1. Introduction
The Penman–Monteith equation has been recommended by the Food and Agriculture Organization of the United Nations as a standard method to calculate LE (Allen et al. 1998, pp. 17–28 and 65–77). The Penman–Monteith equation requires Rn and G, which are not measured routinely and are unavailable at regional or global scale, thus limiting its application. Furthermore, the Penman–Monteith equation needs canopy resistance rc, which is difficult to measure directly (Wang and Dickinson 2012).
Therefore, many studies have tried to simplify the Penman–Monteith equation (Bailey et al. 1993; Kra 2010; Priestley and Taylor 1972; Rivas and Caselles 2004; Valiantzas 2006, 2013). One of the most widely used simplifications, the Priestley and Taylor equation, can be used to calculate LE under adequate moisture conditions (Priestley and Taylor 1972). The Priestley and Taylor equation is not suitable for water-limited conditions, and it does not consider the impact of vegetation on LE either. In addition, the Priestley and Taylor equation does not fully consider the impact of atmospheric evaporative demand, that is, the impacts of wind speed (WS) and water vapor deficit.
Some remote sensing–based models to estimate LE are widely used (Mu et al. 2007a, 2011), but their disadvantages are obvious in terms of high sensitivity to errors of input data and limited availability in different conditions (Kalma et al. 2008; Teixeira et al. 2009a,b; Wang and Dickinson 2012). The use of satellite-derived surface temperature Ts for the aerodynamic temperature results in great uncertainty of surface flux estimates in one-source models, which has been questioned (Friedl 2002; Hall et al. 1992; Shuttleworth 1991). Two-source models require an unbiased gradient between Ts and surface air temperature Ta (Timmermans et al. 2007), but the uncertainty of Ts retrievals is several kelvin (Norman et al. 2000; Wang and Liang 2008). The Ts–vegetation space methods suffer from their key assumption that LE is negatively correlated with temperature (Wang et al. 2006). Therefore, some empirical models were proposed to estimate the global LE over different land-cover types. Take two cases as examples: 1) three suites of empirical models were proposed with routine meteorological observations including Rn, Ta, relative humidity (RH), diurnal temperature range (DTR), WS, and normalized difference vegetation index (NDVI) to obtain long-term series of LE (Wang et al. 2010, 2007; Wang and Liang 2008) and 2) the tree ensemble model was constructed with satellite remote sensing and surface meteorological observations to acquire the temporal variance and global spatial distribution of LE (Jung et al. 2009, 2010).
There are numerous published studies on LE for its connection of surface energy and water balance, but studies on EF and H are many fewer. As H heats air temperature above the surface, EF or H is more directly relevant for climatic-change study—for example, spatial warming contrast (Wang 2014; Wang and Zhou 2015). Even though some land-surface models are designed to provide EF or H, their accuracy is low (Best et al. 2015). Despite an accurate LE estimate, uncertainty of EF or H estimates through the energy-balance method is still large, particularly so when H dominates the available energy over dry regions and seasons.
Therefore, taking advantage of long-time measurements from 81 “AmeriFlux” sites, this study explored the biological and environmental controls on monthly EF for different ecosystems and types of climate. On the basis of the quantitative relationships between EF and its controls, empirical models were further established to estimate EF that can be widely used to estimate the long-term variance in EF from conventional weather observations. These will help in understanding the effect of land–atmosphere interactions on climatic change.
2. Data and methods
a. AmeriFlux data
The AmeriFlux network is a community of sites measuring ecosystem carbon, water, and energy fluxes across America for better understanding of terrestrial ecosystems in a changing world. The AmeriFlux network measures Ta, DTR, RH, WS, H, and LE at every 30 or 60 min over ~140 stations across a range of land-cover types (Baldocchi et al. 2001). These data are publicly available online (http://ameriflux.ornl.gov/). DTR quantifies the difference between the daily maximum and minimum air temperature. After quality control (see section 2b), a total of 81 sites with data spanning over 20 months were selected in this study. These sites (74 in America, 5 in Canada, and 2 in Brazil; Fig. 1) were divided into two groups that were each as well distributed as possible over all of the land-cover types: one group with 43 sites (Table 1) was used to parameterize EF, and the other group with 38 sites (Table 2) was used to validate the accuracy of the parameterizations. In this way, it makes the parameterizations of EF globally applicable. The data collected at all of the sites were used to investigate the biological and environmental controls on EF.
