Ecosystem-dynamics link to hydrologic variations for different landcover types

The soil moisture and evapotranspiration (ET) influence on ecosystem dynamics has been studied only in a limited way owing to the lack of large-scale measurements. The Normalized Difference Vegetation Index (NDVI) data retrieved using the Moderate Resolution Imaging Spectroradiometer (MODIS) was successfully used in this study to identify the ecological relationships that involve soil moisture and ET at 132 sites located on different continents around the world. Optimal relationships exist between NDVI and soil moisture within time lags of 10 days at forest and grassland sites, and 25 days at cropland and shrub land sites. The ecological correlations between NDVI and the hydrological variables are affected mainly by the land-cover type. The densely vegetated areas show shorter time lags for NDVI to ET owing to canopy evaporation and plant transpiration, which are almost simultaneous with NDVI. Article history: Received 22 March 2016 Revised 12 September 2016 Accepted 13 September 2016


IntroductIon
Vegetation production is the source of all food, fiber and fuel available for human consumption.Vegetation is therefore a fundamental defining aspect of Earth's habitability (Running et al. 2004).Ecological processes including vegetation activities have been recently lengthened by the advancement of biological spring and delay of biological winter through the global warming process (Walther et al. 2002).This global-warming climate has caused irreversible feedbacks and impacts regarding ecosystems such as reductions in the global net-primary-production amount (Zhao and Running 2010) and global evapotranspiration (ET) (Jung et al. 2010).Under such climatic conditions the incidences of persistent drought may increase (Dai et al. 2004;Dai 2011) along with a rapid increase the demand for the world's scarce freshwater supply (Vörösmarty et al. 2010).These factors may restrict the availability of water for food production, placing global food security at risk.A clear understanding of the relationships between ecological and hydrological components is essential to estimate the dynamics of ecological processes (Santos and Negri 1997;Pielke et al. 1998;Fisher et al. 2009;Konings and Gentine 2017).However, the direct relationships between these components have not been intensively studied owing to the paucity of regional datasets (Méndez-Barroso et al. 2009).Remote sensing by making use of satellite imagery has been recognized as a successful tool for monitoring ecological and hydrological variables such as soil moisture, ET, and vegetation grossness with different spatial resolutions (Schmugge et al. 2002).
The Moderate Resolution Imaging Spectroradiometer (MODIS), mounted on Terra and Aqua satellites, provides unprecedented information regarding the vegetation and surface-energy conditions at a variety of scales, from watersheds to continents and even the entire planet (Justice et al. 2002).The Normalized Difference Vegetation Index (NDVI), derived from the MODIS is calculated as the difference between the near-infrared and red-reflectance values Terr. Atmos. Ocean. Sci., Vol. 28, No. 3, 437-462, June 2017 that are normalized with their sum.This index is responsive to the conditions and vegetation growing states on the planet surface.The NDVI has been successfully used to monitor global photosynthetic activity (Tucker 1979;Huete et al. 2002;Justice et al. 2002).Note that the background effect can be removed by the SVI, but the NDVI shows a better representation for monitoring the ecosystem biomass dynamics (Huete et al. 2002).Climate change has recently been linked to a vegetation response observed through vegetationgreenness changes according to land-atmosphere water, carbon and energy fluxes, and the associated climatic feedbacks (Atkinson et al. 2011;Mu et al. 2013).
The relationship between NDVI and hydrologic variables such as ET and soil moisture has helped to elucidate the manner in which hydrological changes impact ecological variation (Szilagyi et al. 1998;Adegoke and Carleton 2002;Wang et al. 2007;Schnur et al. 2010).Most of the previous studies on this relationship have pointed out a time lag between NDVI and hydrologic variables.Investigations of the relationships between ecological variables and hydrologic components have thus far been limited to the few local regions with mostly semi-arid climatic conditions (Schultz and Halpert 1993;Nicholson and Farrar 1994;Farrar et al. 1994;Szilagyi et al. 1998;Wang et al. 2001Wang et al. , 2007;;Adegoke and Carleton 2002;Nagler et al. 2005;Kurc and Small 2007;Suzuki et al. 2007;Méndez-Barroso et al. 2009;Nandintsetseg et al. 2010;Zribi et al. 2010).We estimate the relationships between soil moisture and ET in this study with MODIS NDVI at 132 stations located on different continents around the world (Fig. 1; Table S1).The main objective is to identify an ecological relationship with hydrologic variables considering a time lag.

