PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2013WR014573

Special Section: Patterns in Soil-VegetationAtmosphere Systems: Monitoring, Modelling and Data Assimilation Key Points:  A novel data assimilation framework is developed  Remotely sensed LST and FPAR observations are assimilated  Surface heat fluxes and vegetation dynamics are estimated

Correspondence to: S. M. Bateni, [email protected]

Citation: Bateni, S. M., D. Entekhabi, S. Margulis, F. Castelli, and L. Kergoat (2014), Coupled estimation of surface heat fluxes and vegetation dynamics from remotely sensed land surface temperature and fraction of photosynthetically active radiation, Water Resour. Res., 50, doi:10.1002/ 2013WR014573. Received 20 AUG 2013 Accepted 29 SEP 2014 Accepted article online 9 OCT 2014

Coupled estimation of surface heat fluxes and vegetation dynamics from remotely sensed land surface temperature and fraction of photosynthetically active radiation S. M. Bateni1, D. Entekhabi2, S. Margulis3, F. Castelli4, and L. Kergoat5 1

Department of Civil and Environmental Engineering and Water Resources Research Center, University of Hawaii at Manoa, Honolulu, Hawaii, USA, 2Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, 3Department of Civil and Environmental Engineering, University of California Los Angeles, Los Angeles, California, USA, 4Dipartimento di Ingegneria Civile, Universita degli Studli di Firenze, Firenze, Italy, 5Geosciences Environment Toulouse (CNRS/UPS/IRD), Toulouse, France

Abstract Remotely sensed Land Surface Temperature (LST) and Fraction of Photosynthetically Active Radiation absorbed by vegetation (FPAR) are assimilated, respectively, into the Surface Energy Balance (SEB) equation and a Vegetation Dynamics Model (VDM) in order to estimate surface fluxes and vegetation dynamics. The problem is posed in terms of three unknown and dimensionless parameters: (1) neutral bulk heat transfer coefficient, which scales the sum of turbulent heat fluxes, (2) soil and canopy evaporative fractions that characterize partitioning among the turbulent heat fluxes over soil and vegetation, and (3) specific leaf area, which captures seasonal phenology and vegetation dynamics. The model is applied over the Gourma site in Mali, the northern region of the West African Monsoon (WAM) domain. The application of the model over the Gourma site shows that spaceborne LST observations can be used to constrain the SEB equation and obtain its key two unknown parameters (i.e., neutral bulk heat transfer coefficient and evaporative fraction). We demonstrate that the spatial patterns of estimated neutral bulk heat transfer coefficient and evaporative fraction resemble, respectively, those of independently observed vegetation index and soil moisture. The framework also yields estimates of surface energy balance components. The daily sensible, latent, and ground heat flux estimates at the Agoufou site that is located in the south of the Gourma region have, respectively, a root-mean-square error (RMSE) of 53.6, 34.4, and 45.1 Wm22. The daily sensible heat flux estimates at the Bamba site, which is located in the north of the Gourma domain, have a RMSE of 42.6 Wm22. The results also show that remotely sensed FPAR observations can constrain the VDM and retrieve its main unknown parameter (specific leaf area) over large-scale domains without costly in situ measurements. The results indicate that the estimated specific leaf area values vary reasonably with the expected influential environmental variables such as precipitation, air temperature, and solar radiation. Assimilating FPAR observations into the VDM can also provide an estimate of Leaf Area Index (LAI) dynamics. The estimated LAI values are comparable in magnitude, spatial pattern and temporal evolution with satellite retrievals.

1. Introduction The surface heat fluxes, drivers of numerous atmospheric, hydrologic, and environmental processes, are linked to the seasonal phenology of vegetation [Lemon et al., 2007; Alfieri et al., 2009]. Specifically, in regions with a monsoonal hydroclimate where the vegetation seasonal phenology is pronounced, the temporal and spatial dynamics of surface fluxes significantly impact the regional land-atmosphere interaction [Rosnay et al., 2009]. In situ measurement of the surface heat fluxes is costly and difficult, and hence there are a finite number of flux tower networks across the globe (e.g., AmeriFlux, Fluxnet, EuroFlux, etc.). Even with the availability of these measurements, large-scale flux mapping is difficult due to significant spatial heterogeneity in surface properties such as topography, soil moisture, vegetation cover, etc. [Jung et al., 2009, 2011]. Spaceborne measurements of land surface temperature (LST) provide an important constraint for the estimation of surface energy balance components over large spatial domains [Bateni and Entekhabi, 2012b]. As a result, a multitude of approaches have been introduced to retrieve surface fluxes from remotely sensed LST and LST sequences. The majority of the existing surface heat flux retrieval approaches fall into one of

