Introduction
Ice fronts in polar and alpine regions are retreating as a result of climate
warming, and as a consequence, glacier forefield areas in high-latitude and
high-altitude regions are rapidly expanding (Graversen et al., 2008; ACIA,
2005). Glacier coverage in upland Alpine regions in Europe has declined by
up to 30 % from the 1970s to 2003, exposing roughly 860 km2 of
previously ice-covered land area (Paul et al., 2011). Similarly, rapid
glacial retreat has been observed in Iceland (Staines et al., 2014), North
America (Insam and Haselwandter, 1989; Hahn and Quideau, 2013; Ohtonen et
al., 1999; Sattin et al., 2009), Asia (Liu et al., 2012) and Svalbard
(Moreau et al., 2008). These vast expanses of newly uncovered land have been
locked under ice for tens of thousands of years, are typically highly
oligotrophic, with low nutrient budgets and are subject to harsh and rapidly
fluctuating environmental conditions. They potentially play a significant yet
largely unexplored role in large-scale biogeochemical cycling and climate
(Dessert et al., 2003; Anderson et al., 2000; Smittenberg et al., 2012;
Berner et al., 1983), global methane budgets (Kirschke et al., 2013), the
global phosphorus cycle (Filippelli, 2002; Follmi et al., 2009) and the
productivity of downstream and coastal ecosystems (Anesio et al., 2009;
Mindl et al., 2007; Fountain et al., 2008; Anderson et al., 2000).
Furthermore, the initial stages of microbial community development in soils
are fundamental to understanding life in extreme environments, which may
serve as an analogue for survival and habitability of environments currently
assumed devoid of life on this planet and others.
A conceptual overview of the main transformations and fluxes of
nutrients and organic matter in and along a typical de-glaciated forefield.
Outline of quantitative and predictive modelling strategy.
Quantitative modelling
Details
Do initial microbial communities rely on autochthonous or allochthonous carbon?
Explore scenarios of carbon loading to determine the reliance on allochthonous carbon vs. autochthonous production.
Assess the role of nitrogen as a key limiting nutrient.
Quantify nitrogen budget to assess relative importance of nitrogen fixation vs. DIN assimilation in recently exposed and old soils.
Assess how microbial diversity affects soil development.
Test various community assemblages and characterise the soil environment they create.
Predictive modelling
Details
Identifying tipping points within the system.
Do population dynamics, external nutrient loading, seasonal changes, disturbance events and climate change trigger significant changes in soil development?
Assess importance of seasonality.
Explore the dynamics of the “non-growing season”, where there is little observational data due to inaccessibility and difficult field work conditions.
Assess importance of disturbance events and community reset.
Test the effect of hydrological disturbance in proglacial zone (rich in nutrients and organic matter, but may reset established communities and enhance leaching of substrate)
Assess sensitivity to future climate change
Explore the effect of climate and anthropogenic impact using scenario-based predictions.
Draw attention to gaps in our understanding and areas of future research.
Models are driven primarily by empirical relationships and observational data; henceforth it is likely to become apparent where future fieldwork and lab work efforts should be focussed.
Microbial communities are the primary colonisers of recently exposed soils,
and are thought to be fundamental in soil stabilisation, the build-up of
carbon and nutrient pools, and facilitating the establishment of higher-order plants (Schulz et al., 2013; Bradley et al., 2014). A conceptual
overview of forefield nutrient cycling is presented in Fig. 1. Recently
de-glaciated soils vary in their mineralogical and microbial compositions.
Total organic carbon (TOC), total nitrogen (TN), and total phosphorus (TP)
content of newly exposed glacial forefield soils is low, in the range of
0.1–40.0 mgCg-1, 0.1–2.0 mgNg-1, and 2–8 µgPg-1
(Bradley et al., 2014). However, these concentrations typically increase by 1 to 2 orders
of magnitude with ageing from newly exposed to well-developed (decades old)
soil. Three distinct sources contribute carbon to recently exposed soils:
autochthonous primary production by autotrophic microorganisms,
allochthonous material deposited on the soil surface (from wind, hydrology,
biology and precipitation) and ancient organic pools derived from under the
glacier. Organic matter accumulation from all three sources supports the
development of heterotrophic communities, yet their relative significance
remains unknown. The continual autotrophic production, heterotrophic
re-working and allochthonous deposition lead to the accumulation of organic
material, which supports higher abundances and diversity of microorganisms
(Bradley et al., 2014; Schulz et al., 2013). Nitrogen is derived from active
nitrogen-fixing organisms, allochthonous deposition and degradation of
organic substrate. Bioavailable phosphorus is usually abundant in the
topsoil or bedrock of glaciated regions from weathering of the mineral
surface, and can also be liberated due to the degradation of organic
molecules.
Hypotheses relating accumulation of carbon and nutrients to increasing
species richness and diversification have tended to be descriptive and
qualitative, rather than quantitative. Little is known about the main
drivers of microbial succession and controls on abundance, diversity and
activity, and this limits our understanding of glacier forefield
contribution to global nutrient pathways and our ability to predict how
these rapidly expanding ecosystems may respond in the future, including
their potential impact on atmospheric CO2, global climate and
downstream productivity. This lack of understanding can be partly attributed
to the difficulty of quantifying the different external organic matter and
nutrient fluxes, as well as disentangling the complexity of biogeochemical
processes underlying the microbial dynamics and soil carbon and nutrient
build-up along the chronosequence by observations and/or laboratory
experiments alone. Numerical models are useful tools in this context as they
can not only help to disentangle the complex process interplay, diagnose the
fluxes between ecosystem components and, ultimately, predict the sensitivity
and response of an environment to changing environmental and climatic
conditions, but also help identify important data and knowledge gaps and
hence guide the design of efficient field campaigns and laboratory studies
directly targeted at closing these gaps. Nevertheless, a modelling framework
that could be used to explore microbial dynamics and associated nutrient
cycling in glacier forefields currently does not exist.
The development of soil models has been common in the past and important in
informing soil management, policy and prediction (McGill, 2007,
1996), for example in understanding the contribution of soil organic matter
(SOM) to the formation of stable aggregate soils, the ease of soil
cultivation, water holding characteristics and the risk of physical damage
and compaction. The explicit inclusion of soil microbial dynamics has been
shown to drastically improve the performance of these models (Wieder et al.,
2013). There are many different types of soil models in use today across a
range of scales and purposes, such as informing agricultural policy,
understanding biogeochemical cycling and soil food webs and the feedbacks
between soil processes, hydrology and the atmosphere (Stapleton et al.,
2005; Blagodatsky and Richter, 1998; Knapp et al., 1983; Grant et al., 1993;
German et al., 2012; Ingwersen et al., 2008; Leffelaar and Wessel, 1988;
Kuijper et al., 2005; Kravchenko et al., 2004; Parton et al., 1988; Garnier
et al., 2001; Darrah, 1991; Foereid and Yearsley, 2004; Vandewerf and
Verstraete, 1987b; Long and Or, 2005; Maggi and Porporato, 2007; Moorhead
and Sinsabaugh, 2006; Panikov and Sizova, 1996; Toal et al., 2000; Zelenev
et al., 2000; Scott et al., 1995). However, although these models include an
explicit microbial component, SOM models are tailored towards research
questions that are focussed on geochemistry and specifically organic matter
dynamics rather than biology. Forefield ecosystems are characterised by
extreme and highly variable environmental conditions and rapidly changing
compositions of microbial communities whose interplay results in unique
chronosequence dynamics (Bradley et al., 2014). There is not a single model
that can represent the unique forefield development without an unacceptable
level of abstraction and simplification of the system.
Iterative, fully integrated interdisciplinary framework of
SHIMMER, aimed at continuing model development as new data sets emerge and
knowledge of the field evolves.
Therefore, we developed the new model framework SHIMMER (Soil biogeocHemIcal
Model for Microbial Ecosystem Response) to quantitatively
simulate the initial stages of ecosystem development and assess
biogeochemical processes in the forefield of glaciers. The code is written
and executed in the free open-source computing environment and programming
language R, which is available to download on the web
(http://www.r-project.org/). The current version of the model is designed to
represent the microbial community prior to the establishment of plants, and
therefore only the initial stages of chronosequence development will be
assessed. Microbial communities may be heavily structured by establishing
vegetation (Brown and Jumpponen, 2014), and the physical properties of
vegetated soils are considerably different in terms of water retention,
ultraviolet exposure, temperature fluctuations (Ensign et al., 2006; King
et al., 2008) and nutrient status (Kastovska et al., 2005; Schutte et al.,
2009).
This paper provides a comprehensive description of the modelling framework.
