Introduction

Paddy fields are sometimes cultivated with upland crops (Popp et al. 2005; Timsina and Connor 2001) and are known as rotational paddy fields (RPFs). RPFs increase the flexibility of land use in paddy fields, which possibly helps alleviate the imbalance between crop supply, which may decrease owing to climate change, and demand, which may increase owing to the rapidly increasing human population. However, because crop productivity in RPFs is lower than the potential productivity of an individual site (Timsina and Connor 2001), more precise irrigation and drainage management techniques than those applied in upland fields are necessary.

The main reason for the low crop productivity in RPFs is the presence of a plow sole, which is dense and has low permeability to maintain water ponding for cultivating paddy rice (Nishida et al. 2020). Because of this dense soil layer, plant roots are prevented from entering the subsoil (Zhou et al. 2014), resulting in a relatively shallow root zone (Mochida et al. 1990). In addition, plow soles often induce soil saturation for several days after irrigation and precipitation, resulting in a lack of O2 in the root zone (Araki 2006). Hence, upland crops cultivated in RPFs can be more vulnerable to topsoil saturation and drought than those cultivated in upland fields, potentially resulting in wet or drought damage to crops (Timsina and Connor 2001). Furthermore, increased intensive precipitation and continuous clear days caused by climate change (IPCC 2014) may increase both soil saturation and drought in RPFs in the future. Thus, it is important to construct optimal irrigation and drainage systems (Manik et al. 2019) in RPFs to maintain suitable soil water conditions for upland crop cultivation.

Numerous studies have been conducted to determine the optimal soil water conditions for designing irrigation and drainage systems in RPFs under humid climates. For irrigation, a relatively high soil water potential (e.g., − 5 to − 20 mH2O; Kanamori et al. 1999) is recommended as an indicator of irrigation timing to improve the productivity of upland crops. For drainage, the relationship between soil saturation duration and plant yield has been extensively investigated (Linkemer et al. 1998; Rhine et al. 2010). Subsurface drainage systems in Japan are designed to drain perched groundwater in plowed soil within 24 h, based on changes in drainage over time. In recent years, the depth of the groundwater table has also been recommended as an indicator of optimal soil water conditions for both irrigation and drainage management in RPFs (Fidantemiz et al. 2019; Matsuo et al. 2013). Although previous studies have provided valuable information on optimal soil water conditions in RPFs, the application of these results to different fields may be inappropriate because the optimal soil water conditions strongly depend on the soil type, meteorological conditions, and cultivated plant species. Therefore, the effects of these environmental factors on plant growth must be considered in optimal water conditions studies.

To increase plant gas exchange (photosynthesis, transpiration, and respiration), which strongly affects plant growth, it is necessary to maintain high leaf water potential for stomatal aperture. In addition, leaf water potential is the driving force of the root water uptake, and thus the leaf water potential balances transpiration and root water uptake (Bittelli et al. 2015). Therefore, to maintain stomatal aperture and high leaf water potential, root water uptake must satisfy the evaporative demand, which is determined by meteorological conditions. Root water uptake rate S [m s−1] is proportional to the difference in water potential between the soil and leaves and inversely proportional to the series hydraulic resistance of soil and plants; this relationship is simply described as follows (Bittelli et al. 2015):

$$S = \left( {\psi_{{\text{s}}} - \psi_{{\text{l}}} } \right)/\left( {R_{{\text{s}}} + R_{{\text{p}}} } \right)$$
(1)

where Ψs and Ψl are water potential [m] of the soil and leaf, respectively, and Rs and Rp are the hydraulic resistance [s] of the soil and plant, respectively. This equation indicates that Rs and Rp should be maintained at low values to achieve high S with high Ψl.

