1 Introduction

Maize (Zea mays L.) is the most extensively cultivated cereal globally, with a production of 1.1 billion metric tons and a harvested area of 197 million hectares (2017–2019) [1]. Global production of maize has increased due to the expansion of cropland and increased yield per unit of land. Maize is primarily used as feed [2] and fuel bioethanol [3]. Nigeria and Ethiopia are the largest producers of maize in Africa, with a combined production of nearly 32 million metric tonnes on 6.8 million ha of land in 2019, which constituted 39% of Africa’s maize production in the year [4].

Poor or declining soil fertility is a constraint to the improvement of maize yield in sub-Saharan Africa (SSA). The degradation of soil fertility is a serious problem in Nigeria. Therefore, soil fertility management is an issue to consider because it is a prerequisite for sustainable production, food security, and livelihoods in the SSA [5]. The application of fertilizer in the production of maize is important to replenish nutrients lost through the harvested product and crop residues that are removed. Management of Nitrogen (N) is a key challenge in agronomy. It is very essential to produce more food with fewer agricultural inputs and minimal environmental impact. The application of fertilizer in the production of maize is important to replenish nutrients lost through the harvested product and crop residues that are removed. The availability of Nitrogen could influence the grain yield of maize [6]. Yields of maize are about 2 t ha−1 in Nigeria and other sub-Saharan African (SSA) countries [4]. This is considered low compared with higher yields in other parts of the world [7]. Low yields of maize in SSA have been attributed to the considerably low input of Nitrogen fertilizers by subsistence and smallholder farmers [8]. Nitrogen fertilizer affects biomass accumulation in maize by influencing leaf area development, Nitrogen, and radiation efficiencies [6, 9].

Crop model has made significant contributions to agriculture [10]. Crop simulation models are used to monitor and capture information in agronomy to explain and predict crop growth and development [11]. They help to explore the soil–water–plant–atmosphere systems and can be used to examine quantitative hypotheses concerning reality. In addition, researchers use them to extrapolate data beyond field experiments, test the effect of soil fertility and water on biomass, yield and water productivity (WP) and assess adaptation to climate change [12]. Crop models have been used to manage water-limited yield potential for specific fields [13, 14], estimate yield potential, and manage soil Nitrogen for maize [15, 16], support decision making for sustainable crop production [17, 18] and to complement field trials [19]. AquaCrop has been calibrated and tested under varied water and Nitrogen management for rice [20], validated for wheat under full and deficit irrigation [21]. AquaCrop has been used to calibrate and validate the grain yield and biomass of winter maize under different irrigation scenarios [22]. Other models include Soil–Water–Heat–Carbon–Nitrogen–Simulator [23, 24]; Decision Support System for Agrotechnology Transfer (DSSAT) for water and nutrient management [25, 26], Agricultural Production Systems Simulator [27, 28] and Crop Environment Resource Synthesis [29]. Most of these crop models a adopt water-nutrient balanced approach in simulating the effect of soil fertility and the development and yields of crops. Although these models are complex and have high reliability, they require advanced computational and analytical skills and parameters for their calibration and testing which cannot be found easily. Most of the input parameters are obtained using sophisticated equipment during field experiments or laboratory trials. These models are mechanistic and highly sophisticated for applications by non-scientists such as policymakers and extension service providers. This limits the use of such advanced models for theoretical, scientific, and analytical research only [30]. Smallholder farmers especially in SSA and other developing countries could not use them for impact analysis and prediction [31]. Hence, the need for a simplified model that balances simplicity and accuracy in order to achieve broad usage of the models by all end-users and the targeted groups. The AquaCrop model was developed by the Food and Agriculture Organization of the United Nations (FAO) to address these challenges. AquaCrop Model originated from the concept of crop yield response to water availability [32]. The AquaCrop model was developed by Steduto et al. [33], Raes et al. [34] and Steduto et al. [35] to address these challenges. The model was parametised and validated for maize by Hsaio et al. [36] and Heng et al. [37].

