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Agricultural and Forest Meteorology 198–199 (2014) 168–180

Contents lists available at ScienceDirect

Agricultural and Forest Meteorology

j o ur na l ho me pag e: www.elsev ier .com/ locate /agr formet

ime variable hydraulic parameters improve the performance of aechanistic stand transpiration model. A case study of Mediterranean

cots pine sap flow data assimilation

liver Susa,∗, Rafael Poyatosa, Josep Barbaa, Nuno Carvalhaisb,c, Pilar Llorensd,athew Williamse, Jordi Martínez Vilaltaa,f

CREAF, Cerdanyola del Vallès 08193, SpainMax-Planck Institut für Biogeochemie, P.O. Box 10 01 64, 07701 Jena, GermanyCENSE Center for Environmental and Sustainability Research, Departamento de Ciências e Engenharia do Ambiente, Faculdade de Ciências e Tecnologia,niversidade Nova de Lisboa, 2829-516 Caparica, PortugalInstitute of Environmental Assessment and Water Research (IDAEA), CSIC, 08034 Barcelona, SpainSchool of Geosciences, University of Edinburgh, Edinburgh EH9 3JN, UKUniversitat Autònoma Barcelona, Cerdanyola del Vallès 08193, Spain

r t i c l e i n f o

rticle history:eceived 16 December 2013eceived in revised form 11 August 2014ccepted 22 August 2014

eywords:ap flowata assimilationlant hydraulicsediterranean

cosystem modellingrought

a b s t r a c t

Tree transpiration is regulated by short-term physiological adjustments and long-term shifts in hydraulicarchitecture in response to fluctuating evaporative demand and water supply. Despite the tight interde-pendence of plant water loss and carbon uptake and its crucial implications for plant growth and survivalunder drought conditions, the underlying mechanisms remain incompletely represented in most state-of-the-art mechanistic models. Important process information is resolved in tree transpiration (sap flow)data, which are the measurable outcome of water transport through the soil-plant-atmosphere con-tinuum under variable environmental conditions. Here, we assimilated sap flow data measured in twoScots pine stands from climatically contrasting sites – one of which experiencing a strong drought duringthe study period – in NE Spain into a process-based ecophysiological model (SPA) using the EnsembleKalman Filter (EnKF) in order to: (1) distinguish differences in hydraulic characteristics between sites andbetween healthy and defoliated individuals within a site; (2) identify possible structural model deficien-cies, particularly regarding temporal changes in plant hydraulic conductance which the model assumesconstant; and (3) derive implications for gross photosynthesis and carbon cycling. In terms of stomatalcontrol, the assimilation of sap flow data into SPA showed a more conservative water use under dry condi-tions. Time-varying plant conductivity substantially improved model performance under severe drought,

while seasonally varying capacitance and stomatal efficiency only resulted in marginal improvements.Not accounting for this seasonal variability would translate into a 30–60% overestimation of modelledGPP during drought. Our results suggest that an explicit representation of mechanisms leading to tem-poral changes in hydraulic conductivity (i.e., xylem embolism) is required for models to reproduce treefunctioning under extreme drought.

. Introduction

In order to model the water and carbon balance of a forest

cosystem and predict its response to environmental changes,ree transpiration needs to be simulated as a function of ambientonditions (van der Molen et al., 2011). On a global scale, plant

∗ Corresponding author. Present address: Deutscher Wetterdienst, Frankfurtertraße 135, 63067 Offenbach, Germany. Tel.: +49 6980622485.

E-mail addresses: osus79@gmail.com, oliver.sus@dwd.de (O. Sus).

ttp://dx.doi.org/10.1016/j.agrformet.2014.08.009168-1923/© 2014 Elsevier B.V. All rights reserved.

© 2014 Elsevier B.V. All rights reserved.

transpiration considerably influences climate through the releaseof latent heat and water vapour (Alton et al., 2009; Bodin et al.,2013). Transpiration is embedded within and controlled by a soil-plant-atmosphere continuum, which can be conceptualized as aseries of hydraulic resistances. The flow of water between anytwo locations of this system is proportional to the hydraulic con-ductivity and the water potential gradient linking them (Tyree

and Zimmermann, 2002). For some tree species, reductions insoil hydraulic conductivity are sufficient to explain transpirationdecline during drought (Duursma et al., 2008; Fisher et al., 2007).However, the different components of the plant hydraulic system

t Mete

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O. Sus et al. / Agricultural and Fores

an also change during drought as a result of varying stomatalonductance, xylem embolism, and the regulation of leaf and rootrea (Chaves et al., 2003; Maseda and Fernández, 2006). Moreover,lants adopt various strategies to cope with short- and long-erm effects of drought conditions, and can be broadly categorizedlong a continuum from drought avoiders (isohydric behaviour) torought tolerators (anisohydric behaviour, Tardieu and Simonneau,998).

During the last decade, the understanding of mechanismsffecting water and carbon cycling during drought improved con-iderably. However, predictions of post-drought behaviour foronths and years to follow are still highly uncertain (van der Molen

t al., 2011) and large uncertainties remain in the understandingnd modelling of species-specific responses to drought, includ-ng drought-induced mortality (McDowell et al., 2013). Importantnowledge gaps exist, for instance, on the interactions betweeneaf microclimate, leaf water potential, and stomatal regulation ofranspiration (Meinzer et al., 2009; Misson et al., 2004), on the rolef light intensity (Pieruschka et al., 2010) and quality (Sellin et al.,011), or on the mechanisms behind the seasonal variation of keyydraulic traits (Franks et al., 2007; Martínez-Vilalta et al., 2007).

These unknown processes are not represented within state-f-the-art ecosystem transpiration models. Consequently, missingechanisms are partly compensated for when model parameters

re calibrated using observational constraints (i.e., model structuraleficiencies are “absorbed” by parameter calibration). Even thoughuch a calibrated model might be able to reliably reproduce theeasured data, the true causes of model-data discrepancy have not

een addressed, limiting the predictive ability of the model. Today, wealth of temporally highly resolved tree sap flow data is beingollected and readily available. These data are of particular interesto modellers, as they bear the potential for extraction of informa-ion on important hydraulic mechanisms which current models failo simulate.

Data assimilation (DA) methodology, applying the Ensemblealman Filter (EnKF) among others, has shown to be a useful

echnique for model state and/or parameter estimation in variousisciplines of the geosciences. Early efforts were made in the fieldsf hydrology, oceanography, or meteorology (see review in Evensen2009)). More recently, eddy covariance (EC) flux data were used toonstrain ecosystem carbon (C) mass balance models using diverseA techniques (e.g. Chen et al., 2008; Mo et al., 2008; Reichsteint al., 2003; Richardson et al., 2010; Sus et al., 2013; Williams et al.,005; Wu et al., 2012). Posterior (i.e. after DA) temporal parame-er variability within some of these carbon models was interpretedither as ecosystem functional change (Rowland et al., 2013; Wut al., 2012) or, more commonly, as a result of model structural defi-iencies. These results show that temporally highly resolved carbonux data bear important model constraints. However, the mod-ls applied for parameter estimation showed different degrees oftructural completeness and, consequently, the discussion of modelesults is confined to attributing parameter temporal variabilityo known sources of model deficiency. If we intend to use mea-urements within a DA scheme for the identification of currentlynknown sources of model deficiency or even of processes hithertonknown to ecophysiologists, models need to reflect the state-f-the-art of process understanding of the scientific community.ithout a doubt, uncertainties in observations, model drivers, and

epresentation of known processes will exist and influence param-ter adjustment. However, the discussion of model results couldhen go further and associate parameter variability to unexplainedcosystem responses under given climatic constraints. Such a study

ill allow researchers to formulate more robust hypotheses about

cosystem functioning, which then can be used to guide furthereld studies and model development.

orology 198–199 (2014) 168–180 169

In contrast to EC carbon flux data, studies that have appliedsap flow DA to constrain hydraulic parameters of forest transpira-tion models are rare (see Reichstein et al. (2003) as an exception).Sap flow data are likely to contain important process informa-tion on plant hydraulics, as they are the measurable outcomeof water transport through the soil-plant-atmosphere continuumin response to environmental conditions. Accordingly, these dataprovide temporally highly resolved (sub-hourly) constraints onassociated key parameters within models. Sap flow data are moreuseful for this purpose than latent energy flux data from EC, as theEC data include poorly quantified evaporation terms not connectedwith plant processes. With this study, we aim for highlighting thepotential of sap flow data for assimilation into models, followed byan ecophysiological interpretation of parameter variability, and ananalysis of hypotheses on plant hydraulic behaviour. This study canthus be regarded as a detailed manuscript of sap flow DA method-ology.

