# Influence of Climate Conditions on the Temporal Development of Wheat Yields in a Long-Term Experiment in an Area with Pleistocene Loess

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

_{2}concentrations affect plant growth (e.g., [4]).

`flowering`, and ripening, the authors found no common trend for effects on yields. However, the authors described that increasing temperatures harmfully affect pre-heading (yield determination) and post-heading (achievement of yield potential) periods for spring and winter barley, as well as during pre-heading of spring wheat and post-heading of winter wheat.

_{2}concentration in the soil. After a certain time, oxygen is no longer present. This influences the seed during germination and root formation. Waterlogging during the tillering phase damages the roots. This means that nutrients can no longer be absorbed, or are absorbed, but to a lesser degree. Another problem is that the redox potential decreases with decreasing oxygen content. Nitrate, sulfate, manganese, and iron oxides serve as electron acceptors, which can lead to a changed availability of the nutrients.

#### 1.2. Objectives of this Study

_{3}values in groundwater. However, there are no clear findings on the effects of this reduced fertilization on yields. Here, this experiment provides essential insights into such a reduction depending on varieties, management and also climate conditions.

**Table 1.**Literature overview of various studies investigating the influence of climate on grain yield.

Author | Location | Crop | Described Factors of Influence |
---|---|---|---|

[26] | Germany | Wheat, barley, | Yield fluctuations of wheat and barley are mainly caused by precipitation and temperature in June in selected federal states of Germany |

[27] | Germany | Wheat, barley, | The influence of precipitation and temperature on the yield development of wheat, barley and maize in selected districts in Bavaria with special consideration of development stages |

[13] | Germany | Wheat | Development of heat and drought events and the change in wheat yield |

[9] | Germany | Wheat | Influence of temporary waterlogging on growth, nutrient concentration, and yield of wheat |

[7] | Denmark | Wheat | Effect of average temperature, global radiation, and daily precipitation on wheat yields in Denmark (over 17 years) |

[6] | Europe | Wheat | Effect of mean monthly temperature, global radiation, and cumulative rainfall on the yields of winter wheat (over 34 years) |

[5] | Europe | Wheat, barley | Temperature explains most of the yield fluctuations in Europe |

[4] | Canada | - | Effects of climate change and CO_{2} increase on potential agricultural production in Southern Québec, Canada |

[28] | Mexico | Wheat | Mexico: 25% increase in wheat yield in the last two decades due to higher night temperatures |

[29] | USA | Spring wheat | Impacts of day versus night temperatures on spring wheat yields: A comparison of empirical and CERES wheat 2.0 model predictions in three locations |

[30] | USA | Wheat | Simulating the influence of vernalization, photoperiod, and optimum temperature on wheat developmental rates |

[31] | USA | Wheat, maize | Sensitivity of seeds to brief episodes of hot temperatures (e.g., flowering) |

[32] | Europe | Wheat | Sensitivity of wheat varieties grown in Europe to heat, drought, frost, and precipitation |

[33] | India | Wheat | Effect of lack of water on the yield of winter wheat |

[15] | Australia | Wheat | Influence of temperature increases on the yield |

[34] | Australia | Wheat | The effect of duration of heat stress during grain filling on two wheat varieties differing in heat tolerance: grain growth and fractional protein accumulation |

[11] | China | Wheat | Influence of frost on yield in the jointing stage |

[35] | China | Wheat | Influence of heat on the grain filling phase in wheat |

[14] | - | Cereal | Influence of heat on different stages of development of the reproductive phase in different cereal varieties |

[12] | - | Wheat | Summary of frost and heat damage models that can estimate the impact on the yield |

[36] | - | Wheat | Summary of optimal and lethal temperatures of wheat during different stages of development |

[37] | - | Wheat | Influence of waterlogging in different growth phases on the yield |

## 2. Materials and Methods

#### 2.1. General Description, Soil, and Physiography of the Dürnast Long-Term Study Area

#### 2.2. General Description Experimental Design, Wheat Varieties, and Amount of Fertilizer

^{−1}at an adequate fertilization level. This soil and tillage numbers indicate the level of the site-specific soil fertility. The number is derived mainly from the parameters geology, texture and soil condition (dry, wet, acid, calcareous) and the number 100 shows the most fertile site within Germany.

^{2}.

^{−1}on the reduced fertilized plots and 150 kg N ha

^{−1}on the higher fertilized plots. Later, the fertilization level increased to 140 and 180 kg N ha

^{−1}, respectively.

