# Evaluating Maize Drought and Wet Stress in a Converted Japanese Paddy Field Using a SWAP Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. SWAP Model Description

#### 2.1.1. Soil Water Movement

^{3}cm

^{−3}), t is time (d), K(h) is the unsaturated hydraulic conductivity (cm d

^{−1}), h is the matric potential head (−cm), z is the vertical coordinate (cm), and S

_{a}(z,h) is the soil water extraction rate by plant roots (cm

^{3}cm

^{−3}d

^{−1}). The SWAP model can function with a time-step varying from 10

^{−6}to 0.2 days to obtain calculation convergence.

_{sat}is the saturated water content (cm

^{3}cm

^{−3}), θ

_{res}is the residual water content (cm

^{3}cm

^{−3}), α (cm

^{−1}), n, and m (−) are empirical shape factors; and m is 1−1/n. K(h) is calculated using the following equations:

_{sat}is the saturated hydraulic conductivity (cm d

^{−1}) and λ is a shape parameter (=0.5).

#### 2.1.2. Boundary Conditions

_{p}is the potential transpiration of a dry canopy (mm d

^{−1}), W

_{frac}is the fraction of the day in which the canopy is wet (−), V

_{c}is the vegetation cover (−), ∆

_{v}is the slope of the vapor pressure curve (kPa C

^{−1}), L

_{w}is the latent heat of vaporization (J kg

^{−1}), R

_{n}is the net radiation flux at the canopy surface (J m

^{−2}d

^{−1}), G is the soil heat flux (J m

^{−2}d

^{−1}), p

_{1}accounts for unit conversion (=86,400 s d

^{−1}), ρ

_{a}is the air density (kg m

^{−3}), C

_{a}is the heat capacity of moist air (J kg

^{−1}C

^{−1}), e

_{sat}is the saturation vapor pressure (kPa), e

_{a}is the actual vapor pressure (kPa), r

_{a,can}is the aerodynamic resistance of the crop (s m

^{−1}), γ

_{a}is the psychrometric constant (kPa C

^{−1}), r

_{s,min}is the minimal stomatal resistance (s m

^{−1}), LAI

_{eff}is the effective leaf area index (−), E

_{p}is the potential evaporation (mm d

^{−1}), r

_{soil}is the soil resistance of wet soil (s m

^{−1}), and r

_{a,soil}is the aerodynamic resistance of the soil surface (s m

^{−1}). On a daily basis, the soil heat flux G is assumed to be negligible. The vegetation cover V

_{c}is obtained by the following equation:

_{dir}and κ

_{dif}are the extinction coefficients for direct (0.80) and diffuse (0.72) solar light, respectively, and LAI is the actual leaf area index (−). LAI

_{eff}is derived from LAI:

_{a,can}is determined using the resistance for uniform crop r

_{a,can,}

_{0}:

_{m}is the height of wind speed measurements (m), z

_{h}is the height of temperature and humidity measurements (m), d is the zero plane displacement of wind profile (m), z

_{om}is the roughness parameter for momentum (m), z

_{oh}is the roughness parameter for heat and vapor (m), κ

_{vk}is the von Karman constant (0.41), and u is the wind speed measurement at z

_{m}(m s

^{−}

^{1}). The parameters d, z

_{om}, and z

_{oh}are defined as:

_{crop}is the crop height (cm).

#### 2.1.3. Crop Water Stress

_{p}(z) is calculated by the following equation using the potential transpiration T

_{p}(cm d

^{−1}):

_{root}(z) is the root length density at a certain depth (cm cm

^{−3}) and D

_{root}is the root layer thickness (cm).

_{a}(z,h) is calculated considering the water stress described by the function proposed by Feddes et al. [13]:

_{rw}is the reduction factor for excessive wet and dry conditions (−). The reduction factor α

_{rw}changes from 0 to 1.0 depending on the critical pressure heads h

_{1}, h

_{2}, h

_{3}, and h

_{4}(Figure 1). Root water extraction is optimal between h

_{2}and h

_{3}; the reduction under wet conditions occurs when wetter than h

_{2}; under dry conditions, the reduction occurs when drier than h

_{3}. The value of h

_{3}depends on the water demand of the atmosphere and varies with T

_{p}; it is expressed by following equations:

_{3l}and h

_{3h}are the critical pressure heads for low and high transpiration rates, T

_{low}and T

_{high}, respectively (−cm). We used the default values for T

_{low}and T

_{high}: 0.1 and 0.5 cm d

^{−1}.

_{a}(cm d

^{−1}) is yielded by integrating S

_{a}(z,h) over the root layer. Drought and wet stresses are evaluated by subtracting T

_{a}from T

_{p}.