In situ Measurements data
The Global Energy and Water Cycle Experiment in cooperation with the Group on Earth Observations and the Committee on Earth Observation Satellites initiated the International Soil Moisture Network (ISMN) to maintain standardized and quality-controlled databases for soil moisture around the world (Dorigo et al. 2011).More than 30 networks and 1100 stations voluntarily contribute to this initiative by providing continuous hydrometeorological measurements on a long-term basis.ISMN provides a direct-download service for global in situ data at multiple depths through its website (http://ismn.geo.tuwien.ac.at/).The ground soil-moisture measurements from 132 stations belonging to several networks were used in this study (Table 1).According to the MODIS 12 land-cover product, the ISMN stations are surrounded by a variety of land-cover types.Using the International Geosphere-Biosphere Programme (IGBP) land-cover classification, 41 Soil Climate Analysis Network (SCAN) stations in the United States were categorized as 12 cropland, 2 forest, 16 grassland, and 11 shrub land sites (Table 1).SCAN has been operated by the Natural Resources Conservation Service (NRCS) to provide nationwide hydrometeorological variables including soil temperature and soil moisture (Schaefer and Paetzold 2000).The 36 OzNet sites, which are based in Australia,  Ground in situ measurements at 10 Ameriflux sites and a single Asiaflux site were also used.Ameriflux and Asiaflux are regional coordinated networks of the International Network Measuring Terrestrial Carbon, Water and Energy Fluxes (FLUXNET).Over 500 flux-tower sites located in a variety of land-surface conditions have produced micrometeorological measurements continuously through FLUX-NET as a part of an integrated global network (Baldocchi et al. 2001).FLUXNET provides a valuable opportunity to quantify water, energy, and carbon circulation at a variety of scales.Soil-moisture data collected every 30 min were downloaded through the Ameriflux (http://public.ornl.gov/ameriflux/dataproducts.html) and Asiaflux (http://asiaflux.net/) Web services.All of the Ameriflux sites are classified as forest, whereas the Asiaflux site is located on grassland (Table 1).
The Rural Development Administration (RDA) of South Korea observes the surface-depth soil moisture in numerous domestic regions for agricultural purposes.Alongside other international networks, the RDA provides quality-controlled soil-moisture data every 30 min.Eight datasets composed of six cropland and two forest sites, the leading land-cover types in Korea, were selected in this study owing to an insufficient number of Asia-based study sites.The datasets were downloaded from the RDA website (http:// www.rda.go.kr/).
Different types of soil-moisture instruments were used in different networks (Table 1).The in situ soil moisture was measured using six electronic sensors including the following two time-domain reflectometry (TDR) sensors: the TDR100 (Campbell) and the D-LOG/mpts (Easy Test).The following four frequency-domain reflectometry (FDR) sensors were also included: the Theta Probe ML2X (Delta-T Devices), the Hydra Probe (Stevens), and the CS615 and CS616 probes (Campbell; Table 1).Explanations are given with respect to the devices' electronic sensors used to mea-sure soil moisture, as well as the measurement accuracy and device calibrations.Details of the TDR-and FDR-sensor characteristics can be found in Topp et al. (1980) and Mittelbach et al. (2012).Geographic station profiles including latitude, longitude and altitude were also obtained together with the meteorological measurements (Table S1).We note that the in situ soil moisture data used in this study may be used as a representative value of larger areas based on the normality of the data (Vachaud et al. 1985;Choi and Jacobs 2007;Brocca et al. 2009).

