# The moisture response of soil heterotrophic respiration: interaction with soil properties

F. E. Moyano, N. Vasilyeva, L. Bouckaert, F. Cook, J. Craine, J. Curiel Yuste, A. Don, D. Epron, P. Formanek, A. Franzluebbers, et al.

► To cite this version:

F. E. Moyano, N. Vasilyeva, L. Bouckaert, F. Cook, J. Craine, et al. The moisture response of soil heterotrophic respiration: interaction with soil properties. Biogeosciences, 2012, 9 (3), pp.1173–1182. 10.5194/bg-9-1173-2012. hal-01567157

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# The moisture response of soil heterotrophic respiration: interaction with soil properties

F. E. Moyano<fnref n="1" />, N. Vasilyeva<fnref n="1" />, L. Bouckaert<fnref n="2" />, F. Cook<fnref n="3" />, J. Craine<fnref n="4" />, J. Curiel Yuste<fnref n="5" />, A. Don<fnref n="6" />, D. Epron<fnref n="7" />, P. Formanek<fnref n="8" />, A. Franzluebbers<fnref n="9" />, U. Ilstedt<fnref n="10" />, T. Kätterer<fnref n="11" />, V. Orchard<fnref n="12" />, M. Reichstein<fnref n="13" />, A. Rey<fnref n="5" />, L. Ruamps<fnref n="1" />, J.-A. Subke<fnref n="14" />, I. K. Thomsen<fnref n="15" />, and C. Chenu<fnref n="1" />

Correspondence to: F. E. Moyano (fernando.moyano@grignon.inra.fr)

Received: 21 October 2011 – Published in Biogeosciences Discuss.: 2 December 2011

Revised: 5 February 2012 – Accepted: 12 March 2012 – Published: 28 March 2012

**Abstract.** Soil moisture is of primary importance for predicting the evolution of soil carbon stocks and fluxes, both because it strongly controls organic matter decomposition and because it is predicted to change at global scales in the following decades. However, the soil functions used to model the heterotrophic respiration response to moisture have limited empirical support and introduce an uncertainty of at least 4% in global soil carbon stock predictions by 2100. The necessity of improving the representation of this relationship in models has been highlighted in recent studies. Here we present a data-driven analysis of soil moisture-respiration relations based on 90 soils. With the use of linear models we show how the relationship between soil heterotrophic respiration and different measures of soil moisture is consistently affected by soil properties. The empirical models derived include main effects and moisture interaction effects of soil texture, organic carbon content and bulk density. When

compared to other functions currently used in different soil biogeochemical models, we observe that our results can correct biases and reconcile differences within and between such functions. Ultimately, accurate predictions of the response of soil carbon to future climate scenarios will require the integration of soil-dependent moisture-respiration functions coupled with realistic representations of soil water dynamics.

## 1 Introduction

Soil moisture is one of the most important environmental factors driving productivity and carbon cycling in terrestrial ecosystems. Next to temperature, it is a primary determinant of the rate at which soil carbon is mineralized by microbes into carbon dioxide (Greaves and Carter, 1922; Davidson et al., 2000; Davidson and Janssens, 2006; Cook and Orchard,

<footnote n="1">¹CNRS-UPMC-AgroParisTech, UMR Bioemco 7618, 78850 Thiverval-Grignon, France</footnote>

<footnote n="2">²Department of soil management and soil care, Ghent University, Ghent, Coupure Links 653, Belgium</footnote>

<footnote n="3">³Environmental Physicist/Director, Freeman Cook & Associates, Pty Ltd, P.O. Box 948, Mt Ommaney Q4074, Australia</footnote>

<footnote n="4">⁴Division of Biology, Kansas State University, Manhattan KS 66506-4901, USA</footnote>

<footnote n="5">⁵Museo Nacional de Ciencias Naturales CSIC, Serrano 115 dpdo, 28006 Madrid, Spain</footnote>

<footnote n="6">⁶Johann Heinrich von Thünen-Institut, Institut für Agrarrelevante Klimaforschung, Bundesallee 50, 38116 Braunschweig, Germany</footnote>

<footnote n="7">⁷Nancy-Université, UMR Ecologie et Ecophysiologie Forestières, 54506 Vandoeuvre Les Nancy, France</footnote>

<footnote n="8">⁸Mendel University Brno, Department of Geology and Soil Science, Zemedelska 3, 613 00 Brno, Czech Republic</footnote>

<footnote n="9">⁹USDA – Agricultural Research Service, 1420 Experiment Station Road, Watkinsville GA 30677, USA</footnote>

<footnote n="10">¹⁰Department of Forest Ecology and Management, SLU, SE-901 83 Umeå, USA</footnote>

<footnote n="11">¹¹Professor, SLU, Dept. Soil and Environment, P.O. Box 7014, 75007 Uppsala, Sweden</footnote>

<footnote n="12">¹²Strategic Manager, Science and Research, ESR, New Zealand</footnote>

<footnote n="13">¹³Biogeochemical Model-Data Integration Group, Max-Planck Institute for Biogeochemistry, 07701 Jena, Germany</footnote>

<footnote n="14">¹⁴University of Stirling, School of Natural Sciences, Biological and Environmental Sciences, Stirling FK9 4LA, Scotland, UK</footnote>

<footnote n="15">¹⁵Department of Agroecology, Organic Matter, Blichers Allé 20, 8830, Tjele, Denmark</footnote>
2008) and the main driver of soil microbial activity in many ecosystems (Davidson et al., 2000; Jassal et al., 2008; Liu et al., 2009). It is also expected to change significantly at global scales as a result of climate change in the coming decades (IPCC, 2007; Burke and Brown, 2010), potentially leading to large scale changes in soil carbon stocks in different regions, such as the Amazon basin (Falloon et al., 2011).

