Integration of the GG model with SEBAL to produce time series of evapotranspiration of high spatial resolution at watershed scales

Authors


Abstract

[1] Lack of good quality satellite images because of cloud contamination or long revisit time severely degrades predictions of evapotranspiration (ET) time series at watershed/regional scales from satellite-based surface flux models. We integrate the feedback model developed by Granger and Gray (the GG model) with the Surface Energy Balance Algorithm for Land (SEBAL), with the objective to generate ET time series of high spatial resolution and reliable temporal distribution at watershed scales. First, SEBAL is employed to yield estimates of ET for the Baiyangdian watershed in a semihumid climatic zone in north China on cloud-free days, where there exists the complementary relationship (CR) between actual ET and pan ET. These estimates constitute input to the GG model to inversely derive the relationship between the relative evaporation and the relative drying power of the air. Second, the modified GG model is used to yield ET time series on a daily basis simply by using routine meteorological data and Moderate Resolution Imaging Spectroradiometer (MODIS) albedo and leaf area index products. Results suggest that the modified GG model that has incorporated remotely sensed ET can effectively extend remote sensing based ET to days without images and improve spatial representation of ET at watershed scales. Utility of the evaporative fraction method and the crop coefficients approaches to extrapolate ET time series depends largely on the number and interval of good quality satellite images. Comparison of ET time series from the two techniques and the proposed integration method for days with daily net radiation larger than 100 W m−2 and corresponding pan ET clearly shows that only the integration method can exhibit an asymmetric CR at the watershed scale and daily time scale. Validation performed using hydrologic budget calculations indicate that the proposed method has the highest accuracy in terms of annual estimates of ET for both watersheds in north China.

1. Introduction

[2] Evapotranspiration (ET), including evaporation from the soil surface and transpiration from vegetation, is a key variable for understanding the hydrological cycle and the energy balance on the Earth's surface. Numerous models built on the surface energy balance equation have been developed to make predictions of surface fluxes across different spatial scales by incorporating remotely sensed variables like land surface temperature (LST), surface albedo, vegetation cover fraction, and land cover type in conjunction with less meteorological data [Bastiaanssen et al., 1998a, 1998b; Jiang and Islam, 2001; Nishida et al., 2003; Norman et al., 1995; Su, 2002; Wang et al., 2007]. Estimates of ET from these models can be gainfully employed in crop water consumption estimation, forest management, water resources management, hydrologic modeling, and weather and climate predictions.

[3] Because of the assimilation of remotely sensed LST and other key surface variables, satellite-based models tend to generate reasonable spatial representation of latent heat flux [Anderson et al., 2007a, 2007b; Bastiaanssen et al., 2002; Batra et al., 2006; Gao and Long, 2008; Jiang and Islam, 2001; Krajewski et al., 2006; Kustas et al., 2007; Nishida et al., 2003; Zhang, 2009]. Satellite images, however, are often blurred or obstructed by clouds, especially during rainy season, which makes such models constrained to work under cloud-free conditions. At most, these models may offer temporally integrated daily ET by assuming the instantaneous evaporative fraction (defined as the ratio between the latent heat flux to the available energy) to be fairly invariant during daytime and then utilizing the derived evaporative fraction to partition daily net radiation [Ahmad et al., 2006; Bastiaanssen et al., 1998a; Bastiaanssen, 2000; Bastiaanssen et al., 2005; Jiang and Islam, 2001; Norman et al., 2003; Su, 2002]. Nevertheless, estimates of latent heat flux or daily ET under cloud-free conditions cannot satisfy the requirement of ET time series in practical applications; in particular, monthly, seasonal, and yearly ET estimates are desired for quantifying total water consumption by agriculture or for assisting professionals in water resources allocation and management [Ahmad et al., 2006; Allen et al., 2007].

[4] We suggest that integration of the feedback method [Granger, 1989; Granger and Gray, 1989], (hereinafter the GG model) with a remote sensing based model has the potential to make reliable predictions of ET time series of high spatial resolution simply by using routine weather data. The point here is that for a specific region where the complementary relationship (hereinafter CR) between pan ET and actual ET has been shown to be valid, the time series of ET would clearly exhibit complementary features over time and space. If the integration approach has demonstrated skill in generating ET time series estimates showing CR with pan ET and of high spatial resolution due to the assimilation of remotely sensed variables and/or fluxes, it would successfully extend remotely sensed information on cloud-free days to days without good quality images. This would substantially improve the accuracy of ET time series estimates and be greatly beneficial to a variety of practical applications.

[5] The GG model has been shown to have the potential to yield reliable magnitudes of ET over large areas in different regions throughout different climatic zones [Allen et al., 2007; Armstrong et al., 2008; Crago and Crowley, 2005; Liu et al., 2006; Xu and Singh, 2005]. To account for departures from the saturated condition and obtain a more general expression for calculating actual ET, Granger and Gray [1989] introduced a concept of relative evaporation G (defined as the ratio of actual to potential evaporation) to this method, in which the potential evaporation is defined as the evaporation rate that would occur under certain atmospheric conditions for wind and humidity if the surface was saturated at the temperature of the surface. Moreover, they related G to the relative drying power of air D on the basis of an assumption that meteorological variables (e.g., air temperature and vapor pressure) can be indicative of changes in soil moisture status and thus potential and actual ET [Brutsaert, 1982; Morton, 1983]. The GG model eliminates the need for surface variables like LST and surface vapor pressure in that D not only drives the actual ET but also reflects the effects of actual ET on regional advection [Hobbins et al., 2004]. Furthermore, it avoids a prior calculation of potential evaporation which has not been clearly defined in a universally accepted manner [Biftu and Gan, 2000; Granger and Gray, 1989; Wu et al., 2006].

[6] It is noted that the relationship between D and G should be applied with caution. In Granger and Gray's original work [1989], limited data points (158) of actual ET and the values of G larger than 0.7 (wet environment) did not allow for a more universally applicable functional relation over large heterogeneous areas with widely different land covers. Later, Granger modified this relationship which is also an exponential function [Granger, 1996, 1998]. Nevertheless, Biftu and Gan [2000] suggested that the modified relationship cannot represent heterogeneities in landscape properties governing the mechanisms of water-heat transfer either. Furthermore, it should also be noted that although the GG model has the capability to make reliable predictions of areal ET, its spatial representation has yet to be well examined. It is logical that spatial distribution of ET from the GG model relies highly on the spatial scale of meteorological forcing. The remote sensing based model tends to produce estimates of ET with reasonable spatial distribution over an entire scene on cloud-free days; meanwhile, the GG model can yield reasonable magnitudes of ET over large regions using routine meteorological data provided an effective relationship between D and G is well established. This has important implications. If the relationship between D and G can be established by the ET outputs from a remote sensing based model of large heterogeneous areas with a range of atmospheric and surface conditions, the modified GG model would probably make reliable predictions of ET with reasonable magnitude and distribution throughout a study region simply by using routine meteorological data. The integration method would greatly improve the utility of methods to extend estimates of daily ET from satellite-based approaches on cloud-free days to days without good quality images.

[7] Of remote sensing based models for simulating land surface fluxes, Surface Energy Balance Algorithm for Land (SEBAL) has been shown to be one of the most promising tools to capture spatial variability in ET at watershed/regional scales [Allen et al., 2007; Compaore et al., 2008; French et al., 2005; Gao et al., 2008; Hong et al., 2009; Immerzeel and Droogers, 2008; Immerzeel et al., 2008; Kongo and Jewitt, 2006; Oberg and Melesse, 2006; Ramos et al., 2009; Teixeira et al., 2009]. A watershed with a variety of land covers exhibiting distinct surface and atmospheric conditions can be selected as a study site, which would likely satisfy the prerequisite of the presence of two hydrological extremes, termed the hottest and the coldest pixels in SEBAL. Remote sensing sources are available from Moderate Resolution Imaging Spectroradiometer (MODIS) land and atmospheric products, which are widely used in regional ET estimation.

