Combining field data and modeling to better understand maize growth response to phosphorus (P) fertilizer application and soil P dynamics in calcareous soils

Weina Zhang ,Zhigan Zhao ,Di He ,Junhe Liu ,Haigang Li ,Enli Wang#

1 School of Biological and Food Processing Engineering, Huanghuai University, Zhumadian 463000, China

2 Key Laboratory of Plant–Soil Interactions, Ministry of Education/College of Resources and Environmental Sciences, China Agricultural University, Beijing 100193, China

3 Inner Mongolia Key Laboratory of Soil Quality and Nutrient Resources/Key Laboratory of Grassland Resource (IMAU), Ministry of Education/College of Grassland, Resources and Environment, Inner Mongolia Agricultural University, Hohhot 010018, China

4 CSIRO Agriculture and Food, Canberra, ACT 2601, Australia

Abstract We used field experimental data to evaluate the ability of the agricultural production system model (APSIM) to simulate soil P availability,maize biomass and grain yield in response to P fertilizer applications on a fluvo-aquic soil in the North China Plain. Crop and soil data from a 2-year experiment with three P fertilizer application rates(0,75 and 300 kg P2O5 ha–1) were used to calibrate the model. Sensitivity analysis was carried out to investigate the influence of APSIM SoilP parameters on the simulated P availability in soil and maize growth. Crop and soil P parameters were then derived by matching or relating the simulation results to observed crop biomass,yield,P uptake and Olsen-P in soil. The re-parameterized model was further validated against 2 years of independent data at the same sites. The re-parameterized model enabled good simulation of the maize leaf area index (LAI),biomass,grain yield,P uptake,and grain P content in response to different levels of P additions against both the calibration and validation datasets. Our results showed that APSIM needs to be re-parameterized for simulation of maize LAI dynamics through modification of leaf size curve and a reduction in the rate of leaf senescence for modern staygreen maize cultivars in China. The P concentration limits (maximum and minimum P concentrations in organs)at different stages also need to be adjusted. Our results further showed a curvilinear relationship between the measured Olsen-P concentration and simulated labile P content,which could facilitate the initialization of APSIM P pools in the NCP with Olsen-P measurements in future studies. It remains difficult to parameterize the APSIM SoilP module due to the conceptual nature of the pools and simplified conceptualization of key P transformation processes.A fundamental understanding still needs to be developed for modelling and predicting the fate of applied P fertilizers in soils with contrasting physical and chemical characteristics.

Keywords: maize,phosphorus availability,modeling,APSIM maize,APSIM SoilP

1.Introduction

Phosphorus (P) is one of the most limiting macronutrients for plant growth and development (Vanceet al.2003;Zhanget al.2022). To maintain or increase crop yields,P fertilizers often need to be applied to soils (Cordellet al.2009;Lynchet al.2011;Johnstonet al.2014;Zhanget al.2019). However,the majority of P is strongly absorbed by soil minerals,e.g.,clay minerals and aluminum (Al) and iron (Fe) oxides,causing low P use efficiency (PUE),with average in-season PUE of usually less than 20% (Cornishet al.2009;Shenet al.2011;Bushonget al.2014;Wanget al.2019). Excessive application of P fertilizers could pose a potential risk to surface water quality due to P transportationviasurface runoff and soil erosion (Zhanget al.2019).

Maintaining an appropriate P supply level and improving the exploitation and utilization of soil-absorbed P could help to reduce the input of P fertilizers and improve PUE. In calcareous soils,the main processes involved in soil P transformation include sorption/desorption and precipitation/dissolution (Frossardet al.2000;Shenet al.2004;Devauet al.2010). Several studies on soil P fractionation in response to long-term P fertilization have been conducted involving calcareous soils but have only investigated various soil P pools,such as labile P,moderately labile P and nonlabile P(Shenet al.2004;Liet al.2015;Liaoet al.2021). Little information is available to quantify the dynamics of soil P transformation processes. One of the reasons is that long-term experimental data on crop responses to various P additions are required to develop an understanding of P dynamics and transformation processes within the soil–plant continuum. In addition,the findings at one location cannot be extended to other locations with different soil types and climatic conditions. Process-based soil–plant modeling can provide an efficient approach to model crop growth responses to various P supplies across a wide range of soil types and climatic conditions.