The AquaCrop model has been applied successfully in many areas and for cereal crops such as maize to determine the impacts of varying irrigation and Nitrogen regimes [38]; evapotranspiration and yield under rainfed and irrigated conditions [39,40,41]; assess impacts of diverse soil conditioners [42]; calibrate and validate under deficit irrigated conditions [43]; evaluate cultivation and irrigation methods [44]; validate different sowing dates [45]; access soil water balance and response to Nitrogen stress [46, 47]; predict yields under future water availability scenarios [48]; access impact of climate change on yield and evapotranspiration [49,50,51,52,53]; propose estimation methods for crop WP [54]. Despite the importance of maize and Nitrogen fertilizer in the cropping systems in Nigeria, an in-depth study of the assessment of AquaCrop in modelling evapotranspiration (ETa), yields, and real-time data under a rainfed system in the agrarian areas of the sub-humid areas has not been done. Scanty studies reported were done in the Arid and semi-arid areas of Nigeria [41]. Hybrid maize has not been simulated using the AquaCrop model in the study area. There will be high demand for maize in West and Central Africa and research to improve the yields has been a priority in the agricultural agenda in the sub-region [55]. Therefore, predicting maize productivity in response to NPK fertilizer under seasonal variations in rainfall using handy model which are easily accessible to smallholder farmers will improve its management prospects [35]. Therefore, the objective of the study was to assess AquaCrop in simulating canopy cover (CC), soil water storages (SWS), evapotranspiration (ETa), yield, and WP of rainfed maize and to recommend management options for sustainable land and WP of the crop in the sub-humid areas of Nigeria. We hereby hypothesise that the AquaCrop model can be used in selecting the best soil fertility management options in order to improve the growth and yields of maize in the sub-humid agroecology of Nigeria.

2 Materials and methods

2.1 Study area

The studies were carried out at the Teaching and Research Farms of Obafemi Awolowo University, Ile-Ife, Nigeria, latitude 7′330 00ʹ N and longitude 4′340 00ʹ E, 271 m + MSL (mean sea level) in the sub-humid areas of Southwest Nigeria during the rainy seasons of the years 2021 and 2022.

2.1.1 Weather conditions

Daily minimum and maximum air temperatures, relative humidity, wind speed, and solar radiation measured at 2 m above the soil surface were obtained from an automated weather station located at about 300 m from the experimental field. The quality of the weather data considering the environment and seasonal variations were analysed using the standard method [56]. Daily rainfall was measured throughout the growing seasons by using a standard rain gauge and the seasonal rainfall in 2021 and 2022 were 621 mm and 673 mm, respectively. Penman–Monteith model was used to determine reference evapotranspiration (ETo) under standard environmental conditions [57]. The minimum seasonal air temperatures in 2021 and 2022 were 20.4 and 19.9 °C while the maximum temperatures were 30.5 and 30 °C respectively (Figs. 1 and 2).

Fig. 1
figure 1

Climatic variables consisting of air temperatures, rainfall and solar radiation, wind speed, and reference evapotranspiration of the field during the year 2021 growing season

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Fig. 2
figure 2

Climatic parameters consisting of a air temperatures, b rainfall and solar radiation, c wind speed, and d reference evapotranspiration of the field during the year 2022 growing season

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2.2 Experimental design and treatment

2.2.1 Experimental treatments

Two varieties of maize, SUWAN 1-SR (V1) and PVA (V2) obtained from the International Institute for Tropical Agriculture, Ibadan, Nigeria were used for the study. Five levels of soil fertility: 0, 25, 50, 75, 100, and 150% of the recommended NPK fertilizer [58] were used and the combination produced a 2 by 6 factorial set of experimental treatments. NPK fertilizer was applied at the vegetative stage, three weeks after planting. Phosphorus and potassium were applied at a rate of 60 kg ha−1 to all the plots. SUWAN 1-SR has a yellow kernel and was released in 1996. It is very resistant to streak and downy mildew [59]. Provitamin A (PVA) biofortified maize was developed to alleviate vitamin A deficiency and has a low aflatoxin contamination. The twelve treatments were laid out in a randomized complete block design and replicated four times after ploughing and harrowing. The intra-row and inter-row spacing were 0.5 m and 0.75 m respectively and each plot measured 18 m by 20 m (360 m2).

