Timing and intensity of heat and drought stress determine wheat yield losses in Germany

Abstract

Crop yields are increasingly affected by climate change-induced weather extremes in Germany. However, there is still little knowledge of the specific crop-climate relations and respective heat and drought stress-induced yield losses. Therefore, we configure weather indices (WIs) that differ in the timing and intensity of heat and drought stress in wheat (Triticum aestivum L.). We construct these WIs using gridded weather and phenology time series data from 1995 to 2019 and aggregate them with Germany-wide municipality level on-farm wheat yield data. We statistically analyze the WI’s explanatory power and region-specific effect size for wheat yield using linear mixed models. We found the highest explanatory power during the stem elongation and booting phase under moderate drought stress and during the reproductive phase under moderate heat stress. Furthermore, we observed the highest average yield losses due to moderate and extreme heat stress during the reproductive phase. The highest heat and drought stress-induced yield losses were observed in Brandenburg, Saxony-Anhalt, and northern Bavaria, while similar heat and drought stresses cause much lower yield losses in other regions of Germany.

Full text

RESEARCH ARTICLE
Timing and intensity of heat and drought
stress determine wheat yield losses in
Germany
Ludwig RiedeselID
1
*, Markus Mo
¨ller
2
, Peter Horney
1
, Burkhard Golla
1
, Hans-
Peter Piepho
3
, Timo Kautz
4
, Til FeikeID
1
1Julius Ku¨hn Institute (JKI) – Federal Research Centre for Cultivated Plants, Institute for Strategies and
Technology Assessment, Kleinmachnow, Germany, 2Julius Ku¨hn Institute (JKI) – Federal Research Centre
for Cultivated Plants, Institute for Crop and Soil Science, Braunschweig, Germany, 3Institute of Crop
Science, Biostatistics Unit, University of Hohenheim, Stuttgart, Germany, 4Humboldt University of Berlin,
Thaer-Institute of Agricultural and Horticultural Sciences, Berlin, Germany
*ludwig.riedesel@julius-kuehn.de
Abstract
Crop yields are increasingly affected by climate change-induced weather extremes in Ger-
many. However, there is still little knowledge of the specific crop-climate relations and
respective heat and drought stress-induced yield losses. Therefore, we configure weather
indices (WIs) that differ in the timing and intensity of heat and drought stress in wheat (Triti-
cum aestivum L.). We construct these WIs using gridded weather and phenology time series
data from 1995 to 2019 and aggregate them with Germany-wide municipality level on-farm
wheat yield data. We statistically analyze the WI’s explanatory power and region-specific
effect size for wheat yield using linear mixed models. We found the highest explanatory
power during the stem elongation and booting phase under moderate drought stress and
during the reproductive phase under moderate heat stress. Furthermore, we observed the
highest average yield losses due to moderate and extreme heat stress during the reproduc-
tive phase. The highest heat and drought stress-induced yield losses were observed in
Brandenburg, Saxony-Anhalt, and northern Bavaria, while similar heat and drought stresses
cause much lower yield losses in other regions of Germany.
Introduction
Wheat (Triticum aestivum L.) stands out for its high-yielding varieties, high level of disease
resistance, nutritional properties, and excellent baking characteristics [1]. Consequently,
wheat covers the largest production area globally [2] and is one of the most important crops
for global food security [3]. Due to a growing world population, economic growth, and chang-
ing dietary habits, the global demand for wheat is continuously increasing [4,5]. As the second
largest wheat producer in the European Union with high yield levels in international compari-
son [2], Germany plays an important role in the global wheat supply. However, while wheat
yields have continuously increased in Germany in recent decades [6], stagnation of yields has
been observed in Western Europe, including Germany, in recent years [7]. This stagnation can
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OPEN ACCESS
Citation: Riedesel L, Mo¨ller M, Horney P, Golla B,
Piepho H-P, Kautz T, et al. (2023) Timing and
intensity of heat and drought stress determine
wheat yield losses in Germany. PLoS ONE 18(7):
e0288202. https://doi.org/10.1371/journal.
pone.0288202
Editor: Mohammed Magdy Hamed, Arab Academy
for Science Technology and Maritime Transport,
EGYPT
Received: January 9, 2023
Accepted: June 21, 2023
Published: July 25, 2023
Copyright: ©2023 Riedesel et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: The data sources on
which the results of these studies are based are
given in the References section. The yield data
from the FADN dataset are not freely available and
may be requested from the German Federal
Ministry of Food and Agriculture at the following e-
mail address 723@bmel.bund.de. All results can be
reproduced using the minimal dataset, which is
published only at the following Zenodo link: https://
doi.org/10.5281/zenodo.8076295. The minimal
dataset can be freely used and does not need to be

be explained by several factors, such as a slight extensification of production [8], reduced
breeding progress [9], the expansion of winter wheat cultivation to more marginal sites [10]
and, in particular, adverse effects of global climate change [11].
Against this background, wheat yield losses due to weather extremes are increasing in Ger-
many [12–15], with heat stress (high-temperature stress) and drought stress (soil water stress)
considered the most important abiotic stress factors [15–23]. However, the relationships
between regional weather extremes and on-farm yield losses are still insufficiently described
for wheat in Germany [22,24–26]. Hence, a better understanding of the spatiotemporal effects
of heat and drought stress on wheat yields is required [13,25].
