Mechanisms of moisture stress in a mid-latitude temperate forest: Implications for feedforward and feedback controls from an irrigation experiment

While it is well established that stomata close during moisture stress, strong correlations among environmental (e.g., vapor pressure deficit, soil moisture, air temperature, radiation) and internal (e.g., leaf water potential, sap flow, root-shoot signaling) variables obscure the identification of causal mechanisms from field experiments. Models of stomatal control fitted to field data therefore suffer from ambiguous parameter identification, with multiple acceptable (i.e., nearly optimal) model structures emphasizing different moisture status indicators and different processes. In an effort to minimize these correlations and improve parameter and process identification, we conducted an irrigation experiment on red maples (Acer rubrum L.) at Harvard Forest (summers of 2005 and 2006). Control and irrigated trees experienced similar radiative and boundary layer forcings, but different soil moisture status, and thus presumably different diurnal cycles of internal leaf water potential. Measured soil moisture and atmospheric forcing were used to drive a transient tree hydraulic model that incorporated a Jarvis-type leaf conductance in a Penman–Monteith framework with a Cowan-type (resistance and capacitance) tree hydraulic representation. The leaf conductance model included dependence on both leaf matric potential, Ψ_L (so-called feedback control) and on vapor pressure deficit, D (so-called feedforward control). Model parameters were estimated by minimizing the error between predicted and measured sap flow. The whole-tree irrigation treatment had the effect of elevating measured transpiration during summer dry-downs, demonstrating the limiting effect that subsurface resistance may have on transpiration during these times of moisture stress. From the best fitted model, we infer that during dry downs, moisture stress manifests itself in an increase of soil resistance with a resulting decrease in Ψ_L, leading to both feedforward and feedback controls in the control trees, but only feedforward control for the irrigated set. Increases in the sum-of-squares error when individual model components were disabled allow us to reject the following three null hypotheses: (1) the f(D) stress is statistically insignificant (p = 0.01); (2) the f(Ψ_L) stress is statistically insignificant (p = 0.07); and (3) plant storage capacitance is independent of moisture status (p = 0.07).     

Integrating effects of leaf nitrogen,age, rank,and growth temperature into the photosynthesis-stomatal conductance model LEAFC3-N parameterised for barley (Hordeum vulgare L.)

A crucial challenge for including biophysical photosynthesis–transpiration models into complex crop growth models is to integrate the plasticity of photosynthetic processes that is related to factors like nitrogen (N) content, age, and rank of leaves, or to the adaptation of plants to growth temperature (T_g). Here we present a new version of the combined photosynthesis-stomatal conductance model LEAFC3-N [Müller, J., Wernecke, P., Diepenbrock, W., 2005. LEAFC3-N: a nitrogen sensitive extension of the CO₂ and H₂O gas exchange model LEAFC3 parameterised and tested for winter wheat (Triticum aestivum L.). Ecological Modelling 183, 183–210.] that was revised, extended and completely re-parameterised for barley (Hordeum vulgare L.) with special regard for these factors to facilitate the use of the model in ecophysiological studies and in crop modelling. The analysis is based on novel comprehensive data on photosynthetic CO₂ and light response curves measured at two oxygen concentrations and different temperatures on leaves of barley (H. vulgare L.) differing in leaf N and chlorophyll content. Plants were grown in climatic chambers or in the field at different N and T_g.We thoroughly revised the existing and introduced new nitrogen relations for key model parameters that account for a linear increase with leaf N of V_max, J_max, T_p, and R_dmax (maximum rates of carboxylation, electron transport, triose phosphate export, and mitochondrial respiration), a saturation-type increase of φ (quantum yield of electron transport), and a non-linear decrease of θ and m (curvature of the light dependence of electron transport rate, scaling factor of the stomata model). The adaptation of photosynthetic characteristics to T_g was included into the model by linear relations that were observed between T_g and the activation energy ΔH_a of the temperature response characteristics of V_max, J_max, and T_p as well as of the nitrogen dependency of these characteristics. Based on an analysis of diurnal time courses of gas exchange rates it was found necessary including not only the relation between leaf water potential (Ψ) and stomatal conductance as used originally in LEAFC3, but additional effects on V_max and J_max. With the above-listed extensions, the model was capable to reproduce the observed plasticity and the recorded diurnal time courses of gas exchange rates fairly well. Thus, we conclude that the new model version can be used under a broad range of conditions, both for ecophysiological studies and as a submodel of crop growth models. The results presented here for barley will facilitate adapting photosynthesis models like LEAFC3-N to other C₃-species as well. The modelling of the effects of drought stress should be further elaborated in future based on more specific experiments.     