[8] The objectives of this study were to (1) estimate actual ET of a selected watershed with SEBAL on cloud-free days, (2) reestablish the relationship between D and G in the GG model using the retrievals of ET from SEBAL, (3) generate ET time series with the modified GG model, and (4) compare and contrast the performance of the evaporative fraction method, the crop coefficient method and the proposed integration method to produce ET time series at watershed scales and evaluate their utility in the light of hydrologic budget calculations.

2. Critique of Methods to Generate Time Series of ET

[9] Existing methods to produce time series of ET include (1) utilization of evaporative fraction derived in cloud-free days as a surrogate to partition daily net radiation between satellite overpass dates or for days without good quality images [Bastiaanssen et al., 2002; Farah, 2000; Farah et al., 2004] (hereinafter the evaporative fraction method), (2) utilization of crop coefficients derived from remotely sensed actual ET and corresponding weather-based potential or reference ET for the days of image acquisition to partition potential or reference ET between satellite overpass dates [Allen et al., 2007; Li et al., 2008; Mohamed et al., 2004; Mohamed et al., 2006; Oberg and Melesse, 2006; Singh et al., 2008] (hereinafter the crop coefficient method), and (3) utilization of physically based, distributed hydrological models to produce time series of ET estimates over large heterogeneous domains [Arnold et al., 1993; Bastiaanssen et al., 2002; Droogers and Bastiaanssen, 2002; Flerchinger et al., 1996; Gao and Long, 2008; Refsgaard, 1997; Schuurmans et al., 2003; Xu and Li, 2003].

2.1. Evaporative Fraction Method

[10] The evaporative fraction method utilizes the evaporative fraction deduced from days with good quality images as a surrogate to partition daily net radiation to extrapolate ET for cloudy days or days without good quality images. As Bastiaanssen et al. [2002] pointed out that this is a chief assumption in SEBAL, the evaporative fraction remains constant between satellite overpass dates. It may hold true when soil moisture and meteorological conditions do not significantly change. Farah [2000] stated that the accumulated ET for a period of around 10–20 days can be predicted satisfactorily from the remotely sensed evaporative fraction amid the period. However, use of the evaporative fraction retrieved for a particular day to predict ET for the other days within a 10 day period fails. Bastiaanssen et al. [2002] implied that temporarily integrated ET from the temporal constancy of evaporative fraction for a week or so can be sufficiently accurate as systematic errors would cancel out over relatively longer periods of time:

equation image

where ETperiod is the accumulated actual ET for a period beginning on day b and ending on day f, 86400 converts from seconds to 24 h, and Λd is the evaporative fraction derived on days with good quality satellite images. Rn24i is the daily net radiation for day i, and λi is the daily latent heat of vaporization (J kg−1). In the presence of notable differences in soil moisture availability, daily net radiation, and meteorological conditions between clear sky satellite image dates, uncertainties may exist in the extrapolated ET from the method.

2.2. Crop Coefficient Method

[11] The crop coefficient method interpolates the crop coefficient between satellite overpass dates on the basis of remote sensing based crop coefficient on cloud-free days using a linear or spline interpolation. Combining the interpolated crop coefficient with reference evaporation, actual ET predictions for the days between satellite overpass or days without good quality images can be inferred. Allen et al. [2007] indicated that one satellite image per month is generally sufficient to construct an accurate crop coefficient curve for purposes of estimating seasonal ET. However, during periods of rapid vegetation change, a more frequent image interval may be desirable. Note that this approach assumes the actual ET for the entire area of interest to change in proportion to changes in the weather-based reference ET. This means the larger the reference ET, the larger the actual ET for the entire scene under a constant crop coefficient for a pixel:

equation image

where ETd is the actual ET inferred from days with good quality images, ET0d is the corresponding reference ET, and ET0i is the reference ET for day i. In this study, the reference ET is calculated with the FAO56 equation [Allen, 2000]

equation image

where ET0 is the reference ET (mm d−1), Rn is the net radiation at the crop surface (MJ m−2 d−1), and Gs is the soil heat flux (MJ m−2 d−1). In applications having a 24 h calculation time step, Gs is assumed to be zero. Ta is the air temperature at a 2 m height (°C), u2 is the wind speed at 2 m height (m s−1), and esea is the saturation vapor pressure deficit (kPa). ET0 predicts ET from a hypothetical grass reference surface that is 0.12 m in height having a surface resistance of 70 s m−1 and albedo of 0.23. Sensitivity analysis (Figure 1) for ET0 shows that daily net radiation is the most sensitive variable in this equation, with a 10% increase in daily net radiation resulting in around 7.5% increase in ET0. A 10% increase in saturation vapor pressure deficit, daily mean temperature, and wind speed would result in a 2.5%, 0.9%, and 0.8% increase in resulting ET0, respectively.

Figure 1.

Sensitivity analyses of the FAO56 reference ET equation and the GG model (initial condition, Rn = 200 W m−2, D = esea = 1 kPa, u2 = 2 m s−1, Ta = 27°C).

3. Proposed Integration Method

[12] Integration of the GG model and SEBAL is hypothesized to produce ET time series with high spatial resolution at watershed scales as the following steps: (1) the proposed method makes the use of SEBAL to simulate spatially consistent and reasonably distributed ET for cloud-free days; (2) the output from SEBAL constitutes input into the GG model to inversely derive G; (3) the new relationship between D and G can be explored and constructed; and (4) the modified GG model in conjunction with associated weather data and remotely sensed albedo, roughness length, and zero plane displacement will be utilized to generate the ET time series.

3.1. SEBAL Model

[13] SEBAL is an energy balance based method for modeling land surface fluxes with remotely sensed surface characteristic variables and relatively less routine meteorological data. The theoretical and computational basis of SEBAL is from Bastiaanssen et al. [1998a], Bastiaanssen [2000], and Bastiaanssen et al. [2005]. The latent heat flux is calculated as the residual of the surface energy balance equation for circumventing the lack of surface vapor content and surface resistance that cannot be measured through satellite techniques at the current stage. Assuming advection and light energy for photosynthesis to be negligible, the energy balance equation can be expressed as

equation image

where Rn denotes the instantaneous (typically at the satellite overpass time) net radiation (W m−2), Gs denotes the soil heat flux (W m−2), H denotes the sensible heat flux (W m−2), and λE denotes the latent heat flux (W m−2).

[14] Instantaneous net radiation consists of net shortwave radiation from direct and diffuse solar radiation and net longwave radiation from the land and atmosphere systems:

equation image

where α is the surface albedo (dimensionless) which can be derived from visible and near infrared wavebands of satellite images and Sin is the instantaneous shortwave radiation (W m−2) which is a function of extraterrestrial solar radiation, solar zenith angle, and atmospheric transmissivity at satellite overpass time. Given that the incident shortwave radiation varies greatly with terrain factors like slope and azimuth for sloping land surfaces, the parameterization scheme of Sin in the study accounts for the entire watershed [Allen et al., 2007; Gao et al., 2008]. Ld and Lu are the downwelling and upwelling longwave radiation (W m−2), respectively; ɛa is the atmospheric emissivity (dimensionless) which can be derived as a function of atmospheric temperature and vapor pressure [Brutsaert, 1975]; ɛ is the surface emissivity (dimensionless) which can be estimated using an empirical relationship between the normalized difference vegetation index (NDVI) from the red and near infrared wavebands of satellite images [Bastiaanssen et al., 1998a]; σ is the Stefan-Boltzmann constant (5.67 × 10−8 W m−2 K−4); Ta is the atmospheric temperature (K) at screen level which can be obtained from weather stations, and distributed air temperature maps can be produced by a multivariate regression analysis of longitude, latitude, and elevation of a study site; and Ts is the land surface temperature (K) which can be retrieved through thermal infrared wavebands of satellite measurements.

