RETRACTED: Evaluating the complementary relationship of evapotranspiration in an arid shrublands, Heihe river basin

Accepted Manuscript Research papers Evaluating the complimentary relationship of evapotranspiration in an arid shrublands Zhongbo Yu, Shiqin Xu, Xibin Ji, Edward A. Sudicky PII: DOI: Reference:

S0022-1694(18)30274-9 https://doi.org/10.1016/j.jhydrol.2018.04.021 HYDROL 22724

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

13 October 2017 17 December 2017 6 April 2018

Please cite this article as: Yu, Z., Xu, S., Ji, X., Sudicky, E.A., Evaluating the complimentary relationship of evapotranspiration in an arid shrublands, Journal of Hydrology (2018), doi: https://doi.org/10.1016/j.jhydrol. 2018.04.021

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Evaluating the complimentary relationship of evapotranspiration in an arid shrublands Zhongbo Yu1,2, Shiqin Xu1,2*, Xibin Ji3*, Edward A. Sudicky1,4 1

State Key Laboratory of Hydrology‒Water Resources and Hydraulic Engineering, Hohai University,

Nanjing 210098, China 2

College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China

3

Linze Inland River Basin Research Station, Laboratory of Inland River Ecohydrology, Northwest Institute

of Eco‒Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China 4

Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1,

Canada

Zhongbo Yu E-mail: [email protected]

*Corresponding author: Shiqin Xu E-mail: [email protected] Phone: 86‒25‒83786721 Fax: 86‒25‒83786996 Postal address: No.1, Xikang Road, Nanjing 210098, China

*Corresponding author: Xibin Ji E-mail: [email protected]

Edward A. Sudicky E-mail: [email protected]

1

Abstract: Accurate estimates of evapotranspiration and its components are essential for quantifying the water and energy fluxes and water resources management in arid regions. To this end, daily actual evapotranspiration (ETa), pan evaporation, and concurrent microclimate from an arid shrublands were measured over two growing seasons (2014-2015) to determine water budgets and to test the validity of the complementary relationship (CR) at this temporal scale. The average ETa is 229.32 ±45.86 mm during two growing seasons, while canopy transpiration, soil evaporation, and interception accounted for 68.1 ±16.5%, 29.1 ±2.5% and 2.8 ±0.6%, respectively. Actual evapotranspiration and Penman potential evapotranspiration, or pan evaporation exhibit complementary behavior, where the complementary relationship is asymmetric. Daily ETa rates are significantly overestimated by the symmetric Advection-Aridity (AA) model. Employing the modified AA model, where parameters are calibrated locally and wet environment evapotranspiration is evaluated at wet environment air temperature as opposed to the measured air temperature, the prediction accuracy of ETa is dramatically improved. With calibrated parameters, the E601B sunken pan can satisfactorily describe the dynamics of daily ETa, while the D20 aboveground pan underestimates it to some extent. Moreover, the modified AA model is able to capture the dynamics of groundwater usage by vegetation during drying summer. These findings gain our new knowledge on the capability of CR theory to resolve special issue occurred in phreatophytic shrublands, and can also provide beneficial reference to water resource and eco-environment management in arid regions. Key words: Evapotranspiration partition; Advection-Aridity model; Genetic Algorithm; Phreatophytic shrub; Arid climate

1. Introduction Terrestrial evapotranspiration (ET) is an important component in the water and energy cycles (Jung et al., 2010; Vinukollu et al., 2011; Zhang et al., 2016). ET returns approximately 62% of annual land precipitation to the atmosphere and may account for much as 95% of all precipitation inputs in water-limited ecosystems (Wilcox and Thurow, 2006). It is a major component not only of the terrestrial water cycle but also of the surface energy balance. From the later, on average, terrestrial latent heat (LE) uses approximately three fifths of surface net radiation, with estimates from different models varying from 48% to 88% (Trenberth et al., 2009). Accurate quantification and modeling of ET, therefore, is not only crucial to estimate and predict 2

hydrologic budgets and climate dynamics, but is also crucial for sustainable water resource management. Over the past half century, numerous studies have reported observations of decreasing pan evaporation (ETpan) and potential evapotranspiration (ETp) over large areas in different regions throughout the world (Hobbins et al., 2004; Roderick and Farquhar, 2002). This declining trend, however, contrasts with the reported general increases in actual evapotranspiration (ETa) in the same period (Walter et al., 2004; Milly and Dunne, 2001). Two hypotheses have been proposed to explain this contradiction. One is the so-called complementary relationship hypothesis (Bouchet, 1963), and the other is that a decrease in solar radiation or an increase in cloud cover plays a major role in the decrease of ETpan or ETp. These conflicting interpretations and other recent studies indicate that further studies are needed to examine the relationship between ETp and ETa. Many observational and estimation methods have been used for quantifying ETa at multiple spatiotemporal scales including lysimeter, scintillometer, energy balance Bowen ratio, and eddy covariance (Allen et al., 2011; Wang and Dickinson, 2012), but these methods require expensive instrumentation and expert labor. Although recent advances in satellite remote sensing technology and retrieval algorithms now enable large-scale mapping and monitoring of ETa (Zhang et al., 2010; Gokmen et al., 2012), most remote-sensing-based methods only provide us with instantaneous ETa values. Using single-source or two-source physically models to estimate ETa is equally difficult to apply in arid shrublands environments with confidence because of uncertainties in parameters relating complex aerodynamic, canopy, and soil resistances to sensible and latent heat fluxes. An approach based on general feedback mechanisms is attractive because it allows us to avoid extremely detailed knowledge of the complex processes and interaction between soil, vegetation, and atmosphere. For this reason, methods employing the complementary relationship (CR) of evapotranspiration have become popular, because they rely on general feedbacks between ETa and ETp and require only routine measured meteorological variables. The key idea behind the CR formalism is that as a surface dries, a fraction of the energy not used for evaporation becomes available in the form of increased sensible heat flux that increases potential evaporation and gives rise to a complementary relation between actual evaporation and potential evaporation (Brutsaert and Parlange, 1998; Brutsaert, 2005). Such a relation offers a simple approach for estimating ETa based on calculated potential evaporation or measured pan evaporation without detailed knowledge of surface properties (Aminzadeh et al., 2016). Different implementations of the CR theory have been tested experimentally in a number of studies. 3

