Comparison of four steady-state models of increasing complexity for assessing the leaching requirement in agricultural salt-threatened soils

Irrigation scheduling in salt-threatened soils must include an estimation of the leaching requirement (LR). Many models have been developed over the last 40 years for assessing the LR, and they should be compared on common grounds to guide potential users. The LR for salts (LRY), chloride (LRCl) and SAR (LRSAR) and therefore the eventual LR was assessed with simple equations and three steady-state computer models of increasing complexity, WATSUIT, SALSODIMAR and SALTIRSOIL. These models were assessed in 30 scenarios characterised by different crops and water qualities in the irrigated area of the Vega Baja del Segura (SE Spain). The simple equations, WATSUIT and SALTIRSOIL calculated quite similar eventual LRs, which were between < 0.01 and > 0.99 depending on crop species and water quality. The SALSODIMAR gave remarkably higher eventual LRs (between 0.31 and > 0.99). This occurred because SALSODIMAR uses the hypothesis that the saturation extract is more concentrated than the drainage water, contrary to what is assumed by the simple equations or calculated by WATSUIT and SALTIRSOIL. Rainfall, which is not taken into account by the simple equations and WATSUIT, and soil calcite weathering, which is not taken into account by SALSODIMAR, were revealed, respectively, as important and very important aspects to be included in steady-state models. Although the SALTIRSOIL appears to be the most complete model, the simple equations give acceptably similar irrigation doses for many of the situations considered in this study. Irrigation doses lower than presently used could be profitably applied in the Vega Baja del Segura. Additional key words: irrigation scheduling; SALSODIMAR; SALTIRSOIL; Segura River Lowland; WATSUIT.

Comparison of four models for assessing the leaching requirement in salt-threatened soils irrigation water, and the critical soil average saturation extract EC beyond which crop yield excessively declines, that is, crop yield falls below a limit (Y ).
However, this equation is strictly valid provided several assumptions are met, which are, more or less matched depending on the particular characteristics of the irrigation project.The most important are the following: i) steady-state movement of water and salts through soil, ii) negligible amount of rainfall compared to irrigation, iii) neither precipitation of salts nor weathering of soil minerals, iv) total mixing of the infiltrating water with the soil solution, that is, no by-pass flow, and v) bijective and linear relationship between electrical conductivity and salinity.
Several models of increasing complexity appropriate for situations in which one or more of the previous assumptions fail have been developed from the mid-1960s onwards.Specifically, the steady-state assumption has been the most controversial, and this has led to the development of transient models (Corwin et al., 2007;Letey et al., 2011).These usually provide more precise predictions of soil salinity than steady-state models.However, transient models also require data that are difficult to obtain, which limits their applicability to research purposes.As a consequence, the traditional LR model is still used and recommended for irrigation management worldwide, largely supplementing crop water requirement models.The only practical alternatives are steady-state models that overcome one or more of the other four assumptions (ii to v) upon which the traditional LR model is based.

Introduction
In irrigated areas, the control of soil salt build-up is essential to guarantee sustainable agriculture.When changing to a safer water supply is not possible, the primary method used to control soil salinity is to leach the soil salts with an excess of percolating water.Achievement of this objective demands application of water in excess of that required by the crops and, more importantly, the installation and maintenance of drainage systems to collect and dispose of the excess percolating water.The provision of capable drainage systems is essential where one or both of the following situations exist: i) shallow water tables, and/or ii) surface irrigation systems.These two characteristics, in addition to the aggravating factor of clayey soils, are commonly present in alluvial flat bottom areas, such as the Vega Baja del Segura (SE Spain).
Over-irrigation and drainage have been performed in many agricultural areas, providing farmers control over soil salinity.However, uncontrolled over-irrigation is no longer possible because of the growing lack of water, difficulties for drainage disposal, losses of nitrogen from soils and concomitant pollution (Tanji & Kielen, 2002).It is necessary to know precisely how much water in excess of the crop requirement is needed to leach the soil salts while preserving the environment.This demands the calculation of the leaching requirement (LR).
The fraction of the infiltrating water (i.e., rainfall (R) plus irrigation (I)) that passes through the root zone is known as the leaching fraction (LF) and is expressed as LF = D / (I + R), where D is drainage.The LR is defined as the minimum LF required to keep the soil salinity below a critical value that would otherwise excessively reduce crop yield.Expressing water salinity in terms of electrical conductivity (EC) and ignoring rainfall, the LR is usually calculated with the following formula (Eq.[1], Rhoades, 1974), where EC iw and EC se (Y ) stand, respectively, for the EC of the SALTIRSOIL.La lluvia, que no es tenida en cuenta en las ecuaciones sencillas ni en WATSUIT, y la disolución de calcita del suelo, que no es tenida en cuenta por SALSODIMAR, se revelaron, respectivamente, como aspectos importantes y muy importantes a tener en cuenta en los modelos de estado estacionario.Aunque SALTIRSOIL resulta el modelo más completo, las ecuaciones sencillas dan riegos aceptablemente similares para muchas de las situaciones consideradas en este estudio.Riegos inferiores a los que se utilizan actualmente en la Vega Baja del Segura se podrían aplicar productivamente.
Palabras clave adicionales: programación de riegos; SALSODIMAR; SALTIRSOIL; Vega Baja del Segura; WATSUIT.traditional LR equation.They all are steady-state models, which data needs increase gradually starting from the traditional LR model in the sequence WATSUIT < SALSODIMAR < SALTIRSOIL, but without being onerous to fulfil.
The objectives of this investigation were i) to evaluate the adequacy of the traditional LR model for estimating the leaching requirement in comparison to the steadystate models WATSUIT, SALSODIMAR and SALTIR-SOIL by searching for differences, measuring the magnitude of the differences, and understanding the reasons behind them, and ii) to discuss the implications these findings could have for developing irrigation recommendations for traditionally irrigated salt-threatened areas and particularly the Vega Baja del Segura (SE Spain).

