Evolving Soil Water Limitation Changes Maize Production Potential and Biomass Accumulation but Not Its Relationship with Grain Yield

: As a key indicator of agricultural production capacity, crop production potential is critical to evaluate the impacts of climate variability on agriculture. However, less attention has been paid to the pattern of biomass accumulation in response to crop climatic production potential and its relation to grain yield formation at an intra-seasonal time scale, especially under evolving soil water limitation. In this study, we combined a mechanism-based empirical model with ﬁeld experiments conducted at different growth stages of maize on the Northern China Plain (NCP) to assess the dynamic response of biomass accumulation to climatic production potential and its relation to grain yield. The results showed that the ability of climatic production potential to estimate biomass was signiﬁcantly improved when a vapor pressure deﬁcit (VPD) was incorporated, with the root mean square error (RMSE) reduced by 33.3~41.7% and 45.6~47.2% under rainfed and evolving soil water limitation conditions, respectively. Drought signiﬁcantly decreased biomass accumulation mainly by decreasing the intrinsic growth rate and delaying the occurrence timing of maximum growth. Moreover, grain yield shared a nonlinear and saturating relationship with biomass across rainfed and water deﬁcit conditions. The results imply that evolving soil water limitation changes the process of biomass accumulation but not its relationship with grain yield. These ﬁndings provide useful information to estimate crop production potential under abiotic stresses and improve the accuracy of crop yield prediction.


Introduction
Global climate change, characterized by increasing temperature, high spatial-temporal variation in precipitation, and growing numbers of extreme weather events, has been one of the major environmental problems facing humankind in the 21st century [1,2].The impacts of global climate change on agriculture cannot only be reflected by crop growth and development at the plant scale but also by the shifts of agricultural climate zones and cropping systems at landscape scale, which induce great uncertainties in global food safety [3][4][5].As a key index for quantifying the effects of climate change on crop production, crop production potential refers to the biomass production or grain yield of a crop when grown under optimum conditions [6,7].Photosynthetic, light-temperature, and climatic production potential are the maximum crop outputs determined by solar radiation, light-temperature, and light-temperature-precipitation conditions, respectively, when soil and agricultural management (e.g., seed, insect, and disease) are suitable [8,9].These measures provide important theoretical guidance for evaluating crop growth and development, assessing resource use efficiency [10][11][12], and predicting crop production under stresses.
Many studies have estimated the spatial-temporal changes in crop production potential with various statistical and simulation methods around the world [13].Crop models, like WOFOST [14,15], DSSAT-CERES [16], APSIM [17,18], STICS [19], AquaCrop [20], and ORYZA [21], and mechanism-based empirical methods, e.g., Miami [22], Thornthwaite memorial [23], and GAEZ [24], have been widely applied in evaluating crop production potential in China, especially in the semiarid-humid regions [25][26][27][28][29][30][31].Mostly, the abovementioned methods often assume that grain yield is a fixed proportion of aboveground or total biomass, known as the harvest index (HI) [32,33].In fact, HI varies with environmental changes, especially under extreme temperature and drought stress [34][35][36].Therefore, it is not reliable to use a constant value of HI to estimate crop yield.An alternative approach for the HI method is to build a directly quantitative relationship between biomass and grain yield [37].In addition, previous studies mainly focused on the gaps between grain yield potential and actual yield at inter-seasonal time scale [11,[38][39][40], and less attention has been paid to the response of biomass accumulation to production potential at an intra-seasonal time scale, which plays an important role in final yield formation [33,41,42].
The Northern China Plain (NCP) is a major maize production region, accounting for 35% of maize planting areas and 40% of maize production in China [43].Meanwhile, the NCP is one of the most vulnerable areas to the impacts of climate change in China.The average air temperature on the NCP increased by 0.30 • C per decade during 1961-2020, which was significantly higher than the global average level in the same period.Moreover, the precipitation amount, diurnal temperature range, and solar radiation within the crop growing season decreased by 5.8 mm per decade   [44], 0.12 • C per decade   [45], and 55 MJ per decade   [46], respectively.In addition, there is growing evidence that vapor pressure deficit (VPD), denoting the dryness of air, plays a vital role in crop growth, which is comparative to temperature and CO 2 [4,[47][48][49][50].However, the effect of VPD on crop growth is often confounded with temperature because of their tight correlation [51].With an increasing trend for temperature and decreasing trends for both radiation and rainfall within the growing season, climate change has posed a great challenge for the stability of maize production on the NCP [1,52].Therefore, it is urgent to explore the response mechanism of plant growth to climatic production potential, particularly in the context of increasing extreme climate events.
In this study, a field experiment with various irrigation regimes at different growth stages was designed and conducted to explore biomass accumulation in response to crop production potential and its relation to grain yield and, further, to investigate their underlying mechanisms.Specifically, the objectives were to address the following questions.
(1) Are there any differences in the dynamics of crop production potential affected by the droughts that happened at different growth stages?(2) What role does VPD play in determining crop production potential?(3) How does biomass accumulation respond to crop production potential under rainfed and evolving soil water limitation conditions?(4) Is there a unified relationship between biomass and grain yield across rainfed and evolving soil water limitation conditions?

