Systems model of carbon transformations in soil subsidence

Ecological Modelling, 5 (1978) 269--292 269 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

SYSTEMS M O D E L OF C A R B O N T R A N S F O R M A T I O N S IN SOIL SUBSIDENCE

JOAN A. BROWDER and BOB G. VOLK *

Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Fla. 33149 (U.S.A.)

• Soil Science Department, University of Florida, Gainesville, Fla. 32611 (U.S.A.)

Florida Agricultural Experiment Stations Journal Series No. 854.

(Received 11 August 1977; revised 14 October 1977)

ABSTRACT

Browder, J.A. and Volk, B.G., 1978. Systems model of carbon transformations in soil subsidence. Ecol. Modelling, 5 : 269--292.

A systems model was designed to simulate the interaction of climatologic and biologic factors in the biological oxidation of organic soils in order to stimulate research on this diminishing resource and attendant water quality problems in the Florida Everglades area. This is a mass balance model in which carbon and nitrogen are conserved in the transformations. It was designed to test different management alternatives for slowing the rate of soil subsidence and to estimate their potential effect on water quality by simulating subsidence rates and the release rates of nitrates, nitrites, and organic acids to ground and surface waters.

The biological submodel is structured about two major compartments -- the total nonliving carbon compartment and a living carbon compartment that includes the microbial biomass and functioning extracellular enzymes.

Simulations of the model show the effects of temperature, organic composition, and water table height on carbon dioxide evolution from the soil.

INTRODUCTION

The agricultural area in the Everglades o f sou the rn Flor ida encompasses app rox ima te ly 283 ,000 ha o f drained organic soils (Histosols) which are subsiding at the rate o f 3 cm/year . These organic softs are very fertile and are used for the p r o d u c t i o n o f sugarcane, vegetables, and livestock. I t is es t imated tha t farming on these Histosols will e i ther change drastically or largely disap- pear by the year 2000 (Stephens and Speir, 1969).

The major end p roduc t s result ing f rom subsidence are ca rbon dioxide, water, and water-soluble ca rbon c o m p o u n d s , nitrates, and nitrites. Subsi- dence involves consol ida t ion and the relatively rapid microbial oxidat ive deg- rada t ion o f the organic mat ter . The volumetr ic loss o f organic soil accompa- nying biological ox ida t ion has been described in detail by Clay ton and Neller (1943) , S tephens and J o h n s o n (1951) , Allison (1956) , S tephens (1956,

2 7 0

1974), Broadbent (1960), Stephens and Speir (1969), and others. The changing chemical characteristics of Histosols undergoing biological oxidation were described by Volk and Schnitzer (1973) and Zelazny and Carlisle (1974). Volk (1973) measured carbon dioxide evolution rates in the oxidation process at various water table depths and temperatures.

Clayton et al. (1942), Allison (1947), Stephens {1974), and others have suggested that subsidence can be slowed by raising the water table maintained in the area by a system of levees and canals. Other management techniques that have been suggested to slow subsidence are the addition of soil amendments such as clays (Mortland et al., 1957; Zelazny and Carlisle, 1974) and sewage sludge, and the "plowing under" of crop residues (Broadbent, 1960; Thomas, 1965).

The effect of changing the control level of the water table was simulated by a digital computer model. Also simulated was the biological oxidation rate of an equal quanti ty of fresh organic material for comparison with the subsidence rate of Histosols. Major environmental factors affecting the simulated system were temperature, rainfall, and evaporation, which varied daffy with seasonal extremes.

M O D E L - - G E N E R A L D E S C R I P T I O N

The model employs the energy circuit language and concepts of energy flow of Odum (1971) to track carbon transformations from organic soil carbon to carbon dioxide. Diagrams of the model are given in Figs. 1 and 2. A digital computer program for the model was written in DYNAMO (Pugh, 1973). Other models of the soil ecosystem using Odum's (1971) energy circuit language can be found in Richards (1976).

The systems modelling approach

Design of a model is the first step in the systems approach to addressing a problem. In the systems methodology a model is drawn to define the major compartments, interactions, and driving forces of the system. When the energy circuit language of Odum (1971) is used, basic equations of the interactions are inherent in the model design. Classical or derived empirical expressions can be incorporated in the model. Where mathematical relationships are not exactly known, equations estimating the relationships believed to exist are formulated. The model is further developed into a computer program of the equations, necessary constants, and sets of fixed variables ("table functions"}. Where possible, good estimates for the constants and table functions are obtained from the literature. Where such information is not available, values are approximated. Early quantification, although often based primarily on gross estimates, makes it possible to execute the model near the beginning of a s tudy when simulations can help researchers to develop a general understanding of the way the system functions as a whole unit and also

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to identify those parameters which have the greatest impact on systems "behavior", so that research efforts can be concentrated in the areas.

Research oriented toward establishing a firmer data base for the model follows early executions. As this research progresses the model "evolves" so that its structure may become more well defined as more precise relationships become known. Successive executions of the model utilizing new information to produce new simulations are carried out concurrent with research in the field and in laboratories. With the model as a guide, research is directed toward filling vacuums in preexisting knowledge and reaching predetermined goals. With this approach the end product of research is more likely to be a full picture of the system, the problem, and possible solutions.

The model herein described was the model designed to organize research. The simulations presented represent results of early executions of the model to test its general performance and to observe the way in which variations in the values of some parameters affected its overall behavior.

