# A Critical Evaluation on the Role of Aerodynamic and Canopy–Surface Conductance Parameterization in SEB and SVAT Models for Simulating Evapotranspiration: A Case Study in the Upper Biebrza National Park Wetland in Poland

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## Abstract

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_{A}and g

_{S}) for heat and water vapor transfers. This study critically assessed the impact of conductance parameterizations on ET simulation using three structurally different SEB and SVAT models for an ecologically important North-Eastern European wetland, Upper Biebrza National Park (UBNP) in two consecutive years 2015 and 2016. A pronounced ET underestimation (mean bias −0.48 to −0.68 mm day

^{−1}) in SEBS (Surface Energy Balance System) was associated with an overestimation of g

_{A}due to uncertain parameterization of momentum roughness length and bare soil’s excess resistance to heat transfer (kB

^{−1}) under low vegetation cover. The systematic ET overestimation (0.65–0.80 mm day

^{−1}) in SCOPE (Soil Canopy Observation, Photochemistry and Energy fluxes) was attributed to the overestimation of both the conductances. Conductance parameterizations in SEBS and SCOPE appeared to be very sensitive to the general ecohydrological conditions, with a tendency of overestimating g

_{A}(g

_{S}) under humid (arid) conditions. Low ET bias in the analytical STIC (Surface Temperature Initiated Closure) model as compared to SEBS/SCOPE indicated the critical need for calibration-free conductance parameterizations for improved ET estimation.

## 1. Introduction

_{A}and g

_{S}) for heat and water transfer. Previous studies showed ±25% error in simulated SEB fluxes due to the use of different g

_{A}and g

_{S}parameterizations [18]. Some of the major bottlenecks in retrieving g

_{A}and g

_{S}for simulating ET through SEB models are, (a) the lack of a benchmark parameterization to estimate both the conductances across a broad range of hydrometeorological and vegetation cover conditions [19,20,21,22], (b) the use of empirical response functions to characterize the conductances at the canopy-scale that have uncertain transferability in space and time [23,24,25], and (c) the sensitivity of the empirical models of g

_{A}and g

_{S}to different calibration parameters [20,25]. An extended description of g

_{A}–g

_{S}uncertainties are given in Section 3.

_{S}) is combined with radiation, meteorological, and vegetation index or leaf area index to simulate the sensible and latent heat fluxes (H and λE) [12,13]. In the SEB models, λE is derived either as a residual of the SEB or through partitioning of the net available energy (ϕ) (i.e., net radiation, R

_{N}—soil heat flux, G) [14,15,16]. One-source [19] and two-source [17,26] SEB models can be differentiated, which either simulate lumped λE from the canopy-substrate complex (one-source) or λE from canopy and substrate individually (two-source). Contrarily, SVAT models also simulate λE but without the need of any a priori Ts information, instead the SVAT models simultaneously simulate λE, H, and Ts through SEB subroutines. While SEB and SVAT models have been extensively used for understanding the hydrological and environmental impact on ET in various parts of the world [27,28,29,30,31,32], their performance has not been rigorously compared in the wetlands, particularly in the European wetland such as in the Upper Biebrza National Park (UBNP).

- What is the performance of the three structurally different SEB/SVAT models in the UBNP wetland when simulated with high temporal frequency measurements?
- What are the effects of aerodynamic and surface conductances parameterizations and associated state variables in determining the model errors with respect to ET?
- To what extent the ET modelling errors and conductance parameterizations are impacted by a range of environmental and ecohydrological conditions?

## 2. Materials and Methods

#### 2.1. Model Description

_{0M}is critical. In this study we used NDVI (Normalized Difference Vegetation Index) to compute z

_{0M}[62]. Using five (March, April, June, July, and August) Landsat-8 Near Infra-red (NIR) and Red reflectance spectral bands, we computed NDVI as NDVI = (NIR − Red)/(NIR + Red). We proceeded to interpolate the NDVI into 8-day composites and assigned each day to the nearest distance based on the observed trend.

#### 2.2. Uncertainties in g_{A} and g_{S} Parameterizations in SEB and SVAT

_{S}to constrain the energy-water fluxes [16,28,63]. The central aspect of contemporary SEB simulation is based on estimating g

_{A}and sensible heat flux (H), while solving λE as a residual SEB component. Estimation of g

_{A}relies on the Monin–Obukhov Similarity Theory (MOST) or Richardson Number (Ri) criteria, and g

_{A}estimates are subjected to uncertainties due to (a) empirical approximation of the displacement height (d

_{0}) either as a simple function of vegetation height or leaf area index [64,65], (b) uncertainties in estimating the roughness length of momentum transfer (z

_{0M}) and associated surface geometry [66], (c) challenges in accommodating the aerodynamic versus surface temperature inequalities, and (d) complexities in kB

^{−1}parameterization [67,68] to compensate for the differences in the scalar roughness lengths of heat (z

_{0H}) and momentum (z

_{0M}) transfer. The parameters d

_{0}, z

_{0M}, z

_{0H}, and kB

^{−1}are the highly variable components in SEB models, and the commonly used empirical response functions of these components to characterize g

_{A}have an uncertain transferability in space and time [69,70]. An extended description of the impacts of ambiguous parameterization of d

_{0}, z

_{0M}, kB

^{−1}on ET estimates is detailed by [67,71,72].

_{S}model matches best with the observed surface energy balance fluxes [74]. Therefore, there is a critical need to assess the impact of aerodynamic and canopy–surface conductance representation on the performance of SEB and SVAT models.