The agricultural production system model (APSIM)has been widely used in various countries to simulate the growth,yield and resource use efficiency of major crops (e.g.,maize,wheat,and rice) and cropping systems (e.g.,wheat–maize and wheat–rice cropping systems) as affected by variable climatic conditions and management interventions,including different water and nitrogen input levels (Probertet al.1995,1998;Wanget al.2003;Assenget al.2008;Hochmanet al.2009;Chenet al.2010;Wanget al.2012). The APSIM SoilP module was developed to simulate the soil P availability based on soil P sorption/desorption processes and to study the effectiveness of P fertilizer applications (Delveet al.2009). Several studies have demonstrated that the APSIM SoilP module can simulate crop growth in response to P additions in soils where sorption/desorption is the major process controlling P availability (Shenet al.2011). However,it remains unknown whether the APSIM SoilP model can be used to correctly simulate the P availability in soils (e.g.,calcareous soils) where other processes (e.g.,precipitation/dissolution) also control the P availability. A more recent study showed that the APSIM model could not predict the response of the crop yield to soil P dynamics within seasons on Vertisols,which was mainly due to the lack of a linear correlation between the labile P concentration obtained with the SoilP module and the measured Colwell-P concentration (Raymondet al.2021). Calcareous soil is a major soil type in the North China Plain (NCP). No studies have focused on evaluating the APSIM SoilP module performance in the simulation of crop growth and yield responses to various P additions in this soil.

The objectives of this paper were: 1) to determine whether the APSIM model could adequately simulate the observed crop growth and soil P dynamics in response to P fertilizer applications;and 2) to examine ways of improving the model performance in terms of the maize crop response to P fertilizer application in calcareous soils. We first presented experimental data on maize growth,yield,P uptake and soil P dynamics in response to different levels of P addition to the NCP calcareous soil.We then evaluated the ability of the APSIM to simulate maize growth and soil P dynamics,and analyzed the main reasons for the poor performance of the original APSIM.We further re-parameterized the maize and SoilP modules to improve APSIM performance for the simulation of both crop growth and soil P dynamics. Finally,we discussed future work that will be needed to improve the modelling of crop-P relations.

2.Materials and methods

2.1.Study site

Field experiment was conducted at the Quzhou Experimental Station of China Agricultural University(36.9°N,115.0°E) from May to October in 2016 and 2017 in Quzhou County,Hebei Province,China. This site is characterized by a temperate continental monsoon climate,with an average annual temperature of 13.1°C and annual precipitation of 556 mm (1990–2017). Sixtytwo percent of the total precipitation occurs in the summer months from the start of July to the end of September.The fortnightly total precipitation,mean daily radiation per week and mean air temperature per week during the maize growing season from late May to late September are shown in Fig.1. The soil type is classified as a typical calcareous fluvo-aquic soil with a composition of 14.7%clay,74.0% silt and 11.3% sand. At the beginning of the experiment in 2016,topsoil (0–20 cm) chemical properties were measured: pH of 8.5 (1:2.5 w/v in water),mineral N content of 17.7 mg kg–1,exchangeable K content of 80.2 mg kg–1and organic matter content of 10.3 g kg–1.Detailed soil properties are listed in Table 1.

2.2.Field experiments and data measurement

The field experiment was started in 2010 and entailed a completely randomized block design with four replicates of five different P application rates as treatments: 0 kg P2O5ha–1(P0),37.5 kg P2O5ha–1(P37.5),75 kg P2O5ha–1(P75),150 kg P2O5ha–1(P150),and 300 kg P2O5ha–1(P300). Based on the yield responses to P application rates in 2010–2015 (Jiao 2016),the maize shoot biomass and yield plateaued (did not further increase) at around 75 kg P2O5ha–1(P75),implying that 75 kg P2O5ha–1per year was enough to meet the maize P demand for growth. Thus,the P0,P75 and P300 treatments in this study roughly represent P-stress,P-optimal and P-luxury soil conditions,respectively (Zhanget al.2022). The initial soil Olsen-P concentrations before sowing in 2016 were measured,and were 6.6,23.2 and 49.5 mg kg–1,respectively,for those three treatment levels.

Fig. 1 Fortnightly precipitation,mean daily radiation and mean air temperature per week during the maize growing seasons in 2016 and 2017. The position of the arrow denotes the silking growth stage.