Assessment of the maximum permissible salinity for a given crop
According to the three-piece linear (threshold-slope) function model, the yield (Y(%)) of most crops decreases from a threshold electrical conductivity value (EC t ) as a linear function of soil saturation extract electrical conductivity (Eq.[2]).The EC t and the slope of the line (s) are characteristics of each crop (Maas & Hoffman, 1976).

 
With the selection of a minimum crop yield (Y(%)), the corresponding maximum permissible EC se(Y) can be calculated with the reciprocal form of Eq. [2].The target EC se(Y) can be subsequently substituted in Eq. [1] for the calculation of the corresponding LR Y .

The traditional LR model and extensions for chloride and SAR control
The traditional LR model starts from Eq. [3] where EC dw(Y) is the critical drainage water EC from which crop yield excessively declines.

LR EC EC
According to the steady-state hypothesis, the salinity of the soil solution increases as depth increases, while the soil water content is constant.Under such conditions, the EC of the drainage water (EC dw ) in Eq. [3] represents the maximum soil solution EC (EC ss ) to which the plant roots are likely to be exposed.A more reasonable assumption is that the plant responds mainly to the average soil solution EC (EC ss ).Therefore, EC dw was related to EC ss by Rhoades (1974), who proposed an empirical expression (Eq.[4]), where, for convenience, EC ss was substituted by the average saturation extract critical EC beyond which crop yield falls below Y (EC se (Y ) ).
The substitution of Eq. [4] in Eq. [3] led to what has been called the traditional model for the LR calculation (Eq.[1]).
Apart from salt stress, crops are sensitive to particular ions and solutes such as chloride, sodium and boron.Toxicity to chloride has been studied particularly in the case of citrus, which can withstand, without experiencing leaf burn, no more than 10 to 25 mmol L -1 of chloride in the saturation extract ([Cl -] se ) depending on species (Ayers & Westcot, 1985).Providing chloride is readily mobile in the soil under the influence of water, the traditional LR model (Eq.[1]) can be extended to calculate the LR for chloride (Eq.[5], Ayers & Westcot, 1985).
Waters high in sodium with regard to calcium and magnesium increase the soil solution sodium adsorption ratio (SAR), defined as SAR = [Na + ] / ([Mg 2+ ] + [Ca 2+ ]) 1/2 .Comparison of four models for assessing the leaching requirement in salt-threatened soils Increments in the soil solution SAR can on the one hand, cause toxic effects on plants, and on the other hand, increase the soil exchangeable sodium percentage (ESP), which in turn can severely reduce the soil hydraulic conductivity (HC) depending on the soil solution overall salinity.Low HC is favoured by high SAR, in addition to low overall salinity of the soil solution.However, the SAR may also be controlled achieving a minimum LF, that is, a LR (Rhoades, 1968).
The traditional LR model was extended to calculate the LR for SAR control (LR SAR ) by combining the traditional LR model (Eq.[1]) with the calculation of the adjusted SAR according to Suarez (1981).The LR SAR to achieve a target SAR in the saturation extract (SAR se ) is thus obtained by solving the following second order equation (Eq.[6]) for the plus sign where all concentrations in the irrigation water ([Mg 2+ ] iw and [Na + ] iw ) are expressed in mmol L -1 and SAR in (mmol L -1 ) 1/2 .
In Eq. [6], [Ca 2+ ] eq is the calcium concentration at equilibrium with calcite and the carbon dioxide partial pressure in the saturated extract (pCO 2 ).This calcium concentration is calculated with the following metamodel based on the work of Suarez (1981), where EC iw is in dS m -1 , calcium ([Ca 2+ ] iw ) and alkalinity ([Alk] iw ) concentrations in the irrigation water are in mmol L -1 and meq L -1 respectively, and pCO 2 is in atm (Eq. [7]