Biological submodel

The biological submodel (Fig. 1) is structured around two major compartments. The larger compartment is that of total nonliving carbon compounds in the soft. The compounds in this compartment originate as dead plant ma-

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terial but also include "recycled" carbon from microbes, deposited as dena- tured extracellular metaboli tes and dead cells, as described by Given and Dickinson (1975). The second compar tment represents active living carbon as it is found in microbial biomass and functioning extracellular enzymes. In the model, all microbe populations are treated as a single functioning unit. Distinctions are not made between microbe populations with different roles in the decomposi t ion process or at different trophic levels. Internal cycling of materials between populations within this compar tment is not considered.

The larger compar tment is divided into six subcompartments to track the change in different types of carbon compounds. One compar tment represents proteins, peptides, and amino acids; another represents easily hydrolyzable polysaccharides such as sugars and starches. Less easily hydrolyzable polysaccharides such as cellulose and hemicellulose, as well as soluble aromatics and insoluble aromatics, are each in separate compartments. Included also is a compar tment for organic amendments such as sewage sludge that might be added as a management technique. The naturally-occurring carbon compounds are compartmental ized based on their degree of resistence to breakdown by bacteria and other microorganisms, which is assumed in this model to reflect the relative energy cost to the microbes for substrate utilization. The substrate was subdivided into carbon compounds according to ease of breakdown by microbes in a similar manner in a model of the decomposi t ion process by Ausmus (1972).

The rate of assimilation of carbon compounds is represented by the pathway from nonliving carbon to the compar tment of living carbon in microbes. The basic assimilation rate is assumed to be a function of the concentrat ion of total carbon in the soil and approximated by the Michaelis-Menten expression. The proport ion of each compound assimilated is assumed to be the same as the proport ion of that compound present in the substrate (nonliving carbon compartment) .

Assimilation rate is undoubted ly a function of the amount of active living carbon (which is thought to be directly related to the amount of the enzyme, dehydrogenase, in the soil). This relationship is indicated by the "positive feedback" connection between active microbial carbon and assimilation rate in the model diagram. In the model this rate is assumed to approach an asymptote at high levels of active living carbon and decline exponentially with low levels. The level of active living carbon is the cumulative difference between assimilation by microbes and the sum of microbial respiration and death. Microbial respiration is relative to active living carbon bu t also is affected by the proport ion of different carbon compounds, which determines the amount of " w o r k " the microbe communi ty must perform to degrade them. For instance, lignins and other aromatic compounds require a greater investment of energy in the formation of enzymes for breakdown than is required by cellulose. Cellulose, on the other hand, requires more energy invested in enzymes for breakdown than is required by monosaccharides. The presence of available amino acids decreases the energy expenditure by

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microbes because less energy is needed for the synthesis of protein by the microbes. Respiration is the loss of energy and carbon from the system in the evolution of carbon dioxide as ATP is formed and used.

Because of differences in energy required for the breakdown of the different compounds, the size of the active living carbon compar tment is smaller when the substrate is made primarily of lignin and other insoluble aromatic compounds than when it is composed primarily of sugars and cellulose. When the size of the active living carbon compar tment is smaller, the assimilation rate is reduced, because the size of the microbial population and the quanti ty of active enzymes produced by microbes directly affect assimilation rate.

Both assimilation and respiration rates are affected by temperature (Broadbent, 1960; Knipling et al., 1970; Volk, 1973) and the availability of water and oxygen (Neller, 1944; Waksman and Purvis, 1932). A Q10 relationship exists; the standard rate is increased 1.5 times by a 10°C temperature rise (Volk, 1973). Water and air volume are complementary; increases in percent water volume decrease available oxygen so that, although activity is stim- ulated by increased water volume up to a point, beyond that point oxygen is excluded to the extent that microbial activity is suppressed. Sudden decreases in available water or oxygen may cause dramatic decreases in assimilation and respiration rates.

On a sustained basis some percentage of microbial material is continuously returned to the nonliving carbon compar tment through cell senescence, autol- ysis, fragmentation during predation, cell exudation, and enzyme denaturiza- tion. This recycling process, which is indicated in the model diagram, is assumed to be proportional to the active living carbon in the soil. The pro- portions of the different types of carbon compounds (i.e., sugars, amines, cellulose, soluble aromatics, insoluble aromatics, organic acids, and related compounds) in the recycled material has not to our knowledge been quanti- fied, but estimates can be made based on the differences in the composit ion of fresh organic material and well-decomposed Histosols.

Nitrogen transformations that occur concurrently with carbon t ransforma- tion in organic soils also are considered in the model. Included are a compartment for available nitrogen (RNH2, NH3, NH4, NO2, NO3), living nitrogen in microbes, and nonliving nitrogen in carbon compounds. Pathways are included for nitrogen fixation, nitrogen uptake, the release of nitrites and nitrates by microbes, and denitrification. Nitrogen fixation is made proportional to the concentration of easily available carbon energy sources such as sugars, starches, and compounds hydrolyzed by microbial activity, because nitrogen-fixing bacteria appear to utilize these forms rather than the less easily degraded forms (suggested by data in Ausmus and Witkamp, 1974). Deni- trification is made inversely proportional to the oxygen content (air volume) of the soil and is dependent on the concentration of nitrate and nitrite.

Release of nitrite and nitrate is considered to be proportional to the evolution of carbon dioxide. Nitrogen uptake by microbes is made a function of the increase in carbon per unit t ime in the microbial compartment . Nitrogen

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can be limiting to the rate of assimilation of carbon by the microbes. This relationship is expressed by a Michaelis-Menten expression on the assimilation pathway (in addition to that described for carbon). A model by Parnas (1975) that examined microbial decomposi t ion as a function of available nitrogen as well as available carbon also utilized the Michaelis-Menten expression. In the Parnas (1975) model, amino acids were used as both a carbon source and a nitrogen source for the microbes unless other forms of available nitrogen were present.