To ensure that Rs and Rp maintain low values, precise water management is required in RPFs where both topsoil drought and saturation occur, as the resistances significantly depend on the soil water conditions (Carminati and Javaux 2020; Toral-Juarez et al. 2021). For example, soil drought dramatically increases Rs by decreasing soil hydraulic conductivity (Abdalla et al. 2020). Thus, in dry lands, Rs rather than Rp controls the stomatal aperture and plant gas exchange (Carminati and Javaux 2020), emphasizing the importance of irrigation. By contrast, excess soil water decreases soil O2 concentration and increases soil CO2 concentration (Araki 2006), inducing a decrease in root respiration (Araki 2012). Therefore, long-term soil saturation increases Rp by decreasing root growth (Arduini 2019) and root water absorption capacity (Rodriguez-Gamir 2011; Ruiz-Sanchez 1996; Toral-Juarez et al. 2021), emphasizing the importance of drainage. Limiting factors for root water uptake have been investigated extensively. However, these investigations focused only on soil drought conditions (Abdalla et al. 2020; Carminati and Javaux 2020). Therefore, it remains unknown whether Rs or Rp controls root water uptake in RPFs, where crops are subjected to both drought and saturation stresses. It is essential to determine which type of resistance is more important for improving crop productivity in RPFs, because water management measures differ depending on whether Rs or Rp has a greater effect on root water uptake. However, conventional field experiments for evaluating crop yield (Rhine et al. 2010; Matsuo et al. 2013) cannot distinguish which type of resistance is more important for crop yield in RPFS. Thus, changes in resistance must be evaluated over time based on comprehensive measurement of soil and plant water conditions and transpiration rates.

This study was conducted to evaluate whether the hydraulic resistance of soil (Rs) or plants (Rp) principally controlled transpiration in RPFs in humid regions. Field measurements of the soil water conditions, transpiration rate, and leaf water potential, which are required to determine Rs and Rp, were conducted. Temporal changes in Rs and Rp were determined and compared. Based on the comparison, an importance of drainage system in RPFs under humid climates was discussed.

Materials and methods

Study site

Field measurements were conducted in RPFs located in Ishikawa Prefecture, Japan (latitude 36° 29′ N, longitude 136° 32′ E), from late July to late September in 2018 and 2019. Rotational cropping of soybeans and paddy rice is widespread in this area, with soybeans being cultivated once every 3 years. Because of crop rotation, two fields surrounded by RPFs cultivating soybean for at least 50 m in all directions were chosen in 2018 and 2019. Both fields were approximately 30 m × 100 m. Open drainage ditches were installed in the fields to facilitate surface drainage, but a subsurface drainage system was not installed. The soil in the fields was classified as light clay (12.7% coarse sand, 37.0% fine sand, 25.1% silt, and 25.2% clay). The soil physical and hydraulic properties of the fields are shown in Table 1 and the water retention and unsaturated hydraulic conductivity are depicted in Fig. 1 (detailed determination methods are described in “Calculation of soil hydraulic resistance and plant hydraulic resistance” Section).

Table 1 Soil physical properties of the experimental sites
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Fig. 1
figure 1

Water retention curve and unsaturated hydraulic conductivity of plowed soil. The approximate water retention curve (solid line) and unsaturated hydraulic conductivity (broken line) were estimated using the van Genuchten–Mualem model (van Genuchten 1980). The parameters used to calculate curves \(\alpha\), n, and \(\theta_{r}\) were 1.38, 1.51, and 0.08, respectively

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Ridges of 15 cm in height and 40 cm in width were established at 70 cm intervals. Soybean (Glycine max L. Merr. cv Enrei) seeds were sown at a depth of 5 cm from the top of the ridge on May 28 and 27 in 2018 and 2019, respectively. Chemical fertilizer (51 kg ha−1 P2O5, 51 kg ha−1 K2O, and 98 kg ha−1 N) was applied on the same days. The thickness of the plowed layer was approximately 10 cm, and a plow sole was observed below it.

Although there is as much as 799 mm of rainfall (average over the last 30 years) during the cultivation period in this area, irrigation is often conducted from late July to early August because precipitation temporarily becomes scarce. Furrow irrigation was performed twice in 2018 (July 20 and August 1), and once in 2019 (August 7) in the fields. Average temperature in this area during the cultivation period was 24.5 °C.