We assimilated sap flow data from two Scots pine (Pinussylvestris L.) stands with contrasting water availability (mesic:Vallcebre, xeric: Prades) into a process-based ecophysiologicalecosystem model (SPA, Williams et al., 1996, 2001b). In contrast tothe mesic Vallcebre site, Prades is located at the southern dry limitof Scots pine distribution, and drought-induced tree defoliation andmortality events have been reported previously (Martıınez-Vilaltaand Pinol, 2002; Poyatos et al., 2013). As the SPA model containsan advanced process representation of forest transpiration (Bodinet al., 2013; Misson et al., 2004), it is especially suitable for improv-ing our understanding of ecosystem hydraulic functioning throughconfronting the model with the observed data.

The SPA model assumes an isohydric stomatal behaviour (Fisheret al., 2006), as has been repeatedly showed for Scots pine(Irvine et al., 1998; Poyatos et al., 2013). However, the basicmodel structure is mechanistically incomplete by not represent-ing drought-induced damage of the hydraulic water pathway(although see Williams et al. (2001a) for alternate structures).Applying a sequential DA technique (EnKF), we constrained keyhydraulic and structural parameters (aboveground plant conduc-tance, stomatal efficiency, plant capacitance, root to leaf mass ratio)and further analyzed apparent patterns of their seasonal variability.We conducted the assimilation experiments with both synthetic(i.e. model generated) and measured sap flow data in order toestimate the applicability of the DA methodology. Our results arecomplementary to field site experiments by providing independentinsights into stand-scale plant hydraulics, which bear further impli-cations on water use efficiency and hydraulic limitations on carbonassimilation.

We pursued the following key research questions and hypothe-ses: (1) Are there between-site differences in hydraulic parameters,both in terms of magnitude and seasonality? We expect only minorparameter seasonality at the wetter Vallcebre site and larger val-ues of water storage capacity, plant hydraulic conductance, andstomatal conductance than at Prades. (2) According to recent obser-vations (Poyatos et al., 2013), we expect maximum plant hydraulicconductance per unit of leaf area to be higher but more sensitiveto drought in defoliated (DF) than in non-defoliated (NDF) trees atthe xeric Prades site. (3) We further hypothesize that a measureddecrease in tree transpiration during extreme drought is accom-panied by (partial) embolism of the hydraulic pathway, which isnot fully accounted by reductions in stomatal conductance. Wethus expect that a temporal decline in plant hydraulic conductancesignificantly improves model goodness-of-fit at Prades. (4) For thesame reason, at the Prades site the posterior model will show con-

siderable reductions in gross primary productivity (GPP) comparedto a standard model run with temporally constant parameters, withimportant implications for the local carbon balance.

170 O. Sus et al. / Agricultural and Forest Mete

Table 1Stand characteristics for the Prades (NDF = nondefoliated, DF = defoliated) and Vall-cebre sites. Vcmax and Jmax values were derived from Wullschleger (1993) and Aaltoet al. (2002), root resistivity was calibrated so that belowground plant resistance is∼40% of total plant resistance. All other values are local observations.

Prades NDF Prades DF Vallcebre

Max. LAI [m2 m−2] 0.42 0.16 2.4Canopy height [m] 14 14 11LMA [g C m−2 LA] 159 146 218Vcmax | Jmax [�mol m−2 s−1] 57.7 | 148 57.57 | 148 57.7 | 148Foliar N [g N m−2 LA] 4.37 3.49 4.59Density [stems ha−1] 151 106 2165

2

2

cr(dcltr(spstlcthCoisaai

i(1aolcb

a(GvscafdbmVV

Basal area [m2 ha−1] 11.5 12.3 44.7Root resistivity [MPa s g mmol−1] 200 100 65Minimum LWP [MPa] −2.5 −2.5 −2.1

. Data and methods

.1. Study sites and field methods

The Prades site (41◦19′58.05′′ N, 1◦0′52.26′′ E; 1015 m a.s.l.) isharacterized by a Mediterranean climate (664 mm mean annualainfall) and moderate temperatures (11.3 ◦C mean, Poyatos et al.2013)). Soils are fairly rocky and shallow (∼40 cm deep), well-rained xerochrepts with a loamy texture (49% sand, 32% silt, 19%lay) and a relatively high gravel content of 46% (J. Barba, unpub-ished results). The local slope is 35◦, facing NW. This site is close tohe southern dry limit of the distribution of Scots pine, and expe-iences a process of drought-induced tree decline since the 1990sHeres et al., 2012; Martıınez-Vilalta and Pinol, 2002). The over-tory cover comprises both non-defoliated and defoliated Scotsine (Table 1). This defoliation should be seen as an inevitableymptom of drought stress rather than as an adaptive mechanismo water stress (Poyatos et al., 2013). Scots pines which had 50% oress green leaves than a healthy canopy of similarly sized trees wereonsidered defoliated, and experienced on average a ∼62% reduc-ion in green leaves. Maximum tree age is > 150 years and the siteas not been managed for the past 30 years (Heres et al., 2012; Vilà-abrera et al., 2013). The understory cover is dominated by holmak (Quercus ilex, LAI = 1.4 m2 m−2, density = 1736 stems ha−1). Formproved estimation of soil water content (SWC), holm oak tran-piration is directly accounted for within model runs by addingssociated measured sap flow to SPA’s total water loss flux. Aver-ge standing dead and defoliated pine population in the catchments 12% and 52% of the total, respectively (Vilà-Cabrera et al., 2013).

The Vallcebre site (42◦12′ N, 1◦49′ E, 1260 m a.s.l.) is locatedn the Eastern Pyrenees, and has a sub-Mediterranean climate862 mm mean annual rainfall, 7.3 ◦C average air temperature at440 m a.s.l., Llorens et al. (2010)). The Scots pine stand colonizedbandoned, former cultivated terraces (oldest trees are ∼60 yearsld), and the understory is scarce (Poyatos et al., 2007b). The sandy-oam soils (∼60% sand, 20% silt, 20% clay) are ∼65 cm deep andomparably low in gravel content (19%). This wetter site has noteen affected by drought-induced mortality events.

