Effects of changing climate on water and nitrogen availability with implications on the productivity of Norway spruce stands in Southern Finland

An integrated process-based model was used to study how the changing climate affects the availability of water and nitrogen, and consequently the dynamics of productivity of Norway spruce (Picea abies) on sites with different initial soil water conditions in southern Finland over a 100-year period. The sensitivity of the total stem volume growth in relation to short-term availability of water and nitrogen was also analyzed. We found that a high proportion (about 88–92%) of the total precipitation was lost in total evapotranspiration (incl. canopy evaporation (E_c), transpiration (E_t) and ground surface evaporation (E_g)), under both current and changing climate. Furthermore, under the changing climate the cumulative amount of E_c and E_g were significantly higher, while E_t was largely lower than under the current climate. Additionally, the elevated temperature and increased expansion of needle area index (L) enhanced E_c. Under the changing climate, the increasing soil water deficit (W_d) reduced the canopy stomatal conductance (g_cs), the E_t, humus yield (H, available nitrogen source) and nitrogen uptake (N_up) of the trees. During the latter phases of the simulation period, the canopy net photosynthesis (P_nc) was lower due to the reduced N_up and soil water availability. This also reduced the total stem volume production (V_s) on the site with the lower initial soil moisture content. The growth was slightly more sensitive to the change in precipitation than to the change in nitrogen content of the needles, when the elevated temperature was assumed. According to our findings, drought stress episodes may become more frequent under the changing climate. Thus, adaptive management strategies should be developed to sustain the productivity of Norway spruce in these conditions, and thus, to mitigate the adverse impacts of climate change.     

Evaluating weather effects on interannual variation in net ecosystem productivity of a coastal temperate forest landscape: A model intercomparison

Forest productivity is strongly affected by seasonal weather patterns and by natural or anthropogenic disturbances. However weather effects on forest productivity are not currently represented in inventory-based models such as CBM-CFS3 used in national forest C accounting programs. To evaluate different approaches to modelling these effects, a model intercomparison was conducted among CBM-CFS3 and four process models (ecosys, CN-CLASS, Can-IBIS and 3PG) over a 2500 ha landscape in the Oyster River (OR) area of British Columbia, Canada. The process models used local weather data to simulate net primary productivity (NPP), net ecosystem productivity (NEP) and net biome productivity (NBP) from 1920 to 2005. Other inputs used by the process and inventory models were generated from soil, land cover and disturbance records. During a period of intense disturbance from 1928 to 1943, simulated NBP diverged considerably among the models. This divergence was attributed to differences among models in the sizes of detrital and humus C stocks in different soil layers to which a uniform set of soil C transformation coefficients was applied during disturbances. After the disturbance period, divergence in modelled NBP among models was much smaller, and attributed mainly to differences in simulated NPP caused by different approaches to modelling weather effects on productivity. In spite of these differences, age-detrended variation in annual NPP and NEP of closed canopy forest stands was negatively correlated with mean daily maximum air temperature during July-September (T_amax) in all process models (R² = 0.4-0.6), indicating that these correlations were robust. The negative correlation between T_amax and NEP was attributed to different processes in different models, which were tested by comparing CO₂ fluxes from these models with those measured by eddy covariance (EC) under contrasting air temperatures (T_a). The general agreement in sensitivity of annual NPP to T_amax among the process models led to the development of a generalized algorithm for weather effects on NPP of coastal temperate coniferous forests for use in inventory-based models such as CBM-CFS3: NPP′ = NPP − 57.1 (T_amax − 18.6), where NPP and NPP′ are the current and temperature-adjusted annual NPP estimates from the inventory-based model, 18.6 is the long-term mean daily maximum air temperature during July-September, and T_amax is the mean value for the current year. Our analysis indicated that the sensitivity of NPP to T_amax was nonlinear, so that this algorithm should not be extrapolated beyond the conditions of this study. However the process-based methodology to estimate weather effects on NPP and NEP developed in this study is widely applicable to other forest types and may be adopted for other inventory based forest carbon cycle models.     