The relationship between soil moisture and soil respiration is known to be variable. It depends not only on the soil type (Franzluebbers, 1999; Vincent et al., 2006) but also on the diversity of measures used to express water conditions in soils, each having a unique relationship with soil microbial activity (Ilstedt et al., 2000; Paul et al., 2003). Soil factors including total pore space, bulk density and texture have been shown to influence this relationship (Franzluebbers, 1999; Thomsen et al., 1999). However, such studies have been few with most concentrating on finding the measure of moisture that best predicts respiration rates (e.g. water potential, water-filled pore space, etc.) or the single function that best describes this relationship (e.g. linear, polynomial, etc.). A systematic analysis of variations in response to a wide range of soil types has been lacking.

Soil carbon models use soil moisture-respiration functions that, in theory, represent an average response of microbial respiration to soil moisture content, i.e. they do not account for any possible variation in this relationship (Rodrigo et al., 1997). In addition, these functions are generally developed and validated using soils from specific sites and, as a consequence, are not suitable for a wider range of soil types. Accordingly, a few studies indicate that the variability in soil carbon budget predictions related to the use of different moisture-respiration functions can be important (Rodrigo et al., 1997; Bauer et al., 2008; Falloon et al., 2011). Fallon et al. (2011) showed that the divergence in simulations related to the choice of moisture function alone is nearly 4% of global carbon stocks by 2100. However, since all the compared functions still represent an “average” response, the real uncertainty may be larger than reported. A better understanding of how this relationship actually depends on soil properties will help to quantify and reduce such uncertainties (Franzluebbers, 1999; Schjonning et al., 1999; Thomsen et al., 1999).

Here we present results from a meta-analysis of multiple soil incubation datasets that describe how soil properties regulate the relationship between soil microbial respiration and moisture. We use the terms “soil respiration” or simply “respiration” referring to soil CO₂ emissions from heterotrophic microbial activity. The soil respiration response to moisture is the result of several processes – including osmotic stress, diffusion and oxygen limitations – that combined produce a net effect on the rate of carbon decomposition. Consequently, we did not look for a function that acts as the best single average predictor, as it would invariably underperform in most soil types. Instead, we treated the respiration response as a variable that changes freely at different levels

of moisture and is explained by moisture itself and other soil properties.

The main outcome of this analysis is statistical models that predict the proportional response of soil respiration to moisture as a soil-type dependent variable. This can then be used to derive relative soil respiration curves for a given soil type. We illustrate the results by comparing the model we derive, using data from soils of England and Wales (Bellamy et al., 2005), with other currently used functions.

# 2 Materials and methods

## 2.1 Data processing

Data were assembled from studies where soil carbon dioxide emissions were measured together with variations in soil moisture under controlled laboratory conditions. Treatments varied across studies (e.g. intact vs. homogenized soils) but only homogenous samples with respect to soil properties were used. Incubations with temperatures outside the 10 to 35 °C range were excluded. Respiration data from incubations where moisture decreased over time were corrected for substrate depletion effects using data from control (constant moisture) samples. Pore space, if not available, was calculated assuming a mineral density of 2.65 and organic matter density of 1.4 (Rühlmann et al., 2006). We converted the measures of soil CO₂ emissions, moisture and soil properties to the same units and individually normalized soil respiration data sets to a 0–1 scale. The latter facilitated data manipulation but did not affect the results since we analyzed the proportional response rather than the absolute changes, as described below.