ModIs ndVI Products
The Global MODIS NDVI was designed to provide consistent spatio-temporal comparisons of vegetation conditions (Suzuki et al. 2007).NDVI is calculated from spectral measurements, as follows: where NIR and RED are the spectral-reflectance measurements in the red and near-infrared bands, respectively.The MOD13A2-series data including NDVI are provided by the United States Geological Survey (https://lpdaac.usgs.gov/products) as a gridded level-3 product.This data product has been provided since 2000 as a 16-day composite at 1-km resolution (Masuoka et al. 1998).Because the satellite NDVI contains a large amount of noise owing to corrupted spectral reflectance during the non-growing season (Zhao and Running 2010), the MODIS NDVI comparisons with both soil moisture and ET were conducted during the growing seasons, from May to September.

ModIs 16 Global terrestrial-Et Products
The MODIS global terrestrial-ET products were produced using an algorithm developed by Mu et al. (2007Mu et al. ( , 2011)), based on the Penman-Monteith equation (Monteith 1965), as follows: (1 where λE is the latent heat flux (W m -2 ), λ is the latent heat of vaporization (J kg -1 ), s is the slope of the curve that relates the saturated water-vapor pressure to temperature (kPa K -1 ), A is available energy (W m -2 ), t is air density (kg m -3 ), C P is the specific heat capacity of air (J kg -1 K -1 ), e sat is the saturated water-vapor pressure (Pa), e is the actual water-vapor pressure (Pa), r a is the aerodynamic resistance (s m -1 ), c is the psychrometric constant of 0.66 Pa K -1 , and r s is the surface resistance (s m -1 ).
The model uses spatially interpolated Modern Era Retrospective-Analysis for Research and Applications for the Global Modeling and Assimilation Office (MERRA GMAO) meteorological data at 1-km resolution as meteorological inputs (Mu et al. 2007).The algorithm also needs Collection 4 MODIS MOD12Q1 land cover 2, MOD15A2 FPAR/LAI (Myneni et al. 2002), and the MCD43B2/B3 albedo as remote sensing inputs.
The revised Penman-Monteith-based model (Mu et al. 2007) was used to produce the MODIS-based global landsurface ET data at 1-km resolution.The revised algorithm significantly improved the model accuracy (e.g., additional computation of stomatal conductance and canopy conductance, additional soil-evaporation procedure, etc.), and the revised Penman-Monteith-based-model data were then employed for the ET estimation.The biome properties look-up table categorized using different land cover types was used to estimate land surface parameters for MODIS ET products (Mu et al. 2007).Note that the ET time lag signal may be affected by these biome properties depending on the different land cover types.
The MODIS ET products were provided by the Numerical Terradynamic Simulation Group at the University of Montana (http://www.ntsg.umt.edu/project/mod16).The MODIS Land Subsets website (http://daac.ornl.gov/modisglobal) produces spatial subsets of the MOD16A2 ET products at the regional scale in addition to the NDVI.To avoid any temporal mismatches with MODIS NDVI, two consecutive eight-day-composite ET datasets were summed and correlated with the corresponding NDVI data (Méndez-Barroso et al. 2009).

