Modeling of mineral nutrient uptake of spruce tree roots as affected by the ion dynamics in the rhizosphere: Upscaling of model results to field plot scale

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Modeling of mineral nutrient uptake of spruce tree roots as affected by the ion dynamics in the rhizosphere: Upscaling of model results to field plot scale H. Nietfeld a,∗ , J. Prenzel a , H.-S. Helmisaari b , A. Polle c , F. Beese a a

Büsgen-Institute, Department of Soil Science of Temperate Ecosystems, Georg August University, Büsgenweg 2, D-37073 Göttingen, Germany Department of Forest Sciences, University of Helsinki, FI-00014 Helsinki, Finland c Büsgen-Institute, Deptartment of Forest Botany and Tree Physiology, Georg August University, Büsgenweg 2, D-37073 Göttingen, Germany b

a r t i c l e

i n f o

Article history: Received 22 March 2016 Received in revised form 17 August 2016 Accepted 5 September 2016 Available online xxx

a b s t r a c t The effects of acid soil conditions on mineral nutrition and growth of forest trees are discussed controversially. It is hypothesized that approaches are needed which determine the root nutrient uptake rates as affected by root-induced processes in the rhizosphere. A multi-ion rhizosphere model (MIM) has been developed which calculates the reactive dynamics of all major ions (H+ , Al3+ , Mn2+ , Fe3+ , Ca2+ , Mg2+ , K+ , Na+ , NO3 − , SO4 2− and Cl− ) in the rhizosphere of forest tree roots growing in acid soils. MIM calculates fine-scaled ion concentration gradients extending from the unrooted bulk soil (Bulk) to the root surface (RS) and the temporal dynamics of the average concentrations in rhizospheric sub-volumes termed as soil-root-interface (SRI), inner rhizosphere (Rh) and outer rhizosphere (oRh) of all ions (Mi ) involved. SRI, Rh and oRh are defined as cylindrical soil volumes around the root which have distances to the root surface of 0.5 mm, 2.0 mm and 8–12 mm, respectively. The SRI-to-Bulk, Rh-to-Bulk and Rh-to-oRh ion concentration ratios (VMi -SRI , VMi -Rh , RMi ) and the actual rates of root nutrient uptake (UMi ) and H+ or OH− root excretion (EH/OH ) are determined. The model is used in a Monte Carlo upscaling-procedure to calculate the UMi - and EH/OH -rates of non-mycorrhizal long roots of spruce trees growing on a long-term monitoring plot in Solling, Germany. The objectives of this study are (i) to show the plot-specific heterogeneity of modeled VMi -Rh - and VMi -SRI -values of H+ , base cations (Ca2+ , Mg2+ , K+ ; Mb -cations), NO3 − and SO4 2− , to present a comparison with rhizospheric measurement data and, to model the UMi and EH/OH rates and (ii) to present the impact of major influencing processes. The VMi -Rh -data comprise a range of about 0.5 up to 3.0 and more depending on the ion considered. In an equivalence-testing the modeled RMi -ratios of Ca2+ , SO4 2− , Fe3+ and Na+ agree with corresponding ratios (Rˆ Mi ) of measured concentrations in Rh and oRh if extreme Rˆ Mi -values are neglected. Means of modeled UMi -rates are 0.27, 0.126, 0.09, 1.09 and 0.12 mmol m−2 d−1 for Ca2+ , Mg2+ , K+ , NO3 − and SO4 2− , respectively. The UMb -rates are determined by root uptake capacities (UMb -max ), height of water fluxes, Mb concentrations in bulk and rhizosphere soil, amounts of desorbed exchangeable Mb cations and EH/OH -rates. In most calculations OH− root excretions (EOH ) have been calculated. Low UMb -rates have been calculated at low water fluxes and low bulk soil solution concentrations even at high UMb -max -values and are associated with EOH -rates. Based on the UMi rates an assessment of the contribution of long roots on the total annual nutrient uptake of the spruce stand is given. It is concluded that the measured proceeding reduction of Mb -solution concentrations and the prospective NO3 − saturation in the bulk soil of the spruce plot will lead to extreme low Mb /NO3 root uptake ratios. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Trees growing in acid soils often suffer from nutrient imbalances, nutrient deficiencies and restricted growth. But correlations

∗ Corresponding author. E-mail address: [email protected] (H. Nietfeld).

between soil chemical conditions and nutritional status of trees often are inconclusive (De Wit et al., 2010). Even the effects of experimentally induced acid irrigations or enhanced levels of nitrogen on tree mineral nutrition are discussed controversially (Nyberg et al., 2001; Magill et al., 2004; Mellert et al., 2004; Högberg et al., 2006). In view of these investigations an assessment of the effects of acid soil conditions on tree mineral nutrition is still uncertain. Therefore, as stated by Lucas et al. (2007) investigations might

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Please cite this article in press as: Nietfeld, H., et al., Modeling of mineral nutrient uptake of spruce tree roots as affected by the ion dynamics in the rhizosphere: Upscaling of model results to field plot scale. Ecol. Model. (2016), http://dx.doi.org/10.1016/j.ecolmodel.2016.09.006

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be helpful which address the nutrient acquisition potential of the absorbing fine roots on a process-related basis. The construction of nutrient budgets (Watmough et al., 2005) has been previously the most common approach to estimate nutrient uptake by trees, but it does not provide any information on processes at the root scale. Long-term ecosystem models usually determine tree nutrient uptake rates as being proportional to fine root biomass and soil solution concentrations of nutrients. But the used proportionality factors are often not well-validated. Therefore, it is hypothesized in this study that root-centered, deterministic approaches are needed which determine the actual root nutrient uptake rates as affected by root-induced processes in the rhizosphere. This has already been demanded by Högberg and Jensen (1994) because the chemical conditions in the rhizosphere differ substantially from the bulk soil conditions in many aspects (Gobran et al., 1999). Indeed, previous investigations show ion-specific rhizospheric accumulations and depletions in experimental studies (Braun et al., 2001; Dieffenbach and Matzner, 2000; Dieffenbach et al., 1997; Majdi and Bergholm, 1995; Majdi and Rosengren-Brink, 1994) and in field studies (Clegg et al., 1997; Collignon et al., 2011; Fritz et al., 1994; Gobran et al., 1999; Gobran and Clegg, 1996; Majdi and Bergholm, 1995; Majdi and Rosengren-Brink, 1994; Knoche, 1994; Turpault et al., 2007). But, this measurement information on rhizospheric ion concentration changes has been hardly used to quantify root nutrient uptake rates. More generally, investigations are missing which give a quantitative assessment of tree nutrient uptake rates under field conditions deduced from rhizospheric soil conditions thereby considering numerous influencing processes, their mutual interaction and, in particular, the spatial–temporal heterogeneity of the values of process variables (Hinsinger et al., 2005; Schöttelndreier and Falkengren-Grerup, 2009). Therefore, a multi-ion rhizosphere model (MIM; Nietfeld and Prenzel, 2015) is applied in this study. It calculates the actual root nutrient uptake rates under consideration of rhizospheric processes and the overall ion dynamics in the rhizosphere. MIM-results show the temporal dynamics of the spatially fine-scaled ion concentrations extending from the unrooted bulk soil (Bulk) to the root surface (RS) and the averaged ion concentrations in rhizospheric sub-volumes denoted as soil–root interface (SRI), inner rhizosphere (Rh) and outer rhizosphere (oRh) as defined by Seguin et al. (2004) and Gobran et al. (1999). SRI, Rh and oRh are defined as cylindrical soil volumes around the root with distances to the root surface of 0.5 mm, 2.0 mm and 8–12 mm, respectively. It has been shown that various model parameter values produce different rhizospheric concentration gradients and uptake rates of any of the nutrients involved (Nietfeld and Prenzel, 2015). Hence, MIM can be used in an upscaling procedure in which the heterogeneity of actual nutrient uptake rates is calculated under the conditions of the measured site-specific variability of model parameter values as demanded by Darrah et al. (2006). According to Bierkens et al. (2000), for an upscaling of the results provided by the rhizosphere model calculations a Monte Carlo procedure has to be used. The use of average parameter values can produce a severe bias of model output because the ions in the non-linear rhizosphere model behave asynchronously. The Monte Carlo analysis is an adequate method to examine the effects of the variability of the model input values to the range and shape of the model output and has been applied for an assessment of root nutrient acquisition in heterogeneous soil environments (Ryel and Caldwell, 1998; Jackson and Caldwell, 1996). In this study a general approach is presented in which MIM is used in a Monte Carlo upscaling procedure. The approach is applied to the specific conditions on a long-term monitoring spruce plot in Solling (F1-plot), Germany. The heterogeneities of rhizospheric ion concentrations around and nutrient uptake rates of