WATSUIT
The calcite equilibrium in the soils where its existence or precipitation is feasible has a remarkable influence not only on the value of the SAR, but also on its overall salinity.In addition to calcite, gypsum is another mineral the precipitation or weathering of which can have a profound effect on soil salinity and SAR.WATSUIT extends the capabilities of the traditional LR model by taking into account the possibilities of calcite and gypsum precipitation and weathering.
Given a user-selected leaching fraction (LF), the WATSUIT model calculates the concentration factor of the soil solution at field capacity (f d ) for five different depths d or nodes, from the surface (d = 0) to the bottom (d = 4), according to a 40:30:20:10 plant water uptake pattern (Eq.[8]).
Next, the model multiplies the composition of the irrigation water (Na + , K + , Ca 2+ , Mg 2+ , Cl -, alkalinity and SO 4 2-concentrations) by each concentration factor (f 0 , f 1 , etc).Provided built-in carbon dioxide partial pressures (pCO 2d ), WATSUIT solves for the composition at the chemical equilibrium at each depth by means of a semi-thermodynamic equilibrium module allowing for calcite and gypsum precipitation and, optionally, weathering.Next, it calculates the corresponding soil solution ECs at each depth d (EC d ) by means of the model by McNeal et al. (1970).Finally, the depth average values of EC, SAR and chloride concentration at field capacity (EC fc , SAR fc and [Cl -] fc , respectively) are calculated with Eq. [9], where P fc stands for the property of interest.
The average values for the saturation extract must be calculated separately.A proportionality factor of ½ is usually used in this regard (P sat = ½ P fc ; Rhoades et al., 1992).

SALSODIMAR
Similarly to the WATSUIT model previously described, SALSODIMAR also considers the composition of the irrigation water and the possibility of calcite and gypsum precipitation, although not weathering, from the soil solids.Furthermore, it includes a factor for leaching efficiency.
The calculation of the LR for salts starts from Eq. [3] but it considers the main soluble cations instead of EC as the measure of salinity as expressed by Eq. [10], where TS iw and TS dw are the sum of Na + , Ca 2+ and Mg 2+ concentrations in meq L -1 in the irrigation and drainage water, respectively.
Next, the main assumption of SALSODIMAR is that the sum of cations in the saturation extract (TS se ) is related to that of the drainage water (TS dw ) by Eq. [11], where F is labelled as a parameter of leaching efficiency bounded between 0 and 1 (0 < F ≤ 1).Its specific value depends mainly on soil texture and irrigation method: medium to coarse soils have F values between 0.6 and 1, and medium to fine soils lower than 0.6 (Van Hoorn & Van Alphen, 1994;Pla, 1996).Regardless of the texture, F decreases with surface irrigation and increases with drip and sprinkler irrigation (Van Hoorn & Van Alphen, 1994).
The likely precipitation of calcite, gypsum and also magnesian calcite is taken into account by subtracting adequate quantities (Table 1) from TS iw and TS se respectively, giving the general expression upon which the SALSODIMAR leaching requirement calculation for soil salinity is based (Eq.[12]): Similarly to the LR Y , the LR for chloride toxicity is calculated by SALSODIMAR with Eq. [13] regardless of precipitation.
The LR for SAR (LR SAR ) is calculated by SALSODI-MAR starting from the following equation: LR SAR = SAR2 iw /SAR 2 se , which is the one specifically used when no mineral precipitates (case a, Table 1).When precipitations occur (cases b, c, d, e, Table 1), the SAR of the irrigation water (SAR iw ) and the target SAR of the saturated extract (SAR se ) are corrected similarly to what has been previously shown (Eq. [12] and Table 1).This gives a particular formula for the LR SAR calculation for each precipitation case (Pla, 1988).

SALTIRSOIL
SALTIRSOIL shares the foundations of the WAT-SUIT but extends its calculation capabilities.SALTIR-SOIL carries out a monthly multilayer soil water balance from climate, soil, crop and irrigation management data.From this balance, SALTIRSOIL calculates an average soil solution concentration factor at field capacity (f fc ) by means of Eq. [14], where I and R are the irrigation and rainfall in mm yr -1 , ET j is the actual evapotranspiration from the soil layer j also in mm yr -1 and n is the number of soil layers or nodes in which the soil is conceptually split.
From f fc and the soil water contents at field capacity and at saturation, SALTIRSOIL calculates the soil solution concentration factor at saturation (f sat ).The irrigation water composition (Na + , K + , Ca 2+ , Mg 2+ , Cl -, NO 3 -, SO 4 2-and alkalinity) is multiplied by f sat to obtain a soil solution away from equilibrium.These data are the inputs to a semi-thermodynamic equilibrium module that calculates the saturation extract composition Comparison of four models for assessing the leaching requirement in salt-threatened soils at equilibrium with the mean soil pCO 2 and allows for calcite and gypsum precipitation and weathering.Finally, the EC is calculated with the equation developed by Visconti et al. (2010).