#### 2.3. Independent Parameters for the Derivation of Yield

#### 2.4. Statistical Analyses

#### 2.4.1. Calculation of Dataset 1

_{t}

_{−1}, y

_{t}

_{−2}, y

_{t}

_{−p}) and the information from the actual variable. The parameter q ≥ 0 specifies how many past values of the residuals (ε) affect the time series. The terms α and β are additional coefficients

_{observed}):

_{residual}was then the dependent input data for the regressions.

#### 2.4.2. Calculation of Dataset 2

#### 2.5. Statistical Procedures

_{i}) indicates the wheat yield for every fertilization level; x

_{i}, …, x

_{n}indicate the climatic variables; b

_{0}, …, b

_{n}are the empirical regression model coefficients; and e

_{j}is the residual error component of the model.

- Autocorrelation of regression residuals: Durbin–Watson test;If residuals are not independent, there is autocorrelation. This means that a variable correlates with itself at a different time. We use SPSS to test first-order autocorrelation and thus whether a residual correlates with its direct neighbor. However, in this study, it would make little sense to check autocorrelation because it is very unlikely that the measurements or residuals with a distance of three years are dependent. In such cases, testing the independence of the residuals can be omitted.
- Homoscedasticity (no autocorrelation in regression residuals, homogeneity of variance): plot of residuals against predicted values;
- Normally distributed residuals; and
- Multicollinearity (two independent variables are highly correlated): tolerance and variance inflation factor (VIF).

_{si}is the observed value, and z*

_{si}is the predicted value.

## 3. Results

#### 3.1. Temporal Course of the Yields

^{−1}for the low and high fertilized experimental plots with a range of 57 to 91 and 59 to 96 dt ha

^{−1}, respectively. The higher level of N fertilization produced less than 5% higher yields in comparison to the low fertilized plots, which however was statistically not significant. The mean yield of non-fertilized plots was 35.2 dt ha

^{−1}, which was approximately half of the yield of the fertilized treatments.

#### 3.2. Derivation of Yields with Monthly Predictors

^{2}) higher than 0.77, the derivation quality of the yields was distinctly weaker. In the latter, the same plant cultivar combined with the same treatment produced different yield-influencing effects. Soil differences between plots were also conceivable.

^{−1}, in combination with an R

^{2}of higher than 0.77, indicated sufficient accuracy.

#### 3.3. Derivation of Yields with Annual Predictors

^{2}and lower RMSE (Table 6). The R

^{2}of the unfertilized plots was weak with the single predictor aridity index (AI). The derivation of the residuals of the fertilized plots with the independent variables early frost index (EFI) and winter index (WI) had a lower R

^{2}. The accuracy of the regression improved the more predictors were included. However, the quality of the yearly predictors was poor. In all cases, the temporal duration was expressed as number of days.

## 4. Discussion

^{2}values of at least 0.7.

^{2}values were 0.4 for the unfertilized control and low fertilization, and 0.65 for the highly fertilized plots. Winter values were also significant here (EFI and WI). In the following, the significant climate variables are presented.

^{−1}. Brown rust (Puccinia triticina) also occurred in all German federal states and were second most important in both occurrence and yield loss [47]. No surveys of this kind were conducted on the trial site investigated here. However, losses cannot be ruled out.

^{2}of 0.76–0.95, in 1980, 1983, 1989, 1995, 1998, 2001, 2004, 2007, and 2012 and R

^{2}of 0.46–0.66 in 1986, 1992, and 2010) [39].

## 5. Conclusions

^{−1}on a multi-annual average due to a reduction of fertilizing by 20–30%. In other words, 20–30% less fertilization reduced the sensitivity to a lack of precipitation on this site. However, this hypothesis needs further verification.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of experimental plots (4 × 8 m), fertilized with calcium ammonium nitrate throughout the whole long-term field experiment.

**Figure 2.**Annual yields of winter wheat between 1983 and 2010 with the smoothing lines for the fertilized and control plots (N0 unfertilized plots, low fertilized plots N1, high fertilized plots N2).

**Figure 3.**Measured and predicted (see Table 3) residuals with monthly predictors for the different fertilization levels (N0 unfertilized plots, low fertilized plots N1, high fertilized plots N2, N0 expressed as transformed variable).

**Figure 4.**Measured and predicted (Table 3) residuals with yearly predictors for the different fertilization levels. N0, unfertilized plots; N1, low fertilized plots; N2, high fertilized plots.