non-mycorrhizal long roots are determined as affected by the F1specific variability of measured bulk soil conditions and parameter values involved in rhizosphere processes. In detail, the following hypotheses and objectives are addressed: (1) The tree’s demand of nutrients and water, implemented in MIM as root water and potential nutrient uptake rates, creates heterogeneous patterns of ion-specific and fast-changing accumulations and depletions. This is shown by presenting the variabilities of modeled SRI-to-Bulk and Rh-to-Bulk concentration ratios of H+ , Mb cations (Ca2+ , Mg2+ , K+ ), NO3 − , and SO4 2− ions in soil solution and exchanger. Furthermore, the hypothesis is tested whether the Rh-to-oRh ratios of Ca2+ , K+ , Fe3+ , Na+ , and SO4 2− concentrations measured in Rh and oRh can be corroborated by the corresponding ratios of modeled Rh- and oRh-concentrations. (2) The actual root uptake rates of Mb cations, NO3 − and SO4 2− and the actual root excretion rates of H+ or OH− are calculated and the shapes and ranges of their variabilities are presented. It is hypothesized that the actual root uptake rates of Mb cations are clearly lower than their uptake capacities and low Mb /NO3 − ratios of actual root uptake rates exist. Due to the results presented in Nietfeld and Prenzel (2015) it is hypothesized that the actual root uptake rates of Mb cations are determined by water flux and their own availability in bulk and rhizosphere soil and are additionally affected by the concentrations of H+ ions in bulk and rhizosphere soil and the H+ /OH− root excretions. 2. Materials and methods 2.1. Rhizosphere model (MIM) and model calculations The rhizosphere is defined as a cylindrical soil volume around the root which extents from the root surface to the unrooted bulk soil. In the modeling approach it is generally assumed that the root exerts its influence on the rhizosphere soil via uptake of nutrients and water and the excretion of H+ or OH− ions. The ions included in the rhizosphere soil solution are H+ , Al3+ , Mn2+ , Fe3+ , Ca2+ , Mg2+ , K+ , Na+ , HCO3 − , NO3 − , SO4 2− , Cl− . Additionally, the water equilibrium, the dissolution or formation of the solution complexes H2 CO3 , AlSO4 + , AlOH2+ , Al(OH)2 + , the competitive adsorption of the cations on the soil exchanger and the formation and, optional, the dissolution of gibbsite (Al(OH)3 (s)) are considered in MIMcalculations. But, according to Matzner and Prenzel (1992) it is assumed that in the bulk soil no Al(OH)3 (s) exists at the beginning of the model calculations; the possible formation of Al(OH)3 (s) (gibbsite) is induced by the root activity only. The ions involved in this study are generally denoted as Mi if not explicitly designated and Mi -related model variables are indexed by Mi or merely i. The ion transport in MIM takes place by diffusion and transpirationinduced water flux. MIM calculates the spatial–temporal dynamics of the Mi -concentrations in the solution (CMi ) and exchanger (SMi ) of the whole rhizosphere soil up to a defined point of time, tmax (maximum simulation time), thereby starting with rhizosphere ion concentrations equal to their concentrations in the bulk soil (CMi -Bulk , SMi -Bulk ). The ion concentrations in the rhizospheric subvolumes SRI (soil–root-interface; CMi -SRI , SMi -SRI ), Rh (inner rhizosphere; CMi -Rh , SMi -Rh ) and oRh (outer rhizosphere; CMi -oRh ) are computed at specified points of time within tmax . For the mathematical definitions of the rhizospheric subvolumes see Eqs. (1a) and (1b). Moreover, the ratios of CMi -Rh , CMi -SRI and SMi -Rh , SMi -SRI to their concentrations in the outer rhizosphere (RMi = CMi -Rh /CMi -oRh ) and in the bulk soil (VMi -Rh = CMi -Rh /CMi -Bulk , VMi -SRI = CMi -SRI /CMi -Bulk , V Mi -Rh = SMi -Rh /SMi -Bulk , V Mi -SRI = SMi -Rh /SMi -Bulk ) are determined which are shortly termed as SRI-Bulk-, Rh-Bulk- and Rh-oRh-ratios

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of Mi in soil solution and exchanger. The actual root nutrient uptake rate of Mi (IMi ) is formulated according to the Michaelis–Menten kinetics which is characterized by the root nutrient uptake capacity (maximum root nutrient uptake rate; IMi -max )and the Michaelis–Menten constant (KMi ). The excess of actual cation or anion root uptake is balanced by the excretion of H+ (IH ) or OH− ions (IOH ), respectively. From the actual rates of root nutrient uptake (IMi ) and H+ or OH− root excretion (IH , IOH ) calculated up to tmax the averaged root uptake rates of the mineral nutrients (UMi ) and the averaged net root excretion rates of H+ or OH− ions are determined (EH/OH ; for details see Eqs. (2a) and (2b)). 2.2. Upscaling concept The characteristics of the upscaling concept is schematically illustrated in Fig. 1. The particular output of a model calculation is determined by the specific values of model input variables and model parameters. It is assumed that the ion concentrations in solution (CMi -Bulk ) and exchanger (SMi -Bulk ) of the bulk soil, the root uptake capacities of nutrients (IMi,max ) and water (q0 ), the volumetric soil water content () and its related soil impedance factor (fl ), the soil bulk density () and the radius (r0 ) of long roots have a site-specific variability. The variability of these variables and parameters is described by probability density functions (PDFs) which are assumed to represent the intrinsic variability of these values on the F1 spruce plot. They are the results of approximations (R-routine fitdist in R-pakage fitdistplus; Delignette-Muller et al., 2013) of data obtained from measurements on the F1 spruce plot or from other measurements whose results are supposed to be transferable to the conditions on the F1 plot (e.g. see approximation of maximum water flux rate presented in Fig. B.5 in Appendix B). The whole of the PDFs are used to be sampled in a Monte Carlo procedure via the Latin hypercube sampling procedure which is optionally realized in the SIMLAB program (Saltelli et al., 2004). The Iman-Conover method (Saltelli et al., 2000) is used to induce the desired rank correlations on pairs of model variables which approximately preserves the correlations existing between the original data. Inconsistencies in the total correlation matrix are corrected by using the routine nearPD (R-package Matrix; Bates and Mechler, 2008) in order to compute the nearest positive definite correlation matrix. A sample size which is about seven times greater than the number of variables is sufficient for reproduce the PDFs under consideration of the defined correlations (Saltelli et al., 2000). The collection of combinations of the model variable and parameter values is processed in rhizosphere model calculations. The collection of the modeled CMi -Rh -values is characterized by a Mi -specific variability whose range and shape is assumed to be representative for the Rh-concentrations of Mi around long roots of spruce trees growing on the F1 plot. This prediction is supported by measurements ˆ M -Rh ) of the ion solution concentrations in the inner rhizosphere (C i ˆ M -oRh ) via X-ray microanalysis. In and in the outer rhizosphere (C i

ˆ M -Rh /C ˆ M -oRh , an equivalence testing procedure the ratios, Rˆ Mi = C i i are compared with corresponding modeled ratios, RMi . The measurements involve the ions Ca2+ , Na+ , Fe3+ , Al3+ (not shown) and SO4 2− . A description of the measurement procedure is given in Fritz et al. (1994), Knoche (1994) and Fritz (2007). Information on rhizospheric ion interactions is provided by the model calculations and is preserved by simultaneous measurements of the ion concentrations in the sampled rhizosphere subvolumes. It should be noted that the averaged root uptake rates, UMi (and the other model results) have been determined on the basis of the agreement between RMi and Rˆ Mi . It is a distinctive characteristic of this study that the measurements of both, most of the model input parameters and the ionic concentrations in the rhizosphere have been conducted on the F1 plot in the 5–15 cm soil depth layer in 1991.

3

Table 1 Parameter values of lognormal PDFs of ionic bulk soil solution concentrations and amounts on soil exchanger. Ion

Soil solution sd

m lognormal

sd

PDF-type

m lognormal

H+ Al Mn2+ Fe3+ Ca2+ Mg2+ K+ Na+ NO3 − SO4 Cl−

−1.71 −1.52 −3.65 −5.07 −2.33 −3.01 −4.81a −1.89 −0.462b −1.62 −2.23

0.576 0.190 0.267 0.490 0.357 0.286 0.955 0.116 0.553 0.141 0.222

1.54d 3.98 c 0.45 −1.50d −0.21 −0.79 −0.26 −0.74

1.178 0.179 0.553 2.961 0.580 0.591 0.335 0.267

a b c d

Soil exchanger

Left truncation factor: 0.4. Right truncation factor: 0.85. Left truncation factor: 0.25. Left and right truncation factors of 0.1 and 0.9, respectively.