The resulting database consisted of data from 90 different soils originating from 42 sites and characterized by a broad range of soil properties (Tables 1 and 2). From this data we obtained a total of 310 respiration-moisture relationships by plotting soil respiration from a given soil against related soil moisture data expressed in one or more out of four available measures. These measures are: mass related or gravimetric moisture ($\theta_m$), volumetric moisture ($\theta_v$), fraction of water saturation ($\theta_s$), and the logarithm of water potential ($\psi_{log}$). $\theta_m$ is a laboratory standard while $\theta_v$ is the most widely used field measure, often associated with high frequency carbon flux data. $\theta_s$ and $\psi_{log}$ are often considered optimal predictors of microbial respiration as they are related to air space and water energy status respectively (Orchard and Cook, 1983; Skopp et al., 1990). In order to obtain an approximate range of 0 to 1, convenient for the analysis, the unit used for $\psi_{log}$ was (–log₁₀|$\psi$|ₖₚₐ)/5 + 1. Those for the other measures are: g H₂O gSoil⁻¹ ($\theta_m$), cm³ H₂O cm⁻³ ($\theta_v$), and cm³ H₂O cm⁻³ pore-space ($\theta_s$). When possible, missing moisture measures were derived, e.g. using bulk density or pore space for converting $\theta_v$ to $\theta_m$ or $\theta_s$, respectively, and vice versa.
<table><caption>**Table 1.** Description of the data used in the analysis. Each line represents a specific site or location. DS is number of data sets, representing different soil types related to each site. Site averages of soil properties used in the analysis are shown. BD = bulk density, SOC = soil organic carbon, N = soil nitrogen.</caption><thead><tr><th>Reference</th><th>DS</th><th>Country</th><th>Ecosystem</th><th>BD (g cm<sup>-3</sup>)</th><th>SOC (mg g<sup>-1</sup>)</th><th>N (mg g<sup>-1</sup>)</th><th>Clay (%)</th><th>Silt (%)</th><th>Sand (%)</th><th>pH</th></tr></thead><tbody><tr><td>Bouckaert (unpublished data)</td><td>3</td><td>Belgium</td><td>Forest</td><td>1.6</td><td>44</td><td>3.5</td><td>18</td><td>49</td><td>33</td><td>5.4</td></tr><tr><td>Bowden et al. (1998)</td><td>1</td><td>USA</td><td>Forest</td><td>0.3</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>3.3</td></tr><tr><td>Cook (unpublished data)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>1.3</td><td>64</td><td>4.7</td><td>16</td><td>6</td><td>79</td><td>5.4</td></tr><tr><td>Cook (unpublished data)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>0.9</td><td>55</td><td>5.5</td><td>17</td><td>33</td><td>50</td><td>5.7</td></tr><tr><td>Cook (unpublished data)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>0.8</td><td>71</td><td>6.2</td><td>52</td><td>34</td><td>14</td><td>6.1</td></tr><tr><td>Cook et al. (1985)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>Craine and Gelderman (2011)</td><td>8</td><td>USA</td><td>Grassland</td><td>NA</td><td>46</td><td>3.3</td><td>33</td><td>60</td><td>8</td><td>6.7</td></tr><tr><td>Curiel Yuste et al. (2007)</td><td>2</td><td>USA</td><td>Forest</td><td>0.9</td><td>102</td><td>3.5</td><td>11</td><td>29</td><td>60</td><td>5.5</td></tr><tr><td>Curiel Yuste et al. (2007)</td><td>2</td><td>USA</td><td>Grassland</td><td>1.5</td><td>28</td><td>2.5</td><td>14</td><td>44</td><td>43</td><td>6.4</td></tr><tr><td>Don (unpublished data)</td><td>1</td><td>Germany</td><td>Grassland</td><td>1.5</td><td>11</td><td>1.1</td><td>9</td><td>10</td><td>81</td><td>4.5</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Forest</td><td>1.1</td><td>31</td><td>NA</td><td>14</td><td>16</td><td>70</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.2</td><td>14</td><td>NA</td><td>18</td><td>29</td><td>53</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.1</td><td>21</td><td>NA</td><td>22</td><td>75</td><td>3</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Grassland</td><td>1.2</td><td>8</td><td>NA</td><td>26</td><td>19</td><td>55</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Grassland</td><td>1.1</td><td>22</td><td>NA</td><td>17</td><td>64</td><td>19</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Grassland</td><td>1.0</td><td>16</td><td>NA</td><td>46</td><td>42</td><td>12</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>NA</td><td>1.1</td><td>35</td><td>NA</td><td>14</td><td>37</td><td>49</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.2</td><td>13</td><td>NA</td><td>20</td><td>51</td><td>29</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Grassland</td><td>1.2</td><td>7</td><td>NA</td><td>22</td><td>24</td><td>54</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.1</td><td>13</td><td>NA</td><td>58</td><td>35</td><td>7</td><td>6.8</td></tr><tr><td>Doran (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.1</td><td>11</td><td>NA</td><td>16</td><td>68</td><td>16</td><td>6.8</td></tr><tr><td>Skopp et al. (1990)</td><td>1</td><td>USA</td><td>Grassland</td><td>1.2</td><td>13</td><td>NA</td><td>24</td><td>54</td><td>22</td><td>6.8</td></tr><tr><td>Epron (unpublished data)</td><td>1</td><td>France</td><td>Forest</td><td>0.8</td><td>27</td><td>2.5</td><td>20</td><td>66</td><td>14</td><td>4.6</td></tr><tr><td>Formanek (unpublished data)</td><td>3</td><td>Czech Republic</td><td>Forest</td><td>NA</td><td>318</td><td>11.2</td><td>NA</td><td>NA</td><td>NA</td><td>4.8</td></tr><tr><td>Franzluebbers (1999)</td><td>15</td><td>USA</td><td>Grassland</td><td>1.2</td><td>16</td><td>1.1</td><td>19</td><td>16</td><td>65</td><td>6.2</td></tr><tr><td>Gulledge and Schimel (1998)</td><td>2</td><td>USA</td><td>Grassland</td><td>NA</td><td>61</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>Ilstedt et al. (2000)</td><td>3</td><td>Malaysia</td><td>Forest</td><td>0.6</td><td>52</td><td>4.1</td><td>27</td><td>32</td><td>42</td><td>4.7</td></tr><tr><td>Ilstedt et al. (2000)</td><td>1</td><td>Sweden</td><td>Forest</td><td>0.5</td><td>556</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>4.1</td></tr><tr><td>Linn and Doran (1984)</td><td>1</td><td>USA</td><td>Cultivated</td><td>NA</td><td>21</td><td>1.6</td><td>34</td><td>54</td><td>12</td><td>5.8</td></tr><tr><td>Liu et al. (2009)</td><td>1</td><td>China</td><td>Grassland</td><td>NA</td><td>16</td><td>1.5</td><td>17</td><td>20</td><td>63</td><td>6.8</td></tr><tr><td>Lomander et al. (1998)</td><td>2</td><td>Sweden</td><td>Cultivated</td><td>NA</td><td>18</td><td>1.9</td><td>57</td><td>38</td><td>5</td><td>8.2</td></tr><tr><td>Nyhan (1976)</td><td>1</td><td>USA</td><td>NA</td><td>1.4</td><td>9</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>6.8</td></tr><tr><td>Orchard and Cook (1983)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>Orchard et al. (1992)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>NA</td><td>56</td><td>3.5</td><td>24</td><td>NA</td><td>NA</td><td>5.2</td></tr><tr><td>Orchard et al. (1992)</td><td>1</td><td>New Zealand</td><td>Grassland</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>Reichstein et al. (2005)</td><td>1</td><td>Germany</td><td>Forest</td><td>0.9</td><td>45</td><td>2.0</td><td>10</td><td>38</td><td>52</td><td>2.9</td></tr><tr><td>Rey et al. (2005)</td><td>2</td><td>Italy</td><td>Forest</td><td>1.0</td><td>49</td><td>6.0</td><td>NA</td><td>NA</td><td>NA</td><td>5.7</td></tr><tr><td>Ruamps (unpublished data)</td><td>1</td><td>France</td><td>Cultivated</td><td>1.5</td><td>14</td><td>1.2</td><td>17</td><td>53</td><td>30</td><td>6.8</td></tr><tr><td>Thomsen et al. (1999)</td><td>15</td><td>Denmark</td><td>Cultivated</td><td>1.3</td><td>15</td><td>1.5</td><td>23</td><td>14</td><td>64</td><td>6.9</td></tr><tr><td>Skopp et al. (1990)</td><td>1</td><td>USA</td><td>Cultivated</td><td>1.4</td><td>9</td><td>NA</td><td>3</td><td>7</td><td>90</td><td>6.8</td></tr><tr><td>Stott et al. (1986)</td><td>1</td><td>USA</td><td>Cultivated</td><td>NA</td><td>4</td><td>0.6</td><td>NA</td><td>NA</td><td>NA</td><td>7.0</td></tr><tr><td>Wickland and Neff (2008)</td><td>3</td><td>USA</td><td>Forest</td><td>NA</td><td>318</td><td>14.5</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr></tbody></table>