**Table 2.**Site description of the long-term nitrogen fertilization experiment in Dürnast [39].

Parameter | Value (Range) | |||
---|---|---|---|---|

Elevation (m) | 470 (469–472) | |||

Slope (rad) | 0.05 (0.05–0.09) | |||

Aspect (rad) | 2.64 (1.97–3.46) | |||

Soil vertical layer | 0–25 cm | 25–50 cm | 50–75 cm | |

Soil texture (kg kg^{−1}) | Clay | 20.8 (15.7–27.3) | 23.3 (15.2–34.9) | 26.2 (13.6–34.8) |

Silt | 61.5 (54.4–67.5) | 61.7 (35.7–72.9) | 60.7 (32.8–76.8) | |

Sand | 16.6 (11.9–21.3) | 14.4 (8.5–40.5) | 12.4 (5.3–46.8) | |

Skeleton | 1.2 (0.0–3.0) | 0.6 (0.0–7.0) | 0.4 (0.0–3.0) | |

pH | 6.44 (5.94–6.84) | 6.36 (5.96–7.12) | 6.31 (5.98–7.18) | |

C content (%) | 1.18 (0.94–1.38) | 0.56 (0.35–1.14) | 0.4 (0.22–1.11) | |

N content (%) | 0.1 (0.08–0.12) | 0.06 (0.03–0.12) | 0.04 (0.02–0.12) |

Year | Wheat Cultivar | N Fertilizer (kg ha^{−1}) | |
---|---|---|---|

Low | High | ||

1980 | Winter Caribo | 100 | 150 |

1983 | Winter Caribo | 100 | 150 |

1986 | Winter Kronjuwel | 100 | 150 |

1989 | Winter Obelisk | 100 | 150 |

1992 | Winter Orestis | 100 | 150 |

1995 | Winter Astron | 100 | 150 |

1998 | Winter Astron | 100 | 150 |

1992 | Winter Obelisk | 100 | 150 |

1995 | Winter Astron | 100 | 150 |

1998 | Winter Astron | 100 | 150 |

2001 | Winter Ludwig | 100 | 150 |

2004 | Winter Tommi | 140 | 180 |

2007 | Winter Tommi | 140 | 180 |

2010 | Winter Tommi | 140 | 180 |

2012 | Spring Kadrilj | 120 | 180 |

2015 | Spring Lennox | 120 | 180 |

Variable | Definition/Time Range | Formula for the Derivation of the Indices |

Precipitation intensity (PI) | Sum of days on which a certain amount of precipitation occurs | |

PI1: >0–1 mm per day | $\mathrm{PI}1={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{P}>0\mathrm{mm}+\mathrm{P}\le 1\mathrm{mm}$ | |

PI2: >1–10 mm per day | $\mathrm{PI}2={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{P}>1\mathrm{mm}+\mathrm{P}10\mathrm{mm}$ | |

PI3: >10 mm per day | $\mathrm{PI}3={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{P}>10\mathrm{mm}+\mathrm{P}\ge 10\mathrm{mm}$ | |

Monthly values from October to August | where P is precipitation (mm) and n denotes number of days | |

Rain-free days (P0) | Sum of days without precipitation (P0); monthly values from October to August | $\mathrm{P}0={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{N}=0\mathrm{mm}$ where N is height of precipitation |

Temperature threshold (TT) | Sum of the days on which the threshold values of 5 or 10 °C are exceeded; monthly values from October to August | $\mathrm{TT}1={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{Tmax}\ge 5\xb0\mathrm{C}$ $\mathrm{TT}2={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{Tmax}\ge 10\xb0\mathrm{C}$ where Tmax is the daily maximum temperature (°C) |

Summer days (SD) | Sum of the days on which the air temperature exceeds 25 °C; monthly values from October to August | $\mathrm{SD}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}\ge 25\xb0\mathrm{C}$ |

Heat days (HD) | Sum of the days on which the air temperature exceeds 30 °C; monthly values from October to August | $\mathrm{HD}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}\ge 30\xb0\mathrm{C}$ |

Frost days (FT) | Sum of the days on which the air temperature falls below the value 0 °C; monthly values from October to August | $\mathrm{FT}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\mathrm{Tmin}\ge 0\xb0\mathrm{C}$ where Tmin is the daily minimum temperature (°C) |