GPcP 1dd daily Precipitation dataset
The Global Precipitation Climatology Project (GPCP) One-Degree Daily (1DD) precipitation data were accepted as an official GPCP product in August 2000 and have been subsequently provided by the World Data Center (WDC) System for Meteorology, Asheville, which is based at the National Oceanic and Atmospheric Administration's (NO-AA's) National Climatic Data Center (http://lwf.ncdc.noaa.gov/oa/wmo/wdcamet-ncdc.html).GPCP 1DD, a satellitebased 1° daily precipitation product provided at the global scale, has been widely applied in a variety of fields.GPCP 1DD is informed by the Geostationary Operational Environmental Satellite (GOES) Precipitation Index (GPI), a rainfall-estimation technique that uses infrared (IR) estimates from geostationary satellites that are within the 40°N to 40°S band (Huffman et al. 2001).The threshold-matched precipitation index (TMPI), which is suggested in probability matching concepts (Xu et al. 1999), was used to compute precipitation at 1° and a 3-h resolution, and these were summed to estimate the daily products.Because geostationary IR datasets do not provide coverage outside the 40°N to 40°S band, the Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) precipitation datasets from the polar-orbiting NOAA-12 and NOAA-14 satellites were used.Rain-rate estimations in the 39 -40°N and 39 -40°S bands are formed using the empirical relationships of TOVS-derived cloud-top pressure, fractional cloud cover and the relative humidity profile.The GPCP 1DD datasets were extracted for each study site.Because 1DD datasets from 1997 -2008 were available, the extracted point data from 2000 -2008 were summed into 16-day composites to match the point data of the other parameters (Fig. 2a).

scale Adjustment
The ground-measured soil-moisture data were obtained on an hourly basis and the satellite-driven ET data were provided as eight-day composites.Regarding the MODIS NDVI that was processed to represent each 16-day period, a direct comparison can cause severe temporal-discordance problems.A scale adjustment was conducted in advance to match the eco-hydrologic variables.Because NDVI has the longest interval among the variables, the temporal resolutions of the soil moisture and ET were adjusted to correspond with NDVI.
Initially, the hourly soil-moisture data were averaged for each day.The daily soil-moisture data averages were further averaged over the corresponding periods in an analysis of the contemporaneous relationship with NDVI.In the time-lag analysis, each of the 16 daily-soil-moisture-data groups for 5, 10, 15, 20, 25, and 30 preceding days was averaged and compared with the corresponding NDVI (Fig. 3; Table S2).For instance, when MODIS NDVI represented the data between day 129 and day 144 of a year, the 16 dailysoil-moisture data from day 129 to day 144 were averaged to obtain the representative data, and the two 16-day variables with the same period were compared.In the time-lag analysis of 5 and 10 days, the data of 5 previous days and 10 previous days were applied, respectively, to obtain the representative soil-moisture data, and the average values of the periods day 124 to day 139 and day 119 to day 134 were related to NDVI composed of the period day 129 to day 144 (Fig. 2b).
Although the soil-moisture and NDVI data represent the average values for any period, the MODIS eight-day composite ET is defined as the total amount for the eightday period.Therefore, the extracted ET data at each site were summed over the corresponding periods for the temporal trend analysis.In the time-lag analysis, each ET-data pair of the previous 8, 16, 24, and 32 days was summed and compared with the corresponding NDVI (Fig. 4; Table S2).Similarly, if the MODIS NDVI represents the data between day 129 and day 144, two 8-day composites of the ET data each comprised of the periods day 129 to day 136 and day   137 to day 144 were summed and compared with the NDVI data.In the time-lag analysis of 8 and 16 days, the total ET amount for the periods day 121 to day 136 and day 113 to day 128, respectively, were compared with the NDVI data that represents day 129 to day 144 (Fig. 2c).

Linear regression Analysis
A simple linear-regression method was adopted to describe the covariation between the eco-hydrologic variables (Helsel and Hirsch 1992).If a pair of datasets has a linear relationship, a simple linear equation can show how a variable changes in response to the other variable.The following is the model for a simple linear regression (Helsel and Hirsch 1992): , ,..., where y i and x i are the i th observations of the dependent and independent variables, respectively; 0 b is the intercept; 1 b is the slope; i f is the random variable; and n is the sample size.The mean of i f is zero.In a least-squares method, the sum of square i f is minimized to zero so that the following applies: , ,..., y b b x i n 1 2 where y i is the estimate of y given

correlation coefficient
The linear-correlation coefficient r was employed to verify the direct relationship between NDVI and the hydrologic variables.Pearson's r is widely used to reflect the degree of linear relationship between two variables.The coefficient is obtained from the standardization of two different parameters that are invariant in scale (Helsel and Hirsch 1992), and it can be estimated using the following formula: where n is number of samples, x i and y i are the i th observations of the two different variables, x and y are the means, and s x and s y are the standard deviations.This coefficient can vary in a range of -1 to 1. Correlations of -1 and 1 indicate that the data lie exactly on straight lines with negative and positive slopes, respectively, while a correlation of 0 indicates that a linear relation does not exist between the two variables (Helsel and Hirsch 1992).