Study Area Description
A two-year field experiment was conducted at the Hebei Gucheng Agricultural Meteorology National Observation and Research Station (39 • 08 N, 115 • 40 E and 15.2 m above sea level) in Baoding, Hebei Province, China [53].The experimental region is in the central part of the NCP, which is a typical maize production area in China.The climate in this region is classified as warm continental and temperate monsoon.The 30-year (1981The 30-year ( -2010) ) average annual temperature, annual active cumulative temperature (≥10 • C), and sunshine duration were 12.2 • C, 4910 • C d, and 2264 h, respectively.The average annual precipitation is 515.5 mm, and approximately 60~70% of it occurs in the summer.Within a depth of 50 cm, the soil is a sandy loam, with a soil bulk density of 1.37 g cm −3 and a pH of 8.19.In addition, the average field capacity and wilting point were 22.7% (cm 3 cm −3 ) and 5.0% (cm 3 cm −3 ), respectively.The average organic carbon, total nitrogen, total phosphorus, and total potassium contents were 13.67 g kg −1 , 0.98 g kg −1 , 1.02 g kg −1 , and 17.26 g kg −1 , respectively.The farming practice in this region is double cropping with a wheat-maize rotation system.

Experimental Design and Field Management
The field experiment was conducted with a randomized complete block design.The area of each plot was 8.0 m 2 (4 m long and 2 m wide).A large electric-powered waterproof shelter (about 4.0 m high) over the experimental plots was applied to block the rainfall.When it was not raining, the waterproof shelter was moved away and the plots were exposed to the ambient conditions [53].A concrete wall with a depth of 3.0 m was constructed to prevent horizontal soil water exchange between plots.The maize variety used for this study was a drought-tolerant cultivar named Zhengdan-958, which has been the most popular maize variety on the NCP since 2003.The soil moisture within a depth of 1.0 m was measured with the drying method before seeding.Then, each plot was irrigated and maintained to keep the same soil water moisture content.During the growing seasons of 2013 and 2014, the sowing dates were 27 June 2013 and 24 June 2014, respectively.Before the irrigation treatments, some irrigation was applied in each plot to improve seedling emergence.At the local scale, the average precipitation in July from 1981 to 2010 was 150 mm, which was the basic reference for the irrigation amounts in this study.Five different irrigation amounts were applied on 24 July 2013 (at the seven-leaf stage) and 2 July 2014 (at the three-leaf stage), respectively, as detailed in Table 1 [54,55].After irrigation, no more water was applied, and the plots were sheltered from precipitation during the remaining growing season.At the same time, two rainfed treatments, T0 and W0 (not sheltered by waterproof shelter; the only input water was rainfall), were also established in 2013 and 2014, respectively.Each treatment had three replicate plots with a planting density of 6.5 plants m −2 .The controlled-release fertilizer diammonium phosphate (CRP) was applied at a rate of 320 kg ha −1 in all the treatments.The yield harvest dates were 8 October 2013 and 9 October 2014, respectively.Weeds, insects, and diseases were well controlled during the entire maize growing season.
where e s is the mean saturation vapor pressure (kPa), e a is the actual saturation vapor pressure (kPa), e T max and e T min are the saturation vapor pressure at the daily minimum and maximum air temperatures (kPa), respectively, and RH is air relative humidity (%).

Soil Water Availability
The soil water content was determined by the oven-drying method with an interval of 7-14 days throughout the growing season, with eight field observations each year.As more than 95% of the maize root biomass grew within a soil depth of 30 cm [57], the sampling depth was set to 50 cm.In each treatment, three different sampling sites were selected in the middle area of each plot.Soil samples were collected at every 10 cm soil depth with an auger, and then, the remaining soils were returned.The collected samples were dried in a ventilated oven at 105 • C until they reached a constant weight.The available soil water content (ASWC, %) was calculated according to the following equation [58]: where SWC (%) is the measured soil water content as a percentage of the dry soil weight, and FC (%) and WP (%) are the field capacity and wilting point, respectively.

Crop Biomass Production and Grain Yield
To obtain maize biomass, three healthy maize plants were randomly selected from each treatment and harvested during each observation.The sampling interval was identical to that of the soil water content measurements.All aboveground parts and root biomass within a depth of 35 cm were harvested and then weighed in timely manner.The fresh plant organs were placed in an oven with a temperature of 105 • C for one hour, followed by 80 • C until a constant dry weight was obtained.At maturity, maize ears were harvested in each plot and then dried at 80 • C to constant weight.In each plot, 10 representative ears were harvested to determine grain yield at 14% grain moisture content.The grain yield used for this analysis was averaged across three replications.

Maize Biomass Production Potential
Maize biomass production potential is calculated by the crop growth dynamics statistical method, which divided the production potential into three levels: photosynthetic, light-temperature, and climatic production potential [9,59].

