Leaf seasonality impacts a variety of important biological, chemical, and physical Earth system processes, which makes it essential to represent leaf phenology in ecosystem and climate models. However, we are still lacking a general, robust parametrisation of phenology at global scales. In this study, we use a simple process-based model, which describes phenology as a strategy for carbon optimality, to test the effects of the common simplification in global modelling studies that plant species within the same plant functional type (PFT) have the same parameter values, implying they are assumed to have the same species traits. In a previous study this model was shown to predict spatial and temporal dynamics of leaf area index (LAI) well across the entire global land surface provided local grid cell parameters were used, and is able to explain 96 % of the spatial variation in average LAI and 87 % of the variation in amplitude. In contrast, we find here that a PFT level parametrisation is unable to capture the spatial variability in seasonal cycles, explaining on average only 28 % of the spatial variation in mean leaf area index and 12 % of the variation in seasonal amplitude. However, we also show that allowing only two parameters, light compensation point and leaf age, to be spatially variable dramatically improves the model predictions, increasing the model's capability of explaining spatial variations in leaf seasonality to 70 and 57 % of the variation in LAI average and amplitude, respectively. This highlights the importance of identifying the spatial scale of variation of plant traits and the necessity to critically analyse the use of the plant functional type assumption in Earth system models.

The ability to understand and predict leaf seasonal cycles, a process known
as leaf phenology, is essential to our understanding of Earth systems
processes, through its impact on the carbon and water cycles

One of the aspects of global vegetation models that is currently under
scrutiny is the way parameters are assigned to the simulated vegetation
within a given model grid cell. Traditionally, models make use of the plant functional type (PFT) concept. In this approach, a small number of PFTs are
defined, each with a corresponding set of parameters, then a given grid cell
is assigned to one, or a mixture of, these PFTs. However, more recently
efforts are being made to include a more biologically detailed representation
in the form of plant traits. PFTs are classes of plant species with similar
characteristics and roles within ecosystems

The main advantage of using PFTs in vegetation models is the simplicity of
the concept and the relatively small number of parameters, minimising both
the amount of data and computational effort required. Using PFTs to represent
ecological processes at global scales would be the obvious initial choice for
parameter inference because the number of parameters can be kept low while
still representing the various types of vegetation. PFTs are also a useful
concept for future climate predictions where expected changes in vegetation
type can be easily represented in this way. Dynamic global vegetation models
predict PFT distributions based either on pre-defined climate envelopes

However, there are a number of disadvantages to using the PFT approach,
mainly due to the fact that a PFT-type categorisation imposes fixed parameter
values and cannot capture the continuous variation observed in plant traits
within and among PFTs

Given the potential advantages and disadvantages of the PFT approach, it is important to formally evaluate it in comparison to alternative approaches, such as using location-specific traits, but such a formal comparison has not been carried out to date.

In the current paper we aim to investigate the use of PFT and trait-based
parameters within the framework of a data-constrained global phenology model.
We have chosen to use a previously developed leaf phenology model

We use LAI data from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Terra platform. We use the MODIS
collection 5 product MOD15A, which is available at 1 km spatial resolution
and an 8-day time step (

To drive the model, we use temperature and photosynthetically active
radiation (PAR) data from assimilated meteorological data products of the
Goddard Earth Observing System (GEOS-4)

Model parameters for leaf gain and loss processes.

We use a global PFT map, which is used in the Integrated Biosphere Simulator
Model (IBIS)

We use a global-scale mechanistic phenology model

To describe leaf gain, we define the concept of target LAI as the optimum
number of leaf layers for a given light level at the top of the canopy

Following the optimality hypothesis, leaves are lost when their carbon
assimilation is less than their respiration and maintenance costs, defined as
the limit assimilation value

To account for water limitation to assimilation and, implicitly, phenological
processes, we introduce a factor

Similarly, we define an age factor

To calculate the overall canopy LAI loss, we can then sum over all age groups.

We use five different model parametrisation to explore the extent to which
the PFT approach is applicable to a data-constrained phenology model. The
first such model setup, previously used in

The second model setup is using one set of parameters for each PFT, resulting
in only 182 parameters for the entire globe. We term this the

To test the extent to which each parameter represents local characteristics,
in the final model setup one or more parameters are location specific while
the rest have PFT-wide values. We then term a parameter local if it has a
specific value at each grid cell. This setup is the

We fitted all models to the data using a custom Markov chain Monte Carlo (MCMC)
algorithm, known as the Filzbach algorithm
(

Goodness of fit metrics for all five model parametrisations: root mean square error (RMSE) normalised by mean LAI value, difference in observed and predicted mean LAI and difference in observed and predicted annual amplitude. All metrics here are median values across the globe and the two difference values are shown as absolute values.

