We examined parameter optimisation in the JSBACH

The tuning provided estimates for full distribution of possible parameters, along with information about correlation, sensitivity and identifiability. Some parameters were correlated with each other due to a phenomenological connection between carbon uptake and water stress or other connections due to the set-up of the model formulations. The latter holds especially for vegetation phenology parameters. The least identifiable parameters include phenology parameters, parameters connecting relative humidity and soil dryness, and the field capacity of the skin reservoir. These soil parameters were masked by the large contribution from vegetation transpiration.

In addition to leaf area index and the maximum carboxylation rate, the most
effective parameters adjusting the gross primary production (GPP) and
evapotranspiration (ET) fluxes in seasonal tuning were related to soil
wilting point, drainage and moisture stress imposed on vegetation. For daily
and half-hourly tunings the most important parameters were the ratio of leaf
internal CO

The seasonal tuning improved the month-to-month development of GPP and ET, and produced the most stable estimates of water use efficiency. When compared to the seasonal tuning, the daily tuning is worse on the seasonal scale. However, daily parametrisation reproduced the observations for average diurnal cycle best, except for the GPP for Sodankylä validation period, where half-hourly tuned parameters were better. In general, the daily tuning provided the largest reduction in model–data mismatch.

The models response to drought was unaffected by our parametrisations and further studies are needed into enhancing the dry response in JSBACH.

Inverse modelling of ecosystem model parameters against in situ observations
is an established way to tune model parameters

In this study we perform site level parameter optimisation in the JSBACH
model

The motivation for this study comes from results showing that CMIP5 model
simulations, one of which is MPI-ESM, have systematic evapotranspiration
biases over continental areas

In this study we apply the JSBACH ecosystem model for Hyytiälä

The goals of this study are to test the applicability of the AM optimisation method for JSBACH and the impact of different temporal resolutions on the optimisation process, and to improve the models response to environmental drivers, focusing on dryness.

In this study we use site level data from two Finnish measurement sites:
Hyytiälä (61

Hyytiälä site is a Finnish Scots pine (

The Sodankylä forest, in Sodankylä at the Finnish Meteorological
Institute's Arctic Research Centre, is also a Scots pine forest (

The CO

The EC instrumentation in Hyytiälä consisted of a Solent 1012R3
three-axis sonic anemometer (Gill Instruments Ltd., Lymington, UK) and a
LI-6262 closed-path CO

The measurement error in the EC flux data may be classified into two
categories: systematic errors and random errors. The main systematic errors
(density fluctuations, high-frequency losses, calibration issues) are mostly
corrected for as part of the post-processing of the data, and the random
errors tend to dominate the uncertainty of the instantaneous fluxes. The
random error is often assumed Gaussian but can be more accurately
approximated by a symmetric exponential distribution

JSBACH is a process-based ecosystem model and the land surface component of
the MPI-ESM. We
used JSBACH offline using an observational atmospheric data set to force the
model. Implications of this one-way coupling with the atmosphere include lack
of feedback from the surface energy balance to the atmosphere; i.e. latent
and sensible heat fluxes and surface thermal radiation do not directly affect
prescribed air temperature or humidity. Similarly, the feedback of surface to
the vertical transfer coefficients within the atmospheric surface layer is
missing, as the wind speed that drives mixing is prescribed. Furthermore,
since we use site level data (a single grid point), the grid resolution does
not affect the results

In JSBACH the land surface is a fractional structure where the land
grid cells are divided into tiles representing the most prevalent vegetation
classes called plant functional types (PFTs) within each grid cell

Coniferous evergreen trees are characterised by a set of parameters that
control vegetation-related biological and physical processes accounting for
the land–atmosphere interactions. We made use of expert knowledge to set
these parameters for our local sites and verified that they are in line with
those presented by

The seasonal development of LAI is regulated by air temperature and soil moisture with a specific maximum LAI as a limiting value. The cycle is driven by a pseudo soil temperature that is a weighted running mean of air temperature. The predictions of phenology are produced by the Logistic Growth Phenology (LoGro-P) model of JSBACH.

Photosynthesis is described by the biochemical photosynthesis model

The photosynthetic rate is resolved in two steps. First the stomatal
conductance under conditions with no water stress is assumed to be controlled
by photosynthetic activity

Radiation absorption is estimated by a two-stream approximation within a
three-layer canopy

Before tuning the JSBACH model, some of the more slowly changing variables (e.g. LAI) need to be equilibrated in order to bring the model into a (semi-)steady state. We achieve this by running the model through a spin-up period generated by looping the measurement interval over itself. During this period the necessary variables are equilibrated and their values become acceptable for the tuning process. At the end of the spin-up a restart file is generated so that the model can be restarted from this state.