#### 2.3. Eddy Covariance Estimation of g_{A} and g_{S} for Model Evaluation

_{A}measurements, a rigorous evaluation of g

_{A}from the models is challenging. However, an indirect evaluation of g

_{A}retrievals from the three models was performed using the micrometeorological measurements from the EC towers. By using the measured friction velocity (u*) and wind speed (u) at the EC towers and using the equation of [75] we estimated g

_{A}as the sum of turbulent conductance and canopy (quasi-laminar) boundary-layer conductance as follows.

_{A}(EC tower) = [(u/u*

^{2}) + (2/ku*

^{2})(Sc/Pr)

^{0.67}]

^{−1}

_{A}, a direct evaluation modeled g

_{S}could not be performed, as independent ecosystem-scale g

_{S}observations are not possible with current measurement techniques. Assuming u*-based g

_{A}as the baseline aerodynamic conductance, we estimated g

_{S}by inverting the Penman-Monteith equation [76] to evaluate the modeled g

_{S}. Here u*-based g

_{A}was used in conjunction with the net available energy, λE, air temperature, and humidity measurements from the EC towers [57] as follows.

_{N}− G is the net available energy, ρ and c

_{p}are the density and specific heat of air, respectively.

_{S}. However, from the estimated g

_{A}and λE (of SEBS), an inverse estimation of SEBS-based g

_{S}was also performed for comparing with the EC g

_{S}estimates in the framework of Penman-Monteith equation.

#### 2.4. Study Site: Ecological and Hydrological Significance of UBNP Wetland

^{−1}and evapotranspiration between 460 and 480 mm year

^{−1}[40]. It is located 230 km North East of Warsaw being serviced by the Biebrza River which is a right sided tributary of the Narew River. The UBNP wetland is situated within the upper Biebrza river catchment (22°30′–23°60′ E, 53°30′–53°75′ N). While the lower part of Biebrza experiences a sequence of flood events often after snowmelt in early spring, the upper part of the Biebrza river basin rarely experiences flooding. Most part of the surface runoff takes place within the drainage network [46]. During the dry periods, the wetland is groundwater fed. Most part of the surface runoff in UBNP takes place within the drainage network [46].

#### 2.5. Datasets

_{N}, λE, H, and G), shortwave and longwave radiation components (RS

_{in}, RS

_{out}, RL

_{in}, RL

_{out}), and hydrometeorological variables (e.g., T

_{A}, R

_{H}, u, u*, θ, and P). Assuming nighttime ET to be negligible in the wetland [10,81], daily ET (in mm) was computed by integrating half-hourly λE from sunrise to sunset (corresponds to positive magnitude of RS

_{in}). However, it is also important to mention that wetlands in the arid and semi-arid regions could show substantial amount of ET during night and careful daily ET averaging is needed in such cases [82]. Weekly ET (in mm) was computed by summing daily ET. We did not perform any gap filling, which implies that missing observed or estimated sub-daily or daily ET values were not included in the computation. The energy balance closure of the EC site was 92% and the surface energy balance was closed using the Bowen ratio energy balance method as described in [27,56,83].

_{s}) was assumed to be 0.98 and Ts was computed by inverting the longwave radiation measurements as follows.

#### 2.6. Model Evaluation and Comparison

^{2}), the root mean square error (RMSE), the mean absolute percentage deviation (MAPD), the regression slope, and the regression intercept, respectively.

_{i}and p

_{i}are observed and estimated λE and ET; $\overline{{o}_{i}}$ is the mean of observations.

#### 2.7. Relationship between ET Modeling Errors, Conductances, and Ecohydrological Factors

_{P}/P) [84] which are considered to represent the general ecohydrological characteristics of ecosystems. UBNP wetland ecosystem generally has high magnitude of soil moisture and low E

_{P}/P (low evaporative demand and high precipitation). Therefore, an independent assessment of the effects of E

_{P}/P and θ on the predictive capacity of the SEB and SVAT models is crucial. Results of the correlation analysis between MB in weekly ET with weekly θ and weekly E

_{P}/P are presented in Section 3.3, and discussions on the effects of θ and weekly E

_{P}/P on the biophysical conductance simulations are elaborated in Section 5.

## 3. Results

#### 3.1. Statistical Intercomparison of the Conductances and λE (ET) Estimates from SCOPE1.7, STIC1.2 and SEBS Models

#### 3.1.1. Evaluation of g_{A} and g_{S} Estimates from Models

_{A}is illustrated in Figure 3a combining data from both the years. While the estimated g

_{A}values ranged between 0–0.06 m s

^{−1}for STIC1.2 and SEBS, it was 0–0.6 m s

^{−1}for SCOPE1.7, with R

^{2}ranged between 0.13 to 0.80 between the tower-observed g

_{A}and modelled g

_{A}. Statistical comparisons between the models revealed that although SCOPE1.7 had a good R

^{2}, but the magnitude of g

_{A}from SCOPE1.7 is ten times higher with respect to the tower observations. As seen in Figure 3a, there appears to be a strong systematic bias in SCOPE1.7 g

_{A}which led to very high BIAS and MAPD. Overall, the mean bias and MAPD in modeled g

_{A}varied between 0.003–0.12 m s

^{−1}and 81 to 93%, respectively.

_{S}is presented in Figure 3b and the estimated values ranged between 0–0.06 m s

^{−1}for STIC1.2, 0–0.2 m s

^{−1}for SCOPE1.7, and 0–0.01 m s

^{−1}for SEBS. The magnitude of R

^{2}varied from 0.15–0.53, with mean bias and MAPD of −0.004–0.1 m s

^{−1}and 73–86%, respectively. Like g

_{A}, a systematic overestimation of g

_{S}was also found in SCOPE1.7 which is consequently revealed in very high mean bias and MAPD.