Locations of the 81 AmeriFlux sites used in this study. These sites were divided into two groups for training and validating empirical methods to estimate EF; these groups were summarized in Tables 1 and 2, respectively. Light-green circles represent the 16 deciduous forest sites, dark-green circles represent the 17 evergreen forest sites, blue circles represent the 14 shrubland sites, green circles represent the 26 grassland sites, and red circles represent the 8 cropland sites. Land-cover types in the legend are deciduous broadleaf forest (DBF), mixed forest (MF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), closed shrubland (CSH), open shrubland (OSH), grassland (GRA), woody savanna (WSA), and cropland (CRO).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Locations of the 81 AmeriFlux sites used in this study. These sites were divided into two groups for training and validating empirical methods to estimate EF; these groups were summarized in Tables 1 and 2, respectively. Light-green circles represent the 16 deciduous forest sites, dark-green circles represent the 17 evergreen forest sites, blue circles represent the 14 shrubland sites, green circles represent the 26 grassland sites, and red circles represent the 8 cropland sites. Land-cover types in the legend are deciduous broadleaf forest (DBF), mixed forest (MF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), closed shrubland (CSH), open shrubland (OSH), grassland (GRA), woody savanna (WSA), and cropland (CRO).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Locations of the 81 AmeriFlux sites used in this study. These sites were divided into two groups for training and validating empirical methods to estimate EF; these groups were summarized in Tables 1 and 2, respectively. Light-green circles represent the 16 deciduous forest sites, dark-green circles represent the 17 evergreen forest sites, blue circles represent the 14 shrubland sites, green circles represent the 26 grassland sites, and red circles represent the 8 cropland sites. Land-cover types in the legend are deciduous broadleaf forest (DBF), mixed forest (MF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), closed shrubland (CSH), open shrubland (OSH), grassland (GRA), woody savanna (WSA), and cropland (CRO).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
A description of the AmeriFlux sites used to parameterize EF in this study. More information about the sites can be found online (http://ameriflux.lbl.gov/AmeriFluxSites/Pages/Site-Map.aspx.) The MODIS NDVI product is the 16-day composite data. The multiyear average values were calculated to depict the climatological behavior of the sites. IGBP land-cover types are as in Fig. 1. Köppen–Geiger (K–G) climatic classes are as follows: the climates are arid (B), warm temperate (C), and snow (D); the precipitation is steppe (S), fully humid (f), and summer dry (s); and the temperature is cold arid (k), hot summer (a), warm summer (b), and cool summer (c).
As in Table 1, but for the AmeriFlux sites used to evaluate the accuracy of the EF parameterizations in this study.
The flux data at study sites were measured by an eddy covariance (EC) system with the flux-tower height varying from 1.5 to 60 m above the ground surface. The elevation of the selected sites ranges from 1 to over 3000 m above sea level. The land-cover types include deciduous and evergreen forest, closed shrubland, grassland, cropland, and woody savanna (Tables 1 and 2). The climates vary from tropical and temperate to Mediterranean and from humid to arid.
b. Quality control of the AmeriFlux data
Before releasing the data, AmeriFlux implemented extensive quality control on them (Baldocchi et al. 2001); the data still contain outliers and erroneous records, and additional quality-control procedures were thus implemented. The additional quality control included the following procedures. 1) On the basis of historical records, H and LE values over 1600 W m−2 or less than −500 W m−2 (Zahumenský 2004), Ta values outside the range from 56.67° to −62.22°C, DTR values exceeding 39.44°C, and WS values over 45 m s−1 were excluded (Cerveny et al. 2007). 2) On the basis of physical characteristics, RH values outside the range 0%–100% were excluded. 3) Outliers beyond 5 standard deviations σ for all of the above variables were also excluded. Chebyshev’s theorem demonstrates that this threshold results in more than 96% of the statistically acceptable data with any data distribution (Amidan et al. 2005; Schmidt et al. 2011).