A first model performance test is conducted on the basis of existing
published data from the Damma Glacier forefield in Switzerland (Bernasconi
et al., 2011; Brankatschk et al., 2011; Guelland et al., 2013b) and from the
Athabasca Glacier in Canada (Insam and Haselwandter, 1989). The newly
developed model is then used to conduct an extensive parameter sensitivity
study. SHIMMER is not only a new model framework but also part of an
interdisciplinary, iterative, open-source, model-data-based approach fully
integrating fieldwork and laboratory experiments with model development,
testing and application. The model scope and complexity of the first
version of SHIMMER is informed by a comprehensive review of glacier
forefield research (Bradley et al., 2014) and the data set collected during
a first field campaign to characterise the forefield of a retreating
Svalbard glacier. The model is kept as general as possible, and thus is easily
transferable to other microbial ecosystems such as desert soils, ice
surfaces (e.g. cryoconite), microbial mats and the built environment (e.g. fuel and chemical storage). The model is dynamically sufficient; i.e. the
minimum processes that are needed to resolve the system and provide useful
output are included. In addition, it is intended that new model developments
will guide and inform future field and laboratory studies so that subsequent
versions of the model will run with narrower plausible ranges of parameters,
and explicitly resolve processes that currently cannot be constrained on the
basis of available data. SHIMMER can thus be considered as the first step of
an interdisciplinary, iterative approach (illustrated in Fig. 2 and Table 1)
where new data inform new model developments that will result in new
insights, which in turn will inform new laboratory and field experiments, etc. It thus not only contributes to more accurate quantitative
predictions that enable a deeper understanding of the processes that control
microbial communities, their role on global biogeochemical cycles and their
response to climate variations, but also provides an ideal platform for the
synthesis and exchange of knowledge and information across different
disciplines.
The final developed model presented here is:
structurally (i.e. spatial resolution, number of species,
processes included) and mechanistically (i.e. process formulation) complex
enough to describe the required properties for carbon, nitrogen and
phosphorus turnover necessary to address the questions identified in the main
aims (Table 1);
structurally and mechanistically simple enough to
constrain and validate parameters and simulation results by available data and
literature;
able to operate with numerical efficiency on various timescales from days to decades, in order to represent an entire chronosequence development in sufficient
detail;
applicable to a range of environments;
structurally stable, conserves mass and provides robust numerical output.
A conceptual model showing the components and transfers of
SHIMMER. State variables are indicated with shading.
State variables and initial values.
State
Units
Description
Damma Glacier,
Reference
Athabasca Glacier,
Reference
variable
Switzerland
Canada
A1
µgCg-1
Subglacial chemolithoautotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
A2
µgCg-1
Generic soil autotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
A3
µgCg-1
Nitrogen-fixing soil autotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
H1
µgCg-1
Subglacial heterotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
H2
µgCg-1
Generic soil heterotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
H3
µgCg-1
Nitrogen-fixing soil heterotrophs
0.617
Bernasconi et al. (2011)
0.950
Insam and Haselwandter (1989)
S1
µgCg-1
Labile carbon substrate
278.520
Bernasconi et al. (2011)
117.720
Insam and Haselwandter (1989)
S2
µgCg-1
Refractory carbon substrate
417.780
Bernasconi et al. (2011)
176.580
Insam and Haselwandter (1989)
DIN
µgNg-1
Dissolved inorganic nitrogen
0.160
Brankatschk et al. (2011)
0.070
Stoichiometric
DIP
µgPg-1
Dissolved inorganic phosphorus
0.500
Bernasconi et al. (2011)
0.210
Stoichiometric
ON1
µgNg-1
Labile nitrogen substrate
39.440
Bernasconi et al. (2011)
16.600
Stoichiometric
ON2
µgNg-1
Refractory nitrogen substrate
59.160
Bernasconi et al. (2011)
24.900
Stoichiometric
OP1
µgPg-1
Labile phosphorus substrate
23.120
Stoichiometric
9.770
Stoichiometric
OP2
µgPg-1
Refractory phosphorus substrate
34.680
Stoichiometric
14.660
Stoichiometric
Derived variables.
Derived variable
Description
Formulation
cum_A1
Increase in biomass of A1
UA1
cum_A2
Increase in biomass of A2
UA2
cum_A3
Increase in biomass of A3
UA3
cum_H1
Increase in biomass of H1
UH1
cum_H2
Increase in biomass of H2
UH2
cum_H3
Increase in biomass of H3
UH3
cum_A
Increase in autotrophic biomass
ΣUA1-3
cum_H
Increase in heterotrophic biomass
ΣUH1-3
cum_BP
Bacterial production
ΣUA1-3+ΣUH1-3
cum_DIC_A
DIC produced by autotrophs
1-YA⋅1YA⋅UA1+1-YA⋅1YA⋅UA2+1-YA⋅nf⋅1YA⋅nf⋅UA3
cum_DIC_H
DIC produced by heterotrophs
1-YH⋅1YH⋅UH1+1-YH⋅1YH⋅UH2+1-YH⋅nf⋅1YH⋅nf⋅UH3
cum_DIC
Total DIC produced
cum_DIC_A + cum_DIC_H
cum_DIN
DIN consumed by all microbes
DINConsumed
cum_nf
DIN fixed by A3 and H3
NC ⋅((1-β)⋅UA3+(1-β)⋅UH3)
SHIMMER model formulation.
Fundamental balance equations
Rate of change of autotrophic biomass (A1-3)
dAidt=UAi-GAi-XAi
Rate of change of heterotrophic biomass (H1-3)
dHidt=UHi-GHi-XHi
Rate of change of labile carbon substrate (S1)
dS1dt=vSub⋅IS1+q⋅GAi+q⋅GHi+XA+XH-US1Hi-WS1
Rate of change of refractory carbon substrate (S2)
dS2dt=vCS2⋅IS2+(1-q)⋅GAi+(1-q)⋅GHi-US2Hi-WS2
Rate of change of dissolved inorganic nitrogen (DIN)
dDINdt=vDIN⋅IDIN-DINConsumed+DINReleased-WDIN
Rate of change of dissolved inorganic phosphorus (DIP)
dDIPdt=vDIP⋅IDIP-DIPConsumed+DIPReleased-WDIP
Rate of change of labile organic nitrogen (ON1)
dON1dt=vSub⋅ION1-ON1Accumulation-ON1Degraded-WON1
Rate of change of refractory organic nitrogen (ON2)
dON2dt=vSub⋅IOP2-OP2Accumulation-OP2Degraded-WOP2
Rate of change of labile organic phosphorus (OP1)
dOP1dt=vSub⋅IOP1-OP1Accumulation-OP1Degraded-WOP1
Rate of change of refractory organic phosphorus (OP2)
dOP2dt=vSub⋅IOP2-OP2Accumulation-OP2Degraded-WOP2
Carbon cycle – biomass component
Growth of subglacial autotrophs (A1)
UA1=A1⋅Tf⋅d⋅psub⋅ImaxA⋅DINDIN+Kn⋅kSub⋅DIPDIP+Kp⋅kSub
Growth of soil autotrophs (A2)
UA2=A2⋅Tf⋅d⋅ImaxA⋅PARPAR+KL⋅DINDIN+Kn⋅DIPDIP+Kp
Growth of N-fixing soil autotrophs (A3)
UA3=UA3_N2+UA3_DIN
Growth of N-fixing soil autotrophs (A3) with nitrogen fixation
UA3_N2=A3⋅Tf⋅d⋅nf⋅ImaxA3⋅PARPAR+KL⋅DIPDIP+Kp⋅1-mDIN
Growth of N-fixing soil autotrophs (A3) with DIN
UA3_DIN=A3⋅Tf⋅d⋅ImaxA3⋅PARPAR+KL⋅DINDIN+Kn⋅DIPDIP+Kp⋅mDIN
Growth of subglacial heterotrophs (H1) from labile substrate
UH1L=H1⋅Tf⋅d⋅psub⋅ImaxH⋅JS1⋅S1S1+Ks⋅kSub⋅DINDIN+Kn⋅kSub⋅DIPDIP+Kp⋅kSub
Growth of soil heterotrophs (H2) from labile substrate
UH2L=H2⋅Tf⋅d⋅ImaxH⋅JS1⋅S1S1+Ks⋅DINDIN+Kn⋅DIPDIP+Kp
Growth of N-fixing soil heterotrophs (H3) from labile substrate and nitrogen fixation
UH3L_N2=H3⋅Tf⋅d⋅nf⋅ImaxH3⋅JS1⋅S1S1+Ks⋅DIPDIP+Kp⋅1-mDIN
Growth of N-fixing soil heterotrophs (H3) from labile substrate and DIN
UH3L_DIN=H3⋅Tf⋅d⋅ImaxH3⋅JS1⋅S1S1+Ks⋅DINDIN+Kn⋅DIPDIP+Kp⋅mDIN
Growth of subglacial heterotrophs (H1) from refractory substrate
UH1R=H1⋅Tf⋅d⋅ImaxH⋅psub⋅JS2⋅S2S2+Ks⋅kSub⋅DINDIN+Kn⋅kSub⋅DIPDIP+Kp⋅kSub
Growth of soil heterotrophs (H2) from refractory substrate
UH2R=H2⋅Tf⋅d⋅ImaxH⋅JS2⋅S2S2+Ks⋅DINDIN+Kn⋅DIPDIP+Kp
Growth of N-fixing soil heterotrophs (H3) from refractory substrate and nitrogen fixation
UH3R_N2=H3⋅Tf⋅d⋅nf⋅ImaxH3⋅JS2⋅S2S2+Ks⋅DIPDIP+Kp⋅1-mDIN
Growth of N-fixing soil heterotrophs (H3) from refractory substrate and DIN
UH3R_DIN=H3⋅Tf⋅d⋅ImaxH3⋅JS2⋅S2S2+Ks⋅DINDIN+Kn⋅DIPDIP+Kp⋅mDIN
Growth of N-fixing soil heterotrophs (H3) from labile substrate
UH3L=UH3L_N2+UH3L_DIN
Growth of N-fixing soil heterotrophs (H3) from refractory substrate
UH3R=UH3R_N2+UH3R_DIN
Continued.