We use half-hourly measurements from 1999 to 2008 for Hyytiälä. The spin-up finishes at the end of 1999 and is followed by a calibration period (abbreviated as HC for Hyytiälä calibration) of 2000–2004 and a validation period (HV for Hyytiälä validation) of 2005–2008, including an exceptionally dry summer in 2006. The set-up for Sodankylä is similar but we use measurements from 2000 to 2008, where the spin-up finishes at the end of 2008. The model is then restarted from the start of 2000, but we only examine the Sodankylä validation period (SV) of 2005–2008. The main reason to exclude the Sodankylä calibration period is that essentially we do not calibrate (or tune) the model for Sodankylä and we do not want to appear to do so.

The meteorological data used to drive the climate were air temperature, air
pressure, atmospheric CO

Parameter descriptions with references to equations in Appendix

The JSBACH model was modified to fit our custom-built test bed so that all
parameters of interest could be read from an external file. We examined
15 parameters (Table 1) that are for convenience separated into three classes.
The class I parameters are used differently from those of class II and III –
namely,
class I parameters are only tuned in the seasonal tuning
(explained in detail in Sect. 3.1). Additionally, the only distinction
between class II and III parameters is that the latter belong to a specific
part of JSBACH called the LoGro-P – there
is no difference in how these parameters are used. We also note that the only
parameter (of those examined) that can vary from site to site is veg

The parameter sampling in this study was done with the AM
algorithm. The AM algorithm is an adaptive Markov chain Monte Carlo (MCMC)
process described below (it is not strictly Markovian but satisfies
the necessary ergodicity requirements). AM is based on the classical
Metropolis algorithm, extended with the adaptation of the parameter proposal
distribution. Due to the adaptive nature of AM, it does not rely on the
choice of the initial proposal distribution. AM is a sampling method that
produces estimates of the full distribution of possible parameter values
(unlike straightforward optimisation methods), thus enabling, e.g., the study of
parameter identifiability, sensitivity and (nonlinear) correlation – this
information is paramount to understanding the optimisation process in
contrast to merely receiving the optimised parameter values. The rigorous
mathematical presentation of the AM algorithm is given in

The AM algorithm draws samples (sets of parameters) from the parameter space
to generate probability distributions for the parameters. The consecutive
draws form an MCMC chain. We used the algorithm simultaneously for several
independent chains that are parallel adaptations of the algorithmic process

Draw a new sample (

Calculate the acceptance ratio (

Accept the new candidate (

The cost function (Eq.

The optimised parameter values are taken as the mean values of all chains in the sampling process. In the case that the parameter chains converge to a bound of an a priori prescribed range of allowed values, the maximum a posteriori (MAP) value is used instead. After tuning the model, we analysed different aspects of this process. Class I parameters are excluded from this analysis since they are used to bring the model to an “acceptable initial state”; hence, we regard them as a part of the model initialisation (our motivation is explained in Sect. 3.1).

We calculated the correlations and correlation matrices between different
parameters for different tunings using the tested parameter vectors in the AM
process. Then we performed a principal component analysis (PCA) on the
correlation matrices to get the eigenvectors (

The information derived with PCA could be extracted by analysing the
parameters posterior probability distributions, but PCA yields a simple,
straightforward method for the same purpose. The main caveat of the standard
PCA method is that it is not applicable to cases with strong nonlinear
correlations. Therefore, we also calculate kernel density estimates (KDE) for
the parameters to show that there are no nonlinear correlations. The KDE
method places a Gaussian distribution (kernels) centred at each parameter of
the MCMC chain and then sums these kernels to produce an estimate for the
whole distribution. The bandwidth is calculated using the Scott's rule

We also wanted to examine which parameters contributed the most to the change
in the cost function values as we switched from one parameter set to another.
This was done by calculating the change in the cost function values of the
tuned parameter set and a set where one parameter has been reverted to the
value the tuning started with (henceforth, the reference values are for seasonal
tuning the default values and for daily and half-hourly tuning the
seasonally tuned values). We call this method “relative
effectiveness”, since we want to analyse the effect of the parameters to the
cost function. For each tuned set of parameter values, the relative
effectiveness of a parameter is calculated as follows:

change one parameter from the set of tuned parameter values to a reference value and calculate the difference in the cost function for the changed set and the tuned set;

return the changed parameter to the tuned value and repeat for all parameters (sum up the differences);

the relative effectiveness for each parameter is the difference obtained from step 1 divided by the sum from step 2.