Weather Indices (WIs) can help explain the impact of extreme weather events on crop
yields [13,27–30]. WIs are based on the calculation of statistical indicators (e.g., temperature
sum) or the number of thresholds exceeded by an indicator (e.g., days with a maximum tem-
perature above 31˚C) within a reference period relevant for crop growth. A particular chal-
lenge in defining relevant WIs is the complexity and limited knowledge of the relationships
between crop yields, regional site conditions, and changing weather conditions during sensi-
tive growing periods [13,26,31]. In this regard, high quality spatiotemporal data are essential
for designing suitable WIs [29]. This challenge is particularly evident in relation to 1. the spa-
tial accuracy of yield data sets, 2. the consideration of physiologically relevant and spatiotem-
porally accurate crop growing periods and 3. the selection of suitable threshold values:
1. Some studies use yield data on a national level but at low spatial resolution [13,23,27,28],
and others examine yield data as point data for individual locations [29,31,32] or smaller
regions [15,16], but only very few studies use high-resolution on-farm yield data collected
nationwide [14,33].
2. Most studies assume fixed growing periods based on calendric days [13], ignoring regional
and temporal differences in plant development. Others follow more dynamic approaches
by calculating phenological phases using growing degree day (GDD) methods [31–35].
Deriving GDD values allows a more spatiotemporally dynamic approach, but it is limited to
assumptions such as sowing date [36]. Time series of gridded phenological observation data
sets create the possibility of computing WIs within phenological phases for each year and
location, promising to better describe the crop-climate relations than static calendric
approaches [29,36]. Thus far, however, there have been hardly any studies that make use of
such data sets [14,16].
3. Determining suitable yield-effective threshold values is challenging and handled very differ-
ently in the literature [23,25,27,37]. Some studies define their thresholds according to
plant physiological reactions based on controlled experiments [38] ignoring possible spatial
and temporal differences in their occurrence out in the field [31,32,39]. Other studies, do
not take plant physiology into account and base the threshold values on the extremes of
local weather phenomena [14,23,27,40]. To the best of our knowledge, no study has com-
pared the spatial effects of moderate vs. extreme stress nationwide.
With this in mind, the aim of this study is to analyze wheat yield effects with WIs that differ
in the intensity and timing of heat and drought stress based on region-specific interpolated
weather and phenology data. Therefore, our objectives are as follows:
1. To analyze the differences in explanatory power between the timing and intensity of heat
and drought WIs
2. To evaluate the regional differences in heat and drought stress-related yield effects on win-
ter wheat
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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requested from the Federal Ministry of Food and
Agriculture.
Funding: The author(s) received no specific
funding for this work.
Competing interests: The authors have declared
that no competing interests exist.

Consequently, we create WIs that differ in the intensity and timing of heat and drought
stress based on region-specific interpolated weather and phenology data. We then evaluate
these WIs for their explanatory power and region-specific effect size using mixed linear mod-
els. Based on this, we calculate and present the region-specific yield effects of the different WIs.
Material and methods
Study design
Fig 1 illustrates the study design along with the various data integration steps:
1. We compile all required data sets, including yield, weather, phenology, soil, and land use
data sets (Sec. Data sets).
2. We blend phenological data with weather data and derive a set of dynamic WIs based on
the resulting nationwide 1 ×1 km
2
grid data base (Sec. Dynamic WI configuration).
3. We merge the soil data and WI data with the land use data for each grid cell. That way, we
consider only the weather and soil data for cropland in each grid cell, excluding other land
use types (e.g., grassland, forests, and specialty crops) from the analysis. We then aggregate
the data at the municipality level, using weighted averages depending on the share of crop-
land per grid cell. Since the municipality boundaries have been changed in several munici-
pal reforms, with respect to year, we base the WI aggregation on the geometries of the
respective last reform.
4. We assign municipality-specific WIs and soil parameters from Step 3 to each farm-specific
yield data point for each year and municipality.
5. Finally, we statistically analyze the resulting data using a mixed model approach (Sec. Statis-
tical analysis).
Fig 1. Overview of the study design and respective five working steps: From 1) listing the data sets used, 2) aggregation of
spatiotemporal weather indices (WIs), 3) spatial aggregation of the soil and WI data, 4) integration of all data into one
comprehensive data set and 5) statistical analysis.
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Data sets
Yield data. The Federal Ministry of Food and Agriculture (BMEL) provided data from
the Farm Accountancy Data Network (FADN) for this study [41]. In the FADN, the crop-spe-
cific yield data (in dt ha
−1
) and cropland size (in ha) of approximately 11,500 representative
farms were collected annually between 1995 and 2019 and analyzed anonymously. Each farm
is assigned a municipality index and a farm code so that it is possible to distinguish the farms
from each other at the municipality level without sharing their identity and exact location.
Weather data. The German Weather Service (DWD) provided daily meteorological data,
including minimum, mean and maximum temperature, cumulative precipitation, mean wind
speed, and solar radiation. Daily measures from weather stations have been available since
1993 and interpolated to a 1 ×1 km
2
grid-based resolution [42]. Furthermore, the DWD also
provided drought-related data since 1993 on the plant available water capacity (PAWC) in the
0 to 60 cm soil layer generated by the AMBAV model [43]. The model inputs include plant-
specific height, the leaf area index, rooting depth and density, and water fluxes in the soil.
Phenology data. The DWD operates a phenological network of annual and immediate
observers. Approximately 1200 observers monitor 160 phenological phases of wild and culti-
vated plants. The observations are mapped according to a standardized protocol [44]. The
PHASE model was developed to interpolate the phenological observations for the entire terri-
tory of Germany [45]. Since temperature can be considered the most crucial factor influencing
phenology in Central Europe [46], the model combines the concept of GDDs with a geostatis-
tical interpolation procedure. An essential application of the data sets is the derivation of
dynamic time windows for specific years, phases, and test sites [47], which can be defined as
growing periods between two crop-specific, consecutively observed phenological events [48].
As shown by Bucheli et al. [16], considering adverse weather conditions during specific pheno-
logical phases vs. static calendric time windows helps explain weather-yield relations.