Fundamental balance equations
Total growth of heterotrophs (Hi)
UHi=UHiL+UHiR
Loss of autotrophic biomass
GAi=Tf⋅d⋅αA⋅Ai2
Loss of heterotrophic biomass
GHi=Tf⋅d⋅αH⋅Hi2
Total deaths that become labile
GL=q⋅GA1+GA2+GA3+GH1+GH2+GH3
Total deaths that become refractory
GR=1-q⋅GA1+GA2+GA3+GH1+GH2+GH3
Rate of exudate and EPS production by autotrophs
XAi=exA⋅UAi
Rate of exudate and EPS production by heterotrophs
XHi=exH⋅UHi
Total exudate production
XTotal=XA1+XA2+XA3+XH1+XH2+XH3
Carbon cycle – substrate component
Consumption of labile substrate
S1Consumed=1YH⋅UH1L+1YH⋅UH2L+1nf⋅YH⋅UH3L_N2+1YH⋅UH3L_DIN
Consumption of refractory substrate
S2Consumed=1YH⋅UH1R+1YH⋅UH2R+1nf⋅YH⋅UH3R_N2+1YH⋅UH3R_DIN
Leaching
WX=gX⋅X
Nitrogen cycle
Labile organic nitrogen degraded
ON1Degraded=ON1S1⋅S1Consumed
Refractory organic nitrogen degraded
ON2Degraded=ON2S2⋅S2Consumed
Labile organic nitrogen accumulated
ON1Accumulation=NC⋅GL+XT
Refractory organic nitrogen accumulated
ON2Accumulation=NC⋅GR
DIN consumed
DINConsumed=NC⋅UA1+UA2+UA3_DIN+UH1+UH2+UH3L_DIN+UH3R_DIN
DIN released
DINReleased=ON1Degraded+ON2Degraded
Phosphorus cycle
Labile organic phosphorus degraded
OP1Degraded=OP1S1⋅S1Consumed
Refractory organic phosphorus degraded
OP2Degraded=OP2S2⋅S2Consumed
Labile organic phosphorus accumulated
OP1Accumulation=PC⋅GL+XT
Refractory organic phosphorus accumulated
OP2Accumulation=PC⋅GR
DIP consumed
DIPConsumed=PC⋅UA1+UA2+UA3+UH1+UH2+UH3
DIP released
DIPReleased=OP1Degraded+OP2Degraded
Environmental and scaling equations
Temperature factor response
Tf=expT-Tref10loge(Q10)
Monod expression for nitrogen fixation inhibition in the presence of DIN
if DIN≤DINt
mDIN=0
else mDIN=DIN-DINtDIN-DINt+KN2
Parameters.
Parameter
Description
Units
Nominal value (reference)
Lower range (reference)
Upper range (reference)
Damma Glacier, Switzerland
Athabasca Glacier, Canada
Tref
Reference temperature for rates
∘C
25 (Frey et al., 2010)
Fixed
Fixed
–
–
NC
C:N ratio (mass)
Unitless
0.141 (Bernasconi et al., 2011)
Fixed
Fixed
–
–
PC
C:P ratio (mass)
Unitless
0.083 (Bernasconi et al., 2011)
Fixed
Fixed
–
–
Q10
Temperature sensitivity
Unitless
2.0 (Soetaert and Herman, 2009)
1.5
3.1 (Yoshitake et al., 2010)
2.2
2.2
αA
Death rate (autotrophs)
d-1
0.0120 (German et al., 2012)
0.0060 (Grant et al., 1993)
0.4800 (Scott et al., 1995)
–
0.0340
αH
Death rate (heterotrophs)
d-1
0.0120 (German et al., 2012)
0.0060 (Grant et al., 1993)
0.4800 (Scott et al., 1995)
–
0.0340
ImaxA
Maximum growth rate (autotrophs)
d-1
1.21 (Frey et al., 2010)
0.30 (Mur et al., 1999)
1.40 (Mur et al., 1999)
1.40
1.4
ImaxH
Maximum growth rate (heterotrophs)
d-1
1.21 (Frey et al., 2010)
0.24 (Ingwersen et al., 2008)
4.80 (Darrah, 1991; Blagodatsky and Richter, 1998)
1.24
1.24
exA
Exudates and EPS production (autotrophs)
Unitless
0.014 (Allison, 2005)
0.007 (Allison, 2005)
0.021 (Allison, 2005)
–
–
exH
Exudates and EPS production (heterotrophs)
Unitless
0.014 (Allison, 2005)
0.007 (Allison, 2005)
0.021 (Allison, 2005)
–
–
pSub
Slow down of subglacial microbial growth rate
Unitless
0.2
0.1
1.0
–
–
kSub
Lower half-saturation constants (KS, KN and KP) for subglacial microbes
Unitless
0.8
0.1
1.0
–
–
KL
Light half-saturation constant for autotrophs (A2 and A3)
Wm-2 (PAR)
1.85 (Van Liere and Walsby, 1982)
0.70 (Van Liere and Walsby, 1982)
3.00 (Van Liere and Walsby, 1982)
–
–
KS
Substrate half-saturation constant for heterotrophs
µgg-1
349 (Vandewerf and Verstraete, 1987b)
50 (Darrah, 1991)
1000 (Knapp et al., 1983)
–
–
KN
DIN half-saturation constant
µgg-1
49.209 (stoichiometric)
7.050 (stoichiometric)
141.000 (stoichiometric)
–
–
KP
DIP half-saturation constant
µgg-1
28.967 (stoichiometric)
4.150 (stoichiometric)
83.000 (stoichiometric)
–
–
nf
Downscaling of Y and Imax when fixing nitrogen
Unitless
0.50 (Bottomley and Myrold, 2007)
0.10 (LaRoche and Breitbarth, 2005; Breitbarth et al., 2008; Goebel et al., 2008)
0.80
–
–
KN2
Nitrogen fixation inhibition
µgg-1
393.672 (Holl and Montoya, 2005; Rabouille et al., 2006)
56.4 (Holl and Montoya, 2005; Rabouille et al., 2006)
1128 (Holl and Montoya, 2005; Rabouille et al., 2006)
–
–
DINt
Threshold value of DIN for nitrogen fixation inhibition
µgg-1
0
0
0
–
–
q
Proportion of necromass that becomes labile (S1)
Unitless
0.3
0.1
0.5
–
–
JS1
Bioavailability (preference) of S1
Unitless
0.50
0.50
1.00
0.68
0.50
JS2
Bioavailability (preference) of S2
Unitless
0.10
0.10
0.50
0.15
0.10
gSub
Leaching of substrate
d-1
0
0
0
–
–
gDIN
Leaching of DIN
d-1
0
0
0
–
–
gDIP
Leaching of DIP
d-1
0
0
0
–
–
YA
Growth efficiency of autotrophs
g C (g C consumed)-1
0.200 (Scott et al., 1995)
0.100 (Foereid and Yearsley, 2004)
0.848 (Blagodatsky and Richter, 1998)
–
–
YH
Growth efficiency of heterotrophs
g C (g C consumed)-1
0.200 (Scott et al., 1995)
0.134 (German et al., 2012)
0.848 (Blagodatsky and Richter, 1998)
–
–
Continued.
Parameter
Description
Units
Nominal value (reference)
Lower range (reference)
Upper range (reference)
Damma Glacier, Switzerland
Athabasca Glacier, Canada
d
Active fraction of microbial biomass
Unitless
0.285 (Wang et al., 2014)
0.100 (Blagodatsky and Richter, 1998)
0.580 (Blagodatsky and Richter, 1998)
0.285
0.100
vSub
Proportion of allochthonous substrate deposition retained
Unitless
0.60
0.00
1.00
–
0.05
vDIN
Proportion of allochthonous DIN deposition retained
Unitless
0.01
0.00
1.00
–
–
vDIP
Proportion of allochthonous DIP deposition retained
Unitless
0.01
0.00
1.00
–
–
Model runs
Nominal
The model is run with nominal parameters for a period representing 75 years
of succession (the approximate length of the test data sets), starting on the
1 January, in order to provide a baseline model output from which parameters
are varied to determine sensitivity. Leap years are ignored. The model is
forced with meteorological data collected from the Damma Glacier,
Switzerland (case study 1 – see Sect. 4.3.1 for details).