After quality control, when both LE and H were available, other environmental variables were interpolated using a cubic method at points with adjacent gaps of less than 6 h. The most-interpolated variable is Ta with a ratio of 0.21% (the interpolated data length/the whole data length used in this study). It required the common record lengths of H, LE, Ta, NDVI, RH, and WS to be no less than 20 months. A total of 81 sites met the above requirements.
c. MODIS VI products
Three vegetation indices (VI) that quantify vegetation coverage are available from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite land products after 2000 (http://modis.gsfc.nasa.gov/data/): leaf area index (LAI) from the “MOD15A2” dataset (version 5) and NDVI and enhanced vegetation index (EVI) from the “MOD13Q1” dataset (version 5). Some preprocessing was done to obtain a high-quality NDVI dataset. First, on the basis of their quality-control information, the satellite VI data collected under unfavorable conditions (e.g., cloud and snow/ice cover) and from water bodies were filtered. Second, for each site, the 16-day composite data in pixels with a size of 2 × 2 km2 centered on the tower were composited (Xiao et al. 2008). Third, a cubic smoothing spline was used for interpolation (Horn and Schulz 2010) at points with adjacent gaps of less than 1 month, and the data were then averaged into the monthly value. After these processes, a robust method that is based on the Savitzky–Golay filter that was widely recommended for smoothing out noise in NDVI time series was used to obtain the high-quality NDVI time series. This method is to make NDVI data approach the upper NDVI envelope and to reflect the changes in NDVI patterns by an iteration process (Chen et al. 2004).
d. Land-cover and climate types
The classification of vegetation types at the study sites followed the 17 International Geosphere–Biosphere Programme (IGBP) land-cover types of the MODIS land-cover product (i.e., MCD12Q1), which is publicly available online (https://lpdaac.usgs.gov/). Details of this land-cover product can be found in Friedl et al. (2010). Nine different vegetation types were identified at the study sites.
The world map of the Köppen–Geiger classification of climate, which displays 31 types of climate at a resolution of 0.5° × 0.5° on the basis of temperature and precipitation observations for the period of 1951–2000 (Kottek et al. 2006), was used to extract the climatic information for each site (Tables 1 and 2). The usable digital map is provided freely online (http://koeppen-geiger.vu-wien.ac.at/).
e. Calculation of monthly EF
Although the EC method suffers an important issue of energy imbalance, that is, the sum of LE and H is not equal to Rn − G, most applications and correction methods assume that the Bowen ratio is kept for the EC method (Twine et al. 2000; Wang and Dickinson 2012; Wilson et al. 2002). Under this assumption, EF is independent of the energy-closure problem and does not need correction. Monthly EF here is obtained to estimate the long-term variance of EF, which not only avoids the effect of the average error from daily to monthly EF but also makes the following parameterizations (in section 3b) globally applicable because most climatic datasets—for example, those used as input data for the parameterization—are only available at monthly scale.
The diurnal cycle of available energy (H plus LE), LE, and EF during the daytime at the US-NC1 site (35.81°N, 76.71°W; land-cover type: evergreen needleleaf forest). The red dots are calculated by the fluxes at moment t, demonstrating little variance in daytime EF. The black dashed line is a daytime mean (0.75) calculated from the summation of monthly diurnal fluxes [i.e., Eq. (2)].
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The diurnal cycle of available energy (H plus LE), LE, and EF during the daytime at the US-NC1 site (35.81°N, 76.71°W; land-cover type: evergreen needleleaf forest). The red dots are calculated by the fluxes at moment t, demonstrating little variance in daytime EF. The black dashed line is a daytime mean (0.75) calculated from the summation of monthly diurnal fluxes [i.e., Eq. (2)].
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The diurnal cycle of available energy (H plus LE), LE, and EF during the daytime at the US-NC1 site (35.81°N, 76.71°W; land-cover type: evergreen needleleaf forest). The red dots are calculated by the fluxes at moment t, demonstrating little variance in daytime EF. The black dashed line is a daytime mean (0.75) calculated from the summation of monthly diurnal fluxes [i.e., Eq. (2)].
