NGEN02 Ecosystem Modelling
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Ecosystem Modelling Project
In the final project of the course you will build, test and apply a model which simulates the
dynamics of a forest ecosystem at the stand scale, focusing your main attention on one major
ecosystem process. The idea is to experience all the major steps involved in the modelling
process, from choosing and setting up an appropriate model for the task at hand, to coding the
equations, evaluating the output in comparison to observations, analysis of the sensitivity of the
model to its parameters and forcing data, and interpretation of output from a model simulation.
You will work in pairs (i.e. groups of TWO students), and the whole class will be divided into
two larger groups for presentations and feedback. Each pair will work on one of the following
processes. At most two pairs may work on one and the same process:
Photosynthesis
Ecosystem respiration
Canopy conductance
Evapotranspiration
Soil hydrology
Light extinction
Given the relatively limited time available for the project work, a recommended modelling
approach and some advice on how to get underway is provided further down in this document.
The level of detail varies because some processes are more complicated than others to simulate,
calibrate and/or analyse with respect to the available observational data. You should implement
your model as a MATLAB script.
You will work with actual measurement data from two forest study sites (Norunda in central
Sweden and Hyytiälä in Finland). The data consist for the most part of values of a large number
of variables at 30 minutes‟ resolution. Data on most of the variables you are likely to need have
been quality-controlled and some gap filling has been done to save you time and effort on
technical data processing. However, some data-related problems and issues, such as missing
values and measurement errors, may be expected. Depending on what process you are working
with, you may also need to perform post-processing on the observational data to infer values of a
variable or parameter that was not measured, but that you require for validation or calibration of
your model.
Some background to the processes and measurements will be provided in the lecture on Monday
23 February.
Supervision, feedback and milestones
We will meet as a group about once a week throughout the three weeks of the project. In-between
you will have access to supervision and teacher advice at set times each day, according to the
schedule for the course. Michael Mischurow and Wenxin Zhang are the day-to-day
supervisors, whom you should approach in the first instance with your questions and problems.
Presentations and feedback will be held at intervals of one week throughout the project. For each
presentation you should aim to have achieved certain milestones, as follows:
 27 February – Model implemented in MATLAB and technically tested (verified), input
and calibration data extracted, any needed data post-processing done, consistency of units
between model and data confirmed. Progress presentations, 10 minutes (max 5
powerpoint slides) per group, highlighting one or two issues or problems on which you
would like to obtain feedback.
 6 March – Model calibrated, evaluated in comparison to an independent subset of the
observations, sensitivity to major parameters and input variables analysed. Presentations,
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10 minutes (max 5 slides) of results from evaluation and sensitivity analysis and any
arising issues.
 12 March – Project completed. Formal presentation of results including background –
model description – results from evaluation and sensitivity analysis – insights and
interpretation. 15 minutes per group, max 8 slides. The presentation will be assessed and
may influence the overall mark for the project.
Final report
Each group should submit a report which will be marked and contribute the major part of the
assessment for the project work (i.e. 30% of the final mark for the course).
 Format: The report should follow the usual structure for a scientific study, Introduction –
Methods – Results – Discussion/conclusions. Results and Discussion/conclusions may be
combined into one subsection if you prefer, and an appendix, e.g. with your Matlab code, may
optionally be included.
 Length: Max 5 pages not including figures and any appendices. Overly lengthy reports may
result in reduced marks.
 Methods: should be concise but comprehensive; others should be able to reproduce your study
based on your description of the approach.
 Equations and symbols: should follow mathematical style rather than „computer speak‟ as far
as possible. All symbols should be defined, including units, in the running text or a table.
 Figures: Should be clear and legible with axes labelled (including units!) and a caption/figure
text that may be understood without reference back to the main text. Figures should be
numbered and referred to in the main text. If you are showing time series, the x-axis should
preferably show the dates and/or time, not the „timestep number‟. Time-filter your data (i.e.
compute averages for longer time intervals) where this is necessary or appropriate to convey
patterns or trends in a clear way.
 Discussion: your chance to convey your own thoughts and interpretation. Suggested topics:
strengths/weaknesses with your approach versus other alternatives; uncertainty versus what is