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five main categories. The first group empirically relates the correlation between a vegetation index (VI) (e.g., normalized difference vegetation index (NDVI), leaf area index (LAI), crop water stress index (CWSI), etc.) and LST measurements to surface evaporation [Gillies et al., 1997; Sandholt et al., 2002; Carlson, 2007; Tang et al., 2010; Shu et al., 2011]. These studies have led to the so-called triangle method and its variants for retrieving surface evaporation rate from the NDVI-LST relationship. The second group solves the surface energy balance diagnostically and predicts surface heat fluxes by using instantaneous LST observations [Bastiaanssen et al., 1998a, 1998b; Su, 2002; Timmermans et al., 2007; Cammalleri et al., 2010]. Since the land surface temperature (T) and its time derivative (dT/dt) both appear in the surface energy balance equation, typically closure assumptions are required. The most widespread closure assumption is that the ratio of ground heat flux (G) to net radiation (Rn) (i.e., G=Rn ) is taken to be constant or a function of vegetation indices. The third group is called the combination method and estimates turbulent heat fluxes by incorporating the LST observations into the Penman-Monteith equation [Mallick et al., 2013, 2014]. These models combine LST data with energy balance closure models to eliminate the need to the specification of surface to atmosphere conductance terms (i.e., aerodynamic and stomatal conductances). The fourth group (known as the land data assimilation system (LDAS)) merges soil moisture and temperature, vegetation properties, topography, and meteorological forcings with a land surface model (e.g., Noah) within an Ensemble Kalman Filter data assimilation system to estimate water and energy fluxes [Peters-Lidard et al., 2011; Xia et al., 2012a, 2012b]. Beyond these methods, the fifth group, known as variational data assimilation (VDA) approaches, assimilates sequences of LST observations into the surface energy balance (SEB) to estimate heat and moisture fluxes between the land and atmosphere [Caparrini et al., 2004; Sini et al., 2008; Bateni and Entekhabi, 2012a, 2012b; Bateni and Liang, 2012; Bateni et al., 2013a, 2013b; Xu et al., 2014a, 2014b]. The VDA approach has a number of advantages over observations-only and model-only driven approaches. VDA approach applied to the estimation of surface energy balance can generate surface heat fluxes even, for instances, in which remotely sensed LST observations are not available or there are data gaps and constrains the model with observations. They do not require any calibration and empirical fitting. The ground heat flux estimates from the VDA approach is based on the heat diffusion equation. It allows better characterization of the diurnal and synoptic variations in heat flux dynamics when compared to diagnostic approaches. It does however require basic information on soil thermal properties [Bateni et al., 2013a, 2013b]. The partitioning of available energy into surface heat fluxes is controlled by the distribution and dynamics of vegetation in addition to other variables such as LST and soil moisture [Segal et al., 1988; Alfieri et al., 2009; Bateni and Liang, 2012; Bateni et al., 2013b]. Therefore, understanding, modeling, and predicting plant phenology is critical for the correct prediction of surface heat fluxes. A vegetation dynamics model (VDM) can be coupled to the SEB to take into account the effect of vegetation density on the surface heat fluxes. Although such a coupling accounts for changes in vegetation dynamics, it necessarily increases number of variables considerably. To overcome this problem and build a VDA system which performs robustly even with the increased number of model variables, remotely sensed fraction of photosynthetically active radiation absorbed by vegetation (FPAR) data is assimilated into the VDA framework. The assimilation of FPAR provides a constraint on the key unknown variable of the VDA (i.e., specific leaf area; described in more detail in section 6.2) and also estimates LAI dynamics. Literature [e.g., Hipps et al., 1983; Monica et al., 2005] shows that FPAR is generally well correlated with LAI, and thus has valuable information on vegetation dynamics. In this paper, we develop a novel VDA framework that yields surface heat fluxes, LAI, and specific leaf area estimates that are constrained by remotely sensed LST and FPAR data. The beginning point of this study is the VDA model developed by Bateni et al. [2013b], but it enhances that study in two important new directions. First, it couples the SEB equation and the VDM via the linkage between transpiration and photosynthesis. The SEB scheme provides estimates of transpiration, which is used as the key environmental input variable to the VDM. The VDM predicts the LAI variations in time, which is then utilized by the SEB scheme for the partitioning of available energy among heat fluxes. This coupling allows the SEB and VDM to operate in a consistent and dynamic way and eliminates the need for ancillary information on soil moisture, the state of vegetation, and empirical assumptions. Second, this study assimilates FPAR data in order to constrain the key unknown variable of the utilized VDM, i.e., specific leaf area (that captures seasonal phenology and vegetation dynamics).

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The developed methodology is applied over the Gourma mesoscale region in West Africa, which has sharp spatial gradients and seasonality in rainfall, incoming solar radiation, and air temperature. The region is well suited to examine the effect of environmental factors on retrieved surface heat fluxes and vegetation dynamics. Section 2 presents the outline of the SEB and VDM and their coupling. Section 3 describes Figure 1. Schematic diagram showing the resistance network for the dual-source scheme. the variational approach for the estimation of the key unknown parameters. Section 4 provides information on the application site. The results are included in section 6. Finally, a summary of results, conclusions, and future extensions are reported in section 7.

2. Models and Methods 2.1. Heat Diffusion Equation The heat diffusion equation describes the variation of temperature in the soil over time. In one-dimensional form, the heat diffusion can be written as:   @Ts ðz; tÞ @ @Ts ðz; tÞ c 5 p (1) @t @z @z where Ts ðz; tÞ is soil temperature at depth z and time t, p is the soil thermal conductivity, and c is the soil volumetric heat capacity. The heat diffusion equation can be solved by the specification of boundary conditions at the top and bottom of soil column. The boundary condition at the top of soil column is obtained by solving the surface forcing equation ðp@Ts ðz50; tÞ=@t52GðtÞÞ for the soil surface temperature, Ts ðz50; tÞ, where G is the ground heat flux. The diurnal heat wave does not penetrate beyond 0.3–0.5 m. The temperature of soil at these depths varies slightly over a day and can be considered constant [Hu and Islam, 1995; Hirota et al., 2002; Bateni et al., 2013a]. Thus, a Neumann boundary condition is used at the bottom of the soil column. 2.2. Dual Source (DS) Surface Energy Balance A dual source (DS) model treats an inhomogeneous land surface as two distinct heat and moisture flux sources: the canopy and the soil [Shuttleworth and Wallace, 1985; Norman et al., 1995; Anderson et al., 1997]. Since in this study the SEB and VDM are coupled (section 2.5) based on the relationship between transpiration and photosynthesis (section 2.4), a DS scheme is required to provide estimates of transpiration rather than a combined source scheme that yields total evapotranspiration and not transpiration and evaporation separately. The DS scheme is built upon Kustas et al. [1996] model. In this model, the soil-vegetation-atmosphere transfer scheme is characterized by a series of resistances connecting the soil and canopy leaves to the air within canopy, and the within-canopy air to the boundary layer air above it (Figure 1). Heat transfer from soil to air within the canopy is represented by the soil turbulent heat transfer coefficient (CHS). Likewise, heat transfer from canopy to the within-canopy air is represented by the canopy turbulent heat transfer coefficient (CHC). The sensible heat fluxes for the canopy (Hc) and soil (Hs) can be written as: Hc 5qcp CHC Uw ðTc 2Tw Þ

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(2a)

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Hs 5qcp CHS Uw ðTs 2Tw Þ

(2b)

where q is the density of air, cp is the air specific heat at constant pressure, Tc and Ts are the canopy and soil temperatures, and Tw and Uw are the air temperature and wind speed at a reference height within the canopy volume. Using the bulk heat transfer coefficient CH for heat transfer from the within-canopy air (subscript w) to the above-canopy air (subscript a), the total sensible heat flux (H) can be expressed as: H5qcp CH UðTw 2Ta Þ

(3)

where U is the above-canopy wind speed. Following Caparrini et al. [2004], the heat transfer coefficient CH can be written as the product of heat transfer coefficient under neutral atmospheric condition (CHN) and an atmospheric stability correction function, f(Ri) [i.e., CH 5CHN f ðRiÞ, where Ri is the Richardson number]. The atmospheric correction function proposed by Caparrini et al. [2004] is used in this study. CHN mainly depends on the properties of the landscape, evolves on the time scale of changing vegetation phenology (monthly), and is a key unknown in the DS scheme. The other unknowns of the DS model are the canopy and soil evaporative fractions (EFc and EFs), which are given by LEc LEc 1Hc LEs EFs 5 LEs 1Hs

