Mississippi Basin Carbon Project Science Plan

Modeling landscape mass balance

By building on existing models, we can take advantage of a wide range of excellent tools developed to simulate many of the fundamental processes controlling carbon transport across the landscape. The available models most directly useful to our project are those that simulate landscape hydrology, erosion, sediment transport and deposition, soil development, and global carbon cycling. Rather than attempting a complete review of existing models here, we describe prominent examples of each type of model and discuss their benefits and limitations in relation to the Mississippi Basin Carbon Project.

A characterization of surface runoff is the first step in simulating transport of any substance across the land surface. A characterization of soil moisture is also essential to modeling many of the processes that control SOC development and turnover. Simulations of surface runoff and soil moisture are accomplished by landscape hydrology models such as TOPMODEL (Beven and Kirkby, 1979; Beven and others, 1995). This model simulates the distribution of recharge, soil water throughflow, and runoff using a hydrological similarity index based entirely on topographic and soil properties. The principal benefit of this approach to our work is that it provides an efficient means of simulating both soil moisture (needed to simulate soil development) and overland flow (needed to simulate erosion and transport) based on available topographic and soil data. In principle this approach is scalable to the entire Mississippi basin; in practice the application of this approach to large regions and agricultural settings will require careful adaptation of methods heretofore applied usually to small forested watersheds. For example, TOPMODEL does not include erosion, deposition or sediment transport. We will require a modeling framework that accounts for these processes in a way that assures conservation of water, sediment, and carbon. Additional limitations may arise from the limited data available for calibration of extreme events, which dominate erosion and transport of sediments across the land surface.

Because of their practical importance to agriculture, empirical approaches dominate existing models of erosion. The most widely used erosion model is the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1965, 1978; Wolman, 1986). This equation is simply

A = RK(LS)CP

(3)

where A is the rate of erosion in mass per unit area and time; andR,K,(LS),C, andPare empirical terms representing the influences of rainfall, soil erodibility, slope (length and steepness), cropping practices, and erosion control measures, respectively. The usefulness of this approach is apparent in its derivation from numerous studies of rates of erosion in farm fields throughout the Mississippi basin (Wischmeier and Smith, 1965, 1978) and its continuing extension to a wide range of settings and applications (see, for example, Ferreira and others, 1995; Toy and Osterkamp, 1995). Its relevance to our project is enhanced by its separation of terms representing natural influences (the productRK(LS), sometimes termed "inherent erosion potential") from those representing effects of land use (CandP). However, values used for the empirical terms may be somewhat subjective, and the equation may not be suitable for areas subject to wind erosion, ephemeral gully erosion, snowmelt, or rangeland use. Moreover, extension of the model to soil organic matter will require an assessment of the extent to which organic matter is selectively eroded.

An independent approach to the assessment of human effects on erosion is the concept of "steady-state" erosion. This concept refers to the assumption of balance between sediment production (erosion) and transport. Clearly human activities have disrupted any such balance that may have existed in the Mississippi basin. However, recent assessments (Gaillardet and others, 1995; Stallard, 1995a,b) have suggested that pre-existing steady-state erosion rates may be estimated by modeling chemical weathering rates implied by present-day transport of certain dissolved weathering products. This approach can be used to test other estimates of human effects, and to further develop theories linking chemical and physical erosion.

Our requirement for mass balance across the landscape implies a need to directly link erosion models to models of sediment transport and deposition. One approach to this problem is represented by the Simulation for Water Resources in Rural Basins (SWRRB) and the Hydrologic Unit Model of the United States (HUMUS) (Williams and others, 1985). These interrelated models link sediment yield from a Modified Universal Soil Loss Equation (MUSLE) to sediment deposition in ponds, reservoirs, channels, and floodplains. The MUSLE is identical in form to the USLE except that the term for rainfall is derived from an explicit hydrologic model. Thus, this approach demonstrates the possibility of linking models of erosion, sediment transport and deposition, and landscape hydrology. However, its sedimentation algorithms depend on information about travel times and particle-size distributions that will be difficult to estimate, and extending this model to carbon will require treatment of differential transport and degradation.

To successfully model the mass balance of sediments transported across the land surface, we require an approach that can be applied to all of our basic spatial scales: field site, sub-basin, and full Mississippi basin. Testing at the sub-basin scale will serve as a basis for extension to the whole basin and for identification of key problems requiring model refinement in studies of processes at field sites.

