Development of a General Ecosystem Model for a Range of Scales and Ecosystems

E(OLOGI(gL mODELLInG ELSEVIER Ecological Modelling 88 (1996) 263-295

Development of a general ecosystem model for a range of scales and ecosystems

H.C. Fitz a,,, E.B. DeBellevue a, R. Costanza a, R. Boumans b,1 5 T. Maxwell a L. Wainger a, F.H. Sklar c a Maryland International Institute for Ecological Economics, Center for Environmental and Estuarine Studies, University of Maryland, P.O. Box 38, Solomons, MD 20688, USA b Coastal Ecology Institute, Center for Wetland Resources, Louisiana State University, Baton Rouge, LA, USA c South Florida Water Management District, Everglades Systems Research Division, West Palm Beach, FL, USA Received 24 June 1993; accepted 24 March 1995

Abstract

We have developed a General Ecosystem Model (GEM) that is designed to simulate a variety of ecosystem types using a fixed model structure. Driven largely by hydrologic algorithms for upland, wetland and shallow-water habitats, the model captures the response of macrophyte and algal communities to simulated levels of nutrients, water, and environmental inputs. It explicitly incorporates ecological processes that determine water levels, plant production, nutrient cycling associated with organic matter decomposition, consumer dynamics, and fire. While the model may be used to simulate ecosystem dynamics for a single homogenous habitat, our primary objective is to replicate it as a "unit" model in heterogeneous, grid-based dynamic spatial models using different parameter sets for each habitat. Thus, we constrained the process (i.e., computational) complexity, yet targeted a level of disaggregation that would effectively capture the feedbacks among important ecosystem processes. A basic version was used to simulate the response of sedge and hardwood communities to varying hydrologic regimes and associated water quality. Sensitivity analyses provided examples of the model dynamics, showing the varying response of macrophyte production to different nutrient requirements, with subsequent changes in the sediment water nutrient concentrations and total water head. Changes in the macrophyte canopy structure resulted in differences in transpiration, and thus the total water levels and macrophyte production. The GEM's modular design facilitates understanding the model structure and objectives, inviting variants of the basic version for other research goals. Importantly, we hope that the generic nature of the model will help alleviate the "reinventing-the-wheel" syndrome of model development, and we are implementing it in a variety of systems to help understand their basic dynamics.

Keywords: GEM; Hydrology; Nutrients; Process-oriented models; Sensitivity analysis

I. Introduction

1.1. Why a general model? * Corresponding author. Fax: (+ 1-410) 326-7354. i Present address: Jackson Estuarine Laboratory, Univer- Process-oriented ecological models can be use- sity of New Hampshire, Durham, NH, USA. ful tools in ecosystem research and management,

0304-3800/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0304-3800(95)00112-3 264 H. C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 but there are a relatively large number of models tern on process, with feedbacks among the physi- for a relative handful of simulated ecosystem cal and biological processes, are needed for the types. Much of the rationale, and necessity, for next generation of models that incorporate the this perceived redundancy in modeling efforts landscape, regional and global scales. involves differing research objectives, the scale A general ecosystem model can eliminate the associated with those objectives, and the varying need for continuous remaking of models for dif- importance of different ecological processes as ferent systems and/or sites and can form the one crosses system boundaries. Widely varying basis of spatially explicit ecosystem process mod- ecosystem model objectives may range from those els. Such characteristics logically lead to one of involving predictions on the scale of individual the broader objectives in ecosystem research: with organisms or groups of organisms to models that a standard structure for developing a (model) focus more on theoretical constructs of identify- synthesis of a system, comparisons among systems ing/quantifying important interactions, feed- may be facilitated. A model that can be generally backs, and/or cycling in ecosystems. Moreover, applied to ecosystems that range from wetlands model objectives that are similar for different to upland forests could provide at least two useful biomes or regions may still involve different phys- functions in synthesizing our broader understand- ical forcing functions or feedback mechanisms ing of ecosystem properties. One involves using that significantly affect the system behavior. For the model as a quantitative template for compar- these reasons, there will continue to be questions isons of the different controls on each ecosystem, in ecosystem research that require the creation of including the process-related parameters to which completely new models. However, we feel that the systems are most sensitive. Secondly, a simu- there exists a significant void in our understand- lation model which is general in process-orienta- ing of basic ecosystem properties that can be tion and structure could provide one of the tools addressed with the aid of a general model of to analyze the influence of scale on actual and ecosystems, looking for the broad similarities in perceived ecosystem structure. For example, what comparison instead of the unique details. In this is the relative sensitivity of different ecosystems paper, we present a computer simulation model to changes in nutrient concentrations? To what that is a step in that direction. extent, and under what set of conditions, are The utility of a generalized ecosystem model transpiration losses controlled by the fine-scale for research has been recognized for some time, plant physiology versus field-scale radiative flux? with CLEANER/MS.CLEANER (Park et al., 1974, Models that can be consistently applied across 19"79) and CENTUnY (Parton et al., 1987, 1988) systems and across geographic regions would al- being efforts for freshwater and grassland ecosys- low different levels of process aggregation to be tems, respectively. These models have been use- evaluated, and would allow us to discern the fully applied to a variety of sites of the targeted more sensitive parameters of the biological and ecosystem types, alleviating the need to exten- physical processes that vary in importance with sively recode the model for each new application. different ecosystems. To this end, with a general However, central to these and most other ecosys- ecosystem model as a fundamental building block tem-level models has been the assumed homo- for analysis and prediction, hypotheses on scaling geneity within the system, using lumped (aver- within ecosystem dynamics could be analyzed aged) parameters. Due to the heterogeneity in- (Holling, 1992). herent in natural systems, more recent research has accentuated the need for general ecological 1.2. Existing models models that can be reparameterized and applied to different ecosystems for distributed, or spa- A survey of the modeling literature revealed tially explicit, simulation (Costanza et al., 1990; no general ecosystem simulation model that had Band et al., 1991; Costanza and Maxwell, 1991). been developed for use across a wide range of Such models that incorporate the effects of pat- ecosystem types. However, several models have H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 265 been formulated for general application to a spe- corporate some form of chemical or sediment cific type of system. Before presenting the struc- transport and fate (Shoemaker et al., 1992). The ture of the General Ecosystem Model (GEM) ¢nEAMS model (Knisel, 1980) used a variety of that we have developed, we discuss some of the process-oriented algorithms to measure runoff existing models that we borrowed from, or that and sediment/nutrient transport relatively homo- parallel our design in some component. In order geneous "field"-scale regions using a daily time to present where the GEM fits into the scheme of step. The simpler 6WLF model (Haith and Shoe- general ecosystem models, we briefly review some maker, 1987) was a generalized watershed model ecosystem level models that have been designed for nutrient loadings, based largely on empiri- to be general enough to be used for different cally-derived loading functions and simple runoff sites without extensive recoding. Several of these and groundwater relationships. These models in- models were intended to be used in spatial appli- corporated varying degrees of process- and statis- cations to accommodate within-site heterogene- tically-derived algorithms to describe hydrologic ity. functions, reducing the complexity from that of a Physical hydrology is a critical component of more purely process-oriented approach. many ecological systems and the hydrologic com- A versatile ecological model for freshwater ponent of the GEM is an important aspect of the lakes, CLEANER/MS.CLEANERcontained up to 20 model's generality. Models of water processes biotic state variables including: phytoplankton, operate within a well-understood set of physical macrophytes, zooplankton, fish, and benthic fauna constraints that allows these models to be applied (Park et al., 1974, 1979). It also had 20 abiotic to a broad range of landscapes, differentiated by state variables including dissolved and particulate terrain-related parameters and quantified by organic matter, inorganic nutrients, carbon and physical laws. Thus, hydrologic components may oxygen, as well as external environmental forcing generalize well within a general model of ecosys- functions. According to the authors, the full model tem processes. The hydrologic models are those complexity was seldom used; normal application which include water movement among storages in required only 20 state variables. Users were able aquifers, sediment zones, ponded surface water, to run parts of the model by specifying the state and the atmosphere, including the horizontal variables of interest using an editing routine con- component of surface water and groundwater tained in the model package. MS.CLEANER was flows along hydraulic gradients. designed as a user-oriented model with a simple The large number of existing process-based set of commands. hydrologic models use different spatial/temporal The model CENTUaY (Parton et al., 1987, 1988) scales and have varying objectives. Compared to was used to simulate very long-term, regional changes in living biomass or nutrient cycling, hy- patterns for plant production in the US central drology encompasses fast ecosystem processes: grasslands region. This model evaluated plant many hydrologic models of small catchments or growth and the cycles of carbon, nitrogen, and watersheds work with time scales of seconds to phosphorus using a monthly time step over cen- hours to effectively capture fine-scale detail of tury-long periods. Soil moisture and temperature rainfall events and subsequent runoff or variable affected decomposition rates of the five organic infiltration through finely partitioned soil layers. matter components which had very different Recent examples (Binley and Beven, 1992; turnover times (from 0.5 yr to 1000 yr). Soil Grayson et al., 1992) of such distributed hydro- moisture was a function of the ratio of monthly logic models with fine temporal/spatial scales precipitation to monthly potential evapotranspi- and high hydrologic process detail are computa- ration. The plant production submodel simulated tionally complex and not readily amenable to monthly dynamics of C, N, and P in live and dead applications that involve many other ecosystem above-ground plant material, live roots, and sur- processes. face and root detritus. Some simpler watershed hydrologic models in- Another model for describing biogeochemistry 266 14. C. Fitz et al. /Ecological Modelling 88 (1996) 263-295 and plant growth in terrestrial ecosystems (500 m 2) for the scale of forest assemblages (Smith (Rastetter et al., 1991) was applied to Arctic and Urban, 1988), using the coupling framework tundra and temperate hardwood forested sys- of VE6OMAT (Smith et al., 1989). This in turn is tems. The model contained 23 state variables designed to be linked with an existing compart- including four plant compartments and four soil ment model of nutrient cycling and plant produc- organic compartments. Focusing on monthly tion, CENTVRY (Parton et al., 1987), and a soil changes in distribution of C and N between vege- water model, SO~LWAT (Parton, 1978). The design tation and soils, the model simulated the stoichio- for linking the models will rely upon running the metric shifts in plant tissues and had a variety of models concurrently over a network in a UNIX controls on production, but excluded hydrologic processing environment. Preliminary simulations processes. Rastetter et al. (1991) demonstrated linking STEPPE with CENTURY and STEPPE with that a similarly structured model could capture SO1LWAT demonstrated the rich dynamics that are selected ecosystem dynamics of two rather differ- possible to explore by integrating realistic models ently structured ecosystems. of vegetative dynamics with physically based FOREST-BGC (Running and Coughlan, 1988; ecosystem processes. Running and Gower, 1991) was a general forest Our objectives are very similar to those for ecosystem model to describe basic components of most general models: we seek to integrate biolog- carbon, nitrogen and water cycling. They used ical and physical processes in a simulation of daily time steps for canopy gas exchange and basic ecosystem dynamics for applications to more basic hydrology (precipitation and transpiration), than one ecosystem. To be most useful, the model with yearly time resolution for carbon allocation, should be readily understood and be used at litterfall and decomposition processes. The leaf other sites with minimal recoding. All GEMs, area index was a prominent control over a num- using different approaches and simulation algo- ber of the process rates involving three compart- rithms, will provide useful comparisons of model ments for tree biomass; detrital dynamics involve assumptions, design, and results. Furthermore, two compartments with different decomposition such models will aid in evaluating and under- rates. standing how scale can affect results (Alien and A general terrestrial ecosystem model (TEM) Starr, 1982). with 5 state variables was used in a spatial model of South America (Raich et al., 1991) to estimate 1.3. GEM primary production for the region. The TEM was intended to be spatially distributed at the conti- The GEM is a physically driven model that nental and global scales, using monthly time steps incorporates the processes that we hypothesize for decadal output. State variables included or- are most important in influencing plant produc- ganic carbon and nitrogen in both living and dead tion and modify that ecosystem's properties. For matter, with a pool of available inorganic N. To this manuscript, we will first present the basic incorporate feedbacks between moisture and the tools used to develop, modify, and use the GEM. ecosystem dynamics, a water-balance model Following that is a description of the model struc- (V6r6smarty et al., 1989) was linked to the TEM. ture (variables and pathways of material and in- The model was calibrated with data for a variety formation flow) and function (algorithms control- of non-wetland ecosystems from different sites ling model behavior). For that presentation, the that were assumed to be relatively undisturbed. GEM may be best understood by considering the Lauenroth et al. (1993) recently began linking following. separate biotic ecosystem models with abiotic en- • We assume homogeneity of the modeled sys- vironmental process models. The effort involved tem. Spatial heterogeneity of the landscape is the linking of two individual-based plant models, accommodated by replicating this model in a STEPPE for the (0.1 m 2) scale of plots in grass- grid-cell array for explicit spatial simulations lands (Coffin and Lauenroth, 1990) and ZELIG (Costanza and Maxwell, 1991). H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 267