relationship between Ecological Variability and hydrologic components
The time series of the average 16-day MODIS NDVI, soil moisture, and MODIS ET during the study periods at several of the sample locations for each land-cover type in different continents are illustrated in Fig. 3.The soil moisture shows a temporal up/down phase along with the rainfall events.Similar fluctuation patterns are shown between ET and the rainfall with different peaks for different continents observed around July and August in the Northern Hemisphere and January and February in the Southern Hemisphere (Fig. S1).
Regardless of the corresponding continent, the ET data were routinely higher for forest compared with other land-cover types (Fig. S1).Although the soil-moisture data showed direct responses to rainfall events, the ET data showed less-direct responses to rainfall events and gradually increased until the start of the vegetation senescence (Fig. S1).Afterward, a relatively rapid or similar decay compared with NDVI was observed.Regarding soil moisture, NDVI showed similar fluctuation patterns, especially with ET.From the initial stage of the growing season, NDVI increased in a similar time phase with rainfall events and gradually increased until the start of the vegetation senescence.However, these temporal fluctuation patterns were not easily identified at a number of stations in Europe.
NDVI was positively correlated to soil moisture, ET, and precipitation without time lags at most of the sites, with the exception of six forests, two shrub lands, and two cropland sites, as shown by the white bar for 0-day lags in Figs. 4 -6.A higher number of negative correlations were observed at the forest sites (Fig. 4b).The likely explanation for these negative correlations is the temperature limitations at the forest sites, whereby the vegetation activities are predominantly controlled by temperature rather than wetness (Schultz and Halpert 1993;Suzuki et al. 2007).Suzuki et al. (2007) demonstrated that NDVI was either positively or negatively correlated with the precipitation at different regions that were characterized as "wetness-" or "warmthdominated," respectively.
The correlation coefficients (r) between NDVI and soil moisture ranged from -0.55 -0.92 (Fig. 4; Table S2); those between NDVI and ET were from -0.36 -0.89 (Figs. 4, 5; Table S2).The positive r values of NDVI in relation to soil moisture at most of the sites are similar to those of the previous studies (Adegoke and Carleton 2002;Wang et al. 2007;Schnur et al. 2010).The results show that NDVI reflects the phenological changes at the study sites and that soil moisture is a dominant controlling factor for vegetation activities.The different soil moisture spatial scales with NDVI and ET at each site may explain the lower correlations between NDVI and soil moisture compared with those between NDVI and ET.The point-based measurements of the soil moisture represent only limited samples of the entire study area (Choi 2012).In principle, NDVI reflects vegetation-growing conditions that are controlled by climate, such as soil moisture, atmospheric vapor-pressure deficit, air temperature, and radiation (Gu et al. 2009).Photosynthesis and vegetation transpiration are closely coupled through stomata; therefore, NDVI is more responsive to ET (Figs. 4,5,and S1).