However, this has mostly been done with annual or other long-term evaporation data, often obtained with water budget studies over entire river basins, and the research at higher temporal resolution is still limited (Han et al., 2014; Kahler and Brusaert, 2006; Ma et al., 2015). In addition, the widely accepted Advection-Aridity (AA) model as well as other CR-based models produces considerable bias under arid conditions (Lemeur and Zhang, 1990; Matin et al., 2013). For instance, Hobbins’s et al. (2001a) reported that the predictive power of the AA model and the complementary relationship areal evaporation (CRAE) model derived by Morton (1983) increased in moving toward regions of increased climate control (i.e. humid regions) of evapotranspiration rates and decreased in moving toward regions of increased soil control (i.e. arid regions). Xu and Singh (2005) also found the performance of three models based on CR theory was significantly decreased in semiarid region in the Cyprus. Recent researches have focused on various assumptions of model formulations, such as considering the wet environment temperature to estimate wet environment evapotranspiration (Szilagyi, 2007; Szilagyi and Jozsa, 2008). These new assumptions on CR theory make it possible to improve ETa estimation in arid regions which cover 40% of the Earth’s terrestrial surface and face the problem of serious water scarcity in the context of global warming. Based on in situ measurements of actual evapotranspiration, pan evaporation, and microclimate over two growing seasons (2014-2015) in the desert region, northwestern China, the objectives of the present study are (1) to partition annual actual evapotranspiration into transpiration, interception, and soil evaporation, (2) to test the existence of the CR in arid shrublands, (3) to determine the local parameter values of the CR-based AA model, and (4) to estimate actual evapotranspiration rates with the help of the Penman equation as well as with the evaporation pan at daily scale. 2. Study site and material 2.1. Site description Our experiments were conducted in a desert-oasis ecotone in the middle reaches of the Heihe River basin of northwestern China (Fig. 1). The climate in this region is a typical continental arid temperate climate. The annual mean temperature is about 8.9 °C and the annual mean precipitation is about 125 mm. Vegetation at the site was characterized by an open shrub canopy dominated by Haloxylon ammodendron, Nitraria tangutorum, and Calligonum mongolicum. Three desert shrubs species contribute more than 99% of the standing biomass at the site and are typical psammophytes, with extensive and deep root systems. A representative 1ha (100×100 m) plot was selected to conduct a stand vegetation survey during intensive field experiments (from DOY 196 to DOY 222 in 2014). We surveyed the species-specific locations, height, 4

crown area, stand density, basal diameter (5 cm above ground level), and leaf area of the sampling shrub stems. Please refer to Ji’s et al. (2016) study for more detailed information on vegetation survey and mean stand characteristics of the three dominant shrubs in the study plot. < Fig. 1: Line 1 in the document called “Figures” please > 2.2. Microclimate and pan evaporation measurements An automatic weather station was constructed to measure net radiation (Rn, W m-2), ground heat flux (G, W m-2), air temperature (Ta, ºC), relative humidity (%), precipitation (mm day-1), and wind speed (U, m s-1). We also measured volumetric soil water content (cm3 cm-3) with the time domain reflectometers (TDR, CS616, Campbell Scientific Inc., Logan, Utah, USA) using 12 probes at depths of 10, 20, 40, 60, 80 and 120 cm. Meteorological data sets were aggregated from 30 min to daily time steps. Daily pan evaporation (mm d-1) was measured by China D20 model. We also measured daily pan evaporation using the China D20 model and the China E601B model at the Linze Inland River Basin Research Station, Chinese Academy of Sciences near the study site 3 km in 2015. The D20 pan is an aboveground pan, while the E601B pan is a sunken pan, according to the World Meteorological Orgnization’s (2008) pan classification. 2.3. Estimation of canopy transpiration and actual evapotranspiration Canopy transpiration during growing period in 2014 and 2015 was measured by sap flow gauges (Flow32 meters, Dynamax Inc., Houston, TX, USA). For H. ammodendron, sap flow in nine stems was measured using nine gauges in total. For C. mongolicum, three stems were monitored using three gauges. For N. tangutorum, sap flow in three stems was measured used three gauges. Specific model for each gauge and installing process can be found in Xu’s et al. (2017a) study. Raw signal data from the gauge was recorded at 10-s interval and stored as 30-min averaged by a Campbell CR1000 data logger (Cambell Scientific Inc., Logan, Utah, USA). Note that the sap flow of N. tangutorum in 2015 were estimated from DOY 143 to DOY 181 owing to gauges malfunction, which will results in a relative underestimation of its contribution to total ETa in this year. To scale sap flow rates from individual stems to the stand level, we adopted the scaling method used by Allen and Grime (1995) in their study of savannah shrubs, where it was assumed that sap flow rate of each stem was proportional to its basal cross-sectional area. Species-specific area-average transpiration rate, Tc (mm h-1), across the 1-ha sampling plot was calculated by scaling up from sap flow measurements in the stem samples to the whole plot using the species-specific frequency distribution of stem diameter (Fig. S1). (1) 5

