Potassium estimation in the soil solution based on electrical conductivity and soil water content

The objective of this work was to evaluate and to validate models for estimating potassium in the soil solution as a function of bulk electrical conductivity (ECw), soil water content () and a soil solution electrical conductivity (ECss). Treatments consisted of using three concentrations of injecting solution of potassium chloride (1.0, 2.5 and 4.0 g L-1) which were applied by two trickle irrigation systems (microsprinkler and drip) during the first cycle of the banana crop cv. Terra Maranhão. Results showed that it is feasible to estimate potassium concentration in the soil solution from data of ECss and  obtained by time domain reflectometry (TDR) using an equation that combined a linear and a potential model. The estimated values of potassium concentration were close to the ones measured along the crop cycle under field conditions, with a mean normalized deviation of 10.0%, maximum and minimum deviation of 5.0 and 13.0%, respectively.


INTRODUCTION
The use of fertilizers by means of irrigation water has been increasing in the irrigation districts due mainly to the increase of trickle systems and the positive effects of fertirrigation (Santana et al., 2006).Fertirrigation is being practiced without technical criteria in Brazilian irrigation districts with consequences in soil chemical properties such as transient salinity and leaching of íons with risk of groundwater contamination (Pinto, 2001).On the other hand, this technique has contributed for optimizing fertilizer use in irrigated agriculture (Oliveira & Villas-Boas, 2008).
An adequate fertirrigation is the one in which nutrients are applied at right moment according to crop needs.The soil chemical analysis demands long time since sampling in the field.The use of the soil solution might be a good alternative that provides the knowledge of ionic state of the soil solution in a short time.The soil solution may be an alternative for obtaining nutrient levels by laboratory analysis or by using kits for fast determination of levelsof these nutrients.Nutrient levels in soil solution may also be estimated by models from bulk electrical conductivity (ECw) or soil solution electrical conductivity (ECss) (Rhoades et al., 1976;Vogeler & Clotheir, 1996;Muñoz-Carpena et al., 2001;Santana et al., 2007).
Time domain reflectometry might be a feasible alternative in order to obtain a better precision of soil ion dynamics as for soil water dynamics (Nobório, 2001;Muñoz-Carpena et al., 2001) since it provides soil water content and bulk electrical conductivity data at different locations in the soil space along time.
This work had as objective to evaluate and validate a model for estimating potassium concentration in the soil solution as a function of bulk electrical conductivity (ECw), soil water content () and soil solution electrical conductivity (ECss) under field conditions.

MATERIAL AND METHODS
The work was carried out in the experimental area of Embrapa Cassava & Tropical Fruits, located at Cruz das Almas municipality, Bahia State, (12º 48" S, 39° 06" W, 225 m).The climate is classified as humid to sub humid.The soil is an Yellow Alic and Distrofic Latossol silty textured with 444 g kg -1 total sand, 131 g kg -1 silt, 425 g kg -1 clay, bulk density of 1.55 kg dm -3 , 0.23 m 3 m -3 soil water content at the superior limit of soil water availability and 0.16 m 3 m -3 for inferior limit of soil water availability for the Coastal Tablelands soils of Northeast Brazil.The chemical characteristics at the beginning of the experiment were: pH 6.3; 11.0 mg dm -3 -P; 0.06 cmol c dm -3 -K; 3.4 cmol c dm -3 -Ca + Mg; 0.09 cmol c dm -3 -Na; 1.32 cmol c dm -3 -H + Al; 3.56 cmol c dm -3sum of bases; CTC of 4.88 cmol c dm -3 ; 73% for base saturation.
The work was performed inside an experiment with banana crop, cv.Terra Maranhão in a 0.1 ha area to evaluate the effect of three irrigation water with different potassium chloride concentrations (1.0; 2.5 and 4.0 g L -1 ) on chemical soil attributes.Two irrigation systems considered were: micro sprinkler with 43.0 L h -1 emitter per four plants and drip with three 4.0 L h -1 emitters per plant in one lateral line per plant row.The amount of water per irrigation event was calculated based upon reference evapotranspiration and crop coefficients as recommended by Allen et al. (1998).Fertirrigation was applied every week and the injection solution was based on Borges & Caldas (2004).
A parametric model was fitted to data of soil water content and electrical conductivity as a function of potassium concentration.At least twenty different values of independent and dependent variables of the model were used in the optimization process.The optimization process was based upon minimization of the sum of square differences between observed and estimated dependent variables (objective function).