Soil quality data. We use the Soil Quality Rating (SQR) soil map from the BGR to
describe soil quality. The SQR classifies soils globally according to their suitability for agricul-
tural land use and yield potential. This classification is available at a 250 ×250 m
2
grid-based
resolution [49].
Land use data. The ATKIS data set from the Federal Agency for Cartography and Geod-
esy (BKG) enables GIS-based area surveys. Hence, we can carry out area-wide quantification
of land use types (i.e., cropland, grassland, and specialty cropland) at the polygon level [50].
Dynamic WI configuration
To configure a WI, we first choose the crop (i.e., winter wheat) and weather event (i.e., heat
and drought stress), set the regional expanse (i.e., nationwide), and depict the spatial aggrega-
tion (i.e., municipality level). Second, we express the configuration conditions in setting the
parameter (i.e., daily maximum temperature, daily average plant available water capacity) and
the index (i.e., accumulated days above the threshold). Finally, we define timing and intensity
to build up the WI structure.
Timing refers to the year- and location-specific phenological development phases [15,31,
51]. We select three growing periods where heat and drought stress are of specific crop physio-
logical relevance [19,20,52]. Hence, we select the “stem elongation and booting phase” (SEB;
BBCH 31—50), “reproductive phase” (RP; BBCH 51—75), and “generative phase” (GP; BBCH
51—87). We illustrate the respective growing phases in Fig 2.
Intensity refers in our study to a fixed threshold value of a weather variable that must be
exceeded for the WIs to take effect [36]. We base the thresholds on crop physiological under-
standing, describing moderate, severe, and extreme stress intensities. We calculate the heat-
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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related WIs from the accumulated number of days with a maximum temperature exceeding
27, 29 or 31˚C, i.e., T
max
>[27, 29, 31]˚C [20,31,32]. We further calculate the drought-related
WIs from the accumulated number of days with plant available water (PAW) below 50, 30 and
10% of the plant available water capacity (PAWC), i.e., PAWC <[10, 30, 50]% [32,54]. We
form all timing ×intensity combinations and thus obtain 18 WIs with moderate, severe, and
extreme intensities for the three growing periods (Table 1).
Spatial aggregation
To evaluate the weather-yield relations while considering spatial differences, we utilize the 50
SCRs within Germany in our analysis according to Roßberg et al. [55]. SCRs represent regions
of similar agricultural growth conditions. SCRs were derived considering soil (i.e., the
weighted soil quality) and weather information (i.e., mean monthly temperature and mean
monthly precipitation sum for the period March–August in 1981–2000) at the municipality
level. We present the federal states and SCR within the federal states in Fig 3. Furthermore, we
list a detailed description of the individual SCRs in Table A in S1 File.
Statistical analysis
Mixed linear model. We use linear mixed models based on Bo¨necke et al. and Hadasch
et al. [31,32]. In the first part of the model, we depict the fixed regression terms (first line) and
the random main and interaction effects (second line). Our model can be expressed according
to Eq (1)
zjklm ¼mþgtjþBnlþSmþdðwSÞjlm
þMlþYjþFkl þ ðMYÞlj þ ðMFÞlk þ ðYFÞjk þejklm ð1Þ
Fig 2. Phenological phases with values according to the BBCH scale available from the PHASE model and growing
phases (colored) for winter wheat along the vegetation period.
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where z
jklm
represents the mean yield of the j-th harvesting year in the k-th farm location in
the l-th municipality of the m-th SCRs. μis the overall intercept, γt
j
represents the genetic and
nongenetic time trend where γis a fixed regression coefficient for the time trend and tj is the
continuous covariate for the j-th harvesting year. The covariate B
nl
accounts for the continuous
Table 1. List of moderate, severe, and extreme heat and drought WIs for the growing periods stem elongation and booting phase (SEB), reproductive phase (RP)
and generative phase (GP).
Name Weather event Intensity Intensity threshold Timing
H27_SEB heat moderate T
max
>27˚C BBCH 31–50
H29_SEB heat severe T
max
>29˚C BBCH 31–50
H31_SEB heat extreme T
max
>31˚C BBCH 31–50
H27_RP heat moderate T
max
>27˚C BBCH 51–75
H29_RP heat severe T
max
>29˚C BBCH 51–75
H31_RP heat extreme T
max
>31˚C BBCH 51–75
H27_GP heat moderate T
max
>27˚C BBCH 51–87
H29_GP heat severe T
max
>29˚C BBCH 51–87
H31_GP heat extreme T
max
>31˚C BBCH 51–87
D50_SEB drought moderate <50% PAWC BBCH 31–50
D30_SEB drought severe <30% PAWC BBCH 31–50
D10_SEB drought extreme <10% PAWC BBCH 31–50
D50_RP drought moderate <50% PAWC BBCH 51–75
D30_RP drought severe <30% PAWC BBCH 51–75
D10_RP drought extreme <10% PAWC BBCH 51–75
D50_GP drought moderate <50% PAWC BBCH 51–87
D30_GP drought severe <30% PAWC BBCH 51–87
D10_GP drought extreme <10% PAWC BBCH 51–87
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Fig 3. A Federal states in Germany. BFifty Soil Climate Regions (SCRs) within the federal states of Germany. The
designation of the numbered SCRs is shown in Table A in S1 File. The maps were reprinted from [53] under a CC BY
license, with permission from [GeoBasis-DE/ BKG], original copyright [2023].