2.3. Model input variables and parameter values The F1 research plot is located in the Solling area, which is a mountain range in the northern centre of Germany. The F1-plot is stocked with over 100 years old Picea abies (L.) Karst. trees. A general description of the plot characteristics and a more detailed description of the variability of the measured model parameter values are given in Appendix B. 2.3.1. Variability of soil chemical and physical variables and parameter values The ion concentrations measured in water samples attained by suction lysimeters are considered as ionic bulk soil solution concentrations (CMi -Bulk ; Fig. B.1) and the cationic amounts extracted from soil samples in 1990 (Widey, unpubl. data; soil depth of 5–15 cm) are interpreted as exchangeable cations of the bulk soil (SMi -Bulk ; Fig. B.2). The heterogeneities of the ionic concentrations are approximated by log-normal PDFs whose parameter values are listed in Table 1. Empirical correlations between measured CMi -Bulk data and measured exchangeable cations are listed in Tables B.1a and B.1b, respectively. The cation selectivity coefficients, expressed as pKMi /Ca values (Fig. B.3), are implicitly determined by the CMi -Bulk and SMi -Bulk values. The variabilities of the volumetric soil water content, , and the soil bulk density, , are approximated by lognormal (meanlog=−1.167, sdlog= 0.154) and normal (mean = 1.1, sd = 0.025; Widey, unpubl. data) PDFs, respectively. The -data in a soil depth layer of 5–15 cm have been obtained from water balance model calculations conducted on the F1-plot (Schulte-Bisping; Manderscheid; unpubl. studies). 2.3.2. Variability of root parameter values The variability of long root diameter values, d0 (lognormal-type PDF; meanlog=−0.58, sdlog= 0.23; Fig. B.4), was adapted to the monitoring data obtained from mini-rhizotrone experiments with adult spruce trees (Leppälammi-Kujansuu et al., 2014) and field measurements on the roofed spruce D0-plot in Solling in 0–10 cm depth (Borken, pers. comm.; Lammersdorf and Borken, 2004) and on other plots (Borken et al., 2007). Root water uptake in the course of a day is modeled by a sinusoidal curve (see Eq. (1d) in Nietfeld and Prenzel (2015)) which are due to the diurnal-patterned measurement results reported by Coners and Leuschner (2005) and Coners (pers. comm.). The q0 -values used in the MIM-calculations are defined by the daily sunlight length and the maximum root water uptake rates, qmax . The qmax -data (histogram in Fig. B.5) were determined by the results of water balance model calculations and are approximated by a Weibull distribution (shape = 2.39, scale = 5.79;

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4

Measurements Measurements

Monte Carlo procedure

Ions (Mi): H, Al, Mn, Fe, Ca, Mg K, Na, NO3, SO4, Cl Bulk soil chacteristics:

Repeated model calculations

Samples

Probability

density • Ion solution concentrations functions (CMi-Bulk) (PDFs) • Amounts of exchangeable & ions (SMi-Bulk) Correlations

Sample generation

Constellation of model input parameters

•

Input Parameter

• Rhizosphere ion concentration gradients • Ion concentrations - root surface (CMi-RS) - inner,outer rhizosphere, soil-root-interface (CMi-Rh, CMi-oRh, CMi-SRI)

Root chacteristics: • Water uptake rates • Nutrient uptake capacities

• Root morphological parameters (root diameters, root length)

• Average mineral nutrient root uptake rates (UMi)

Validation Rhizosphere:

Equivalence Testing

• Ion concentrations in inner (ĈMi-Rh) and outer (ĈMi-oRh) rhizosphere • Ratios: Mi= ĈMi-Rh/ĈMi-oRh

Rhizosphere Model

Model Output

• Average net H or OH root excretion rates (EH/OH) • Ion concentration ratios: RMi=CMi-Rh/CMi-oRh

Fig. 1. Schematic diagram of the upscaling concept.

Table 2 Parameter values of triangle PDFs of the root uptake capacities of mineral nutrients, IMi,max . IMi,max , ˛, and ˇ are mode and limiting points of triangular distributions. Mi

˛1

1 IM ,max

ˇ1

0.135 0.07 0.563 0.187 0.5 1.5 0.025

0.325 0.017 2.5 1.5 0.65 3.5 0.5

i

[10−11 mmol mm−2 s−1 ] Mn2+ Fe3+ Ca2+ Mg2+ K+ NO3 − SO4 2−

0.001 0.0001 0.001 0.001 0.001 0.001 0.001

KMi mmol L−1 0.05 0.075 0.05 0.05 0.01 0.025 0.035

see presentation in Fig. B.5). The variability of root nutrient uptake capacities (IMi,max ) is extremely high and are determined by a variety of influencing processes (Appendix B). The range of root nutrient uptake capacities used in this study were determined according to the measured values reported in the literature. The variability of the IMi,max values are represented by asymmetrical triangle distributions in order to take into account the different nutrient uptake capacities of the apical and basal zone of long roots (e.g. Häussling et al., 1988; Table 2). 2.3.3. Values of unchanged model parameters A more detailed description of the unchanged model parameters is presented in Nietfeld and Prenzel (2015). The ion self-diffusion coefficients in solutions are found in Li and Gregory (1974). For the calculation of the ion diffusion coefficients in soils relations between  and fl are needed and have been determined for the Solling site soil (Beese, 1986). It is fl = 1.25 ·  + 0.35 for 0.225 ≤  ≤ 0.45 and fl = 1.25 · e0.001· for  ≤ 0.225. The pK values of the equilibrium constants of the ion solution complexes are 6.46, 3.2, 5.02 and 9.3 for H2 CO3 , AlSO4 + , AlOH2+ and Al(OH)2 + , respectively (Lindsay, 1979). The dissolution constant of CO2 is KH = 10−1.27 MPa−1 and the CO2 partial pressure is set to 0.4 kPa

(Lemke, 2005). The solubility product of Al(OH)3 (s) is set to pKsoc =−9.35 in accordance with the value used by Wesseling and Mulder (1995) for the Solling sites. The kinetical retardation factor of the formation of Al(OH)3 (s) is defined to 1.0 · 10−6 . The ionspecific Michaelis–Menten constants are unchanged (Table 2) and CMin is determined to 2.0 · 10−9 mmol mm−3 for all nutrients. The outer rhizosphere boundary is set to r1 = r0 + 18.6 mm. The maximum simulation time, t max , is set to 10 d. 2.4. Average ion concentrations in rhizospheric subvolumes (SRI, Rh, oRh), Rh-Bulk and Rh-oRh concentration ratios and average rates of root nutrient uptake and net H+ or OH− root excretion The radius of the inner rhizosphere soil cylinder is r2 = r0 + 2.0 mm and the solution fraction and solid phase weight of the Rh-volume of unit length (mm) are VRh = a ·  ·  · ((r0 + 2.0)2 − r02 ) (mm3 ) and V Rh = a ·  ·  · ((r0 + 2.0)2 − r02 ) [mg], respectively,

where a = 1 or a = 10−6 if VRh and V Rh are expressed in L and kg, respectively. The mean solution concentration and exchanger concentration of Mi in Rh (CMi -Rh , SMi -Rh ) are 1 CMi -Rh (t) = VRh and SMi -Rh (t) =

1 V Rh







r2

2·a··

r · CMi (r, t) dr

(1a)

r0





r2

2·a··

 r · SMi (r, t)

dr

(1b)

r0

respectively, where CMi -Rh (t) and SMi -Rh (t) are the concentrations of Mi in the Rh-solution (mmol mm−3 ) and Rh-exchanger (mmolc mg−1 ), respectively at time t. Similarly, the average Mi concentrations in SRI and oRh are calculated. Mi -concentrations in SRI, Rh, and oRh, CMi -SRI , CMi -Rh , CMi -oRh , SMi -SRI , and SMi -Rh are collected in hourly intervals of the whole simulation period or in the last time section denoted by T10 (9.5 d ≤ t ≤ 10 d). From these

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data the ratios VMi -Rh , V Mi -Rh and VMi -SRI , V Mi -SRI are determined. The averaged Mi -root uptake rate of a root with radius r0 , UMi (mmol m−2 d−1 ), is calculated as



IMi (t) dt

V Mi -Rh > 1) and soil-root-interface (SRI; VMi -SRI , V Mi -SRI > 1).

