# Simulations of the Soil Evaporation and Crop Transpiration Beneath a Maize Crop Canopy in a Humid Area

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.85, D = 0.96, p < 0.001); and (2) The trend of the simulated Tc can present the actual Tc variation, but the accuracy was not as high as the evaporation (R

^{2}= 0.74, D = 0.87, p < 0.001), therefore, the simulation of water balance process by APSIM will be helpful in calculating Es and Tc in a humid area of Nanjing, and its application also could predict the production of maize fields in Nanjing.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measurement Field

^{3}and a soil pH (H

_{2}O) value of 6.3. The total carbon and nitrogen contents are 19.95 g/kg and 1.19 g/kg, respectively, and the maize variety was “Jundan 66”. Basic soil characteristics and parameters of the experimental site are shown in Table 1, where it can be seen that all of the characteristics of the soil increased layer-by-layer, but DUL, LL15 and SAT of the soil from the ground surface to the depth of 40 cm have little changes among the 4 soil layers. However, the Airdry changed a lot with the soil layers varied (Table 1).

#### 2.2. Measurements and Variations of Meteorological Factors in Maize Growing Periods

_{n}), maximum temperature/low temperature, rainfall, wind speed (at 2 m height above the land surface) and relative humidity (RH) in the whole corn growth period are shown in Figure 2a–c, respectively. It is worth noting that as a source of energy for crop evapotranspiration [16], the R

_{n}has the highest correlation coefficient to transpiration among all of the related factors [27]. As shown in Figure 2a, the radiation was relatively large and its value fluctuated obviously during the whole 3 growth periods, with the highest value of 26.82 MJ/m

^{2}/d on 15 June 2018, and the lowest value of 1.96 MJ/m

^{2}/d on 15 September 2016. In addition, the values on sunny days were larger than those of rainy weather. Meanwhile, the wind speed was basically stable and relatively small during the 3 growth periods, values of it were generally below 1.5 m/s, but its maximum value reached 2.4 m/s, which appeared on 26 August 2016. As can be seen from Figure 2b, during the 3 growth periods, the daily maximum temperature had larger fluctuations annually; however, the daily minimum temperature had larger fluctuations in 2016, and smaller fluctuations in 2017 and 2018. The lowest value was 5.08 °C, which appeared on 21 June 2016, and the highest was 30.12 °C, which appeared on 28 July 2017. In terms of the whole 3 growth periods, the diurnal temperature range in 2016 was relatively larger than that of the other years. As we can see from Figure 2c, the total rainfall in 2016 was less and concentrated in the final days of June and early days of July, and the concentrating period of precipitation in 2017 and 2018 was August. The maximum rainfall reached 182.4 on 15 August 2018, and the secondary peak appeared with a value of 82.7 on 11 July 2018. It can be seen that the annual variation of RH had little change, but its diurnal variation was very large and fluctuated greatly with a highest value of 99.7% and a lowest level of 47.1% during the 3 years. The fluctuation of RH was related to the fluctuation of rainfall and radiation. When the rainfall was large at the beginning and the radiation was low, the relative humidity was relatively large accordingly. Whereas at the end of August and the beginning of September in 2016, the precipitation was basically zero, so the relative humidity was relatively low.

#### 2.3. APSIM Model

#### 2.3.1. Es Model in APSIM

_{so}is the amount of potential soil evaporation (replaced with observed evaporation here) each day during stage 1, ${t}_{1}$ is the total number of Es days in stage 1, and α (mm/d

^{0.5}) is the coefficient in stage 2, and it is assumed to be a constant value for particular soil and mainly depends on soil hydraulic characteristic, ∆ (kPa/°C) is the slope of saturated water vapor pressure, γ (kPa/°C) is the psychrometer constant, R

_{ns}(MJ/m

^{2}/d) is the average net radiation at the soil surface, R

_{no}(MJ/m

^{2}/d) is the average net radiation at canopy, R

_{s}(MJ/m

^{2}/d) is the solar radiation, ${\mathsf{\u03f5}}_{s}$ is the albedo for bare soil with a value of 0.1 here [31], $\mathsf{\u03f5}$ is the developing canopy albedo varying with Lai, which is the leaf area index. What is noteworthy is that different soils have different U values. According to the Ritchie experiment, U values of clay, loam and sandy soil are 12 mm, 9 mm and 6 mm, respectively.