Measurements

The following meteorological conditions were monitored to determine the evapotranspiration rate. The net radiation Rn [W m−2] was measured at a height of 1.7 m from the inter-ridge surface using a net radiometer (NR-LITE, Campbell Scientific, Inc., Logan, USA). The wind speed uz [m s−1] was measured at a height of 2.4 m using wind anemometer (03,301 R.M., Campbell Scientific, Inc., Logan, USA). Both air temperature T [°C] and relative humidity [%] were measured at heights of 1.2 and 2.0 m using temperature–humidity probes (HMP155A, Campbell Scientific, Inc., Logan, USA). Precipitation [mm] was measured using a rain gauge (TE525-L, Campbell Scientific, Inc., Logan, USA). The incoming short-wave radiation [W m−2] was measured using a pyranometer (LI200R, Campbell Scientific, Inc., Logan, USA). The soil heat flux G [W m−2] was calculated by the heat balance in the surface layer. The change in soil heat storage in the plowed soil layer was estimated from the soil temperature distribution and volumetric water content in the plowed soil. The soil temperature was measured at depth of 1, 4, 9, and 16 cm from the top of the ridge using copper–constantan thermocouples. The volumetric water content of the plowed soil was measured using a water content reflectometer (CS655, Campbell Scientific Inc., Logan, CA, USA) to estimate the heat capacity. The heat flux across the bottom boundary of the plow layer was measured using a heat–flux plate (HFP01SC, Campbell Scientific, Inc., Logan, USA). These measurements were conducted at 10 s intervals, and average values for 10 min periods were recorded using data–loggers (CR-1000, Campbell Scientific Inc., Logan, USA).

The soil matric potential Ψm [mH2O] and volumetric water content θ [m3 m−3] were measured on the ridge where the plants were standing. In this paper, water potential is represented by hydraulic head [m]. Water potential sensors (TEROS21, Decagon Devices Inc., Pullman, USA) and water content reflectometers (5TE, Decagon Devices Inc., Pullman, USA) were installed at the level of the inter-ridge surface and at the bottom of the plowed soil. These conducted measurements at 60 s intervals, and average values of 10 min period were recorded using data–loggers (Em50, Decagon Devices Inc., Pullman, USA). In our study area, the soil water potential was assumed to be equal to the soil matric potential because the precipitation amount was much higher than the potential evapotranspiration amount, indicating low soil salinity. Water levels in the plowed layer were measured using pressure transducers (HTV-100KP; Sensez Co., Tokyo, Japan) and perforated standing tubes at depths of 17 and 12 cm from the inter-ridge ground surface. These data were sampled at 10 s intervals, and average values of 10 min periods were recorded using data–loggers (CR-1000, Campbell Scientific Inc., Logan, USA).

To evaluate the plant water status, leaf water potential Ψl [m] was measured using a pressure chamber (Pump-Up Chamber; PMS Instrument Co., Albany, USA). Measurements were conducted on clear days close to the days of irrigation and intensive rainfall. For each measurement, the Ψl of 4–6 leaves were determined and averaged.

Calculation of actual evapotranspiration rate and potential evapotranspiration rate

The actual evapotranspiration rate ETa was calculated using the energy balance Bowen ratio method (EBBR method) as follows:

$${\text{ET}}_{{\text{a}}} = \frac{1}{{\rho_{{\text{w}}} l}}\frac{{R_{{\text{n}}} - G}}{1 + \beta }$$
(2)

where ρw is the density of water [1000 kg m−3] and l is the latent heat of vaporization of water [2.44 × 106 J kg−1]. β is the Bowen ratio, which is derived from the air temperature and relative humidity:

$$\beta = \gamma \frac{{T_{2.0} - T_{1.2} }}{{e_{2.0} - e_{1.2} }}$$
(3)

where γ is the psychrometric constant [kPa °C−1], e is the vapor pressure [kPa], and the subscripts indicate the measurement height [m]. The evapotranspiration rate estimated from the EBBR method needs to be corrected when β → − 1 (e.g., around sunrise, sunset, or heavy rain) because the denominator approaches zero in Eq. (2) (Ma et al. 2015). Thus, in this study, the dynamic effective range of the Bowen ratio (Wu 2016) was applied for the correction of β, as follows:

$$- 1 - \left| {\frac{{\delta_{1} - \gamma \delta_{2} }}{\Delta e}} \right| < \beta < - 1 + \left| {\frac{{\delta_{1} - \gamma \delta_{2} }}{\Delta e}} \right|$$
(4)

where \(\delta_{1}\) and \(\delta_{2}\) are the accuracies of the potential temperature and vapor pressure measurements, respectively. When β was within the range of Eq. (4), it was set to − 0.5 according to Ito and Maruyama (2019).

