
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12115-9
10.1016/j.heliyon.2024.e36084
e36084
Research Article
Modeling the response of sesame (Sesamum indicum L.) to different soil fertility levels under rain-fed conditions in the semi-arid areas of western Tigray, Ethiopia
Berhane Abadi aabay2003@gmail.com
a⁎
Abrha Berhanu berhanuabrha@gmail.com
b
Worku Walelign walelignworku@yahoo.co.uk
c
Hadgu Gebre g.hadgu27@gmail.com
d
a Department of Plant Sciences, Aksum University, Tigray, Ethiopia
b Department of Dryland Crop and Horticulture Science, Mekelle University, Ethiopia
c School of Plant and Horticultural Sciences, Hawassa University, Ethiopia
d Tigray Agricultural Research Institute, Ethiopia
⁎ Corresponding author. aabay2003@gmail.com
10 8 2024
15 9 2024
10 8 2024
10 17 e360847 10 2023
3 8 2024
9 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Sesame, a crucial oilseed crop in Ethiopia, ranks second only to coffee in its importance as an exported agricultural commodity. However, inadequate soil fertility management has hampered its productivity despite its substantial international market demand. Hence, this study was conducted to model the response of sesame to different nitrogen fertilizer levels using the AquaCrop model, and to assess the capability of the model as a decision-support tool for optimizing soil fertility management strategies in the study area. The experiment was laid out in a randomized complete block design, consisting of four nitrogen fertilizer rates (0, 23, 46, and 69 kg/ha nitrogen) and three distinct sesame varieties (Setit-1, Setit-2, and Humera-1). Over the course of the three cropping seasons, data on soil physical and chemical properties, crop growth, yield and yield components were collected for each treatment. Evaluation of model performance relied upon established metrics of coefficient of determination (R2), root mean square error (RMSE), normalized root mean square error (N-RMSE), model efficiency (E), and degree of agreement (D). Analysis of results revealed the AquaCrop model appropriately calibrated for simulation of soil water content, showing R2 values ranging from 0.92 to 0.98, RMSE values varying from 6.5 to 13.9 mm, E values from 0.78 to 0.94, and D values from 0.95 to 0.99. Similarly, simulation outputs for aboveground biomass (AB) demonstrated good accuracy of the model, with R2 values varying from 0.92 to 0.98, RMSE values ranging from 0.33 to 0.54 tons/ha, and D values from 0.9 to 0.98. Notable accuracy was also observed in the simulation of canopy cover (CC), revealing R2 values between 0.95 and 0.99, and RMSE values ranging from 5.3 to 8.6 %. In conclusion, this study substantiates the successful calibration and validation of the AquaCrop model for predicting sesame response to diverse nitrogen fertilizer levels. The performance of the model in predicting soil water content, CC, AB, and yield highlights its potential as a valuable tool for optimizing soil fertility management and enhancing sesame cultivation practices in Ethiopia.

Keywords

AquaCrop model
Calibration
Canopy cover
Nitrogen fertilizer
Validation
Abbreviations

DAE days after emergence

CC canopy cover

CCx maximum canopy cover

Kc crop coefficient

ETo reference evapotranspiration

RCPs Representative Concentration Pathways

WP* water productivity normalized for evapotranspiration and atmospheric CO2
==== Body
pmc1 Introduction

1.1 Background

Sesame (Sesamum indicum L.) is one of the oldest and historically significant oilseed crops, valued for its high quality seed oil [1]. Sesame has been produced globally for many years as a versatile oilseed crop [2]. In addition, sesame is utilized in a variety of products, including cake, flour, paste, and confectionery. This widespread usage of sesame is attributed to its highly stable oil content, nutritious proteins, and distinctive savory, nutty flavor profile when roasted [3]. It has been cultivated for over 5000 years for its oil-rich seeds, which have culinary, medicinal, and industrial applications [4].

Sesame is predominantly grown in tropical and subtropical regions [5] 400 north and south of the equator, mainly in areas having well-drained soils, fertile soils of medium texture (typically sandy loam) at neutral pH [1], and moderate rainfall [6]. Its cultivation is characterized by its adaptability to various environmental conditions, making it suitable for both small-scale and large-scale farming operations [[7], [8]]. Over the last decades, the global cultivation and production volume of sesame have increased [[1], [9]]. In 2022, the average global yield of sesame was 6.7 million metric tons, grown on an area of 12.7 million hectares [10]. The major sesame-producing countries, accounting for more than 76 % of global production, are Sudan, India, Myanmar, Tanzania, Nigeria, China, Burkina Faso, Chad, Central Africa, and Ethiopia [10]. Furthermore, Sudan, India, and Ethiopia were the top sesame exporters, while China, Japan, and Turkey were the major sesame importers in 2022 [10].

