Characterization of subtropical soils by mineral magnetic measurements

Abstract

This paper reports the use of mineral magnetic measurement techniques to characterize the iron oxide assemblage within soils of varying parent material type and water regime from subtropical region in Zhejiang Province, China. Results show that dryland soils formed on Quaternary red clay, limestone, arenaceous shale, and diluvium, exhibit a distinct ferrimagnetic profile with a magnetic susceptibility (χ) enhancement in surface horizon. This enhancement is interpreted as being due to pedogenic superparamagnetic (SP) ferrimagnetic grains, which is supported by a higher frequency dependent susceptibility (χ_fd) values. The χ and χ_fd have highly significant positive linear relationship with dithionite‐citrate‐bicarbonate (DCB) extractable iron (Fed) content. The upper horizon of paddy soil has extremely lower χ and χ_fd values than dryland soils formed on the same parent material. Soil with poorly‐drained condition has distinctly lower absolute χ and saturation isothermal remanent magnetization (SIRM) value than associated well‐drained soil. It indicates that reduction state is an important factor responsible for loss of SP ferrimagnetic minerals in soils.     

Evaluating soil salinity status from bulk electrical conductivity and permittivity

In the range of volumetric water content, θ, from about 0.12 cm³ cm^–3 to saturation the relation between bulk electrical conductivity, C_b, and bulk electrical permittivity, ε, of mineral soils was observed to be linear. The partial derivative ?C_b/?ε appeared independent of the moisture content and directly proportional to soil salinity. We found that the variable X_s = ?C_b/?ε determined from in situ measurements of C_b(θ > 0.2) and ε(θ > 0.2) can be considered as an index of soil salinity, and we call it the ‘salinity index’. Knowing the index and sand content for a given soil we could calculate the electrical conductivity of the soil water, C_w, which is a widely accepted measure of soil salinity. The two variables from which the salinity index can be calculated, i.e. C_b and ε, can be read simultaneously from the same sensor by time-domain reflectometry. Quantities and symbols a constant /dS m^–1 b constant c constant /dS m^–1 C _b electrical conductivity of bulk soil /dS m^–1 C _b′ constant equal to 0.08 dS m^–1 C _s electrical conductivity of a solution used to moisten soil samples /dS m^–1 C _w electrical conductivity of soil water defined as the soil salinity /dS m^–1 C _wref reference salinity (that truly existing) resulting from the procedure of moistening samples, expressed as C_s + C_r/dS m^–1 C _r baseline value of C_s due to residual soluble salts present in the soil /dS m^–1 d constant D dry soil bulk density /g cm^–3 l slope r ratio S sand content /% by weight t time /s X _s salinity index /dS m^–1 X _si initial salinity index when distilled water is used to moisten soil samples /dS m^–1 Y a moisture-independent salinity-dependent variable /dS m^–1 z coordinate along direction of flow of the soil solution ε′ constant equal to 6.2 ε relative bulk electrical permittivity (dielectric constant) of the soil θ volumetric water content determined thermogravimetrically using oven-drying /cm³ cm^–3     

Determination of chemical transport properties for different textures of undisturbed soils

Agrichemicals usually contaminate groundwater via preferential flow, therefore determination of the preferential flow characteristics of soil is needed. One model that predicts solute transport due to preferential flow is the mobile–immobile (MIM) solute-transport model, which partitions total water content (θ; m³ m^?3) into mobile (θ_m) and immobile fractions (θ_im). In undisturbed soils, a method is proposed for determining the MIM model parameters, i.e. immobile water fraction (θ_im), mass transfer coefficient (α) and hydrodynamic dispersion coefficient (D _h). Breakthrough curves were obtained for five different soil textures in three replicates, by miscible displacement of Cl^? in undisturbed soil columns. Cl^? breakthrough curves were evaluated in terms of the MIM model. Analysis suggests that the values of D _h and α increased with lighter soil textures and θ_im increased with heavier soil textures. The values of θ_im ranged from 5.31 to 14.28% in different soil textures. Furthermore, values of θ_im were found to be related to soil clay content. Values of α ranged from 0.0257 to 0.32 h^?1 and values of D _h ranged from 0.36 to 11.2 cm² h^?1 in different soil textures. A significant linear correlation was obtained between α, θ_im, D _h and soil saturated hydraulic conductivity (K _s) and pore water velocity (v). A multivariate pedotransfer function was developed to estimate α, θ_im and D _h based on the geometric mean (d _g) and the standard deviation (σ_g) of the diameter of soil particles and soil organic matter content. The pedotransfer functions for D _h, θ_im and α were validated by independent data sets from other investigators.     

