The Surface Urban Energy and Water Balance Scheme (SUEWS) is a local-scale land surface model for simulating the surface energy and hydrological fluxes (Grimmond and Oke, 1986, 1991; Järvi et al., 2011, 2014; Offerle et al., 2003; Ward et al., 2016) without requiring specialised computing facilities. It has been extensively evaluated and applied in many cities (Lindberg et al., 2018, their Table 3; Sun and Grimmond, 2019, their Table 1). Other details of how SUEWS computes the surface energy, water and carbon fluxes are given in recent model description papers (Järvi et al., 2011, 2019; Ward et al., 2016).

The surface energy and water balances are directly linked by the turbulent latent heat flux (QE) or its mass equivalent evaporation (E) (Grimmond and Oke, 1986, 1991): 1Q∗+QF=QH+QE+ΔQS,2P+Ie=E+R+ΔS, where Q∗ is the net all-wave radiation flux; QF is the anthropogenic heat flux; QH is the turbulent sensible heat flux; ΔQS the net storage heat flux; and P, Ie, ΔS and R are precipitation, external water use, net change in the water storage (e.g. canopy, soil moisture, water bodies) and runoff, respectively. The sites selected in this work are assumed to have no irrigation, so Ie is assumed to be 0 mms-1.

In SUEWS, a modified Penman–Monteith equation (Penman, 1948; Monteith, 1965) is used to compute QE with an expectation in cities that the anthropogenic heat flux (QF) is greater than zero (Grimmond and Oke, 1991): 3QE=sQ∗+QF-ΔQS+ρcpVPDras+γ1+rsra.

However, with our current focus on extensive (non-urban) pervious areas QF is assumed to be 0 Wm-2. The atmospheric state is obtained from the slope of saturation water vapour pressure curve with respect to air temperature (s, PaK-1), density of air (ρ, kgm-3), specific heat of air at constant pressure (cp, JK-1kg-1), vapour pressure deficit (VPD, Pa), psychrometric “constant” (γ, PaK-1) and the aerodynamic resistance for water vapour (ra,  sm-1).

Under given ambient meteorological conditions (e.g. incoming solar radiation K↓, air temperature Ta, humidity) at an extensive vegetated site, QE from this method is sensitive to the estimation of available energy (i.e. Q∗-ΔQS), aerodynamic resistance ra and surface resistance rs. Hence, the critical vegetation-related parameters (Table 1) are addressed with these caveats and/or assumptions:

Surface emissivity ε0 and canopy water storage capacity Si are assumed to be the same as reported in Ward et al. (2016).

The FLUXNET2015 dataset (Pastorello et al., 2020) is the newest version of the FLUXNET data products. The gap-filled dataset includes 212 flux sites from around the world. Although the FLUXNET focus is on local-scale ecosystem CO2 eddy covariance (EC) fluxes, it also includes water and energy EC fluxes plus other meteorological and biological data. The biosphere–atmosphere exchange dataset contains more than 1500 site years for the period to the end of 2014. The open-source package ONEFlux (Open Network-Enabled Flux processing pipeline; https://github.com/fluxnet/ONEFlux, last access: 4 November 2021) is used to produce FLUXNET2015 (Pastorello et al., 2020).

Half-hourly observations (Table 2) are used from 38 sites (Table 3) in three regions (Fig. 2). These sites are selected to meet the following criteria (number of remaining sites that met the criteria):

Sites with CC-BY 4.0 license (206/212).

Unfortunately, no datasets are left after selection based on the above criteria for some regions (Fig. 2), including Africa, Asia and South America.

As SUEWS allows any grid cell to have three vegetation or plant functional types (PFTs), with the sub-type or properties varying between grids, we subdivide the 38 sites into three classes using IGBP (Table 3) (code, number of sites): a.

Evergreen trees/shrubs (EveTr, 13). Evergreen needleleaf forests (ENF, 12), evergreen broadleaf forests (EBF, 1).

The landscape heterogeneity of many FLUXNET EC flux measurements sites have been systematically examined by Stoy et al. (2013) using satellite imagery. Of the sites they examined, they found them to be located within homogeneous parts of the targeted PFT, but the larger landscape (∼ 20 km) may have considerable variability. As a FLUXNET site is typically assigned to one PFT for land surface model development and evaluation (e.g. Stöckli et al., 2008; Zhang et al., 2017; Chu et al., 2021), we configure each as a homogeneous grid cell and assume fi=1.