#### 2.3.2. Tc Model in APSIM

_{n}(MJ/m

^{2}/d) is energy available for evapotranspiration, λ (J/kg) is the latent heat of vaporization, ${\rho}_{air}$ and ${\rho}_{water}$ (kg/m

^{3}) represent the density of air and water, D (kPa) is the specific vapor pressure deficit, and G

_{a}and G

_{c}are the (bulk) aerodynamic and surface resistances. Most of the factors can be calculated by the formulas in FAO Irrigation and Drainage Paper No. 56 [34]. In addition, this formula involves the slope of the vapor saturation-temperature curve Δ (kPa/°C), the calculation in the model code are as follows:

_{p}(J/kg) is the specific heat of air at constant temperature, P

_{air}is the air pressure,${\scriptscriptstyle \frac{d{e}_{sat}(T)}{dT}}$ is the slope of sat. vapor pressure-temperature, T is the average daily temperature, T

_{abs}is 273.16, and e

_{sat}(T) is the saturated vapor pressure.

#### 2.4. Methods for Parameters Tuning and Model Evaluation

#### 2.4.1. Parameters Calibration of Es

_{o}in the early growth periods when E

_{s}/E

_{o}remained > 0.9. As mentioned before, “Magan soil” belongs to loam clay, so it can be concluded that the CONA varies from 9 to 12, and trial and error was the first choice. The E

_{o}is calculated as follows [35]:

_{sat}(mb) is the saturated vapor pressure at mean air temperature, e

_{a}(mb) is the vapor pressure at mean air temperature, R

_{no}(MJ/m

^{2}/d) is the average net radiation at canopy (1 mm/d is equivalent to an energy flux of 2.5 MJ/m

^{2}/d), and u (km/d) is the wind speed at a height of 2 m.

^{0.5}) was the average slope of 4 precipitation cycles in the 2 years.

#### 2.4.2. Determination of Stemflow

#### 2.4.3. Methods of Model Evaluation

^{2}) alone, in general, is often inappropriate and has deficiencies when used to compare predicted and observed values. Therefore, an index of agreement (D), as well as the systematic root mean square error (RMSE

_{s}) and unsystematic error (RMSE

_{u}), were suggested to use for comparisons of model-predicted and observed variables [36,37,38,39].

^{2}and D, ranged from 0 to 1, represents the consistency between the simulated and measured values. The closer that the value is to 1, the higher the fitting degree is. Herein, X

_{i}and Y

_{i}are measured and simulated values, respectively, $\overline{X}$ and $\overline{Y}$ are the average of measured and simulated values, respectively, ${\widehat{Y}}_{i}$ is the regression estimate for the observation, and n is the number of observations. The smaller the RMSE value is, the better the fitting effect.

## 3. Results

#### 3.1. Simulated and Observed Es from Maize

#### 3.1.1. Es Variation in the Maize Growth Periods

#### 3.1.2. Comparison of Simulated and Observed Es

^{2}= 0.85 (p < 0.01), the adjusted determination coefficient R

^{2}= 0.85 and the index of agreement D = 0.96 (Figure 4, Table 2), which means the relationship between the simulated and the measured values reaches an extremely significant level. The RMSEs = 0.0783 mm/d, RMSEu = 0.4435 mm/d (Table 2), and the fitted slope was 0.9647 (Figure 4), which means the ratio of the simulated value to the measured value was close to 1:1 and the model had a small regression error. The variation curves of the simulated value in the two years were basically consistent with the responsive measured values, except that the simulated value was obviously higher than the measured value in August 2016 (Figure 3). The Es was in stage 2, and the simulated values were the potential evaporation; however, the soil moisture was not sufficient to support theoretical amounts for there was little rain during this period. Individually, the fitting degree in 2016 (R

^{2}= 0.81) was better than that in 2017 (R

^{2}= 0.80), and yet there was no remarkable difference between the two. However, compared with the total fitting degree, both the two fitting degrees in 2016 and 2017 were significantly lower than the total one.

#### 3.2. Simulated and Observed Tc from Maize

#### 3.2.1. Tc Variation in the Maize Growth Periods

#### 3.2.2. Comparison of Simulated and Observed Tc

^{2}= 0.74 (p < 0.001) (Figure 6). The RMSEs = 1.2261 mm/d and the RMSEu = 1.4197 mm/d (Table 2) means that the predicted ratings slightly deviated from the true ones. However, the simulated and observed Tc had good agreement, connoted by the index agreement D = 0.82. and the fitted slope was 0.8553 (Figure 6), all of which meant that the fitting degree between the simulated and observed Tc was not “high” but statistically significant. Compared with the observed Tc, it was shown that the trends of fluctuation in the two growth periods of 2016 and 2017 were basically consistent (Figure 6). The fluctuation frequencies of the simulated Tc were basically consistent with the observed, but the values of the simulated Tc were higher than the observed.

