NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-889-2018The effect of soil moisture anomalies on maize yield in GermanyPeichlMichaelmichael.peichl@ufz.dehttps://orcid.org/0000-0002-9865-1885ThoberStephanhttps://orcid.org/0000-0003-3939-1523MeyerVolkerSamaniegoLuishttps://orcid.org/0000-0002-8449-4428UFZ – Helmholtz Centre for Environmental Research, Leipzig, GermanyMichael Peichl (michael.peichl@ufz.de)20March201818388990613April201725April201722December20172January2018This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/18/889/2018/nhess-18-889-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/889/2018/nhess-18-889-2018.pdf
Crop models routinely use meteorological variations to estimate
crop yield. Soil moisture, however, is the primary source of water for plant
growth. The aim of this study is to investigate the intraseasonal
predictability of soil moisture to estimate silage maize yield in Germany. We
also evaluate how approaches considering soil moisture perform compare
to those using only meteorological variables. Silage maize is one of the most
widely cultivated crops in Germany because it is used as a main biomass
supplier for energy production in the course of the German Energiewende (energy transition).
Reduced form fixed effect panel models are employed to investigate the
relationships in this study. These models are estimated for each month of the
growing season to gain insights into the time-varying effects of soil
moisture and meteorological variables. Temperature, precipitation, and
potential evapotranspiration are used as meteorological variables. Soil
moisture is transformed into anomalies which provide a measure for the
interannual variation within each month. The main result of this study is
that soil moisture anomalies have predictive skills which vary in magnitude
and direction depending on the month. For instance, dry soil moisture
anomalies in August and September reduce silage maize yield more than
10 %,
other factors being equal. In contrast, dry anomalies in May increase
crop yield up to 7 % because absolute soil water content is higher in May
compared to August due to its seasonality. With respect to the meteorological
terms, models using both temperature and precipitation have higher
predictability than models using only one meteorological variable. Also,
models employing only temperature exhibit elevated effects.
Introduction
In the course of the German Energiewende (energy transition), the demand for biomass has
increased considerably with silage maize being an important plant for high
dry matter yields. The share of the total production in agriculture was 18 %
in 2014 , with an increasing share of
agricultural area used for silage maize from 15.4 % in 2010 to 17.7 % in
2015 . With
that in mind, the observed susceptibility of silage maize towards extreme dry
conditions during summer time supports the detection of relevant factors for
yield variation for instance in 2015;.
Knowing the determinants of maize variation can help to mitigate welfare
losses. For instance, detrimental effects of soil moisture shortage and
abundance can be mitigated by the means of irrigation and drainage and thus
are key for targeted and efficient development of adaptation measures
.
In general, two different kinds of modeling approaches are employed to assess
the impact of weather or climate on the agricultural sector. These are
structural (integrated assessment) models and reduced form models
. Whilst structural approaches specify the economic
behavior based on theoretical models and assumptions and thus have “the
ability to make predictions about counterfactual outcomes and welfare”
, the advantage of reduced form approaches is “transparent
and credible identification” by exploiting the exogenous
variation of key parameters . Regression models are used
to estimate the variation in the dependent variable within various sectors by
the means of damage or dose-response functions
. In the agricultural sector, the major
explanatory variables are temperature based . The use of temperature as the
main explanatory variable is questioned in this study by using reduced form
models to identify the impact of different determinants on crop yield.
In the agricultural context, most advances have been made regarding
dose-response functions through the development of temperature estimates on
high spatial and temporal resolutions . Based on these data,
many studies employ a precise term which integrates cumulative exposure to
specific temperature ranges over the growing period as major explanatory
variable. Those are defined as growing degree days and accumulated measures of extreme heat above a certain
threshold, for instance extreme, heat, killing, or damage degree days
.
showed that the time in which a plant is exposed to a
temperature above a threshold during each day of the growing season can
explain almost half of its yield variations. For corn, this threshold is
estimated to be 29 ∘C. Thus, it is highly recommended to account
for nonlinearity in temperature. This is particularly important in the
context of climate change, as the likelihood of significant and non-marginal
changes in relevant factors increases. Currently, nonlinear measures with
thresholds such as extreme degree days (EDD) are considered to be the best
predictor of crop yield variation .
Recent research suggests that the main reason of the importance of EDD is
the high correlation with measures of cumulative evaporative demand
, for instance vapor pressure deficit
VPD;. There is evidence that the effect
of EDD and measures for evapotranspirative demand is overstated when
neglecting proper control for water supply . For instance, soil moisture is considered a major limiting factor
to maize growth . Extreme high temperature amplifies the
impact of soil moisture deficit because of surface–atmosphere coupling
, but the opposite is not necessarily the case as droughts
occur independently of heat . highlight
the impact of interactive effects between VPD and water supply to further
improve model predictability. In Germany, a recent statistical impact
assessment of weather fluctuations affecting maize and winter wheat
recognizes water shortage as a major limiting factor . These studies employ proxies to control for the
primary source of water, such as precipitation and measures for
evapotranspirative demand. The water holding capacity of the soil and the
persistence of soil moisture is often not considered.
One basic assumption in EDD is that temperature effects are additive
substitutable, which means that their impact is constant for all development
stages of the plant. This assumption is rejected in both agronomic studies
and large-scale
empirical analyses . For example, the susceptibility to high temperatures is increased
during flowering (i.e., tasseling, silkening, and pollination) and the
reproductive period. Similar to heat measurements, the sensitivity to water
stress is dependent on the development stage of the plant
. For instance, it is shown for climate projections in
India that a more uneven distribution of precipitation within a season
overturns positive effects of an increase in total precipitation
. It is argued to control for intraseasonal-varying
weather induced effects on crop yield variation. This issue is amplified for
precipitation controls compared to temperature. The distribution of measures
such as EDD partially overlaps with the sensitive phase of plant growth
see Fig. A14 of, but precipitation, as a control for
water supply, is commonly aggregated for the entire growing season
among others. These studies do not explicitly account for seasonality of
water-supply-related effects. Overall, controls for meteorological effects
averaged over the entire season may bias the estimated dose-response function
and diminish the predictive power of the models because they do not account
for the seasonal interaction between water supply and water demand
.
Based on this analysis, it is the main aim of this study to investigate the
intraseasonal predictability of soil moisture to estimate silage maize yield
in Germany. It is also evaluated how approaches considering soil moisture
perform compared to those using meteorological variables. The examined
hypotheses are that (a) models with soil moisture are better able to predict
yield than meteorology-only approaches and (b) temporal patterns in the
seasonal effects of the explanatory variables matter, i.e., there is no
additive substitutability. In order to analyze these hypotheses, the
intraseasonal effects of soil moisture and meteorological variables for
nonirrigated arable land in Germany are examined in this study. In detail,
the following research questions are addressed: (1) is there predictability of
soil moisture additionally to meteorology? (2) If so, how does it compare to
the one by meteorological determinants? (3) Is there temporal pattern in the
seasonal effects of all explanatory variables (meteorology and soil
moisture)? Along with this analysis we also evaluate (4) how models based on
different meteorological determinants perform compared to each other.