Lastly, we calculate the root mean squared error (RMSE;

The model was optimised for Hyytiälä with the AM algorithm using three different timescales: seasonal, daily and half-hourly tuning, which are described below. Tuning was done on a powerful laptop with an Intel Core i7-3520M processor. We removed unwanted output streams from the model and tweaked the I/O. With a single core the spin-up generation takes approximately 150 s, the run through calibration period with daily output takes 20 s and with half-hourly output 320 s. We used daily output also for the seasonal tuning.

The fundamental motivation for the seasonal tuning is to ensure that the
model reproduces the observed growing season maximum of LAI, since we have
previously noticed that JSBACH underestimates LAI at the site level (even the
default value of

All three class I parameters are tuned with four independent chains each consisting of 3000 samples. This step required a 30-year spin-up for each sample separately.

Class II and III parameters are each separately tested with 24 evenly separated values for an extensive range and those nine parameters that did not yield a negligible difference in the maximal and minimal values in the objective function are tuned. The consequent tuning was done with eight independent chains each consisting of 10 000 samples. A single spin-up, common for all samples, used optimal parameter values from step 1 and default values for the rest of the parameters.

All the previously tuned 12 parameters with eight independent chains each consisting of 10 000 samples are returned. Initial proposal covariance was generated from previous step and spin-up was generated separately for each sample.

The highest correlations between parameters.

The difference in daily and half-hourly tuning is the time interval used in
the model output and observations in the cost function (Eq.

It should be noted that even though the cost function (Eq.

After tuning the model for Hyytiälä we took the parameter set from
seasonal tuning and re-tuned only the maximum LAI parameter (

The parameters and cost function components involved in the different phases of the optimisation process need to be studied before the performance of the optimisation method can be evaluated.

As noted above, we decided to reject the unreliable wintertime ET values. This masking leaves out the start of the growing season, which reduces the reliability of some of the tuned parameters, including all the LoGro phenology model parameters (class III), which mostly affect the timing of the spring event and regulate the development of the LAI towards the peak season. However, as a result of the tuning processes, all the analysed parameters were revealed to have unimodal posterior probability distributions, with different skewness and deviations.

We analysed the correlations and effectiveness of the parameters in the seasonal, daily and half-hourly optimisations on the Hyytiälä site for the calibration period. We also analysed the contributions from the cost function components referring to ET, GPP and LAI and generated the time series and daily cycles of GPP and ET for both Hyytiälä and Sodankylä sites. For all these examinations, individual spin-ups were generated using the optimised parameter values.

The parameter correlations (Table 2) do not reveal much information, which is common for larger systems where the underlying parameter dependencies are more complex. Usually more sophisticated methods are used to analyse the parameters, but we omit these examinations here since pairwise Kernel density estimates (Fig. 1) did not reveal any new insights.

The strongest correlation was between the ratio of leaf internal CO

Approximately half of the parameters with high correlation are also the least identifiable (Table 3) with the given data and cost function. This means that the values these parameters acquire, as a result of the tuning process, are the most unreliable – it does not reflect on the parameters contribution to the cost function. The PCA merely highlights where most of the parametric unreliability lies.

Significant components of principal component analysis for the different tunings. The given parameters are the most dominant within the component and the ratio is how many times larger the factor related to the first parameter is when compared to that of the second. Coverage reveals how much of the component is accounted for by the given parameters (sum of the weights of given vector components).

Kernel density estimates of the last 20 000 parameter samples with
daily (upper triangle) and half-hourly tunings. The contours correspond to
densities in a two-dimensional Gaussian distribution (

The PCA analysis revealed that most of the unreliability is explained by a
handful of parameters. Disregarding those of the LoGro phenology model, the
two most dominantly unreliable parameters in every tuning were the fraction
depicting relative humidity based on soil dryness (

Default and optimised parameter values using the last 20 000 samples (if no value is given, the parameter was not part of that tuning, and the default value was used instead). The percentage next to a parameter value is the effectiveness of that parameter for that tuning. The reference values for seasonal tuning are the default values and for daily and half-hourly tunings the seasonal values.

The default and optimised parameter values from the different tuning metrics are presented in Table 4 along with their relative effectiveness. The reference values for seasonal tuning are the default values. Since we fixed class I parameters with seasonal tuning, the realistic reference values for daily and half-hourly tunings are the seasonal parameter values. Here we note that using one spin-up for all daily and half-hourly optimisation runs is computationally justifiable but generates errors as the general spin-up differs from those generated by the optimised parameters. These errors are relatively small but give rise to, e.g., the negative relative effectiveness values in daily and half-hourly parametrisations.