[15] In SEBAL, soil heat flux Gs is taken to be a fraction of net radiation. The fraction is a function of LST, albedo, and NDVI for vegetated cover [Bastiaanssen, 2000]:

equation image

For bare soil surfaces and water bodies, Gs can be estimated with the following equation, respectively [Zhang, 2009].

equation image
equation image

[16] Parameterization of sensible heat flux is a key component of energy balance based methods for modeling land surface fluxes from satellite images. The innovative component of SEBAL is that the difference between air temperature at a reference height and aerodynamic temperature at the land surface has been shown to be proportional to remotely sensed LST through a host of experiments and applications [Bastiaanssen et al., 1998b, 2002, 2005; French et al., 2005; Gao et al., 2008; Hong et al., 2009; Immerzeel and Droogers, 2008; Kongo and Jewitt, 2006; Oberg and Melesse, 2006; Ramos et al., 2009; Teixeira et al., 2009]. This eliminates the need for the aerodynamic temperature that is not readily available from conventional methods. Coefficients of the linear relationship are specified through two pixels with extreme hydrologic conditions, termed the hottest pixel and the coldest pixel, which are manually identified via contextual interpretation of the maps of LST and NDVI/albedo. For the hottest pixel, the latent heat flux is considered zero, and the sensible heat flux is thus equal to its available net energy. For the coldest pixel, the sensible heat flux is regarded as zero, and its latent heat flux is equal to the available net energy:

equation image

where ρ is the air density (kg m−3), cp is the air specific heat at constant pressure (J kg−1 K−1), dT is the near-surface temperature difference between z1 (0.1 m) and z2 (2 m), a0 and b0 are the linear regression coefficients that are scene specific, and rah is the aerodynamic resistance for heat transfer (s m−1), which is a function of friction velocity u* (m s−1) and stability correction factors for momentum transfer ψm (dimensionless) and sensible heat transfer ψh (dimensionless):

equation image
equation image

where k is the von Karman constant 0.41; u200 is the wind velocity (m s−1) at an assumed blending height (200 m), which can be inferred using the wind velocity at a certain height observed at a weather station within the area of interest; and zm is the roughness length for momentum transfer (m), which can be related to the remotely sensed vegetation index or leaf area index in the calculation of regional surface fluxes and ET.

[17] In terms of the assumption regarding the hottest and coldest pixels in SEBAL, linear coefficients a0 and b0 can be derived as follows:

equation image
equation image

where rah,hot is the aerodynamic resistance for heat transfer for the hottest pixel; ρhot is the air density of the hottest pixel; Rn,hot and Ghot are the instantaneous net radiation and soil heat flux for the hottest pixel; and Ts,hot and Ts,cold are the LST for the hottest and coldest pixels, respectively. Since the stability correction factors ψm and ψh are functions of the sensible heat flux, equation (9) through equation (13) have to be solved in an iterative manner. First, the stability correction factors are assumed to be zero, and the first approximation of H can be obtained. Second, the first approximation of H is used to calculate stability factors, and then the second approximation of H is obtained. These procedures are repeated iteratively until linear coefficients a0 and b0 are convergent. After Rn, Gs, and H are computed, λE can be obtained as the residual of equation (4). Evaporative fraction [Λ = λE/(RGs)] is introduced into SEBAL as a link between the instantaneous latent heat flux and daily ET (in the unit of mm d−1):

equation image

where Rn24 is the daily net radiation (W m−2) and λ is the latent heat of vaporization (J kg−1). There are two critical assumptions in equation (14) that the evaporative fraction keeps fairly invariant throughout the day, and there is no regional advection for cloud-free days [Bastiaanssen et al., 1998a; Bastiaanssen, 2000; Su, 2002]. The approach to extrapolating ET from satellite overpass time to periods of 24 h has been shown to be capable of providing reliable estimates of daily ET compared with ground-based measurements (e.g., ET from lysimeter, Bowen ratio, and eddy correlation system) [Ahmad et al., 2006; Norman et al., 2003]. Daily net radiation is a key variable for determining the magnitude of ET. It is parameterized with the algorithm proposed by Long et al. [2010] in conjunction with LST, DEM, and ancillary weather data.

3.2. GG model

[18] The GG model [Granger and Gray, 1989] is intended to estimate terrestrial actual ET across different spatial and temporal scales with routine meteorological data. This model was derived on the basis of energy budget and aerodynamic principles, similar in form to the Penman equation but differs in the inclusion of the relative evaporation G. ET is driven primarily by two components: daily net radiation Rn24 and drying power of the air Ea in terms of the model:

equation image

where Δ is the slope of saturated vapor pressure (kPa °C°1), and γ is the psychrometric constant (kPa °C−1):

equation image

where e*a is the saturated vapor pressure at the daily average temperature (kPa), ea is the daily average vapor pressure (kPa), and f(u) is a function of wind speed:

equation image

where P is the atmospheric pressure (Pa). The wind speed function does not call for the stability correction for daily and longer time steps, assuming that the atmospheric stability is, on average, neutral.

[19] Granger and Gray [1989] related G to a concept of the relative drying power of the air D through experimental data, establishing an exponential function of the two variables:

equation image
equation image

where a and b are the regression coefficients. In the first formation (1989) of the GG model (hereinafter GG 1989), a is 0.028, and b is 8.045 for experimental data of 158 samples. As they indicated, the lack of measurements from wet environments (G > 0.7) does not allow for the development of a functional relation between D and G that can be treated with confidence over the entire range of G. As a result, its utility should be explored in depth when applied to a broad range of underlying surface conditions with distinct soil moisture availability and landscape properties. Granger [1996] modified the original relationship between D and G as follows (hereinafter GG 1996):

equation image

where a is 0.2 and b is 4.902.

[20] Sensitivity analysis of GG 1989 was performed in order to examine how inputs of the GG model affect the magnitude of resulting estimates of ET (Figure 1). Results suggested that a 10% increase in Rn24 can lead to around an 18.4% increase in estimates of actual ET. A 10% increase in G, D, and daily mean temperature can create 8.0%, −3.8%, and −0.7% variations in the resulting ET, respectively. Therefore, G is positively correlated with ET estimates. Reestablishing the functional relationship between D and G is critical to improving spatial representation of the ET time series with finer resolution. Figure 2 shows the flow diagram of the GG model.

Figure 2.

A flow diagram of the input and output of the GG model.

[21] The relationship between D and G involved in the GG model creates an opportunity to make predictions of ET time series of reasonably good resolution at watershed/regional scales through incorporating remotely sensed variables compared with coarse ET predictions from other CR-based models which are merely reliant on meteorological forcing.

4. Application

4.1. Study Site

[22] The study was conducted in the Baiyangdian watershed with an area of 31,200 km2, a subbasin of the Haihe River basin in north China and extending in latitude from around 37.8°N to 40.4°N and in longitude from around 113.3°E to 116.6°E (Figure 3). Hebei and Shanxi provinces and Beijing Municipality contribute 80.4%, 12.3%, and 7.3% of the total area of the watershed, respectively. Elevation generally decreases from the northwest of the watershed, the Taihang mountainous areas, to the southeast plain, ranging from around 2784 m to 0 m. Mountainous areas (elevation above 100 m) occupy approximately 53% of this watershed. Eight streams of the Daqing River provide major water sources for four irrigation districts, reservoirs, and municipal and industrial water use in this watershed, finally converging to the outlet, Lake Baiyangdian, the largest lake on the North China Plain. Woodlands and grasslands generally dominate the northwestern mountainous areas, and cropland prevails over the plain areas (Figure 3), showing that dry land, shrubs, and moderate grasslands account for 33.6%, 12.1%, and 12.0% of the watershed, respectively. Historical weather records in the recent 50 years from the Baoding, Shijiazhuang, Wutaishan, Weixian, and Huailai weather stations within or adjacent to the watershed reveal that the mean annual temperature of this watershed is between 6.8°C and 12.7°C (the daily maximum value is 43.3°C and the daily minimum value is −30.6°C), a mean annual precipitation of 548 mm falls in the watershed, and mean annual pan evaporation is roughly 1500∼2000 mm.

Figure 3.