where n is the number of gauged stems, Fi is the sap flow velocity measured in stem i (kg h-1), Ai is the basal cross-sectional area (cm2), A is the basal cross-sectional area per ground area (cm2 m-2), and ρw is the density of water (kg m-3). For each species, we estimated hourly transpiration (mm h-1) from sap flow measurements using Eq. (1) and summed hourly transpiration to obtain daily transpiration (mm day-1). < Fig. S1: Line 156 in the document called “Figures” please > The Penman-Monteith equation (Monteith, 1981) was solved to derive measurements for actual evapotranspiration. (2) Where ∆ is the slope of the saturation vapor pressure curve at air temperature (kPa °C -1), Rn and G are net radiation and soil heat flux (W m-2), ρa is the density of air (kg m-3), cp is the specific heat of air at constant pressure (W kg-1 ºC-1), es and ea are the saturated and actual vapor pressure of the air (kPa), ga is the aerodynamic conductance (mm s-1). Canopy conductance, gc (mm s-1), was estimated from canopy transpiration as (Granier et al., 1996) (3) where λ is the latent heat of vaporization of water (W kg-1). 2.4. Partition of actual evapotranspiration and soil water balance Actual evapotranspiration was partitioned into three components including canopy transpiration (Tc, mm), canopy interception (I, mm), and soil evaporation (Es, mm). The model developed by De Groen (2002) was used to calculate monthly interception. (4) where I is the monthly interception, P is the monthly precipitation, and nr is the number of rainy days per month. The interception capacity of vegetation, Dv (mm day-1), depends on vegetation type and meteorological conditions. It varies from 0.5 mm day-1 for grass to 2 mm day-1 for coniferous forest (De Groen, 2002). Pitman (1973) recommended a value of 0 mm day-1 for bare soil and a value of 8 mm day-1 for densely vegetated area. In our study, a threshold value of 0.2 mm day-1 was used empirically. Then, Es can be determined by (5) Because annual precipitation is very low and the infiltration rate into the sandy soil is high, surface runoff and deep percolation at the study sites were negligible. Soil water balance during measuring period 6

was estimated as (Allen et al., 1998) (6) where ∆SWC is the soil water storage (mm), and GW is the groundwater usage by vegetation (mm). 3. Method 3.1. Advection-Aridity approach Bouchet (1963) first hypothesized that there are complementary feedbacks between ETa and ETp, and related these fluxes to the available energy-limited wet environment evapotranspiration, termed equilibrium evapotranspiration, ETw. The complementary relationship can be expressed as (7) where b is a constant of proportionality. However, in its original formulation, it was not clear how the different terms should be calculated. Morton (1969) and Brutsaert and Stricker (1979) further developed the idea and proposed quantitative approach for estimating ETp, ETw, and ETa on the basis of a symmetric CR where b is unity (Fig. 2). (8) this is the widely accepted Advection-Aridity model, and the ETp term (mm day-1) can generally be defined by the Penman (1948) equation (9) where Ea is the drying power of the air (mm d−1), calculated using Penman’s original Rome wind function (Brutsaert, 1982) (10) where U2 is the measured wind speed at 2 m height (m s-1). < Fig. 2: Line 15 in the document called “Figures” please > The Priestley-Taylor equation (Priestley and Taylor, 1972) is used to estimate the wet environment evapotranspiration rate, ETw (mm day−1), as (11) where α is the well-known Priestley-Taylor coefficient, commonly having a default value of 1.26. 3.2. Estimating actual evapotranspiration with pan evaporation Kahler and Brutsaert (2006) employed class A pan evaporation (ETpan) data to estimate daily actual evapotranspiration. However, they found the assumed symmetric nature of the CR becomes asymmetric.