Water budget and the consequent duration of canopy carbon gain in a teak plantation in a dry tropical region: Analysis using a soil–plant–air continuum multilayer model

A soil–plant–air continuum multilayer model was used to numerically simulate canopy net assimilation (A_n), evapotranspiration (ET), and soil moisture in a deciduous teak plantation in a dry tropical climate of northern Thailand to examine the influence of soil drought on A_n. The timings of leaf flush and the end of the canopy duration period (CDP) were also investigated from the perspective of the temporal positive carbon gain. Two numerical experiments with different seasonal patterns of leaf area index (LAI) were carried out using above-canopy hydrometeorological data as input data. The first experiment involved seasonally varying LAI estimated based on time-series of radiative transmittance through the canopy, and the second experiment applied an annually constant LAI. The first simulation captured the measured seasonal changes in soil surface moisture; the simulated transpiration agreed with seasonal changes in heat pulse velocity, corresponding to the water use of individual trees, and the simulated A_n became slightly negative. However, in the second simulation, A_n became negative in the dry season because the decline in stomatal conductance due to severe soil drought limited the assimilation, and the simultaneous increase in leaf temperature increased dark respiration. Thus, these experiments revealed that the leaflessness in the dry season is reasonable for carbon gain and emphasized the unfavorable soil water status for carbon gain in the dry season. Examining the duration of positive A_n (DPA) in the second simulation showed that the start of the longest DPA (LDPA) in a year approached the timing of leaf flush in the teak plantation after the spring equinox. On the other hand, the end appeared earlier than that of all CDPs. This result is consistent with the sap flow stopping earlier than the complete leaf fall, implying that the carbon assimilation period ends before the completion of defoliation. The model sensitivity analysis in the second simulation suggests that a smaller LAI and slower maximum rate of carboxylation likely extend the LDPA because soil water from the surface to rooting depth is maintained longer at levels adequate for carbon gain by decreased canopy transpiration. The experiments also suggest that lower soil hydraulic conductivity and deeper rooting depth can postpone the end of the LDPA by increasing soil water retention and the soil water capacity, respectively.     

Development of a hydrothermal time seed germination model which uses the Weibull distribution to describe base water potential

Seed germination has been modelled extensively using hydrothermal time (HTT) models, that predict time to germination as a function of the extent to which seedbed temperature, T, and water potential, Ψ, exceed the base temperature, T_b, and base water potential, Ψ_b, of each seed percentile, g. Within a seed population the variation in time to germination arises from variation in Ψ_b(g) modelled by a normal distribution. We tested the assumption of normality in the distribution of Ψ_b(g) by germinating seed of two unrelated species with non-dormant seed (Buddleja davidii (Franch.) and Pinus radiata D. Don) across a range of constant Ψ at sub-optimal T. When incorporated into a HTT model the Weibull distribution more accurately described both the right skewed distribution of Ψ_b(g) and germination time course over sub-optimal T than the HTT based on the normal distribution, for both species. Given the flexibility of the Weibull distribution this model not only provides a useful method for predicting germination but also a means of determining the distribution of Ψ_b(g).     

Theoretical analysis of change in forest carbon use efficiency with stand development: A case study on Hinoki Cypress (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.) plantation from the seedling stage

Changes in carbon use efficiency (CUE), which is defined as the ratio of net primary production (NPP) to gross primary production (GPP), were estimated for the aerial parts of the Hinoki Cypress (Chamaecyparis obtusa (Sieb. et Zucc.) Endl.) with respect to stand development. The analysis incorporated previously published data from the early stages of stand development, namely the seedling stages of the cypress. For this analysis, a simple mathematical model to assess the changes in CUE was developed by incorporating data on physiological variables and mass of woody species. The CUE tended to increase with increases in the aboveground biomass of the stand, and then decreased gradually despite increases in the aboveground biomass. The CUE-value (0.28, 0.39) of the seedling stage was lower than that (0.33-0.58) of the young or mature trees. To examine the effect of physiological variables and mass on CUE, the ratios of the specific respiration rate to the specific photosynthetic rate (r/a) and the leaf biomass to the aboveground biomass or leaf mass ratio (y_L/y_T) were calculated. The low value of CUE at the seedling stage was due to the high ratio of specific respiration rate to specific photosynthetic rate r/a, but was not due to the high value of the leaf mass ratio y_L/y_T. In addition, the decline in CUE associated with older stages of stand development was due to the decreasing changes in y_L/y_T, and the r/a ratio did not influence the change in CUE.     