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soil quality ratings (SQRs) from 1 to 100 points, where Bis the regression coefficient, and n
l
represents the SQR value for the l-th municipality. S
m
is a categorical covariate with 50 levels
(m) considering the different SCRs. δ(wS)
jlm
is the interaction term between the WI and SCR,
where δis the fixed regression coefficient for the interaction of w
jl
and S
m
, with w
jl
represent-
ing the continuous covariate of the WI in the j-th year and l-th municipality. For the random
effects, M
l
is the main effect of the l-th municipality, Y
j
is the main effect of the j-th year, and
F
kl
is the main effect of the k-th farm within the l-th municipality. (MY)
lj
is the lj-th
municipality ×year interaction effect, (MF)
lk
is the lk-th municipality ×farm interaction effect,
(YF)
jk
is the jk-th year ×farm interaction effect and e
jklm
is a random residual.
Explanatory power. To quantify the explanatory power of the various heat and drought
WIs, we analyze the variance reduction (VR) of each WI by estimating the coefficient of deter-
mination (R
2
) for mixed models following Piepho [56]. In this regard, we analyze the variance
of the random effects (M,Eq (1)) twice—first without (Var
y(M−x
)) and second with (Var
y(M+x
))
the WI-term δ(wS)
jlm
as our variable under assessment. Next, we derive the VR (%Var
y
) of
every WI one by one by calculating the relative change () in the total variance of the random
effects between the two models as described in Eq (2).
%Vary¼VaryðMxÞVaryðMþxÞ
VaryðMxÞ�100 ð2Þ
Region-specific effect size and yield effects. We analyze the region-specific effect size of
each WI in each SCR individually by deriving the estimated coefficients (δ) of the regression
term δ(wS)
jlm
. To obtain the resulting annual yield effects on municipality level, we multiply
the estimated coefficient (δ) per SCR (S
m
) with the respective WI value (w
jl
).
Selection of covariates. We again use the VR with the coefficient of determination for
mixed models after Piepho [56] to select covariates (Sec. Explanatory power). In this context,
we select a covariate when the VR of M+ 1 is at least -0.5% compared to the baseline model
given in Eq (3). below:
zjkl ¼m
þMlþYjþFkl þ ðMYÞlj þ ðMFÞlk þ ðYFÞjk þejkl ð3Þ
We also compare the models according to the Akaike information criterion (AIC) and
select the covariates if, in addition to a VR >0.5%, they have a smaller AIC value than the base-
line model [57]. To guarantee comparability with the AIC methodology, we follow Faraway
[58] and change the estimation scheme of the mixed linear models from restricted maximum
likelihood (REML) to maximum likelihood (ML). In addition, we also test the variance infla-
tion factor (VIF) to check for multicollinearity. The VIF measures how much the variance of a
regression coefficient is increased due to collinearity. If the VIF exceeds five, the multicolli-
nearity is considerably high, and we reject the covariate [59]. To apply the VIF, we need to
remove the random effects from the models. We list the covariates used in the analyses and
their VR and VIF values in Table C in S1 File.
Results
Explanatory power of heat and drought WIs
In Fig 4, we observe the highest VR for the moderate heat WI during the reproductive phase
with a T
max
above 27˚C (H27_RP, -2.10%), followed by the severe heat WI with a T
max
above
29˚C (H29_RP, -1.64%), and the extreme heat WI with a T
max
above 31˚C (H31_RP, -0.87%).
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Looking at the heat WIs during the generative phase, the moderate heat WI with a T
max
above
27˚C again shows the highest VR (H27_GP, -0.92%), followed by the severe heat WI
(H29_GP, -0.65%) and the extreme heat WI (H31_GP, -0.30%). During the stem elongation
and booting phase, all heat WIs show comparatively low VR values, where the moderate WI
with a T
max
above 27˚C (H27_SEB) ranks highest (-0.35%), followed by the severe WI with a
T
max
above 29˚C (H29_SEB, 0.08%) and the extreme WI with a T
max
above 31˚C (H31_SEB,
0.02%).
In contrast to the pattern observed for heat WIs, the highest VR is observed for drought
during the stem elongation and booting phase, where the moderate drought WI with PAW
below 50% PAWC (-1.26%; D50_SEB) ranks highest, followed by the severe drought WI with
PAW below 30% PAWC (-0.96%, D30_SEB). In comparison, the extreme drought WI with
PAW below 10% PAWC shows an almost zero VR (-0.03%; D10_SEB). During the reproduc-
tive phase, the severe and extreme drought WIs at PAW below 30% PAWC (D30_GP) and
PAW below 10% PAWC show approximately double the VR (-0.76%, -0,74%) of the moderate
drought WI at PAW below 50% PAWC (D50_RP, -0.34%). For drought stress during the gen-
erative phase, the severe drought WI has the highest VR at PAW below 30% PAWC (D30_GP,
-0.69%), followed by the moderate drought WI at PAW below 50% PAWC (D50_GP,—
0.29%), while the extreme drought WI at PAW below 10% PAWC shows almost no VR
(D10_GP, -0.09%). We list the VR of every WI in Table B in S1 File.
Region-specific effect size and yield effects of heat and drought WIs
Below, we analyze the region-specific effect size and yield effect of the drought WIs during the
stem elongation and booting phase and the heat and drought WIs during the reproductive
phase. As the heat WIs during the stem elongation and booting phase and the heat and
Fig 4. Variance reduction (VR) of the analyzed heat and drought WIs. For WI abbreviations, see Table 1. VR is
calculated based on (Eq (2)).
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drought WIs during the generative phase show almost no explanatory power across all intensi-
ties, we do not further illustrate their regional yield effects. However, we list the model outputs
for all WIs in Tables D-V in S1 File. All model outputs are based on (1).