To answer these research questions, a reduced form panel approach is employed
to examine the nonlinear intraseasonal partial effects of soil moisture
anomalies and the meteorological variables temperature, potential
evapotranspiration, and precipitation. For this purpose, we use a new data
set which is additionally comprised of soil moisture anomaly data. The aim is
to evaluate whether soil moisture anomalies have predictive skills and how
the effects differ from those using only meteorological variables. Soil
moisture and any derived index are highly autocorrelated in time and thus
provide an integrated signal of the meteorological conditions in the
preceding and subsequent months e.g.,.
This persistence does not allow for cumulative measures as those used for
temperature, but it avoids the inflation of the error terms. Commonly, the
predictive power of models only employing meteorological variables can be
improved by accounting for the regional-specific temporal distribution of the
phenological stages . The integrated signal of the
meteorological conditions provided by any measure derived from soil moisture,
however, allows the employment of monthly averages to account for these
intraseasonal effects. In our study, it is implicitly controlled for the
interaction of both variables controlling for water supply and water demand
because these show high correlation on a monthly basis. Different model
configurations for each month of the growing season are compared by model
selection criteria to allow conclusions about the effect of soil moisture
anomalies on the explanatory power of the model and to test the assumption of
additive substitutability. Further, the difference in explanatory power of
models either using potential evapotranspiration or average temperature is
evaluated. The partial effects of all covariates of the best model for each
month are examined. For the purpose of a comprehensive examination, we also
investigate the effects of wet anomalies.
DataYield data
Annual yield data for silage maize are provided by the Federal Statistical
Office of Germany for the administrative districts (rural districts,
district-free towns, and urban districts) since the year 1999
. The yield data are detrended
using linear regression for the period 1999 to 2015 to control for technical
progress. A log transformation is applied afterwards to better satisfy the
normality assumption. This transformation also mitigates issues related to
heteroscedasticity and the estimates are less sensitive to outliers. All
administrative districts with less than nine observations are removed from
the analysis because the influence of individual observations is too
strong in these cases. The threshold of nine has been chosen after exploring
Cook's distance and evaluating the systematic omission of yield data by the
administrative districts .
Soil moisture anomalies and meteorology
The explanatory variables used in the study are the observed meteorological
variables precipitation (P), average temperature (T), and potential
evapotranspiration (E), as well as model-derived soil moisture. The mesoscale
Hydrologic Model (mHM) has been used to estimate the soil moisture
. The model uses grid cells as the primary unit
and accounts for various hydrological processes such as infiltration,
percolation, evapotranspiration, snow accumulation, groundwater recharge and
storage, and fast and slow runoff. The parametrization process of the
model is based on physical characteristic, for instance soil texture.
Three different forms of land cover are also integrated in the model, which
are based on the CORINE Land Cover maps of 2006 . However, no
endogenous processes of land use management, for instance drainage or
irrigation, are considered within the model. The depth of the soil in each
grid depends on the soil type used in mHM. Details can be found in
.
Soil moisture is further transformed into a soil moisture index (SMI),
which is a nonparametric cumulative distribution function (cdf) derived from
the absolute soil moisture estimated by mHM. A nonparametric kernel smoother
algorithm has been used for the calculation of the cdf for each calendar
month in accordance to the proposed method by . It
ranges from 0 to 1 and represents an anomaly with respect to the monthly
long-term median in soil water (SMI =0.5). Low values represent extreme dry
soils and high values extreme wet ones. The SMI is calculated for all of
Germany at a spatial resolution of 4 km. Monthly values of soil moisture are
transformed to SMI for the period from 1951 to 2015. These values have also
been used for drought reconstruction . A similar
procedure has been applied for the seasonal forecasts of agricultural
droughts .
The monthly SMI values are categorized into seven classes which follow the
notion of the US and German drought monitors
. This stepwise approach allows to measure nonlinear effects
of soil moisture. The dry categories SMI ≤0.1, 0.1< SMI ≤0.2, and
0.2< SMI ≤0.3 are denoted as severe drought, moderate drought, and
abnormally dry, respectively. The wet quantile intervals between
0.7< SMI ≤0.8, 0.8< SMI ≤0.9, and 0.9< SMI are labeled as
abnormally wet, abundantly wet, and severely wet, respectively. The interval
of 0.3< SMI ≤0.7 serves as reference and characterizes normal
situations. This classification uses location-dependent cdfs and thus allows
comparison of classes across locations. In the following, the terms soil
moisture anomalies and SMI are used synonymously
because of this categorization.
Daily data of precipitation and temperature are obtained from a station
network operated by the German Weather Service . Details on
interpolation can be found in . These daily values are also
used to force mHM. For the analysis in this study, all daily values are
aggregated to monthly ones conserving the mass and energy of the daily
observations.
Further, we introduce potential evapotranspiration (E) as a measure for
evaporative demand. E is calculated by the equation of
based upon extraterrestrial radiation and temperature and is estimated in
millimeters per day:
E=κRTδ(T+17.8),
where κ is a free parameter (∘C-1.5) that
compensates for advection of water vapor (mm d-1), R is
extraterrestrial radiation converted into equivalent water evaporation, and
Tδ is the temperature difference between daily maximum and
daily minimum temperature (∘C). The term T+17.8 is an
approximation of saturated vapor pressure, whereas the term
Tδ is an approximation of cloudiness; 17.8 is an empirical
constant found by calibration.
More complex alternatives exist, for instance the standard method of
United Nations Food and Agriculture Organization after Penman and Monteith
. These data use, for example, net radiation that is more
difficult to estimate on the national scale in comparison to temperature,
particularly due to the lack of consistent observations. Similar to VPD, which has been introduced as an effective crop yield predictor
, potential evapotranspiration has a more
direct physical link to crop water requirements than temperature. One goal of
this study is to evaluate whether potential evapotranspiration provides
improved yield estimates in comparison to temperature.
Mean and standard deviation of the meteorological
variables, averaged over Germany. Data are obtained by the
Germany Weather Service.
May June July August September October MeanSDMeanSDMeanSDMeanSDMeanSDMeanSDP (monthly sum in mm)75.7439.8469.7133.1589.4839.7284.0443.6863.8832.6257.7227.28T (monthly average in ∘C)13.461.4216.521.4518.481.7417.901.5714.071.639.641.83E (monthly average in mm)115.2312.15133.4212.21139.1016.52115.2413.5570.338.7336.824.69
All meteorological variables are standardized to ease the comparison among
different months. After this transformation, the variables have a mean of
0 and a standard deviation (SD) of 1. The original mean and SD of the meteorological variables are depicted in Table 1 for
completeness.