EFc 5

(4a) (4b)

where LEc and LEs are latent heat fluxes for the canopy and soil. EFc and EFs are almost constant for nearpeak radiation hours on days without precipitation [Gentine et al., 2007]. The total sensible (latent) heat flux is given by the sum of sensible (latent) heat fluxes from soil and vegetation, weighted by the fractional canopy cover fc [Bateni and Liang, 2012]. The net radiation absorbed by the canopy (Rnc) and soil (Rns) are estimated by creating a balance among the incoming and outgoing shortwave and longwave radiation fluxes for canopy and soil components [Bateni and Liang, 2012]. The unknown parameters of the DS scheme are CHS, CHC, CHN, EFs, and EFc. Following Bateni and Liang [2012], the soil and canopy conductance (CHS Uw and CHC Uw ) are related to CHN U in order to decrease the unknown parameters of the DS scheme to CHN, EFs, and EFc. 2.3. Vegetation Dynamics Model (VDM) Vegetation dynamic models predict the seasonal variability of plant structure. A review of available VDMs and representation of ecophysiological processes (respiration, photosynthesis, and carbon allocation) is given in Arora [2002]. The VDM suggested by Montaldo et al. [2005] is used in this study due to its simplicity and physically based nature. They showed that it is possible to simplify the more complicated VDM of Nouvellon et al. [2000] by excluding its root and dead biomass modeling compartments, and finally proposed a parsimonious VDM, which only models the green aboveground biomass. In their model, the green aboveground biomass evolution through time is calculated via the balance between the rate of biomass generation that occurs through photosynthesis and the rate of biomass loss through respiration and senescence. This can be captured through the daily dynamic model for aboveground biomass, Bg (gr DM m22): dBg 5aa Pg 2Rg 2Sg dt

(5)

where Pg is the gross daily photosynthesis (gr DM m22 d21) (in section 2.4, the model for Pg is presented), t is the daily time step (day), aa is the allocation coefficient to the green aboveground compartment, Rg is the respiration from aboveground biomass (gr DM m22 d21), and Sg is the senescence of aboveground green biomass (gr DM m22 d21). As in previous studies [e.g., Nouvellon et al., 2000; Cayrol et al., 2000a, 2000b; Montaldo et al., 2005, 2008; Cervarolo et al., 2010], aa is set to 0.5 herein.

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The maintenance and growth respiration constitute total respiration from aboveground biomass (Rg) [Amthor, 1986, 1989; Cayrol et al., 2000a; Montaldo et al., 2005, 2008]: Rg 5ms Bg 1ga aa Pg

(6)

where ms and ga are maintenance and growth respiration coefficients for the green aboveground biomass. Maintenance respiration (ms Bg ) keeps the available biomass alive and functioning and thus is related to the maintenance of existing green aboveground biomass. Growth respiration (ga aa Pg ) is associated with the new biomass production and is strongly correlated with the growth of green aboveground compartment of plant. The maintenance coefficient (ms) may be different among various species and is strongly affected by air temperature [Amthor, 1986, 1989; Atkin et al., 2005]. Its dependence on air temperature is captured by the common Q10 relationship [Montaldo et al., 2005]: T =10

ms 5mso Q10m

(7)

where Tm is the mean daily air temperature ( C), and mso is the maintenance respiration coefficient at 0 C. Q10 shows the logarithmic increase in respiration for every 10 C increase in the air temperature. Its measured values range from less than 2 to more than 3. In this study, a typical value of 2 is used for Q10 and a value of 0.02 day21 is chosen for ms at 20 C as suggested by previous work [e.g., Amthor, 1986, 1989; Cayrol et al., 2000a, 2000b; Montaldo et al., 2005; Lebel et al., 2009]. The growth respiration coefficient (ga) depends on the plant functional type (PFT). Following Amthor [1986, 1989], Nouvellon et al. [2000], and Montaldo et al. [2005, 2008], ga is set to 0.25 in this study. Senescence of aboveground green biomass (Sg) is given by [Nouvellon et al., 2000; Cayrol et al., 2000a, 2000b; Montaldo et al., 2005, 2008; Cervarolo et al., 2010]: Sg 5dT Bg

(8)

where dT (day21) is the total biomass destruction coefficient. The readers are referred to Detling et al. [1979] and Nouvellon et al. [2000] for detailed information on dT and its specification. Finally, leaf area index is related to the biomass via the following relationship [Nouvellon et al., 2000; Montaldo et al., 2005, 2008]: LAI5cg Bg

(9)

where cg (m2 gr DM21) is the specific leaf area of the green biomass and is a measure of leaf thickness. Substituting equations (6), (8), and (9) into equation (5) leads to: dLAI 5aa cg ð12ga ÞPg 2ðms 1dT ÞLAI dt

(10)

Montaldo et al. [2005] showed that cg varies on a seasonal time scale, and in the growing season its values is almost twice of its value in the senescence season. Therefore, in this study, cg is treated as a variable that changes on a monthly time scale. 2.4. Transpiration-Photosynthesis Relationship Transpiration can be considered as the necessary cost that is paid by plants to assimilate carbon through photosynthesis [Chen and Coughenour, 2004]. The gradient of water vapor concentration from the intercellular spaces of the leaf to ambient air and the diffusive resistance in the water vapor pathway determine transpiration [Monteith, 1988; Mcdowell et al., 2010]. Similarly, the gradient of CO2 concentration from the ambient air to the leaf and the related diffusive resistances determine photosynthesis. Based on Fick’s law, transpiration can be written as [Monteith, 1988; Mcdowell et al., 2010]: Ec 5qw ðmi 2ma Þ=ðrs 1rb Þ

(11)

where Ec (kg/m2 s) is transpiration, ma (kg/kg) and mi (kg/kg) are water vapor mixing ratios in ambient air and leaf intercellular spaces, qw (kg/m3) is the density of water vapor, and rb (s/m) and rs (s/m) are diffusion resistances of the leaf boundary layer and stomata for the water vapor flux.

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In the same way that transpiration is formulated in (11), photosynthesis can be written as: Pg 5qc ðm0a 2m0i Þ=ðrs0 1rb0 Þ

(12)

where m0a (kg/kg) and m0i (kg/kg) are CO2 mixing ratios in ambient air and in the intercellular spaces of a leaf, qc (kg/m3) is the density of CO2, and rb0 (s/m) and rs0 (s/m) are diffusion resistances of the leaf boundary layer and stomata for CO2 flux. Considering (11) and (12) results in: Pg qc ðm0a 2m0i Þ=ðrs0 1rb0 Þ Mc ðm0a 2m0i Þ ðrs 1rb Þ 5 5 Ec qw ðmi 2ma Þ=ðrs 1rb Þ Mw ðmi 2ma Þ ðrs0 1rb0 Þ

(13)

where Mw is the molar mass of water (18 gr) and Mc is the molar mass of CO2 (44 gr). The ratio (rs 1rb )/ (rs0 1rb0 ) is proportional to the inverse of ratio of the diffusion coefficient (Di) for water vapor and CO2 [Monteith, 1988; Damour et al., 2010]. Substituting the ratio of diffusion coefficients for water vapor (0.209 cm2 s21) and CO2 (0.103 cm2 s21) (i.e., 0.209/0.103 5 1.6) in equation (13) and taking x5ð12m0i =m0a Þ yields [Marrero and Mason, 1972]: Pg m0a 51:52x Ec mi 2ma