Influence of temperature and drought on seasonal and interannual variations of soil, bole and ecosystem respiration in a boreal aspen stand

Continuous half-hourly measurements of soil (R_s) and bole respiration (R_b), as well as whole-ecosystem CO₂ exchange, were made with a non steady-state automated chamber system and with the eddy covariance (EC) technique, respectively, in a mature trembling aspen stand between January 2001 and December 2003. Our main objective was to investigate the influence of long-term variations of environmental and biological variables on component-specific and whole-ecosystem respiration (R_e) processes. During the study period, the stand was exposed to severe drought conditions that affected much of the western plains of North America. Over the 3 years, daily mean R_s varied from a minimum of 0.1 μmol m⁻² s⁻¹ during winter to a maximum of 9.2 μmol m⁻² s⁻¹ in mid-summer. Seasonal variations of R_s were highly correlated with variations of soil temperature (T_s) and water content (θ) in the surface soil layers. Both variables explained 96, 95 and 90% of the variance in daily mean R_s from 2001 to 2003. Aspen daily mean R_b varied from negligible during winter to a maximum of 2.5 μmol m⁻² bark s⁻¹ (2.2 μmol m⁻² ground s⁻¹) during the growing season. Maximum R_b occurred at the end of the aspen radial growth increment and leaf emergence period during each year. This was 2 months before the peak in bole temperature (T_b) in 2001 and 2003. Nonetheless, R_b was highly correlated with T_b and this variable explained 77, 87 and 62% of the variance in R_b in the respective years. Partitioning of R_b between its maintenance (R_bm) and growth (R_bg) components using the mature tissue method showed that daily mean R_bg occurred at the same time as aspen radial growth increment during each growing season. This method led, however, to systematic over- and underestimations of R_bm and R_bg, respectively, during each year. Annual totals of R_s, R_b and estimated foliage respiration (R_f) from hazelnut and aspen trees were, on average, 829, 159 and 202 g C m⁻² year⁻¹, respectively, over the 3 years. These totals corresponded to 70, 14 and 16%, respectively, of scaled-up respiration estimates of R_e from chamber measurements. Scaled R_e estimates were 25% higher (1190 g C m⁻² year⁻¹) than the annual totals of R_e obtained from EC (949 g C m⁻² year⁻¹). The independent effects of temperature and drought on annual totals of R_e and its components were difficult to separate because the two variables co-varied during the 3 years. However, recalculation of annual totals of R_s to remove the limitations imposed by low θ, suggests that drought played a more important role than temperature in explaining interannual variations of R_s and R_e.     

Cation exchange properties of acid forest soils of the northeastern USA

Negative correlations between soil pH and cation exchange capacity (CEC) or base saturation in soils of the northeastern USA and Scandinavia have raised questions regarding the nature of cation exchange in acid forest soils. Using data from three small‐catchment studies and an extensive regional survey of soils in the northeastern USA, I examined relationships among total carbon, effective CEC (CEC_e), soil pH_s (in 0.01 m CaCl₂) and base saturation. Organic matter is the predominant source of soil surface charge in these coarse‐grained, glacially derived soils. Correlation coefficients (r) between total carbon and CEC_e ranged from 0.43 to 0.74 in organic horizons and from 0.46 to 0.83 in mineral horizons. In all cases, the intercepts of functional relations between CEC_e and total C were near zero. In O horizons, the CEC_e per unit mass of organic carbon (CEC_e:C) was positively correlated with pH_s in three of the four data sets, consistent with the weak‐acid behaviour of the organic matter. However, CEC_e:C was negatively correlated with pH_s in mineral soils in two data sets, and uncorrelated in the other two. The CEC_e in mineral soils represents the portion of total CEC not occupied by organically bound Al. The negative correlations between CEC_e:C and pH_s can therefore be explained by increased Al binding at higher pH_s. Aluminium behaves like a base cation in these soils. When Al was considered a base cation, the relation between base saturation and pH_s could be effectively modelled by the extended Henderson–Hasselbalch equation. When modelled without Al as a base cation, however, there were no consistent relationships between pH_s and base saturation across sites or soil horizons. Because of the non‐acidic behaviour of Al, it is difficult to predict the effect of ongoing reductions in acid deposition on the base status of soils in the northeastern USA.     

