Modelling environmental heterogeneity in forested landscapes

Journal of Hydrology, 150 (1993) 717-747 0022-1694/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved

717

[3]

Modelling environmental heterogeneity in forested landscapes Ian D. Moore *'a, T.W. Norton a, Jann E. Williams b aCentre for Resource and Environmental Studies, Institute of Advanced Studies, The Australian National University, Canberra, A.C.T. 0200, Australia bEcosystem Dynamics Group, Research School of Biological Sciences, Institute of Advanced Studies, The Australian National University, Canberra, A.C.T. 0200, Australia (Received 4 September 1992; revision accepted 20 May 1993)

Abstract Models for estimating the spatial distribution of radiation, thermal and hydrologic regimes in topographically complex forested catchments are presented. These models use topographic attributes derived from a grid-based digital elevation model (DEM) as the primary input data. The models are based on simplified representations of the underlying physics of the processes, but include the key factors that modulate system behaviour. They represent an attempt to relate pattern to process. Model SRAD is an approximate method for estimating the spatial distribution of global short-wave radiation, net long-wave radiation, net radiation and maximum, minimum and average temperature, and accounts for the effects of topographic shading. Model WET estimates spatially distributed soil water content and evapotranspiration and catchment runoff`. SRAD and WET were applied to a 21.65 km 2 forested area within the Brindabella Range in south-eastern Australia to illustrate the potential applications of the approach. A 20 m x 20 m grid DEM was developed for the area. The computed radiation fluxes are consistent with measurements made at Canberra. The computed average annual runoff'conversionefficiency was 18.6%, which compares reasonably well with the annual runoff` conversion efficiency of 17.6% measured over an 11 year period on a 97.5 ha catchment located near the study area. The study area contains five main sub-alpine forest types, as well as a small area of exotics. The computed fluxes were used to characterize the fine-scale environmental heterogeneity and environmental domains of these forest types. Average minimum temperature in the coldest month (July) and annual net radiation were two environmental variables differentiating the occurrence of the three eucalypt species (Eucalyptus paueiflora, E. fastigata and E. delegatensis) investigated.

Introduction Many of the ecological patterns observed in landscapes result from common processes operating at various spatial and temporal scales. The nature of, and interactions between water, radiation, nutrient and * C o r r e s p o n d i n g author. Telephone: (06) 249 0660. Fax: (06) 249 0757.

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LD. Moore et al./ Journal of Hydrology 150 (1993) 717- 747

disturbance regimes are, for example, often critical in determining the composition, productivity and persistence of biotic assemblages in forests. At the micro-scale, combinations of these regimes may influence the types of plants that can occupy a site and their rate of growth and phenology. At the meso-scale, these regimes can markedly influence the floristic composition and structure of a forest. This, in turn, can influence the composition and species diversity of fauna using the forest and the quantity and quality of water flowing from it. An ability to characterize such regimes accurately is an important requisite for developing a predictive understanding of the relationship between environmental heterogeneity and ecological patterns and processes from the level of a forest site to a landscape. The concept of vegetation as a continuum with the composition of species changing along environmental gradients has been employed for some time as a basis for predicting plant distribution and interactions (e.g. Whittaker, 1967, 1975; Austin, 1971, 1979, 1987; Tilman, 1987; Williams, 1989; Westman, 1991; Oksanen and Ranta, 1992). In the developing field of landscape ecology, the effects of landform on ecosystem patterns and processes have been recognized (Forman and Godron, 1986; Bridgewater, 1987) and were categorized generally by Swanson et al. (1988) in their discussion of the ways in which geomorphic features of the Earth's surface can regulate the distribution of organisms and ecological processes. The term 'phytogeomorphology' was coined by Howard and Mitchell (1985) in recognition of the interdependence of plants and landforms. They stated that phytogeomorphology 'reflects those sensitive landform vegetation relationships that are visibly dominant in the landscape'. Similarly, 'hydrogeomorphology' refers to landform-hydrology relationships. Water is a major erosive agent and transporting mechanism for land surface processes, and water flow processes are significantly influenced by topography. In recent years, considerable progress has been made in the development of computer-based mathematical and computational techniques to model a number of climatological, hydrological, geomorphological and biological processes at various scales of analysis in terrestrial landscapes (e.g. Moore et al., 1988a, b; Davis and Dozier, 1990; Hutchinson and Dowling, 1991; Band et al., 1991, 1993; Moore et al., 1991, 1993; Quinn et al., 1991; Hutchinson et al., 1992). For example, Band et al. (1993) recently described RHESSys (Regional HydroEcological Simulation System), which is an integration of a forest ecosystem process model, FOREST-BGC (Running and Coughlan, 1988), and a spatially distributed hydrological model TOPMODEL (Beven and Kirkby, 1979). The model was used to examine hydrological and ecological linkages, and specifically to model forest canopy net photosynthesis and total evaporation. In RHESSys, landform elements defined by

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717-747

719

stream links and hillslopes represented the basic scale of modelling, with frequency distributions of key variables used to describe the within land unit (hillslope) variability. These techniques permit the characterization of environmental variation across regions with a precision and resolution previously unattainable, and have enormous potential application to the study and predictive modelling of ecological phenomena. This is particularly the case in complex terrain, where relatively small changes in slope, aspect and catchment area can markedly influence local climate and hydrology and fine-scale variation in biotic communities (Tajchman and Lacey, 1986). In this paper, we present a process-based approach to modelling soil water-plant terrain interactions in forests using a combination of this suite of bioclimatic, terrain, hydrological and ecological models. Our study site is the sub-alpine forests in the northern part of the Brindabella Range in south-eastern Australia. First, we examine the relationships between terrain complexity and environmental heterogeneity as defined by site radiation, temperature and soil water regime. We then present a preliminary analysis of the relationships between the spatial distribution of Eucalyptus communities and species in the Brindabella Range and the regimes characterized by environmental heterogeneity.