Sensitivity and uncertainty analysis
A sensitivity study involving 24 model parameters is carried out to assess
the stability of model output given variation in all key parameters. This is
important when accounting for uncertainty, since high sensitivity of key
parameters that have a relatively wide plausible range of values would lead
to large uncertainties in predictions. Sensitivity analysis is considered
across all state variables to assess the extent to which parameter variation
influences whole model behaviour or only single variables. The model is run
for 75 years under each sensitivity scenario, starting on 1 January,
forced with data from the Damma Glacier (since results can be interpreted
alongside the more detailed contextual observations). The following model
output (X) is explored:
total autotrophic biomass (average over the entire simulation run)
total heterotrophic biomass (average over the entire simulation run)
total C substrate (average over the entire simulation run)
DIN (average over the entire simulation run)
DIP (average over the entire simulation run)
total ON (average over the entire simulation run)
total OP (average over the entire simulation run)
total nitrogen fixed (cumulative)
seasonal variation in microbial biomass (final year of simulation).
Plausible ranges for model parameter values are constrained from values in
published literature (Table 5). Many of the parameters show considerable
variation, but the most confident values (their applicability to the glacier
forefield system, the method by which the value was determined, and their
occurrence in the literature) are used as nominal values. To explore
sensitivity, uncertainty and linearity, plausible ranges are split into
tenths, and simulations are run sequentially through all eleven possible
values for each parameter.
Illustration of calculation of sensitivity (λ) where
(a) the value of λ is representative of the sensitivity; (b) the value
of λ is not representative of the sensitivity. In (b) the apparent
sensitivity (λ) will be low due to model behaviour either side of
the nominal parameter value having an opposite sign, even though the model
may be truly sensitive to that parameter.
Simulated response of autotrophic (A1-3) biomass (blue line)
and heterotrophic (H1-3) biomass (red line) to variation in (a) Q10
and (b) ImaxH across the entire range of plausible values, forced with
meteorological data from the Damma Glacier over 75 years. The shaded segment
shows the region in which model sensitivity (λ) is calculated.
Sensitivity around nominal values is quantified using a variation on the
method presented in Xenakis et al. (2008). The relative sensitivity
(λ) of a certain model output (X) to a parameter (p) is estimated
according to
λX,p=pX⋅δXδp,
where p is the nominal value for the parameter, X is the model output from
nominal parameter values, δp is the difference in parameter value
either side of the nominal value, and δX is the change in model
output (simulated over the range of parameters identified in δp). For
clarity, this is illustrated in Fig. 5a. The sensitivity (λ)
quantifies the relation between the model output and variation in a single
parameter as a first derivative of their relationship either side of the
nominal value, and is normalised based on the magnitude of parameter and
model output values. Thus, λ indicates the sensitivity of model
output to parameter variation and also the direction (sign) of the change. A
positive λ value indicates that an increase in the parameter value
yields an increased value in the model output, whereas a negative λ
value indicates that an increase in the parameter causes a decrease in the
value of the model output. Values of λ further from zero indicate
that the model output is highly sensitive to variation in the parameter.
Model output is assessed graphically for each parameter (e.g. Fig. 6).
First, the shape of the model output variation is assessed to see if the
value for λ is representative of sensitivity. An unrealistic
λ may be calculated if the nominal parameter is near a vertex and
the variation in model output either side of the nominal value has an
opposite sign (i.e. a parabola). This is illustrated in Fig. 5b, whereby
δX is low, and thus a low λ value is obtained, even though the
sensitivity is relatively high (i.e. X depends strongly on p). Second, each
plot is assessed and a linear (e.g. Fig. 6a) or non-linear (e.g. Fig. 6b)
relationship is attributed to each parameter. Finally, non-linear results
are assessed to determine if the highest sensitivity is around the nominal
parameter value, since this has implications in interpreting the model
output. If parameters are most sensitive near to the nominal values, there
is a higher potential variation in model output and therefore potentially
greater uncertainty in interpreting results.
To explore uncertainty (ø) associated with each parameter, the percentage
variation in model output is calculated according to
∅=Xmax-XminX×100,
where Xmax and Xmin are the highest and lowest values for model
output over the entire plausible range in parameter variation, and X is the
model output with nominal parameters.
Optimisation
Model parameters implicitly account for all processes that are not
explicitly accounted for in the model and, therefore, may vary across
different environments. Based on the outcome of the sensitivity and
uncertainty analysis, parameters are adjusted in an optimisation exercise to
improve model fit to the validation data sets. Parameters are varied
incrementally to determine the effect on the accumulation of microbial
biomass and mean squared error is calculated with each model run. Parameters
JS1 and JS2 (the relative bioavailability of labile and refractory
substrate) are artefacts of the SHIMMER modelling structure. Therefore,
these two parameters are the primary free parameters, which are adjusted to
reduce mean squared error. Once a known optimum range for these parameters
has been determined, the parameters that bear the highest sensitivity,
uncertainty and non-linearity are adjusted. Parameters for which there is a high degree of confidence (narrow plausible ranges, lower sensitivity,
linear behaviour and low uncertainty) are not adjusted in the optimisation
exercise, since even relatively large changes in their value would cause
only a small change in model output.
Given the wealth of physical, biological, genomic and chemical data
available for the Damma Glacier, the focus of the analysis of model dynamics
is on this data set. However, data from the Athabasca Glacier forefield
provide additional support that the model can respond dynamically to
predict the development of soils from a range of environments and study
sites. This data set is more representative of the quality of data that is
typically available for de-glaciated forefields.
Case study 1: Damma Glacier, Switzerland
Published data sets of the biogeochemical development of the Damma Glacier
forefield in Canton Uri, Switzerland (46.6∘ N, 8.5∘ E),
are used to test and validate the model, and explore detailed model
behaviour (Bernasconi et al., 2011). Over the last 2 decades, plant and
microbial succession at this site has been extensively studied.
Comprehensive data sets have been collected as part of the BigLink project
(Bernasconi et al., 2011), with further detailed studies on nutrient cycling
(Brankatschk et al., 2011; Bernasconi et al., 2011; Guelland et al., 2013a;
Göransson et al., 2014; Smittenberg et al., 2012; Tamburini et al.,
2012), microbial community composition (Duc et al., 2009; Frey et al., 2013;
Lazzaro et al., 2012; Meola et al., 2014; Sigler and Zeyer, 2002; Zumsteg et
al., 2012), soil depths (Rime et al., 2014) and soil activity (Goransson et
al., 2011; Guelland et al., 2013b; Zumsteg et al., 2011). Therefore, the
site is highly appropriate to gain insight into model behaviour and
biogeochemical processes.
The forefield chronosequence is roughly 650 m long and represents a range of
soil ages from 0 years old to around 120 years old (Brankatschk et al.,
2011). The underlying bedrock is mainly granitic gneiss (Frey et al., 2010)
with a silty, sandy soil texture (Lazzaro et al., 2009). The site has a
northeast exposition (Bernasconi et al., 2011) and an inclination of 25 %
(Sigler and Zeyer, 2002). Soil pH decreases from pH 5.1 in initial soils (10 years ice free) to 4.1 in developed soils (ice free for 2000 years) and
water holding capacity increases from 26 to 33 % (Brankatschk et al.,
2011). Recently exposed sites at the Damma Glacier (ice free for 6 to 13 years)
are characterised by mostly unvegetated, sandy-silty sediment, gravel
and large rocks. Intermediate soils (ice free for 60 to 80 years) are
characterised by increasing vegetation cover and soil structure resembling a
typical soil profile. The old sites (ice free for roughly 120 years) are
fully vegetated, with clearly visible soil horizons (Bernasconi et al.,
2011). Molecular characterisation suggests that both specialised
heterotrophs (α-, β-, γ-Proteobacteria), autotrophs (Cyanobacteria) and other nitrogen-fixing microbes are found in all samples from all ages (Duc et al., 2009).
There is a clear increase in TOC with soil age (Bernasconi et al., 2011)
from around 700 µgCg-1 in recently exposed soils to around
30 000 µgCg-1 in developed soils. Similarly, microbial
biomass, TN and phosphorus increase by roughly an order of magnitude from
recently exposed soils to developed soils (Bernasconi et al., 2011;
Goransson et al., 2011).
The model is evaluated using least-squares error against four chemical analyses
presented in the BigLink data set (Bernasconi et al., 2011):
total microbial biomass (A1+A2+A3+H1+H2+H3): presented as
Cmic;
carbon substrate (S1+S2): calculated as TOC-Cmic;
ON (ON1+ ON2): calculated as TN-Nmic;
available DIP: presented as Presin.
Observational data were collected on 7 September (day 244 of the year), and are therefore compared to model output from day 244 of each year. The
omission of sites older than 77 years (due to vegetation influence) leaves
16 samples ranging from 5 years to 77 years since ice retreat. The 5-year
data are used as initial conditions, leaving 3 data points in the “early
soils” category and 12 from later stages of succession where there is relatively
high plant abundance. Least-square error calculation and minimisation of
errors are done only on those data points. The remaining data points
from the later stages of succession are used as a test to see if microbial
abundance in older soils falls within a plausible range, given the scatter in
the observational data. A secondary data set of DIP accumulation complements the BigLink data set (Goransson et al., 2011).