Photosynthetic Production Potential of Biomass
Photosynthetic production potential of biomass (B q ) refers to the biomass production potential determined by solar radiation, with optimal temperature, water, nutrient conditions, and field management.Based on radiation-use efficiency theory, Loomis and Williams [60] proposed a classic algorithm for daily photosynthetic production, which is calculated as follows: where B q is the photosynthetic production potential of biomass (t ha −1 ), C is the unit conversion factor with a value of 10, and ∑ Q i is the total solar radiation reached above the maize canopy from sowing to physiological maturity (MJ m −2 ).f (Q) is the photosynthetic coefficient [59], as shown by Equation (8).
Here, the values and meanings of µ, ϕ, α, β, ρ, γ, ω, f (L), ξ, and q are detailed in Table 2 [59,61].Light-temperature production potential of biomass (B qt ) represents the production potential as a function of solar radiation and temperature with other environmental conditions (water, nutrients, etc.) being optimal.B qt is calculated as follows [59]: where B qt is the light-temperature production potential of biomass (t ha −1 ), f (T) is the downregulating scalar for the effect of temperature on B q , T is the daily air temperature ( • C), and b is a temperature coefficient.T minp , T opt , and T maxp are the minimum, optimum, and maximum air temperatures, respectively, for photosynthetic activity at different growth stages (Table 3), which were obtained from previous research across many different maize varieties based on the theory of three critical points of temperature [62,63].

Climatic Production Potential of Biomass
Climatic production potential of biomass (B qtw ) is the production potential depending upon climatic conditions, such as solar radiation, temperature, and precipitation.In this study, we adopted ASWC to represent the effects of precipitation on crop production potential, which was in accordance with previous studies [61].The climatic production potential of biomass was determined as follows: where B qtw is the climatic production potential of biomass (t ha −1 ).f (w) is the downregu- lating scalar for the effect of soil water on B qt , which is represented by ASWC.
In addition, due to the impact mechanism of VPD on crop growth and development that differs from that of temperature [4,47,48], VPD was also taken into consideration in this study.Climatic production potential of biomass after being corrected by VPD (B qtwv ) was calculated as follows: where B qtwv is the climatic production potential of biomass after being corrected by VPD (t ha −1 ).f (VPD) is the downregulating scalar for the effect of VPD on B qtw [47], and VPD 0 is the empirical coefficient of the VPD constraint equation.

Data and Statistical Analysis
Daily ASWC values were calculated via cubic spline interpolation between measured points of the ASWC, assuming that there is a linear relationship between subsequent sampling dates [64].Cubic spline interpolation was performed by using the "stata" package in R 4.0.4(R Core Team, 2021).One-way analysis of variance (ANOVA) was applied to evaluate the effects of evolving soil water limitations on biomass production and grain yield among the different treatments.The least significant difference (LSD) test was employed to distinguish the differences in biomass production and grain yield among treatments with Duncan's test.The linear regression model was applied to compare observed biomass versus the climatic production potential of biomass corrected by VPD (B qtwv ).In addition, the coefficient of determination (R 2 ), mean absolute error (MAE), and square root mean square error (RMSE) were calculated to evaluate model performance.
Seasonal biomass dynamics were often simulated using linear, exponential, monomolecular, and logistic functions [65,66].A logistic function (Equation ( 16)) was introduced to explore how the biomass responded to climatic production potential under evolving soil water limitation conditions during the growing season because this function is often used to quantify plant growth [67,68].
where y represents the crop biomass (t ha −1 ), and x is the production potential.L is the predicted maximum biomass (t ha −1 ), k indicates the intrinsic rate of plant growth, and a denotes the timing of maximum growth.In all cases, the differences were deemed to be significant if p < 0.05.All the figures were constructed with Origin 9.1 (Origin Lab Corporation, Northampton, MA, USA).

Meteorological Conditions during the Experimental Growing Seasons
Except for the daily air temperature, the other meteorological variables were significantly different between the two growing seasons.The daily air temperature showed a trend of first increasing and then decreasing, with a peak appearing in early August (Figure 1a).The mean temperatures in the 2013 and 2014 growing seasons were 23.6 • C and 23.2 • C, respectively, which were comparable (Figure 1b).Total precipitation of the ambient condition in 2013 was 401.9 mm, which was 1.4 times that of 287.2 mm in 2014 (Figure 1c,d).However, the cumulative solar radiation of 2678.4MJ m −2 during the 2013 growing season was significantly less than the 3547.13MJ m −2 in 2014 (Figure 1e,f).Moreover, the mean VPD was 0.58 kPa in 2013, which was significantly lower than the 0.75 kPa in 2014 (Figure 1g,h).Overall, the thermal conditions were analogous in the 2013 and 2014 growing seasons; the moisture conditions in 2013 were better than those in 2014, while the solar radiation conditions were the opposite.
where  represents the crop biomass (t ha −1 ), and  is the production potential. is the predicted maximum biomass (t ha −1 ),  indicates the intrinsic rate of plant growth, and  denotes the timing of maximum growth.In all cases, the differences were deemed to be significant if p < 0.05.All the figures were constructed with Origin 9.1 (Origin Lab Corporation, Northampton, MA, USA).