The potential evapotranspiration rate ETp [m s−1] was calculated using the Penman–Monteith equation (Allen et al. 1998).

$${\text{ET}}_{{\text{p}}} = \frac{{K_{{\text{c}}} }}{{\rho_{{\text{w}}} l}}\frac{{\Delta \left( {R_{{\text{n}}} - G} \right) + \rho_{{\text{a}}} C_{{\text{p}}} r_{{\text{a}}}^{ - 1} \left( {e_{{\text{s}}} - e_{{\text{a}}} } \right)}}{{\Delta + \gamma \left( {1 + r_{{\text{c}}} /r_{{\text{a}}} } \right)}}$$
(5)

where ∆ is the slope of the saturated vapor pressure–temperature curve [kPa °C−2], ρa is the density of air [kg m−3], Cp is the specific heat of air at constant pressure [1007 J kg−1 °C−1], es is the saturated vapor pressure at the air temperature [kPa], ea is the vapor pressure of air [kPa], ra is the aerodynamic resistance [s m−1], rc is the canopy resistance [s m−1], and Kc is the crop coefficient. According to Allen et al. (1998), Kc was set to 1.15 for mid-season soybean, and ra was calculated from the wind speed. According to Walter et al. (2000), rc was set to 50 s m−1 for the daytime (from 6:00 to 18:00) and 200 s m−1 for the night-time (from 18:00 to 6:00).

Because the measurement periods were after the flowering stage of soybean when leaves were fully expanded, ETa and ETp could be regarded as the actual and potential transpiration rates of soybean, respectively. Thus, the evapotranspiration ratio ETr (= ETa/ETp) represented the transpiration ratio. Because transpiration decreases with a reduction in Ψl due to stomatal closure, ETr was expressed as a linear function of Ψl.

Calculation of soil hydraulic resistance and plant hydraulic resistance

Soil hydraulic resistance Rs was calculated according to Gardner (1960) as follows:

$$R_{{\text{s}}} = K_{{\text{h}}}^{ - 1} \sqrt {\frac{1}{{\pi \cdot {\text{RLD}}}}}$$
(6)

where Kh is the soil hydraulic conductivity [m s−1] and RLD is the root length density [m m−3]. Although RLD depends on the soil layer, we used a uniform value of 2.0 × 104 m m−3 according to Myers et al. (2007) who investigated the RLD at 15 cm intervals from the soil surface to a depth of 1.2 m in the soybean field. Kh was estimated from the van Genuchiten–Mualem model (van Genuchiten 1980).

$$\theta = \theta_{{\text{r}}} + \frac{{\theta_{s} - \theta_{r} }}{{\left[ {1 + \left| {\alpha \psi_{{\text{s}}} } \right|^{n} } \right]^{m} }}$$
(7)
$$K_{h} = K_{s} \left( {\frac{{\theta - \theta_{r} }}{{\theta_{s} - \theta_{r} }}} \right)^{\tau } \left[ {1 - \left( {1 - \left( {\frac{{\theta - \theta_{r} }}{{\theta_{s} - \theta_{r} }}} \right)^{\frac{1}{m}} } \right)^{m} } \right]^{2}$$
(8)

where θs is the saturated volumetric water content [m3 m−3], θr is the residual volumetric water content [m3 m−3], Ks is the saturated soil hydraulic conductivity [m s−1], τ is tortuosity parameter (0.5), α and n are fitting parameters, and m = 1–1/n. The measured values of θs and Ks (Table 1) were used as the parameters in Eqs. (7) and (8). Other parameter (α, n, and θr) values were 1.38, 1.51, and 0.08, respectively, which were determined by applying the least square method to the observed relationship between Ψs and θ of the plowed layer during the drying process from August 1 to 7 in 2019 (Fig. 1). These calculations were conducted in Microsoft Excel 2016. From Eq. (1), Rp can be described as follows:

$$R_{{\text{p}}} = \left( {\psi_{{\text{s}}} - \psi_{{\text{l}}} } \right)/{\text{ET}}_{{\text{a}}} - R_{{\text{s}}}$$
(9)

As Ψs is not uniform throughout the root zone, the selection of a representative soil layer to define Rs influences the evaluation of Rp. Thus, Ψs and Rs in both the plowed soil and plow sole were used to calculate of Rp to compare the difference.