Simulation area
The Vega Baja del Segura (SE Spain) is a very important agricultural area where approximately 80% of the irrigated soils are salt-affected (de Paz et al., 2011).The main crops (Visconti, 2009) that cover 61% of the irrigated area are citrus such as orange, mandarin and Verna lemon grafted onto various different rootstocks.The moderately salt-tolerant Sour Orange and especially Cleopatra mandarin are used as rootstocks for more than 60% of citrus.Vegetables (including tubers) cover 16% of the area.These are globe artichoke, lettuce, melon, broccoli, and potato.Non-citrus fruit trees cover 12% of the area, specifically almond, pomegranate and date palm.All crops grown in the area, but especially date palm, pomegranate and globe artichoke, are more or less tolerant to salinity (Table 2).
The average Penman-Monteith reference evapotranspiration and precipitation in the period of 2007-2009 were 1215 and 385 mm yr -1 , respectively.The main irrigation water supply in the area is the Segura River.Since the early 1980s, water from the Tajo-Segura transfer has also been available for some farmers.
Beginning in 2011, up to 40 hm 3 yr -1 of desalinated water will be available for irrigation by the Sindicato Central de Regantes del Acueducto Tajo-Segura (Tajo-Segura Aqueduct Irrigators Union) (MMA, 2006).Although new irrigation projects use drip systems, at least 50% of the area is still irrigated by surface (Visconti, 2009).

Set up of simulations
Ten crops, namely i) globe artichoke, ii) cantaloupe melon and broccoli rotation, iii) cantaloupe melon and potato rotation, iv) date palm, v) orange, vi) Verna lemon grafted onto sour orange, vii) Verna lemon grafted onto Cleopatra mandarin, and viii) Verna lemon grafted onto Citrus macrophylla, ix) nongrafted Verna lemon, and x) pomegranate, were combined with three different water supplies, the Segura River, Tajo-Segura transfer and desalinated water, to simulate 30 scenarios.These crops and crop rotations exhibit different salt tolerances and were selected to be representative of at least 75% of the irrigated area.The LR Y values were calculated for 90% potential yield (Table 2).The water quality data (Table 3) for the Segura River and Tajo-Segura transfer are average values for the river and transfer, respectively, in the area for the years 2007-2009 (Confederación Hidrográfica del Segura).The desalinated water characteristics are from a reverse osmosis desalination plant with treatment for boron removal located on the Mediterranean coast of Spain (Hernández-Suárez, 2010).The soil data (Table 4) A leaching efficiency (F) equal to 0.6 was selected for the SALSODIMAR simulations according to the soil texture and the predominant surface irrigation.

Calculation of leaching requirements and irrigation doses
As management oriented models, both the traditional LR model with extensions and SALSODIMAR calculate the LR as their key output.Moreover, SAL-SODIMAR calculates the irrigation and drainage volumes required to fulfil the LR provided that the crop evapotranspiration and rainfall are known.As more predictive oriented models, WATSUIT and particularly SALTIRSOIL, do not calculate the LR per se.
In the case of WATSUIT, the user calculates the soil solution EC caused by different leaching fractions (LFs).Then, the LR is taken equal to the LF that produces the target value of soil solution EC.Next, the irrigation doses have to be assessed separately, which include the crop evapotranspiration calculations.
The use of SALTIRSOIL to calculate the LR is similar to WATSUIT, except that the LF is a model output jointly with the soil solution salinity.In this case, the user tests some irrigation volumes instead of some LFs.When, instead of EC, the SAR or chloride are the parameters of interest, the procedure is the same but then logically searching for a target SAR or [Cl -] respectively.In SALTIRSOIL, the irrigation doses are calculated with the dual crop coefficient paradigm (Allen et al., 1998) using appropriate monthly basal crop coefficients (Table 5).For the vegetable crops, these were assessed on basis usual planting and harvest dates in the area: artichoke from October 1 st until July 8 th , melon from April 1 st until August 19 th , broccoli from September 14 th until January 27 th and potato from September 14 th until January 22 nd .