Most seasonally tuned parameters are near their default values and the most
effective parameters are the fraction of soil moisture above which
transpiration is unaffected by soil moisture stress (

When we compare the model output streams with seasonal against those with
default parametrisation, we notice that the average evapotranspiration for
the calibration period has increased 15 %. Most of this is due to not only added
transpiration (18 % increase) but also increased evaporation (6 %). In
addition drainage was accelerated by 11 %. These increases are mostly
compensated by a 15 % reduction in average soil moisture. In addition soil
moisture values that are under the limit when transpiration is affected by
soil moisture stress (below the value of

The daily and half-hourly tunings lower the average evapotranspiration by
22 and 35 % respectively, when compared to the seasonal values.
Transpiration is decreased by 28 and 37 %, whereas evaporation is increased
by 0.5 % and decreased by 28 % respectively, for daily tuning and half-hourly
tuning. Soil moisture is increased by 11 and 8 % and the amount of values
below

Cost function components for each parametrisation for Hyytiälä
calibration (HC), Hyytiälä validation (HV) and Sodankylä validation (SV) periods.

Using the optimised values (parametrisations), we calculated the components of each cost function for Hyytiälä calibration period and Hyytiälä and Sodankylä validation period (Table 5).

First, we note that with the default parameters

Second, the value of the

Third, for the cost function (Eq.

Lastly, we examine how the algorithm and cost functions have performed. The
best parameter set (the lowest cost function value) for a given cost function, in
each of the three different periods (HC, HV, SV), is the same as that used
in the corresponding tuning process. For example the lowest value for cf

The overall structure of the model time series was not affected by the
parametrisations obtained with different tunings (Figs. 2 and 3). Some
time series characteristics have been enhanced and others reduced but the
timing of the peaks and dips in GPP and ET are the same as before. The
corresponding RMSE and bias estimates are given in Table 6. In comparison we
estimated the PRELES model biases for Hyytiälä from Fig. 5 in

RMSE and bias of ET and GPP calculated from half-hourly data for first two summers of the validation period for Hyytiälä (corresponding to Fig. 2) and last two summers of the validation period for Sodankylä (corresponding to Fig. 3).

Hyytiälä 7-day-running mean time series for different tunings for the first two summers of the validation period. Solid black line represents the observations.

Sodankylä 7-day-running mean time series for different tunings for the last two summers of the validation period. Solid black line represents the observations.

The best seasonal performance was obtained by seasonal tuning as we previously noted from the cost function components (Table 5). Even though the optimisation is done on the seasonal level, especially the GPP cycle is noticeably improved from that generated by the default parameters. This tuning also gives rise to the most stable (least fluctuating) water use efficiency (WUE), when calculated as a pointwise ratio of GPP and ET. We use WUE here only as a diagnostic variable to examine the balance between the GPP and ET.

When compared to the seasonal tuning, the daily tuning is worse on the seasonal scale and lowers both the ET and GPP cycles. WUE follows the observations better but starts to give rise to some fluctuation. With half-hourly tuning, this behaviour is further enhanced and especially ET is lowered to too low levels, which manifests the high WUE values. The worsening in the model time series with daily and half-hourly tunings are explained by biases in the diurnal cycle.

Average diurnal cycle from May to September for the validation period.

Daily averages for ET, GPP and WUE on a dry event in 2006 for Hyytiälä.

Average diurnal cycles with different parametrisations (Fig. 4) show that modelled night-time ET values are too low when compared to the observed and this behaviour was not affected by the tunings. Low night-time values are compensated by too high midday values in the default and seasonal tuning so that the average daily and seasonal values are on an acceptable level. For the daily and half-hourly tuning, the algorithm lowers the daytime values, which results in too low average daily and half-hourly values. It is noteworthy to mention that with the default setting we get too low GPP for Hyytiälä but too high GPP for Sodankylä. The unrealistic wintertime and the biased night-time ET values actually have the same origin. Since we do not have the coupling from the land surface model (LSM) back to the atmosphere, we get an erroneous energy balance as we lose the energy released by condensation.