The following analysis was performed in parallel for each moisture measure using the R statistical software version 2.13.1 (Supplement: R Code and data files MRD.txt, DD.txt and funs.txt). We started by assuming that a response to a change in soil moisture is proportional to the value of respiration itself, as normally done in soil carbon models. By using the proportional response we make our results generalizable, avoiding the problem of comparing absolute respi-

ration values which vary largely across soils. Since the response of respiration varies along the moisture axis, we defined the Proportional Response of Soil Respiration (PR<sub>SR</sub>) related to a 0.01 increase in soil moisture as the central unit for analysis, with the unit of this 0.01 value depending on the moisture measure applied. We then tested how PR<sub>SR</sub> is affected by diverse soil properties.
<table><caption>**Table 2.** Range of values for soil moisture (SM), soil organic carbon (SOC), clay, and bulk density (BD) used to fit linear regression models using different measures of soil moisture. Numbers in italics are for descriptive purposes only since the respective variables were not used in that particular model. $\theta_m$ is gravimetric moisture (g H₂O gSoil⁻¹), $\theta_v$ is volumetric moisture (cm³ H₂O cm⁻³), $\theta_s$ is relative water saturation (cm³ H₂O cm⁻³ pore-space), and $\Psi^{log}$ is water potential [(-log10|Ψ|kPa)/5 + 1].</caption><thead><tr><th rowspan="2">Model and Moisture Measure</th><th colspan="2">SM</th><th colspan="2">SOC (g g<sup>-1</sup> soil)</th><th colspan="2">Clay (fraction)</th><th colspan="2">BD (g cm<sup>-3</sup>)</th></tr><tr><th>min</th><th>max</th><th>min</th><th>max</th><th>min</th><th>max</th><th>min</th><th>max</th></tr></thead><tbody><tr><td colspan="9"><strong>Model 1 (mineral soils)</strong></td></tr><tr><td>θ<sub>m</sub></td><td>0.04</td><td>0.65</td><td>0.01</td><td>0.05</td><td>0.09</td><td>0.45</td><td>0.8</td><td>1.5</td></tr><tr><td>θ<sub>v</sub></td><td>0.05</td><td>0.60</td><td>0.01</td><td>0.05</td><td>0.03</td><td>0.58</td><td>0.8</td><td>1.5</td></tr><tr><td>θ<sub>s</sub></td><td>0.07</td><td>1.00</td><td>0.01</td><td>0.05</td><td>0.03</td><td>0.58</td><td>0.8</td><td>1.5</td></tr><tr><td>ψ<sub>log</sub></td><td>0.22</td><td>1.02</td><td>0.01</td><td>0.03</td><td>0.09</td><td>0.45</td><td>0.6</td><td>1.5</td></tr><tr><td colspan="9"><strong>Model 2 (mineral soils)</strong></td></tr><tr><td>θ<sub>m</sub></td><td>0.04</td><td>0.66</td><td>0.01</td><td>0.05</td><td>0.09</td><td>0.57</td><td>—</td><td>—</td></tr><tr><td>θ<sub>v</sub></td><td>0.05</td><td>0.60</td><td>0.01</td><td>0.05</td><td>0.03</td><td>0.58</td><td>—</td><td>—</td></tr><tr><td>θ<sub>s</sub></td><td>0.07</td><td>1.00</td><td>0.01</td><td>0.05</td><td>0.03</td><td>0.58</td><td>—</td><td>—</td></tr><tr><td>ψ<sub>log</sub></td><td>0.22</td><td>1.02</td><td>0.01</td><td>0.03</td><td>0.09</td><td>0.45</td><td>—</td><td>—</td></tr><tr><td colspan="9"><strong>Model 3 (organic soils)</strong></td></tr><tr><td>θ<sub>m</sub></td><td>0.05</td><td>1.1</td><td>0.05</td><td>0.40</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>θ<sub>v</sub></td><td>0.05</td><td>0.85</td><td>0.06</td><td>0.35</td><td>—</td><td>—</td><td>0.24</td><td>0.9</td></tr><tr><td>θ<sub>s</sub></td><td>0.07</td><td>0.99</td><td>0.06</td><td>0.35</td><td>—</td><td>—</td><td>0.24</td><td>0.9</td></tr><tr><td>ψ<sub>log</sub></td><td>0.27</td><td>0.97</td><td>0.06</td><td>0.56</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

To obtain PR<sub>SR</sub> values we used general additive models (GAMs) to fit smooth curves to each of the 310 relationships. Linear or polynomial fits were used instead if the number of moisture points in a dataset was less than 4. Respiration values at each 0.01 moisture interval were then predicted from the fitted curves between the minimum and maximum moisture value of each relationship (as to avoid extrapolations). With the resulting set of predicted values, the PR<sub>SR</sub> of each 0.01 increase in moisture was calculated, at moisture M, as the average of SR(M)/SR(M-0.01) and SR(M+0.01)/SR(M).

## 2.2 Regression models

The dependence of PR<sub>SR</sub> on soil properties was analyzed using soil pore space, bulk density, soil organic carbon, and sand, silt and clay content. We also tested soil pH and the interaction between organic carbon and clay but found no significant effects. To isolate the effect of each soil property we used linear regression models of the form:

$$PR_{SR} = \beta_{1}M + \beta_{2}M^{2} + \beta_{3}M^{3} + \beta_{i}SP_{i} + \beta_{i}M \cdot SP_{i} + \varepsilon \quad (1)$$

where M is soil moisture (either $\theta_m$, $\theta_v$, $\theta_s$ or $\psi_{log}$) and SP are soil properties which can interact with M. Stepwise model selection was applied.