Traditional LR model extended for chloride and SAR control
The LR Y values for the Segura river water were between 0.17 and 0.52 for vegetable crops and between 0.15 and > 0.99 for tree crops (Table 6).The lower limit in each group corresponded to the most tolerant crop, that is, artichoke and date palm with EC 90 equal to 5.8 and 6.8 dS m -1 , respectively.The higher limit corresponds to the most sensitive crops, that is, potato and lemon tree grafted onto C. macrophylla with EC 90 equal to 2.5 and 1.7 dS m -1 , respectively.Citrus are known to be sensitive to soil salinity.However, the differences among rootstocks are reflected in the LR Y values, for example, the lower LR Y was 0.44 and corresponded to lemon grafted onto Cleopatra mandarin, which exhibited an EC 90 of 2.8 dS m -1 .The maximum chloride concentrations in mmol L -1 for the citrus trees are 10 for orange, 15 for lemon grafted onto sour orange and also non-grafted lemon tree, and 25 for lemon grafted onto Cleopatra mandarin (Ayers and Westcot, 1985).These differences gave rise to remarkable differences in LR Cl , which ranged from 0.83 for the most sensitive to 0.22 for the least.A SAR up to 10 (mmol L -1 ) 1/2 may be permissible at whatever the expected soil solution EC attainable with the Segura water.This produced a LR SAR equal to 0.14.As expected, when the Tajo-Segura transfer was the water supply, all LRs were lower.The LR Y was between 0.04 and 0.11 for vegetable crops and between 0.04 and 0.17 for tree crops.For citrus, the LR Cl was always below LR Y and, although the maximum permissible SAR with this water was 7 (mmol L -1 ) 1/2 , the LR SAR was even lower than before (0.02).
As expected, when irrigating with desalinated water, all LR Y values decreased compared to the Tajo-Segura.However, the LR Cl increased because the desalinated water is higher in chloride than the Tajo-Segura (Table 3).Furthermore, the maximum permissible SAR of 7 (mmol L -1 ) 1/2 and the high SAR of the desalinated water (Table 3) produced a LR SAR equal to 0.08, which was higher than the previous value.This increment was expected because of the high SAR of the desalinated water (Table 3).

WATSUIT
The LR Y values for the Segura water were between 0.13 and 0.79 for vegetables and between 0.09 and > 0.99 for trees (Table 6).When the target EC (EC 90 ) was higher than 4.8 dS m -1 , WATSUIT gave lower LR Y values than the traditional model, whereas the opposite occurred when the target EC was lower than 4.8 dS m -1 (Fig. 1a).The LR Cl values for citrus were between 0.27 and > 0.99, all higher than those calculated with the traditional model.Similarly to the LR Y calculation, WATSUIT gave higher LR Cl values than the extended traditional model when the target [Cl -] se was under 38 mmol L -1 , which is common for all citrus (Fig. 1g).The LR SAR was 0.08, lower than the LR SAR calculated with the extended traditional model.
For the Tajo-Segura water, the LR Y values were between < 0.01 and 0.04 for vegetables and between < 0.01 and 0.11 for trees.These values are lower than those calculated with the traditional model.For the Tajo-Segura water, WATSUIT gives lower LR Y values than the traditional model when the target EC is higher than 1.2 dS m -1 (Fig. 1b).The LR Cl values were between 0.01 and 0.05.In contrast to what occurred with the Segura water, the LR Cl values were lower than those calculated with the traditional model.This is because for a target [Cl -] se over 7 mmol L -1 , which is surpassed by all citrus, the LR Cl calculated with WATSUIT is lower than the LR Cl calculated with the traditional model (Fig. 1h).The LR SAR was lower than 0.01 and, therefore, lower than the LR SAR calculated with the extended traditional model.
For the desalinated water, the LR Y values were between < 0.01 and 0.02 for vegetables and between < 0.01 and 0.03 for trees.They were again lower than those calculated with the traditional model.Over a target EC of 1.2 dS m -1 , WATSUIT gave lower LR Y values than the traditional model with this water (Fig. 1c).The LR Cl values were between 0.02 and 0.08 and were lower than those calculated by the traditional model.The LR SAR was equal to 0.06, again lower than the value calculated with the traditional model.For a target SAR over 5 (mmol L -1 ) 1/2 , the WATSUIT model calculated lower LR SAR than the extended traditional model (Fig. 1f).