Meteorological Conditions during the Experimental Growing Seasons
Except for the daily air temperature, the other meteorological variables were significantly different between the two growing seasons.The daily air temperature showed a trend of first increasing and then decreasing, with a peak appearing in early August (Figure 1a).The mean temperatures in the 2013 and 2014 growing seasons were 23.6 °C and 23.2 °C, respectively, which were comparable (Figure 1b).Total precipitation of the ambient condition in 2013 was 401.9 mm, which was 1.4 times that of 287.2 mm in 2014 (Figure 1c,d).However, the cumulative solar radiation of 2678.4MJ m −2 during the 2013 growing season was significantly less than the 3547.13MJ m −2 in 2014 (Figure 1e,f).Moreover, the mean  was 0.58 kPa in 2013, which was significantly lower than the 0.75 kPa in 2014 (Figure 1g,h).Overall, the thermal conditions were analogous in the 2013 and 2014 growing seasons; the moisture conditions in 2013 were better than those in 2014, while the solar radiation conditions were the opposite.

Dynamics of Downregulation Scalars for the Effects of Temperature and VPD on Climatic Production Potential
As the thermal conditions were similar in the 2013 and 2014 growing seasons, the downregulating scalars for the effect on climatic production potential were difficult to distinguish, and both showed a strong negative effect (indicated by lower positive values) in the later growth period (Figure 2a,b).The positive effect of VPD on climatic production potential roughly showed an increasing trend during the 2013 and 2014 growing seasons.In addition, the mean value of 0.63 was higher than the 0.57 in 2014 (p < 0.05), which suggested that the positive effect of VPD on climatic production potential was larger than that in 2014 (Figure 2c,d).The interaction scalar between temperature and VPD (represented by f (T) * f (VPD)) was 0.55 and 0.49 in 2013 and 2014, respectively (Figure 2e,f).Therefore, the relative effects of temperature and VPD on climatic production potential were more dominated by VPD.
downregulating scalars for the effect on climatic production potential were difficult to distinguish, and both showed a strong negative effect (indicated by lower positive values) in the later growth period (Figure 2a,b).The positive effect of  on climatic production potential roughly showed an increasing trend during the 2013 and 2014 growing seasons.In addition, the mean value of 0.63 was higher than the 0.57 in 2014 (p < 0.05), which suggested that the positive effect of  on climatic production potential was larger than that in 2014 (Figure 2c,d).The interaction scalar between temperature and  (represented by () * ()) was 0.55 and 0.49 in 2013 and 2014, respectively (Figure 2e,f).Therefore, the relative effects of temperature and  on climatic production potential were more dominated by .

Climatic Production Potential across Rainfed and Soil Water Deficit Treatments
Due to the differences in soil water availability (Figure S1), the dynamics of  among rainfed and evolving soil water limitation treatments were significantly different in both growing seasons (Figure 3).In 2013, daily  of the rainfed treatment (T0) fluctuated significantly within 0.10~0.72 t ha −1 , with a mean value of 0.36 t ha −1 (Figure 3a).Meanwhile, the daily  among evolving soil water limitation treatments (T1-T5) shared similar patterns with an obvious declining trend after drought (applied on July 24, seven-leaf stage) (Figure 3a).In 2014, the rainfed treatment (W0) had a higher mean value of 0.42 t ha −1 compared with T0.The declining trend of the W1-W5 treatments was also observed after drought (applied on July 2, three-leaf stage) (Figure 3b).Both the T0 and W0 treatments had a higher accumulative  than the evolving soil water limitation treatments across the growing seasons (p < 0.01).In addition, the accumulative  of the evolving soil water limitation treatments showed a cut-off point after the limited water

Climatic Production Potential across Rainfed and Soil Water Deficit Treatments
Due to the differences in soil water availability (Figure S1), the dynamics of B qtw among rainfed and evolving soil water limitation treatments were significantly different in both growing seasons (Figure 3).In 2013, daily B qtw of the rainfed treatment (T0) fluctuated significantly within 0.10~0.72 t ha −1 , with a mean value of 0.36 t ha −1 (Figure 3a).Meanwhile, the daily B qtw among evolving soil water limitation treatments (T1-T5) shared similar patterns with an obvious declining trend after drought (applied on July 24, sevenleaf stage) (Figure 3a).In 2014, the rainfed treatment (W0) had a higher mean value of 0.42 t ha −1 compared with T0.The declining trend of the W1-W5 treatments was also observed after drought (applied on July 2, three-leaf stage) (Figure 3b).Both the T0 and W0 treatments had a higher accumulative B qtw than the evolving soil water limitation treatments across the growing seasons (p < 0.01).In addition, the accumulative B qtw of the evolving soil water limitation treatments showed a cut-off point after the limited water was applied, respectively, and the differences among treatments gradually increased with soil drying (Figure 3c,d).
After being corrected by VPD, the variations of B qtwv under rainfed and evolving soil water limitation treatments shared a similar trend with B qtw , although with smaller fluctuations (Figure 4a,b).In addition, the cumulative B qtwv also had a similar dynamic pattern to B qtw in the 2013 and 2014 growing seasons, respectively.However, the amount of accumulative B qtwv was about half of B qtw (Figure 4c,d).was applied, respectively, and the differences among treatments gradually increased with soil drying (Figure 3c,d).After being corrected by , the variations of  under rainfed and evolving soil water limitation treatments shared a similar trend with  , although with smaller fluctuations (Figure 4a,b).In addition, the cumulative  also had a similar dynamic pattern to  in the 2013 and 2014 growing seasons, respectively.However, the amount of accumulative  was about half of  (Figure 4c,d).Under rainfed conditions, linear regression analysis (B qtw vs. Biomass and B qtwv vs. Biomass) indicated that the R 2 value did not significantly increase, while the MAE and RMSE were significantly reduced after the production potential was corrected by VPD.The MAE and RMSE decreased by 34.3% and 33.3%, respectively, in 2013 (Figure 5a), compared to those of 45.9% and 47.2% in 2014 (Figure 5b).Similar results were also obtained for evolving soil water limitation treatments.There was no significant change in R 2 according to linear regression; however, a 41.6% reduction in the MAE and a 41.7% reduction in the RMSE were obtained during the 2013 growing season (Figure 5c), while they were 47.2% and 45.6% during the 2014 growing season, respectively (Figure 5d).