Terrain-based hydrological modelling for vegetation gradient analysis Contemporary studies of the processes affecting the distribution, productivity and interactions between vegetation along environmental gradients are likely to be more informative if these gradients are characterized more specifically and at a finer resolution than has typically been employed in the past. For example, rather than using elevation as a crude surrogate for spatial variation in temperature and/or precipitation in a region, it is more accurate to employ quantified gradients of these and other climatic attributes associated with elevation to model vegetation patterns. Similarly, rather than using estimates of spatial variation in mean annual temperature or rainfall, for example, as variables to model plant distribution, it is more realistic to use climatic indices that more closely reflect the ambient conditions to which plants are exposed (Austin, 1971). This is now possible at a fine spatial scale using computer-based mathematical algorithms and spatial analysis techniques, coupled to spatially related data sets including digital terrain models, to derive estimates of climate surfaces and various site attributes or indices of environmental processes that are considered indicative of landscape processes. Procedures to derive spatial and temporal estimates of various biophysical site-based and

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I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

catchment-based attributes which are relevant to vegetation gradient analysis are discussed below. Solar radiation dependent processes The surface energy budget is a driving force for evaporation and photosynthesis processes occurring at the land surface and is highly dependent on topography. Evapotranspiration accounts for a major part of the total water budget of a catchment. Vegetation diversity and biomass production have been shown to be related to radiation input (Hutchins et al., 1976; Austin et al., 1983, 1984; Tajchman and Lacey, 1986; Takahashi, 1987). The net radiative flux density, Rn, received by an inclined surface can be written as R n = (1 - c~)(Rair + Rdif q- Rref) -'k esLin - Lou t = (1 - c~)Rt + Ln

(1)

where c~is the surface albedo, es is the surface emissivity, Rdir, Rdi f and Rref are the direct, diffuse and reflected short-wave irradiance, respectively, for which Rdi r q- Rdi f q- Rre f ---- Rt, the global short-wave irradiance, Lin is the incoming or atmospheric long-wave irradiance and Lout is the outgoing or surface longwave irradiance, for which esLin - Lou t = Ln, the net long-wave irradiance. The long-wave irradiance components are approximated by Lout, i : ~soTs4i

t i n i = ~ a o r : i / y -F (1 - / ] ) L o u t , i

(2)

where ¢a is the atmospheric emissivity (a function of air temperature, vapour pressure and cloudiness), a is the Stefan-Boltzman constant, Ts is the mean surface temperature, Ta is the mean air temperature, and u is the skyview factor, which is the fraction of the sky that can be seen by the sloping surface (typically more than 0.9). A useful approximation is u = cos2(/3/2), where ,~ is the slope angle, but this is correct only for slopes that are unobstructed by surrounding terrain. We have developed an approximate method of calculating R n and its components at any point in a topographically heterogeneous landscape (the program is called SRAD), based on the work of Idso (1969), Kondratyev (1977), Dozier et al. (1981), Bristow and Campbell (1985), Isard (1986), P.M. Fleming (unpublished work, 1987) and Duguay (1989). The variables of the model, such as albedo, emissivity, sunshine fraction, mean air and surface temperatures, and clear sky transmittance, were varied on a monthly basis in the application described here. The short-wave irradiance components are calculated using the CLOUDY algorithm of P.M. Fleming (unpublished work, 1987) modified to account for the effects of shading from direct sunlight by surrounding terrain at enclaved sites via Dozier et al.'s (1981) solution of the horizon problem. The total short-wave

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717-747

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irradiance can be approximated by R t = ( R t h -- R d h ) f +

RdhtY nt- R t h ( 1 -- u ) c t

(3)

where Rth and Rdh are the total and diffuse radiation on a horizontal surface, and F is the potential solar radiation ratio (= Ro/Roh), which is the ratio of the potential solar radiation (Ro) on a sloping surface to that on a horizontal surface (Roh). The total and diffuse short-wave irradiances on a horizontal surface are often expressed as functions of the total and diffuse transmittances of the atmosphere and the potential solar radiation on a horizontal surface, Roh. These transmittances are functions of the thickness and composition of the atmosphere, particularly the water vapour (i.e. cloudiness), dust and aerosol content (Hounam, 1963; Lee, 1978). The potential solar radiation, Ro, is the radiation received at a sloping site in the absence of the atmosphere, and can be expressed as 24I Ro = ~2r2cos qScos ~(sin r / - r/cos r/)

(4)

where I is the solar constant, ~ is the solar declination, r is the ratio of the Earth Sun distance to its mean, and q5 and r/are functions of the terrestrial latitude and the topographic attributes of slope,/3, and aspect, % respectively (Lee, 1978). Eq. (4) can be numerically integrated over any time period ranging from 1 day to 1 year to estimate the seasonal potential solar radiation on an inclined surface. Hence, on a given catchment, the variation in potential solar radiation over the catchment is a function of only slope, aspect and the time of year. The potential solar radiation ratio, F, has been used widely in hydrological and ecological contexts as an approximate method of examining the spatial distribution of radiation across a catchment (Lee, 1978). The potential solar radiation ratio in combination with the wetness index also has potential for characterizing biological distribution and species diversity (Moore et al., 1988b).

Temperature The spatial distribution of minimum, maximum and average air temperature is computed using a modification of the simple approach proposed by Running et al. (1987), Hungerford et al. (1989) and Running (1991). It corrects for elevation via a lapse rate, for slope aspect via the ratio of short-wave radiation on a sloping surface to that on an unobstructed horizontal surface, S, and for vegetative effects via a leaf area index, LAI. In the southern hemisphere, this approach increases temperatures on north-facing slopes and decreases temperature on south-facing slopes relative to a flat surface. This effect is greatest on

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LD. Moore et al./ Journal of Hydrology 150 (1993) 717 747

poorly vegetated slopes (low LAI) and negligible in closed forests (high LAI). The temperature, T, at a site i can be written as T i = T b - Tlapse(Zi -

Zb)/1000 +

Ti :

Zb)/1000-~-i

T b - rlapse(Zi-

CISi(1

LAIi LAimaxj for

Si > 1

LAIi _~ 1 -~ LAlm~xJ for S~ < 1

(5a) (5b)

where Z is elevation (m), Tlapse is the elevation lapse rate (°C per 1000m) for minimum or maximum temperatures, C~ is a constant, LAImax is the maximum leaf area index (about 10), and subscript b refers to the base station. No LAI/radiation corrections are applied to estimates of minimum temperature as these occur during the night. Eqs. (1)-(5) are the basis of the program SRAD. Two effects are not included in Eq. (5): the effects of the diurnal thermal inertia and cold air drainage. Air temperatures are higher on north-west than on north-east aspects in the southern hemisphere, owing to the warming of the air mass during the morning. In the Brindabella Range, cold air drainage from higher to lower elevations along drainage-ways can have a significant impact on temperatures in depression areas over relatively small distances. Soil water and evapotranspiration distribution

In mountainous or hilly terrain, such as the Brindabella Range, soil water distribution is controlled by vertical and horizontal water divergence and convergence, infiltration recharge and evapotranspiration. The last two terms are affected by solar insolation and vegetation canopy, and vary strongly with exposure. The divergence and convergence, and solar insolation are dependent on hillslope position. Beven and Kirkby (1979) and O'Loughlin (1986) independently derived wetness indices that characterize the spatial distribution and size of zones of saturation or variable source areas of runoff generation in a landscape. These wetness indices were derived from simple catchment drainage theory, and in their simplest form can be expressed in terms of terrain attributes and soil hydraulic properties (Moore and Foster, 1990) as Xi : In [bTt~n/31 dA ] i= In [ta-~] i+ ln[Te]- ln[Ti]

(6)

where Xi is the wetness index, d A i is the element area (m2), b i is the outflow width (m), fli is the slope angle (degrees) and T i is the transmissivity (m 2 day- 1) in the ith element, As is the specific catchment area (catchment area draining