Drought effects during the stem elongation and booting phase (BBCH 31–50). The
median number of drought days during the stem elongation and booting phase ranges from
3.9 days at PAW below 50% PAWC (i.e., moderate WI) to 0.8 days at PAW below 30% PAWC
(i.e., severe WI), down to 0 days at PAW below 10% PAWC (i.e., extreme WI). Moreover, the
number of drought days is highest in Brandenburg and the northern regions of Lower Saxony
and Saxony-Anhalt, as well as Bavaria and Baden-Wuerttemberg. At the same time, it is the
lowest in the southern regions of Bavaria and Baden-Wuerttemberg (Fig 5A, 5C and 5G).
The Germany-wide median effect size increases with increasing stress intensity and ranges
from -0.18 dt ha
−1
day above threshold
−1
(<50% PAWC), to -0.24 dt ha
−1
day above
threshold
−1
(<30% PAWC), down to -2.31 dt ha
−1
day above threshold
−1
(<10% PAWC). The
moderate and severe WIs both show a north-south gradient in the effect size, with estimated
coefficients being significantly negative in the north and east and positive in the south. In the
west, both WIs show no significant effects in many regions (Fig 5B and 5E). The extreme WI
reveals only three regions in the center of Germany with significant effects and estimated coef-
ficients ranging up to -9.3 dt ha
−1
day above threshold
−1
.
Drought in the stem elongation and booting phase exhibits the most substantial yield losses
under moderate drought intensities. For the moderate WIs, we observe the highest adverse
Fig 5. Drought stress during the stem elongation and booting phase (SEB, BBCH 31–50) for moderate (<50%
PAWC), severe (<30% PAWC) and extreme (<10% PAWC) stress intensities. Mean occurrence (A, D, G) describes
the average number of days above the respective thresholds between 1995 and 2019 at the municipality level.
Estimated coefficients (B, E, H) describe the WI x SCR regression coefficients of Eq 1 for each SCR. Nonsignificant
values are given in dark gray. Significant values are given in red (negative effect) or blue (positive effect). The
regression coefficients and p-values are displayed in Tables P-R in S1 File.Mean yield effects (C, F, I) describe the
average yield change in dt ha
−1
per municipality between 1995 and 2019. The median values below each map refer to
the median of all municipalities’ SCRs with significant effects on the respective index. The maps were reprinted from
[53] under a CC BY license, with permission from [GeoBasis-DE/ BKG], original copyright [2023].
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yield effects (2—5 dt ha
−1
) in the north and southeast of Saxony-Anhalt and the predominant
municipalities of Brandenburg. The remaining regions with significantly adverse yield effects
show average yield losses between 0.01 and 2 dt ha
−1
. In Bavaria and Baden-Wuerttemberg, we
note yield gains between 0.01 and 2 dt ha
−1
(Fig 3C). An increase in intensity from moderate
to severe drought thresholds causes a considerable reduction of the observed number of days
above the threshold (−80%) but a minor increase in the effect strength (+33%). Thus, the cap-
tured yield effects are comparably low for severe drought intensities, where we observe the
highest yield losses (2—5 dt ha
−1
) in a few municipalities in southwestern Brandenburg and
southeastern and northeastern Saxony-Anhalt. The remaining regions with significant nega-
tive effect strengths reveal yield losses between 0.01—2 dt ha
−1
. In central Bavaria and eastern
Baden-Wuerttemberg, yield increases between 0.01—2 dt ha
−1
are still prevalent (Fig 5F). As
the number of days above the threshold is zero for extreme drought intensities, yield effects are
also zero for extreme drought during the stem elongation and booting phase.
Drought effects during the reproductive phase (BBCH 51–75). The average number of
drought days during the reproductive phase ranges from 0 to 39. The Germany-wide median
decreases with increasing drought intensities from 14.1 days at PAW below 50% PAWC (i.e.,
moderate WI) to 6.7 days at PAW below 30% PAWC (i.e., severe WI), and down to 1.5 days at
PAW below 10% PAWC (i.e., extreme WI). Most drought days occur in northeastern Ger-
many and the northern regions of Bavaria and Baden-Wuerttemberg, and the fewest drought
days occur in southern Bavaria and Baden-Wuerttemberg (Fig 6A, 6C, 6G).
Fig 6. Drought stress during the reproductive phase (RP, BBCH 51–75) for moderate (<50% PAWC), severe
(<30% PAWC) and extreme (<10% PAWC) intensities. Mean occurrence (A, D, G) describes the average number
of days above the respective thresholds between 1995 and 2019 at the municipality level. Estimated coefficients (B, E,
H) describe the WI x SCR regression coefficients of Eq 1 for each SCR. Nonsignificant values are given in dark gray.
Significant values are given in red (negative effect) or blue (positive effect). The regression coefficients and p values are
displayed in Tables M-O in S1 File.Mean yield effects (C, F, I) describe the average yield change in dt ha
−1
per
municipality between 1995 and 2019. The median values below each map refer to the median of all municipalities’
SCRs with significant effects on the respective index. The maps were reprinted from [53] under a CC BY license, with
permission from [GeoBasis-DE/ BKG], original copyright [2023].
https://doi.org/10.1371/journal.pone.0288202.g006
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The median effect size increases with increasing intensity (i.e., decreasing PAWC) from
−0.09 dt ha
−1
day above threshold
−1
at PAW below 50% PAWC to −0.19 dt ha
−1
day above
threshold
−1
at PAW below 30% PAWC and up to −0.36 dt ha
−1
day above threshold
−1
at PAW
below 10% PAWC. All drought WIs show a similar pattern of region-specific effect size, where
significant adverse yield effects are predominantly seen in the north, east, and southwest (Fig
6A and 6C). The number of regions with significant adverse yield effects increases in the west
and south with increasing intensity. The moderate WI reveals regions with positive effect size
in the south and the northwest. Positive effect sizes with PAW below 10% PAWC occur only in
southern Bavaria (Fig 6H).