Preliminary results revealed important differences between soils with high and low organic carbon content. After empirically testing the influence of different soils on the models' root mean square deviation, we set a threshold of 50 mg C g⁻¹ soil, with soils above this value considered organic for the purpose of this analysis. These soils were analyzed separately from mineral soils.

The PR<sub>SR</sub> tended to be very large at respiration values near 0. Such PR<sub>SR</sub> are related to very low respiration rates and do not have a large absolute impact, but can still represent a real response. However, our model failed to accurately predict them and, as a consequence, a few of such values produced a strong general bias. To avoid this we excluded any PR<sub>SR</sub> value further than 3 standard deviations from the mean.

Model simplification led to excluding pore space (strongly correlated with BD), sand, silt and the SOC-M interaction. As bulk density is often not available for use in large scale soil simulations, we fitted a second model for mineral soils including only clay and organic carbon. The final linear models predicting PR<sub>SR</sub> were:

$$PR_{SR} = \beta_{1}M + \beta_{2}M^{2} + \beta_{3}M^{3} + \beta_{4}BD + \beta_{5}M \cdot BD + \beta_{6}clay + \beta_{7}M \cdot clay + \beta_{8}SOC \quad (2)$$

$$PR_{SR} = \beta_{1}M + \beta_{2}M^{2} + \beta_{3}M^{3} + \beta_{4}clay + \beta_{5}M \cdot clay + \beta_{6}SOC \quad (3)$$
$$PR_{SR} = \beta_1 M + \beta_2 M^2 + \beta_3 M^3 \quad (4)$$

where M is soil moisture, BD is bulk density, SOC is soil organic carbon and β are model coefficients. Model 1 (Eq. 2) and Model 2 (Eq. 3) are mineral soil models, with the latter excluding bulk density (Table 3). Model 3 (Eq. 4) is for organic soils and has only moisture as a predictor. Few datasets were available for these soils and significant correlations with soil properties were not found (Table 3).

## 2.3 Soil respiration predictions

With the PR<sub>SR</sub> values obtained from the above models, respiration was predicted using the equation:

$$SR(M) = (\Pi_{k=M_0}^{M} PR_{SR_k}) \cdot SR_0 \quad (5)$$

where soil respiration (SR) as a function of soil moisture (M) is equal to an initial respiration value (SR<sub>0</sub>) multiplied by the product of all PR<sub>SR</sub> values (denoted by the Π symbol) at each 0.01 moisture interval (k) from the initial moisture (M<sub>0</sub>) to M (for M<sub>0</sub> < M; otherwise the product term divides SR<sub>0</sub>). PR<sub>SR</sub> values at each k interval are predicted with the above PR<sub>SR</sub> models.

Relative respiration curves, which scale respiration from 0 to 1, were obtained in a two-step calculation: (1) using Eq. (2) to predict PR<sub>SR</sub> values for each 0.01 moisture interval and (2) using Eq. (5) to calculate respiration values along the moisture axis (with an arbitrary SR<sub>0</sub> of 1) and dividing all values by the maximum obtained. As data at low moistures extremes was generally missing, regression models did not well reproduce the high PR<sub>SR</sub> related to respiration values approaching 0. As a result, depending on the soil type, curve intercepts were variably higher than 0. To obtain curves with a 0 intercept we applied a rescaling of respiration from 0 to 1 in the range of 0 to optimum moisture. For this, we subtracted the minimum respiration value (R<sub>min</sub>) and divided by 1-R<sub>min</sub> (Supplement: R Code lines 463–467). This resulted in a scaling down that was strongest at lower moisture levels but minimal when approaching optimal moisture.

In order to compare our results with existing functions, we applied Eq. (3) using θ<sub>s</sub> or ψ<sub>log</sub> to predict respiration curves for 106 soil series from England and Wales covering an area of ca. 50 000 km<sup>2</sup> Soil organic carbon and clay content in these soils ranged between 0.01–0.05 g g<sup>-1</sup> and 80–610 g clay kg<sup>-1</sup> soil. We compared these results with functions from six other models using the same moisture measures, plotting the resulting range of respiration values next to θ<sub>s</sub> functions belonging to the RothC (Coleman and Jenkinson, 1999; Bauer et al., 2008), CANDY (Franko et al., 1995; Powlson et al., 1996), Bethy (Knorr, 2000) and SimCycle (Ito and Oikawa, 2002) models and ψ<sub>log</sub> functions from the Daisy (Abrahamsen and Hansen, 2000; Bauer et al., 2008) and SOILCO2 (Simunek and Suarez, 1993; Bauer et al., 2008) models. To use θ<sub>s</sub> with the RothC function we followed the same procedure as Bauer et al. (2008), assuming

<figure><img src="image_4.png" /><figcaption>Fig. 1. Proportional response of soil microbial respiration (PR<sub>SR</sub>) to moisture. PR<sub>SR</sub> values correspond to a 0.01 increase in soil moisture. Values are shown for all datasets and for θ<sub>m</sub> (gravimetric moisture, (a)), θ<sub>v</sub> (volumetric moisture, (b)), θ<sub>s</sub> (fraction of saturation, (c)), and ψ<sub>log</sub> (log water potential, (d)). Units of soil moisture in the x-axis are: g H<sub>2</sub>O gSoil<sup>-1</sup> (a), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> (b), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> pore-space (c) and (-log<sub>10</sub>|ψ<sub>kPa</sub>)/5+1 (d). Grey circles represent the PR<sub>SR</sub> of each 0.01 moisture increase. The black and dashed lines are mean and standard deviations, respectively.</figcaption></figure>

that the accumulated total soil moisture deficit equals θ<sub>v</sub> at saturation minus actual θ<sub>v</sub> and maximum total soil moisture deficit is equal to θ<sub>v</sub> at saturation.