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.     

Climate, canopy conductance and leaf area development controls on evapotranspiration in a boreal coniferous forest over a 10-year period: A united model assessment

The aim of this work was to test a process-based model (hydrological model combined with forest growth model) on the simulation of seasonal variability of evapotranspiration (ET) in an even-aged boreal Scots pine (Pinus sylvestris L.) stand over a 10 year period (1999-2008). The water flux components (including canopy transpiration (E_t) and evaporation from canopy (E_c) and ground surface (E_g) were estimated in order to output the long-term stand water budget considering the interaction between climate variations and stand development. For validation, half-hourly data on eddy water vapor fluxes were measured during the 10 growing seasons (May-September). The model predicted well the seasonal course of ET compared to the measured values, but slightly underestimated the water fluxes both in non-drought and drought (2000, 2003 and 2006) years. The prediction accuracy was, on average, higher in drought years. The simulated ET over the 10 years explained, on average, 58% of the daily variations and 84% of the monthly amount of ET. Water amount from E_t contributed most to the ET, with the fractions of E_t, E_c and E_g being, on average, 67, 11 and 23% over the 10-year period, respectively. Regardless of weather conditions, the daily ET was strongly dependent on air temperature (T_a) and vapor pressure deficit (D_a), but less dependent on soil moisture (W_s). On cloudy and rainy days, there was a non-linear relationship between the ET and solar radiation (R_o). During drought years, the model predicted lower daily canopy stomatal conductance (g_cs) compared with non-drought years, leading to a lower level of E_t. The modeled daily g_cs responded well to D_a and W_s. In the model simulation, the annual LAI increased by 35% between 1999 and 2008. The ratio of E_c: ET correlated strongly with LAI. Furthermore, LAI reduced the proportion of E_g as a result of the increased share of E_c and E_t and radiation interception. Although the increase of LAI affected positively E_t, the contribution of E_t in ET was not significantly correlated with LAI. To conclude, although the model predicted reasonably well the seasonal course of ET, the calculation time steps of different processes in the model should be homogenized in the future to increase the prediction accuracy.     

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.     

A Modelling Study of Transient,Buoyancy-Driven Exchange Flow over a Descending Barrier

Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density ₀ and ₀+()₀, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7% and 3% are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show (and the theoretical model predictions confirm) that (i) the dimensionless time of detection t _det(g/H _b)^1/2 of the brackish water pool fed by the dense outflow increases (at a given distance from the barrier) with increasing values of the descent rate parameter g'H _b/(dh _b/dt)² and (ii) the normalised thickness (x,t)/H _b of the pool at a given reference station increases monotonically with increasing values of the modified time (t–t _det)/(H _b/g)^1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g'H _b(dh _b/dt)². Here, g=(g/₀)()₀ is the modified gravitational acceleration, H _b is the mean depth of the water and dh _b/dt denotes the rate of descent of the barrier height h _b with elapsed time t after the two water bodies are first brought into contact.     

Parameter fitting in dynamic models

We consider the numerical approaches for the least squares estimation of the parameter vector p in the initial value problem y′ = g(t, y, p), y(t₀) = y₀(p) when observations are available on some or all components of the vector y(t). Special attention is paid to the development of techniques which, although not global, are less sensitive to initial parameter estimates than the standard approach employing the sensitivity equations. Experience indicates that interactive approaches can be very valuable when good starting parameter approximations are unavailable. We describe the main features of our interactive parameter fitting package PARFIT. This package contains standard techniques employing the sensitivity equations as well as special algorithms designed to improve poor parameter estimates. These special algorithms have been selected and developed with user interaction in mind. We describe in detail one special approach designed for the case when observations are not available on all state variables. An example (using computer generated observations) is presented to illustrate this approach. Finally, the power of an interactive approach is demonstrated with two examples involving attempts to model physically observed phenomena.     

A peaked function for modeling temperature dependence of plant productivity

We suggests that temperature response of plant productivity can be modeled by the Arrhenius function modified to describe the effect of temperature on enzyme activity: G_A(T) = 2f(T)/(1 + f²(T)), where f(T) = exp(E_a/RT_opt − E_a/RT), R the universal gas constant, E_a the activation energy and T_opt is the optimal temperature. In common with other functions used for modeling the temperature response of plant productivity, the curve of function G is almost symmetrical and bell-shaped. The special convenience of G_A is that it relates the width of the “bell” to thermodynamic concepts, such as activation energy of chemical reactions converting carbon dioxide and water to carbohydrates.     

