Quantifying how vegetation phenology responds to climate variability is a key prerequisite to
predicting how ecosystem dynamics will shift with climate change. So far, many studies have focused
on responses of classical phenological events (e.g., budburst or flowering) to climatic variability
for individual species. Comparatively little is known on the dynamics of physio-phenological
events such as the timing of maximum gross primary production (

Phenology is the study of the timing of biological events that can be observed at either the
organismic level or the ecosystem scale

The eddy covariance (EC) technique allows us to continuously measure the exchange of energy and
matter between ecosystems and the atmosphere

In this study we focus on understanding how climate variability affects the time when ecosystems
reach their maximum potential for

The challenge of understanding phenology is generally to characterize a discrete event that repeats
periodically. Classically, phenological analyses have been performed using linear regression models

Conceptual distribution of GPPmax timing (

Figure

In recent years, circular statistics have gained some attention as they offer a solution to problems
of this kind

In this paper, we aim to identify the factors controlling the timing of the maximal seasonal GPP
(

We use 52 EC sites (with at least 7 years of data) located throughout the latitudinal gradient of
the globe from the FLUXNET2015 database

Given that the past climate conditions affect the

The decay function gives the instantaneous value a weight of 1 (

Due to the high colinearity between the exponential weighted variables of Tair, SWin, and VPD, we
perform a principal component analysis (PCA) on the matrix of variables and FLUXNET sites and retain
the leading principal component of these variables as well as precipitation as input for the circular
statistics model

Since units of the circular response variable must be in radians or degrees, we transform the days
of the year to radians using Eq. (

A basic circular regression model was proposed by

Relevant interpretations of fitted circular regression models are (1) the sign of the

To estimate the relative sensitivity of

Interpretation of the coefficients in the circular regression considering a reference point
(black) generated with a circular–linear model with mean angular direction (

To assess the performance of linear versus circular regressions we perform an experiment with
simulated data in which we evaluate the accuracy and precision of both approaches to recover original
regression coefficients in a circular setting (Eq.

To quantify the accuracy of each model per coefficient we estimate the mean absolute error per model
and coefficient (Eq.

We estimate regression coefficients for the bootstrap sample

The target variable

To quantify the contribution of each climate variable, we count the number of sites per vegetation type where the regression coefficient is statistically significant. We perform a leave-one-out cross-validation per vegetation type to evaluate the predictive power of the circular regression using climate conditions. We only consider vegetation types with more than five sites. In this case the standardization of the climate variables is not applied. Finally, we use the mean of the optimum half-time parameter per vegetation type to weigh the climate conditions.

Here, we first report results from simulated data to describe the performance of the circular regression approach compared to a linear model. Second, we compare the performance of circular and linear regression using empirical data. Third, we analyze the sensitivity of

Figure

Accuracy and precision of linear and circular regression models by recovering the original regression coefficients of a circular regression.

To illustrate the method in practice, we compare the circular and linear models using data from two
sites: US-Ha1 (Northern Hemisphere, deciduous broadleaf forest) and AU-How (Southern Hemisphere,
woody savanna). We relate the climate variables with

Correlation coefficient between the observed and predicted

From the 52 sites analyzed in this study, only one site (ES-LJu) shows bimodal growing seasons (see
Supplement 1.2). As expected, in most cases

For half of the sites, the JS correlation coefficients are between 0.70 and 0.97 (Supplement 1,
Fig. S5), showing that the interannual variability of

We find that air temperature, shortwave incoming radiation, and vapor pressure
deficit appear as the dominant drivers worldwide at 43 of the total sites (84 %; Supplement 3). Precipitation
is the main driver for five sites (AU-How US-Ton ZA-Kru US-SRM US-Wkg; Supplement 3). Interestingly,
precipitation was the most important factor for all the woody savanna sites (Supplement 3). For
three sites (DE-Gri, IT-Ro2, BRSa1), any climatic variable is significant. In terms of the sign of
the coefficients, all the variables are predominantly negative
(Table

Number of FLUXNET sites where each regression coefficient is statistically significant to
explain the physio-phenology of GPPmax (

The PCA between shortwave incoming radiation, air temperature, and vapor pressure deficit has the
highest frequency of significant correlation coefficients by number of sites for all the vegetation
types with the exception of woody savannas (WSAs), where precipitation is shown to be more important for most
sites than the dimensionality reduction between Tair, SWin, and VPD
(Fig.

