2 x scalars relating soil resistance to fractional soil wetness
Tree Physiological Parameters:
C content of leaves on a per-area basis
Fractional C content of leaves
Turnover rate of plant wood C
(no units)
mg CO2 · kPa · g-1 H2O
cm (precipitation equivalent)
cm (precipitation equivalent)
(no units)
(no units)
cm (water equivalent) · °C-1 · day-1
cm (water equivalent) · day-1
(no units)
(no units)
g C · m-2 (leaf area)
g C · g-1 (leaf biomass)
g C · g-1 C · day-1
25
R.K. Monson
Table 2. Derived values for components of the annual net ecosystem CO2 exchange (NEE) for
the Niwot Ridge Ameriflux site during five consecutive years.
Winter cum NEE
(mol m-2)b
Growing-season
cum NEE
(mol m-2)c
Annual
cum NEE
(mol m-2)d
Ratio winter:summer
cum NEE
1998-1999
12.21
-18.92
-6.71
64.5
1999-2000
12.02
-16.82
-4.80
71.5
2000-2001
11.44
-17.08
-5.64
67.0
2001-2002
9.58
-10.71
-1.13
89.4
2002-2003
10.07
-15.32
-5.05
67.0
Year
a
a The period used for NEE calculations in any one year spans from November 1 – October 31.
Thus, the first date of the time series considered in this analysis began on November 1, 1998.
b The cumulative (cum) NEE for the forest during the winter period between the cessation of
negative daily NEE (i.e., net CO2 uptake) in the autumn and the initiation of negative daily NEE
in the spring.
c The cumulative (cum) NEE for the forest during the period marked by the initiation of
negative daily NEE in the spring and the return to positive daily NEE (i.e., CO2 loss) in the
autumn.
d The annual cumulative (cum) NEE for the period from November 1-October 31 in each year.
26
R.K. Monson
Figure Legends
Figure 1. Five years of cumulative NEE data for the Niwot Ridge Ameriflux site superimposed
to show interannual variation in the seasonal pattern. Data for all years begins with November 1.
Black = 1998-1999; Blue = 1999-2000; Red = 2000-2001; Green = 2001-2002; Pink = 20022003.
Figure 2. Regression analysis of monthly cumulative NEE against monthly mean air
temperature of monthly total precipitation (as snow water equivalent or liquid precipitation).
The data were binned into seasonal categories as described in the text. The best-fit regression
models and regression coefficients were as follows: December-April (NEE vs. temperature : y =
mx + b; m = 0.17, b = 2.81; r2 = 0.31; P = 0.0082*) (NEE vs. precipitation: y = ax/(b+x) +
cx/(d+x); a = 1.02, b = 2.51, c = 1.63, d = 24.12; r2 = 0.63; P = 0.0006*). May-June (NEE vs.
temperature: y = ax2 + bx +c; a = 0.1057, b = -1.6585, c = 1.5225; r2 = 0.76; P = 0.0071*)
(NEE vs. precipitation: y = mx + b; m = 0.005, b = -4.2112; r2 = 0.010; P = 0.7796). JulySeptember (NEE vs. temperature: y = mx + b; m = 0.15, b = -3.80; r2 = 0.22; P = 0.0803) (NEE
vs. precipitation: y = mx + b; m = -0.019, b = -1.03; r2 = 0.31; P = 0.0318*). OctoberNovember (NEE vs. temperature: y = mx + b; m = -0.26, b = 0.55; r2 = 0.64; P = 0.0057*)
(NEE vs. precipitation: y = ax3 + bx2 + cx + d; a = -0.0001, b = 0.0021, c = 0.0935, d = -1.531;
r2 = 0.55; P = 0.1628). Probability determinations were made using ANOVA.
Figure 3. Observed and simulated cumulative NEE for the Niwot Ridge Ameriflux site over the
five-year period of observations. Observed values are shown with black symbols and simulated
values are shown with gray symbols.
27
R.K. Monson
Figure 4. Observed and simulated daily NEE for the Niwot Ridge Ameriflux site over the fiveyear period of observations. Observed values are shown with black symbols and simulated
values are shown with gray symbols.
Figure 5. Overview showing the process of constraining the Bayesian parameter optimization
through the model-data fusion approach. Following the optimization, diagnosis of model
structure is conducted by analysis of the domains that retain significant mismatch between model
predictions and observations.
28