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.     

Effects of body size and temperature on the metabolic rate of Penaeus monodon

Laboratory measurements of oxygen consumption were made on Penaeus monodon (Fabricius) from protozoea to adult stage at temperatures between 15° and 35°C. The logarithmic relationship between weight-specific respiration rate (WRt) and temperature (T) for two size groups, Protozoea 1 (PZ1) to Postlarva 1 (PL1) and PL to adult, are given as; WRt=10^{0.431+0.0146 (T)} (ml O₂ g^-1 h^-1) and WRt=10^{-0.948+0.0338 (T)} (ml O₂ g^-1 h^-1), respectively. Additionally, equations relating metabolic rate, temperature and size for the two size groups are; PZ1-PL1: log M=0.431+0.0146T+(1.25 (log TL)+0.579), and PL1-adult: log M=-0.948+0.0338T+(2.60(log CL)-0.683), where M=oxygen consumption in ml O₂ individual ^-1h^-1, T=temperature in °C, TL=total length in cm, and CL=carapace length in cm. Activation energies of 6 186.75 J for PZ1-PL1 and 14 066.62 J for PL-adults point to different metabolic pathways or to differences in the ratio between the metabolic pathways used.     

Release thresholds strongly determine the range of seed dispersal by wind

The effect of the seed abscission process on the dispersal distance of seeds has never been studied explicitly and is often ignored in studies that aim to estimate the seed shadows of species. To examine the importance of the abscission process for the seed shadow we used a seed trajectory model that keeps track of the release threshold dynamics of the individual seeds on mother plant. We defined the release threshold as the critical wind speed that induces a mechanical force that is just large enough to release a seed from its mother plant. The model used real wind speed sequences and seed appearance over time on the mother plant.Several calculations were performed to investigate the effect of release thresholds dynamics on seed shadow of two herbaceous species with contrasting terminal velocity values (V_t): Centaurea jacea (V_t = 4.1 m s⁻¹) and Hypochaeris radicata (V_t = 0.49 m s⁻¹).Release thresholds were responsible for a two-fold increase of median dispersal distances in both species. Tails of the seed shadows, the fraction of seeds that travel furthest, were even more sensitive and increased with a factor 4.5 for Centaurea and 7.0 for Hypochaeris. Our work indicates that the abscission process appears to be very important and suggests that dispersal distance of plants is currently severely underestimated, which, in turn, has major consequences for our current understanding of the distribution, metapopulation dynamics and survival of plant species.     

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited ‘universal’ mass scaling exponent (b) of ¾ representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO₂ and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.     

Modelling of leachates from dolomitic mine tailings

The REDEQL.EPAK computer model was used to study speciation of Pb, Cd, Zn, and Ca in leachates from dolomitic Pb mine tailings. By allowing or disallowing precipitation of solids and equilibration of the modelled leachate with atmospheric C0₂, comparison of fresh and aged leachates was made. The effects of treatment of the tailings with phosphate containing fertilizer were studied through addition of P0₄ ^3– to the modelled solution. Equilibrium constants pertaining to metal ion-humic acid complexation were added to the thermodynamic data base of the model in order to study the effects of decaying plant material on tailings leachate.Initial leachate of the tailings is found to be supersaturated with Cd and Zn. Non-complexed (free) Cd²⁺ and Zn²⁺ is predicted to comprise most of the soluble form of these metals in the leachate; Pb is predicted to be present largely as PbCO₃ ion pair. Equilibration of the leachate with the atmosphere is predicted to lead to extensive precipitation of CdCO₃ and ZnSiO₃. Precipitation of Pb₅(PO₄)₃Cl is predicted at high PO₄ ^3– concentration and at low pH. Complexation by the humic acid is predicted to compete effectively with other ligands in the leachate for the metal ions. The results are compared with experimental findings.     

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.     