Root mean squared error (RMSE) of predicted LAI over the model study period for the local, PFT, and combined models. All values have been normalised to the mean observed LAI at all locations.

For the global, regional and PFT models, the likelihood estimation is carried
out at the global, regional or PFT level, the likelihood being calculated as
the sum at all locations

Without separating training and test data in this way, the more parameter-rich models would be guaranteed to give a better fit to the data. Separating the training and test improves our ability to assess model performance, although, given that the training test data are separated by a relatively short time and not separated in space, we expect a tendency for the more parameter-rich models to provide superior performance against the test data.

Difference between predicted and observed annual mean LAI (left) and seasonal amplitude (right) for the local, PFT, and combined models. All values have been normalised to the mean observed LAI at all locations

To compare the different types of models described above, we define several model performance metrics against the test data. The best model should be able to capture both the timing and magnitude of the seasonal cycle at each location and the spatial variability in seasonal cycles across the globe. As an overall measure of fit we use the root mean squared error (RMSE) normalised by the mean LAI, which is a measure of the fit at each particular location. The mean LAI and LAI amplitude describe the magnitude of the seasonal cycle and we use the percent of variation explained to capture the extent to which the model describes their spatial distribution. Similarly, we use the start and end of the growing season to describe the timing. We define the start of the growing season as the first date of the year when the LAI reaches 0.2 of the maximum LAI, while the end of the growing season is the equivalent last date. To capture the timing in tropical areas with a less pronounced seasonal cycle, we also use the timing of maximum LAI. All metrics are reported for the model evaluation period (2006).

Comparison of predicted and observed mean LAI and seasonal amplitude for the local, PFT, and combined models for tropical (green), temperate (red), and boreal (blue) forest PFTs.

Comparison of predicted and observed mean LAI and seasonal amplitude for the local, PFT, and combined models for tropical (green), temperate (red), and boreal (blue) grass PFTs.

We choose not to use statistical information criteria (e.g. Bayesian information criteria) because our model fitting methodology does not easily allow for the computation of a single likelihood metric. The model structure is the same for all parametrisations, with the main model differences being the number of parameters at each grid cell. However, this means that different quantities of data are also used to fit different models. For example, since the local model is fitted separately at each location, it effectively consists of 2041 separate models, each with 14 parameters, while the PFT model contains 13 models each with 14 parameters. Rather than work out a global information criterion-based metric for the models, we instead opt to use the more meaningful metrics of the relationships between the model predictions and the data described

LAI time series for all models for tropical evergreen forests, TEF
(6

Correlations between model error and fraction of each grid occupied
by the dominant PFT in the PFT model as a proxy for grid heterogeneity.

Parameter distributions for the light compensation point and age limit in three representative forest PFTs: tropical evergreen forest (TEF Amazon), temperate deciduous forest (TDF), and boreal evergreen forest (BEF). Parameter values are the mean of the fitted posterior distributions and the represented values reflect the variation in space within one PFT, for the local (top) and combined (bottom) models, as well as for the fitted PFT (black line).

An overall comparison of the five model parametrisations
(Table

Parameter distributions for the light compensation point and age limit in three representative grass PFTs: savanna (S), grassland (G), and tundra (T). Parameter values are the mean of the fitted posterior distributions and the represented values reflect the variation in space within one PFT, for the local (top) and combined (bottom) models, as well as for the fitted PFT (black line).

Figure

Figure

Posterior parameter means for the compensation point

Figures

All models show a similar ability to predict the timing of the seasonal cycle, with an error of 16 days for the start of the growing season and differences of up to 24 days for the maximum and end of the growing season, whereas in tropical evergreen forests the time of maximum LAI is 16 days earlier compared to that shown by the MODIS data.

Figure

Figure

To further investigate the observed differences arising from the model
parametrisation, we can analyse the parameter values for each different
model. Figures

Overall, all metrics show that the PFT model performs poorly across the globe, while the combination model, which has only two location-specific parameters, shows a good fit to the data.