The plot size was 250 m2(12.5 m×20 m). All the plots were treated with 225 kg N ha–1as urea (46% N),60 kg K2O ha–1as K2SO4(50% K2O) and P fertilizer as calcium superphosphate. P and K fertilizers were broadcast and incorporated into the 0–20 cm soil layer before maize sowing. N fertilizer was applied three times: 90 kg N ha–1at sowing,60 kg N ha–1at the 6-leaf (V6) stage,and 75 kg N ha–1at the 12-leaf (V12) stage. The field was flood-irrigated with 110 mm of water before sowing in each year to avoid water stress. Maize (ZeamaysL.cv.ZD958) was planted on 25 May 2016 and 27 May 2017 with a 0.6-m row spacing,and the final plant density reached 75,000 plants per ha. Weeds,insect pests and diseases were controlled by herbicides and pesticides as needed.

Four plants were cut from the stem base in each plot at the seedling,jointing,silking and grain filling stages in 2016 and 2017. The leaf areas of individual leaves were calculated either as leaf length×leaf width×0.75 for fully expanded leaves or as leaf length×leaf width×0.5 for incompletely expanded leaves. All shoot samples were oven-dried at 105°C for 30 min and then dried at 70°C to a constant weight. The shoot biomass was determined at each of the different growth stages (seedling,jointing,silking and filling). Then,all the samples were ground into powder,evenly mixed,and digested in a mixture of H2SO4and H2O2to determine the P concentrationviathe molybdovanadate spectrophotometric method (Johnson and Ulrich 1959). The data of maize shoot biomass,P uptake and grain yield at maturity were obtained from our previous study (Zhanget al.2022). Details of the experiment can be found in Zhanget al.(2022).

Soil samples were collected from the plow layer(0–20 cm) at the maize seedling,jointing,silking,grain filling and maturity stages in 2016 and 2017. Five soil cores (5-cm diameter) were collected in each plot every year. The fresh soil samples were thoroughly mixed,air-dried and sieved through a 2.0-mm sieve. The soil samples were extracted with 0.5 mol L–1NaHCO3(pH 8.5)at 25°C,and Olsen-P was determinedviathe molybdo–vanadophosphate method (Westerman 1990).

The above experimental data and published data(Zhanget al.2022) from 2016 to 2017 were used to test the APSIM v7.9 for the simulation of maize growth in response to P fertilizer addition at Quzhou. These data were then further used to calibrate the APSIM model,to derive the maize and soilP parameters in order to improve the simulation results.

Another independent dataset was used to validate the calibrated APSIM model. That dataset was obtained from a previous study at the same site with six P fertilizer treatments (0,12.5,25,50,100,and 200 kg P ha–1) and a typical maize cultivar (Zhanget al.2017,2018),and included data on biomass,yield and biomass P content.Details of that experiment can be found in Zhanget al.(2017,2018).

2.3.APSlM maize and SoilP modules

APSIM version 7.9 was used to simulate maize growth and yield in response to the soil P availability at a daily time step. The maize module simulates maize growth and P demand,while the SoilP module simulates the soil P availability and the ability to supply P to maize in response to P fertilizer applications. The actual P uptake per day by maize is determined as the minimum of the crop P demand and the soil P supply.

The maize module was developed based on the same model template as the sorghum module to simulate crop development,biomass accumulation and partitioning,which are similar to those described for sorghum by Hammeret al.(2010). The phenology is simulated for successive phenological stages,each with its own specific thermal time target. The maize LAI dynamics is simulated using the final leaf number per plant,individual leaf size,plant density and leaf appearance rate. The final leaf number is estimated at early stages and then determined based on the thermal time duration between emergence and flag leaf initiation and the leaf initiation rate (23.2°C per leaf) (Carberryet al.1989).In the model,the individual leaf size is a function of the final leaf number and leaf position following a bellshaped curve developed by Keating and Wafula (1992).The actual LAI is simulated using the leaf size,leaf appearance rate and leaf senescence rate,and further reduced by soil water and nutrient (N and P) stresses.The cultivar parameters adopted in the current study are summarized in Table 2.

