Performance of Ordinary least Squares (OLS) and Bayesian network (BN) in Exchange sodium percentage prediction based on Sodium adsorption Ratio

Document Type : Complete scientific research article


1 M.Sc. Graduated of Soil Science Department, University of Zanjan

2 Assistant Professor, And Faculty Member of the Ministry of Science, Research and Technology (Corresponding Author)


Background and Objectives: Two different criteria are exist in the soil science as indices of Alkality. These are the Sodium Adsorption Ratio (SAR) and the Exchangeable Sodium Percentage (ESP). As shown for measured of ESP, it is essential to have soil Cation Exchange Capacity (CEC). But, For CEC determined using laborious and time consuming tests, it be more appropriate and economical to develop a model that predict ESP indirectly from a easily-measured properties. Researches showed a relationship between ESP and SAR. So, SAR can be allocated to predict of ESP. For this reason, many attempts have been made to predict ESP from soil. The specific goal of the research develop model to determining ESP based on SAR by OLS and BN models for Bonab soils in East Azarbaijan province, Iran.
Materials and Methods: For arrived presented research, 209 soil samples were taken by grid survey (250˟250) of Bonab, Iran. The site is located at mean 1300 m above mean sea level, in semiarid climate in the Northwest of Iran. Then, some soil chemical properties such as Na+, Ca2+, Mg2+, SAR and ESP of the soil samples were measured using laboratory experiments. Then, two model was developed by OLS and BN. OLS estimators are linear functions of the values of the dependent variable which are linearly combined using weights that are a non-linear function of the values of the explanatory variables. So the OLS estimator is respect to how it uses the values of the dependent variable only, and irrespective of how it uses the values of the explanatory. So A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty.
Results: The Coefficient of Determination (R2) and Root Mean Square error (RMSE) of the soil ESP-SAR model is reported 0.99, 0.71 and 0.98, 1.63 by OLS and BN respectively. Based on the statistical result, both of soil ESP-SAR model was judged acceptable. T-test were used to compare the soil ESP values predicted using the soil ESP-SAR model with the soil ESP values measured by laboratory tests. The paired samples t-test results indicated that the difference between the soil ESP values predicted by the model and measured by laboratory tests were not statistically significant (P>0.05). Therefore, the soil ESP-SAR model can provide an easy, economic and brief methodology to estimate soil ESP. The GMER index also indicated low estimation of two selected land evaluation method.
Conclusion: The results of present study illustrated that OLS and BN models can predict ESP with acceptable limits. OLS and BN are mathematical models between input and output variables and has the ability of modeling between ESP and SAR.


1.Banaei, M.H., Momeni, A., Baybordi, M.,
and Malakouti, J. 2004. Iranian Soils.
Sana Press, Tehran, Iran.
2.Bouyoucos, G.J. 1962. Hydrometer
method improved for making particle size
analysis of soils. Agron. J. 56: 464-466.
3.Bower, CA., Reitemeier, RF., and
Fireman, M. 1952. Exchangeable cation
analysis of saline and alkali soils. Soil
Science. 73: 251-261.
4.Chi, Ch.M., Zhao, Ch.W., Sun, X.J.,
and Wang, Z.C. 2011. Estimating
exchangeable sodium percentage from
sodium adsorption ratio of salt-affected
soil in The Songnen plain of Northeast
China. Soil Science Society of China
Pedosphere 21: 2. 271-276.
5.Dahiya, I.S., Richter, J., and Malik, R.S.
1984. Soil spatial variability: A review.
Inter. J. Trop. Agric. 11: 91-102.
6.Evangelou, V.P., and Marsi, M. 2003.
Influence of ionic strength on sodiumcalcium exchange of two temperate
climate soils. Plant and Soil. 250: 307-313.
7.Farahmand, A., Oustan, S.H., Jafarzadeh,
A.J., and Asgarzad, A.N. 2011. The
parameters of sodium and salinity in
some salt affected soils of the Tabriz
Plain. J of Soil and Water, 19: 2. 22. 1-15.
(In Persian)
8.Heckerman, D. 1997. Bayesian networks
for data mining. Data Mining and
Knowledge Discovery. 1: 1. 79-119.
9.Jurinak, J.J., and Suarez, D.L. 1990. The
chemistry of salt-affected soils, P 42-63.
In: Tanji, K.K. (ed). Agricultural Salinity
Assessment and Management, No, 71.
American Society of Civil Engineers,
New York, N.Y.
10.Kevin, B., and Nicholson, E. 2010.
Bayesian artificial intelligence. Second
Edition, United states. 3: 1. 370-450.
11.Lake, H.R., Akbarzadeh, A., and
Mehrjardi, R.T. 2009. Development of
pedotransfer functions (PTFs) to predict
soil physico-chemical and hydrological
characteristics in southern coastal zones
of the Caspian Sea. J. Ecol. Natur.
Environ. 1: 7. 160-172.
12.Lal, P., Chippa, B.R., and Arvind,
K. 2003. Salt affected soils and
crop production, a modern synthesis,
AGROBIS (India). Pp: 42-61.
13.Lesch, S.M., Strauss, D.J., and Rhoades,
J.D. 1995. Spatial prediction of soil
salinity using electromagnetic induction
techniques 1. Statistical prediction
models: A comparison of multiple
linear regression and cokriging. Water
Resources Research, 31: 373-386.
14.Nguyen, R.T., Prentiss, D., and Shively,
J.E. 1998. Rainfall interpolation for
Santa Barbara County. UCSB,
Department Geography. USA.
15.Rhoades, J.D. 1982. Cation exchange
capacity. P 149-157. In: Page, A.L.,
Miller, R.H. and Keeney, D.R. (eds).
Methods of Soil Analysis. Part 2. Agron.
Monogr. 9, American Society of
Agronomy, Madison, WI, USA.
16.Richards, L.A. 1954. USDA Handbook
60. U.S. Department of Agriculture,
Washington DC. USA
17.Rowell, D.L. 1994. Soil Science:
Methods and Application. Longman
Group, Harlow, England, 345p.
18.Seilsepour, M., Rashidi, M., and
Khabbaz, B.G. 2009. Prediction of soil
exchangeable sodium percentage based
on soil sodium adsorption ratio. Amer.-
Euras. J. Agric. Environ. Sci. 5: 1. 1-4.
19.Sumner, M.E. 1993. Sodic soils:
New perspectives. Austr. J. Soil Res.
31: 683-750.
20.Tamari, S., WoÈsten, J.H.M., and
Ruiz-SuaÂrez, J.C. 1996. Testing an
artificial neural network for predicting
soil hydraulic conductivity. Soil Sci.
Soc. Amer. J. 60: 1732-1741.
21.Tu, J. 2011. Spatially varying
relationships between land use and
water quality across an urbanization
gradient explored by geographically
weighted regression. Applied Geography,
31: 1. 376-392.
22.USDA. 1996. Soil Survey Laboratory
Methods Manual. Soil Survey
Investigations Republic, Washington:
United States Government Print.
23.Wagner, B., Tarnawski, V.R., Hennings,
V., Muller, U., Wessolek, G., and
Plagge, R. 2001. Evaluation of
pedotransfer function for unsaturated
soil hydraulic conductivity using
an independent data set. Geoderma.
102: 275-297.
24.Zare, M., Ordookhani, K., Emadi, A.,
and Azarpanah, A. 2014. Relationship
between soil exchangeable sodium
percentage and soil sodium adsorption
ratio in Marvdasht plain, Iran. Inter. J.
Adv. Biol. Biom. Res. 2: 12. 2934-2939