2.3 Data collection

2.3.1 Soil data

Soil samples were collected to a depth of 1 m on the experimental field using a 0.053 m core sampler. Guelph permeameter was used in situ to measure saturated hydraulic conductivity [60]. Standard laboratory procedures were used in measuring and estimating the soil’s physical and chemical properties [61]. Investigation reveals that the soil in the study area is sandy clay loam (Vertisol) using the USDA classification. The lower soil profile, 0.40–0.80 m contains sandy clay loam while the upper 0.40 m contains sandy loam [62]). The upper soil profile has higher organic matter than the lower profile (Table 1). The field has a lower BD in the upper than the lower layer which could be attributed to seasonal tillage operations. The study area is in the sub-humid agro-ecology of the Southwest Nigeria. The predominant crops in the area are maize, cassava, cocoa, kolanut and oil palm.

Table 1 Soil properties in the experimental site indicate the textural classifications and nutrient compositions
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Three seeds were planted per hole at 4 cm soil depth on the 12th of June, 163 Days of the year (DOY) in 2021 (first season) and 23rd of May, 143 DOY in 2022 (second season), thinned to two seedlings after full establishment and produced a plant population of 53,333 plants/ha. The treatments were applied 21 days after planting. Insects were controlled using Caterpillar force™ (Emamectin benzoate 5% WDG) at 2 l ha−1 twice during each season. Weeds were controlled manually using local hoes. Crops within 20 m2 were harvested on the 18th of September, 2021, (DOY 261) and 29th of August, 2022, (DOY 243), 98 DAP, and the yields per ha were estimated.

2.3.2 Soil water storage

TEROS 12 (Meter Groups, USA) were installed to 0.60 m soil depth at intervals of 0.10 m and the water contents (m3 m−3) in the soil profiles were measured at intervals of one week until maturity. The soil water storage (SWS) was determined using the Eq. (1) [63]:

$$\int_{i}^{z} {\theta dz} = \sum\nolimits_{{i = 1}}^{m} {\theta \times di}$$
(1)

where z is the maximum soil profile depth (mm); θ is the soil water content at the soil depth z, m3 m−3; θi is the soil water content of layer i, (m3 m−3); di is the thickness of the layer i (mm); and m is the number of calculation layers.

2.3.3 Biomass

The aboveground biomass was measured from 7 DAP and subsequently at intervals of 1 week until physiological maturity. Plants within 0.94 m2 were harvested and oven dried at 70 °C (Memmert, Sweden) for 48 h. Fourteen consecutive measurements of the dry above-ground biomass (DAB) were made in each season. The DAB (t ha−1) was estimated by multiplying the oven-dried mass by the plant population.

2.3.4 Canopy cover

The photosynthetically active radiation and the leaf area index (LAI) (m2 m−2) near solar noon were measured at average intervals of seven days using AccuPAR LP 80 (Meter Group, USA). Fourteen measurements of the LAI were taken in the canopy each season. The average seasonal extinction coefficient was determined using the approach by [64]. Canopy cover (CC) was determined by using Eq. (2):

$$CC = \left[ {100\left( {1 - e^{{\left( { - {{\varvec{\uplambda}}}LAI} \right)}} } \right)} \right]$$
(2)

where LAI is the leaf area index (m2 m−2), λ is the extinction coefficient (0.47).

2.3.5 Soil water balance and evapotranspiration

Surface runoff was determined using a micro runoff plot within 1.0 m2. Water percolation beyond 100 cm was assumed negligible. Deep percolation beyond the root zone (60 cm) was computed using the soil water contents measured at regular intervals. The groundwater table is at about 25 m and couldn’t contribute to the root zone therefore capillary contribution was ignored. Changes in SWS were determined from the difference between water storages on the sampling dates. Therefore, the evapotranspiration was determined using Eq. (3) [62]:

$$ET_{a} = P - RO - DP \pm \left( {\Delta S_{2} - \Delta S_{1} } \right)$$
(3)

ETa is the actual evapotranspiration (mm), P is the rainfall (mm), DP is the percolation (mm), RO is the surface runoff (mm), ΔS2 − \(\Delta\)S1 is the change in SWS (mm).