time Lags of the relationship between Ecological Variability and hydrologic components
Soil moisture is an important water-stress factor that limits stomatal conductance, and precedent soil moisture may control current photosynthesis and ET (Wang et al. 2007).When spring starts, increasing temperature and precipitation levels trigger soil thawing and the soil moisture consequently increases.The increased soil moisture stimulates vegetation growth and the NDVI increases.In fall, the decreasing temperature, radiation and precipitation reduce the soil moisture and levels of plant photosynthesis (Waring and Running 2007).The vegetation begins to brown down and the NDVI decreases, explaining the best correlation among the soil moisture, ET, and NDVI with time lags.The current NDVI and ET values should be more closely correlated to the soil moisture at precedent conditions.
Significantly stronger relationships (p < 0.05) were observed between NDVI and soil moisture with a variety of time lags within a 25-day period (Fig. 4).The highest correlation-coefficient value was 0.94 between NDVI and the 10-day-earlier soil moisture at the Cabrières-d'Avignon site in Europe.Generally, stronger relationships were observed with the 25-day time lag at the cropland and shrub land sites, and with the 10-day time lag at the forest and grassland sites (Fig. 4a).Typically, tree roots can access water at deeper soil levels and have less fluctuating variations than those at shallow soil depths (Canadell et al. 1996).General croplands that are characterized as shallow-rooted plants have a shorter time lag (i.e., less than one month) than those of deep-rooted trees and shrubs (i.e., longer than a one month) (Savenije 2004).In this study, however, the NDVI time lags of the forest sites following the soil-moisture measurement were relatively shorter compared with those of the croplands because the soil-moisture data were measured only at 5 -10 cm surface depths (Table 1).Even if the absolute root depth and lateral spread of the plants are related to growth forms, climate systems, and soil mechanisms, the minimum root depth of the trees is typically considered to be 1 m (Schenk and Jackson 2002); therefore, the current soilmoisture data measured at the top surface depths might not be consistent for detecting the behaviors of deeply rooted plants such as forests.
As with the time-lag analyses between NDVI and the soil moisture, stronger relationships were found between NDVI with time lags and ET (Fig. 5).The strongest correlations occurred with different time lags of 0 -32 days at different sites.The NDVI time lags to ET were usually shorter than those of the NDVI to soil moisture, as shown by white bars with red boxes in Fig. 5. ET not only comprises plant transpiration, but also the evaporation from the soil surface and plant-canopy-intercepted precipitation.The  ET rates are influenced mainly by plant types characterized by different root distributions, phenology, stomatal conductance, and leaf-area index (Kurc and Small 2007).During the growing seasons, the high temperatures and wetness from frequent rainfall events induce optimal conditions for ET composed of evaporation and plant transpiration (Han et al. 2010).Transpiration, the largest ET component in areas where vegetation grows well, is the water that is simultaneously lost via the stomata with the carbon-flux exchanges, and a time lag to NDVI may not exist.Moreover, the large amount of precipitation intercepted by the fertile vegetation canopy triggers a rapid wet-canopy evaporation process (Savenije 2004;Suzuki et al. 2007;Miralles et al. 2010;Cui and Li 2014), resulting in a short time lag.Approximately 20 -40% of annual rainfall is intercepted in forest sites, and the evaporation from the interception is a rapid feedback to the atmosphere that occurs within a time lag of one day (Savenije 2004).For example, at the sites where the NDVI is high in summer, such as the forest site at Créon d'Armagnac (CRE) and the cropland site at Perthshire (PER), the ET responded to the NDVI almost simultaneously with no time lag (Figs. 5, S1; Table S2).At Chestnut Ridge (CHR), another forest site, and the cropland site in Haenam (HAE), the strongest relationship occurred between the eight-day-earlier ET and NDVI (Figs. 5, S1; Table S2).A relatively low NDVI, however, corresponds with a low leaf area and a low level of intercepted precipitation, and ET is mainly a result of soil evaporation controlled by soil moisture; therefore, NDVI has a longer time lag of 16 days to ET at a number of sites such as Balranald-Bolton Park (BBP) and Bundure (BUN) (Fig. 5; Table S2).