Table 2 Maize cultivar parameters used in the simulation

The SoilP module was developed by Probert (2004)to simulate P dynamics in soil and the response of soil P availability to different P fertilizer application rates. The SoilP module comprises six major pools (Fig.2),including the rock P pool,banded P pool (water-soluble fertilizer P applied as a band),unavailable organic P pool (P contained in soil organic matter or the microbial biomass),unavailable inorganic P pool (P that cannot be readilyused by crops but can replenish the labile P pool over time),labile P pool (P weakly absorbed onto soil particles)and solution P pool. The size of the labile P pool in the model is affected by several processes,including fertilizer input,crop uptake,and soil P transformation processes between the different P pools. APSIM simulates the dynamic changes in the sizes of P pools in response to soil temperature and moisture and P fertilizer additions to capture the short-and long-term P availability in soil.

Fig. 2 Diagram of the structure and simulated processes of the APSIM SoilP module (modified from Wang et al.2014).

The SoilP module considers the differences in P fertilizer forms and placement effects in fertilizer application methods (Probert 2004). Rock phosphate,which can release P into the labile P pool,is assigned to the rock P pool. Water-soluble P fertilizer,which is appliedviabroadcasting or mixing with soil,is assigned to the labile P pool. However,water-soluble P fertilizer is added to the banded P pool when it is banded,assuming a higher effectiveness.

There are three soil P transformation processes in the SoilP module (Fig.2),including mineralization and immobilization between the unavailable organic P and labile P pools,gain and loss of availability between the unavailable inorganic P and labile P pools,and sorption and desorption between the labile P and solution P pools.The SoilP module assumes that the unavailable organic P pool can be estimated from the soil organic matter pool and the C:P ratio (Westerman 1990). The gain/loss of availability between the labile and unavailable inorganic P pools can be estimatedviathe relative rate of loss,which is affected by the soil temperature and moisture.The relative rates of the forward and reverse processes determine the magnitude of the ratio of the unavailable P pool replenishing the labile P pool under steady-state conditions (Joneset al.1984). It is assumed that the unavailable P pool is typically 10 times the labile P pool under steady-state conditions. In the model,the annual fraction of the loss of the available P pool at 25°C and optimal soil moisture is an input parameter (=0.3/year),which can be modified by the user (Wanget al.2014).The solution P pool is directly linked to crop P uptake.

The SoilP module assumes that P in the soil solution is in equilibrium with the labile P in soil,which is controlled by sorption/desorption processes. The solution P concentration (Ps) can then be determined from the labile P concentration (PL) using the Freundlich isotherm in eq.(1).

The coefficientsaandbin eq.(1) define the shape of the Freundlich isotherm,and their values vary with the soil P sorption characteristics. Sorption curves have not been routinely used to obtain sorption coefficient values,and the first coefficientais sometimes derived from the P buffering capacity of soil while the value of the second coefficientbis estimatedviareference to previous work on soil P sorption.Psdenotes the inorganic P concentration in the soil solution.

2.4.APSlM parameterization

For the simulation of maize growth in this study,cultivar parameters were derived according to the field experimental data under the P300 treatment (i.e.,no P stress condition). The maximum grain number and grainfilling rate were calculated based on our observed data(Table 2). In addition,the thermal time for the different phenology periods was derived based on the observed dates of emergence,silking and maturity (Table 2).Using the above cultivar parameters,APSIM severely underestimated LAI and maize biomass (Fig.3-A). The underestimation of LAI was due to the overestimation of leaf death and dead leaf number for the modern maize cultivar used in this study. We re-parameterized the bellshaped leaf size function used in APSIM-Maize according to Zhenet al.(2018) for local cultivars. We reduced the values of the two parameters for the simulation of the leaf senescence rate and dead leaf number,i.e.,deadLeafConstanddeadLeafSlop(Table 3) in eq.(2).The underestimation of leaf biomass (Fig.3-B) was related to the lower simulated biomass partitioning to leaves,as calculated in eq.(3). We further reduced the value ofleaf_partition_ratefrom 0.0182 to 0.006 (Table 3).

In APSIM,the P concentration limits (senescent,minimum and maximum P concentrations) of different maize organs are related to the phenological stages of maize,which are used to calculate the P demand.Compared to our data,these P concentrations (Pc) were inconsistent with the field measurements (P0,P75 and P300). We therefore replaced the default maximum Pc in APSIM with the Pc values measured under our P300 treatment,and the default minimum Pc with the measured Pc values under our P0 treatment for all stages.