2.3.6 AquaCrop model

The AquaCrop model is a dynamic crop growth model that simulates potential herbaceous crop yields using the water transpired [35]. The AquaCrop Model is a water-driven model because transpiration is converted into biomass using conservative crop parameters, the biomass WP that is normalized for atmospheric evaporative demand and concentration of CO2 in the air. Normalization of WP makes the AquaCrop model suitable for diverse agroecological conditions.

and cropping seasons. The AquaCrop model simulates transpiration and separates evaporation from productive transpiration using CC, which can be estimated using remote sensing, LAI, or visually. The AquaCrop model estimates potential yields from the product of final DAB and HI [33]. In the AquaCrop model, the relative dry above-ground biomass (Brel) is related to the dry above-ground biomass from fertility stress-free conditions (Bref) and DAB from well fertilized, stressed conditions (Bstress) by using Eq. (4) [35]:

$$B_{rel} = \frac{{B_{stress} }}{{B_{ref} }}$$
(4)

where Brel is the maximum relative dry above-ground biomass (%), Bstress is the total DAB at maturity in a soil fertility-stressed field and Bref is the total DAB at maturity in a non-fertility stressed field. In order to simulate the daily growth and development of crops, AquaCrop models requires local weather data such as rainfall, air temperature, and reference evapotranspiration (ETo). The model simulates the responses of crops to water by using four coefficients: canopy expansion, stomata control of transpiration, canopy senescence, and HI. Under field conditions, pests and diseases can limit crop yields [65]. However, the AquaCrop model does not simulate the effects of pests and diseases. AquaCrop model is less satisfactory in simulating severe water stress treatments during senescence [37]. The AquaCrop model applies conservative [36] and non-conservative parameters during the simulation of outputs (Table 2). Conservative parameters do not change due to time, management, location, cultivars but could be adjusted to improve the simulations [35, 66]. Generally, the non-conservative parameters are adjusted during simulation.

Table 2 The conservative parameters from Hsiao et al., 33 of the crop data files of AquaCrop used for the simulation of maize
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2.3.7 Calibration and validation of AquaCrop model

AquaCrop model ver. 7.1 was used for the simulation in this study. The minimum and maximum air temperatures, rainfall, relative humidity, wind speed, solar radiation and ETo were used to generate the climate file. The soil file was generated using the soil data. The non-conservative parameters were estimated by using the field data obtained during the 2021 and 2022 agronomic seasons. Due to the sensitivity of the model to water, the data for the year 2022 were used for the calibration of the model. The plant population, sowing date, time to attain maximum CC, time to the commencement of senescence and its duration, and date of physiological maturity were used. The AquaCrop model was run in growing degree days (GDD) to accommodate the effects of temperatures on the simulations. Grain yields were simulated by entering the date and duration of flowering, reference HIo and duration of building up of HI for each treatment. In this study, N00, N25 and N50 represent 100, 75 and 50% soil fertility stresses, respectively, while N75 and N100 indicated 25 and 0% soil fertility stresses, respectively. The impacts of soil fertility on seed and biomass yields were simulated in the crop subcomponent of the AquaCrop model by selecting the degree of the effects of soil fertility. The N00, N25 and N50 represented very poor, poor and about half while N75, N100 and N150 represented moderate and non-limiting soil Nitrogen fertilities respectively. In addition, the impacts of the soil fertility on the crop were calibrated by using field data for the year 2022. The biomass yields for N00 for full fertility stress without water stress are divided by a reference biomass (Bref.) where there was no soil fertility and water stresses and for calibrating crop responses to soil fertility stresses were later applying the model to predict yields for other treatments (Fig. 3). Soil water storage was simulated by using the daily rainfall and the physical characteristics of the soil profiles in [62]. The crop coefficient for transpiration (KcTr,x) and the readily evaporable water were adjusted to ensure good correlations. Other non-conservative parameters were adjusted based on observations and measurements on the field (Table 3).