robust in your results; scope of applicability of your model.
 References: should be cited in the usual manner for a scientific report. Check any published
paper or a journal‟s instructions for authors if you are unsure.
 Deadline: 13 March, e-mail PDF to [email protected].
Ben Smith
Paul Miller
VT2015.
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Photosynthesis
A suitable model that can be applied to Norunda, with some simplifications and assumptions, is
the non-rectangular hyperbola model of photosynthesis proposed by Cannell & Thornley (1998,
Annals of Botany 82: 883-892). This model represents leaf-level gross photosynthesis as a
function of irradiance (I) and three parameters: photosynthesis rate at saturating light intensity
(Asat), quantum yield () and a shape parameter  (Equation A2 in Cannell & Thornley):
Aleaf 
I  Asat  (I  Asat ) 2  4I Asat
2
All three parameters are expected to vary with temperature and CO2 concentration, but for the
purposes of this study, in which the model will be applied on a seasonal cycle for one or two
years, and at one particular forest site, it will be sufficient to account for the temperaturedependence of Asat and  . Equations expressing these parameters as a function of temperature are
available in the appendix of Cannell & Thornley‟s paper. A constant ambient CO2 concentration
(Ca) of 370 mol mol1 (global value for year 2000) may be assumed. However, you will have to
calibrate the model to a representative subset of the available data from Norunda.
Making the simplification that the overall response of canopy photosynthesis to APAR is the
same as the response of an individual leaf to I, we can estimate Astand using the equation above,
substituting APAR for I. Several of the parameters in the photosynthesis model may potentially
vary between vegetation types or climate zones and may be subject to calibration. However, as it
is difficult to calibrate several parameters simultaneously to obtain the best global fit, you are
advised to focus on two parameters to which the photosynthesis model is quite sensitive, namely
 and Asat,20. Ranges and notional „first guess‟ values of these and other needed parameters are
available in Cannell and Thornley‟s paper. [Note that due to a typographic error, the symbol ,
quantum yield, is missing from Equations A1, A2, A3 and associated text in Cannell and
Thornley‟s paper. Further, there is a missing minus sign in Equation A8, where “(Tref T0)2” should
read “(Tref –T0)2”].
Ecosystem respiration
The total ecosystem respiration (RE) consists of two major components, heterotrophic (RH) and
autotrophic (RA) respiration. RA is often further divided in belowground (RAb) and aboveground
(RAa) as the respiring tissues operates at different temperatures. In short and medium time
perspective the respiration rate is strongly dependent on temperature and the relationship is often
expressed as an exponential form:
(( T TREF ) / 10)
R  RTREF  Q10
where RTREF is the respiration rate at a reference temperature, TREF and Q10 is the relative change
in R for a 10 degree change in temperature. From the measurements of NEE the night-time data
(where NEE is only a result of RE) have been extrapolated to daytime by fitting data to
temperature. Very roughly you could say that RH, RAb, and RAa make up about 1/3 each of RAb but
it is really hard to measure the fractions and they are not constant over the season. In Lagergren et
al (2005) there is simple model based on limited data from Norunda that could be tested. Your
task would be to model RE with help of different temperatures that you give different weight
depending on their contribution. There are data of air temperature, soil temperature in different
layers and for Norunda also bole temperature. You could consider that TREF and Q10 could vary
over the season and that the simple concept of plain Q10 relationships is somewhat questioned.
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Lagergren, F., Eklundh, L., Grelle, A., Lundblad, M., Mölder, M., Lankreijer, H. and Lindroth,
A., 2005. Net primary production and light use efficiency in a mixed coniferous forest in
Sweden. Plant, Cell & Environment 28: 412-423.
Davidson, E.A., Janssens, I. and Luo, Y., 2006. On the variability of respiration in terrestrial
ecosystems: moving beyond Q10. Global Change Biology 12: 154-164.
Canopy conductance
Canopy conductance refers to aggregate stomatal conductance (gc) of leaves or the inverse of
surface resistance (1/rs) at the stand scale. Two alternative approaches focus on the dependency of
gc on photosynthesis or on humidity/evapotranspiration. Ball and Berry‟s model (Collatz et al.
1991 Agricultural & Forest Meteorology 54: 107-136), which includes photosynthesis (Aleaf) as a
dependent variable, has the potential advantage of accounting for the commonly observed
reduction in stomatal conductance under elevated atmospheric CO2:
gc  m
Aleaf h
b
CO2 
(Eqn 1 in Collatz et al. 1991) where Aleaf is leaf-level net photosynthesis, h is relative humidity,
[CO2] is the concentration of CO2 in the air and m and b are empirical parameters.
Direct measurements of gc are not available for Norunda or Hyytiälä. In order to calibrate the
empirical parameters m and b you will therefore need to construct artificial time-series of gc using
an independent approach. For this purpose you are recommended to utilise a rearrangement of the
Penman-Monteith equation which expresses the surface resistance as a function of latent heat flux
or evapotranspiration:
D


