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

In the course of the German

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

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

Recent research suggests that the main reason of the importance of EDD is
the high correlation with measures of cumulative evaporative demand

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

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

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 explanatory variables used in the study are the observed meteorological
variables precipitation (

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

The monthly SMI values are categorized into seven classes which follow the
notion of the US and German drought monitors

Daily data of precipitation and temperature are obtained from a station
network operated by the German Weather Service

Further, we introduce potential evapotranspiration (

More complex alternatives exist, for instance the standard method of
United Nations Food and Agriculture Organization after Penman and Monteith

Mean and standard deviation of the meteorological variables, averaged over Germany. Data are obtained by the Germany Weather Service.

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

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

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 (

The index

Comparison of Pearson correlation coefficients of the exogenous variables.

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,

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

Endogenous variables are not included because these are considered as bad
control in frameworks as those defined by

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

Additionally, the models are evaluated according to their adjusted
coefficient of determination (adj.

The standard errors of the coefficients are corrected for spatial
autocorrelation. For this purpose, the robust covariance matrix estimator
proposed by

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

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

The difference in BIC between configuration 08 (

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

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.

In this and the next section, we present the quantitative results for
the “full” model with polynomials of degree three of the variables

Comparison of the adjusted coefficients of determination

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
(

The adjusted

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

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

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.

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

The partial dose-response functions of the meteorological variables are depicted for
the range between

Sensitivity of the functional form of temperature partial effects for various controls for water supply.

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 (

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

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.

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

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

The general functional forms of temperature are hardly affected by neglecting
SMI (Fig. 3d). For example, crop yield changes from

As mentioned before, a substantial amount of studies employed temperature as
the major explanatory variable neglecting knowledge about plant physiology
and plant growth

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

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(

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

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

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

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.

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 (

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

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

Second, the definition of an index as anomaly has general implications for
climate econometrics. Such an index is less prone to systematic errors

Finally, this study has also several implications for the design of
adaptation measures on weather realizations to reduce current welfare losses
of climate events

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.

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 (