#### 3.1.2. Evaluation of λE (ET) Estimates from Models

^{2}= 0.80–0.91) and 91–92% (R

^{2}= 0.91–0.92) of the variations in observed λE for the entire growing season in both years (Figure 4a,b). Seasonal evaluation of the models revealed marginal differences between STIC1.2 and SCOPE1.7 performance in both years, although both models captured relatively low λE variations (R

^{2}= 0.74 and 0.90) in summer 2015 as compared to the summer 2016 (Figure 4c–f).

^{2}= 0.67–0.80) and seasonally (R

^{2}= 0.62–0.83) in both years (Figure 4). Comparison of the statistical error metrics of the model performance (Table 2) revealed SEBS to produce the highest RMSE (62–75 W m

^{−2}) and MAPD (24–46%) (for the entire growing season as well as summer and spring), followed by SCOPE1.7 (37–52 W m

^{−2}, 22–32%) and STIC1.2 (29–31 W m

^{−2}, 18–19%). As evident from the slope of the linear regressions and mean bias (Table 2), while SEBS and STIC1.2 underestimated λE; SCOPE1.7 had overestimated λE in both years, regardless of the season.

^{−1}) (Figure 5) showed large variability in day-to-day ET during the summer months (June–July) (1–7 mm) which is reasonably captured by all the models. Maximum ET was found to occur during June–July (7 mm) and minimum ET was observed during spring (1–3 mm). Among the three models, SEBS revealed consistent underestimation which was more pronounced during the spring. However, SEBS captured the daily ET trend slightly better than the other two models during the dry-down phase of late summer in the year 2016, whereas SCOPE1.7 (STIC1.2) revealed substantial (little) overestimation tendency during this period.

^{2}and RMSE of SCOPE1.7 (and STIC1.2) to be 0.87–0.95 (0.89–0.92) and 0.89–0.92 mm day

^{−1}(0.37–0.46 mm day

^{−1}) (Table 3), with a consistent overestimation (underestimation) of daily ET from SCOPE1.7 (STIC1.2). While the MAPD of STIC1.2 varied between 16–21%, it was 38–44% for SCOPE1.7, and both models showed relatively high MAPD in 2016. For SEBS, the RMSE and MAPD in daily ET was 0.74–0.95 mm and 33–40%, respectively (Table 3).

#### 3.2. Effects of Biophysical Conductance Parameterization on Residual Error of the Models

_{λE}) (= predicted − observed) for different classes of simulated conductances, T

_{0}and T

_{c}for STIC1.2 and SCOPE1.7. Since SEBS does not simulate the surface conductance, the model errors for SEBS are assessed by relating Δ

_{λE}with the aerodynamic conductance, kB

^{−1}and z

_{0M}.

_{λE}from SCOPE1.7 (Δ

_{λE}SCOPE1.7 hereafter) had a significantly positive relationship with the simulated canopy temperature (T

_{c}) (r = 0.46, p-value < 0.05), and a systematic overestimation of λE (Δ

_{λE}SCOPE1.7 increased exponentially) with T

_{c}was evident when T

_{c}increased from 10 to 30 °C (Figure 6a). However, Δ

_{λE}SCOPE1.7 was found to be moderately correlated (r = 0.22 and r = 0.32 for g

_{A}and g

_{S}respectively) with the two biophysical conductances (Figure 6a). The residual λE error from SEBS (Δ

_{λE}SEBS hereafter) was inversely related to g

_{A}and kB

^{−1}(Figure 6b). Here, a systematic underestimation of λE was evident with increasing g

_{A}and kB

^{−1}(Figure 6b) with a correlation of −0.55 and −0.27 (p-value < 0.05, significant), respectively. The mean residual λE error from STIC1.2 (Δ

_{λE}STIC1.2 hereafter) showed an increasing pattern with an increase in g

_{A}and g

_{S}(Figure 6c) having correlation of 0.35 and 0.27 (p-value < 0.05), respectively. However, Δ

_{λE}STIC1.2 appeared to be heteroscedastic with an increase in T

_{0}, which signifies unequal variability of Δ

_{λE}STIC1.2 as the value of T

_{0}increases (Figure 6c).

#### 3.3. Effects of Environmental and Ecohydrological Factors on the Model Performances

_{S}and vegetation index) variables in determining the residual λE error (Δ

_{λE}= predicted − observed) of the individual models through principal component regression (PCR) analysis. This will be followed by assessing the role of general ecohydrological conditions on the weekly ET bias from the individual models.

_{λE}) versus T

_{S}, T

_{A}, ϕ, R

_{H}, u, and normalized difference vegetation index (NDVI) revealed T

_{S}, T

_{A}, ϕ, to be the first principal component (PC1) whereas R

_{H}and u to be the second principal component (PC2) affecting Δ

_{λE}variance in all the three models in both the years (Figure 7). For all the models, the first principal components (PC1), which is on the horizontal axis, had positive coefficients for T

_{S}, T

_{A}, ϕ, and u (exception SCOPE1.7 for year 2016 where u had negative coefficient). Therefore, vectors are directed into the right half of the plot. It is also surprising to see that despite STIC1.2 was not driven by wind speed, there is an apparent relationship between Δ

_{λE}and u in STIC1.2 due to a strong relationship between u and T

_{S}. For all the models, maximum PC1 loading was found for T

_{S}and T

_{A}followed by ϕ (Figure 7) where their correlation with Δ

_{λE}varied between 0.45–0.50 (for T

_{S}), 0.40–0.45 (T

_{A}), and 0.30–0.40 (ϕ), respectively (Figure 7). Relatively high effects of wind speed (u) on the Δ

_{λE}variance were reflected in the second principal component axis (PC2) for SEBS (Figure 7b,c) followed by STIC1.2 and SCOPE1.7, with correlation varying from 0.40 to 0.60.

