Interactive comment on “ Simultaneous parameterization of the two-source evapotranspiration model by Bayesian approach : application to spring maize in an arid region of northwest China ”

Parameter optimization by MCMC method for the evapotranspiration model is one of the best solutions for improving the estimation accuracy. Zhu et al. did an interesting work on simultaneous assimilation of two different data streams: 30min evapotranspiration (ET) and daily evaporation (E), then finally gained the moderately good accordance between the simulations and the observations. The efforts proved a new feature for optimizing the canopy transpiration and soil evaporation parameters, and also brought the direction for further improvement of such ET model. However, this paper is suffering


Introduction
In agriculture ecosystem, more than 90 % of all water inputs is lost by evapotranspiration (ET) (Morison et al., 2008), which is defined as the sum of water loss by evaporation (E ) from soil and transpiration (T ) from plants (Rana and Katerji, 2000).E and T are influenced by different abiotic and biotic factors (Wang and Yakir, 2000), and the contributions of E and T to the total ecosystem ET are highly variable in space and time (Ferretti et al., 2003).Thus, accurate measurement or estimation of ET and its components (E and T ) is essential for many applications in agriculture, such as irrigation scheduling, drainage, and yield forecasts (Wallace and Verhoef, 2000;Flumignan et al., Introduction Conclusions References Tables Figures

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Full 2011; Sun et al., 2012).The Shuttleworth-Wallace model (S-W model) (Shuttleworth and Wallace, 1985) takes the interactions between the fluxes from soil and canopy into account, and is physically sound and rigorous.Previous studies have proved that it has good performances for row crops such as maize, wheat, cotton, sorghun and vine (Stannard, 1993;Tourula and Heikinheimo, 1998;Anadranistakis et al., 2000;Teh et al., 2001;Lund and Soegaard, 2003;Kato et al., 2004;Ortega-Farias et al., 2007;Zhang et al., 2008).Despite these studies, there are still some insufficiencies in the application of the S-W model (Hu et al., 2009;Zhu et al., 2013).First, the S-W model is sensitive to the errors in the values of canopy and soil resistances (Lund and Soegaard, 2003).Previous studies mainly focused on the parameterization of the canopy resistance (Hanan and Prince, 1997;Samanta et al., 2007;Zhu et al., 2013), and less attentions has been committed to the parameterization of the soil surface resistance (Sellers et al., 1992;van de Griend and Owe, 1994;Villagarcía et al., 2010).In crop ecosystem, E may contribute significantly to the total ET when leaf area index (LAI) is low (Lund and Soegaard, 2003;Zhang et al., 2008).Thus, simultaneous parameterization of the canopy and soil resistances in the S-W model, based on direct measurement of ET and its components by using a combination of micro-meteorological (e.g.eddy covariance methods, Bowen ratio), hydrological (e.g.chambers, microlysimeters) and ecophysiological techniques (e.g.sap-flow, stable isotopes) (Williams et al., 2004;Scott et al., 2006), is important to reduce the model error.However, such studies are relative rare or non-existent.Secondly, as far as the parameterization method is concerned, abundant evidence has shown that the Bayesian method provides a powerful new tool to simultaneously optimized many or all model parameters against all available measurements (Clark and Gelfand, 2006).Although some pioneering efforts have been made (e.g.Samanta et al., 2007;Zhu et al., 2013), the Bayesian method has been much less frequently used in parameterization of ET model than in the other environmental sciences (van Oijen et al., 2005).Moreover, the Bayesian method, to our knowledge, has not been used to simultaneously optimized the parameters of the S-W Introduction

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Full model against multiple measuring dataset (Sect.2.5).Finally, arid northwest China, one of the driest area in the world (Zhu et al., 2007(Zhu et al., , 2008)), is characterized by a widely distributed desert/Gobi interspersed with many oases in different sizes and shapes.Land surface processes of this heterogeneous region are much complex than in other regions (Zhang and Huang, 2004).Thus, the applicability of the S-W model in such regions need to be investigated in details.
Based on direct measurements of different components of ET obtained by using the eddy covariance technique and microlysimeters over a spring maize field in arid region of northwest China from 27 May to 14 September in 2013, the objectives of the present study were to: (1) simultaneously parameterize the S-W model using the Bayesian method against multiple measuring dataset; (2) verify the performances of the S-W model, and identify the causes of failure and success in simulating ET over the crop ecosystem in arid desert oasis of northwest China.It is expected that this study can not only promote the developments of ET model parameterization, but also help us to find a proper direction in modifying the S-W model used in arid regions.