In the period from 1995 to 2019, the median yield effects of the moderate and severe
drought WIs are at a similar level (−0.4 dt ha
−1
) across Germany, while the captured median
yield effect for the extreme WI is 50% lower (−0.2 dt ha
−1
). Shifting the thresholds from mod-
erate to severe intensity, a decrease in the observed number of days above the threshold
(−52%) and a substantial increase in the effect size (+111%) are evident. However, a further
increase from moderate to extreme intensity reduces the number of days above the threshold
(−90%), displaying an approximately 50% lower yield loss than moderate or severe stress. In
particular, Saxony-Anhalt, northwestern Bavaria, northeastern Baden-Wuerttemberg, almost
all municipalities in Brandenburg, and parts of Mecklenburg-Western-Pomerania show the
highest average yield losses (-2 to -5 dt ha
−1
). The few municipalities with positive yield effects
display yield gains in the range of 2−4 dt ha
−1
for the moderate WI, 0.01−2 dt ha
−1
for the
severe WI and 0 dt ha
−1
for the extreme WI.
Heat effects during the reproductive phase (BBCH 51–75). Germany’s mean annual
number of heat days during the reproductive phase ranged from 0 to 9.7 days between 1995
and 2019. The Germany-wide median decreases with increasing heat stress intensity (i.e.,
increasing daily maximum temperature, T
max
) from 4.5 days at T
max
>27˚C (i.e. moderate
WI) to 2.3 days at T
max
>29˚C (i.e., severe WI), and down to 0.8 days at T
max
>31˚C (i.e.,
extreme WI). During the reproductive phase, most heat days occur in eastern and southern
Germany, and the fewest heat days occur along the northern coastline in Schleswig-Holstein
and Mecklenburg-Western Pomerania (Fig 7A, 7C and 7G).
The median effect sizes increase with increasing intensity from −0.39 dt ha
−1
day above
threshold
−1
at T
max
>27˚C to −0.73 dt ha
−1
day above threshold
−1
at T
max
>29˚C and up to
−1.1 dt ha
−1
day above threshold
−1
at T
max
>31˚C. At all heat intensities, the negative effect
size is highest in the northeast and east and is lowest in the southern Germany. With increas-
ing intensity, the regions with significant negative effect sizes increase in the south and west
and decrease in the north. Consequently, the moderate WI reveals regions with nonsignificant
or positive effect sizes in the south and west. In contrast, the severe and extreme WIs show pos-
itive and nonsignificant effect sizes in the north along the coastline (Fig 7B, 7E and 7H).
The median yield effects are strongest for the moderate WI (−2.2 dt ha
−1
), followed by the
extreme WI (−2.0 dt ha
−1
), and are lowest for the severe WI (−1.4 dt ha
−1
). In that regard, a
shift from moderate to severe intensities leads to a subtle drop in the observed number of days
above the threshold (−48%) and an increase in the effect size (+87%), whereas a shift from
moderate to extreme intensities leads to a substantial drop in days above the threshold (−82%)
and an increase in the effect size (+182%). For all intensities, the largest yield losses appear in
almost all parts of Saxony-Anhalt and Brandenburg (Fig 7C, 7F and 7I). In these regions aver-
age yield losses are greater than −8 dt ha
−1
for moderate intensities, between -5 and -8 dt ha
−1
for extreme intensities and between −2 and −5 dt ha
−1
for severe intensities. The second high-
est yield losses are observed area-wide in Mecklenburg-Western-Pomerania (except on the
coasts), in the northeastern and southern parts of Lower Saxony, in Saxony, and in northwest-
ern Bavaria (−2 to −5 dt ha
−1
) for the moderate WI. In contrast to the north, large parts of the
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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south (i.e., Bavaria and Baden-Wuerttemberg) show just significantly negative yield effects
with severe (−0.1 to −2 dt ha
−1
) and extreme (−2 to −5 dt ha
−1
) intensities.
Discussion
This study investigates the effects of the timing and intensity of heat and drought stress on
wheat yields in Germany using WIs. For this purpose, we first study the VR of all 18 WIs to
determine differences in explanatory power. Second, we analyze the region-specific effect sizes
of the various WIs and identify local yield effects at the municipality level.
Differences in explanatory power due to timing and intensity
During the reproductive phase, heat WIs generally help better explain wheat yields than
drought WIs. However, this pattern is reversed during the stem elongation and booting phase,
which is consistent with the findings of previous studies [20,31,52]. For heat WIs during the
reproductive phase, a moderate stress intensity helps to explain heat-induced yield changes
better than severe and extreme stress intensities. In contrast, several studies report especially
strong yield effects caused by short-term, extremely high temperature stress [22,60–64]. Nev-
ertheless, the findings of Ben-Ari et al. [27] and Bucheli et al. [16] confirm that moderate but
long-lasting and spatially uniform heat stress helps explain wheat yields in France and eastern
Germany better than short-lived regional extremes.
Fig 7. Heat stress during the reproductive phase (RP, BBCH 51–75) for moderate (T
max
>27˚C), severe (T
max
>
29˚C) and extreme (T
max
>31˚C) intensities. Mean occurrence (A, D, G) describes the average number of days
above the respective thresholds between 1995 and 2019 at the municipality level. Estimated coefficients (B, E, H)
describe the WI x SCR regression coefficients of Eq 1 for each SCR. Nonsignificant values are given in dark gray.
