Soil Science Society of America Journal 63:1101-1105 (1999)
© 1999 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
The Effect of Hysteresis on Microbial Activity in Computer Simulation Models
Andrew P. Whitmorea and
Marius Heinenb
a Silsoe Research Institute, Wrest Park, Silsoe, Bedfordshire, MK45 4HS, UK
b DLO Research Institute for Agrobiology and Soil Fertility (AB-DLO), P.O. Box 14, NL-6700 AA Wageningen, The Netherlands
andy.whitmore{at}bbsrc.ac.uk
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ABSTRACT
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Microbial activity in soils depends on the status of the soil water, which is expressed by pressure head (h) or water content (
). There is no unique relationship between and h because moisture relations exhibit hysteresis. For convenience microbial activity has usually been related to the main drying curve but in general this will lead to bias in computer models that aim to simulate microbial activity. This article aims to evaluate the magnitude of the bias resulting from the use of computer simulation models of mineralization coupled to a model that follows the hysteresis of water relations in soil. Simulations of mineralization were found to accumulate a bias of more than 15% of the mean annual mineralization by harvest. This bias was found to be most serious where soil is continually subject to severe wetting and drying cycles such as can be found in irrigated and tropical agriculture.
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INTRODUCTION
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THE RELATIONSHIP between the volumetric water content (, L3L-3) of a soil and the pressure head at which it is held (h, L) differs depending upon whether the soil is wetting or drying; this path dependence is known as hysteresis. The (h) relationship is characterized by a main drying curve and a main wetting curve but the actual state of a porous medium may lie within or on these envelopes. During wetting and drying cycles there are an infinitely large number of pathways that can be followed, known as scanning curves (see e.g., Topp, 1969). Fortunately, empirical and mechanistic models exist that can describe scanning curves. In most experimental studies the main drying curve only is determined, but this curve always overestimates for any given value of h. For convenience, microbial activity is measured only in relation to this same drying curve; Stanford and Epstein (1974) and Stott et al. (1986) showed how nitrogen mineralization changes in relation to h. Groffman and Tiedje (1988) also observed the effect of hysteresis in moisture relations on denitrification. Computer modelers have made extensive use of the relationships between mineralization and either or h to simulate the change in microbial activity in soil with drying. Like the experiments, the models fail to take into account the effect of hysteresis on the moisture relations in soil.
This note aims to evaluate the magnitude of the bias resulting from the use of computer simulation models that calculate mineralization without including the effects of hysteresis. Clearly there are no soils that do not exhibit hysteresis yet their existence is automatically assumed by models that relate microbial activity to laboratory measurements made on the main drying curve only. Predictions of mineralization may be in error from day to day depending on whether the soil is wetting or drying. Here we demonstrate how these errors may be estimated and assess their likely magnitude.
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Methods
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Climate and Soils Data Used in the Models
Real, daily meteorological data close to the 40-yr mean for Wageningen in the Netherlands, longitude 5.67°E, latitude 51.97°N, was used for a series of simulations under temperate conditions (see Whitmore and Schröder, 1996, for a description of how the weather data was derived) and weather from Sanpatong, Thailand, longitude 98.95°E and latitude 18.75°N for a series under tropical conditions. Three rainfall regimes were tried under temperate conditions: (i) natural (unaltered), (ii) allowing 75-mm rain to fall each month in the first 5 d and none for the remainder of that month, (iii) spreading each month's rainfall uniformly over every day of that month. Daily (40-yr) mean values of evapotranspiration (cropped) or evaporation (bare soil) were used with the uniform and alternating rainfall regimes. For the temperate region we used a loam topsoil above a sand subsoil [for (h) relations see the `Staringreeks', Wösten et al., 1994: 1 m `zavelb7' on top of 1 m `zand01']. For the tropical region we used the physical properties of a Korat series profile from northeastern Thailand (Vichai Sribuule and Vidhaya Trifo-goes, 1996). Simulations were carried out for a total of two consecutive growing seasons in each instance: the first season with the water model only to establish realistic initial conditions and the second with mineralization to produce the data discussed here.
Description of the Water Movement Simulation Model
Heinen (1997) developed a simulation model for describing water movement, solute transport, and root uptake. Water movement is described by the Richards equation, which states that the change of water content as a function of time is due to a gradient of water flux density and a source–sink [e.g., root uptake U (L3L-3T-1)]. The flux density is given by Darcy's law, which gives the flux density as the product of the hydraulic conductivity K (LT-1) and a gradient in hydraulic head H (L). H equals the sum of the pressure head h and gravitational head. The simulation model of Heinen (1997) uses relationships between K, , and h as given by van Genuchten (1980) and Mualem (1976):
 | (1) |
and
 | (2) |
where Se is the effective saturation, r is the residual water content, s is at saturation, Ks is K at saturation,
, and 
are shape parameters. Topp (1969) showed experimentally that (h) is hysteretic, while K() has negligible hysteresis. Heinen (1997) used the modified dependent domain model of Mualem (1984) to describe the scanning curves in the hysteretic (h) domain. This model performed the best in a comparison study (Viaene et al., 1994). It goes beyond the scope of this note to present the detail of this model (see Heinen, 1997; Heinen and de Willigen, 1998).