(14)

The value of m0i =m0a is constant for plants assimilating CO2 through the C3 pathway, and constant with a differing value for those plants assimilating CO2 by the C4 pathway [Sinclair et al., 1984; Prentice and Harrison, 2009]. The value of m0i =m0a (x512m0i =m0a ) for C3 and C4 plants is approximately 0.7 (0.3) and 0.35 (0.65), respectively [Sinclair et al., 1984; Prentice and Harrison, 2009]. An x value of 0.65 is used in this study because the Gourma site is covered by C4 grasses [Mougin et al., 2009]. The mixing ratio of CO2 in ambient air (m0a ) in equation (14) is set to 235 3 1026 (kg/kg) according to the measurement of atmospheric CO2 concentration at the Mauna Los Observatory. The measurements are available on the NOAA archive (http://www.esrl.noaa.gov/gmd/ccgg/trends/). The value for mi in equation (14) is obtained from the estimate of water vapor pressure in the leaf (el) and the measurement of atmospheric air pressure (P) via [Rogers and Yau, 1989] mi 5e

el P2el

(15)

where e50:622. Because the air in the intercellular spaces of a leaf is effectively saturated, the water vapor pressure in a leaf (el) can be considered to be saturated and can be easily estimated from the ClausiusClapeyron equation [Monteith, 1988; Rogers and Yau, 1989].

2.5. Coupling SEB and VDM This study couples the VDM with the SEB model based on the linkage between Pg and Ec (14). The core of this coupling is that the VDM estimates the LAI dynamics, which is then exploited by the SEB scheme for the partitioning of available energy among soil and vegetation SEB components. The SEB scheme provides estimates of transpiration that are used by the VDM. This coupling not only eliminates the need for the ancillary input variables such as soil moisture and PAR but also makes the SEB and VDM operate in a consistent and dynamic way. In order to couple the VDM (10) with the SEB model, the key term of VDM (i.e., Pg) is replaced by transpiration (Ec) using (14), dLAI m0a Ec 2ðms 1dT ÞLAI 51:52aa cg ð12ga Þx mi 2ma dt

(16)

Equation (16) couples transpiration and canopy growth processes in a dynamic and functional way. Also, the model keeps only the most relevant environmental variables influencing LAI dynamics and operates on a daily time step using a limited number of parameters. The unknown parameter of the VDM is cg, which varies on the scale of changing vegetation phenology (monthly) [Montaldo et al., 2005, 2008]. Specific leaf area represents the ratio of leaf area to its dry weight, and therefore, is considered as a measure of leaf thickness. The value of cg is affected by complicated

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physiological processes that vary with time (on a monthly time scale) and space and control the leaf growth and development.

3. Data Assimilation In this study, FPAR observations are assimilated within a data assimilation framework to constrain the key unknown parameter of the utilized VDM, i.e., specific leaf area (cg). We also assimilate LST observations because they can constrain the unknown parameters of the SEB model (CHN, EFs, and EFc) [Caparrini et al., 2004; Bateni and Liang, 2012; Bateni et al., 2013b]. To retrieve statistically optimal values for cg, CHN, EFs, and EFc, we define a cost function (J) based on the misfits between LST and FPAR observations and simulations, uncertain prior parameter value estimates, and physical (SEB and VDM) constraints. Two integral time scales are used in the cost function. The first time scale is daily with an assimilation window of [s0,s1] during which EFs and EFc can be assumed to be invariant in each pixel. The second time scale spans an assimilation period of N days in which CHN and cg can be assumed to be constant for each pixel. The cost function can be shown as: JðT; LAI; R; EFS ; EFC ;cg ;K1;K2Þ5 N ð s1 X

1

i51 s0

1

½Ti ð0; tÞ2Tobs;i ð0; tÞT K21 T ½Ti ð0; tÞ2Tobs;i ð0; tÞdt

N X 0 T 21 0 ½FPARi 2FPARobs;i T K21 FPAR ½FPARi 2FPARobs;i 1ðR2R Þ KR ðR2R Þ i51

1

N N X X 0 0 0 0 ðEFSi 2EF Si ÞT K21 ðEFCi 2EF Ci ÞT K21 EFs ðEFSi 2EF Si Þ1 EFc ðEFCi 2EF Ci Þ i51

(17)

i51

  @Tsi ðz; tÞ @ @Tsi ðz; tÞ 2 p dzdt @t @z @z i51 s0 0   ðN dLAIi 1:52aa ð12ga Þxm0a Ec K2i cg 1ðms 1dT ÞLAIi dt 1 2 dt mi 2ma i51 0

1ðcg -c0g ÞT K21 Cg ðcg -c g Þ1

N ð s1 X

ðl



K1i c

where Tobs ð0; tÞ and FPARobs are the vectors containing remotely sensed LST and FPAR data, respectively. T ð0; tÞ and FPAR are the vectors that contain the modeled equivalents of the observations. The first and second terms of the cost function quantify the quadratic difference between the LST and FPAR observations and the model predictions. Primed variables are the prior estimates of the parameter values. To maintain CHN as a nonnegative variable, it is transformed into R via CHN 5eR . The third through sixth terms are penalty terms for deviations from the prior estimates. The seventh term is the heat diffusion equation (that estimates the temperature dynamics, T(z, t), in the soil column at depth z and time t) and is incorporated into the model as the physical constraint (adjoint) using Lagrange multiplier function K1. The last term is the VDM that is incorporated into the model as the second physical constraint using Lagrange multiplier function K2. The estimated LAI values from the VDM are used in the Lambert-Beer extinction law to obtain FPAR estimates (in the second term) as follows [Hipps et al., 1983; Sellers et al., 1996]: FPAR512exp ð2ke LAIÞ

(18)

where ke is the extinction coefficient and depends on the plant species. 21 The matrices K21 T and KFPAR are the spatial error-covariance matrices for LST and FPAR observations, respec21 21 21 tively. KR ; KEFS ; KEFC , and K21 Cg are the spatial error-covariance matrices of the prior values for the sub21 21 21 21 21 scripted components. The relative magnitude of the matrices K21 T ; KFPAR ; KR ; KEFS ; KEFC , and KCg controls the rate of convergence of the iterative procedure. Over the scale of a computational pixel, lateral heat fluxes are negligible compared to vertical fluxes. In this study, the lateral heat exchanges among the pixels are neglected. This assumption results in diagonal covariance matrices. 21 21 21 Following Bateni and Liang [2012], the diagonal components of K21 T ; KR ; KEFS , and KEFC matrices are taken 22 21 equal to 0.01 K , 1000, 1000, and 1000, respectively. The value of KFPAR is chosen such that the magnitude of the first and second terms in the cost function would be comparable. From the results in Bateni and Liang