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across a unit width of contour: m 2 m -1) and ln(Te) is the areal average value of ln(Ti). The integral term represents the upslope area draining across a contour segment of width b orthogonal to the fow. In Eq. (6), As is a measure of the steady-state subsurface drainage flux wherefis the net runoff rate; mm day 1), but assumes uniform infiltration over the entire catchment. Wood et al. (1990) demonstrated that the variation in the topographic variable, ln[AJ tan 3], is far greater than the local variation in transmissivity, ln(T/). The topographic variable alone is therefore a useful approximation. However, during interstorm periods the mean transmissivity, ln(Te) plays a dominant role. One rationale for using only topographic attributes to predict soil water content is that in many landscapes pedogenesis of the soil catena occurs in response to the way water moves through the landscape. The spatial distribution of topographic attributes that characterize these flow paths inherently captures the spatial variability of soil properties at the meso-scale as well (Moore et al., 1993). Eq. (6) is often used to characterize the spatial distribution of soil water content. For example, Burt and Butcher (1986) and Moore et al. (1988a) found strong relationships between terrain attributes such as In[As/tan/3], plane curvature and aspect (i.e. solar radiation) and surface soil water content. Jones (1986, 1987) discussed the usefulness and limitations of wetness indices as indicators of the spatial distribution of soil water content and soil water drainage. Eq. (6) can be generalized to account for the effects of topography, soil properties, deep seepage, rainfall and evapotranspiration to yield (Moore and Hutchinson, 1991; Moore et al., 1993)

(q cxfAs,

xi=lnlbt@n3[#PdAl i+[ln(Te)-

ln(~)]

(7)

Pi

where #i is an area weighting coefficient and is the precipitation rate (mmday-l). In Eq. (7), 0 _< #i-< 1 and is dependent on the evapotranspiration (i.e. solar radiation and vegetation characteristics), deep drainage losses and precipitation in each element. It represents the fraction of precipitation that is converted to runoff in each element. The weighting coefficient can be written as

where E is the actual evapotranspiration (mm day-l), P is the precipitation (mmday -1) and D is the deep drainage loss (mmday -l) on a monthly, seasonal or annual basis. Water lost as deep drainage is not assumed to contribute to baseflow. On an annual basis, the lumped catchment term

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724

(E + D)/P can be estimated directly from an analysis of long-term catchment precipitation and runoff records. For example, forested catchments along the south-east coast of Australia have an average value of (E + D)/P of about 0.70-0.95. This index can characterize soil water distribution in a landscape only if evapotranspiration is conservative over the land area (to maintain stationary mean soil water content). The actual evapotranspiration, E, can be expressed as a function of soil water content and potential evapotranspiration, Ep (i.e. the evapotranspiration under non-limiting soil water conditions). Various functional forms have been proposed to describe this relationship. We use the following parametrically efficient relationship proposed by Kristensen and Jensen (1975), which produces a range of responses under different evaporative demands: E = Ep[l - (1 E = Ep

O)c/Ep] for 0 < 0 < 1.0 for 0 > 1.0

(9a) (9b)

where 0 is the relative available soil water content (0.0 1.0), Ep is the evaporative demand ( m m d a y -1) and C is a constant (approximately 6 1 5 m m d a y - l ) . The deep drainage loss, D, can be expressed as the product of the subsoil saturated hydraulic conductivity, Ks, and a power function of 0. The available energy, Qn, can be approximated by the net radiation, Rn, obtained from Eq. (1), above. The energy budget at the Earth's surface can be written as Rn ~ Qn ~- pAEp + H - ? G

(10)

where H is the sensible heat flux (MJ m -2 day-l), pAEp is the latent heat flux (MJ m -2 day -1), G is the soil heat flux (MJ m -2 day l), A is the latent heat of vaporization (2.477 MJ kg -l at 10°C) and p is the density of water (Mg m-3). Priestley and Taylor (1972) proposed that the evaporative demand from wellwatered vegetation under conditions of minimal advection can be written as a function of Rn - G: O~e(R n -

G)

(ll)

where a e is an empirical constant (= 1.26), A is the slope of the saturation specific humidity curve and 7 is the psychometric constant (functions of air temperature and pressure). This expression is equivalent to the Bowen ratio

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725

method, in which the Bowen ratio Bo = H/(pAEp), if B o - +(1~ ) ~e

1

(12)

If these equations are applied at time intervals of 1 day or greater, then the ground heat flux can be neglected. Therefore, the weighting terms in Eqs. (7) and (8) can be expressed as a function of the relative soil water content, net radiation, precipitation and drainage rates, and four constants (C, p, A and/30). Finally, as a first approximation, the relative available soil water content can be related to the wetness index via an empirical equation of the form 0-

X Xcr

(13)

where Xcr is a critical wetness index corresponding to 0 = 1.0 (field capacity soil water content). Using the form of the weighting function given by Eq. (8), and its components Eqs. (9)-(12), the wetness index appears on the left- and right-hand (via the # term) side of Eq. (7) and must be solved iteratively. The solution technique is most efficient if it begins with the elemental area of highest elevation and finishes with the element of lowest elevation at the catchment outlet. In the application described here, we have applied these equations on both a monthly and an annual basis and have assumed that the four constants (C, p, ~ and Bo) and the mean precipitation and maximum deep seepage rates (expressed as mm day -l) are spatially invariant. This means that the evaporation, runoff and soil water regime are characterized using an equilibrium approach. Therefore, with these assumptions, Eq. (7) can be written as Xi =-in Ib ta~

J # dA] i+ ln[P] + [ln(Te) - ln(~)]

(14)

with

#i ~ 1 --

Xcr/ P

J

and Ep, i given by Eq. (11). These equations are solved iteratively.

(15)

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726

0 0

0 0

I 6088300

m

6082500

m

I

Fig. 1. Shaded relief diagram of the 21.65 km 2 study area in the northern section of the Brindabella Range, south-eastern Australia (35°22 ~S, 148°48' E), derived from a 20m x 20m grid DEM. The coordinates shown use the Australian Map Grid (UTM) from false origin Zone 55/3. Elevations are based on the Australian Geodetic Datum.