The rate equation for assimilation of carbon by microbes is composed of nine expressions describing the rate as a function of:

(a) concentrat ion of nonliving carbon

V W(it)/(KMc+ W(it) 1 (1) V T ( t ) = MAX L(t) S L ( t ) / '

where t is t ime in days, i is type of carbon compound, VMAX is maximum velocity of assimilation reaction, W(it) is weight per gram mineral soil of each nonliving carbon compound, and KMC is Michaelis-Menten rate constant for effect of carbon substrate concentration on velocity;

(b) concentrat ion of available nitrogen

NT(t) KMN + (2) NEF(t) - SL(t ) Sb(t)] ,

where NT< t ) is total available nitrogen, and KMN is Michaelis-Menten rate constant for effect of nitrogen concentrat ion on velocity;

(c) concentration of carbon compound.~ known to be inhibiting to microbial activity

(3) I N H ( t ) = 1 - - exp --a~ 1 -- b(o W(~t)] '

where al is a constant estimating the total negative exponential effect of cer- tain carbon compounds, b(i) is constants estimating inhibitory effect of each carbon compound (zero for some compounds);

(d) concentration of active living carbon

T L C ( t ) = (see Eq. (15)) ;

(e) temperature effect

TEF(t) = 1 + 0.1 (Qlo -- 1)(Tc¢t) -- TsT) , (4)

where Qt0 is factor by which reactions of microbes are increased by a 10°C increase above standard temperature, Tc(t) is average daily soil temperature (at 10 cm below surface), and TST is standard temperature (25°C);

(f) oxygen effect

P o R - Vw(t) (5) Ox(t) = az + KM 0 + POR -- Vw(t) '

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WA(t)

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and; (i) total amount of soil (per gram mineral soil)

SL(t) = TORG(t) + TMIN ,

where a 3 is fraction of maximum assimilation rate attributable to anaerobic activity, POR is porosity of the soil (percent volume occupied by water) and KMO is Michaelis-Menten rate constant for effect of soil air on assimilation velocity;

(g) water effect

Vw(t) - VH

= KMW + Yw(t) - - VH ' (6)

KMW is Michaelis-Menten rate constant for effect of soil air on assimi- velocity and VH is hydroscopic water as fraction total volume; percent total nonliving carbon represented by each carbon compound

W(it) = W(it) (7)

(8) where TORG(t) is total organic soil per gram naturally occurring mineral soil (includes organic amendment, A c(t)), and TMIN is total mineral soil per gram naturally occurring mineral soil (includes inorganic amendment, AMEN). The equation is prevented from achieving unrealistically high values by a negative- density-dependent (crowding) function:

1 -- a2TLc(t ) , (9)

where a2 is crowding coefficient and TLc(t) is the concentration of active living carbon (see Eq. (15)).

Loss of hydrolyzed material through leaching is proportional to the amount of material solubilized and the percolation rate. This loss of a fraction of the material solubilized through bacterial action is included in the equation by multiplying by:

1 -- k(i)PERK(t) (I0)

where k(i ) is concentration of solubilized material in the percolating water and PERK(t) is the percolation rate in centimeters soil depth per day.

The equation for assimilation rates, which encorporates all the above factors, is:

R(it) = (VT(t)NEF(t)INH(t)TLc(t)TEF(t)Ox(t) WA(t) Yp(it)SL(t))

(I - - a2TLc(t))(l - - k(i)PERK(t) )LIM(t) , (II)

where LIM (t) is a factor preventing the equation from going below zero. The balance between rate of assimilation and rate of respiration determines

whether active living carbon grows, declines, or remains constant. The model's equation for microbial respiration is basically the equation for exponen-

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tial decay of the active living carbon compartment . This basic rate, however, is modified by the percent composi t ion of carbon compounds in the organic substrate serving as the energy source. Increase in respiration due to differences in substrate composit ion are assumed to be linearly related to the percent composi t ion of cellulose and insoluble and soluble aromatic compounds, with a different coefficient weighting the effect of each form. Decreases in the basic respiration rate are assumed to be linearly proportional to the percent composit ion of protein and amino acids of the substrate. Respiration rate is affected by temperature, water, and air (oxygen) in the same way that assimilation rate is affected. The equation for respiration in the model is as follows:

W(it) (12) RESP(t) =k3TLc(t)TEF(t)Ox(t)WA(t) C(i) W(it )

where k3 is the basic rate constant of respiration and c(/) is a positive or negative coefficient weighting the effect of percent composition of each carbon compound in the substrate on microbial respiration rate.

The contribution to carbon compounds of different types by routine death and excretion of metabolites by microbes is represented by:

DRs(t) = F(i)(klTLc(t )) (13)

where F(i) is fraction of each carbon compound in material recycled from microbes and k I is rate constant of microbial death and enzyme denaturiza- tion.

The six nonliving carbon compound compartments and the one active living carbon compartment can thus be described by differential equations as follows:

dW(it) R(it) (14) dt - L(it) + DRs(i t) -- 1 - - k(i)PERK(t) '

d TLc( t ) dt - R ( i t ) - REsP(t)--DRs(t) , (15)

where L(it) is the contribution of fresh nonliving carbon material by the death of living plant parts.