Effect of Evolving Soil Water Limitation on the Response Pattern of Biomass Accumulation to Climatic Production Potential
Compared with the rainfed conditions, evolving soil water limitation treatments significantly decreased biomass accumulation.In addition, biomass accumulation decreased with the reduction in irrigation in both years (Figure 6).
Using the final observed biomass and accumulative B qtwv under the rainfed treatment in 2013 and 2014 as references, respectively, we normalized the T1-T5 and W1-W5 treatments (Figure 7).Then, the response of the normalized biomass to normalized B qtwv was well represented by a three-parameter logistic function.The fitting results suggested that the standardized intrinsic growth rate of 9.98 in 2013 was significantly greater than the 7.38 in 2014 (Figure 7a,b).In addition, the standardized timing of maximum growth was 0.53 and 0.69 during the 2013 and 2014 growing seasons, respectively.In other words, the timing for maximum growth rate to occur in 2014 was also significantly postponed by the soil water limitation applied at the three-leaf stage, compared with that applied at the seven-leaf stage in 2013 (Figure 7a,b).These findings suggested that evolving soil water limitation significantly reduced the biomass accumulation of maize plants, as reflected by the decrease in the intrinsic growth rate response to climate production potential and delayed timing of the maximum growth.Under rainfed conditions, linear regression analysis ( vs. Biomass and  vs. Biomass) indicated that the R 2 value did not significantly increase, while the MAE and RMSE were significantly reduced after the production potential was corrected by .The MAE and RMSE decreased by 34.3% and 33.3%, respectively, in 2013 (Figure 5a), compared to those of 45.9% and 47.2% in 2014 (Figure 5b).Similar results were also obtained for evolving soil water limitation treatments.There was no significant change in R 2 according to linear regression; however, a 41.6% reduction in the MAE and a 41.7% reduction in the RMSE were obtained during the 2013 growing season (Figure 5c), while they were 47.2% and 45.6% during the 2014 growing season, respectively (Figure 5d).

The Relationship between Biomass and Grain Yield across Rainfed and Evolving Soil Water Limitiation Conditions
The one-way ANOVA analysis showed that grain yields of evolving soil water limitation treatments were much lower compared to rainfed treatments (Figure 8a,b).In addition, evolving soil water limitation treatments applied at the three-leaf stage and seven-leaf stage significantly decreased maize yield (Figure 8a,b).In 2013, maize grain yield obviously decreased with the reduction in irrigation, such as the grain yield of the T5 treatment (3.02 t ha −1 ) being only 55.7% of the T1 treatment (5.22 t ha −1 ) (Figure 8a).In 2014, the grain yields of T1-T3 were 1.32 t ha −1 , 1.09 t ha −1 , and 0.84 t ha −1 , respectively, while no yield was obtained in the T4-T5 treatments (Figure 8b).According to the pooled data (rainfed and evolving soil water limitation treatments), grain yield was shown to be a saturating function of biomass (Figure 8c).The response rate of grain yield to biomass first increased and then decreased.At the high end of biomass values, the increment in yield diminishes with the increment in biomass.The results indicate that the nonlinear, saturating relationship of grain yield to biomass applies across rainfed and soil water limitation conditions.

Effect of Evolving Soil Water Limitation on the Response Pattern of Biomass Accumulation to Climatic Production Potential
Compared with the rainfed conditions, evolving soil water limitation treatments significantly decreased biomass accumulation.In addition, biomass accumulation decreased with the reduction in irrigation in both years (Figure 6).

Effect of Evolving Soil Water Limitation on the Response Pattern of Biomass Accumulation to Climatic Production Potential
Compared with the rainfed conditions, evolving soil water limitation treatments significantly decreased biomass accumulation.In addition, biomass accumulation decreased with the reduction in irrigation in both years (Figure 6).was 0.53 and 0.69 during the 2013 and 2014 growing seasons, respectively.In other words, the timing for maximum growth rate to occur in 2014 was also significantly postponed by the soil water limitation applied at the three-leaf stage, compared with that applied at the seven-leaf stage in 2013 (Figure 7a,b).These findings suggested that evolving soil water limitation significantly reduced the biomass accumulation of maize plants, as reflected by the decrease in the intrinsic growth rate response to climate production potential and delayed timing of the maximum growth.