Average temperature (T_{y}) per year | ${\mathrm{T}}_{\mathrm{y}}=\frac{\left({{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Temp}}_{\mathrm{d}}\right)}{\mathrm{n}}$ where Temp _{d} is the diurnal mean air temperature of the day, n is the number of days per year | |

Average temperature (T_{v}) main vegetation period | ${\mathrm{T}}_{\mathrm{v}}=\frac{\left({{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Temp}}_{\mathrm{d}}\right)}{\mathrm{n}}$ where n is the number of days per main vegetation period | |

Precipitation sum (P_{y}) | Sum of precipitation per year, (calculated for every year) | ${\mathrm{P}}_{\mathrm{y}}={{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{d}}\mathrm{mm}$ where P _{d} is precipitation per day |

Rain factor (RF) | Relationship of precipitation/temperature per year, (calculated for every year) | $\mathrm{RF}=\frac{{\mathrm{P}}_{\mathrm{y}}}{{\mathrm{T}}_{\mathrm{y}}}$ where P _{y} is the annual precipitation and T_{y} is the average annual temperature |

Dryness index de Martonne-Reichel (DI) | Evaluates the effect of precipitation on plant physiology and precipitation distribution during the main vegetation period | $\mathrm{DI}=\frac{{\mathrm{P}}_{\mathrm{y}}}{{\mathrm{T}}_{\mathrm{y}}+10}\times \frac{\mathrm{K}}{120}$ where 10 indicates that negative values in the denominator should be avoided, K is the number of days with precipitation ≥ 1.0 mm, and 120 is the multiannual average number of days with precipitation in Germany (main vegetation period) |

Air humidity (AH) | Evaluates the effect of precipitation on plant physiology; annual values | $\mathrm{AH}=\frac{{\mathrm{P}}_{\mathrm{y}}}{{\mathrm{T}}_{\mathrm{y}}+10}$ |

Aridity index (AI) | Evaluates the effect of precipitation on plant physiology; main vegetation period | $\mathrm{AI}=\frac{{\mathrm{P}}_{\mathrm{v}}}{{\mathrm{T}}_{\mathrm{v}}+10}$ |

Summer index (SI_{y}) | Sum of days with daily maximum of air temperature above 5 °C; yearly | ${\mathrm{SI}}_{\mathrm{y}}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}\ge 5\xb0\mathrm{C}$ |

Summer index (SI_{v}) | Sum of days with daily maximum of air temperature above 5 °C; main vegetation period | ${\mathrm{SI}}_{\mathrm{v}}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}\ge 5\xb0\mathrm{C}$ |

Winter index (WI) | Sum of days with daily maximum of air temperature above 5 °C from November to April | $\mathrm{WI}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}\ge 5\xb0\mathrm{C}$ |

Frost alternating days (FAD) | Sum of days (October to April) with a change of temperatures above and below 0 °C within a day, between consecutive days | $\mathrm{FAD}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmax}>0+{\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmin}<0$ |

Early frost index (EFI) | Sum of the days on which the minimum air temperature falls below 0 °C from July to October | $\mathrm{EFI}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmin}<0\xb0\mathrm{C}$ |

Late frost index (LFI) | Sum of the days on which the minimum air temperature falls below 0 °C from April to July | $\mathrm{LFI}={\displaystyle {\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}}\mathrm{Tmin}0\xb0\mathrm{C}$ |

Variable | Definition/Time Range | |

Frost severity (FS) | Annual minimum of temperature | |

Begin/end of the main vegetation period | First week of the year on which the threshold value of 5 °C is permanently exceeded (at least 5 days)/mid-August | |

Frost index per Liu (FI_Liu) | Sum of the days on which the minimum air temperature is below −3 °C and the temperature difference is at least 8 °C from the mean value of the last 20 days; from September to May | |

Frost shock (FS) | Sum of the days on which the air temperature drops by 15 °C within 24 h and the minimum air temperature falls below −3 °C; annual values | |

Summer cold per Liu (SC_Liu) | Sum of the difference between the minimum temperature and the mean minimum temperature of the last 20 days exceeding 8 °C | |

Climatic main vegetation time duration 1 (CL1) | Number of days with the longest period in which the air temperature exceeds 10 °C; values per year | |

Climatic main vegetation time duration 2 (CL2) | Number of 5-day periods with a maximum diurnal air temperature above 10 °C; values per year | |

Global radiation (GR) | Sum of global radiation; annual values |

**Table 5.**Overview of the effects on the temporal yield development and the effects that are eliminated by calculating residuals.