The hysteresis model needs as input both the main drying and main wetting curves. Kool and Parker (1987) proposed that both curves could be described by Eq. [1] if 
is allowed to differ; d for the drying curve, and w for the wetting curve, where w > d. This approach is adopted in this note. If only the main drying curve is known and no information on wetting data is available, Kool and Parker (1987) further suggested that
, which was the average ratio they obtained from different kinds of soils. However, this ratio may be different for other porous media, e.g., Otten (1994) obtained a value of 6.9 for w:d in a peat-perlite potting medium. Here we used ratios of 1 (no hysteresis), 2, or 5 and consider a soil profile with a deep or no water table. The simulations assume a soil column of 2-m depth, with a unit H-gradient condition at the lower boundary. For slowly varying flow fields together with a pressure head or flux specified at some depth, a unit-gradient condition may be appropriate (McCord, 1991; McCord et al., 1991; Sisson, 1987). Where water tables are high, hysteresis may exert less effect than is averred in this note.
Root Uptake
Root water uptake U was assumed to be as described by (Feddes et al., 1978):
 | (3) |
with 
(h) a prescribed reduction function of h and Um the maximum possible uptake rate at a particular depth z (see Fig. 1)
. Two relationships for Um(z) were used. The first is based on an exponential decrease in root length density with depth (e.g., Addiscott and Whitmore, 1987), defined as:
 | (4) |
Here a is defined as –loge(0.01)/zr if 99% of the required uptake takes place between 0 < z < zr, E is the potential transpiration rate (L3 L-2 T-1), and zr is the maximum rooting depth in the vertical dimension z (L). The rooting depth, z, is assumed to increase linearly with time to reach zr at flowering. Equation [4] was used for all simulations under temperate conditions. The second relationship defined by Feddes et al. (1978) is:
 | (5) |
Equation [5] describes a uniform Um in the root zone and was used with the simulations under tropical conditions.
In the temperate simulations, a wheat (Triticum aesitvum L.) crop was grown from mid-October to the end of July;
. Parameters for (h) (Fig. 1) were as follows: h1 = 0 cm, h2 = -1 cm, h3 = -700 cm and h4 = -16000 cm (Wesseling, 1993). For the tropical simulations, we used a corn (Zea mays L.) crop grown from September to the end of January, with: zr = 35 cm (assuming that aluminum toxicity below this depth prevents root exploration in this soil, Whitmore et al., 1998), parameters describing (h) in this case were as follows: h1 = -15 cm, h2 = -30 cm, h3 = -450 cm and h4 = -8000 cm (Wesseling, 1993). To permit proper comparison with temperate conditions, a series of simulations was also carried out for the tropical soil with
. Drying of uncropped soils (after harvest) was limited by reducing the permitted evaporation in proportion to in the top 5 cm of soil (Addiscott and Whitmore, 1987).
Relationships Used to Estimate Mineralization
We simulated microbial activity by tracing the decomposition of a single pool of organic matter assuming a first-order turnover (e.g., Bradbury et al., 1993):
 | (6) |
where C is the total amount of carbon mineralized by time t, k is the first order-rate constant, and C0 is the initial amount of C present at the start of the simulations. The parameter M (0 < M < 1) reduces mineralization if the moisture constant of the soil is less than optimal (see below) and T (0 < T < 1) reduces mineralization if the temperature is less than optimal. To allow direct comparison of the effects of hysteresis, the same function describing T was used for all simulations (Bradbury et al., 1993) with the appropriate daily temperature (climate and soils section). Suitable values chosen for C0 and k were 20 g C kg-1 soil and 0.00006 d-1, respectively, and a C:N of 10 in soil organic matter was chosen to translate the results into N mineralization. Total net, potential mineralization is then 143 kg N ha-1 annually in a soil with a bulk density of 1.32 g cm-3, which is well within the range given by Hassink (1995). The results should be assessed in the context of this potential mineralization.
Four different functions describing M were used to evaluate the change in mineralization with changes in soil-moisture relations, they derive from Sundial (Bradbury et al., 1993) and Daisy (Hansen et al., 1991), which relate mineralization to h; Van Veen (Van Veen and Paul, 1981); and NCSOIL (Clay et al., 1985), which relate mineralization to . There are other functions in the literature (see e.g., Rodrigo et al., 1997) and our choice is meant to be illustrative only and does not imply that the selected functions are better or worse than others. The different effects that dryness (referred to the main drying curve) has on mineralization reduction factor M in each function can be seen in Fig. 2
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Fig. 2 Magnitude of the factor M reducing microbial activity and its relationship with (a) pressure head, h, as described by Sundial (—— Bradbury et al., 1993), Daisy (---- Hansen et al., 1991), and with (b) volumetric moisture content, , as described by Van Veen (—— Van Veen and Paul, 1981), and NCSOIL (---- Clay et al., 1984)
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We define here a quantity 
as the accumulated difference in daily mineralization (kg N ha-1) at any time between simulations without or with hysteresis. The quantity represents the effect of ignoring hysteresis; > 0 means that more mineralization occurred in the simulations where hysteresis was ignored
; < 0 means that more mineralization occurred in the simulations where hysteresis was taken into account (w:d > 1).