(2a)

0

where b= 2 · 1· r · 105 is a conversion factor. For reasons of compara0 bility a modified root uptake capacity is set to UMi ,max = b · IMi ,max . UMi /UMi ,max is shortly termed as uptake reduction. Similarly, the averaged excretion rates of protons or hydroxyl-ions, EH and EOH (mmol m−2 d−1 ), respectively are calculated according to



EH/OH = EH − EOH = 2 · b · r0 ·  ·



tmax



tmax

IH (t) dt − 0

IOH (t) dt 0

(2b)

and where EH/OH is denoted as averaged net H+ or OH− root excretion rate. 2.5. Comparison of the ratios of measured and modeled rhizospheric ion concentrations Hourly RMi -values calculated at water flux during the last day of the simulation period (9.2d < t < 9.8d) are collected. In an equivalence testing procedure the RMi -data are compared with the ratios, ˆ M -Rh and C ˆ M -oRh , Rˆ M , determined from measured concentrations, C i

i

i

thereby assuming that also the measurements represent spatially averaged ion concentrations of Mi in Rh and oRh, respectively. According to Robinson and Froese (2004) the means of modeling and measurement data are compared each other; i.e. the differences of the means xMi = m(Rˆ Mi ) − m(RMi ) are within a margin of 0. The boundaries of the predefined interval of equivalence, TMi = [-dM ,+dM ] are specified as a fraction of m(Rˆ M ). The nulli

Table 3 Relative proportions (%) of ion accumulations in inner rhizosphere (Rh; VMi -Rh ,

Ion

tmax

UMi = 2 · b ·  · r0

i

i

hypothesis (H0 ) is taken as non-equivalence, i.e. xMi is not near zero but less than the lower equivalence bound (-dMi ) or greater than the upper equivalence bound (+dMi ). The level of tolerance is given by the boundaries of the confidence interval around xMi , (–C˛− ,+C˛+ ), which are calculated on a 5% significance level (˛=0.05). In summary, it is H0 : −C˛− ≤ −dMi or + C˛+ ≥ +dMi

(3a)

the H0 hypothesis and HA : −C˛− > −dMi and + C˛+ < +dMi

(3b)

the alternative hypothesis, HA . To reject H0 means, that the confidence interval is entirely included within the interval of equivalence, i.e. (–C˛− , +C˛+ ) ⊂ TMi . For calculations of the confidence intervals the procedure etc.diff implemented in the R-package ETC (Haseler, 2009) has been used. Moreover, for illustration, the comparisons between Rh-oRh ratios of measured and modeled Rh- and oRh-concentrations are demonstrated in Q–Q-plots. 3. Results The MIM-calculations produce spatially and temporarily finescaled ion-specific concentration gradients in the rhizosphere which differ in terms of shape (depletion: CMi ≤ CMi -Bulk or accumulation: CMi ≥ CMi -Bulk ), steepness and spatial extent. The MIM-calculated concentration gradients of a mineral nutrient considered are determined by its root uptake (IMi -max , IMi ) and the transport via water flux (qmax , q0 ) and diffusion (e.g. Mi soil diffusion coefficient, DMi ). This process interaction is already simulated by the single ion rhizosphere models. But the main characteristics of the MIM-results is that the concentration gradients of an ion considered may be strongly affected by the rhizospheric dynamics of all

5

H+ Ca2+ Mg2+ K+ NO3 − SO4 2− a

Enrichment factorsa VMi -Rh >1

V Mi -Rh > 1

VMi -SRI >1

V Mi -SRI > 1

50.7 50.7 58.4 55.1 48.1 66.5

30.9 14.5 15.1 4.5 – –

61.2 31.6 42.1 21.9 48.8 68.0

23.4 12.9 14.6 3.8 – –

in time period T10

other ions involved. Ionic interactions occur, for example, by interand counter-diffusion fluxes, the competitive cation exchange, the H+ or OH− excretion rates of the root and the ion concentration levels in bulk and rhizosphere soil. In two calculation examples (Appendix C) the rhizospheric concentration gradients of H+ ions, Mb cations and NO3 − and SO4 2− anions are shown. The parameter values assumed in these calculation examples differ only in terms of the availability and root uptake of NO3 − and SO4 2− . The effects of H+ and OH− root excretions on the rhizospheric pH and the concentrations of Mb , NO3 − and SO4 2− ions and their actual root uptake rates are demonstrated. It is shown that the ionic concentration changes mainly occur in the Rh-volume; only the rhizospheric pH-changes cover a larger soil volume around the root. The concentrations in the outer rhizosphere are only slightly affected by the root’s impact. The temporal slopes of the ionic solution concentrations in Rh and SRI and the ratios to their bulk soil concentrations show that ion concentration changes may already occur in less than one day (especially in SRI and on RS) and they are characterized by fluctuating short-term decreases and increases which are due to the daily-patterned water fluxes. MIM-calculations including the total sample of model variable and parameter values result in a variety of rhizospheric ion concentration gradients and concentration decreases and increases in Rh and SRI which are described by the concentration ratios VMi -SRI , VMi -Rh , V Mi -SRI and V Mi -Rh . The VMi -Rh - and VMi -SRI -values are ion specific and may change during the simulation period (see Appendix C). The magnitudes and frequencies of the VMi -Rh - and V Mi -Rh -concentration ratios collected in hourly intervals within the T10 -period are presented in Figs. 2 and 3, respectively. The VMi -Rh -values include a range of about 0.5 up to 3.0 and more; especially for NO3 − , Mg2+ , Na+ , Fe3+ and Al3+ (not shown) Rh-toBulk concentration ratios higher than 3.0 have been calculated. The ion concentration changes in the SRI-volume collected in T10 (VMi -SRI , Appendix D) are much more extreme and range between about 0.3 and about 5.0 and more; especially for NO3 − more extreme values were calculated. It is shown that the frequency of Mb -accumulations in Rh is higher if compared with SRI-accumulations, i.e. Mb -depletions in SRI are superimposed by Mb -accumulations in Rh (Table 3). The VMi -RS enrichment factors (not shown) have approximately the same orders of magnitude as the VMi -SRI -enrichment factors but may include extreme depletions with root surface concentrations near Cmin -level. The changes of Rh-concentrations of exchangeable cations (V H−Rh , V Mb -Rh ) include a range of about 0.6 up to 1.5. Mostly depletions of exchangeable Mb cations have been calculated (Table 3) which indicates opposite concentration gradients in Rh-solution and Rh-exchanger and variable ion distribution coefficients. The differences between V Mi -Rh and V Mi -SRI are smaller (with the exception of H+ ions) if compared with differences between VMi -Rh and VMi -SRI . The Rh- and SRI-concentrations of H+ -ions take an exceptional position as they are additionally affected by H+ or OH− root excretions and a possible precipitation of gibbsite (AlOH3 (s)).

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Fig. 2. Range and shape of modeled Rh-to-Bulk concentration ratios, VMi -Rh = CMi -Rh /CMi -Bulk , of H+ , Ca2+ , Mg2+ , K+ , NO3 − and SO4 2− . The histograms show VMi -Rh -data calculated in hourly intervals within the T10 time section (T10 : 9.5 d ≤ t ≤ 10 d).

Predominantly OH− ions are excreted by the root due to an anion root uptake excess (Fig. 5a) which may cause pH increases near the root surface especially during the diffusion-periods (e.g. Fig. C.1). But, nevertheless mostly pH-decreases in Rh and especially in SRI have been calculated. The pHRh -decreases are caused by protons transported via water flux towards the root and H+ root excretions but occur also at OH− root excretions. The root-released OH− ions may be neutralized by protons desorbed from the soil exchanger (Fig. 3; Table 3) and transported via mass flow. In fact, high CH−Bulk concentrations cause high rates of H+ -ions convectively transported due to the assumed proportionality between CH−Bulk and water flux rate. Moreover, high amounts of exchangeable protons may be desorbed (Table 3) due to high SH−Bulk values. Hence, pH-increases in Rh and SRI are modeled only if the amounts of these rhizospheric H+ -sources are smaller than the amount of OH− ions released by the root. In Fig. E.1 (Appendix E) the variabilities of the Rˆ Mi -ratios determined from measured ion concentrations in Rh and oRh are shown and include the ions Ca2+ , SO4 2− , K+ , Na+ and Fe3+ . It is assumed that the defined time section (9.2d < t < 9.8d) used for the collection of modeled RhMi -ratios, corresponds to the day time of collecting Rh- and oRh soil samples for measurement. The Q–Q-plots in Fig. 4 illustrate that the model calculations cannot produce extreme Mi -depletions and -accumulations with the same

frequency as documented by the measurement results. While the agreement is quite well for SO4 −2 the deviations are highest for Na+ even if the most extreme Rˆ Na -values were not considered. Also, the equivalence tests have been conducted only with subsets of Rˆ Mi -values and some of the most extreme Rˆ Mi -values were excluded. The ion-specific boundaries (±dMi ; Table 4) of the intervals of equivalence (TMi ), which have been determined as fractions of the m(Rˆ M )-values, cover 9.5%–16.5% of the particular i

m(Rˆ Mi )-value. It is shown that the boundaries of the calculated ± , are completely included ion-specific confidence intervals, ±C0.05 in the corresponding TMi -intervals. The test results indicate that the H0 -hypothesis of non-equivalence can be rejected. It should be noted, however, that for K+ the test is failed. MIM cannot produce the extremely large range of Rˆ K -ratios (see Fig. E.1). In most cases net root excretion rates of OH− ions have been calculated; only in about 25.0% of all cases net excretions of protons have been determined (Fig. 5a). Fig. 5a also shows the variability of H+ or OH− root excretions if the root nutrient uptake capacities are used for the calculations (UMi,max ; dashed histograms in Fig. 5). A significant shift from H+ to OH− root excretion rates is shown which is caused by an anion excess of the actual nutrient uptake rates. The actual root uptake rates of Mb cations (ICa , IMg , IK ) are considerably lower if compared with their particular root

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Fig. 4. Comparison of RMi and Rˆ Mi distributions via Q–Q-plots. RMi = CMi -Rh /CMi -oRh and Rˆ Mi = CMi -Rh /CMi -oRh are the Rh-oRh-ratios of modeled (CMi -Rh , CMi -oRh ) and measured concentrations (Cˆ Mi -Rh , Cˆ Mi -oRh ) of Ca2+ , SO4 2− , Fe3+ and Na+ . The RMi -data have been calculated in hourly intervals within the time section 9.2 d ≤ t ≤ 9.8 d.

