Development of a Novel Hydrodynamic Approach for Modeling Whole-Plant Transpiration

Development of a Novel Hydrodynamic Approach for Modeling Whole-plant Transpiration

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Golnazalsadat Mirfenderesgi

Graduate Program in Civil Engineering

The Ohio State University

2017

Dissertation Committee:

Gil Bohrer, Advisor

Peter S. Curtis

Ethan Kubatko

Andrew A. May

Copyrighted by

Golnazalsadat Mirfenderesgi

2017

Abstract

The Finite-difference Ecosystem-scale Tree-Crown Hydrodynamics model

(FETCH2) is a novel tree-scale hydrodynamic model of transpiration. The FETCH2 model employs a finite difference numerical methodology and a simplified single-beam conduit system and simulates water flow through the tree as a continuum of porous media conduits.

It explicitly resolves xylem water potential throughout the tree’s vertical extent (from root to shoot). Empirical equations relate water potential within the stem to stomatal conductance of the leaves at each height throughout the crown. While highly simplified, this approach brings additional realism to the simulation of transpiration by linking stomatal responses to stem water potential rather than directly to soil moisture, as is currently the case in the majority of land-surface models. FETCH2 accounts for plant hydraulic traits, such as the degree of anisohydric/isohydric response of stomata, maximal xylem conductivity, vertical distribution of leaf area, rooting depth, and maximal and minimal stem water content.

We used FETCH2 along with sap flow and eddy covariance data sets to conduct an analysis of the inter-genera variation of hydraulic strategies and their effects on diurnal and seasonal transpiration dynamics. We define these strategies through the parameters that describe the genus-level transpiration and xylem conductivity responses to changes in stem water potential. Using a virtual experiment, we showed that the model was able to capture

ii the effect of hydraulic strategies such as isohydric/anisohydric behavior on stomatal conductance under different soil-water availability conditions. Our evaluation revealed that

FETCH2 considerably improved the simulation of ecosystem transpiration and latent heat flux than more conventional models.

Whole-plant hydraulic performance depends on the integrated function of complexes of traits, such as embolism resistance and xylem anatomy, stomatal closure mechanisms, hydraulic architecture, and root properties. The diversity of such traits produces a wide range of response strategies to both short-term variation of environmental conditions and long-term changes to climate and hydrological cycles which affect water availability. FETCH2 resolves plant functional traits at the root, stem and leaf levels and simulates the integrated plant-level transpiration, provided hydraulic traits and environmental forcing. This framework may be helpful in studying the influence of each suits of plant hydraulic traits independently and assess how the different trait groups interact with each other to form viable hydraulic strategies for different environmental conditions.

We define a multi-dimensional hydraulic “strategy space” by considering a broad continuum of hydraulic traits at each of the leaf, stem, and root levels, and test the consequences of different strategies under a range of environmental conditions in a research forest in Northern Michigan, USA. We evaluated the degree to which simulated trees suffer hydraulic failure due to cavitation resulting in loss of xylem conductivity or carbon starvation through leaf-water-potential-driven reduction of stomatal conductance.

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Finally we concluded that incorporation of the plant functional traits into FETCH2 allows us to simulate the dissimilar water use patterns of species with contrasting hydraulic strategies. This will improve predictions of transpiration, growth, and mortality, and consequently simulations of the surface energy budget and the global carbon and water balances.

Dedication

To my parents,

For their love, support, and kind guidance. I owe them everything I have achieved in my life

To my husband

For being the best thing happened to me in this life and for supporting me during my PhD studies

And to the memory of my grandfather

Acknowledgments

I would like to thank my advisor, Gil Bohrer, for his mentorship, support, and encouragement; Karina Schäfer for providing data for parametrization of FETCH2, including sap flux and meteorological observations collected from Silas little experimental forest; Peter Curtis, Ethan Kubatko, Gaj Sivandran, and Andrew May for their guidance as my thesis committee; Simone Fatichi for his assistance and direction in development of the capacitance term for FETCH2; Renato Frasson for his assistance in the process of data preparation for the model and learning ED2; Tim Morin, Ashley Matheny, Camilo Rey

Sanchez, and Stephano Manzoni for providing the data for model simulation and parameterizations of FETCH2; And all of my current and previous lab members.

Funding for this study was provided the National Science Foundation Hydrological

Science grant 1521238. Meteorological observations at the UMBS are supported in part by

U.S. Department of Energy’s Office of Science, Ameriflux Management Program under

Flux Core Site Agreement No. 7096915 through Lawrence Berkeley National Laboratory.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

Vita

May 2005 ...... Isfahan University of Technology high

School, Isfahan, Iran

Summer 2007 ...... Structural Design Intern, Organization for

development, Renovation and Equipping

Schools of I.R.Iran, Isfahan, Iran

Summer 2007 ...... Structural Engineer, Tara Tahlil Sazeh

Consulting Firm, Isfahan, Iran

June 2008 ...... B.S. Civil Engineering (Structural

Engineering), Isfahan University of

Technology, Isfahan, Iran

Summer 2008 ...... Structural Engineer, Saraman Isfahan Co,

Isfahan, Iran

2011...... M.Sc Civil Engineering (Water

Engineering), AmirKabir University of

Technology (Tehran Polytechnic), Tehran,

Iran vii

2012-2013 ...... Graduate Research Associate, Portland State

University, Portland, OR

Jan 2013 ...... Graduate Teaching Associate, Portland State

University, Portland, OR

2013 to resent ...... Graduate Research Associate, Civil,

Environmental and Geodetic Engineering,

the Ohio State University, Columbus, OH

Spring 2015 ...... Graduate Teaching Associate, Civil,

Environmental and Geodetic Engineering,

the Ohio State University, Columbus, OH

Spring 2017 ...... Instructure, Civil, Environmental and

Geodetic Engineering, the Ohio State

University, Columbus, OH

Publications

 Mirfenderesgi, G., G. Bohrer, A. M. Matheny, (2017), “Hydrodynamic Trait

Coordination and Cost-Benefit Tradeoffs throughout the Isohydric-Anisohydric

Continuum in Trees”, Ecohydrology (under submission).

 Rey-Sánchez, C., Bohrer, G., Morin, T. H., Sclomo, D., Mirfenderesgi, G., Gildor, H.,

Genin, A, (2017), “Evaporation and CO2 flux in a coastal reef lagoon: Comparing eddy

viii

covariance measurements to model estimates”, Ecosystem Health and Sustainability

(under review).

 J.C. Angle, T.H. Morin, G.J. Smith, L.M. Solden, A.B. Narrowe, M.A. Borton, R.A.

Daly, D.W. Hoyt, A.C. Rey-Sanchez, G. Mirfenderesgi, W.R. Riley, C.S. Miller, G.

Bohrer, K.C. Wrighton, (2017), “Methanogenesis in oxygenated soils is a substantial

fraction of wetland methane emissions”, Nature Communications (under review).

 Matheny, A.M., Mirfenderesgi, G., Bohrer, G., (2016) “Trait-based representation of

hydrological functional properties of plants in weather and ecosystem models”, Plant

Diversity, doi: 10.1016/j.pld.2016.10.001.

 Mirfenderesgi, G., G. Bohrer, A. M. Matheny, S. Fatichi, R. P. de M. Frasson, and K.

V. R. Schäfer, (2016), Tree level hydrodynamic approach for resolving aboveground

water storage and stomatal conductance and modeling the effects of tree hydraulic

strategy, J. Geophys. Res. Biogeosci., 121, doi:10.1002/2016JG003467.

 Mirfenderesgi, G., Mousavi, S.J., (2015) “Adaptive meta-modeling-based simulation

optimization in basin-scale optimum water allocation: a comparative analysis of meta-

models”, Journal of HydroiInformatics, 2015, DOI: 10.2166/hydro.2015.157.

 Matheny, M, A., Bohrer, G., Vogel, S, C., Morin, H, T., He, L., Mirfenderesgi, G.,

Schafer, V, K., Gough, M, C., Ivanov, V., Curtis, S, P., (2014) “Species-specific

transpiration responses to intermediate disturbance in a northern hardwood forest”,

Journal of Geophysical Research: Biogeosciences,

119, 2014JG002804. DOI:10.1002/2014JG002804.

Fields of Study

Major Field: Civil Engineering

Table of Contents

Abstract ...... ii

Dedication ...... v

Acknowledgments...... vi

Vita ...... vii

Table of Contents ...... xi

List of Tables ...... xv

List of Figures ...... xvii

Chapter 1: Introduction and Motivation ...... 1

1.1 Transpiration and Vegetation-Climate Feedbacks ...... 1

1.2 Modeling Vegetation Dynamics and Stomatal Functioning ...... 3

1.3 Hydraulic Functional Traits ...... 7

1.3.1 Leaf Traits ...... 8

1.3.2 Xylem Traits ...... 9

1.3.3 Root Traits ...... 10

1.4 Future Development ...... 12

1.5 Document Structure...... 13

Chapter 2: Finite difference Ecosystem-scale Tree Crown Hydrodynamics Model version

2 (FETCH2) Using Porous Media Flow Approach to Represent Whole Trees ...... 14

2.1 Introduction ...... 14

2.2 Governing Equations ...... 21

2.2.1 Stem Water Hydraulics ...... 23

2.2.2 Root Water Hydraulics ...... 27

2.2.3 Soil Water Hydraulics ...... 31

2.3 Vertically Discretized Forcing ...... 32

2.4 Discrete Approximation of The Continuous Flow Equation ...... 36

2.5 Boundary Condition ...... 40

2.6 Hydrological Outputs of FETCH2 ...... 42

2.7 Scaling to Plot Level ...... 42

Chapter 3: Tree-Level Hydrodynamic Approach for Modeling Aboveground Water

Storage and Stomatal Conductance Illuminates the Effects of Tree Hydraulic Strategy . 44

3.1 Introduction ...... 44

3.2 Materials and methods ...... 47

3.2.1 Study Site ...... 47

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3.2.2 Site Level Observations ...... 49

3.2.3 Aboveground-FETCH2 ...... 50

3.2.4 Hysteresis Calculation ...... 53

3.2.5 Parameter Estimation ...... 54

3.2.6 Evaluation of Model Performance ...... 59

3.2.7 Performance Measures ...... 62

3.2.8 Site-specific Simulation Setup...... 63

3.3 Results and Discussion ...... 65

3.3.1 Model Performance Evaluation ...... 65

3.3.2 Model Evaluation ...... 67

3.4 Identifying Differences in Hydraulic Strategies Between Oak and Pine ...... 73

3.5 Conclusions ...... 80

Chapter 4: Hydrodynamic Trait Coordination and Cost-Benefit Tradeoffs throughout the

Isohydric-Anisohydric Continuum in Trees ...... 82

4.1 Introduction ...... 82

4.2 Materials and Methods ...... 84

4.2.1 Site Description ...... 84

4.2.2 Model Parameters ...... 86

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4.2.3 Reducing Degrees of Freedom in the Leaf, Stem, and Root Trait Parameter

Space ...... 89

4.2.4 Quantifying the Cost of Hydraulic Stress ...... 97

4.2.5 Classification of “Wet”, “Intermediate” and “Dry” Days ...... 98

4.2.6 Numerical Experiment to Test the Consequences of Limited Water Availability

Under Different Hydraulic Traits ...... 100

4.3 Results and Discussion ...... 101

4.3.1 Quantifying the Safety-efficiency Trade-off ...... 108

4.4 Conclusions ...... 111

Chapter 5: Conclusions ...... 112

References: ...... 115

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List of Tables

Table 1. List of all variables, used in FETCH2 formulation ...... 17

Table 2. List of all the parameters selected for calibration. References relate to selection criteria for acceptable ranges...... 56

Table 3. List of all variables, used in PM formulation ...... 61

Table 4. Site-specific atmospheric and soil properties during the experiment’s period in

2009 and 2011...... 64

Table 5. Average of main attributes of the existing genera (oak/pine) at Silas Little experimental forest, New Jersey. The first four attributes are averages of the 21 trees with sap-flow measurements...... 65

Table 6. Performance metrics of NHL model, FETCH2, and Penman Monteith based on plot level transpiration hysteresis and half-hourly and mean daily simulations of transpiration (the bold numbers are the performance metrics that have been improved by

FETCH2 simulation) ...... 68

Table 7. Comparison between the Akaike Information Criteria (AIC) and Relative

Likelihood of NHL, PM and FETCH2 models ...... 69

Table 8. FETCH2 parameters, associated with plant traits at the root, stem and leaf levels, that assumed to be constant ...... 96

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List of Figures

Figure 1. Schematic view of the FETCH2. Left: dynamics of water flow within the tree xylem (roots and stem), water exchange between soil and roots, and water exchange between leaves and atmosphere. Middle: FETCH2 simplified the tree into a one- dimensional (1-D) conduit system, including the aboveground vertical distribution of leaf area and belowground root-mass distribution within the rooting depth. Right: finite difference discretization of the soil and xylem to solve for soil, root, and stem water potentials, and forcing through non-hydraulically limiting transpirational water sink. ... 16

Figure 2. Sensitivity analysis of the stomata response curve describing leaf vulnerability to stem water potential with respect to changes in c3 and Ф50,stomata. The parameters were selected according to the standard values found in Cruiziat et al. [2002]. c3 was allowed to vary between 1 and 10 (within each of the colored curve bundles) and Ф50,stomata was allowed to vary between 0.5 and 8 MPa (among the different colored curve bundles, light yellow for Ф50,stomata=-0.5 MPa gradually changing to dark blue for Ф50,stomata=-8 MPa). For water potentials larger than Ф50,stomata, larger c3 will lead to higher conductivity. For water potentials smaller than Ф50,stomata, smaller c3 leads to higher conductivity...... 24

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Figure 3. Sensitivity analysis of the xylem conductance response curve describing xylem vulnerability to stem water potential with to the changes in c2 and Ф50,stem. The parameters selected according to the standard values presented by Mayr et al. [2003]. c2,stem was allowed to vary between 1 and 10 (within each of the colored curve bundles) and Ф50,stem was allowed to vary between 0.5 and 8 MPa (among the different colored curve bundles, light yellow for Ф50,stem=-0.5 MPa gradually changing to dark blue for Ф50,stem=-8 MPa).

For water potentials larger than Ф50,stem larger c2,stem will lead to higher xylem conductivity.

For water potentials smaller than Ф50,stem, smaller c2 leads to higher xylem conductivity.

...... 26

Figure 4. Schematic representation of the finite difference method (backward Euler with fully implicit Picard method) adopted by FETCH2, following Celia et al. [1990] ...... 37

Figure 5. Silas little experimental forest, NJ (Oak Ridge National Laboratory Distributed

Active Archive Center (ORNL, DAAC). 2014. FLUXNET Maps & Graphics Web Page.

Available online [http://fluxnet.ornl.gov/] from ORNL, DAAC, Oak Ridge, Tennessee,

U.S.A...... 48

Figure 6. Schematic view of aboveground simulation of water flow in the aboveground-

FETCH2. Left side figure: dynamics of water flow within tree xylem (stem), water exchange between soil and roots, and water exchange between leaves and atmosphere.

Middle figure: FETCH2 simplified the tree into a one-dimensional (1-D) single beam conduit system within aboveground level with the aboveground leaf area distribution.

Right side figure: finite difference discretization of aboveground xylem to solve for stem water potentials...... 52 xviii

(RWC) response to changes in the stem water potential for the parameterized oak (solid line) and parametrized pine (dashed line). We plotted the curves over an arbitrary range of stem water potential with the optimized parameters from Table 2 to compare the hydraulic properties of the two existing genera qualitatively...... 66

Figure 8. Mean daily plot level NHL (blue square), FETCH2 (magenta diamond), Penman-

Monteith (red circle), and observed (black triangle) transpiration...... 67

Figure 9. Mean hysteresis loop of observed (black triangle), NHL (blue square), FETCH2

(magenta diamond), and PM (red circle) simulated transpirations under intermediate soil moisture condition...... 71

Figure 10. Total daily tree level observed (black) and FETCH2-simulated (magenta) sap flux during the simulation period for (a) oak and (b) pine...... 72

Figure 11. Ten days dynamics of (a) left y-axis: Oak’s tree level NHL (solid blue line),

FETCH2- simulated (solid magenta line), and observed (dashed-dot black line) transpiration, right y-axis: soil water content (solid green line), (b) left y-axis: Oak’s tree level observed (dashed black line), and FETCH2-simulated (solid magenta line) sap flux, right y-axis: Oak’s water storage (solid blue line)...... 73

Figure 12. Left column: Normalized (with respect to total daily) mean daily cycle of transpiration during (a) wet days, (b) intermediate soil moisture, and (c) dry condition for

xix oak (solid blue line) and pine (solid magenta line). The blue and magenta dashed lines represent the peak of normalized transpiration. Right column: Relative mean hysteresis loop of transpiration with their corresponding hysteresis values, during (a) wet days, (b) intermediate soil moisture, and (c) dry condition for oak (solid blue line) and pine (solid magenta line). Hysteresis was calculated using the method explained in section 3.2.4. .. 76

Figure 13. Dynamics of diurnal relative hysteresis of tree level sap flux for oak (black) and pine (magenta) ...... 79

Figure 14. UMBS site map showing the locations of the control tower (blue) and the

FASET tower (red)...... 85

2002]. c3 was allowed to vary between 1 and 10 (within each of the colored curve bundles) and Ф50,stomata was allowed to vary between 0.5 and 8 MPa (among the different colored curve bundles, light yellow for Ф50,stomata=-0.5 MPa gradually changing to dark blue for

Ф50,stomata=-8 MPa). For water potentials larger than Ф50,stomata, larger c3 will lead to higher conductivity. For water potentials smaller than Ф50,stomata, smaller c3 leads to higher conductivity. Black solid lines are the stomatal response curves with slope (c3) equal to 3.

...... 91

Figure 16. Correlation between maximal xylem conductance (kstem,max) and water potential

2 at 50% loss of conductivity (Ф50,stem). We found a significant (p=0.01, r =0.28) exponential relationship, kstem,max=3.154×exp(-2.08 Ф50,stem)...... 93

(solid blue line), and dry (solid green line) conditions. The root cross sectional area index is defined as the total cross-sectional area of roots per unit ground area measured at each layer of the soil...... 95

Figure 18. (a) Correlation analysis between water supply (shallow SWC) and water demand

(VPD) during summer period of 2013; (b) Days with lowest correlation error from shallow parts of the soil, located in the dry (low SWC and high VPD, light yellow), Intermediate

(intermediate SWC and medium VPD, light blue), and wet (high SWC and low VPD, dark blue) regions...... 99

Figure 19. Time series of the non-hydraulically limited transpirational forcing (black stars) and the hydrodynamically limited transpiration over a 9-day period of diurnally recycled atmospheric conditions and constant moisture for four different combinations of xylem and leaf traits during an intermediate dry day with deep rooting depth strategy...... 102

Figure 20. Continuum of plant responses to different wet, intermediate, and dry conditions considering either a deep (right side) or shallow (left side) root strategy and a continuous range of xylem and stomatal traits, defined through Ф50,stem and Ф50,stomata. PLCs is the

xxi percent loss of conductivity of leaf stomata (Eq. 9). The hashed areas are related to the areas under which plants experience more than 50% xylem loss of conductivity (PLCx, Eq.