Foliage profiles of individual trees determine competition,self-thinning,biomass and NPP of a Cryptomeria japonica forest stand: A simulation study based on a stand-scale process-based forest model

A simulation study was carried out to investigate simultaneously the effects of eco-physiological parameters on competitive asymmetry, self-thinning, stand biomass and NPP in a temperate forest using an atmosphere–vegetation dynamics interactive model (MINoSGI). In this study, we selected three eco-physiological relevant parameters as foliage profiles (i.e. vertical distribution of leaf area density) of individual trees (distribution pattern is described by the parameter η), biomass allocation pattern in individual tree growth (χ) and the maximum carboxylation velocity (V_max). The position of the maximal leaf area density shifts upward in the canopy with increasing η. For scenarios with η < 4 (foliage concentrated in the lowest canopy layer) or η > 12 (foliage concentrated in the uppermost canopy layer), a low degree of competitive asymmetry was produced. These scenarios resulted in the survival of subordinate trees due to a brighter lower canopy environment when η < 4 or the generation of spatially separated foliage profiles between dominant and subordinate trees when η > 12. In contrast, competition between trees was most asymmetric when 4 ≤ η ≤ 12 (vertically widespread foliage profile in the canopy), especially when η = 8. In such cases, vertically widespread foliage of dominant trees lowered the opportunity of light acquisition for subordinate trees and reduced their carbon gain. The resulting reduction in carbon gain of subordinate trees yielded a higher degree of competitive asymmetry and ultimately higher mortality of subordinate trees. It was also shown that 4 ≤ η ≤ 12 generated higher self-thinning speed, smaller accumulated NPP, litter-fall and potential stand biomass as compared with the scenarios with η < 4 or η > 12. In contrast, our simulation revealed small effects of χ or V_max on the above-mentioned variables as compared with those of η. In particular, it is notable that greater V_max would not produce greater potential stand biomass and accumulated NPP although it has been thought that physiological parameters relevant to photosynthesis such as V_max influence dynamic changes in forest stand biomass and NPP (e.g. the greater the V_max, the greater the NPP). Overall, it is suggested that foliage profiles rather than biomass allocation or maximum carboxylation velocity greatly govern forest dynamics, stand biomass, NPP and litter-fall.     

Modeling seasonal course of carbon fluxes and evapotranspiration in response to low temperature and moisture in a boreal Scots pine ecosystem

Environmental conditions act above and below ground, and regulate carbon fluxes and evapotranspiration. The productivity of boreal forest ecosystems is strongly governed by low temperature and moisture conditions, but the understanding of various feedbacks between vegetation and environmental conditions is still unclear. In order to quantify the seasonal responses of vegetation to environmental factors, the seasonality of carbon and heat fluxes and the corresponding responses for temperature and moisture in air and soil were simulated by merging a process-based model (CoupModel) with detailed measurements representing various components of a forest ecosystem in Hyytiälä, southern Finland. The uncertainties in parameters, model assumptions, and measurements were identified by generalized likelihood uncertainty estimation (GLUE). Seasonal and diurnal courses of sensible and latent heat fluxes and net ecosystem exchange (NEE) of CO₂ were successfully simulated for two contrasting years. Moreover, systematic increases in efficiency of photosynthesis, water uptake, and decomposition occurred from spring to summer, demonstrating the strong coupling between processes. Evapotranspiration and NEE flux both showed a strong response to soil temperature conditions via different direct and indirect ecosystem mechanisms. The rate of photosynthesis was strongly correlated with the corresponding water uptake response and the light use efficiency. With the present data and model assumptions, it was not possible to precisely distinguish the various regulating ecosystem mechanisms. Our approach proved robust for modeling the seasonal course of carbon fluxes and evapotranspiration by combining different independent measurements. It will be highly interesting to continue using long-term series data and to make additional tests of optional stomatal conductance models in order to improve our understanding of the boreal forest ecosystem in response to climate variability and environmental conditions.     

Der einfluß der temperatur auf die substrat-affinität der laktat-dehydrogenase aus fischen