In Africa, sesame cultivation is widespread and significant. In 2020, the area allocated to sesame cultivation was more than 8.2 million hectares, which generated 4.0 million metric tons of sesame [10]. This production accounts for approximately 59 % of the world's total sesame production and 64 % of the world's sesame cultivated area. The major sesame-producing countries in Africa are Sudan, Tanzania, Nigeria, Burkina Faso, Chad, Central Africa, and Ethiopia [10]. These African nations are crucial players in the global sesame market. For instance, in 2022, Africa exported more than 63 % of the world sesame market, earned about 16 billion USD [10]. This demonstrates Africa's significant contribution to the worldwide production and export of this valuable oilseed crop. However, the yield of sesame is very low in Ethiopia with a national average of 0.7 tons/ha [11], which is very low compared to the potential grain yield of 3.6 tons/ha recorded in China [12]. Hence, this low crop productivity could be due to several reasons; such as soil water and soil fertility stress, shattering of the seed during harvest, and losses from pests and diseases. It has also been stated that climate change and inappropriate fertilizer management also affect the growth, and yield of sesame [13].

Sesame is among the most important oil crops grown in Ethiopia [8]. In fact, the country is among the top sesame producers globally. In terms of foreign exchange earnings, sesame ranks second only to coffee [14]. Sesame is a cash crop that supports the livelihoods of thousands of small-scale farmers, a medium to large-scale private farms along with thousands of other actors involved in the value chain [15]. Sesame production in Ethiopia has experienced rapid growth in recent years, mainly due to the growing awareness of sesame's nutritional and health advantages; the consumption of sesame seeds and oil has been steadily rising; the crop is ideally suited to various types of soil and weather conditions; and high remuneration [8]. In addition, sesame is a strategic priority commodity to generate foreign exchange earnings and improve the food security and livelihood of growers in Ethiopia. It predominantly grows in the northern and northwestern parts of the country, with a vast potential to expand to various areas. In this regard, the area allotted to the production of sesame has increased by 4.9 % and 10.6 %, respectively, between 2010 and 2015 [10].

Tigray is one of the major sesame producing regions in Ethiopia, comprising 31 % of the total area allotted to sesame [16]. Sesame is an important agricultural activity in the region, contributing significantly to the region's economy and the livelihoods of farmers. However, the production of sesame is very low compared to the national average, which might be caused by various factors like soil fertility, water availability, pest and disease management, and agronomic practices [14]. It has also been stated that climate change and inappropriate fertilizer management also affect the growth, and yield of sesame [13]. Recent studies conducted in the Humera area found that sesame responded positively to nitrogen application rates ranging from 52.5 to 110 kg N/ha, with an optimal rate of 64 kg N/ha [17]. On the other hand, experiences revealed that agronomic practices, including nitrogen application, are site and variety specific. Therefore, models that have been trained based on observations can be used as decision-making supports to optimize field management practices.

Agricultural systems modeling can be traced back to 1957 [18]. Robust predictions of crop yield responses to varying climate and management practices can be obtained using process-based crop models [19]. Recent studies indicate that several crop models have been used for many years to provide, and support decision-making on crop management, climate change impacts, socio-economics, and land use management [18]. Such models organize information from experiments into crop physiological processes [20] by integrating mathematical equations. Recently, crop simulation models like the Decision Support System for Agrotechnology Transfer (DSSAT) [21], Agricultural Production Simulator Model (APSIM) [[22], [23]], AquaCrop [24]; [[25], [26]], Cropsyst; cropping system model [27], and WOFOST [28] models have been applied to simulate the growth and yield of crops under different management and environmental conditions. These models provide insight into understanding crop physiological processes under different environments and management practices.

The Food and Agricultural Organization of the United States (FAO) has developed a water-driven model, the “AquaCrop model,” with a semi-quantitative performance to quantify soil fertility stress using stress coefficient variables on different crop parameters [25]; [[26], [29]]. The model was evolved from the concept of yield response factor to water [30] and later designed based on the concept of normalized water productivity for evaporative demand and atmospheric carbon dioxide concentration (CO2) [26]. In addition to its performance to simulate soil water content, green canopy cover, aboveground biomass, and yield, the AquaCrop model is capable of simulating the effect of soil fertility on the growth and yield of crops, green canopy cover, and water productivity using a semi-quantitative approach using soil fertility stress coefficients [29]. It is capable of predicting crop growth and yield, crop water requirements, and water use efficiency under water-limiting conditions [24].

The AquaCrop model adjusts soil fertility effects with a set of soil fertility stress coefficients in four important ways: the canopy growth coefficient (CGC), maximum canopy cover (CCx), canopy decline (CDC), and water productivity (WP*) [[29], [31]]. The soil fertility stress indicator varies from 0 %, at which soil fertility is non-limiting, to 100 % when soil fertility stress is so high that crop production is no longer possible, with soil fertility coefficients (Ks) ranging from 1 (no soil fertility stress) to 0 (full soil fertility stress) [32].