Model parameters for estimating electrical conductivity and potassium concentration in the soil solution
Experimental activity was carried inside banana crop where TDR probes and water samplers were installed in the soil at depths of 0.20 and 0.40 m at 0.30 m from plant between two emitters along lateral line (drip system) and between plant and emitter (micro sprinkler).TDR probes were installed at these locations for evaluating bulk electrical conductivity (ECw) and soil water content ().TDR probes of 0.10 m length were built (Silva et al., 2005) and soil water content was determined by Eq. 1 (Ledieu et al., 1986).Electrical conductivity of soil solution was estimated (Giese & Tiemann, 1975) and their values were corrected to 25 ºC temperature, according to Eq. 2 proposed by Richards (1954).0,1785 ECw 0,1138 θ  where:  -soil water content, cm 3 cm -3 ECw -soil bulk electrical conductivity Soil solution samples were collected at the same time of readings of ECw and , these readings were made every 15 min beginning at the suction application with a vacuum hand pump until soil solution be collected two hours after suction.Soil solution electrical conductivity (ECss) was measured by means of a desk conductivity meter and potassium concentration [K] was estimated by using a kit for quick determination (Card Horiba).The average reading of  and ECw taken during soil (1) (2) solution suction in water sampler, ECss and [K] data were related by mathematical models.The model of Vogeler & Clothier (1996) was used for estimating ECss as a function of ECw and  according to Eq. 3: where: ECss -soil solution electrical conductivity ECw -Soil bulk electrical conductivity a, b, c and d -parameters of Vogeler & Clothier (1996) equation The data of [K] and ECss were related by a potential function in order to yield ECss as a function [K]: The substitution of Eq. 4 in Eq. 3 resulted in the model:

Statistical evaluation of model performance
The adjustment of the mathematical model and data was accomplished by means of minimization of root square deviation among estimated and observed values.The statistical indices ME (mean errors), RMSE (root mean square error), d (Willmott agreement index) and R 2 (goodness of fit) were used for model evaluation.The root mean square error (RMSE) was defined by the equation: where: n -number of data Oi -measured value Ei -estimated value The absolute mean error (MEA) was calculated according to the equation: The normalized error mean (MEN) was also calculated: Borges et al. (2010) reported that these statistical parameters are good indicators for model efficiency.The units used for the deviations were the same as used in the evaluation of variables in order to facilitate interpretation of results (Legates & McCabe Jr., 1999).Also a regression analysis considering measured and estimated dependent variable with zero intercept was evaluated by the angular coefficient and goodness of fit.

Validation of the model under field conditions
Soil solution samples were collected every 15 days in each plot with three replications by using water samplers installed radially to the micro sprinkle at 0.30 m from plant at depths of 0.20 and 0.40 m during one cycle of banana crop.The water samplers were installed at 0.3 m from plant in the direction of plant-dripper at a fixed distance of 0.15 m from the dripper at two depths (0.20 and 0.40 m) with three replications.The porous cup of the sampler were located in the wetted volume between two drippers.
Water samples were colleted followed by a suction with a vacuum hand pump (-70 kPa) and the suction period lasted for two hours.Afterwards, soil solution samples were taken to laboratory and ECss and [K] were determined.Therefore, data of ECw, ECss and [K] were registered at an interval of 15 days during a whole banana cycle for the three irrigation waters with different potassium chloride concentrations (1.0; 2.5 and 4.0 g L -1 ).
Once the parameters for the models for estimating [K] as a function of ECw and [K] as a function of ECss and  were defined (Eq.5); the model was applied to the data of ECss, ECw and  which were collected every 15 days along the crop cycle.The efficiency of the model for estimating [K] concentration related to the measured concentrations along banana cycle was calculated by using Nash & Suttcliffe (1970) where: EF -efficiency of the model Oi -potassium measured Pi -potassium estimated Besides efficiency, RMSE and MEA were evaluated for comparing data of [K] observed in the field and estimated by modeling.Statistical analysis was made considering [K] observed along crop cycle and estimated at 0.30 m depth for the two irrigation systems by using the t test for comparing means of estimated and measured values.