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727

Study site: Brindabella Range The study site is a 21.65km 2 area located in the northern section of the Brindabella Range, south-eastern Australia (see Fig. 1 for geocode). Elevations range from 842 to 1370m above sea-level (a.s.1.), with a mean elevation of lll3ma.s.1. Slopes range from 0.4 to 114%, with a mean of 32% and a standard deviation of 15%. The site has a predominantly eastern aspect, although a wide range of aspects are present. The fractal dimension of the site, calculated using a power spectrum approach (Moore et al., 1991), is 2.54, indicating a rugged and topographically complex landscape. A shaded relief diagram of the site is presented in Fig. 1. Climate

Regional climate is cool, temperate continental (Cotter Report, Anon., 1973). In summer, high-pressure systems dominate but are sometimes penetrated by the southerly extension of tropical cyclone depressions. In winter, a succession of frontal systems occur in association with low-pressure air masses moving from west to east across southern Australia and the region. Above 1000ma.s.l., there are occasional snow falls and persistent fogs that may envelop areas for up to 20h (Pryor and Brewer, 1954). Table 1 gives the long-term mean monthly air temperature and precipitation in the region. Annual precipitation for Bull's Head Table 1 Long-term mean monthly values for minimum and maximum temperature (Bull's Head, 1366 m) and precipitation (Blundell's Trig, 1040 m) Month

January February March April May June July August September October November December

Maximum temperature

Minimum temperature

(~c)

(°c)

20.8 20.7 17.5 13.5 8.0 6.0 4.7 5.3 9.5 12.7 15.0 18.5

9.5 10.5 8.0 5.3 1.7 0.0 - 1.5 0.5 1.0 4.3 5.3 7.7

Precipitation (mm)

85.9 90.6 87.4 94.8 95.1 69.1 104.1 133.1 125.4 127.4 99.0 79.6

728

(1366ma.s.1.), which (Talsma, 1983).

I.D. Moore et al. ~Journal of Hydrology 150 (1993) 717 747

is located

near

the

study

area,

is

ll00mm

Soils and geology The lithological base of the region is typically Ordovician meta-sediments (Owen and Wyborn, 1979), although there are also areas of Silurian granitoids and volcanic outcrops (Pryor and Brewer, 1954). Our study area principally covers one geological substrate, the Ordovician meta-sediments. The main soil types in the region are yellow and red podzolics, red loams, transitional alpine humus soils and alpine humus soils (Anon., 1973). The spatial pattern of soil types in the Brindabella Range is complex but appears to be related generally to geology, topography and climate (Talsma, 1983). Soils can be relatively stony, with weathered rock fragments occurring throughout and forming the base of the profile.

Vegetation The Brindabella Range supports a diversity of sub-alpine forest communities, of which the floristic composition and structure can change markedly over relatively small geographic distances as the elevation, aspect, slope and geology of sites vary. Six of the eight forest types identified in the region (Anon., 1973) are incorporated in the study area (Table 2), one being a small area of exotics. The spatial distribution of these forest types is presented in Fig. 2. The vegetation types are distinguished by one or more key species, one of which is always present as either the major or minor stand component. In at least three of the vegetation types (Snow Gum Mountain Gum, Alpine Ash and Brown Barrel), however, there is one dominant species of Eucalyptus (E. pauciflora, E. delegatensis and E. fastigata, respectively). Table 2 Vegetation types used in this study, with key eucalypt species, one of which is always present as either a major or minor stand component Vegetation type

Key species

Snow Gum Mountain Gum Upper Peppermint Lower Peppermint Alpine Ash Brown Barrel Exotics

E. pauciflora, E. dalrympleana E. dives, E. radiata, E. dalrympleana E. dives, E. radiata, E. viminalis, E. mannifera E. delegatensis, E. dalrympleana E. fastigata, E. viminalis Pinus radiata plantation

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729

Upper Peppermint Snow Gum / Mountain Gum Lower Peppermint Exotics Brown Barrel Alpine Ash No data

Fig. 2. Spatial distribution of the six forest types in the study area (data available for 76.5% of the study region).

In general, the forest types represent a broad altitudinal zonation from the Snow Gum Mountain Gum type at higher altitudes to the Lower Peppermint type at lower altitudes (generally on the drier, exposed slopes). Within this zonation, a number of 'types' are associated with specialized habitats. For instance, both E. delegatensis (Alpine Ash) and E. fastigata (Brown Barrel) occur primarily on sheltered, southeastern aspects, with E. fastigata occurring at lower altitudes (Anon., 1973). Non-forested communities are limited in distribution, generally occurring on broad open flats or in saddles along the ranges where temperature and soil moisture are probably significant in restricting tree growth (Anon., 1973).

730

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

Results Using the above computer-based techniques, spatio-temporal variation in many key environmental factors, such as monthly minimum temperature, radiation and relative available soil water content, can be estimated at a high resolution (e.g. for gridded data sets, individual grid ceils may represent a geographic area of less than 20 m x 20 m, i.e. 0.04 ha) across complex terrain in one or more forested catchments. These techniques provide a basis for the explicit and quantitative characterization of environmental gradients in the field. Digital elevation data for this study were initially obtained by line-digitizing stream lines and contour lines at 50 m contour intervals from the 1:25 000 Cotter Dam 8627-11-N map sheet (available from the Land Information Centre). The digitizing was carried out in Australian Map Grid (UTM) coordinates from the false origin of Zone 55/3. A 5 m x 5 m digital elevation model (DEM) was developed from these data using the program A N U D E M (Hutchinson, 1989), a finite-difference method of interpolating grid DEMs that has a drainage enforcement algorithm that automatically removes spurious sinks or pits, and therefore maintains fidelity with the drainage network. This DEM was then sub-sampled to yield a 20m x 20m DEM containing 54 126 grid points, which was the basis of the subsequent analysis. A shaded relief plot of the 20 m x 20 m DEM is presented in Fig. 1.

Terra& complexity and environmental heterogeneity The spatial distribution of several topographic attributes including elevation, slope, aspect, profile and plan curvature, specific catchment area and maximum flow path length were calculated from the DEM using T A P E S - - G (Terrain Analysis Programs for the Environmental Sciences - - Grid version). The algorithm initially creates a depressionless DEM, using the method of Jenson and Domingue (1988), if desired. Specific catchment areas can be estimated using either the classical D8 algorithm, which allows drainage from one node to only one of eight nearest neighbours based on the direction of steepest descent, the quasi-random Rho8 algorithm, or the FRho8 algorithm, which permits drainage from a node to multiple nearest neighbours on a slope-weighted basis. The Rho8 algorithm produces more realistic flow networks than does the D8 algorithm, and the FRho8 algorithm permits the modelling of flow dispersion in upland areas, which is important in convex topography (Moore, 1992; Moore et al., 1993). Slope and aspect are the principal factors determining

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

731

the variability of global radiation, and hence potential evapotranspiration, received across a landscape. The spatial distributions of global short-wave radiation, net long-wave radiation, net radiation, and maximum, minimum and average temperature were computed with program SRAD (Moore, 1992), based on Eqs. (1) (3) and (5). These estimates are derived from average monthly climatic data (maximum and minimum temperatures, and sunshine fraction) measured at Bull's Head and Blundell's Trig (Table 1), which are near the study site, estimated monthly values of atmospheric transmittance at sea-level (0.65 0.71) and average annual values of albedo (0.15), LAI (2.25) and the appropriate temperature lapse rates. These model 'parameters' were assumed to be spatially invariant. The predicted distributions of net radiation and average air temperature in July are presented in Fig. 3. The predicted monthly values of global short-wave radiation on horizontal and sloping surfaces and net radiation are compared with measured (Paltridge, 1975; Paltridge and Proctor, 1976) monthly global short-wave radiation and seasonal values of net radiation on a horizontal surface at Canberra (35°17'S, 149°07'E; 640ma.s.l.) in Table 3. The predicted monthly values of short-wave radiation on a horizontal surface at the study site range Table 3 Short-wave and net radiation ( W m 2) predicted for the study site (mean and standard deviation) and measured on a horizontal surface at Canberra Month