The NASA Moderate Resolution Imaging Spectroradiometer (MODIS; Nishihama et al., 1997) four-day composite product MCD15A3H (Myneni et al., 2015) with 500 m resolution is treated as “observed” LAI. Product data are available from 2002. We use the Fixed Sites Subsetting and Visualization Tool (ORNL DAAC, 2018) for the FLUXNET dataset to extract the MCD15A3H time series. To obtain a daily time series we linearly interpolate between values, for parameter derivation (Sect. 4.1).

The SoilGrids (Hengl et al., 2014) database provides soil properties (i.e. organic carbon, bulk density, cation exchange capacity (CEC), pH, soil texture fractions and coarse fragments) at seven depths (0, 0.05, 0.15, 0.30, 0.60, 1.00 and 2.00 m), as well as a bedrock depth prediction, World Reference Base (WRB) and USDA soil classes. We use the SoilGrids250m (Hengl et al., 2017) version, with its ∼ 280 raster layers, to obtain the parameters (Table 4) to derive soil moisture deficit at wilting point (ΔθWP in mm) for soil-moisture-related calculations (e.g. Eq. 18).

The difference in soil moisture between field capacity (θFC in mm) and wilting point (θWP in mm) are used with parameters defined as follows (Saxon and Rawls, 2006): 23ΔθWP=θFC-θWP=(WFC-WWP)(1-fCF)dr with 24WFC=kFC+1.283⋅kFC2-0.374⋅kFC-0.015, using the weight fractions of sand fsand, clay fclay and organic matter fOM: 25kFC=-0.251⋅fsand+0.195⋅fclay+0.011⋅fOM+0.006⋅(fsandfOM)-0.027⋅(fclayfOM)+0.452⋅(fsandfclay)+0.299 and 26WWP=kWP+(0.14⋅kWP-0.02), where 27kWP=-0.024⋅fsand+0.487⋅fclay+0.006⋅fOM+0.005⋅(fsandfOM)-0.013⋅(fclayfOM)+0.068⋅(fsandfclay)+0.031.

LAI is a key phenology parameter in SUEWS; it moderates albedo (α) and therefore surface radiative exchanges. LAI changes also modify both aerodynamic roughness parameters (roughness length z0, zero plane displacement height zd) (e.g. Kent et al., 2017a, b) impacting aerodynamic resistance (ra) and surface resistance (rs). LAI directly moderates QE and canopy interception capacity, which modifies when potential evaporation occurs and aspects of the water balance.

As the SUEWS LAI equation (Eq. 4) makes global optimisation techniques numerically challenging to derive all the required parameters, we take a two-step approach (Fig. 3).

To calculate the storage heat flux ΔQS, the required OHM coefficients (Eq. 7) can be determined from observed net all-wave radiation and observed storage heat flux, using ordinary linear regression. As the FLUXNET sites chosen are considered to be homogeneous, we derive coefficients for each site.

Ideally the storage heat flux measurements would include each of the components that are heating and cooling down on a daily basis, such as the soil, trunk, branches, leaves and air volume in a forest (e.g. McCaughey et al., 1985; Oliphant et al., 2004). However, these measurements are unavailable in the FLUXNET2015 dataset. Hence, we calculate a residual flux ΔQS,res=Q∗-(QH+QE) by assuming energy balance closure. This has the problem of accumulating the net measurement errors in this term (Grimmond et al., 1991; Grimmond and Oke, 1999).

The derived OHM coefficients (Fig. 6) can be determined by season (Anandakumar, 1999; Ward et al., 2016; Sun et al., 2017). We distinguish warm (“summer”) and cold (“winter”) seasons using months (summer: Northern Hemisphere JJA; Southern Hemisphere: DJF; winter: DJF (JJA), respectively). For simplicity, we omit periods when LAI may be changing rapidly. If the daily mean air temperature is warmer (cooler) than the annual mean of daily median temperature, then summer (winter) OHM coefficients are used in the simulations.