Initial microbial biomass is assumed to be evenly distributed between all
microbial groups of autotrophs and heterotrophs, and initial substrate
bioavailability is assumed to be 40 % labile and 60 % refractory.
Initial values for OP were not presented in the BigLink data set (Bernasconi
et al., 2011), but were assumed to follow a stoichiometric ratio (Bernasconi
et al., 2011). An initial value for DIN was taken from Brankatschk et al. (2011).
PAR, snow depth and soil temperature at 3 cm depth (collected by an
automatic weather station in the Damma Glacier forefield) were provided by
the WSL Institute for Snow and Avalanche Research SLF, Switzerland. Light
intensity is provided in units of photons (µmolm-2s-1)
which are converted to PAR (Wm-2) by a conversion factor (0.219). PAR
(Wm-2), snow depth (m) and soil temperature (∘C)
are
averaged to provide daily forcing to the model, and linear interpolation is
used between any (very infrequent) missing data points. The seasonal data set
is repeated for the duration of the model run (75 years) (Fig. 4).
Allochthonous inputs to the Damma Glacier forefield are estimated in
Brankatschk et al. (2011) based on chemical analyses of the snowpack and
model simulations:
carbon substrate: 75 µgCcm-2yr-1
DIN: 80 µgNcm-2yr-1
ON: 6.3 µgNcm-2yr-1.
Inputs of OP are assumed to be stoichiometrically linked to carbon substrate
according to the measured C:P ratio of microbial biomass (Bernasconi et al.,
2011). Allochthonous substrate input is assumed to be 30 % labile and
70 % refractory. Several additional assumptions are required to convert
units of deposition per surface area to units of weight. When considering a
1cm deep soil profile, 1 g dry soil occupies a surface area of
0.869 cm2
(Guelland et al., 2013b). Since substrate material and DIN is liberated when
the snowpack melts, the yearly accumulation is prescribed evenly over 10
days when there is significant snowmelt: days 158–167 (7–16 May).
DIP is typically liberated by rock weathering; however Frey et al. (2010)
analysed the minerals liberated from the weathering of the granitic
Damma Glacier bedrock material and did not find any traceable amounts of
phosphorus. Different mineralogy is likely to considerably alter the
importance of rock weathering as a source of phosphorus between locations,
increasing the uncertainty for the amount of DIP generated by weathering
processes. The annual input of DIP is prescribed as 80 µgPcm-2yr-1 (equal to DIN input), but this release is spread evenly over the
first snow-free months of each year, from day 167 to 206 (16 June–25 July). Prescribed allochthonous inputs are presented in Table 6.
The proportion of the allochthonous nutrient input that is available to the
soil represented by the model is adjusted by parameters vSub (for all
substrate pools), vDIN (for DIN) and vDIP (for DIP).
Allochthonous deposition.
Nutrient species
Input (µgg-1d-1)
S1
1.955
S2
4.562
DIN
6.952
DIP
1.738
ON1
0.164
ON2
0.383
OP1
0.162
OP2
0.378
Model output of the Damma Glacier forefield for a 75 year time
series with nominal parameter values (Table 4).
Case study 2: Athabasca Glacier, Canada
Published data from the Athabasca Glacier forefield, Canada (52.2∘ N,
117.2∘ W), are used as a second case study in the validation
exercise (Insam and Haselwandter, 1989). The Athabasca Glacier forefield is
a high-altitude (2740 m) site with soil ages from 5 to 225 years. The
mineralogy is medium textured, mostly calcareous and neutral to slightly
alkaline pH (Insam and Haselwandter, 1989). The Athabasca glacier forefield
is less intensively studied, and accordingly there is less contextual
information on the biogeochemical development of soils than the Damma
Glacier. However, the soils in the earlier stages of development (<100 years) provide a robust test of model behaviour and underlying system
dynamics due to the sparseness of vegetation and lack of interference in the
microbial signal from vascular plants.
The model is evaluated using least-squares error against two observed bulk
biogeochemical variables (Insam and Haselwandter, 1989):
Total microbial biomass (A1+A2+A3+H1+H2+H3);
Carbon substrate (S1+S2): calculated as Corg – microbial biomass.
Observational data were collected in July and are compared to model output
from day 196 of each year. Sites older than 50 years should be interpreted
cautiously due to the influence of establishing vegetation. The 5-year data
are used as initial conditions. Initial microbial biomass is assumed to be
evenly distributed between all microbial groups of autotrophs and
heterotrophs, and initial substrate bioavailability is assumed to be 40 %
labile and 60 % refractory. Since there are no quantitative estimates of
DIN, DIP, ON and OP, initial inorganic nutrient concentrations are assumed
to follow the same ratio as the Damma Glacier case study, and organic
material follows a stoichiometric ratio (Bernasconi et al., 2011). Annual
profiles of monthly average soil temperature (at 5 cm depth) and snow depth
are obtained from published literature (Achuff and Coen, 1980) and linearly
interpolated to provide daily forcing data (Fig. 4). Daily solar irradiance
data from 2014 are obtained from the Alberta Agriculture and Rural
Development Agroclimatic Information Service for a nearby meteorological
station (Stavely AAFC, 50.2∘ N, 113.9∘ NW; 1360 m). These
are repeated year-on-year for the duration of the model run. There is no
observational, experimental or modelled data of sufficient quality to
provide forcings of allochthonous inputs to the Athabasca Glacier forefield.
Therefore estimations from the Damma Glacier are used and parameters
vSub, vDIN and vDIP are adjusted. As with case study 1,
optimisation is carried out based on the results of the sensitivity study,
and a minimisation of least-squared error and visual fit to data is carried
out based on numerous model runs varying parameters that were identified in
the sensitivity test.
Sensitivity of model outputs (λ) to individual parameter
variation. The model is forced with meteorological data from the Damma
Glacier (Fig. 4) over 75 years.
Results and discussion
Nominal
The model behaviour under nominal parameters, and forced with meteorological
data and initial conditions from the Damma Glacier is presented in Fig. 7.
Total microbial biomass is initially stable at roughly 3.4 µgCg-1 (year 1),
followed by an exponential growth phase to 46.8 µgCg-1 (year 15),
and then a decline to near-steady-state around 31.0 µgCg-1,
varying seasonally by roughly 12.0 µgCg-1. By the final year of simulation (year 75), the community has
evolved (from an even split 16.7 % per pool) such that the most dominant
pool is soil autotrophs (A2=35.8 %), followed by nitrogen-fixing
autotrophs (A3=27.4 %) and subglacial chemolithoautotrophs
(A1=12.3 %), with all heterotrophic biomass (H1-3) making up
the remaining 24.5 %. Total bacterial production rises steadily from 0.3 µgCg-1yr-1 (year 1) to 114.2 µgCg-1yr-1
(year 15), after which (year 31 onwards) bacterial production
declines by roughly a half. Autotrophs are consistently the highest
producers, responsible for between 72.6 and 89.2 % of the total bacterial
production.
There is a steady accumulation of carbon substrate throughout the entire
simulation, from 735.4 µgCg-1 (year 1) to 4129.2 µgCg-1
(year 75); however substrate becomes more refractory (39.4 % labile in
year 1, 3.7 % labile in year 75). ON and OP follow similar dynamics to
carbon substrate (S1 and S2). The accumulation of substrate is
derived from autotrophic activity, the build-up of microbial necromass and
allochthonous deposition. DIN and DIP accumulate during the first 14 years
of the simulation, after which DIN increases and DIP declines.
Sensitivity and linearity
Sensitivity
Sensitivity analysis is presented in Fig. 8. The accumulation of autotrophic
and heterotrophic biomass is most sensitive to variation in Q10
(λ≥0.70). Biomass accumulation is also highly sensitive to
adjustments in the active fraction (d) (-0.55≤λ≤-0.52), the bioavailability of refractory substrate (JS2) (0.44≤λ≤0.64), the partitioning of microbial necromass into labile
and refractory pools (q) (0.31≤λ≤λ0.45) and
microbial growth rates (Imax) (-0.55≤λ≤0.67).
Biomass accumulation is moderately sensitive to death rates (αA
and αH), the efficiency of heterotrophic growth (YH) and
the allochthonous substrate input (vSub) (±0.15≤λ≤±0.41). Biomass accumulation has relatively low sensitivity
(λ≤±0.15) to variation in half-saturation constants
(KL, KS, KN and KP), parameters affecting only the dynamics
of subglacial microbes (A1 and H1) (pSub and kSub) and
nitrogen fixers (A3 and H3) (nf, KN2), the bioavailability
of labile substrate (JS1), exudate rates (exA and exH), the input
of allochthonous nutrients (vDIN and vDIP) and the efficiency of
autotrophic growth (YA). Variation in the half saturation for nitrogen
(KN) and phosphorus (KP) causes little change to the accumulation of
biomass (-0.02≤λ≤0.00 and -0.05≤λ≤0.03, respectively), but has a proportionally large effect on the
accumulation of DIN, DIP and total nitrogen fixation (0.22≤λ≤0.95). Similarly, the reduction of efficiency and growth rates
(nf) for nitrogen fixers whilst fixing nitrogen (rather than
assimilating DIN) has a relatively minor effect on the accumulation of
biomass (λ≤±0.09) but strongly affects DIN, DIP and
total nitrogen fixed (λ=0.96, λ=-0.96 and λ=0.60, respectively).