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[2012], it is evident that the absolute value of (T2Tobs ) has an order of magnitude of 1 K [i.e., (T2Tobs )  O(1)], and therefore, ðT2Tobs ÞT K21 T ðT2Tobs Þ  O(0.01). FPAR varies from 0 to 1, and we anticipate that the order of magnitude for the absolute value of ðFPAR2FPARobs Þ would be 0.01. Thus, the diagonal elements T 21 of K21 FPAR are set to 100 so that ðFPAR2FPARobs Þ KFPAR ðFPAR2FPARobs Þ would have the order of magnitude of 0.01 (comparable with that of the first term). Finally, to find the magnitude for the diagonal elements of 21 21 K21 Cg , the VDA model is run for three different KCg values of 1, 10, and 100. For KCg 51 and 10, the model is 21 unstable, while for the KCg values of 100, the model converges to a physically reasonable solution, and the misfit between observed and predicted FPAR will be minimized. In this study, K21 Cg is set to 100. The optimal values for cg, R, EFs, and EFc are obtained by minimizing the cost function J. In order to minimize J, its first variation should be set equal to zero (dJ 5 0). Setting dJ 5 0 yields the Euler-Lagrange equations, which has to be solved simultaneously on a monthly basis within an iterative loop. The VDA scheme begins with an initial (prior) guess of model parameters (cg, EFs, EFc, and CHN), which are uniform over the domain and improves them iteratively through minimizing the misfit between the estimated and satellite-observed LST and FPAR.

4. Gourma Site The Gourma mesoscale site (located in Mali, West Africa) is part of the AMMA (African Monsoon Multidisciplinary Analysis) project [Mougin et al., 2009] (Figure 2). It is the northernmost site of the AMMA ‘‘Couplage de l’Atmosphere Tropicale et du Cycle Hydrologique’’ (CATCH) observatory. The site spans 1 in longitude from 1 W to 2 W and covers 3 in latitude from 14.5 N to 17.5 N. The site is mostly flat and its elevations vary from about 250 to 350 m above sea level, with isolated sandstone buttes reaching up to 600 m. It is covered by semiarid natural vegetation (annual grasses and shrubs) [Lebel et al., 2009]. Only 3% of vegetation cover over the Gourma site is scattered trees [Mougin et al., 2009]. Sahelian meteorological conditions are generally characterized by a short rainy season (due to the West African Monsoon, WAM) from early July to mid-September, followed by a long dry season from midSeptember until the next July [Gruhier et al., 2009; Mougin et al., 2009; Timouk et al., 2009]. Mean annual rainfall increases from 100 mm in the north to 450 mm in the south of the Gourma site [Timouk et al., 2009]. The vegetation dynamics at the Gourma site are strongly affected by the seasonal rainfall pattern with a strong latitudinal gradient [Jarlan et al., 2008b]. The north-south gradient of rainfall, soil moisture, vegetation cover, and net radiation as well as high interannual variability of climate over the Gourma site provide a unique opportunity to test the developed model across diverse conditions.

5. Data Set The Gourma site has been instrumented with three automatic micrometeorological stations along the north-south climatological gradient (in Bamba (17.1 N), Agoufou (15.3 N), and Kobou (14.7 N)). These stations perform a continuous monitoring of micrometeorological data (air temperature, humidity, and wind speed) at a 15 in time step. The micrometeorological data are obtained from the AMMA archive (http://database. amma-international.org/) and were spatially interpolated over the computational grid. Air temperature, humidity, wind speed, and incident solar radiation are the only meteorological inputs to the VDA scheme. Two flux staFigure 2. Graphical location of the Gourma mesoscale site (surrounded by red lines) in West tions [in Agoufou (15.3 N) Africa. Figure adapted from http://www.ecmwf.int/research/ESA_projects/SMOS/calval/ and Bamba (17.1 N)] provide smos-amma_index.html.

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a continuous measurement of surface heat fluxes at a 30 min time step [Timouk et al., 2009]. These measurements are used to validate the estimated surface heat fluxes. Fluxes were measured by an open-path eddy covariance system at a reference height of 3.5 m. For detailed information on the analysis and process of measured fluxes and their closure errors, the readers are referred to Timouk et al. [2009]. Remotely sensed LST, incoming solar radiation (R#s ), FPAR, and albedo are obtained from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor on the METEOSAT Second Generation (MSG) satellite. LST, R#s , albedo, and FPAR are provided, respectively, with 15 min, 30 min, daily, and weekly frequencies and are available on the Land Surface Analysis Satellite Applications Facility (LSA-SAF) archive (http://landsaf. meteo.pt/). The frequent measurements of LST (every 15 min) from the SEVIRI sensor allow to characterize the diurnal cycle of LST. This is particularly important since the VDA system derives the signature of partitioning of surface heat fluxes from the LST diurnal cycle [Bateni and Entekhabi, 2012b]. Furthermore, the geostationary MSG observing platform observations over the region are at low incidence angles near nadir, which enhances their quality relative to applications at other (higher) latitudes. The values of extinction coefficient (ke) are available in the literature for different plant types from field experiments [Hipps et al., 1983; Eagleson, 2002]. In this study, the pixels for which remotely sensed FPAR observations are zero during the monthly assimilation period are considered as bare soil, with a ke value set 0 for them. In contrast, the pixels for which FPAR observations are not zero are mainly covered by grasses. Based on reported values of ke in the literature for grasslands [e.g., Agata, 1985; Kiniry et al., 1999], a value of 0.35 is used in this study. The soil type at the Gourma site mainly consists of sand. The soil volumetric heat capacity can be estimated from c5cs 1hcw [Campbell, 1985; Bateni et al., 2012] (where h is the soil volumetric water content, and cs and cw are the volumetric heat capacity of dry soil and water). The literature values for cw and cs are, respectively, 4 3 106 (J m23  K21) and 1.4 3 106 (J m23  K21) [Hillel, 1998]. Later, it will be shown that h varies from about 0 to 0.3 over the Gourma site. A nominal h value of 0.15 is used herein. Sensitivity analyses showed that other nominal values yield similar final results. Based on soil type (sand) and the nominal water content, the soil heat conductivity (p) is set to 1.5 (J m21  K21 s21) [Hillel, 1998; Chen, 2008]. Precipitation is not an input and hence not used in the estimation. As an independent data source, it is used to interpret the patterns and trends in the estimated fields. Precipitation data are obtained from the University of California, Irvine archive (http://chrs.web.uci.edu/PERSIANN-CCS/data.html). The assimilation domain covers the Gourma region. The size of computational grid is 3 km, which yields 3744 computational pixels over the region. The period of analysis covers the summer of 2007 (AMMA field experiment Enhanced Observing Period [EOP]) from Julian day 152 to 273 (from 1 June to 30 September) due to the availability of quality controlled surface heat flux measurements and occurrence of monsoon. The daily assimilation window ranges from s0 5 0900 to s1 5 1600 local time, when EFs and EFc are selfpreserved, i.e., constant for the day. The assimilation is implemented in 30 day subperiods (N 5 30 days). FPAR values are retrieved from the red and near infrared spectral bands by defining a vegetation index called RDVI (Renormalized Difference Vegetation Index) and using the FPAR-RDVI linear relationship developed by Roujean and Breon [1995]. The linear relationship between FPAR and RDVI (spectral reflectance) can be found on the LSA-SAF archive (http://landsaf.meteo.pt). Alternatively, we could assimilate LAI product available on the LSA-SAF archive to constrain the key unknown of the VDM (specific leaf area). LAI values are obtained from fc data, which themselves are found via a Bidirectional Reflectance Distribution Function (BRDF). The reader is referred to the LSA-SAF archive for detailed information on LAI retrieval. Based on the above mentioned explanations about FPAR and LAI, it is more reasonable to assimilate FPAR as it is directly obtained from the reflectance data measured by MSG-SEVIRI rather than LAI that is obtained from fc through an intricate algorithm.