The OHM coefficients derived for the 38 FLUXNET sites (Table 6, Fig. 7) vary between land cover types and seasons. For each land cover type, a1 and a3 are notably larger in winter than in summer while the seasonal difference in a2 is relatively small. Thus the overall fraction of heat stored does not vary much, but the diurnal hysteresis effect is weaker in winter. These results are consistent with previous analytical results (Sun et al., 2017). Within each PFT, there is larger variability in a2 and a3 (cf. a1), notably for evergreen and deciduous trees, suggesting using the most appropriate site values (e.g. medians) may improve predictions of the storage heat flux. In addition to the values derived here, we note that more detailed ΔQS observations are available for vegetated sites to derive such OHM coefficients (e.g. McCaughey, 1985; Oliphant et al., 2004).

As the Jarvis-type formulation of stomatal and surface conductance is widely used for many land cover types, many parameter sets exist (e.g. Stewart, 1988; Grimmond and Oke, 1991; Ogink-Hendriks, 1995; Wright et al., 1995; Bosveld and Bouten, 2001; Järvi et al., 2011). Hoshika et al.'s (2018) comprehensive meta-analysis of published Jarvis-type stomatal conductance parameter values includes major woody and crop plants broadly similar to PFTs examined here.

Conventionally, the surface conductance parameters are derived by minimising the bias between the parameterised (Eq. 14) and so-called “observed” values derived from an inverse form of the Penman–Monteith equation (Eq. 3): 301gs=rs=sγQHQE-1ra+ρcpVPDγQE.

This requires the surface be dry (Sect. 2.2.4) which we define as being without recorded rainfall in 24 h.

However, as the optimisation may not return values because of the complexity in Eq. (13) and the challenge of interpreting the derived parameter values, we adopt Matsumoto et al.'s (2008) approach to derive these parameters. Rather than using all the data combinations for gs, the upper boundary of each forcing variable component (e.g. g(K↓)) is considered as the response for unconstrained conditions. Specifically, the workflow is as follows (Fig. 8):

Calculate aerodynamic resistance ra (Eq. 8) with roughness length z0m and displacement height zd derived from observed wind speed under neutral conditions (Appendix B).

The derived surface conductance parameters for the 38 FLUXNET sites (Tables 7 and C3) have different intra-PFT variability based on the IQR (dotted lines, Fig. 10) and demonstrates the benefit of the observations and of deriving site values when possible. It may help in selecting appropriate PFTs from other sources (e.g. NOAH values in Appendix A). The gmax⁡ results are consistent with Hoshika et al. (2018) in terms of inter-PFT ordering (Grass > EveTr and DecTr). The grass and crop values are comparable (Table C3) to Hoshika et al. (2018); however, our derived deciduous trees values are smaller (22 vs. 31 mms-1) and evergreen trees values larger (20 vs. 12 mms-1).

A consistent Gq,shape (Eq. 16) value (0.9 units) is obtained for all sites, implying potential for improvements to the g(Δq) relation between gs and Δq (e.g. other formulations gs(Δq) in Matsumoto et al., 2008) in future SUEWS development. This would be beneficial as there is a clear “plateau” observed for low Δq (Fig. 9c). Similar issues are found in g(Δθ) for soil-moisture-related parameters. Although the parameters derived here are the “best” fit to the gs forms in SUEWS v2020a, for each component variable multiple gs formulations exist with a range of variable fitting performance (e.g. Fig. A1 in Ward et al., 2016). Here, we focus on deriving the parameters rather than proposing new or more appropriate formulations.

The solar-radiation-related GK parameter is linked to the level of incoming solar radiation needed for evapotranspiration to occur. Given incoming solar radiation intensity varies with latitude, we see GK generally decreases polewards (Fig. 11a), suggesting geographical location could be used as a proxy for deriving GK.

The air-temperature-related GT parameter indicates the optimal temperature for evapotranspiration to reach its probable maxima. GT appears to have a negative relation with latitude, but the two other temperature parameters (TL and TH) have a very weak (or no) relation with latitude (Fig. 11b). This suggests a universal temperature range between TL and TH might be applicable across different sites while GT should be determined on a site-by-site basis.