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(12) Rearrangement of Eq. (12) leads to (13) where c is the pan coefficient, assumed to be unity (Szilagyi, 2007). In this model, the parameter α in Eq. (11) and parameter b in Eq. (12) can be determined by local calibrating. 3.3. Calculating ∆ under wet environment air temperature Szilagyi and Jozsa (2008) argued that ∆ in Eq. (11) should be evaluated at the wet environment air temperature (Twea, °C) as appose to the actual air temperature (Ta, °C) because ETw represents the wet environment evapotranspiration. This modification is very important when the AA model is applied in arid/semiarid regions because of the possible large difference between Twea and Ta. However, it is difficult to determine Twea from nonhumid observations. Szilagyi and Jozsa (2008) proposed that Twea can be approximated by the wet environment surface temperature, Twes (°C). (14) where βw is the Bowen ratio of the wet patch, es(Twes) is the saturated vapor pressure taken at the wet surface temperature (kPa). By applying Eq. (9) with the measured Rn, G, Ta and ea to estimate ETp, all terms are known except for Twes and es(Twes) and therefore can be solved iteratively. When Twes is larger than Ta, Twes should be replaced by Ta (Kahler and Brutsaert, 2006). With Twes estimated, Eq. (11) becomes (15) Now Eq. (7) can be rearranged for estimating ETa as (16) Fig. 3 illustrates the average daily Ta and the computed Twea for the study site, where it is evident that Twea differs significantly from Ta as Ta becomes large. < Fig. 3: Line 27 in the document called “Figures” please > 3.4. Normalization of Complementary Relationship Following Brutsaert (2005), the ETa and ETp values can be normalized by dividing Eq. (7) with ETw to obtain dimensionless expression. (17) (18)

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where EMI is the humidity index (= ETa/ETp). According to previous studies, the use of humidity index EMI provides strong support for the complementary relationship. One drawback of this ratio is that it involves the variables under consideration. Although this can usually not be avoided in the process of nondimensionalization, some more independent moisture indices can be used to investigate the possibility to validate the complementary relationship (Kahler and Brutsaert, 2006). Accordingly, the relationship between ETa and ETP as well as ETpan is tested as a function of two other measured of the moisture status of the surface, namely, the measured soil water content and the antecedent precipitation index of Kohler and Linsley (1951). In this study, soil water content averaged from 0 to 120 cm depth is used to represent soil moisture status in the site rather than surface soil water content (0-20 cm). 3.5. Local calibration of key parameter values in CR In previous studies, a nested trial-and-error method was employed for parameter calibrating (Kahler and Brutsaert, 2006; Szilagyi, 2007). However, the parameter α was calibrated empirically using this method. For example, Ma et al. (2015) determined α value according to 8 days’ observed data with ETa/ETp ranging from 0.90 to 1.07. Obviously, it will results in uncertainties in parameter calibrating and thus large errors on ETa estimation, because on a shorter time interval (such as daily scale) a passing weather front can significantly upset any dynamic equilibrium in the fluxes between the land and atmosphere and cause large variation of the ratio of ETa/ETp. De-Jong (1975) first used the Genetic algorithms (GAs) to solve optimization problem. In recent years, it has been a popular technique for solving hydrology and water resources problems (Chen et al., 2002). We use GA to determine parameter values in CR, which were obtained by finding the minimum of objective function F to determine the best fit for ETa. (19) where Mi is the observed ETa, Ei is the estimated ETa, n is the number of ETa records. According to previous studies, the threshold of parameter α and b was set as 0.1 to 1.5, and 1 to 10, respectively. Data from DOY 152 to DOY 212 in 2014 was used to calibrate parameters, and the remaining data was used to validate CR models. Noting that the daily pan evaporation measured at the Linze Station was just used to validate the model. The model performance was evaluated using the coefficient of determination (R2) of linear regression and the root mean square error (RMSE). 4. Results and Discussion 4.1 Actual evapotranspiration partitioning and groundwater usage by vegetation 9

The annual actual evapotranspiration (ETa) is 227.93 ±52.32 mm in 2014 and 242.36 ±39.41 mm in 2015 during the growing period (Fig. 4). The annual canopy transpiration (Tc) is 167.44 ±45.77 mm in 2014 and 151.87 ±31.35 mm in 2015, which accounted for 73.5 ±20.1% and 62.7 ±12.9% of the total ETa. The annual soil evaporation (Es) is 53.78 ±4.95 mm in 2014 and 83.94 ±6.88 mm in 2015, which accounted for 23.6 ±2.2% and 34.6 ±2.8% of the total ETa. The annual canopy interception (I) is 6.72 ±1.60 mm in 2014 and 6.55 ±1.18 mm in 2015, which only accounted for 2.9 ±0.7% and 2.7 ±0.5% of the total ETa, and for 6.8% and 8.8% of the total precipitation. Zhao et al. (2016) conducted rainfall partition experiments during growing period near our study site, and found that annual I of C. mongolicum community (one of our target species) accounted for 8% of total precipitation. Therefore, the estimated threshold value of 0.2 mm day-1 of interception capacity (i.e. the parameter Dv in Eq. (4)) is reasonable for calculating monthly I. These results show that Tc is the largest component of ETa, following by Es and I. < Fig. 4: Line 42 in the document called “Figures” please > Soil water storage (∆SWC) is -0.15 mm ±0.02 in 2014, and -0.05 ±0.007 mm in 2015 during the growing season. This net loss is offset by inputs of water from melting snow during the dormant season. Groundwater usage by vegetation (GW) is 129.08 ±52.30 mm in 2014, and 167.51 ±39.40 mm in 2015, accounting for 56.7 ±22.9% and 69.1 ±16.3% of total water consumption, respectively. Therefore, groundwater is the largest water source for our study arid shrublands. 4.2. The relationship between actual and potential evapotranspiration Daily observed ETa and calculated ETp values using Penman equation are displayed in Fig. 5a, against the humidity index, ETMI (= ETa/ETp). The result shows that the data points are quite scattered and a CR behavior is not evident, which is mainly because for the same moisture status of the surface widely different evaporation rates are possible, all depending on the atmospheric conditions. As stated by Kahler and Brutsaert (2006), a relationship can be considered truly universal only when it can be expressed in terms of dimensionless variables, which in this case is accomplished by normalizing the ETa and ETp by the ETw. The normalized ETa and ETp as a function of the EMI is shown in Fig. 5b. It is clearly evident that a complementary relationship between ETa and ETp exists, in which the difference between ETa and ETp increases with the decrease in EMI. In addition, the daily ETp and ETa does not converge under the limited soil moisture (i.e. small EMI values), indicating an extremely arid environment in the study area during the measurement period. < Fig.5: Line 57 in the document called “Figures” please > 10