 s ( Rn  G )   a c p

ra s 

1 / g c  rs  ra 
 1


E  





Where Rn is net radiation (incoming minus outgoing radiation in all wavelengths, Wm2); G is
soil heat flux (Wm2); a is the density of air, kg m3; cp is the specific heat of air, J kg1 [°C]1; D
is vapour pressure deficit (kPa); E is evapotranspiration (mm s1, or kg m2 s-1);  is the
psychrometric constant, 0.066 kPa [°C]1;  = latent heat of vaporisation of water, 2.42 MJ kg1; s
is the slope of the response of saturation vapour pressure to temperature, 0.212 kPa [°C]1. In
reality, ,  and s vary with temperature, but may be assumed constant at the values given above
under a normal growing-season temperature range of 5-25 °C. Finally, ra is the aerodynamic
resistance, given by:
ra
2

ln(( z  d ) / z 0 )

k 2u
where k is the von Karman constant, 0.41; u is wind speed (ms1), z is height at which wind
measurements were made; d is 2/3 of the height of the forest canopy; and z0 is roughness length,
given by 0.02d.
Evapotranspiration
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You may use the Priestley-Taylor equation for canopy evapotranspiration E (mm s1, or kg m2 s1
):
E  
s( Rn  G )
s 
where  is an empirical parameter, the Priestley-Taylor coefficient; Rn is net radiation (incoming
minus outgoing radiation in all wavelengths, Wm2); G is soil heat flux (Wm2);  is the
psychrometric constant, 0.066 kPa [°C]1;  = latent heat of vaporisation of water, 2.42 MJ kg1; s
is the slope of the response of saturation vapour pressure to temperature, 0.212 kPa [°C]1. In
reality, ,  and s vary with temperature, but may be assumed constant at the values given above
under a normal growing-season temperature range of 5-25 °C.
You are advised to calibrate your model to a subset of your data, encompassing a full growing
season, by fitting the modelled E to measured evapotranspiration from the study site, by adjusting
. Rainy days should be avoided in the calibration data, as evaporation of water intercepted by
the canopy will interfere with the estimates of E. Keep careful track of units in your model and in
the measured data. The resultant model may then be applied to and validated for another subset of
the measurement data.
Soil hydrology
A simple but often adequate model of soil water balance treats the soil as a „leaky bucket‟ that is
filled by rain and depleted through evapotranspiration and groundwater discharge. The bucket is
implemented as a dynamic model with a single state variable, the soil water content  (mm).
Every timestep, the net change (flux) of soil water is computed as:
  P  E  Q
where P is precipitation, E is evapotranspiration and Q is groundwater recharge, all in mm.
Excess rainfall over and above the capacity of the bucket (the available water holding capacity of
the soil, max, in mm), results in loss through surface runoff. E may be estimated following the
Priestley-Taylor approach (see Evapotranspiration above). Q typically depends on  and soil
texture, e.g. (Neilson et al. 1995; Ecological Applications 5: 362-386):
 
Q   k 
  max



2
where k is an empirical parameter that may be calibrated for a subset of the available
measurement data.
Light extinction
Attenuation of light in the canopy of a forest stand is often characterised by Beer‟s law:
I  I 0 exp( k  LAI)
where I is the attenuated (remaining) amount of the incident (incoming) light I0 at the top of a
canopy with a given leaf area index (LAI), and k is an extinction coefficient that depends on the
architecture and density of the canopy. You are advised to implement a more advanced light
extinction model based on Beer‟s law, dividing the canopy into layers, and calculating the
attenuation in each layer according to the fraction of LAI in that layer, i.e.
NGEN02 Ecosystem Modelling
I z where I i  I i 1 exp( k  LAIi )
for z layers, where LAIi is the leaf area index of a given layer, counting from i=1 for the topmost
layer. LAI values for different depths within the canopy are available in the meta-data for
Norunda. Simultaneous measurements of PAR (photosynthetically active radiation) above and
below the canopy are available for two seasons, 2001 and 2004. You may calibrate k using the
data for one of these seasons, and may validate the model using data for the other season.
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