8)...... 103

Figure 21. Maximum variation in the daily xylem water potential under two extreme environmental conditions (dry and wet), and a continuous range of xylem and stomatal traits, defined through Фstem,50 and Ф50,stomata...... 107

Figure 22. FETCH2 simulations show that the plant safety margin, (Ф88,stomata - Ф50,stem), defined as the degree of isohydricity, changes with the stem level hydraulic safety margin

(Фmin,stem - Ф50,stem). The dashed red line marks a linear regression...... 110

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Chapter 1: Introduction and Motivation

1.1 Transpiration and Vegetation-Climate Feedbacks

Transpiration is the end result of water transfer from the soil to the atmosphere through plant tissues. During transpiration liquid water changes its phase and exits from the plant into the atmosphere as water vapor [Katul et al., 2012]. Transpiration occurs through small openings in the leaves called stomata, which is the same pathway plants use for carbon uptake. Stomata are epidermal “valves” that are essential for plant survival because they regulate water loss and the entry of carbon dioxide, needed for assimilation in photosynthesis. By controlling both water loss and carbon uptake, stomata effectively determine the plants water use efficiency [Bergmann and Sack, 2007]. Stomata form the dynamic control on biosphere-atmosphere exchanges. This control has significant impacts on the global carbon and water cycles [van der Molen et al., 2011; Williams et al., 2012], as well as for the ecosystem function.

Plants are the most common land cover in the terrestrial ecosystem. The land cover determined the surface energy budget of Earth. Incoming energy is intercepted by the land cover, and either reflected, re-emitted as long-wave radiation, used to transfer heat from the surface to the atmosphere (sensible heat flux) or evaporate water from the surface

(latent heat flux). As stomata control the amount of water that can be evaporated through 1 plants, it has a strong impact on the total surface energy budget. Decrease in transpiration alters the leaf energy budget by decreasing the latent heat and increasing the sensible heat fluxes, which eventually leads to an increase in the long wave radiation. The main reason is that given constant forcing, decrease in stomatal conductance increases the leaf temperature [Strengers et al., 2010].

Overall, plant-covered terrestrial ecosystems influence climate through fluxes of energy, water, momentum, CO2, trace gases, and mineral aerosols [Bonan et al., 2003].

Therefore, it can be concluded that large scale patterns of climate may be influenced significantly by regional variability of these vegetation fluxes, as regulated by stomata.

Transpiration serves as the largest component of the terrestrial water cycle and the main component of the latent heat flux portion of the earth surface energy budget [Eagleson,

1978; Jasechko et al., 2013; Schlesinger and Jasechko, 2014]. At a longer time scale, vegetation carbon uptake, through stomata, influences the global CO2 concentrations.

Therefore, Study the transpiration process and its link to the atmospheric circulation is central for a better understanding of the feedbacks between the surface water components and the atmosphere, as well as assessing the effects of climate and water resources on the terrestrial carbon cycle [Fisher et al., 2005; Savabi and Stockle, 2001]. For example, canopy-scale eddy covariance studies have shown that drought significantly influence the net ecosystem exchange (e.g. Baldocchi and Xu [2007]). Here are further examples of vegetation-climate feedbacks:

Vegetation can also change the radiation balance of the canopies that intercept snow by producing shading for the ground snowpack from direct radiation. However, they 2 typically increase the longwave radiation accessibility to ground during the snow melting periods [Pomeroy et al., 2009]. There is a strong association between canopy-structure characteristics and the surface roughness of the canopy, which controls the characteristics of turbulent eddies that are responsible for the vertical mixing of mass between the biosphere and atmosphere and modifying the wind profile [Bohrer et al., 2009; Maurer et al., 2015; Thomas and Foken, 2007].

Precipitation, as an input to the hydrological cycle, can fall directly on the ground or be intercepted by the canopy and eventually evaporate or drip. Vegetation canopy structure and leaf area index (LAI) determine the fraction of precipitation that is intercepted and evaporated, and that which fall to the ground [Peng et al., 2014]. On the other hand, the amount of water that is taken up by vegetation through root uptake can further influence the soil water content, groundwater availability and even transpiration [Fatichi et al.,

2016]. Furthermore, transpiration plays an important role in the continental moisture recycling, precipitation patterns, and cloud formation especially in the regions with tropical atmospheric conditions [Aemisegger et al., 2014; Cox et al., 2004]. Also species-specific mortality, which results in shifts in forest compositions, has been shown to have some impacts on the hydrological cycle and climate change [Matheny et al., 2014b].

1.2 Modeling Vegetation Dynamics and Stomatal Functioning

Given the central role of water-plant interactions in the climate system, adequate representation of vegetation dynamics and especially stomatal functioning within

3 hydrologic and climate models is essential in understanding and predicting the effects of changes in climate on landscape and on water resources [Bonan et al., 2003; Fatichi, 2014;

Fatichi et al., 2014; Fisher et al., 2014; Sellers et al., 1997; Sellers et al., 1996; Sellers et al., 1986]. Despite the strong association between vegetation and hydrology, historically, vegetation has been represented with static parameters embedded in equations to calculate the bulk evapotranspiration. For example, Penman-Monteith is a physically based simple model of evapotranspiration that uses available meteorological observations including incoming solar radiation, wind speed, air temperature and vapor pressure deficit [Federer et al., 1996; Sumner and Jacobs, 2005; Vörösmarty et al., 1998]. These simple models typically estimate potential evapotranspiration (PET), assuming a specific vegetation characteristics under well-watered surface condition [Fisher et al., 2005]. The actual evapotranspiration (AET) is then estimated by reducing the potential evapotranspiration based on the limitations in available water (i.e. soil moisture) [Federer et al., 1996;

Stannard, 1993]. Although the space & time-static representation of vegetation functioning provides a reasonable approximation, however, this method faces numerous shortcomings

[Bonan, 2008; Deckmyn et al., 2008].

Shuttleworth [1991] defined two categories of PETs modeling approaches: reference-surface PET methods and surface-dependent PET methods. Reference-surface evapotranspiration compute PET from a ‘reference crop’ (normally a short, uniform, green plant cover such as alfalfa or grass) under the designed weather, assuming well-watered condition. The focus of these type of models is the relationship between temperature and

PET while they neglect vegetation [Allen et al., 1998]. In contrast, the surface-dependent

PET method, estimates the PET from a specified land surface, considering a combination of vegetation and soil characteristics [Priestley and Taylor, 1972]. AET is more robustly computed using land surface-atmosphere models (LSMs) commonly named soil- vegetation-atmosphere-transfer (SVAT) models. This land surface scheme has been used in many weather, climate, hydrologic, and ecologic models for simulating water and surface energy balance [Dai et al., 2003; Mohr et al., 2000; Whitfield et al., 2006]. LSMs and dynamic global vegetation models (DGVMs), typically indicated as terrestrial biosphere models (e.g. Fisher et al. [2014]), are types of models that resolve the surface energy budget as an upper or lower boundary condition for the atmospheric, hydrological, or combined Earth-system models of which they are often a component [Fisher et al.,

2014]. LSMs explicitly resolve the effects of vegetation and its interactions with climate while representing the vegetation as a static set of parameters. DGVMs likewise represent vegetation using static parameters, but dynamically develop the vegetative state over time following plant ecological dynamics of establishment, growth, competition and mortality

[Matheny et al., 2017]. In order to mimic plant trait diversity, both LSMs and DGVMs group vegetation into broad categories, called Plant functional types (PFTs). This grouping is mainly based on phonological, environmental, and leaf shape characteristics including leaf size, leaf life span, leaf area-to-mass ratio, leaf moisture retention, leaf nutrients, radiation absorption, tree height, and successional stage [Fisher et al., 2014; Pappas et al.,

2016].

Although grouping plant traits into PFTs, to some extent, captures the trait variation

[Kattge et al., 2011], however the course resolution at which PFTs have been defined has

5 shown to be a major source of error, specifically for long-term simulations [Matheny et al.,

2014; Matthes et al., 2016; Ostle et al., 2009; Pavlick et al., 2013; Poulter et al., 2011; Van

Bodegom et al., 2012]. Therefore, the responses obtained using mean plant attributes cannot represent the ecosystem responses of the highly diverse plant characteristics

(Jensen’s inequality; [Jensen, 1906]). Representing plant trait diversity within PFT classification has been shown to improve the prediction of carbon assimilation and vegetation distribution [Verheijen et al., 2013]. This approach is named “trait-based” vegetation modeling, which is developed based upon multivariate plant trait spectrum, such as leaf traits (leaf economics spectrum; Reich et al. [1997]; Wright et al. [2005]), plant hydraulic properties and drought tolerance strategies (Manzoni et al. [2013]; Anderegg et al. [2015]), wood properties (wood economics spectrum; Chave et al. [2009]), and nutrient availability [Maire et al., 2012; Ordonez et al., 2009; Reich and Oleksyn, 2004; Reich et al., 1997; Wright et al., 2004]. Replacing the coarse resolution PFTs with the trait-based approach can result in better representation of the plant functional diversity [Fyllas et al.,

2014; Sakschewski et al., 2015].

In this study, we mainly focus on the importance of representing diversity among hydraulic traits [Christoffersen et al., 2016; Jasechko et al., 2013; Matheny et al., 2014a].

Currently, PFT-based vegetation schemes do not represent the physical process of water transport and storage from roots to leaves. Therefore, may not be able to accurately model variation among different plant species in the effects of drought and disturbance.

1.3 Hydraulic Functional Traits

To simulate the stomata behavior, some models use simple assumptions about the functional relations calibrated through observation [Damour et al., 2010; Jarvis, 1976;

1976; Tuzet et al., 2003], while Some other use the mechanistic representation of stomata to reproduce the dynamics in leaf fluxes [Buckley et al., 2003; de Boer et al., 2012; Dewar,

1995; 2002; Franks, 2004; Franks et al., 2007; Gao et al., 2002; Mott and Peak, 2013;

Peak and Mott, 2011]. While most of the plant physiological studies apply mechanistic models, ESMs adopt empirical/conceptual solutions [Jarvis, 1976]. Another approach characterizes stomatal regulation such that it maximizes carbon gain, while minimizing water losses [Lin et al., 2015; Medlyn et al., 2013]. This approach has recently been started to be used in ESMs [Bonan et al., 2014].

In the above modeling approaches, plant-water stress is typically driven only by external factors, including precipitation, humidity, and vapor pressure deficit (VPD), and soil moisture. However, it would be more realistic to characterize plant-water stress through the water potential in the leaves. A decline in leaf water potential may result in downregulation of maximum carboxylation rates and electron transport rates, as found by studies in tropical dry forest [Brodribb et al., 2002] and other ecosystems [Brodribb et al.,

2003; Manzoni, 2014; Xu et al., 2016], as well as leaf shedding if leaf turgor cannot be maintained [Sobrado, 1986].

The dynamics of stomatal conductance are affected externally by meteorological conditions, such as photosynthetic active radiation (PAR), wind speed, and vapor pressure

7 deficit (VPD), and internally by leaf water potential. Leaf water potential is controlled by multiple structural and functional hydraulic traits throughout the plant, along the soil-root- stem-branch-leaf continuum of water flow [Matheny et al., 2016; Meinzer et al., 2013;

Sperry et al., 2002; Taneda and Sperry, 2008]. The diversity of hydraulic traits in plants may produce a wide range of response strategies to both short-term variation of environmental condition and long-term changes to climate and hydrological cycles which affect the availability of water [Rogiers et al., 2012; Skelton et al., 2015; Will et al., 2013].

Whole-plant hydraulic performance depends on the integrated function of complexes of traits. Species-specific patterns of transpiration and growth among coexisting species normally occur through adopting contrasting whole-plant hydraulic strategies [e.g. Anderegg, 2015; Kocher et al., 2013; Martinez-Vilalta et al., 2014; Matheny et al., 2014; McCulloh et al., 2012; Meinzer et al., 2014; Thomsen et al., 2013]. Species coordinates their hydraulic traits through tradeoffs defined within the plant economics spectrum [Chave et al., 2009; Freschet et al., 2012; Freschet et al., 2010; Liu et al., 2010;

Reich, 2014; Wright et al., 2004] and potentially through the proposed hydraulic safety- efficiency tradeoff [Manzoni et al., 2013; Skelton et al., 2015].

1.3.1 Leaf Traits

At the leaf level, hydraulic strategies vary along an iso- to anisohydric behavior continuum [Domec and Johnson, 2012; Jones, 1998; Klein, 2014; Larcher, 2003;

Martínez‐Vilalta et al., 2014; Meinzer et al., 2017; Tardieu and Simonneau, 1998].

Isohydric behavior is characterized by the tendency of species to maintain a relatively constant leaf water potential by down-regulating stomatal conductance when the transpiration rate is higher than the rate of leaf-water recharge. Alternatively, anisohydric species allow leaf water potential to decline substantially during the day and during dry conditions.

Estimating the degree of iso/anisohydric is essential in accurate prediction of ecosystem drought resilience but is difficult to measure, and instead can be quantifies through other easy-to-measure parameters. Martínez‐Vilalta et al. [2014] suggested using the relationship between midday and predawn leaf water potential to evaluate the leaf water regulation strategy. Oren et al. [1999] Suggested that responses of stomata conductance to

VPD could be another way to quantify the hydraulic strategy leaves adopt. Konings and

Gentine [2017] defined a metric for the degree of iso/anisohydry using AMSR-E satellite data. This metric is evaluated based on diurnal variations in microwave vegetation optical depth (VOD), which is directly related to leaf water potential.

1.3.2 Xylem Traits

Xylem provides the pathway for water movement from roots to leaves. Structural properties of the xylem, such as conduit number and diameter and pit membrane structure determine the hydraulic traits of xylem, including maximum conductivity, median cavitation pressure, and xylem capacitance [Bush et al., 2008; Lens et al., 2011; Pockman and Sperry, 2000; Sperry et al., 2002; Thomsen et al., 2013]. Xylem hydraulic properties

9 can be described using the vulnerability curve of the xylem to cavitation [Maherali et al.,

2006; Sperry et al., 1994]. For example, xylem with large-diameter vessels would result in higher maximum conductivity in well-hydrated conditions, yet may have higher median cavitation pressure and with it greater cavitation vulnerability at a given water potential deficit [Li et al., 2008; Pockman and Sperry, 2000; Sperry, 2004; Taneda and Sperry,

2008]. Xylem with smaller diameter vessels may result in lower maximum conductivity, but is more resistant to cavitation under water-limited conditions [Bovard et al., 2005;

Hacke et al., 2001; Taneda and Sperry, 2008; Thomsen et al., 2013]

1.3.3 Root Traits

Previous studies have identified roots as one of the controlling components of the hydraulic pathway [Meinzer, 2002; Sperry et al., 2002]. Root branching structure, rooting-depth distribution, and root water-uptake efficiency regulate plant water status at the root level [Allen, 2009; Brooks et al., 2010; Canadell et al., 2007; Matheny et al., 2017].

Rooting structure and depth primarily determine the fraction of soil water available for uptake. Deeply-rooted species have the potential to access soil waters that shallowly-rooted species cannot, which may increase drought tolerance [Ivanov et al., 2012; Miller et al.,

2010; Phillips and Ehleringer, 1995; Pinto et al., 2014; Thomsen et al., 2013].

Studies have shown that plants whose roots are concentrated in shallower part of the soil are more reliant on soil moisture near the surface [Barnes and Turner, 1998]. These plants increase their water uptake after each rainfall event and start to experience water

10 stress as soil moisture declines in layers near the surface of the ground due to evaporation during the dry interstorm periods. This also decreases root water compensation due to the drier upper layer soil. Miller et al. [2010], Phillips and Ehleringer [1995], and Matheny et al. [2015] show evidences of water uptake from deeper parts of the soil by plants with deeper rooting system. The deeper-rooted plants that have access to the deep soil water content are less sensitive to the surface soil moisture variations. Having access to a more stable source of water, these plants experience less water stress and can maintain high transpiration under low leaf water potential despite their risk-prone vasculature and anisohydric stomatal regulation strategies [Abrams, 1990; Baldocchi and Xu, 2007; Bovard et al., 2005; Hernandez-Santana et al., 2008; Matheny et al., 2014b; Oren and Pataki,

2001; Thomsen et al., 2013; von Allmen et al., 2015].

The effectiveness of hydraulic lift, which is the transport of water through the roots from the wetter to dryer regions to delay the onset of water stress [Brooks et al., 2002;

Burgess et al., 1998; Caldwell et al., 1998; Dawson, 1993; Emerman and Dawson, 1996;

Mendel et al., 2002; Williams et al., 1993], has been shown to be mainly controlled by the root vertical distribution. However, the soil moisture level, at which hydraulic lift is most effective, depends on soil hydraulic properties and atmospheric water vapor demand

[Siqueira et al., 2008].

1.4 Future Development

Adding hydraulic traits that describe the plant mechanisms for controlling root water uptake, xylem water transport, and leaf-level hydraulic limitations to stomata conductance into LSMS and DGVMs will help to more accurately simulate ecosystem responses to land use and climate changes [Boulangeat et al., 2012; McIntyre and Lavorel,

2007; Quillet et al., 2010]. Recently, efforts have been made to more realistically represent vegetative responses to the effects of climate and land use change by incorporating the whole-plant hydraulic strategy into models [Gough et al., 2013; Matheny et al., 2014;

Quillet et al., 2010; Shellito and Sloan, 2006]. This approach will potentially improve the simulation of water and carbon fluxes, specifically during severe conditions like drought or disturbance [Matheny et al., 2014; McDowell et al., 2013]; However the high temporal resolutions of the hydraulic trait necessitates the incorporation of mechanistic processed based models to capture the dynamic responses to these traits (e.g. FETCH2 [Bohrer et al.,

2005; Mirfenderesgi et al., 2016], ExpertN [Bittner et al., 2012; Janott et al., 2011], SPAC

[Gentine et al., 2015], one-dimensional root model by Siqueira et al. [2008], and a two dimensional root model by Vrugt et al. [2001]). These plant hydrodynamic sub-models simulate water flow through the entire or part of the plant vascular system. They resolve plant functional traits at different hydraulic levels and calculate the vegetation soil water uptake, stomatal conductance and transpiration based on the integrated whole-plant hydraulic strategy [Mirfenderesgi et al., 2016]. Statistical approaches can be applied to the model outputs to scale them to the patch or ecosystem level based on the relative fraction

12 of leaf area or basal area represented by these simulated individuals [Matheny et al., 2014b;

Mirfenderesgi et al., 2016].

1.5 Document Structure

The manuscript is structured as follows: Chapter 2 provides the detailed descriptions of the underlying theories and governing equations of the Finite-difference

Ecosystem-scale Tree-Crown Hydrodynamics model version 2 (FETCH2). In Chapter 3, we applied FETCH2 along with sap-flow and eddy-covariance data collected from a mixed plot of two genera (oak/pine) in Silas Little Experimental Forest, NJ, USA, to conduct an analysis of the intergeneric variation of hydraulic strategies and their effects on diurnal and seasonal transpiration dynamics. In chapter 4, we used FETCH2 to conduct a virtual experiment, simulating the consequences of plant functional traits at the root, stem and leaf levels to the integrated whole-plant transpirational response. We define a multi- dimensional “strategy space” and test the consequences of different strategies under different environmental conditions, representing typical wet, intermediate, and dry conditions, based on observations collected from a research plot in Northern Michigan.

Chapter 5 provides the conclusion of this study.