In this paper we have investigated the capacity of a global phenology model
parametrised at the PFT level to represent observed phenological behaviour.
We show that the PFT model cannot fully capture spatial variations in LAI
mean and amplitude. In contrast, a model with local parameters results in a
better model fit, but has a very large number of parameters, which make it
very difficult to use. However, a combination model, where two of the model
parameters are local while the others are fitted at the PFT scale, performs
well with a reduced number of parameters. Our analysis shows that two
specific parameters need to have local values, the direct compensation point

The most straightforward biological explanation for the observed results of
the combined model is that the two local parameters – the light compensation
point and leaf age limit – are location-specific plant traits that vary
within a PFT sufficiently to affect model performance. Previous studies, which
have included traits as a replacement for the PFT concept, have done so
starting from biological principles, either based on trait databases

The light compensation point is not a trait commonly used in models or
included in trait data, but it is closely related to leaf photosynthetic
parameters, such as

While the light compensation point is not a common parameter in vegetation
models, measured values can be obtained from light response curves measured
for individual plant species. Reported values range from 0.5 to
16.2 Wm

Leaf longevity is one of the main parameters used in vegetation models, which
employ plant traits

Our results show that allowing two critical traits to vary within a PFT among locations provides a superior model performance. It is likely that such traits vary due to underlying factors that are not explicitly included in our model. Two likely candidates for such hidden factors are nutrient availability and canopy structure. If the effects of these factors on traits could be understood and modelled explicitly, this could dramatically reduce the number of parameters required by the model, without making the assumption that the traits are constant within any PFT.

Leaf photosynthetic capacity is a function of leaf nitrogen content

Canopy structure determines the light environment in the canopy and controls
the actual amount of light that reaches the leaves for a given light
intensity above the canopy. This means it can be of important value in
determining the compensation point, both through model structure and
long-term impact on plant behaviour. Within the model used in this study, we
assume a homogeneous canopy, with a random distribution of leaf angles and no
clumping, assumptions that can be considered valid at very large scales, but
can potentially introduce errors for certain forest structure types. It has
been shown

One of the main possible sources of error in our conclusion is the way we
have parametrised the PFT model. In most models, which use the PFT concept,
grid cells are represented as a mix of PFTs, with PFT-specific parameters
assigned to each fraction

We use space borne vegetation data from the MODIS Terra sensor, as satellite
measurements are one of the only sources of data for constraining global
level vegetation models, although they suffer from instrument error and
atmospheric contamination. We have attempted to filter the data robustly
using data quality flags, as discussed in Sect.

As more studies begin to acknowledge that the PFT concept is not necessarily the best approach to vegetation modelling, we need to quantify the extent to which the inclusion of spatially distributed parameters or plant traits improve our predictive capability and to identify the optimal number of parameters that both give a good model fit and minimise computational cost. In this study we have attempted not only to build a model with locally distributed parameters but also to quantify the extent to which a model with local parameters and one with PFT level parameters can capture the spatial variability in global LAI observations. Furthermore, we quantitatively identified which parameters need to be local to improve model performance with a view to reduce data and computational needs. We believe that the method used here for investigating the use of PFT level parameters has a high degree of generality and can be applied to a large variety of models and input data sets.

One of the advantages of the PFT concept is its capacity to represent future
changes in vegetation distribution within DGVMs. Given a predicted change in
climate, models using PFTs can then predict a change in PFT distribution,
using either predefined climate envelopes

In this paper we explored the extent to which plants within the same PFT exhibit the same phenological characteristics using a process-based global phenology model. We showed that a model with PFT-wide parameters cannot explain the observed spatial variation in seasonal cycles, but that an intermediate model with two location-specific parameters gives a good overall model fit and can reliably be used for phenological studies. The spatial patterns of these local parameters, the light compensation point, and leaf age limit might be explained by species adaptation to the local climate or nutrient and water availability, and further data are needed to fully understand the observed distribution. The modelling approach used to determine the validity of PFT level models can provide further insight for global vegetation models, which use plant functional types as a basis for upscaling measured or fitted parameter values and can hence improve global simulations of ecosystem processes.

Table

Figure

Results of principal component analysis performed for parameters obtained from the local model. The table shows correlation coefficients between the two principal axes of variation and each parameter. The first two axes of variation explain 95 % of the spatial variation in parameters.

Model goodness of fit for preliminary model runs. The parameter name shows which parameter was made local for that particular run.

Root mean squared error (RMSE) and difference in mean and amplitude of predicted LAI over the model study period for a selecion of regions in the regional model. All values have been normalised to the mean observed LAI at all locations.

We would like to thank the developers of the MODIS LAI product for providing the data that form the basis for our work. Edited by: K. Thonicke