## 4. Discussions

^{2}was between 0.959~0.973). Li et al. [43] showed that the relationship was found between predicted and observed soil storage water (R > 0.7) with a variation of ±20%. As inferred, the method of model parameter optimization and experimental observations in different tests are different, which could affect the results and fitting degrees. The validation water balance process of the APSIM model gives a convenient method to simulate the Es and Tc by crop growing models. After calibrating the parameters needed in the simulation, the water consumption of the maize field would be predicted under both climate change and crop growth variation. Moreover, the APSIM helps simulate the production of the maize field.

^{2}= 0.70). Moreover, Li et al. and Yan et al. [46,47] demonstrated that the simulated and measured values of Tc had good agreement. In similarity with the above, the result of the simulated Tc in this paper was also good (R

^{2}= 0.74). The reason may be the APSIM model separated ET into Es and Tc, which improves the Es and Tc simulation, respectively. In addition, it is worthless that there are not unified standards for the calculation of some parameters needed in the Penman-Monteith. Different formulas for parameters calculation may influence the estimation values. As well, the Penman-Monteith neglected the energy consumption of inner dissipation and photosynthesis and did not take the airflow exchange and the atmospheric stratification into account [32]. Moreover, the Penman-Monteith water demand in the APSIM amplifies the effects of the VPD (vapor pressure deficit), which may lead to errors. Therefore, the applicability of the Penman-Monteith model and the method of parameters determination are still controversial [48].

## 5. Conclusions

^{2}and adjusted R

^{2}was 0.85, (p < 0.001) and the index agreement D was 0.96, which connoted that the correlation degree reached a significant level. Based on the results, it was concluded that the calibrated Ritchie model in the APSIM can simulate the Es during maize growth periods in Nanjing. From the results that the RMSEs and RMSEu were 1.22 and 1.42 mm/d, respectively, the R

^{2}was 0.74 and the index agreement D was 0.88 in the simulation of Tc, it can be concluded that compared with the Es simulation, the Tc simulation error of the APSIM should be further reduced and the performance of the model should be further improved in Nanjing. However, it also has a good agreement with the observed values. The results of this project may be beneficial to further research on field moisture. Both of the Es and Tc simulations can provide a reference for water-saving irrigation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Radiation and wind speed (

**a**), maximum/low temperatures (

**b**), rain and relative humidity (RH) (

**c**) during maize growth during 2016–2018.

**Figure 3.**Comparison of APSIM simulated and field observed daily evaporation in 2016 and 2017. The observed data was obtained by weighing micro-lysimeter every day, and calculating differences between two successive days.

**Figure 4.**The linear regression between simulated and observed evaporation values during maize growth in 2016 and 2017.

**Figure 6.**The linear regression between simulated and observed transpiration values during partial maize growth in 2016 and 2017.

Soil Depth (cm) | Air Dry (mm/mm) | DUL (mm/mm) | LL15 (mm/mm) | SAT (mm/mm) |
---|---|---|---|---|

0~5 | 0.038 | 0.221 | 0/119 | 0.300 |

5~15 | 0.136 | 0.250 | 0.136 | 0.300 |

15~25 | 0.150 | 0.268 | 0.160 | 0.322 |

25~40 | 0.158 | 0.274 | 0.167 | 0.311 |

Sub-Models | R^{2} | D | p-Value | RMSEs (mm/d) | RMSEu (mm/d) |
---|---|---|---|---|---|

Es | 0.85 | 0.96 | 0.000 | 0.0783 | 0.4435 |

Tc | 0.74 | 0.88 | 0.000 | 1.2261 | 1.4197 |

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**MDPI and ACS Style**

Guo, T.; Liu, C.; Xiang, Y.; Zhang, P.; Wang, R.
Simulations of the Soil Evaporation and Crop Transpiration Beneath a Maize Crop Canopy in a Humid Area. *Water* **2021**, *13*, 1975.
https://doi.org/10.3390/w13141975

**AMA Style**

Guo T, Liu C, Xiang Y, Zhang P, Wang R.
Simulations of the Soil Evaporation and Crop Transpiration Beneath a Maize Crop Canopy in a Humid Area. *Water*. 2021; 13(14):1975.
https://doi.org/10.3390/w13141975

**Chicago/Turabian Style**

Guo, Tianting, Chunwei Liu, Ying Xiang, Pei Zhang, and Ranghui Wang.
2021. "Simulations of the Soil Evaporation and Crop Transpiration Beneath a Maize Crop Canopy in a Humid Area" *Water* 13, no. 14: 1975.
https://doi.org/10.3390/w13141975