Many of the limitations of available models, for our purposes, lie in their inability to address conservation of mass across the landscape. Our choice of existing models will therefore be guided by their compatibility with GIS techniques and suitability to spatial integration. A landscape hydrology model is the first logical step in developing the unique integrative capability we require. We will begin with an approach similar to that of TOPMODEL, developing similarity indices from appropriately scaled digital elevation models (DEM’s) and digital soil maps. Particular attention will be devoted to problems of extending this approach to large agricultural basins and to extreme flood events. The resulting landscape representation will provide a platform for parallel development of modeling capabilities to simulate (1) material transport, (2) soil development, and (3) contributions to carbon cycling. Indices of landscape and soil characteristics will be incorporated into models of material transport, as exemplified by the soil erodibility and topography terms in the USLE. Other models – such as the SWRRB/HUMUS -- will then be used to link sediment transport and deposition directly to calculations of erosion. Thus, we will have a framework of models of runoff, erosion, and sedimentation which can be used to develop estimates of carbon mass balance across the landscape. The final stage of this effort will involve model assessment of the historical effects of land use; and comparison of "natural" erosion estimates from this approach to steady-state erosion estimates.‹

Modeling carbon budgets

Our modeling of material transport will be combined with estimates of the concentration of organic carbon in runoff, suspended material, and sediments to provide a basis for modeling carbon erosion, transport, and deposition across the land surface. We will focus initially on testing the approach of Stallard (in press), who considered riverine suspended material to be comprised of autochthonous (i.e., produced by aquatic organisms) and allochthonous (i.e., soil-derived) components. Following Stallard, we hypothesize that each of these two components can be associated with a characteristic organic carbon concentration, and that the concentration of autochthonous suspended material is relatively constant. These hypothesized conditions imply an inverse relationship between the concentration of total suspended material and the fraction of organic carbon in the suspended load. This relationship appears to be reasonable for suspended sediment in large rivers (Stallard, in press); we will further test it using data from streams and rivers in the Mississippi basin. We will also examine ways of improving this simple approach by exploring other systematic relationships, such as those between autochthonous production and nutrient loads, and between suspended particle size and organic carbon concentration.

Our carbon modeling effort must include major emphasis on the processes that control carbon accumulation in soils. Many field and experimental studies have shown that, for given land use and landscape characteristics, the amount of organic carbon in soils tends toward an equilibrium or steady-state value. The trend toward equilibrium can often be approximated by an equation for the first-order kinetics of change in soil organic carbon:

dC/dt = I - L = I - kC

(4)

where C is the soil organic carbon content, t is time, I is the rate of addition of organic carbon to the system, and k is a constant that determines the proportion of organic carbon removed from the system in unit time (see, for example, Jenny and others, 1949; Olson, 1963; Schlesinger, 1977; Greenland, 1995). In relatively undisturbed soils, the addition rate (I) reflects primarily thein situproduction of SOC from plant litter and roots, while carbon loss (L) occurs primarily throughin situdecomposition, loss as DOC, and, in some cases, burning. At equilibrium or steady state, the inputs of C are balanced by outputs (I = L = kC), and there is no net change in the amount of stored C (dC/dt = 0). A positive sign for the term (I - kC) indicates that the soil is a carbon sink (sequestration) and a negative sign indicates that the soil is a carbon source.

Equation (4) can be used to illustrate some of the basic principles and difficulties in applying soil carbon models to areas where cultivation has caused erosion and deposition to contribute significantly to the carbon mass balance. For example, consider an undisturbed soil at steady state in whichin situproduction is the primary source of SOC andin situdecomposition is the primary removal mechanism. Then, following equations (1) and (4),

I = L = kC = Iprod= Ldecomp

(5)

The SOC production rate (I) in agricultural soils includes not only in situ production from plant litter and roots, but also crop residue returned to the soil, sediment deposition, addition of compost and farmyard manure, dung from grazing cattle, and any other source of carbon added to the soil (Lal and others, 1995). The loss rate (L) represents erosion as well as the removal processes that affect undisturbed soils. In simplest form, these alterations can be represented by,

 in areas of erosion,

I = Iprod+ Iadded

(6)

L = Ldecomp+ Leros= kC + Leros

(7)

and in areas of deposition,

I = Iprod+ Iadded + Idep

(8)

L = kC = Ldecomp

(9)