We assume that hydrology is a critical process Sectors such as fire dynamics or hydrodynam- of most ecosystems. Thus the model is largely ics may easily be removed (or turned off) from driven by hydrologic algorithms; some are the model just as other components may be novel, others are patterned after previous work replicated or revised. such as Haith and Shoemaker (1987). Three After the complete description, we present (variable) layers of vertical zonation are estab- some sensitivity analyses of the type that could be lished as a minimum for plant response to useful in determining the level of process aggre- available water and its dissolved inorganic nu- gation for a site and its parameterization. These trients. simulation results are indicative of the model's Hydrology is a "fast" process (Holling, 1992) internal feedbacks and constraints within biotic which dictates the minimum (fixed) time unit and abiotic sectors for habitats representative of of the model. We chose daily time steps as the different ecosystems of the Everglades in south minimum that would adequately represent Florida. From there we indicate the future direc- broad, field-scale hydrologic responses to daily tions for this model in terms of its use in compar- rainfall data. Yearly to decadal simulations are ative ecosystem ecology and research in ecosys- feasible depending on data constraints. tem- and landscape-level dynamics via modeling. Beyond hydrology, the GEM extends the simple unit ecosystem processes of CELSS (Costanza et al., 1990) by including significantly more 2. Modeling tools explicit process details for both wetland and terrestrial habitats. 2.1. Model development environment Inorganic and organic components of the sediment are simulated as a determinant of sedi- Central to the GEM modeling framework is ment elevation. the use of STELLA 2 as a model development tool. Nitrogen and phosphorus cycling are devel- This program is a graphically based simulation oped with very similar model functions, aggre- development environment that alleviates the need gating the speciation of each nutrient into one for being expert in a high level programming inorganic form. Inorganic nutrient stocks in language in order to develop new models or homogenous zones of the water and understand existing models (Costanza, 1987). The sediment/soils are one constraint on plant extensive amount of code needed to execute a production. large ecosystem level model inevitably is difficult Maximum rates of carbon fixation, ingestion, for a potential user to fully understand and mod- and decomposition are limited by control func- ify. STELLA allows for rapid conversion of con- tions; for macrophyte growth, these are nutri- cepts to logical and mathematical expressions, ents, water, temperature and light. while providing graphical information maps of We target plant (macrophytes and algae) pro- the linkages among variables. Importantly, a duction as indicative of the most basic ecosys- STELLA model can be divided into functional sub- tem dynamic. Trophic dynamics are only models called sectors that can be run indepen- crudely incorporated into GEM. Thus, feed- dently or as a part of the whole model. Such backs resulting from multi-species consumer modularity allows convenient revision, and facili- interactions are implicit. tates the development/debugging phase for indi- Having made the above statement, we hope to vidual process components. The advantage of show that modularity of the GEM is such that communicating both general model structure plus detailed trophic structure can be built into specific mathematical algorithms - in a runtime GEM to explicitly test hypotheses regarding the relative importance of top-down and bottom-up controls on different wetland and ter- 2 STELLA ® is available from High Performance Systems, restrial systems. The building blocks are there. Inc., 45 Lyme Road, Hanover, NH 03755, USA. 268 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 environment with graphical and tabular output - of which are not necessarily needed for each is important for a model that is intended to be project objective. These data include rate param- communicated to other people and actually get eters, initial conditions, threshold values, and used. other parameters that are used in the GEM and Models developed using STELLA may be run that vary from one habitat or ecosystem type to under the Macintosh or MS DOS (using Win- another. When the GEM is run to compare dif- dows 3.1) operating systems with no translation. ferent habitats or in a spatial context within a Acceptable performance with GEM, however, heterogeneous landscape (Maxwell and Costanza, dictates the use of strictly high end processors for 1994), the efficient compilation and organization these machines. For those familiar with the C of the data is critical. We have designed a set of programming language, the GEM may be con- linked databases in order to automate the trans- verted into C code using an existing translator, fer of the parameters to the model. The database and executed using drivers for a variety of differ- parameters for different habitats are dynamically ent computer platforms (Maxwell and Costanza, linked to the model using calls in the Macintosh 1994). operating system, with each habitat-specific data set being selected by changing the value of the 2.2. Linked databases model's habitat variable. The databases are organized to match the sec- A vital component of any model is the data tors of the unit model, with a separate database used in its parameterization. For a general model for each sector such as Macrophytes, Hydrology, designed to run in different systems with differ- or Dissolved Inorganic Nitrogen. Within each ent parameter sets, database access for reviewing sector's database, we provide the user with three simulation parameters and implementing a simu- different perspectives on viewing information lation becomes even more important. The GEM about the data. These include the parameter value has 103 input parameters that vary among ecosys- and name as it is used in the STELLA unit model, tems (Table 1). The model varies in sensitivity to documentation from the model regarding how these ecosystem/habitat-specific parameters, all the parameter is used, and a field for the user to

Table 1 The number of parameters needed for 13 sectors (submodels), classified into seven categories: Stoichiometry (C:N:P of organic matter, etc.); Nutrient Flux (plant nutrient requirements, coefficients of nutrient adsorption to sediments, etc.); Rate Parameters (hydraulic conductivity, specific rates of growth, respiration, etc.); Initial Conditions (initial mass or concentration for each state variable); Physical Structure (related to height of macrophytes, hydraulic roughness, etc.); Environmental (related to response to temperature, solar radiation, etc.); Other parameters, such as allocation of dead organic material to particular detritus pools Stoich NutFlux RateParm InitCond PhysStruct Environ Other Sum Hydrology 4 3 3 10 Hydrodynamics 0 Macrophytes 6 2 5 2 9 6 30 Algae 3 2 4 1 2 12 Consumer 3 3 1 1 1 9 St Detritus 3 1 1 2 7 In~)rgSeds 1 1 SOM 3 1 2 6 DOM 3 2 1 1 1 3 11 DIN 3 3 1 7 PO4 3 3 6 Salt 2 2 Fire 1 1 2 Sum 21 10 19 19 13 11 10 103 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 269 provide comments that include the source of data and any assumptions involved in its use. More- over, we provide a numeric (range = 1-5) grade attribute, whereby the subjective quality of the data can be evaluated (Costanza et al., 1992). For Dead example, a plant's carbon : nitrogen : phosphorus Organic ratio that was measured in the modeled region during four seasons may be considered high-quality information and ranked 1 or 2. Conversely, growth data obtained from the literature for a I Consumers congener plant species in a climatic region different from the model area would be ranked inter- Fire mediate (3) to poor (5) in grade depending on an l 1 evaluation of the assumptions involved in the Fig. 1. The process-oriented feedbacks among the biotic and data utilization. This system provides users with abiotic sectors of the GEM. Dynamics of live and standing full access to the critical model data in a format dead macrophytes alter surface water runoff through changes in structure and thus surface roughness. Water losses via that allows one to easily focus on and evaluate transpiration vary with changes in biomass (leaf area index) particular areas of interest. Importantly, anyone and physical canopy structure. Availability of water in surface, can view the data, its source and perceived qual- unsaturated and saturated storage is one control on plant ity, and subsequently further evaluate that aspect growth and mortality. Hydrologic algorithms also transport of the model. dissolved nutrients and control their remineralization, while nutrient availability and uptake kinetics can control plant growth. Dead organic matter, in different forms of storage 2.3. Revision control software and with different C:N:P ratios, is the source for nutrient cycling. Consumers sequester plant biomass, delaying its in- Because by design the GEM and its databases corporation into detrital pools. Fire may generally affect the will change with refinements or different user whole system. objectives, we felt that it was important to track the model and databases as such changes are made. The current version of GEM is the basic and implementation of the GEM and associated building block for model development, and is databases in different projects with varying objec- functional as it stands. However, refinements in tives. algorithms and sector enhancements will result in new versions and variants of the basic model. Revision control software (Voodoo 3) manages 3. Model implementation the structure and sequence of changes as they occur within a user's site; new versions during a 3.1. GEM structure development/debugging process are stored (with changes in compressed form) along a develop- The structure of the model is designed to ment path. Moreover, completely new variants of capture the feedbacks among abiotic and biotic the model project may branch off of the main components. The (primary) ecosystem process development path. This management scheme al- feedbacks in the model are outlined in (Fig. 1). lows effective organization of the development Nutrient availability and changes in surface and subsurface water have explicit controls on algae and macrophyte growth, whereas the macrophytes affect hydrology via the surface roughness 3 Voodoo Lite is a shareware version of Voodoo (Versions of Outdated Documents Organized Orthogonally), available and transpiration. Plant mortality and consumer from anonymous ftp sites or the author: [email protected] dynamics alter detrital storages, and mineraliza- linz.ac.al. tion of this organic matter of different quality is 270 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 influenced by hydrology, which also transports the flow of material or information. In order to nutrients. Fire may be one of the major distur- maintain a seamless link between the STELLA bances that alter many of the system components. model and the description, we maintain the full These direct and indirect interactions built into variable names in accordance with their use in the model provide a rich variety of dynamics, the STELLA model. The system of non-linear and directly coupling biological and physical compo- linear equations employs a variety of built-in logi- nents of the whole system. A diagram of the cal and mathematical functions that are built into model structure is provided in Fig. 2, including STELLA. The software carries out the solution of most of the linkages among state variables (ex- the finite difference equations using the Euler cluding hydrology). Also indicated is the distinc- integration technique and provides graphical and tion between above- and below-sediment zones. tabular output of results. We describe the model in order of sectors that We assume that the area included in the model distinguish among fundamental physical and bio- boundaries is homogenous in most respects. The logical processes within the system. The following model boundary area is referred to as a cell, in descriptions of the different sectors of the model reference to the typical situation where the GEM incorporate many of the principal equations that is a unit model embedded in a cell of a spatial describe the fluxes associated with state variables model. The vertical dimension varies dynamically and the functions that provide feedbacks to some according to changing sediment and water levels of the biological and/or physical processes. The as indicated in the descriptions below. text descriptions present the logic of many of the Text in ALL CAPS indicates a state variable, algorithms that are used in the model to generate and is given in this format when first defined in

W I--

W 0

n~ W I--

Fig. 2. The state variables and most of the linkages of material or information in the GEM, excluding hydrology (Fig. 3). Hydrology drives many of the vertical fluxes shown and the unshown horizontal fluxes of materials into and out off the system (cell). State variables are enclosed within rectangles in ALL CAPS. Environmental forcing functions are in oval boxes; simulations of fire, hydrology, and hydrodynamics affect model dynamics. Metabolic sinks are not indicated. Dissolved Inorganic Nitrogen (DIN) and PO4 are separate state variables with slightly different dynamics. Although not shown, both nutrients are involved in uptake and mineralization processes. H.C. Fitz et al. /Ecological Modelling 88 (1996) 263-295 271 the text and in all equations. Auxiliary variables and parameters are italic&ed when first defined within a sector and when used in equations. Pa- Precipit at ion rameters preceded by rc_, such as rc alg prod, l Evap°,ati°n are rate constants; variables appended by _cf are Transpiration control functions. Within the equations, bold standard text represent common intrinsic func- Overland flow tions that are defined in STELLA software.