#### 2.2. Field Experiment

#### 2.2.1. Field Experiment for Model Calibration

#### 2.2.2. Field Experiment for Model Validation

#### 2.3. Model Calibration and Validation

#### 2.3.1. Data for SWAP Model Simulation

#### 2.3.2. Model Calibration

#### 2.3.3. Model Validation

#### 2.3.4. Evaluation of Calculation Error

_{obs}) and calculated (θ

_{cal}) volumetric water content using the root mean square error (RMSE):

_{obs}and h

_{cal}) in the calibration plot to consider possible error in water stress estimation; the matric potential head was converted from θ

_{obs}and θ

_{cal}by using calibrated Mualem–van Genuchten parameters.

#### 2.3.5. Evaluation of Water Stress under Actual and Scenario Conditions

_{p}, T

_{a}, drought stress, and wet stress using the 2019 observations as the actual conditions. We then evaluated the difference in water stress between the actual and a scenario in which tillage reached 11 cm deeper than under actual conditions; the soil hydraulic properties of layer 2 were therefore the same as those of layer 1. The tillage depth in the scenario conditions assumed to exceed a depth where hardpans usually exist.

## 3. Results and Discussion

#### 3.1. Model Calibration

^{−1}, on 15 June 2019. Thereafter, precipitation occurred more frequently. The highest groundwater level, −14.6 cm, was recorded on 2 May 2019, after which it gradually decreased to its lowest value, approximately −85 cm; we note that this was the limit of observation for the water level monitoring sensor. The groundwater level changed frequently after 15 June 2019, and high groundwater levels of approximately −20 cm appeared on 16 June and 15 July 2019.

_{obs}, θ

_{cal}, and the volumetric water content with initial parameter θ

_{ini}at depths of 10, 20, and 30 cm, respectively. The initial parameters and soil dry bulk density are shown in Table 4; Table 5 shows calibrated parameters. At a depth of 10 cm, θ

_{ini}was higher than θ

_{obs}and θ

_{cal}during the simulation period, except between 2 and 12 June 2019, when precipitation was less frequent. The values of θ

_{obs}and θ

_{cal}at a depth of 10 cm varied between 0.3 and 0.5 cm

^{3}cm

^{−3}, and the change in these two values was more frequent than in their equivalents at the other two depths. At a depth of 10 cm, θ

_{obs}and θ

_{cal}increased with rising precipitation (Figure 4a,b). Before 14 June 2019, θ

_{obs}and θ

_{cal}changed moderately and had three peaks, namely, 30 April, 20 May, and 7 June 2019, when precipitation was more than 20 mm d

^{−1}. After 15 June 2019, when precipitation occurred frequently, θ

_{obs}and θ

_{cal}increased, and θ

_{cal}changed more frequently than θ

_{obs}. At a depth of 20 cm, θ

_{ini}was higher than θ

_{obs}and θ

_{cal}throughout the simulation period: θ

_{obs}and θ

_{cal}were between 0.4 and 0.5 cm

^{3}cm

^{−3}. At a depth of 30 cm, θ

_{obs}was between 0.4 and 0.6 cm

^{3}cm

^{−3}, whereas θ

_{cal}was around 0.5 cm

^{3}cm

^{−3}: θ

_{ini}was almost the same as θ

_{cal}. Between 27 May and 14 June 2019, θ

_{obs}at a depth of 30 cm gradually decreased; in contrast, θ

_{cal}changed minimally. During this period, the lowest groundwater level was applied in the simulation. However, the actual ground water level at this time might have exceeded the sensor’s measurement limit, causing the difference between θ

_{obs}and θ

_{cal}.

_{obs}and θ

_{cal}at depths of 10, 20, and 30 cm were 0.030, 0.012, and 0.027 cm

^{3}cm

^{−3}, respectively. Crescimanno and Garofalo [24], also using a SWAP model, reported that their largest RMSE (0.037 cm

^{3}cm

^{−3}) related to volumetric water content was low enough to indicate good model accuracy. Similarly, our largest RMSE (0.030 cm

^{3}cm

^{−3}) was sufficiently low for this purpose.

#### 3.2. Model Validation

^{−1}) occurred on 29 September 2018. Thereafter, the groundwater level gradually decreased to its lowest value (−90 cm), and precipitation became less frequent. Figure 6b shows the temporal changes in θ

_{obs}and θ

_{cal}at a depth of 10 cm: the trends in θ

_{cal}and θ

_{obs}were matched; both values changed with the precipitation. The RMSE between θ

_{cal}and θ

_{obs}was 0.029 cm

^{3}cm

^{−3}. This result indicates that, even with high levels of precipitation and groundwater, the model was able to reproduce actual volumetric water content using our calibrated parameters.