The Relationship between Biomass and Grain Yield across Rainfed and Evolving Soil Water Limitiation Conditions
The one-way ANOVA analysis showed that grain yields of evolving soil water limitation treatments were much lower compared to rainfed treatments (Figure 8a,b).In addition, evolving soil water limitation treatments applied at the three-leaf stage and sevenleaf stage significantly decreased maize yield (Figure 8a,b).In 2013, maize grain yield obviously decreased with the reduction in irrigation, such as the grain yield of the T5 treatment (3.02 t ha −1 ) being only 55.7% of the T1 treatment (5.22 t ha −1 ) (Figure 8a).In 2014, the grain yields of T1-T3 were 1.32 t ha −1 , 1.09 t ha −1 , and 0.84 t ha −1 , respectively, while no yield was obtained in the T4-T5 treatments (Figure 8b).According to the pooled data (rainfed and evolving soil water limitation treatments), grain yield was shown to be a saturating function of biomass (Figure 8c).The response rate of grain yield to biomass first increased and then decreased.At the high end of biomass values, the increment in yield diminishes with the increment in biomass.The results indicate that the nonlinear, saturating relationship of grain yield to biomass applies across rainfed and soil water limitation conditions.

Climate Change Influences Crop Growth and Production Potential
Climate change has profound impacts on global agriculture and will continue to have them [1,5].Solar dimming or brightening can substantially change the net amount of radiation arriving at the crop vegetation canopies and then affect crop photosynthesis and growth and, ultimately, crop yields [46,69].In recent years, there is increasing interest from researchers over the impact of solar radiation on agricultural production [70,71].The approximately 27% increase in maize yield in the US Corn Belt from 1984-2013 could be attributed to solar brightening [72]; meanwhile, an approximately 19% decrease was induced by solar dimming on the NCP during 1960-2015 [46].In this study, we found that the cumulative solar radiation during the growing season in 2013 was less than that in 2014, with a deficit of 868.7 MJ m −2 (Figure 1).These results suggested that the seasonal variation of solar radiation input needs to be addressed when studying the impacts of climate change on agriculture production.
Relative to wheat and rice, maize is more sensitive to climate warming.Each 1 °C increase in global mean temperature is predicted to reduce global yields of maize by 7.4%,

Climate Change Influences Crop Growth and Production Potential
Climate change has profound impacts on global agriculture and will continue to have them [1,5].Solar dimming or brightening can substantially change the net amount of radiation arriving at the crop vegetation canopies and then affect crop photosynthesis and growth and, ultimately, crop yields [46,69].In recent years, there is increasing interest from researchers over the impact of solar radiation on agricultural production [70,71].The approximately 27% increase in maize yield in the US Corn Belt from 1984-2013 could be attributed to solar brightening [72]; meanwhile, an approximately 19% decrease was induced by solar dimming on the NCP during 1960-2015 [46].In this study, we found that the cumulative solar radiation during the growing season in 2013 was less than that in 2014, with a deficit of 868.7 MJ m −2 (Figure 1).These results suggested that the seasonal variation of solar radiation input needs to be addressed when studying the impacts of climate change on agriculture production.
Relative to wheat and rice, maize is more sensitive to climate warming.Each 1 • C increase in global mean temperature is predicted to reduce global yields of maize by 7.4%, of wheat by 6.0%, and of rice by 3.2% [73].In addition, rainfed maize is more vulnerable to increasing temperatures than irrigated maize [74].In general, maize tends to display a higher stomatal conductance, transpiration rate, and intercellular CO 2 concentration under high VPD conditions, ultimately leading to reduced total biomass [48].Each 100 Pa increase in VPD during the milking stage would reduce maize yield by 127 kg ha −1 , and it decreased sharply by 82 kg ha −1 when the maximum temperature was higher than 29 • C [75].The effect of heat damage caused by increased temperature on maize yield loss is mainly caused by decreased pollen vitality, resulting in a decrease in pollination, and ultimately, this decreases the number of grains and grain weight [68,76].Interestingly, the impact mechanisms of temperature and VPD on crop growth and development are different.In detail, temperature influences plants primarily through the temperature dependence of biochemical and developmental processes, such as photosynthesis and respiration [51], whereas a VPD influences plants mainly by increasing atmospheric water demand and plant water loss [77].Because of the intimate connection between temperature and VPD, the effect of VPD on crop growth and development is often neglected or attributed to temperature.In this study, the temperature conditions were found to be similar, while the VPDs were significantly different the during two growing seasons (Figure 1).If the effect of VPD on production potential was not incorporated (Figure 2), the climatic production potential would be largely overestimated (Figure 5).Therefore, it is necessary to consider the impact of VPD on climatic production potential, especially under severe weather and climatic conditions.