Sap flow data analyzed here are for years 2004 (Vallcebre)nd 2011 (Prades). At both sites, 15-minute means of sap flowusing heat dissipation sensors according to the Granier method,ranier (1985)) were measured together with key meteorologicalariables (air temperature and relative humidity, precipitation,olar radiation, wind speed), and SWC (30 cm depth using waterontent reflectometers). At Prades, measured SWC was regressedgainst independent volumetric measurements of SWC to accountor soil stoniness in the calibration of the sensors. Tree leaf area wasetermined as a function of site-specific allometric relationships

etween stem/branch diameter and leaf mass/area. Additionalethodological details can be found in Poyatos et al. (2007b) forallcebre and in Poyatos et al. (2013) for Prades. Whereas forallcebre the year 2004 was drier than average but sufficiently

orology 198–199 (2014) 168–180

wet (644 mm total annual precipitation, daytime average of VPD<2 kPa and min. SWC ∼14% Vol. for June–August, Poyatos et al.(2007b)), Prades experienced a severe drought in 2011, with just113 mm of precipitation from May to October (31% of the climaticaverage, min. SWC ∼8% Vol.).

2.2. The SPA model: structure and setup

SPA is a process-based model simulating ecosystem photosyn-thesis and water balance at fine spatiotemporal scales (Williamset al., 1996). It is a tool for diagnosing eddy flux and sap flow dataand for scaling up leaf level processes to canopy and landscapescales (Williams et al., 2001c). Plant and leaf ecophysiology arerepresented within SPA through well tested theoretical represen-tations of leaf-level photosynthesis (the Farquhar model, Farquharand Caemmerer (1982)) and transpiration (Penman-Monteith, seealso Williams et al. (2001b) for a detailed description of modelcomponents).

The flow of water from soil to leaf is simulated by SPA adoptingan electric circuit analogue (Williams et al., 2001a). Along a networkof parallel resistors, water travels from soil to atmosphere downa gradient of water potential. Water loss is determined throughchanges in leaf water potential (� l), which in turn is estimated fromthe soil-canopy water potential gradient, hydraulic resistances (inthe rhizosphere (Rs), plant fine roots (Rr), and stems (Rp)), and thecapacitance of the soil-canopy pathway. Here, we assume that Rp,the reciprocal of leaf area per canopy layer (LA, m2 m−2) times plantstem conductivity Gp (mmol m−2 leaves s−1 Mpa−1), is indepen-dent of canopy height. Rs is a function of soil conductivity (Saxtonand Rawls, 2006), soil layer depth, fine root radius and length, anddistance between roots. The relationship between Rr and fine rootbiomass is inverse:

Rr = R′r

DMr,

where Rr′ is root resistivity (MPa s g mmol−1), and DMr is dry mat-

ter of fine roots (g m−2). Root distribution is assumed to declineexponentially with soil depth. Total belowground resistance Rb isthe sum of Rr and Rs, with Rs being particularly large for low SWC(here <∼20%Vol.). Thus when the soil is moist, DMr is the primarydriver of Rb. In this calibration of SPA, DMr is estimated as a fractionof leaf dry matter (DMl):

DMr = DMl × ratiorl,

where ratiorl is the ratio of fine root to leaf dry matter.The change of � l per timestep is given by

d�l

dt= �s − h d − E(Ra + Rb) − �l

C(Ra + Rb),

where E is evaporation (mmol m−2 s−1), � s the soil water potential(MPa), h is the height above the ground (m), and d is the gravita-tional head of pressure (MPa m−1). The capacitance parameter C(mmol MPa−1 m−2 leaves) is defined as the ratio of the change intissue water content (W, mmol m−2) to change in � l

C = dW

d�l.

where W is the difference between sap flow into the stem (J,mmol m−2 s−1) and evaporative losses (E), hence J at the base ofthe tree can be determined from E and buffering fluxes from/intoplant capacitors (Cflux) by

J = E + Cflux,

with Cflux = C × ��l

�t.

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2

fitSshoEre2rcTmab

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O. Sus et al. / Agricultural and Fores

An optimizing procedure is applied within SPA to determinehe stomatal conductance (gs, mmol m−2 s−1) and the associatedarbon assimilation rate (A, �mol m−2 s−1). Based on Farquhar andaemmerer (1982) equations, photosynthetic parameters Vcmax

maximum carboxylation capacity) and Jmax (maximum electronransport rate, Table 1) are calculated as a function of foliar Noncentration and leaf temperature. Internal CO2 concentrations simulated considering both diffusion and metabolic uptake periven gs, providing A (i.e. photosynthesis or gross primary produc-ivity, GPP). The approach aims for maximizing water use efficiencyWUE), as the response of A to increments in gs is asymptotic. Theimulation determines the value of gs for which either a furtherncrement fails to increase A by more than 1 − � (the dimensionlesshreshold parameter iota, or “stomatal efficiency”), or for which

l = � crit. � crit limits stomatal conductance to maintain � l at orbove this critical level, thus minimizing the risk of xylem cavita-ion and subsequent decline in stem hydraulic conductivity. Iotaan be estimated from leaf level data by comparing modelled withbserved maximum gs. We initially calibrated key hydraulic param-ters in SPA based on site-specific empirical evidence (whenevervailable) and literature values. A calibration spreadsheet was usedor finding values of Gp and Rr′ so that Rr is ∼40% of Rr + Rp (cf.

artínez-Vilalta et al. (2007)) whilst meeting observational con-traints of leaf specific conductance (LSC). Iota was set so thataximum gs is ∼300 mmol m−2 s−1. We set � crit to the minimum

bserved � l value at Prades (−2.5 MPa) and Vallcebre (−2.1 MPa).nitial SWC was set to the observed value. For Vallcebre, we scaledrom bulk (as observed) to matric (as modelled) SWC by accountingor gravel content (Saxton and Rawls, 2006). Canopy phenology waserived from filtered and smoothed (Chen et al., 2004) time seriesf MODIS 250 m EVI data, downloaded with input site coordinatesf the closest representative forest canopy of sufficient spatial cov-rage (≥ 500 m × 500 m). For both sites, the seasonal minimum ofAI was assumed to be ∼75% of its maximum, and these valuesere used to convert from EVI to LAI. All model experiments were

onducted with a timestep size of 15 min.

.3. Data assimilation methodology

Data assimilation (DA) is a set of techniques that is used fornding an optimal combination of observations and models, withhis combination being referred to as the analysis (Evensen, 2003).equential DA provides the opportunity to explicitly analyze sea-onal changes of model parameters and formulate or even testypotheses on corresponding model deficiencies and ecophysi-logical mechanisms. One such sequential DA technique is thensemble Kalman Filter (EnKF, Evensen, 2003), which recently haseceived increasing attention in ecological modelling (e.g. Chent al., 2008; Moradkhani et al., 2005; Quaife et al., 2008; Stöckli et al.,011; Williams et al. 2005). Through the EnKF, a system can be rep-esented by an ensemble of model state and observation estimatesreated by Monte Carlo sampling and uncertainty perturbation.he EnKF aims for finding the optimal solution through weightingodel forecast and observations with their intrinsic uncertainties

s defined by the Kalman gain term, and hereby reduces the ensem-le variance.

A potential deficiency of the EnKF is that by adjusting the stateariables it can break the strict mass balance (but see Moradkhani2008) for other approaches that can avoid this problem). In ourtudy, a mass balance breach is not possible, as we assimilatend constrain instantaneous flux values and parameters but not

he water budget. However, when the EnKF analysis produces anpdate in model transpiration, this water flux change (the so-calledinnovation”) is not added to total evapotranspiration and ecosys-em water loss. Consequently, innovations in water fluxes have no

orology 198–199 (2014) 168–180 171

impact on soil water balance, leading to a bias in the water balanceif the forward model transpiration was biased. In our case how-ever, these innovations are only a fraction of a comparably smallflux value within the total water balance, and their effect on soilwater content was negligible. Next to J, we selected four modelparameters as members of the model state vector, all of which arekey controls on plant hydraulics that require constraint by data:stomatal efficiency (iota), plant conductivity (Gp), capacitance (C),and root to leaf mass ratio (ratiorl).