3.1.1. Global Inputs Sector lnf lit rat ion The GEM used daily rate coefficients and a Surface - Saturated time step of 0.5 day or less. The area of the exchanges I modeled system is input by the user, but the ~l'percolat ion / example simulations here use a 1.0-km 2 cell size. ~ & upflow ( Daily precipitation and temperature data are required, with humidity data useful, but not essen- SAllJRAllED WATm tial. Daily solar radiation is simulated using an GroUndwaterflo~ [ algorithm derived from Nikolov and Zeller (1992) that begins with a calculation of daily solar radiation at the top of the atmosphere based on Julian Fig. 3. Simplified diagram of water storages and flows for the Hydrology sector. The depths associated with water in sur- date, latitude, solar declination, and other fac- face, unsaturated, and saturated storages all vary dynamically, tors. For the GEM, mean monthly cloud cover is and calculations determine the variable soil moisture propor- calculated using a regressed relationship based tion of the unsaturated zone. on daily precipitation, humidity, and temperature. This monthly cloud cover value is used to attenuate the daily radiation reaching the sur- low the sediment/soil level. Flux among the vari- face. Daily radiation (SolRadGrd in cal. cm -2. ables depends on a variety of processes. Horizon- d-l) received at the earth surface at a particular tal flow of surface and saturated ground water, elevation, latitude, or time of year in the northern evaporation, infiltration, and saturated/un- hemisphere is calculated using the Beer's law saturated water transpiration are some of the relationship to account for attenuation through more critical fluxes for accurate simulation of the atmosphere (Nikolov and Zeller, 1992). Other water storages at daily time scales. We ignore components of their radiation model can accom- details of processes that occur on a time scale modate slope and aspect of mountainous terrain, faster than the daily time step, such as vertical but are not used in this GEM version. movement of a saturated wetting front in infiltration events. The longer-term results of storage in 3.1.2. Hydrology Sector a small landscape can be effectively captured Water is held in three state variables: (1) SUR- within the day-to-weekly time scale. FACE WAT is water that is stored above the sediment/soil surface; (2) UNSAT WAT is 3.1.2.1. Surface water. The volume of surface wa- stored in the pore spaces of the sediment/soil ter that is runoff from the cell in one time step is complex, but not saturating that zone; and (3) calculated first. Runoff is determined using the SAT WAT is water saturating the pore spaces of Manning's equation (Chow, 1964) for overland the s~diment/soil complex. Simulating the fluxes flow which is based on the hydraulic head differ- among variables (Fig. 3) allows the depiction of ence between the current cell and external cells. wet, moist and dry environments by simulating We provide only one directional pathway of net the water movement between storages and calcu- flow to/from the external environment for sim- lating the water level movements above and be- plicity. In the spatial modeling context, the flux 272 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 equations would operate in the four directions of the compass. Flow associated with the current cell is: ~ Sf wt._.head - Sf___wt headExt (dynamic) Sf _wt__flow = --c-e[l__width Manning's Sf wt._.avgS/3 . cell width n - (1) Manningscoef Min. __ I (static) I where Sf._wt__flow is the net flux of water (m 3. I d -1) into or out of the cell, Sf_wtheadExt, O0 0,0 Sf_wt_Head, and Sf wt avg are the hydraulic Plant height (m) (dynamic) heads (m) of the external cell, of the current cell, Increasing water depth (m) and their average, respectively; cell width is the width (m) of the square cell that-qs uniformly Fig. 4. The relationship between Manning's roughness-coeffi- covered with water; and Mannings._.coef is Man- cient n to water depth and to plant height, both of which chance dynamically in the model. The maximum Manning's n ning's coefficient of surface roughness. varies with the plant density; the minimum Manning's n is The Manning's roughness coefficient is a func- fixed for a vegetation-free cell. Maximum roughness for a tion of the sediment type and the interaction of given plant density occurs when water depth equals the plant the vegetation height/density and water depth. height. Mannings._.coef = - ( Mac_max__rough rate of water loss in saturated storage. Both of these vertical flows are explained in more detail Sf_wt depth) in the next section. -sed --Material) • (2 (1 mac. height -- 11 Any remaining surface water is available for + Mac_max._.rough ) (2) evaporation. Surface water evaporation is simulated separately from water loss due to transpira- The sed Material roughness is the minimum tion by plants. Potential evaporation (m. d -1) is Manning's coefficient for a vegetation-free cell, calculated from Christiansen (1968). The model the Mac_max_rough is the maximum roughness uses temperature, solar radiation, wind speed and associated with the (dynamic) vegetation density humidity as the independent variables such that: in the cell, and macheight is the (dynamic) height of the macrophytes in the cell. This func- evap._pot tion (Fig. 4) returns a positive roughness coeffi- = 0.0000482" C T • C w • C," SolRadGrd/585, cient whose value ranges from a vegetation-free where minimum to a maximum at the point of full plant immersion (Petryk et al., 1975). As water depth C:r = 0.463 + 0.425( T/To) + 0.112(T/To) 2, increases over that of the macrophyte height, the roughness decreases to an asymptote at the base- Cw= 0.672 + 0.406( W/Wo) - O.078( W/Wo) 2, line sediment roughness (Nalluri and Judy, 1989). (3) Surface water loss to storage in the C H = 1.305 + 0.240(H/Ho) sediment/soil is determined after runoff and can -0.275(H/Ho) 3, occur via two pathways: (1) infiltration from the 585 cal/g is the latent heat of vaporization to surface water to an unsaturated soil water zone, convert solar radiation from cal • cm- 2. d- 1 to its based on measured infiltration rates for different water equivalent of cm. d-l, and Cr, Cw, and soil types; and (2) surface water flow to the satu- C, are coefficients related to temperature (T in rated water storage at a rate that depends on the °C), wind speed (W in km/h), and humidity (H, H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 273 proportion from 0-1), respectively. Parameters subscripted with 0 (such as T 0) are reference tI°°°~ iiii iiii iiii ii iiii iiii iiii fi~] o.oo3°'°°°'"Put o.ooO,.oooOUtput values in the model of Christiansen (1968). = [ ...... ii i' yi :,:: t o.,,70.250 lo.Doo0.030 o } 0.333 0.I00

3.1.2.2. Saturated and unsaturated water. Vertical -~ li...... / ilo4.0.500 o2400.415 ~,}" • 0.583 0.570 fluxes of water occur among all three of the water .... i...... 0.667 0.725 ~ ..i i y ...... 0.750 0.035 storage compartments. If surface water from pre- • .... 0.033 1.920 j~. : . •... 0.917 0,975 cipitation is present, and there is available vol- O.O~ i : i~/" : : i II I .OOO I .POD ume in the unsaturated storage of the sediment, ~i I~i[ 0ata Pei.ts: 113 L '°°° U ~ Edit Output: ~i-~ then water infiltrates into the unsaturated zone at unsat_moist_prp a rate determined by the infiltration rate (m • d- ~) ~_ To equation I Q Delete graph ] ~ for the habitat type multiplied by the cell size (m2). The available capacity of the unsaturated Fig. 5. An example of a control function that is determined by zone is calculated from the porosity and current data, graphically represented in a ST dialog box. The unsaturated hydraulic conductivity (0-1) multiplier (unsat hyd volume of water in unsaturated storage, which condcf along the Y axis and listed in the Output column of also determines the moisture proportion in unsat- data) is a function of the (0-1) unsaturated moisture propor- urated storage (unsatmoist__prp). We assume tion (unsatmoist_prp along the X axis and listed in the Input that the water in unsaturated storage is dis- column). The multiplier reduces the value of saturated hy- tributed homogeneously within that zone, ignor- draulic conductivity for the current soil moisture; STELLA performs a linear interpolation between data points. The user ing the presence of any wetted front and the may input tabular experimental data or manipulate the curve heterogeneities associated with processes occur- to some hypothesized relationship between the X and Y ring on faster time scales than the daily time step variables. used in the GEM. When the sediment is fully saturated, surface water may flow into the saturated layer to replace water (sf. wt depth). The function max(x,y) re- outflow from the saturated storage at the rate turns the greater of either argument x or y, and determined by the loss of saturated water. We exp(x) returns e raised to the x power. The equa- assume that the rate of vertical movement of tion returns a (dimensionless) value near 0.0 for a water from the surface to the saturated zone is at small unsaturated zone, resulting in most water least as fast as that of losses from saturated flux to the saturated zone; the function rapidly storage via horizontal flow, transpiration, and approaches 1.0 as the unsaturated depth becomes deep aquifer recharge. Similarly, water from the significant, resulting in all surface water infiltra- saturated storage zone flows into surface water tion to the unsaturated layer. storage when the total capacity of the sediment is Any moisture in excess of field capacity may exceeded. Because the unsaturated zone varies in percolate from the unsaturated storage to satu- depth, the GEM has a function to determine the rated storage, determined by the hydraulic con- relative degree to which surface water flows to- ductivity of the sediment for unsaturated condi- wards the unsaturated and saturated storage tions. The unsaturated hydraulic conductivity (m. zones in the transition from significant depths of d -1) for each habitat (sediment) type is de- ponded surface water to little surface water and creased from the saturated hydraulic conductivity increasing depths of unsaturated storage: as a function of decreasing sediment moisture (unsat_moist__prp). This (0-1) multiplier varies sat us unsat = 1/exp(100* max((Sfwt_depth with soil type (Dominico and Schwartz, 1990) as - unsat._depth), 0) ). (4) shown in Fig. 5. Downward percolation, then, is simply the cal- This equation allows for the presence of a vanish- culated hydraulic conductivity multiplied by the ingly small unsaturated depth (unsatdepth) in cell size (m2). When the water table rises (due to the presence of small depth of overlying surface groundwater inflow or percolation), the volume 274 H. C. Fitz et al. /Ecological Modelling 88 (1996) 263-295 of water held in pore space in the previously This (0-1) decoupling factor is an approximate unsaturated zone is incorporated into saturated scaling measure that varies with gross canopy water storage. Thus, the total flux of water from morphology, with forests generally being near 0.2 the unsaturated to saturated zone (m 3. d -l) is and grasslands being near 0.8 (strongly decou- the sum of percolation and that due to groundwa- pled). The decoupling factor will be discussed ter inflow. further in the context of sensitivity analyses. Loss of water by plant transpiration occurs The equation below determines the relative either from the unsaturated or saturated water importance of these controls in determining po- storages depending on the presence/absence of tential transpiration (m. d -~) for a unit area of roots within the zone. The GEM has a gradation plant canopy: between physical and biological controls on this transp._pot flux term, dictated by the vegetation type, water availability, and model scale. There are two basic = ( transp._canop( 1 - maccanopdecoup) mechanisms of evaporative loss through the plant • mac wat str_cf+ evap_pot canopy. First, the degree of coupling of air masses . mac canop decoup ) in the canopy and the lower atmosphere influ- ences the degree to which purely physical pro- • mac LAI (5) cesses (Eq. 3) drive the transpirative loss. Sec- where transp__canop is the canopy conductance ondly, the degree to which water is limiting, and (m. d-l), which varies from a plant's maximum thus stressing plants, simulates the reduction in rate depending on the atmospheric saturation transpiration (and thus primary production at deficit. The mac__canopdecoupl is the dimen- some point) due to stomatal closure and changed sionless decoupling factor for the macrophyte canopy conductance. canopy, mac wat_..str._.cf the dimensionless (0-1) In the general sense, transpiration is con- control function indicating the relative extent of trolled by canopy conductance, net radiation, the water stress of the plant, mac LAI is the variable air saturation deficit, temperature, and wind (linked to biomass) ratio of pTant canopy surface speed. The algorithm used in GEM depends on area to ground area, and evap__pot is the calcu- several factors associated with the plant assem- lated (Eq. 3) potential evaporation (m-d-l). blage and with the physical environment. Total Thus, transpiration potential may be significantly transpiration is determined along a continuum of controlled by plant responses to water limitations the relative importance of the physical versus the on one extreme of canopy morphology, but re- plant-related factors for the given ecosystem. spond primarily to radiative heat flux when the First, we calculate the part of the potential tran- canopy is strongly decoupled. spiration that is based on the leaf canopy conduc- Actual transpiration is a function of available tance, the water saturation deficit of the local water in the saturated and the unsaturated zones, (canopy) environment, and water stress of the partitioned relative to the depth to which roots plant. Next, the potential evaporation model (Eq. exist. When the root zone depth is greater than 3) is used to determine the potential rate of or equal to the depth to the saturated zone, all evaporative flux given the solar radiation, tem- transpiration flux is assumed to be from the satu- perature, humidity and wind speed. For the GEM, rated zone. As the saturated water table drops the degree to which these two processes control below the root zone, the roots draw water from the total transpirative flux depends on the extent the saturated zone via capillary action in an expo- to which the saturation deficit at the canopy nentially decreasing amount, with the remainder surface is decoupled from the saturation deficit in being drawn from the soil moisture in unsatu- the atmosphere above the boundary layer of the rated storage: canopy (Jarvis and McNaughton, 1986), here sat wt transp taken to be the mixed Planetary Boundary Layer on the order of hundreds of meters in height. = transp_pot, cell._.area H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 275