Significant values are given in red (negative effect) or blue (positive effect). The regression coefficients and p values are
displayed in Tables G-I in S1 File.Mean yield effects (C, F, I) describe the average yield change in dt ha
−1
per
municipality between 1995 and 2019. The median values below each map refer to the median of all municipalities’
SCRs with significant effects of the respective index. The maps were reprinted from [53] under a CC BY license, with
permission from [GeoBasis-DE/ BKG], original copyright [2023].
https://doi.org/10.1371/journal.pone.0288202.g007
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Furthermore, during the stem elongation and booting phase, drought WIs have the highest
explanatory power at moderate intensities. However, during the reproductive phase, severe
and extreme drought have the highest explanatory power, which is in line with te results of
previous studies [31,65–67]. Hence, we confirm the findings from Le Gouis et al. [7] and
Makinen et al. [66], which emphasize early-season droughts as particularly harmful in central
Europe, where the intensity is already moderate. We also confirm the findings of Sarto et al.
[68] and Schmitt et al. [14] who reported anthesis and grain filling as the most sensitive phases
to heat and drought, as stress intensities increase during these phases.
Apparent differences between heat and drought stress are visible when comparing the
effects of stress timing, i.e., during the generative vs. reproductive phase. The late growth
phase from milk ripening to hard dough, which is excluded from the reproductive phase but
included in the generative phase, is of limited relevance for yield formation. Drought stress
can contribute to the ripening process in this late phenological phase and hence has no adverse
yield effects. Thus, the explanatory power of the stress WI is higher during the reproductive
phase than during the generative phase. Also, for the heat WIs during the generative phase, the
explanatory power is two to three times higher when we restrict the observed period to the
reproductive phase. Various studies confirm these findings and explicitly find a yield effect
only during the reproductive phase [17,20,52]. Hadasch et al. [32] even found positive yield
effects due to drought toward the end of the growth period for wheat in Germany.
The explanatory power of all tested WIs is small, with a maximum VR of -2.1%. In compari-
son, in Bo¨necke et al. [31], similar WIs displayed a VR of up to −25%. The difference from our
study is that Bo¨necke et al. [31] analyze experimental data from 43 German experimental sites
obtained between 1953 and 2006. Compared to our on-farm data at the municipality level,
these experimental data can better reduce external effects that influence variance for two rea-
sons: First, the point-based yield data can be linked with the respective weather and soil data
with higher local resolution. Second, experimental data are obtained under rather constant
and standardized management conditions. Hence, experimental data can better isolate the
individual effect of WIs than our on-farm yield data from more than 10,000 practical farms,
which are influenced by unknown factors related to local agronomic practices [26,33].
Regional yield impacts of timing and intensity
At the national level, our results reveal higher adverse yield effects due to heat than due to
drought. This is confirmed by the findings of Lu¨ttger & Feike, Trnka et al. and Zampieri et al.
[13,23,69], who underline that heat plays a more substantial role than drought in the late
growing period in Germany and Central Europe. Additionally, Semenov & Shewry [70]
reported a higher risk due to heat than drought during flowering in northern Europe, as wheat
matures earlier with climate change, avoiding extreme drought stress. In contrast, Schmitt
et al. [14] described extreme drought as the main driver of yield losses in Germany during the
reproductive phase, whereas the effect of extreme heat was not significant in their analysis.
However, Schmitt et al. [14] considered only very extreme heat stress events, while we investi-
gated moderate, severe and extreme WIs for each SCRs individually. Our approach reveals
great regional differences regarding heat- and drought-related yield effects.
In that regard, the heat and drought stress-induced yield effects in our study are a function
of the number of days above the threshold and the statistical effect size (i.e., estimated coeffi-
cient) of the SCR. The analysis reveals that the municipalities in Brandenburg, Saxony-Anhalt,
and in northwestern Bavaria consistently show the most days above the threshold and the
highest effect size per day above the threshold. Consequently, these regions display the highest
yield losses with heat and drought stress off all intensities and timings, which is also in line
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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with the findings of other studies [13,14]. Our analysis reveals that a higher stress intensity
generally accompanies (1) fewer days above the threshold and (2) a larger effect size per day
above the threshold. However, there are considerable variations in the response of these two
parameters. Hence, an increase in intensity leads to regionally very distinct yield effects. For
example, for heat in the reproductive phase, we see almost twice as many days above the
threshold in the south compared with the north at all intensities. However, we still observe
much stronger adverse yield effects in the north and the east than in the south. Several studies
also confirm regional variations in heat-induced yield effects. In that regard, Zampieri et al.
[23] found varying yield effects for similar heat intensities at national and global levels. Addi-
tionally, Dreccer et al. [28] show that low temperatures reduce yields in western Australia,
while the opposite trend dominates in norther and southern Australia.
For drought in the reproductive phase, we find relatively linear relationships between
the number of days above the threshold, effect size, and yield loss. As a result, a few days
above the threshold, such as in the south and west, is associated with the smallest effect size
and yield losses, while in the north and east, a large number of days above the threshold
accompanies large effect sizes and the highest yield losses. However, during the stem elon-
gation and booting phase, we can see considerable regional differences in the magnitude of
the effect size and yield effect. Thus, we observe a few days above the threshold and a large
effect size in the north but not in the south. Lu¨ttger & Feike [13] also revealed spatial differ-
ences in drought-induced yield effects and showed that drought stress increases yield vari-
ability in northeastern and eastern Germany. In contrast, southern Germany is consistently
spared from yield-altering drought stress. Additionally, Ben-Ari et al. [27] illustrate how
identical heat and drought WIs show opposite effects in France compared to Spain. They
highlight that heat and drought effects differ significantly at global, national, and subna-
tional levels.