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Table 4 Results of equivalence testing: (mRˆ Mi ) and (mRMi ) are the means of Rh-to-oRh-concentration ratios, Rˆ Mi and RMi , of measured and modeled concentrations. It is Rˆ Mi = Cˆ M -Rh /Cˆ M -oRh and RM = CM -Rh /CM -oRh , where Cˆ M -Rh , Cˆ M -oRh and CM -Rh , CM -oRh are the measured and modeled concentrations, respectively of Mi in the inner (Rh) and outer i

i

i

i

i

i

i

i

i

− + rhizosphere (oRh). It is xMi = m(Rˆ Mi ) − m(RMi ), ±dMi are the boundaries of the predefined intervals of equivalence and −C0.05 and +C0.05 are the boundaries of the calculated confidence intervals.

Mi

m(Rˆ Mi )

m(RMi )

xMi

±dMi

− C0.05

+ C0.05

p value

Ca2+ Fe3+ Na+ SO4

1.06 1.34a 1.45c 1.14

1.02 1.22b 1.40 1.085

−0.04 −0.12 −0.05 −0.055

±0.12 ± 0.13 ± 0.239 ± 0.108

−0.11 −0.129 −0.239 −0.102

0.065 0.067 0.13 0.014

0.032 0.049 0.049 0.03

a b c

0.55 ≤ Rˆ Fe ≤ 3.5. RFe ≤ 3.75. 0.5 ≤ Rˆ Na ≤ 3.25.

Table 5 Means and standard deviations of actual root nutrient uptake rates and H+ and OH− root excretion rates and means of nutrient reduction factors. Ion

Average root uptake (excretion) ratea , b UMi (EH/OH ) [mmol m−2 d−1 ]

Uptake reduction factorsa UMi /UMi -max –

H+ OH− Ca2+ Mg2+ K+ NO3 − SO4 2−

0.52 (0.48) 0.56 (0.39) 0.27 (0.19) 0.126 (0.074) 0.09 (0.058) 1.09 (0.58) 0.12 (0.078)

– – 0.41 0.33 0.285 0.79 0.81

a b

Means. Standard deviation (in brackets).

uptake capacities (ICa,max , IMg,max , IK,max ). Hence, the heterogeneities of the averaged root uptake rates (UCa , UMg , UK ) differ from the variabilities of the corresponding root uptake capacities. Means and sd-values (in brackets) of the UMi -values and separately calculated OH− and H+ root excretion rates are listed in Table 5. The low uptake reductions of Mb cations (Table 5) show that actual uptake rates are considerably determined by the bulk soil concentrations while the modeled actual anion uptake rates are mostly close to their root uptake capacities. The variabilities of UMi -data as shown in Fig. 5 have been set in relation to the variabilities of the respective root uptake capacities, UMi -max , which are exemplarily presented for Ca2+ and NO3 − ions (Figs. 6a, 7a; F.1a, F.1b). The individual UCa - and UNO3 values were classified according to predefined subsets of U Ca−max and U NO3−max -values. The curves A and C in Fig. 6a represent both, the highest and lowest UCa -values, respectively, at increasing UCa-max -values while curve B shows the UCa -increases at constantly highest UCa-max -values. The other classified values are between these boundaries. A similar relationship for NO3 − (Fig. 7a) shows that most of the NO3 − uptake rates (about 87.5%) amounts to at least 75% of the UNO3−max -rates as already shown in Fig. 5e. The specific heterogeneity of the actual root uptake rates (UCa , UNO3 ) can be explained by differences in the values of model variables and parameters. Obviously, the lowest UCa-max -values (label 1 in Fig. 6a) produce lowest actual root uptake rates and high accumulations in the rhizospheric soil solution (Fig. 6e) irrespective of the maximum water flux rates (Fig. 6b) and are the only cases in which accumulations of exchangeable Ca2+ cations have been calculated (Fig. 6f). Low actual root uptake rates at highest UCa-max -values (label a in Fig. 6a) are caused by Rh-depletions (Fig. 6e), low maximum water flux rates (Fig. 6b), low to medium Ca2+ bulk soil solution concentrations (Fig. 6c) and low amounts of desorbed exchangeable Ca2+ cations (Fig. 6f). The low UCa -rates at increasing UCa-max -rates (curve C in Fig. 6a) are caused by low bulk soil solution concentrations and low up to moderate water fluxes (Appendix F). The highest UCa -rates (curve points labeled by markers d and 4 in Fig. 6) were calculated due to high root

uptake capacities, highest maximum water flux rates (Fig. 6b), high concentrations in bulk soil solution (Fig. 6c), high amounts of desorbed exchangeable Ca2+ cations (Fig. 6e) and are associated with H+ root excretions (Fig. 6d). The amount of desorbed exchangeable Mb cations is high at H+ root excretions because both, H+ and Al3+ cations compete effectively with Mb cations for the soil exchanger sites and increase the availability of Mb cations in the rhizospheric soil solution. In opposite, OH− root excretions lead to depletions of exchangeable H+ ions and less amounts of desorbed Mb cations and less availability of Mb cations for root uptake even at high water flux rates. Increases of water fluxes and Ca2+ bulk soil solution concentrations and amounts of desorbed exchangeable cations lead to increases of the UCa -values; the letter one is associated with the predominant excretion of H+ ions instead of OH− ions. The OH− root excretions are due to high NO3 − root uptake capacities. The Ca2+ /NO3 − uptake ratios (UCa /UNO3 ) range between about 0.05 and 1.0 with a few higher values at extremely low NO3 − bulk soil solution concentrations (Fig. 7c). In 70% of all cases the Ca2+ /NO3 − uptake ratios are lower than about 0.325 and are associated with OH− root excretions. The UCa /UNO3 -values which are associated with a root excretion of H+ ions are higher than 0.325 (Fig. 7b). The CCa-Bulk /CNO3 -Bulk ratios are between 0.1 and 0.3 due to the high correlation between Ca2+ and NO− concentrations in 3 the bulk soil solution (Fig. 7d). The range of CCa-Bulk /CNO3 -Bulk ratios corresponds to the whole range of the Ca2+ /NO3 − uptake ratios.

4. Discussion 4.1. Methodical approach The collections of measured and modeled rhizospheric ion concentrations (Cˆ Mi -Rh , Cˆ Mi -oRh , CMi -Rh , CMi -SRI , SMi -Rh , Cˆ Mi -oRh ) may be considered as representative samples which show the heterogeneity of rhizospheric ion concentration changes (Rˆ Mi , RMi , VMi -Rh , VMi -SRI , V Mi -Rh , V Mi -SRI , Figs. 2, 3; Figs. in Appendices C, D) around long roots in a soil depth layer of 5–15 cm during a vegetation period in the F1 spruce plot. The actual rates of root nutrient uptake and H+ or OH− root excretion (UMi , EH , EOH ; Fig. 5) and their heterogeneities on the F1-plot scale were presented. The modeling results were obtained in a Monte Carlo upscaling approach as proposed by Bierkens et al. (2000). The F1-plot specific variability of the values of all relevant MIM parameters and variables was determined from measurement data and used in MIM-calculations as demanded by Darrah et al. (2006). The model results provide a transfer of validated information on the ion concentrations and their F1-specific variability between the scales of bulk soil, rhizosphere and root surface. Nutrient uptake rates on the field plot scale are predicted as derived from the actual nutrient uptake rates on the singleroot scale. The concept of scale encompases both, extent and grain, which generally define the upper and lower limits of resolution of data obtained in an investigation (Wu and Li, 2006; Bierkens

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Fig. 5. Variabilites of average net H+ (positive values) or OH− (negative values) root excretion rates, EH/OH (Eq. (2b)), and average root uptake rates, UMi (Eq. (2a)), of Ca2+ , Mg2+ , K+ , NO3 − and SO4 2− . Dashed lines show the variabilites of root nutrient uptake capacities, UMi,max , and the associated H+ or OH− root excretion rates.