Nitrogen transformations within the system and losses of nitrogen from the system occur by the following processes:

(a) assimilation of nitrogen in proteins and amino acids of the natural carbon substrate by microbes

N ( p t ) = R N c p R ( p t ) , (16)

where RNC P is nitrogen/carbon ratio in protein and R(pt) is assimilation rate for proteins and amino acids;

(b) assimilation of nitrogen in proteins and amino acids in organic amend-

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ments by microbes

N¢oAt~ = NcoAR( OAt~, (17)

where NCOA is nitrogen/carbon ratio in organic amendment and R(oAt ~ is assimilation rate for organic amendment;

(c) fixation of nitrogen by microbes

W~st~ (18) NF(t) = a s R ( i t ) -I-a6SL(t ) ,

where a5 is rate constant for nitrogen fixation fueled by hydrolyzed carbon compounds and a6 is rate constant for nitrogen fixation fueled by sugars and starches;

(d) release of nitrogen in respiration of microbes

NREs(t~ = aTREsI,(t } , (19)

where a7 is rate constant of nitrogen released in microbial respiration; (e) incorporation of nitrogen into living microbes

NLM(t) = Nc(TLc( t~ - - TLCCt--1}) , (20)

where Nc is nitrogen/carbon ratio in microbes; (f) loss of nitrogen through denitrification

NDN(t) = (a9 - -a loOx( t~ ) (NF( t~ + NaEs(t~) , (21)

where a9 is rate constant of nitrogen loss by denitrification; and (g) loss of nitrogen through leaching, computed by the factor

1 -- a~PERK(t) , (22)

where as is the proport ion of total nitrogen carried in percolating water. The differential equation that encorporates the above expressions to

describe the compar tment of total available nitrogen is:

dNw(t ) d t - ( N ( p t ) +N(oAt) +NF(t) +NREs(t) --NLM(t) --NDN(t))

(1 -- asPERK(t ; ) • (23)

Phys ica l s u b m o d e l

In the quantification of the model (Fig. 1) 1 g mineral soil is the reference base, and initial and instantaneous values for all material quantities are relative to this unit.

Fig. 2. shows how the basic unit in Fig. 1 is used to estimate total loss of soil per unit area over time. The model assumes that only: the soil layer above the water table is subject to appreciable biological oxidation. Total gravimet-

279

ric losses are calculated for a 1 cm X 1 cm column above the water table. Gravimetric losses are converted to volumetric losses so that cumulative loss of soil over time can be described in centimeters.

The biological submodel in Fig. 1 is interfaced with the physical submodel in Fig. 2 by means of the following equations:

(a) grams naturally occurring soil per gram mineral soil

W(it) (24) 0RG(t) -- PCAR '

where W<it) is weight in grams per gram mineral soil of each of the nonliving carbon compounds and PCAR is fraction carbon in naturally occurring organic soil;

(b) grams total organic soil per gram mineral soil

TORG(t) = ORG( t ) "{- AC(t)CARF, (25)

where Ac(t) is grams carbon in organic amendment per gram naturally occurring mineral soil and CARF is reciprocal of fraction carbon in organic amendment;

(c) grams total soil per gram mineral soil

SL(t) = (see Eq. (8));

(d) fraction total mineral soil

TMIN M I N F S ( t ) -- SL( t ) ; (26)

(e) fraction naturally occurring mineral soil

MIN (27) MNFS( t ) -- SL( t ) ,

where MIN is grams naturally occurring mineral soil (defined as 1). The bulk density (g/cc) of the soil above the water table is a variable calcu-

lated by the equation:

BLKDN(t ) ---- MINBDMINFS( t )ORGBD(1 - - MINFS(t ) ) , (28)

where MINBD is bulk density of the mineral fraction and ORGBD is bulk density of the organic fraction.

The following equation calculates the instantaneous weight (in g) of soil in a 1 cm X 1 cm column above the water table:

SWT(t ) = WTA(t)BLKDN(t ) , (29)

where WTA(t ) is depth to water table in centimeters (see Eq. (34)). The depth loss (in cm) of organic soft from a 1 cm X 1 cm column above

the water table is calculated by determining the total number of grams of naturally occurring mineral soil in the soil column and multiplying this value

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by the cumulative loss of organic material per gram naturally occurring mineral soft. The following equations are used:

WMIN(t) = SWT(t)MNFs(t), (30)

W M I N ( t ) ( O G G - - ORG(t) ) (31) DEPLS(t ) -- BLKDN(t) '

where OG6 is initial weight in grams of organic component of soil per gram mineral soil and DEPLS(t ) is the total soil loss (in cm) incurred through microbial respiration and leaching.

The depth soil loss (in cm) due to microbial respiration alone is calculated by the integral equation:

1 WMIN(t)REsP(t) dt (32) CuLs(t) -- PCAR BLKDN(t)

An important controlling variable in the model is water table depth (in cm), WTA(t), which determines total quanti ty of organic soil subject to biological oxidation and also determines the percent volume of soil moisture. Water table depth is partially a function of rainfall (R AI N(t)) and evapotranspiration (EvAP(t)), but is also under the influence of logic functions representing drainage (PERK(t)) and irrigation (INF(t)), which a t tempt to maintain the water table at a constant (or seasonally varying) control depth (WTc or WTc(t)). Water values were divided by soil porosity minus fraction water volume to convert centimeters of water into centimeters of change in the water table.

The equation for the drainage effect is:

D2Sw2(t) (33) PERK(t) -- POR -- Vw(t) '

where D2 is pumping capacity (in cm water depth) of primary canals, Sw2 is 1 when WTA(t ) WTC and zero when WTACt) WTC, POR is porosity of the soil as a fraction of total volume (same as VWSAT), and Vw(t) is a function of WTA(t) determined by a table function based on a curve from Weaver and Speir (1960). WTA(t) is the water table, in centimeters below surface (see Eq. (35)).