Study site
The study site is located in Daman (DM) Oasis, in the middle Heihe River Basin, Gansu province, China (100 • 22 20 E, 38 • 51 20 N; 1556 m a.s.l.; Fig. 1).The annual average temperature and precipitation was 7.2 • C and 125 mm (1960-2000), respectively.The potential evaporation is around 2365 mm yr −1 , and the dryness index is 15.9.The soil type is silt clay loam on the surface and silt loam in the deeper layer.
The 10 days of July, while the maize (Zea mays L.) is sown in the late April and harvested in the middle 10 days of September.

Measurements and data processing
The field observation systems at this site were constructed in May 2013 as part of the Heihe Watershed Allied Telemetry Experimental Research (HiWATER) project (see details in Li et al., 2013b).The fluxes of sensible heat (H), latent heat (λET) and carbon dioxide were measured at the height 4.5 m using the eddy covariance (EC) system (Liu et al., 2014), which consists of an open-path infrared gas analyzer (Li-7500, LiCor Inc., Lincoln, NE, USA) and a 3-D sonic anemometer (CSAT-3, Campbell Scientific Inc., Logan, UT, USA).The EC data were sampled at a frequency of 10 Hz by a data logger (CR5000, Campbell Scientific Inc.), and then were processed with an average time of 30 min.Post-processing calculations, using EdiRe software, included spike detection, lag correction of H 2 O/CO 2 relative to the vertical wind component, sonic virtual temperature conversion, planar fit coordinate rotation, the WPL density fluctuation correction and frequency response correction (Xu et al., 2014).Data gaps due to instrument malfunction, power failure and bad weather conditions were filled using artificial neural network (ANN) and mean diurnal variations (MDV) methods (Falge et al., 2001).The ANN method was applied when the synchronously meteorological data were available; otherwise, the MDV method was used.The gap-filling data were used only to analyze the seasonal and annual variations in ET.
Continuous complementary measurements also included standard hydrometeorological variables.Rainfall was measuring using a tipping bucket rain gauge (TE525MM, Campbell Scientific Instruments Inc.).Air temperature and relative humidity (HMP45C, Vaisala Inc., Helsinki, Finland) and wind speed/direction (034B, Met One Instruments, Inc. USA) were measured at heights of 3, 5, 10 15, 20, 30 and 40 m above the ground.Downward and upward solar and longwave radiation (PSP, The EPPLEY Laboratory Inc., USA) and photosynthetic photon flux density (PPFD) (LI-190SA, LI-COR Inc.) were measured at height of 6 m.Soil temperature Introduction

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Full (Campbell-107, Campbell Scientific Instruments Inc.) and moisture (CS616, Campbell Scientific Instruments Inc.) were measured at 0.02, 0.04, 0.1, 0.2, 0.4, 0.8, 1.2 and 1.6 m depths.Three heat flux plates (HFT3, Campbell Scientific Instruments Inc.) were randomly buried at the depths of 0.01 m.The average soil heat fluxes were calculated using the three randomly buried plates.These data were logged every 10 min by a digital micrologger (CR23X, Campbell Scientific Inc.) equipped with an analog multiplexer (AM416) was used for sampling and logging data.
Daily soil evaporation was measured using three microlysimeters randomly placed between crop rows.The microlysimeters with an internal diameter of 10 cm and a depth of 20 cm were filled with an intact soil core and pushed into soil with the top slightly above the soil surface (Daamen et al., 1993;Liu et al., 2002).The average weight loss of these microlysimeters measured using electronic scales with 0.01 g precision was nearly equal to soil evaporation.In order to keep the soil moisture in microlysimeters similar to that between the rows, the soil in the microlysimeters was replaced daily or every two days.
Leaf area index (LAI) was measured using AM300 portable leaf area meter (ADC BioScientific Ltd., UK).The fraction of land cover (f ) was estimated by measuring the projected crop canopy area of selected stands in corresponding field plot.LAI, f and crop height were measured approximately every 10 days during the growing season, and the gaps were linearly interpolated to daily interval.