Fig. 3 Dynamics of the simulated (lines) and observed (symbols) leaf area index (LAI;A) and leaf biomass (B) of maize under the different P fertilization treatments. P0,0 kg P2O5 ha–1;P75,75 kg P2O5 ha–1;P300,300 kg P2O5 ha–1. The bars denote the standard errors of four replicates (n=4). Simulated values were produced with the original APSIM v7.9 using the maize phenology and grain parameters derived in this study (Table 2).

For parameterization of soil P,due to the lack of detailed data and a process understanding of the P transformation processes,we conducted a sensitivity analysis to explore the impacts of the changes in the three parameters that control P availability (i.e.,sorption coefficientsaandband the rate of gain/loss availability).We used the sensitivity analysis to investigate how the simulated labile P corresponds to measured Olsen-P concentrations over time and how they impact maize biomass growth and yield (Assenget al.2002;Luoet al.2014;Gunarathnaet al.2019). The intervals and the lower and upper bounds for these three parameters were specified based on expert opinions in the sensitivity analysis. Two model outputs,i.e.,the soil labile P concentration and shoot biomass at maturity,were used to assess the crop response and soil P availability. We derived a set of SoilP module parameters based on the best match between the simulated and measured biomasses and the best correlation between the simulated labile P and measured Olsen-P concentrations. Table 3 provides the parameters with their values in the original and modified APSIM models.

2.5.Evaluation of the APSlM performance

With the derived parameters,the APSIM model was tested against both datasets to evaluate model performance. The performance of the modified APSIM model was evaluated by comparing the simulated and measured values of the LAI,shoot biomass,grain yield and P content in the shoot biomass and grains under the three P fertilizer application treatments. The coefficient of determination (R2) and root mean squared error(RMSE) between the simulated and measured values were used to evaluate the model performance. The higher theR2,the lower the RMSE and the better the APSIM performance.

whereXiandYiare the measured and simulated values,andnandiare the sample numbers,respectively.

3.Results

3.1.Performance of the original APSlM v7.9

Maize growth significantly responded to P fertilization application in both 2016 and 2017 (Fig.4). The shoot biomass increased from P0 to P75 but did not further increase under the P300 treatment (Fig.3),and similar trends were observed for LAI and grain yield (Fig.4-A and C). In general,compared to the observed values,the APSIM captured the early season dynamics of LAI,biomass,and biomass P reasonably well until the jointing stage,but underestimated all of these quantities at the later stages (LAI:R2=0.22,RMSE=1.96;biomass:R2=0.87,RMSE=5.20 t ha–1;biomass P:R2=0.87,RMSE=14.9 kg ha–1) (Figs.3-A,4 and 5). The shoot biomass underestimation at the later growth stages was mainly due to the underestimation of the peak LAI (Fig.3-A) and the simulation of a more rapid leaf senescence toward maturity (Fig.3-B).

3.2.Modified maize module parameters

The modified maize module parameters for simulating leaf senescence are given in Table 3. According to our previous study (Zhanget al.2022),the modified senescent,minimum and maximum P concentrations for leaves,stems and grain are shown in Fig.6.

3.3.Response of labile P to the SoilP module parameters

The soil labile P concentration was not sensitive to the change inaor the relative rate of P availability gain/loss under the P75 and P300 treatments,but it was very sensitive to the changes inband P application rates(Fig.7). The soil labile P concentration was positively correlated with the change in P application rate,but it was negatively correlated with the change inbunder the P75 and P300 treatments. The soil labile P concentration under the P0 treatment was positively correlated with the relative rate of P availability gain/loss,under loweraand higherbvalues (Fig.8).

Fig. 5 Comparison of the simulated and observed values of the shoot biomass (A),biomass P content (B),grain yield (C),grain P content at maturity (D),leaf area index (LAI) at silking (E) and leaf biomass at maturity (F) for maize under the different P fertilization treatments. P0,0 kg P2O5 ha–1;P75,75 kg P2O5 ha–1;P300,300 kg P2O5 ha–1. The dotted lines are 1:1 lines,and the thick lines are regression lines. The bars indicate the standard errors of four replicates (n=4). Simulated values were produced with the original APSIM v.7.9. with the maize phenology and grain parameters derived in this study (Table 2).

Fig. 6 The senescent,minimum and maximum P concentrations in leaves (A),stems (B) and grains (C) at different growth stages,modified from Zhang et al.(2022).