^{3}m

^{−3}), followed by a progressive overestimation of weekly ET (2–3 mm/week) with increasing θ (θ > 0.75 m

^{3}m

^{−3}) (r = 0.24, p-value < 0.05) (Figure 8a). While SCOPE1.7 showed a general overestimation tendency in weekly ET across the entire range of soil moisture (2–8 mm/week), scatters of STIC1.2 revealed predominant underestimation of ET (0–(−5) mm/week) up to θ range of 0.7–0.8 m

^{3}m

^{−3}after which a moderate overestimation in weekly ET was noted (Figure 8a). A consistent positive bias in weekly ET from SCOPE1.7 (2–8 mm/week) was evident with increasing climatological dryness (E

_{p}/P) with a significant correlation of 0.27 (p-value < 0.05) (Figure 8b); whereas ET underestimation tendency in SEBS was reduced with increasing E

_{p}/P ratio (Figure 8b). Contrarily, STIC1.2 showed an overestimation tendency in weekly ET (positive bias) (2–6 mm/week) for low E

_{p}/P which progressively declined with increasing E

_{p}/P ratio, with a correlation of 0.21 (p-value < 0.05).

## 4. Discussion

#### 4.1. Effects of Model Structure and Biophysical Parameterizations on Residual λE or ET Errors

_{A}and g

_{S}(Figure 6). Uncertainty in the relationship between thermal infrared temperature (T

_{S}) and aggregated moisture availability (M) in STIC1.2 could be a considerable source of underestimation of the conductances which is reflected in the simulation of λE (and ET) through STIC1.2. In STIC1.2, M is modeled as a fraction of the dewpoint temperature difference between the evaporating front and atmosphere (T

_{0D}–T

_{D}) and of infrared temperature—dewpoint differences between surface to atmosphere (T

_{S}–T

_{D}), weighted by two different slopes of saturation vapor pressure temperature relationships (s

_{1}and s

_{2}; equation S26 in [56], [M = s

_{1}(T

_{0D}− T

_{D})/s

_{2}(T

_{S}− T

_{D})]. The estimation of T

_{0D}plays a critical role in the water unlimited wetland ecosystem because estimation of T

_{0D}further requires sound estimation of s

_{1}. From the definition, s

_{1}is the slope of the saturation vapor pressure versus temperature curve between the evaporating front and air [s

_{1}= (e

_{0}− e

_{A})/(T

_{0D}− T

_{D})]. However, in the wetland, e

_{0}tends to approach saturation vapor pressure of wet surface and s

_{1}tend to be the slope of the wet surface to air saturation-vapor pressure versus temperature. In the present case, the estimates of s

_{1}as a function of air dewpoint temperature (T

_{D}) tend to be lower than the possible s

_{1}-limits for the water-unlimited surfaces, which is likely to introduce underestimation errors in T

_{0D}[56,57]. Underestimation of s

_{1}and T

_{0D}would also lead to an underestimation of M (through the denominator in equation S26 in [56], thus leading to an underestimation of the conductances and λE. As demonstrated by [56], the ratio of g

_{S}/g

_{A}increases with increasing M and the sensitivity of g

_{S}to M is substantially higher as compared to the sensitivity of g

_{A}to M. An underestimation M would lead to an underestimation of g

_{S}, and consequently an overestimation of the denominator [i.e., s + γ(1 + g

_{A}/g

_{S})] in the Penman-Monteith equation (because g

_{A}/g

_{S}in the denominator is overestimated). Thus underestimation errors could be introduced in λE simulation in STIC1.2 for high soil moisture conditions.

_{A}(as seen in Figure 3a). The impact of g

_{A}and associated roughness length parameterization (z

_{0M}and kB

^{−1}) is therefore evident in the residual λE error in SEBS (Figure 6). In SEBS, z

_{0M}is estimated as a function of the leaf area index and vegetation index [77], and low values of both the variables in the start of the growing season would tend to an underestimation of z

_{0M}, which would lead to an overestimation of kB

^{−1}and g

_{A}, and an underestimation of λE (as see in Figure 6). Despite the strong dependence of kB

^{−1}on T

_{S}, radiation, and meteorological variables [64]; no common consensus on a physically-based model for both z

_{0M}and kB

^{−1}is available [67,68]. Empirical parameterization of z

_{0M}and ±50% uncertainties in z

_{0M}can also lead to 25% errors in g

_{A}estimation [18,64,77], which would lead to more than 30% uncertainty in ET estimates. This is also evident from the semi-exponential pattern between z

_{0M}and mean Δ

_{λE}SEBS (Figure 6b) that showed a positive correlation (r = 0.26, p-value < 0.05). Major λE differences for kB

^{−1}range greater than 6 (typical range for the wet/saturated surfaces) (Figure 6b) indicates uncertainties in kB

^{−1}parameterization for simulating λE in the water-unlimited extremes. This is further reflected in the weekly ET bias versus soil moisture and E

_{p}/P scatters (Figure 8) where a negative bias was found for low values of soil moisture and E

_{p}/P ratio, conditions that presumably exist in the start of the growing season.