Description of the S-W model
In the S-W model, the ecosystem evapotranspiration (λET; W m −2 ) is separated into evaporation from the soil surface (λE ; W m −2 ) and transpiration from the vegetation canopy (λT ; W m −2 ) (Fig. 2), which are calculated as (Shuttleworth and Wallace, 1985;Lhomme et al., 2012):

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Full (2) (3) (10) −1 ), and r a a is aerodynamic resistances from canopy height to reference height (s m −1 ).A and A s (W m −2 ) are the available energy input above the canopy and above the soil surface, respectively, and are calculated as: where R n and R ns are net radiation fluxes into the canopy and the substrate (W m −2 ), respectively; G is the soil heat flux (W m −2 ).R ns was calculated using a Beer's law relationship of the form: in which K A is the extinction coefficient of light attenuation, and is approximately 0.41 for spring maize (Mo et al., 2000).

Calculation of resistances in the S-W model
The resistance network of the S-W model is shown in Fig. 2. In this paper, the three aerodynamic resistance (i.e., r a a , r c a and r s a ) were calculated using the same approach suggested by Shuttleworth and Wallace (1985), Shuttleworth and Gurney (1990) and Lhomme et al. (2012).
The canopy resistance (r c s ), which is the equivalent resistance of all the individual stomates in a canopy and depends on the environmental variables, can be calculated using the Jarvis-type model (Jarvis, 1976)  Full where r STmin represents the minimal stomatal resistance of individual leaves under optimal conditions.F i (X i ) is the stress function of a specific environmental variable X i , with 0 ≤ F i (X i ) ≤ 1.Following Stewart (1998) and Verhoef and Allen (2000), the stress functions were expressed as: where k 1 − k 3 are constants (units see Table 1); R s is the incoming solar radiation (W m −2 ); T a is the air temperature ( The soil surface resistances (r s s ; Fig. 2) was expressed as a function of near-surface soil water content (Sellers, 1992;Verhoef et al., 2006Verhoef et al., , 2012;;Zhu et al., 2013): in which b 1 and b 2 are empirical constants (s m −1 ); θ s is soil water content in the top layer of soil (at depth of 2 cm); θ sat is the saturated soil water content (m 3 m −3 ), which was estimated empirically through the near-surface soil texture.In summary, there are 6 site-and species-specific parameters needed to be estimated in the S-W model associated with soil and canopy resistances, which are b 1 , b 2 , r STmin and k 1 − k 3 .

Model calibration and evaluation
A Bayesian approach was applied to simultaneously estimate the parameters associated with the soil (b 1 , b 2 ) and canopy (r ST min , k 1 , k 2 , k 3 ) resistances in the S-W model (van Oijen et al., 2005;Svensson et al., 2008;Zhu et al., 2011Zhu et al., , 2013)).The two dataset used to simultaneously optimize the parameter values were: EC-measured half-hourly evapotranspiration (λET; W m −2 ) and microlysimeters-measured daily soil evaporation (E ; mm d −1 ).
Corresponding to each of the data sets (e.g., λET and E ), the model error e i (t) (i = 1, 2) is expressed by: where O i (t) and f i (t) is observed and modeled (Eqs. 1 and 9) values of the i th dataset at time t, respectively.Assuming the model error e i (t) follows a Gaussian distribution with a zero mean, the data likelihood function can be expressed by:

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Full where c is the parameter vector; O is the observed data sets; m is the number of dataset (= 2 in this study); σ 2 i (i = 1, 2) is the measurement error variance of the i th dataset; n i is the number of observations of i th dataset.Then with Bayes' theorem, the posterior distribution of parameters c is generated by: where p(c) represents prior probability distributions of parameters c, and p(c|O) is the posterior distributions of parameters c.The posterior distribution was sampled using the Metropolis-Hasting (M-H) algorithm (Metropolis et al., 1953;Hastings, 1970), a version of the Markov Chain Monte Carlo (MCMC) technique.To generate a Markov chain in the parameter space, the M-H algorithm was run by repeating two steps: a proposing step and a moving step.In the proposing step, a candidate point c new is generated according to a proposal density P (c new |c k−1 ), where c k−1 is the accepted point at the previous step.In the moving step, point c new is treated against the Metropolis criterion to examine if it should be accepted or rejected (see Zhu et al., 2011Zhu et al., , 2013 for detailed description on MCMC sampling procedure).We ran at least three parallel MCMC chains with 20 000 iterations each, evaluated the chains for convergence (Gelman and Rubin, 1992), and thinned the chains (every 20th iteration) when appropriate to reduce within chain autocorrelation, thereby producing an independent sample of 3000 values for each parameter from the joint posterior distribution.
During the whole growing season, the measurements were split into two independent dataset by taking alternate days.The model parameters were derived using one dataset.Then the optimized S-W model was used with the second data set to predict the different components of ET and these values were compared to the measured values in the second dataset.The performance of the S-W model was evaluated using the coefficient of determination of the linear regression between measured and estimated values of water vapor fluxes, R 2 , representing how much the variation in the observations was explained by the models.Also, the root mean square error (RMSE), Introduction