Illustration of the spatial processing of the SMI data of May 2003. On
the left side, one can see the SMI with the 4×4km2 grids.
In the middle, the data are masked with the 0.1×0.1km2
“nonirrigated arable land” class of the CORINE Land Cover. Those data are
than averaged over all the grid cells which are inside an administrative district.
This is done for each district and the map on the right is derived. The processing steps
shown in panels (a) and (b) are shown here exemplary for the soil moisture index for
consistency, but these processing steps are applied to soil moisture fractions.
Spatial processing
The explanatory variables (meteorology and soil moisture) are mapped onto the
level of administrative districts to align with the spatial scale of the
yield data. Maps of the different processing steps are shown in Fig. 1.
Figure 1a depicts the 4×4km2 grid. These absolute soil
moisture fractions are masked for “nonirrigated arable land” class of
the CORINE Land Cover (2006) at a 0.1×0.1km2
resolution to account for the variability due to heterogeneous land use
within the administrative districts (Fig. 1b). The 0.1 km values are then
averaged for each of the administrative district to obtain district level
values (Fig. 1c). Blank administrative districts occur because of the absence
of nonirrigated arable land grid cells. These processing steps are
also applied to the meteorological variables (P, T, E). The soil moisture
fractions of each administrative district are then transformed into a
percentile index (SMI) using the kernel density estimator explained above
. An index reduces the
probability of measurement errors and the estimated coefficients in the
regression models are supposed to be less prone to attenuation bias
.
Regression analysis
The main aim of this study is the identification of the monthly effects of
soil moisture anomalies on crop yield. The model relates silage maize yield
deviation (Y) to a stepwise function of soil moisture anomalies (SMI) and
polynomials of the meteorological variables (P, T, E). Also, an error term is
included which is composed of the fixed effects (c), a time-invariant
categorical administrative district identifier, and the observation-specific
zero-mean random-error term, which is allowed to vary over time (ϵ). Each monthly model can be written as
Yik=∑n=16αnI(SMIikm∈Cn)+∑j=13βj(Pikm)j+∑j=13γj(Tikm)j+∑j=13δj(Eikm)j+cim+ϵikm.
The index i represents the administrative districts, k the years, and m
each month of the growing season, while the superscript j refers to degrees
of the polynomials. I(⋅) is the indicator function of the soil
moisture categories Cn, which is 1 if the SMI belong to class n and 0
otherwise. The six classes are defined as severe drought (SMI ≤0.1),
moderate drought (0.1< SMI ≤0.2), abnormally dry
(0.2< SMI ≤0.3), abnormally wet (0.7< SMI ≤0.8),
abundantly wet (0.8< SMI ≤0.9), and severely wet (0.9< SMI),
respectively. The estimated coefficients of the model are α, β,
γ, and δ and are constrained to be the same for all
administrative districts. Time-invariant differences between administrative
districts are taken into account by the fixed effects. These consist of the
districts specific mean values of the individual variables on the right and
left sides of the equation.
Comparison of Pearson correlation coefficients of the exogenous variables.
MayJuneJulyAugustSeptemberOctoberAverageAvg. June to Aug.E/T0.840.860.920.840.650.40.750.87E/P-0.38-0.38-0.52-0.52-0.56-0.150.420.47P/T-0.31-0.22-0.54-0.47-0.47-0.060.350.41SMI /E-0.27-0.28-0.44-0.49-0.46-0.020.330.40SMI /P0.190.310.430.430.50.090.330.39SMI /T-0.04-0.16-0.35-0.35-0.270.130.220.29
Absolute values of the Pearson correlation coefficients
are employed to calculate the averages presented in the last two columns.
The explanatory variables are correlated to each other (Table 2). Thus,
higher nonorthogonal polynomials induce singularity in the moment matrix
which cannot be inverted as required by the ordinary least-squares estimation
of the coefficient. The polynomials are limited to a degree of three to avoid this
and other detrimental consequences of multicollinearity such as the inflation
of the standard errors. Additionally, E and T are treated as mutually
exclusive because of the high correlation of E and T (Table 2). The
coefficients γ or δ are set to 0, accordingly.
In addition to soil moisture, a meteorological and a fixed effect term are
included. The fixed effects potentially reduce omitted variable bias because
they take into account the time-variant confounding factors specific to each
spatial unit, such as average weather conditions and the water storage
capacity of the respective soil. It is also assumed that farmers have
optimized the entire production process at their location given their
experience at that location. Soil and plant management, such as the choice
of varieties, is adapted based on this long-term experience. Therefore, the
coefficients of the exogenous variables are determined on the basis of
year-to-year variations. By restricting the coefficients to be same in all
administrative districts, it is implicitly assumed that the response of
plants to interannual stressors is the same across all locations.
Differences in the sensitivity to exogenous weather and soil moisture
fluctuations implied by the use of different silage maize varieties could
thus be neglected by the model. If it is also assumed that these interannual
fluctuations in weather and soil moisture are not fully taken into account by
the farmer in the cultivation decisions, this corresponds to a randomized
allocation of the farmer to a treatment group and can therefore be regarded
as a natural experiment . The outlined
interpretation of the coefficients is particularly suitable for SMI, because
this index, which describes deviations from the median, is per definition an
anomaly.
Endogenous variables are not included because these are considered as bad
control in frameworks as those defined by . For instance,
prices are affected by weather realizations and climate and are thus defined
as endogenous . Other
studies additionally use annual fixed effects and interaction terms of both
time- and entity-specific fixed effects to control for time-specific
confounding factors e.g.,. These terms are not used in
this study because annual variation should be explicitly accounted for by the
weather variation of the exogenous variables. Annual fixed effects would
diminish the entity-specific interannual variation of the exogenous
variables and thereby potentially amplify measurement errors
.
Various estimation approaches are used to evaluate the quality of the models.
Models can be distinguished by the explanatory variables they use and the
degree of polynomials in the meteorological terms. The maximum number of
parameters estimated in a model is 12. The Bayesian information criterion
(BIC) is used for model selection in the next section. The BIC is composed of
the maximum of the likelihood function for a particular set of variables as
well as a penalty term . The latter adjusts the model
selection criterion for the number of parameters to account for overfitting.
This allows to choose across models with different number of variables. The
BIC imposes a higher penalty on overfitting compared to other
model selection criteria based on maximum likelihood such as the Akaike
information criterion . The penalty particularly affects
the soil moisture anomaly term because it always adds six parameters.