To evaluate the time course of Rp over the entire period using Eq. (9), estimates of continuous Ψl were necessary. However, Ψl was measured only on a limited number of dates because it was measured manually and destructively. Thus, we estimated the midday Ψl from the measured midday ETr using linear regression between Ψl and ETr (Eq. (10) in “Impact of leaf water potential reduction on evapotranspiration ratio and stomatal conductance” Section). In the following sections, the Rp evaluated from the measured Ψl is denoted as Rp,mes, while the estimated midday Ψl explained above is denoted as Rp,est. To determine the accuracy of the estimation, the root-mean-square error (RMSE) for the estimation of Rp was calculated.

Result

Soil water conditions throughout the measurement period

Total precipitation during the measurement period was 579 and 314 mm in 2018 and 2019, respectively. In both years, early August was dryer with little precipitation (2018: 6.7 mm, 2019: 7.8 mm) whereas late August was rainy (2018: 213.3 mm, 2019: 204.8 mm). In September, the precipitation was no less than 357 mm in 2018, but no more than 49 mm in 2019 (Figs. 2a, 3a). The number of clear days for which midday short-wave radiation was higher than 400 W m−2 was 28 in 2018 and 36 in 2019 (Figs. 2a, 3a).

Fig. 2
figure 2

Variation in daily precipitation and midday (10:00–15:00 h) solar radiation (a), soil matric potential Ψm and water level in the plow layer (b), volumetric water content θ (c), daily actual and potential evapotranspiration rate (d), and midday evapotranspiration ratio (e) in 2018. Water level plotted as 0 cm represents the bottom of the plow layer, 12 cm represents the surface of the furrow soil, and 27 cm represents the top of the ridge. Saturated volumetric water content θs measured from sampled soil was 0.56 and 0.47 in plowed soil and plow sole, respectively (Table 1). Evapotranspiration ratio was derived by dividing ETa by ETp

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Fig. 3
figure 3

Variation in daily precipitation and midday (10:00–15:00 h) solar radiation (a), soil matric potential Ψm and water level in the plow layer (b), volumetric water content θ (c), daily actual and potential evapotranspiration rate (d), and midday evapotranspiration ratio (d) in 2019. Water level plotted as 0 cm represents the bottom of the plow layer, 10 cm represents the surface of the furrow soil, and 25 cm represents the top of the ridge. Saturated volumetric water content θs measured from sampled soil was 0.56 and 0.47 in plowed soil and plow sole, respectively (Table 1). Evapotranspiration ratio was calculated by dividing ETa by ETp

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The dry period occurred in early August in both years. The minimum \(\psi_{{\text{s}}}\) for both layers was observed just before irrigation (August 1, 2018, and August 7, 2019). For example, \(\psi_{{\text{s}}}\) value of the plow layer and plow sole layer were − 112.2 and − 25.5 m on August 1, 2018, respectively. By contrast, the groundwater level frequently rose to the plow layer due to frequent rainfall, and both the plow layer and plow sole layer were often saturated in late August in both years (Figs. 2b, c, 3b, c). In particular, the perched water continuously remained in the plowed layer for more than 90 h because of the intermittent rainfall from August 28 and August 27 in 2018 and 2019, respectively. Thus, the root zone was under anaerobic conditions for several days despite the existence of open drainage ditches.

Evapotranspiration rate and evapotranspiration ratio

ETa fluctuated from 0.1 to 6.9 mm d−1, and ETp fluctuated from 0.7 to 9.7 mm d−1 over the 2 years mainly due to the fluctuation of solar radiation (Fig. 2d and Fig. 3d). On clear days, the average ETa was 5.4 mm d−1 and 3.9 mm d−1, and the average ETp was 6.8 mm d−1 and 6.3 mm d−1 in August and in September, respectively. Accordingly, the average midday ETr on the clear days was 0.92 in August, but 0.73 in September, decreasing to approximately 0.5 by the end of September (Figs. 2e, 3e). The average midday ETp on clear days was 0.75 mm h−1. Moreover, the maximum value of midday ETr on clear days was 1.00 and 1.01 in 2018 and 2019, respectively, indicating the reasonable selection of crop coefficient value used for the calculation of ETp.