et al., 2000). Any characterization of a system is scale dependent and is constrained by the extent and grain of the data. There are often incompatibilities between the rhizosphere modeling scale (RhMS), the scale of model input variables and parameters and the rhizosphere observation (measurement) scale (RhOS) as identified similarly in other studies (Wu and Li, 2006). On RhMS, the results represent the proposed processes operating in the rhizosphere, provide information on the rhizospheric ion concentration gradients in a high spatial–temporal resolution (grain) and show in detail the ion-specific total size of the root’s impact on its soil environment (extent). The grain values are clearly in a sub-mmrange and the extent differs between 2.0 and 5.0 mm (Figs. 2, 3; Figs. in Appendix C) around the root, sometimes more, depending on the ion considered as already reported by Hinsinger et al. (2005). The ionic concentrations changes in larger soil volumes around the root (e.g. soil volumes around the root of 5.0 mm distance to the root surface or the oRh-volume as used here) are less significant because in larger rhizospheric subvolumes the average ion concentrations differ only slightly from the concentrations in the bulk soil (Figs. in Appendix C). Hence, differences between modeled concentrations in oRh and bulk soil are small. On RhOS the measurement results are spatially much coarser, because the

achievable results are often dictated by the technical capabilities of the measurement sensors and do not fulfil the RhMS-related values of grain. Hence, the measurement results usually represent spatially averaged values, e.g. in the SRI- or Rh-volumes (Gobran and Clegg, 1996; Gobran et al., 1999; Majdi and Perrson, 1995; Knoche, 1994) or in larger soil volumes around the root (Braun et al., 2001; Dieffenbach and Matzner, 2000). It is documented by the simulation results (Figures in Appendix D) that measurements in the SRI-soil volume have a high content of information because the ionic SRI-concentrations provide good approximations of the non-measureable root surface concentrations. Therefore, it is very reasonable to measure ion concentrations in the SRI-volume (Gobran and Clegg, 1996; Gobran et al., 1999). But, it should be noted that an accurate determination of the volumes of the sampled rhizosphere soil (Gobran and Clegg, 1996) is important and non-adequate sampling may produce erroneous results as stated by Hinsinger et al. (2005). Moreover, as shown in this study the modeled enrichment factors in Rh and SRI demonstrate that ion concentration gradients in the rhizosphere are not stable over long time intervals but have a diurnal dynamics and opposite concentration gradients are possible in short time intervals of a few hours. Therefore, the temporal variability of rhizospheric concentration

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Fig. 6. Grouped actual uptake rates of Ca2+ , UCa , as related to predefined classes of Ca2+ root uptake capacities (UCa-max ; 6a), the maximum root water uptake rates (qmax ; 6b) the Ca2+ solution concentrations in the bulk soil (CCa-Bulk , 6c), the H+ or OH− root excretions (EH /EOH ; 6d), the Rh-to-Bulk ratios (VCa−Rh , 6e) of Ca2+ concentrations in solution and exchanger (V Ca−Rh , 6f) in Rh and Bulk soil. The data present means and ±sd-values.

changes should be considered with regard to sampling date and sample size in order to avoid a biased emphasis on certain process constallations and small sampling sizes may not include at least approximately the whole spectrum of rhizospheric changes. It is shown in this study that the average concentrations in the 2.0 mm soil volume around the root preserves enough information for using in rhizosphere model calculations. But, a comparability of data on RhMS and RhOS level is possible only if the fine-grained modeling data are lumped via a volume-weighted averaging (Eqs. (1a) and (1b)) as proposed by Bierkens et al., 2000; p. 59 ff). The X-ray method as applied here for measurements of ion Rh-concentrations has been well-calibrated and has been tested in comparision with conventional measurement methods (Fritz et al., 1994; Fritz, 2007).

The repeated measurements of the ion concentrations in single rhizosphere soil solutions only differ by 3–6%. In any Monte Carlo analysis the determination of probability distributions of the model parameter values and their dependencies used in the model calculations is the step that leads to the most controversies over its use, because the used PDFs of the model variables and the correlations between them greatly affect the model outcome. Indeed, although in this study appropriate, measurement-based PDFs have been used several aspects still may produce uncertainty because most of the PDFs have been derived from measurements conducted on a broader, not root-near scale. For downscaling of this information various methods may be applied depending on the pre-information on the relations between

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0.4

CCa−Bulk / CNO3−Bulk

Fig. 7. Actual uptake rates of NO3 − , UNO3 , as related to predefined classes of NO3 − root uptake capacities (U NO3−max ; (a)), the H/OH root excretion rates (EH/OH ) as related to Ca2+ /NO3 − uptake ratios, UCa /UNO3 (b), the actual root uptake rate of Ca2+ as related to the actual uptake rate of NO3 − (c) and Ca2+ /NO3 − concentration ratios in the bulk soil solution as related to UCa /UNO3 ratios (d). The data present means and ±sd-values.

the scales concerning a certain property (Bierkens et al., 2000, p 101 ff). If available, functional relations between the measured data on the coarse scale and their proposed resolution on the finer scale can be used as formally described by Bierkens et al., 2000, p. 120 ff). A functional relation (Appendix B) has been used here for getting temporarily fine-resolved root water uptake rates calculated in water budget models (see also Raats, 2007). The soil solution sampled on the F1 plot by convential suction lysimeters obtains information on the ionic concentrations in large bulk soil solution volumes and the heterogeneities of spatially small-scale differences herein are averaged. The derived PDFs possibly may not represent the variabilities of the ion concentrations in direct proximity of the roots (potential rhizosphere soil pore space) and the strong correlations between Mb and NO3 − as found on F1 (Table B.1) may no longer valid. It should be noted that MIMcalculations disregarding these strong correlations produce more frequently extreme rhizospheric gradients and a better agreement with Rh-measurements (not shown). Moreover, the spectrum of ion concentrations in the bulk soil solution may include small-scale differences of over one order of magnitude (Göttlein and Matzner, 1997) and in aggregated soils the nutrient concentrations in the inter-aggregate pore space, i.e. in the proximity of the roots, may follow a concentration spectrum which is clearly different to that what is measured via conventional suction lysimeters (Hildebrand, 1991). Also, the cationic composition of the exchanger of naturally layered soils may differ on aggregate surfaces and what is determined in homogenized soil samples and fine roots predominantly grow on aggregate surfaces where exchangeable nutrients may have low concentrations (Hildebrand, 1994). But the soil on the F1 plot is characterized by a coherent texture with a volumetric stone fraction lower than 5% which may assure that

the ionic concentrations measured in the solutions sampled with conventional suction lysimeters approximately represent bulk soil solution concentrations in the potential rhizosphere pore space. A further critical aspect is the assumption made implicitly in this study that the soil rooting zone is completely and almost homogeneously exploited by roots and that the roots meet the whole range of the measured ionic bulk soil concentrations. But, spatial heterogeneity in root distribution is characterized by patchiness in soil resources such as nutrients and water or adverse soil conditions (Pregitzer et al., 1993) as shown at the clear vertical gradients of the fine root biomass (Perrson and Stadenberg, 2009). In the horizontal direction the heterogeneity of the root abundance can be expected to follow the unevently distributed soil resources (Schmid and Kazda, 2005) and, hence, roots may meet only a subrange of the CMi -Bulk -PDFs as used here. Moreover, the soil root environment affects morphological root characterics such as root diameter (Zobel et al., 2007; Richter et al., 2007; Ostonen et al., 2007) and roots adjust their nutrient uptake capacities to the external nutrient availability even during the day-time (Gessler et al., 2002; Lucas et al., 2005). It is a shortcoming of this study that the nutrient uptake capacities have not been measured explicitely of the spruce long roots on the F1 plot. But the experimental methods used in determing nutrient root uptake capacities under field conditions (BassiriRad, 2005) not yet differentiate between long roots and mycorrhizal roots and their nutrient uptake capacities have been determined only under experimental conditions. In any case, the applied triangle distributions of the nutrient uptake capacities not only represent the possible ranges of their variabilities but represent also an uncertainty in their specification. Beyond, no correlative relations have been made between ion bulk soil concentrations and root abundance and root nutrient uptake capacities.