SUEWS v2020a (Tang et al., 2021) is evaluated using its Python wrapper SuPy v2021.3.18 (Sun and Grimmond, 2019) with parameters (Table 1) and gap-filled 30 or 60 min meteorological forcing data (Table 2) based on FLUXNET2015 dataset. Simulations are conducted, with forcing data interpolated to a 5 min time step (Ward et al., 2016), for 3 years (Table 3, Evaluation period) starting in mid-winter. The first year is discarded to allow for model spin-up. The two subsequent years are evaluated when observed latent heat flux data are available. In these model runs, the z0m and zdm values used are derived (Appendix B) by LAI state using observations for each LAI season (approximately nine values per site; see Sun et al. (2021) for values). All other parameters (Table 1) are determined for the parameter derivation period indicated in Table 3. At one site (AU-Gin), there are insufficient data for independent evaluation period from the parameter derivation period.

For the periods with 30 or 60 min QE EC observations (Yobs) available, the 5 min simulated values (Ymod) are averaged to 30 or 60 min to evaluate the j cases between 1 and the number of data points (N). The following metrics are used:

Hit rate (HR).31HR=∑j=1NH(δY,j-|Ymod,j-Yobs,j|)N,with Heaviside step function H defined by32H(x)=0,x<0,1,x≥0,and the threshold δY,jbeing a value dependent on evaluation variable Y.

In particular, δY,j for QE is determined as a function of net all-wave radiation Q∗ following Hollinger and Richardson (2005) to be δY,j=0.1Qj∗+10 (in Wm-2) based on measurement uncertainties.

Both the MAE and MBE would ideally be 0 (with units of parameter and variable assessed), whereas if the HR = 1 it indicates all model predictions fall within the acceptable threshold set, while HR = 0 would suggest none are within the acceptance threshold.

A performance score PS as a function for each metric (x; i.e. HR, MAE, |MBE|) is used to rank the sites: 35PS=1N∑k=1N(wxx̃)k, where x̃ is the rescaled ranking score of a given metric after being ranked from poorest to best, and wx is a weight associated with the temporal analysis type k which varies from 1 to N (number of component periods; e.g. N = 24 for hourly results). Equal weights (1/3) are used in the PS calculations for HR, MAE and |MBE|.

Given the many parameters in SUEWS, first we assess the relative importance of the parameters. We assume in this analysis our derived parameters (Sect. 4) are “perfect”, so we can undertake a sensitivity analysis (McCuen, 1974; Beven, 1979) of the Penman–Monteith equation (i.e. Eq. 3, denoted by PM hereafter):

36ΔQE=PM(AE+ΔAE,ra+Δra,rs+Δrs)-QE, where AE=Q∗-ΔQS is the available energy, incorporating parameter influences related to LAI, albedo and OHM. Similarly, multiple parameters influence the resistance terms. In Eq. (36)​​​​​​​ the prefix Δ indicates bias terms. For simplicity, we consider the direct impacts only (i.e. secondary impacts from parameters inter-dependence are ignored). Expanding Eq. (36) in Taylor series, gives the following: 37ΔQE≈PM′(AE)⋅ΔAE+PM′(ra)⋅Δra+PM′(rs)⋅Δrs, where PM′(x), the first-order derivative of x, indicates the sensitivity of modelled QE. Note “≈” implies the approximation of ΔQE as the sum of bias from the chosen parameters. To examine the influences of different parameters in model performance, we use two non-dimensional metrics derived from Eq. (37):

Sensitivity coefficient (SC) (McCuen, 1974).38SC=PM′(x)⋅xQE=∂QE∂xxQE≈ΔQE/QEΔx/xgives the fractional change in x causing a change in QE, indicating a relative sensitivity of PM to x. For instance, SC = 0.5 suggests a 20 % increase in x may increase QE by 10 % (= 20 % × 0.5).

Ideally, the sum of all AF contributors would equal 1, but as we omit inter-dependence of impacts of parameters, this may not occur. However, comparing the different contributors is indicative of their relative importance in modelled QE.

Both SCAE and SCra generally show a similar type of pattern (Fig. 12a–f) with seasonal and diurnal variations for the three PFTs. During warm periods (summer and noon), with an increase in ΔAE and Δra it is found to lead to larger positive bias in modelled QE, whereas in cooler periods (winter and night-time) the ΔAE and Δra is found to increase the negative bias.