where I_added and I_dep are the inputs of carbon added to the soil by crop management and deposition, respectively; and L_eros is the loss of carbon due to erosion. Thus, cultivation introduces factors that will certainly alter the steady state toward which relatively undisturbed soils might be expected to evolve. In fact, because carbon inputs and losses (particularly sedimentation and erosion) are much more likely to be episodic rather than continuous in cultivated soils, the attainment of "steady state" may have little practical meaning. Comparison of equation (5) to equations (6) - (9) suggests some important non-steady-state generalizations. In areas of erosion, the carbon content (C) and rate of decomposition (kC) will tend to decrease due to the loss of SOC to erosion (L_eros). In these areas the likelihood of SOC being oxidized in situ is reduced because some of it is eroded before it can be oxidized. This effect may be somewhat offset by oxidation during transport, but most eroded SOC is probably redeposited before it can be oxidized. In areas of deposition, the carbon content (C) and rate of decomposition (kC) will likely rise in response to the increased carbon input from sedimentation (I_dep). However, accretion tends to favor SOC preservation, and areas of deposition also tend to have higher soil moisture contents (or may even be under water), further enhancing the probability of preservation. Thus the probability of in situ decomposition (represented by k) in areas of deposition is almost certainly less than that in areas of erosion. In other words, the simple equations above suggest that SOC that is eroded and redeposited is less likely to be decomposed than SOC that remains in upland soils. Moreover, the equations indicate that any enhancement of soil carbon inputs by cultivation will tend to accelerate the delivery of SOC to sites of both erosion and sedimentation, thereby accelerating the likelihood of preservation.

Of course the modeling of agricultural soils is not this simple. Cultivation usually decreases rates of addition of organic matter to the soil; however, soil amendments which lead to greater crop yields, larger root systems, and more crop residues will tend to enhance levels of soil organic matter (Greenland, 1995). The magnitude of the decomposition constant k depends on climate, geomorphic setting, the composition of the soil organic matter (particularly the lignin content), intrinsic soil properties (such as acidity, texture, and clay content), land use, and soil and crop management practices. For a given geographic area, the magnitude of k can be expected to be relatively low for natural ecosystems and for agricultural soils subject to soil and crop management practices that involve prudent off-farm inputs, conservation tillage, crop residue return, and other soil restorative measures. On the other hand, relatively high values of k can be expected for soils subject to deforestation, biomass burning, plow-based tillage, and other cropping systems that exacerbate soil degradative processes. Enhancements of k values may also occur in cases of expansion of agricultural activities to marginal or ecologically-sensitive areas (Lal and others, 1995).

Fortunately, a number of existing soil organic carbon models have been applied to a wide range of soils and land-use settings (e.g., Jenkinson, 1990; Parton and others, 1987; Li and others, 1994). For example, the CENTURY model (Parton and others, 1994) has been applied to a particularly broad range of soil responses to observed and potential human influences, including cropping practices, fertilizer addition, tillage, and climate change (Parton and others., 1996). Such models typically subdivide soil organic carbon into various fractions with different susceptibilities to decomposition. This scheme is convenient for us because we are concerned only with the fraction of SOC that decomposes over time scales greater than a few years. However, an important limitation is that the modeled soil organic fractions cannot be physically or chemically separated by generally accepted methods; thus these models must be highly parameterized for particular settings. Another specific problem for our purposes is that the models do not generally accommodate erosion or deposition in a manner that assures conservation of mass across the landscape. Even model implementations that include explicit erosion effects (e.g., Voroney and others, 1981; Barnwell and others, 1992; Donigian and others, 1995) do not account for the fate of carbon removed from sites of erosion.

To complete our assessment of carbon mass balance across the landscape, we will need to link models of soil carbon dynamics to models of landscape hydrology and material transport. For example, we can adapt the CENTURY model through spatial allocation of parameters consistent with TOPMODEL indices and with the soil erosion and deposition simulations. In this manner, CENTURY can become one component in a landscape model with the capacity to accommodate carbon mass balance across the landscape. The time-dependent characteristics of CENTURY also enable us to simulate historical effects of changing land use and soil development accompanied by erosion and deposition.

Much of the debate concerning the modern global carbon dioxide budget focuses on the results of models of terrestrial carbon cycling. A variety of models have been applied to the diagnosis of historical effects of land use (Houghton and others, 1987) and the forecasting of future terrestrial carbon budgets (Melillo and others, 1993, 1995). These issues are fundamental motivations for our project and we must be able to relate our results to those of other approaches to terrestrial carbon modeling. Unfortunately none of the existing terrestrial carbon cycle models addresses the effects of carbon transport across the land surface. Moreover, very few models have examined the linkages among terrestrial carbon cycling, river fluxes to the oceans, and marine carbon cycling. One such model is that of Sundquist (1990), which has been used to simulate the contribution of river fluxes to the annual carbon dioxide budget (Sarmiento and Sundquist, 1992). Although this model has been used to model past carbon cycle changes and interactions between terrestrial and marine CO₂ budgets, it must be substantially updated if it is to be used as a link between USGS studies of the Mississippi basin and models of global carbon cycling. We will use this model as a starting point for linking our studies of carbon in the Mississippi basin to estimates of effects on the global carbon dioxide budget. We will focus on placing our "first cut" whole-basin carbon budget in the context of a global carbon cycle model. This task will require rectifying the land-surface characterizations of our whole-basin analysis with those used in ecological models of terrestrial carbon cycling.

	Contents
	Identification and field study of key processes
	Reconstructing effects of historical human land use