Effect of Evolving Soil Water Limitation on Biomass Accumulation and Its Relation to Climatic Production Potential
Crop biomass accumulation is a result of the growth of different organs (e.g., leaves, stems, roots, and ears), which is a complex and dynamic process regulated by interactions between genetic factors and the environment [55,78].In addition, growth is also a reflection of intricate source-sink dynamics [78].Source and sink strength are highly responsive to environmental changes, and they are particularly susceptible to drought conditions [79].Reduced source and sink strengths during soil drying can lead to a large reduction in crop biomass accumulation and grain yield [80,81]. Prolonged drought decreased the growth rate of plant organs, reduced plant biomass accumulation, and delayed flowering time, although an extension of growth duration has been observed [78,82].However, the highly organized succession of maximum growth rates of the distinct organs was proved to be unchanged in response to prolonged drought [78].
In this study, evolving soil water limitation was applied at the seven-leaf stage and three-leaf stage during the 2013 and 2014 growing seasons, respectively.The biomass accumulations of maize were significantly decreased with irrigation reductions.The highest recorded yield in this region was 15.4 t ha −1 (equivalent to 30.8 t ha −1 B qtwv ) [40], which was much higher than those obtained values of B qtwv among the T1-T5 treatments (3.19~22.60t ha −1 ) and the W0-W5 treatments (2.35~22.85t ha −1 ).According to the continuous observations and pooled data, a gradient of soil water limitations was obtained at the flowering-milking stage.The response patterns of biomass accumulation to climatic production potential were logistic, with three distinct stages under both evolving soil water limitation and rainfed conditions, implying that the biomass accumulation pattern was conservative.Moreover, the dynamic pattern of biomass accumulation suggested that the reduced biomass was achieved by lowering the intrinsic growth rate and delaying the timing of the maximum growth rate (Figure 7).These findings could be considered as a further confirmation and complement for the previous findings [78].

The Relationship between Biomass and Grain Yield Affected by Soil Water Condition
In recent years, the technology used for the genetic breeding of maize has significantly advanced, contributing to approximately 75% of the yield increase [83,84].Genetic gains have been associated with improved stress tolerance related to a higher leaf area index and HI.Maize grain yield is strongly related to the number of kernels, which depends on the accumulation of ear biomass and the efficiency of using this biomass for kernel set [85].Therefore, the impact of drought on the relationship between biomass and grain yield involved two aspects: the rate of plant biomass accumulation and the proportion of this biomass that is allocated to the grain after flowering [36].In contrast to that of wheat, sorghum, and soybean [86][87][88], the proportion of biomass for maize allocated to the ear is not constant and even approaches zero under severe drought conditions.However, a constant HI is often adopted in most crop models [39], and it is not reliable for crop yield estimation, especially under drought or other abiotic stresses.An alternate way is to build a directly general relationship between biomass and grain yield.There is evidence that wheat grain yield is a saturation function of the above biomass within and across varieties [37].Our results also indicated that the relationship between biomass and grain yield appeared to be nonlinear and saturating across rainfed and drought conditions (Figure 8).Therefore, quantifying the relationship between plant biomass and grain yields across climate environments, varieties, and agricultural management is necessary to optimize yield estimation in a future study.

Limitations and Future Perspectives
The data collected from the field experiments provided us with an opportunity to assess the dynamic response of biomass accumulation to climatic production potential and its relation to grain yield under a range of evolving soil water limitations applied at two different growth stages.However, there are still some limitations in the implication and generalization of the results, although the data were collected from standardized measurements and processed by strict data quality control and analysis.First, droughts occurring at the three-leaf and seven-leaf growth stages of maize were only evaluated in a single growing season, which did not capture the climate variability range over decades.Nonetheless, due to the field experimental design with various irrigation levels, the response differences in biomass accumulation among different treatments appeared gradually with soil drying, which covered a wide range of soil water content.Therefore, the findings in this study would be robust and reasonable.Second, the production potential calculated by the mechanism-based empirical model was susceptible to the selection of parameters and crop species.In this study, we only used one drought-tolerant maize cultivar, while different genetic characteristics (e.g., growth duration, canopy structure, and optimal temperature for photosynthetic activity) of crop species were not considered.In addition, there was still a large gap between climatic production potential after being corrected by VPD and observed biomass, which should be noticed and remained to be explained.Therefore, future studies are needed to correct the main parameters for production potential calculation with more field data of maize to improve the universality of the results and enhance the understanding of crop production potential response to climate change.

Conclusions
Crop climatic production potential is useful for identifying the critical factors limiting resource use efficiency and productivity.However, previous studies on this topic have mostly focused on crop grain yield at an inter-seasonal time scale, and less attention has been paid to the process of biomass accumulation and its relation to grain yield in response to climatic production potential within the growing season, especially under evolving soil water limitations.In addition, the effect of VPD on crop growth and development is often neglected or attributed to temperature.In this study, we used a mechanism-based empirical model and a set of field experiment data to explore the dynamic response of biomass accumulation to climatic production potential and its relation to grain yield.We found that the ability of climate production potential to estimate biomass was well improved when VPD was involved.Soil water limitation significantly inhibited the biomass accumulation of maize plants, mainly by reducing the intrinsic growth rate and delaying the timing of maximum growth.Grain yield showed a nonlinear and saturating relationship with biomass across rainfed and evolving soil water limitation conditions.Overall, VPD cannot be neglected in determining climatic production potential, and drought changed the biomass accumulation pattern but not the relationship between grain yield and biomass in maize.This study provides useful information to estimate crop production potential under soil water limitations and the optimization of maize farming and management under the background of climate change.

Figure 2 .
Figure 2. Variations of the downregulation scalars for the respective effects of temperature (a,b), vapor pressure deficit (; (c,d)), and their interaction (e,f) on climatic production potential during the 2013-2014 growing seasons.f(T) and f(VPD) denote the downregulating scalars for the effects of temperature and VPD on crop climatic production potential, respectively; meanwhile, f(T) × f(VPD) means the interaction effects of temperature and VPD on crop climatic production potential.