However, the temporal patterns in SCrs differ (Fig. 13g–i) from those in SCAE (Fig. 13a–c) and SCra (Fig. 13d–f): the SCrs values are always negative, and consistently larger in magnitude (cf. SCAE and SCra), implying a particularly strong sensitivity of QE to rs. This is consistent with Beven (1979), who found it to dominate the modelled summertime QE sensitivity in the PM framework.

The relative (cf. total) bias from the parameters is assessed in modelled QE at monthly and hourly temporal scales using the median AF (Fig. 13). AFrs is larger than both AFAE and AFra; i.e. rs imposes a dominant influence in modelled QE bias. There is more temporal variability in AFrs (cf. AFAEand AFra) with cooler periods (morning and evening, whole winter) generally having values greater than 1, indicating the bias in rs dominates modelled QE. As AFrs is still generally larger than ∼ 0.3 (except for transitional periods in summer, 08:00–09:00 LST, when AFrs≲0.3), rs remains an important control on modelled QE. These results together indicate that it is critical to assign accurate rs to obtain accurate estimates of QE.

Given the critical importance of surface resistance to model performance in QE (Sect. 5.2), we assess the impact of two different sources of gs parameters (keeping all other site parameters the same, with the values as indicated in Sect. 5.1): (i) site-specific values derived from FLUXNET2015 data (Sect. 4) and (ii) PFT-specific NOAH values modified for SUEWS (Appendix A). Errors in the other derived parameters (e.g. LAI-related parameters, storage heat flux coefficients via available energy) will impact both sets of results, but they are assumed to be equal, allowing the impacts of using site- and PFT-specific gs parameters on SUEWS-simulated QE to be assessed. Given NOAH is extensively used in NWP systems (e.g. WRF, Skamarock and Klemp, 2008), the result also allows the applicability of NOAH-based gs parameters at FLUXNET sites to be assessed.

Analysis using 2 years of QE EC flux data (after a 1-year spin-up) uses three metrics (Sect. 5.1). The overall median results are similar between the two sets of parameters across the 38 sites split into the three PFTs (Fig. 14, red lines). The median HRs are between 0.6 and 0.7, median MAEs are less than 25 Wm-2, and median MBEs are ∼ 5 Wm-2. At the Grass site, HR and MAE (Fig. 14a and b) performance is very similar, suggesting the NOAH-based parameters could be used for these sites at annual scales as a first-order proxy.

Evaluation using three different time periods (annual, monthly and hourly) shows differences in performance between using the FLUXNET2015 and NOAH-based parameters (Fig. 15). The HR is similar for all three temporal scales (Fig. 15a–c) for the three site types (colour). Both the MAE (Fig. 15d–f) and MBE (Fig. 15g–i) indicate better model performance can be obtained using the FLUXNET2015-based parameters (i.e. not above the 1:1 line). When using the NOAH parameters (Fig. 15h and i), some monthly MBEs are ∼ 40 Wm-2 larger at EveTr sites for 8 of 156 cases and 5 of 312 for DecTr sites. Similarly, at the hourly scale the NOAH MBEs are on occasions ∼ 30 Wm-2 larger (4 of 132 EveTr cases and 6 of 264 DecTr cases). However, the NOAH results have similar metrics at Grass sites. This suggests at the EveTr and DecTr sites, the NOAH-based gs parameters may on occasion be less appropriate, suggesting that the individual sites' values may be better.

Given the results in Sect. 5.3, the performance of individual sites using the FLUXNET2015-derived parameters (Sect. 4) at monthly (Fig. 16) and hourly (Fig. 17) timescales are investigated.

As expected (Sect. 5.2), the HR values are consistently better at all sites during cooler (winter) than warmer (summer) seasons (Fig. 16a–c), and similarly for night rather midday time periods (Fig. 17a–c). Given the consistency in MAE and HR (Figs. 16 and 17d–f) patterns, the sites identified to be simulated the “best” (blue) and “poorest” (orange) are the same (Sect. 5.1).

