Article acceptance date: XXX

This R-Markdown document provides step-by-step instructions for executing the analysis and producing figures presented in the paper XXX by Stocker et al. (XXX). By using RMarkdown and open access code available through this github repository, this is supposed to allow for full reproducibility of published results - from publicly accessible data files to published figures.

IP information

All code in this github repository is free software. It may be redistributed and/or modified under the terms of the GNU General Public License as published by the Free Software Foundation, version 3. Present code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License (file ./LICENSE) for more details.

Copyright (C) 2018 Benjamin D. Stocker

Below, the workflow is described to reproduce the analysis of the paper.

Environment setup

Install required R packages. The execution of the scripts provided here requires the following R packages. Install them if missing (Sorry if some are missing - It’s hard to keep the overview):

list.of.packages <- c( "dplyr", "readr", "ggplot2", "tibble", "lubridate", "ncdf4", "abind", "maptools", "sp", "fields", "RColorBrewer", "LSD", "minpack.lm", "neuroim", "raster", "Metrics", "R.matlab", "pracma" )
new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if( length(new.packages) ) install.packages(new.packages)

Define working directory:

myhome <- gsub( "soilm_global", "", getwd() )

Get additional utility functions, available from this github repository and place them in a directory that sits in the same parent directory as where you placed this repository. To test it, make sure the following returns TRUE:

if (!dir.exists("../utilities")){
  system("git clone https://github.com/stineb/utilities ../utilities")
}
print( dir.exists("../utilities") )
## [1] TRUE

Data preparation

Collect FLUXNET 2015 data, daily, from Tier 1 sites, respective environmental forcing data (meteorological variables from FLUXNET, fAPAR from MODIS FPAR). This performs a data “cleaning” of FLUXNET 2015 data (see clean_fluxnet.R), calculates additional variables and writes all data as an R data frame (tibble, data/df_modobs_<simsuite>_*.Rdata).

This step requires access to open access datasets (FLUXNET 2015, Tier 1 and MODIS FPAR MCD15A3H, extracted at FLUXNET sites), and P-model outputs from site-level simulations. For ease of reproducibility, the Rdata file (df_modobs_fluxnet2015_s16_with_SWC_v5.Rdata), created by the commands below, is made directly accessible here via this link. Download this Rdata file and place it in ./data/ by the following:

filn <- "df_modobs_fluxnet2015_s16_with_SWC_v5.Rdata"
dir <- "./data/"
if (!file.exists( paste0(dir, filn) )) {
  system( paste0( "wget http://bstocker.net/downloads/", filn ) )
  system( paste( "mv", filn, dir ) )
}

Alternatively, here’s the command for executing the functions to create this Rdata file:

source("get_modobs.R")
simsuite <- "fluxnet2015"
outputset <- c( "s16" )
if (!file.exists( paste0( "data/df_modobs_fluxnet2015_", paste( outputset, collapse="_"), "_with_SWC_v5.Rdata" ) ) ) get_modobs( simsuite = simsuite, outputset = outputset )

Data aggregation

Combine this with site-level GPP data from BESS, VPM, MODIS and MTE, and aggregate all site data into a single dataframe (tibble, data/nice_nn_agg_lue_obs_evi.Rdata for daily data, and data/nice_nn_8d_agg_lue_obs_evi.Rdata for data aggregated to 8-days periods, defined by MODIS data frequency).

if (!file.exists("data/nice_nn_agg_lue_obs_evi.Rdata") || !file.exists("data/nice_nn_8d_agg_lue_obs_evi.Rdata")){
  source("aggregate_nn_fluxnet2015.R")
}

Data filtering for soil moisture effects

The comparison of GPP from RS-models and FLUXNET observations is limited to data from a subset of sites, where soil moisture effects had reliably been identified, and to periods with clearly identified soil moisture effects. The site selection is determined by the amount of data available from respective sites (at least 500 days data for the site after data cleaning) and the reliability by which the importance of soil moisture effects was identified. This is based on the analysis by (???) and selects for sites that experience clear episodic or recurrent soil water stress and is, i.a., limited by fAPAR (MODIS FPAR) data quality (necessary to determine \(\text{LUE}=\text{GPP}/(\text{fAPAR}\cdot\text{PAR})\)). An overview of selected and not selected sites is given below.