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
f. Partial correlation analysis
To identify further the impacts of individual parameters on monthly EF, a partial correlation analysis was applied to statistically remove the effect of other factors (Cohen et al. 2013); partial correlation coefficients ρ at a significance level p of 0.05 were used. To parameterize the monthly EF, a stepwise-regression model was applied at a p of 0.05 for entry and 0.1 for removal to avoid collinearity with in-model variables at a p of 0.1 (Montgomery et al. 2012). A stepwise regression is a systematic method for adding and removing terms from a multilinear model on the basis of their statistical significance in a regression. At each step, the p value of an F statistic is computed to test models with and without a potential variable. The model proceeds as follows:
Fit the initial model with the most explanatory power variable.
If any variables not in the model have p values of less than 0.05 (forward selection), add the one with the smallest p value and repeat this step; otherwise, go to step 3.
If any variables in the model have p values greater than 0.1 (backward elimination), remove the one with the largest p value and go to step 2; otherwise, end.
After these three steps, no more variables can be entered and removed. To quantify the collinearity of in-model variables, the variance inflation factor (VIF) is recommended as a criterion, and its value in excess of 10 is a threshold for an unreliable regression (Chatterjee and Price 1977). Also, the correlation coefficient r at a p of 0.05 and root-mean-square error (RMSE) were used to evaluate the accuracy of fitting and parameterization of monthly EF.
g. Selection of determining variables
The LE is strongly controlled by vegetation-growth demand, atmospheric demand, and water supply (Bucci et al. 2008; Chang et al. 2006; Hu et al. 2009; Maximov et al. 2008; Monteith 1965; Saugier et al. 1997; Si et al. 2007; Tanaka et al. 2008; Wang et al. 2010, 2007; Wang and Liang 2008; Zha et al. 2010), including rc, VI, RH, Rn, Ta, vapor pressure deficit, WS, and soil moisture (SM). On the basis of the physical simplification of EF, standardized by its definition of EF = LE/(Rn − G) (Wang and Liang 2009; Wang et al. 2010), the relationships between EF and vegetation demand (expressed by VI), atmospheric demand (expressed by Ta, DTR, and WS), and water supply (expressed by SM or RH) were investigated. These factors are as independent as possible and have specific physical meanings.
Three similar temperature measurements are available: the maximum air temperature Tmax, minimum air temperature Tmin, and daily mean air temperature. The correlation between EF and Tmin is slightly better than those of EF with Tmax and averaged air temperature at monthly scale, likely because Tmin may control respiratory enzyme activity. The Tmin data have been widely collected at weather stations and are easily accessible; therefore, Tmin was analyzed in this study. Similarly, the partial correlation between EF and NDVI is a little better than those of EF with EVI and LAI. The availability of NDVI is much higher than that of EVI and LAI; therefore, the results using the NDVI are reported in this study.
In developing the equations to calculate EF and based on the findings mentioned in section 3a, the 81 sites were divided into five categories: deciduous forests, evergreen forests, shrublands, grasslands, and cropland. An empirical equation was created for each category with climatic parameters (Tmin, DTR, WS, RH) and satellite vegetation index (NDVI) as input data. It is found that the equations derived from such a process can well reflect the impacts of land-cover types and climates on EF (section 3b).
3. Results
a. Biological and environmental controls on monthly EF
The analyses in this section aim to identify the relationships between EF and biological/environmental parameters but cannot determine the causes or results. These relationships can actually be a mixture of cause and result. Such analyses at daily and monthly scales were conducted, and similar conclusions were derived. To coordinate with the following parameterizations of monthly EF for its long-term variance, the results at monthly scale are reported here.