The Aquacrop model maintains the balance between simplicity, robustness, and accuracy [25] and requires a relatively small number of explicit crop parameters [24]. The model can be used by irrigation and water experts, extension workers, government and/or non-government (NGO), and researchers for irrigation planning and farm management strategies. It has been used to predict the growth and productivity of many herbaceous crops under different water, soil, and management conditions [26]; [[32], [33]].

The AquaCrop model has been evaluated for its capability, accuracy, and robustness to simulate the growth and yield of major cereal crops, including maize [33]; [[34], [35]], tef [[36], [37]], barley [[38], [39]], wheat [[40], [41]], cowpea [42], potato [[43], [44]], and common bean [45].

In this view, crop models can be used as decision-support tools in optimizing field management practices [41] in order to improve crop growth and productivity. The primary objectives of this study are to model the response of sesame to different nitrogen fertilizer levels by calibrating and validating the AquaCrop model. Additionally, the study aims to assess the effectiveness of the AquaCrop model as a decision-support tool for optimizing sesame cultivation practices in the study area. This entails establishing a well-calibrated and validated crop model that can reliably simulate sesame growth dynamics and yield responses to different management practices and environmental factors. Ultimately, the research seeks to provide valuable insights for farmers, investors and stakeholders to enhance productivity and sustainability in sesame production.

2 Materials and methods

2.1 Description of the study area

Humera is located in the western zone of Tigray in northern Ethiopia, which is bordered by Sudan in the western, Eritrea in the western, and the Amhara region in the southwest. This experiment was conducted at the Humera Agricultural Research Center, which is located at 14015′ North latitude and 36037’ East longitude, with an altitude of 580 m above sea level. The study site is classified as having a hot to warm semi-arid climate, with temperatures rising up to 42 °C from April to June, and declining 25–35 °C from late June to February [46]. The average maximum and minimum temperature of the area is 37 and 20 °C respectively. The annual average precipitation ranges from 300 to 860 mm. The monthly climatic conditions of the study area are presented in Fig. 1. The experimental site is predominantly composed of black clay soils with a pH ranging from 8.6 to 8.7.Fig. 1 Monthly average rainfall, maximum and minimum temperature of the study area from 2016 to 2018 (Data was obtained from National Meteorological Agency [47]).

Fig. 1

Fig. 2 Digital photograph captured for canopy cover analysis.

Fig. 2

2.2 Experimental setup

This study was carried out during the 2016, 2017, and 2018 main cropping seasons. In 2016, a one-way Randomized Complete Block Design (RCBD) was implemented, with four nitrogen levels (0, 23, 37.5, and 46 kg nitrogen/ha) in combination with a popular variety of sesame known as Setit-1. In the subsequent years, 2017 and 2018, a randomized complete block design (RCBD) design was applied in a two-factorial arrangement, comprising of four nitrogen fertilizer rates (0, 23, 46, and 69 kg/ha) and three sesame varieties (Setit-1, Setit-2, and Humera-1). Each treatment combination was replicated three times to reduce statistical bias. The plot size was 3 m by 4 m, with a row spacing of 0.4 m, and a 0.1 m between plants.

2.2.1 Crop management

Urea (46-0-0) served as the source of nitrogen fertilizer, was applied in two split applications. Initially, half of the designated dosage was applied during the sowing time, and the remaining second half was applied thirty days after emergence. Keeping all recommended agronomic practices to ensure appropriate plantation niche of the crop, we applied carefully including weeding, pesticide application, and hoeing throughout all field experiments. Furthermore, thinning out was systematically implemented to regulate plant density, adjusting spacing to 0.1 m between plants and 0.4 m between rows when the plants develop two to three true leaves at seedling stage to achieve a targeted plant population of 250,000 plants/ha.

2.2.2 Data collection and analysis

1 Climate data: observed climate data of the study area for the 2016, 2017 and 2018 were obtained from the Ethiopian Meteorological Agency, and Humera Agricultural Research Center. Maximum and minimum temperature, rainfall, relative humidity, sunshine hour, and wind speed were collected. Reference evapotranspiration (ETO) was computed using FAO Penn Man-Minteith equation [48]. Finally, climate dataset was prepared based on the AquaCrop model climate data input requirement for the 2016, 2017, and 2018 cropping seasons.