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Also, the assumption made in this model study that the factors of influence , , CEC and the bulk soil concentrations CMi -Bulk and SMi -Bulk are unaffected by root activity can not be maintained. Rhizospheric gradients of  and  due to compacting of root surrounding soil and an increase of CEC caused by the accumulation of organic matter have been measured (Gobran et al., 1999). Moreover, the bulk soil concentrations CMi -Bulk and SMi -Bulk may be affected by the root activity. All these determing factors have been addressed in this study at most rudimentary by considering the bulk soil conditions (CMi -Bulk , SMi -Bulk , , ) specific for the soil depth layer of 5–15 cm and the differention between the characteristics of non-mycorrhizal long roots and mycorrhizal roots (in preparation) as it has been realized in similar investigations by measuring the bulk soil chemistry, rhizosphere chemistry and fine root biomass in various soil layers (Majdi and Persson, 1995; Perrson and Stadenberg, 2009). 4.2. Comparison of measured and modeled rhizospheric ion concentrations changes The comparison between measured and modeled data has been realized on the basis of the ionic enrichment factors, (RMi , Rˆ Mi ; Fig. E.1) because of the methodically conditioned dilution of the soil extracts (Knoche, 1994). This proceeding is in agreement with Rykiel (1996) who stated that any comparison of model results with measurement-derived data may serve for a validation. Although it is shown that the heterogeneity of the sampled parameter constellations cannot produce the complete range of RMi -enrichment factors as it is shown by the measurement data (except for SO4 2− ) it can be stated that, with exception of K+ and partially also Na+ , the means of the modeled ion-specific enrichment factors, RMi , agree within certain margins with corresponding ratios, Rˆ M , determined i

from measurement data. The results presented in Table 4 show that the ion-specific confidence intervals are included in the predefined intervals of equivalence which means a rejection the H0 hypothesis in Eq. (3a). The boundaries of the equivalence intervals have been determined to be about 9.5%–16.5% of the particular mean of the rhizospheric measurement data, Rˆ Mi . In most applications a 10% margin of the mean of the reference data is considered to be an acceptable tolerance of difference between tested data sets (Robinson and Froese, 2004). Despite remaining uncertainties of the approach developed in this study the partially satisfying agreement of measured and modeled concentration changes of Ca2+ , Al (in prep.), Fe3+ , Na+ and SO4 2− ions demonstrate that the model results may be considered as partly validated by measurements. Moreover, this validation approach fullfils the postulates formulated by Darrah et al. (2006) who demanded rhizospheric measurements on the single-root level for a corroboration of rhizosphere model results. 4.3. Rhizospheric ion concentration changes, H+ and OH− root excretions and actual root nutrient uptake rates The enrichment factors determined from measurements or model calculations (VMi , RMi , Rˆ Mi ) cover a large range between 0.5 and over 3.0, i.e. they show that both, extreme depletions of less than half and accumulations of the threefold or even more of the particular reference concentration are possible. These values correspond to the range of results measured on other plots. On a spruce plot with a bulk soil chemistry similar to that on the F1-plot Majdi and Bergholm (1995) and Majdi and Rosengren-Brink (1994) found ion concentration increases in 2.0 mm-rhizosphere-solution volumes which were by factors of about 1.2 up to 4.5 higher than the concentrations in the bulk soil solution. Only in some cases no changes or moderate depletions were measured. In contrast,

in soil volumes of less than 2.5 mm distance to spruce long roots Dieffenbach and Matzner (2000) mostly measured concentration decreases of Ca2+ , Mg2+ and NO3 − between 10% and 20% (only for K+ an accumulation factor of about 1.5 was determined). Braun et al. (2001) found in 5.0-mm rhizosphere solution volumes depletions (untreated soil samples) of all relevant nutrients in the same magnitude. The different results measured in the various rhizosphere studies may not be interpreted as contradictory as stated sometimes in the literature but should be considered as the result of different rhizospheric process constellations. Therefore, interpretation and comparison of measured rhizospheric ion concentration changes should be conducted on the basis of presumed processes operating in the rhizosphere. Hence, the often applied focus in many studies on showing significant differences between ion concentrations in rhizosphere and bulk soil is less reasonable, because VMi values close to one (Fig. 2) are possible and ionic Rh-fluxes exist even if no ionic Rh-concentration changes have been measured or modeled. It is shown, that the root-induced water flux is a driving force of the accumulation of ions in the inner rhizosphere (Figs. in Appendix C) which may result in higher actual uptake rates of Mb cations (Fig. 6). But due to the proportionality between water flux rate and soil solution concentration the mass flow rates of Mb cations at low Mb bulk soil solution concentrations are low even at high water flux rates and, hence, their actual root uptake rates are low. Rhizospheric depletions of Mb cations lead to low actual root uptake rates and are caused by high nutrient uptake capacities, exclusive diffusion transport or low water fluxes and low CMb -Bulk values and are mostly associated with OH− root excretions induced by a high availability and root uptake of NO3 − . The predominantly low simulated pHRh and pHSRI changes is confirmed by the low rhizospheric pH changes (about ±0.15 pH units) measured in the upper soil layers on the F1 plot (Maarth, 1995). The range of modeled H+ or OH− root excretion rates corresponds to rates measured in solution culture experiments. Marschner et al. (1991) measured H+ efflux rates of spruce seedlings of up to about 5.0 mmol m−2 d−1 . Also Keltjens and van Loenen (1989) measured 1.9–9.0 mmol m−2 d−1 H+ root efflux rates depending on the tree species and OH− root effluxes in a similar order of magnitude. Here, the root OH− excretion rates modeled in most calculations are neutralized by high amounts of H+ ions desorbed from the soil exchanger (Fig. 3) and convectively transported towards the root (Fig. C.1a). This modeled process dynamics of protons in the rhizosphere is supported by the results presented by Turpault et al. (2007). They used a soil which is chemically similar to the bulk soil of the F1-plot, especially concerning the CEC and high H+ saturation. They measured only less pH increases but considerable decreases of exchangeable protons of up to 22.0% which they attributed to OH− root excretions as response to a NO3 − -induced root anion uptake excess. Turpault et al. (2007) also measured depletions of exchangeable Mg2+ and Ca2+ cations of about 70% and 17%, respectively; the latter is similar to the modeling results presented here. But in constrast to the result presented here (Fig. 3) they found an increased K+ saturation in the rhizosphere. The actual uptake rates of Mb cations are considerably lower if compared with their particular root uptake capacities (Fig. 5). The UCa and UMg values correspond on average to about 40% and 30%, respectively of their root uptake capacities. The actual uptake rates of potassium as modeled here probably underestimates the K+ uptake rates of the roots. It can be assumed that the measured high K+ accumulations in Rh may lead to higher K+ uptake rates. Measured high Rh-accumulations of K+ also have been found by Dieffenbach and Matzner (2000) and Gobran et al. (1999) which they explain by increased weathering rates in the rhizosphere (Calvaruso et al., 2009). A release of non-exchangeable K+ ions from the Illite minerals in the Solling soil, as it has been found by Claassen et al. (1986) in other soils, may lead to the measured accumulations

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and probably to higher actual uptake rates of K+ . The results show that there are considerable uptake reductions of Mb cations (Fig. 6) even at Mb -accumulations in Rh. This is all the more remarkable because the uptake capacities defined in this study correspond to the lower values of nutrient uptake capacities measured in solution culture experiments (Marschner et al., 1991; Häussling et al., 1988). Moreover, from the results presented in this study it may be concluded that the characteristics of the heterogeneity of rhizospheric changes can be related to and is strongly affected by the ionic concentrations in the bulk soil and its inherent heterogeneity. For example, the strong positive correlations between H+ , Mb and NO3 − ions (Table C.1a) determines that the availability of Mb cations in the bulk soil is mostly accompanied by the availability of NO3 − . It can be predicted that a more asynchronous availability of NO3 − and Mb ions would produce higher root excretion rates of both, OH− and H+ ions. Moreover, if in addition NH4 + is available or is even the main N-source, preferential root uptake of NH4 + will produce high H+ root excretion rates and considerable decreases of pHSRI and pHRh . Increases of rhizopsheric H+ -concentrations result in an enhanced H+ -induced desorption of Mb cations from the rhizospheric soil exchanger sites and could lead to an increased availability and possibly higher actual uptake rates of Mb cations (see Figs. in Appendix C; Nietfeld and Prenzel, 2015). This is supported by the results of fertilization experiments with (NH4 )2 SO4 in which strong acidifications of the rhizospheres were measured (Braun et al., 2001; Clegg et al., 1997). The NH4 + -treated soils show less Rh-depletions of nutrients if compared with results achieved on untreated soils (Braun et al., 2001). On the other hand, it can be concluded from the results presented in Figs. 6 and 7 and in Appendix F that a proposed considerable reduction of the bulk soil solution concentrations of Mb cations and other cationic nutrients (and the other model parameter values leaving unchanged) would mostly lead to high OH− root excretions rates. Beyond, an increased availability of NO3 − in the bulk soil solution and NO3 − -root uptake capacities higher as defined here would lead to considerable pH increases in the rhizosphere and a possible formation of Al(OH)3 (s) (gibbsite). Due to the model results presented in Nietfeld and Prenzel (2015) a formation of gibbsite produces depletions of Al3+ cations in rhizospheric soil solution and soil exchanger, increases of exchangeable Mb cations, and leads to a low actual root uptake of Mb cations. These rootinduced feed-back mechanisms are demonstrated and discussed in detail in the MIM-model analysis of Nietfeld and Prenzel (2015). In any case, for an understanding the differences between the bulk and the rhizosphere soil measurements of rhizospheric ion concentrations have to include the inherent heterogeneity of the bulk soil chemistry on a small spatial scale in a direct vicinity of the root. This aspect has been pointed out by Schöttelndreier and Falkengren-Grerup (2009) and may be realized as conducted in this study and in the investigations of Seguin et al. (2004) by separating inner and outer rhizosphere and bulk soil.