Figure 3 shows the typical scatterplots of monthly EF against monthly Tmin, NDVI, RH, DTR, and WS for deciduous forests, evergreen forests, shrublands, grasslands, and cropland sites. In general, vegetation influences water and heat exchange through biophysical and ecophysiological responses to different environmental conditions. In different ecosystems and climates, the magnitude and mode of these responses are obviously inconsistent (Wang and Dickinson 2012). With the exception of cropland (Fig. 3e1), monthly EF increases linearly with Tmin; the different result for cropland is partly due to agricultural management (e.g., irrigation during seeding periods). The NDVI loses its sensitivity to vegetation coverage when vegetation is dense (Wang et al. 2010); thus, monthly EF increases at a greater rate at high NDVI than at low NDVI in deciduous forests (Fig. 3a2). Because of crop growth and transpiration demand, monthly EF increases linearly with NDVI in cropland sites with high NDVI, whereas significant soil evaporation may contribute to the high monthly EF when the NDVI is low (Fig. 3e2) in the seeding period.
Scatterplots of monthly EF against Tmin, NDVI, RH, DTR, and WS for the example sites US-Dk2 (35.97°N, 79.10°W), US-Ho1 (45.20°N, 68.74°W), US-Ced (39.84°N, 74.38°W), US-ArB (35.55°N, 98.04°W), and US-IB1 (41.86°N, 88.22°W), representing the five land-cover types of deciduous forests, evergreen forests, shrublands, grasslands, and cropland, respectively. The red, green, blue, black, and cyan dots represent the relationships of monthly EF with Tmin, NDVI, RH, DTR, and WS, respectively. The corresponding correlation coefficient is shown at the bottom right of each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Scatterplots of monthly EF against Tmin, NDVI, RH, DTR, and WS for the example sites US-Dk2 (35.97°N, 79.10°W), US-Ho1 (45.20°N, 68.74°W), US-Ced (39.84°N, 74.38°W), US-ArB (35.55°N, 98.04°W), and US-IB1 (41.86°N, 88.22°W), representing the five land-cover types of deciduous forests, evergreen forests, shrublands, grasslands, and cropland, respectively. The red, green, blue, black, and cyan dots represent the relationships of monthly EF with Tmin, NDVI, RH, DTR, and WS, respectively. The corresponding correlation coefficient is shown at the bottom right of each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Scatterplots of monthly EF against Tmin, NDVI, RH, DTR, and WS for the example sites US-Dk2 (35.97°N, 79.10°W), US-Ho1 (45.20°N, 68.74°W), US-Ced (39.84°N, 74.38°W), US-ArB (35.55°N, 98.04°W), and US-IB1 (41.86°N, 88.22°W), representing the five land-cover types of deciduous forests, evergreen forests, shrublands, grasslands, and cropland, respectively. The red, green, blue, black, and cyan dots represent the relationships of monthly EF with Tmin, NDVI, RH, DTR, and WS, respectively. The corresponding correlation coefficient is shown at the bottom right of each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Monthly EF agrees well with RH (Figs. 3a3,b3,c3,d3,e3), which represents impacts of surface aridity (or soil moisture) and water vapor deficit on LE. The DTR is negatively related to monthly EF because as the amount of energy heating Earth’s surface increases it makes Tmax high and then DTR large, and thus energy consumption by LE decreases; consequently, monthly EF decreases (Figs. 3a4,b4,c4,d4,e4). DTR also is closely related to surface aridity or soil moisture (Mu et al. 2007b; Wang and Liang 2008).
The monthly EF values over forests and grasslands have different responses to WS. To be specific, monthly EF negatively correlates with WS over deciduous and evergreen forests but positively correlates over shrublands, grasslands, and cropland (Figs. 3a5,b5,c5,d5,e5). This opposite correlation over different land-cover types results from the complicated effects of WS on LE (e.g., transpiration) and H through the intricate impacts of WS on the aerodynamic resistance, leaf boundary layer resistance, and stomatal resistance (Dixon and Grace 1984; Gutiérrez et al. 1994). The stomatal resistance increases by ~40% with an increase of ~0.7–4.7 m s−1 in WS in a mixed broadleaved deciduous forest (Kim et al. 2014), whereas the aerodynamic resistance decreases in forests and grasslands; thus, the EF decreases more dramatically with WS in the forest region. Lei et al. (2010) reported that WS accelerates the transpiration of Artemisia ordosica (a shrub) in the Tengger Desert of China. Therefore, the relationship between EF and WS depends on the aerodynamic resistance and rc to thermal and vapor transfer. In all, the aerodynamic resistance decreases with increasing WS as based on the MOST, and the rc increases with increasing WS as based on the rearranged Penman–Monteith equation.