The equation for the irrigation effect is:

D2Sws(t) (34) INF(t) -- POR - - Vw(t)

where Sw3 is 1 when WTA (t) WTC and zero when WTA(t) WTC. The water table equation is:

dWTA(t) = --RAIN(t) + EVAP(t) + PERK(t) --/NF(t) , (35) dt

where RAIN(t) is a table of daffy rainfall (in cm) and EvAPCt) is a table of pan

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evaporation, multiplied by 0.75 (Chow, 1964) to approximate evapotranspiration from soil.

The fraction of total volume as soil water is determined by a table function relating fraction soil water volume ( Vw(t ) ) to water table depth ( WTA ( t ) )- An average curve from a set of curves from Weaver and Speir (1960) is the basis of the table function. Fraction soil air volume (VA(t)) is porosity (PoR) minus soil water (Vw(t)). These equations are:

(a) fraction soil water volume

Y w ( t ) = f W w A ( t ) ; (36)

(b) fraction soil air volume

VA(t) = POR -- Vw(t) • (37)

The effect of fraction soil water and fraction soil air on the rate of breakdown of carbon compounds by soil microbes (assimilation and respiration rates) is given by the Michaelis-Menten functions in Eqs. (5) and (6).

R E S U L T S - - S I M U L A T I O N S

Measured daily values from January 1 through December 31, 1975, at Belle Glade (Florida Agricultural Experiment Station, Belle Glade, personal communicat ion) were used for rainfall (RAIN(t) ), pan evaporation (EvAP (t)), and average soil temperature (Tc(t)) in all executions of the model. The ranges of daily values for these parameters were 0--5.38 cm, 0.127--0.813 cm, and 18.3--30.3 ° C, respectively. The At used in the simulations was 0.0625 day. Other At's were tested for their effect on model performance.

Table I gives values for initial conditions and constants that were used in executions of the model. Tables II and III give some assumed values representing different conditions that were used in different executions. Table II shows assumed initial-condition values for fractions composit ion of carbon compounds (Ve(it)) in Histosol and another set of assumed initial condition values to approximate the fraction composit ion of carbon compounds in relatively fresh soil organic material. Executions were made with each of the sets of initial conditions to simulate the rate of decomposi t ion of the two different types of material. A different coefficient for the crowding effect (a2) was used for the simulations of the decomposi t ion of the two different materials (see Table I). Table III gives two different sets of proport ions of the different types of carbon compounds in carbon material recycled from microbes (F(i)). The purpose of executing the model using two different sets of these proport ions was to test the sensitivity of the model to these parameters, because good data was not available on them, and it was necessary to know how important their values might be to overall model performance in. order to evaluate the need for obtaining sounder data through future research.

Figs. 3 through 10 present some simulations from the model. Fig. 3 follows the decline in nonliving carbon and the seasonal c"cillation in the level of

2 8 2

T A B L E I

C o n s t a n t s a n d in i t ia l c o n d i t i o n s

C o n s t a n t s CARF = 0 .0 Q10 = 1.5 a t = 5 .0 D 1 = 3 6 4 RNC P = 0 . 2 3 3 3 a 2 = 1 X 103 D 2 = 1 . 9 0 5 TMI N = 1 .0 a 3 = 1 × 10 -3 F( i ) see T a b l e I I I TST = 25 a s = 0 .0 k I = 2 .0 VH = 0 . 1 5 a 6 = 0 .0 k 3 = 1 . 5 9 5 VMAX = 12 a 7 = 0 .0 k ( i ) VWSAT = 0 . 8 9 a s = 0 .0 k (A ) = 0 .0 WT C see T a b l e IV a 9 = 0 .0 k(AC) = 0 .0 a l 0 = 0 .0 k ( c ) = 0 .0 I n i t i a l c o n d i t i o n s AMEN = 0 .0 k(H) = 0 .01 A c = 0 .0 b(i) k (L) = 0 .0 CMI.S = 0.0

b(a) = 0 . 0 k(OA) = 0 . 0 1 N T = 0 . 4 7 7 7 b(AC3 = 0 .0 k(p) = 1 X 10 -3 OP, G = 1 1 . 9 1 b(c ) = 0 .0 k ( ~ I ) = 0 .01 T I C = 1 . 2 5 3 X 10 -4 b(L) = 0 . 3 7 8 5 KMC ffi I X 10 -5 Vp(A) -- 0 . 0 b(oA) = 0 .9 KMN = 1 X 10 -3 VP(AC) = 0 .0 b(p) = 0 .0 KMO = 1 . 7 5 × 10 -3 VP(O see T a b l e II b(sI-D = 0.0 KMW = 5 × 10 -3 VP(L) see Table II

c(i) MIN = 1.0 VP(OA) see Table II C(A) = 0 .0 MINBD = 1 .3 W A = 0 .0 C(AO = 0 .0 N C = 0 . 2 9 1 7 WAC = 0 .0 C(C) = 3 .0 NCOA = 0 .5 WC see T a b l e II c(L) ffi 5 .0 Oc_~ = 1 1 . 9 1 WL see T a b l e II c(OA) ffi 5 .0 O R G a n = 0 . 0 8 9 8 WOA see T a b l e II C(p) ffi 0 . 5 P C AR = 0 . 5 9 8 3 Wp see T a b l e II c(~-l) = 1 .0 P O R = 0 . 8 9 Wsz-I see T a b l e II

a c t i v e l i v i n g c a r b o n i n H i s t o s o l s o v e r a 1 - y e a r p e r i o d . F i g . 4 f o l l o w s t h e r e s p i r a -

t i o n p e r u n i t a c t i v e l i v i n g c a r b o n o v e r t i m e . R e s p i r a t i o n i s a f f e c t e d b y t h e r e l -

a t i v e p r o p o r t i o n s o f t h e d i f f e r e n t c a r b o n c o m p o u n d s ( i . e . , s u g a r s a n d s t a r c h e s ,