2 Data on physico-chemical properties of the soil and soil water content (SWC):

Data pertaining to soil physical and chemical properties were collected for analysis. Specifically, soil water content (% volume) measurements were conducted to determine field capacity (FC) and permanent wilting point (PWP) across three soil depths: 0–0.20, 0.21–0.40, and 0.41–0.60 m. Electrical conductivity, available phosphorus, percent organic carbon, percent nitrogen content and cation exchange capacity of the soil were analyzed as presented in Table 1. Soil pH and electrical conductivity were determined with pH meter 1:2.5 [49] and EC meter [50], respectively. Organic carbon (%), available phosphorus (ppm), and total nitrogen were determined with Walkley and Black method [51], Sodium bicarbonate method [52], and Kjeldahl method [53], respectively. Cation exchanging capacity was also analyzed using Ammonium acetate method. Soil samples were collected from 0 to 0.20, 0.21–0.40 and 0.41–0.60 m soil depths, and dried for 24 h at 105 °C; and after executing these procedures, water content of was estimated based on gravimeteric basis.3. Crop data: Crop data encompassing various parameters such as aboveground biomass, canopy cover, rooting depth, plant density, and grain yield were carefully recorded for each experiment at all cropping seasons. In addition, key phenological stages including sowing date, days to 90 % emergence, days to start of flowering, days to attain maximum rooting depth, days to start of senescence, days to reach maximum canopy cover (CCx), and days to physiological maturity were recorded during the three main cropping seasons. We also recorded sequential aboveground biomass and digital photographs every 10 days intervals from each treatment. The harvest index (HI) was determined by dividing grain yield by aboveground biomass. Notably, aerial photographs collected from the different treatments were analyzed using the SamplePoint software to quantify green canopy development, which is available at www.SamplePoint.org. Photographs were captured from a standardized height of 2.0 m above the soil surface (Fig. 2), ensuring the distance from the soil surface to the top of the crop canopy and accommodating maximum solar ration distribution.

Table 1 Soil physical and chemical properties of the study area.

Table 1Depth (cm)	pH	EC (mhos/cm)	P (ppm)	% OC	%TN	CEC (meq/100 g)	FC (vol%)	WP (vol%)	TAW (mm/m)	
0–20	8.77	0.45	3.23	0.51	0.06	57.4	44.8	30.5	143.0	
21–40	8.93	0.395	3.23	0.51	0.06	59.4	44.7	30.5	142.0	
41–60	9.16	0.46	3.30	0.49	0.06	60.8	45.4	31.0	144.0	
Where; EC = electrical conductivity, P = phosphorus, %OC = percent of organic carbon, % TN = total soil nitrogen, CEC = cation exchange capacity, FC = field capacity, WP = wilting point, and AW = available soil water content (mm).

2.3 Description of AquaCrop model

The AquaCrop model [26] is a water-driven model that only needs a few parameters to operate [24] and maintains a balance between accuracy, simplicity, robustness, and practitioner-friendliness [33]. The AquaCrop model must be calibrated and validated using observed field data under various conditions before being used to simulate the response of sesame to various water, fertilizer, and other crop management approaches. Because of this, measured field data from three consecutive cropping seasons: 2016, 2017, and 2018 were used to calibrate and validate the model at various nitrogen fertilizer rates.

2.3.1 Model calibration

In order to fit model parameters to measured values under specific environmental and management conditions, a procedure known as calibration is performed [54]. Sesame, however, does not have any predefined parameters in the AquaCrop model database. Therefore, to calibrate the model at the predefined nitrogen fertilizer settings, crop-specific crop parameters were gathered during the 2016 cropping season from a separate plot treated with a 46 kg/ha nitrogen, treated with recommended agronomic practices for the growth and development of the crop. We also used data recorded from the 46 kg/ha treatment in 2016, which is the recommended nitrogen fertilizer level. We used a popular sesame variety (Setit-1), which is commonly cultivated by farmers and researchers at different research centers for the calibration purpose.

Maximum canopy cover (97 %), time from sowing to emergence (6 days), days to maximum canopy cover (60 days after emergence, DAE), days to start of senescence (70 DAE), days to start of flowering (34 DAE), days to maximum rooting depth (70 DAE), maximum rooting depth (0.6 m), and days to physiological maturity (93 days) were recorded (Table 1). Reference harvest index (HIo), and normalized water productivity (15 g/m2) were also estimated to calibrate the model (Table 2). As part of the calibration of the AquaCrop model, the normalized water productivity (WP), which is central to the AquaCrop model function [33] was also determined using Equation (1).Equation 1 WP*=B∑i=1nTrETo

where, WP* is normalized water productivity (g/m2) normalized under the prevailing CO2 and transpiration in a given location, Tr is daily transpiration, ETo is daily reference evapotranspiration and n is the length of growing period of the crop during the entire growing season.

Conservative crop parameters were adjusted repeatedly until the best fit of the model was obtained. To calibrate the Aquacrop model, climate, soil, crop, and initial soil water content (SWC) files were created for all field experiments and treatments.

The climate file includes daily minimum and maximum air temperature, reference evapotranspiration (ETo), rainfall, and the mean annual atmospheric CO2 concentration. On the other hand, the soil file was created containing volumetric soil water contents at field capacity, at the permanent wilting point, and at saturation for 0.0–0.2 m, 0.2–0.4 m, and 0.4–0.6 m soil depths. The volumetric soil water content, and hydraulic conductivity were estimated using pedotransfer function [55], based on the particle size distribution analysis of the sampled soils from the experimental sites. Similarly, the crop files were generated whereby crop development was described in a growing calendar from the observed crop development stages under non-stressed conditions. Field management files were also created.