Fig. 7 Impacts of coefficients a (bottom) and b (left) in eq.(1),and the rate loss available coefficient and P fertilization rate (kg ha–1)on the labile P concentration (mg kg–1).

Under P stress conditions (P0),the measured soil P concentrations slowly decreased from the seedling to maturity stages in both 2016 and 2017. It slightly increased from the maize maturity stage in 2016 to the maize seedling stage in 2017 (Fig.9). The original APSIM simulated a sharp decrease in soil P from the maize maturity stage in 2016 to the maize seedling stage in 2017,which is different from the measured trend (Fig.9). The measured LAI at the silking stage was higher in 2017 than that in 2016,while the simulated LAI at the silking stage in 2017 was lower than both the simulated LAI at the silking stage in 2016 and the measured LAI in 2017 (Fig.3-A). The underestimation of the LAI in 2017 was mainly caused by the underestimation of the labile P concentration in 2017 and the consequent P stress. Based on the effects of parameter changes on the resulting biomass and correlations between the labile P and Olsen-P concentrations,parameterb(affecting the shape of the soil P Freundlich isotherm) was increased from 0.7 to 0.75,and the parameter for the P loss availability (affecting soil P transformation between the labile P and unavailable P pools) was increased from 0.3 to 0.9 (Table 3).

3.4.Response of maize growth to the SoilP model parameters

Fig. 8 Impacts of coefficients a (bottom) and b (left) in eq.(1),and the rate loss available coefficient on the labile P concentration (mg kg–1) under the P0 (0 kg P2O5 ha–1) treatment in 2016 and 2017. The circles of different sizes denote different levels of soil labile P.

Fig. 9 Comparison of the measured Olsen-P (extracted with 0.5 mol L–1 NaHCO3 (pH=8.5)) and labile P concentrations (mg kg–1) simulated with the original and modified APSIM models at the different maize growth stages under the P0 (0 kg P2O5 ha–1) treatment in 2016 and 2017. The bars denote the standard errors of four replicates (n=4). Arrow illustrates the significant decrease trend.

Fig.10 shows the effects of changingaandbof the Freundlich isotherm,the rate of P availability gain/loss and the P fertilization application rate on simulated maize biomass at maturity. Simulated biomass was not sensitive1)to the changes in the rate of P availability gain/lossunder P0,P75 and P300 treatments,but it was very sensitive to the changes ina,band P fertilization rate. The biomass was negatively correlated withaand positively correlated withb.

3.5.Performance of the modified version of APSlM v7.9

Modifications of parameterband the rate of P availability loss/gain improved the simulated dynamics of soil labile P from 2016 to 2017 (Fig.9). The modified APSIM could capture the dynamics of LAI (Fig.11-E),and accurately simulate the biomass dynamics (Fig.11-A) and grain yield(Fig.11-C) across the different P fertilization treatments.The model explained 91 and 88% of the biomass and yield variations,respectively,and the RMSE values for the biomass and yield were 1.03 and 0.49 t ha–1,respectively(Fig.12-A and C). The new parameterization also led to a more accurate simulation of crop P uptake (Fig.11-B) and grain P content (Fig.11-D) in both 2016 and 2017. This model explained 92% (Fig.12-B) and 82% (Fig.12-D) of the variations in final biomass and grain P contents,with RMSE values of 3.53 and 4.17 kg ha–1,respectively.

The performance of the calibrated model against the independent 2014–2015 experimental data by Zhanget al.(2017,2018) is shown in Fig.13. The modified APSIM could explain 77,82 and 78% of the variations in the shoot biomass (Fig.13-A),yield (Fig.13-B) and biomass P content (Fig.13-C),respectively,with corresponding RMSE values of 1.95,0.90 and 2.50 kg ha–1.

Fig. 10 Effects of coefficients a (bottom) and b (left) in eq.(1),and the rate loss available coefficient (top) and P fertilization rate on the biomass (t ha–1). The circles of different sizes denote different biomasses.

3.6.Relationship between the simulated and measured soil Olsen-P concentrations

The measured soil Olsen-P concentrations were much lower than the simulated labile P concentrations under the P75 and P300 treatments (Fig.14-A). The measured soil Olsen-P and simulated soil labile P concentrations showed similar patterns of change,and they correlated well in a curvilinear relationship(Fig.14-B). The simulated soil labile P could explain 92% of the variation in the measured soil Olsen-P concentration across the different P fertilization application treatments and successive planting years from 2016 to 2017.