•exp ( - 10" max ( Unsat__.depth therefore assume that: (1) water density is constant; (2) surface tension is negligible; (3) Coriolis - NPhBio_root_depth, 0)), (6) force is negligible; (4) only one set of waves is where sat wt transp is the actual transpiration considered at a time; (5) the sediment surface is a flux from saturated storage (m3 . d-~), horizontal, fixed boundary that does not absorb NPhBio__root_depth is the root depth (m), and energy; and (6) wave amplitude is small and the transp._pot is the potential flux (m" 0-1); a com- wave form invariant within the time and space plementary relationship exists for flux from the scales considered. While the first three assump- unsaturated storage. tions are reasonable for most situations, assump- In the GEM, horizontal flow of water in satu- tions 4 through 6 involve issues of the area con- rated storage is assumed to be steady, unidirec- sidered in the model, and can be considered tional flow in an homogenous, unconfined aquifer. reasonable in most situations if sufficiently small The basic Darcy equation is applied to flux be- cells are used in a spatial model. Factors within tween two cells as follows: the equations of motion not relevant to coastal Sat_wt._flow and shallow water conditions are not considered. Wave predictions and formulae are based on the ( tot_water head - tot_.watheadExt) axioms of linear wave theory (USACOE, 1984). cell width . sat_hydr__.conduct, cellwidth 3.1.3.1. Wave and current simulation. Wave dynamics in GEM are estimated by wave prediction • satavghd, (7) equations for transitional water depth in which where Sat_wt_.flow is the net flux of water (m 3 • the depth :wavelength ratio is between 1 : 25 and d- 1) into or out of the cell, tot water head is the 1:2 (USACOE, 1984). These equations are used total hydraulic head (m) and is the sum of the to estimate significant wave heights based on saturated water head plus the surface water fetch within a grid cell and wind speed. Linear depth, for the case when the saturated water wave theory makes use of these wave heights to height reaches the sediment surface• The calculate wave dynamics such as orbital velocities tot wat headExt is the analogous total water and wave energy. We use USACOE (1984) for hea-d (m) of an external cell, cell width is the determining the wave height and period in the width (m) of a square grid cell, sat~hydr__.conduct following series of Eqs. 8-10. After determining is the saturated hydraulic conductivity (m. d-l), the fetch distance for a given wind direction and sat_.avg_hd is the average hydraulic head of within the cell, a local wave height is calculated the water in saturated storage (m) in the two based on wind speed, fetch distance and water cells. The total water head is used to accommo- depth. Both of the latter corrections convert dis- date any difference in elevation among two cells tances into dimensionless parameters using the when surface water is present to alter the hy- gravitational constant. For instance, the dimen- draulic gradient. sionless depth parameter used in determining local wave height is determined by: 3.1.3. Hydrodynamics Sector Sf__wt_depth . G In shallow surface water (< ~ 3 m), the GEM D less_depth = Wind speed 2 , (8) simulates the hydrodynamics associated with the transfer of wind energy to water and calculates the stress effect of wave- and current-induced where Dless__depth is the dimensionless fetch turbulence near the bottom sediments. This tur- parameter, Sf_wtdepth is the distance of open bulence drives the suspension and deposition of water over which waves travel (m), G the gravita- sediments, which in turn affects water clarity tional acceleration (m-s-Z), and Wind_speed is within the system. We envision the GEM as a in m • s-~. We developed a graphical algorithm to terrestrial and wetland modeling system, and approximate an intrinsic hyperbolic tangent func- 276 H.C. Fitz et al./ Ecological Modelling 88 (1996) 263-295 tion needed in the calculation of wave height, tanh(X), where X is any expression. This algorithm is then used to calculate intermediate parameters involving depth and fetch parameters, + exp ( - 2. PI. Sf__.wt_depth solving the following relationship: (12) depth H corr = tanh(0.530 . Dless__depth°75), where Wave_height is the actual wave height (m), (9) and Sf_wt_depth is the depth of the surface where depth H corr is the intermediate result water (m). involving the hyperbolic tangent of the dimensionless depth parameter; tanh, the hyperbolic 3.1.3.2. Shear stress. Shear stress is used to calcu- tangent function; and 0.530, an empirical con- late the amount of sediment suspended above stant. A similar technique is used to determine a threshold resistances in the Inorganic Sediments second intermediate result involving fetch, Sector and the Deposited Organic Matter Sector. fetch H corr. These intermediate results are then This version of GEM does not account for ero- used in solving the following equation for local sional and depositional processes in streams. wave height: Shear stress is calculated as a function of the wind-induced wave orbital motion modified by Loc_Wave_height any current (Grant and Madsen, 1979). = (0.283" Wind_._speedZ.depth H corr Shear stress •fetch H corr)/G, (10) = 0.5 .friccoef. Fluid._.density where 0.283 is a dimensionless empirical con- • [1.0 + currentcorr 2 + 2.0 "current__corr stant. This local wave height is then expressed as •cos ( ( abs ( Current._direction wave energy (USACOE, 1984). The actual wave - Wind_.direction )" 0.8))] height (Wave__height) within the system is calculated by combining the local wave height with •abs ( Wa ve_orbitvelo ), (13) wave energy propagated from outside the cell, and energy dissipated due to bottom friction. where fric__coef is the friction coefficient that The wave period is determined from algo- varies with the extent to which the turbulence is rithms similar to those used in wave height calcu- due to wave rather than current velocities, lations (USACOE, 1984). The wave period is Fluid_density is the density of water (kg. m-3), determined by: current corr is the ratio of current velocity to wave orbital velocity, and abs(expression) is the Wave__period = (7.54. Wind__speed. depth_T corr function that returns the absolute value of the •fetch T corr)/G, (11) expression in parentheses. where depth T corr and fetch T corr are the 3.1.4. Inorganic Sediments Sector intermediate results involving depth and fetch. This sector includes a state variable for de- The wave_Length is also calculated based on posited (DEP INORG_SEDS) and for sus- USACOE (1984). We then determine the wave pended (SUS INORG SEDS) sediments that orbital velocity for waves in water of transitional represent an aggregate of all sizes of mineral relative depth using (USACOE, 1984). particles. Deposited inorganic sediments are sus- Wave orbit velo pended in the presence of surface water as a Waveheight. G . Wave_period function of the shear stress calculated in the Hydrodynamics Sector. As described in the Hy- 2" WaveLength drodynamics Sector, a shear stress due to waves H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 277 and currents is determined for each time step. and the inorganic sediment (without pore space) This shear stress on the sediments is compared to is determined from the mass and the standard a shear resistance value. Soil shear resistance density of the organic and of the inorganic con- varies with habitat and is expressed using an stituents. The total sediment volume is then the algorithm composed of the root density of macro- sum of the volume of inorganic sediment/soil, phytes and the inverse of the proportion of or- plus the volume of the organic component, plus ganic material in the sediments. Sediment sus- the pore space volume. Over long time scales, pension depends on the extent of erosion during sediments can also downwarp, moving part of the the prior time step. If the potential erosion at sediment/soil down below the base datum of time t i is less than that which occurred one time reference, thus effectively being lost from the unit previously ti_ 1, then no erosion will occur system. We describe this as a simple constant (sediments underlying the eroded material are rate: assumed to be more consolidated and less erod- DIS dn warp able). However, a layer is subject to erosion if the erosion potential is greater than that during the = rcdownwarp • cellarea prior time step: • ( 1.0 - Porosity ). DISpartdensity, (15) eros = max [ PotEros - delay(Pot__.Eros,a), 0] where rc__downwarp is the rate of geologic down- warping (m. d-l), porosity is the proportion of • cellarea, (14) sediment/soil structure that is occupied by pore where eros is the volume (m 3) of (organic and space, and DIS._partdensity is the average den- inorganic) sediment that is actually eroded in one sity of inorganic material in the sediments (kg. time unit, Pot Eros is the depth (m) of (organic m-3). These dynamics of sediment elevation are and inorganic)-sediment that may be potentially most important in coastal areas in relation to the eroded due to the difference between shear stress height of the surface (sea) water. and shear resistance, and cell area is the surface area (m 2) of the cell. In thisexample, the delay 3.1.5. Chemical Constituent Sectors: general dy- function, which is intrinsic to STELLA, returns the namics value of Pot eros from the prior (1) time unit. The three model sectors involving salts, inor- The mass of inorganic sediments eroded are de- ganic nitrogen, and orthophosphate share a vari- termined by eros by the proportion of sediments ety of common structures and logic. Each is di- that are inorganic, and their bulk density. vided into those portions that are dissolved in Suspended inorganic sediments that enter a surface water (constituent SF WT) and those cell as a function of the surface water inflow and that are dissolved in sediment/soil pore water outflow can be deposited from the suspended (constituent_SEDWT), the latter being the total stock when shear stress is less than fluid yield. of saturated and unsaturated water storage stocks. The fluid yield is the minimum shear stress value The concentration of dissolved constituents is at which a particular mud/sediment concentra- assumed to be distributed homogeneously through tion can be kept in suspension. To obtain this their storage volumes. All constituents dissolved fluid mud yield, the concentration of mud is in surface water and saturated water can move multiplied by 10 to account for increases in con- into and out of the cell determined by their centration when the water column becomes strat- concentration in the water volumes of the hori- ified during low energy conditions. zontal water flows described in the Hydrology The sediment depth may change due to de- Sector. Similarly, advective vertical movement of composition of organic material and the suspen- dissolved constituents are controlled by calcu- sion/deposition of sediment/soil. We dynami- lated water flows, in addition to diffusion across cally determine sediment elevation depending on the surface water-sediment/soil water gradient. the sediment volume. The volume of the organic Diffusion is generally small relative to the advec- 278 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 tive fluxes, and is modeled by the difference in mined by means analogous to those for surface concentration multiplied by the diffusion coeffi- water phosphorus, with the replacement of algae cient for the constituent across a 1-cm distance. and suspended organic matter by macrophytes We assume that the vertical fluxes of dissolved (Macrophytes Sector) and deposited organic mat- constituents between the unsaturated and satu- ter (Deposited Organic Matter Sector), respec- rated zones is rapid enough for equilibrium to tively. Mineralization and biotic uptake of nutri- occur between the different dissolved compo- ents in the sediment/soil aerobic zone are verti- nents in the vertical sediment/soil profile. Be- cally stratified processes. However, the model cause of the assumed homogeneity of concentra- assumption of equilibrium within this zone ap- tion in both the saturated and unsaturated water pears reasonable when most of the dynamic pro- components, a loss of chemicals such as nutrients cesses occur within the shallow, upper zone of via saturated (groundwater) flow also decreases the profile. the concentration in the unsaturated water zone. Adsorption and desorption of phosphorus to soil particles in the sediment also assumes equi- 3.1.6. Salt Sector librium conditions over daily periods. This pro- The dynamics in this sector are those de- cess is modeled by: scribed above for the general model of con- P04 sorbtion stituent flows. Although salts are not actively =P04 K" (P04 sed wt conc °8) taken up or released by the biotic components in the GEM, they may affect certain biological pro- • DEPOS_ORG_MAT - PO4_SORB, cesses and the habitat type. This is one example (16) of where a sector structure is established for where PO4 sorbtion is the daily net mass flux of future use, e.g., salinity constraints on macro- PO 4 among the PO4 SED WT (kg PO 4) and the phyte growth. mass of phosphorus so-rbed to sediments PO4 SORB (kg pO4), P04 K is the phosphorus 3.1.7. Orthophosphate Sector sorpTion coefficient (m-~ • kg-1) for the Phosphorus is one of two nutrients that can DEPOS_ORG MAT, P04 sed wt conc is the potentially limit the growth of plants in a GEM concentration of PO 4 in the sediment/soil water simulation. Available inorganic phosphorus is (kg" m-3), and DEPOS ORG MAT is the mass simulated as orthophosphate. In addition to the (kg) of deposited organic matter (Deposited Or- general constituent dynamics outlined above, ganic Matter Sector). there are losses due to plant uptake and gains due to decomposition of organic material. 3.1.8. Dissolced Nitrogen Sector Phosphorus dissolved in surface water The other potentially limiting nutrient is nitro- (PO4 SF WT) may increase as a result of the gen. Dissolved inorganic nitrogen is stored in nutrient concentration in rainfall. PO4 SF WT surface water (DIN SF WT, kg) and sediment uptake is directly linked to the amount of carbon water (DIN_SED WT, kg). NO~, NO 3 and NH~- fixed by algae (see the Algae Sector) and its are aggregated into one value of nitrogen to carbon to phosphorus (C:P) ratio. Likewise, the represent all forms of nitrogen that are directly rate of decomposition of organic material sus- available for plant uptake. There are a number of pended in the water column (Suspended Organic redox reactions that determine the species of Matter Sector determines the rate of remineral- nitrogen present in a given type of environment, ization of PO4 SF WT via the C:P ratio of the and thus the extent to which the inorganic nitro- organic material. Currently, the detrital and algal gen is available for plant uptake. We assume that C: P ratios are not temporally dynamic in the the proportion of the available inorganic nitrogen model and vary only by habitat type. is a function of particular environmental condi- Uptake and mineralization of phosphorus in tions that are typical for different habitats (e.g., the sediment water (PO4 SED WT) are deter- anaerobic sediments, aerobic water column, and H.C. Fitz et al./ Ecological Modelling 88 (1996) 263-295 279 shallow aerobic sediments)• It is also assumed where Alg._.gross_PP is the flux of carbon fixed that the daily concentrations of NO3-N in the by algae (kg.d-1), rc alg prod is the specific surface water and NH4-N in the sediment water rate of carbon fixation (l/d), alg_max is the are in equilibrium. maximum biomass of algae (kg), and alg._.prod._fb The primary functional difference between the is the (dimensionless) control function incorporat- simulated dynamics of phosphorus and nitrogen ing environmental factors. This combined func- is the addition of denitrification losses from the tion is a multiplicative expression that has 3 con- sediment water storage• Gaseous denitrification trol functions of light intensity, temperature, and losses occur in the anaerobic portion of the sedi- nutrient availability. ment profile, the depth of which is determined in The dimensionless control function due to light the Deposited Organic Matter Sector• Denitrifi- intensity in the water column is based on the cation is determined by: Steele (1965) photoinhibition formulation inte- din sed wt denitrific grated over depth (Bowie et al., 1985): = sed anaerob vol" DIN sed wt conc alglight_.cf • rc DIN denit" 1.2 (min(wat-temp-Tc'O'O)), = 2.718 ( daylength/24 (17) mide~ ~inct ) where sed anaerob c,ol is the volume (m 3) of the water in ~he anaerobic layer in the sediments, • exp alg sat light "exp(-lightextinct DIN sed wt conc the concentration (kg. m -3) of DIN in the sediment water, rc DIN denit is ) (-incidentlight)] the specific rate (I-d -~) of denitr]}ication, •midepth) - exp alg sat light (19) wattemp is the water temperature, and Tc is the critical temperature, at which denitrification is at where midepth is the midpoint of the surface its maximum rate. water depth (m). The light_extinct variable is the 3.1.9. Algae Sector light extinction (l/m) resulting from concentrations of algae and suspended organic and inor- This sector contains one state variable which ganic matter, and is determined by multiplying may be used to represent either phytoplankton or the concentrations by the appropriate extinction periphyton/algae. If both types of communities coefficient. The incidentlight (kcal. cm -2. d -l) are to be included, then the sector as described is light reaching the water surface, and is deter- here for phytoplankton is duplicated and modi- mined by solar radiation at ground surface level fied to remove flows with surface water runoff (SolRadGrd), corrected for shading by macro- and depth of residence of the community (be- phytes. The alg sat light is the saturating light nthic vs. within the water column)• Carbon fixa- intensity for algae (kcal • cm- 2. d- 1). tion in primary production increases the aggre- The temperature control function, based on gate value for organic carbon in algal biomass Lassiter (1975), describes the biological responses (ALGAE). to temperature in the other living biotic sectors, Growth of the standing stock of algae is de- with an example shown here for algae: scribed by a maximum growth rate multiplied by the standing stock, a density-dependent feedback, Algtempcf = exp[ C( H2O temp - Tot,) ] and a control function involving several environmental parameters: ( Tm,- H2Otemp ) c(rmx-r°p~, Alg_gross PP = rc alg prod. ALGAE x rmx - Top ALGAE (20) where C is a curvature parameter, H2Otemp (18) the water temperature, Tmx the maximum tern- 280 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 perature (°C), and Top the optimal temperature and the concomitant carbon:nutrient ratios in (°C). This constraint rises to 1 at the optimal subsequent detrital dynamics from the two stocks. temperature at an exponential rate which de- As in the Algae Sector, this sector aggregates all pends on a curvature parameter. The interval macrophyte species into one stock using weighted width between the optimal temperature (re- averages for the parameter values. sponse = 1) and maximum temperature (response Biomass is added to the sector through the = 0) determines the rate at which the function photosynthetic pathway that determines net pro- decreases to 0. duction of MAC PH BIOMAS, with the maxi- Nutrient limitation is based on the standard mum rate of net production limited by a multi- Michaelis-Menten relations for nitrogen and for plicative environmental control function that in- phosphorus. The formulation assumes that one cludes light, nutrients, temperature, and water. nutrient is most limiting: Using a form similar to Eq. 18 for algal gross Algal_._nut._cf production, the rate is further constrained by maximum density considerations. The light con- [( DlN_sf. wtconc) trol function is based on the Steele (1965) for- = min DIN sf._wtconc + DIN._half ' mula representing the effects of photoinhibition, without selfshading: POasf. .wt conc 1] mac light_.cf PO 4_.sf_wt__conc + PO 4__half ] ] ' (21) SolRadGrd [ SolRadGrd where DIN_sf. wt conc and PO4_sf. wt conc are = exp l- --- the surface-water concentrations (g. 1-1 =kg. mac sat light ~ mac sat l--~ght ) ' m -3) of inorganic nitrogen and phosphorus, re- (23) spectively, and DIN_half and PO4_half are the half-saturation constants for the respective nutri- where mac sat light is the saturating light inten- ents. sity (kcal-cm -2. d-l), and SolRadGrd is solar Export and import of phytoplankton biomass radiation (kcal.cm-Z.d -1) received at ground depends on the direction and magnitude of the level (see the Global Inputs Sector). associated water flux and ingestion by consumers. The nutrient control function is similar to Eq. The rate of algal mortality is constant when water 21 for algae, but uses nutrients in the surface is present, but increases to a high value near 1.0 water instead of in the sediment water. The tem- when the algae are exposed to desiccation. The perature control function also uses the form of standard respiratory losses for biotic components that in the Algae Sector, but replaces water tem- in the GEM has the form: perature with air temperature. Water availability to plants is a dimensionless Alg._.resp = rc alg resp " algtempcf . ALGAE, (0-1) function of the soil moisture, the depth of (22) the unsaturated zone and the root depth: where rc alg resp is the maximum specific rate water avail cf of respiration, and (1. d-l), algtemp._fb is the = mini1.0, unsatmoist__prp dimensionless temperature control function analogous to Eq. 20. + exp ( - 10. max ( unsat_depth - NPhBio__rootdepth, 0)) ], (24) 3.1.10. Macrophytes Sector Macrophytes are modeled using two state vari- where unsatmoist._.prp is the (dimensionless) ables, photosynthetic (MAC PH BIOMAS) and moisture proportion in the unsaturated zone of non-photosynthetic carbon biomass the sediment/soil, unsat_depth the depth (m) of (MAC NOPH BIOMAS). This partition is used the unsaturated zone, and NPhBioroot_depth to represent variations in plant carbon storage the root depth (m) of the macrophytes. Water is H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 281 not limiting at all (returning 1.0) if the roots reach the saturated zone• When the unsaturated ...... 0.000 0,000 0.005 0,545 water table is shallower than the root zone depth, , i i/ ~ : ~ ~ .i.i ...'o.,07 0.635 ~' .... :: i : : ! "~,i :: 0.250 0.060 the value returned is the unsat acail water pro- ...... 0.333 1.000 " ::~' ..... ~] 0.417 ;0.995 portion plus an exponentially decrea~-ng amount 0.500 0.910 from the saturated zone• Thus water may be - t00070.583 o0.005 35 I 0.750 0.660 available to the root system when the roots do ...... 0,833 0,590 0.917 0.520 not reach the saturated zone due to the capillary I 0.000 -' : : ..... 1.000 0.475 ' ';il I'@ ' ' Paints:f13 draw of water from a nearby saturated layer• 0.000 .000 Oata Edit Output: Ii__ Shoot growth is related to simulated net pro- mac_rel_biomass duction, but is used in determining the extent of Io equation ~ [ Delete graph ) ~1 translocation between the photosynthetic and nonphotosynthetic stocks• Fig. 6. The STELLA dialog box containing the relationship between the ratio of the current macrophyte biomass to its PhBio._.shoot._.grow maximum (mac tel biomass) and the ratio of the number of = rc PhBio NPP" MAC PH BIOMAS stems or trunks to its maximum (mac tel #dens). • PhBio shoot seas photosynthetic module is assumed to occur at a constant rate. The effects of salinity and other - 1- PhBio_max ' factors simulated in the model could be incorpo- where PhBio_shoot_.grow is the biomass increase rated into a control function depending on the (kg-d -1) in the MAC PH BIOMAS (kg), model requirements• rc PhBio NPP is the maximum specific rate (d -1) The carbon : nitrogen : phosphorus (C : N : P) of-net production (used in the photosynthetic ratios of MAC NOPH BIOMAS and MAC pathway above), PhBio shoot seas is an empiri- PH BIOMAS are different, but do not change cally derived (0-1) funci~on that operates primar- for a given habitat (plant) type. The significance ily during peak periods of new-shoot develop- of these ratios lies principally in their influence ment, and PhBio max is the maximum photo- on the rate of decomposition (described below). synthetic bioma'-ss (kg). If shoot growth Consumers ingest both types of biomass depend- (PhBio_.shoot_grow) requires more carbon than ing on their relative availability. Fire (described is fixed in the photosynthetic pathway simulated below) may also burn both types of biomass de- above, that carbon is translocated from the avail- pending on their fuel quality and content, as able nonphotosynthetic pool. That available re- determined in the Fire Sector• serve of labile carbon is calculated by Macrophytes have direct feedbacks on the NPhBio avail (using the form of Eq. 31) multi- physical environment that are important to over- plied by the proportion of labile carbon in plant all model dynamics. The areal density of stems biomass for the habitat. If carbon fixed by the and trunks is calculated based on data for the photosynthetic pathway is in excess of that needed plant type such as those shown in Fig. 6 based on for net growth of shoot and leaf biomass, that Steward and Ornes (1975) for a subtropical sedge. carbon is translocated to the nonphotosynthetic These data and the plant height are used in stock, thus assuming a homeostatic mechanism determining a Manning's roughness coefficient between roots and shoots. (see the Hydrology Sector) for the system's (cell's) Mortality within the photosynthetic stock is community type. determined from seasonal cues and current water stress. The maximum specific rate of mortality is 3.1.11. Suspended Organic Matter Sector limited by the unweighted average of seasonal The stock of suspended organic matter litterfall (from empirical data) and water stress (SUS ORG MAT) in this sector includes an ag- limitations (both range 0,1). Mortality of the non- gregate mass of live and dead organic matter 282 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 suspended in surface water. As indicated in the is described in the Deposited Organic Matter Inorganic Sediments Sector above, the GEM is Sector• designed to be able to simulate the dynamics of Outflows from this stock include decomposi- suspension and deposition of both organic and tion, deposition, consumer ingestion, and export inorganic material. Thus, for the purposes of with surface water. Decomposition is implicitly tracking such changes in the sediment/soil depth driven by the microbial community, with no inter- via suspension and deposition, the units for the nal feedback mechanism or recycling within the suspended (and deposited) organic material stocks sector• This mineralization of organic material is are in mass of total organic matter, as opposed to assumed to be an aerobic process in the water only organic carbon. The GEM assumes that the column, and thus there are two control functions stock of suspended organic matter is homoge- in the decomposition equation: neously distributed throughout the water column, SOMdecomp and that organic material of all size fractions have the same characteristics• = rcdecomp • SUS_ORG MAT Mortality of algae, macrophytes, and consumers, along with consumer egestion, are inputs • decomp._temp_cf, rain - ,1 , to the Suspended Organic Matter Sector• The SOM NCop, ratios of carbon to organic matter for these living (27) carbon stocks determine the mass of total organic material associated with each input. Depending where rc_decomp is the maximum specific rate of on the habitat and thus the type of living plants decomposition in aerobic conditions (d -~) and organisms, specific proportions of the organic SUS ORG MAT the biomass of organic matter mortality pool are then allocated to either sus- (kg O-M), d~comptemp._.cf a temperature control pended, deposited, or (in the case of macro- function (Eq. 20), and SOMNC and SOMNCop t phytes) standing dead detritus• For example, sus- the current and the optimal nitrogen:carbon sub- pended organic matter input to this stock from strate ratios, respectively• consumers (kg. OM- d-l) is given by: Suspended material can flow into and out of the system with surface water flux determined in S OM__fr__consum the Hydrology Sector• Ingestion of suspended or- = Cons_prop to SOM ganic matter is controlled by the consumption ( cons mort_biom + consegest ) rate determined in the Consumer Sector, assuming complete availability of this resource to the Cons C to OM , (26) consumers. Deposition of organic matter is con- where Consprop to SOM is the dimensionless trolled by the shear stress calculated in the Hy- proportion of consumer losses that is directly drodynamics Sector. If the shear stress is below a allocated to the suspended stock, threshold value, then all of the suspended organic cons mort biom is consumer mortality (kg. C" material is deposited in one time step. Above the d-1)_consegest is the egestion by consumers threshold, a constant proportion of the organic (kg. C. d-i3, and Cons C to OM is the ratio of material is deposited in each time step. carbon to total organic matter of consumers (kg C • kg OM-I). The complement of 3.1.12. Deposited Organic Matter Sector Consprop to SOM is the proportion that is al- The organic matter (DEPOS ORG MAT) located to the deposited organic matter stock stock in this sector includes the mass of non-liv- (described below)• A similar relationship is used ing organic matter and of living microscopic de- for the flux of carbon due to mortality of macro- composers that are deposited into the sediment/ phytes and algae and due to degradation of soil complex• All non-living organic material is standing dead detritus. Inputs to this stock from included within this sector, from particulates to suspension of organic matter from the sediments dead plant roots. Thus, changes in sediment or- H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 283 ganic biomass are part of the sediment elevation DepOM_max_avail that is calculated in the Inorganic Sediments Sec- sed elev , DEPOS_ORG_MAT tor. Inputs to this stock are from deposition of suspended organic matter, mortality of macro- sed_._aerob__depthsed_elev ) ' (29) phyte nonphotosynthetic biomass, and from consumer mortality and egestion. Outputs occur via suspension, fire, decomposition, and ingestion by where DepOM_max_avail is the depth of sedi- consumers. ment that is accessible by fire and consumers of a Suspension and deposition are driven by the particular habitat. The mass of carbon available shear stress calculated in the Hydrodynamics Sec- to consumer ingestion is determined by the car- tor; deposition was described in the Suspended bon to organic matter ratio for the sediment type. Organic Matter Sector, and erosion was de- As with the inorganic sediments, there is down- scribed in the Inorganic Sediments Sector. How- warping of organic sediments past the base da- ever, decomposition in sediments differs from tum of measurement. that in the water column due to the extent of the aerobic/anaerobic zonation of the sediments. 3.1.13. Standing Detritus Sector Decomposition in the sediments takes the same Dead organic matter attached to plants or basic functional form as decomposition in the earth, and which can not be moved under normal water column, but with fluxes described sepa- hydrologic flows, is defined as standing detritus rately for the aerobic and the anaerobic zones. (STAND DETRITUS). This stock includes dead For the aerobic sediment/soil zone, an analogous standing grass and marsh grass leaves, snags, dead form of Eq. 27 was further constrained by: brush, matted leaf litter, and fallen stems and sed_aerob depth trunks. The stock is increased by plant mortality (28) sed elev • unsat moist prp, and decreased by fire, consumer ingestion, and where sed._.aerobdepth is the depth (m) of the fragmentation to the suspended or deposited or- aerobic layer and unsat_moist__prp is the (dimen- ganic matter stock. sionless) moisture proportion in the zone of un- Mortality of macrophytes is the only input to saturated water of the sediments. The depth of this stock, with the rate determined in the Macro- the aerobic layer is taken to be the depth of the phytes Sector. The flux from nonphotosynthetic unsaturated zone of the sediment plus a constant biomass is partitioned between deposited organic depth of a (habitat-specific) thin aerobic zone at material and standing detritus, whereas the flux the surface. Thus, in situations where the sedi- of dead photosynthetic biomass is partitioned be- ment is entirely saturated, a thin aerobic zone tween suspended organic matter and standing will be present. The same form is used for the detritus. anaerobic decomposition, replacing aerobic depth Wind and animal consumers contribute to the with the depth of the anaerobic zone of the fragmentation and shredding of standing detritus, sediments, and a dimensionless factor that re- whereby the standing detritus becomes part of duces the maximum anaerobic decomposition rate the suspended or deposited organic material. The from the maximum aerobic rate. Total decompo- rate of loss to suspended organic matter is calcu- sition in the sediment/soil is the addition of the lated as: aerobic plus the anaerobic fluxes. St det to SOM Not all of the deposited organic material is available to consumer and fire consumption. The = consingest std detr. StDet_shred to ingest mass of organic material that is available is: + STAND DETRITUS-0.9