Figure 4 displays the partial correlation coefficients ρ of monthly EF with Tmin, NDVI, RH, DTR, and WS at all of the sites. In comparing the results over each land-cover type shown in Fig. 4 with each other and trying our best to merge different land-cover types into a class, the study sites were divided into five categories: deciduous forests, evergreen forests, shrublands, grasslands, and cropland. Strong relationships are observed between monthly EF and Tmin, NDVI, and RH in deciduous forests, with site-averaged ρ values of 0.53, 0.52, and 0.46 (p < 0.05), respectively (Fig. 4). When compared with deciduous forests, stronger relationships are found between monthly EF and Tmin and NDVI in evergreen forests, with site-averaged ρ values of 0.65 and 0.51 (p < 0.05), respectively. Monthly EF is less sensitive to NDVI in evergreen forests because of the low perennial variance of NDVI. Similarly, Tmin, RH, NDVI, and WS mainly control monthly EF in shrublands, with site-averaged ρ values of 0.53, 0.50, 0.42, and −0.37 (p < 0.05), respectively. The strongest correlation of monthly EF with NDVI occurs in grasslands, with a site-averaged ρ of 0.66 (p < 0.05); similar relationships among RH, Tmin, DTR, and WS and monthly EF are observed for grasslands, with site-averaged ρ values of 0.46, 0.44, −0.40, and 0.36 (p < 0.05), respectively. Because of the efficient use of water and energy by agricultural management, NDVI, WS, Tmin, RH, and DTR have very similar relationships with monthly EF in cropland, with site-averaged ρ values of 0.42, 0.36, 0.35, 0.33, and −0.27 (p < 0.05), respectively.
The partial correlation coefficients of monthly EF with (a) Tmin, (b) NDVI, (c) RH, (d) DTR, and (e) WS for the five vegetation classes (deciduous forests, evergreen forests, shrublands, grasslands, and cropland). The white bar represents a partial correlation that does not pass the t test at a significance level of 0.05, and the bars with other colors pass that test. Each bar in the figure represents one station in Tables 1 and 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The partial correlation coefficients of monthly EF with (a) Tmin, (b) NDVI, (c) RH, (d) DTR, and (e) WS for the five vegetation classes (deciduous forests, evergreen forests, shrublands, grasslands, and cropland). The white bar represents a partial correlation that does not pass the t test at a significance level of 0.05, and the bars with other colors pass that test. Each bar in the figure represents one station in Tables 1 and 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The partial correlation coefficients of monthly EF with (a) Tmin, (b) NDVI, (c) RH, (d) DTR, and (e) WS for the five vegetation classes (deciduous forests, evergreen forests, shrublands, grasslands, and cropland). The white bar represents a partial correlation that does not pass the t test at a significance level of 0.05, and the bars with other colors pass that test. Each bar in the figure represents one station in Tables 1 and 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Figure 5 demonstrates the maximum explanation of monthly EF by the most explanatory power variable independently. The explanatory variance of monthly EF is defined by the square of partial correlation coefficient of monthly EF with Tmin, NDVI, RH, DTR, and WS, ranging from 0 to 1. NDVI, Tmin, and RH are main factors over different land-cover types, as indicated by the green, red, and blue bars, respectively (Fig. 5). The maximum variances of monthly EF explained by NDVI, Tmin, and RH are 0.83, 0.72, and 0.71, respectively, and their means are 0.31, 0.29, and 0.23, respectively. To be more specific, 0.45 of the variance of EF can be explained by NDVI in grasslands, whereas this value is only 0.22 in forests. In contrast, Tmin can explain 0.35 of the variance in EF in forests but only 0.20 of the variance of EF in grasslands.