SALTIRSOIL
The LR Y values with the Segura water were between 0.10 and > 0.99 for vegetables and between 0.09 and > 0.99 for trees (Table 6).Only artichoke, melon and broccoli rotation, date palm and pomegranate presented LR Y values under 0.99.The LR Y values corresponding to artichoke (0.10), date palm (0.09) and pomegranate (0.25) were slightly lower than those calculated with WATSUIT, which were 0.13, 0.09 and 0.27, respectively.On basis the SALSODIMAR simulations, the LR Y values were all over 0.99.The LR Y values calculated with SALTIRSOIL led to irrigation doses of 368, 746 and 593 mm yr -1 , respectively (Table 7), which are reasonable values.The LR Y values calculated with SALTIR-SOIL for the other crops were higher than 0.99, that is, the same as those calculated with SALSODIMAR.The LR Cl values were between 0.10 and > 0.99, this latter corresponding to the least tolerant orange.These LR Y were, with the exception of orange, well under the corresponding values calculated with WATSUIT.The LR SAR for a target SAR of 10 (mmol L -1 ) 1/2 was between < 0.01 and 0.05, that is, lower than the values calculated with WATSUIT (0.08) and remarkably lower than those calculated with SALSODIMAR (0.67).
For the Tajo-Segura water, the LR Y values were between < 0.01 and 0.10 for vegetables and between < 0.01 and 0.50 for trees.The LR Y values obtained for artichoke, melon and broccoli, date palm, pomegranate, non-grafted lemon and lemon grafted onto Sour Orange and Cleopatra mandarin are very similar to the LR Y values obtained with WATSUIT, with differences less than 0.03.The LR Y values obtained for melon and potato and orange tree were more similar to the values obtained with the traditional The LR Cl values obtained with SALTIRSOIL and SALSODIMAR were again very different, ranging from 0.22 to 0.51.The LR SAR for a target SAR of 7 (mmol L -1 ) 1/2 was less than 0.01 which matches the LR SAR obtained with WATSUIT and was remarkably lower than the value calculated with SALSODIMAR (0.11).
For the desalinated water, the LR Y was between < 0.01 and 0.04 for vegetables and between < 0.01 and 0.08 for trees.Again, the LR Y values obtained for seven crops (artichoke, melon and broccoli, date palm, pomegranate, non-grafted lemon and lemon grafted onto Sour Orange and Cleopatra mandarin were very similar to the LR Y values obtained with WATSUIT, with differences less than 0.03.The LR Y for the other three crops were more similar to the LR Y obtained with the traditional model, with differences of less than 0.02.The corresponding differences with the LR Y values obtained with the SALSODIMAR were within 0.11 and 0.33.The LR Cl values were between < 0.01 and 0.07, which were between 0.03 and 0.01 lower than those obtained with WATSUIT and between 0.32 and 0.72 lower than those obtained with SALSODIMAR.The LR SAR for a target SAR se of 7 (mmol L -1 ) 1/2 was between < 0.01 and 0.02, which was somewhat lower than the LR SAR calculated with WATSUIT and the extended traditional model.These values were very far from the SALSODI-MAR result (> 0.99).