Correlation of properties of Brazilian Haplustalfs with magnetic susceptibility measurements

Magnetic susceptibility (χ, mass specific) is useful for easy indirect estimation of other soil properties at a low cost. The aim of this study was to assess the use of χ as measured with an analytical balance for predicting properties with a substantial influence on the management of Typic Haplustalfs in southern Brazil. To achieve this 48 topsoil samples were taken at the intersection points in a rectangular grid of 20 m × 20 m cells, with 38 of these used for calibration and 10 for validation in regression analyses. The obtained χ values were slightly higher than, and highly correlated (r = 0.970; P < 0.001) with those measured with a susceptibility meter. Highly significant (P < 0.001) correlations were also found between χ and other soil properties relevant to soil classification and management such as clay content (r = 0.68), cation exchange capacity (r = 0.62), P sorption capacity (r = 0.76) and haematite content (r = 0.82). Results from a principal component analysis of eight properties important for soil classification explained 11% of the variance in the data set. The good predictive ability of χ was consistent with current knowledge on the formation pathways for pedogenic ferrimagnets. In summary, χ, which can be readily measured with an analytical balance, has the potential for quantifying soil attributes and may therefore be used in pedotransfer functions.     

Simple Formulation of the Soil Water Effect on Residue Decomposition

Soil water content, θ, is a major factor affecting residue decomposition, but simple formulation of this factor is often lacking. We observed that θ significantly (P < 0.001) affected the residue decomposition constant, k _d. When θ varied from 0.09 g g^?1 to 0.23 g g^?1, k _d ranged from 0.009 to 0.013 d^?1 and from 0.009 to 0.022 d^?1 for residues with carbon to nitrogen ratio (C/N) > 30 and C/N < 25, respectively. A θ factor was formulated in terms of the field capacity θ _FC and the air‐dry θ _d in the form f _w = (θ ? θ _d) / (θ _FC ? θ _d), and this was used to modify the potential k _d as θ varied. Coupling f _w with a first‐order residue decomposition equation resulted in the prediction of the decomposition of four residue types in the greenhouse (R² = 0.94; relative root mean square error, RRMSE, = 0.06) and in the field (R² = 0.93; RRMSE = 0.11).     

Nitrate loss in soil drainage waters in relation to by-passing flow and discharge on an arable site

In a well-structured soil at or close to pedal saturation, rainfall intensity in excess of pedal K_sat is predicted to result in by-passing flow through well connected structural voids. The depth of solute penetration (tracer dye and nitrate) under by-passing flow has been predicted by D_f=(P-C_p)/θ_f, where D_f is the depth of penetration of the leading edge of solute in by-passing flow, P is gross precipitation, C_p is the input volume transmitted through the soil peds and θ_f is the operational volumetric moisture content in by-passing. The timing of surface applied nitrate arrival at a channel bank is demonstrated to be related to by-passing flow rather than uniform displacement. The relationship between nitrate load in soil drainage waters (Y, mg s^-1) and water discharge (X, dm³ s^?1) was Y～6X after nitrate fertilizer application but subsequently declined to Y 0.5X It is deduced that the decline resulted from inefficient leaching under by-passing conditions once surface applied nitrate had become relocated within the soil peds.     

THE EFFECT OF DENSITY ON WATER RETENTION PROPERTIES OF FIELD SOILS

The bulk density, available water (A_ν), air capacity (C_α), and retained water capacity (θ_ν) were determined for 158 A, B, and C horizons of field soils. Clay (< 2 μm) and silt (2=60 μm) were also determined. Statistical analysis of the results demonstrated that bulk density exerts a profound influence on A_ν, C_α, and θ_ν, but the effect varies between texture groups and horizons. Significant negative correlations were obtained between bulk density and C_α for most texture and horizon groups. In B and C horizons A_ν and θ_ν also decrease with increasing density, whereas in A horizons A_ν and θ_ν tend to increase with bulk density except in silty soils. Within a limited range it is feasible to control these parameters by using field techniques to achieve optimum bulk density for particular soils.     