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Results and Discussion
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Mean values of under natural temperate rainfall ranged from -21 to 20 kg ha-1 (Table 1
;
) and these differences represent more than 10% of the potential annual mineralization. Large though these mean values of are under natural rainfall, the absolute maxima were much greater (Table 1). The maxima were generally found towards the end of the growing season (final values in Table 1 are similar in many instances to the maxima) suggesting that the bias resulting from ignoring hysteresis is cumulative and can be carried over from one season to the next. This problem is most acute with Van Veen and NCSOIL (carry-over 27 and -23 kg N ha-1, respectively), under natural, temperate conditions with
. The effect of disregarding hysteresis in these models reached more than 15% of the potential annual mineralization by the end of the simulations.
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Table 1 Differences in mineralization, (kg ha-1 yr-1), between stimulations where hysteresis was not taken into account and where it was
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Mean, maximum, and final absolute values of were much greater where soil was alternately very wet and then dry than under either natural or uniform rainfall (Table 1): Daisy is surprisingly sensitive to periodic drying of the soil; the reason is a small but consistent accumulated difference between the simulations with and without hysteresis. Repeated wetting and drying cycles in soil had the greatest influence on ; the maximum effect in some models was almost 60 kg N ha-1, which is 40% of the potential annual mineralization. This effect too appears to be carried over from one year to the next (Table 1). Under realistic tropical rainfall mean, maximum, and final values of || were about equal to or less than under temperate conditions (with the exception of Daisy). This was a surprising result but probably comes about because the corn crop was not allowed to extract water beyond h = -8000 cm in contrast to the cereal under temperate agriculture which extracted water to h = -16000 cm (see Materials and Methods section). If the tropical soils were allowed to dry to -16000 cm, values of became similar to or exceeded those found in temperate soils.
Changing the ratio w:d from 2 to 5 produced a roughly similar change in the magnitude of (Table 1) but the change was not consistent and varied with rainfall treatment. The position on, and shape of, the main wetting curve may thus be important; in addition the magnitude of will almost certainly depend on soil type. Measurements made by Heinen (1997) in a coarse sand suggest that the simple description of the main wetting curve given in Eq. [1] using
, where n is a number, may not be adequate.
The effect of ignoring hysteresis was quite different depending upon which model was chosen. Mineralization in Sundial was least affected by hysteresis but this is because it is least affected by moisture (Fig. 2). Van Veen and NCSOIL were most affected (Table 1), but this is partly because they relate microbial activity to and not h (Fig. 2). Strictly, Sundial does this too (see model description in Bradbury et al., 1993) but confines changes in M to the range where (h) relations are approximately linear (on the main drying curve; Stanford and Epstein, 1974).
It is not only the magnitude of in Table 1 that indicates the importance of taking account of hysteresis, it is also the inconsistency of the sign of . This inconsistency is in part due to the fact that three of the models use a function describing M that has a maximum (Fig. 2) so that small shifts in soil moisture bring about inconsistent changes in depending upon whether M increases or decreases. This suggests that it is unlikely that any simple function could compensate for the absence of hysteresis in computer simulation models of mineralization.
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Conclusions
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Most models of mineralization employ at least an element of calibration and since all soils exhibit hysteresis, hysteresis must have been taken up in the residual during calibration of the models. In many cases, this residual might be reduced or bias in the use of models removed by taking account of hysteretic moisture relations in soil. The bias is likely to be particularly problematic (i) where soils are alternately very wet or very dry such as in irrigated agriculture, (ii) where the soil is also allowed to dry much further than a pressure head of 1000 cm, (iii) after the harvest of crops such as cereals, or (iv) after any crop in the tropics that extracts much water from soil. The results indicate that the shape of the response of mineralization to moisture relations is important with respect to hysteresis; models that simulate a sharp reversal in response to changes in moisture will be sensitive to hysteresis to a disproportionate extent and would probably be improved by including the effect of hysteresis.Wösten Veerman Stolte 1994
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ACKNOWLEDGMENTS
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We thank P.A.C. Raats and H. Terburg for their helpful comments on the manuscript.
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NOTES
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This work was carried out while A.P. Whitmore was employed at AB-DLO.
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REFERENCES
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ABSTRACT
INTRODUCTION
and
; and under maize:
and