DepOM_avail .max[1 max(wind storm-Wind speed,O) , t ~-- ~ 0 / =min(DEPOS ORG MAT wind__storm - windthresh J' (30) 284 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 where cons._ingest std detr is the flux of stand- (coNs)) • 1 ,OM tot C avail (32) ing detritus to consumer ingestion (kg-C. d-l), cons max StDet shred to ingest is the ratio of mass shred- ded to mass ingested, 0.9 is a calibrated rate where Constemp__cf is the dimensionless tem- constant (1-d-~), wind storm is the wind speed perature control function analogous to Eq. 20, (m. s-1) at which max'Tmal damage to standing rc._.consingest is the maximum specific rate of detritus occurs, and wind thresh is the threshold ingestion (d- ~), cons max the maximum biomass wind speed (m. s -1) below which wind does not of consumers for t-he modeled habitat, and affect the standing dead detritus. OM tot C avail the sum of all available carbon resources for ingestion (kg). Ingestion of each 3.1.14. Consumer Sector resource is then partitioned among the resources The consumer module represents an aggregate in accordance with availability. carbon mass of all consumers (CONS). At this Losses within the consumer stock include res- level of aggregation it is used primarily as a piration and mortality (including emigration), us- processor of organic matter, producing a time lag ing maximum specific rates that are constrained in the mineralization of nutrients. The consumer by the same form of temperature control function is omnivorous, ingesting all carbon stocks in the used in the Algae and Macrophyte Sectors. Eges- model with equal preference and has a maximum tion is a proportion of the material ingested, or rate of ingestion which is applied to all equations the complement of an average (carbon) assimila- of ingestion of resources. For each carbon food tion efficiency. source, the realized ingestion rate is limited by functions of temperature, the availability of that 3.1.15. Fire Sector resource, and density dependent regulation of the Fire can burn living and non-living plant consumer. biomass in GEM, whether the material is emer- The control function for the availability of a gent vegetation, peat or other organic material in particular resource X (kg organic carbon) to in- the soil. The probability of a lightning Strike is a gestion by consumers follows the general form of random function of time, using a pseudo random Wiegert and Wetzel (1979): number generator in STELLA. However, the X avail m threshold probability of a strike occurrence varies seasonally, allowing for varying probability distri- butions of fire source• The distribution of threshold values for a lightning strike is: • Xbiomass, (31) lightn._strike thresh where X~ is the saturation density of resource X ( DayJul ) at which ingestion by consumers is maximal, X is = 0.02. cos 36~ " 2" PI + 0.98, (33) the current density of the food resource, X r is the density of the resource at which consumption which ranges from 1.0 in January and December does not occur, and X biomass the standing stock (Julian dates 1 and 365) to 0.96 in July. If the of the resource X. This availability function is random number generator returns a value larger used for all living and dead food carbon re- than the threshold, a lightning strike is generated. sources. Ignition from a fire source and the rate of fire Total ingestion of combined carbon resources propagation within the system are calculated us- is: ing a formulation similar to the fire model of Consingest Kessell (1977). A state variable is used to store the attribute of a new lightning strike or a contin- = rain (Constempcf" CONS - rcconsingest ued fire presence• If this FIRE ORIG value is non-zero, then the fire spread rate across the H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 285 horizontal area of the system (m.d -1) is de- order of 70% of the Everglades (Loveless, 1959). scribed by: Sawgrass does well in an oligotrophic environ- fire spread__.rate ment with variable surface water depths that are characteristic of much of the Everglades (Steward = ( fuelheatcontent "fuelloading and Ornes, 1975; Herndon et al., 1991). However, •fire rx veloc .fuelmoist .fuelash._free) phosphorus appears to be a limiting nutrient for these marsh communities, and cattail (Typha sp.) • ( fuelbulkdens "fireheat__forignit) - ', is replacing sawgrass in some areas that are un- (34) dergoing apparent eutrophication (Davis, 1991, 1994)• The relative nutrient requirements of these where fuelheal._.content is the potential heat plants may be a factor in determining their rela- content of the fuel type (kcal. g-1), fuel_loading tive proportions in the marsh ecosystem. In the is the biomass of available fuel (g. m-Z), first set of sensitivity examples we compared the fire rx ~'eloc is the consumption rate of the fire model response to variations in plant nutrient (d-l), fuel_moist is a dimensionless function of requirements. the moisture of the fuel, fuel_ash_free is the The second major ecosystem type considered dimensionless proportion of the fuel that is or- in these simulation examples is that of a forested ganic material, fuelbulk dens is the effective ecosystem dominated by cypress (Taxodinum sp.). bulk density of the f'uel (kg-m-3), and Various forms of cypress communities exist in fireheat_forignit is the threshold heat required areas with hydroperiods (time of inundation) to ignite the given fuel (kcal • g-l). around 0.25-0.75 year, and plant production may Vegetation height and root depth modify the decrease by an order of magnitude if the soil is bulk density, with the effective bulk density being drained (Carter et al., 1973). Both the marsh and equal to the biomass of the fuel divided by the the forest ecosystem types may exist in proximity mean height and depth of the vegetation; higher to each other depending on a variety of controls densities slow down the spreading rate of fire. due to hydroperiod, fire and other environmental The algorithm for determining the moisture con- attributes (Duever et al., 1986)• In the second set ditions includes current rainfall, soil moisture, of sensitivity analysis examples, differences in and surface ponding; moisture can either prevent canopy morphology and their link to biological fire ignition, modify the rate of fire spread, or and physical controls on transpiration were com- extinguish a present fire. pared between model ecosystems• Although both are wetland systems, we used 3•2• Model dynamics them to indicate the ability of the GEM to simulate ecosystems with variable water tables whose We are in the process of parameterizing and range may include the lower water tables charac- calibrating the GEM for a range of ecosystem teristic of upland communities. The full set of types in regions in Maryland and Florida, US. sensitivity analyses and calibration for a large Prior to, and during this process we have been number of systems is beyond the scope of this testing its submodels and determining which pa- paper, and will be the topic of future manuscripts. rameters should be most closely scrutinized• The Our objective here was to indicate the range of basic sensitivity analyses that we present are a dynamics of the model and its response to spe- representative subset of those model analyses for cific parameter changes• These simulations were the Florida Everglades. not designed to incorporate finely calibrated re- These simulations were parameterized to rep- sponses, but rather to demonstrate the modeled resent two ecosystem types from the Everglades/ system behaviors. Big Cypress region. The fresh marsh system is All simulation runs were based on daily rate dominated by sawgrass (Cladium jamaicense), a parameters using a 0.5-d time step. One (repeat- perennial sedge that historically covered on the ing) year of rainfall, humidity and temperature 286 H.C. Fitz et aL / Ecological Modelling 88 (1996) 263-295