The key purpose of iota is to set an upper limit to rates of sap flowas long as � l > � crit, whilst C is an important constraint when J islow. Then, water fluxes from tissue capacitors towards the canopysustain sap flow despite reduced evaporation (e.g. around dawn),thus extending the duration of sap flow. Moreover, the timing ofstomatal closure depends strongly on C (Alton et al., 2009; Williamset al., 2001a). Gp and ratiorl constrain above- and belowgroundplant conductivity.

2.4. Uncertainty quantification and model experiments

2.4.1. Uncertainty quantificationWe based our experimental setup (Fig. 1) on a best-practice

framework for data assimilation studies as recently proposedby Keenan et al. (2011). We quantified uncertainty in sap flowdata applying the Hollinger–Richardson paired-days approach(Hollinger and Richardson, 2005). We derived average sap flowuncertainties of 0.0014 (Vallcebre) and 0.00012 (Prades) mm m−2

ground area (GA) timestep (ts)−1 by fitting a laplacian, double-exponential distribution to the histogram of paired-differences.Values vary by an order of magnitude due to larger canopy areaand thus transpiration at Vallcebre. A likely heteroscedasticity(Hill et al., 2012; Hollinger and Richardson, 2005) of observationswas not explicitly accounted for. Instead, the above uncertaintieswere introduced as absolute values when generating the per-turbed observation ensemble. To account for deficiencies in modelstructure, the same absolute uncertainties were used for generat-ing the simulated ensembles of transpiration. Moreover, the fourparameters in the model state vector were perturbed by Gaussianrandom noise of zero mean and a standard deviation of 0.001 ts−1.This perturbation was quantified iteratively to provide an optimalcompromise between parameter stability and temporal variability.Consequently, total model uncertainty is the sum of uncertaintyin both parameters and model state and thus at least as large asobservational uncertainty itself.

2.4.2. Best-guess experiment (BGE)The BGE was conducted in order to provide a constraint on base-

line model performance when hydraulic parameters are consideredconstant. A Monte Carlo-type approach was applied to randomlysample 5000 parameter sets within ecophysiologically meaningfullimits (Table 2). These limits were defined as a ±50% deviation inparameter values from their a priori calibrated estimates. A searchstrategy was not adopted for sake of simplicity, which was deemedsufficient as we merely needed an approximated estimate of themodel baseline rather than a robust batch-calibration (Wang et al.,2009). Best-guess model output (Fig. 3a–c) was then produced byaveraging the output of 100 SPA runs with highest Kling-Guptaefficiency (KGE, Section 2.6) values. The mean and standard devi-ation of these top 100 parameter sets were used as initial guessesof parameter state and uncertainty in subsequent real-data EnKFexperiments (Tables 2 and 3).

2.4.3. Synthetic data experiment (SDE)We conducted a range of SDE (Vallcebre only) to test the gen-

eral applicability of the DA framework. We generated synthetic datausing the model output from the simulation with the highest KGE

172 O. Sus et al. / Agricultural and Forest Meteorology 198–199 (2014) 168–180

Fig. 1. Flowchart of study experiments.

Table 2Overview of parameter setup values. iota = stomatal efficiency (unitless), Gp = aboveground plant conductance (mmol MPa−1 m−2 leaves s−1), C = capacitance (mmol MPa−1 m−2

leaves), ratiorl = root to leaf carbon mass (ratio). VC = Vallcebre, PR = Prades, NDF = non-defoliated, DF = defoliated.

BGE estimate Bounds Timestep uncertaintya

VC PR NDF PR DF BGE RDE

Mean SDA Mean SDA Mean SDA Low High Low High SDE RDE

iota 1.0037 0.001 1.0241 0.008 1.0056 0.002 1.002 1.04 1.00001 1.1 0.0001 0.001Gp 1.23 0.12 1.45 0.26 1.81 0.29 1.00 3.00 0.05 5.00 0.0001 0.001

.25

.09

osmpmtivem

TO

C 3179 0.29 2828 0.23 3659 0ratiorl 0.54 0.31 0.32 0.05 0.33 0

a Relative to the mean.

f all 5000 runs. Before assimilation, we added random noise to theynthetic data by sampling from a normal distribution with zeroean and sd = 0.0024 mm 15 min−1 to attain similar uncertainty

roperties as for the observed sap flow data. Uncertainty on bothodel transpiration and parameters is an order of magnitude lower

han for the real data experiment (Section 2.4.4), as the SDE model

s structurally complete. The experiments were conducted underariable DA setups, such as magnitude and sign of initial param-ter perturbation (±10%, 25%, 33%, and 50% of truth), ensembleember size (10, 20, 50, 100, 200, and 500), and added parameter

able 3verview of experiment setup.

BGE SDE

DA method Batch-calibration Sequential

Model sap flow uncertainty NA Minus one orderof obs, parameteadded

Ensemble size NA Various tested (Parameter variability Constant Variable

1725 5175 100 10000 0.0001 0.0010.3 0.9 0.1 2.0 0.0001 0.001

uncertainty (perturbation per timestep: 1E-06 and 5E-06 to 1E-03and 5E-03 sd, given as fractions of mean instantaneous parametervalue, Tables 2 and 3).

2.4.4. Real data experiment (RDE)For the RDE, all data of a given year were assimilated into SPA

with a 500 ensemble member EnKF. The experiments were contin-ued by subsequent looping over the same data five times. We didnot renormalize the ensemble spread after each loop year to strictlycomply with Bayes’ theorem, but conducted a sensitivity study

RDE PGE

Sequential Forward mode of magnituder uncertainty

= obs, parameteruncertainty added

NA

10–500) 500 NAVariable Constant and variable

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O. Sus et al. / Agricultural and Fores

or Vallcebre for technical correctness (data not shown). We findhat ensemble renormalization, including an increase of ensem-le spread to its prior estimate, has no obvious effect on posteriorarameter time series and can thus be omitted without reducinghe credibility of our methodology. Looping output was used to testepeatability of parameter magnitude and seasonality by analysing1) whether parameters stabilize around their posterior estimatesrom the previous loop year and (2) whether the pattern of time-ariability is a persistent feature in all loop runs. Upper and lowerounds on parameter space were increased (Table 2) in order toeduce the risk of a parameter being edge-hitting.

.4.5. Posterior-guess experiment (PGE)The parameter time-series produced by the RDE were then used

s “drivers” of SPA (forward mode, i.e. no DA) in a range of PGE. Theim of the PGE was to see whether model performance improvedhrough temporal parameter variability compared to the prior best-uess. SPA was run with all possible combinations of constant (i.e.GE-derived) and variable (i.e. RDE-derived, last loop year ana-

yzed only) parameters to isolate a parameter combination whoseemporal variability brings most improvement (Table 3).

.5. Correlation analysis of residuals and parameter time-series

Finally, we analyzed correlations between model residuals (bothGE and PGE), RDE-derived parameter time-series, and modelrivers, with these correlations having been quantified once peray (n = 96 per day without data gaps) over the entire time series toesolve temporal changes. This analysis aims to determine in a qual-tative manner whether systematic deficiencies in the prior model,ndicated by correlations between model residuals and drivers, areompensated for by temporal variability of parameters.