Location and relevant information of the Baiyangdian watershed in a semihumid climatic zone in north China and its land use map.

[23] Analyses of hydrometeorological data of the watershed suggest that the climate over the areas has shown a general warming trend since the 1950s, especially during the recent two decades, with the air temperature rising at a rate of around 0.4∼1.2°C/10 yr. Precipitation basically presents a decreasing trend at a rate of around 22.9 mm/10 yr. Pan ET decreases at a rate of around 52.2 mm/10 yr, which may be indicative of an increase in water use due to a rapid expansion of irrigation and an increase of wetness. Mean annual runoff shows a decreasing trend at a rate of around 3.5 m3 s−1/10 yr, which could be attributed to a decreasing trend in precipitation and increases in reservoirs and agricultural, industrial, and municipal water uses across this watershed. It is noted that Bouchet's [1963] CR of potential and actual evaporation has been shown to be valid over the nonhumid region in north China and under the condition of elevation lower than 1000 m [Qiu et al., 2004; Yang et al., 2006; Yu et al., 2009]. This suggests that the CR can be a powerful means to interpret variability in potential and actual evaporation and to estimate watershed/regional actual ET across the watershed.

4.2. Data Description

[24] A common data set encompassing hydrometeorological data, remote sensing data, digital elevation models (DEMs), and ancillary parameters in the year 2007 was built to simulate daily and time series of ET by the evaporative fraction method, the crop coefficient method, and the proposed integrated method.

4.2.1. Hydrometeorological Data

[25] Meteorological data on a daily basis relevant to parameterization schemes of daily net radiation, daily reference ET, and D, such as daily maximum, minimum, and mean temperatures; daily vapor pressure and saturated vapor pressure deficit; and daily atmospheric pressure, were determined by an average of in situ measurements from 18 weather stations within the study watershed. Maps of those variables were produced using multiple linear regression analysis of longitude, latitude, elevation, and observations. Of the 18 weather stations, the Baoding and Fuping stations provide observations of air temperature, vapor pressure, and atmospheric pressure at a 1 h interval. The other stations provide relevant observations at a 6 h interval. Daily actual sunshine duration was available by accumulating in situ measurements at a 1 h interval during daytime for all 18 weather stations. Daily observations of wind speed were also obtained by an average of 24 automatic measurements on the hour for all 18 stations.

[26] In simulation of instantaneous land surface fluxes by SEBAL, instantaneous atmospheric pressure, air temperature, and vapor pressure for 16 weather stations at the satellite overpass time were inferred by a sinusoidal model incorporating 4 observations of these variables. For the Baoding and Fuping stations, the instantaneous counterparts were estimated by linear interpolation between two measurements on an hourly basis.

[27] Observations of precipitation on a daily basis from 18 weather stations, surface runoff at 12 hydrological stations on the main streams, reservoir storage change, and groundwater observation well levels in the watershed were utilized to estimate water budget for the entire watershed in the year 2007. Daily pan ET values from 18 weather stations were used to interpret trends in estimates of actual ET from the three approaches assessed in this study.

4.2.2. Remote Sensing Data

[28] Remote sensing data for this study are available from MODIS land and atmospheric data products (http://modis.gsfc.nasa.gov/), given their relatively high temporal resolution and sufficient spatial resolution (250 m, 500 m, and 1000 m for visible wavebands and near infrared wavebands; 1000 m for thermal infrared wavebands) as well as the area of the watershed (31,250 km2). A reasonable tradeoff between spatial and temporal resolution makes MODIS data widely used in research regarding global dynamics and processes occurring on the land, in the oceans, and in the lower atmosphere. Furthermore, remotely sensed information of 36 spectral bands from visible to thermal near-infrared wavelengths (20 for visible, near infrared, and shortwave infrared wavebands; 16 for thermal infrared wavebands) offers an extremely valuable data source for assessing current land and vegetation states at watershed scales.

[29] MOD11_L2, the level 2 MODIS LST and emissivities for bands 31 and 32 daily data, and MOD11A1 and MYD11A1 from Terra-MODIS and Aqua-MODIS, the level 3 MODIS LST and emissivities for bands 31 and 32 daily data, were utilized to simulate instantaneous and daily surface upwelling longwave radiation for the net radiation component in SEBAL and GG. All maps of LST were adjusted to eliminate elevation and viewing angle effects before calculating the sensible heat flux by SEBAL. MCD43A3, the 16 day composite level 3 gridded albedo product, and MOD04, the daily level 2 aerosol depth at 0.550 μm wavelength product, were jointly utilized to simulate albedo using the algorithm developed by Lucht et al. [2000]. MOD13A2 data, the level 3 NDVI product, were utilized to simulate soil heat flux as required in equation (6) for SEBAL and to facilitate manual identification of the hottest and coldest pixels in the calculation of sensible heat flux required by SEBAL. MOD15A2, the level 4 MODIS global leaf area index (LAI), was used as an input to SEBAL and GG to estimate the roughness length for momentum transfer. The remote sensing data used are shown in Table 1.

Table 1. MODIS Data Sets Used in This Study and Their Associated Properties
NameUsed VariablesTemporal ResolutionSpatial ResolutionPlatform
MOD11_L2LST and emissivity5 min1000 mTerra
MOD11A1LST and emissivityDaily1000 mTerra
MYD11A1LST and emissivityDaily1000 mAqua
MCD43A3Albedo16 days500 mTerra & Aqua
MOD13A2NDVI16 days500 mTerra
MOD15A2Leaf area index8 days1000 mTerra
MOD04_L2Aerosol depthDaily10 kmTerra

4.2.3. DEM and Ancillary Data

[30] Shuttle Radar Topography Mission (SRTM) digital elevation models for the study site are available from the U.S. Geological Survey Earth Resources Observation and Science Center (http://edcsns17.cr.usgs.gov/EarthExplorer/). Terrain variables (e.g., slope, azimuth, and elevation) can be directly extracted from DEMs for simulating terrain-dependent instantaneous net radiation for SEBAL and daily net radiation for both SEBAL and GG [Gao et al., 2008; Long et al., 2010]. They also aided in producing maps of meteorological variables through multivariate regression analysis. Ancillary parameters comprise day of year (DOY) to calculate solar declination and Earth-Sun distance and the satellite overpass time for jointly simulating extraterrestrial shortwave radiation involved in the instantaneous and daily net radiation.

4.3. Daily ET Modeling by SEBAL

[31] As LST is the most critical remotely sensed variable required by SEBAL, we selected one day having the best quality remotely sensed LST from MOD11_L2 in each month in the year 2007 for modeling surface fluxes and then reestablishing relationships between D and G. It is noted that for some months in spring and winter (e.g., January, February, March, November, and December) and rainy season in summer (e.g., June, July, and August), scarcity of good quality MODIS LST products due to cloud contamination makes ET time series reconstruction depending only on remote sensing images infeasible. MODIS LST images in January, February, March, November, December, and July were inevitably contaminated to varying degrees by clouds.

[32] Correctly selecting the hottest pixel and the coldest pixel is critical to the simulation of surface fluxes by SEBAL. However, the selection is a manually identified procedure, which frequently requires the aid of contextual maps of LST and NDVI and/or albedo [Gao et al., 2008; Timmermans et al., 2007]. Sometimes it even requires a priori knowledge of land use type or even expertise/experience [Allen et al., 2007]. Uncertainties in H estimates stemming from the uncertainties in Ts,hot and Ts,cold were quantified by performing a sensitivity analysis in this study. It is apparent that variations in H estimates caused by variations in inputs are determined by both the magnitude of the variations and the initial value conditions. We tested the sensitivity of H estimates to Ts,hot and Ts,cold using 28 sets of initial values of variables in equations (9) through (13) for cloud-free days in 2007. Figure 4 illustrates the variations in a0 and b0 and subsequently H resulting from the variations in Ts,hot and Ts,cold. Results indicate that a 2 K increase in Ts,hot would likely result in an average of 9.3% and 11.3% decrease in a0 and H, respectively, and an average of 9.3% increase in b0; a 2 K increase in Ts,cold would cause an average of around 12.5% and 13.5% decrease in a0 and H, respectively, and an average of 11.7% increase in b0.