Chapter 2: Finite difference Ecosystem-scale Tree Crown Hydrodynamics Model version

2 (FETCH2) Using Porous Media Flow Approach to Represent Whole Trees

2.1 Introduction

The Finite-difference Ecosystem-scale Tree-Crown Hydrodynamics model version

2 (FETCH2) is a novel tree-scale hydrodynamic model of transpiration. The FETCH2 model employs a finite difference numerical methodology and a simplified single-beam conduit system and simulates water flow through the tree as a continuum of porous media conduits. It explicitly resolves xylem water potential throughout the tree’s vertical extent.

Empirical equations relate water potential within the stem to stomatal conductance of the leaves at each height throughout the crown. While highly simplified, this approach brings additional realism to the simulation of transpiration by linking stomatal responses to stem water potential rather than directly to soil moisture, as is currently the case in the majority of land-surface models. FETCH2 accounts for plant hydraulic traits, such as the degree of anisohydric/isohydric response of stomata, maximal xylem conductivity, vertical distribution of leaf area, rooting depth, and maximal and minimal stem water content.

We developed the Finite difference Ecosystem-scale Tree-Crown Hydrodynamics model version 2 (FETCH2). FETCH2 solves Richards' equation to simulate xylem water pressure and consequent stomatal conductance of a tree crown. The Richards' equation

14 analogy for xylem water flow established by Sperry et al. [1998] has been broadly applied

[Arbogast et al., 1993; Chuang et al., 2006; Früh and Kurth, 1999; Kumagai, 2001;

Mackay et al., 2015; Verma et al., 2014]. Some advanced models include a capacitance term to account for canopy water storage using an analogous electric circuit formulation

[e.g., Boersma et al., 1991; Bonan et al., 2014; Cowan, 1972; Lee, 1992; Sheriff, 1973;

Sperry et al., 1998; Steppe et al., 2006; Tyree et al., 1994; Van den Honert, 1948], or by water mass-budget through the stem volume [Gentine et al., 2015]. However, the hydrodynamics of water flow through xylem is more complex than the dynamics described by electric-equivalence capacitor models [Chuang et al., 2006]. Therefore, a few models that resolve stem water potential using a mechanistic representation of porous medium flow through the stem have been introduced [Bohrer et al., 2005; Janott et al., 2011; Nikinmaa et al., 2014]. Nevertheless, such models are computationally intensive and can currently be applied solely to single trees. As a response to the need for a mechanistic approach that can be applied to entire ecosystems and coupled with land-atmosphere models, we developed FETCH2, which allows the scaling of simulations to the plot scale, and enables resolving xylem water potential and the corresponding tree hydraulic strategies at the regional and larger scales.

FETCH2 is an evolution upon its predecessor model, FETCH [Bohrer et al., 2005].

To reduce simulation time and the inputs required regarding tree-crown structure, it uses a finite difference numerical solver scheme and simplified 1-dimentional (1-D) single beam conduit system. FETCH2 resolves processes at the resolution of an individual tree and subsequently scales representative single-tree model output to the plot-level based on the

15 genus-size distribution of trees in a forest. The tree is represented as a single beam (i.e.,

"stem") with a realistic vertical leaf area distribution. The model is forced by atmospheric demand for water vapor and light availability to the leaves at each layer of the canopy, which are estimated using above-canopy atmospheric conditions. FETCH2 also simulates water flow in the soil and root, and includes the 2-way exchange of water between soil and roots. Figure 1 provides a schematic representation of FETCH2.

Table 1 includes a list of all symbols and units of the variables and parameters listed in the formulations and evaluation of the FETCH2 model (Eq. 1-50, below).

Table 1. List of all variables, used in FETCH2 formulation

Parameter Description Units Values 2 Abasal Basal area m m2 ACrown Genus-based mean crown area m2 ACrown,tot Genus-based total crown area m2 Ap Total plot area m2 Ap,tot Genus-based total sapwood area

Genus-based mean sapwood area (stem 2 Astem,sap m active xylem) Genus-based total sapwood area (Active 2 ASap,tot m xylem) 2 AStem Cross-section area of the entire stem m Genus-based mean sapwood area (root 2 Aroot,sap m active xylem) 2 Aroot Cross-section area of the entire root m -2 -1 Az Net CO2 assimilation rate μmol m s B Empirical shape parameter - bstem Stem empirical shape parameter - broot Root empirical shape parameter -

Capacitance of the active xylem of the -1 -1 Cstem kgH2O m MPa stem Capacitance of the active xylem of the -1 -1 Croot kgH2O m MPa root - -1 Cp Specific heat of air Jg K Empirical dimensionless shape parameter c - for the root distribution -1 ci Internal leaf CO2 partial pressure mmol mol -1 cs Atmospheric concentration of CO2 μmol mol Shape parameter for conductance (stem c2,stem - xylem) Shape parameter- cavitation pressure c1,root Pa (root xylem) Shape parameter for conductance (root c2,root - Continued xylem)

Table 1 Continued c3 Shape parameter for stomatal response - Cross section area index of the root 2 -2 CAIroot m root m ground system DBH Diameter at breast height cm D0 Reference vapor pressure kPa -1 Elroot,c Root water uptake kg s -1 Elsoil,c Soil sink/source term kg s -1 Elstem,c Tree (crown) level root water sink/uptake kg s Plot level water-limited transpiration -2 Elp W m ground water sink Tree (crown) level NHL transpiration -1 ENHLstem kg s forcing -2 ENHLp Plot level NHL transpiration forcing Wm ground -2 EOBSp Plot level observed transpiration Wm ground -1 EOBSc Crown level observed transpiration kg s -2 Esim Simulated plot level transpiration Wm ground Froot Cumulative Root distribution - f Fraction of total root biomass % Rate of change of the mean root length -1 flz mroot m soil with respect to the soil depth g Gravitational acceleration ms-2 9.807 -2 -1 gb Leaf boundary layer conductance mol m s -2 -1 gs Stomatal conductance mol m s -2 -1 g0 Cuticular conductance mol m s -1 Jc Tree-level sap flux kg s -2 Jp Plot-level sap flux Wm ground -1 -1 JOBSc Observed tree sap flux kg m s -2 JOBSp Plot level observed sap flux W m ground Temperature adjusted Michaelis-Menten -1 Kc μmol mol constants for CO2 2 Kstem Conductivity of the stem active xylem m s 2 Krad.root Radial conductivity of the root xylem m s

s Specific radial hydraulic conductivity 2 K rad,root m s under saturated soil condition 2 Kax.root Axial conductivity of the root xylem m s Specific axial conductivity of the root 2 Kax.root,max m s system, measured on isolated roots 2 Ksoil Conductivity of the soil m s Temperature adjusted Michaelis-Menten -1 Ko mmol mol constants for O2 Conductance of the active xylem of the kstem s Continued stem 18

Table 1 Continued Maximum xylem conductance of the kstem,max s stem Genus level total leaf area to the total 2 -2 LAICrown m leaf m crown crown area of trees -2 LEOBSp Plot level observed latent heat flux W m ground Lpath Mean length of root m Total mass of water in the xylem of the -2 Mstem,c kg m stem tree stem Total mass of water in the xylem of the -2 Mroot,c kg m stem tree root Total mass of water in the xylem of the -2 Mc kg m stem tree m Fit parameter - NO Number of free parameters in the model - -1 oi O2 partial pressure mmol mol P Atmospheric pressure kPa P0 Standard sea level atmospheric pressure kPa 101.3 PLCx Percent loss of xylem conductivity % PLCz Percent loss of stomata conductivity % PAR Photosynthetic active radiation μmol m-2s-1 Absorbed photosynthetically active -2 -1 Qp μmol m s radiation R Molar density of an ideal gas mol m-3 44.46 RWCstem Stem xylem relative water content - RWCroot Root xylem relative water content - Rd Dark respiration - -1 rh Aerodynamic resistance to heat flux sm 2 -1 -1 rc Stomatal resistance m mol s Probability of information loss in a RL - model RWC Xylem relative water content - 2 -2 SAIroot Surface area index of the root m root m ground Sc Total storage of the tree kg Sp Plot level total storage of the tree kg SD Sapwood depth cm t Time s Ta Air temperature °C tmax End of simulation time s Ta Air temperature °C T0 Temperature conversion from °C to °K - 273 U Wind speed m s-1 Continued 19

Table 1 Continued Maximum carboxylation capacity of -2 -1 Vcmax25 μmol m leaf s Rubisco at 25 ͦC VPD Vapor pressure deficit kPa Total occupied volume of the stem active 3 -2 Vstem,ToT m sapwood m stem xylem (including water and wood) Total occupied volume of the root active 3 -2 Vroot,ToT xylem (including water and root m sapwood m stem biomass) 9 Xstem,E Stem xylem elasticity module Pa 10 9 Xroot,E Root xylem elasticity module Pa 10 Ratio of horizontal to vertical projections x - of leaves assumed spherical 9 XE Xylem elasticity module Pa 10 z Vertical height of the tree m zbottom Height at the base of the tree m Height of the topmost element of the tree ztop m (tree height) Depth above which 50% of the roots are z50 m located Depth above which 95% of the roots are z95 m located α Quantum efficiency (%) - βp Leaf absorptivity of PAR - βs Soil water stress function - Psychometric constant as a function of γ kPa K-1 air density and the heat Capacity of air Slope of the saturation vapor pressure Δ kPaK-1 curve Length of the vertical elements of the Δz m tree Δt Time step s 3 -3 θres Residual soil water content cm H2O cm soil 3 -3 θsat Saturated soil water content cm H2O cm soil 3 -3 θsoil Soil water content cm H2O cm soil Water content of saturated stem active -3 θstem,sap kgwater m sapwood xylem -3 θstem,sap Water content of saturated stem sapwood kgwater m sapwood Θsoil Dimensionless soil water content - λ Latent heat of vaporization kJ kg-1 2240 -1 Γ* CO2 compensation point μmol mol -3 ρ Water density kg H2O m sapwood 1000 -3 ρh Density of water gm Continued 20

Table 1 Continued σ2 Variance of the error term - Standard deviation of the observed plot -2 σobs Wm level transpiration Shape parameter – xylem water potential ϕstem,z50 Pa at 50% relative water content (stem) Shape parameter – xylem water potential ϕstem,z88 Pa at 88% relative water content (stem) Shape parameter – xylem water potential ϕroot,z50 Pa at 50% relative water content (root) Shape parameter – xylem water potential ϕroot,z88 Pa at 88% relative water content (root) Фstem Stem water potential Pa Φroot Root water potential Pa Φsoil Soil water potential Pa Φsoil,sat Soil water potential at saturation Pa Shape parameter- cavitation pressure Φ50,stem Pa (stem xylem) Shape parameter – inflection point of Φ50,stomata Pa stomata response to xylem pressure Empirical minimal root-top (stem-base) Φroot_min Pa pressure Shape parameter – inflection point of Φs50 Pa stomata response to xylem pressure Soil water potential when stomata or root Ψ0 MPa are not limited by water availability Ψe Soil water potential MPa Ψw Limiting soil water potential MPa

2.2 Governing Equations

FETCH2 resolves xylem water pressure, both below and aboveground, Фroot(z, t) and Фstem(z, t), using Eq. 1, updated at each time step, t, and at each vertical layer, z. This formulation represents a physically based approach to resolve water potential, which combines the continuity equation with a physical transport law applied to both root and stem segment, leading to a nonlinear partial differential equation, which resembles

Richards’ equation for soil water movement, including sources and sinks. In essence, this approach assumes that water movement through a collection of interconnected tracheids or xylem elements resembles porous media flow [Chuang et al., 2006; Siau, 1983; Sperry et al., 1998; Sperry, 2000]. The formulation of tree hydrodynamics we use here is based on the Finite-Elements Tree-Crown Hydrodynamics (FETCH) model [Bohrer et al., 2005].

The key assumption of FETCH2 is that water transport is primarily driven by pressure and gravitational potential differences as opposed to other forcing, such as solute potential differences. In this equation and throughout the manuscript, subscript c represents the tree level and subscript p represents the plot level. Superscript (c) indicates that the parameter or variable is genus-specific. Xylem capacitance is defined as follows:

 rootz,t C z,t(c) 0    root  t   (c)   z,t  0 Cstem z,t   stem   t  (1)    rootz,t   El root,z z,t  (c)     K root 0   z,t        root  z  g   z    (c)   z,t   El z,t  z 0 K stem  z,t  stem    stem,c      stem          z    z 

At each time step we solve the combined above-belowground Richards’ equation for the xylem water potential within the soil, roots, and stem. To make it easier, we break the vector form of Richards’ equation to the Richards’ equation aboveground (stem water hydraulics, section 2.2.1) and belowground (soil & root water hydraulics, section 2.2.2 &

2.2.3).

2.2.1 Stem Water Hydraulics

The aboveground plant hydrodynamics represents the water transport dynamics in the stem [Mirfenderesgi et al., 2016].

(c) stemz,t   (c)  stemz,t  Elstem,c z,t Cstemz,t  Kstemstemz,t   g   (2) t z   z  z

ρ is water density, g is gravity, and ρg represents the hydrostatic water potential.

The sink term Elstem,c/Δz is the simulated transpiration from each vertical layer of a particular tree crown at height z and time t. The transpirational water sink is determined using a response function, which limits the water loss through the stomata as a function of the Non-Hydrodynamically Limited transpiration (NHL transpiration) and stem water potential. At each vertical element of the stem system, transpiration (Elstem,c) is calculated by restricting the NHL transpiration (NHLc) due to the hydrodynamic effects of xylem water potential. The second term in Eq. 3 mimics the stomatal regulation effect using an empirical response function of transpirational water loss related to stem water pressure at the previous time step (Figure 2):

c(c)  3     z,t 1 El (z,t)  NHL z,t exp   stem   (3) stem,c c   (c)     50,stomata  

(c) where Ф50,stomata is an empirical shape parameter describing the inflection point of the leaf-stem water potential response curve (Figure 2). The time step difference between transpiration, Elstem,c, and the xylem water pressure it responds to, Фstem(z,t-1), is quasi- 23

Figure 2. Sensitivity analysis of the stomata response curve describing leaf

vulnerability to stem water potential with respect to changes in c3 and

Ф50,stomata. The parameters were selected according to the standard values

found in Cruiziat et al. [2002]. c3 was allowed to vary between 1 and 10

(within each of the colored curve bundles) and Ф50,stomata was allowed to vary between 0.5 and 8 MPa (among the different colored curve bundles,

light yellow for Ф50,stomata=-0.5 MPa gradually changing to dark blue for

Ф50,stomata=-8 MPa). For water potentials larger than Ф50,stomata, larger c3 will lead to higher conductivity. For water potentials smaller than

Ф50,stomata, smaller c3 leads to higher conductivity.

realistic as stomata do not respond instantaneously. Furthermore, this ‘lag time’ allows greater numerical efficiency in the solution as it limits the implicit contribution of stem

24 water potential to the water sink term. Our tests show that provided a reasonably small time step (order of minutes), it does not lead to numerical instability. The sensitivity of the

(c) and c3 ) determines the plant’s leaf hydraulic strategy, or expressed in another way the degree of (an) isohydric behavior.

Due to the characteristics of a porous medium, the conductivity and capacitance are not fixed properties, but are dynamic functions of the water pressure (Eqs. 4 & 6). The relationship between water potential and conductivity is known as the xylem vulnerability or cavitation curve [Sperry et al., 2003]. Conductivity in unsaturated media drops rapidly with further decreases of water content. Plants have evolved to dynamically minimize the risk of cavitation by closing their stomata before critically low water contents are reached

c(c)  2,stem  (c)    z,t K  z,t  A(c) k (c) exp   stem   (4) stem stem stem,sap stem,max   (c)     50,stem  

8 MPa (among the different colored curve bundles, light yellow for Ф50,stem=-

0.5 MPa gradually changing to dark blue for Ф50,stem=-8 MPa). For water potentials larger than Ф50,stem larger c2,stem will lead to higher xylem conductivity. For water potentials smaller than Ф50,stem, smaller c2 leads to higher xylem conductivity.

Capacitance is defined using the formulation proposed by Fatichi [2014] based on the relationship between stem relative water content and water potential, RWC(Фstem(z, t)), observed by Barnard et al. [2011] (see also Domec and Gartner [2003]).

stemz,t RWCstemstem z,t 1 (c) (c) (c) (5) bstem stemz,tstem,z502  bstem 

The capacitance is a prognostic variable related to the water potential in the stem:

A(c) dM C  z,t  stem,sap stem,c  stem stem V d stem,TOT stem (6)  (c) A(c) dz   (c) 2  b (c)   (c)  stem,sap stem,sap  stem,z50 stem     Astem,Sap  (c)  (c) (c) (c) 2   AstemV stem,TOT b  z,t  2  b X stem,E     stem stem   stem,z50 stem    where

 (c)  0.24 (c) (c) stem,z88 stem,z50 bstem  (c) (c) (7) 0.12stem,z50 stem,z88

(c) (c) (c) the term θstem,sap Astem,sap dz/Astem represents the mass of water in the numerical stem segment, i.e., the element between each two nodes that result from the numerical discretization, when it is saturated, and is related to ratio between the cross-section area of

2.2.2 Root Water Hydraulics

Water flow in the roots can be also explained through the Richards’ equation:

(c) rootz,t   (c)  rootz,t  Elroot,c z,t Crootz,t  Kax,rootrootz,t   g   (8) t z   z  z

(c) where Kax,root is the effective axial conductivity of the roots that represents the capacity of the root system to axially transport water within the roots:

c(c) (c) (c)  2,root  (c) CAI z K    z,t K  z,t  root root,ax,max exp   root   (9) ax,root stem f   c(c)   lz   1,root  

(c) where Kroot,ax,max is the specific axial conductivity of the root system obtained from isolated roots measurements, which serves as a measure of root efficiency in transporting water in the axial

(c) direction per unit of cross-sectional area of root. CAIroot is the cross sectional area index of the root system, which represents the total cross-sectional area working in parallel at a

(c) certain depth (z) per unit of ground area. CAIroot is an important variable that regulate the axial conductance of the root system; however determining this variable is challenging,

(c) the root distribution. Therefore, CAIroot distribution was calculated at each particular layer i within the soil domain using the root distribution and the basal area for the entire rooting system:

f i CAI (c) z  A(c) (10) root f 1 basal

28 where fi is the fraction of the total root biomass in layer i. We assumed that the root distribution follows a logistic dose-response relation as suggested by Schenk and Jackson

[2002].

    c  1   z95  F  ,    0.052 cum,root  c   z  (11)  z   50  1          z50  

where Fcum,root is the cumulative fraction of root biomass above z, z50 is the depth at which

Fcum,root equals 0.5, and c is an empirical dimensionless shape parameter that can be determined from z50 and z95 (Eq.11). flz is the rate of change of mean root length with respect to z:

Lpath f  (12) lz z

where Lpath is the mean length of the root in a soil layer with Δz thickness. Elroot,c, which serves as the sink/source term of the root, can be calculated as:

where Фsoil and Фroot are the water potential in the soil and roots, respectively. The effective

(c) radial conductivity (Krad,root ) indicated the capacity of the root system to transport water from the surrounding soil to the roots.

g K (c) z,t  K s z SAI (c) z (14) rad,root rad,root root z

s where Krad,root is the specific root radial conductivity, is the root radial conductivity per unit surface of root area. This conductivity refers to the discharge of water per unit area of

(c) root under a given water potential gradient between soil and root. SAIroot is the root surface area index, which is the ratio of root surface area and ground surface area. Δz is the vertical element length in the soil over which the flux of water between soil and root takes place. Similar to the stem, root capacitance is also defined based on the relationship between root relative water content and root water potential, RWCroot(Фroot(z, t)):

 z,t RWC  z,t 1 root root root  (c) (c) (c) (15) broot rootz,troot,z502  broot 

The capacitance term in Eq. 16 can also derived similar to the aboveground formulation

(Eq. 6):

A(c) dM C  z,t  root,sap root,c  root root V d root,TOT stem (16)  (c) A(c) dz   (c) 2  b (c)   (c)  root,sap root,sap  root,z50 root     Aroot,active  (c)  (c) (c) (c) 2   ArootV root,TOT b  z,t  2  b X root,E     root root  root,z50 root   

Where

 (c)  0.24 (c) (c) root,z88 root,z50 broot  (c) (c) (17) 0.12root,z50 root,z88

(c) (c) (c) where the term θroot,sap Aroot,sap dz/Aroot represents the mass of water in the numerical root segment, i.e., the element between each two nodes that result from the numerical discretization, when it is saturated, and is related to ratio between the cross-section area of

2.2.3 Soil Water Hydraulics

Similar to the stem and root hydraulics, Richards’ equation was used to solve the soil water potential in different layers of the soil:

soilz,t    soilz,t  Elsoilz,t  Ksoilsoilz,t  g   (18) t z   z  z

The sink/source term in the above equation (Elsoil) is equals to the source/sink term in the root equation (Elroot,c). Ksoil is the conductivity of the soil can be calculated using Van

Genuchten [1980] formulation,

2 1/ 2 1/ m m Ksoilz,t   1 1   

where   (19) z,t  soil res , sat res 1 m  1 , 0  m  1 n

where θsat and θres indicate the saturated and residual values of the soil water content respectively, and θsoil is the soil water content.