6. Results Retrieved LAI maps from the VDA system are shown in section 6.1. Estimated specific leaf area, neutral bulk heat transfer coefficient, and evaporative fraction maps from the VDA approach are shown, respectively, in sections 6.2–6.4. Finally, surface heat flux estimates are presented in section 6.5.

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Figure 3. Comparison of monthly mean LAI maps from the (top) LSA-SAF and (bottom) VDA framework over four assimilation periods [days 152–181 (June), days 182–212 (July), days 213–243 (August), days 244–273 (September)]. Regions with insufficient remotely sensed LST observations (less than 5 days with at least three observations) are shown by blank (white) pixels.

6.1. Vegetation Dynamics The Gourma site is mainly covered by C4 annual grasses, which have a very high photosynthesis rate and sustain a rapid growth whenever soil moisture is available [Mougin et al., 2009]. The vegetation cover increases rapidly during the monsoon season. In general, in arid areas, canopy growth follows rainfall since it fully depends on water availability at the surface. Figure 3 compares maps of LAI from the LSA-SAF (top) and the VDA approach (bottom). LAI values from the LSA-SAF and VDA are comparable in spatial pattern, temporal evolution, and magnitude although no explicit information on vegetation phenology is used in the model. However, there is a weaker consistency between the LSA-SAF and VDA LAI maps in period 3. This weaker consistency is due to the erroneous FPAR values (not shown), which are close to zero over most parts of the domain in period 3. Regions with insufficient remotely sensed LST observations (less than 5 days with at least three observations) are shown by blank (white) pixels. The vegetation cover increases during the core of the monsoon season (period 3) and reaches its peak value in the last period. This occurs because the Gourma site is mainly covered by C4 annual grasses that have high photosynthesis rates and sustain fast growth when soil moisture is accessible [Mougin et al., 2009; Jing et al., 2011]. Also, due to the time lag between rainfall and vegetation greenness [e.g., Wang et al., 2003; Zhang et al., 2010], rainfall peaks in period 3 while vegetation reaches its peak in period 4. The spatial and temporal consistency between the LAI maps from LSA-SAF and VDA indicates that the VDA framework can effectively use the information contained in the FPAR data to calibrate the VDM for largescale applications. This is particularly useful in large-scale applications because the SEVIRI sensor on the MSG satellite provides a spatially comprehensive FPAR dataset that can be used to constrain the VDM, create LAI maps, and predict the response of vegetation cover to variations in environmental factors and climate in the future. Overall, the results indicate a significant step toward controlling the VDM’s simulation at large scale using new generation satellite data.

6.2. Specific Leaf Area Specific leaf area (cg) is strongly and negatively correlated to leaf thickness, and the variations in leaf thickness can be well captured by it [Vile et al., 2005]. Therefore, specific leaf area values can be used to monitor

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Figure 4. Retrieved values for the specific leaf area of the green biomass (cg) over four periods.

the changes in leaf thickness [White and Montes, 2005; Vile et al., 2005]. This is particularly important since leaf thickness has a significant role in plant and leaf functioning and CO2 assimilation rate. Specific leaf area plays a vital role in explaining variation in relative growth rate [Nielsen et al., 1996; Li et al., 2005], maximum rate of photosynthesis, and leaf functioning [Garnier et al., 2001]. Plants with high cg values (i.e., a large leaf area with small tissue) show a rapid production of biomass, while the ones with low cg tend to efficiently conserve nutrients, and reduce the photosynthesis and relative growth rates [Wright and Westoby, 1999]. Plants inhabiting arid and semiarid regions tend to have inherently low cg (i.e., high leaf thickness). Arid and semiarid plants with thick leaves have denser tissue that provides extra structural strength, and consequently are resistant against unfavorable environmental conditions (e.g., low rainfall or nutrient) and allows continued leaf function [Warren et al., 2005]. The variable cg has been used regularly as a means to monitor plants’ productivity [White and Montes, 2005] or ecological behavior [Diaz et al., 2004]. Specific leaf area is an indicator of complicated physiological processes that vary with time and space and control the leaf growth and development. According to Montaldo et al. [2005, 2008], cg can vary on a monthly time scale. Also, Bouriaud et al. [2003] showed that the spatial variation of specific leaf area can be large even within a small area with a uniform vegetation cover. They concluded that cg estimate in one particular location should not be applied in other locations to convert biomass (Bg) to LAI since soil conditions can significantly affect cg Many manual destructive sampling campaigns are aimed at measuring cg [Westoby, 1998; Weiher et al., 1999; Wilson et al., 1999]. However, due to the large spatial and temporal variability of cg, its manual measurement over large-scale domains is impractical. The approach outlined and demonstrated in this study allows retrieval and mapping specific leaf area based on remotely sensed FPAR observations. Figure 4 shows the retrieved monthly cg values over the domain. Specific leaf area is affected by water availability [Cunningham et al., 1999; Hobbie, 2000], solar radiation [Reddy et al., 1989], air temperature [Acock et al., 1979; Niinemets, 2001], vapor pressure deficit [Wright et al., 2004], nutrient resources [Cunningham et al., 1999], leaf maturity and growth stage [Jonckheere et al., 2004], soil properties and its nitrogen content [Bouriaud et al., 2003], altitude [Korner, 1989], season [Field and Mooney, 1983], and plant type [Vile et al., 2005; Li et al., 2005]. It is evident that numerous factors are responsible for the spatiotemporal variability of cg, and therefore the spatial patterns of the retrieved cg (Figure 4) cannot be attributed to only one environmental variable. This is one key reason why its a priori estimation is difficult. As mentioned above, the Gourma site is covered with annual C4 grasses [Lebel et al., 2009]. The main objective here is to study the effect of climatic variables (i.e., precipitation, temperature, solar radiation, and vapor pressure) on the specific leaf area of C4 grass vegetation type and explore if variations in cg estimates in response to the climatic factors are physically meaningful. Leaf thickness (specific leaf area) typically increases (decreases) by decreasing rainfall [Cunningham et al., 1999; Warren et al., 2005]. Thick leaves provide extra structural strength and consequently increase the ability of leaves to resist wilting (or postpone leaf death under very dry circumstances) [Wright et al., 2004]. Water availability is one of the controlling factors of vegetation development in the Gourma site,