## 3 Results

For each dataset, PR<sub>SR</sub> values are highest at dry conditions and decrease progressively with increasing moisture (Fig. 1), with values below 1 corresponding to a negative trend in respiration rates. Mean PR<sub>SR</sub> values for θ<sub>s</sub> and ψ<sub>log</sub> decreased monotonically with increasing moisture (Fig. 1c and d) while those for θ<sub>m</sub> and θ<sub>v</sub> showed more discontinuities related to sharp variations in soil types (Fig. 1a and b). All moisture measures had a wide range of soil moisture associated to an optimum for respiration, defined as the point where PR<sub>SR</sub> crosses 1. Taking θ<sub>s</sub> as an example, the PR<sub>SR</sub> mean value reaches 1 at 0.63 θ<sub>s</sub>, consistent with the commonly reported range of 0.6–0.7, but different datasets had values of optimum moisture as low as 0.4 and as high as 0.9 water saturation.

For mineral soils, significant correlations were found between PR<sub>SR</sub> and all soil properties, with the correlation strength and significance being strongly dependent on the moisture range and type of moisture measure (Fig. 2). With θ<sub>m</sub> and θ<sub>v</sub>, correlation coefficients of PR<sub>SR</sub> versus bulk density were negative and tended to increase with increasing moisture. Correlations with pore space, not shown in Fig. 2, were identical but of opposite sign, i.e. positive. Fewer or no
<table><caption>**Table 3.** Variables and coefficients for linear models predicting the proportional response of soil respiration (PR<sub>SR</sub>) at 0.01 moisture intervals. SM = soil moisture, BD = bulk density, SOC = soil organic carbon. Coefficient values and standard errors are given under the corresponding moisture measure. All terms are significant at *p* < 0.001. In addition, values are given for the number of data points (*n*) and datasets used, and the model root mean square deviation (RMSD) with the improvement relative to a moisture-only fit in brackets.</caption><thead><tr><th>Variables</th><th>Gravimetric moisture (θ<sub>m</sub>)</th><th>Volumetric moisture (θ<sub>v</sub>)</th><th>Fraction of saturation (θ<sub>s</sub>)</th><th>Log water potential (ψ<sub>log</sub>)</th></tr></thead><tbody><tr><td colspan="5"><strong>Model 1 (mineral soils)</strong></td></tr><tr><td><em>n</em></td><td>1233</td><td>1936</td><td>3610</td><td>2193</td></tr><tr><td><em>n</em>-datasets</td><td>50</td><td>52</td><td>52</td><td>42</td></tr><tr><td>RMSD</td><td>0.023 (0.006)</td><td>0.024 (0.003)</td><td>0.014 (0.002)</td><td>0.012 (0.001)</td></tr><tr><td>Intercept</td><td>1.00 ± 0.02</td><td>0.98 ± 0.01</td><td>1.02 ± 0.00</td><td>1.26 ± 0.02</td></tr><tr><td>SM</td><td>-0.80 ± 0.09</td><td>-0.48 ± 0.08</td><td>-0.29 ± 0.02</td><td>-1.36 ± 0.05</td></tr><tr><td>(SM)<sup>2</sup></td><td>3.5 ± 0.2</td><td>1.8 ± 0.3</td><td>0.37 ± 0.04</td><td>2.26 ± 0.08</td></tr><tr><td>(SM)<sup>3</sup></td><td>-3.1 ± 0.2</td><td>-1.6 ± 0.3</td><td>-0.19 ± 0.03</td><td>-1.12 ± 0.04</td></tr><tr><td>BD (g cm<sup>-3</sup>)</td><td>0.10 ± 0.01</td><td>0.1 ± 0.01</td><td>0.03 ± 0.00</td><td>0.05 ± 0.01</td></tr><tr><td>BD (g cm<sup>-3</sup>) SM</td><td>-0.44 ± 0.05</td><td>-0.3 ± 0.04</td><td>—</td><td>-0.09 ± 0.01</td></tr><tr><td>Clay (fraction)</td><td>0.33 ± 0.03</td><td>0.18 ± 0.02</td><td>0.09 ± 0.01</td><td>0.17 ± 0.02</td></tr><tr><td>Clay (fraction) SM</td><td>-0.7 ± 0.1</td><td>-0.31 ± 0.06</td><td>-0.08 ± 0.01</td><td>-0.25 ± 0.02</td></tr><tr><td>SOC (g gSoil<sup>-1</sup>)</td><td>1.5 ± 0.1</td><td>1.4 ± 0.09</td><td>0.8 ± 0.04</td><td>—</td></tr><tr><td colspan="5"><strong>Model 2 (mineral soils)</strong></td></tr><tr><td><em>n</em></td><td>1474</td><td>1951</td><td>3710</td><td>2232</td></tr><tr><td><em>n</em>-datasets</td><td>59</td><td>65</td><td>66</td><td>43</td></tr><tr><td>RMSD</td><td>0.025 (0.006)</td><td>0.025 (0.002)</td><td>0.015 (0.001)</td><td>0.013 (0.0003)</td></tr><tr><td>Intercept</td><td>1.13 ± 0.01</td><td>1.11 ± 0.01</td><td>1.059 ± 0.003</td><td>1.31 ± 0.01</td></tr><tr><td>SM</td><td>-1.31 ± 0.05</td><td>-0.83 ± 0.07</td><td>-0.26 ± 0.02</td><td>-1.45 ± 0.05</td></tr><tr><td>(SM)<sup>2</sup></td><td>3.0 ± 0.2</td><td>1.5 ± 0.3</td><td>0.32 ± 0.04</td><td>2.18 ± 0.08</td></tr><tr><td>(SM)<sup>3</sup></td><td>-2.23 ± 0.2</td><td>-1.0 ± 0.3</td><td>-0.15 ± 0.03</td><td>-1.07 ± 0.04</td></tr><tr><td>Clay (fraction)</td><td>0.26 ± 0.02</td><td>0.08 ± 0.01</td><td>0.08 ± 0.01</td><td>0.12 ± 0.01</td></tr><tr><td>Clay (fraction) SM</td><td>-0.39 ± 0.05</td><td>—</td><td>-0.09 ± 0.01</td><td>-0.16 ± 0.02</td></tr><tr><td>SOC (g gSoil<sup>-1</sup>)</td><td>1.07 ± 0.07</td><td>1.28 ± 0.08</td><td>0.57 ± 0.04</td><td>0.19 ± 0.06</td></tr><tr><td colspan="5"><strong>Model 3 (organic soils)</strong></td></tr><tr><td><em>n</em></td><td>682</td><td>286</td><td>355</td><td>159</td></tr><tr><td><em>n</em>-datasets</td><td>16</td><td>6</td><td>6</td><td>3</td></tr><tr><td>RMSD</td><td>0.020</td><td>0.010</td><td>0.008</td><td>0.014</td></tr><tr><td>Intercept</td><td>1.146 ± 0.005</td><td>1.178 ± 0.004</td><td>1.134 ± 0.003</td><td>1.42 ± 0.04</td></tr><tr><td>SM</td><td>-0.57 ± 0.03</td><td>-1.12 ± 0.03</td><td>-0.67 ± 0.02</td><td>-1.9 ± 0.2</td></tr><tr><td>(SM)<sup>2</sup></td><td>0.79 ± 0.07</td><td>2.22 ± 0.09</td><td>1.08 ± 0.05</td><td>2.9 ± 0.4</td></tr><tr><td>(SM)<sup>3</sup></td><td>-0.37 ± 0.04</td><td>-1.40 ± 0.06</td><td>-0.57 ± 0.03</td><td>-1.4 ± 0.2</td></tr></tbody></table>