2.3 Vertically Discretized Forcing

The FETCH2 model is forced by the tree level NHL transpiration (NHLc), at each vertical layer z, throughout the canopy. By our definition, NHL transpiration is the transpiration predicted considering the stomatal conductance as a function of atmospheric demand and photosynthetic capacity, but without any limiting effects of soil water availability (Eq. 20). Most current models of transpiration can be used to generate NHL transpiration by simply removing the function that represents soil water availability limitations. We modified the formulation developed by Ewers and Oren [2000], which is driven by observed, half-hourly mean, gap-filled, above-canopy values of photosynthetically active radiation (PAR), air temperature (Ta), wind speed (u), and vapor pressure deficit (VPD):

A LAI (c)  g VPD  NHL  Crown Crown  eff , z  c     K  (20) T0 Pt  g  R    Ta tT0  P0 

where geff,z is the effective leaf conductance of layer z, VPD is vapor pressure deficit assumed constant throughout the canopy, ACrown is the genus-specific crown area,

(c) LAI Crown is the genus level total leaf area to the total crown area of trees, R is the Molar density of an ideal gas, Ta is the air temperature, and Kg is a temperature dependent conductance coefficient defined as Ewers et al. [2007]:

Kg 115.8  0.4236Ta (21) where Ta is the air temperature assumed to be constant throughout the canopy.

ggbzsz,, (22) geffz,  ggbzsz,,

where gb,z is the leaf boundary layer conductance and gs,z is stomatal conductance

[Campbell and Norman, 1998].

u (23) g  0.147 z b, z d where uz is the wind speed at canopy height z and d is the characteristic leaf length.

(24) u Uzz U *

The vertical profile of wind through the canopy, Uz is adjusted by the friction velocity, U*. The vertical wind profile is calculated using the mean momentum equation.

The measured above canopy wind U forms the upper boundary condition, and a no-slip boundary condition is applied at the ground surface following Poggi et al. [2004] and Katul et al. [2004].

2 (25) d UdU dKmz, dp KC LAIUzz U 0 m,, zDndzdzdzdz zzz2 where Km,z is the turbulent diffusivity of momentum, dz is the discretization height, CD is the drag coefficient (unitless) assumed to be 0.2 [Katul et al., 2004], LAIn,z is the normalized leaf area index at height z, and dp is the change in kinematic pressure which we assume dz to be negligible due to the relative flat topography of the site [Katul et al., 2004].

dU (26) Kl z mmixz , dz

where lmix,z [m] is the characteristic mixing length. The mixing length profile is defined as linear within the subcanopy, constant throughout the canopy, and linear above the canopy

[Leuning et al., 1995; Poggi et al., 2004]:

mA (27) z g s,z  g0   VPD    cs  * 1   D0 

-2 -1 where g0 [mol m s ] is the cuticular conductance, m is a fit parameter (unitless), cs is the atmospheric concentration of CO2 assumed to be constant throughout the canopy, Γ* is the

CO2 compensation point, and D0 is a reference vapor pressure assumed to be 3.0 kPa. Az is the net CO2 assimilation rate discretized throughout the canopy and calculated following.

(28) AwVwzccj zmin(), max, 

Where wc is the Rubisco limited rate of carboxylation and wj is the light limited rate of carboxylation.

Vc() cimax * (29) wRcd oi cKic1 Ko

()cQi*, p p z (30) wRj, z d ci 2 *

34 wc is a function of the maximum carboxylation rate, Vcmax. ci is the internal leaf CO2 partial pressure, and oi is the O2 partial pressure. Qp,z is the absorbed photosynthetically active radiation at each level within the canopy, α is the quantum efficiency (%), βp is leaf absorptivity of PAR (unitless), and Kc and Ko are the temperature adjusted Michaelis-

Menten constants for CO2 and O2, respectively. Rd is dark respiration calculated as

0.015Vcmax. The temperature dependence of Vcmax is modeled from the maximum carboxylation rate at 25 C, Vcmax25, following Farquhar et al. [1980]:

VTexp0.08825  (31) camax 25    Vcmax  1exp0.2941 Ta 

QPPARpzo,, z (32)

where Po,z (unitless) is the attenuation fraction of PAR penetrating the canopy at each level, z.

(33) PkLAICo,, zn zf exp 

Where k is the light extinction coefficient (unitless) and Cf is the unitless clumping fraction, assumed to be 0.85 [Forseth and Norman, 1993].

1/2 2 2 (34) x  tancos    k  xx1.7441.182 0.773 where x (unitless) represents the ratio of horizontal to vertical projections of leaves, assumed spherical, and θ (°) is the zenith angle of the sun.

2.4 Discrete Approximation of The Continuous Flow Equation

FETCH2 is discretized in finite differences to be compatible with the numerical scheme of most land surface models. It resolves the water pressure in a 1-D single beam stem to reduce computational and data requirements. A reduction in branching complexity was necessary because, while there are good sources of knowledge for stem height, diameter, and crown area from plot census and from remote sensing [Garrity et al., 2012], there is no good theory or data resource, to date, that allows generalizing and prescribing individual tree crown structures detailed to the branch level over a large scale that represent an entire forest area and region.

The simulations must be started before dawn, when an initial condition that prescribes hydrostatic pressure throughout the root and stem is realistic. Unlike the previously developed FETCH, FETCH2 uses finite difference method to solve the resulted

PDE in Eq. 1 considering all the constraints, and initial and boundary conditions. Celia et al. [1990] demonstrated that the convergence of the finite difference solutions occurs at a rapid speed once the number of iterations increasing slowly over the acceptable ranges of the initial condition. We adopted the backward Euler with fully implicit Picard method to discretize the resulting PDE temporally and spatially (Figure 4) and solved the final approximated equation using the tridiagonal matrix algorithm.

Figure 4. Schematic representation of the finite difference method (backward Euler with fully implicit Picard method) adopted by FETCH2, following Celia et al. [1990]

Considering the general form of the Richard’s equation: 37

z,t    z,t  Elc z,t C  K  g   (35) t z   z  z here is how FETCH2 discretizes Eq. 35 following Celia et al. [1990]:

n1 n n1 n1  stem  K EL Cn1  K n1n1 g  c (36) t z z z

Where Δt=tn+1- tn is the time step and Фn denotes the approximate value of Ф at the discrete time level t while Cn+1 and Kn+1are the hydraulic capacity and hydraulic conductivity

evaluated using Ф at the next time step n+1. Since both C and K are functions of Ф, a sequential method is incorporated to estimate the unknown Фn+1 using the latest estimates of Cn+1 and Kn+1. If m denotes the iteration number of Picard method, the discrete form of the governing equation can be rewritten as:

n1,m1 n n1,m n1 n1,m     n1,m n1,m1 K EL C  K   g  c (37) t z z z if subscript i denotes the spatial location (zi=i×Δz), the standard finite difference discretization to Eq. 35 is:

n1,m1 n n1,m1 n1,m1 n1,m1 n1,m1 n1,m     n1,m     n1,m     C i i  K i1 i  K i i1  i t i1/ 2 z2 i1/ 2 z2

c n1,m n1,m n1   n 3  (K  K ) EL      g i1/ 2 i1/ 2  c  exp     z z         50,stomata     (38) where 1 K n1,m  K n1,m  K n1,m  i1/ 2 2 i1 i 1 K n1,m  K n1,m  K n1,m  i1/ 2 2 i i1

n+1,m+1 Writing the discretization in the general format A(Ф i-

n+1,m+1 n+1,m+1 1)+B(Ф i)+C(Ф i+1)=D we have:

  K n1,m    K n1,m  K n1,m C n1,m    K n1,m   i1/ 2  n1,m1   i1/ 2  i1/ 2  i  n1,m1   i1/ 2  n1,m1   2  i1   2 2  i   2  i1   z   z z t   z  c (39) n1,m n1,m n1,m n1   n 3   C  n K  K  EL       i   g i1/ 2 i1/ 2  c exp      t  i z z            50,stomata  

n+1,m n+1,m+1 n+1,m Substituting the iteration increment (δФ i= (Ф i - Ф i)) in the equation we have:

 C n1,m  1  i  n1,m  K n1,m m  m  K n1,m m  m    i  2  i1/ 2  i1 i  i1/ 2  i i1   t  z 1 [K n1,m n1,m  n1,m  K n1,m n1,m  n1,m ]  z2 i1/ 2 i1 i i1/ 2 i i1 (40) c n1,m n1,m n1,m n1   n 3  K  K   C  n1,m n EL      g i1/ 2 i1/ 2   i     c exp     z  t  i i z            50,stomata  

Finally the system of algebraic equations can be written in the following general format: 39

  An1,m B (41)   ~  where Matrix A is a tridiagonal matrix, so we use the tridiagonal matrix algorithm to solve

n+1,m the equation above. Upon convergence in iteration, the δФ i term, which is the difference between two successive calculated pressure heads in each node, should approach to zero. This is the most basic convergence criteria named “standard convergence criteria”

[Shahraiyni and Ataie-Ashtiani, 2011]:

n1,m1  n1,m  a (42)

In the above criteria δa is a predefined tolerance that can be defined by the user.

2.5 Boundary Condition

FETCH2 discretizes and solves the stem, root, and soil equations together. For the root and stem FETCH2 assumes a single beam element that extends from soil depth to the canopy top, while for the soil equation, it solves the Richards equation for a column element inside the soil. A Neumann no-flux condition is prescribed at the topmost stem element (top of the root-stem continuum beam element) such that water may only leave the stem through a sink term (in Eq. 2) and not as a direct gradient flux:

  0 z (43) zztop

We also applied the Neumann no-flux condition to the bottom boundary of the root model

(bottom of the root-stem continuum beam element).

  0 (44) z zz0

The boundary condition for the soil model at the bottom soil layer is set to the hydraulic conductivity of the bottom soil layer. the upper boundary layer of the soil model is also set to the infiltration rate, which is the minimum of through fall (qthrough) and available capacity in the top soil layer as suggested by Amenu and Kumar [2008].

  z   top  qinf  minqthrough, sat,top soil,top    t  (45)   LAI qthroug  qraine

where qrain is the precipitation rate, LAI is the leaf area index, Δztop is the thickness of the soil layer if different from other layers, θsat,top is the top soil layer water content at saturation, and θsat,top is the water content of the top soil layer. Δz is the model time step and

ζ is a constant. In this equation it is assumed that the amount of rain intercepted is a function of LAI. This indicates that the infiltration should not surpass the available capacity of the top soil layer [Amenu and Kumar, 2008].

2.6 Hydrological Outputs of FETCH2

The model explicitly solves for the within-tree spatial and temporal dynamics of xylem water pressure. Eq. 1, combined with the NHL transpiration relates xylem water potential to transpiration. Besides xylem water potential and transpiration, FETCH2 also computes the aboveground water storage (Sc), and sap flux (Jc). The aboveground water storage of the stem (Sc) can be estimated from:

ztop S t  RWC  z,t  V  A c    stem stem  stem,sat stem,TOT stem  (46) zzbottom

where zbottom and ztop are the height at the base and top of the tree. Tree level sap flux (Jc) through the stem at each time step can be calculated through the water mass balance:

S t S t 1 ztop J t  c c  El z,t/ z (47) c t  stem,c zzbottom

Tree-level stem water storage can be inferred through in-situ measurements of xylem RWC using frequency domain reflectometry (FDR, [Matheny et al., 2015]), or dendrometer-based approaches [Steppe and Lemeur, 2007]. Jc can be directly comparable with tree-level sap-flow observations. Storage and sap flux can be scaled to the plot-level following section 2.7.

2.7 Scaling to Plot Level

In order to efficiently scale individual-based FETCH2 simulations to a forest plot

(corresponding, for example, to a grid-cell of a coupled hydrologic or atmospheric model, 42 or the footprint area of a flux tower), we followed the approach of Matheny et al. [2014b].

We classified the individual trees found in the forest census into groups according to their genus. Predictions of tree level transpiration for each representative individual (Elstem,c) were scaled to the plot level (Elp) using the following equation:

El z,t A(c) (48) El z,t   stem,c Crown,tot p  A(c) A c Crown p

(c) (c) where ACrown is the simulated tree’s crown area, ACrown,tot is the total crown area of all the trees of that genus, Ap is the total plot area of the study site, and λ is the latent heat of vaporization. Sap flux at the plot level (Jp) can be derived from the tree level sap flux (Jc):

(c) (c) where Astem,sap is the computed tree’s sapwood area, ASap,tot is the total sapwood area of all the trees of that genus. Plot level storage (Sp) is equal to the sum over all simulated trees of tree level stem water storage (Sc) divided by that tree’s total occupied volume of the

S t (50) S t  c V (c) p  V (c)  TOT c TOT c

The Next two chapters of the manuscript focus on the research application of FETCH2 model.

Chapter 3: Tree-Level Hydrodynamic Approach for Modeling Aboveground Water

Storage and Stomatal Conductance Illuminates the Effects of Tree Hydraulic Strategy

3.1 Introduction

Transpiration is controlled by the atmospheric demand for moisture and limited by stomatal conductance that is regulated to a certain extent by the plant water status and thus water availability. Most current land-surface and hydrologic models impose water availability limitations on stomatal conductance using simple linear Feddes‐type [Feddes et al., 2001; Feddes et al., 1976] or sigmoidal [Jarvis, 1976] empirical relationships between stomatal conductance or photosynthetic capacity and soil moisture. These parameterizations link leaf stomatal conductance directly and instantaneously to soil moisture, and do not incorporate mechanistic representation of the internal water storage and flow through the vegetation, xylem hydraulic properties, or stem and canopy structure.

Models that do not represent the plant water storage-mediated regulation of stomatal conductance are potentially too sensitive to soil water potential or atmospheric vapor pressure deficit (VPD) variations, and may misrepresent the intra-daily dynamics of transpiration [Matheny et al., 2014b].

Plant water storage and its diurnal dynamics provide one of the mechanisms that influence the magnitude of the diurnal hysteretic pattern of transpiration. The hysteretic

44 pattern is formed when, for the same atmospheric demand for water vapor and soil moisture conditions, plants transpire more before noon than during the afternoon [Matheny et al.,

2014b; Novick et al., 2014; O'Brien et al., 2004; Unsworth et al., 2004; Verbeeck et al.,

2007; Zhang et al., 2014]. Regulation of stomatal conductance due to leaf-level water stress is known to affect transpiration when the soil is dry or when VPD is high [Brodribb and

Holbrook, 2004; Davis et al., 2002; McCulloh and Sperry, 2005; Monteith, 1995; Turner et al., 1984]. Nonetheless, it can also impact stomatal apertures under conditions of adequate soil moisture and lower evaporative demand, if depletion of water in the leaves occurs at a faster rate than recharge of the stem xylem [Brodribb and Holbrook, 2004;

Ewers et al., 2007; McCulloh et al., 2012; Sperry et al., 2002]. As such, photosynthesis and the coupled water and energy cycles substantially deviate from the predictions of models that employ a direct link to soil moisture, which, in turn, leads to biases in diurnal dynamics of simulated transpiration [Matheny et al., 2014a].

The physiological mechanisms for avoidance of hydraulic failure modify stomatal opening and control water loss at the cost of reduced carbon assimilation [Cowan and

Farquhar, 1977; Katul et al., 2003; McDowell et al., 2008; McDowell et al., 2013; Meinzer et al., 2013]. The degree and intensity of this hydraulic regulation vary among species, and with the size and structure of the plant [Buckley, 2005; Maherali et al., 2006; Maherali et al., 2004; Matheny et al., 2014a; Meinzer et al., 2003; Meinzer and McCulloh, 2013;

Meinzer et al., 2014; Pittermann et al., 2005; Tardieu and Davies, 1993; Tardieu and

Simonneau, 1998; Thomsen et al., 2013; Whitehead, 1998]. Plants regulate their leaf-water status by modifying stomatal conductance using a range of strategies: from isohydric –

45 relatively constant leaf water potential actively maintained by stomatal regulation – to anisohydric – minimal stomatal regulation resulting in varying leaf water potential typically driven by the balance of water supply to the leaf and atmospheric demand.

Isohydric versus anisohydric regulation of leaf-water status affects transpiration and carbon assimilation under regular conditions and in response to disturbance and drought

[Anderegg et al., 2012; Franks et al., 2007; Gentine et al., 2015; Güneralp and Gertner,

2007; Kolb and McCormick, 1993; McDowell et al., 2008; Meinzer et al., 2014; Ogle et al., 2000; Roman et al., 2015; Tardieu and Simonneau, 1998].

We hypothesize that, because of their more dynamic stomatal control, Isohydric trees typically close their stomata earlier in days when low soil moisture and high atmospheric demand reduce xylem water pressure faster than during days when soil moisture is non-limiting. Anisohydric trees show less severe daily fluctuations in stomatal conductance, but stronger fluctuations in xylem water potential and thus, the amount of aboveground water storage [Matheny et al., 2015; Meinzer et al., 2014]. These differences between trees will affect the overall plot-level transpiration, and particularly the intra-daily dynamics of transpiration, especially when soil moisture is intermediate.

Mechanistically resolving xylem water potential allows the quantification of differences in transpiration and water stress between isohydric and anisohydric trees in the same site and soil moisture conditions, and define the parameters that describe the traits that control these aspects of plant hydraulic response. We will demonstrate that by mechanistically resolving the aboveground xylem water potentials, stem water storage, and leaf hydraulic strategies of trees we will be able to model the distinct behaviors of species 46 throughout the isohydric-anisohydric trait continuum in response to drying soil conditions.