Overall, the model with the lowest BIC is preferred. To derive the BIC, a
generalized linear model is fitted using the glm function
.
Additionally, the models are evaluated according to their adjusted
coefficient of determination (adj. R2, Sect. 4.2). Ordinary least
squares using the lm function are employed
with a dummy variable for each administrative districts to explicitly account
for the fixed effects. As default, a demeaning framework
has been applied to investigate the model performance
in terms of R2. The demeaning framework involves converting the data by
subtracting the administrative district average from each variable. The
estimated coefficients are the same for the least-squares dummy variable
regression, a demeaning framework, and maximum likelihood (BIC). This is in
accordance with the theory that normal distributed error terms estimators based on
maximum likelihood and least squares are the same.
The standard errors of the coefficients are corrected for spatial
autocorrelation. For this purpose, the robust covariance matrix estimator
proposed by is employed to construct standard errors
based on asymptotic formulas. No weights capturing decaying effects in space
are used because the administrative districts have different areas and the
spatial extent of SMI occurrences is heterogeneous. This can be regarded as
comparable to block-bootstrapping at a country level, which has been used in
many comparable studies relying on resampling methods
e.g.,.
Further, serial correlation and heteroscedasticity are also controlled for
. Overall, this approach is rather
conservative but in alignment with the proposal of to
take the largest robust standard error as measure of precision.
Results and discussionQualitative evaluation of different model configurations within the growing season
In this section, the BIC is applied to
evaluate the best combination with respect to soil moisture, meteorological
variables, and the polynomial degrees of the latter. The BIC is calculated
separately for each month to assess the intraseasonal variability.
Each panel shows the BIC distribution of 1 month. Within the panels various
models are compared, whilst the lowest marker is preferred. Each column represents a
particular selection of variables. The markers represent different degrees of the
polynomials in the meteorological term. The gray markers denote those models that
neglect the SMI, whilst the black include it.
The distribution of the BIC for the various model configurations is presented
in Fig. 2, which shows one panel for each month of the growing season.
Within the panels, models with different variable combinations in the
meteorological term are separated by vertical lines. A model configuration is
defined by a set of meteorological variables, the polynomial degree of each
variable, and the stepwise function of the soil moisture anomalies. The
complexity of the configurations increase stepwise from the left to right
within each panel. The model employing SMI as single explanatory variable is
represented by a point on the left in each panel. The black markers indicate
the models with soil moisture and gray markers without. The models 02–07
employ one meteorological variable each. These have three markers for the
different degrees of the polynomials. The models 08–11 employ two
meteorological variables and thus have nine markers.
The explanatory power is different across the months as indicated by the
lowest marker within each panel. Overall, July has the highest explanatory
power. Nonlinear meteorological terms improve the fit of the model on the
data in all model configurations (not shown). The preferred polynomial in the
meteorological term is of a degree of three. The only exception is June, where the
best model employs a second-degree polynomial for P. These observations are
consistent with agronomic studies. Curvilinear relationships between maize
yield and meteorological variables are already investigated in previous
research. The rationale behind this is that optimal conditions exist for
certain growth stages and deviations from them are detrimental. For example,
found for corn in the US Corn Belt that precipitation
in July above and temperature in August below the monthly average are
desirable. Nonlinear configurations have been neglected so far in comparable
approaches employing constant elasticity models in Germany
.
The composition of the meteorological term is evaluated by comparing the gray
markers in Fig. 2. It is possible to asses the impact on the model fit of the
single variables P, T, and E by the comparison of the configurations
02, 04, and 06, respectively. In May, most of the yield variation is explained by
E. In June and July, P contributes to model fit the most. In July, for
instance, the explanatory power of a nonlinear P term is almost as good as
the best combined configuration. September and October are determined by T.
However, in most months, using more than one meteorological variable results
in the highest explanatory power. The only exception is October, where model
05 (SMI and T) exhibits the lowest BIC.
The difference in BIC between configuration 08 (P and T) and 10 (P and
E) is small from June to August. This result can be expected because T
and E are highly correlated in our sample (Table 2). The models with mixed
meteorological terms in July and August slightly prefer E, while in June it
is T. In the other months, the difference between T and E is
comparatively larger. E is preferred in May and T is the better measure in
September and October. Both measures, T and E, account for similar
determinants of silage maize growth. The latter, however, is more complex
because it contains information on subdaily radiation additionally to daily
temperature . It can be assumed that this additional
information is averaged out using monthly values and monthly temperature
becomes a close estimate of monthly E. This is in alignment with results of
different time resolutions, which indicate that measures of
evapotranspirative demand are highly correlated with temperature extremes
. Therefore, it is sufficient to account for
temperature when simultaneously controlling for water supply (P, SMI)
because it is easier to measure temperature data and there is a smaller
chance of attenuation bias.
The extent of the model improvement by adding soil moisture anomalies varies
across the months. This can be evaluated by comparing the gray and black
markers in Fig. 2. Including soil moisture anomalies only improves model fit
to a small extent in May and July. In all the other months, large
improvement can be made when additionally controlling for soil moisture. In
the second half of the season, i.e., August and September, the models using
only SMI have a similar or even lower BIC compared to all meteorology-only
models.
These results indicate that soil moisture builds memory over the season that
adds relevant information, which are not integrated in the monthly
meteorological variables. There are several reasons for this postulation. First, the seasonality of soil moisture must be considered. The
fraction of the saturated soil changes over time and thus the base value for
the index. For Germany, this seasonality is depicted in Fig. 4 in
. In March, soil water content is the highest while
soils are usually driest in August and September. This also implies that an
agricultural drought has a lower absolute soil moisture in August and
September compared to the preceding months. Second, the anomalies in the
later months integrate information about the water balance in the preceding
months because of the persistent character of soil moisture (evident from the
autocorrelation of the soil moisture indexes). For instance, extreme dry
conditions during flowering and grain filling are reflected in a dry soil
moisture anomaly in the second half of the agricultural season of silage
maize. The observation that the SMI represents additional information to the
meteorology is also supported by the fact that the pairwise correlations
including SMI are lower compared to any other combination of the exogenous
variables (Table 2). Further, dry anomalies in the late part of the season
may indicate a long lasting water shortage condition, as soil moisture
drought lasts several months or potentially even years
.
Similar results may be achieved by cumulated measures of the meteorology or
the climatic water balance. However, the comparison of soil moisture
measurements and different cumulates of precipitation (1 to 6 months)
shows that it would be necessary to consider different precipitation
accumulations for different sites in order to include the same information as
for soil moisture (not shown). For example, southern Germany exhibits higher
water-retaining capacities and also higher correlation with 3-month
precipitation as compared to eastern Germany. Further, a substantial share of
the variability of soil moisture is not explained by precipitation (the mean
coefficient of determination is at most 50 %). One advantage of using soil
moisture in such a study is that the coefficients can be restricted to be the
same at all locations, whilst assuming that the water-retaining capacity is
not the same everywhere.