Discussion
Generally, the saturation extract electrical conductivity simulated by the four models decreases with the LF, at first steeply and then more softly before becoming almost flat (Fig. 1a,b,c).From a point that depends on the salinity of the irrigation water, progressive increments of the LF hardly decrease the soil salinity.Although this general trend is followed by every model, there are differences among them concerning the specific magnitudes involved.The SALSODIMAR model gives remarkably higher LFs than the other three models for any water quality and EC.Therefore, the differences between the LR values calculated with SAL-SODIMAR and the other three models decrease as function of the EC of the irrigation water.
According to the SALSODIMAR model, the relationship between the drainage water and saturation extract salinities is given by a parameter labelled as leaching efficiency F (Eq. [11]).Because this parameter is a positive value never higher than 1, the drainage water is, by definition, less saline than the saturation in SALSODIMAR.In the other three models, this relationship is provided empirically (traditional LR; Eq. [4]) or by calculation (WATSUIT and SALTIRSOIL).Whatever the particular method, and contrary to SAL-SODIMAR, the drainage water is always more saline than the saturation extract in the three other models, that is, the quotient EC dw / EC se is variable and never less than one.Specifically, this quotient is never less than 4.3, 4.7 and 1.7 for the Tajo-Segura transfer water according to the traditional LR, WATSUIT and SALTIR-SOIL models, respectively (Table 8).Similar values for are obtained with the Segura and desalinated waters.
In Figure 1 (d to f), we observe similar graphs, although SAR is the variable on the ordinate axis rather than EC.As for EC, the SAR decreases steeply at low LFs and then progressively flattens as LF approaches one.Again from a point, SAR hardly decreases with the LF.All four models follow similar trends.The corresponding lines for the traditional LR, WATSUIT and SALTIRSOIL remain very close and cross each other.However, the SALSODIMAR line is very far apart, that is, it gives remarkably higher LR SAR for any water quality and target SAR.As previously indicated, in SALSODIMAR, the saturation extract is more saline than the drainage water by definition, which explains part of this behaviour.However, with SAR, higher differences between SALSODIMAR and the other models are found when considering desalinated water, and not the more saline Segura river water.
The desalinated water is characterised by very low calcium and relatively high sodium, which results in a high SAR.It is also undersaturated regarding calcium carbonate and, consequently, tends to dissolve calcite from soil solids (Hernández-Suarez, 2010).The soils from the Vega Baja del Segura are very high in the calcium carbonate equivalent (Table 4), and the weathering of some little calcite compensates for the initial lack of calcium in the desalinated water.The extended traditional LR, WATSUIT and SALTIRSOIL models include the weathering of calcite, and therefore, they calculate low LRs for SAR control in soils irrigated with desalinated water.However, SALSODIMAR only takes account of calcite precipitation, not weathering, giving rise to very high, and in fact unattainable, LRs for SAR control using desalinated water.
The traditional LR, WATSUIT and SALTIRSOIL models are very similar.However, for SALTIRSOIL, both EC and SAR change faster with LF at low LFs and slower at medium and high LFs, that is, the SAL-TIRSOIL line is the steepest.Following SALTIRSOIL, there is WATSUIT and finally the traditional LR, which gives softer transitions from low to high LFs.As a consequence, SALTIRSOIL gives the lowest LR Y values for target ECs higher than approximately 1.5 times the irrigation water EC and the highest for much lower target ECs.The LR Y values calculated on the basis of transient-state models are usually lower than those calculated on the basis of steady-state models (Letey et al., 2011).The refinements introduced in SALTIR-SOIL have been sufficient to have lower LR values than those usually calculated with other steady-state models and, specifically, the traditional LR model.
SALTIRSOIL takes into account the rainfall, whereas the traditional LR and WATSUIT do not.Under Mediterranean climate conditions, rainfall is seldom negligible when compared to irrigation, so it should be included in the LR assessment.This is shown by using the following two equations (Eq.[15] and Eq.[16]), together with the traditional LR model: If the non-linear system of three equations, [1], [15] and [16], is solved for every scenario, between 34 and 63% lower LR Y values than those obtained with the traditional LR model alone are obtained.These differences are similar to those produced by the inclusion of soil calcite and gypsum precipitation and weathering into steady-state models (Corwin et al., 2007).
As we observe in the graphs of chloride against LF (Figs. 1g,h,i), SALTIRSOIL gives somewhat lower LR Cl at high [Cl -] se than WATSUIT, which follows the behaviour of LR Y and LR SAR .However, the differences between both models almost disappear as LF increases.At low LF, the magnitude of the irrigation water is similar to that of the rainfall and, therefore, the inclusion of this variable in SALTIRSOIL and not WAT-SUIT makes a difference between these models when compared with the traditional LR model.Nevertheless, as LF increases, the irrigation increases and for medium to high LFs, the LR Cl calculated with both models is almost the same.The calculation methods for the average concentration factor at field capacity in WATSUIT and SALTIRSOIL (Eqs.[8], [9] and [14]) are therefore very similar, and thus the different results for LR Y and LR SAR (Fig. 1a to 1f) could only be explained by either the different way in which the calcite and gypsum equilibria are included in the models or by the different conversion of concentrations at field capacity to saturation.
In WATSUIT, the carbon dioxide partial pressures (log pCO 2 ) at the five different depths from top to bottom are -2.99,-2.20, -1.74, -1.54 and -1.39 atm, with a mean of -1.97, which is lower than the log pCO 2 used in SALTIRSOIL that is equal to -2.43 atm.This elevated pCO 2 along with the higher calcite solubility products (pKs) used in WATSUIT (from top to bottom 8.12, 8.22,    et al., 1992).This conversion has little effect on ions not controlled by any equilibrium but it has a profound effect ions such as calcium, the concentration of which is strongly dependent on calcite equilibrium.As we observe in Table 9, this makes the calcium concentration to have half the value it has at equilibrium.Thus, its concentration is underestimated, and the SAR is concomitantly overestimated.Similar reasons apply for the underestimation of the EC.
The eventual LR recommendation is given by the maximum value among LR Y , LR Cl and LR SAR .However, SALTIRSOIL also calculates a LF caused by the crop water requirement (LF CWR ).This accounts for the minimum water loss produced by irrigation avoiding water stress.Therefore, the irrigation scheduling for each scenario has to be calculated based on the maximum value among LR Y , LR Cl , LR SAR and LF CWR .Taking 90% as the minimum profitable yield, the irrigation water demand in Vega Baja del Segura is between 368 and 1823 mm yr -1 for the Segura River, between 343 and 957 mm yr -1 for the Tajo-Segura transfer and between 340 and 660 mm yr -1 for desalinated waters (Table 7, last column).If the availability of irrigation water does not surpass 800 mm yr -1 (MMA, 1997), acceptable yields could have been obtained using Segura River water for the melon and broccoli, melon and potato, lemon grafted onto Sour Orange and Cleopatra mandarin with 86, 70, 79 and 80% yields, respectively.The irrigation doses calculated with the traditional LR model are, with the exception of saltsensitive crops, within -22 and 31% of those calculated with SALTIRSOIL (Table 7).The irrigation doses actually applied to citrus and pomegranate in the Vega Baja del Segura have been estimated to be approximately 1600 and 750 mm yr -1 , respectively (MAPA, 2004).Using rootstocks moderately tolerant to salinity, no more than 800 mm yr -1 would be necessary to have citrus yields of at least 80%, even with the salty Segura River water.The water requirements for citrus would further decrease to 500 mm yr -1 or less if using Tajo-Segura transfer or desalinated waters.For pomegranate, no more than 600 mm yr -1 would be necessary with Segura water and less than 450 mm yr -1 with Tajo-Segura and desalinated waters.