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0.00 I / i I I 1 I i i i gO 180 270 360 Julian days Fig. 8. A series of one-year model runs showing the sensitivity of hydrologic, macrophyte and nutrient variables to changes in the half-saturation coefficients of PO 4 for the Michaelis Menten uptake kinetics. Values close to 0.05 mg/l are in the range appropriate for the natural system. Higher and lower values show the model behavior to extreme nutrient limitation and low levels of limitation.

Fig. 7. (see p. 286.) A 4-yr run of GEM in a fresh marsh habitat, with selected hydrologic, macrophyte, and nutrient dynamics. The top graph shows the total water head relative to a constant (6 m) land elevation. The next graph contains (repeated, one-year) daily rainfall input and simulated transpiration. The third graph shows changes in macrophyte biomass density and the overall production control function (0-1 multiplier). The bottom panel shows the concentration of PO 4 dissolved in the sediment water and the resulting control function that is part of the macrophyte production control. 288 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 data was used to drive the model. Fig. 7 shows the simulations, whose results are summarized in some of the results from a four-year run for a Fig. 8. At the lowest K s value (0.001 mg/l), marsh habitat. The total water (Hydrology Sec- nutrients had some constraint on the growth away tor) head dropped below the land elevation in the from its maximum rate, indicated by the curve of spring dry period, then increased to flooded con- the production control function which includes ditions through the rest of each year in response controls from temperature, light, water and nutri- to precipitation and varying amounts of transpira- ents. Macrophyte biomass increased during the tion (and runoff, etc.). Seasonal changes in year-long simulation, with nutrients lowering in macrophyte biomass density were small, but concentration due to the relative uptake and min- showed a slight interannual decrease in response eralization imbalance. After significantly increas- to changing nutrient levels during the period of ing the plant requirements to a K s value of 0.045 this example.. mg/l, the macrophyte production was more limited than the prior run for most of the year. 3.2.1. Nutrient limitation Macrophyte biomass was less than that of the As described above, macrophytes are con- first run, and nutrient concentrations concomi- trolled by several functions, one of which is that tantly decreased to a lesser extent. Very little involving plant nutrient requirements. Laboratory change was observed in the water levels in the experiments indicated that cattails appeared to cell between runs, but transpiration losses were take up PO 4 at a faster rate than sawgrass, with a very slightly decreased with lowered plant lower saturation coefficient for maximum uptake biomass. An approximately 20% further increase rate (R. Reddy, Soil and Water Science Depart- in the K s value (to 0.055 rag/l) resulted in a ment, University of Florida, pers. commun.). Cat- further observable decrease in plant biomass, but tails appear to have better competitive ability large differences were not apparent in the pro- than sawgrass under enriched nutrient conditions duction control function, biomass, or nutrient (Davis, 1994), and may have higher transpiration concentrations between the two runs (using K s rates (Koch and Rawlik, 1993). Under different values that are near those for the marsh commu- ambient nutrient concentrations, the varying plant nity). Using a high K s value of 0.5 mg/1, plant growth response may alter the biomass of plants production was severely limited by nutrient levels, in a mixed sawgrass/cattail marsh, with associ- and plant biomass dropped rapidly, with nutrient ated changes in the water losses via transpiration levels remaining approximately level. Total water and overland flow. For this first model exercise, levels were higher during the dry season, with a we varied the Michaelis-Menten half-saturation significant decrease in transpiration losses. coefficients (K s) near the appropriate ranges re- ported for these plant species. In addition, we 3.2.2. Transpiration modified the coefficient significantly above and Evaporation and transpiration are known to be below the experimental values in order to explore critical "loss" components within the hydrologic the extremes that would mimic (a) relatively low cycle, particularly in areas such as wetlands where ambient nutrients and high plant requirements, water is generally stored at or near the land limiting growth, and (b) relatively high ambient surface (Duever, 1988; Ewel and Smith, 1992). nutrient concentrations with low plant require- Evaporation occurs from water in contact with ments. the atmosphere, whereas transpiration is the simi- Four runs were made using half-saturation co- lar process of evaporation from plant tissues. efficients for the Michaelis-Menten kinetics of While there is a critical difference in that the nutrient limitation on net production (K s = 0.001, latter evaporative flux can be controlled by plant 0.045, 0.055, and 0.5 mg PO 4" 1-1). The nutrient physiology, the fluxes are often combined into concentration in incoming surface water was set one term, evapotranspiration (ET), for ease of equal to that currently in the system cell. There measuring or modeling. Depending on the scale were no other changes in input or parameters for of measurement, researchers have come to widely H.C. Fitz et al./ Ecological Modelling 88 (1996) 263-293 289 varying views on what controls the transpiration approach does not exist, and we agree with the part of this flux. As summarized by Jarvis and suggestion by Jarvis and McNaughton (1986) that MeNaughton (1986) meteorologists concerned quantifying the controls on transpiration depends with large-scale fluxes of water (over hundreds to on the scale with which one is addressing the thousands of meters distance) emphasize the objectives. evaporative energy and thus the heat and radia- We analyzed the total atmospheric water loss tive flux involved, whereas the stomata of plants for a GEM parameterized for a cypress- may control transpiration at some level in re- dominated community and for a sawgrass- sponse to differences in its internal and external dominated freshwater marsh. The sensitivity ex- environments. At the moment, a single "best" ercise indicates the range of relative losses in the

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Fig. 9. A series of one-year model runs showing the sensitivity of hydrologic and macrophyte variables to changes in the parameter representing the degree of decoupling of the canopy from the atmospheric saturation deficit. A decouple factor (range = 0-1) of 0.2 is typical of a forested canopy, whereas 0.8 is representative of a grassland type canopy. 290 H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 two different canopy types with changes in tran- tion dynamics, and nutrient cycling are the focus spiration-related parameters which include the of the model, which may operate for a single decoupling factor related to canopy morphology ecosystem or a cell in a spatial landscape model and the maximum rate of canopy conductance. with distributed ecosystem types. The range of For simplification, we parameterized the model scales and ecosystems for which the model is to represent situations where the maximum Leaf suitable depends upon the questions being ad- Area Indices (LAD and other pertinent parame- dressed, but this version is being applied to wet- ters were equivalent among the two communities land and upland terrestrial sites to evaluate basic (such as a may be the situation in sparse cypress system dynamics. The GEM requires a large scrub habitat). Thus, the transpiration sensitivity number (~ 100) of parameters that may change analyses only incorporate differences as a result with ecosystem (habitat) type, and ongoing sensi- of the identified parameter changes. tivity analyses indicate which parameters are most With the canopy conductance held at a refer- important to quantify for application to particular ence rate of 0.1 mol.m-2.s -1, varying the de- systems. The biological thresholds built into the coupling factor (Hydrology Sector) from that model make the model robust to changes in pa- characteristic of a marsh (0.2) to an intermediate rameter sets and constrain stocks to levels that (0.5) value resulted in a decreased transpiration are realistic, while control functions affect the loss in the colder months, and similar losses dur- biological and physical dynamics in accordance ing the dry season when the water table dropped with their basic underlying mechanisms. near or below the root zone (Fig. 9). This lowered Using this model formalism, we are imple- water availability decreased the plant production menting the GEM in a range of ecosystems and control function, a growth constraint that de- incorporating refinements where the need is indi- creased plant biomass during that simulation run cated. Changes to the model structure are easily compared to the prior run. A further increase in accomplished by duplicating or modifying the dif- the decoupling factor to that approximating a ferent sector modules. For example, explicit forested canopy further reduced the transpiration trophic dynamics would be incorporated into the losses in this particular analysis, resulting in a model by replicating the Consumer Sector and water table that did not reach much below the varying feeding preferences to represent different (0.3 m) root depth and no negative influence on trophic levels. Phytoplankton may replace algae the plant growth. In all three runs, transpiration by making such changes as the depth at which was linked to the saturation deficit and could be light is considered to control production in its potentially the same for the different canopy de- control function, and incorporating fluxes into coupling factors (such as shown for the fall pe- and out of the system with surface water. Fire riod). However, differences in canopy morphol- disturbances or hydrodynamic control of suspen- ogy altered the extent to which transpiration was sion of sediments may be unimportant to certain controlled by plant water stress and canopy con- model objectives and either made inoperative ductance, significantly modifying the transpira- within the model (by software commands), or the tion water losses in the GEM. sector modules may be easily deleted altogether. Control functions may be modified for sites that have different control mechanisms from the basic 4. Discussion set included in this version. Whereas salinity is currently used only as a tracer for spatial model The GEM was used to model ecosystem level application, an hypothesis of salinity effects on dynamics for different ecosystems. The simula- plant production could be introduced into its tion examples indicated the linkages and feed- control function as needed. Different versions, backs among the biotic and abiotic components and new sector modules, may be maintained of the model, which are the more critical features within the version control software component of of the model structure. Hydrology, plant produc- this general modeling system. H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 291