In summary, soil moisture anomalies improve the model fit in all model
configurations. This is the case even though soil moisture is strongly
affected by the penalty for additional parameters within the BIC. Further,
the evidence of nonlinear effects in the meteorological terms is confirmed.
The results also indicate that there is substantial seasonal variability in
the impact of exogenous variables. This is investigated further
quantitatively in the next sections for the meteorological variables and soil
moisture.
Quantitative assessment: coefficient of determination for models using different explanatory variables
In this and the next section, we present the quantitative results for
the “full” model with polynomials of degree three of the variables
T and P in the meteorological term and
additionally the soil moisture anomalies (SMI). Using the same model
configuration for each month allows the comparison of partial effects and
ensures that the source of variation is the same within the meteorological
term . In this section, the coefficient of
determination is employed to evaluate the share of the sample variation only
explained by the exogenous variables. Additionally, it is used to assess the
in-sample goodness of fit of the models 03 (SMI and P), 05 (SMI and T), 08
(P
and T), and 09 (SMI, P, and T), each using polynomials of degree three.
Comparison of the adjusted coefficients of determination R2.
The results from the demeaning framework serve as reference to the ones obtained
by least-squares dummy variable regression (LSDV). The latter explicitly accounts
for the fixed effects. Additionally, model configurations without either T, P,
or SMI are shown.
MayJuneJulyAugustSeptemberOctoberAverageJune–August(a) Adjusted R2 demeaning0.110.160.310.170.130.120.160.21(b1) Adjusted R2 LSDV0.560.590.660.590.570.560.590.61(b2) ((b1) - (a)) / (a) in %409.1268.8112.9247.1338.5366.7290.5209.6(c1) Adjusted R2 no T0.070.130.280.160.080.080.130.19(c2) ((c1) - (a)) / (a) in %-36.4-18.8-9.7-5.9-38.5-33.3-23.7-11.4(d1) Adjusted R2 no P0.080.110.220.140.120.120.130.16(d2) ((d1) - (a)) / (a) in %-27.3-31.3-29.0-17.6-7.70.0-18.8-26.0(e1) Adjusted R2 no SMI0.070.080.300.110.060.070.110.16(e2) ((e1) - (a)) / (a) in %-36.4-50.0-3.2-35.3-53.8-41.7-36.7-29.5
**p< 0.05. ***p< 0.01; 5376 observations used in each model.
The coefficients of determination for two model settings are evaluated to
show the ability of exogenous explanatory variables, e.g., the meteorological
term and the soil moisture anomalies, to improve the in-sample goodness of
fit of the full model: first, the model that only accounts for the variation
in the exogenous explanatory variables, which is derived by the demeaning
framework (row a in Table 3); second, the least-squares dummy variable
model that accounts for both the variation in the exogenous explanatory
variables and the administrative district-specific average yield (row b1 in
Table 3). The ratio of the coefficient of determination derived by these two
model setups is investigated (row b2 in Table 3) to quantify the share of
variance explained only by the exogenous explanatory variables, e.g., the
meteorological term and soil moisture anomalies. Expectedly, the exogenous
variation in weather and soil moisture improves the model fit in all months,
but the level of improvement varies. The month which gains the least in
explanatory power when additionally accounting for the share of variation
explained by the average crop yield of each administrative district is July
(+112.9 %). This suggests that a large part of the yield variation is
explained only by exogenous explanatory variables. The month with the
greatest variation, which is explained only by the average yield of the
districts, is May. During this month, 409.1 % of the explanatory power is
added if the average yield of each county is explicitly taken into account in
comparison to the models that only use soil moisture and weather variation as
explanatory variables (line b2 in Table 3).
The adjusted R2 presented in this study explicitly including fixed effects
for each month of the period June (0.59), July (0.66), and August (0.59) is
comparable to related approaches. , who employed a
comparable period to estimate their results, reported R2 of 0.65 and 0.67
for a model that successfully accounts for the interaction between heat and
moisture for a 61–90-day period following sowing for Iowa, Illinois, and
Indiana. Their study additionally employed time fixed effects which usually
lead to higher R2. The seminal approach employing EDD
reported R2 between 0.77 and 0.78. In their
sample, a comparatively large share of the variation was explained by the
fixed effects and trend, which exhibited an R2 of 0.66. A study using
updated data of and controlling for evaporative demand
in July and August achieved adjusted R2 between 0.66 and 0.72
.
In the previous section, all the models have been evaluated with respect to
the BIC criterion, which penalizes overfitting. The focus here is on reducing
the sample bias of the model. The in-sample adjusted R2 of the models is
additionally compared when either one of the variables SMI, P, or T is
not considered (rows c1–e1 in Table 1). The relative change in
model fit when one variable is removed from the full model can be found in
rows c2–e2 of Table 3. In all months but May and July, the strongest
loss in in-sample goodness of fit is seen for removing soil moisture (for
instance -50.0 % in June and -35.3 % in August). In July, which
is the month with the highest overall in-sample goodness of fit, the largest
effect is accounted for by precipitation (-29.0 %). The average
relative model loss is largest for soil moisture for the entire season
(-36.7 %) as well as the period June to August (-29.5 %). As
observed in the section before, the effect of each particular variable is
dependent on the month. For instance, the largest relative loss in adjusted
R2 for SMI is estimated in June (-50.0 %) and September
(-53.8 %). The largest effect of precipitation is observed in June
(-31.3 %) and July (-29.0 %). Temperature is relevant the most in
September (-38.5 %) and May (-36.4 %).
To summarize, the in-sample explanatory power of the full models are
comparable to those reported in the previous literature. The largest average
gain in goodness of fit is achieved by including SMI. In July, the month with
the largest in-sample goodness of fit, most of the variation in yield is
explained by precipitation. This section has only presented a quantitative
analysis of the explanatory power in terms of adjusted R2. A detailed
assessment of the partial functional form of individual explanatory variables
is presented in the next section to better understand their ceteris paribus
impact on the crop yield.
Results of regression models employing precipitation and temperature
to account for meteorology (both with polynomials of degree 3; superscripts
denote the degree of individual polynomials) and a stepwise function of SMI.