Furthermore, tree-level results can be statistically scaled to the plot level and achieve increased accuracy in the simulation of ecosystem-scale transpiration fluxes. We used a novel tree-hydrodynamic model, and observations of tree-level sap flow and plot-level eddy flux from an oak/pine forest in the New Jersey Pine Barrens, a nutrient poor and water limited environment [Dighton et al., 2004; Pan et al., 2006; Renninger et al., 2014; Schäfer et al., 2010], to test our hypothesis.

3.2 Materials and methods

3.2.1 Study Site

The Silas Little Experimental Forest, also known as Rutgers University Pinelands

Research Station is located at northwestern part of the New Jersey Pine Barrens in

Pemberton Township of Burlington County, NJ, USA (N 39º 55’, W 74º 36’) (Figure 5).

This study area is an oak/pine dominated plot consisting of: 58% chestnut oak (Quercus prinus Willd), 14% black oak (Quercus velutina Lam), 6% scarlet oak (Quercus coccinia

Münchh), 8% scattered pitch pine (Pinus rigida Mill), 6% white oak (Quercus alba L), and

3% post oak (Quercus stellata Wangenh) (see Schäfer et al. [2010]). The species-specific

LAI was measured in the study site from 2005 to 2009 [Schäfer et al., 2014]. For the following years, we used the species-specific LAI litter-fall campaign of 2009 in addition to the annual census data and revised the LAI of each species based on the percentage

47 increment in the basal area. The canopy leaf area index (LAI) derived from litterfall was

1.7 in 2009. The composition and canopy LAI of the plot are reported on a yearly basis.

Figure 5. Silas little experimental forest, NJ (Oak Ridge National Laboratory Distributed Active Archive Center (ORNL, DAAC). 2014. FLUXNET Maps & Graphics Web Page. Available online [http://fluxnet.ornl.gov/] from ORNL, DAAC, Oak Ridge, Tennessee, U.S.A.

3.2.2 Site Level Observations

Methods for sap flux measurements and the meteorological observations at the study site are described in detail by Schäfer et al. [2014]. Half-hourly meteorological and flux data are available through the Ameriflux database (http://ameriflux.lbl.gov/), site-ID

US-Slt. A complete dataset of the observations used in this study, including sap flux is available as an electronic supplementary material to this manuscript. The soil moisture content in the upper 30 cm of the soil was measured in four locations using CS616 sensors

(Campbell Scientific Inc.). The sensors were attached to CR3000 datalogger (Campbell

Scientific Inc.), which collected data every 30 s and averaged data every 30 min [Renninger et al., 2014]. Flux measurements were conducted using the eddy covariance technique from a 19 m tower [Clark et al., 2012; Clark et al., 2010]. Total plot area of the study site is 0.3 ha, in which the tree and sapling diameters at breast height (DBH, cm) greater than 2.5 cm were measured at the end of each year from 2005 to 2013. For oak, sapwood area (Asap, cm2) was established based on the allometric relationships (r2 = 0.6), determined by

Renninger and Schäfer [2012], (Eq. 1).

ASap    SDDBH  SD where SD  0.0832 DBH (1) where SD is the sapwood depth of the tree individual in cm. For pine, we used the equation

2 reported by Renninger et al. [2013] for calculating Asap from DBH (Eq. 2, r = 0.99).

2.0473 ASap  0.3733 DBH (2)

Species-specific and canopy total growing season LAI were provided by Clark et al. [2010] and Schäfer et al. [2010]. Realistic vertical distribution of leaf area density 49

(LAD) was obtained for trees of the same genus in a similar plot in Michigan using a portable canopy LiDAR system (PCL) [Hardiman et al., 2011].

3.2.3 Aboveground-FETCH2

As comprehensively explained in chapter 2, FETCH2 is transpiration model, developed as an evolution upon its predecessor FETCH [Bohrer et al., 2005]. To reduce simulation time and the inputs required regarding tree-crown structure, it uses a finite difference numerical solver scheme and simplified 1-dimentional (1-D) single beam conduit system. FETCH2 resolves processes at the resolution of an individual tree and subsequently scales representative single-tree model output to the plot-level based on the genus-size distribution of trees in a forest. The tree is represented as a single beam (i.e.,

In this study, we chose to focus on aboveground hydrodynamic processes, and show what improvements of ecosystem representation and accuracy in transpiration prediction are provided by resolving these processes (Figure 6). We treated all other processes that affect water fluxes as forcing using the same formulations commonly used in large-scale ecosystem models. In order to allow an easier integration with large-scale ecosystem and earth system models, we purposefully represented the effects of soil water availability through the Feddes approach, which is similar to almost all large-scale ecosystem and

50 earth-system models representations [e.g., Bonan, 2002; Fatichi et al., 2012; Fatichi et al.,

2016; Ivanov et al., 2012; Janott et al., 2011; Siqueira et al., 2008; Sivandran and Bras,

2013]. This does not imply that the hydrodynamic processes at the soil-root interface are not important. In fact, one can easily claim that root-water storage, root conductivity and structure, and other root processes such as hydraulic nighttime water redistribution and hormonal controls on the leaves all have important roles in the whole plant hydrodynamics.

Examples of more sophisticated approaches to describe soil-root interface dynamics include Bleby et al. [2010], Caldwell and Richards [1989], Domec et al. [2004], Doussan et al. [2006], Mackay et al. [2015], Verma et al. [2014], Bittner et al. [2012], and Vrugt et al. [2001].

Figure 6. Schematic view of aboveground simulation of water flow in the aboveground- FETCH2. Left side figure: dynamics of water flow within tree xylem (stem), water exchange between soil and roots, and water exchange between leaves and atmosphere. Middle figure: FETCH2 simplified the tree into a one-dimensional (1-D) single beam conduit system within aboveground level with the aboveground leaf area distribution. Right side figure: finite difference discretization of aboveground xylem to solve for stem water potentials.

The bottom boundary condition to the model represents the integrated effect of soil water availability on the water potential at the top of the root system. A Dirichlet boundary condition is enforced at the base of the trunk, based on a Feddes-like [Feddes et al., 1976] formulation of soil moisture and rooting profile:

  (c)      1    1 r  w e  t0 s root_ min   e  (c) (c)  root_ min (3)  e  w  0  where βs is the soil water stress function, Ψw is the limiting soil water potential, and Ψ0 is the soil water potential when stomata or roots are not limited by water availability.

Subscript e represents a particular vertical soil layer. re is the fraction of the root system in each soil layer e. In this work, we assumed the distribution of roots to be vertically uniform, and used a single layer to represent the mean response from the surface to a depth of 30 cm where the soil moisture probes were installed [Renninger et al., 2014]. Ψw – Ψ0 represents an empirical range of soil moisture within which stomata move from being fully open, to fully closed. Φroot_min is an empirical minimal pressure (negative number) used to scale soil water potential to root-system-top xylem water potential, and can be determined from observations of the minimal pre-dawn water potential, during days when the soil is extremely dry.

3.2.4 Hysteresis Calculation

Despite being subjected to the same VPD, plants tend to transpire more during the morning hours, as compared to the afternoon, partially because of higher water storage in the stem during the morning hours, which becomes depleted later in the day [Bohrer et al.,

2005; Phillips et al., 2003; Verbeeck et al., 2007]. Therefore, a hysteretic loop is created when transpiration is plotted against VPD during the course of a day [Chen et al., 2011;

O'Grady et al., 2008]. This hysteretic loop depends on different factors including the time lag between daily maximum VPD and PAR, and the hydrodynamic cycle of water storage 53 within a plant. We define the magnitude of the hysteresis as the area enclosed by the daily hysteretic loop. The magnitude of the hysteresis was shown to be indicative of plant water status during the day and may be used to represent the hydrodynamic stress (expressed as the degree of imbalance between leaf water demand and soil water supply) incurred by the plant [Matheny et al., 2014a; Novick et al., 2014; Zhang et al., 2014]. We computed and analyzed the relative mean hysteresis of transpiration between genera. We calculated the mean hysteresis by normalizing daily transpiration and VPD by their respective daily maximum values, plotting the normalized transpiration against the normalized VPD, and averaging this normalized daily hysteresis over all day with similar soil moisture conditions for the trees representing each genus.

3.2.5 Parameter Estimation

We classify the FETCH2 model parameters into four distinct groups, based on the processes they affect:

(1) Transpirational demand parameters: As described in chapter 2, The NHL transpiration is calculated through stomatal conductance for a given atmospheric condition, while excluding limitations based on soil water availability. The physiological module of the NHL transpiration has three different parameters: (1) Vcmax the maximum carboxylation rate at 25°C [Farquhar et al., 1980], (2) m, the slope of the Ball-Woodrow-Berry stomatal conductance model [Ball et al., 1987], and (3) x, ratio of horizontal to vertical projections of leaves.

(2) Stomatal response parameters: This set determines the shape and sensitivity of the stomatal response to stem water potential: Φ50,stomata and c3, which define the simulated tree’s hydraulic strategy on the isohydric-anisohydric continuum.

(3) Xylem hydraulics parameters: The xylem cavitation curve and water storage capacity are described by kstem,max, θsat, Φ50,stem, c2, ϕstem,z50, and ϕstem,z88. We expect these parameters to define specific xylem architectures, for example non-porous, diffuse-porous, or ring-porous xylem as well as the degree of coupling between xylem conduits and storage tissues.

(4) Soil water availability regulation parameters: Φroot_min, re, and βs determine root- depth distribution, the relationship between soil water potential in the root zone and stem- base water potential, and the soil water stress function. These parameters can be modified to represent the rooting depth as well as other root strategies that affect water availability such as rooting vertical distribution, rooting length and diameter, and efficiency of water extraction.

Among all the parameters defined in FETCH2 formulations, we chose to perform the model calibration on the parameters listed in Table 1. This selection was carried out based on the predicted sensitivity of the model outputs (simulated transpiration and sap flux) to the selected parameters, which was evaluated by reviewing the literature and from some preliminary model simulations. The initial values and ranges of these parameters along with their corresponding references are listed in columns 2, 3 and 4 of Table 2. For this study we used only one soil layer, such that the root distribution function was equal to

1 (re=1). The discrete spatial and temporal increments used to numerically solve Eq. 1 were 55

fixed and did not change throughout the simulation or the stem model, with Δz= 200 mm

and Δt = 180 s.

Table 2. List of all the parameters selected for calibration. References relate to selection criteria for acceptable ranges.

Optimized Initial Acceptable range z References parameters values [min, max] Oak Pine Non-hydrodynamically limited (NHL)1 Vcmax25 40 [20, 85] Renninger et al. [2015] 59.9 31.1 m 5 [4, 9] Renninger et al. [2015] 6.7 7.3 x 4 [2, 6] 3.1 3.5 FETCH2 2,3 Stomata response to stem water potential 2 5 6 5 5 5 Φ50,stomata -1×10 [-2×10 , -1×10 ] Cruiziat et al. [2002] -9.1×10 -1.8×10 c3 0.10 [0.1, 20] Cruiziat et al. [2002] 12.3 10.3 Xylem cavitation and capacitance curve 3 -7 -7 -6 -6 -6 Kstem,max 9×10 [9×10 , 12×10 ] Bohrer et al. [2005] 1.6×10 1.2×10 6 6 6 6 6 Φ50,stem 1×10 [1×10 , 2×10 ] Mayr et al. [2003] 1.7×10 1.2×10 c2 2 [2, 6] Chuang et al. [2006] 3.0 2.8 6 6 6 6 6 ϕstem,z50 -0.5×10 [-6×10 , -0.5×10 ] -2.5×10 -2.2×10 6 6 6 6 6 ϕ stem,z88 -0.1×10 [-2×10 , -0.1×10 ] -0.5×10 -0.5×10 Soil water stress function 4 Ψ0 -0.3 [-0.75, -0.3] Feddes et al. [1978] -0.51 Ψw -2.1 [-2.7, -2.1] Feddes et al. [1978] -2.56 Penman-Monteith+β Optimized parameters Plot level Renninger et al. Vcmax25 30 [20, 85] 55 [2015] Α 0.4 [0.4, 1.2] Feddes et al. [1978] 0.8 Ψ0 -0.3 [-0.75, -0.3] Feddes et al. [1978] -0.64 Ψw -2.1 [-2.7, -2.1] Feddes et al. [1978] -2.49 1 parameter type (1), 2 parameter type (2), 3 parameter type (3), 4 parameter type (4)

As is customary with land-atmosphere and ecosystem models such as CLM [Bonan

et al., 2002], ED2 [Medvigy et al., 2009], and T&C [Pappas et al., 2016], we assume that 56 the aforementioned physiologic and hydraulic parameters (Table 2) are not age/size- specific, but are properties of the plant functional type or species (in this study represented as two different genera). Therefore, we parameterized the genus-specific NHL and

FETCH2 formulations through an optimization algorithm considering a predefined objective function, which includes the measurement of latent heat flux. We used a two-step parameterization process. First, we calibrated the NHL transpiration (forcing), using the sum of squared error between the NHL transpiration and observed plot level transpiration as an objective function. Derivation procedures of the observed plot level transpiration are outlined in the following paragraph. Optimizing the NHL transpiration guarantees that any further improvement to the simulated transpiration by FETCH2 relative to the NHL transpiration model is a result of the improved dynamics in FETCH2 and not an artifact of poor parameterization of the NHL transpiration model. Next, we used the parameterized

NHL transpiration component to optimize the other FETCH2 parameters, based on the double exponential error distribution.

The NHL calibration required determination of the plot level observed transpiration

(EOBSp) from the observed plot level latent heat flux (evapotranspiration, LEOBSp) using the approach introduced by Williams et al. [2004]. This approach assumes that during dry conditions the differences between the eddy covariance observed latent heat flux (LEOBSp) and transpiration approximated through plot-scaled sap flux (JOBSp, scaled from tree level observed sap flux (JOBSc) using Eq. 49 in chapter 2) correspond to errors in sap flux scaling. However, during non-water limited conditions and shortly after precipitation events, the deviations between scaled sap flux and LEOBSp are the result of the inclusion

57 of evaporation from the soil and intercepted-precipitation in LEOBSp [Williams et al.,

2004]. The ratio of evapotranspiration/transpiration calculated for this study site was, on average, 70% during 2009 and 65% during 2011.

2.6 Optimization of the Model Parameters Using Markov Chain Monte Carlo Algorithm

The FETCH2 parameterization was performed using a delayed rejection-adaptation

Markov-Chain Monte Carlo-Metropolis Hasting algorithm (DRAM-MCMC-MH). This approach is a modified version of the adaptive MCMC algorithm [Haario et al., 2006;

Haario et al., 2001], which tends to improve the convergence efficiency of the algorithm.

The algorithm assumes Gaussian distribution for each of the parameters. In the first iteration, MCMC creates a prior distribution for each parameter assuming infinite variance and the mean equal to expected value of the initial parameter (Table 2). The distribution is updated at each iteration adaptively considering the mean at current point and covariance determined by the spatial distribution of the parameter states [Haario et al., 2001].

The MCMC technique evolves the parameter values iteratively until the distribution associated with each optimized parameter converges to a stable posterior distribution. The optimum parameter set is selected as the parameter set that maximizes the likelihood. The

MCMC algorithm requires the user to pick initial, lower bound and upper-bound values for each of the parameters to be optimized, and the maximum number of iteration for the sampling process. We set the algorithm to run for 1000 iterations, 200 of which are discarded as burn-in. The initial, lower bound and upper bound values for the parameters

58 were determined based on the existing literature (columns 3 & 4, Table 2). There are different methods to ensure that the algorithms have found a true global optimum [Brooks and Roberts, 1998]. In this study, we used a “burn-in” method, which rejects a certain fraction of the neighborhood explorations before accepting points.

3.2.6 Evaluation of Model Performance

The Penman-Monteith (PM) model [Monteith, 1965; Penman, 1948; Thom, 1972] is a widely used evapotranspiration model that does not include any mechanistic link between soil water potential and stomatal conductance [Ershadi et al., 2014; Stannard,

1993]. The PM model was driven by the atmospheric forcing including net radiation, ground heat flux, VPD, wind speed, humidity, and temperature and calculates the plot level expected evapotranspiration. We parameterized the PM model using the half hourly transpiration derived from the observed latent heat flux using Williams et al. [2004] (Table

2), assuming that transpiration is the primary component of evapotranspiration in PM model.

The specific version of the Penman Monteith model (PM, W/m-2) [Monteith, 1965;

Penman, 1948; Thom, 1972] we used to predict evapotranspiration was:

 g g  T  Pt  R  G   C VPD44.6 b,z s,z  0    n  h p     gb,z  gs,z  Ta tT0  P0  EPM    (4)  r  r    c h rh

59 where

 (c)    mA r  w e  z  e  (c) (c)  e  w  0  g  g  (5) s,z 0  VPD    cs  * 1   Do  where

 V exp0.088T  25    cmax 25 a c       1 exp 0.29 T  41  i * c    Q      a   i * p p,z Az  min  Rd ,  Rd  (6)  o  c  2  c  K 1 i  i *   i c      Ko  

All the variables and parameter definitions and values are presented in Table 3.

Table 3. List of all variables, used in PM formulation

Parameter Description Δ [kPaK-1] Slope of the saturation vapor pressure curve VPD [kPa] Vapor pressure deficit -2 -1 gb [mol m s ] Leaf boundary layer conductance -2 -1 gs [mol m s ] Stomatal conductance Ta [°C] Air temperature -2 -1 g0 [mol m s ] Cuticular conductance m [-] Fit parameter -2 -1 Az [μmol m s ] Net CO2 assimilation rate Ψw [kPa] Limiting soil water potential Ψe [kPa] Soil water potential Soil water potential when stomata or root are not limited by Ψ0 [kPa] water availability -1 cs [μmol mol ] Atmospheric concentration of CO2 -1 Γ* [μmol mol ] CO2 compensation point D0 [kPa] Reference vapor pressure -2 -1 Vcmax25 [μmol m s ] Maximum carboxylation rate at 25 °C -1 ci [mmol mol ] Internal leaf CO2 partial pressure -1 Kc [μmol mol ] Temperature adjusted Michaelis-Menten constants for CO2 -1 Ko [mmol mol ] Temperature adjusted Michaelis-Menten constants for O2 -1 oi [mmol mol ] O2 partial pressure βp [-] Leaf absorptivity of PAR -2 -1 Qp [μmol m s ] Absorbed photosynthetically active radiation α [-] Quantum efficiency (%) Rd Dark respiration calculated -3 ρh [gm ] Density of water - -1 Cp [Jg K ] Specific heat of air Psychrometric constant as a function of air density and the γ [kPaK-1] heat Capacity of air -1 rh [sm ] Aerodynamic resistance to heat flux 2 -1 -1 rc [m mol s ] Stomatal resistance

As depicted in Table 2 We chose to perform calibration on Vcmax25, α, Ψw, and Ψ0.

To demonstrate how well the mechanistic representation of tree hydrodynamics by

FETCH2 improves the simulation of transpiration beyond current, broadly used

transpiration models, we compared the FETCH2 predictions of plot level transpiration with 61 the plot level transpiration determined by the parameterized NHL and PM models. To make this comparison meaningful, we incorporated the direct soil water limitation effect on the stomatal conductance of the NHL and PM models by multiplying their resolved stomatal conductance by the soil water stress function (βs).