T A B L E II

In i t i a l c o n d i t i o n s o f c a r b o n c o m p o u n d c o m p o s i t i o n fo r M o n t v e r d e m u c k a n d f r e sh o r g a n i c m a t e r i a l

Carbon compound M o n t v e r d e m u c k Fresh o r g a n i c

g/g % g % m i n e r a l f r a c t i o n f r a c t i o n

E a s i l y h y d r o l y z a b l e p o l y s a c c h a r i d e s 0 . 2 8 5 1 D i f f i c u l t y h y d r o l y z a b l e p o l y s a c c h a r i d e s 0 . 3 5 6 3 A m i n o a c i d s 0 . 3 5 6 3 I n s o l u b l e a r o m a t i c s 5 . 9 8 6 S o l u b l e a r o m a t i c s 0 . 1 4 2 5

0 . 0 4 0 . 5 0 7 1 0 . 0 8 0 . 0 5 4 . 6 3 2 1 0 . 6 5 0 . 0 5 0 . 3 5 6 3 0 . 0 5 0 . 8 4 1 . 4 2 5 2 0 . 2 0 0 . 0 2 0 . 1 4 2 5 0 . 0 2

TABLE III

Test parameters of carbon compound fractions recycled by microbes

283

Carbon compound Test Test 1 2

Easily hydrolyzable polysaccharides (SH) 0.10 0.15 Difficulty hydrolyzable polysaccharides (C) 0.10 0.10 Amino acids (P) 0.20 0.15 Insoluble aromatics (L) 0.50 0.45 Soluble aromatics (O) 0.10 0.15

amino acids, lignins, cellulose) in the Histosol substrate, which also are shown in Fig. 4. In each graph are two sets of curves, each curve a simulation produced by executions of the model using the two different sets of fractions of recycled carbon given in Table III.

Figs. 5, 6a, and 6b provide simulations for the breakdown of relatively fresh soil organic material. Fig. 5 shows a decline in nonliving carbon, with a complete loss of carbon in about 195 days. There is an initial increase in active living carbon over the same initial value used in the organic soils, fol- lowed by a leveling until the point when the nonliving carbon is entirely gone, at which time the simulation ends. Figs. 6a and 6b show respiration

7.2

. J

<~ 7.0

Z

6.B

-~, 6.6

Z

6 . 4 I 0 50

• non-living

I I I I I I

I00 150 200 250 :500 350

TIME (days)

4

Z

_J

Z

2 g

~J <

Fig. 3. Nonliving and active living carbon in a drained Histosol (Montverde) with water table controlled at 60 cm (see Table II for assumed initial conditions for fractions of carbon compounds).

284

Z 7.24 ~ 1.0

0 ~ @ , ' rn [E

(.9 (.9 Z 7.25 0.875 > lignin

-~ ;~-- . . . . . . . . . . . . ~ . . . . . . . . . . . ~-I z m > o F- ,;" m

~r0h0n q 7.22 0.75 o o

o z i

._1

z 7.21 0.625 0 o z I-- LJ- < 0 rr

Z o W -- C~ P-

7.20 I , , _ , , I i 0.5 o n--

ce l lu l0se- l ike ®~®t 0.0625" soluble 0 romat ics . . . . . . . . . . . . 5 ]

. . . . . p_ m_ i_n_ 9_ £¢_ _Ld s_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ° t ~ l 0.06£5 suga rs ®j l t I 1 I I l

0 50 I00 150 200 250 500 550 TIME (d0ys)

Fig. 4. Resp i ra t ion (CO2-C e v o l u t i o n / d a y ) per g a c t i v e l i v i n g c a r b o n , a n d t h e con t ro l l i ng factors , f r ac t ions c o m p o s i t i o n of energy source: easily h y d r o l y z a b l e po lysacchar ides (sugars), d i f f icu l ty h y d r o l y z e d po lysacchar ides (cellulose-like), amino acids, so luble aromatics , and insoluble a roma t i c s (l ignins). Note : T h e circled (1) refers to the curves s imula ted f rom the mode l using the n u m b e r 1 c o n d i t i o n s f rom Table I I I f o r f r a c t i o n s c o m p o s i t i o n o f c a r b o n c o m p o u n d s recycled f rom microorganisms . The circled (2) refers to the curves s imula ted using the n u m b e r 2 condi- t ions f rom Table III.

per unit of active living carbon for the fresh soil organic condition. Also shown is the change over time in the fractions of different nonliving carbon compounds. The difference in relative composit ion of the recycled carbon material appeared to have a greater effect on decomposit ion of fresh organic materials than on Histosols because of the greater turnover rate of the fresh material.