Midday ETr when Ψs in the plowed soil almost approached the wilting point was 0.90 and 0.88 in 2018 and 2019, respectively, recovering to 0.96 and 0.91 after irrigation. Although ETr increased slightly with irrigation, ETr before irrigation did not decrease considerably.

On the contrary, midday ETr decreased considerably from 0.60 to 0.36 in late September 2019. Because Ψs was even higher than it was before irrigation, the low ETr observed in the late September may be affected by leaf aging. In fact, we observed that the leaves gradually turned yellow after mid-September. Because photosynthetic rate and stomatal conductance significantly decreased in yellow soybean leaves (Locke and Ort 2014), the data obtained after September 15 were excluded from further analysis.

Impact of leaf water potential reduction on evapotranspiration ratio and stomatal conductance

A decrease in Ψl decreases stomatal conductance, inducing the suppression of transpiration (Hamlyn 2014). Our results are consistent with this relationship (Fig. 4). The linear regression equation for ETr and Ψl was as follows (R2 = 0.57):

$${\text{ET}}_{{\text{r}}} = \, 0.00248\Psi_{{\text{l}}} + \, 1.22$$
(10)
Fig. 4
figure 4

Relationship between leaf water potential measured at noon and midday evapotranspiration ratio. Leaf water potential was measured for 3–7 leaves on each day. Mean ± standard error is shown in the plots and horizontal bars

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This equation indicates that ETr started to decrease from 1.0 when Ψl exceeded − 87 m. The Ψl threshold when stomatal conductance began to decrease was − 82 m, which is close to that for ETr (data are not shown). Previous studies on the relationship between Ψl and stomatal conductance in soybean have also reported that critical Ψl when stomatal conductance begins to decrease ranges between − 64 and − 125 m (Lawn 1982; Turner et al. 1978). Our results were within the range indicated in previous studies.

Measured and estimated hydraulic resistance of soil and plant

Except before irrigation (August 1, 2018), Rs was at least three orders of magnitude lower than Rp,mes regardless of the representative layer where Ψs was measured to calculate Rs (Table 2). Rp,mes fluctuated from 4.4 × 108 to 10.3 × 108 s, and the mean value of Rp,mes under wet soil conditions was 6.6 × 108 s (Table 2). On exceptionally dry days, such as August 1, 2018, Rs calculated from Ψs in the plowed layer was two orders of magnitude higher than the average Rp,mes (Table 2).

Table 2 Hydraulic resistance of soil (Rs) and plant (Rp,mes) in 2018 and 2019
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Figure 5 compares Rs and average Rp,mes as a function of Ψs. A decrease in Ψs from − 1 to − 100 m monotonically increased Rs from 3.5 × 105 to 1.5 × 1011 s. On the contrary, Rs + Rp,mes was almost constant when Ψs was higher than − 6 m. However, beyond this range, it increased gradually with a decrease in Ψs. A comparison of Rs and Rp,mes indicates that Rs was the same as the average Rp,mes when the soil matric potential was − 16 m. These values are almost consistent with empirically determined irrigation thresholds from − 5 to − 20 m, which enable maximum yields (Kanmori et al. 1999).

Fig. 5
figure 5

Relationship between soil water potential and hydraulic resistance of soil (Rs) and plants (Rp,mes) The mean and range of ± standard deviations for Rp,mes are shown by the dotted line and gray stripe, respectively

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Rp,mes and Rp,est exhibited almost the same values and trends (Fig. 6). The RMSE for the estimated value was 7.2 × 107 s, being one order of magnitude lower than the average Rp,mes. A comparison of Rp,est and Rs indicates that Rp was much higher than Rs for most of the investigation period (Fig. 6). Rp,est increased gradually from approximately 5.0 × 108 s in early August to approximately 1.0 × 109 s in early September in both years. Furthermore, a gradual increase in both Rp,mes and Rp,est was observed during the measurement period. In particular, Rp increased after the soil saturation event, during which a perched water level was present in the plowed soil (Table 2 and Fig. 6b).