Due to the effect of soil compaction from heavy tractors in the study area, the effective rooting depth was adjusted to be 0.6 m. The time to reach maximum effective rooting depth was set between time to maximum CC, and the start of crop senescence. In AquaCrop, the leaf expansion and canopy senescence are regulated by the canopy growth coefficient (CGC) and canopy decline coefficient (CDC), respectively. CGC was calibrated based on the initial canopy cover (CC0), the maximum canopy cover (CCx), and the days after planting when CCx was attained. The CDC was calibrated by specifying CCx, and the date of start of senescence and maturity after sowing [[25], [26]].

By changing soil water depletion thresholds (p) that affect leaf growth and early canopy senescence, crop canopy development in response to soil water stress was calibrated in AquaCrop. The soil water depletion threshold is expressed as a fraction of the total accessible soil water (TAW); therefore, p was set to 0.6 [48]. Canopy growth coefficient (CGC), canopy decline coefficient (CDC), and soil water depletion thresholds for inhibition of leaf expansion and for the acceleration of canopy senescence were calibrated repeatedly until the simulated and observed crop canopy development in the unstressed plots matched precisely.

As a function of water productivity normalized for daily transpiration and atmospheric CO2, AquaCrop model predicts daily biomass production (equation (1)), and it is calculated as the slope of cumulative aboveground biomass and cumulative evapotranspiration [25]; [[26], [33]]. Data gathered from irrigation experiments conducted in 2018 and 2019 were used to calculate water productivity [56]. For most crops, only part of the biomass produced is partitioned to the harvested organs to give yield (Y), and the ratio of yield to biomass is known as harvest index (HI). Grain yield is determined by multiplying aboveground biomass by the harvest index equation (2).Equation 2 Y=HI*B

The reference harvest index (HI0) was the harvest index (HI) recorded under unstressed conditions. The impact of soil water stress on HI was calibrated for crop yield response to soil water stress at (i) the phases before flowering, (ii) during flowering, and (iii) during grain filling. A trial and error adjustment was used to find the water stress coefficients for HI in the model that best matched the observed and simulated harvestable yield. Table 1 shows the conservative and user-specific parameters that were utilized to calibrate the AquaCrop.

2.3.2 Model validation and statistical indices

The AquaCrop model was validated for its performance in predicting green canopy, soil water balance, aboveground biomass, and yield of sesame varieties under different nitrogen fertilizer rates based on the calibrated parameters. Separate datasets recorded in 2016, 2017 and 2018 main cropping seasons from three sesame varieties (Setit-1, Setit-2 and Humera-1) treated with the different nitrogen fertilizer levels, except the data used during calibration. The coefficient of determination, root mean square error, normalized root mean square error, model efficiency, and degree of agreement were used to evaluate the performance of the model for prediction based on the calibrated parameters. The performance of the model was considered when five of the evaluation indicator values ranged from good to very good.1. Coefficient of determination (Equation (3)): R2 estimates the combined dispersion between the observed and predicted series [57]. The value of R2 varies between 0 and 1; where, values closer to 1 indicate good prediction and values closer to zero show poor prediction.

2. Nash-Sutcliffe efficiency (Equation (4)): The coefficient of efficiency (E) expresses how much the overall deviation between observed and simulated values departs from the overall deviation between observed values and their mean value [58]. The range of E lies between 1 (perfect fit) and infinity; whereas, an E value of 0 indicates that the model predictions are as accurate as the average of the observed data.

3. Willmotts Index of agreement (Equation (5)): The index of agreement (D) indicates the ratio of the mean square error and the potential error 59.

4. Root mean squared error (Equation (6)): root mean square error (RMSE) represents a measure of the overall or mean deviations between observed and simulated values [58].

Equation 3 R2=(∑i=1n(Oi−O‾)(Si−S‾)∑i=1n(Oi−O‾)2∑i=1n(Oi−S‾)2)

Equation 4 E=1−∑i=1n(Oi−Si)2∑n(Oi−O‾)2

Equation 5 d=1−∑i=1n(Si−Oi)2∑(|Si−S‾|+|Oi−S‾|)2

Equation 6 RMSE=1(N)∑i=1n(Oi−Si)2

Where, S is simulated value, S‾ is the mean of the simulated value, O is observed value, O‾ is the mean of the observed value, and N or n is the number of observations

3 Results

3.1 Calibration

Following rigorous calibration efforts, the AquaCrop model was utilized to conduct a daily assessment of soil water balance, accounting for both incoming and outgoing water fluxes relative to the root zone [25]. Through meticulous calibration procedures, the model was fine-tuned to simulate soil water content (SWC), as illustrated in Fig. 3, considering the soil properties and maximum rooting depth specific to the crop, as outlined in Table 2. Statistical performance metrics such as R2, RMSE, N-RMSE, E, and D achieved impressive values of 0.98, 9.5 mm, 4.3 %, 0.97, and 0.97, respectively, signifying the model's ability to accurately capture SWC dynamics during calibration. Moreover, the AquaCrop model was specifically adjusted to replicate the green canopy cover of sesame under conditions of full nitrogen fertilization (46 kg/ha nitrogen) documented in 2016, yielding satisfactory performance with an R2 of 0.96 and RMSE of 8.5 % (see Table 3).Fig. 3 Observed versus simulated soil water content (mm), aboveground biomass and canopy cover of sesame used for calibration in 2016 under full nitrogen fertilizer conditions (filled squares/diamonds are observed values and filled circles with lines are simulated values).