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and therefore, the variations in cg are controlled to some extent by the changes in rainfall. In 0.013 order to evaluate the effect of 0.012 rainfall on specific leaf area, cg values are plotted versus the 0.011 monthly precipitation data for 0.01 the four modeling periods (Fig0.009 ure 5). As shown, with increasing rainfall, cg rises rapidly. At a 0.008 monthly precipitation rate of 0.007 about 25 (mm/month), cg is 0.006 equal to 0.008 (m2 gr DM21), 0 100 200 300 400 Rainfall (mm/month) while with increasing rainfall up to 350 (mm/month), specific Figure 5. Diagnosed variation of specific leaf area of the green biomass (cg) versus monthly leaf area reaches about 0.011 rainfall with one standard deviation variability in each monthly rainfall bin. (m2 gr DM21). The increase of cg with rainfall is consistent with the findings of several other studies such as Cunningham et al. [1999] and Hobbie [2000], which showed that cg increases with an increase in rainfall. −1 cg (m2 gr DM )

0.014

The plot of cg versus monthly mean solar radiation indicates an inverse relationship. This is in agreement with the results of a number of studies [e.g., Reddy et al., 1989; Witkowski and Lamont, 1991; Ackerly et al., 2002; Lee and Heuvelink, 2003] that reported a reduction in cg as solar radiation increases. Analogously, Figure 7 indicates that cg is negatively correlated with mean monthly air temperature. A similar negative correlation between cg and air temperature was also found by Niinemets [2001]. The negative scaling of cg with solar radiation and air temperature yields from adaptive modification in leaf thickness [Niinemets, 2001]. As air temperature or solar radiation rises, leaf thickness increases (cg decreases) since thicker leaves have the capability to survive longer and withstand tougher environmental conditions [Mooney and Dunn, 1970; Ackerly et al., 2002]. Two important conclusions can be drawn from Figures 5–7: (1) the specific leaf area estimates from the developed methodology show physically meaningful variations in response to changes in environmental factors, and (2) the specific leaf area of herbaceous grassland species change significantly in response to environmental gradients, and therefore they have a high capability for adaptation to variations in climatic variables.

2 −1 cg (m gr DM )

In addition to illustrating the reasonable variation of cg estimates with environmental variables, their magnitude is also compared with the reported values in the literature (Table 1). For the last period, cg values are close to 0.007 (m2 gr DM21) over the very short and sparse grassland in the north of the domain (from about 15.5 N to 16.5 N), and they increase to about 0.015 (m2 gr DM21) in the south. As indicated in Table 1, the range of retrieved cg values is comparable to those reported in the literature [e.g., Goff, 1985; Cayrol et al., 2000b; Li et al., 2005; Montaldo et al., 0.016 2005, 2008; Cervarolo et al., 0.015 2010]. It is worth noting that 0.014 in the parts of the domain where the magnitude of 0.013 remotely sensed FPAR data is 0.012 zero (e.g., over most parts in periods 1 and 2, and the 0.011 northern part in periods 3 and 0.01 4), the prior spatially uniform value of cg is not updated, and 0.009 therefore cg maps remain 0.008 equal to the initial guess. 700 720 740 760 780 800 820 840 Mean monthly irradiance (Wm−2) Figure 6. Diagnosed variation of specific leaf area of the green biomass (cg) versus mean monthly irradiance with one standard deviation variability in each mean monthly irradiance bin.

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Overall, the results indicate that assimilating remotely sensed FPAR observations into

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the VDM model can efficiently constrain the key unknown parameter of VDM (i.e., cg) and retrieve it over large domains. This is particularly important since cg is highly variable, and its retrieval over large scales by in situ measurements is very time consuming and costly.

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Future studies should be directed toward using mapped specific leaf area values to monitor variations in leaf thickness, plants productivity, ecological behavior, and CO2 assimilation rate.

6.3. Neutral Bulk Heat Transfer Coefficient Figure 8 shows CHN estimates over the domain for all periods. In periods 1 and 2, the CHN estimates are more spatially homogeneous compared to periods 3 and 4. During the monsoon season (periods 3 and 4), a pronounced north-south pattern develops in the retrieved CHN maps. In these two periods, the estimated CHN values in the southern part of the domain increase relative to the north. The spatial patterns of the estimated CHN maps correspond with those in the vegetation phenology across the Gourma site. The magnitude of CHN is comparable to the reported values in the literature [Stull, 1994]. Over the bare soil to the north, the estimated CHN values are about 0.0031. They increase with spatial consistency to 0.0125 over the grassland in the south. It is worth mentioning that the initial guess for the CHN in all pixels across the Gourma site is assumed to be 0.01. Figure 9 shows CHN estimates over the Gourma site from all the four modeling periods versus LAI values. LAI has an appreciable effect on CHN, and CHN increases with an increase in LAI. This figure characterizes variations in CHN as LAI changes, and thus it allows for improvement in future studies by taking CHN as a function of LAI instead of assuming invariant CHN in each monthly assimilation block. This is particularly important because in only a few weeks the bare soil can be fully covered by vegetation, and hence assuming CHN to be constant in each monthly period can degrade surface heat flux estimation. In a similar attempt, Sugita and Brutsaert [1990], Kubota and Sugita [1994], and Qualls and Brutsaert [1996] investigated the relationship between CHN and LAI, but they all used a very limited number of in situ field measurements. In contrast, the CHN-LAI relationship herein is derived via a large number of CHN estimates over the Gourma site, thereby is more robust to those of the above mentioned studies. The CHN-LAI relationships from the aforementioned studies are also shown in Figure 9 for comparison. As indicated, the increasing rate of CHN estimates from the VDA with LAI is comparable with those of Sugita and Brutsaert [1990] and Qualls and Brutsaert [1996]. Also, estimated CHN values from the VDA model fall within Table 1. Comparing the Magnitude of cg Estimates With the Reported Values in the Literature the range of variability of CHN Locationa Study Range of cg (m2 gr DM21) Values estimates from other studies. Goff [1985] 0.0105 1 The discrepancy among CHN Cayrol et al. [2000b] 0.023 2 estimates from different studLi et al. [2005] 0.006–0.028 3 ies can be partially explained Montaldo et al. [2005] 0.0135 4 Montaldo et al. [2008] 0.01 5 by the fact that CHN is plotted Cervarolo et al. [2010] 0.011 4 versus only LAI (Figure 9), thus, This study 0.007–0.015 6 the effect of other factors such a 1. Kendall grassland site in Arizona, 2. Hydrological Atmospheric Pilot Experiment as friction velocity, wind speed, (HAPEX)-Sahel grassland site, 3. Grass fields in Kerqin Sandy Land (northern China), 4. and solar elevation on CHN is Grassland site in Iona, California (U.S.), 5. Grassland cover in a water-limited Mediterranean ecosystem on Sardinia, Italy, 6. Grassland in the Gourma site. overlooked.