遗传算法率定参照作物腾发量相关参数的研究

用气象资料计算参照作物腾发量(ET0)的方法需要各种气象(候)和物理参数,净辐射是其中的重要数据之一,而专业测量净辐射的设备在农业气象站里很少安装。为解决计算ET0时缺少太阳净辐射(Rn)测量值这一实际问题,该文采用浑善达克沙地东南缘南沙梁草甸草原区气象站观测的气象资料,用遗传算法模型对联合国粮农组织56号文本(FAO56)推荐值(as和bs)进行率定,计算了对应夏半年(4—9月)和冬半年(1—3月和10—12月)的太阳净辐射和参照作物腾发量,并将率定前后的模拟太阳辐射进行对比分析,用残差估计指数法对该方法模拟的参照作物腾发量模拟精度进行了分析。结果表明:在缺少太阳净辐射测量值的地区,采用FAO56参数(as和bs)推荐值与遗传算法模型率定参数(as和bs)相比,净辐射年内变化趋势一致,采用率定后参数计算的净辐射相对更不稳定,波动更大,但能有效提高参照作物腾发量计算精度。误差较大的模拟值均出现在降雨日前后,降雨虽然并未直接出现在Penman-Monteith公式中,但是降雨必然会对湿度和温度等气象条件造成一定影响,而as和bs是受湿度等因素影响而变化的,其深层次的原因有待进一步分析。     

Empirical binomial sampling plans: model calibration and testing using Williams’ method III for generalized linear models with overdispersion

Binomial sampling plans that use presence/absence data for estimating pest population density are commonly used in cropprotection when counting individual pest units is not cost effective. These plans are often based on the empirical relationship between the proportion of presences, p, and a count-based estimate of the mean population density, [(m)\tilde]\tilde \mu , given by ln{ - ln(1 - p) } = a₀ + a₁ ln([(m)\tilde] )\ln \left\{ { - \ln (1 - p)} \right\} = \alpha _0 + \alpha _1 ln(\tilde \mu ), which is typically fitted as a simple linear regression. However, correctly incorporating all of (i) binomial sampling errors, (ii) biological errors (i.e., overdispersion), and (iii) errors in variables is not possible using linear regression. Here, model calibration and testing is carried out using William’s method III for fitting a binomial generalized linear model with overdispersion (GLMw) in order to handle (i) and (ii), and simulation is used to study the effect of using the sample estimate of μ as the predictor variable. Calculation of the operating characteristics function of the decision rule for an action threshold of p ₀ is compared for linear and GLM_w models, with the former shown to substantially underestimate the probability of correct decisions and overestimate the probability of incorrect decisions. A binomial sampling plan for populations of the leaf beetle Chrysophtharta bimaculata, a defoliator of Eucalyptusnitens plantations, is used to demonstrate the methods.     

KINETICS OF ISOTOPIC EXCHANGE OF PHOSPHATE ADSORBED ON GIBBSITE

An Elovich-type equation has been used to describe the kinetics of isotopic exchange of phosphate adsorbed on the surface of gibbsite. The equation is where A and B are parameters; θ=bF/[b+a(I-F]; a and b are the molar concentrations of the phosphate on the crystal surface and in solution respectively and F is the fraction exchange of the radio-isotope at time t. First-order rate constants were obtained from the equation. The reference state for the first-order rate constants, and the distribution of activation energies, for exchange can be related to the Elovich equation parameters. The kinetic results are consistent with S_N1 dissociation or S_N2 bimolecular solvolysis for the phosphate ligand. The eschange reaction is subject to an acid-base catalysis the exact nature of which could not be determined from the available data.     

Estimation of the diffusion coefficients of adsorbed and non-adsorbed solutes in soil