Figure 2 .
Figure 2. Variations of the downregulation scalars for the respective effects of temperature (a,b), vapor pressure deficit (VPD; (c,d)), and their interaction (e,f) on climatic production potential during the 2013-2014 growing seasons.f (T) and f (VPD) denote the downregulating scalars for the effects of temperature and VPD on crop climatic production potential, respectively; meanwhile, f (T) × f (VPD) means the interaction effects of temperature and VPD on crop climatic production potential.

Figure 3 .
Figure 3. Daily and accumulative climatic production potential of biomass ( ) during the 2013-2014 growing seasons.Daily  in 2013 (a) and 2014 (b), accumulative  in 2013 (c) and 2014 (d).T0, rainfed treatment in 2013; T1-T5, evolving soil water limitation treatments with different irrigation amounts applied at seven-leaf stage in 2013.W0, rainfed treatment in 2014; W1-W5, evolving soil water limitation treatments with different irrigation amounts applied at three-leaf stage in 2014. , climatic production potential of biomass.

Figure 3 .
Figure 3. Daily and accumulative climatic production potential of biomass (B qtw ) during the 2013-2014 growing seasons.Daily B qtw in 2013 (a) and 2014 (b), accumulative B qtw in 2013 (c) and 2014 (d).T0, rainfed treatment in 2013; T1-T5, evolving soil water limitation treatments with different irrigation amounts applied at seven-leaf stage in 2013.W0, rainfed treatment in 2014; W1-W5, evolving soil water limitation treatments with different irrigation amounts applied at three-leaf stage in 2014.B qtw , climatic production potential of biomass.

Figure 4 .
Figure 4. Daily and cumulative climatic production potential of biomass after being corrected by  ( ) during the 2013-2014 growing seasons.Daily  in 2013 (a) and 2014 (b); accumulative  in 2013 (c) and 2014 (d).T0, rainfed treatment in 2013; T1-T5, evolving soil water limitation treatments applied at seven-leaf stage in 2013.W0, rainfed treatment in 2014; W1-W5, evolving soil water limitation treatments applied at three-leaf stage in 2014. , climatic production potential of biomass after being corrected by .

Figure 4 .
Figure 4. Daily and cumulative climatic production potential of biomass after being corrected by VPD (B qtwv ) during the 2013-2014 growing seasons.Daily B qtwv in 2013 (a) and 2014 (b); accumulative B qtwv in 2013 (c) and 2014 (d).T0, rainfed treatment in 2013; T1-T5, evolving soil water limitation treatments applied at seven-leaf stage in 2013.W0, rainfed treatment in 2014; W1-W5, evolving soil water limitation treatments applied at three-leaf stage in 2014.B qtwv , climatic production potential of biomass after being corrected by VPD.

Agronomy 2023 , 19 Figure 5 .
Figure 5.Comparison of the climatic production potential of biomass ( ) and climatic production potential of biomass after being corrected by  ( ) with observed biomass under rainfed (a,b) and drought treatments (c,d) during the 2013-2014 growing seasons.

Figure 5 .
Figure 5.Comparison of the climatic production potential of biomass (B qtw ) and climatic production potential of biomass after being corrected by VPD (B qtwv ) with observed biomass under rainfed (a,b) and drought treatments (c,d) during the 2013-2014 growing seasons.

Figure 5 .
Figure 5.Comparison of the climatic production potential of biomass ( ) and climatic production potential of biomass after being corrected by  ( ) with observed biomass under rainfed (a,b) and drought treatments (c,d) during the 2013-2014 growing seasons.

Figure 6 .
Figure 6.Variations of observed biomass under rainfed and evolving soil water limitation treatments during the 2013 (a) and 2014 (b) growing seasons.The error bars denote the standard errors of three or five replications.

Figure 7 .
Figure 7. Response of normalized climatic biomass production potential after being corrected by  (normalized  ) to normalized observed biomass during the 2013-2014 growing seasons: (a) 2013; (b) 2014; (c) 2013 and 2014.The colored areas are the 95% confidence bands of the nonlinear fitting.The error bars denote the standard errors for three replications.

Figure 7 . 19 Figure 8 .
Figure 7. Response of normalized climatic biomass production potential after being corrected by VPD (normalized B qtwv ) to normalized observed biomass during the 2013-2014 growing seasons: (a) 2013; (b) 2014; (c) 2013 and 2014.The colored areas are the 95% confidence bands of the nonlinear fitting.The error bars denote the standard errors for three replications.Agronomy 2023, 13, x FOR PEER REVIEW 13 of 19

Figure 8 .
Figure 8. Grain yield under different treatments and its relationship to biomass during the 2013-2014 growing seasons.Grain yields among different treatments in 2013 (a) and 2014 (b), respectively; the relationship between grain yield and biomass production under rainfed and evolving soil water limitation treatments (c).The error bars denote the standard errors of three or five replications.The different lowercase letters indicate a significant difference between treatments (p < 0.05).

Table 1 .
Experimental design of evolving soil water limitations treatments during the 2013-2014 maize growing seasons.

Table 2 .
Values and meanings of photosynthetic production potential parameters for maize.

Table 3 .
The minimum, optimum, and maximum temperatures for the photosynthetic activity of maize at different growth stages.