#### 3.3. Change in Matric Potential in the Calibration Plot

_{cal}) in the calibration plot captured the trend of change in observed value (h

_{obs}) except after 15 June 2019, when precipitation was more frequent (Figure 4a and Figure 7). We excluded positive pressure head in Figure 6. Before 15 June 2019, h

_{cal}at a depth of 10 cm changed similarly to h

_{obs}except between 30 April and 19 May 2019. In this period, h

_{cal}was almost 10 times higher than h

_{obs}; this reflected lower θ

_{cal}than θ

_{obs}in the same period (Figure 4b and Figure 7a). At depths of 20 and 30 cm, the changes in h

_{obs}and h

_{cal}were similar. After 27 May 2019, h

_{obs}at a depth of 30 cm became larger than h

_{cal}due to the decrease in θ

_{obs}in this period (Figure 4d and Figure 7c). Except at a depth of 30 cm, h

_{cal}differed from h

_{obs}after 15 June 2019. At a depth of 10 cm, h

_{cal}tended to be smaller than h

_{obs}; h

_{cal}was larger than h

_{obs}at a depth of 20 cm. The RMSEs between h

_{obs}and h

_{cal}at depths of 10, 20, and 30 cm were 1.0, 0.7, and 0.6 log

_{10}(−cm), respectively. These results indicate that the calculated water stress after 15 June 2019 might contain larger error than that before the day.

#### 3.4. Water Stress under Actual Conditions

_{p}and T

_{a}in the calibration plot in 2019 as estimated by the SWAP model. T

_{a}was significantly lower than T

_{p}during most of the simulation period, reaching an approximate extreme of only 20% of T

_{p}. From 28 May to 15 June 2019, less precipitation occurred, and the groundwater level was low (Figure 4a). Thus, the difference between T

_{p}and T

_{a}might have been induced by dry conditions. After 15 June 2019, groundwater level and precipitation increased; T

_{a}during this period may have decreased due to the wet conditions. However, several zero-precipitation days (namely, 17–20 June, 23–25 June, and 4–8 July 2019) occurred during this period. Although the comparison between T

_{p}and T

_{a}indicates that water stress occurred, we could not distinguish whether it was drought or wet stress that affected T

_{a}.

#### 3.5. Illustrative Example: Reduction of Water Stress by Changing Tillage Depth

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The reduction factor for excessive wet and dry conditions, α

_{rw}, as a function of matric potential head; h

_{1}, h

_{2}, h

_{3}, and h

_{4}are critical pressure heads (−cm); h

_{3}is between h

_{3h}and h

_{3l}values for high and low transpiration rates, respectively; h

_{3}depends on the water demand of the atmosphere (T

_{low}and T

_{high}) and varies with the potential transpiration rate T

_{p}. Wet stress occurs when wetter than h

_{2}, whereas drought stress occurs when drier than h

_{3}.

**Figure 2.**The converted field in this study. The field was divided into a calibration plot and a validation plot.

**Figure 4.**Volumetric water content in the calibration plot in 2019. (

**a**) Groundwater level and precipitation; (

**b**–

**d**) results at depths of 10, 20, and 30 cm, respectively. The maximum daily precipitation, 51.7 mm d

^{−1}, occurred on 15 June 2019. The results with initial and calibrated soil hydraulic parameters were generated using the data in Table 4 and Table 5, respectively.

**Figure 5.**The analytical soil water retention curves generated by initial and calibrated Mualem–van Genuchten parameters. (

**a**–

**c**) Results for layers 1, 2, and 3, respectively. The grey area represents the zero-water-stress zone; drought or wet stresses occur outside this area. In the scenario condition, layers 1 and 2 used the calibrated soil water retention curve of layer 1.

**Figure 6.**Volumetric water content in the validation plot in 2018. (

**a**) Groundwater level and precipitation; (

**b**) θ

_{cal}and θ

_{obs}at a depth of 10 cm. The maximum daily precipitation, 82.7 mm d

^{−1}, occurred on 29 September 2018.

**Figure 7.**Matric potential head in the calibration plot in 2019. (

**a**–

**c**) Results at depths of 10, 20, and 30 cm, respectively. Those results were converted from observed and calculated volumetric water content by using calibrated Mualem–van Genuchten parameters (Table 5). We excluded data that showed positive values.