Fig. 7 shows the distance of the water table from ground surface every 5th day over the 1-year period of the simulation with the control level at 60 cm. At the rates of removal and irrigation assumed in the model (1 .905 cm/day, which is the pumping capacity of the primary canals), there is little fluctua- tion and an almost steady level is maintained. Fig. 8 shows two important

285

d

03

_J <[ or" UJ Z Z 0 m Or" <~

8 l

6 ~non-living I orbo°

2

0 I [ i 50 I00 150

TIME (days)

'_o X

.J

~4 Z

g2 E~

active living carbon

~ ,

1

I I I 50 I00 150

TIME (days)

Fig. 5. Nonl iv ing carbon and active living carbon in relatively fresh organic material' in soil (see Table II for assumed initial condi t ions for fractions o f carbon compounds ) . Note : The circled (1) refers to the curves s imulated from the m o d e l using the number 1 condi t ions from Table III for fractions compos i t ion of carbon c o m p o u n d s recycled from microorganisms. The circled (2) refers to the curves s imulated using the number 2 condi- t ions from Table III.

functions influencing the rate of assimilation and respiration by microbes, Ox, the soil air effect, and WA, the soil water effect. Fig. 9 shows another important function controlling biological rates, TEF, the soil temperature effect. The variation in the temperature effect is shown to be much greater than the variation in either soil air or water effects. Fig. 10 shows the fraction of soft volume as air and fraction of soil volume as water at the three different control water levels.

Fig. 11 fol lows the change in grams nonliving carbon per gram mineral soil over a 1-year period at three different control water levels.

Table IV shows the simulated loss of organic soil (in cm of depth) over a 1-year period from the total soil co lumn above the water table at the three different control levels. The simulations indicate that raising the water table slows subsidence in two ways: first by reducing the loss of carbon per unit soil (reference base is one gram mineral soil), and second by reducing the number of units exposed to biological action. With the estimated Michaelis- Menten coefficients (KMo and KMw ) used in the executions there is only a slight decrease in subsidence rate per unit soil; the major saving results from the fact that fewer units of soil are exposed when the water levels axe higher. The rate of loss is considerably reduced due to this latter effect. These sinm-

286

5.4

z o m cr 5.5 < (..) £.9 z

d

LIJ > 5.2 I- <

7 0 rn ~ 5.1

5.0

1.0

~ l 0.75

_ cel lul0se i l

,,Jrespirati0n 10.25

I I I I 0 . 0

50 I00 150 TIME (days)

z o

(.9 _z > d

z o z LL 0 Z 12) I---

I J-

q

0

FRACTION OF NON-LIVING CARBON 0.5 0.25 co

z ~ z 0.25 lignin .. '~ (-9

12' •

soluble 0~0~0%~__.~___.__.~_~

O I I i 50 I00 150

TIME [days)

co 0,25 /

0.125 p I"~ "

sugars . . . . . . . . . . • f . . . . . . . . j . . s

(Y') _ _ _ r - - - (T~

OI i i l

50 I00 150 TIME (days)

I - - <

o IT O.125 <

UJ d G3 E3 . J o

o co

0.25

(/)

(D <~

0.125 o z

<

Figs. 6a and 6b. Respirat ion (CO2-C evolu t ion /day) per g active living carbon, and the control l ing factors, fract ions compos i t ion o f energy source: easily hydrolyzable polysaccharides (sugars), d i f f icul ty hydro lyzed polysaccharides (cellulose-like), amino acids, soluble aromatics, and insoluble aromatics (lignins), in fresh organic material in soil (see Table II for assumed initial condi t ions for fract ions carbon compounds) . N o t e : The circled (1) refers to the curves simulated f rom the model using the number 1 condi t ions f rom Table III for fractions compos i t ion o f carbon compounds recycled f rom microorganisms. The circled (2) refers to the curves s imulated using the number 2 condi- t ions f rom Table III. ?

O.72

g o.52

~5

~" 0 . 4 2 5 I I I I I I I O O tOO 150 200 250 300 350

TIME (doys) Fig. 7. The water table control led at 60 cm f rom ground surface.

I.O l 50cm water table ! ~_ water (WA) ~

0 99 / [ (o×)

0 . 9 8 ~

0.97 i I ~ J , i I i i Ld u_ I.O EL- | 60cm water table

uJ t water (WA) 0 .99 - - z oxygen (Ox)

o 098[ c~ 0 9 7 ! t L L I I I Z " < i.O n.- I 90cm water table

[ L~ water (WA) I- 0 .99 ~ ,,---v < oxygen (Ox)

0.98 [

0 . 9 7 " I I i i I L 1 50 I00 150 200 250 500 550

TIME (days) Fig. 8. S imula t ions of t he m o d e l showing the e f fec ts of soil wa te r (WA) and o x y g e n ( O x ) on mic roo rgan i sms ass imi la t ion and resp i ra t ion ra tes at 30, 60, and 90 cm wate r tab le levels. Note: The wate r e f fec t is a Michae l i s -Menten express ion using f r ac t ion vo lume as soil wa te r and a Kra o f 0 .005 and assuming no act iv i ty at 0 .15 vo lume as water . The o x y g e n ef fec t is a Michae l i s -Menten express ion using f r ac t ion vo lume as soil air and a Km of 0 .00175 .

L4 I

u hl Ii Ii UJ

bJ

0.8

0,6 i i I i L VI~ 50 I00 t50 200 250 300 350

TIME (days) Fig. 9. F u n c t i o n s of the mode l showing t he e f fec ts of t e m p e r a t u r e (TEF), o n ass imi la t ion and resp i ra t ion rates . Note: T e m p e r a t u r e e f fec t is based o n a Q10 of 1.5.