Fig. 3

Table 2 Phenological stages of sesame at different growth stages from 2016 to 2018 main cropping seasons.

Table 2Parameter	Year	
2016	2017	2018	
Date of sowing	July 15	July 16	July 18	
Days to 90 % emergence	6	6	6	
Days to start of flowering (DAE)	40	40	40	
Days to start of senescence (DAE)	70	70	70	
Days to maximum rooting depth (DAE)	70	70	70	
Days to maximum canopy cover (DAE)	60	60	60	
Total days to 50 % physiological maturity	93	93	93	

Table 3 Conservative and user-specific model parameters used for calibrating AquaCrop model.

Table 3Parameter	value	Units	
Base temperature	11	0C	
Upper temperature	40	0C	
Cover per seedling	5	cm2 per plant	
 Canopy growth coefficient (CGC)	11.7	%/day	
Canopy decline coefficient (CDC)	14.1	%/day	
Soil water depletion factor for canopy expansion, upper limit	0.1		
Soil water depletion factor for canopy expansion, lower limit	0.45		
Shape factor for water stress coefficient for canopy expansion	3		
Soil water depletion factor for stomatal closure	0.6		
Shape factor for water stress coefficient for stomatal control	4		
Soil water depletion factor for canopy senescence	0.6		
Shape factor for water stress coefficient for canopy senescence	3		
Normalized water productivity (WP*)	15	g/m2	
Plant density	250,000	plants/ha	
Initial canopy cover (CCo)	1.25	%	
Maximum canopy cover (CCx)	97	%	
Time to maximum canopy cover	66	days	
Time to start of flowering	41	days	
Time to start of senescence	76	days	
Time to physiological maturity	91	days	
Time to maximum rooting depth	66	days	
Maximum effective rooting depth	0.6	meter	

The calibration of green canopy cover of sesame using the AquaCrop model resulted in acceptable performance metrics, with RMSE, N-RMSE, E, and D values of 6 %, 14.7 %, 0.92, and 0.98, respectively. These outcomes indicate successful calibration of the model under full nitrogen fertilizer regimes. In addition, the model underwent calibration for aboveground biomass (AB) simulation, demonstrating effective performance as illustrated in Fig. 3. The results showed satisfactory agreement between simulated and observed AB values, with R2, RMSE, N-RMSE, E, and D values of 0.98, 0.3 tons/ha, 8.1 %, 0.96 %, and 0.99, respectively, as presented in Table 4. These findings affirm the model's pertinent calibration for accurately simulating sesame's AB under conditions of full nitrogen fertilization.Table 4 Statistical indicator values of the AquaCrop model during calibration.

Table 4Parameters	R2	RMSE	N-RMSE (%)	E	D	
SWC	0.96	10.7 mm	4.9	0.96	0.98	
CC	0.99	6.0 %	10.9	0.96	0.99	
AB	0.98	0.38 tons/ha	11.9	0.91	0.98	

3.2 Validation

3.2.1 Soil water content (SWC)

The AquaCrop model successfully simulated SWC with high levels of accuracy and consistency across multiple cropping seasons. The model demonstrated strong performance with R2 values ranging from 0.88 to 0.97, revealing a good fit between simulated and observed values. Besides, the coefficients of determination (D) varied from 0.92 to 0.96, indicating a strong correlation between predicted and actual SWC levels. Evaluation metrics such as RMSE and N-RMSE fell within acceptable ranges, with values ranging between 8.8 and 15.0 mm and 4.0–19.03 %, respectively, over different cropping seasons. The model efficiency index (E) for SWC ranged from 0.78 to 0.84, highlighting its capability to moderately capture the dynamics of soil water content. The results also showed high levels of agreement, with a degree of agreement reaching 0.96 in certain cases. Overall, the AquaCrop model demonstrated consistent and acceptable performance in simulating SWC for sesame crops across various cropping seasons, providing valuable insights for agricultural management practices.