Short-wave radiation

Net radiation

Canberra a

Predicted horizontal

Predicted sloping

December January February March April May June July August September October November

309 300 269 214 167 128 100 110 147 206 244 288

288 311 252 215 143 106 101 96 136 185 211 272

271 292 238 205 138 103 98 93 130 176 200 256

Annual

207

193 ± 3

± 4 ± 4 + 3 + 3 4- 2 ± 2 + 2 ± 2 i 2 ± 3 ± 3 ± 4

i 16 ± 19 ± 22 ± 32 ± 33 ± 34 + 37 =l- 33 4- 36 ± 33 ± 22 -4- 18

Canberra b

180

70

25

135

183 ± 26

Measured on a horizontal surface (Paltridge and Proctor, 1976). Measured average seasonal values on a horizontal surface (Paltridge, 1975).

Predicted sloping 183 4- 13 195 ± 15 158 ± 16 123 ± 25 72 :tz 25 39 + 26 21 + 28 36 ± 25 63 + 28 99 ± 26 130 ± 17 170 ± 14 107 ± 20

"ig. 3. Predicted spatial distributions of (a) net radiation (W m 2) and (b) average air temperature (°C) over the study site for July, calculated by program ;RAD.

~2

-q

<3

.2

"4

t-3

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733

from 104 to 83 % of those recorded at Canberra; the annual value is 6.8% less. The predicted mean net radiation (i.e. on sloping surfaces) is about 5% less than predicted values on a horizontal surface. As expected, the standard deviation of predicted short-wave radiation is greatest in winter and least in summer; the coefficients of variation range from 5.9 to 38%. Table 3 shows that the predicted mean monthly net radiation for the study site compares reasonably well with the seasonal values on a horizontal surface measured at Canberra. The coefficient of variation of the predicted values of net radiation range from 7.1 to 133%. Table 4 shows that the variations in predicted maximum and average temperatures across the landscape are greatest in winter and lowest in summer. In winter, the interpolation of maximum and average temperatures across the landscape (Fig. 3(b)) is dominated by the short-wave radiation terms in Eqs. (5a) and (5b) - - the average temperature pattern is similar to the net radiation pattern (Fig. 3(a)). In summer, however, the pattern of temperature variation is different, and the elevation correction dominates. The ratio of the short-wave radiation on sloping surfaces to that on a horizontal surface, which is the basis of the radiation correction in the temperature interpolation equations (Eqs. (5a) and (5b)), displays much greater variability in winter than in summer. Figure 4 presents the computed distribution of average annual relative available soil water content (0--wilting point; 1--field capacity) and average Table 4 Mean and standard deviation of predicted maximum, minimum and average monthly temperatures (°C) Month

Maximum temperature

Minimum temperature

Average temperature

January February March April May June July August September October November December

21.1 ± 0.8 21.5 4. 1.2 18.5 + 1.3 14.6 ± 1.5 9.0 4, 1.7 6.9 J- 1.9 5 . 6 + 1.8 6.3 4. 1.6 10.5 :[: 1.4 13.7 4, 1.3 15.5 :t: 0.9 18.7 ± 0.7

11.3 4. 0.9 12.3 -t: 0.9 9.8 4. 0.9 7.1 4. 0.9 3.5 4. 0.9 1.8 + 0.9 0.34-0.9 1.3 ± 0.9 2.8 + 0.9 6.1 4. 0.9 7.1 4- 0.9 9.5 4. 0.9

16.2 ± 0.8 16.9 4, 0.9 14.2 i 0.9 10.9 + 1.1 6.3 4. 1.1 4.4 ± 1.1 3 . 0 ± 1.1 3.8 ± 1.0 6.7 -t: 1.0 9.9 4. 0.8 11.3 4- 0.8 14.1 4. 0.8

Annual

13.7 + 1.2

6.2 J- 0.9

9.9 ± 0.9

~

Fig. 4. Predicted spatial distributions of (a) average annual relative available soil water content (0 wilting point; 1 field capacity or greater) and (b) average annual evapotranspiration (mm day l), calculated by program WET.

0.5

1.o

1.5

2.0

2.5

3.0

3.5

~2 -.q

-.q

,:~

.~

4~

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

735

annual evapotranspiration ( m m d a y 1). The average annual precipitation is 3.264mmday -l. The computed annual evapotranspiration, deep seepage and total runoff are 2.472 ± 0.414 mm day 1 (75.8% of gross precipitation), 0.183 ± 0 . 9 2 7 m m d a y - ~ (5.6% of gross precipitation) and 0.608 mm day i (18.6% of gross rainfall), respectively. These estimates were based on values of the exponent in the soil water content actual evaporation relationship (Eq. (9a)), C = 12 mm day -I, and a subsoil saturated hydraulic conductivity for estimating the deep drainage loss, Ks = 6 mm day 1. Kristensen and Jensen (1975) used a value of C -- 10 mm day -1 for a variety of crops, and Moore et al. (1986) achieved good hydrologic simulation results in a forested catchment in south-eastern Australia assuming C = 1 2 m m d a y -~. For C = 12 mm day -1 and an evaporative demand of 5 mm day ~, the predicted E/Ep ratios are 0.50, 0.81 and 0.96 for relative soil water contents of 0.25, 0.5 and 0.75, respectively. Measured C horizon saturated hydraulic conductivities (0.7-1.0m depths) for the Brindabella Range vary considerably from virtually impermeable to greater than 400 mm day -1, with a mean value of about 2 4 0 m m d a y 1 (Talsma and Hallam, 1980, 1982; Talsma, 1983). These values of Ks produced unrealistically large values of deep drainage losses. Limited fitting indicated that a value of Ks = 6 m m d a y -1 produced more realistic results. This suggests that most of the deep seepage, as defined here, contributes to baseflow and is thus an integral part of the total catchment runoff. The computed Bowen ratio equivalent (Eq. (12)) used in the annual equilibrium model was 0.368, based on an average annual air temperature of 9.4°C and a mean elevation of 1115 m. Rainfall and runoff from the 97.5ha Bushrangers catchment have been measured since 1967 (O'Loughlin et al., 1982). This catchment is located about 2kin south of the study area, and has a similar environment and vegetation to the study area. For the 11 year period 1968-1978 the average annual gross precipitation and total runoff for the Bushrangers catchment were 3.502mmday ~ and 0.616mmday z (17.6% of gross precipitation), respectively (P. Crapper, personal communication, 1992). The close agreement between the observed and predicted runoff conversion efficiencies (17.6% and 18.6%, respectively) provides some verification for the application of the equilibrium soil water and evapotranspiration relationships represented by Eqs. (7)-(15) in characterizing the spatial distribution of hydrologic processes (i.e. environmental heterogeneity) in complex landscapes on an annual basis. It should be noted that we had difficulty in applying these equilibrium equations on a monthly basis and in predicting monthly runoff conversion efficiencies that agreed with the observed values for the Bushrangers catchment (varying from 12.9% in January to 22.5% in July). There is a significant seasonal carry-over of soil water content, but in the equilibrium