Optimizing the configuration of a clearwell by integrating pilot and full-scale tracer testing

In this paper, the main factors impacting the plug flow pattern of a clearwell were investigated by integrating pilot-scale, full-scale clearwell tracer testing and computational fluid dynamics (CFD) simulation. It was found that pilot tracer testing, full-scale tracer testing and CFD simulation all demonstrated that the correlation between the ratio of t ₁₀/T and L/W can be approximately expressed by: t ₁₀/T = 0.189 4ln(L/W)-0.049 4. This study confirmed that the installation of baffles within clearwells is an efficient way to optimize their configuration. In addition, the inlet velocity has a minimal contribution to the ratio of t ₁₀/T. However, the ratio of turning channel width to channel width (d/W) significantly contributes to the ratio of t ₁₀/T. The optimal ratio of d/W is 0.8–1.2 for maintaining better plug flow pattern. The number of turning channels is one of the main factors that impact the ratio of t ₁₀/T. When increasing the number of turning channels, a lower ratio of t ₁₀/T is obtained.     

The theoretical basis for estimating phytoplankton production and specific growth rate from chlorophyll, light and temperature data

Phytoplankton maximum specific growth rate, μ_max, and maximum photosynthetic quantum yield, Φ_max, can be related mathematically via the photosynthetic light curve, P(I). A model is presented in which maximum quantum yield defines the initial slope of the light curve and is assumed to be a known constant, while maximum specific growth rate defines the light-saturated region of the curve and is assumed to be a known function of temperature. The effect of introducing μ_max(T) into P(I, Φ_max) is to replace the unknown, temperature-dependent light saturation parameter with a term involving the ratio μ_max/Φ_max. The advantage of writing P(I) in terms of both μ_max and Φ_max is that those parameters are particularly well documented in the literature. Consequently, estimates of nutrient-unlimited phytoplankton growth and production rates can be based solely on the constants μ_max, Φ_max and k_c (light absorption per unit of chlorophyll) and the free variables light, temperature and chlorophyll concentration. Rate estimates appear to be accurate to within a factor of two for an extremely wide range of conditions.One particularly significant result of introducing μ_max into P(I, Φ_max) is that the carbon : chlorophyll ration, θ, appears explicitly. It is possible to derive an expression for optimum θ based on the assumption that adaptive changes in carbon/chlorophyll occur so as to maximize the specific growth rate for given conditions of light and temperature. Laboratory and field data are compiled from the literature to test the formulae presented here.     

The effect of estimated PAR uncertainties on the physiological processes of biosphere models

Photosynthetically active radiation (PAR) energy reaching on the vegetated surface is a key determinant of plant physiological processes. Most of biosphere or crop models use the ratio of PAR to incoming solar radiation (R_s), PAR/R_s, to convert R_s into PAR in order to reduce weather data-input requirements. Several existing models simply specify a constant ratio, PAR/R_s = 0.5. However, some field experiments have reported that the ratio PAR/R_s may not be constant. Previous empirical equations of PAR/R_s were derived based on the data of monthly or daily timescales collected from only a few measurement sites, hence they may not be appropriate to be used in current global biosphere models usually with hourly simulation time steps. Here, we represent the exponential correlation between PAR/R_s and sky clearness index (0-1) using hourly data from 54 Ameriflux measurement sites. It is found that PAR/R_s increases up to 0.6 in cloudy conditions when the clearness index (CI) is below ∼0.2, whereas it is nearly constant at ∼0.42 when CI is above 0.2. When the identified empirical equation is used in the model simulation, it results in −4 to 2% difference in the stomatal conductance compared to that using the constant ratio PAR/R_s = 0.5.     

Energy conservation in hibernating endotherms: Why “suboptimal” temperatures are optimal

Many endotherms use facultative heterothermic responses of torpor or hibernation to conserve energy during periods of low energy availability. A common assumption when estimating winter energy budgets is that endotherms should hibernate at the ambient temperature (T_a) that minimizes torpid metabolic rate (TMR) and maximizes the duration of torpor bouts. However, previous studies of the energetic benefits of hibernation have assumed constant T_a within hibernacula. Here we use an individual-based energetic model to estimate overwinter energy expenditure of mammals hibernating at T_as that vary temporally. We show that, in accordance with the principles of Jenson's inequality, hibernators can conserve energy by selecting microclimates warmer than the single T_a value that minimizes TMR (T_min). As temporal variation in T_a increases, endotherms should choose microclimates with mean T_as progressively warmer than T_min. Further, as thermal conductance decreases, as it does with increasing body mass and use of social thermoregulation, the mean T_a that minimizes overwinter energy expenditure approaches, but never equals, T_min. We suggest that the commonly held assumption of stable microclimates in hibernacula has skewed the interpretation of the optimal expression of hibernation for energy conservation. Our results contradict much of the accepted understanding of hibernation energetics and add to a growing body of literature proposing that hibernating at a T_a warmer than T_min is optimal.