Figure 4.

Sensitivity analyses of sensible heat flux to the temperatures of the extreme pixels in SEBAL.

[33] We selected the extreme pixels in the light of scatterplots of LST and NDVI (see Figure 5), a land use map for the study watershed (see Figure 3), and geomorphologic features. As for the selection of the hottest pixel, first, the pixels with a group of highest temperatures and relatively lower NDVI values are selected. It is interesting to note that the pixel with the highest LST value does not necessarily correspond to the lowest NDVI value. In this case, the land cover map is utilized. It appears that the hottest pixel tends to occur in the bare soil surface, sandy land, urban built-up land, or dry land. Such pixels with a group of highest temperatures are ordered in a sequence of descending LST values. The hottest one is thus selected by a qualitative judgment starting with the highest LST pixel until the pixel corresponding to bare surface, sandy land, urban built-up land, or dry land is identified.

Figure 5.

Selection of the hottest and coldest pixels from the contextual map of NDVI and LST for simulation of daily ET from SEBAL under cloud-free conditions.

[34] Regarding the selection of the coldest pixel, it is evident that a small group of pixels distributed on the lower edges of the scatterplots are contaminated by clouds. They show relatively low LST values whereas they do not show reasonable high NDVI values, an implication of no dense vegetation cover. This does not satisfy the hypothesis of the coldest pixel in SEBAL. In this case, the MOD11_L2 quality information is utilized to facilitate excluding all pixels that may be contaminated by clouds or other factors. Then, the pixel with the lowest temperature is regarded as the coldest pixel. In addition, if the Landsat Thematic Mapper/Enhanced Thematic Mapper Plus (TM/ETM+) images were used to identify the coldest pixel, the cloud effects would not be readily isolated as the MODIS data do. In this case, the standardized alfalfa reference ET could be used to determine the ET at the coldest pixel [Allen et al., 2007; Tasumi, 2003]. Figure 5 shows the selection of the extreme pixels for one typical cloud-free day in each month in the year 2007. In general, the scatterplots between NDVI and LST exhibit a kind of triangular or trapezoidal shape (e.g., April–October). For January–March and November–December, as cloud significantly obscured the land surface, the contextual spaces showed a vertically scattered distribution for pixels with lower LST values. The hottest pixel is frequently observed on the upper left portion of the triangle or trapezoid, where the pixel has a relatively greater value of LST but a smaller value of NDVI. By contrast, the coldest pixel is generally found to be located on the lower right portion of the triangle or trapezoid, where the pixel often shows a relatively lower value of LST but a higher value of NDVI. Combined with associated remotely sensed variables, routine meteorological data, ancillary parameters, maps described in section 4.2, and the manually identified extreme pixels, daily ET for selected typical cloud-free days was simulated with SEBAL.

4.4. Inverse Procedures for Incorporating Remotely Sensed ET into the GG model

[35] Resulting estimates of ET from SEBAL constitute input to the GG model to inversely derive G on the basis of equation (15). The D values were calculated in terms of equation (19) using meteorological forcing in combination with remotely sensed albedo and LAI. Scatterplots between D and G for typical cloud-free days are shown in Figure 6, with associated statistics contained in Table 2.

Figure 6.

Calibration of the functional relationship between the relative drying power of the air D and the relative evaporation G in the GG model using SEBAL-based ET estimates for the Baiyangdian watershed on 12 cloud-free days in year 2007, showing GG 1989 and GG 1996.

Table 2. Regression Coefficients of the Exponential Relationship Between D and G and Associated Statisticsa
DateabnRSSR2
  • a

    Value n, number of samples; RSS, residual sum of squares; R2, coefficient of determination.

17 Jan0.004609.9322819437187.670.82
9 Feb0.0023711.0997722911155.610.86
11 Mar0.0005714.3007318568203.270.80
25 Apr0.0013210.643713073626.580.96
9 May0.006399.8835329400190.530.77
15 Jun0.0005812.830992205568.580.89
19 July0.028917.4948625232200.340.72
13 Aug0.167495.0703924956125.320.81
19 Sep0.017348.6329227372167.300.85
14 Oct0.0047610.4414426258121.800.90
1 Nov0.0026010.2475026745166.810.88
3 Dec0.003669.506072474691.290.89

[36] Results definitely show that G decreases nonlinearly with an increase in D, consistent with the finding reported by Granger and Gray [1989], in which they made use of ET calculated as the residual term in a soil water balance applied at field sites to derive the relationship between D and G. The relationship between D and G is approximately curvilinear and fitted using an exponential function. The highest and lowest R2 were found to be 0.96 on 25 April and 0.77 on 9 May, respectively. It is observed that with decreases in D (e.g., D < 0.6), the variation ranges in G tend to be larger. This may be as a consequence of a weakened CR effect at higher elevations and suggests that the remote sensing based SEBAL can detect more variations in ET. Nevertheless, the relationship between D and G can generally be represented by the fitted functions.

5. Results and Discussion

[37] The time series of ET from the evaporative fraction method, the crop coefficient method, and the proposed integration method of the study watershed on a daily basis in the year 2007 were generated by virtue of the methodologies illustrated above. There were totally 28 cloud-free days selected for generating daily evaporative fractions and crop coefficients on the basis of satellite images and meteorological data. Then the simulated daily evaporative fractions and crop coefficients were employed to extrapolate daily counterparts and ET for all cloudy days in terms of equations (1) and (2). The integration method yielded the ET time series on the basis of the newly established relationship between D and G in conjunction with routine meteorological data. The usefulness and robustness of the three methods were carefully compared and evaluated.

5.1. ET Time Series from the Evaporative Fraction Method

[38] The evaporative fractions and crop coefficients of the entire watershed for the 28 cloud-free days are shown in Figure 7 and Table 3. The evaporative fraction varied irregularly throughout the whole year, showing a mean of 0.518. This demonstrates that there does not exist a regular variation trend in the evaporative fraction during the year. The daily evaporative fraction is, to a large extent, influenced by the combined effect of soil moisture and net radiation availability, vegetation, and metrological states for that day, considerably varying from day to day. The evaporative fraction method suffers serious theoretical and technical limitations in yielding ET time series as shown below.

Figure 7.

Evaporative fractions and crop coefficients from SEBAL of the Baiyangdian watershed on 28 cloud-free days in year 2007, presenting corresponding daily precipitation and the mean annual predictions.

Table 3. Simulated Evaporative Fractions and Crop Coefficients From the Evaporative Fraction Method and Crop Coefficient Method of the Entire Watershed for 28 Cloud-Free Days
DateDaily Radiation (W m−2)Evaporative FractionActual ET From SEBAL (mm d−1)FAO56 ET (mm d−1)Crop Coefficients
17 Jan1.1400.5080.020.100.20
9 Feb10.0250.4600.160.710.23
11 Mar14.8890.3880.201.260.16
9 Apr89.7830.6101.992.950.67
13 Apr100.0330.6182.202.540.87
25 Apr140.7270.6453.003.890.77
6 May116.4270.5522.413.760.64
9 May142.6060.4832.083.250.64
14 May128.2340.4412.104.250.49
25 May159.1020.4262.434.640.52
5 Jun116.9000.4412.084.070.51
8 Jun146.6370.6363.474.170.83
15 Jun108.0770.3001.193.910.30
2 Jul176.7520.4093.594.220.85
10 Jul149.2210.6193.304.510.73
19 Jul155.5840.5452.974.410.67
11 Aug115.0430.5012.043.580.57
13 Aug116.1270.5092.103.800.55
15 Aug105.4570.5041.853.660.51
4 Sep104.0110.5982.192.700.81
8 Sep114.6170.3012.152.620.82
19 Sep88.2910.5251.682.200.76
23 Sep68.2640.7311.761.890.93
14 Oct61.6130.5181.181.071.10
16 Oct52.4980.5821.060.801.33
28 Oct34.6310.4350.570.880.65
1 Nov27.2140.5610.530.600.88
3 Dec0.8710.6640.020.080.25

[39] First, good quality images of LST were rarely obtained in January, February, March, November, and December, with only one day in each month being selected for performing the simulation. In the worst case, there is no good quality satellite image available for routine ET estimation, particularly during rainy season when water supply is ample and actual ET is likely to be very large between rain events. Therefore, the use of the satellite-deduced evaporative fraction (in the worst case, there is no evaporative fraction estimate) for a cloud-free day in each month to extrapolate ET time series for the month would lead to large uncertainties in the resulting ET. The applicability of the evaporative fraction method depends largely on the frequency and quality of images available, which cause large difficulties in operational ET estimation and associated applications.