Microbial communities alter their metabolic state (through the Q10
formulation) to persist during long periods of cold. At cold temperatures
typical of glacier forefield environments, high Q10 responses to
temperature variation (Schipper et al., 2014) promote the survival of
biomass under prolonged periods of harsh environmental conditions (soil
temperatures <Tref).
Heterotrophic production is critical in supporting the overall establishment
of biomass and activity of the entire microbial community. Increasing the
maximum growth rate of heterotrophs (ImaxH) leads to a substantial
increase in both heterotrophic and autotrophic biomass (λ=0.47
and λ=0.67, respectively). However, strikingly, an increase in
the maximum growth rate of autotrophs (ImaxA) has the net effect of
lowering autotrophic and heterotrophic biomass (λ=-0.36 and
λ=-0.55, respectively). Autotrophic growth is responsible for
the build-up of substrate during the initial stages of soil development,
thus supporting heterotrophic production. However, the dominance of
autotrophic communities rapidly consumes available nutrients, at the expense
of heterotrophs. If autotrophs are given a competitive advantage (i.e. increasing ImaxA), their rapid growth increases nutrient scarcity
(λDIN=-0.57, λDIP=-1.58) and
heterotrophic growth becomes nutrient limited. However, if heterotrophs are
given a competitive advantage (i.e. increasing ImaxH), substrate is
degraded more rapidly, liberating DIN (λ=0.76) and DIP
(λ=0.38). This is an effective positive feedback effect,
whereby the additional nutrients recycled from rapid heterotrophic
degradation are able to support the growth of all microbial populations
(including autotrophs (λ=0.47)) in this oligotrophic and
relatively nutrient poor environment. Similarly, increasing autotrophic
death rates (αA) reduces competition for nutrient resources
whilst also increasing the availability of degradable organic matter
(autotrophic necromass), thereby increasing heterotrophic biomass (λ=0.24).
An increase in the heterotrophic growth efficiency (YH) leads to an
overall more rapid accumulation of heterotrophic biomass (λ=0.14) at the expense of autotrophs (λ=-0.41), since
heterotrophic nutrient uptake is higher. A decrease in heterotrophic growth
efficiency effectively means that for heterotrophs to grow by the same
amount, they must degrade more organic matter per mole of carbon
incorporated in biomass, thereby liberating nutrients and in turn supporting
autotrophic growth. Previous modelling studies have consistently found
microbial growth efficiency (Y) to be the most sensitive parameter in
determining overall biomass accumulation and the compartmentalisation of
carbon between biotic and abiotic pools (Blagodatsky and Richter, 1998;
Ingwersen et al., 2008; Toal et al., 2000).
Linearity
Linearity of parameter sensitivity is explored qualitatively over the range
of parameter values by plotting the change in model output and visually
fitting a linear or polynomial relationship to the trend (Fig. 9). Sensitivity and
linearity evaluation have important implications in model optimisation. The
highest degrees of freedom can be given to those parameters with fairly low
sensitivity and a high degree of linearity (Q10, exA, exH,
KL, KS, KN and KP), since these parameters affect model
output minimally and in a reasonably predictable way (illustrated in Fig. 6a).
The parameters vSub, pSub, q and YH also behave fairly
linearly. Changes in model output respond non-linearly to changes in
ImaxA, ImaxH, JS2, d, αA, αH,
vDIN and vDIP. Therefore, the sensitivity value λ is likely
to change when looking at values away from the nominal parameter value, as
illustrated for ImaxA in Fig. 6b. For non-linear parameters αA, αH, vDIN and vDIP, the maximum sensitivity is
found in the region near the nominal value. This means that slight changes
in parameter values will greatly affect the model output. Parameters
ImaxA, ImaxH, JS2, and d behave fairly linearly with
comparatively little sensitivity around the nominal value; however their
sensitivity increases with distance from the nominal value. This may give
the impression of stability around the nominal values however a tipping
point may be reached when parameters deviate too much from the nominal
value. As such, non-linear parameters (identified in Fig. 9) must be given
due caution in optimisation exercises since changes in these parameters may yield
unexpected model behaviour.
Heat map showing parameter linearity and non-linearity over a
range of model outputs. The model is forced with meteorological data from
the Damma Glacier (Fig. 4) over 75 years.
Heat map showing uncertainty of model outputs (ø) arising from
individual parameters. The model is forced with meteorological data from the
Damma Glacier (Fig. 4) over 75 years.
Uncertainty
Uncertainty is evaluated over the entire plausible parameter range and
results are presented in Fig. 10. The parameters that bear the highest
uncertainty in the accumulation of autotrophic and heterotrophic biomass are
ImaxH (397 and 685 %, respectively) and JS2 (333 and
606 %, respectively). A high degree of uncertainty (≥60 %) also
results from variation in αA, αH, ImaxA, q,
YH, d, vSub and vDIP. This is due to a combination of high
sensitivity and large plausible ranges. There is minimal uncertainty (≤30 %) resulting from variation in parameters exA, exH, pSub,
kSub, KL, KN, KP, KN2, JS1, YA and vDIN.
Parameters that bear high uncertainty in the accumulation of biomass also
tend to cause high degrees of uncertainty in other model outputs, most
notably the accumulation of DIN and DIP, total nitrogen fixed and
seasonality.
Measurements of bacterial growth are fundamental to most aspects of
microbial ecology. Consequently, there are many estimates for ImaxA and ImaxH
from literature and related modelling studies; however they span over an
order of magnitude (0.24 to 4.80 d-1) (Mur et al., 1999; Van Liere and
Walsby, 1982; Frey et al., 2010; Ingwersen et al., 2008; Knapp et al., 1983;
Zelenev et al., 2000; Stapleton et al., 2005; Darrah, 1991; Blagodatsky and
Richter, 1998; Vandewerf and Verstraete, 1987a; Foereid and Yearsley, 2004;
Toal et al., 2000; Scott et al., 1995), greatly increasing the uncertainty
associated with ImaxA and ImaxH (average uncertainty =265 and
693 %, respectively). Maximum growth rates have been experimentally
measured for soils from the Damma Glacier, with a value roughly in the
middle of the plausible range (Frey et al., 2010); however there is inherent
abstraction when incorporating laboratory measurements into models because
of the assumptions and simplifications in model design.
Microbial death rates (αAand αH), however, are
difficult and problematic to define experimentally (Toal et al., 2000), and
there is a great deal of variation in how losses from microbial biomass are
modelled. Death rates bear moderate sensitivity in model outputs (λ≤-0.13 and λ≥0.24), and very high uncertainty (77
to 178 %), as a consequence of the large plausible parameter range, which
spans almost 2 orders of magnitude (0.006 to 0.48 d-1). Furthermore,
the transferability of microbial death rate constants is compromised by the
different mathematical formulations used to describe death rates (e.g. constant fixed rate (German et al., 2012; Grant et al., 1993; Scott et al.,
1995; Toal et al., 2000): logistic (Boudreau, 1999; Kravchenko et al.,
2004) and variable, depending on model conditions (Knapp et al., 1983;
Blagodatsky and Richter, 1998; Ingwersen et al., 2008; Zelenev et al., 2000;
Lancelot et al., 2005)).
Model output optimised to observational data from the Damma
Glacier, Switzerland.
The allochthonous deposition of organic matter and nutrients is a source of
considerable uncertainty. Published literature provides estimates of snow
nutrient concentrations at the Damma Glacier (Brankatschk et al., 2011);
however the fate of these nutrients once deposited on the soil surface is
largely unknown. Accordingly, the plausible parameter ranges for
vSub, vDIN and vDIP are wide, and the resulting uncertainty is
very high (75 to 2503 %). Furthermore, variation in parameters
vDIN and vDIP results in highly non-linear behaviour, with
comparatively large changes resulting from small changes in the parameter
value. However, the effect of vDIN on the accumulation of autotrophic
and heterotrophic biomass is minimal (5 and 9 %), due to the
substantial inputs of nitrogen from nitrogen fixers throughout the
development of the forefield. Analysis of the BACWAVE model (Zelenev et al.,
2000) found high sensitivity of the spatial and temporal response of
bacterial populations to changes in allochthonous carbon sources in soil.
The partitioning of organic matter compounds into a limited number of substrate pools (e.g. labile and refractory) is, although common practice, artificial, and a meaningful value cannot be determined experimentally or
from literature (e.g. Arndt et al., 2013). Therefore, these parameters are
ideal for initial tuning and optimisation exercises. Adjustment in q,
JS1 and JS2 causes considerable variation in the accumulation of
autotrophic and heterotrophic biomass (0.07≤λ≤0.64)
and relatively large uncertainty (4 to 606 %).