Table: Sites used for bias evaluation
site lon lat year_start year_end classid group
AR-Vir -56.19 -28.24 2009 2012 ENF 1
AU-Ade 131.12 -13.08 2007 2009 WSA 1
AU-ASM 133.25 -22.28 2010 2013 ENF 1
AU-DaP 131.32 -14.06 2007 2013 GRA 1
AU-DaS 131.39 -14.16 2008 2014 SAV 1
AU-Dry 132.37 -15.26 2008 2014 SAV 1
AU-Fog 131.31 -12.55 2006 2008 WET 1
AU-Gin 115.71 -31.38 2011 2014 WSA 1
AU-How 131.15 -12.49 2001 2014 WSA 1
AU-Stp 133.35 -17.15 2008 2014 GRA 1
AU-Whr 145.03 -36.67 2011 2014 EBF 1
AU-Wom 144.09 -37.42 2010 2012 EBF 2
BE-Bra 4.52 51.31 1996 2014 MF 2
BE-Vie 6.00 50.31 1996 2014 MF 2
CH-Fru 8.54 47.12 2005 2014 GRA 2
CH-Lae 8.37 47.48 2004 2014 MF 2
CH-Oe1 7.73 47.29 2002 2008 GRA 1
CN-Cng 123.51 44.59 2007 2010 GRA 2
CN-Qia 115.06 26.74 2003 2005 ENF 1
CZ-wet 14.77 49.02 2006 2014 WET 2
DE-Akm 13.68 53.87 2009 2014 WET 2
DE-Geb 10.91 51.10 2001 2014 CRO 2
DE-Gri 13.51 50.95 2004 2014 GRA 2
DE-Hai 10.45 51.08 2000 2012 DBF 2
DE-Kli 13.52 50.89 2004 2014 CRO 1
DE-Obe 13.72 50.78 2008 2014 ENF 2
DE-RuR 6.30 50.62 2011 2014 GRA 2
DE-Spw 14.03 51.89 2010 2014 WET 2
DE-Tha 13.57 50.96 1996 2014 ENF 1
DK-NuF -51.39 64.13 2008 2014 WET 1
DK-Sor 11.64 55.49 1996 2014 DBF 1
FI-Hyy 24.30 61.85 1996 2014 ENF 1
FI-Sod 26.64 67.36 2001 2014 ENF 2
FR-Fon 2.78 48.48 2005 2014 DBF 2
FR-LBr -0.77 44.72 1996 2008 ENF 1
FR-Pue 3.60 43.74 2000 2014 EBF 1
IT-Col 13.59 41.85 1996 2014 DBF 2
IT-Cp2 12.36 41.70 2012 2014 EBF 1
IT-Cpz 12.38 41.71 1997 2009 EBF 1
IT-Isp 8.63 45.81 2013 2014 DBF 2
IT-Lav 11.28 45.96 2003 2014 ENF 2
IT-MBo 11.05 46.01 2003 2013 GRA 2
IT-Noe 8.15 40.61 2004 2014 CSH 1
IT-PT1 9.06 45.20 2002 2004 DBF 1
IT-Ren 11.43 46.59 1998 2013 ENF 2
IT-Ro1 11.93 42.41 2000 2008 DBF 1
IT-SR2 10.29 43.73 2013 2014 ENF 1
IT-SRo 10.28 43.73 1999 2012 ENF 1
IT-Tor 7.58 45.84 2008 2014 GRA 2
JP-SMF 137.08 35.26 2002 2006 MF 2
NL-Hor 5.07 52.24 2004 2011 GRA 2
NL-Loo 5.74 52.17 1996 2013 ENF 2
RU-Fyo 32.92 56.46 1998 2014 ENF 1
SD-Dem 30.48 13.28 2005 2009 SAV 1
SN-Dhr -15.43 15.40 2010 2013 SAV 1
US-GLE -106.24 41.37 2004 2014 ENF 2
US-Ha1 -72.17 42.54 1991 2012 DBF 2
US-Los -89.98 46.08 2000 2014 WET 2
US-Me2 -121.56 44.45 2002 2014 ENF 1
US-MMS -86.41 39.32 1999 2014 DBF 2
US-PFa -90.27 45.95 1995 2014 MF 2
US-SRG -110.83 31.79 2008 2014 GRA 1
US-SRM -110.87 31.82 2004 2014 WSA 1
US-Syv -89.35 46.24 2001 2014 MF 2
US-Ton -120.97 38.43 2001 2014 WSA 1
US-UMB -84.71 45.56 2000 2014 DBF 2
US-UMd -84.70 45.56 2007 2014 DBF 2
US-Var -120.95 38.41 2000 2014 GRA 1
US-WCr -90.08 45.81 1999 2014 DBF 2
US-Wi4 -91.17 46.74 2002 2005 ENF 2
ZM-Mon 23.25 -15.44 2000 2009 DBF 1

Fig. above: Geographical distribution of sites selected for the bias evaluation. Sites listed in Table XXX as group 1 are in green, sites of group 2 are in black. The color of land area represents aridity, quantified as the ratio of potential evapotranspiration over precipitation from (???).