.6. Statistical evaluation of model goodness-of-fit

We use Taylor-diagrams in order to provide a graphical eval-ation of how well observed patterns are matched by a model

n terms of mutual correlation (Pearson correlation coefficient R),oot-mean-square difference (RMSD), and the ratio of variancesTaylor, 2001). Additionally, the following statistical functions weresed for quantification of model goodness-of-fit (contained in Rackage “hydroGOF”, Zambrano-Bigiarini (2012)):

normalized root mean squared error (nRMSE) = RMSE in % ofobservational rangepercent bias (PBIAS) = sum of residuals/sum of observations in %modified Nash-Sutcliffe efficiency (mNSE) = sum of residuals/sumof deviations in observationsKling-Gupta efficiency (KGE):

KGE = 1 −√

(r − 1)2 + (vr − 1)2 + ( − 1)2, with r = Pearsonorrelation coefficient, vr = ratio of modelled and observedtandard deviations, and = ratio of means.

Data ranges are [−∞,1] for KGE and mNSE, with a value of 1ndicating a perfect goodness-of-fit. All statistical analyses shownn this study are based on comparisons of quarter-hourly simula-ions and observational data. We applied bootstrapping analysis torovide 95% confidence intervals (CI, ±2 sd) on model goodness-of-t statistics (Efron and Tibshirani, 1993; Reichstein et al., 2003). Foruantification of uncertainty, we used an approach where residu-ls were shuffled and randomly added back to model estimates for

n entire study year. The KGE between model and observationsas determined for each of 500 repeated shufflings, thus provid-

ng means and standard deviations of KGE metrics for all modelxperiments.

orology 198–199 (2014) 168–180 173

3. Results

3.1. Measured sap flow data analysis

Temporal correlations between observed sap flow and localdriver data revealed differences between sites in ecosystemresponses to local climate (Fig. 2). Until ∼July, all three data streamsshowed a similar pattern of correlations of measured sap flow withdriver data: correlations were significant and positive (Pearson cor-relation coefficient R > 0.4), with R for T > RAD > VPD. Whereas thispattern continues throughout the remainder of the season at Vall-cebre, these statistical relationships diminished at Prades during atransition phase from mid-July to early October. We refer to thisperiod as the drought phase, which was characterized by dimin-ishing tree transpiration throughout July followed by continuouslylow values until end of season (Fig. 3).

3.2. Synthetic data experiment (SDE)

The various SDE simulations generally reproduced parametertruth when assimilating synthetic data, and so the DA methodol-ogy passed the minimum requirement for parameter estimationreliability (Fig. S1). For most experiments, parameters stabilizedaround their true value after assimilation of ∼1 month of data.Iota was most constrained and stabilized most quickly at its truevalue. Constraints were also strong for the remaining three param-eters, but true Gp was less well identified in cases when ratiorlwas edge-hitting. In general, only in simulations for which com-binations of initial parameter perturbation and ensemble sizewere most unfavourable, e.g. perturbation = 50% and ensemble size<=20, parameter truths were not found. Parameter equifinality(i.e. many parameters acceptably reproduce the behaviour of theobserved process) was never observed when ensemble size was>100, independent of initial perturbation. Moreover, for magni-tudes of uncertainty >0.0005 per timestep and parameter unit,parameter time series became considerably noisy and truths werenot identified when uncertainty = 0.005.

Supplementary Fig. S1 related to this article can befound, in the online version, at http://dx.doi.org/10.1016/j.agrformet.2014.08.009.

3.3. Best-guess experiment (BGE)

Observed sap flow was reproduced better at Vallcebre(KGE = 0.89) than at Prades for both data streams NDF (non-defoliated, 0.59) and DF (defoliated, 0.75, Fig. 3 and Table S1) whenSPA was run with time-constant BGE parameters. This was alsotrue for values of nRMSE, which were Vallcebre (35.1%) < Prades DF(55.3%) < Prades NDF (61.1%). Percent bias was negative and rela-tively low for Vallcebre (-9.7%), but positive and of larger magnitudefor Prades DF (17.5%) and NDF (37.9%). For Prades, SPA-BGE was notcapable of reproducing the timing and rate of the observed rapiddecline of sap flow in late June to July. Moreover, sap flow wasunderestimated during April for both NDF and DF, but observationswere reproduced well in May.

Supplementary Table S1 related to this article can befound, in the online version, at http://dx.doi.org/10.1016/j.agrformet.2014.08.009.

Differences between modelled and observed �l over all sitesindicated that model pre-dawn � l appeared sensitive to grad-ual changes in soil water content (SWC) but positively biasedby ∼0.5 MPa on average (Fig. 4). Simulated mid-day � l on the

other hand mostly fell to � crit, whereas observations were higherthroughout. At Prades, observations showed that absolute differ-ences between pre-dawn and mid-day � l continually decreasedduring drought (from ∼0.7 in June towards 0.1–0.2 in August),

174 O. Sus et al. / Agricultural and Forest Meteorology 198–199 (2014) 168–180

F per dT d greyV

ittawwtiPistSpttd

ww(pT

ig. 2. Time series of daily (i.e. estimated over 96 quarter-hourly timesteps, onceair = air temperature, VPD = vapour pressure deficit, RAD = global radiation. Dotteallcebre: 2004, Prades: 2011.

ndicating that reductions in SWC were forcing pre-dawn � l closerowards � crit. Whereas simulated SWC agreed well with observa-ions at Vallcebre, there was a positive model bias during droughtt Prades (overestimation of ∼0.04%Vol from July to October),hich possibly explained the bias in predawn � l. Even thoughe implemented updated Saxton equations in order to account for

he effects of gravel content on matric SWC and soil conductiv-ty, model difficulties remained in reproducing observed values atrades. This was likely due to a combination of several complicat-ng factors, such as the locally steep slope, effects of macropores onoil conductivity, and the spatial heterogeneity in soil characteris-ics and depth. However, we conducted a separate RDE for whichPA’s soil water balance was driven by measured SWC. Resultingosterior parameters (data not shown) were very similar to theemporal patterns shown in Fig. 5, with the exception of a con-inuous trend of C decline for Prades (NDF + DF) throughout therought.

In terms of BGE parameters our simulations showed that ratiorlas not well constrained and largest for Vallcebre. Moreover, iotaas considerably larger for Prades NDF (1.024) than for Prades DF

1.006) and Vallcebre (1.004), and G was largest for defoliated

p

ines (1.81 (Prades DF) vs. 1.23 (Vallcebre) and 1.45 (Prades NDF),able 2).

ay) Pearson correlation coefficient R for measured sap flow vs. measured drivers: horizontal lines indicate R values for significance levels p = 0.01, 0.05, and 0.001.

3.4. Real data experiment-derived posterior parameters

3.4.1. Temporal variabilityThe sequential assimilation of all sap flow data sets produced

clear seasonality and differences in magnitude in all parametersbut ratiorl (Fig. 5). Except for this parameter, repeated looping overthe study years did not show any obvious trends in parametersbut instead a high degree of repeatability. Magnitude of stoma-tal efficiency (∼the reciprocal of maximum stomatal conductance)was Prades NDF > Prades DF > Vallcebre. These differences werelowest in March but grew quickly during the following months.Values of Gp were similar for Vallcebre and Prades DF from Marchuntil end of May, and were about half for Prades NDF during thatphase. Prades Gp followed a negative trend from May onwards.This decrease accelerated during June and July and caused Gp tofinally fall towards its lower limit in mid-July, where it remainedwithout recovering in autumn. Interestingly, time-variable Gp

parameters were always considerably lower than time-constantBGE parameters for all data sets. All three sites showed early sea-son maxima for C in March/April followed by a continuous decreaseuntil July, with C = Prades DF > Vallcebre > Prades NDF. For param-

eter ratiorl, values showed strong temporal fluctuations and neverstabilized.