Fig. 3
figure 3

Responses of the maize (Brel) to soil fertility stress. The point of calibration for full soil fertility stress (in red colour) was used to obtain the orientation of the curve

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Table 3 Non-conservative parameters used in calibrating and validating AquaCrop model for rainfed maize in sub-humid area of Nigeria
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2.3.8 Performances of the AquaCrop model

Arrays of parameters are recommended for the evaluation of crop models [67, 68]. In this study, we used statistical indices and graphs to assess the performance of the model in simulating the CC, SWS in the root zone, seed yield, DAB, ET, and WP. Regression lines relating the observed and simulated data were forced through the origin and the regression coefficient (b) was determined [69]. Values of b close to 1.0 indicates that there is a close relationship between the measured and the simulated data [70, 71]. Other statistics used for evaluation are the coefficient of determination (R2), percentage deviation (Pd), Root Mean Square Error (RMSE), Normalised Root Mean Square Error (NRMSE) [72]; Nash–Sutcliffe efficiency coefficient (EF), Willmott’s index of agreement (d-index) [73] in Eqns. (5–9).

$$R^{2} = \left( {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - \overline{O}} \right)\left( {P_{i} - \overline{P}} \right)}}{{\sqrt {\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - \overline{O}} \right)^{2} } \sqrt {\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - \overline{P}} \right)^{2} } }}} \right)^{2}$$
(5)
$$RMSE = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{n}}$$
(6)
$$NRMSE = \frac{1}{{\overline{O}}}\sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{n}} \times 100$$
(7)
$$EF = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - \overline{O}} \right)^{2} }}$$
(8)
$$d - index = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {P_{i} - O_{i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {\left| {\left. {P_{i} - \overline{O}} \right| + \left| {\left. {O_{i} - \overline{O}} \right|} \right.} \right.} \right)^{2} }}$$
(9)

where Oi is the measured data, \(\overline{O}\) is the mean of measured data, Pi is the simulated data, \(\overline{P}\) is the average of simulated data, N is the number of measurements taken.

3 Results

3.1 Canopy cover

3.1.1 Calibration

The correlation between the measured and simulated CC was excellent, R2 = 0.98 for the calibrated. The model accounted for up to 98% of the variations in the CC throughout the season (Fig. 4). The errors were low (2.8% ≤ RMSE ≤ 10.4%) for the calibrated data set. The measured and simulated data set fit excellently into the line 1:1 with (0.86 ≤ EF ≤ 0.99) for the calibrated data.

Fig. 4
figure 4

Trends of observed and simulated canopy cover for PVA maize with varying soil fertility management (NPK fertilizer) in the year 2022

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3.1.2 Validation

The correlations (0.88 ≤ R2 ≤ 0.98) for the validated data set (Table 4) and with high errors (4.9% ≤ RMSE ≤ 14.4%) for the validated data sets and were considered good for the simulation. The EF ranged from 0.85 to 0.97 for the validated data sets.

Table 4 Parametric evaluation criteria for the simulations of the canopy cover for maize under different levels of soil fertility management using AquaCrop in the Sub-humid Nigeria
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3.2 Soil water storage

The measured and simulated SWSs were well correlated, 0.71 ≤ R2 ≤ 0.96 for the calibrated and R2 ≥ 0.83 for the validated data (Table 5). Most of the variances in the SWS were well captured by the model (Fig. 5). The RMSE ≤ 10.7 mm, and is below 5.4% of the average measured SWS for the calibrated data and less than 7.4% calibration data set for the AquaCrop model indicating its suitability for crop modelling[74]. The NRMSE ≤ 20% for the calibrated and the validated data set is judged good for agricultural crop simulations [75]. The EF ≥ 0.97 for the calibration and 0.95 for the validation show that the measured and the observed are close.

Table 5 Assessment of the measured and simulated soil water storages for maize under varying soil soil fertility management (NPK fertilizer) in Ile-Ife, Nigeria
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Fig. 5
figure 5

Temporal variation of the observed and simulated soil water storage for PVA maize in the year 2022 cropping season. SAT (Saturation), FC (Field capacity), and PWP (Permanent wilting point)

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3.3 Evapotranspiration

The measured seasonal ETa ranged from 468 mm in 2022 to 555 mm in 2021 (Table 6). PBIAS was 8% and indicating that the AquaCrop model tends to underestimate ETa under soil Nitrogen stress in sub-humid areas (Fig. 6). There were very low overestimations of ETa (b = 1.02) in the calibrated and validated data sets.