Estimation of the inhibition of nitrogen fixation with DIN (KN2) is
based on published literature and a relatively large range is considered in
the uncertainty analysis (56.4µgNg-1≤KN2≤1128µgNg-1) (LaRoche and Breitbarth, 2005; Rabouille et al.,
2006; Holl and Montoya, 2005). The total nitrogen fixed and total
accumulation of DIN is fairly sensitive to variation in KN2 (λ=0.08 and λ=0.11, respectively), however the resulting
uncertainty in the overall accumulation of autotrophic and heterotrophic
biomass is low (3 and 1 %, respectively). Therefore, although this
parameter is not well defined, its importance is outweighed by other much
more sensitive parameters such as the active fraction (d) and microbial death
rates (αA and αH).
Many of the fairly well-constrained parameters result in low uncertainty
values. This can be explained by relatively tight parameter bounds explored
in the uncertainty analysis, or relatively low sensitivity of model output
to variation in this parameter, or a combination of both of these factors.
For example, exudate production rates (exA and exH) (uncertainty ≤2 %) have relatively tight parameter bounds (Allison, 2005), as well as
low overall sensitivity (-0.01≤λ≤0.02).
Half-saturation constants for carbon substrate (KS) have been estimated
experimentally (Vandewerf and Verstraete, 1987a; Vandewerf and Verstraete,
1987b; Blagodatsky et al., 1998; Anderson and Domsch, 1985) and fitted using
models (Darrah, 1991; Ingwersen et al., 2008; Stapleton et al., 2005), with
values between 50 and 1000 µgCg-1. This
variation can be attributed to differences in experimental technique and
medium of substrate used, and differences in model structure and
optimisation; however overall model sensitivity is low (λ=-0.07), as is reflected in other models (Ingwersen et al., 2008; Blagodatsky
and Richter, 1998).
Evolution of the microbial community composition in model output
optimised from the Damma Glacier, Switzerland, over the first 20 years of
soil formation.
Optimisation and model dynamics
Case study 1: Damma Glacier
Model parameters are optimised to obtain the best possible fit to
observational data from the Damma Glacier, Switzerland (Table 5 and Fig. 11).
Total microbial biomass increases rapidly during the initial stages of
the soil development to a peak of 61.6 µgCg-1 (year 12),
followed by a decline over the following 10 years, after which biomass is
fairly stable at roughly 37.0 µgCg-1 (years 30 to 75). The
microbial community evolves from an even split between all six pools of
microbial biomass (16.7 %) to a community dominated by autotrophs
(A1-3 comprises 78.5 % of biomass in year 13) (Fig. 12). Nitrogen-fixing autotrophs (A3) are the dominant functional group during the
first 10 years of the simulation (up to 56.1 % of biomass), after which
soil autotrophs (A2) increase in relative abundance (up to 35.6 % of
biomass) as DIN concentrations increase. Subglacial microbes (A1 and
H1) are consistently outcompeted by soil microbes (A2 and
H2) (Fig. 12).
Evolution of (a) substrate dynamics, (b) bacterial production and
(c) nitrogen (N) assimilation of model output from the first 20 years of
soil formation at the Damma Glacier, Switzerland.
Primary production (A1-3) accounts for between 68.7 and 88.9 % of
total bacterial production, whereas heterotrophic production (H1-3)
accounts for the remaining 11.1 to 31.3 % (Fig. 13b). This trend is
also reflected in independent field studies, whereby autotrophic production
has been identified as a major source of carbon in young soils at the Damma
Glacier (Zumsteg et al., 2013b; Esperschütz et al., 2011; Frey et al., 2013)
and elsewhere including the Puca Glacier in Peru (Schmidt et al., 2008).
Heterotrophic production is closely associated with the abundance and
availability of carbon substrate. A high proportion of labile substrate
(39.4 % in year 1) supports high rates of heterotrophic production and
rapid accumulation of heterotrophic biomass. Labile substrate is rapidly
depleted (Fig. 13a) followed by a sharp decline in biomass (Fig. 11).
Following the exhaustion of labile organic carbon substrate, heterotrophic
production is sustained at lower steady rate (roughly 10.0 µgCg-1yr-1) and predicted microbial biomass is within the natural
variability of the observational data. Chemical analysis of substrate from
the Damma Glacier forefield suggests that organic matter becomes
increasingly refractory in the later stages of development due to continual
re-working and cycling by microbial communities (Goransson et al., 2011), as
reflected in the model. Soil respiration (net DIC efflux) follows a broadly
similar pattern to total microbial production, and is relatively stable
(roughly 312.0 µgCg-1yr-1) in the later stages of soil
development (years 30 to 75). Soil respiration rates in the Damma Glacier
have been estimated to be in the range of 130.0 µgCg-1yr-1
(Schulz et al., 2013; Guelland et al., 2013a), which is within the range
predicted by the SHIMMER model.
No parameter combination could reproduce the high substrate accumulation
observed at the Damma Glacier (Fig. 11). Even under extremely high
allochthonous substrate loading (vSub=3.0, equivalent of 195.5 µgCg-1yr-1), carbon substrate accumulates to roughly half of the
highest maximum substrate sampled in the BigLink project (31 363.1 µgCg-1)
(Bernasconi et al., 2011). We attribute this to the extremely
rapid onset of vegetation (Bernasconi et al., 2011). Duc et al. (2009)
compare rhizosphere and bulk soils in the Damma Glacier, and find
substantially higher total organic carbon concentrations in soils sampled in
close proximity to plants. The SHIMMER model does not include a vegetation
component and is thus not able to account for the effect of plants.
Field-based nutrient enrichment experiments show that microbial growth is
limited by carbon and nitrogen (Goransson et al., 2011; Yoshitake et al.,
2007). Furthermore, a high diversity of diazotrophs has been associated with
soil nitrogen accumulation in initial soils at the Damma Glacier (Duc et
al., 2009), the Puca Glacier (Peru) (Schmidt et al., 2008; Nemergut et al.,
2007), Mendenhall Glacier (Alaska) (Sattin et al., 2009; Knelman et al.,
2012) and Anvers Island (Antarctica) (Strauss et al., 2012). This is
reflected in the model. DIN is the primary limiting nutrient for subglacial
and soil species (A1, A2, H1 and H2) during the first 5
years of simulated soil development, after which there is sufficient DIN in
the soil (6.22 µgNg-1) to support the net accumulation of
microbial biomass in all pools. However, nitrogen fixers (A3 and
H3) are able to alleviate DIN limitation and experience net growth
immediately, contributing 85.7 % of all nitrogen assimilated in microbial
biomass during the first 10 years (Fig. 13c). The main supply of phosphorus
to natural terrestrial ecosystems is the underlying parent rock, especially
in glaciated settings whereby relatively high erosion rates and crushed rock
flour give rise to increased mineral dissolution rates. However, phosphate
is a relatively immobile macronutrient due to sorption and interaction with
other soil constituents, making it a potential growth-limiting nutrient in
terrestrial ecosystems (Hinsinger, 2001). Initial phosphorus limitation is
rapidly alleviated by the accumulation of DIP at an average rate of 2.0 µgPg-1yr-1
(years 1 to 10). Predicted DIP closely
resembles field data (Goransson et al., 2011). Isotopic analysis (Tamburini
et al., 2012) and modelling suggests that biological activity is the main
driver of phosphorus cycling in developing soils at the Damma Glacier.
The seasonal evolution of the Damma Glacier forefield is not well
understood; however transplantation studies have indicated that microbial
communities respond dynamically to changing environmental conditions
(Zumsteg et al., 2013a) and soil bacteria photosynthesise, degrade organic
material and fix nitrogen at varying rates over spring, summer and autumn
(Lazzaro et al., 2012). Microbial abundance and production calculated over
winter (January, February, March) and summer (July, August, September)
varies seasonally (Fig. 11a). Snow cover attenuates PAR in the winter period
causing large seasonal fluctuations in the biomass and overall production of
photosynthetic organisms (A2 and A3). Whilst heterotrophic
production is also higher in the summer (0.13 µgCg-1d-1)
than winter (0.05 µgCg-1d-1), populations remain more
stable. SHIMMER estimates that 69.6 to 74.5 % of total net CO2 efflux
occurs during the 4 month snow-free summer period between June and
October, which agrees well with estimations from field studies at the Damma
Glacier (62 to 70 %) (Guelland et al., 2013b).
Model output optimised to observational data from the Athabasca
Glacier, Canada.
Case study 2: Athabasca Glacier, Canada
The model is calibrated and validated against a second test data set from the
Athabasca Glacier forefield in Canada. Parameters (Table 5) are varied
sequentially to provide a best fit to observations of microbial biomass and
carbon substrate (Fig. 14). Microbial biomass accumulates throughout the
simulation from 2.6 µgCg-1 in year 1 to 11.5 µgCg-1 in year 40,
and at roughly 0.02 µgCg-1yr-1 in
years 50 to 75. These results agree with the observed accumulation of
microbial biomass in the validation data set. During the early stages of
succession (<15 years), nitrogen-fixing autotrophs account for up
to 62.5 % of the total biomass. Heterotrophs (H1-3) make up 17.2 %
of the biomass in year 15. Soil heterotrophs (H2) account for only
4.7 % of biomass in year 15 (0.33 µgCg-1), and are severely
limited by DIN (11.3 µgNg-1); however later increase to a
similar relative abundance to nitrogen-fixing heterotrophs when DIN stocks
are more plentiful.