_{r}) which was estimated by scaling the actual sensible heat flux (H) with the sensible heat fluxes for the driest (H

_{dry}) and wettest (H

_{wet}) conditions [Λ

_{r}= 1 − (H − H

_{wet})/(H

_{dry}− H

_{wet}); and H

_{dry}= Rn − G] [19]. In the start of the growing season (spring), when λE is low, any condition that produces H ≈ H

_{dry}would tend to simulate substantially low relative evaporation (Λ

_{r}≈ 0), and λE will be consequently underestimated (Figure 9a). As seen in Figure 9b, the residual daily ET error (Δ

_{ET}) in SEBS had a rather linear relationship with daily Λ

_{r}(r = 0.35–0.37, p-value < 0.05) and a systematic underestimation in daily ET (up to − mm day

^{−1}) was revealed for 0 < Λ

_{r}< 0.4.

_{wet}) and associated aerodynamic conductance in the wet limits (g

_{Awet}) are also responsible for the systematic underestimation of λE and ET in SEBS (Figure 9c,d). A consistent negative bias in daily ET was evident (−1 to −2 mm day

^{−1}) for high magnitude of H

_{wet}(Figure 9c) [r = (−0.29)–(−0.31), p-value < 0.05]. This was mainly due to the inverse exponential relationship between H

_{wet}and g

_{Awet}(inset of Figure 9d) which was consequently propagated in ET as evident from the scatter between Δ

_{ET}versus g

_{Awet}[r = (−0.15)–(−0.19), p-value < 0.05] (Figure 9d).

_{A}estimation in SCOPE1.7 is also based on the Monin–Obukhov Similarity Theory and similar empirical sub-models for the roughness lengths (z

_{0M}and z

_{0H}) [58]. Therefore, the errors in λE and ET in SCOPE1.7 due to large overestimation of g

_{A}appear to be similar to SEBS. However, an additional source of uncertainty in SCOPE1.7 is due to a consistent overestimation of g

_{S}(Figure 3b) which was consequently propagated into overestimation of λE. In SCOPE1.7, g

_{S}parameterization is based on the Ball-Woodrow-Berry (BWB) g

_{S}-photosynthesis model [85]. BWB model was originally developed at the leaf-scale and no universally agreed scaling method is available to extrapolate this model for the ecosystem scale [86]. Photosynthesis simulation in SCOPE1.7 depends on the calibration of V

_{cmax}(i.e., maximum carboxylation capacity) [87], parameter for dark respiration, Extinction coefficient for vertical profile of V

_{cmax}. Uncertainty in photosynthesis simulation in SCOPE1.7 would lead to erroneous g

_{S}(due to the g

_{S}-photosynthesis feedback in the model) and λE. The major problem of using BWB or BWB-Leuning class of models is that they are valid only for saturated soil water conditions and cannot accommodate the soil drying process or when the soil drying is coupled with high atmospheric vapor pressure deficit. However, there are new generation g

_{S}models that could be used to predict stomatal conductance during soil dry-down when accounting for the soil-xylem hydraulics and detailed plant physiological attributes [88,89,90,91]. Assessing the photosynthesis related uncertainty in SCOPE1.7 is beyond the scope of this study, but, the consistent overestimation tendency in ET (Figure 8b) indicates the uncertainty in g

_{S}and g

_{A}simulation (Figure 3) under high atmospheric aridity (high E

_{P}and low P) (Figure 10 below) to be one of the main sources of errors in SCOPE1.7.

#### 4.2. Effects of Ecohydrological Conditions on Conductance Estimation and Implication on Model Performances

_{p}/P ratio (as seen in Figure 8), the effects of ecohydrological conditions on the two biophysical conductance retrievals are presented in Figure 10, which showed the scatters between weekly g

_{S}/g

_{A}ratio from STIC1.2 and SCOPE1.7 with weekly θ and E

_{p}/P ratio. For STIC1.2, a weak and nearly invariant relationship (r = 0.02, p-value > 0.05) was found between g

_{S}/g

_{A}ratio versus θ (Figure 10a). Since the soil moisture was predominantly high (to the level of saturation) in the UBNP wetland, the conductances retrieved through STIC1.2 appeared to be unaffected due the underlying soil moisture conditions. However, g

_{S}/g

_{A}ratio from STIC1.2 progressively diminished with increasing E

_{p}/P (Figure 10b) with a significant correlation (r = 0.64, p-value < 0.05), which means low g

_{S}as compared to g

_{A}with increasing atmospheric aridity and evaporative demand. This further emphasizes the uncertainties due to surface moisture characterization in STIC1.2 especially the assumptions associated with the slope of temperature-vapor pressure relationship as described in Section 6.1. For SCOPE1.7, although g

_{S}/g

_{A}ratio varied between 0.8–1.0 for the entire range of soil moisture, but, there was a significantly positive relationship (r = 0.41, p-value < 0.05) between SCOPE1.7-derived g

_{S}/g

_{A}ratio with E

_{p}/P. This signifies relatively high values of g

_{S}(as compared to g

_{A}) with increasing evaporative demand (and atmospheric aridity). The tendency of simulating high g

_{S}as compared to g

_{A}with increasing evaporative demand (i.e., high E

_{P}) was eventually propagated into an overestimation of λE (and ET) in SCOPE1.7. With the progress of the growing season from spring onwards, an increase in the atmospheric vapor pressure deficit, air temperature and radiative load led to an increase in the evaporative demand of the atmosphere where λE overestimation (due to g

_{S}) was predominant.