Soil hydraulic data | ||

Estimated by nonlinear optimization using the Mualem–van Genuchten model | ||

Saturated hydraulic conductivity K_{sat} | Measured | |

Soil water retention curve | Measured | |

Meteorological data | ||

Obtained from the Agro-Meteorological Grid Square Data, NARO, which generates the Japanese meteorological data for every 1 km^{2} [18] | ||

Crop data | ||

Crop height | Measured | |

Rooting depth | Measured | |

LAI | Determined based on Maddonni and Otegui [19] | |

Critical pressure heads of water stress | Data from Wesseling et al. [20] | |

Initial and bottom boundary conditions | ||

Matric potential head | Converted from observed volumetric water content | |

Groundwater level | Measured | |

Data for calibration | ||

Volumetric water content | Measured |

Depth (cm) | 0–3 | 3–23 | 23–35 | 35–100 |

Nodal spacing (cm) | 0.2 | 1.0 | 2.0 | 5.0 |

Maximum rooting depth (cm) | 50.0 | (17 July 2019; observed) |

Crop height in the calibration plot (cm) | 27.2 | (9 May 2019; observed) |

58.0 | (23 May 2019; observed) | |

158.5 | (12 June 2019; observed) | |

230.1 | (25 June 2019; observed) | |

258.6 | (17 July 2019; interpolated) | |

Crop height in the validation plot (cm) | 17.7 | (10 August 2018; observed) |

246.1 | (5 November 2018; observed) | |

Critical pressure heads: h_{1}, h_{2}, h_{3h}, h_{3l}, h_{4} (−cm) | 15, 30, 325, 600, 8000 |

Layer No. | Depth (cm) | θ_{res}(cm ^{3} cm^{−3}) | θ_{sat}(cm ^{3} cm^{−3}) | α (cm ^{−1}) | n (-) | K_{sat}(cm s ^{−1}) | λ (-) | Dry Bulk Density (g cm ^{−3}) |
---|---|---|---|---|---|---|---|---|

1 | 0–12 | 0.010 | 0.500 | 0.090 | 1.07 | 1.06 × 10^{−3} | 0.50 | 1.15 |

2 | 12–23 | 0.010 | 0.502 | 0.047 | 1.05 | 5.89 × 10^{−4} | 0.50 | 1.31 |

3 | 23–100 | 0.010 | 0.509 | 0.008 | 1.08 | 1.44 × 10^{−4} | 0.50 | 1.31 |

_{res}: residual water content; θ

_{sat}: saturated water content; α and n: empirical shape factors; K

_{sat}: saturated hydraulic conductivity; λ: a shape parameter.

Layer No. | Depth (cm) | θ_{res}(cm ^{3} cm^{−3}) | θ_{sat}(cm ^{3} cm^{−3}) | α (cm ^{−1}) | n (-) | K_{sat}(cm s ^{−1}) | λ (-) |
---|---|---|---|---|---|---|---|

1 | 0–12 | 0.050 | 0.430 | 0.100 | 1.05 | 5.21 × 10^{−3} | 0.50 |

2 | 12–23 | 0.010 | 0.440 | 0.090 | 1.02 | 2.91 × 10^{−4} | 0.50 |

3 | 23–100 | 0.010 | 0.520 | 0.010 | 1.08 | 5.86 × 10^{−4} | 0.50 |

_{res}: residual water content; θ

_{sat}: saturated water content; α and n: empirical shape factors; K

_{sat}: saturated hydraulic conductivity; λ: a shape parameter.

**Table 6.**Average volumetric water content per day and the number of days under stress, under actual and scenario conditions.

Depth | Condition | Drought-Dominant Period (3–15 June 2019; 12 days) | Wet Stress Critical Period (23 June–13 July 2019; 20 days) | ||
---|---|---|---|---|---|

Average Volumetric Water Content (cm ^{3} cm^{−3}) | Stress Occurrence Days | Average Volumetric Water Content (cm ^{3} cm^{−3}) | Stress Occurrence Days | ||

10 cm | Actual | 0.330 | 12 | 0.405 | 13 |

Scenario | 0.331 | 12 | 0.375 | 4 | |

20 cm | Actual | 0.393 | 12 | 0.416 | 8 |

Scenario | 0.380 | 0 | 0.390 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Hamada, K.; Inoue, H.; Mochizuki, H.; Asakura, M.; Shimizu, Y.; Takemura, T.
Evaluating Maize Drought and Wet Stress in a Converted Japanese Paddy Field Using a SWAP Model. *Water* **2020**, *12*, 1363.
https://doi.org/10.3390/w12051363

**AMA Style**

Hamada K, Inoue H, Mochizuki H, Asakura M, Shimizu Y, Takemura T.
Evaluating Maize Drought and Wet Stress in a Converted Japanese Paddy Field Using a SWAP Model. *Water*. 2020; 12(5):1363.
https://doi.org/10.3390/w12051363

**Chicago/Turabian Style**

Hamada, Kosuke, Hisayoshi Inoue, Hidetoshi Mochizuki, Mayuko Asakura, Yuta Shimizu, and Takeshi Takemura.
2020. "Evaluating Maize Drought and Wet Stress in a Converted Japanese Paddy Field Using a SWAP Model" *Water* 12, no. 5: 1363.
https://doi.org/10.3390/w12051363