However, using the MBE different sites are selected. For example, monthly MBE at AU-ASM stays close to zero throughout the year while at AU-Das it varies between -40 and 60 Wm-2 (Fig. 16h). The largest intra-month MBE range for an EveTr site is 87.1 Wm-2, which occurs at FR-LBr. The equivalent range for DecTr sites is larger (96.1 Wm-2 at AU-DaS) but smaller at Grass sites (69.6 Wm-2; US-Ne3). The intra-hourly MBE ranges are smaller than intra-monthly values, with a DecTr and a Grass site having a larger range than the largest EveTr site (AU-DaS (61.9 Wm-2), US-Goo (60.0 Wm-2), FR-LBr (53.1 Wm-2), respectively).

To investigate QE performance relative to key parameters (LAI, ra and gs) we select the sites with contrasting results from each PFT to understand the drivers. The hourly and monthly ranked performances (Eq. 35) are broadly consistent within each PFT (Fig. 18). Sites with higher hourly scores generally have better monthly scores, except for IT-SRo within the EveTr cohort. It has the highest hourly PS (0.86) but is ranked fourth based on PSmonthly (0.64), whereas the highest PSmonthly (0.91) is for FI-Hyy which also has the second rank PShourly (0.83). To select sites for further analysis we rank based on the mean of monthly and hourly PS results. The six sites chosen are the best and poorest sites for the three PFTs (i.e. extremes in Fig. 18, highlighted in Figs. 16 and 17).

Comparing the contrasting site QE performance (best vs. poorest) for the three PFTs (Figs. 19 vs. 20; 21 vs. 22; 23 vs. 24), we identify the skill of capturing the annual LAI dynamics is crucial to seasonal model performance (Figs. 19–24a). At the “best” sites (except for BE-Lona, a Grass site whose performance is more controlled by surface conductance gs skill and shall be discussed later) the phenology generally has the correct timing, while at the poorest onsets of some stages are missed (e.g. Fig. 22a). Timing appears to be more critical than magnitude, as although the LAI magnitude at AU-ASM has a large bias in year 2 (0.5 m2m-2, Fig. 21a) the phenology timing is well captured. This result for a first rank site (i.e. best performance) implies the rescaling nature of LAI in parameterisation of albedo (Eq. 6) and surface conductance (Eq. 14) plays an important role. This indicates the importance of assigning appropriate LAI parameters, notably those influencing the timing (i.e. temperature thresholds Tbase,GDD and Tbase,SDD in Eq. 4), in SUEWS modelling QE at vegetated sites.

As expected (Sect 5.2), SUEWS performance is critically impacted by surface conductance gs skill (Figs. 19–24b–e vs. j–m): sites and seasons with better model gs skill (i.e. simulations and observations closer) show overall better performance (e.g. for Grass sites, BE-Lon vs. US-CRT, cf. Figs. 23c and 24c). gs is better modelled in warmer (JJA and SON) than cooler seasons (MAM and DJF). At night, gs is generally underestimated, by a similar order of magnitude to that in cooler seasons (∼ 3 mms-1). These results, consistent with SUEWS results for two UK urban sites (Ward et al., 2016), suggest improvements are needed in the Jarvis-type gs parameterisation during cooler periods. Given the method adopted here of using summertime observations, as used by many other land surface models (e.g. NOAH – Chen and Dudhia, 2001; HTESSEL – Balsamo et al., 2009), it is implied that the widely adopted Jarvis-type gs parameterisations and/or related parameter values (see Sect. 4.3) may be biased towards vegetation canopies in warmer periods. The “cool” bias in modelled gs found here, and in earlier SUEWS work (e.g. Ward et al., 2016), should be considered a more common issue beyond the SUEWS model. Given the needs in long-term climate modelling, systematic biases should be removed, suggesting other land surface models that adopt the Jarvis-type gs parameterisation might need revisions as well.

The aerodynamic resistance ra is modelled well at all sites (Figs. 19–24f–i), with nocturnal biases larger (e.g. underestimate of ∼ 50 sm-1 at AT-Neu, Fig. 23f–i). This good performance may be largely attributed to the use of local growth-stage-derived aerodynamic roughness parameters (Appendix B) rather than estimated using a morphometric model (e.g. based on canopy height). To estimate z0m and zd using Eqs. (9) and (10) the f0 and fd parameters can be derived using Sun et al. (2021) for different growing stages with the FLUXNET2015 data when canopy heights are available. The largest intra-PFT variability occurs for “Grass” sites (Fig. B1).