significant correlations of these properties were seen for θ<sub>s</sub> and ψ<sub>log</sub>.

Significant PR<sub>SR</sub> correlations with texture and organic carbon were found for all moisture measures but most importantly for θ<sub>m</sub> and θ<sub>v</sub>. Correlations were generally negative for sand and positive for clay, silt and organic carbon. Correlations with clay and silt followed a similar pattern that mirrored the behavior of sand. Correlations with organic carbon content were similar to those of clay and silt. In contrast, organic soils showed no significant correlations between PR<sub>SR</sub> and carbon content (data not shown).

The range of values used for fitting the multiple linear regression models is given in Table 2. Models using θ<sub>m</sub> and θ<sub>v</sub> showed the largest improvement in their root mean square deviation (RMSD) after adding soil properties to the basic moisture polynomial. However, the much lower RMSD values of the models using θ<sub>s</sub> and ψ<sub>log</sub>, which only decreased slightly after adding soil properties, show that they are better predictors, with ψ<sub>log</sub> having a slightly better performance (Table 3). An analysis of model residuals resulted in no trend or significant correlation with soil incubation temperature and incubation duration. Note that models using different measures of moisture were fitted with different sets
<figure><img src="image_5.png" /></figure>

**Fig. 2.** The respiration response to moisture (PR<sub>SR</sub>) correlated with soil properties of mineral soils. Correlation coefficients of PR<sub>SR</sub> vs. bulk density (black circles), organic carbon (green squares), sand (yellow inverted triangles), silt (brown triangles) and clay (red diamonds) on the y-axis are shown for different levels of soil moisture (SM) on the x-axis. Full symbols denote correlations significant at *p* < 0.05. Units of soil moisture in the x-axis are: g H<sub>2</sub>O gSoil<sup>-1</sup> (**a**), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> (**b**), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> pore-space (**c**) and [-log<sub>10</sub>|ψ|<sub>kPa</sub>]<sup>1/5</sup> + 1 (**d**).

of observations, one reason why R² values were not used to compare them.

Relative respiration curves are shown in Fig. 3. The effect of clay content on respiration was mainly at low (aerobic) moisture ranges and strongly affected the spread in the curve. Less clay resulted in a wider range of soil moisture values associated to optimal respiration and a respiration peak at lower water contents. Soil organic carbon produced a shift in the curve under all moisture measures with the exception of water potential. More carbon content did not affect the spread of the curve but drove the point of maximum respiration towards higher values of moisture. With changes in bulk density, respiration changed relatively little for a constant volumetric moisture (θ<sub>v</sub> curve) or water potential (ψ<sub>log</sub> curve) but changed strongly under a constant gravimetric moisture (θ<sub>m</sub> curve) or water saturation fraction (θ<sub>s</sub> curve).

When compared to currently used models (Fig. 4), results from our model covered much of the range of variability between other functions based on θs, which either under- or overestimate average respiration, with a strong tendency towards the latter. Functions using ψlog were comparable to our predictions, where we observed a limited influence of soil properties, but they showed a general overestimation of respiration values in most of the range of suboptimal moisture conditions.

<figure><img src="image_6.png" /></figure>

**Fig. 3.** The response of predicted soil moisture-respiration curves to variations in soil properties for mineral soils. Darker lines represent higher values of a given property. Variations are shown for clay content from 0.1 to 1 fraction (**a–d**), organic carbon from 0.005 to 0.05 g g<sup>-1</sup> (**e–h**), and bulk density from 0.6 to 1.6 g cm<sup>-3</sup> (**i–l**). The respective values for the variables held constant are: 0.3 fraction, 0.02 g g<sup>-1</sup> and 1.2 g cm<sup>-3</sup>. Moisture units are: g H<sub>2</sub>O gSoil<sup>-1</sup> (**a**, **e**, **i**), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> (**b**, **f**, **j**), cm<sup>3</sup> H<sub>2</sub>O cm<sup>-3</sup> pore-space (**c**, **g**, **k**), and -log<sub>10</sub>|ψ|<sub>kPa</sub> (**d**, **f**, **l**).

<figure><img src="image_7.png" /></figure>

**Fig. 4.** Comparison of predicted relative soil heterotrophic respiration as a function of soil moisture. The grey area marks the full range of values obtained with Eqs. (3) and (5) using θs (**a**) or ψlog (**b**) for 106 soil series from England and Wales ranging from 8 to 50 mg g<sup>-1</sup> SOC and 0.08 to 0.61 clay fraction. Other lines are moisture-respiration functions from existing models using either θs (**a**) or ψlog (**b**) as a predictor. (**a**): CANDY model (full line), Bethy model (dashed line), SimCycle model (dotted line), RothC model (dot-dash line). (**b**): Daisy model (full line), SOILCO2 model (dashed line).