Table 6 Variabilities of the measured and predicted ET, maize yield, and water productivity of rainfed maize in the years 2021 and 2022 with varying soil fertility management (NPK fertilizer) by using the AquaCrop model in the sub-humid area of Nigeria
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Fig. 6
figure 6

Simulated and measured evapotranspiration for varied soil Nitrogen stresses in the cropping seasons in Ile-Ife, Southwest Nigeria

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3.4 Biomass

There were good correlations, 0.90 ≤ R2 ≤ 1.00 between the measured and simulated aboveground biomass (Table 7 and Fig. 7). The AquaCrop model tends to overestimate aboveground biomass at harvest soil Nitrogen stress, 0.96 ≤ b ≤ 1.12 (Fig. 8), which is still within the acceptable limit [73]. This is similar to the findings of [62]. The RMSE ranged from 0.29 t ha−1 to 0.73 t ha−1 with EF ≥ 0.97, d-index ≥ 0.98 for the calibrated data, and EF ≥ 0.92, d-index ≥ 0.95 for the validated data set.

Table 7 Statistical criteria for assessing modelled aboveground biomass for SUWAN-1 SR and PVA
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Fig. 7
figure 7

Progressions of the cumulative aboveground biomass under varying Nitrogen stresses for maize in the year 2022 in Ile-Ife, Nigeria

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Fig. 8
figure 8

Aboveground biomass at harvest for the SUWAN 1 SR and PVA under varying soil Nitrogen stresses and temporal variability in daily rainfall in Ile-Ife, Nigeria in the year 2022

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3.5 Crop yield

There were variabilities of the maize yields in response to the soil fertility management (NPK fertilizer) (Table 6). This compared well with the significant impacts of Nitrogen on yields of maize [76, 77]. There was a strong correlation between the measured and the simulated grain yields for the calibrated and validated data sets (Fig. 9). For the calibrated data set, the RMSE = 0.06 t ha−1 which is less than 1% of the average of the measured grain yields, NRMSE = 1%, EF and d-index = 1.00 while for the validated data, the corresponding RMSE was 0.1 t ha−1 (less than 2% of the averaged measured yields), 2% and 1.00 respectively. The deviations in the calibration, − 1.10 ≤ Pd ≤ 3.41 is lower than the range in the validation (− 1.67 ≤ Pb ≤ 5.40) data sets (Table 4) and far below the 15% threshold for crop yield simulations [66, 78]. The b = 1.00 shows that the grain yields in the seasons fit excellently into the 1:1 line and that the underestimations in the calibrated data set were very low (Fig. 9).

Fig. 9
figure 9

Simulated and measured maize yields using AquaCrop and with varying NPK fertilizer during the growing seasons in the study area

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3.6 Water productivity

There were variabilities in the WP of maize in the seasons. It ranged from 0.53–0.76 kg m−3 in the year 2021 to 0.53–0.80 kg m−3 in the year 2022 (Table 6). AquaCrop model accounted for 98% of the variances in the measured WP of the crop in the seasons (Fig. 10). Deviations of the simulated WP were lower for the calibrated (− 3.54 ≤ Pb ≤ 2.75) data set than for the validated (− 3.33 ≤ Pb ≤ 4.52) data sets. The RMSE, 0.02 kg m−3 was low and constituted 1.82% of the mean of the measured WP. The NRMSE = 2% is considered excellent, while EF and d-index ≥ 0.97. Low NRMSE, positive and high EF means that the AquaCrop model can explain well the pattern of the WP in the maize and that the parametrization adopted in the calibration was adequate. There was an overestimation bias of WP in the AquaCrop model under NPK stress. Despite this tendency, the predicted WP is still within the reference of the measured data sets.

Fig. 10
figure 10

Simulated and the measured water productivity of maize using AquaCrop with varying nitrogen stresses in the years 2021 and 2022 in the study area