The most explanatory power variable at each site is shown as a bar graph with the square of spatial correlation coefficient of monthly EF with this variable at a significance level of 0.05, on a base map of the IGBP land-cover types (MCD12Q1; 2007). IGBP types: barren or sparsely vegetated (BSV), snow ice (SNI), cropland/natural vegetation mosaics (CVM), cropland (CRO), wetland (WET), grassland (GRA), savanna (SAV), woody savanna (WSA), open shrubland (OSH), closed shrubland (CSH), mixed forest (MF), deciduous broadleaf forest (DBF), deciduous needleleaf forest (DNF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), and water body (WB). Data collected at all sites in Tables 1 and 2 are shown.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The most explanatory power variable at each site is shown as a bar graph with the square of spatial correlation coefficient of monthly EF with this variable at a significance level of 0.05, on a base map of the IGBP land-cover types (MCD12Q1; 2007). IGBP types: barren or sparsely vegetated (BSV), snow ice (SNI), cropland/natural vegetation mosaics (CVM), cropland (CRO), wetland (WET), grassland (GRA), savanna (SAV), woody savanna (WSA), open shrubland (OSH), closed shrubland (CSH), mixed forest (MF), deciduous broadleaf forest (DBF), deciduous needleleaf forest (DNF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), and water body (WB). Data collected at all sites in Tables 1 and 2 are shown.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The most explanatory power variable at each site is shown as a bar graph with the square of spatial correlation coefficient of monthly EF with this variable at a significance level of 0.05, on a base map of the IGBP land-cover types (MCD12Q1; 2007). IGBP types: barren or sparsely vegetated (BSV), snow ice (SNI), cropland/natural vegetation mosaics (CVM), cropland (CRO), wetland (WET), grassland (GRA), savanna (SAV), woody savanna (WSA), open shrubland (OSH), closed shrubland (CSH), mixed forest (MF), deciduous broadleaf forest (DBF), deciduous needleleaf forest (DNF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), and water body (WB). Data collected at all sites in Tables 1 and 2 are shown.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
b. Empirical methods to estimate monthly EF and their validation
The fitting coefficients are listed in Table 3 and are in agreement with the above correlation analysis (section 3b). The scatterplots of the fitting results are shown in Fig. 6. For Eq. (3), the r values range from 0.80 to 0.92, and the RMSE values range from 0.07 to 0.14 for five categories. The vegetation growth has a larger impact on the EF over the deciduous forests, grasslands, and cropland than over evergreen forests and shrublands by comparison of the equation coefficients of NDVI. Moreover, WS acts to obviously promote LE for short vegetation, such as shrublands, grasslands, and cropland. The VIF that is recommended to evaluate the multicollinearity among the predictors with a threshold of 10 (Chatterjee and Price 1977) indicates that the fitting equations are reliable regression over five vegetation classes (Table 3).
The fitted coefficients in Eq. (3) for five categories on a monthly scale are calculated by stepwise-regression models with the sites in Table 1. The correlation coefficients r and RMSE values between the measured and fitted EFs are listed. The multicollinearities among the predictor variables are evaluated by the VIF. A VIF in excess of 10 is suggested to be a criterion for an unreliable regression. An em dash indicates that this parameter does not enter the model.
The scatterplots of fitting results for (a) deciduous forests including deciduous broadleaf forests and mixed forest, (b) evergreen forests including evergreen broadleaf forest and evergreen needleleaf forest, (c) shrublands including closed shrubland and open shrubland, (d) grasslands including grassland and woody savanna, and (e) cropland. Using the data collected at sites in Table 1, the monthly EF is fitted by the stepwise-regression model [Eq. (3)]. The correlation coefficient r and RMSE are listed in each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The scatterplots of fitting results for (a) deciduous forests including deciduous broadleaf forests and mixed forest, (b) evergreen forests including evergreen broadleaf forest and evergreen needleleaf forest, (c) shrublands including closed shrubland and open shrubland, (d) grasslands including grassland and woody savanna, and (e) cropland. Using the data collected at sites in Table 1, the monthly EF is fitted by the stepwise-regression model [Eq. (3)]. The correlation coefficient r and RMSE are listed in each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The scatterplots of fitting results for (a) deciduous forests including deciduous broadleaf forests and mixed forest, (b) evergreen forests including evergreen broadleaf forest and evergreen needleleaf forest, (c) shrublands including closed shrubland and open shrubland, (d) grasslands including grassland and woody savanna, and (e) cropland. Using the data collected at sites in Table 1, the monthly EF is fitted by the stepwise-regression model [Eq. (3)]. The correlation coefficient r and RMSE are listed in each panel.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Figures 7 and 8 illustrate the validation results for each site over deciduous forests, evergreen forests, shrublands, grasslands, and cropland (listed in Table 2). The predicted monthly EF values are in good agreement with the measured monthly EF values over five categories (Fig. 7). The r values between predicted and measured monthly EF range from 0.80 to 0.93, and the RMSE values range from 0.09 to 0.12 for five categories (Fig. 8). These results show that the equations for EF can be used to accurately estimate the long-term variance in EF from conventional weather observations and NDVI, which are measured and available globally.