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Full mean bias error (MBE), index of agreement (IA) and model efficiency (EF) (Legates and McCabe, 1999;Poblete-Echeverria and Ortega-Farias, 2009) were included in the statistical analysis, which are calculated as follows: where n is the total number of observations, O(t) is the observed values at time t, O is the mean of the observed values, and f (t) is the simulation which was calculated using the posterior expectancy of parameter.

Environmental and biological factors
Detailed information on the seasonality of key environmental and biological variables is essential to assess seasonal variation in the actual ET and its partitioning.The Introduction

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Full  -195).The variation of mean daily air temperature (T a ) has a similar trend to R n , varying from 8.8 to 24.9 • C with an average value of around 19.0 • C. D exhibited large diurnal variation ranging from 0 to 3.5 kPa, and the daily mean D was relative small when the LAI was larger than 3 m 2 m −2 (DOY197-230).Daily mean wind speed (u) ranged from 0.5 to 3.2 m s −1 , and was close to normal long-term values.Total precipitation during the study period was 104.2 mm with eight events over 5.0 mm (Fig. 3).θ varied greatly over the whole growing season.The variability of θ mainly depended on irrigation scheduling of local government (irrigation quota and timing).Soil water content had a peak value (about 0.35 m 3 m −3 ) after irrigation and gradually reduced till the next irrigation (Fig. 3).The LAI showed a clear "one peak" pattern over the whole growing season with relative high values of 3.5 m −2 m −2 from early July to late August (DOY184-221).

Posterior distribution of S-W model parameters
The posterior parameter distributions are shown as histograms in Fig. 4 and summarized in Table 1 by posterior means and 95 % probability intervals.The results showed that the Bayesian calibration against the multiple dataset was in most cases successful in reducing the assumed prior ranges of the parameters values.Among the parameters, r STmin has the least posterior variability relative to its prior range, followed by the key parameters in the S-W model were well estimated by the Bayesian method against the multiple measuring dataset.In addition, the six calibrated parameters were not significantly inter-correlated with each other except for the pair b 1 and b 2 , which was positively correlated with a correlation coefficient of 0.85.The responses of soil surface resistances (r s s ) to soil water content computed using our posterior mean b 1 and b 2 values were very similar to that calculated using equation developed by Ortega-Farias et al. (2010) based on direct soil evaporation measurements, but seemed to be more sensitive to changes in soil water contents compared with some other studies (e.g., Sun, 1982;Sellers, 1992;Zhu et al., 2013;Fig. 5).The posterior mean value of r STmin from our study was very close to that (20 s m −1 ) reported for spring maize growing in northwest China obtained by using the least squares fitting method (Li et al., 2013a).The variations of the minimal stomatal resistance (r STmin ) for many natural and cultivated plantshave been widely investigated by previous studies (Korner et al., 1979;Pospisilova and Solarova, 1980).Typical values for r STmin vary considerably from about 20-100 s m −1 for crops to 200-300 s m −1 for many types of trees.Thus, our results fell within the range of previous studies.