Contribution of each climate variable to explain the interannual variation in

A special case for understanding the sensitivity of

The leave-one-out cross-validation for several vegetation types shows that the predictive power
of the model for grassland (GRA) and evergreen broadleaf forest (EBF) is

Cross-validation of the circular regression model to predict

We explored whether circular regression is a suitable tool for analyzing phenological events. Our results suggest that circular regressions can recover predefined coefficients in a set of simulations with higher accuracy and precision than linear regressions. Hence, we would generally suggest that circular regressions may be advantageous when the aim is analyzing the effect of climatic variables on phenological events. We also found cases where the classical linear regression may be either more robust or equally suitable, e.g., when phenological events are reached close to midyear. In the overall view, however, we consider that circular regressions are to be preferred over linear regression for their conceptual capacity to analyze the physio-phenology of ecosystems regardless of the day of the year when an event of interest occurs. This allows us to analyze phenological studies at the global scale regardless of geographic location or the distribution of the observations during the year.

Different phenological models have been developed, ranging from empirical approaches

The geographical location of the FLUXNET2015 sites represents an advantage when capturing the

The high values of the JS correlation coefficients for most of the sites demonstrate that the
interannual variability of

Our results suggest that there is no pattern between the

While there is no clear relationship between the

On a global scale, our analysis shows that the combination of air temperature, shortwave incoming
radiation, and vapor pressure deficit as well as precipitation has a negative sign. This means that
if these variables increase during the growing season, the GPPmax will be reached earlier. Our
results are similar to those obtained by

Ecosystems with two growing seasons per year represent a very interesting case of the effect of
climate drivers on

Phenology in Mediterranean ecosystems is mainly controlled by water availability

Complex interactions between climate variables and phenological response and the interspecificity of
the sensitivity at the site level explain in part the poor predictive power of the model for grasslands,
evergreen broadleaf forest, evergreen needleleaf forest, and deciduous broadleaf forests in the
cross-validation analysis (Fig.

In this study we explored the potential of “circular regressions” to explain the physio-phenology of
maximal

FLUXNET sites used in our study. We report the name of the sites, the time period used for the analysis, and the climate class of each site following Köppen–Geiger classification: tropical monsoon climate (Am), tropical savanna climate (Aw), cold semiarid climate (BSk), humid subtropical climate (Cfa), oceanic climate (Cfb), hot summer Mediterranean climate (Csa), warm summer Mediterranean climate (Csb), humid subtropical climate (Cwa), humid continental climate (Dfb), subarctic climate (Dfc, Dsc), and tundra climate (ET). We also report the vegetation type of the sites: closed shrubland (CSH), deciduous broadleaf forest (DBF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), grassland (GRA), mixed forest (MF), open shrubland (OSH), savanna (SAV), permanent wetland (WET), and woody savanna (WSA).

Code is available under GPL-3 license at

FLUXNET database is available online at

The supplement related to this article is available online at:

DEPM, TM, MM, and MDM designed the study in collaboration with MR and CR. DEPM conducted the analysis and wrote the manuscript, with substantial contributions from all coauthors.

The authors declare that they have no conflict of interest.

We thank the reviewers for their helpful suggestions and Guido Kraemer for his help with the mathematical notation. This project has received funding from the European Union's Horizon 2020 research and innovation program via the TRuStEE project under the Marie Skłodowska-Curie grant agreement no. 721995. 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 ERA-Interim reanalysis data are provided by ECMWF and processed by LSCE. The FLUXNET eddy covariance data processing and harmonization were carried out by the European Fluxes Database Cluster, AmeriFlux Management Project, and the Fluxdata project of FLUXNET, with the support of CDIAC and ICOS Ecosystem Thematic Center, as well as the OzFlux, ChinaFlux, and AsiaFlux offices.

This research has been supported by the H2020 Marie Skłodowska-Curie Actions (TRuStEE grant no. 721995).The article processing charges for this open-access publication were covered by the Max Planck Society.

This paper was edited by David Bowling and reviewed by two anonymous referees.