controlling Factor of the relationship between Ecological Variability and hydrologic components
The relationship between the ecological variability and the hydrologic components in worldwide regions shows the existence of different time lags between NDVI-soil moisture and NDVI-ET, depending on the land-cover type.Precedent soil moisture is the controlling factor for vegetation growth.Several previous studies have demonstrated that the response times of the NDVI to soil moisture are shorter in arid climate conditions than those in humid climate conditions (Kerr et al. 1989;Szilagyi et al. 1998;Wang et al. 2007;Schnur et al. 2010).
Although transpiration and carbon-flux exchanges through stomata are simultaneous and the evaporation from canopy-intercepted water has almost no time lag to NDVI, the NDVI that represents vegetation-growth status has a time lag to ET because, soil evaporation is controlled primarily by soil moisture.In this study, the land-cover type was identified as a major controlling factor of the relationship between the ecological variability and the hydrologic components in global regions.These relationships found in this study may enrich our knowledge for environmental managements in response to climate change and human activities.

concLusIons
The ecological relationships among MODIS NDVI, soil moisture, and ET were investigated at 132 global sites in this study.Positive relationships between NDVI and soil moisture and between NDVI and ET were observed at most of the sites.An optimal relationship exists between NDVI and soil moisture within time lags of 10 days at the forest and grassland sites and time lags of 25 days exists at the cropland and shrub land sites.Generally, the time lags between NDVI and ET are shorter than those between NDVI and soil moisture.Densely vegetated areas show shorter time lags for NDVI to ET because ET is largely composed of evaporation from canopy-intercepted precipitation and plant transpiration, both of which are almost simultaneous with the NDVI.The relationship between ecological variability and the hydrologic components is affected mainly by the corresponding land-cover type.The results from this study are useful for understanding carbon-, water-, and energy-feedback mechanisms and for an estimation of ecosystem dynamics that uses time-lag information from regional and continental climate systems.

Fig. 1 .
Fig. 1.Geographic locations of the study sites and the land-cover-classification pie charts for all of the sites on each continent.(Color online only) Fig. 2. Scale adjustment procedure for direct comparison between the NDVI and the precipitation (PR), soil moisture (SM), and ET.(a) Precipitation procedure -Step 1. Sum the i day, 3-h precipitation data; Step 2. Preceding k-day, form n-k day to n-k + 15 day of the daily precipitation data were summed.(b) Soil-moisture procedure -Step 1.Average the i day, hourly soil-moisture data; Step 2. Preceding k-day, from n-k day to n-k + 15 day of the daily soil-moisture data were averaged.(c) ET procedure -Preceding k-day, sum the two 8-day composites of the ET data with the periods from n-k day to n-k + 7 day and from n-k + 8 day to n-k + 15 day.

Fig. 3 .
Fig. 3.The time-series graphs describe the 16-day mean values of the precipitation, NDVI, soil moisture, and ET at the selected sites, which show the representative temporal trends for each continent.
x i ; b 0 is the estimate of 0 b and is solved by b y x b 0 1 = -; and b 1 , the estimate of 1 b , is given by b S SS xy x 1 = .S xy is the sum of the xy cross products and y are the means.S Sx is the sum of squares x so that

Fig. 4 .
Fig. 4. Correlation coefficients among the NDVI with 16-day soil moisture and 0-to 30-day time lags.(a) Cropland, (b) forest, (c) grassland, and (d) shrubland.Each bar-height represents the absolute value of correlation coefficient (shown in legend box).The red boxes of the box graph suggest the highest correlation coefficients at each site, with significance at the 99% confidence levels.(Color online only)

Fig
Fig. S1.Time-series graphs for the growing season.The MODIS 16-day NDVI values from 2000 -2010 for each period were averaged to prevent a misleading representation due to extreme values; similarly, the MODIS ET values for the 11-year period were summed into 16-day composites and then averaged for each year to match the corresponding periods.All of the available 16-day average values of the in situ soil-moisture data were averaged again for given periods.The GPCP 1DD precipitation values from 2000 -2008 were summed into 16-day composites and then averaged as the ET values were.

Table S2 .
Correlation coefficients among the NDVI with 16-day ET, 16-day mean soil moisture, and 16-day precipitation with a variety of time lags.The bold numbers in the table suggest the highest correlation coefficients at each site.* and ** indicate significance at the 95 and 99% confidence levels, respectively.