3.2.2 Green canopy cover (CC)

The accuracy of the AquaCrop model in predicting sesame canopy cover under varying nitrogen fertilizer rates was evaluated for the 2016, 2017, and 2018 main cropping seasons. Fig. 4, Fig. 5, Fig. 6, Fig. 7 illustrate that the model exhibited high levels of performance, as evidenced by R2 values ranging from 0.94 to 0.98. Evaluation metrics such as RMSE, N-RMSE, D, and E varied between 6.2 and 11 %, 8.3–22 %, 0.86 to 0.96, and 0.95 to 0.99, respectively. The AquaCrop model tended to slightly overestimate CC during late-season growth stages across all cropping seasons. These findings confirm the model's ability to accurately simulate sesame CC under varying nitrogen fertilizer regimes throughout different crop growth periods.Fig. 4 Observed and simulated canopy cover of sesame (A) 0 kg/ha, (B) 23 kg/ha and (C) 37.5 kg/ha and (D) 46 kg/ha nitrogen in 2016 (cv. Setit-1.

Fig. 4

Fig. 5 Observed and simulated canopy cover of sesame under (A) 0 kg/ha, (B) 23 kg/ha, (C) 46 kg/ha and (D) 69 kg/ha nitrogen fertilizer in 2017 (cv. Humera-1).

Fig. 5

Fig. 6 Observed and simulated canopy cover of sesame (A) 23 kg N/ha, (B) 0 kg N/ha, (C) 46 kg N/ha, and (D) 69 kg N/ha in 2017 (Cv. Setit-2). Points with Diamonds are measured and points with solid circles are simulated values.

Fig. 6

Fig. 7 Observed and simulated canopy cover of sesame under (A) 0 kg/ha, (B) 23 kg/ha, (C) 46 kg/ha, and (D) 69 kg/ha of nitrogen in 2018 (cv. Setit-1).

Fig. 7

The AquaCrop model slightly under estimated CC of sesame during the mid-growth stage under the different nitrogen fertilizer applications in 2018. Green canopy cover of sesame was also appropriately simulated under the different nitrogen fertilizer conditions in the 2016, and 2017 crop growing seasons (Fig. 4, Fig. 5, Fig. 6, Fig. 7). The model consistently over-estimated CC of sesame during the late-growth stage in all cropping seasons; whereas, the model appropriately estimated CC of sesame under the different nitrogen fertilizer applications during the initial growth stage of the crop.

3.2.3 Aboveground biomass and yield

The results show that the AquaCrop model accurately predicted the aboveground biomass of sesame. The statistical measures R2, RMSE, and NRMSE ranged from 0.93 to 0.96, 0.39–0.48 tons/ha, and 12.12–14.13 %, respectively. Additionally, the model efficiency (E) and degree of agreement (D) ranged from 0.77 to 0.90 and 0.92 to 0.97, respectively. These findings demonstrate that the model effectively simulated the AB of sesame during the main cropping seasons of 2016, 2017, and 2018. (Fig. 8).Fig. 8 Observed versus simulated aboveground biomass of sesame under 0, 23, 46 and 69 kg/ha different nitrogen fertilizer levels in the 2016, 2017 and 2018 main cropping seasons.

Fig. 8

The performance of the AquaCrop model was evaluated in predicting sesame yield under various nitrogen fertilizer levels, demonstrating satisfactory simulation results. Statistical measures such as R2, RMSE, N-RMSE, E, and D indicated that the model achieved an R2 value of 0.88, RMSE of 0.24 tons/ha, N-RMSE of 15 %, and both E and D of 0.80 (Fig. 9). The model tended to slightly overestimate sesame yield across the range of nitrogen fertilizer rates tested in comparison to the actual measurements.Fig. 9 Observed and simulated yield of sesame under different nitrogen fertilizer rates in 2016, 2017 and 2018 (the average of three sesame varieties).

Fig. 9

4 Discussions

1 Soil water content (SWC)

In this study, the AquaCrop model was thoroughly calibrated and validated to accurately predict the incoming and outgoing water in the root zone under the different nitrogen fertilizer levels. Prior studies have highlighted the model's performance in capturing soil water fluxes within the root zones of diverse crops [[41], [60]]. The results obtained in this study are in agreement with similar studies, which have conducted under different crop management strategies and environmental conditions. Similarly, evaluation of the performance of AquaCrop model in predicting SWC of tef, with statistical indicators including R2 (0.90), E (0.90), D (0.97), and RMSE (15 mm), demonstrated its ability to model soil water dynamics under different fertilizer treatments [36]. Furthermore, the accuracy and robustness of the model in simulating SWC under differing nitrogen levels for maize production was evaluated, resulting in RMSE, R2, and mean bias error (MBE) values spanning 3.92 %–10.78 %, 0.80 to 0.82, and −0.19 % to −0.25 %, respectively [61], which were comparably lower than the findings observed in the present study.2 Green canopy cover development (CC)