With the assumption of c = 1 in Eq. (13), the daily evaporation rates of the D20 pan at the study site are used to evaluate the relationship with daily observed ETa. Fig. 6a definitely shows some degree of complementary behavior of ETa and ETpan, because large values of ETpan generally appear to correspond with small values of ETa, and vice versa. However, the relationship between the two variables is not very clear, nor very consistent, as the data appear as clouds of points with considerable scatter. The CR between the observed ETa and ETpan becomes more obvious when the dimensionless rates, ETa+ and ETp+, are plotted against the humidity index, ETMI, in Fig. 6b. < Fig. 6: Line 75 in the document called “Figures” please > The data points in Fig. 5b and Fig. 6b definitely show a more pronounced complementary behavior than their unscaled counterparts in Fig. 5a and Fig. 6a, respectively. The theoretical curves obtained with Eq. (13) and Eq. (16) are also shown in Fig. 5b and Fig. 6b, which generally give a good description of these scaled evapotranspiration using the measured air temperature or the iterated wet environment air temperature, Twea. The complementarity of the data and the good agreement with the curves support the notion that with proper calibration the equilibrium evapotranspiration, as defined in Eq. (11) and Eq. (15), can serve as a robust measure of the evaporation from wet surface to normalize ETa and ETp in the context of the complementary concept. We also carry out the analysis with monthly averages of the variables to test the effect of timescale on the values of the parameter. For the available data sets of 11 months, it is found that the monthly values fell nearly perfectly on the curves, and cannot be distinguished from daily values, as described by Fig. 5b and Fig. 6b. Due to limited measurement of long time annual actual evapotranspiration, the analysis is not carried out at annual scale. Applying the soil water content and the antecedent precipitation index, Fig. 7 definitely shows some degree of complementary behavior of ETa and ETp either, although the data points are relatively scattered. When the analysis is carried out at monthly scale, the complementary relationship becomes more evident (data not shown) which indicates that selection of such moisture indices may be more effective at longer temporal scale (such as monthly or annual scale) for illuminating the relationship between ETa and ETp. For instance, Wang et al. (2013) and Zhang et al. (2007) found that the precipitation standardized by ETw was a good indicator to reveal the complementary relationship between these two variables at annual scale. < Fig. 7: Line 92 in the document called “Figures” please > 4.3. Local calibration of parameter b and α in CR 11

Employing Penman equation to calculate potential evapotranspiration, the calibrated b value is 4.76 using Ta for obtaining ETw, and 7.03 using Te. This value becomes 7.93 using Ta and 8.87 using Te when pan evaporation is regarded as a practical measure of ETp. The magnitude of b indicates an asymmetric CR in the study area between ETa and ETP calculated either using Penman equation or pan evaporation. However, using Penman equation to calculate potential evapotranspiration, our asymmetric CR contradicts previous research which applied the calibrated parameter value of α, and obtained a symmetric CR for alpine steppe of the Tibetan Plateau (Ma et al., 2015) and Nevada shrublands (Huntington et al., 2011). It is mainly because the study area was in a heterogeneous arid shrublands, which was affected by strong advection and secondary circulation. In addition, Ma et al. (2015) calculated the drying power of the air in Eq. (10) using the Moin-Obukhov Similarity theory (Monin and Obukhov, 1954) rather than the Rome wind function, which may be another reason for our contrary results. These results indicate the importance of local calibration of key parameters in CR in arid regions. The calibrated α value ranges from 0.38 to 0.44, which is significantly smaller than the typically employed 1.26. Field experiments showed that the value of α was empirically related to soil moisture, and that the value decreased from its standard value for water stressed surfaces (Stannard, 1993). For example, Garcia et al. (2009) reported α values ranging from 0.25 to 1.4 for nearly constant volumetric soil moisture of 0.05 and α values ranging from 0.75 to 1.75 for nearly constant volumetric soil moisture of 0.20. As ETp and ETa is linked by ETw in the AA model, the value of α is very important for accurate ETa estimation. It is therefore necessary to specify α for local conditions, especially for arid environment (Hobbins et al., 2001b). 4.4. Practical application of CR Using Penman equation to estimate potential evapotranspiration, the results of employing the original AA model proposed by Brutsaert and Stricker (1979) and two locally calibrated AA models using the measured air temperature (Ta) to obtain ETw and the iterated wet environment air temperature (Twea) are given in Fig. 8, where R2 is 0.834, 0.834, and 0.845, respectively. It can be seen that the rate of daily ETa is considerably overestimated without local calibration (Fig. 8a). When the calibrated parameters are used, the predicted ETa is close to 1:1 line, and the RMSE significantly decreases from 6.26 mm day-1 to 0.3 mm day-1 (Fig. 8b). The model performance is further improved when Twea is used for obtaining ETw, as reflected by higher R2 and lower RMSE (Fig. 8c). < Fig. 8: Line 107 in the document called “Figures” please > It is not true only for the study desert shrublands that the CR-based ETa estimates can be significantly 12