_{0M}and kB

^{−1}that is eventually propagated to z

_{0H}[77]. To further understand the role of general ecohydrological conditions on g

_{A}simulation and its impact on ET estimation in SEBS (SEBS does not simulate g

_{S}), the scatterplots of weekly kB

^{−1}versus weekly soil moisture and E

_{p}/P ratio are also showed in Figure 10. This figure highlights a significant impact of these two ecohydrological factors on the estimation of kB

^{−1}(r = −0.26 to −0.29, p-value < 0.05). The prevailing soil moisture and E

_{p}/P ratio in the UBNP wetland during the start of the spring typically varying between 0.7–0.8 m

^{3}m

^{−3}and 0–2 and the underestimation tendency of SEBS is maximally noted in this range of soil moisture and E

_{p}/P ratio. Majority of the λE (ET) underestimation was evident when kB

^{−1}values exceeded 6 which is a typical range of kB

^{−1}in the humid ecosystems with low E

_{p}/P ratio (0–2), and the underestimation trend was consistent for E

_{P}/P ratio of 0–2. Thus, underestimation of z

_{0M}(due to low NDVI in the start of the growing season) in conjunction with an overestimation of kB

^{−1}would lead to an underestimation of z

_{0H}[z

_{0H}= z

_{0M}/exp(kB

^{−1})]. Underestimation of z

_{0H}consequently led to an overestimation of g

_{A}and H both for the actual and the wet limits, and a consistent underestimation of λE (ET) was discernible. Previous studies ([77,92]) also revealed substantial uncertainties in z

_{0M}and kB

^{−1}that eventually led to uncertain estimation of ET. Our results demonstrated the critical role of surface to aerodynamic conductance parameterizations on the performance of the SVAT and SEB models.

_{A}from the models were mainly attributed to their structural differences and the nature of the parameterization of g

_{A}from all the three models. Therefore, the difference in g

_{A}estimates markedly contributed to the different statistical metric between simulated versus observed λE (and ET) from the models. In general, the accuracies in commonly used parametric g

_{A}estimates based on wind speed and surface roughness parameters several meters distant from canopy foliage are limited due to the uncertainties related to the attenuation of wind speed close to the vegetation surface [93,94]. The wind speed close to the foliage can be substantially lower than that measured at some reference location above the vegetation canopy [95]. Notwithstanding the inequalities of g

_{A}estimated with different methods, inferring the accuracy of the different g

_{A}estimates is beyond the scope of the manuscript. However, g

_{A}is one of the main anchors in the SVAT and SEB models because it provides feedback to g

_{S}[96]. Therefore, ET estimation using SVAT and SEB models are very sensitive to g

_{A}and a universally agreed g

_{A}parameterization is needed to obtain similar λE results from the models [97,98]. Given the lack of consensus in the community on the “true” g

_{A}and from the nature of surface flux validation results (Figure 4), it appears that g

_{A}from STIC1.2 tends to be the appropriate aerodynamic conductance that tend to produce the lowest λE error.

## 5. Conclusions

_{A}and g

_{S}) parameterizations in estimating ET from SVAT and SEB models. By using high temporal frequency eddy covariance measurements and three different SVAT and SEB models (SCOPE1.7, SEBS, and STIC1.2), we showed the critical role of ecohydrological conditions in influencing the conductance and latent heat flux simulation, and consequently daily ET. Independent validation of the models using observed latent heat flux data from an anomalous and a normal precipitation year (2015 and 2016) from one of the most ecologically important wetlands (Upper Biebrza National Park, Poland) (UBNP) led us to the following conclusions.

- (a)
- Notable differences were found out in the g
_{A}and g_{S}estimates from the three models. While SCOPE1.7 revealed substantial overestimation of both g_{A}and g_{S}with respect to the EC tower estimates, STIC1.2 derived g_{A}and g_{S}were within the range of EC tower estimates. SEBS revealed a consistent overestimation of g_{A}during the start of the growing season in spring, and g_{A}estimates were is good agreement with the EC tower during the active vegetative phase in summer. - (b)
- All the models explained significant variability in the observed ET with a root mean square error (RMSE) of 0.4–1 mm day
^{−1}and mean absolute percent error (MAPE) of 16–44%. Model intercomparison showed STIC1.2 to produce the least bias and good agreement with the observations, whereas SEBS and SCOPE1.7 revealed consistent underestimation and overestimation, respectively, in both years. - (c)
- Underestimation of λE (and ET) in SEBS was mainly attributed to the underestimation in the roughness lengths of momentum and heat transfers (z
_{0M}and z_{0H}). While the underestimation of z_{0M}is associated with the empirical modeling structure, the underestimation of z_{0H}was associated with the overestimation of ‘kB^{−1}-term’ under high soil moisture and low atmospheric aridity conditions. Underestimation of both z_{0M}and z_{0H}led to an overestimation of the aerodynamic conductance (g_{A}) and sensible heat flux (H), which was consequently reflected in the underestimation of ET. - (d)
- Although both SEBS and SCOPE1.7 had similar empirical parameterization of g
_{A}, a consistent overestimation of λE (and ET) in SCOPE1.7 was associated with the overestimation of the canopy–surface conductance (g_{S}) under high atmospheric aridity and also presumably due to the g_{S}-photosynthesis modeling uncertainty in SCOPE1.7 under high atmospheric vapor pressure deficit. - (e)
- Despite all the three model captured substantial variability in λE (and ET), the principal difference between the models appear to be associated with the differences in g
_{A}and g_{S}. Different magnitude g_{A}and g_{S}from all the models indicate the critical role of ambiguous parameterizations of these two important conductances for a broad spectrum of ecohydrological conditions. While SEBS require improved roughness length representation for enhancing the performance of g_{A}sub-models under low fractional vegetation cover conditions; SCOPE1.7 requires robust parameterizations for both g_{A}and g_{S}, and default calibration parameters prior to large-scale ET monitoring in the wetlands. - (f)
- The models showed promise as a quick and simple monitoring tool for wetland evapotranspiration. The simplified analytical model STIC1.2, requiring only surface-air temperature, humidity, and radiation data, can produce comparable results to more complex methods like SEBS under fully vegetated conditions and relatively better results under low fractional vegetation cover. Furthermore, this study demonstrated the model’s potential for large scale ET mapping in the wetlands to capture the spatio-temporal ET dynamics. A dense network of radiation, temperature and humidity monitoring stations would also help create near-real time ET maps for the eco-hydrological studies in the Upper Biebrza National Park region.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**An example of simulated Landsat-8 reflectance within a 3 × 3-pixel window around the Eddy covariance (EC) tower location acquired in Spring and Summer of 2015 by forward modelling and corresponding retrievals of the leaf and canopy properties obtained through model inversion using iterative optimization approach.