Disregarding the default parametrisation we notice that seasonal parametrisation show the highest values, daily in the middle and half-hourly show the lowest values. Daily parametrisation reproduces the observations for average diurnal cycle better than the others in every occasion except the GPP for Sodankylä, where half-hourly tuning is better (verified by pointwise RMSE from the average diurnal cycle). We also notice that Sodankylä daily patterns, and to some extent Hyytiälä as well, are slightly out of phase. Our current understanding is that this is (at least partly) due to a slightly misaligned sensor (which can cause significant errors on high latitudes), measuring radiation fluxes. Fortunately this affects mainly the cost function for half-hourly tuning since it is the only one operating on the densest half-hourly timescale.

Dry period in the summer 2006 can be clearly located by the massive drawdown in observed GPP, and to a lesser extent in ET, at Hyytiälä (Fig. 2). In a closer look at this event (Fig. 5) it is evident that none of our parametrisation schemes were able to capture it correctly. As it was with the time series, the overall structure of the daily time series during this event remains the same (there are no divergent aspects in the model output between the different tunings).

During the drought event (defined here as 31 July–15 August 2006), the soil moisture
is on average 27 % lower for default, daily and half-hourly tuning and 40 %
lower for seasonal tuning when compared to the corresponding values from
other years – seasonal tuning has the lowest overall soil moisture. During
this event the modelled soil moisture decreases monotonically for all tunings
and reaches the lowest values on 13 August, after which it starts to
rise. During the period the modelled ET and GPP are predominantly higher than
the observations. WUE on the other hand follows the “observations” remarkably well and deviates from the observed only towards the end of the
event when modelled ET drops to near-zero values, coinciding with the lowest
modelled soil moisture values.

Initially we tuned the model to produce near-measured seasonal ET, GPP and especially maximum LAI to enhance the vegetation transpiration and to emphasise the response to precipitation. This was done successfully with seasonal tuning in the hopes of bringing forth the underlying model responses to dryness. With the consecutive daily and half-hourly tunings, we managed to improve the average diurnal cycles of both ET and GPP, but failed in reproducing the low ET and GPP levels during the dry event in 2006. Effectively we first (seasonal tuning) transferred water from soil moisture into (too high levels of) ET, and later (with daily and half-hourly tunings) transferred some of it back.

In addition to the maximum LAI (

Despite the fact that we were unable to enhance the dry response of the model, we are confident in saying that the algorithm itself worked well and performed as intended with the daily tuning providing the most reduction in model–data mismatch. We optimised 12 parameters simultaneously (with daily and half-hourly tunings) using eight fairly short chains (8000 samples). With daily tuning the resulting estimates are well matured, but with half-hourly tuning the parameter deviations are larger (which is probably due modelling inefficiencies and noise in measurements). Nevertheless, all optimisation procedures worked well with regard to what was optimised (seasonality, daily averages or diurnal cycle).

Recently,

The measurement data required to run and tune the model can be procured from the
FLUXNET database (

In this Appendix we present the main equations that the parameters in this study affect.

The parameters from the LoGro-P model, which are of interest here, are mainly
used to determine the spring event for JSBACH. The maximum all-sided leaf area index (

The Farquhar model is based on the observation that the assimilation rate in
the chloropast is limited either by the carboxylation rate (

In JSBACH, the soil water budget is based on several reservoirs (skin,
soil, bare soil, rain intercepted by canopy, etc.) and the different
formulations are plentiful. We present here only the most crucial of these.
Changes in soil water (

Evaporation from wet surfaces (

Tuula Aalto, Heikki Järvinen, Tiina Markkanen and Stefan Hagemann chose the parameters in the optimisation process and provided support throughout the experiments. Mika Aurela and Ivan Mammarella provided knowledge on the observations. Jouni Susiluoto provided the algorithm test bed and Jarmo Mäkelä integrated the model into the test bed, ran the experiments and prepared the manuscript with contributions from all co-authors.

This work was funded by the European Commission's 7th Framework Programme, under grant agreement no. 282672, EMBRACE project, and the Nordic Centre of Excellence “Tools for Investigating Climate Change at High Northern Latitudes” (eSTICC) under the Nordic Top-Level Research Initiative. This work was also supported by the Academy of Finland Center of Excellence (no. 272041), ICOS-Finland (no. 281255) and ICOS-ERIC (no. 281250) funded by Academy of Finland. This work used eddy covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia and USCCC. The FLUXNET eddy covariance data processing and harmonisation was carried out by the ICOS Ecosystem Thematic Center, AmeriFlux Management Project and Fluxdata project of FLUXNET, with the support of CDIAC, and the OzFlux, ChinaFlux and AsiaFlux offices. Edited by: O. Talagrand Reviewed by: two anonymous referees