O. Sus et al. / Agricultural and Forest Meteorology 198–199 (2014) 168–180 175

F ) and

r comp(

3

r(

Fc

ig. 3. Daily observed and modelled sap flow for best-guess experiments (BGE, a,b,cesiduals (g–i). Positive values in polar plots indicate that the PGE model improvedNDF, row 2), and Prades defoliated pines (DF, row 3).

.4.2. Correlation with prior residuals and model drivers

Daily correlations between posterior parameters and prior

esiduals were generally larger and more significant for Pradesexcept for ratiorl p < 0.001 from July onwards) than for Vallcebre

ig. 4. Observed (obs) and modelled (best-guess (BGE) and posterior-guess (PGE) experiontent (g–i) for Vallcebre (2004) and Prades non-defoliated (NDF) + defoliated pines (DF

posterior-guess experiments (PGE, d–f), and polar plots of BGE residuals minus PGEared to the BGE. Data are shown for Vallcebre (row 1), Prades non-defoliated pines

(p > 0.001, Fig. S2a–c). Prades correlations during drought were

0.4 < |R| < 0.5. Ratiorl was least strongly and often not significantly(p > 0.05 for defoliated pines) correlated with residuals at Prades.As the analysis aimed for reducing prior residuals, these results

ments) values of leaf water potential (pre-dawn: a–c, mid-day: d–f) and soil water, 2011).

176 O. Sus et al. / Agricultural and Forest Meteorology 198–199 (2014) 168–180

Fig. 5. Parameter time series for Vallcebre (blue), Prades non-defoliated (green), and Prades defoliated pines (red). Thick lines are monthly moving averages of 15-min data(thin lines) for all loop years. Horizontal dashed lines are best-guess experiment parameter values. Data are shown for parameters iota (stomatal efficiency), Gp (abovegroundp

iaaiPat

i2

mwAbrptt

3

3

rd2rnVss04c

ftTe

lant conductance), C (capacitance), and ratiorl (root to leaf carbon mass ratio).

ndicated that (1) DA model adjustments were primarily broughtbout by temporal adjustments of iota, C, and Gp, and that (2) thesedjustments were larger at Prades. Moreover, the obvious increasen parameter correlations with prior residuals during drought atrades compared to preceding months supported the notion thatforementioned supposed functional changes (Fig. 2) were not cap-ured by the forward model.

Supplementary Fig. 2 related to this article can be found,n the online version, at http://dx.doi.org/10.1016/j.agrformet.014.08.009.

Correlations between environmental drivers T and VPD andodel residuals were generally smaller when the model was drivenith time variable posterior parameters for all data sets (Fig. S2d–f).

fraction of the information that was resolved within T and VPDut not captured by the forward model was absorbed by tempo-al parameter variability, consequently leading to improved modelerformance. This effect was less obvious for driver RAD, indicatinghat DA model adjustments were primarily related to air tempera-ure and humidity, and largely independent of levels of irradiance.

.5. Posterior-guess experiment (PGE)

.5.1. All parameters variableResiduals between model output and observations were clearly

educed when SPA was run with time-variable parameters (nRMSEecreased by 9% (absolute value, Vallcebre), 32% (Prades NDF), and2% (Prades DF), Fig. 3d–i, Table S1). In particular, the timing andate of reduction of sap flow during drought at Prades appearedow well captured. In other months, and for the whole season atallcebre, model improvement was somewhat smaller. For Prades,tatistics describing model goodness-of-fit (Table S1) were con-iderably improved (KGE rising from 0.59 to 0.88 (NDF), and from.75 to 0.85 (DF)). BGE percent bias was only slightly lowered by% (absolute value) for Vallcebre and 8% for Prades DF, but wasonsiderably reduced for Prades NDF (34%).

At all sites, pre-dawn � l was considerably closer to observations

or the posterior model, with lower � l (i.e., more negative) evenhough SWC increased slightly compared to the BGE run (Fig. 4).here was little effect of DA on mid-day � l, which was almostxclusively underestimated at both sites and often falls to � crit.

3.5.2. Constant and variable parameter combinationsFor each of the three data sets, the various PGE could be

classified into four different groups that formed clusters inthe Taylor diagrams and thus had similar model fit values(Fig. 6):

• cluster 1: runs with variable ratiorl but constant Gp• cluster 2: runs with variable C and/or iota but with constant Gp

and ratiorl• cluster 3: runs with variable Gp but constant ratiorl• cluster 4: runs with both variable Gp and variable ratiorl

For Prades data, cluster 1 was associated with lowest Taylorscores and thus poorest model performance throughout. Cluster2 had about similar fit scores as the BGE for Prades NDF, butmodel performance somewhat improved for Prades DF. Cluster 3had improved values in correlation coefficients and RMSD com-pared to BGE, but underestimated observed sap flow variability.Performance of cluster 4 experiments improved most and wasabout as good as the PGE run with all four parameters beingtime-variant. For Vallcebre, model improvement due to chang-ing combinations of time constant and variable parameters wasless obvious (see also Table S1). Bootstrap analysis of KGE scoresshowed that for Vallcebre differences between model experimentswere, except for cluster 1, generally significant. For Prades NDF,cluster 4 goodness-of-fit was significantly superior to all other clus-ters. For defoliated pines however, differences between clusters 2,4, and the “all parameters variable” experiment were not significantoverall (Table S1).

Model performance was best when time-variability of bothGp and ratiorl was introduced simultaneously, and lowest oth-erwise. As we found repeatable seasonality patterns in Gp butnot ratiorl (Fig. 5), this probably indicated that short-term (≤daily) fluctuations of observations were resolved within thetime-variability of ratiorl, and temporal changes in Gp werenecessary to reproduce the long-term (≥daily) trend in sap

flow. Whereas parameter ratiorl appeared to have absorbedhigher frequency, potentially noisy information, seasonality inGp was crucial for enabling SPA to reproduce Prades droughtbehaviour.

O. Sus et al. / Agricultural and Forest Meteorology 198–199 (2014) 168–180 177

Fig. 6. Taylor diagrams of posterior-guess experiments (PGE) for a) Vallcebre, b) Prades nexperiment (BGE) and all PGEs. Letters indicate which model parameters were temporally

i = stomatal efficiency, r = root to leaf carbon mass ratio.

Fig. 7. Modelled daily gross primary productivity (GPP) for Vallcebre (a, 2004) andPrades non-defoliated (b, 2011) and defoliated pines (c, 2011). Best-guess experi-ment (BGE) values are shown as a dark-grey surface, and posterior-guess experiment(PGE) values as light-grey points. At the top of each panel, values indicate percentagecP

3

ipctmepGPtts

2012; Katul et al., 2009). There is still debate about what is the key

hange of cumulative GPP for PGE (2 months) vs. BGE (2 months), and in parenthesesGE (2 months) vs. BGE (annual sum).

.6. Gross primary productivity – BGE vs. PGE estimates

The introduction of time variable plant hydraulic parametersnto SPA caused negligible changes in cumulative gross primaryroductivity (GPP) over the whole season for Vallcebre (−1.6%ompared to BGE), but lead to a considerable reduction in pho-osynthesis at Prades DF (−15.5%) and NDF (−25.3%, Fig. 7). The

agnitude of these values depended to some extent on the param-terization of the BGE model, as percentage changes in GPP wereroportional to BGE model bias in simulated sap flow (Table S1).PP as simulated by the PGE model was considerably reduced forrades NDF in July (−54.1%) and August (−40.5%), with 63.2% of

he annual total reduction in GPP having been associated with thatime period only. Photosynthesis of defoliated pines was also con-iderably affected by time variable parameters in July (−40.5%) and

on-defoliated, and c) Prades defoliated pines. Scores are shown for the best-guessvariable in the PGE model runs: c = capacitance, g = aboveground plant conductance,

August (−31.1%), which was equivalent to 74% of the annual totalreduction.