Model performance compared with measurements
Having parameterized the S-W model as described above, we ran the model to simulate the half-hourly λET (Eq. 1) and λE (Eq.9) values (W m −2 ).The daily estimations of evapotranspiration (ET; mm d −1 ) and soil evaporation (E ; mm d −1 ) was obtained by summing up the half-hourly simulated values.The statistical analysis of observed vs. estimated values of water vapor fluxes at different time-scales were summarized in Table 2.These results indicated that the parameterized S-W model was able to predicate λET on a half-hourly basis with values of R 2 , IA and EF equal to 0.83, 0.93 and 0.74, respectively.However, there still existed the difference between measured and modeled half-hourly λET values for the spring maize in the arid desert oasis.The slope (0.84) of regressive equation between the measured and modeled half-hourly λET values was lower than one (Table 2 and Fig. 6a), which indicated that the S-W 754 Introduction

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Full  2010) also reported that the S-W model underestimated on halfhourly time intervals compared the EC-measured λET over a drip-irrigated vineyard in Mediterranean semiarid region during the growing season in 2006.On the contrary, some studies showed that the S-W model overestimated half-hourly λET (e.g., Li et al., 2013a;Ortega-Farias et al., 2007;Zhang et al., 2008).Therefore, the performances of the S-W model seemed to be variable for different crops and places, and there is a need to identify the causes that induced the disagreements between observed and modeled values (discussed below).
The fluctuation of measured and estimated daily ET and E was illustrated in Fig. 7.
In this case, a good agreement between measured and estimated daily E was obtained with values of R 2 , IA and EF equal to 0.82, 0.94 and 0.76 (Table 2).The points in plots of measured-vs.-modeleddaily E fell tightly along the 1 : 1 line (slope = 1.01 and intercept = 0.01 with RMSE = 0.05 and MBE = −0.01;Fig. 6b and Table 2).Thus, we thought that the soil resistance in the S-W model was properly parameterized for the spring maize by the measured soil evaporation data.From Fig. 7, we can also observed that the estimated daily ET generally fluctuated tightly with the measured values.The values of RMSE, MBE, IA and EF were equal to 0.05, 0.14 mm d −1 , 0.94 and 0.79, respectively (Table 2).However, great underestimations (> 0.5 mm d −1 ) were observed on 12 days during the study period (111 days).For example, on 5 July, the estimated and measured daily ET was 2.9 and 4.3 mm d −1 , respectively (Fig. 7).Thus, the causes of the underestimations of ET by the S-W on these days needed to be carefully checked based on detailed micrometeorological data.This work would help us to modify the model in a correct way and improve the precision of prediction.

GMDD Introduction
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Identification of the disagreement/agreement between observed and modeled ET values
The diurnal variation of R n , H and λET (measured and modeled) above the spring maize ecosystem for some selected days was presented in Fig. 8. Resulting from the high surface heterogeneities, one special phenomenon, known as the "oasis effect" (Lemon et al., 1957) or "cold island effect" (Wang et al., 1992;Zhang and Huang, 2004), was often observed on clear days in July and August in the study area and it is characterized as follows: (1) H is very small and even negative (downward) in the afternoon (Fig. 8a-c) due to the micro-scale advection of hot dry air over the desert to crop surface in the oasis.For an example, on 5 July, H was continuously negative from 12 : 00 to 20 : 00 (Fig. 8a).A strong advection process can be distinctly detected from the temperature and relative humidity profiles (Fig. 9a and b), in which the highest temperature occurred at a height of 8-18 m; (2) measured actual λET often exceeded (Fig. 8a) or was equal to (Figs. 8b and c) the local net radiation because of the added energy in the form of downward fluxes of H to the ET process (Evett et al., 2012).Under such conditions, the S-W model significantly underestimated the actual ET values due to the real atmospheric flows do not correspond to its assumption of horizontal homogeneities (Rao et al., 1974).Thus, how to properly representing the advection process in the S-W model should be paid special attentions in simulating ET over crop ecosystems in arid desert oasis in the future studies.In addition to this situation, slight underestimations were also observed on or shortly after rainy days (Fig. 7).For example, the simulated half-hourly λET was lower than that measured by EC after the rainfall event occurred in 13:00 LT on 17 June (Fig. 8d).We thought that the underestimations by the model on or shortly after rainy days were mainly due to ignoring the direct evaporation of liquid water intercepted in the crop canopy, because no downward H and temperature inversion were observed on this day (Figs.9c and d).

