Abstract

Sorghum is considered as a cereal in the world but in Iran forage sorghum is preferred due to lack of forage. This research was conducted considering the importance of forage sorghum and the conditions of sorghum cultivation under salinity stress in Mazandaran province. The aims of this research were: 1) to investigate the functional response of forage sorghum (variety Speedfeed) to irrigation water salinity and soil salinity, and 2) to quantify the sorghum functional response to salinity during maturation, using several empirical models. Water salinity treatments included well water (control), ratios of 1:4, 2:4, and 3:4 sea water to well water, and pure sea water which were applied in a column study. Salinity-Yield threshold models (Mass and Hoffman, van Genuchten and Hoffman, Dirksen et al., Homaee et al., modified Weibull, bi-exponential and Gompertz( were fitted to the data obtained (relative yield of sorghum at maturation stage vs. electrical conductivity, EC) and the parameters of models were estimated. The van Genuchten model and the Hoffman and Gompertz model were better than other models in fitting the relative yield data as a function of the EC of the saturated soil extract, due to the lower root mean square errors (RMSE) and Akaike’s information criterion (AIC) in these models (2.84 and –157.34 for the van Genuchten model and 3.11 and –152.53 for the Hoffmann and Gompertz model, respectively). The van Genuchten and Hoffmann model (–205.77, -1.09) and the corrected Weibull model (-213.21 and 0.95) were superior in fitting relative yield data as a function of EC of irrigation water. The salinity tolerance thresholds of sorghum based on fitting relative yield data as a function of EC of saturated soil extract and irrigation water were also estimated to be 3.65 and 2.33 dS m^{-1}, respectively. Also, no significant difference was observed between the relative yield obtained from the models as a function of the EC of saturated soil extract or irrigation water. In other words, the mentioned models are capable to estimate the yield based on the salinity of the irrigation water.

**Background and Objective:** Currently, the increasing growth of the world's population and the need for more agricultural products are important issues that human being is facing today. Limitation in water and soil resources is mentioned as the main restriction for agricultural production. Therefore, the proper use of available water resources and poor-quality saline waters, is at the forefront of the activities of different countries (2). The detrimental effect of salinity on plant growth is due to low osmotic potential in the soil, unbalanced nutrition, specific ionic effects or a combination of these factors (1). Usually, the sensitivity of plants to salinity varies during the growing season (3). Therefore, proper water management requires analysis of plant sensitivity to salinity at each growth stage, in areas with unfavorable water and soil quality.

**Methods:** Five sorghum seeds were planted in 15 polyethylene columns filled with a clay loam soil, and after germination, they were reduced to three seedlings. The treatments included well water as control, 1:4, 2:4 and 3:4 ratios of sea water to well water, and pure sea water with the EC values of 0.99, 4.7, 8.1, 13.7 and 15.9 dS m^{-1}, respectively. After 56 days of plant growth, the effect of salinity on the growth and yield of sorghum was assessed and the salinity threshold for this plant was determined. The relative yield as a function of salinity was also calculated using the models of Mass and Hoffman, van Genuchten and Hoffman, Dirksen et al., Homaee et al., modified Weibull, bi-exponential and Gompertz. Quantitative comparison of the models was also conducted using some statistical indices. In order to fit and determine the optimized parameters of the root water uptake models, the Solver tool in Excel was used. Also, the mean comparison was statistically analyzed using *t*-test by MSTATC software.