Fig. 6
figure 6

Variation in estimated and measured midday Rp and Rs in (a) 2018 and (b) 2019. Error bars denote the standard deviations (n = 3–7). Gray-shaded area indicates the duration that perched groundwater level existed in the plowed soil layer

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Discussion

Frequent rainfall and low-permeable plow soles lead to frequent soil saturation in RPFs under humid climates. In our fields, because of the irrigation and frequent rainfall (Fig. 2a,  3a), both plowed soil and plow sole were sufficiently wet for Rs (Ψs > − 16 m). Thus, soil drying periods with Ψs decreased to below − 16 m on only 3 and 16 days in 2018 and 2019, respectively. By contrast, frequent soil saturation was observed (Fig. 2b, 3b). Similar to our fields, frequent rainfall and subsequent soil water saturation often occur in RPFs under humid climates (Nishida et al. 2020). Therefore, the appropriate irrigation and drainage management to improve crop productivity in RPF under humid climate are discussed.

Comparing variations in Rp and Rs over time is important to determine the optimal soil water condition for improving the productivity of upland crops in RPFs under humid climates, wherein both drought and wet damage to crops can occur. In our study sites, the Rp during most of the measurement period after the flowering stage was one to three orders of magnitude higher than the Rs (Fig. 6), indicating that Rp controls root water uptake (transpiration). Although Rs was negligibly small compared with Rp, the average ETr on clear days was 0.90 and rarely reached 1.0 (Fig. 2e, 3e), indicating that the stomata were not completely open. Thus, the transpiration of soybeans cultivated under humid climate may not be controlled by Rs but by Rp for majority of the growing period. Under drought conditions, Rs becomes significantly higher than Rp, indicating that transpiration rate was constrained by Rs (Abdalla et al. 2020; Carminati and Javaux 2020; Tuzet et al. 2003). On the contrary, under wet soil conditions, transpiration rate decreases with increasing Rp (Hirasawa and Ishihara 1991), consistent with our results. Therefore, a high Rp, which may induce stomatal closure and decrease crop yield, is one of the main causes of low crop productivity in RPFs under humid climates.

The upper limit of Rp that satisfies the midday evaporative demand (potential transpiration rate) under very wet soil conditions can be determined from Eq. (9). This upper limit was estimated as 4.2 × 108 s using a Ψl = − 87 m (Fig. 4) and ETp = 0.75 mm h−1 under sufficiently wet conditions (Rs <  < Rp). However, the mean Rp,mes was 6.6 × 108 s (Table 2), which was higher than the upper limit. This result indicates that, even under well-wet soil conditions, the maximum root water uptake rate of soybeans was less than ETp, and thus midday transpiration rate was constrained by Rp. These stomatal closure and reduction of transpiration due to high Rp under well-wet soil conditions have been reported in several crop species (Hirasawa et al. 1992; Hu et al. 2009; Yokoyama et al. 2019). Root hydraulic resistance, which is the main constituent of Rp, is determined by root surface area (function of RLD) and hydraulic resistance per unit root length (Bittelli et al. 2015). Soybeans grown under frequent irrigation treatment until pre-flowering were reported to have a lower RLD, and, thus, higher Rp than non-irrigated soybeans, resulting in significant midday depression of stomatal conductance and photosynthesis rate (Hirasawa et al. 1998). In Japan, frequent precipitation during the rainy season, which overlaps with crop development stage, can also induce the formation of a shallow and poor root system and higher Rp. Thus, the observed high Rp,mes may be induced under wet soil conditions until the flowering stage. This result supports the importance of drainage management for decreasing Rp to improve crop productivity.