Dependent variable: log(silage maize) Model of the month MayJuneJulyAugustSeptemberOctoberPrecipitation10.0040.036***0.039***-0.014-0.011-0.003(0.011)(0.014)(0.013)(0.011)(0.013)(0.010)Precipitation2-0.023*-0.014*-0.023***-0.019***-0.0050.002(0.014)(0.007)(0.004)(0.006)(0.005)(0.008)Precipitation30.0040.0010.005***0.004***0.002-0.0001(0.002)(0.001)(0.002)(0.002)(0.001)(0.002)Temperature10.024-0.006-0.036*-0.0030.038-0.002(0.021)(0.015)(0.021)(0.014)(0.024)(0.018)Temperature2-0.005-0.006-0.007***-0.008**-0.009*-0.016**(0.007)(0.006)(0.002)(0.003)(0.005)(0.008)Temperature30.0004-0.0020.004*-0.002-0.013*0.005(0.003)(0.003)(0.003)(0.002)(0.006)(0.003)SMI: severe drought0.068***0.024-0.044**-0.110***-0.126***-0.149***(0.012)(0.020)(0.019)(0.035)(0.028)(0.037)SMI: moderate drought0.044***0.016-0.007-0.055***-0.041*-0.024(0.011)(0.017)(0.011)(0.017)(0.023)(0.030)SMI: abnormally dry0.0110.023***-0.005-0.024**-0.017-0.005(0.011)(0.007)(0.007)(0.011)(0.015)(0.017)SMI: abnormally wet-0.007-0.034***-0.0110.026***0.007-0.006(0.014)(0.011)(0.007)(0.008)(0.011)(0.019)SMI: abundantly wet-0.014-0.052**-0.0040.027***0.012-0.001(0.020)(0.025)(0.009)(0.008)(0.017)(0.015)SMI: severely wet-0.009-0.202***-0.041***0.037***0.0300.025(0.019)(0.047)(0.016)(0.013)(0.027)(0.017)Observations537653765376537653765376R20.1130.1730.3260.1790.1360.129Adjusted R20.1050.1620.3050.1680.1270.121F statistic53.151***87.531***203.025***91.409***65.891***62.296***
*p< 0.1. **p< 0.05. ***p< 0.01.
Quantitative assessment: partial effects of the meteorological variables
A better understanding of the relationship between individual explanatory
variables allows to design effective adaptation measures. The partial
functions of the meteorological covariates are presented in the next two
sections and those of soil moisture in Sect. 4.3.3. Those functional forms,
which are significant at least in the first or second order, are presented
for individual months in Fig. 3. The range of the meteorological variables is
depicted from -2 to +2 SD. It can be assumed that
larger deviations from the mean are related to higher uncertainties in the
estimated crop yield. A table with the estimated coefficients and standard
errors of all models can be found in Table 4.
The partial dose-response functions of the meteorological variables are depicted for
the range between -2 and +2 standard deviations (SD). The upper row represents those models
considering SMI, whilst the lower row neglects SMI.
A solid line is used for those variables which are significant in both the first- and second-degree polynomials.
A dashed line is employed when only one of the
first two polynomials is
significant. The vertical axis represents the change in silage maize converted into percent.
These are approximate values, either by the formula 100(exp(∑j=13βj(Pikm)j)-1)
for precipitation (left column) or 100(exp(∑j=13γj(Tikm)j)- 1) for temperature (right column).
Both formulas refer to Eq. (2).
Under the assumption that the variables are normally distributed, the range depicted accounts
for about 95 % of the observations. The dark gray areas denote the interval between
the 0.023 % (-2 SD) and the 10 % quantiles as well as the 90 and 97.7 % (+2 SD) quantiles.
Similar, in medium gray the range between either the 10 and the 20 % quantiles or
the 80 and 90 % quantiles is marked. The light gray quantifies the impact
between the between either the 20 and the 30 % quantiles or the
70 and 80 % quantiles.
Sensitivity of the functional form of temperature
partial effects for various controls for water supply.
Partial effects of precipitation
The partial precipitation effects for the months May to August are shown in
panel a of Fig. 3. Given constant soil moisture and temperature effects,
negative precipitation anomalies are associated with reduced yield in these
months. The largest effect is observed for June (-5 % at -1 SD) and July
(-6.5 % at -1 SD). These are the overall most significant months, but with
different patterns compared to the remaining two. In June and July, more than
average precipitation is associated with comparatively higher yield (at 1 SD:
+2.2 % in June and +2.1 % in July), whilst the opposite is the case for
May and August.
The results indicate the importance of sufficient water supply provided to
plants by precipitation, especially in June and July. In Germany, the begin
of flowering is usually in July and extends into August based on data
provided by the. Maize plants are
susceptible to water stress during this growing phase . Despite the necessity to control for
intraseasonal variability of precipitation effects, explicitly controlling
for this sensitive phase is not very common in recent reduced form studies
. Notable exceptions are , who used
precipitation centered around flowering (anthesis) in statistical models
based on historical data of trials in Africa, and ,
who controlled for the vegetative, flowering, and grain-filling stages.
Instead, many approaches employ total precipitation over the growing season
,
monthly mean growing season precipitation , or the average of
a subset of the season . Studies for Germany commonly
separate the season into the periods May to July and August to October
, thus dividing exactly the
time interval most susceptible to water stress and averaging over periods
with diverse effects (e.g., May and June in Fig. 3a). This may hide water-related effects. Other studies neglect precipitation entirely and only rely
on temperature measures .
According to their results, the explanatory power is not improved when adding
precipitation. This is contradictory to our observations that precipitation
is particularly relevant (see also Sect. 4.1 and 4.2).
The models employed here do not explicitly account for interactions between
the meteorological and the soil moisture terms. Nevertheless, soil moisture
is a function of the meteorological variables and all effects are correlated
to each other (see Table 2). The overall pattern in the effects of the
meteorological variables only changes to a small extent when estimating the
standard model configuration without the term for soil moisture anomalies
(Fig. 3b). One of the most pronounced differences is that the positive effect
of precipitation in June diminishes when not accounting for soil moisture.
The coefficients in June are also less significant. The effects in September
become significant in the second and third polynomial degree when not
considering SMI (blue dashed line in Fig. 3b). In contrast, May is less
significant and thus not included in this panel. SMI improves the model fit
but only slightly affects the functional form of precipitation, which
highlights that soil moisture adds relevant but different information as
those entailed in precipitation. The next section presents an analogue
analysis for temperature.
Partial effects of temperature
The significant partial temperature effects are depicted in Fig. 3c. A
significant effect in all polynomials is only estimated for July, whilst in
May and June no significant coefficients can be found at all. In all months
but September, higher than average temperatures are associated with reduced
crop yield. The extent of the effects, however, varies over time. In July,
less than average temperature is associated with above-normal crop yield. The
estimated function peaks at -1.24 SD, which is 16.18 ∘C (mean in July
is 18.34 ∘C). Additional 2.66 % crop yield can be expected at this
temperature, if all other variables are held constant. In August, elevated
temperatures are associated with negative effects. September exhibits a large
but not significant linear effect, whilst the second and third polynomials
are significant. Because maize is maturing during this time, higher
temperatures up to a threshold are favorable as shown in Fig. 3c. Crop yield
is reduced beyond this threshold, which might be related to heat waves. Cold
temperatures have a negative effect in October, which is the strongest one
observed. Harvesting commonly begins at the end of September within the
period from 1999 to 2015 . Thus, low temperatures may be related
to early harvesting and result in lower yield.