Soil solution electrical conductivity as a function of bulk electrical conductivity and soil water content
Table 1 illustrates the adjustment of Vogeler & Clothier (1996) model to data of ECss as a function of ECw and  for 1.0, 2.5 and 4.0 g L -1 concentrations of K in water by micro sprinkler and drip irrigation.Results showed that 70, 78 and 93% of ECss variations were due to the variation of ECw and  for 4.0; 2.3 e 1.0 g L -1 concentrations, respectively, in drip system.These results were in agreement to the ones obtained by Silva et al. (2005), they verified that 92% of variation of ECss were due to variations of ECw and  in a similar study.Santana et al. (2006) noticed that the empirical model of Vogeler & Clothier (1996) resulted in best estimate of ECss as a function of ECw and  compared to other models, in which, 82.7% of ECss variations was explained by ECw e  variations.Vogeler & Clothier (1996) models fitted reasonably to the data of ECss as a function of ECw and  only for 4.0 g L -1 concentration.This result is in agreement to the ones of Santana et al. (2007), who observed that 79% of ECss variation was explained by variation of ECw and  using Vogeler & Clothier (1996) model for a loam soil.The minimum RMSE value and the smaller MEA, which indicate the best fitting of data to Eq. 3 was verified for the irrigation water concentration of 1.0 g L -1 for drip system.The ECss model underestimated the measured values for 1.0 g L -1 concentration in case of drip system and for 4.0 g L -1 in case of micro sprinkler.The model overestimated the measured values with small fitting coefficients in case of micro sprinkler.This result did not agree to the one verified by Santana et al. (2007).These authors found that ECss from the model underestimed the measured values by about 5%.

Potassium concentration as a function of bulk electrical conductivity and soil water content
Table 2 shows model parameters as a result of adjustment of Eq. 5 to potassium data as a function of ECw and .Also correlation and difference coefficients are shown in the same table for both drip and sprayer systems and considering the irrigation water concentrations.Eq. 5 explained 92.42; 81.52 and 84.29% of variations in [K] due to variations of ECw and  for water concentrations respectively of 1.0; 2.5 and 4.0 g L -1 , in case of drip system.These coefficients were near to the ones obtained by Santana et al. (2007), who noticed that 81% of variations of [K] were explained by variations of ECw and  in a sandy silty soil.The same occurred for sprayer system, i.e., the Eq. 5 explained 87, 84 e 80.1% of variation of [K] as a function of ECw and  for concentrations of potassium chloride in irrigation water of 1.0, 2.5 and 4.0 g L -1 .The results were in agreement to the ones of Santana et al. (2007), the model explained 81,78% of [K] as function of ECw and  in a sandy silty soil.
Treatments that showed the smallest value of RMSE were the ones that presented the largest goodness of fit as observed by Borges et al. (2010), except for the concentration of 2.5 g L -1 in micro sprinkler.Eq. 5 overestimated about 2.5% the measured values of [K] for concentrations of 4.0 g L -1 in drip system and about 1.4% the measured values for 2.5 g L -1 concentration in micro sprinkler, however the model underestimated measured [K] values in the range of 1.16 to 1.45% for the other irrigation water concentrations in both irrigation systems.
The goodnes of fit for relations K es = b K med (K es -estimated potassium concentration and K med -measured concentration) for all irrigation water concentrations were larger than those obtained by Santana et al. (2007), who worked with different models for estimating [K] and obtained 74% of [K] variations explained by ECw and  variations.There was statistical difference of deviation modules between the averages of measured and estimated [K] by the t test, considering the three concentrations of irrigation water.Only the average deviation (1) Parameters of Vogeler & Clothier (1996) equation for estimating ECss (soil solution electrical conductivity) from ECw (bulk electrical conductivity) and  (soil water content); (2) R 2 -goodness of fit; (3) RMSE -root mean square errors; (4) MEA -mean absolute errors;   for 1.0 g L -1 potassium chloride concentration of irrigation water in drip system and for 4.0 g L -1 in micro sprinkler.The model overstimated measured values with poor fit to data for the other concentrations in case of sprinkler.2. Eq. 5 showed larger performance coefficients for estimating potassium ion concentration compared to Eq. 3 for estimating ECss.
3. Eq. 5 showed efficiencies ranged from 0.89 to 0.97 for all concentrations of irrigation water potassium chloride, with mean variation of normalized errors of 5 to 13% in both irrigation systems.

Table 1 .
Vogeler & Clothier (1996)othier (1996)model as a result of fitting the model to data of ECss as a function of ECw and  and statistical coefficients for the different potassium chloride concentrations, considering micro sprinkler and drip irrigation systems

Table 2 .
Parameters of Eq. 5 as a result of fitting the model to data of [K] as a function of ECw and  and statistical coefficients for the different potassium chloride concentrations, considering micro sprinkler and drip irrigation systems