A method is proposed which follows Darrah's experimental procedure and takes advantage of a mathematical solution provided by Carslaw & Jaeger to estimate the diffusion coefficients of adsorbed and non-adsorbed solutes in soil. The method requires only the values of the concentration of the solute at the input face of a uniform column of soil, C^s, and of the total amount, Q_t, that has entered the soil after a specified time during which the surface of the block is in contact with a thin porous pad containing a known initial amount of solute, Q₀, at concentration C₀, expressed in the same units as C^s. In the C^s/C₀ vs. Q_t/Q₀ space there is a unique relationship between the effective diffusion coefficient, D_e, of the solute in the soil and the contact conductance for this solute, h, between the pad and the soil surface. The proposed procedure is firstly to determine D_e, and h for a non-adsorbed solute in the experimental soil using the experimental values of C^s/C₀ and Q/_Q for that solute. This value of D_e, gives the diffusion impedance factor for the solute in the soil, f, which is assumed also to apply to adsorbed solutes. A first estimate of the effective diffusion coefficient of an adsorbed solute, ¹D_ea, is then made using f and the diffusion coefficient of the free solute in water, D_L, obtained from the literature (i.e. ¹D_ea= D_Lf). Only if the solute is weakly adsorbed will the values of C^s/C₀, and Q_t/Q₀ lie in C^s/C₀, vs. Q_t/Q₀, space as defined by ¹D_ea and the contact conductance, h. Instead a second space relating C^s/C₀ and Q_t/Q₀, is now constructed from nominated values of h and D_e, where D_e, is defined in terms of ¹D_ea, the adsorption coefficient, F , and the volumetric moisture content of the soil, θ. The position of the experimental values of C^s/C₀, and Q_t/Q₀ within this new space defines h and the actual D_e, and F of the solute as it diffuses and is adsorbed in the soil. The advantages and limitations of the method are discussed. In particular, the method assumes that the adsorption process is linear and reversible.     

Magnetic susceptibility changes in relation to pedogenesis in a Xeralf chronosequence in northwestern Spain

Pedogenesis under aerobic conditions is usually associated with an increase in magnetic susceptibility (χ, mass‐specific), which results from the formation of nano‐sized magnetite and/or maghaemite. In this study, we systematically investigated the χ trend in Xeralfs from a chronosequence of 13 river terraces in an area with a Mediterranean climate in Spain. The soils in the younger terraces are well drained and reddened, but those of the older terraces exhibit redoximorphic features and reduced χ values, because of the presence of a perched water table. In the well‐drained members of the chronosequence, the frequency dependent magnetic susceptibility, χ_FD, which is a proxy for the concentration of nano‐sized pedogenic ferrimagnets such as maghaemite, was highly correlated with the concentration of haematite (Hm), but not with that of goethite (Gt). Also, the peak χ_FD increased with increasing age in the younger freely drained soils, indicating that no steady state had been reached, and decreased with increasing depth. The formation of maghaemite can be explained by either or both of two formation models, namely: (i) ferrihydrite → maghaemite → haematite solid state transformations; and (ii) the reaction of bacterially produced Fe(II) with an Fe hydroxide phase to form magnetite, which is later oxidized to maghaemite. Comparison between these soils and those in other climatic regions indicates that the Hm/χ_FD ratio increases with increasing soil temperature and with the degree of weathering. In the horizons exhibiting redoximorphic features on the higher terraces, there was significantly less Hm and χ_FD in clay than in the well‐drained younger soils, possibly because of reductive dissolution of haematite and maghaemite. Laboratory experiments showed that susceptibility to reductive dissolution increased in the sequence goethite < maghaemite < haematite, which is consistent with the relative abundance of these minerals in the redoximorphic horizons.     

宁夏中部干旱带砂土混合覆盖下土壤蒸发估算

为寻求一种能够有效估算宁夏中部干旱带压砂地土壤蒸发量的方法,通过微型蒸渗仪大田试验,研究了 0(S1),20％(S2),40％(S3),60％(S4),80％(S5),100％(S6)6种砂土混合比条件下土水蒸发比与表层土壤含水量的关系,并构建了压砂地土壤蒸发量估算模型.结果表明:土水蒸发比随表层土壤含水量呈分阶段变化...     

Environmental and physiological control of transpiration by groundnut crops

In central India, four populations of groundnut were grown to assess the interaction between population and water stress.Transpiration was calculated from measurements or estimates of stomatal resistance, r_s, boundary layer resistance, r_a, vapour concentration difference between leaf and air, δ_χ, and leaf area index, L.The frequency distributions of r_s, r_a, δ_χ and seasonal changes in L were plotted to analyse the dependence of transpiration rate on each variable, both per unit area of leaf surface, E_l, and per unit land surface, E_e. For estimates of E_l, both r_s and δ_χ were of similar importance, exerting a far greater influence than changes in r_a. However, in terms of E_e, changes in L were far more important than in any other variable, particularly late in the season when water was scarce.This study provides further experimental support for estimates of evaporation based on stomatal resistance and allied measurements and confirms similar estimates obtained earlier for crops of pearl millet maintained on stored water. The ability of the technique to describe temporal and spatial variations as well as the dominant environmental and physiological influences on transpiration may outweigh any small loss in accuracy of estimates thus obtained.     