If the activity of lactate-dehydrogenase (LDH) at small pyruvate concentrations (e.g. 20μM), as found in vivo, is measured, no temperature-dependence of the reaction-velocity is noted. This finding implies, for a poikilothermic animal (e.g. the fish Rhodeus amarus), that in physiological substrate concentrations, the velocity of enzymatic reaction is temperature-independent. In the LDH of R. amarus acclimated to 10° or 20°C, the enzyme-substrate-affinity, as judged by the Michaelis-constant (K _M), changes inversely with temperature. In contrast to R. amarus, K _M-values of Idus idus have a minimum temperature range identical to the adaptation temperature (AT). The momentary AT (e.g. 10°, 20°C) induces the disposition of an enzyme with greatest substrate-affinity at that temperature, which coincides with the AT. Estimating the activation energy (′E _a=μ) through the Arrhenius-plot, ′E _a for LDH of I. idus amounts to 8.2 kcal/mol in the experimental temperature (ET) range of 5° to 15°C. For ETs above 15°C, a value of ′E _a=12 kcal/mol is found. LDH of I. idus of 20°C, however, shows a smaller value of ′E _a=7.8 kcal/mol beyond ET=15°C; below ET=15°C, ′E _a=10 kcal/mol. If the AT of R. amarus of 10°C is raised to 25°C, and the K _M of LDH for substrate pyruvate and cosubstrate NADH (ET always 25°C) is measured, a dampened oscillation-like curve will be found, depending on time.     

Assessment of canopy stomatal conductance models using flux measurements

Stomatal conductance (g) is a key parameter in controlling energy and water exchanges between canopy and the atmosphere. Stomatal conductance models proposed by Ball, Woodrow and Berry (BWB) and Leuning have been increasingly used in land surface schemes. In a recent study, a new diagnostic index was developed by Wang et al. to examine the response of g to humidity and new models were proposed to resolve problems identified in the BWB and Leuning models. This approach is theoretically sound, but relies on canopy latent heat and CO₂ fluxes and environmental variables at the leaf surface which are not available at most eddy correlation (EC) observation sites. In this study, we tested the diagnostic index by empirically correcting EC measurements to canopy-level fluxes and by replacing leaf surface variables by their corresponding ambient air variables, and re-examined the stomatal conductance models of BWB, Leuning, and Wang et al. We found that the impact of the above modifications on the evaluation of g–humidity relationships is very small. This study provides a practical approach to investigate the stomatal response to humidity using routine EC measurements.     

Modeling amphibian energetics, habitat suitability, and movements of western toads, Anaxyrus (=Bufo) boreas, across present and future landscapes

Effective conservation of amphibian populations requires the prediction of how amphibians use and move through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach that uses the physiological attributes of amphibians, together with knowledge of their natural history, should be helpful. We used Niche Mapper™ to model the known movements and habitat use patterns of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern Idaho. Niche Mapper uses first principles of environmental biophysics to combine features of topography, climate, land cover, and animal features to model microclimates and animal physiology and behavior across landscapes. Niche Mapper reproduced core body temperatures (T_c) and evaporation rates of live toads with average errors of 1.6 ± 0.4 °C and 0.8 ± 0.2 g/h, respectively. For four different habitat types, it reproduced similar mid-summer daily temperature patterns as those measured in the field and calculated evaporation rates (g/h) with an average error rate of 7.2 ± 5.5%. Sensitivity analyses indicate these errors do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male toads (74.2 ± 6.8% and 53.6 ± 15.8%, respectively), reflecting the stronger patterns of habitat selection among females. Using these changing to construct a cost surface, we also reconstructed movement paths that were consistent with field observations. The effect of climate warming on toads depends on the interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby limiting the activity for toads in different habitats.     

Sensitivity of modelled gross primary productivity to topographic effects on surface radiation: A case study in the Cotter River Catchment, Australia

Gross primary productivity (GPP) is a critical response variable for many environmental problems, including terrestrial carbon accounting and the calculation of catchment water balances. Various approaches for modelling GPP have been developed and applied at continental and landscapes scales, but little attention has been given to the sensitivity of GPP to the spatial scale of its driving variables. A key driving variable is surface radiation (R_s) which is influenced by both meso-scale factors (latitude, time of year, cloudiness) and the topographic variables of slope, aspect and horizon shading. We compared the sensitivity of modelled GPP to two different sources of surface radiation (R_s): (1) the ANUCLIM method which only captures the meso-scaled factors; and (2) the SRAD method which incorporates the topographic effects GPP was calculated using the radiation use efficiency (RUE) model (Roderick et al., 2001) to discern general patterns of vegetation productivity at a sub-catchment (i.e. sub-water shed) scale. The radiation use efficiency approach uses the normalized difference vegetation index (NDVI) derived from satellite data (MODIS TERRA), along with estimates of solar radiation at the top of the atmosphere (R_o) and canopy (R_s). In this approach, R_o and R_s capture the influence of diffuse irradiance in canopy photosynthesis and vegetation productivity respectively. This research showed that R_s calculated using the SRAD program provides important discrimination of GPP regimes at a sub-catchment scale, as the result of minimum and maximum daily radiation varying between shaded and exposed surfaces. However, mean daily radiation at a whole-of-catchment scale did not differ between the two sources as the differences in the minimum and maximum daily values tend to cancel each other out. Applications of GPP models therefore need to consider whether topographic factors are important and select the appropriate source of R_s values. GPP models should also reflect understanding of radiation use efficiency. However, further research is required especially with respect to the influence of water stress on plant response.     