[40] Second, one may obtain several good quality images for consecutive cloud-free days (e.g., 11, 13, and 15 August in this study) when the evaporative fraction for the entire watershed probably shows similar patterns and magnitudes. These images, however, cannot capture variations in the evaporative fraction for a relatively longer period during rainy season, which is likely to exhibit marked variations in soil moisture, energy availability, and subsequently the ET. Hence, there is somewhat of a tradeoff between the quantity of good quality images and their distribution over time. This means, even in the case of sufficient scenes of good quality images available, such images are probably centered on a short period of cloud-free days exhibiting similar evaporative fraction patterns and magnitudes. As such, the evaporative fraction method seems to be of less capability to estimate ET for a longer period of time when the evaporative fraction essentially changes greatly over time. The case of sufficient satellite images with regular temporal intervals rarely occurs in practical applications.

[41] Third, there would exist large differences in evaporative fractions in rainy season (e.g., from May to September in this study). Though the intervals between dates of image acquisition were not large in June, the estimates of evaporative fraction of 0.441, 0.636, and 0.300 on 5, 8, and 15 June, respectively, suggest that use of any of them to extrapolate accumulated ET for a period centered on these days would give rise to large uncertainties if the intervals between image acquisition are not appropriately spaced.

[42] In summary, the evaporative fraction shows high spatial-temporal variability at the watershed scale during a year. Therefore, the utility of the evaporative fraction method to extrapolate ET time series depends largely on good quality satellite images available, their temporal frequency, corresponding energy and soil moisture availability as well as vegetation states. Uncertainties in the evaporative fraction method would introduce gross errors in the resulting ET time series at the watershed scale.

5.2. ET Time Series From the Crop Coefficient Method

[43] Reference ET from the FAO56 equation was first calculated on a daily basis for 18 weather stations across the study watershed. Variations in daily reference ET, pan ET, and precipitation for the Anxin, Fuping, Yixian, and Anguo stations in 2007 are shown in Figure 8, illustrating that trends in the variation in daily reference ET are highly consistent with that of pan ET. Moreover, reference ET and pan ET in rainy season (e.g., from June DOY 152 to August DOY 243) were both relatively lower than that in May, showing a general decreasing trend in the reference ET and pan ET with days in rainy season. However, they were generally higher than in other months in the year. The trends in reference and pan ET in rainy season described can be ascribed to larger daily net radiation but relatively higher water vapor pressure compared to May and other months.

Figure 8.

Variations in the FAO56-based reference ET, pan ET and precipitation of the Baiyangdian watershed for the Anxin, Fuping, Yixian, and Anguo stations in year 2007.

[44] It is observed that there does not exist a distinct intermonthly low and high variation in the crop coefficient throughout the year, showing a mean of 0.651 (see Figure 7 and Table 3). It is apparent that the crop coefficient of the entire watershed from January to March was relatively small because of domination of bare or nearly bare soil combined with lower ambient temperature and solar radiation. With large increases in irrigation water supply in the four irrigation districts in April, the crop water consumption increased steeply and showed a pronounced increase in the crop coefficient. The crop coefficient continued to increase during the growing seasons and peaked in July, showing the largest value of around 0.85 on 2 July.

[45] It should, however, be noted that relatively small values of the crop coefficient shown in August and relatively large values shown in September and October do not agree with field experiment results from Chen et al. [1995] in the areas, presenting a counterintuitive trend rather than a typical progressive trend of low-high-low variation in the crop coefficient during a year. This may be because of an underestimate of the reference ET from the FAO56 method in the study watershed in September and October, thereby causing a spurious larger crop coefficient. It is difficult to construct a continuous and realistic crop coefficient curve from a handful of satellite images, especially during periods of rapid vegetation change. In this case, a more frequent image interval may be desirable [Allen et al., 2007], which cannot be readily achieved in practice.

[46] In summary, limited good quality satellite images merely cover a fraction of the crop coefficient cycle during a year. The crop coefficient method cannot provide a realistic and continuous crop coefficient curve primarily because of insufficient good quality satellite images, especially during periods of rapid development of vegetation and crops. Underestimation of the FAO56 reference ET in September and October over this watershed is another reason for overestimation of crop coefficient and thus unreliable estimates of ET.

5.3. ET Time Series From the Integration Method

[47] ET time series at the watershed scale from the evaporative fraction method, the crop coefficient method, and the proposed integrated method on a daily basis are shown in Figure 9. It should be noted that the estimates of watershed ET from the evaporative fraction and crop coefficient methods were produced by extrapolating corresponding variables in terms of equations (1) and (2) from 28 discrete image days. In contrast, the time series of ET from the integration method were generated on a daily basis. In general, the time series of ET from the three methods were lower than corresponding pan ET except rainy days when the pan ET data were suspected to be systematically overestimated and thus were set to zero.

Figure 9.

ET Time series from the proposed integration method, the evaporative fraction method, and the crop coefficient method of the Baiyangdian watershed in year 2007, with showing corresponding observations of daily precipitation and pan ET.

[48] It is interesting to note that exploring the relationship between pan evaporation and actual terrestrial ET at the watershed scale on a daily basis would help clarify and test the validity of different approaches to yielding ET time series. It is indicated that there exists a CR between pan evaporation and terrestrial actual ET across the study areas [Qiu et al., 2004; Yang et al., 2006; Yu et al., 2009]. It is therefore logical that if the produced ET time series and corresponding measurements of pan ET show a complementary behavior at the watershed scale, this would lend support to the credibility of the proposed method. Figure 10 graphically displays the data pairs of the estimates of daily ET from the three tested methods of the entire watershed against corresponding observations of pan ET in an ascending order of pan ET for days with daily net radiation larger than 100 W m−2. The data treatment was intended to unravel the potential CR for different methods under conditions of similar radiative energy import and absence of precipitation, facilitating the analysis of the underlying physical mechanisms of energy partitioning.

Figure 10.

Observations of the pan ET and actual ET estimates from the proposed integration method, and evaporative fraction method and the crop coefficient method of the Baiyangdian watershed for days with daily net radiation greater than 100 W m−2, with showing the complementary features between pan ET and estimated actual ET from the integration method.

[49] Results suggest that observations of pan ET and simulated daily actual ET from the integration method show a pronounced asymmetric CR, with an increase in pan ET being generally an evidence of a decrease in actual terrestrial ET for this watershed. In particular, for those days with a series of largest pan ET observations emerging in mid-May, the simulated actual ET from the integration method was relatively low. This corresponds to relatively large vapor pressure deficit and wind speed in the period, leading to a large magnitude of D and thus small G and actual ET. Conversely, for days with a relatively small pan ET, overall they show relatively large estimated actual ET, approaching the wet environmental ET of around 4.5 mm for this watershed. Higher soil moisture and energy availability and relatively small D were likely together to contribute to the large estimates of actual ET. It is apparent that the pan ET and actual ET from the evaporative fraction and the crop coefficient method do not diverge from each other, which would be a significant drawback of the two methods for producing ET time series at the watershed scale. The asymmetric CR between the pan ET and simulated actual ET from the integration method is basically in correspondence with what Kahler and Brutsaert [2006] found. They demonstrated that the scaled pan ET and locally observed actual ET at the daily timescale show a distinct CR. It should be noted that although the observations of pan ET in our study were not scaled, the selected data pairs of pan ET and simulated actual ET of the entire watershed generally represent similar energy import, which clearly exhibit the CR.