4.Discussion

The results of this study revealed several deficiencies in the APSIM model for simulating maize leaf area dynamics,crop growth and P demand,and their responses to P availability in soil. The results also indicated a close relationship between the model simulated labile P and the measured Olsen-P concentrations in soil,which could help with the initialization of the SoilP module in future modelling studies on similar soils.

4.1.Modeling the maize leaf size and area in the NCP

For LAI,APSIM v7.9 uses a bell-shaped curve function to simulate leaf size along leaf positions (Dwyer 1986),which is further used together with plant density and leaf senescence to calculate the LAI (Birchet al.1998;Soufizadehet al.2018). The parameters for both the leaf size curve and leaf senescence need to be adjusted to local and modern maize cultivars,which are different from those of classical maize hybrids (Carberryet al.1989;Keating and Wafula 1992;Birchet al.1998;Zhenet al.2018). We adopted the revised bell-shaped function for the individual leaf size with the leaf position from Zhenet al.(2018),who derived parameters according to the LAI data of new maize hybrids cultivated in China. For leaf senescence,past maize varieties were early-senescing hybrids,while the new maize varieties currently cultivated in China are staygreen hybrids. Ninget al.(2013) reported that the main maize varieties cultivated in China were early-senescing varieties in the 1950s,two moderate-senescing varieties in the 1960s and two stay-green hybrids currently. The cultivar simulated in this study (ZD 958) is a stay-green hybrid (Zhanget al.2022). Therefore,it was necessaryto change the leaf senescence parameters in APSIM,which resulted in significantly improved simulations of LAI at the different growth stages (Figs.6 and 12,respectively).

Fig. 11 Dynamics of the simulated (lines) and observed(symbols) values of the shoot biomass (A),biomass P content(B),yield (C),grain P content (D) and leaf area index (LAI;E)for maize under the different P fertilization treatments. P0,0 kg P2O5 ha–1;P75,75 kg P2O5 ha–1;P300,300 kg P2O5 ha–1.The symbols indicate the measured values,and the lines indicate the simulated values of the modified APSIM v7.9.The bars denote the standard errors of four replicates (n=4).

4.2.P concentration limits of maize

The shoot P concentration in crops decreases with increasing crop biomass or growth stage,and this dilution phenomenon is used for identifying and quantifying P deficiencies and demand. The APSIM maize model calculates crop P demand,P stress and P re-translocation in crop using crop biomass together with P concentration limits,i.e.,the minimum and maximum P concentrations of different maize organs at the various growth stages(Wanget al.2014). The initial P concentration limits for leaves,stems and grains (Fig.6) were derived from the compositions of samples collected during an experiment of the growth of a short-duration cultivar in eastern Kenya(Probert and Okalebo 1992),together with the published data of Jones (1983). Both sets of data were obtained from experiments conducted before the 1990s and used classical maize hybrids. Wanget al.(2014) compared the P concentration limits defined in the APSIM and the measured P concentrations in their study,and found that the range of the measured P concentrations was quite different from the P concentration limits in the APSIM. In our previous study involving three P fertilizer treatments(P0,P75 and P300),we obtained the minimum and maximum P concentrations of each organ at the differentgrowth stages (Zhanget al.2022). From the datasets of the P concentration limits in the current version of APSIM v7.9 and our previous study,we chose the highest maximum P concentration as the maximum P concentration and the lowest minimum P concentration as the minimum P concentration to re-parameterize APSIMMaize (Fig.6),which improved the performance of the APSIM in simulating the biomass and grain P content(Figs.12 and 13,respectively).

Fig. 12 Comparison of the simulated and observed values of the shoot biomass (A),biomass P content (B),yield (C),grain P content (D) at maturity and leaf area index at silking stage(E) for maize under the different P fertilization treatments. The dotted lines are 1:1 lines,and the thick lines are regression lines. The bars denote the standard errors of four replicates(n=4). All the simulated data were obtained with the modified APSIM v7.9.

Fig. 13 Comparison of the simulated and observed values of the shoot biomass (A) and yield (B) at maturity,and the biomass P content at silking (C) for maize. The dotted lines are 1:1 lines,and the thick lines are regression lines. The bars denote the standard errors of four replicates (n=4). All the simulated data were obtained with the modified APSIM v7.9.