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Full were developed for simulating the rainfall interception by forest ecosystems, and their suitability for crops need to be further investigated.
On the other hand, the diurnal variation of simulated half-hourly λET by the parameterized S-W model has a similar trend to the measurements on clear and advectionabsent days during the whole study periods (Fig. 8e-h).On these days, H was positive (upwards) at day time (Fig. 8e-h) and no temperature inversion was observed (Fig. 9e  and f).Thus, we thought that the parameterization schedule adopted in this study worked well.It also demonstrated that the properly parameterized S-W model can be used in simulating and partitioning ET for homogeneous land surface.Hu et al. (2009) reported that the S-W model parameterized by using Monte Carlo method can successfully simulated ET at four uniform grasslands in China; our previous studies (Zhu et al., 2013) also illustrated that parameterized S-W model can be used to simulate and partition ET over a vast alpine grassland in Qinghai-Tibet Plateau.

Conclusions
This study illustrated the use of the Bayesian method to simultaneously parameterize a two-source ET model against the multiple measuring dataset for a crop ecosystem in a desert oasis of northwest China.The posterior distributions of the model parameters in most cases can be well constrained by the observations.Generally, the parameterized model has a good performance in simulating and partitioning ET.However, underestimations were observed on days when micro-scale advection occurred.Therefore, in the future studies, special attentions should be given to proper descriptions of the effects of advection on estimating ET for heterogeneous land surface.In addition, the canopy interception model should be coupled with the two-source ET model in longterm simulation.Introduction

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Full  euphratica Oliv., Tree Physiol., 31, 178-195, 2011. Zhu, G. F., Su, Y. H., Li, X., Zhang, K., and Li, C. B.: Estimating actual evapotranspiration from an alpine grassland on Qinghai-Tibetan plateau using a two-source model and parameter Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | study area has an agricultural development history of over 2000 yr owing to its flat terrain, adequate sunlight and convenient water resources from Qilian Mountains.The main crops in the DM Oasis are spring wheat and maize.The spring wheat (Triticum aestivum L.) is generally sown in the later March and harvested in the middle Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | s , and ET c are terms to describe evaporation from soil and transpiration from the plant (W m −2 ), respectively; C s and C c are soil surface resistance coefficient and canopy resistance coefficient (dimensionless), respectively; λ is the latent heat of evaporation (J kg −1 ); ∆ is the slope of the saturation vapor pressure vs. temperature curve (kPa K −1 ); ρ is the air density (kg m −3 ); C p is the specific heat capacity of dry air (1013 J kg −1 K −1 ); D and D 0 (kPa) is the air water vapor pressure deficit at the reference height (3 m) and the canopy height, respectively; γ is the psychrometric constant Introduction surface resistance for plant canopy and soil surface (s m −resistances from the leaf to canopy height and soil surface to canopy height (s m Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | • C) at the reference height; T a,min and T a,max are the lower and upper temperatures limits ( • C), respectively, which are T a values when F 2 (T a ) = 0 and are set at values of 0 and 40 • C (Harris et al., 2004); θ r is the actual volumetric soil water content in the root-zone at depth of 0-60 cm (m 3 m −3 ); θ wp is water content at the wilting point (m 3 m −3 ); and θ cr is the critical water content at which plant stress starts and was set as 0.30 m 3 m −3 in this study.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | seasonal change in net solar radiation (R n ; MJ m −2 d −1), air temperature (T a ;• C), air water vapor pressure deficit (D; kPa), wind speed (u, m s −1 ) at the height of 3 m, rainfall and irrigation (mm), soil water content (θ; m 3 m −3 ), and leaf area index (LAI; m 2 m −2 ) was illustrated in Fig.3.During the study period (DOY147-257), the daily mean R n varied from 2.6 to 18.5 MJ m −2 d −1 with an average value of 11.9 MJ m −2 d −1 .The peaked values were recorded from the end of June to the middle of July (DOY180 b 1 , b 2 , k 2 (approximately symmetric with distinctive modes; Fig. 4), while parameters k 1 and k 3 have relative large variability (widely spread on the prior bounds).Ortega-Farias et al. (2007) have demonstrated that the S-W model is very sensitive to errors in r STmin , and much less to uncertainties in other parameters.Thus, we thought that GMDD Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | model tended to underestimate the half-hourly λET with a MBE value of 24.2 W m −2 .Ortega-Farias et al. ( Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Zhu, G. F., Li, X., Su, Y. H., Lu, L., and Huang, C. L.: Seasonal fluctuations and temperature dependence in photosynthetic parameters and stomatal conductance at the leaf scale of Populus