[50] It is highlighted that the modified GG model here departs from GG 1989 and GG 1996 in the use of a set of D and G relationships adjusted by the outputs from satellite-based SEBAL to integrate effects of surface and meteorological conditions on ET during certain period (e.g., 1 month). Consequently, the mechanism of the modified GG model appears to show more similarity to the energy balance methods. In other words, the modified GG model can be of the capability to extend the ET estimates from SEBAL to days regardless of weather conditions.

[51] It could be concluded that temporal trends in the ET time series from the proposed integration method are shown to be more reasonable in comparison to other extrapolation techniques. The new finding that the energy balance based method and mass balance based method both yield complementary features between actual ET estimates, and pan ET lends support to the complementary features between pan ET and actual ET at watershed scales and daily time scale. By contrast, the ET time series from the evaporative fraction and crop coefficient methods seem unable to show similar complementary features. Simple extrapolation and interpolation of the evaporative fraction and crop coefficient on the basis of insufficient images which are unreasonably distributed over time destruct temporal patterns of ET time series estimates at watershed scales.

5.4. Validation

5.4.1. Daily ET Validation Versus SEBAL

[52] To evaluate the performance of the modified relationship between D and G, we used the modified GG model to produce daily estimates of ET for typical cloud-free days with the exception of those days for calibration and compared them with the SEBAL-based ET predictions (see Figure 11 and Table 4). Results indicate that the modified GG model correlates reasonably well with SEBAL, showing overall R2 larger than 0.6 (the highest R2 was 0.8 on 5 June) and relative error smaller than −22.8% (the lowest relative error was −0.5% on 9 April) except 15 August. However, GG 1989 generates systematically lower ET predictions, showing larger relative errors versus SEBAL. As for ET estimates on 15 August, SEBAL may have provided relatively lower predictions because of spurious estimates of H occurring in some pixels with relatively large roughness length. As a result, the estimates of ET for those pixels were postprocessed into zero, making the mean of ET estimates of the entire watershed underestimate. Given this specific case, the relative error with respect to SEBAL would be smaller than 35.4% on 15 August.

Figure 11.

Comparison of predictions of daily ET from the modified GG and GG 1989 for the Baiyangdian watershed in year 2007 and SEBAL-based counterparts.

Table 4. Comparison of the Estimates of ET From GG 1989 and the Modified GG Model Versus SEBAL-Based ET Predictions
DateOriginal GG R2Modified GG R2Original GGModified GGSEBAL ET (mm)
ET (mm)Relative ErrorET (mm)Relative Error
9 Apr0.590.620.954−4.6%1.978−0.5%1.987
14 May0.680.631.605−23.6%1.698−19.2%2.101
5 Jun0.810.801.720−17.2%2.2005.9%2.077
10 Jul0.710.782.723−17.5%3.222−2.3%3.299
15 Aug0.320.431.8902.3%2.05235.4%1.848
23 Sep0.740.771.304−26.0%1.368−22.4%1.763
28 Oct0.740.740.402−29.3%0.410−27.8%0.568

[53] Despite losing certain variations in ET from the modified GG model under small D conditions, the areal mean and basic spatial representation of the ET estimates can be generally captured by the modified GG model. Figure 12 clearly illustrates that the modified GG model can offer a more realistic distribution of ET across the entire watershed compared with GG 1989 and GG 1996, showing a larger standard deviation of 0.909 mm and a closer mean of watershed ET of 2.943 mm on 25 April 2007 relative to the estimates from SEBAL. GG 1989 and GG 1996 systematically underestimate actual ET, indicating relatively lower averages of ET of 1.453 mm and 2.359 mm and standard deviations of 0.499 mm and 0.434 mm, respectively. This suggests that the original relationship between D and G is not sensitive to the variation in surface moisture, land covers, and thus actual ET. The difference between the original GG models and the modified GG model may result from a different hydrologic condition these models are based on. GG 1989 was derived for a semiarid climatic zone of western Canada, leading to a relatively lower magnitude of G and thus lower predictions of ET. However, the modified relationship between D and G in this study was developed in a semihumid climatic zone in north China, suggesting a relatively larger magnitude of G for a given D. The remotely sensed ET from SEBAL at watershed scales provides the potential to deduce a more effective and applicable functional relationship between D and G. The modified GG model obviates the need for a wealth of information on landscape properties and can retain essentially remotely sensed characteristics of ET. Its robustness would be manifested for days without good quality images. The integration technique successfully combines the strengths of both methodologies.

Figure 12.

Spatial distributions of ET estimates from SEBAL, the modified GG model, GG 1989, and GG 1996 of the Baiyangdian watershed on 25 April 2007.

5.4.2. Annual ET Validation Versus the Water Balance Equation

[54] The hydrologic budget calculation for the Baiyangdian watershed in the year 2007 was performed to independently offer annual ET for evaluating the overall accuracy of the time series of ET from the three studied methods. The water balance equation plays a predominant role in hydrologic modeling and has been widely used to perform model validation for satellite-based surface fluxes estimation [Bastiaanssen et al., 2002; Gao and Long, 2008; Mohamed et al., 2006]:

equation image

where P is the annual precipitation for a watershed (mm), which can be obtained from meteorological stations. The Thiessen polygon interpolation method was adopted to provide the areal mean precipitation. R is the surface runoff (mm), which can be obtained from hydrologic stations at the outlet. The dS/dt is the surface water storage change (mm), which can be estimated from records of large reservoirs in a watershed. The dG/dt is the ground water storage change (mm), which can be estimated from phreatic records. dW/dt is the soil water storage change (mm). The ground outflow was neglected in equation (21) in this study.

[55] The precipitation of the Baiyangdian watershed in 2007 was estimated to be 570.0 mm on the basis of records of 18 weather stations using the Thiessen polygon interpolation technique. There was no natural streamflow into the outlet, Baiyangdian Lake, on account of large usage of water resources from irrigation, industrial, and municipal use and reservoir regulation. It is noted that there has been no natural surface runoff to Baiyangdian Lake for recent years; its water resources are exclusively from interbasin water transfer projects and the precipitation of the area. The change in surface water storage was roughly 10.2 mm from the reservoir storage data within this watershed. This amount appears to be relatively larger than other years, because the precipitation of 46.5 mm and 19.0 mm in September and October in 2007, respectively, were generally 50% larger than the yearly average precipitation. This would suggest a small amount of precipitation evaporating back into the atmosphere and hence a large amount reserved in the reservoirs. Groundwater storage change was calculated using the data of groundwater observation wells and the inverse distance weighting method, showing an increase of around 10 mm across the plain areas. In addition, it was assumed that the groundwater storage change for mountainous areas and the soil water storage change were negligible. The actual ET was ultimately calculated as 549.8 mm (see Table 5) by means of equation (21); the integration method has the highest accuracy in terms of the smallest relative error of −7.5% with respect to the ET from the hydrologic budget calculation.

Table 5. Accuracy Assessment for Different Methods to Generate ET Time Series in Terms of Hydrologic Budget Calculations
Watershed NameEvaporative Fraction MethodCrop Coefficient MethodCombination MethodWater Balance Equation-Based ET (mm)
ET (mm)Relative Error (%)ET (mm)Relative Error (%)ET (mm)Relative Error (%)
Baiyangdian395.2−25.4358.7−32.3508.4−7.5549.8
Dage310.2−12.6321.3−9.5360.31.5355.1

5.4.3. Application to Another Watershed

[56] The three studied approaches were applied to another watershed, upper the Dage hydrological station in the Chao River, north China, to further compare their utility and evaluate their accuracy in generating ET time series. This watershed lies in a transition zone between the Inner Mongolia Plateau and the North China Plain, extending in latitude from 41.03°N to 41.62°N and in longitude from 116.13°E to 116.75°E, with an area of 1850 km2. The watershed climate is a transition zone from semihumid to semiarid climatic regimes, showing a mean annual precipitation of 457.1 mm and a mean annual runoff of 54.9 mm. The mean annul temperature is approximately 6.8°C, with the coldest month being January with a mean temperature of −11.7°C and the hottest month being July with a mean temperature of 22.4°C.