Green canopy development of sesame was appropriately simulated by the AquaCrop model under the different nitrogen fertilizer applications. Recent studies also highlight that the AquaCrop model is an important tool for capturing soil water dynamics in the root zone, predicting the growth and yield of several field crops under varying management and environmental conditions [25]; [26,[29], [33]]. In line with this, field experiments reveal that the AquaCrop model acceptably simulated CC of maize with RMSE of 16.2–24.12 % [62]; and a RMSE, R2, and D of 14.1 %, 0.85, and 0.90, respectively for faba bean green CC development [54]. Similarly, the AquaCrop model was also able to adequately simulate the CC of maize under the Nebraska environmental conditions, USA, with RMSE ranging from 5.3 to 12.7 % [58]. Hence, this study demonstrate that the model adequately simulated the green CC development of sesame, with its best performance observed in the 2016 main cropping season with 99 % of the measured and simulated CC values match during calibration and validation processes. In line with this, the AquaCrop model was also tested in simulating CC of rice under different water management practices and simulated CC with acceptable performance with D and E ranging from 0.98 to 0.99, and 0.93 to 0.99, respectively [60].3 Aboveground biomass (AB) and yield of sesame

The AquaCrop model was also calibrated and validated for predicting AB development and yield of sesame under different nitrogen fertilizer levels as illustrated in Fig. 7, Fig. 8. The findings of this study align with prior research studies conducted under different management and environmental conditions to predict AB of diverse field crops, including maize [[25], [33]]; tef [[36], [37]]; barley [[38], [39]], cotton [[63], [64]], and rice [[60], [65]], thus demonstrating to performance of the model in simulating AB under varied management and environmental contexts. Recent findings have highlight the accuracy and robustness of the AquaCrop model in predicting AB of maize, with a degree of agreement (D) exceeding or equal to 0.97 [25], and tef, with D ranging from 0.9 to 0.98 [36]. Conversely, the AquaCrop model was evaluated for its efficacy in simulating maize biomass under different soil fertility regimens [66]. Furthermore, the performance of the model for predicting yeld of maize under differing soil fertility levels, resulting in its efficiency factor (EF) of 0.98 [35], and relative root mean square error (RMSE), coefficient of determination (R2), and mean bias error (MBE) of 5.16 %, 0.96, and 0.28 tons/ha, respectively [61].

The AquaCrop model was also tested for its performance in simulating the yield of sesame, and the statistical indicator values show that the model was able to simulate yield of the crop under the different nitrogen fertilizer rates. Similarly, the AquaCrop model was also tested for its ability to simulate seed yield across several field crops, including maize [35]; [[61], [66]], wheat [[40], [63]]; and barley [38], with the results revealing yield simulations across these crops. Similarly, the model demonstrated moderate capability in simulating rice grain yield, as evidenced by R2 and normalized root mean square error (N-RMSE) values of 0.81 and 13 %, respectively [65]. Additionally, the AquaCrop model was also subjected to thorough assessment for its efficiency in simulating maize grain yield under varied nitrogen fertilizer applications in Iran, resulting in satisfactory performance with root mean square error (RMSE), R2, and mean bias error (MBE) values of 14.64 %, 0.94, and 0.56 tons/ha, respectively [61]. Moreover, previous reports substantiate the model's capability in simulating maize yield, with R2 values ranging from 0.82 to 0.99, degree of agreement (D) ranging from 0.6 to 0.88, and normalized root mean square error (NRMSE) values varying from 8 % to 17 %, indicative of excellent to good agreement [66], which validates the findings of this study.

5 Conclusions

The calibration and validation of the AquaCrop model for predicting the response sesame to different soil fertility levels in the semi-arid areas of western Tigray, demonstrate its accuracy and robustness as a valuable tool for agricultural research and management. Through thorough calibration and validation, the model accurately simulates soil water dynamics, green canopy cover development, aboveground biomass, and yield of sesame across varying nitrogen fertilizer rates. Comparative analyses with other crops highlight the model's efficiency and robustness in capturing plant growth dynamics under diverse environmental and management conditions. The findings obtained in this study demonstrate the robustness, accuracy and reliability of the AquaCrop model in predicting the response of sesame to different soil fertility management strategies, providing valuable insights for sustainable soil fertility management practices in semi-arid regions, with similar agro-climatic conditions of the western Tigray. Overall, this study contributes to enhancing our understanding of sesame cultivation under rain-fed conditions and highlights the importance of application of crop modeling approaches for optimizing agricultural productivity in resource-constrained environments.

Data availability

Field data are available in the hands of the corresponding author, and can be available on legal request of the journal editorial management office.

CRediT authorship contribution statement

Abadi Berhane: Writing – original draft, Software, Resources, Methodology, Funding acquisition, Formal analysis, Conceptualization. Berhanu Abrha: Writing – review & editing, Validation, Supervision. Walelign Worku: Writing – review & editing, Validation, Supervision. Gebre Hadgu: Writing – original draft, Validation, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A Supplementary data

The following is the Supplementary data to this article:Multimedia component 1

Multimedia component 1

Acknowledgement

The authors would like to thank the Ethiopian Agricultural Research Institute, Ministry of Education of the Federal Democratic Republic of Ethiopia and 10.13039/100015666 Aksum University for financially supporting this research project.

Appendix A Supplementary data to this article can be found online at https://doi.org/10.1016/j.heliyon.2024.e36084.
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