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4 Discussions

The (d-index ≥ 0.97) is excellent and acceptable for crop simulation and modelling. There were instances of very low over and under-estimations in the data sets which could be traced to the reactions of the AquaCrop model to the simulation of canopy expansion for the hybrid maize. The CC was high because there was no water stress in the seasons which could trigger early senescence (Fig. 4). RMSE of less than 15.2% [42] and 9.55% [45] were reported for CC in hybrid maize. Our simulation of the CC compared better than RMSE of 16–24% and R2 ≥ 0.67 reported for maize [46] and NRMSE = 23.5%, R2 = 0.91 [79]. The overall assessment shows that the AquaCrop model simulated CC for maize under Nitrogen stresses adequately. AquaCrop responded well to the simulation of the SWS despite temporal variabilities in the rainfall and soil fertility stress [80]. The d-index ≥ 0.97 shows that the AquaCrop model is acceptable for calibration and validation of SWS under Nitrogen stress for maize [81]. The 0.96 ≤ b ≤ 1.12 means that the model did not underestimate or overestimate beyond the acceptable limits for crop modelling. The AquaCrop model simulated SWS often above and below the field capacity in response to the rainfall events (Fig. 5). This means that the model being water driven responded well to the rainfall contributions in the root zone. The simulation compares well with R2 ≥ 0.85, RMSE ≤ 2.59%, and NRMSE ≤ 12.95% [82] and better than R2 of 0.62, and RMSE = 27.4 mm for SWS [83]. The model simulated SWS around the field capacity but not to saturation and wilting point. This is commendable because there were no traces of water logging and water stress in the seasons and the soil is well drained. AquaCrop captured above 98% (R2 ≥ 0.98, slope = 1.08, intercept = -28.55) of the variances in the simulated ETa for the two seasons (Fig. 5). The RMSE = 10.26 mm is considered good [84], NRMSE = 2.1% is excellent [85], EF = 0.88, d-index = 0.97 is acceptable for calibration in environmental agronomy [81]. The simulated final biomass compared well with NRMSE ≤ 15% reported in Van Gaelen et al. [79] under Nitrogen stress. Statistical evaluations indicate that the simulated biomass in the seasons is still within the acceptable limits for crop modelling [73]. This is similar to the findings of Adeboye et al. [62]. Excellent simulations of biomass by the AquaCrop model were also reported with RMSE ranging from 0.10 and 0.59 t ha−1 and d-index from 0.96–0.99 for maize [86] and NRMSE of 9.3% [79].

The simulated grain yields compare well with the findings of Akumaga et al. [41] in Northern Nigeria, NRMSE between 7–19% [79] and R2 ≤ 0.79, d ≥ 0.78 using DSSAT-CERES-Maize and APSIM-Maize [87]. Similarly, the AquaCrop model in this study performs better than DSSAT in modelling maize with NRMSE below 21.6% [88]. The modelling of the maize yields under NPK stresses by AquaCrop is rated well.

The grain yields were reduced by 40% for SUWANI-SR and 39% for the PVA in the seasons due to varied NPK. The WP of the varieties responded well to the changes in the NPK. For instance, the WP of SUWANI-1 SR was reduced between 1 and 30% due to NPK while for PVA, the WP reduced by between 4 to 33% compared with the highest application of NPK. These findings testify that improvement of soil fertility especially NPK could bridge the gaps between the potential and actual yields of maize under rainfed conditions [89]. Under the current trends of changes in climate and fluctuations in seasonal rainfall, effective use of N fertilizer for the cultivation of maize will improve its WP. Maize is a key crop in Nigeria because of its diverse importance. Application of modelling tools to improve predictions in the management of soil NPK and water is very essential. Smallholder farmers in the sub-humid region of Nigeria could adopt our parameters and use AquaCrop model in planning, predicting, and improving the land and WP of maize. This is commendable because there were no traces of water stress in the season and the soil is well drained.

5 Conclusion

Field experiments were conducted in order to assess the impacts of Nitrogen stresses on land and water productivity of rainfed maize for two agronomic seasons and to use AquaCrop ver. 7.0 model to simulate canopy cover, soil water storage, aboveground biomass, evapotranspiration, and water productivity. The 150% of the recommended soil fertility management (NPK fertilizer) is suitable for the desired improvement in land and water productivity of the crop. The AquaCrop model captured the trends in canopy cover well. The model simulated soil water adequately and accurately simulated the progression of cumulative biomass with time, with a high index of agreement. The simulated and measured biomass at harvest were well captured and the evapotranspiration and grain yields were well simulated with very low error for grain yields. In view of these findings, the AquaCrop model can be utilized as a tool in simulating the impacts of soil fertility and available rainfall on land and water productivity of maize in Ile-Ife, Nigeria, and other sub-humid agro-ecological areas in the tropics.