Introducing effects of temperature and CO2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO₂ on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO₂, stand density and the tree's competition status in a stand of Scots pine (Pinus sylvestris), silver birch (Betula pendula) and Norway spruce (Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO₂ elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained.The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO₂. These calculations revealed that the growth response of individual trees to elevated temperature and CO₂ can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.     

Ammonium excretion by the ophiuridOphiothrix fragilis as a function of season and tide

Ammonium excretion of a dense population (~1 500 individuals m^–2) of the ophiuridOphiothrix fragilis (Abildgaard) was measured in the Dover Straits (French coast) between May 1989 and March 1990: the excretion rate varied from 4.8 µg N g^–1 dry wt h^–1 in November to 12.8 µg N g^–1 dry wt h^–1 in June. Mean individual ammonium excretion,E, wasE=0.019t +1.26 (whereE=µg N individual^–1 andt=time in min;r=0.80;N=81). Variations in the ammonium excretion rate during a tidal cycle appeared to arise from variations in the duration of the suspension-feeding activity ofO. fragilis, which was governed by the strength of the tidal current. During short-term starvation, excretion was low (E=0.009t+1.47;r=0.91;N=17), increasing with increasing length of starvation [E=4.62lnt–2.5;r=0.95;N=17], as observed for other echinoderms; this could be due to catabolism of tissue. The daily ammonia flux from thisO. fragilis population to the water column was estimated at 41 mg N m^–2 d^–1.     

Influences of canopy structure and physiological traits on flux partitioning between understory and overstory in an eastern Siberian boreal larch forest

Boreal forests play an important role in the global balance of energy and CO₂. Our previous study of elaborate eddy covariance observations in a Siberian boreal larch forest, conducted both above the forest canopy and at the forest floor, revealed a significant contribution of latent heat flux (LE) from the cowberry understory to the whole ecosystem LE. Thus, in the present study, we examined what factors control the partitioning of whole ecosystem LE and CO₂ flux into the understory and overstory vegetation, using detailed leaf-level physiology (for both understory and overstory vegetation) and soil respiration property measurements as well as a multilayer soil-vegetation-atmosphere transfer (SVAT) model. The modeling results showed that the larch overstory's leaf area index (LAI) and vertical profile of leaf photosynthetic capacity were major factors determining the flux partitioning in this boreal forest ecosystem. This is unlike other forest ecosystems that tend to have dense LAI. We concluded that control of the larch overstory's LAI had a relationship with both the coexistence of the larch with the cowberry understory and with the water resources available to the total forest ecosystem.     

Mathematical analysis of change in forest carbon use efficiency with stand development: A case study on Abies veitchii Lindl.

Changes in carbon use efficiency (CUE), which is defined as the ratio of net primary production (NPP) to gross primary production (GPP), were analyzed for Abies veitchii Lindl. forests with respect to stand development by developing a simple mathematical model incorporating data on physiological variables and leaf mass ratio. A decrease in CUE with stand development was successfully expressed as a function of stand biomass (y) based on the following three assumptions: (1) a power-law relationship between mean respiration and mean individual tree mass, (2) a power-functional relationship between mean gross primary production and mean individual tree mass, and (3) self-thinning relationship between stand biomass and density. Based on this model, a parameter of CUE–y relationship was defined, and it was clarified that CUE decrease with stand development is caused not by the ratio of specific respiration rate to specific gross photosynthetic rate, but by leaf mass ratio. Since CUE is high in young forests, helpful information on selecting woody species when planting seedlings was provided from the viewpoints of reducing CO₂ in the atmosphere and global warming.     