736

LD. Moore et al./ Journal of Hydrology 150 (1993) 717-747

analysis this is ignored. We are currently modifying the approach to account for this carry-over effect and to overcome this limitation. Our aim is to retain a relatively simple model that includes the main forcing functions that determine environmental heterogeneity and that has a firm foundation in basic flow theory.

Forest communities and environmental heterogeneity There have been a number of studies investigating the vegetation dynamics of the Brindabella Range. Broad relationships between landscape attributes and species distribution in the region have been documented in the Cotter Report (Anon., 1973) and by Ingwersen (1983). These researchers found that aspect, slope, altitude and geology were correlated with the distribution of understorey and overstorey species in the region. However, primary topographic attributes such as altitude, slope and aspect are only indirect indices of the bioclimatic forcing variables that determine the distribution and abundance of forest communities. For example, elevation and aspect are incomplete measures of temperature and solar radiation in complex landscapes, respectively. Austin (1971, 1979) investigated the relationships between the occurrence of eucalypt species found on the lower slopes of the Brindabella Range and site attributes such as estimated mean annual rainfall, estimated mean annual evaporation, soil depth, estimated soil moisture storage and pH, as well as indirect indices such as altitude, slope and aspect. The occurrence of Eucalyptus rossii, for example, was related to altitude and estimated mean annual rainfall but was poorly predicted by simple linear regression. Austin (1971, 1979) demonstrated the advantages of using an environmental process model or scalar to estimate the combined effects of site attributes on moisture stress in plants using known physical processes. Several studies have emphasized the influence of fire on forest stand dynamics (Banks, 1982; Noble, 1984; Williams, 1989; Keith, 1991) and its potential role in the distribution of understorey (Griffith, 1977) and overstorey plant species in the Brindabella Range (Park, 1975; Shugart and Noble, 1981; Williams, 1989). Minimum temperature, length of snow cover and soil depth have also been suggested as important factors influencing the ftoristic composition of the understorey (Evans, 1971; Banks, 1982). Minimum air temperature in particular was identified by Williams (1989) as the most important factor controlling the upper altitudinal limit of Eucalyptus dives, whereas competition, with E. dives at least, was hypothesized to cause the lower distributional limit of E. pauciflora. Relatively few studies have investigated the mechanistic basis of plant distribution. Burdon and Chilvers

737

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

(1974a, b) proposed a regulatory role for insect herbivory in the population dynamics of sub-alpine eucalypts, but Williams (1990) suggested that this aspect has been overemphasized. However, no detailed fine-scale spatial analysis of the relationships between terrain complexity, environmental heterogeneity and biotic communities has been undertaken in the area. It is now possible to relate fine-scale environmental heterogeneity, as expressed by the spatial distribution of temperature, solar radiation, evapotranspiration and soil water content, using techniques such as those described above, to the distribution of biotic communities. This section presents a preliminary analysis of the environmental domains associated with the broad forest types listed in Table 2. A single forest type was assigned to each 20m x 20m cell in the study area, based on the generalized map given in Fig. 2. This map represents a modification of the vegetation map given in the Cotter Report (Anon., 1973), based on a large number of quantitative and qualitative observations over the past 5 years on overstorey composition in the study area. The mapped boundaries between forest types have been checked on the ground and are considered accurate. Forest types had been mapped for 76.5% of the study region. The western quarter had not been mapped. A range of environmental variables (monthly and annual maximum, minimum and average air temperatures, annual relative available soil water content, annual deep seepage, annual evapotranspiration, and monthly and annual global shortwave, net long-wave and net radiation) were estimated for each cell using the methods outlined above. The means and standard deviations for selected environmental variables are summarized in Table 5. Table 5 Means and standard deviations of selected environmental variables associated with the key vegetation species in the study area Forest type

Relative available soil water content (annual)

Minimum temperature July CC)

Maximum temperature January (°C)

Net radiation July (W m 2)

Net radiation Annual (W m -2)

Total area Alpine Ash Brown Barrel Pinusradiata Lower Peppermint Upper Peppermint Snow G u m Mountain Gum

0.483+0.148 0.474 ± 0.137 0.481 ±0.153 0.488±0.142 0.461±0.142 0.494 ± 0.158 0.491 ± 0.133

0.51 ±0.86 0.00 ± 0.63 1.05±0.61 1.53±0.30 1.08±0.64 0.62 ± 0.64 -0.65 ± 0.37

21.3±0.8 20.9±0.6 21.6±0.6 22.3 :t: 0.7 21.7±0.6 21.3 ± 0.6 20.5 i 0.8

37±25 38±24 31±25 43±14 47+23 35 4- 25 46±18

108+21 110±18 102±21 114± 10 113±17 105 ± 21 118± 12

738

LD. Moore et al./ Journal of Itydrology 150 (1993) 717-747

Each environmental variable was also divided into 40 equally spaced classes across its range, and the frequency of occurrence in each class was determined for three forest types, to examine the environmental variables differentiating responses by eucalypt species. This analysis was limited to Snow G u m Mountain Gum, Alpine Ash and Brown Barrel forest types because, on the basis of our field observations, we believe that they uniquely define the mapped distribution of E. pauciflora, E. delegatensis and E. fastigata, respectively, in the study area. That is, it is assumed that for each grid cell encompassed by each respective forest type, the relevant eucalypt species will be present. This assumption cannot be made, however, for the other eucalypt species in the study area, as they either occur in more than one forest type (e.g. E. dalrympleana and E. dives) or are restricted to an unknown subset of a single forest type (e.g.E. mannifera). Further field-based sampling would be required before it would be possible to investigate the environmental variables differentiating the response of these eucalypts. The computed probability of occurrence of E. pauciflora, E. delegatensis and E.fastigata as functions of minimum July temperature (°C) (i.e. minimum temperature in the coldest month), annual short-wave radiation (W m -2) and annual relative available soil water content is presented in Fig. 5. Average minimum temperature in the coldest month (July Fig. 5(a)) provides the major differentiation for the occurrence of the three forest types. For example, E. pauciflora is generally restricted to higher elevations where the average minimum July temperature is less than 0°C and E. fastigata rarely occurs where the average minimum July temperature is below 0°C. E. delegatensis is restricted to locations where the average minimum July temperature ranges from about -1.5 to 1.0°C. The occurrence of these eucalypts is further differentiated by the radiation regime (global short-wave radiation or net radiation, on both a monthly and annual basis) as illustrated in Fig. 5(b), which shows the probability of occurrence of each species as a function of annual net radiation. Our data suggest that E. pauciflora has a relatively narrow, but high, net radiation range (about 90-145 W m-Z), and is rarely found at low net radiation sites (southern aspects) at the higher end of its minimum temperature range. E. fastigata appears to have the greatest annual net radiation range (30-140Win -2) and 'dominates' at the low end of this range (less than 100Wm-2). The thermal regime of E. delegatensis overlaps the upper (higher-temperature) end of the thermal regime of E. pauciflora (Fig. 5(a)), but it is found more frequently at sites where net radiation is less than 100Wm -2. Figures 6(a) and 6(b) are plots of the probability of occurrence of E. pauciflora and E. fastigata, respectively, within the two-dimensional environmental domains of annual net radiation vs. minimum July