**Results:** The salinity thresholds of sorghum based on the EC values of saturated soil extract and irrigation water were 3.5 and 1.4 dS m^{-1}, respectively. The slope of the linear relation between relative yield and soil EC was calculated to be about 3% per dS m^{-1}, indicating that sorghum is sensitive to salinity stress. Based on the EC of saturated soil extract, the RMSE and AIC were lower for van Genuchten and Hoffman, and Gompertz models. However, efficiencies of Dirksen et al.'s and bi-exponential models were slightly different and can be suggested. Also Mass and Hoffman's model can also be used due to the simplicity of its equation. The analysis based on the EC of irrigation water also showed that the van Genuchten and Hoffman's model and the modified Weibull model were the best ones according to the lower values of RMSE and AIC. Also, the results of the *t* test showed that there was no significant difference between the fitting of mathematical and statistical models to observational data and between the two groups of models as a function of EC values of saturated soil extract and irrigation water at *p*<0.01. Therefore, at this stage of plant growth, instead of using EC of saturated soil extract, EC of irrigation water can be used directly in the root water uptake models.

**Conclusions:** The results of this research showed that the salinity thresholds of sorghum based on the EC values of saturated soil extract and irrigation water were 3.5 and 1.4 dS m^{-1}, respectively. The non-linear models have better ability in modeling the water uptake by roots. Also, there was not significant difference between the fitting results of mathematical and statistical models with the measured data and the results of the two groups of models as a function of EC values of saturated soil extract and irrigation water. Therefore, by using these models, it is possible to determine the irrigation time for maximum plant growth without the need for field measurements.

**References:**

1. Munns, R., Gilliham, M., 2015. Salinity tolerance of crops–what is the cost?*New Phytologist* 208(3): 668–673.

2. Rhoades, J.D., Kandiah, A., Mashali, A.M., 1992. The Use of Saline Waters for Crop Production. FAO Irrigation and Drainage Paper, FAO, United Nations, Rome.

3. Saadat, S., Homaee, M., 2015. Modeling sorghum response to irrigation water salinity at early growth stage.*Agricultural Water Management* 152: 119–124.

Sorghum is considered as a cereal in the world but in Iran forage sorghum is preferred due to lack of forage. This research was conducted considering the importance of forage sorghum and the conditions of sorghum cultivation under salinity stress in Mazandaran province. The aims of this research were: 1) to investigate the functional response of forage sorghum (variety Speedfeed) to irrigation water salinity and soil salinity, and 2) to quantify the sorghum functional response to salinity during maturation, using several empirical models. Water salinity treatments included well water (control), ratios of 1:4, 2:4, and 3:4 sea water to well water, and pure sea water which were applied in a column study. Salinity-Yield threshold models (Mass and Hoffman, van Genuchten and Hoffman, Dirksen et al., Homaee et al., modified Weibull, bi-exponential and Gompertz( were fitted to the data obtained (relative yield of sorghum at maturation stage vs. electrical conductivity, EC) and the parameters of models were estimated. The van Genuchten model and the Hoffman and Gompertz model were better than other models in fitting the relative yield data as a function of the EC of the saturated soil extract, due to the lower root mean square errors (RMSE) and Akaike’s information criterion (AIC) in these models (2.84 and –157.34 for the van Genuchten model and 3.11 and –152.53 for the Hoffmann and Gompertz model, respectively). The van Genuchten and Hoffmann model (–205.77, -1.09) and the corrected Weibull model (-213.21 and 0.95) were superior in fitting relative yield data as a function of EC of irrigation water. The salinity tolerance thresholds of sorghum based on fitting relative yield data as a function of EC of saturated soil extract and irrigation water were also estimated to be 3.65 and 2.33 dS m

1. Munns, R., Gilliham, M., 2015. Salinity tolerance of crops–what is the cost?

2. Rhoades, J.D., Kandiah, A., Mashali, A.M., 1992. The Use of Saline Waters for Crop Production. FAO Irrigation and Drainage Paper, FAO, United Nations, Rome.

3. Saadat, S., Homaee, M., 2015. Modeling sorghum response to irrigation water salinity at early growth stage.

Type of Study: Research |
Subject:
Modeling of soil-water-plant relations and root water uptake

Received: 2022/11/10 | Accepted: 2023/05/23 | Published: 2023/09/20

Received: 2022/11/10 | Accepted: 2023/05/23 | Published: 2023/09/20

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