improved by calibrating the parameters values locally as well as evaluating ∆ at Twea. For instance, Huntington et al. (2011) compared the results of their CR-based ETa estimation method in the shrublands of Nevada, when the air temperature (Ta) was replaced by the Szilagyi and Jozsa’s (2008) estimate of Twea to calculate ETw, they found that the latter improved the ETa estimates. Besides, Szilagyi (2014) also found the bias of the AA model in estimating ETa in a semiarid savanna in Botswana could be reduced from 53% to 23% when Ta was replaced with Twea. Recently, Ma et al. (2015) reported that, when ETw term was evaluated at Twea with calibrated α, the RMSE values for estimating ETa in the alpine steppe decreased from 0.994 to 0.512 mm day-1, and the mean-absolute-error decreased from 0.86 to 0.40 mm day-1. In the present study, the employment of local calibrated α and b as well as Twea together explains the success of ETa estimating by Eq. (16) at the study site. Estimated ETa using pan evaporation is given in Fig. 9. The R2 between the measured and predicted ETa using the original AA model and two calibrated models using Ta to obtain ETw and Twea is 0.593, 0.751, and 0.891, respectively. The daily rate of ETa is overestimated with high RMSE when the original AA model is used (Fig. 9a), while the model performance dramatically improved when the AA model is locally calibrated (Fig. 9b). Evaluating ETw at Twea, the AA model gives the best performance, as reflected by highest R2 and smallest RMSE (Fig. 9c). < Fig. 9: Line 121 in the document called “Figures” please > With calibrated values of α = 0.38 and b = 8.87 and evaluating ∆ at wet environment air temperature, we also analyze the relationship between daily measured ETa and estimated ETa from the D20 aboveground pan and the E601B sunken pan installed at the Linze Station. The result shows that the performance of the D20 pan is not as good as that of the E601B pan (Fig. 10). The former tends to underestimate ETa to some extent with R2 and RMSE values of 0.71 and 0.54 mm day-1, respectively. It is maybe because the exposing side and bottom as well as small size of the D20 aboveground pan induced significant local advection of energy from the surrounding environment, thus resulted in bias in ETa estimating. The R2 and RMSE values yielded from the E601B pan is 0.84 and 0.33 mm day-1, respectively, indicating a much better performance. < Fig. 10: Line 135 in the document called “Figures” please > Vegetation in arid and semiarid regions often depends on underground water. However, only in recent years, the impact of surface water-underground water interaction on vegetation transpiration becomes a subject of major research interest (Kalbus et al., 2006; Xu et al., 2017a, 2017b, 2018). If this dependence were not considered, ETa would be substantially underestimated during the dry season. At this study site, 13

groundwater is the largest water source for plants to absorb and maintain their survival, which accounts for 62.9% of total water consumption during two main growing seasons. It has also been confirmed by root excavation (Xu et al., 2007; Xu et al., 2017b) and oxygen isotopic tracing experiments (Wu et al., 2014; Zhou et al., 2015). Therefore, it is necessary to evaluate whether the CR model can capture the dynamics of groundwater usage by vegetation for improve understanding of eco-hydrological processes and water resource management in desert-oasis ecotone. During the late spring (from DOY 152 to DOY 181) in 2014, ETa increases with increase of soil moisture while transpiration rate is constant. Therefore, increase of ETa is mainly caused by soil evaporation and canopy interception. During early summer (from DOY 182 to DOY 212) the soil moisture is significantly increased because of strong rainfall events and ETa reached the annual maximum, and ETpan is significantly reduced because of the increase in ETa. During midsummer and late summer (from DOY 213 to DOY 243), soil moisture significantly decreases due to limited precipitation and high evaporative demand, while transpiration as well as ETa was fairly constant. The fairly constant rate of transpiration and ETa could attributed to the utilization of groundwater. After that, ETa is continuing to decrease with the end of growing season, and ETpan also decreases with decrease of solar radiation and temperature. Similar results can be found during the main growing season in 2015 (Fig. 11). From Fig. 11b, it can be seen that the modified AA model is able to predict the utilization of groundwater during drying summer, which suggests its capability to resolve special issue occurred in phreatophytic shrublands. However, detailed field experiment need to be conducted for quantifying groundwater usage by vegetation at daily scale in the future. Such work will improve our understanding on vegetation water use strategy and adaption to changing climate in arid regions. < Fig. 11: Line 146 in the document called “Figures” please > This study shows a success in applying the calibrated CR-based AA model to estimate actual evapotranspiration from a desert shrublands, in which a novel estimation of the wet surface temperature is involved. However, there may be some uncertainties about the quantitative results. Xu et al. (2017b) previously found that, the tap root of H. ammodendron extended to 420 cm, the tap root of C. mongolicum extended to120 cm, and the tap root of N. tangutorum extended to160 cm. Due to limited TDR gauges, we are not able to monitor soil moisture for the whole root zone. It will cause some uncertainty on estimation of soil water storage amount and thus groundwater usage amount during two growing seasons. When apply the AA model, the temporal scale is a debated issue. For example, Brutsaert and Striker (1979) and Morton 14