I.D. Moore et al,/ Journal of Hydrology 150 (1993) 717-747

739

1.0 ;,.,,

0.8

A //

'~- . . . . . . . . . . . . . . . .

Brown Barrel - E. fastigala

', . . . . . . . .

Snow Gum - E. pauciflora

"\

i ':' o-J~ .Q 0 Q.

(a)

Alpine Ash - E. delegatensis

i

0.6

;

0.4

/

\

0.2

0.0 .5

-1.0

-0.5

0.0

Minimum 1.0

i

July

i

0.5

1.0

1.5

Temperature i

2.0

2.5

(°C)

i

i

i

(b) Alpine Ash - E. delegatensis

0.8 ,-.0 ¢3 J~

o

0.6

................. Brown Barrel - E. fastigata

i

........

!

Snow Gum - E. pauciflora

i J J i

m

1",

0.4

,~,\

A

i

J~ i v v

-~,-,,,.

:

0.2

0.0 z0

[.

,

40

60

80

100

120

140

Annual Net Radiation ( W / m 2) 1.0

(c) 0.8

Alpine Ash - E. delegatensis

0.6

Snow Gum - E. pauciflora

Brown Barrel - E. fastigata 0= J~ O Is

0.4

0.2

0.0 U.2

0.4 Relative

0.6 Soil

Water

0.8

.0

Content

Fig. 5. Computed probability of occurrence of E. pauciflora, E. delegatensis and E. fastigata as functions of (a) minimum July temperature, (b) annual net radiation and (c) annual relative available soil water content.

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

740

140.

120.

O

100

I

E. delegatensis E. fastigata E. pauciflora

~5

8O t-

~ Probability< 0,6 Outsidedomain

~lU-_l"

60-~ t

~ ~ 1 1

~I~ •

-2

-1.5

-1

-0.5

0

0,5

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Minimum July air temperature (°C)

Probability

~

-2

-1,5

-1

-0.5

0

0.5

1.0

1.5

2.0

0.2 0.4 0.6 0.8 1.0

No vegetationdata Outsidedomain

2.5

Minimum July air temperature (°C) Fig. 6. Plots of the probability of occurrence of (a) E. pauciflora and (b) E. fastigata, and (c) configuration of E. pauciflora, E. delegatensis and E.fastigata in the two-dimensional environmental space defined by annual net radiation and minimum July temperature where the probability of their occurrence is estimated to exceed 60%.

741

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

140-

il~

,.,.-, 120-

Probability

~. E ,"0 i~ "o ,~

0.2 iO.O 0.4 0.6 0.8 1.0 No vegetationdata L_] Outside domain

I00-

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t=

--~" ,"

60-

40 20 ~ -2

,

-1.5

i

i .............

, ....

i . . . . . . .

-1 -0'.5 0 015 1.0 1.5 2.0 Minimum July air temperature (°C)

215

Fig. 6. Continued.

temperature. This is a similar form of presentation to that of Austin et al.'s (1990) quantitative environmental realized niches (QERN). The limits of the environmental domains for the study site (for which forest type data were available) are also defined on these figures. These plots illustrate the differences in the environmental domains of the two species. For example, E. pauciflora is found only where the minimum July temperature is below 0.0°C. Fig. 6(c) shows the configuration of E. pauciflora, E. fastigata and E. delegatensis within this two-dimensional environmental domain where the probability of the occurrence of each species exceeds 0.6. E. pauciflora and E. delegatensis occur at sites experiencing low minimum July temperatures and can be differentiated generally on the basis of net radiation, whereas E. fastigata occurs at sites experiencing minimum July temperatures greater than 0°C and intermediate annual net radiation regimes. Figure 5(c) presents the frequency distributions of the three eucalypt species as a function of the computed average annual relative available soil water content. There is little difference between any of the forest types. This may suggest that in the Brindabella Range average annual soil water is not a useful correlate of overstorey composition. Previous observations suggesting that shorter-term variations in soil water are important determinants of eucalypt distribution (Anon., 1973; Lamb and Florence, 1978) will be tested as our data and models are developed.

742

I.D, Moore et al.; Journal o f Hydrology 150 (1993) 717-747

Summary and conclusions Modelling spatially distributed environmental processes places great demands on both the modelling technology and the data needed to drive these models. In many management and ecologically oriented applications, the use of sophisticated, physically based distributed parameter models may not be needed or appropriate. We have attempted to develop methods that are consistent with the limited available data, the management questions being posed and the precision with which these questions need to be answered. The key advantages of the models presented are that they provide an improved estimation of physical processes and have an ability to estimate processes for all parts of the landscape using DEM data as the primary model input. As a result of these features, it is possible to predict biological phenomena (e.g. vegetation and fauna) at a fine spatial scale from samples. Model SRAD is an approximate method for estimating the spatial distribution of global short-wave radiation, net long-wave radiation, net radiation, and maximum, minimum and average temperature, and accounts for the effects of topographic shading. The model can be applied on any time increment ranging from 1 day to 1 year. In this study, we applied it on a daily basis to estimate the average daily radiation and thermal regime for each month using long-term average monthly parameters. Model WET estimates spatially distributed soil water content and evapotranspiration, and catchment runoff. The model uses an equilibrium approach. This approach performed well on an annual basis, but needs modification to be accurately applied on a monthly basis because of the carry-over effect of soil water storage from one month to the next. The models were applied to a 21.65km 2 forested area within the Brindabella Range in south-eastern Australia. This work is presented as a preliminary analysis of pattern-process relationships and is used simply to illustrate how the techniques and models could be applied usefully in this research area. A 20 m x 20m grid DEM was developed for the study area. The site has a fractal dimension of 2.54, indicating that it is topographically complex. Computed annual short-wave radiation was 183 ± 26 W m 2• but varied from 2 9 2 ± 1 9 W m -2 in January to 9 3 ± 3 3 W m -2 in July. The computed annual short-wave radiation on a horizontal surface was 193 ± 3 W m 2, which compares with an average annual value of 207 W m" ) observed nearby at Canberra. Annual net radiation was 1 0 7 ± 2 0 W m ~, --9 • and varied from 1 9 5 ± 1 5 W m - m January to 2 1 ± 2 8 W m -2 in June. These values are consistent with average seasonal measurements made at Canberra. Computed average minimum monthly temperatures ranged from 0.3 ± 0 . 9 ° C in July to 11.3 ±0.9~C in January. The computed annual