## 4 Discussion

This comparison of multiple datasets revealed a strong soil-dependent variation of the moisture-respiration relationship, in clear contrast to the simple functions found in all current models. The large range of variability observed (e.g. respiration maximums ranging from 40–100 % water saturation)
reflects differences between ecosystems that are largely ignored in the more common and simplified representations of this relationship. A major difference observed was in the response of organic vs. mineral soils. In the case of organic soils we found little or no effects of soil properties on the PR<sub>SR</sub>. The models derived for organic soils use moisture as the only predictor. It is evident that, with a generally lower bulk density and mineral fraction, the influence of oxygenation and clay content become less important. These models serve as a best approximation, but remain rough averages given the limited availability of data and the often incomplete characterization of soil properties. More data of well characterized soils will be needed to better understand moisture effects in these soils.

For mineral soils (with less than 50 mg C g soil⁻¹) the soil factors having an influence on the moisture-respiration relationship involved aeration and structure (bulk density), texture (clay) and composition (carbon content). The models we derived from the data include clay but not silt or sand. This was a result of the large effect of clay and the relatively small influence of silt or sand when including one or the other in the linear regression. This is probably caused by the much larger specific surface area of clay which affects water retention and availability. The increase in the optimum water content for respiration with increasing clay fraction we observed has also been identified in field studies (Balogh et al., 2011). Water potential is the only measure of soil moisture for which this pattern was not observed.

Biological and physical theory predicts that microbial activity in soils should be tightly regulated by the osmotic and matric potential of water (Parr et al., 1981; Orchard and Cook, 1983). Accordingly, the relation between soil respiration and soil water potential (ψ<sub>log</sub>) was the least affected by soil properties. RMSD values (Table 3) show that this measure was the best predictor of respiration rates with or without including soil properties – except in organic soils, which may be the result of having only three related datasets. However, since large changes in water potential are often associated with small changes in water content, predicting water potential in soils could itself be associated with large errors. Among the models based on measures of water content (θ<sub>s</sub>, θ<sub>m</sub> or θ<sub>v</sub>), those using θ<sub>s</sub> resulted in the lowest root mean square deviation and were thus the best predictor of respiration rates. Ultimately, finding the measure that performs best in large scale simulations will require a validation of model performance against actual field data. It should be noted that R<sup>2</sup> were not reported because, first, different models were fit with different sets of observations, and second, even with a low R<sup>2</sup> a moisture measure may still be a good predictor of respiration, as would be the case of a mostly constant PR<sub>SR</sub> that does not vary with any of the predictor variables.

The main limitation of our models was simulating the respiration response at low values of moisture, usually associated with less than 10% θs. This was partially the result of the lack of data at low moistures (Fig. 1), but also of the

analysis procedure. Because we compared soils with unknown basal respiration rates and incubated under very different conditions, the only comparable measure for this analysis was the proportional or relative change. However, this means that at respiration values approaching 0 this proportional change will tend to increase exponentially, resulting in a wide spread of values and a poor model performance in this range. In this study, we chose to apply a rescaling of predicted values to obtain a zero-intercept (Fig. 3), as described in methods, thus introducing a negative bias but making fluxes at low moisture more realistic. Note that for water potential models this rescaling was not performed.

The data from England and Wales soils used for model comparison represents a large range of properties characteristic of soils in temperate regions. The range of respiration curves we predicted (Fig. 4), related to variations in the properties of these soils, covered most of the differences between strongly differing functions such as those used in the RothC, CANDY and Bethy models. Thus, the variability in model predictions, associated with different moisture functions, can be largely reduced or eliminated by using a common, but generally valid, soil-dependent moisture-respiration function. Depending on the model, soil and climate, significantly different predictions of soil carbon decomposition are expected after including these soil-dependent functions. In most cases this will tend to lower rates of respiration and, consequently, to an increased sequestration of carbon in soils.

Our predictions rely on regression models which are practical and have the advantage of being based on data. As a drawback, they can result in unrealistic values when extrapolating or where data was insufficient or non-linear. This can be avoided by using mechanistic models that integrate, or are parameterized with, the results of empirical studies. A recent study that provides a process based framework of the soil moisture-respiration relationship is that of Davidson et al. (2012). The Dual Arrhenius and Michaelis-Menten kinetics model (DAMM) they describe has the advantage of being process based, so that moisture effects are reproduced by simulating the diffusion of substrates and oxygen depending on water and air space content, respectively. DAMM is, however, in an early stage of development and must be parameterized for individual soils. In this sense, regression models may prove more useful at this stage and for large scale simulations. As mechanistic models incorporate the effects of texture, bulk density, etc., they should reproduce the effects of soil properties in a way that is consistent with the correlations observed here.

## 5 Conclusions

It remains unclear if soils will cause a positive or negative feedback to global warming as global changes in climatic patterns affect soil temperature and moisture (IPCC, 2007; Kendon et al., 2009; Burke and Brown, 2010), but the
moisture response of soil carbon decomposition will likely
have an important role in determining any future evolution.
The empirical analysis presented here is a comprehensive
synthesis of what has been observed to date. But most im-
portantly, it shows that the soil heterotrophic respiration re-
sponse to moisture depends on soil properties in a consistent
and largely predictable way, explaining a significant part of
the variations found across studies. Future studies should
concentrate on reducing uncertainties in these relationships
and on better representing specific field conditions, such as
the depth-dependence of oxygen availability and the dynam-
ics of water in soils. This will require obtaining and analyz-
ing more relevant data while using observed relationships to
develop process-based models.

**Supplementary material related to this**
**article is available online at:**

http://www.biogeosciences.net/9/1173/2012/
bg-9-1173-2012-supplement.zip.

*Acknowledgements.* This work was supported by the Project Carbosoil from GIS Climat-Environnement-Société. England and Wales soils data were used under licence of “Soils Data (c) Cranfield University (NSRI) and for the Controller of HMSO, 2011”.

Edited by: M. Bahn

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