**Figure 2.**Study area in the Upper Biebrza National Park (UBNP) wetland based on a Landsat-8 scene. The distribution of precipitation (P) and soil moisture (θ) for the year 2015 and 2016 is also shown in the primary y-axis (P) and secondary y-axis (θ), respectively.

**Figure 3.**(

**a**) Comparison between model derived g

_{A}estimates with an estimated aerodynamic conductance based on friction velocity (u*) and wind speed (u) according to [75], (

**b**) Comparison between model derived g

_{S}estimates with respect to g

_{S}computed by inverting the penman-Monteith model where g

_{A}estimates from EC tower were used as aerodynamic input in conjunction with tower measurements of λE, radiation and meteorological variables.

**Figure 4.**Evaluation of half-hourly latent heat flux (λE) from STIC1.2, SEBS, and SCOPE1.7 for entire growing season (

**a**,

**b**), for the spring (

**c**,

**d**) and for the summer (

**e**,

**f**) months during the two consecutive years of 2015 and 2016.

**Figure 5.**Time series of simulated and observed daily ET from SCOPE1.7, SEBS and STIC1.2 for years 2015 and 2016.

**Figure 6.**Box and violin plot showing the relationship between the residual errors in half-hourly λE versus (

**a**) simulated g

_{A}, g

_{S}and T

_{c}in SCOPE1.7, (

**b**) simulated g

_{A}, z

_{0M}and kB

^{−1}in SEBS and (

**c**) g

_{A}, g

_{S}, and T

_{0}in STIC1.2.

**Figure 7.**Loadings of Principal Component Regression (PCR) between residual errors simulated λE with T

_{S}, NDVI, and environmental variables showing the contribution of each principal component in explaining the variance of the residual λE error in SCOPE1.7 (

**a**,

**b**), SEBS (

**c**,

**d**), and STIC1.2 (

**e**,

**f**), respectively, for years 2015 (left column) and 2016 (right column).

**Figure 8.**(

**a**) Scatterplots of mean bias in weekly ET (mm week

^{−1}) simulated from STIC1.2, SCOPE1.7, and SEBS versus weekly soil moisture (θ), and (

**b**) Scatterplots of mean bias in weekly ET simulated from STIC1.2, SCOPE1.7, and SEBS versus weekly climatic aridity index (E

_{P}/P ratio).

**Figure 9.**(

**a**) Time-series of daily reference evaporation (Λ

_{r}) from SEBS for 2015 and 2016 which shows low magnitude of Λ

_{r}in the beginning of the growing season where ET underestimation was predominant, (

**b**) Scatterplots showing the relationship between residual error in daily ET (Δ

_{ET}) from SEBS with daily Λ

_{r}, which further confirms the systematic underestimation in ET was associated with estimation errors in Λ

_{r}, (

**c**) Scatterplots showing the relationship between Δ

_{ET}from SEBS with simulated sensible heat flux for the wet limit (H

_{wet}), (

**d**) Scatterplots showing the relationship between Δ

_{ET}from SEBS with simulated aerodynamic conductance for the wet limit (g

_{Awet}). Scatterplot in the inset shows the relationship between H

_{wet}and g

_{Awet}.

**Figure 10.**(

**a**) Scatterplots of weekly g

_{S}/g

_{A}ratio simulated from STIC1.2 and SCOPE1.7 (kB

^{−1}for SEBS) versus weekly soil moisture (θ), and (

**b**) weekly climatic aridity index (E

_{P}/P ratio). Since SEBS does not simulate g

_{A}, the behaviour of kB

^{−1}was assessed with respect to the same ecohydrological conditions (θ and E

_{P}/P ratio). This shows that g

_{S}/g

_{A}ratio simulated through STIC1.2 and SCOPE1.7 was not affected by the soil moisture conditions, but it was strongly affected by E

_{P}/P ratio. In SEBS, kB

^{−1}was found to be affected by both θ and E

_{P}/P ratio.

**Table 1.**A summary overview of features, inputs-outputs and conductance parameterization characteristics of the two SEB and one SVAT model.