More asymmetric tree competition brings about more evapotranspiration and less runoff from the forest ecosystems: A simulation study

The present paper reports how stand size-structure dynamics due to competition between different-sized trees affect long-term forested water balance in Japanese cool-temperate planted stands (evergreen coniferous Cryptomeria japonica and deciduous coniferous Larix kaempferi stands) using a fully coupled multi-layered meteorological surface physics—terrestrial ecosystems model. The simulation captured the well-known annual variation in leaf area index (LAI) accurately with stand age in monocultured and even-aged stands; the occurrence of maximum LAI during the early growth stage and then a gradual decline followed by a steady state after the maximum LAI. The simulations also detected a high dependency of annual evapotranspiration (AETr) on LAI with stand age that is well known by prior observational researches. In the C. japonica (shade-tolerant late-successional species) stand, the relationship between annual net primary productivity of an individual tree (NPP_ind) and individual tree mass (w) changed from linear to a convex curve during self-thinning, indicating that the degree of asymmetric tree competition intensified with forest stand development. The higher degree of competitive asymmetry characterized by the convex-shaped NPPind-w relationship produced greater size inequality, i.e., the formation of trees stratified by height. Under such conditions, AETr and annual transpiration (ATr) were mainly regulated by larger trees. On the other hand, the NPPind-w relationships in the L. kaempferi (shade-intolerant early-successional species) stand were linear throughout the simulated period, indicating the lower degree of competitive asymmetry. Under such conditions, the growth of intermediate-sized trees was enhanced and these trees became a dominant source of AETr (and also ATr) during self-thinning. Furthermore, the sensitivity analysis of the effects of ecophysiological parameters such as foliage profile (i.e., vertical distribution of leaf area density) of an individual tree (distribution pattern is described by the parameter η), the maximum carboxylation velocity (V_cmax0) and biomass allocation pattern of individual plant growth (μ₁) on AETr, ATr and annual runoff (AR_off) showed that the temporal trends of AETr, ATr, AR_off and NPPind-w relationships were completely the same as those in the control simulations. However, the NPPind-w relationship during self-thinning indicated higher degrees of competitive asymmetry when η or V_cmax0 were greater than those in the control simulation and generated greater AETr and ATr and thus smaller AR_off. We found that more asymmetric tree competition brings about greater size inequality between different-sized trees and thus more evapotranspiration and less runoff in a forest stand. Overall, our simulation approach revealed that not only LAI dynamics but also plant competition, and thus size-structure dynamics, in a forest ecosystem are essential to long-term future projections of forested water balance.     

A general solution of Benjamin-type gravity current in a channel of non-rectangular cross-section

We consider the steady-state propagation of a high-Reynolds-number gravity current in a horizontal channel along the horizontal coordinate x. The bottom and top of the channel are at z =?0, H, and the cross-section is given by the quite general form ?f ₁(z) ≤?y ≤?f ₂(z) for 0 ≤?z ≤?H, where f _1,2 are piecewise continuous functions and f ₁ +?f ₂ >?0 for ${z \in(0,H)}$ . The interface of the current is horizontal, the (maximum) thickness is h, its density is ρ _c . The reduced gravity g′ =?|ρ _c /ρ _a ? 1|g (where ${- g\hat{z}}$ is the gravity acceleration and ρ _a the density of the ambient) drives the current with speed U into the stationary ambient fluid. We show that the dimensionless Fr =?U/(g′ h)^1/2, the rate of energy dissipation (scaled with the rate of pressure work), and the dimensionless head-loss Δ/h, can be expressed by compact formulas which involve three integrals over the cross-section areas of the current and ambient. By some standard manipulations these integrals are simplified into quite simple line-integrals of the shape-function of the channel, f(z) =?f ₁(z) +?f ₂(z), and of z f(z). This theory applies to Boussinesq and non-Boussinesq currents of “heavy” (bottom) and “light” (top) type. The classical results of Benjamin (J Fluid Mech 31:209–248, 1968) for a rectangular channel are fully recovered. We also recover the Fr results of Marino and Thomas (J Fluid Eng 131(5):051201, 2009) for channels of shape y =?±b z ^α (where b, α are positive constants); in addition, we consider the energy dissipation of these flows. The results provide insights into the effect of the cross-section shape on the behavior of the steady-state current, in quite general cases, for both heavy-into-light and light-into-heavy fluid systems, Boussinesq and non-Boussinesq. In particular, we show that a very deep current displays ${Fr = \sqrt{2}}$ , and is dissipative; the value of Fr and rate of dissipation (absolute value) decrease when the thickness of the current increases. However, in general, energy considerations restrict the thickness of the current by a clear-cut condition of the form h/H ≤?a _max ?< 1.