4. Discussion and conclusions

4.1. Differences in magnitude and seasonality of hydraulicparameters between mesic and xeric sites and defoliated andnon-defoliated pines

Differences between the xeric (Prades) and the mesic (Vallcebre)sites show that stomatal control of transpiration is more conserva-tive at the xeric site (cf. Poyatos et al. (2007a); but see Héroult et al.(2013)). Here, larger values of stomatal efficiency are equivalent toa larger WUE and lower stomatal conductance. An independentlyoptimized estimate of iota (1 + 10−3, Pinus ponderosa, Misson et al.(2004)) is within the range of the posterior parameter time seriesshown here for Vallcebre. Stomatal control is least conservativeduring spring at all sites, and gradually becomes more restrictiveduring the drier summer months. These absolute and seasonal dif-ferences are realistic and in agreement with previous modellingstudies showing non-conservative water use when SWC is high anda decrease in stomatal conductance when SWC becomes limiting(Misson et al., 2004). In the latter case however, these decreases ings were simulated with time constant parameters, whereas here weobserved an additional reduction in gs through posterior parameterseasonality in iota for all stands. This indicates that the stoma-tal model applied within SPA, and probably that of other models,captures only part of the true variability in stomatal functioningand fails to simulate additional influencing factors (see Bodin et al.(2013) for a long-term decline in SPA modelled WUE fit due tochanging controlling processes). Radiation load effects, i.e. the pro-duction of water vapour in the leaf interior affecting homeostasisof epidermal water potential (Pieruschka et al., 2010), are unlikelyin our case, as time series correlation between radiation and iota isrelatively low for all sites (data not shown). Seasonality in stomatalefficiency appears to be more closely related to VPD and tempera-ture, suggesting that missing processes within SPA are primarily afunction of these two environmental variables. It has been observedthat stomata close despite the absence of actual hydraulic stress,which could reflect a direct response of guard cells to VPD (Fisheret al., 2006) or, more likely, to transpiration rates (Buckley et al.,

driver of stomatal behaviour (Damour et al., 2010), and clearly moreresearch is needed into defining and modelling the mechanismsunderlying stomatal opening.

1 t Mete

qalr2liatevtcrcntod2Tawbacc

phesaAvtamitPoFv(

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e

78 O. Sus et al. / Agricultural and Fores

The larger absolute conductivity of DF vs. NDF is a logical conse-uence of defoliation, leading to a decrease in the leaf-to-sapwoodrea ratio (Mencuccini and Grace, 1995). At Prades however, defo-iation should be seen as an inevitable consequence of droughtather than as an adaptive mechanism to water stress (Poyatos et al.,013). Interestingly, posterior absolute values of Gp are generally

ower for time variable (PGE) compared to constant (BGE) DA exper-ments (Fig. 5). However, these reduced aboveground conductancesre compensated for by a modelled increase in root biomass andhus belowground conductance. This is a classic example of param-ter equifinality: whereas absolute values of Gp and ratiorl can beery different (PGE vs. BGE, Fig. 5), the model will produce rela-ively similar output before drought onset nonetheless (Fig. 3). Inontrast to its definition in the prior model, posterior Gp is thusather representative of total (i.e. above- and belowground) plantonductance, as the location of maximum hydraulic resistance isot resolved within sap flow data (Williams et al., 2001a). Addi-ional data such as sub-daily variation of stem water potentialbtained with stem psychrometers (Fisher et al., 2006) or thoseerived from xylem diameter variations (Martínez-Vilalta et al.,007) could provide further important information in this context.hus, a range of belowground variables and processes which are notppropriately accounted for within model runs could be resolvedithin posterior Gp variability. Deficiencies in simulating total root

iomass and distribution (Fisher et al., 2007; Williams et al., 2001a)nd soil structure (Williams et al., 1998) could explain why plantonductance per unit leaf area is lower for healthy pines at Pradesompared to Vallcebre.

Capacitance is an important and somewhat neglected com-onent of a plant’s hydraulic system (Meinzer et al., 2009), andere our results provide a temporally highly resolved, alternativestimate. The capacitance term provides an advantage over steady-tate simulations of water fluxes (Alton et al., 2009). In our study,n overall decline in C for all sites is observed from March to July.t Prades, this decline has important implications: the short-termariability in transpiration fluxes is increasingly less well bufferedhroughout the season, and hydraulic failure becomes more likelys the drought develops (Meinzer et al., 2009). This C decreaseight reflect depletion of stored water (Meinzer et al., 2009) and

s consistent with observed seasonal patterns of stem shrinkage inhe same Prades population (R. Poyatos et al., unpublished results).arameter values are within the wide range of reported values inther applications of the SPA model (2300–8000 mmol m−2 MPa−1,isher et al., 2006; Williams et al., 1998) and consistent with thealues observed in other conifers (see references in Verbeeck et al.2007)).

Regarding these results, posterior parameter time series appearobust and confirm a previous observation that SPA performsell during wet conditions, but overestimates GPP and transpi-

ation during drought (Williams et al., 1998). The forward modelmploys strict isohydric behaviour by preventing simulated � lo fall below a critical threshold value beyond which dangerousavitation occurs. This makes SPA structurally incomplete duringntense drought, as the isohydric approach is too simplistic for theroad range of ecophysiological conditions under which the modelperates (Misson et al., 2004). Other schemes have been imple-ented within SPA and tested by Williams et al. (2001a) for sap flow

ata, such as a direct dependency of Gp on LWP or – more indirectly on the time spent at low LWP (∼analogue to embolism-inducedydraulic damage). However, the authors found no clear evidenceo support either of the two hypotheses. Here, we present alter-ative results on how SPA deficiencies directly relate to the lack of

odelling certain mechanisms controlling stomatal opening, water

torage, and particularly hydraulic conductance.A recent publication (Poyatos et al., 2013) tested the hypoth-

sis whether defoliated Scots pine at Prades shows enhanced

orology 198–199 (2014) 168–180

sensitivity to drought. The study’s results generally confirm ourfindings regarding differences in seasonality and magnitude ofparameters (Gp: DF > NDF) and state variables (gs: DF > NDF)between healthy and defoliated pines. Further, strict stomatal clo-sure in response to VPD was reported, which our model resultssuggest (but not confirm) through very high late-season stomatalefficiency values (Fig. 5). The authors further reported a continu-ous drop in midday � l during drought despite of stomatal closure.This observation supports the notion that the critical � l thresh-old mechanism within SPA is incomplete, as � l cannot be perfectlyregulated by stomatal closure alone due to cuticular water loss.The isohydric behaviour of Scots pine has functional limits, andxylem embolism cannot be avoided under intense drought condi-tions (Martıınez-Vilalta and Pinol, 2002). No short-term recoveryof hydraulic conductance after post-drought precipitation eventswas observed at Prades (Poyatos et al., 2013), which is in agree-ment with posterior parameter time series and the assumptionof embolism-induced damage of hydraulic pathways. Indepen-dent measurements on the Prades population confirm high levelsof native embolism in stems (>60%) at the peak of the summerdrought, both for DF and NDF trees (Gómez, 2012). Native embolismlevels could be even larger in roots and leaves of the studied trees,due to their higher vulnerability to drought-induced embolism(Gómez (2012), J. M. Torres, unpublished).