4.1. Comparative research that do not fully characterize the system dynamics. Field, laboratory, and model experiments can Two aspects of ecosystem comparison are most be usefully integrated into a comprehension pro- readily evaluated using this general model: across gram of ecosystem ecological research. In order ecosystems and across scales. We are using the to facilitate such integration, the GEM is a gener- GEM framework to evaluate our understanding alized model with an easily perceived, modular of different ecosystems in the Everglades and format and a graphical "map" of flows of matter other sites. Using field data from different and their mathematical controls. Within this ecosystems in a region, the model can be used as modeling environment, the model structure, re- a tool for synthesis and focusing research on the quirements, assumptions, and flaws-to-be-cor- more important processes for each system. rected are readily communicated to the research Whereas eutrophication appears to be a control community. We are using this framework to de- in the development of an Everglades sawgrass/ velop some level of consensus among the re- cattail system, salinity changes may be more criti- search participants on the level of effort needed cal to the development of an ecotone between to study different parts of an ecosystem. In one mangrove and marsh communities in south instance, we are structuring significant compo- Florida. Using available data, we can evaluate the nents of an Everglades research program (at the extent to which these processes are affecting the South Florida Water Management District) using ecosystems under different scenarios of nutrient information outlined by the GEM and its incor- inputs or water flows, comparing such processes poration into a spatial modeling system. More- as the relative transpiration losses in marsh and over, because of its designed generality and focus mangrove communities. on ease-of-use, the basic structure may be used at As part of a new Multiscale Experimental a variety of sites. Ultimately, the model may be Ecosystem Research Center (at the University of used to continually develop hypotheses concern- Maryland), we are using a GEM to evaluate ing the key variables in the structure and function various aspects of scale-effects on ecosystem be- of the system of study. In this context, a coupled havior. Using experimental ecosystems ranging modeling and field/lab research program may from microcosm to mesocosms to small water- provide a better understanding of the ecology of sheds (macrocosms), we can calibrate the GEM the ecosystem. at each scale and see how parameters change Such integration may be one of the greatest with scale. This may allow us to develop scaling strengths of modeling in ecosystem research. rules to extrapolate results to the landscape and Wiegert et al. (1975) initiated a salt marsh ecosys- global scales. The hypotheses to be tested involve tem model that continued to be developed over a the extent to which model algorithms and their decade (Wiegert and Wetzel, 1979; Wiegert, 1986) parameterization may effectively capture the as different hypotheses were incorporated in cross-scale behavior observed in the experimental modeling experiments and evaluated or further ecosystems. Whereas many of the components of parameterized from new field research. The US GEM are derived from calibration and partition- National Science Foundation's Long-Term Eco- ing methods (Rastetter et al., 1992), the experi- logical Research Program (LTER) of the 1980s mental outcomes of this exercise is intended to and 1990s has a commitment to develop long-term facilitate the use of literature and experimental ecological research in different ecosystems across data in models of varying scales. North America. The LTER sites have a basic set of core research topics (Callahan, 1984) aimed at 4.2. Ecosystem dynamics understanding ecosystem level processes, including: (1) pattern and control of primary produc- A model is never completely finished, as its tion, (2) spatial and temporal distribution of pop- use may indicate where knowledge of the ecosys- ulations selected to represent trophic structure, tem is incomplete or the aspects of the model (3) pattern and control of organic matter accumu- 292 H.C. Fitz et aZ / Ecological Modelling 88 (1996) 263-295 lation in surface layers and sediments, (4) pat- landscape mosaic affects the dynamics within the terns of inorganic inputs and movements of nutri- modeled region, and changing ecological pro- ents through soils, groundwater and surface wa- cesses may alter that landscape pattern via rule- ters, and (5) patterns and frequency of site distur- based transition algorithms. bances. The GEM incorporates most of these Various versions of the GEM are now being dynamics in its current structure at a scale that applied using the SMP at three different sites in may be useful for synthesizing site-specific knowl- the United States: Sawmill Creek, Maryland (22 edge, yet general enough to be used for across-site km 2 of a largely urbanized and degraded water- comparisons. The use of general models such as shed in inland Maryland), the Patuxent River the GEM for a range of applications should be watershed, Maryland (2400 km 2 of mixed forest considered an important component of develop- and agricultural uplands draining to wetlands and ing a holistic understanding of ecological pro- open estuary), and the Everglades/Big Cypress cesses, and their controls, in different ecosystems. region, Florida (10000 km 2 of mainly wetland habitats). The combined sites offer the opportu- 4.3. Landscape dynamics nity to test and develop the GEM in sub-tropical and temperate climate zones of open-water, wet- A model (such as the GEM) that assumes land and terrestrial ecosystems. homogeneity within set boundaries may be useful if the system boundaries are appropriately chosen for the stated objectives. However, the hetero- Acknowledgements geneity of large natural systems may significantly alter system dynamics as a result of interactions A copy of the GEM (that can be used either among the varying classes of objects in the sys- on a Macintosh or Windows platform) may be tem. Partitioning parameter values in accordance obtained from our WWW server with the follow- with some attribute class such as habitat or ing URL: http://kabir.umd.edu/MIIEE/MI- ecosystem reduces the aggregation problems in- IEE.html, or directly from the first author. The herent in large scale, lumped parameter models database for multi-system implementation and the (Rastetter et al., 1992). Thus, spatial models for version control history may also be obtained at heterogeneous landscapes hold promise to better this site. understand the interactions of the landscape pat- This work was supported by grants from differ- tern and associated ecological processes within ent institutions including: (1) the National Sci- the landscape components. We have developed a ence Foundation, grants titled: "Landscape Mod- Spatial Modeling Package (SMP), (Costanza and eling: the Synthesis of Ecological Processes over Maxwell, 1991; Maxwell and Costanza, 1994) for Large Geographic Regions and Long Time the development, implementation, and testing of Scales," R. Costanza and F.H. Sklar, Principal spatially explicit ecosystem models in a dis- Investigators, 1989-92; and "Responses of a Ma- tributed computational environment. The land- jor Land Margin Ecosystem to Changes in Ter- scape is divided into square grid cells of an ap- restrial Nutrient Input, Internal Nutrient Cycling, propriate scale, and the GEM (tested for each Production and Export", M. Kemp et al., Princi- ecosystem and translated into C source code) is pal Investigators, 1988-93; (2) The Chesapeake replicated as a unit model within each cell of the Bay Research and Monitoring Division, Tidewa- landscape. The unit model is differently parameter Administration, Maryland Department of terized for each cell's ecosystem type in the land- Natural Resources, "Development of the Patux- scape, and a configuration step allows the user to ent Landscape Model (PLM)," R. Costanza, Prin- link the unit model with spatial data from a GIS. cipal Investigator, 1992-93; (3) The South Florida This generates a dynamic spatial model with fluxes Water Management District, Everglades Re- of water and associated dissolved and suspended search Division, "The Everglades Landscape matter across cells in the landscape. Thus, the Model (ELM)," R. Costanza, Principal Investiga- H.C. Fitz et al. / Ecological Modelling 88 (1996) 263-295 293 tor, 1992-93; (4) the US Environmental Protec- established the goals and objectives for GEM, tion Agency, "The Multiscale Experimental provided guidance for parts of the model, edited Ecosystem Research Center (MEERC)," Univer- the draft, and provided through various grants sity of Maryland, R. Costanza et al., Principal the funding necessary to accomplish the work. R. Investigators, 1992-2002. Boumans provided the algorithms for the hydro- The GEM has been under development for dynamic sector and contributed to the sediment three years. During this time we have opened the and hydrologic sectors. E. DeBellevue provided model to input and criticism from various groups overall early conceptualization of the GEM and of environmental scientists and managers in a parts of the framework development, contributing consensus-building process. These include: (1) a generally to most model sectors and parts of the series of three workshops hosted by the South manuscript. C. Fitz developed a variety of compo- Florida Water Management District in W. Palm nents of the model structure, wrote most of the Beach, FL held in 1992; (2) a series of workshops final GEM equations, and wrote most of the conducted under the above NSF grant held in manuscript. 1991 and 1992 at (a) Chesapeake Biological Lab- oratory, University of Maryland, Solomons, MD, References (b) Baruch Marine Laboratory, University of South Carolina, Georgetown, SC, and (c) Coastal Allen, T.F.H. and Starr, T.B., 1982. Hierarchy: Perspectives Ecology Institute, Louisiana State University, Ba- for Ecological Complexity. University of Chicago Press, ton Rouge LA; (3) NOAA Estuarine Habitat Chicago, IL. Band, L.E., Peterson, D.L., Running, S.W., Coughlan, J., Program Workshops, held in 1992 in Silver Spring, Lammers, R., Dungan, J. and Nemani, R., 1991. Forest MD; (4) an ongoing series of workshops held in ecosystem processes at the watershed scale: basis for dis- 1992-1993, sponsored by the Multiscale Experi- tributed simulation. Ecol. Model., 56: 171-196. mental Ecosystem Research Center, Center for Binley, A. and Beven, K., 1992. Three-dimensional modelling Environmental and Estuarine Studies, University of hillslope hydrology.Hydrol. Processes, 6: 347-359. Bowie, G.L., Mills, W.B., Porcella, D.B., Campbell, C.L., of Maryland, at Wye, MD, and Cambridge, MD. Pagenkopf, J.R., Rupp, G.L., Johnson, K.M., Chan, We would like to extend our gratitude to the P.W.H., Gherini, S,A. and Chamberlin, C.E., 1985. Rates, many workshop participants who have con- constants, and kinetics formulations in surface water qual- tributed in many ways to this present version of ity modeling. US Environmental Protection Agency,Office GEM. of Research and Development, Athens, GA. Callahan, J.T., 1984. Long-term ecological research. Bio- Special appreciation is expressed to S. 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Sklar contributed to various early ver- Costanza, R., 1987. Simulation modeling on the Macintosh sions of the model and worked with the using STELLA. BioScience, 37: 129-132. manuscript text. L. Wainger contributed to the Costanza, R. and Maxwell, T., 1991. Spatial ecosystem model- hydrologic sector and edited drafts. T. Maxwell ing using parallel processors. Ecol. Model., 58: 159-183. contributed to early versions of several sectors, Costanza, R., Sklar, F.H. and White, M.L., 1990. Modeling coastal landscape dynamics. BioScience, 40: 91-107. and developed the framework for GEM spatial Costanza, R., Funtowicz, S.O. and Ravetz, J.R., 1992. Assess- application. He also wrote the STELLA-to-C ing and communicating data quality in policy-relevant re- translator for C versions of GEM. R. Costanza search. Environ. Manage., 16: 121-131. 294 H. C Fitz et al. /Ecological Modelling 88 (1996) 263-295

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