Influence | Effects Eliminated by Residuals | Effects Remain in Residuals |
---|---|---|

Biological and chemical | New varieties Herbicides Insecticides Fertilizer, fertilization level | Diseases Pest infestation |

Mechanical management | Technical Equipment Processing | |

Management advancement | Crop rotation | |

Atmospheric | Climate change | Weather deviations, Extreme weather events |

**Table 6.**Formulas depicting multiple linear regressions derivation of residuals and yields for different levels of fertilization with monthly climate parameters.

Regression Coefficient | Unit Predictor | Sig. | β Coefficient Standardized | RMSE (dt ha^{−1}) | R^{2} Adj. | |
---|---|---|---|---|---|---|

Residuals unfertilized control^3 | 271.42 | ** | 4.27 | 0.775 | ||

−61.007 × temperature threshold 2 (TT2) April | number of days | ** | −0.822 | |||

319.656 × TT2 February | number of days | * | 0.492 | |||

Residuals low fertilization level | −22,035 | * | 2.90 | 0.862 | ||

1.859 × N0 June | number of days | ** | 0.651 | |||

−1.532 × temperature threshold 1 (TT1) December | number of days | ** | −0.446 | |||

Residuals high fertilization level | −46.209 | *** | 4.04 | 0.804 | ||

2.835 × rain-free days (P0) June | number of days | *** | 0.909 | |||

Yield unfertilized control | 43.902 | ** | 3.60 | 0.487 | ||

−1.499 × temperature threshold 2 (TT2) April | number of days | * | −0.738 | |||

Yield low fertilization level | 90.973 | ** | 7.63 | 0.471 | ||

−3.142 × temperature threshold 1 (TT1) December | number of days | * | −0.728 | |||

Yield high fertilization level | 29.120 | n.s. | 8.65 | 0.472 | ||

2.968 × rain-free days (P0) June | number of days | * | 0.729 |

**Table 7.**Formulas depicting multiple linear regressions derivation of residuals and yields for different levels of fertilization with yearly climate parameters.

Regression Coefficient | Unit Predictor | Sig. | β Coefficient, Standardized | RMSE (dt ha^{−1}) | R^{2} Adj. | |
---|---|---|---|---|---|---|

Residuals unfertilized control | 19.697 | ** | 4.41 | 0.403 | ||

−1.056 × aridity index (AI) | number of days | ** | −6.85 | |||

Residuals low fertilization | −5.752 | n.s. | 6.35 | 0.439 | ||

3.595 × early frost index (EFI) | number of days | * | 0.708 | |||

Residuals high fertilization | −11.914 | * | 5.03 | 0.648 | ||

3.526 × early frost index (EFI) | number of days | * | 0.636 | |||

1.960 × winter index (WI) | number of days | * | 0.486 | |||

Crop unfertilized control | 58.083 | ** | 3.73 | 0.45 | ||

−1.171 × aridity index (AI) | number of days | * | −0.715 | |||

Crop low fertilization | 72.608 | ** | 5.07 | 0.733 | ||

−1.830 × summer cold per Liu (SC_Liu) | number of days | ** | −0.686 | |||

3.990 × early frost index (EFI) | number of days | ** | 0.625 | |||

Crop high fertilization | −173.24 | * | 5.90 | 0.719 | ||

−0.00021 × global radiation (GR) | watt-hour m^{2} | ** | 0.692 | |||

4.194 × early frost index (EFI) | number of days | * | 0.579 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Heil, K.; Lehner, A.; Schmidhalter, U.
Influence of Climate Conditions on the Temporal Development of Wheat Yields in a Long-Term Experiment in an Area with Pleistocene Loess. *Climate* **2020**, *8*, 100.
https://doi.org/10.3390/cli8090100

**AMA Style**

Heil K, Lehner A, Schmidhalter U.
Influence of Climate Conditions on the Temporal Development of Wheat Yields in a Long-Term Experiment in an Area with Pleistocene Loess. *Climate*. 2020; 8(9):100.
https://doi.org/10.3390/cli8090100

**Chicago/Turabian Style**

Heil, Kurt, Anna Lehner, and Urs Schmidhalter.
2020. "Influence of Climate Conditions on the Temporal Development of Wheat Yields in a Long-Term Experiment in an Area with Pleistocene Loess" *Climate* 8, no. 9: 100.
https://doi.org/10.3390/cli8090100