4.2. Temporal decline in plant conductance at the xeric sitesignificantly improves model performance

The analyses here suggest that a decline in plant hydraulic con-ductance is the primary cause of reduced sap flow during drought.Model improvement at Prades through introducing time variabil-ity in Gp is significant compared to other PGEs. This is most obviousfor healthy pines, for which model performance is almost indepen-dent of time variability in stomatal efficiency, as long as parametertrends in Gp and ratiorl are introduced simultaneously (Fig. 6).Although there is some degree of parameter equifinality betweenGp and ratiorl, the seasonal signal in Gp from Prades simulationsappears very robust (Fig. 5). These conclusions are somewhatlimited by: (1) possible inaccuracies in estimating soil conductancefrom SWC using the Saxton equations, which could potentiallyintroduce an additional seasonality signal; and (2) parameter spacerestrictions on stomatal efficiency, which prevented near-completestomatal closure. However, iota does not hit the upper bound beforeJuly, when plant conductance is already almost minimal and largelyrestricts transpiration. Thus, further adjustments in stomatal effi-ciency are unlikely to significantly affect model behaviour, as thelocation of largest resistance already lies within plant hydraulicpathways. In fact, seasonal behaviour of stomatal conductance canbe largely reproduced by a simplified mechanistic sap flow modelframework using time constant parameters (Buckley et al., 2012).This is in agreement with our study, suggesting here that non-stomatal adaptation to seasonal changes, and in particular drought,is crucial for an improved simulation of observations.

Even though it is known that SPA parameter sensitivity is largestfor � crit (Williams et al., 1996), the latter was not part of our DAscheme. Introducing time variability in � crit, while possible, wouldmean a radical change in model philosophy, replacing strict iso-hydric by anisohydric behaviour. Moreover, this would contradictwhat we currently know about Scots pine stomatal behaviour dur-ing drought (Martínez-Vilalta et al., 2009; Poyatos et al., 2013).

Prades parameter time-series show that the initial response todecreasing SWC is an increase in stomatal efficiency from early

April onwards. However, Gp stays about constant until early June(Fig. 5). At Vallcebre on the other hand, Gp shows no significantcorrelations with model drivers, whereas iota and, especially, C aresignificantly related to air temperature and VPD (data not shown).

t Mete

Tnrcc

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O. Sus et al. / Agricultural and Fores

his suggests that stomatal efficiency and plant conductance areot completely coupled and respond differently to changing envi-onmental conditions, so that sap flow data bear independentonstraints on SPA modelled stomatal functioning and hydrauliconductance.

The close grouping of Vallcebre PGEs in the Taylor diagram indi-ates that the forward model already captures the most importantrocesses driving transpiration and benefits only little from timeariable parameters. Thus, SPA appears structurally complete inhe absence of drought. However, this is clearly not the case atrades, and confirms statements above that SPA fails to modeley processes such as embolism (Fisher et al., 2007) and leaf con-uctance when SWC is very low. The model could be improvedy implementing an explicit embolism mechanism: plant con-uctance would then be simulated as the product of Gp and andditional embolism scalar (0–1), which is inversely proportionalo the time spent around � crit. A similar approach was alreadymplemented (Williams et al., 2001a).

One major uncertainty in DA studies is defining model uncer-ainty magnitude. There are complex methodologies that estimateer-timestep parameter uncertainty perturbation in sequential DAtudies (Rastetter et al., 2010); these show the model uncertaintyarameter affects the adjustment time of the ensemble, althoughot the final outcome. So, for simplicity, we did not employ theseethodologies, but instead estimated a model error that included

n appropriate adjustment time and used this. While in a Bayesianense it is not correct to set per-timestep prior distributions by esti-ation, the outcomes of the study are not affected significantly. We

epeated the RDE for Vallcebre and Prades non-defoliated pines,unning the assimilation scheme for one loop year and four addi-ional parameter uncertainty values (ensemble perturbation withd = 0.0001, 0.0005, 0.005, and 0.01 relative of the ensemble mean)o analyze the sensitivity of posterior parameter time series tonsemble perturbation magnitude (data not shown). We find thathe choice of parameter uncertainty magnitude does not affect ouresults and conclusions in a considerable way. Further increasingarameter uncertainty leads to an increased absorption of pertur-ation noise by parameters, whilst the overall temporal patterns shown in Fig. 5 is reproduced when parameters are not edge-itting. Moreover, uncertainty magnitude should be large enoughhere >0.0001) so that parameters absorb process information andxhibit temporal variability on a seasonal scale.

.3. Implications of plant hydraulic constraints for carbonssimilation under extreme drought

Whereas at Vallcebre GPP values differed only slightly betweenorward and posterior model runs, at Prades photosynthesis was5.5% (DF) and 25.3% (NDF) lower over the entire year in PGE vs.GE simulations. The largest fraction of GPP reduction occurs dur-

ng drought (a 30–60% reduction PGE vs. BGE), when pronouncedtomatal closure and reduced hydraulic conductivity strongly limitnstantaneous carbon assimilation. These results are expectable, ast is known that the forward model reproduces measured tran-piration fluxes better in the absence of drought (Williams et al.,998). In an artificial drought experiment in the Amazonian rain-orest, SPA modelled GPP declined by 13–14% over two years, and0–45% during the driest period (Fisher et al., 2007). In that study,PA was able to realistically simulate drought constraints on GPP.owever, drought conditions were less severe than in our study

minimum modelled pre-dawn � l >−1.2 MPa). Moreover, our GPP

eductions are derived from comparison against forward modelalues for drought conditions. Whereas Fisher et al. (2007) sug-est that drought conditions of an Amazonian rainforest with a 50%eduction in precipitation can be confidently simulated by SPA, we

orology 198–199 (2014) 168–180 179

show how the same model is less successful when environmentalconditions drive a forest ecosystem towards its physiological limits.

Besides the implications for whole ecosystem carbon exchange,the seasonal distribution of carbon assimilation can have severeimplications for short- and long-term survival of Scots pine. Duringand after drought, trees might struggle with supporting the carbonrequirements of maintenance respiration, repair of hydraulic andstructural damage, and fine root growth. Reductions in assimila-tion, exacerbated by lowered leaf-to-sapwood area ratio throughdefoliation, might thus jeopardize long-term survival (Galianoet al., 2011; McDowell, 2011). Thus, model results could provideinsights into crucial processes during drought, especially if carbonand water flux constraints are assimilated simultaneously.

The study clearly shows that the assimilation of observationsinto mechanistically advanced ecosystem models adds value tothe data’s informational content and helps to visualize and testhypotheses on processes that are otherwise difficult to measure.Sequential data assimilation allows researchers to constrain modelparameter values and their temporal variability, and thus to learnabout missing mechanisms at various time scales. Moreover, ithelps to characterize differences across sites and between treesof varying canopy conditions (defoliation) within a site that arelargely consistent with observations. Our results suggest that anexplicit representation of mechanisms leading to temporal changesin hydraulic conductivity (i.e. xylem embolism) is required for mod-els to reproduce tree functioning during extreme drought.

Acknowledgements

This research has been supported by the Spanish Govern-ment through grants CSD2008-0040 (Consolider Programme) andCGL2010-16373. RP was supported by a Juan de la Cierva postdoc-toral fellowship from the Spanish Government. RP, JMV, JB, and PLprovided the field data on sap flow and stand characteristics. MWdeveloped the SPA model, to which MW and OS then coupled theEnKF. The manuscript was written by OS and JMV, with further sci-entific and editorial input from all other authors. OS produced allfigures and tables shown.

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