Similar to Fig. 6, but for the validation results (comparison of measured and predicted monthly EF). Using the data collected at sites in Table 2, the predicted monthly EF is calculated with Eq. (3).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Similar to Fig. 6, but for the validation results (comparison of measured and predicted monthly EF). Using the data collected at sites in Table 2, the predicted monthly EF is calculated with Eq. (3).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
Similar to Fig. 6, but for the validation results (comparison of measured and predicted monthly EF). Using the data collected at sites in Table 2, the predicted monthly EF is calculated with Eq. (3).
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The validation statistics for the measured and predicted monthly EFs calculated by Eq. (3) from the sites belonging to five vegetation classes in Table 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The validation statistics for the measured and predicted monthly EFs calculated by Eq. (3) from the sites belonging to five vegetation classes in Table 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
The validation statistics for the measured and predicted monthly EFs calculated by Eq. (3) from the sites belonging to five vegetation classes in Table 2.
Citation: Journal of Applied Meteorology and Climatology 55, 1; 10.1175/JAMC-D-15-0126.1
4. Conclusions and discussion
The objectives of this study are to identify the various factors that control monthly EF for different land-cover types and climates and to further parameterize monthly EF. Through partial correlation analyses of EF with relevant factors at 81 sites, the factors controlling monthly EF at different vegetation classes are determined as follows:
Positive correlations of monthly EF with Tmin, NDVI, and RH are found for all sites, whereas the effect of WS and DTR on monthly EF is complicated and depends on land-cover type.
For deciduous forest sites, Tmin, NDVI, and RH are the three main controlling factors on monthly EF and have a saturation effect at high NDVI. For evergreen forests, Tmin and RH are the main controls. For shrubland sites, Tmin, RH, NDVI, and WS mainly control monthly EF. For grasslands, NDVI has the best correlation with monthly EF, whereas RH, Tmin, DTR, and WS all have similar relationships with monthly EF. Because of agricultural management, NDVI, WS, Tmin, RH, and DTR contribute almost equally to the control of monthly EF.
Because Ta, WS, and RH are measured with high frequency at globally distributed stations and because NDVI can be acquired with remotely sensed data, these equations can be used to monitor global ecosystem dynamics and detect long-term trends in EF. Another advantage of these linear equations is that they are insensitive to errors of input data, unlike the nonlinear relationship of aerodynamic resistance with the environmental parameters in one- and two-source models. This study provides a preliminary study on methods to calculate EF, which is of great importance for climatic studies. High precision of parameterization is still a challenge in accurately estimating EF, and further study is needed. In addition, to obtain the global EF over all land-cover types, some effort is being made to collect the relevant data for further validation or even for developing a model of EF over the other land-cover types that were not involved in this study.
Acknowledgments
This study was funded by the National Basic Research Program of China (2012CB955302) and the National Natural Science Foundation of China (91337111, 41525018, and 41205036). AmeriFlux data were downloaded from http://ameriflux.ornl.gov/. MODIS satellite vegetation indices and land-cover-type data were downloaded from https://lpdaac.usgs.gov/. The world map of the Köppen–Geiger climatic classification was downloaded from http://koeppen-geiger.vu-wien.ac.at/.
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