(1983) recommended that the shortest time-period the CR should be applied over is 3-5 days to avoid the influence of the passing weather front on the dynamic equilibrium in the fluxes between land and atmosphere. Kahler and Brutsaert (2006) applied their optimized CR at a daily time step but eliminated days where advection of moist air from a nearby reservoir was suspected. Szilagyi and Jozsa (2008) concluded that application of the AA model at daily or monthly scale did not affect the predicted monthly accumulated ETa values significantly. In our study, we also found the influence of temporal scale on the behavior of CR for the desert shrublands when the soil water content or the antecedent precipitation index was chose as humidity index. In view of these controversial results, more relevant work should be done to obtain more realistic conclusion for long-term variations of evaporation, which is left for future research. 5. Conclusion In the present study, daily actual evapotranspiration from an arid shrublands was compared with the Penman-calculated potential evapotranspiration and pan evaporation. Analysis of these data in the framework of the complementary concept has produced the following findings. 1.

The average ETa is 229.32 ±45.86 mm during two growing seasons, while canopy transpiration, soil evaporation, and canopy interception accounts for 68.1 ±16.5%, 29.1 ±2.5% and 2.8 ±0.6%, respectively. Groundwater is the largest water source for our studied arid shrublands.

2.

When parameters in the CR-based AA model are locally calibrated, the accuracy of ETa estimation is significantly increased. The model performance is further improved when the wet surface temperature is introduced as opposed to the measured air temperature to calculate wet environment evapotranspiration.

3.

Applying the calibrated parameters, the E601B sunken pan performs better than the D20 aboveground pan. Moreover, the modified AA model is able to predict the utilization of groundwater by vegetation during drying summer.

These findings address the importance of local calibration of the CR-based model and reveal its capability to resolve special issue occurred in phreatophytic shrublands. It will promote better understanding of the water and energy budget and can also provide beneficial reference to water resource and eco-environment management in arid regions.

Acknowledgements

This work was funded by the National Key R&D Program of China (Grant No. 2016YFC0402710, 15

2016YFC0402706) and the National Natural Science Foundation of China (Grant No. 41771041, 41271036, 41323001, 51539003, 41471016).

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Fig. 1. Map of study area

Fig. 2. Theoretical symmetric (b = 1) and asymmetric (b > 1) complementary relationship. The ETw is the wet environment evapotranspiration. The ETa+ and ETp+ are normalized actual evapotranspiration and potential evapotranspiration. EMI is a normalized evaporative moisture index (= ETa/ETp). The black line represents the theoretical value of ETa+ and ETp+, where b = 1; the red, green, blue and cyan line represents the theoretical value of ETa+ and ETp+, where b = 2, b = 3, b = 4, b = 5, respectively.

Fig. 3. Daily air temperature (Ta) plotted against calculated wet environment air temperature (Twea).

Fig. 4. Inter-annual amount of actual evapotranspiration (ETa), canopy transpiration (Tc), soil evaporation (Es), and canopy interception (I).

Fig. 5. (a) Plots of the measured actual (ETa) and Penman potential (ETp) evapotranspiration against the humidity index, EMI (= ETa/ETp). (b) Plots of the normalized ETa (ETa+) and ETp (ETp+) plotted against EMI. The solid line and dash line represent the theoretical curves using the measured air temperature (Ta) for obtaining ETw (The optimized b equals 4.76) and the iterated wet environment air temperature (Twea) (The optimized b equals 7.04), respectively.

Fig. 6. (a) Plots of the measured actual evapotranspiration (ETa) and pan evaporation (ETpan) against the humidity index, EMI (= ETa/ETpan). (b) Plots of the normalized ETa and ETpan plotted against EMI. The solid line and dash line represent the theoretical curves using the measured air temperature (Ta) for obtaining ETw (the optimized b equals 7.93) and the iterated wet environment air temperature (Twea) (the optimized b equals 8.87), respectively.

Fig. 7. Normalized daily actual (ETa+) and potential (ETp+) evapotranspiration rates calculated from (a) Penman equation and (b) pan evaporation plotted against the soil water content. Normalized daily actual (ETa+) and potential (ETp+) evapotranspiration rates calculated from (c) Penman equation and (d) pan evaporation plotted against the antecedent precipitation index.