I.D. Moore et al./ Journal of Hydrology 150 (1993) 717 747

743

evapotranspiration, deep seepage and total runoff were 2.472+ 0.414mmday -1, 0.183 + 0 . 9 2 7 m m d a y 1 and 0.608mmday 1, respectively. These fluxes represent 75.8%, 5.6% and 18.6% of the gross precipitation (3.264mm day 1), respectively. Recorded runoff from a 97.5 ha catchment, located within the Brindabella Range, averaged 0.61 mm day -1 or 17.6% of gross precipitation for the period 1968-1978, which is within 6% of the predicted value. The study area contains five main sub-alpine forest types - - Snow Gum-Mountain Gum, Upper and Lower Peppermint, Alpine Ash, Brown Barrel as well as a small area of exotics (Pinus radiata plantation). The computed fluxes were used to characterize the fine-scale environmental heterogeneity and environmental domains of these forest types. Average minimum temperature in the coldest month (July) and the annual net radiation were two environmental variables differentiating the occurrence of the three eucalypt species examined. The spatial distribution of average annual soil water content or evapotranspiration did not appear to differentiate significantly between eucalypts.

Acknowledgements This study was funded in part by Grant 90/82 and Special Project 1991-92: ANU 3 from the Land and Water Resources Research and Development Corporation, by a Postgraduate Fellowship from the Australian Research Council and by the Water Research Foundation of Australia. The authors thank John Gallant and Ursula Grott for assistance with computer program development and digitizing. John Gallant provided invaluable assistance in the production of the final versions of the figures for this manuscript. The manuscript significantly benefited from the comments and suggestions of Dr. Michael Austin and Dr. Larry Band.

References Anon., 1973, Cotter Report. A Resource and Management Survey of the Cotter River Catchment. Department of Forestry, The Australian National University, Canberra, A.C.T., 287 pp. Austin, M.P., 1971. Role of regression analysis in plant ecology. Proc. Ecol. Soc. Aust., 6: 63 75. Austin, M.P., 1979. Current approaches to non-linearity in vegetation analysis: In: G.P. Patil and M.L. Rosenzweig (Editors), Contemporary Quantitative Ecology and Related Ecometrics, International Co-operative Publishing House, Fairland, MD, pp. 197-210. Austin, M.P., 1987. Models for the analysis of species' response to environmental gradients. Vegetatio, 69: 35-45.

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Austin, M.P., Cunningham, R.B. and Good, R.B., 1983. Altitudinal distribution of several eucalypt species in relation to other environmental factors in southern New South Wales. Aust. J. Ecol., 8: 169--180. Austin, M.P., Cunningham, R.B. and Fleming, P.M., 1984. New approaches to direct gradient analysis using environmental scalars and statistical curve-fitting procedures. Vegetatio, 55: 11-27. Austin, M.P., Nicholls, A.O. and Margules, C.R., 1990. Measurement of the realized qualitative niche of plant species: examples of the environmental niches of five Eucalyptus species. Ecol. Monogr., 60: 161-177. Band, L.E., Peterson, D.L., Running, S.W., Coughlan, J.C., Lammers, R.B., Dungan, J. and Nemani, R., 1991. Forest ecosystem processes at the watershed scale: basis for distributed simulation. Ecol. Modeling, 56:151 176. Band, L.E., Patterson, P., Nemani, R. and Running, S.W., 1993. Forest ecosystem processes at the watershed scale: incorporating hillslope hydrology. Agric. For. Meteorol., 63: 93-126. Banks, J.C.G., 1982. The use of dendrochronology in the interpretation of the dynamics of the snow gum forest. Ph.D. Thesis, The Australian National University, Canberra, A.C.T. Beven, K.J. and Kirkby, M.J., 1979. A physically-based variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24:43 69. Bridgewater, P.B., 1987. Connectivity: an Australian perspective. In: D.A. Saunders, G.W. Arnold, A.A. Burbidge and A.J.M. Hopkins (Editors), Nature Conservation: The Role of Remnants of Native Vegetation. Surrey Beatty and CSIRO, Sydney, N.S.W., pp. 195 200. Bristow, K.L. and Campbell, G.S., 1985. An equation for separating daily solar irradiation into direct and diffuse components. Agric. For. Meteorol., 35:123 131. Burdon, J.J. and Chilvers, G.A., 1974a. Leaf parasites on altitudinal populations of Eucalyptus pauciflora Sieb. ex Spreng. Aust. J. Bot., 22:265 269. Burdon, J.J. and Chilvers, G.A., 1974b. Fungal and insect parasites contributing to niche differentiation in mixed species stands of eucalypt saplings. Aust. J. Bot., 22: 103-114. Burt, T.P. and Butcher, D.P., 1986. Development of topographic indices for use in semidistributed hillslope runoff models. In: O. Slaymaker and D. Balteanu (Editors), Geomorphology and Land Management. Gebruder Borntraeger, Berlin, pp. 1 19. Davis, F.W. and Dozier, J., 1990. Information analysis of a spatial database for ecological land classification. Photogramm. Eng. Remote Sensing, 56:605 613. Dozier, J., Bruno, J. and Downey, P., 1981. A faster solution to the horizon problem. Comput. Geosci., 7:145 151. Duguay, C.R., 1989. Net radiation mapping of mountainous terrain using LANDSAT-5 Thematic Mapper imagery and digital terrain data. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., 259 pp. Evans, G.C., 1971. Altitudinal variation in vegetation on the Brindabella Range. B.Sc.(Hons.) Thesis, The Australian National University, Canberra, A.C.T. Forman, R.T.T. and Godron, M., 1986. Landscape Ecology. Wiley, New York. Griffith, L., 1977. Pattern and structure in snow gum understorey. M.Sc. Thesis, The Australian National University, Canberra, A.C.T., 210 pp. Hounam, C.E., 1963. Estimates of solar radiation over Australia. Aust. Meteorol. Mag., 43: 1-14. Howard, J.A. and Mitchell, C.W., 1985. Phytogeomorphology. Wiley, New York, 222 pp. Hungerford, R.D., Nemani, R.R., Running, S.W. and Coughlan, J.C., 1989. MTCLIM: a mountain microclimate simulation model. US For. Serv. Res. Pap. INT-414, 52 pp.

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