Direction-dependent behaviour of hydraulic and mechanical properties in structured soils under conventional and conservation tillage

The development of soil structure units with defined forms and dimensions (e.g. platy by soil compaction or prismatic up to subangular-blocky by swelling–shrinkage processes) can lead to direction-dependent behaviour of mechanical and hydraulic properties. However, little research has investigated direction-dependent behaviour directly. Undisturbed samples were collected at different horizons and orientations (vertical and horizontal) of Stagnic Luvisols derived from glacial till (Weichselian moraine region in Northern Germany). A direct shear test determined the cohesion (c) and the angle of internal friction (φ). The water retention curve (WRC), the saturated hydraulic conductivity (k_s) and the air permeability (k_a) were also measured. The air-filled porosity (_a) was determined and pore continuity indices (N) and blocked porosities (_b) were derived from the relationship between k_a and _a.Although the pore volume as a scalar is isotrop, the saturated hydraulic conductivity and air permeability can be anisotropic. In the seedbed (SB) and plough pan (PP) of conventionally managed soils the effective porosity is non-direction-dependent, however, differences in k_s as a function of sampling direction can reach one order of magnitude in PP (k_sh > k_sv). The shear strength parameters do not present a significant anisotropy, although, a pronounced spatial orientation of soil aggregates (e.g. induced by soil compaction in a plough pan) lead to direction-dependent shear strength (by σ_n: 10 kPa, σ_tv: 12 kPa and σ_th: 19 kPa). This behaviour was especially observed in pore continuity indices (e.g. vertical and horizontal oriented aggregates observed in Bvg and PP presented _bv < _bh and _bv > _bh, respectively) showing that the identification of soil structure can be used as the first parameter to estimate if hydraulic properties present a direction-dependent behaviour at the scale of the soil horizon, which is relevant in modelling transport processes.     

Evaluation of porous medium hydraulic properties using experimental methods and RETC code

Two experimental procedures were used to determine both hydraulic properties, soil water retention θ(h) curve and unsaturated hydraulic conductivity K(θ), of a sand sample. Knowledge of hydraulic properties is essential, since they generally control soil water dynamics. A steady-state laboratory method was used for the simultaneous determination of θ(h) and K(θ). A one-step outflow method was used for the determination of diffusivity D(θ) and subsequently K(θ) from soil water retention data which were measured independently on the same sample and using the same apparatus. The comparison of K(θ) measured values from the above-mentioned methods showed very good agreement of the results. Also, the comparison between the experimental K(θ) and θ(h) functions and the predictions obtained using retention curve (RETC) code by simultaneous fit of experimental soil water retention and hydraulic conductivity data from outflow data, assuming the Mualem-van Genuchten model, showed very good agreement. It is noted that the main disadvantage of the one-step outflow method is the weakness to predict K(θ) values near saturation. This disadvantage could be overcome using RETC code with the above procedures, since the K(θ) values between the predictive approach and the steady-state method were similar.     

Electric charge characteristics of horizons of Ando (B) and Red-Yellow B soils and weathered pumices

The electric charge characteristics of five Ando (B) and two Red-Yellow B horizon soils and two weathered pumices were studied by measuring the retention of NH₄+ and Cl^? at different pH values and NH₄Cl concentrations. The magnitude of their negative charge (CEC; meq/100g) was dependent on pH and NH₄Cl concentration (C; _m) as represented by a regression equation: log CEC =apH +blog C +c. The values of the coefficient a (0.017 to 0.342), b (0.031 to 0.274) and c (1.41 to ? 1.26) were correlated and depended on the kind of clay minerals present. A similar equation: log AEC =a’ pH +b’ log C+c’ was also found for the positive charge in the Ando soils, but there was little difference in the values of a’(?0.204 to ?0.251), b’(0.181 to 0.253) and c’(2.06 to 2.46) between the soils. It was shown that the equations generally hold for soils with constant and/or variable charges and describe adsorption equilibria in which NH₄+ and H⁺, and Cl^? and OH^? compete for cation- and anionexchange sites, respectively. The significance and utility of the coefficients is discussed.