When comparing the effects of precipitation and temperature in the months
most relevant for meteorology, i.e., June and July, those of precipitation
clearly outweigh temperature. The largest effects can be found for negative
anomalies of precipitation in July (compare Fig. 3a and c). The limited
effect of temperature is in alignment with agricultural literature, which
states that maize is tolerant to heat as long as enough water is provided
. This is also the case in our study area given the fact
that Germany lies in a rather temperate and marine climate zone.
Additionally, sufficient provision of water is associated with prolonged
grain filling and hence diminished heat sensitivity .
Recent literature often neglected precipitation and emphasized mostly extreme
temperature instead , which may have lead to biased assessments.
The general functional forms of temperature are hardly affected by neglecting
SMI (Fig. 3d). For example, crop yield changes from -3.82 % with SMI to
-4.11 % without SMI for 1 SD of elevated temperature in July. These effects
are smaller than those seen for precipitation, which highlights again that
soil moisture provides information that is independent of that provided
by T.
As mentioned before, a substantial amount of studies employed temperature as
the major explanatory variable neglecting knowledge about plant physiology
and plant growth . The functional form of
the partial temperature effects derived from different model configurations
for July and August is presented in Fig. 4 to evaluate the magnitude of bias
between the full model (presented in Fig. 3) and a temperature-only model.
In both months, the in-sample explanatory power is reduced compared to the
full model when only using temperature as explanatory variables. In July, the
model fit is -34.2 % lower when employing the temperature-only model
compared to the full model, while it is -45.9 % in August (Fig. 4). In
July, the in-sample goodness of fit is affected stronger by removing
precipitation (-29.0 %) than by doing so for SMI (-3.2 %), (Table 3).
This is not surprising because the partial effect of precipitation in July is
largest, whilst soil moisture anomalies only show negligible effect. In contrast, considering SMI in August (-35.3 %) exceeds the losses in
adjusted R2 compared to a model without precipitation (-17.6 %)
(Table 3). In July, the functional form stays qualitatively the same across
all model configurations (Fig. 4a). The magnitude of the effects is, however,
larger when precipitation is not considered. In August, the temperature
effect is elevated by not considering SMI. Taking out precipitation reverses
the effects found for the full models. This observation clearly demonstrates
that adequate control of water supply is necessary to derive non-biased
estimates of partial temperature effects. These results also indicate that
the biases seen for different model configuration depend on the month
considered. Overall, a model using only temperature as explanatory variable
has larger partial effects and potentially even different ones with regard to
the direction compared to those of the full model. In the next section, the
partial effects of the soil moisture index are investigated.
Percentage change of silage maize yield caused by
significant soil moisture anomalies for each month. The vertical axis
represents the change in silage maize converted into percent, approximated
by the formula 100(exp(∑n=16αnI(SMIikm∈Cn))-1),
where Cn are the soil moisture classes (refers to Eq. 2). The standard errors are
indicated by the black error bars.
Partial effects of the SMI
Similar to the meteorological terms, the susceptibility to SMI changes over
the months (Fig. 5). In particular, a change in the general patterns can be
observed. In May and June, dry conditions are associated with positive yield
(up to +7 % in May and +2.3 % in June), whilst wet conditions are
harmful (up to -18.3 % under severely wet conditions in June). In July,
both extremes have negative impacts of around -4 %. In all of the following
months, dry conditions are associated with reduced crop yield (up to
-10.4 % in August, -11.8 % in September, and -13.8 % in October),
whilst only extreme wet conditions in August are positive for annual silage
maize yield (up to +3.77 %). These deviations are as high as the ones
observed for the meteorological variables (Fig. 3).
For the interpretation of the results, the climatology of mean soil water
content needs to be taken into account. The SMI of each month refers to
different fractions of absolute water saturation in the soil. This
seasonality is depicted in Fig. 4 in for different
locations in Germany. In general, the optimal water content for plant
development is defined as 60 to 80 % of the available field capacity,
whilst less than 40 % field capacity, such as in the year 2003, is
associated with depression in crop yield . In May and
June, dry anomalies represent soil moisture fractions above critical water
content because the soil has been replenished with water in preceding winter
and spring. For silage maize, however, rather dry conditions are preferable
during this time because high soil moisture saturation can induce luxury
consumption and thus reduced root depths . This is
particularly relevant for maize due to its capability to develop deep roots
. This feature allows the plants to access deep soil
water under dry conditions during the sensitive phase of flowering and grain
filling. Empirical studies indicated that early wet conditions slow down the
spreading of seeds and young plants can be damaged through indirect effects,
such as fungus . A detailed analysis indicates that the
large effect of severely wet conditions in June can be partly associated to
the 2013 flood in Germany (not shown), which exhibited wet soils in large
parts of the country. Starting in July, the level of soil water content
decreases see Fig. 4 in. As a consequence, dry
anomalies represent damaging conditions because plant available soil water
starts to be too low to provide enough water during the most susceptible
phase. These effects are increasing over the subsequent months because of the
seasonality, the particular growing stage, and the persistence of soil
moisture. Lower levels in absolute soil water also explain why wet anomalies
have a positive impact in August, but not in July. July exhibits the highest
evapotranspiration among all months. This leads to a highly dynamic soil
moisture in July which is characterized by a transition from a wet regime to
a dry regime. Thus, small deviations from average soil moisture in this month
have no significant effect on yield (Fig. 5). These are only observed for the
very extreme conditions.
Additionally, the growing stage modifies the impact of soil moisture
coefficients. In our sample, flowering commonly begins between the middle and
end of July and milk ripening occurs in the second half of August based
on own calculation from data provided by. Plants exhibit an increased
susceptibility to insufficient water supply during these development stages.
As shown in Sect. 4.3, July has the highest partial effect with respect to
meteorological variables. In August, soil moisture anomalies show a
significantly higher impact on annual silage maize yield than in July. Due
its seasonality, absolute soil moisture values are in general lower in August
than in July. Further, soil moisture in August integrates temperature and
precipitation effects of the preceding months. Thus, dry soil moisture
anomalies show harmful effects, while wet ones are beneficial. In September
and October, soil moisture usually starts to refill see Fig. 4
in. Maize is in the less susceptible phase to dryness of
ripening in September and harvesting usually starts in the second half of
this month . This implies that severe drought anomalies in
September and October might be associated with extended periods of water
stress over the sensitive growing stages in the months before.