In a second step, data is filtered for periods where soil moisture impacts are significant based on the parallel evolution of photosynthetic light use efficiency (LUE), temperature, vapour pressure deficit (VPD), photosynthetically active radiation (PAR), and soil moisture. Impact-relevant drought periods are defined when LUE is significantly reduced by soil moisture effects (‘fLUE droughts’ in (???)). Only data is retained for the 20-day period prior to the onset of droughts and during the duration of fLUE droughts.

if (!file.exists("data/data_aligned_agg.Rdata")){
  source("execute_reshape_align_nn_fluxnet2015.R")
}

For additional analyses with relaxed criteria for site selection and independent of the drought identification by (???), alternative data aggregation is implemented by:

if (!file.exists("data/nice_all_agg_lue_obs_evi.Rdata") || !file.exists("data/nice_all_8d_agg_lue_obs_evi.Rdata")){
  source("aggregate_all_fluxnet2015.R")
}

Bias detection

First, we evaluate the bias of different RS-model versus soil moisture and versus actual over potential evapotranspiration (AET/PET) for 71 sites (corresponding to the full list of sites shown in Table XXX). This corresponds to the selection with relaxed criteria and independent of the drought identification by (???). For all RS-models, the bias generally increases along bins of decreasing AET/PET. Note that below, boxplots are shown for the ratio of modelled over observed GPP.

source("plot_bias_all.R")
plot_bias_all( nice_agg, nice_8d_agg)

Fig. above: Bias of simulated daily GPP by models, in different bins of daily AET/PET. The bias is calculated here as the ratio of simulated GPP over observed GPP. Observational data is derived from flux measurements at 71 sites (all sites in Table XXX).

This pattern becomes clearer when applying the narrower site selection (sites in group 1 in Table XXX) and using only data during apparent droughts, i.e. where soil-moisture appears to reduce the LUE as determined by (???).

Fig. above: Bias of simulated daily GPP by models, in different fLUE bins, calculated as simulated GPP minus observed GPP, derived from flux measurements at 36 sites (sites of group 1 in Table XXX).

All RS-models, except P-model, have a tendency to be biased low under non-soil moisture-limited conditions and biased under strong soil moisture stress. To distill the pattern, independent of the mean absolute bias, we normalised simulated GPP to the median ratio of modelled-over-observed GPP in the highest fLUE bin, i.e., where soil moisture impacts on observed fluxes are small (fLUE bin 0.8-1.0).

Fig. above: Bias of simulated daily GPP by models, in different fLUE bins, calculated as simulated GPP minus observed GPP, derived from flux measurements at 36 sites (sites of group 1 in Table XXX). Simulated GPP is normalised to the median ratio of modelled over observed GPP in the highest fLUE bin (0.8-1.0).

Another way to illustrate the systematic relationship between the RS-models’ bias and the apparent soil moisture-related LUE reductions is given below. Here, the ratio of observed-to-modelled is shown along the y-axes, indicating by how much modelled GPP would have to be scaled in order to match observations. The straight red line is the 1:1 line and the fact that points cluster along it indicates that soil moisture effects on LUE are the dominant factor underlying model bias. Colors indicate the density of points.

source("plot_bias_nn.R")
plot_bias_nn( df_dday_agg, filn="./fig/bias_vs_fvar.pdf" )

Soil moisture stress functions

As documented above, there is a systematic bias of several remote sensing-based GPP models during droughts and this bias is strongly related, both in magnitude and timing, to the apparent effects of soil moisture on light use efficiency (LUE). With sufficient temporal aggregation, GPP can be expressed as a light use efficiency model (???): \[ \text{GPP} = \text{APAR} \cdot \text{LUE} \] Hence, the bias in simulated GPP (\(\text{GPP}_{\text{mod}}\)) can effectively be removed by multiplying GPP with a soil moisture stress function \(\varphi(\theta)\). Corrected GPP estimates are: \[ \text{GPP}_{\text{corr}} = \text{GPP}_{\text{mod}} \cdot \varphi(\theta) \] The apparent soil moisture-related reduction in light use efficiency (termed fLUE), separated from effects by VPD, greenness, other meteorological drivers, has been identified by (???) using a machine-learning algorithm, applied on eddy covariance flux measurement data, combined with co-located soil moisture measurements and remotely-sensed greenness. We use these results here to fit a set of soil moisture stress functions (\(\varphi(\theta)\simeq\text{fLUE}\)) based on two general patterns:

  1. The functional form of \(\varphi(\theta)\) is general across all sites and can be approximated by a quadratic function that approaches 1 for soil moisture at a certain threshold \(\theta_0\) and held constant at 1 for soil moisture values above that. Here \(\theta\) is the plant-available soil water, expressed as a fraction of field capacity. The general form is: \[ \varphi = \begin{cases} \beta(\theta - \theta_0)^2 + 1,& \theta \leq \theta_0\\ 1, & \theta > \theta_0 \end{cases} \]
  2. The sensitivity of \(\varphi(\theta)\) to extreme soil dryness (\(\theta \rightarrow 0\)) is related to the mean aridity at the site. The dryness-related decline in \(\varphi(\theta)\) is particularly strong at the driest sites (mostly deserts, grasslands, savannahs), whereas sites at intermediate aridity (mostly mediterranean) exhibit a smaller reduction in \(\varphi(\theta)\) when soil water gets depleted. In the equation above, the “sensitivity parameter” \(\beta\) is defined by the maximum \(\varphi\) reduction at low soil moisture \(\varphi_0\equiv\varphi(\theta=0)\), leading to \(\beta=(\varphi_0-1)/\theta_0^2\). \(\varphi_0\) is modelled as a linear function of the mean aridity, quantified by the mean annual ratio of AET/PET, termed \(\alpha\): \[ \varphi_0 = a + b \alpha \]

We have tested several approaches to fit parameters \(a\) and \(b\). Final fitted functions based on approaches I-III bracket fLUE values derived at our selection of sites (group 1 in Table XXX). Their definition is described below.

Approach I

Based on fLUE in lowest soil moisture bin and its relationship to mean AET/PET.

This is based on the relationship between minimum fLUE and mean AET/PET, identified in (???). Parameters \(a\) and \(b\) are calculated from a linear regression between each site’s \(\varphi_0\) and \(\alpha\). \(\alpha\) is calculated as the annual mean ratio of AET/PET, calculated from daily AET and PET values from simulations with the SPLASH model (Davis et al. 2017) (the same set of simulations as described in the Methods in the main text, section ‘Global P-model simulations’). \(\varphi_0\) is derived for each site as the mean fLUE value of data in the lowest soil moisture quartile. This defines parameters \(\varphi_0\) and hence \(\beta\) in above equations. This is identical to the linear regression of fLUE\(_0\) to soil moisture shown in Fig. 9 in (???).

In summary, this method derives the following fitting parameters:

print( coef(linearfit_I$linmod) )
## (Intercept)   meanalpha 
##   0.2617121   0.5668587

Given the estimate of \(\varphi_0\) as a function of \(\alpha\) at each site, we can calculate the soil moisture stress function using daily varying soil moisture data and evaluate whether accounting for this resolves the bias of modelled GPP at low soil moisture. Here, we’re assessing this with GPP predictions from the P-model.

Here are the statistics for I, mean across the lower five fLUE bins:

## [1] "With fLUE, mean bias is reduced from 1.76 to 0.0897"
## [1] "With fLUE, RMSE is reduced from 2.53 to 1.18"
## [1] "With I, mean bias is reduced from 1.76 to 0.435"
## [1] "With I, RMSE is reduced from 2.53 to 1.61"

Above figure shows that the bias in predicted GPP is reduced but not fully resolved. Hence, we defined alternative stress functions below.

Approach II

First, a quadratic function of the form described above (Eq. XXX) is fitted to fLUE data for each site individually. The y-axis intersect of the site-specific fitted function is used here as \(\varphi_0\). Second, \(\varphi_0\) is regressed against \(\alpha\) as above.

This method derives the following fitting parameters:

print( coef(linearfit_II$linmod) )
## (Intercept)   meanalpha 
##   0.1073682   0.4779815

Here are the statistics for II, mean across the lower five fLUE bins:

## [1] "With fLUE, mean bias is reduced from 1.76 to 0.0897"
## [1] "With fLUE, RMSE is reduced from 2.53 to 1.18"
## [1] "With II, mean bias is reduced from 1.76 to 0.215"
## [1] "With II, RMSE is reduced from 2.53 to 1.52"

This approach (II) is more effective in reducing the bias in the lower four fLUE bins than approach I, but corrected values still have the tendency to be biased high in the lowest fLUE bin and it also introduces a negative bias in the highest fLUE bin.