3.2.7 Performance Measures

We used four different performance metrics to evaluate the models: (1) coefficient of determination (R2); (2) Bias (B), which is the average difference between observation and simulation; (3) Normalized Mean Absolute Error (NMAE) [Medlyn et al., 2005]:

EOBS t E t (7) NMAE   p sim t nEOBS p t

where EOBSp is the observed plot level transpiration and Esim is the model-simulated transpiration. The over bar indicates averaging across all values of observations (n is the number of observations). Finally, (4) Reduced χ2 statistic [Taylor, 1982]:

2 2 1  EOBS p t Esim t     (8) n t  2 obs  where σobs is the standard deviation of the observations. In this formulation, the coefficient

2 in the denominator normalizes the uncertainty of observed values (EOBSp) to account for the 95% confidence interval. χ2, indicates the model-data mismatch along the range from

0 to infinite. Values of χ2 close to 1 indicate that model result and observations are in agreement relative to existing uncertainty in observations. 62

Akaike Information Criteria (AIC) is a leading method for selecting the best model among several competing models. This selection criterion was based on a combination of model’s goodness of fit (penalized likelihood) and number of parameters. AIC is defined as [Akaike, 1974; Burnham and Anderson, 2002]:

  n / 2  1 2  AIC  2ln 2 2 exp  EOBS  E   2 NO f     2  p sim   (9)    2  where σ2 is the variance of the error term, and NO is the number of free parameters in the model. In the scope of comparing various models, the relative probability that a model f minimizes the estimated information loss (RLf) is defined as [Burnham and Anderson,

2002]:

RL f  expAICmin  AIC f / 2 (10)

where AICmin is the minimum AICf and AICf is the Akaike information number for model f. The minimum AIC, corresponds to the model with the best performance for which RLf is equal to 1.

3.2.8 Site-specific Simulation Setup

We chose the peak-growing season (June 1 to August 31) of 2009 to perform the calibration on PM, NHL and FETCH2 models. Then, we evaluated the performance of the parameterized models using the observed data collected during the peak growing season of

2011. Meteorological data, including humidity, wind speed, air temperature, PAR, and

63 atmospheric pressure, were gap filled using bi-linear, periodic trended interpolation [Morin et al., 2014]. Flux data, including sap flux and latent heat fluxes, were gap filled using the

Artificial Neural Network (ANN) method, which is a common approach to gap-filling of flux data [Papale et al., 2006]. The ANN’s specific setup applied in our study is described in detail in Morin et al. [2014]. In this study, 26.5% of the 2009’s and 26.7% 2011’s latent heat flux were gap filled using the ANN method. In addition, to assure the accuracy of our parameterization, days with more than eight sequentially missing half-hourly sap flux observations were removed from the optimization process.

Table 4 includes the average of maximum daily VPD, mean wind speed, mean air temperature, average of maximum daily PAR, mean soil moisture and total precipitation for the selected simulation periods in 2009 and 2011.

Table 4. Site-specific atmospheric and soil properties during the experiment’s period in 2009 and 2011. Average Average of Mean of Mean Mean air Total Maximum soil Maximum wind temperature precipitation Month daily PAR moisture daily speed (μmol m- VPD (ms-1) (°C) (mm) 2s1) (%) (kPa) 2009 June 1.5 1.4 19.6 1488 8.1 104.6 July 2.2 1.5 22.4 1683 6.9 121.8 August 2.1 1.2 23.7 1560 7.8 133.8 2011 June 2.3 1.4 22.3 1681 5.4 38.9 July 2.8 1.4 25.5 1691 6.3 121.9 August 2.1 1.5 22.7 1509 8.7 370.8

Simulations were performed at the genus-level using a single representative tree for each

(c) (c) (c) (c) genus. DBH , height (ztop ), sapwood area (ASap ), crown area (ACrown ) of a representative ‘average tree’, total sapwood area of the trees with sap-flow measurement

(c) (c) (ASap,tot ) and total crown area (ACrown,tot ) of the two existing genera (oak/pine) in 2009 and 2011 are presented in Table 5.

2009 (c) (c) (c) (c) (c) (c) DBH ztop ASap ACrown ASap,tot ACrown,tot PFT (cm) (m) (cm2) (m2) (m2) (m2) Oaks 19.7 12.0 99 28.8 0.20 10239 Pines 35.9 17.0 509 46.1 0.05 1290 2011 Oaks 18.3 12.0 88 28.8 0.18 7370 Pines 37.3 17.0 616 46.1 0.06 1325

3.3 Results and Discussion

3.3.1 Model Performance Evaluation

We calibrated the PM and NHL models based on observed half-hourly transpiration, and FETCH2 based on observed half-hourly sap flux. We used the MCMC algorithm to optimize NHL and FETCH2 parameters for each of the two genera (oak and pine), and for the PM model for the whole plot. The resulting calibrated PM, NHL, and

FETCH2 parameters are listed in Table 2. We used these parameters to represent the

hydrodynamic variables of FETCH2 for both genera including stomatal response ratio, (the

ratio of FETCH2 simulated water-limited transpiration sink (Elstem,c) to NHL transpiration

forcing (ENHLstem)), xylem conductance (kstem), and finally the RWC.

Figure 7. Differences in hydraulic traits between the oaks and pines predicted by our optimized FETCH2: (a) Stomata response curve describing leaf response to stem water potential, (b) Xylem conductance, and (c) Stem capacitance - relative water content (RWC) response to changes in the stem water potential for the parameterized oak (solid line) and parametrized pine (dashed line). We plotted the curves over an arbitrary range of stem water potential with the optimized parameters from Table 2 to compare the hydraulic properties of the two existing genera qualitatively.

Figure 7 illustrates how genera-specific parameterizations reflect the differences

between oaks’ and pines’ hydrodynamic properties and hence the hydraulic strategies of

the two genera. With the onset of water stress, i.e., the initial drop in stem water potential,

the oak maintains higher stomatal conductance as compared to the pine (Figure 7a). This

characterizes oak as the more anisohydric of the pair. The oak, having higher maximum

xylem conductance (kstem,max, Table 2) maintains a higher conductance within the displayed

range of stem water potential deficit. Changes in relative stem water content per stem water

potential are similar between oak and pine but pine tends to release more water (lower

RWC) for the same drop in water potential (Figure 7c).

3.3.2 Model Evaluation

We simulated the tree level NHL transpiration in 2011 and used it to force the

parameterized FETCH2. Figure 8 illustrates the mean daily dynamics at plot level of

observed and simulated transpiration with NHL, FETCH2-resolved, and Penman Monteith

models.

Figure 8. Mean daily plot level NHL (blue square), FETCH2 (magenta diamond), Penman- Monteith (red circle), and observed (black triangle) transpiration.

Figure 8 visually demonstrates that the mean daily plot level transpiration, simulated by FETCH2 is closer in value to the mean daily-observed transpiration compared to the other two models. To compare the differences between models, model skill metrics were evaluated based on the magnitude of transpiration hysteresis, and half-hourly and mean daily transpiration for all the three models (Table 6).

Models Hysteresis 2 2 NMAE χ B R NHL 0.279 10.696 0.146 0.59 FETCH2 0.062 2.566 -0.133 0.91 PM 0.373 19.207 0.165 0.32 Models Half-hourly Simulation of transpiration 2 2 NMAE χ B R NHL -0.094 5.822 10.873 0.75 FETCH2 0.0098 0.724 -0.002 0.93 PM -0.368 90.609 0.565 0.45 Models Mean daily Simulation of transpiration 2 2 NMAE χ B R NHL -0.093 2.880 67.791 0.58 FETCH2 0.0619 1.270 -6.663 0.78 PM -0.367 44.118 50.117 0.36

FETCH2 outperforms both the optimized NHL and PM models for simulations of transpiration at the half-hourly and daily scale, and for simulations of the hysteresis of transpiration (section 3.2.4). The NMAE and χ2 criteria for FETCH2 were closer to zero and unity, respectively. This indicates that FETCH2 has significantly improved the 68 simulation of transpiration through the incorporation of within-tree hydrodynamic processes, rather than only considering the soil moisture limitations. Simulated NHL transpiration displayed better performance compared to PM, particularly at the half-hourly scale.

Although the performance metrics in Table 6 showed that FETCH2 improves the

NHL simulation of transpiration, since these three models use different numbers of parameters, we used AIC and RL statistics to analyze the effect of over-parameterization.

Considering that the NHL model has 3, the PM model has 4 and the FETCH2 model has

11 parameters that were calibrated, we calculated the AIC and RL numbers for each of the three transpiration models using the Gaussian distribution of the likelihood (Table 7).

Table 7. Comparison between the Akaike Information Criteria (AIC) and Relative Likelihood of NHL, PM and FETCH2 models Akaike Information Relative Likelihood Model Criteria (AIC) (RL)

NHL 26.35 0.11

PM 74.28 4.28×10-12

FETCH2 21.89 1

Despite having more free parameters, FETCH2, with the lowest AIC number, has the highest probability to minimize the modeling error. The NHL model is 0.11 times and the

PM model is 4.28×10-12 as probable as FETCH2 to minimize the simulation error, confirming the advantage of the hydrodynamic approach. 69

We categorized the days within the simulation period (June 1 to August 31, 2011) into three groups: wet (with daily mean soil moisture larger than 10%), intermediate (with daily mean soil moisture between 5% and 10%) and dry days (with daily mean soil moisture less than 5%). For each category, we calculated the relative hysteresis of transpiration (Section 3.2.4). Figure 9 shows the mean relative hysteretic loop for days with intermediate soil moisture, created based on the observed and simulated (FETCH2, PM, and NHL) transpirations. Similar to the performance metrics presented in Table 6, Figure

9 also shows that FETCH2 performed better than the two other models in predicting the magnitude of hysteresis. Neither the PM nor the NHL models are able to reproduce the hysteresis of transpiration as accurately as FETCH2 (Figure 9).

Figure 9. Mean hysteresis loop of observed (black triangle), NHL (blue square), FETCH2 (magenta diamond), and PM (red circle) simulated transpirations under intermediate soil moisture condition.

One of the outputs of FETCH2 is sap flux. This is advantageous in cases where direct observations of sap flux exist as an additional variable for model evaluation. Figure

10 shows the total daily tree-level observed and FETCH2 simulated sap flux for both oak and pine with a very good agreement.

a - Oak

]

/ Sap-OBS g Sap-FETCH2 k 0.04

[

F 0.02

S 0 0 0 1 1 2 2 0 0 1 1 2 2 3 0 1 1 2 2 3 1 6 1 6 1 6 1 6 1 6 1 6 1 5 0 5 0 5 0 -J -J -J -J -J -J -J -J -J -J -J -J -J -A -A -A -A -A -A u u u u u u u u u u u u u u u u u u u n n n n n n l l l l l l l g g g g g g Time b - Pine

] 0.03

g Sap-OBS

[ Sap-FETCH2

0.02

0.01

S 0 0 0 1 1 2 2 0 0 1 1 2 2 3 0 1 1 2 2 3 1 6 1 6 1 6 1 6 1 6 1 6 1 5 0 5 0 5 0 -J -J -J -J -J -J -J -J -J -J -J -J -J -A -A -A -A -A -A u u u u u u u u u u u u u u u u u u u n n n n n n l l l l l l l g g g g g g Time

Figure 10. Total daily tree level observed (black) and FETCH2-simulated (magenta) sap flux during the simulation period for (a) oak and (b) pine.

Figure 11 shows the daily dynamics of the observed soil moisture, tree-level simulated stem water storage and observed and simulated water fluxes (sap flux and transpiration) within a selected period of ten consecutive days during a drying period, with initially high and gradually declining soil moisture. FETCH2 successfully captured the inter- and intra-daily pattern of water flux. FETCH2 predicts higher transpiration rates before noon than afternoon, with the diurnal transpiration curve gradually skewing towards the morning, as the soil becomes dryer and overall daily transpiration declines. The model also shows the diurnal dynamics of stem water storage depletion and nighttime recharge.

× #×10-3 a ]

]

2 10 [

/ EV-Obs t

[ EV-NHL

t 1.5 8

n n EV-FETCH2

1 6

a s 0.5 4

T 0 2 o July-12 July-13 July-14 July-15 July-16 July-17 July-18 July-19 July-20 July-21 S Day

× #×10-3 b 2.5 ]

Sap-FETCH2 g

]

38 k

[ s Sap-Obs

/ 2

[ 36

1.5 r

t l 34

S F 1

a 0.5 32 t

0 30 W July-12 July-13 July-14 July-15 July-16 July-17 July-18 July-19 July-20 July-21 Day

Figure 11. Ten days dynamics of (a) left y-axis: Oak’s tree level NHL (solid blue line), FETCH2- simulated (solid magenta line), and observed (dashed-dot black line) transpiration, right y-axis: soil water content (solid green line), (b) left y-axis: Oak’s tree level observed (dashed black line), and FETCH2-simulated (solid magenta line) sap flux, right y-axis: Oak’s water storage (solid blue line).

3.4 Identifying Differences in Hydraulic Strategies Between Oak and Pine

Plants lose water from storage in the stem and branches during the morning due to faster rate of water loss through transpiration than recharge of the stem xylem [Matheny et al., 2015]. Some trees may reduce their stomatal conductance during and after peak water demand (at midday and early afternoon) by closing the guard cells to prevent further water

73 loss and drop of water potential in the plant [e.g., Sack and Holbrook, 2006]. This process is called “midday stomata closure” [Manzoni et al., 2013; Sperry et al., 1993; Sperry et al.,

2002] which affects the diurnal dynamics of transpiration as well as the long-term totals of transpired water and through its dependence on stomatal conductance, affects carbon fluxes as well.

One of the advantages of FETCH2, is the ability to resolve differences among trees with various hydraulic strategies through multiple parameters that are not typically resolved by other models (Table 2). Genus-specific parameterization of FETCH2 yields groups of parameters that can effectively characterize the hydraulic strategy of the genera.

The FETCH2 model represents stomatal-response sensitivity to stem water potential through two parameters: Φ50,stomata and c3 (Table 2, Figure 7a). Thus, characterizing the relatively anisohydric strategy of oaks versus the more isohydric strategy of pines (Figure

7).

Renninger et al. [2014] and Renninger et al. [2015] showed that pine trees in the

Silas Little experimental forest demonstrate a relatively isohydric response. As shown in

Figure 7a, we determined that stomatal response occurs over a range of less negative stem water potentials for pine (e.g. steeper decline in the stomatal response ratio) than for oak.

This indicates that the transpiration rate is more vulnerable to drops in stem water potential and, over a large range of water potentials, a lower value of stomata conductance

(corresponding to actual transpiration) will be obtained for pine than for oak at the same xylem water potential.

Responses to changes in soil water availability depend on the tree's hydraulic strategy [Tardieu and Simonneau, 1998]. Anisohydric plants experience larger leaf water deficits at midday during dry soil water conditions than in wetter conditions. Isohydric plants demonstrate less variability between midday leaf water potential during dry and wet conditions, mainly due to the strong down-regulation of their transpiration under dry conditions. Similar to Figure 9, we categorized the days into dry, intermediate, and wet days and calculated the normalized mean daily transpiration for each one of these categories.

Figure 12. Left column: Normalized (with respect to total daily) mean daily cycle of transpiration during (a) wet days, (b) intermediate soil moisture, and (c) dry condition for oak (solid blue line) and pine (solid magenta line). The blue and magenta dashed lines represent the peak of normalized transpiration. Right column: Relative mean hysteresis loop of transpiration with their corresponding hysteresis values, during (a) wet days, (b) intermediate soil moisture, and (c) dry condition for oak (solid blue line) and pine (solid magenta line). Hysteresis was calculated using the method explained in section 3.2.4.

Both oak and pine reach their maximum daily transpiration rate around noon under wet conditions (Figure 12a). Under the intermediate conditions, both genera peak earlier, however pine appears to be more sensitive to the drying soil conditions and reaches its peak transpiration rate earlier in the morning (Figure 12b). Pine shifts its peak transpiration earlier, to around 10 am, under extremely dry conditions while oak transpiration continues to peak around 11 am (Figure 12c). Therefore, soil water limitations play a smaller role in regulating oak transpiration than for other, more isohydric species such as pine.

We conducted a paired-sample t-test to determine whether there are any significant differences between daily absolute hysteresis means of oak and pine. We performed the test separately for each soil moisture condition. The test result revealed that there are statistically significant differences between oak’s and pine’s daily absolute hysteresis

(p<0.0001) in all three soil moisture conditions while oak maintains higher daily hysteresis of transpiration. This confirms the results of Matheny et al. [2014b], who showed that a ring porous anisohydric species of oak, Quercus rubra, demonstrated larger mean relative hysteresis as compared to similarly sized isohydric species. We speculate that in order to reduce the effect of soil water stress, oak must either draw water from deeper layers, be more conductive and efficient in overnight recharge, and/or have a more effective hydraulic redistribution than pine [Robinson et al., 2012].

Similarly to transpiration, sap flux also exhibits diurnal hysteresis that is illustrated by plotting the normalized simulated sap flux as a function of normalized VPD during the course of each day [Chen et al., 2011; O’Grady et al., 2008]. Figure 13 shows that throughout the simulation period, oak maintains a larger degree of daily sap flux hysteresis 77 as compared to pine. The diurnal hysteresis of sap flow can be indicative of the diurnal hydrodynamic stress on plants [Matheny et al., 2014b]. Mechanistically, the differences in the vessel and inter-vessel pit structure of plant species cause a trade-off between the water transport capacity ("efficiency") and safety among plants [Manzoni et al., 2013]. The

“efficiency” of plant species can be characterized by the maximal hydraulic conductivity.

High efficiency if often obtained at the cost of larger vulnerability to cavitation (less negative values of water potential at 50% loss of conductivity). “Safety” is characterized by lower xylem conductivity but larger resistance to cavitation, or higher margin between minimum water potentials during droughts and critical cavitation levels [Manzoni et al.,

2013; Meinzer et al., 2010]. Thus, oak, by being on the efficiency side of the “safety- efficiency” continuum and experiences stronger depletion of stem-water storage, requires more time to replenish its water storage and hence has lower sap flux in the afternoon compared to more isohydric species like pine [Manzoni et al., 2013; McCulloh et al., 2012;

Taneda and Sperry, 2008; Tyree and Zimmermann, 2002]. Pine on the other hand as an isohydric coniferous genus demonstrates less sap flow hysteresis [Matheny et al., 2014b;

McAdam and Brodribb, 2014].

s 0.6

r Oak

t 0.4

s Pine

x 0.2

p a 0 S 0 0 1 1 2 2 0 0 1 1 2 2 3 0 1 1 2 2 3 1 6 1 6 1 6 1 6 1 6 1 6 1 5 0 5 0 5 0 -J -J -J -J -J -J -J -J -J -J -J -J -J -A -A -A -A -A -A u u u u u u u u u u u u u u u u u u u n n n n n n l l l l l l l g g g g g g Time

Figure 13. Dynamics of diurnal relative hysteresis of tree level sap flux for oak (black) and pine (magenta)

Xylem architecture is one of the factors that imposes physical limitation on the

water transport rate within a tree, and its variations across species can explain some of their

water-use strategies [Bush et al., 2008; Lens et al., 2011; Sperry et al., 2002; Thomsen et

al., 2013]. Wood anatomy affects wood traits such as xylem conductivity (Kstem) and xylem

capacitance (Cstem). For example, the ring-porous oak with wide vessels in the wood

structure results in higher conductivity during the high water availability condition, yet,

decreases the safety margin of these species during drought [Bovard et al., 2005; Hacke et

al., 2001; Taneda and Sperry, 2008; Thomsen et al., 2013]. This structure causes the plant

to be more conductive, but also more vulnerable to cavitation under water limiting

conditions.