4.3.Modeling the P availability in calcareous soil

Fig. 14 Dynamics (A) and comparision (B) of simulated soil labile P concentration and the measured soil Olsen-P concentration(mg kg–1) in the top soil layer (0-10 cm). P0,0 kg P2O5 ha–1;P75,75 kg P2O5 ha–1;P300,300 kg P2O5 ha–1. The Olsen-P values include the 2016–2017 experimental data,which were measured at the different maize growth stages. All the simulated data were generated with the modified APSIM v7.9.

To the best of our knowledge,this study is the first to model maize crop growth and yield in response to P fertilizer application in fluvo-aquic soil in the NCP.Previous studies have shown that the APSIM could simulate the impact of soil P deficiency and types of P applied as fertilizers or manure on the biomass growth and grain yield of maize in Oxisol soil in western Kenya(Kinyangiet al.2004;Micheniet al.2004;Probert 2004),the response of crop yield in a rotation to P additions in a red Ferrosol soil in Australia (Wanget al.2014),and the impact of P on maize and bean yields on contrasting soil types in Kenya and Colombia (Delveet al.2009). Like the work described here,all these studies required estimation of the soil P parameters based on local data.

In calcareous soils,P retention is controlled by precipitation/dissolution reactions in addition to the sorption/desorption processes (Devauet al.2010;Shenet al.2011). The current APSIM SoilP module only describes the P availability in soil in terms of P sorption/desorption processes,while precipitation/dissolution processes (which are the dominant processes of P transformation in natural and calcareous soils) are ignored. This simplification may pose a limitation in the simulation of labile P in soils where precipitation/dissolution play a dominant role. It also implies that any attempt to derive the sorption parameters in the model will result in empirical values fitting to the local data. Other studies in Vertisols demonstrated that the interaction between the dynamics of precipitation and dissolution of Ca-P minerals and adsorption and desorption processes remains unclear (Raymondet al.2021). Further work is needed to better understand those processes in order to improve the model performance and its applicability to different soil types.

4.4.Relationship between the labile P and Olsen-P concentrations

The soil labile P pool in the current APSIM SoilP module is a conceptual pool which does not equate with any soil test P measurement,although it does respond to crop P uptake or P additions to soil (Wanget al.2014).Thus,difficulties occur in initializing the soil labile P pool before the simulation. The soil Olsen-P concentration is normally derivedviaa laboratory procedure conducted at a constant temperature and with a standard solution,and it is used to define soil P availability. The significant correlation between the measured Olsen-P and simulated labile P concentrations in the surface 0–10 cm soil layer(Fig.14) suggests that Olsen-P measurements may help to initialize the labile P pool in the APSIM. Wanget al.(2014) and Micheniet al.(2004) also reported that the simulated labile P pool was closely related to the Cowell-P or Olsen-P concentration. Micheniet al.(2004) suggested a factor of 2.5 to convert the measured Olsen-P concentration into the simulated labile P concentration,while Wanget al.(2014) proposed a different curvilinear relationship between the Cowell-P and labile P concentrations. As in Wanget al.(2014),a curvilinear relationship was also found between the Olsen-P and labile P concentrations in this study (Fig.14).Although the simulated labile P is closely related to measured Olsen P or Cowell P,their relationships are different on different soil types. These differences may be caused by soil type-specific properties,such as the P buffering capacity and pH,which significantly affect the subsequent change from added P to labile P or the difference in P extractants. Future research should investigate how to quantify the plant available P in soil and how to better conceptualize it so that the P models can be easily initialized to better simulate changes in soil P availability and crop response.

5.Conclusion

The re-parameterized APSIM model could further improve the simulation performance in maize leaf area index,biomass,grain yield,P uptake,grain P content in response to different levels of P additions against both the calibration and validation datasets. However,the significant limitation for improving the model performance is the lack of quantitative data on the soil P pool transformations,especially the precipitation/dissolution processes in NCP.

Acknowledgements

This work was funded by the National Natural Science Program of China (2022YFD1900300),the China Scholarship Council (CSC) through the CSC-CSIRO(Commonwealth Scientific and Industrial Research Organisation) Joint Ph D Program,the Zhumadian Major Scientific and Technological Innovation Project,China(170109564016) and the Huanghuai University Scientific Research Foundation,China (502310020017).

Declaration of competing interests

The authors declare that they have no conflict of interest.