Fig. 8. Scatter plots of daily transpiration simulated from (a) the original AA model, and the calibrated AA model using (b) measured air temperature for obtaining ETw and (c) iterated wet environment air temperature compared to measured actual evapotranspiration (ETa). Penman equation was used to calculate potential evapotranspiration. 21

Fig. 9. Scatter plots of daily transpiration simulated from (a) the original AA model, and the calibrated AA model using (b) measured air temperature for obtaining ETw and (c) iterated wet environment air temperature compared to measured actual evapotranspiration (ETa). Pan evaporation was regarded as a practical measure of potential evapotranspiration.

Fig. 10 Scatter plots of daily measured actual evapotranspiration (ETa) compared to estimated ETa with calibrated values of α = 0.38 and b = 8.87 for the (a) D20 evaporation pan and (b) E601B evaporation pan at Linze Station.

Fig. 11. Temporal variations of (a) pan evapotranspiration (ETpan), (b) measured stand transpiration (Tr), actual evapotranspiration (ETa), and estimated ETa from modified AA model with calibrated parameter value of α = 0.38 and b = 8.87 which gives the best fittings, and (d) precipitation and soil water content.

Fig. S1. The Frequency distribution of stem diameter in 1-cm, 0.1-cm, and 0.5-cm classes for (a) H. ammodendron, (b) N. tangutorum, and (c) C. mongolicum in the 1-ha study plot (Ji et al., 2016).

22

Fig. 1. Map of study area

23

Fig. 2. Theoretical symmetric (b = 1) and asymmetric (b > 1) complementary relationship. The ETw is the wet environment evapotranspiration. The ETa+ and ETp+ are normalized actual evapotranspiration and potential evapotranspiration. EMI is a normalized evaporative moisture index (= ETa/ETp). The black line represents the theoretical value of ETa+ and ETp+, where b = 1; the red, green, blue and cyan line represents the theoretical value of ETa+ and ETp+, where b = 2, b = 3, b = 4, b = 5, respectively.

24

Fig. 3. Daily air temperature (Ta) plotted against calculated wet environment air temperature (Twea).

25

Fig. 4. Inter-annual amount of actual evapotranspiration (ETa), canopy transpiration (Tc), soil evaporation (Es), and canopy interception (I).

26

Fig. 5. (a) Plots of the measured actual (ETa) and Penman potential (ETp) evapotranspiration against the humidity index, EMI (= ETa/ETp). (b) Plots of the normalized ETa (ETa+) and ETp (ETp+) plotted against EMI. The solid line and dash line represent the theoretical curves using the measured air temperature (Ta) for obtaining ETw (The optimized b equals 4.76) and the iterated wet environment air temperature (Twea) (The optimized b equals 7.04), respectively.

Fig. 6. (a) Plots of the measured actual evapotranspiration (ETa) and pan evaporation (ETpan) against the humidity index, EMI (= ETa/ETpan). (b) Plots of the normalized ETa and ETpan plotted against EMI. The solid line and dash line represent the theoretical curves using the measured air temperature (Ta) for obtaining ETw (the optimized b equals 7.93) and the iterated wet environment air temperature (Twea) (the optimized b equals 8.87), respectively.

27

Fig. 7. Normalized daily actual (ETa+) and potential (ETp+) evapotranspiration rates calculated from (a) Penman equation and (b) pan evaporation plotted against the soil water content. Normalized daily actual (ETa+) and potential (ETp+) evapotranspiration rates calculated from (c) Penman equation and (d) pan evaporation plotted against the antecedent precipitation index.

28

Fig. 8. Scatter plots of daily transpiration simulated from (a) the original AA model, and the calibrated AA model using (b) measured air temperature for obtaining ETw and (c) iterated wet environment air temperature compared to measured actual evapotranspiration (ETa). Penman equation was used to calculate potential evapotranspiration.

29

Fig. 9. Scatter plots of daily transpiration simulated from (a) the original AA model, and the calibrated AA model using (b) measured air temperature for obtaining ETw and (c) iterated wet environment air temperature compared to measured actual evapotranspiration (ETa). Pan evaporation was regarded as a practical measure of potential evapotranspiration.

Fig. 10 Scatter plots of daily measured actual evapotranspiration (ETa) compared to estimated ETa with calibrated values of α = 0.38 and b = 8.87 for the (a) D20 evaporation pan and (b) E601B evaporation pan at Linze Station. 30

Fig. 11. Temporal variations of (a) pan evapotranspiration (ETpan), (b) measured stand transpiration (Tr), actual evapotranspiration (ETa), and estimated ETa from modified AA model with calibrated parameter value of α = 0.38 and b = 8.87 which gives the best fittings, and (d) precipitation and soil water content.

31

Fig. S1. The Frequency distribution of stem diameter in 1-cm, 0.1-cm, and 0.5-cm classes for (a) H. ammodendron, (b) N. tangutorum, and (c) C. mongolicum in the 1-ha study plot (Ji et al., 2016).

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Graphical abstract: Modification of the Advection Aridity (AA) model significantly improve its performance in estimating daily actual evapotranspiration from an arid shrublands.

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Highlights Actual evapotranspiration from an arid shrublands was partitioned into three components. Local calibration and introducing wet environment air temperature significantly improved the performance of the AA model. The E601B sunken pan performed better than the D20 aboveground pan. The modified AA model was able to predict the usage of groundwater by desert shrubs.

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