There are several explanations regarding the regionally differing yield effects due to similar
WI occurrences. First, there are reasons for natural region-specific differences in resistance to
heat and drought stress that are associated with soil properties. While the simulated soil mois-
ture data consider soil texture for deriving current plant available water, Mueller et al. and
Trnka et al. [71,72] highlight that during drought, light soils and the associated low soil water
storage capacity exacerbate water stress-induced yield variations, while heavy soils may better
buffer against drought stress. Furthermore, regarding heat effects, soil temperature is decisive
for the yield formation of the plant [73]. Soil temperature alters the rate of organic matter
decomposition and mineralization of different organic materials and soil water content, con-
ductivity, and availability to plants [73,74]. Soil temperature, in turn, is influenced by a wide
variety of local parameters such as soil color, vegetative cover, soil mulch, the slope of the land
surface, organic matter content, evaporation, solar radiation, and their interactions, and can
therefore vary considerably by region [25,74].
For the interpretation of our results, additional aspects may be considered. For example,
Siebert et al. [25] discuss how the above described regionally differing yield effects of the same
WI is challenging to explain from a crop physiological perspective. They emphasize that the
effect of a specific WI may be influenced by (i.e., correlated with) other variables not consid-
ered in the regression analysis. This is highlighted by our results on the positive yield effects of
moderate drought conditions in southern Germany. Here, the drought WI represents a proxy
for a season that is not too wet, leading to drought-related yield increases in the south. In that
regard, Schmitt et al. [14] show that heavy rainfall and water excess are yield-limiting factors
in southern Germany, while excessively wet conditions hardly occur in northern Germany.
Additionally, the heat WIs comprise other weather conditions such as drier conditions with
higher incident radiation. This is supported by findings from Rezaei et al. [75], who found no
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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heat-related yield changes in wheat, when drought stress was fully controlled. In addition,
weather conditions during the growing season before or after the timing of the WIs may influ-
ence their yield effect. For example, Siebert et al. [25] and Taraz [64] emphasize that moderate
stress can be (ultimately) compensated for, especially in early growth phases, if growth condi-
tions are favorable over the rest of the growing season. In contrast, compensation in later
growth phases around flowering is no longer possible in wheat, and the individual weather
effect carries a more substantial weight. Additionally, compound weather events impacted spa-
tial differences in our study, as dry and hot conditions often co-occur. For instance, the
extreme 2003, 2010, and 2018 heatwaves accompanied strong drought events in central Europe
[76]. Many studies highlight that the compound effects between heat and drought lead to
more substantial yield losses than their isolated effects [23,26,76–81]. Hence, compound
effects might occur only in some regions, whereas in other regions, only the isolated weather
event effect shows an impact. Furthermore, individual farm management practices, which
impact weather-yield relations, could not be considered in our analysis due to the lack of
related data. Jones et al. [82] highlight the lack of precise knowledge of farm management prac-
tices influencing the effects of heat and drought stress, and Albers et al. and Bo¨necke et al. [31,
33] stress that individual farm management practices affect yield variation by more than 50%.
In that regard, Macholdt & Honermeier [83] emphasize nitrate fertilization, crop rotation, and
weather extremes as the most important factors influencing yield variations. Furthermore, sev-
eral studies have identified plant breeding as having a primary influence on heat and drought
stress-induced yield losses [26,32,66]. Breeding progress alters the timing of crop develop-
mental phases [84], resource use efficiency, including water use efficiency [85], and resistance
levels against biotic [9] and abiotic stress [72]. However, Albers et al. [33] highlight that
detailed information on inputs would rarely alter the results in a qualitative manner, but most
likely quantitatively. Finally [86] stress that interpolated weather data carry the risk of spatial
autocorrelation, as errors might propagate from one grid cell to the next, resulting in signifi-
cantly larger standard errors, which might affect the WI’s effect sizes. Thus, Mo¨ller et al. [29]
suggest the considering local accuracy metrics, which enable a spatiotemporal quantification
of interpolation errors.
Conclusion
Building on a vast on-farm yield data set, we analyzed the effects of heat and drought on wheat
yields in Germany. We specifically analyzed i) differences in explanatory power between the
timing and intensity of heat and drought WIs and ii) regional differences in heat- and
drought-related yield effects of winter wheat. In that regard, our mixed linear model analysis
reveals the highest explanatory power for moderate heat WIs during the reproductive phase
and for moderate drought WIs during the stem elongation and booting phase. Heat stress
shows only limited relevance during the stem elongation and booting phase. Moreover, we
find higher explanatory power when the yield-sensitive periods are defined more precisely
(i.e., reproductive phase vs. generative phase). In addition, we find large regional differences in
heat and drought stress-related yield effects in winter wheat. Across all WIs, we identify the
strongest heat- and drought-related yield losses in the northeast and east. However, similar
occurrences of heat and drought stress intensities caused much lower yield losses in other
regions. Potential reasons for this finding include region- or farm-specific impacts such as
genetic (G) differences (e.g., different crop varieties), environmental (E) influences (e.g., soil
type) and differences in crop management (M) (e.g., sowing date). Therefore, further studies
should specifically analyze G x E x M effects and respective regional interactions when analyz-
ing crop–climate relations.
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Timing and intensity of heat and drought stress determine wheat yield losses in Germany
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Supporting information
S1 File.
(DOCX)
S1 Data.
(PDF)
Acknowledgments
We thank the German Weather Service (DWD) for providing the weather station and soil
moisture data.
Author Contributions
Conceptualization: Ludwig Riedesel, Markus Mo¨ller, Til Feike.
Data curation: Ludwig Riedesel.
Formal analysis: Ludwig Riedesel.
Investigation: Ludwig Riedesel.
Methodology: Ludwig Riedesel, Hans-Peter Piepho.
Project administration: Til Feike.
Software: Peter Horney.
Supervision: Burkhard Golla, Timo Kautz, Til Feike.
Visualization: Ludwig Riedesel.
Writing – original draft: Ludwig Riedesel.
Writing – review & editing: Ludwig Riedesel, Markus Mo¨ller, Burkhard Golla, Hans-Peter
Piepho, Timo Kautz, Til Feike.
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