However, interactions with leaf traits, which in this case were more isohydric for

pines vs. anisohydric for oaks, and potentially additional interactions with root traits, such

as rooting depth, can lead to a whole-plant level strategy that does not necessarily present 79 the vulnerabilities expected by the xylem structure only. We suggest that these multi-trait whole-plant level combined hydrodynamics may explain the fact that only weak evidence for the safety-efficiency tradeoff was found when studying only xylem traits in many plant species [Gleason et al., 2016]. For example, in the case we studied, the generally more conductive xylem of oaks allowed maintaining high transpiration rates despite decreasing midday xylem-water potentials without signs of widespread cavitation.

3.5 Conclusions

We demonstrated that FETCH2 can effectively represent the continuum of hydraulic properties of stems and leaves over different genera with a wide range of characteristics through its parameterization process as depicted by the differences between wood properties of oak and pine. By incorporating the consequences of tree-water storage and hydraulic strategy to stomatal conductance, the hydrodynamic modeling approach we presented here may have a large impact on revising the structure of hydrologic, land- surface models, DGVM and coupled ESM. Simulating the aboveground water storage in trees enhances our understanding of the role hydrodynamic limitations and intra-daily water stresses play on transpiration. By accounting for tree hydrodynamics, FETCH2 is able to resolve the outcomes of different hydraulic strategies. The difference in the parameter values that represent the traits in FETCH2 correspond to the different trees' hydraulic strategies – namely the continuum between isohydric and anisohydric regulation of stomatal conductance. Through the parameterization process, FETCH2 has the ability

80 to capture differences in xylem anatomy such as conductivity and capacitance of the xylem.

By resolving aboveground stem water flow, storage and potential, it can effectively describe the difference in hydraulic strategies between plants.

The genus-specific parameterization of FETCH2 illustrates that with the same drop in xylem water potential, oak maintains higher stomatal conductance, higher xylem conductance, and higher RWC than pine. The model simulations demonstrated that soil water limitations play a smaller role in regulating oak transpiration than for the more isohydric species, pine, under nearly all water availability conditions. In response to the same changes in soil water availability, oaks experienced larger xylem water deficits at midday during dry soil water conditions compared to the wetter conditions, but maintained high transpiration rates. As expected for a more isohydric species, pine demonstrated less variability between midday leaf-water potential during dry and wet conditions but downregulated transpiration, and closed stomata earlier during the day when the soil was dry. We showed that the diurnal dynamics of transpiration for each genus shows a characteristic and different response to increasing soil moisture stress. These responses integrate at the plot level to a combined diurnal and overall transpiration dynamics that were not easily predictable by non-hydrodynamic models of transpiration, which do not resolve aboveground water storage and its effects. Application of this modeling approach in other mixed forests with trees of different hydraulic strategies will result in better estimation of the plant contribution to the land-surface energy balance and therefore a more accurate assessment of water resources and carbon uptake rates.

Chapter 4: Hydrodynamic Trait Coordination and Cost-Benefit Tradeoffs throughout the

Isohydric-Anisohydric Continuum in Trees

4.1 Introduction

Stomata regulate gas exchanges between leaves and the atmosphere, forming a dynamic control on biosphere-atmosphere exchanges. This control has impacts on the global carbon and water cycles [van der Molen et al., 2011; Williams et al., 2012], as well as on ecosystem function. The dynamics of stomatal conductance are affected externally by meteorological conditions, such as photosynthetic active radiation (PAR), wind speed, and vapor pressure deficit (VPD), and internally by leaf water potential. Leaf water potential is controlled by multiple structural and functional hydraulic traits throughout the plant, along the soil-root-stem-branch-leaf continuum of water flow [Matheny et al., 2016;

Meinzer et al., 2013; Sperry et al., 2002; Taneda and Sperry, 2008]. The diversity of hydraulic traits in plants may produce a wide range of response strategies to both short- term variation of environmental condition and long-term changes to climate and hydrological cycles which affect the availability of water [Rogiers et al., 2012; Skelton et al., 2015; Will et al., 2013].

Whole-plant hydraulic performance depends on the integrated function of complexes of traits [Matheny et al., 2017], such as embolism resistance and xylem anatomy

[Choat et al., 2012; Linton et al., 1998; Ogasa et al., 2013; Willson et al., 2008], stomatal closure mechanisms [Brodribb et al., 2014], hydraulic architecture and root properties

[Rogiers et al., 2012; Will et al., 2013], leaf turgor regulation [Meinzer et al., 2014], and phloem transport [Nikinmaa et al., 2014]. Plants with various trait complexes operate differently and show different dynamics of stomatal conductance, transpiration, carbon uptake, and stem-water storage, even under similar environmental conditions [Garcia-

Forner et al., 2016; Klein, 2014; Martı́nez-Vilalta et al., 2002; Matheny et al., 2015].

Vegetation hydraulic function during water limitation is based on a trade-off between water loss/demand (i.e. transpiration), which is coupled to carbon uptake through stomatal conductance, and water supply, transport from the soil to the leaves. Following the work of McDowell et al. [2008] and McDowell et al. [2013], we divide the causes of drought-induced mortality into carbon starvation as a result of limited stomatal openness and hydraulic failure as a result of cavitation. Avoidance of water-stress limitations is achieved through the coordination of xylem and root hydrodynamics and stomatal regulation [Brodribb and McAdam, 2011; Choat et al., 2012; Sperry, 2000]. The whole- plant hydraulic strategy, therefore, integrates the tradeoffs between root, xylem, and leaf hydraulic traits [Maherali et al., 2006; Matheny et al., 2017; Matheny et al., 2017].

Recently, there has been increased interest in describing the whole-plant hydraulic strategy of species using functional trait complexes, primarily to assess the vulnerability of species-rich communities to drought or other disturbance events [Garcia-Forner et al.,

2016; Klein, 2014; Martínez‐Vilalta et al., 2014; Matheny et al., 2017; Meinzer et al.,

2016; Skelton et al., 2015]. These studies identify variation in hydraulic strategies using an 83 explicit assessment of coordination among stomatal, xylem, and root traits. Functional traits are often well-related to environmental stresses and have been adopted in plant ecology to explore various species’ functional strategies and their mechanisms of mortality

[Choat et al., 2012; Kumagai and Porporato, 2012; Manzoni et al., 2014].

The purpose of this study is to assess the role of different hydraulic trait combinations in trees’ vulnerability to drought using a quantitative hydraulic modeling framework. We utilize an advanced plant hydrodynamic model, FETCH2 [Bohrer et al.,

2005; Mirfenderesgi et al., 2016]. FETCH2 resolves hydraulic functional traits at the root, stem, and leaf levels and simulates plant-level transpiration when provided with these hydraulic traits and environmental forcing. We evaluated the degree to which hypothetical trees, as defined by different combinations of hydraulic traits, suffer hydraulic failure due to cavitation or carbon starvation under the same environmental conditions. We consider a continuum of hydraulic traits at each of the leaf, xylem, and root levels to define a multi- dimensional “hydraulic strategy space”. We test the outcomes of different hydraulic strategies in response to a range of environmental conditions, representing typical wet, intermediate and dry conditions as observed in a research forest in Northern Michigan.

4.2 Materials and Methods

4.2.1 Site Description

The forcing data used in this analysis was collected from the forest flux site at the

University of Michigan Biological Station (UMBS) located at northern lower Michigan, 84

USA (N 45º 33’ 35”, W 84º 42’ 48”). Annual average temperature for UMBS is 6.8 ͦC, and mean annual precipitation is 805 mm [Matheny et al., 2014b]. Soil is characterized as well drained Haplorthods of the Rubicon, Blue Lake, or Cheboygan series and consists of 92.2% sand, 6.5% silt, and 0.6% clay [Nave et al., 2011]. The study site is dominated by declining early successional species Populus grandidentata and Betula papyrifera, with mid- successional species Acer rubrum, Quercus rubra, Pinus strobus, Fagus grandifolia, and

Acer saccharum in increasing abundance. Average stem density of trees with diameter at breast height (DBH) larger than 8 cm is ~750 trees/ha, and the mean peak growing season

LAI is ~3.9 m2/m2.

Figure 14. UMBS site map showing the locations of the control tower (blue) and the FASET tower (red).

Methods for meteorological observations and evapotranspiration measurements at the UMBS site are described in detail by Gough et al. [2013] and Matheny et al. [2014b].

Half-hourly meteorological and eddy flux data are available through the Ameriflux database (http://ameriflux.lbl.gov/), site-ID US-UMB [Gough et al., 1999]. Soil water content is measured and recorded at 4 different locations at depths of 5, 15, 30, and 60 cm, and at 2 different locations at depths of 100, 200, and 300 cm below the soil surface (Hydra probe SDI-12; Stevens Water Monitoring Systems, Portland, Oregon, USA; He et al.

[2013]). Roughly 95% of the fine-root biomass is located in the top 80 cm of the soil depth

2 [He et al., 2013]. Conductive sapwood area (Asap, cm ) was established based on species- specific allometric relationships developed by Bovard et al. [2005] and Matheny et al.

[2014b].

4.2.2 Model Parameters

The three sets of parameters used to represent plant traits at the root, stem and leaf levels in FETCH2 are:

(1) Leaf-traits parameters: This group of parameters determines the shape and sensitivity of the stomatal response to stem water potential: Φ50,stomata is the water potential at which stomata will be 50% closed (i.e., the inflection point of stomata response to xylem pressure); c3,stomata is a shape parameter for the stomata closure response to reduced plant water potential. Together these values effectively define the simulated tree’s leaf hydraulic strategy along the isohydric-anisohydric continuum (Eq. 1).

c  3,stomata    z,t 1 El (z,t)  NHL z,texp    (1) stem stem        50,stomata   where NHLstem(z,t) is the potential evaporative demand, referred to as Non-

Hydrodynamically Limited transpiration (NHL). NHL is the transpiration estimated using the stomatal conductance as a function of atmospheric demand and photosynthetic capacity, while neglecting the soil water limitation effects on plants [Mirfenderesgi et al.,

2016].

(2) Stem-traits parameters: The aboveground xylem vulnerability curve and water storage capacity are described by kstem,max, Φ50,stem, c2,stem, ϕstem,z50, and ϕstem,z88 (defined below, Eqs.

2 & 3). These parameters are the consequence of specific xylem architectures (i.e. tracheids, diffuse-porous, or ring-porous xylem) and the interdependence of xylem conduits and storage tissues.

c  2,stem     z,t K  z,t  A k exp   stem   (2) stem stem stem,sap stem,max        50,stem  

Eq. 2 is the relationship between loss of conductivity and reduction of xylem water potential, frequently referred to as the cavitation curve. Astem,sap is the cross-sectional sapwood area within each vertical levels of an individual tree. Kstem,max is the maximum conductance of saturated xylem, Φ50,stem is the leaf water potential at 50% stomatal closure, and c2,stem is the shape parameters of the cavitation curve. The relative water content,

RWCstem, of the aboveground xylem can be calculated using:

stem z,t RWCstem stem z,t  1 (c) , bstem stem z,tstem,z502  bstem  (3) (c) stem,z88  0.24stem,z50 bstem  0.12stem,z50 stem,z88

where ϕstem,z50 and ϕstem,z88 are xylem water potentials at 50% and 88% relative stem water content. Including the capacitance term in the formulations for FETCH2 may be affected by including the capacitance term in the formulations [Meinzer et al., 2009].

(3) Root-traits parameters: This set of parameters represent the cavitation vulnerability of below ground root xylem (Eq. 4), root-water storage (Eq. 5), soil-to-root conductance (Eq.

6), and rooting depth and root mass vertical distribution within the rooting zone (Eq. 7). kroot,ax,max is specific axial conductivity of the root system as measured on isolated roots. c1,root and c2,root are shape parameters of the root system vulnerability curve,

c  2,root  CAI z K    z,t K  z,t  root root,ax,max exp   root   (4) root,ax stem f   c   lz   1,root  

ϕroot,z50 and ϕroot,z88 are xylem water potential at 50% and 88% relative root water content,

rootz,t RWCrootrootz,t 1 , brootrootz,troot,z502  broot (5) root,z88  0.24root,z50 broot  0.12root,z50 root,z88

s K rad,root is specific radial hydraulic conductivity under saturated soil condition, and bs is an empirical parameter based on soil type as suggested by Clapp and Hornberger [1978].

1/bs   z,t  K z,t  K s z  SAI z  soil  (6) rad,root  rad,root  root    soil,sat z

where, SAIroot is the surface area index of the root, defined as the ratio of root surface area to the ground surface area. Φsoil,sat is soil water potential at saturation,

The distribution of the root biomass is assumed to follow a logistic dose-response relation [Schenk and Jackson, 2002] (Eq. 7). z50 is the depth at which the cumulative fraction of root biomass above z (Fcum,root) equals 0.5, and c is an empirical dimensionless shape parameter that can be determined from z50 and z95.

    c  1   z  F   95  (7) cum,root  c  ,    0.052  z   z50  1          z50  

4.2.3 Reducing Degrees of Freedom in the Leaf, Stem, and Root Trait Parameter Space

To develop a framework that can test the sensitivity of plant response to hydraulic strategy according to whole-plant functional and physical traits, it is necessary, in theory, to test the response along each axis represented by the potential range of each of the parameters that characterize the hydraulic traits and define strategies. Such an analysis, however, would be largely unfeasible. Therefore, we reduced the degrees of freedom along some of the potential parametric variation by fixing some traits to realistic values [Chuang et al., 2006; Cruiziat et al., 2002; Quijano and Kumar, 2015]. For others that could not be

89 easily constrained to a fixed value, we looked for correlations between traits at the same physiological level.

At the leaf level, we fixed the slope of the stomatal response to leaf water potential, thereby reducing the 2-parameter description of stomatal response along the iso- anisohydric continuum to a single variable-parameter, Φ50,stomata, ranging from -0.5 MPa

(strongly isohydric) to -8 MPa (anisohydric) (Figure 15). Stomatal regulation is governed to a large degree by leaf turgor [Brodribb and Holbrook, 2003; Brodribb et al., 2003]; therefore, leaf water potential at 50% stomatal closure, Φ50,stomata, serves as a good representation of the degree of iso- to anisohydry [Meinzer et al., 2016; Skelton et al.,

2015]. We fixed c3,stomata = 3, representing a rather sharp stomatal response. Importantly, the value of c3,stomata has a much smaller effect on the upper part of the curve, when stomata begin to close, than Φ50,stomata.

Figure 15. Sensitivity analysis of the stomatal response curve describing leaf vulnerability to stem water potential with respect to changes in c3 and Ф50,stomata. The parameters were selected according to the standard values found in Cruiziat et al. [2002]. c3,stomata was allowed to vary between 1 and 10 (within each of the colored curve bundles) and Ф50,stomata was allowed to vary between 0.5 and 8 MPa

(among the different colored curve bundles, light yellow for Ф50,stomata=-0.5 MPa gradually changing to dark blue for Ф50,stomata=-8 MPa). For water potentials larger than Ф50,stomata, larger c3,stomata will lead to higher conductivity. For water potentials smaller than Ф50,stomata, smaller c3 leads to higher conductivity. Black solid lines are the stomatal response curves with slope (c3,stomata) equal to 3.

The cavitation vulnerability curve is the most common approach for representation of the xylem hydraulic strategy [Tyree, 1988]. The most commonly used parameter derived from the cavitation curve is the water potential at 50% conductivity loss (Φ50,stem) [Skelton et al., 2015]. Maximum conductivity of well-hydrated xylem (kstem,max) is also a deterministic trait for hydraulic function. Higher maximum conductivity reduces the impact of water stress and postpone xylem cavitation [Gentine et al., 2015]. Similarly, higher Ф50,stem delays the onset of cavitation under water-stressed conditions. We used reported observations of these trait values from a collection of published hydraulic trait data, including water potential at 50% loss of conductivity and sapwood-specific

(maximum) conductivity [Kattge et al., 2011] and found a significant (p = 0.01) correlation between kstem,max and Ф50,stem. We used this correlation to model kstem,max as a function of

Ф50,stem (Figure 16). After fixing the shape parameter, we effectively reduced the 3- parameter description of the xylem conductivity to a single axis driven by variation in

Ф50,stem.

Figure 16. Correlation between maximal xylem conductance

(kstem,max) and water potential at 50% loss of conductivity 2 (Ф50,stem). We found a significant (p=0.01, r =0.28) exponential

relationship, kstem,max=3.154×exp(-2.08 Ф50,stem).

Maherali et al. [2004] show that species vary considerably in Ф50,stem, ranging from

−0.18 MPa (highly cavitation vulnerable) to −14.1 MPa (highly cavitation resistant).

Similar to its effect in the leaf response curves, the shape parameter of the cavitation curve

(c2,stem) had a smaller effect than Ф50,stem at the area corresponding with the onset of loss of conductivity. We therefore picked a reasonable value for c2,stem = 3 [Chuang et al., 2006] and kept it constant throughout the course of this study. In a previous study [Mirfenderesgi

93 et al., 2016], we found that FETCH2 simulated water potential and transpiration are less sensitive to the parameters that define the capacitance term (ϕstem,z50, and ϕstem,z88). Here, we set the values of -2.20 and -0.58 MPa, respectively for ϕstem,z50, and ϕstem,z88.

We selected rooting depth as the representative rooting trait of the plant. Rooting depth is known to control the effect of rainfall variability on soil moisture dynamics and plant water stress [D'Odorico et al., 2000; Gentine et al., 2015]. We varied rooting depth between 50 cm (shallow rooting case) and 300 cm (deep rooting case), which, in our site correspond to the shallow, well-drained surface layer, and the deep layer with less variable soil water content, respectively. We chose a typical vertical rooting profile (Eq. 7) with identical shape parameter (c) for both cases. The vertical distribution of the roots over the existing rooting depth (shallow or deep) was calculated from the cumulative fraction of root biomass above any soil layer, estimated based on Eq. 9 (Figure 17). We kept the remaining parameters constant, all constant values are shown in Table 8.

Figure 17. Vertical profile of root cross sectional area index for deep roots over 300 cm soil depth (black dashed line). Vertical profile of root cross sectional area index for shallow roots over 50 cm soil depth (purple dashed line) for the wet (solid red line), intermediate (solid blue line), and dry (solid green line) conditions. The root cross sectional area index is defined as the total cross- sectional area of roots per unit ground area measured at each layer of the soil

We kept the remaining parameters constant, all constant values are shown in Table 8.