Approach III

In view of the remaining positive bias in the lowest fLUE bin, we derive soil moisture stress functions with an even stronger sensitivity. To achieve that, we use only data from sites where approach II does not effectively remove the bias. The method for finding fit parameters itself is identical to approach II. Sites used here are:

-IT-Noe -FR-Pue -AU-Stp -AU-Fog -AU-DaP -AU-ASM -IT-SRo -US-SRG -US-SRM -US-Var

Here are the statistics for III, mean across the lower five fLUE bins:

## [1] "With fLUE, mean bias is reduced from 1.76 to 0.0897"
## [1] "With fLUE, RMSE is reduced from 2.53 to 1.18"
## [1] "With III, mean bias is reduced from 1.76 to -0.196"
## [1] "With III, RMSE is reduced from 2.53 to 1.46"

Approach IV

In view of the trade-off between resolving the bias in the lowest and highest fLUE bins and remaining biases, we developed a method that uses additional information to distinguish between vegetation types for determining the sensitivity of the soil moisture stress function. We applied the same method as in approach II, but determined fit parameters for grasslands (IGBP vegetation type GRA or CSH) and forest ecosystems separately.

Again, we have a linear relationship between the maximum LUE reduction (y-axis intersect) and mean site aridity (AET/PET).

Here are the statistics for IV, mean across the lower five fLUE bins:

## [1] "With fLUE, mean bias is reduced from 1.76 to 0.0897"
## [1] "With fLUE, RMSE is reduced from 2.53 to 1.18"
## [1] "With IV , mean bias is reduced from 1.76 to 0.108"
## [1] "With IV , RMSE is reduced from 2.53 to 1.4"

Overview

For further analyses, we only retained approaches I, IV, III. Approach IV yields the best performance statistics in removing the bias in simulated GPP (P-model outputs assessed here) and serves as a best estimate. Approaches I and III provide a lower and upper boundary for the uncertainty in the sensitivity of GPP (or LUE) to declining soil moisture. An overview of fitted parameters \(a\) and \(b\) (for Equation XXX) is given below. Note that the different approaches I, IV, and III are used for global P-model simulations s1a, s1b, and s1c, respectively.

Overview of parameters for the empirical soil moisture stress functions.
approach simulation a b a_grass b_grass bias rmse
I s1a 0.262 0.567 NA NA 0.1117268 2.126748
II NA 0.107 0.478 NA NA -0.1886077 2.120031
III s1c 0.009 0.384 NA NA -0.5959219 2.241869
IV s1b 0.179 0.450 0.101 0.0063 -0.1682577 2.082576

Site-by-site evaluations

Site-by-site evaluations of the three different soil moisture stress functions are shown below.

Performance of soil moisture correction

Above, the performance of different empirical soil moisture stress (ESMS) functions was assessed by comparing original and corrected GPP estimates from the P-model against observations. Next, we compare their performance in removing the bias in all RS-models assessed here (MODIS, VPM, BESS, P-model). For this, we pool the normalised bias from all models.

## [1] "With fLUE, mean bias in lower four fLUE bins is reduced from 1.65 to 0.0308"
## [1] "With fLUE, RMSE in lower four fLUE bins is reduced from 2.52 to 0.939"
## [1] "With IV, mean bias in lower four fLUE bins is reduced from 1.65 to 0.247"
## [1] "With IV, RMSE in lower four fLUE bins is reduced from 2.52 to 1.32"

For the site US-Var, apparent soil moisture-related reductions in LUE (fLUE) are excessively large and, while the site is not extremely arid, it is notoriously difficult to appropriately predict its sensitivity from using only information on vegetation type (GRA) and mean annual AET/PET. Therefore, we excluded results from this site for evaluations of the bias after correction below. 

## [1] "With fLUE, mean bias in lower four fLUE bins is reduced from 1.41 to -2.63e-05"
## [1] "With fLUE, RMSE in lower four fLUE bins is reduced from 2.26 to 0.917"
## [1] "With IV, mean bias in lower four fLUE bins is reduced from 1.41 to 0.0438"
## [1] "With IV, RMSE in lower four fLUE bins is reduced from 2.26 to 1.07"

Global P-model simulations

Approaches I, III, and IV are implemented for global simulations with the P-model. This section provides information of the model code version and setup.