The model predicts the observed accumulation of carbon substrate with a
substantially lower allochthonous input of substrate (vSub=0.05)
compared to the Damma Glacier (vSub=0.60). Autotrophic production
accounts for >87.5 % of total bacterial production. DIN
remains low compared to the Damma Glacier. The majority of the DIN
assimilation in young soils (<15 years) is by nitrogen fixation (up
to 96.6 %). The seasonal oscillations in microbial biomass and activity at
the Athabasca Glacier forefield are considerably smaller than the Damma
Glacier forefield, due to increased nutrient scarcity (inhibiting growth and
slowing the biotic response to seasonal variability) and lower microbial
biomass. A high level of bacterial production is sustained by a continuous
pool of labile substrate. Our ability to put these model results into
context with field data is limited since there the Athabasca Glacier
forefield is considerably less intensively studied than the Damma Glacier.
Nevertheless, the Athabasca Glacier site acts as a secondary test and
validation of model behaviour against published observational and
experimental data suggesting an increase in microbial biomass and
accumulation of organic carbon.
Model development, application and recommendations
The SHIMMER framework greatly improves our ability to quantify dominant
biogeochemical processes and make scenario-based predictions of soil
development. An additional result of developing the SHIMMER framework has
been an appreciation of the types of data that are necessary to build a
mechanistic and fully constrained numerical representation of these systems,
and this is presented here as a recommendation to future field and
laboratory efforts.
Data availability
Model development and confidence in model evaluations would be improved by
higher temporal and spatial sampling resolution along the chronosequence and
interdisciplinary (microbial and geochemical) data sets (concentrations and
rates). Resolution of autotrophic and heterotrophic biomass would help in
validating model predictions of community composition and net
autotrophy/heterotrophy. SHIMMER does not explicitly account for vegetation
and thus cannot reproduce the high organic carbon accumulation in vegetated
sites (Fig. 11). Therefore, there is a need for test sites where the
influence of vegetation is not so great. A full mass budget of inputs (e.g.
aerial deposition) and outputs (e.g. leaching) of substrate and nutrients
through the soil surface would greatly improve the predictive power of
SHIMMER, as demonstrated in sensitivity analysis (Sect. 5.2.1).
Death and dormancy
Many biological processes including microbial growth and death are
simplified in order to describe them mathematically. Cell death is not well
constrained, with a lack of empirical measurements, and fundamental
differences in how these rates are defined in models (German et al., 2012;
Grant et al., 1993; Scott et al., 1995; Toal et al., 2000; Boudreau, 1999;
Kravchenko et al., 2004; Knapp et al., 1983; Blagodatsky and Richter, 1998;
Ingwersen et al., 2008; Zelenev et al., 2000; Lancelot et al.,
2005). Additionally, in situ measurements of active and dormant
microbes in field studies are rare, thus making validation difficult. Those
that are provided in the literature (Toal et al., 2000; Blagodatsky and
Richter, 1998; Vandewerf and Verstraete, 1987b) are mostly derived from
models and are a snap shot in time. These rates strongly influence both the
microbial populations' stability in size, and the available substrate and
necromass. Therefore, more focussed empirical observations are
needed to support and inform model processes, increase confidence in
predictions and support future development.
Bacterial growth
Parameters defined as constants in mathematical models are often known to
vary in time depending on prevailing environmental and biogeochemical
conditions, for example sensitivity to temperature, soil moisture, oxygen
availability, C:N ratio and quality of soil organic matter (Manzoni et al.,
2012; Erhagen et al., 2015). Variable growth efficiencies and background
maintenance, for example, would require additional parameters that currently
cannot be defined with sufficient confidence, increasing uncertainty rather
than improving the model. Laboratory incubations are useful to estimate
parameter values experimentally (Blagodatsky et al., 1998). It is our
intention that future laboratory analysis can at least in part inform
parameters such that confidence in model output is increased.
Discrete pools vs. continuum representation
In a real soil system, the composition of the microbial community, along
with the quality of substrate are continua, rather than discreet categories
(as in SHIMMER). Classifying variables into categories (e.g. labile and
refractory) ultimately provides a simplistic view of the system, but also
provides tuning parameters, flexibility and a high degree of generality.
Other modelling approaches such as individual-based modelling (IBM) would
account for population heterogeneity, and the ability to link mechanisms to
population dynamics at the individual level (Hellweger and Bucci, 2009).
However, this is outside the scope of the current model version.
Deterministic vs. stochastic
The biogeochemical development of a de-glaciated forefield is extremely
heterogeneous across a range of spatial scales, which affects the signal of
biogeochemical changes in observations (Bernasconi et al., 2011; Bradley et
al., 2014). Stochastic variability resulting from disturbances,
heterogeneity in biotic and abiotic processes, lateral and vertical particle
movement and diffusion, inter-annual variability, and changing environmental
conditions affect the biogeochemical development of a chronosequence in such
a way that a deterministic model cannot predict. Furthermore, the SHIMMER
model does not predict or account for the effect of plant biomass, which is
highly abundant in the forefield of the Damma Glacier (Bernasconi et al.,
2011). However, a first attempt to gain quantitative insight into glacier
forefield dynamics favours a deterministic framework.
0-D vs. multi-D
Currently, nearly all soil system models assume that at the finest level of
detail, soil is a well-mixed homogeneous particle with respect to its
composition and dynamics, whereas microbial populations and metabolic rates
are known to be heterogeneous across a number of different spatial scales
and directions. A large amount of additional parameters and equations would
need to be incorporated in order to include 1-D or 2-D processes in SHIMMER.
It is currently unfeasible to incorporate this level of detail due to
limitations in the observational data, and the resulting model would not be
useful for the purpose it is intended for, that is to describe, predict and
provide insight on the development of initial ecosystems such as those
exposed due to glacier retreat.
Conclusions
Accurate quantitative prediction of the biogeochemical development of
de-glaciated forefields is important to understand the primary succession of
microbial communities and the formation of organic carbon in extreme
oligotrophic environments. The forefield ecosystem reacts rapidly to climate
change (Smittenberg et al., 2012), and the fine glacial flour, highly
reactive sediments and rapid biological cycling of nutrients typical of
forefields may be significant to global biogeochemical cycles in the context
of future large-scale ice retreat.
Here we present SHIMMER, a novel modelling framework designed to predict
microbial community development during the initial stages of ecosystem
formation. The model accurately predicts the accumulation of microbial
biomass and organic carbon during the initial stages of soil development
from two glacier forefields (Bernasconi et al., 2011; Goransson et al.,
2011; Insam and Haselwandter, 1989), and supports our general understanding
of these ecosystems. Autotrophic production and nitrogen fixation are
fundamental to the establishment of microbial communities and stable and
labile pools of organic substrate and inorganic nutrients, a finding that is
supported by field experiments at the Damma Glacier (Zumsteg et al., 2013b;
Esperschütz et al., 2011; Frey et al., 2013; Duc et al., 2009) and elsewhere
including the Puca Glacier in Peru (Schmidt et al., 2008; Nemergut et al.,
2007), the Mendenhall Glacier in Alaska (Sattin et al., 2009; Knelman et
al., 2012), and Anvers Island in Antarctica (Strauss et al., 2012). Soil respiration is comparable to field observations (Schulz et al.,
2013; Guelland et al., 2013a). The seasonal evolution of glacier forefields
is not well understood (Bradley et al., 2014); however modelling work is
likely to provide insight into the dynamics of the “non-growing season”.
For example, modelled summer production accounts for roughly 70 % of total
annual respiration, in line with field observations from the Damma Glacier
(Guelland et al., 2013b).
The accumulation of microbial biomass is highly sensitive to variation in
the Q10 values, active biomass, the bioavailability of organic matter,
bacterial growth efficiency, and rates of microbial growth and death. These
parameters also bear high uncertainty due to a relatively large range of
plausible values. Many of the well-constrained parameters (e.g. half-saturation constants and exudation rates) have low sensitivity and
uncertainty and show mostly linear behaviour. One of the striking outcomes
of the sensitivity study is the apparent strong dependence between the
heterotrophic and autotrophic microbial communities. Heterotrophic
production degrades organic matter and recycles nutrients, in turn
supporting autotrophic and heterotrophic growth. Increasing heterotrophic
growth rates therefore increases the accumulation in all pools of biomass.
SHIMMER is the first step towards an iterative and interdisciplinary
framework (presented in Fig. 2), integrating fieldwork and laboratory
experiments with model development, testing and application. The development
of SHIMMER (1.0) is informed by previous experimental and field campaigns
(Bradley et al., 2014). It is expected that further quantitative analysis of
forefield dynamics will guide and inform future studies that will provide
new data and insights, which will inform further model development and so
forth. SHIMMER thus contributes to more accurate quantitative predictions
that enable a deeper understanding of the processes which control microbial
communities, their role on global biogeochemical cycles and their response
to climate variations in the future.
Code availability
The source code related to this article is provided as a Supplement
package together with a read me file. The code is written and executed in
the free open-source computing environment and programming language R, which
is available for download on the web (http://www.r-project.org/).