Table 8. FETCH2 parameters, associated with plant traits at the root, stem, and leaf levels, assumed to be constant

Parameter Description Units Values Empirical dimensionless shape parameter c - -1.37 for the root distribution Shape parameter for conductance (stem c2,stem - 3 xylem) Shape parameter- cavitation pressure 4 c1,root Pa 10 (root xylem) Shape parameter for conductance (root c2,root - 3 xylem) c3 Shape parameter for stomatal response - 3 Rate of change of the mean root length -1 flz mroot m soil 0.9 with respect to the soil depth g Gravitational acceleration ms-2 9.807

s Specific radial hydraulic conductivity 2 -6 K rad,root m s 10 under saturated soil condition Specific axial conductivity of the root 2 -6 Kax.root,max m s 10 system, measured on isolated roots P0 Standard sea level atmospheric pressure kPa 101.3 R Molar density of an ideal gas mol m-3 44.46 T0 Temperature conversion from °C to °K - 273 9 Xstem,E Stem xylem elasticity module Pa 10 9 Xroot,E Root xylem elasticity module Pa 10 9 XE Xylem elasticity module Pa 10 Depth above which 50% of the roots are z50 m 0.25-1.5 located Depth above which 95% of the roots are z95 m 0.4-2.4 located λ Latent heat of vaporization kJ kg-1 2240 Shape parameter – xylem water potential 6 ϕstem,z50 Pa -2.2×10 at 50% relative water content (stem) Shape parameter – xylem water potential 5 ϕstem,z88 Pa -5.8×10 at 88% relative water content (stem) Shape parameter – xylem water potential 6 ϕroot,z50 Pa -2.20×10 at 50% relative water content (root) Shape parameter – xylem water potential 5 ϕroot,z88 Pa -5.8×10 at 88% relative water content (root)

4.2.4 Quantifying the Cost of Hydraulic Stress

Water limitations can lead to two detrimental outcomes – hydraulic failure or carbon starvation. Hydraulic failure occurs when cavitation within the xylem system results in a catastrophic loss of xylem conductivity [McDowell et al., 2011; Sperry et al., 2002;

Tyree and Sperry, 1989]. Percent loss of xylem conductivity (PLCx, Eq. 8) is a common metric of the cost of water limitations to the conductive system. We used PLCx and PLCs to quantify hydraulic failure [McDowell et al., 2013].

LADz kstem,max  LADz kstem  stem z,t t z PLCx  100  (8) LADz kstem,max  t z where LAD is the vertical leaf area density. Alternatively, the carbon starvation presented by McDowell et al. [2008] and McDowell et al. [2013] predicts that stomata closure, in avoidance of hydraulic failure, stops the photosynthetic uptake of carbon and results in starvation due to the continued metabolic demand for carbohydrates. Although non- hydraulic factors such as temperature and biotic agents may also influence carbon starvation [Wallin et al., 2003], hydraulic mechanisms are proven to be among its primary drivers. We calculate the percent loss of stomatal conductivity (PLCs, Eq. 9) as a metric of the cost of leaf-level stomata regulation of hydraulic limitations.

NHLz,t El stem (z,t) t z PLCs 100 (9)  NHLz,t t z

4.2.5 Classification of “Wet”, “Intermediate” and “Dry” Days

We used our modeling framework to evaluate responses of a continuum of whole- plant hydraulic strategies to different environmental conditions. We used a combination of vapor pressure deficit (VPD) and soil water content (SWC) to define criteria to select three days, to represent stereotypical dry, intermediate, and wet conditions. We performed our analysis using the meteorological observations from these selected days as environmental forcing. We selected our representative days from the observations collected during the summer (June 1st to August 31th) of 2013. We considered the roots located in the top 30 cm as shallow roots and the roots located between 100 and 300 cm as deep roots. The soil water content at the top three observation depths (5, 15, and 30 cm) were then averaged to estimate the shallow soil water content, and the deeper soil water content was calculated by taking an average of the measurements at depths 100 to 300 cm. Soil water content measurements were converted to soil water potential using the Van Genuchten [1980] hydraulic parameterization and UMBS site-specific parameters [He et al., 2013; Matheny et al., 2014b].

We plotted the maximum daily VPD with respect to the mean daily soil water potential for shallow soils (Figure 18a). We excluded days with total daily precipitation higher than 2 mm as the intra-daily variation of both VPD and SWC was large during these days. We found a significant correlation between daily mean VPD and SWC at shallow depth. We narrowed our search to days when the observed VPD and shallow SWC fell close to both mean regression lines (Figure 18b). Among these few days we selected three days with low, intermediate, and high VPD and SWC. To do this, we first categorized all 98 days within our observation period as dry, intermediate or wet days. The dry days (light yellow area in Figure 18b) are defined as days when mean daily shallow SWC fell in the lowest third of the SWC range (-23.3 to -30 kPa) while maximum daily VPD fell within the highest third of the maximum daily VPD range (1.8 to 2.4 kPa). The intermediate days

(light blue area in Figure 18b) are defined as days when mean daily shallow SWC fell in the middle third of the SWC range (-16.6 to -23.3 kPa) and maximum daily VPD fell within the middle third of the of maximum daily VPD range (1.3 to 1.8 kPa). The wet days (dark blue area in Figure 18b) are defined as days with mean daily shallow SWC in the highest third of the SWC range (-10 to -16.6 kPa) and with maximum daily VPD in the lowest third of the maximum daily VPD range (0.8 to 1.3 kPa).

(a) (b)

Figure 18. (a) Correlation analysis between water supply (shallow SWC) and water demand (VPD) during summer period of 2013; (b) Days with lowest correlation error from shallow parts of the soil, located in the dry (low SWC and high VPD, light yellow), Intermediate (intermediate SWC and medium VPD, light blue), and wet (high SWC and low VPD, dark blue) regions.

After categorizing days into dry, intermediate, and wet conditions, we took an average of the atmospheric and soil observations across all the days in each category to create three ‘stereotypical’ days representing each of the three moisture conditions. The vertical profile of soil water potential over the 3 m soil layer is depicted in Figure 17 for the three conditions.

4.2.6 Numerical Experiment to Test the Consequences of Limited Water Availability

Under Different Hydraulic Traits

For each of the three levels of environmental water limitations (dry, intermediate, and wet) we generated a synthetic set of forcing to drive the simulations. Each environmental water limitation scenario was represented by the observed atmospheric and soil moisture conditions of the averaged ‘stereotypical’ day (see section 4.2.5 and Figure

18). Two sets of prescribed soil moisture values were considered for each environmental water-limitation level: the “deep root” and “shallow root” options (see section 4.2.5 and

Figure 18). For each of these 6 sets (3 water limitation levels and 2 rooting strategies) of forcing data we simulated the transpiration and hydrodynamics of hypothetical trees with different combinations of xylem and leaf trait values within the tested range over all 6 combinations (Φ50,stem ranging from -0.1 MPa to -3 MPa and Φ50,stomata ranging from -0.1

MPa to -3 MPa). Simulations were 9 days long, over which atmospheric forcing was recycled daily with constant SWC. We used the PLCs score (Eq. 9) resulting from each simulation to quantify the whole-plant effect of each trait combination for each of the water limitation levels. 100

4.3 Results and Discussion

We used FETCH2 to simulate the whole-plant hydrodynamics of an average-sized

19-meter high using stereotypical forcing conditions generated based on observations of wet, intermediate, and dry days observed at UMBS. We spanned a parametric space of leaf, stem, and root traits along the range of reasonable values of the three selected parameters which are representative of key traits at each of these levels. For the different combinations of hypothetical hydraulic strategies and environmental water limitations, simulations demonstrated no stress response and transpired as much as the non-hydraulically limited transpiration model predicts (Figure 19, black line), or experienced a rapid hydraulic failure

(Figure 19, magenta line), or experienced an intermediate degree of stress and loss of conductivity between the two extremes (Figure 19, red and blue lines).

101

We demonstrate the consequences of hypothetical trait combinations more broadly by considering all possible combinations of leaf, stem and root strategies under the three environmental water limitation conditions (Figure 20).

102

Deep Roots Shallow Roots

Dry day

Wet day

Intermediate day

Wet day

Figure 20. Continuum of plant responses to different wet, intermediate, and dry conditions considering either a deep (right side) or shallow (left side) root strategy and a continuous range

of xylem and stomatal traits, defined through Ф50,stem and Ф50,stomata. PLCs is the percent loss of conductivity of leaf stomata (Eq. 9). The hashed areas are related to the areas under which plants experience more than 50% xylem loss of conductivity (PLCx, Eq. 8).

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Hypothetical trees with cavitation-resistant xylem parameters (i.e. -3 Mpa > Ф50,stem

> -2 Mpa), experienced a very low degrees of hydraulic stress regardless of their leaf strategy as represented by Ф50,stomata. Hypothetical trees with parameters more characteristic of cavitation sensitivity (Ф50,stem >-1.25 MPa or Ф50,stomata >-0.5 MPa) suffered hydraulic stress under most combinations of root traits and environmental conditions (Figure 20). However, at an intermediate range of Ф50,stem values (-1.75 < Ф50,stem

< -1.25 MPa) combined with relatively isohydric Ф50,stomata (-0.5 < Ф50,stomata < -1.5 MPa) avoided catastrophic hydraulic stress (Figure 20). Under dry conditions, deep rooted trees experience less hydraulic stress, particularly when trait values were within a moderate range (-1.25<Ф50,stem <-1 Mpa and -1<Ф50,stomata <-0.5) (Figure 20). In our experiment, species with more risk-averse xylem strategy were represented through less negative values of Ф50,stem, which indicate that the xylem is more sensitive to cavitation, but also has higher maximal conductance (Figure 16). We also presented more isohydric plants with stronger stomatal regulations (risk-averse leaf strategy) through less negative Ф50,stomata, meaning that these species reduce transpiration through stomatal closure under minor deficits in water potential.

We found that under all three environmental conditions, the risk-averse isohydric leaf strategy (less negative Ф50,stomata) leads to higher risk of mortality due to carbon starvation (Figure 20). Previous studies have also supported the idea that carbon starvation is initiated by stomatal closure [Breshears et al., 2009; Martı́nez-Vilalta et al., 2002;

McDowell et al., 2008; Pedersen, 1998; Skelton et al., 2015]. However, a risk-averse

(isohydric) leaf strategy prevents excessive xylem cavitation even during dry periods,

104 particularly for trees with mildly risk-prone xylem strategy (Figure 20). Our results support

McDowell et al. [2013], prosed that anisohydric species are more likely to die due to hydraulic failure during short but severe drought, while isohydric species are more prone to carbon starvation during a prolonged period of mild drought due to the early closure of their stomata. The response of trees with risk-prone leaf strategy (anisohydric, low stomatal regulation) to environmental conditions depended largely on the xylem traits employed.

When combined with risk-adverse xylem (Ф50,stem > -1.25 MPa) an anisohydric strategy increases the risk of hydraulic failure. This indicates that plants with more risk-prone leaf strategies are more likely to experience mortality due to hydraulic failure under extreme drought [McDowell et al., 2008], when combined with risk-adverse xylem. However, for all cases where Ф50,stem < -1.5 MPa trees experienced less hydraulic stress when combined with a risk-prone leaf strategy.

Stomata integrate the environmental and hydraulic signals originating external to- and internal to the plant including the xylem flow pathway from the roots to the guard cells

[Meinzer et al., 2013; Woodruff et al., 2010]. Stomata response drives a whole-plant strategy defined by specific combinations of traits, or trait complexes. For example, deep roots in anisohydric species makes them less vulnerable to hydraulic failure, while the impact of deeper roots on carbon starvation is only marginal (right panels in Figure 20).

This tradeoff could promote the combination of anisohydric stomatal regulation and deep roots [Burns and Honkala, 1990; Miller et al., 2010; Taneda and Sperry, 2008].

Isohydric behavior is mainly characterized by relatively constant leaf water potential actively maintained by stomatal regulation, and anisohydric behavior is 105 characterized by substantially declining leaf water potential during the day mainly driven by the balance of water supply to the leaf and atmospheric demand [Domec and Johnson,

2012; Jones, 1998; Klein, 2014; Larcher, 2003; Martínez‐Vilalta et al., 2014; Tardieu and Simonneau, 1998]. We show that this definition is not absolute and iso/anisohydry needs to be assessed relative to the environmental conditions, including soil water availability and vapor pressure deficit. We used the daily variability of integrated plant water potential to quantify the ‘whole-tree’ hydraulic strategy. Higher daily water-potential variability is expected under dry condition as compared to wet condition, and among anisohydric plants. Under the same environmental condition the effective degree of iso/anisohydry is not only influenced by leaf sensitivity to the change in water potential, but it can also be influenced by the xylem sensitivity especially when xylem is highly conductive, and simultaneously highly sensitive to the changes in water potential (high

Ф50,stem). For less cavitation-vulnerable xylem (Ф50,stem<-2.5 MPa), the leaf trait (Ф50,stomata) controls the whole-tree’s degree of isohydricity, however with sufficiently large Ф50,stem (>

-2.5 MPa), xylem sensitivity begins to dominate hydraulic control (Figure 21). Under wet conditions, both xylem and leaf traits play a significant role in water regulation as compared to dry conditions (Figure 21).

106

Dry

Wet

107

4.3.1 Quantifying the Safety-efficiency Trade-off

As suggested by Skelton et al. [2015], we quantified the safety margin for stomatal regulation by calculating the difference between the water potential at 88% stomatal closure and the water potential at 50% loss of conductivity (Ф88,stomata-Ф50,stem). This safety margin can be used as a proxy to represent the degree of isohydricity for a plant (Figure

22). Positive safety-margin values are representative of as isohydric traits (low fluctuation in daily water potential) and negative values are representative of anisohydric traits (high fluctuation in daily water potential). Skelton et al. [2015] found a linear correlation between the degree of isohydricity and xylem safety margin. Safety margins are commonly used to describe the degree of conservatism regarding plants’ hydraulic strategy. “Safety margin” is characterized as the distance between minimum water potential during drought and critical cavitation level [Manzoni et al., 2013; Meinzer et al., 2010]. We estimated the safety margin in xylem by comparing the xylem water potential at 50% loss of xylem conductivity (Ф50,stem) to the minimum water potential that xylem experiences [Sperry,

2000]. Based on this definition, the xylem safety margin decreases with the decrease in the diurnal drop in water potential and hydraulic conductivity [Gentine et al., 2015].

The definition of safety margin combines traits that define the potential properties of the xylem (Ф50,stem) that is relatively fixed (per individual, over weeks to seasons) with the effective minimal water potential, observed over a period of time. Therefore, variation in degree of isohydricity of plants with respect to the xylem safety margin can be very different under different environmental conditions (see dry vs. wet conditions in Figure

22). Plants with anisohydric trait complexes (negative stomatal safety margin in Figure 22) 108 are expected to have a lower xylem safety margin as compared to species with isohydric trait complexes (positive stomatal safety margin) [Cochard et al., 1992; Sperry et al., 1993;

Tyree et al., 1993]. The steeper slope of the stomata-xylem safety margin relationship under dry conditions than under wet conditions shows that anisohydry is riskier under dry conditions. Under similar environmental conditions, the slope of the curve describing the degree of isohydricity with respect to the xylem safety margin varies with Ф50,stomata, while the intercept is controlled by Ф50,stem (Figure 22). More isohydric species tend to have larger xylem safety margins, while more anisohydric species tend to have smaller (or negative) xylem safety margin [Brodribb and Holbrook, 2004; Choat et al., 2012; McDowell et al.,

2008; Meinzer et al., 2009].

109

day

Dry

day

Wet Wet day

Figure 22. FETCH2 simulations show that the plant safety margin, (Ф88,stomata -

Ф50,stem), defined as the degree of isohydricity, changes with the stem level hydraulic safety margin (Фmin,stem - Ф50,stem). The dashed red line marks a linear regression.

110

4.4 Conclusions

We conducted a sensitivity analysis of hypothetical hydraulic trait complexes using

FETCH2 modeling framework [Mirfenderesgi et al., 2016], based on which a continuum of hydraulic traits at the leaf, stem, and root levels are simulated to predict the whole-plant response and define a whole-plant strategy to different environmental conditions. These traits prove to be essential in determining the plant strategy under different weather conditions. However understanding the overall strategy of plants cannot be fully achieved without considering the interdependence of these traits. Determining the plant response based solely on one of these traits can be misleading and gives an unrealistic insight to whole-plant mechanisms of survival and mortality.

Our framework predicted that a more risk-prone leaf strategy when combined with a risk-prone xylem trait may expose plants to the risk of hydraulic failure due to declining

Фstem during period of low soil moisture and high VPD. However, if this strategy is coupled with deep roots, the plant is less likely to experience water stress even during periods of low soil water availability and high evaporative demand. Alternatively, a risk-averse leaf strategy coupled with shallow roots, may increase the risk of carbon-starvation, specifically under extended periods of drought. This illustrates the importance of considering coordination between stomatal, xylem, and rooting traits in analysis of species’ response to environmental conditions.

111

Chapter 5: Conclusions

Terrestrial ecosystems influence large patterns of climate through the feedbacks between vegetation and climate. These feedbacks are known to impact the global carbon and water cycle. Transpiration, as the largest component of the terrestrial water cycle, and

CO2 uptake by vegetation are intrinsically coupled through stomatal conductance.

Therefore, study the transpiration process and its contribution to the global atmospheric circulation is integral to understanding the interactions between the surface water components and the atmosphere, as well as assessing the effects of climate and water resources on the terrestrial carbon cycle. This requires the hydrological and climate models to be able to adequately represent the vegetation dynamics and stomatal functioning.

The current land surface models that use the PFT-based vegetation scheme do not represent the physical processes of water transport from roots to leaves; Therefore are not able to accurately simulate the differences between vegetation responses to droughts or disturbances. Representing the vegetative responses to climate and land use changes by incorporating the whole-plant strategy into these models will potentially improve the simulation of water and carbon cycle. This necessitates the incorporation of mechanistic based models that capture the dynamic responses to the high temporal resolutions hydraulic traits. We developed the Finite-difference Ecosystem-scale Tree-Crown Hydrodynamics

112 model version 2 (FETCH2). FETCH2 explicitly resolves xylem water potentials throughout the vertical extent of a tree along the soil-root-stem-branch-leaf continuum of water flow. Calculating the plant functional traits at the root, stem and leaf levels, FETCH2 simulates the integrated plant-level transpiration, provided hydraulic traits and environmental forcing.

We tested the aboveground version of FETCH2 (excluding the root dynamics and replacing it with Fades’ boundary condition) along with sap flow and eddy covariance data set collected from a mixed plot of two genera (oak/pine) in Silas Little Experimental Forest,

NJ, USA, to conduct an analysis of the intergeneric variation of hydraulic strategies and their effects on diurnal and seasonal transpiration dynamics. We define these strategies through the parameters that describe the genus-level transpiration and xylem conductivity responses to changes in stem water potential. Our result demonstrated that FETCH2 can effectively represent the continuum of hydraulic properties of stems and leaves over different genera with a wide range of characteristics through its parameterization process as depicted by the differences between wood properties of oak and pine. By resolving below and aboveground stem water flow, storage and potential, FETCH2 can effectively describe the difference in hydraulic strategies between plants, while the current modeling frameworks do not resolve the outcomes of the species-specific behaviors due to the over- aggregation of dissimilar species into the same functional class.

We used FETCH2 to simulate a continuum of hydraulic traits at leaf, stem, and root levels to predict the whole-plant response and preformed a sensitivity analysis of the hypothetical hydraulic trait complexes to different environmental conditions. We 113 illustrated that although each trait is essential in determining the plant strategy under different environmental conditions, however considering the coordination between leaf, xylem and root traits is essential in understanding the overall strategy of plants.

Finally, we suggest that replacing the current empirical link between soil moisture and stomatal conductance in land surface and ecosystem models with more physically and structurally realistic plant hydraulic sub-models, such as FETCH2, may have a large impact on the simulation of ecosystem response to drought and other changes associated with climate or canopy structure. This may, in turn, improve the prediction of the terrestrial surface energy budget and global carbon and water cycle.

114

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