5. Conclusions The modeled average nutrient root uptake rates, UMi (Fig. 5), can be used to give an assessment of the total annual nutrient uptake rates of the long roots on the F1-stand. But it should be noted that any generalization should consider the soil-layer specific differences in chemistry and physics of the bulk soil and spatial and temporal differences in the fine root biomass with hightest amounts in the vegetation period and in the organic and upper mineral-soil layers (Matzner and Murach, 1995). Irrespective of the restrictions and assumptions which have to be made, the total

13

Table 6 Assessment of annual nutrient uptake via long roots on the F1-plot. Ion

2+

Ca Mg2+ K+ NTotal SO4 2−

Stand uptakea determined via balance approach

Modeled total uptake via long root tipsb

Fractions of measured stand uptake

[mol ha−1 a−1 ]

[mol ha−1 a−1 ]

%

723.5 111.1 793.0 4000.0 200.0

26.2 12.3 8.8 107.6c 11.8

3.6 11.1 1.1 2.7 5.9

Stand uptake using long root uptake rates measured by Marschner et al. (1991) 566.2

1180.2c

a

Matzner (1988), p. 56. Murach (1984): 12 × 106 long root tips ha−1 and an assumed vegation period of 300d. c Uptake as NO3 − . b

annual uptake of Mb cations and of NO3 − and SO4 2− anions can be calculated if a rough estimate of the average number of nonmycorrhizal long roots tips on the F1 plot of 12 × 106 tips ha−1 (Murach, 1984; Marschner et al., 1991) is used as made in the calculations of Marschner et al. (1991). The calculations of Marschner et al. (1991) are based on the results of solution culture experiments In our study these estimates are made under consideration of the rhizospheric conditions. The amounts of Mb cations and NO3 − and SO4 2− taken up via the long roots from the mineral soil depend on the nutrient considered and correspond to about 2.5%–10% (Table 6) of the annual uptake rate determined via the nutrient budget approach (Matzner, 1988). Due to the discrepancy between measured and modeled K+ concentration the uptake rate of potassium may be much higher as modeled here. These results show that the main fraction of mineral nutrient uptake occurs via mycorrhizal fine roots which accounts for about 90–95% of the total root tips in the plot (Murach, 1984). The annual uptake rates of Ca2+ and NO3 − presented in Table 6 are considerably lower as calculated by Marschner et al. (1991); the differences to the results reported by Marschner et al. (1991) are probably due to differing root diameters and lengths. The net OH− root excretions (total of OH− excretion rates minus total of H+ excretion rates) via long roots has been calculated to 31.8 mol ha−1 a−1 . In the matter balance calculations of the F1-plot the internal proton production and consumption on the Solling F1 plot the H+ production induced by tree nutrient uptake has been accounted for about 500.0–1000.0 mol ha−1 a−1 (Bredemeyer, 1987). This indicates that most of the tree-induced proton production will occur via the mycorrhizal fine root biomass in the upper soil layer where NH+ still is available. 4 The soil chemical situation on the F1 plot in the last years and nowadays and probably in the near future is characterized by increasing deposition-induced NO3 − concentrations and a proceeding reduction of the total ion concentrations in the bulk soil solution (Meesenburg, pers. comm.). As shown by the simulation results, under low bulk soil solution concentrations of Mb cations the actual root uptake rates of Mb cations considerably differ from their uptake capacities and the exchangeable Mb -cations have a considerable share on their actual root uptake rates. Assuming that this low actual acquisition of Mb cations is valid to all roots a nutritional stress for the spruce stand may be predicted which may be compensated by an increasing fine root biomass growth. These predictions are supported by the measurement results obtained from investigations on the roofed Solling plot which was treated with “clean”, pre-industrial precipitation but which is also characterized by low nitrogen content. After a ten-years treatment the clear reduction of the total ionic solution concentration in the bulk soil

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corresponds to a considerable increase of the fine root biomass to about the threefold of the value measured on the roofed control plot. This result has been interpreted as the tree’s response to the reduced nutrient availability, especially of Mb cations and nitrogen (Lammersdorf and Borken, 2004). But in contrast to the soil solution chemistry on the “clean” roof plot, the probable prospective chemical situation on the F1 plot is characterized by a proceeding NO3 − saturation (Brumme and Khanna, 2008). An actual NO3 − root uptake of about root uptake capacity (Fig. 7) leads to a high total NO3 − uptake of the F1 stand and an extremely low Mb /NO3 − uptake ratio and possibly an adverse Mb cations – nitrogen stoichiometry on the whole tree scale (Agren, 2008). Acknowledgements We would like to acknowledge M. Hasler, Kiel and G. Robinson, Melbourne for valuable suggestions in applying equivalence tests. S. Tarantola, Ispra, is acknowledged for giving valuable hints in applying the SIMLAB program. We are grateful to H. Meesenburg, Göttingen for providing the measurement data of the ion soil solution concentrations on the spruce F1-plot in Solling, to U. Schwardmann, GWDG Göttingen, for computational support and to an anonymous reviewer for his helpful suggestions. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ecolmodel.2016. 09.006. References Agren, G.I., 2008. Stoichiometry and nutrition of plant growth in natural communities. Annu. Rev. Ecol. Evol. Syst. 39, 153–170. BassiriRad, H. (Ed.), 2005. Nutrient Acquisition by Plants. An Ecological Perspective. Ecological Studies, vol. 181. Springer, Berlin. Bates, D., Mechler, M., 2008. Matrix: Sparse and Dense Matrix Classes and Methods. R-package, version 0.999375-38. Beese, F., 1986. Parameter des Stickstoffumsatzes in Ökosystemen mit Böden unterschiedlicher Acidität. Gött. Bodenkd. Ber. 90, 1–344. Bierkens, M.F.P., Finke, P.A., De Willigen, P., 2000. Upscaling and Downscaling Methods for Environmental Research. Developments in Plant and Soil Sciences, vol. 88. Kluwer Academic Publishers, Dordrecht, The Netherlands. Borken, W., Kossmann, G., Matzner, E., 2007. Biomass, morphology and nutrient content of fine roots in four Norway spruce stands. Plant Soil 292, 79–93. Braun, M., Dieffenbach, A., Matzner, E., 2001. Soil solution chemistry in the rhizosphere of beech (Fagus silvatica L.) roots as influenced by ammonium supply. J. Plant Nutr. Soil Sci. 164, 271–277. Bredemeyer, M., 1987. Quantification of ecosystem-internal proton production from the ion balance of soil. Plant Soil 101, 273–280. Brumme, R., Khanna, P.K., 2008. Ecological and site historical aspects of N dynamics and current N status in temperate forests. Glob. Change Biol. 14, 125–141. Calvaruso, C., Mareschal, L., Turpault, M.P., Leclerc, E., 2009. Rapid clay weathering in the rhizosphere of Norway Spruce and Oak in an acid forest ecosystem. Soil Sci. Soc. Am. J. 73, 331–338. Claassen, N., Syring, K.M., Jungk, A., 1986. Verification of a mathematical model by simulating potassium uptake from soil. Plant Soil 95, 209–220. Clegg, S., Gobran, G.R., Guan, X., 1997. Rhizosphere chemistry in an ammonium sulfate and water manipulated Norway spruce (Picea abies (L.) Karst.) forest. Can. J. Soil Sci. 77, 515–523. Collignon, C., Calvaruso, C., Turpault, M.P., 2011. Temporal dynamics of exchangeable K, Ca and Mg in acidic bulk soil and rhizosphere under Norway spruce (Picea abies K.) and beech (Fagus silvatica L.) stands. Plant Soil 349, 335–366. Coners, H., Leuschner, Ch., 2005. In situ measurement of fine root water absorption in three temperate tree species – temporal variability and control by soil and atmospheric factors. Basic Appl. Ecol. 6, 395–405. Darrah, P.R., Jones, D.L., Kirk, G.J.D., Roose, T., 2006. Modeling the rhizosphere: a review of methods of ‘upscaling’ to the whole-plant scale. Eur. J. Soil Sci. 57, 13–25. De Wit, H.A., Eldhuset, T.D., Mulder, J., 2010. Dissolved Al reduces Mg uptake in Norway spruce forest: results from a long-term field manipulation in Norway. For. Ecol. Manage. 259, 2072–2082. Delignette-Muller, M.L., Pouillot, R., Denis, J.B., 2013. R-pakage ‘fitdistrplus’. Version 1.0-1. http://riskassessment.r-forge.r-project.org.

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Please cite this article in press as: Nietfeld, H., et al., Modeling of mineral nutrient uptake of spruce tree roots as affected by the ion dynamics in the rhizosphere: Upscaling of model results to field plot scale. Ecol. Model. (2016), http://dx.doi.org/10.1016/j.ecolmodel.2016.09.006