[57] The mean annual precipitation and mean annual surface runoff of the Dage watershed during the period of July 2005 to July 2006 was 402.9 mm and 21.4 mm, respectively. The soil moisture storage change was estimated using observations of 25 soil moisture monitoring sites from two field campaigns conducted at the beginning and the end of the study period and by the inverse distance weighting averaging, showing a mean of 26.4 mm. More details about the Dage watershed and the field campaigns can be found in Gao and Long [2008]. Given that the surface water storage change and ground water exchange with adjacent watersheds are negligible caused by the watershed being located in a mountainous area without intensive human activities, the ET amount for the Dage watershed in 2005 can thus be obtained with equation (21) as 355.1 mm (Table 5). The proposed integration method also yielded the highest accuracy in terms of the smallest relative error of 1.5% relative to the annual ET from the hydrologic budget calculation.

5.4.4. Variations in Terrestrial ET and Determinants

[58] Analysis of variation trends in the simulated ET and associated meteorological and remotely sensed variables would help further interpret the utility of the proposed technique. Simulations of monthly watershed ET and corresponding measurements of precipitation and pan ET are shown in Figure 13. It is indicated that precipitation amounts in rainy season (June, July, and August) were 92.5 mm, 124.5 mm, and 105.3 mm, respectively. The estimates of actual watershed ET from the integration technique for the three months were 82.9 mm, 81.8 mm, and 74.2 mm, respectively. Figure 14 presents variation trends in the daily net radiation, drying power of the air, remotely sensed LAI, and surface albedo in 2007. It is again suggested that the daily net radiation is the most critical variable in determining the magnitude of actual ET which has been proved by the sensitivity analysis performed in section 3.2 and other studies [Gao and Long, 2008; Gao et al., 2008; Long et al., 2010]. June showed the largest amount of daily net radiation and relatively small drying power of the air, thereby resulting in the largest actual terrestrial ET. The largest LAI of this watershed occurred in August, which was coincident with consecutive rain events and consequently ample soil moisture. However, estimated actual watershed ET in August was somewhat smaller than was in June and July, which was probably related to the declined energy availability in August compared to June and July.

Figure 13.

Simulated monthly actual ET and corresponding precipitation and pan ET from the studied three techniques of the Baiyangdian watershed in year 2007.

Figure 14.

Variation trends in key variables of determining the magnitude and distribution of watershed ET (error bars represent one standard deviation with reference to the bin mean).

[59] It is important to note that variation trends in observed pan ET were not in accordance with that of actual ET, showing the largest accumulated actual ET of 82.9 mm in June but the largest pan ET of 305.3 mm in May. This further clarifies the “evaporation paradox” initiated by [Brutsaert and Parlange, 1998]. Large evaporation does not necessarily correspond to large terrestrial actual ET; conversely, it is often an indicator of large drying power of the air and thus small terrestrial actual ET. In this study, the largest drying power corresponding to the largest observed pan ET occurred in May, which may have been caused by relatively larger observations of saturation vapor pressure deficit and wind speed. As such, May reflected a smaller estimate of actual terrestrial ET of 50.6 mm compared to that of 68.2 mm in April. The largest water consumption by agriculture and adequate radiative energy jointly contributed to such an amount of actual terrestrial ET in April.

6. Summary and Conclusions

[60] Lack of good quality satellite images because of cloud contamination particularly in rainy season or too long revisit time severely deteriorates predictions of ET time series from remote sensing based models at watershed scales. This significantly limits practical applications of satellite-based operational ET simulation to estimation of water consumption by crops, irrigation scheduling formulation, and water budget calculation for a watershed for water resources planning, allocation, and management as well as climate and weather predictions.

[61] In the present work, we integrate the feedback GG model built on the energy budget and aerodynamic principles simply using routine meteorological data with SEBAL that simulates surface fluxes from satellite images, with the objective to generate ET time series of reasonable spatial and temporal representation. The point here is that for a specific region where the complementary relationship between pan ET and actual ET has been shown to be valid, the ET time series would clearly exhibit the complementary features both in time and space. If the integration method can generate estimates of ET time series showing complementary features and estimates of high spatial resolution due to the assimilation of remotely sensed variables and/or fluxes, it would successfully extend remotely sensed information on cloud-free days to days without good quality images and be greatly beneficial to operational ET time series estimation. The integration approach would improve the overall performance of the feedback method at large spatial scales by incorporating satellite-derived ET.

[62] Results suggest that the modified GG model that has incorporated remotely sensed information can predict reliable ET of high resolution and reasonable spatial representation at watershed scales. GG 1989 and GG 1996 systematically underestimates areal ET at watershed/regional scales because of the limitations in the relationship between D and G, showing unreliable ET distribution. It is found that the utility of the evaporative fraction method depends largely on the number and interval of good quality satellite images and corresponding soil and vegetation states as well as energy availability. Because of limited good quality satellite images solely covering a fraction of the crop coefficient cycle during a year, the crop coefficient method cannot produce a realistic and continuous crop coefficient curve, particularly during periods of rapid development of vegetation and crops. There is a gap between the desired quality and frequency distribution of satellite images over time and practical applications for constructing reliable evaporative fraction and crop coefficient curves. ET time series estimates from the three studied techniques for days with daily net radiation larger than 100 W m−2 and corresponding pan ET clearly show that only the integration method can exhibit an asymmetric complementary relationship at the watershed scale and daily time scale. The findings, in turn, give confidence to the utility of the proposed technique because of its reasonable temporal distribution throughout a year. Validation performed using hydrologic budget calculations indicate that the proposed integration method has the highest accuracy of annual estimates of ET for both the Baiyangdian watershed and the Dage watershed in north China. More work, however, is still required to further validate the proposed model by hydrologic modeling approaches, by spatially and temporally extensive flux, or by lysimeter measurements. Some remote sensing based flux models (e.g., Atmosphere-Land Exchange Inverse (ALEXI), Two-Source Energy Balance (TSEB), and Surface Energy Balance System (SEBS)) can also serve to provide regional estimates of ET for calibration of the GG model if it shows better performance for certain study sites.

[63] Unprecedentedly increasing satellite images nowadays offer new opportunities to study hydrology, meteorology, agronomy, forestry, and environmental issues related disciplines. Adequate utilization of the increasing remotely observed information at different spatial and temporal scales has been a focus for several decades. The available remote sensing information, however, has its inherent limitation in quantity and quality as well as scale effects. It is expected that some conventional techniques will be rejuvenated through incorporation of the strengths of satellite remote sensing and overcoming their deficiencies on the basis of basic nature principles (e.g., the energy balance, water balance, and complementary relationship) and new developments in information extraction techniques. Observations of the surface and lower atmosphere variables and relevant conventional techniques built on them should also be continuously utilized rather than only depending on satellite images. This may, on the one hand, obviate inherent limitations in satellite remote sensing and, on the other hand, provide surface reference for comparing and evaluating predictions that have incorporated satellite data.

Acknowledgments

[64] The authors are grateful to the associate editor and three anonymous reviewers who provided thorough and constructive reviews. The paper is much improved as a result. We would like to thank National Climatic Center of the China Meteorological Administration and the Meteorological Bureau of Baoding City for providing associated hydrometeorological data, and the administration office of Baiyangdian Lake in Hebei Province, China, for providing the hydrologic data in the research. Director Suqin Li in the Meteorological Bureau of Baoding City, Hebei Province, and Director Zhiyong Bian in the administration office of Baiyangdian Lake, Hebei Province, are both greatly appreciated for their assistance in interpreting the study site and usage of data.

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