In this section, it was shown that the seasonality of soil moisture
underlying the soil moisture index needs to be considered to disentangle its
temporal effects on silage maize yield. Thus, it is necessary to consider
seasonality in soil moisture content and silage maize growth when assessing
effects caused by soil moisture anomalies.
Conclusions
In this study, the intraseasonal effects of soil moisture on silage maize
yield in Germany are investigated. It is also evaluated how approaches
considering soil moisture perform compared to meteorology-only ones. A
demeaned reduced form panel approach is applied, which employs polynomials of
degree three for variables of average temperature, potential
evapotranspiration, precipitation, and a stepwise function for soil moisture
anomalies to capture nonlinearities. Potential evapotranspiration and average
temperature are mutually exclusive. The model selection is based on the
BIC and the adjusted coefficient of
determination (R2).
This study provides a proof of concept that (a) soil moisture improves the
capability of models to predict silage maize yield compared to
meteorology-only approaches and (b) temporal patterns in the seasonal
effects of the explanatory variables matter. Results show that soil moisture
anomalies improve the model fit in all model configurations according to both
the BIC and R2. SMI entails the highest explanatory power in all months
but May (most explained by T) and July (most explained by P). This highlights
that soil moisture adds different information than meteorological variables.
All time-invariant variables show seasonal patterns in accordance to each
particular growing stage of silage maize. Furthermore, the dynamic patterns
of the SMI effects originate from the seasonality in absolute soil moisture.
Those results support the supposition that it is necessary to control for
intraseasonal variability in both the index for soil moisture and
meteorology to derive valid impact assessments. Also, the comparison of
various meteorological effects based on BIC shows that potential
evapotranspiration adds no explanatory power compared to average temperature.
Further, partial effects of precipitation outweigh those of temperature when
controlling for intraseasonal variability.
The temporal resolution for the meteorological and soil moisture data is
months. This might be too low to accurately resolve the stage of plant
growth. Future improvements will involve the use of daily data from high-resolution remote sensing campaigns which would allow us to determine growing
seasons more accurately.
Our results have further implications for climate change impact assessment.
First,soil moisture can improve agricultural damage
assessment and enrich the climate adaptation discourse in this realm, which
is mostly based on temperature measures as major explanatory variable
. We recommend controlling for at least those seasonal
dependent pathways that affect plant growth presented in our study. Measures
of soil moisture should be considered to derive evidence about climate
impacts and adaptation possibilities. This particularly concerns climate
econometrics, where frequently used reduced form approaches and dose-response
functions should also control for soil moisture. For example,
derived from a dose-response function only relying on
temperature measures that the sensitivity to EDD is lower in
southern than northern US counties. Based on these estimates, they
concluded that the south is better adapted to hot conditions than the
north. Transferring those adaptation potential to future impacts diminishes
the estimated losses. However, various issues need to be considered when
employing such an approach, such as the costs of adaptation and wrong
institutional incentives . Also,
argued that higher average humidity levels in the south
diminish the correlation between heat and measures based on
evapotranspirative demand. Accordingly, it is recommended to directly control
for evapotranspirative demand by VPD. As shown in
Sect. 4.1, no superior effect of potential evapotranspiration over
temperature was found when controlling for either precipitation or both
precipitation and SMI. Potential evapotranspiration and VPD both account for
the water demand of the atmosphere. Instead, the results of this study show
that controlling for water supply by measures of either soil moisture and
precipitation avoids biased effects in a humid climate. This study further
indicates that it is necessary to account for the seasonal dynamics in both
the meteorological and soil moisture effects that constitute the variation in
crop yield to employ spatial adaptation as surrogate for future adaptation.
Second, the definition of an index as anomaly has general implications for
climate econometrics. Such an index is less prone to systematic errors
because any bias associated to the
spatial processing and the meteorological or climatological modeling is
minimized . Also, the
persistence in soil moisture and the resulting smoother distribution in
comparison to the meteorological variables might deliver more reliable
estimates than climate assessment based on meteorological variables because
climate simulations only show robust trends at coarse temporal resolutions
. An index can also be interpreted as interannual
variability beyond the demeaning framework. Any linear model employing a
categorical variable for each spatial unit is equivalent to joint demeaning
of both the dependent and the independent variables and thus the source of
variation is the deviation from the mean. For instance, anomalies are used
within the adaptation discourse to derive implications for short-term
measures . Again, in such a setting soil moisture can serve
as a more comprehensive measure than the commonly used temperature.
Finally, this study has also several implications for the design of
adaptation measures on weather realizations to reduce current welfare losses
of climate events . First, indexes derived
from soil moisture can be used in risk transfer mechanisms. For instance,
insurance schemes based on a particular weather index can be enhanced in
both developed and developing countries . Second, the
detrimental effects of wet soil moisture anomalies might allow one to extend the
risk portfolio of multi-peril crop insurance and thus foster the advancement
and implementation of those schemes in Germany . Third, the
installation of agricultural infrastructure should be investigated because
negative effects of soil moisture anomalies can be mitigated by irrigation
and drainage. In 2010, only 2.34 % of the agricultural area used for
silage maize was irrigated (own calculation from data provided by
) and the latest numbers about drainage
systems in Germany date back to 1993 .
Overall, an index of soil moisture considering intraseasonal variability has
relevant implications for current and future damage assessment and adaptation
evaluation, which are supposed to gain importance in the course of climate
change.
All datasets can be made available upon request to the
corresponding author.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Damage of natural hazards: assessment and mitigation”.
It is a result of the EGU General Assembly 2016, Vienna, Austria, 17–22 April 2016.
Acknowledgements
We kindly acknowledge the German Meteorological Service (DWD), the Joint
Research Center of the European Commission, the European Environmental
Agency, the Federal Institute for Geosciences and Natural Resources (BGR),
the Federal Agency for Cartography and Geodesy (BKG), the European Water
Archive, the Global Runoff Data Centre at the German Federal Institute of
Hydrology (BfG), and the Federal Statistical Office of Germany for the
provision of data. We especially thank Matthias Zink (UFZ) for processing and
providing the data. We also thank the authors of the R packages
used in this study (). We express our thanks to
Prof. Reimund Schwarze for his comments and the promotion of the project at
the Helmholtz Alliance Climate Initiative REKLIM. This work is also part of
the Integrated Project Water Scarcity at the UFZ – Helmholtz Centre for
Environmental Research, Leipzig, Germany, which served as forum to present
our work. Special thanks to Andreas Marx, head of the Climate Office for
Central Germany, who supported us in the final steps of this
study.The article processing charges for this
open-access publication were covered by a Research
Centre of the Helmholtz Association.Edited by: Thomas Thaler Reviewed by: two
anonymous referees
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