Code

The P-model (???) and SPLASH (Davis et al. 2017) are implemented for site-scale and global applications within a single flexible modelling framework, SOFUN v1.0.0 [stocker18zenodo] available through zenodo and github. This is based on the formulation to predict leaf-level photosynthetis and light use efficiency of (P-model part) (???) and the SPLASH model (Davis et al. 2017) for calculating potential evapotranspiration and simulating the soil water balance. Different implementations of the P-model have been used previously (???). A monthly LUE is calculated based on monthly mean climate conditions, calculated from daily values (see below). Daily GPP is then calculated based on monthly LUE multiplied by daily varying absorbed PAR and aggregated again to longer periods for all evaluations. The time scale at which the light use efficiency concept can be applied is determined by the time scale of allocation into the photosynthetic machinery (turnover of enzymes). The linearity between primary production and absorbed light described by Monteith’s light use efficiency model arises due to acclimation of photosynthesis to light conditions but does not hold at short time scales (e.g., hourly-daily), where the light response curves are strongly non-linear.

Greenness data

The P-model is used here as a light use efficiency model [monteith72] (Eq. 1 in main text), driven by remotely sensed greenness (fAPAR). We use an updated version of FPAR3g (???) here, which covers years 1982-2016 and limits model simulations into the past.

Climate data

Daily data from the WATCH-WFDEI climate forcing dataset (???) is used here for variables temperature, precipitation (sum of rainfall and snowfall), specific humidity (converted to vapour pressure deficit), and shortwave incoming radiation (converted to photosynthetically active radiation).

Vapour pressure deficit

Vapour pressure deficit (VPD, here \(D\), in units of Pa) is calculated from specific humidity (\(q\)) as: \[ D = e_s - e_a \] wehere \(e_s\) is the saturation water vapour pressure, and \(e_a\) is the actual water vapour pressure (both in Pa). \(e_s\) is calculated as: \[ e_s = 611.0 \; \exp \Big( \frac{17.27 \; T}{T + 237.3} \Big) \] \(T\) is temperature. Actual water vapour pressure \(e_a\) is calculated as: \[ e_a = P\frac{w R_v}{R_d + w R_v} \] where \(P\) is the atmospheric pressure, \(w\) is the mass mising ratio of water vapor to dry air (dimensionless), \(R_v\) is the specific gas constant of water vapor (J g\(^{-1}\) K\(^{-1}\)), and \(R_d\) is the specific gas constant of dry air (J g\(^{-1}\) K\(^{-1}\)). \(P\) is calculated from standard conditions and spatially varying elevation. \(w\) is calculated from specific humidity \(q\) data: \[ w = q/(1-q). \]

Photosynthetically active radiation

Photosynthetically active radiation (PAR, in units of mol m\(^{-2}\) d\(^{-1}\)) is calculated from shortwave incoming radiation \(R_s\) (W m\(^{-2}\)) as \[ \text{PAR} = R_s \; k \; 60.0 \cdot 60.0 \cdot 24.0 \cdot 10^{-6} \] where \(k\) is a flux-to-energy conversion factor, here 2.04 \(\mu\)mol J\(^{-1}\).

Soil data

Plant-available soil water holding capacity (WHC) is an essential variable that determines water stress during dry periods. To estimate variations in WHC across the globe, we used texture data from SoilGrids (xxx ref) at 1 km resolution and derived plant wilting point \(F_{\text{PWP}}\) and field capacity \(F_{\text{FC}}\) estimated from sand, clay and organic matter contents following (???). WHC is calculated as \[ \text{WHC} = (F_{\text{PWP}}-F_{\text{FC}})(1-f_{\text{gravel}})\cdot\min(z, z_{\text{max}}) \] where \(f_{\text{gravel}}\) is the coarse fraction (SoilGrids data) and \(z\) is the soil depth to bedrock (SoilGrids data) and \(z_{\text{max}}\) is the maximum soil depth considered here, taken as 2000 mm. For global applications, global WHC fields derived at 1 km resolution are aggregated to 0.5\(^{\circ}\) in longitude and latitude.

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Davis, T. W., I. C. Prentice, B. D. Stocker, R. T. Thomas, R. J. Whitley, H. Wang, B. J. Evans, A. V. Gallego-Sala, M. T. Sykes, and W. Cramer. 2017. “Simple Process-Led Algorithms for Simulating Habitats (Splash V.1.0): Robust Indices of Radiation, Evapotranspiration and Plant-Available Moisture.” Geoscientific Model Development 10 (2): 689–708. doi:10.5194/gmd-10-689-2017.