2 8 7

288

I.O

w

_J 0 >

0.8 .J

0

LL 0

Z O 0.61

F- ~.}

OE LL

r~ W

0.4

_J 5 u~

0.2

s0il w a t e r ^ s, 60cm

......... sS~] -waTe'r" .... 90 c m

- soi l mr 90cm -

soil air 6 0 cm

. . . . . . . . . . . . . . . . . . . . . . . . . . . V - , , - V - - . ~ . V - . , " . . . . . . .%..

soi l air 30cm

I I I I I I • 0 50 I00 150 200 250 300 350

TIME (doys)

0.4

0.3

0.2

O.I

L~

D

0 >

<[ F- 0

b_ 0

Z 0

CD <[ [K t~

0

Fig. 10. Soi l air and soil water as fract ions tota l soil vo lume at three d i f ferent contro l water levels: 30, 60 , and 9 0 cm.

lation results should be considered very preliminary, since many of the values used for initial values and coefficients are rough approximations. Better estimates for KMO and KMW might increase or decrease the simulated effect

7 .2

_---J 7 .0 0 rE)

._1

rr LLI z

: ~ 6 8

Z 0 m

r.)

~ 6.6

6 . 4 , i , l I , ,

5 0 I 0 0 150 2 0 0 2,50 3 0 0 3 5 0

T I M E (d0ys)

Fig. 11. Non- l iv ing carbon over 1-year period at 30, 60, and 90 cm water contro l levels .

TABLE IV

Effect of water table level on subsidence level of Montverde muck

289

Water table level Soil water volume Depth loss due Total (cm below surface) (fraction of total volume) to microbial depth

respiration loss (era/year) (cm/year)

30 0.837--0.877 1.75 2.92 60 0.737--0.752 3.59 5.75 90 0.699--0.707 5.43 8.78

of raising the water table or the loss of carbon per unit of soil above the water table, but would not change the simulated effect of decreasing the number of soil units exposed to biological action by means of raising the water table.

If executed over a long period of time the model will become unrealistic when there is no longer enough soil for the water level to actually be at the stated depth.

DISCUSSION

Despite the absence of firm data for many initial conditions and coefficients of the model, enough reliable information was available for two results of these early executions of the model to be stated with confidence:

(1) temperature is the seasonally varying parameter that has the greatest effect on soil subsidence rate;

(2) a substantial reduction in soil subsidence rate results from reducing the number of units of soil above the water table by raising the control water level.

Although it would be useful to have a bet ter estimate of the relative composition of carbon material recycled from microbes, for which two different sets of estimates used in the model were given in Table III, the simulations indicate that the variation in subsidence rate of Histosols resulting from variation in relative composit ion of this material may not be very large on the short term and possibly is unimportant over the long term. Results, however, are dependent on the coefficients (c¢i)) weighting the effect of percent composition of each carbon compound on microbial respiration rate, for which the values used in the model (see Table I) are gross estimates.

Following is a summary of the data needs suggested by the model and background workers. These are areas where research efforts should be directed.

Research needs

(1) Transpiration rates of sugarcane, pasture, and truck crops relative to pan evaporation (assuming an unlimited supply of water through irrigation),

290

relative to solar radiation, and relative to production. (2) Changes in bulk density relative to degree of decomposition. (3) Change in equilibrium water volume of soil relative to degree of

decomposition. (4) Development of quantitative measures of degree of decomposition,

such as percent humus in organic fraction, C/N ratios, change in percent mineral fraction, etc.

(5) Qualitative and quantitative characterization of microbial constituents of decomposing Everglades Histosols

(a) absolute active living biomass of major groups on a seasonal basis, (b) dominant species of each major group, {c) chemical makeup of each major group in terms of lipids, amino

acids, glucosamines, etc., (d) rate of secretion and excretion of extracellular metabolites relative

to biomass and carbon dioxide evolution, and percent composition in terms of lipids, amino acids, etc. in secretions. (6) Percent composition of Histosols in terms of energy sources for mi-

crobes such as lipids, amino acids, sugars and starches (readily hydrolyzable polysaccharides), cellulose and hemicellulose {less readily hydrolyzable polysaccharides), amino sugars, insoluble aromatic compounds, including lignin, soluble aromatic compounds, including condensed tannins, lactic acid, and other materials produced by plants or soil microbes.

(7) Relative energy cost to microbes of breaking down different energy sources (irregardless of the taxonomic groups involved).

(8) Rate of production of nitrates and nitrites relative to rate of evolution of carbon dioxide from drained Histosols. Rate of nitrogen fixation relative to available sugars in Histosols. Rate of denitrification relative to available oxygen {percent soil air) in drained Histosols.

Future research in the dynamics of soil subsidence should focus on the above questions. A cursory review of the literature suggests that much more is known about the microbial dynamics of forest soils (Sollins et al., 1973; Reichle et al., 1973; Ausmus and Witkamp, 1974) and grassland soils (Macfadyen, 1963) than is known about drained Histosols. More is known about the soils of the Everglades in their natural state (Given and Dickinson, 1975) than is known about these soils in the drained situation. A unique op- portunity for research is thus presented to the microbiologist and soil chem- ist who faces these issues.

ACKNOWLEDGMENTS

This modeling study was financed by the Department of Soil Sciences, Institute of Food and Agricultural Science, University of Florida, Gainesville. Encouragement and information was provided to the authors by J. Davidson and S. Rao of the Soil Sciences Department at Gainesville, by D. Myhre, G. Snyder, W. Mishoe, and R. Tare of the University of Florida Agricultural Ex-

291

periment Station at Belle Glade, and by S. Gerchakov at the University of Miami Microbiology Department in Miami. The authors wish to thank every- one in the Soil Science Department and in other departments at the Univer- sity of Florida for reviewing the manuscript and providing helpful suggestions prior to submission for publication.

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Systems model of carbon transformations in soil subsidence