SEB Model | Feature | Inputs | Outputs | Surface Parameterization | |
---|---|---|---|---|---|

Meteo | Leaf/Canopy | ||||

STIC 1.2 [57,77] | Single source | T_{A}, T_{D}, RS_{in}, RS_{out} | g_{A}, g_{S}, T_{0}, λ_{r}, M, H, λE | Analytically computes g_{A} and g_{S} | |

Derivative of PM-WS | G, φ, T_{s} | Calibration free estimates of conductances | |||

Integrates T_{s} into PM | |||||

λE directly estimated from SEB | |||||

SEBS [19] | Single source | T_{A}, T_{D}, RS_{in}, RS_{out}, | h, fc, z_{0H}, z_{0M}, d_{0} | g_{A}, λ_{r,} kB^{−1}, H, λE | Assumes T_{s} and T_{0} are equal |

Uses MOST to solve for H | G, φ, T_{S} | NDVI, LAI | Assumes kB^{−1} adjusts the inequality between the | ||

Scales H between hypothetical | p_{a}, u | roughness lengths of momentum and heat transfers | |||

wet and dry limit | |||||

Estimates λE as a residual component of SEB | |||||

SCOPE 1.7 [58] | Multi source | T_{A}, e_{A}, RS_{in}, RL_{in} | PROSPECT [78] inputs | g_{A}, g_{S(leaf)}, H, G, λE | Computes g_{A} at (inertial, roughness and canopy) |

Computes g_{S} at leaf level | |||||

Applies SVAT principle | p_{a}, u | Vcmo, m, | R_{N}, RS_{out}, u* | ||

Flux transfer based on K-theory | h_{c}, LAI, LDFa, LIDFb, LW | ||||

[23] | Soil thermal properties, SMC | ||||

z_{0H}, z_{0M}, d_{0} | |||||

rbs, rss, rwc | |||||

VZA, RAA, SZA |

**Table 2.**Error Statistics of half-hourly λE from the two SEB and one SVAT models in the UBNP wetland (Site: Rogozynk) in two contrasting rainfall years.

Full Season | Spring | Summer | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Year | Model | R^{2} | Slope | Intercept | RMSE, W m^{−2} | MAPD, % | MB W m^{−2} | R^{2} | Slope | Intercept | RMSE, W m^{−2} | MAPD, % | MB, W m^{−2} | R^{2} | Slope | Intercept | RMSE, W m^{−2} | MAPD, % | MB, W m^{−2} |

2015 | SCOPE1.7 | 0.8 | 1.06 | 16 | 52 | 32 | 23 | 0.81 | 1.05 | 16 | 49 | 32 | 22 | 0.74 | 1.07 | 15 | 64 | 32 | 25 |

SEBS | 0.67 | 0.84 | −3 | 75 | 40 | −51 | 0.62 | 0.73 | −21 | 80 | 46 | −57 | 0.8 | 1.06 | −43 | 55 | 24 | −33 | |

STIC1.2 | 0.91 | 0.91 | −2 | 29 | 18 | −13 | 0.92 | 0.89 | −1 | 28 | 19 | −13 | 0.9 | 0.96 | −3 | 30 | 15 | −10 | |

2016 | SCOPE1.7 | 0.91 | 1.08 | 5 | 37 | 22 | 14 | 0.9 | 1.09 | 6 | 38 | 23 | 15 | 0.96 | 1.08 | −11 | 21 | 12 | −0 |

SEBS | 0.8 | 0.91 | −30 | 62 | 33 | −43 | 0.79 | 0.91 | −30 | 62 | 33 | −42 | 0.83 | 0.87 | −28 | 61 | 32 | −50 | |

STIC1.2 | 0.92 | 0.88 | 1 | 31 | 19 | −13 | 0.92 | 0.89 | 1 | 30 | 19 | −12 | 0.94 | 0.84 | 0 | 34 | 19 | −23 |

**Table 3.**Error Statistics of daily ET from the three models in the UBNP wetland (Rogozynk) in the two contrasting rainfall years of 2015 and 2016.

Year | Model | R^{2} | RMSE (mm day^{−1}) | MAPD (%) | MB (mm day^{−1}) |
---|---|---|---|---|---|

2015 | SCOPE1.7 | 0.87 | 0.89 | 38 | 0.67 |

SEBS | 0.75 | 0.95 | 40 | −0.68 | |

STIC1.2 | 0.92 | 0.37 | 16 | −0.05 | |

2016 | SCOPE1.7 | 0.95 | 0.92 | 44 | 0.79 |

SEBS | 0.80 | 0.74 | 33 | −0.46 | |

STIC1.2 | 0.89 | 0.46 | 21 | −0.14 |

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## Share and Cite

**MDPI and ACS Style**

Mallick, K.; Wandera, L.; Bhattarai, N.; Hostache, R.; Kleniewska, M.; Chormanski, J.
A Critical Evaluation on the Role of Aerodynamic and Canopy–Surface Conductance Parameterization in SEB and SVAT Models for Simulating Evapotranspiration: A Case Study in the Upper Biebrza National Park Wetland in Poland. *Water* **2018**, *10*, 1753.
https://doi.org/10.3390/w10121753

**AMA Style**

Mallick K, Wandera L, Bhattarai N, Hostache R, Kleniewska M, Chormanski J.
A Critical Evaluation on the Role of Aerodynamic and Canopy–Surface Conductance Parameterization in SEB and SVAT Models for Simulating Evapotranspiration: A Case Study in the Upper Biebrza National Park Wetland in Poland. *Water*. 2018; 10(12):1753.
https://doi.org/10.3390/w10121753

**Chicago/Turabian Style**

Mallick, Kaniska, Loise Wandera, Nishan Bhattarai, Renaud Hostache, Malgorzata Kleniewska, and Jaroslaw Chormanski.
2018. "A Critical Evaluation on the Role of Aerodynamic and Canopy–Surface Conductance Parameterization in SEB and SVAT Models for Simulating Evapotranspiration: A Case Study in the Upper Biebrza National Park Wetland in Poland" *Water* 10, no. 12: 1753.
https://doi.org/10.3390/w10121753