Conclusions
For the simulations performed in the Vega Baja del Segura the SALSODIMAR model gave eventual LRs higher than 0.99 with both the Segura River and the desalinated water and between 0.31 and > 0.99 for the Tajo-Segura transfer, which are remarkably higher than the eventual LRs calculated with the rest of models.Specifically, SALTIRSOIL gave eventual LRs between 0.09 and > 0.99 for the Segura water, between 0.01 and 0.50 for the Tajo-Segura transfer, and between 0.01 and 0.10 for the desalinated water.These differences occur mainly because, in SALSODIMAR, the saturation extract is more concentrated than the drainage water by definition, whereas in the other models, the opposite is either assumed (traditional LR) or calculated (WATSUIT and SALTIRSOIL).Furthermore, SALSODIMAR does not take into account the weathering of soil calcite, which remarkably decreases the SAR of infiltrating desalinated waters as revealed by the other three models.The traditional LR, WATSUIT and SALTIRSOIL models gave similar LRs.The differences were because of i) the rainfall variable, absent in the traditional LR and WATSUIT, and present in SALTIRSOIL, and ii) because WAT-SUIT calculates the calcite equilibrium for the soil solution at field capacity whereas SALTIRSOIL so does at saturation.Therefore, after using WATSUIT, the conversion of ion concentrations from field capacity to saturation underestimates the electrical conductivity and also calcium, which in turn overestimates the SAR.SALTIRSOIL seems to be the most complete model.Therefore, an irrigation dose was finally calculated for each scenario with SALTIRSOIL and compared to the traditional LR model.Despite the differences between the models, the irrigation doses were very similar except when salt-and chloride-sensitive crops are irrigated with waters of EC higher than 1.24 dS m -1 and high in chloride, respectively.The irrigation doses calculated with SALTIRSOIL were lower than the actual irrigation doses presently used in the Vega Baja del Segura.

Figure 1 .
Figure1.Graphs of electrical conductivity (a, b, c), sodium adsorption ratio (d, e, f) and chloride concentration (g, h, i) of the saturation extract against leaching fraction for Segura river, Tajo-Segura transfer and desalinated waters. ).

Table 1 .
Values of the k and w parameters of the SALSODIMAR model (Eq.[12])

Table 2 .
Threshold-slope values and saturation extract electrical conductivity for 90% yield Vega Baja typical clay loam soil sampled in 2006.The 2007-2009 climate data were taken from the records of three agricultural weather stations in the area, Almoradí, Catral and Orihuela -La Murada managed by the SIAR (Sistema de Información Agroclimática para el Regadío).

Table 3 .
Characteristics of the irrigation water supplies

Table 4 .
Soil characteristics of a typical calcaric fluvisol in the Vega Baja del Segura Comparison of four models for assessing the leaching requirement in salt-threatened soils

Table 5 .
Monthly basal crop coefficients used for SALTIRSOIL evapotranspiration assessment

Table 7 .
Irrigation doses (I mm -1 yr -1 ) calculated with all four models , with differences of less than 0.01.The LR Y values obtained with the SALTIRSOIL and SALSODIMAR models are very far apart from each other, with differences ranging from 0.31 to > 0.92.The LR Cl values were between 0.04 and < 0.01, which are no more than 0.02 lower than the corresponding values calculated with WATSUIT. model

Table 8 .
Electrical conductivity of the drainage water (EC dw ) and quotient EC dw /EC se for the Tajo-Segura transfer water Comparison of four models for assessing the leaching requirement in salt-threatened soils the quotient EC dw / EC se [Supplementary Table 1 (pdf)]

Table 9 .
Characteristics of soil solutions obtained with LF = 0.5 and the Segura river water as calculated by WATSUIT at field capacity (A), and then converted to saturation (B), and SALTIRSOIL directly at saturation (C)*