In addition to the high Rp that could not meet the midday evaporative demand, Rp gradually increased (Fig. 6) and ETr gradually decreased (Fig. 2e, 3e) during the measurement period. This result suggests that wet damage occurred because of frequent soil saturation (Fig. 2b, 3b). Hypoxic soil conditions induce a decrease in root elongation rate (Araki et al. 2012; Arduini et al. 2019; Else et al. 2001) and an increase in root hydraulic resistance per unit root length (Araki 2006; Rodriguez-Gamir et al. 2011), resulting in an increase in Rp (Ruiz-Sanchez 1996; Toral-Juarez et al. 2021). Such hypoxic conditions induced by long-term soil saturation at our study site may have increased Rp. As increases in Rp decrease Ψl, resulting in stomatal closure and suppression of photosynthesis (Else et al. 2001; Ziegler et al. 2017), they should be avoided by installing drainage facilities. The increase in Rp in our fields, where only an open drainage ditch has been installed, indicates that further drainage capacity is necessary to improve crop productivity. This result also supports that installing drainage systems, such as surface and subsurface drainage systems and/or raised bed systems (Kaur et al. 2020; Manik et al. 2019), can improve Rp in RPFs under humid climates.

Although severe soil drought rarely occurs in RPFs under humid climates, it is not completely absent. For example, in our fields, Ψs of plow soil decreased close to the permanent wilting point (− 150 m; Hillel 1998) before irrigation in both years. Since the unsaturated soil hydraulic conductivity decreased drastically with plow soil drying (Fig. 1; Abdalla et al. 2020), the Rs of plow soil became two orders of magnitude higher than Rp,mes (Table 2), indicating that root water uptake from plowed soil was almost impossible. Crops grown in RPFs form shallow root systems (Mochida et al. 1990) because RPFs generally have extremely dense plow sole or reduced subsoil, preventing root development to below the plow sole layer (Shinoto et al. 2021). However, the observed ETr before irrigation was maintained at approximately 0.90 (Fig. 2e, 3e), indicating that root water uptake below the plow sole contributed to maintain transpiration before irrigation. Our result indicates the importance of root development into subsoil, enabling water uptake even when the plow layer becomes dry.

Irrigation is the most conventional countermeasure against soil drought; in our study, there was no effective rainfall for more than a week after irrigation (Fig. 2a, 3a); thus, it may be essential for crops to avoid severe drought damage even under humid climate. However, irrigation can also cause wet damage to crop in RPFs because of the poor drainage capacity of plow sole. In our study, the Rp was not decreased after irrigation (Fig. 6), likely because of the presence of open drainage ditches and relatively high plow sole permeability. However, in RPFs with a lower plow sole permeability (e.g., heavy clay soil) than that in our fields, without appropriate drainage systems, irrigation can significantly decrease Rp through long-term soil saturation. Thus, to avoid both soil drought and wet damage in RPFs, irrigation management and drainage facilities is important. These will prevent long-term soil saturation based on the drainage capacity of the fields.

Our results emphasize the importance of Rp, which increases via long-term soil saturation, on transpiration rate of upland crops in RPFs under humid climates, suggesting that installation of drainage systems to improve root water uptake is important for increasing crop productivity. Although drainage systems are important, optimal soil water conditions for crop production remain unknown, requiring the design of an optimal drainage systems. To achieve this, further research to elucidate the relationship between soil water conditions (duration of soil saturation, depth of groundwater level, volumetric water, and air content) and Rp is necessary. Such research may enable the determination of the optimal soil water conditions required for designing drainage facilities in RPFs.

Conclusion

The major conclusions can be summarized as follows:

  1. (1)

    The Rp of soybean after the flowering stage was one to three order magnitude higher than Rs during most of the investigation period, indicating that the transpiration (root water uptake) rate in RPFs under humid climate was mainly controlled by Rp rather than Rs.

  2. (2)

    Although the soil was sufficiently wet to maintain a low Rs, midday ETr rarely reached 1.0, and gradually decreased throughout the investigation period, indicating stomatal closure. This result indicates that the Rp was too high to satisfy the transpiration demand.

  3. (3)

    Rp gradually increased from approximately 5.0 × 108 s in early August to approximately 1.0 × 109 s in early September. This increasing trend in Rp may be due to hypoxic stress induced by intermittent precipitation and poor soil drainage ability.

These results suggest that drainage systems are essential to avoid an increase in Rp, and potentially even induce a decrease in Rp for improving crop productivity in RPFs. Further research on the relationship between soil water conditions and Rp is required to determine an optimal irrigation threshold and drainage systems for crop production in RPFs.