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6.4. Evaporative Fraction Surface soil moisture is the key factor in controlling soil evaporative fraction, and therefore, the spatial patterns in EFs estimates should be consistent with those of surface soil moisture. We explore the relationship between EFs (retrieved from the VDA framework) and soil moisture with an independent data set of surface soil moisture. Comparing three soil moisture products (from the Advanced Microwave Scanning Radiometer on Earth Observing System (AMSR-E) in collaboration with the VU University Amsterdam (VUA), Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), and European Remote Sensing (ERS) scatterometer sensor) with ground station measurements in Mali (Sahel), Gruhier et al. [2009] showed that soil moisture product based on the AMSR-E/VUA has the best match with in situ soil moisture measurements at multiple temporal scales. The AMSR-E/VUA soil moisture dataset is derived via application of the Land Parameter Retrieval Model (LPRM) to the AMSR-E brightness temperature observations at the 6.9 GHz channel [Owe et al., 2001, 2008; Gruhier et al., 2009]. This product gives soil moisture estimates within the soil’s top 10 mm at a spatial resolution of 56 km. The AMSR-E/VUA soil moisture product is regridded from its original resolution onto a 25 km regular grid and is available on (http://geoservices.falw.vu.nl/amsr-soil-moisture-description.html).

CHN

As a test of the robustness of the VDA, estimates of EFs are compared with the independent AMSR-E/VUAderived surface soil moisture, the key factor controlling EFs, for sample days 218, 220, 236, 242, 256, and 259 in Figure 10. For days in which adequate spaceborne LST observations are available for updating EFs (days 220, 236, 242, 256, and 259), the retrieved EFs fields strongly resemble the soil moisture patterns. On the contrary, when remotely 0.012 sensed LST observations are Sugita and Brutsaert (1990) insufficient (day 218), the prior Kubota and Sugita (1994) Qualls and Brutsaert (1996) spatially uniform values of the 0.01 This study EFs are not updated and the estimates do not coincide with 0.008 the soil moisture maps. Overall, the results indicate that the 0.006 developed VDA model can robustly estimate EFs when adequate LST observations are 0.004 available. 0.002

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Figure 9. Diagnosed variation of neutral bulk heat transfer coefficient (CHN) against LAI with one standard deviation variability in each LAI bin.

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6.5. Surface Heat Fluxes Estimated fields of latent and sensible heat fluxes (combined soil and vegetation) are shown in Figures 11 and 12, respectively. The spatial patterns and seasonal evolution of retrieved

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latent heat flux consistently resemble features in the rainfall (not shown herein and not an input to the VDA). Regions and times of higher rainfall have correspondingly higher values of LE. The latent heat flux has its minimum value in the first period (before the beginning of monsoon season), when rainfall is low and the region is dry. By the beginning of monsoon season and initiation of rainfall in period 2, LE values increase and finally reach their maximum in period 3, during which the rainfall is at its seasonal maximum. In this period, there is a north-south gradient in evapotranspiration, consistent with the gradient in the rainfall. Compared to period 3, the retrieved LE values reduce in period 4 due to the decrease in rainfall and vegetation senescence. No information on rainfall and/or soil moisture is used in the VDA system. Yet, the VDA system can robustly capture the variations in LE mainly occurring due to spatial and temporal patterns in rainfall. Compared to the spatially uniform LE estimates in periods 1 and 2, the estimated sensible heat flux in the north of the domain is lower than those in the south. This is due to the fact that the higher albedo in the north (not shown herein) increases reflected short wave radiation (i.e., decreases net radiation) [Samain et al., 2008]. The H estimates in period 3 reach its minimum value because in this period available energy at the land surface is mainly dissipated by LE due to the high rainfall (see Figure 11). In order to test the retrieved LE and H values, the estimated fluxes are compared to available ground-based flux observations during different periods. Figure 13 shows the average diurnal cycles of estimated sensible, latent, and ground heat fluxes as well as net radiation (components of SEB) at Bamba (in the north of the Gourma site) and Agoufou (in the south of the Gourma site) for each of the four periods. Measurements at two flux stations at Bamba and Agoufou provide continuous estimates of surface heat fluxes reported at a 30 min time aggregation interval [Timouk et al., 2009]. It should be noted that the flux station at Bamba recorded only net radiation and sensible heat flux. These ground-based values are plotted in Figure 13 as

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open circles. As shown, latent heat flux estimates at Bamba 17 are insignificant during all four assimilation periods since the soil is dry at that site. At this 16 site, sensible heat flux dominates over latent heat flux. 15 Only in period 3 (peak of monsoon season), estimated LE val−2 −1.5 −1 Longitude ues increase slightly. Also, the 0 50 100 150 200 250 magnitude and phase of esti[Wm−2] mated sensible heat flux correspond well with the groundFigure 11. Maps of average daytime latent heat flux (Wm22). based observations at the Bamba site. The daily sensible heat flux estimates at the Bamba site have a mean-absolute-error (MAE) and root-mean-square-error (RMSE) of 37.1 and 42.6 Wm22, respectively. Days 182−212

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The Agoufou site (Figure 13, bottom) has measurements of all of the main components of the SEB. During the four periods, at this southern station the relative partitioning of available energy among the turbulent fluxes has dramatic changes. During the first two premonsoon periods, the soil is dry. The sensible heat flux dominates over latent heat flux. With the onset of the monsoon and rainfall, the latent heat flux dominates over sensible heat flux. The shifts in partitioning and magnitude of the SEB components during the successive periods are captured well by the VDA system. The daily estimated sensible, latent, and ground heat fluxes at the Agoufou site have, respectively, a MAE of 47.2, 29.8, and 37.2 Wm22. Corresponding RMSE (relative error) values are 53.6 (35.5%), 34.4 (15.2%), and 45.1 Wm22 (38.3%). Figure 13 also indicates that the net radiation increases continuously during the monsoon season at Agoufou due to the growth of vegetation in the south of the domain in the monsoon season. The vegetation growth decreases albedo (reflected short wave radiation) and therefore increases net radiation. Overall, two important conclusions can be drawn from Figure 13: (1) the magnitude of estimated surface heat fluxes compare well with respect to ground-based measurements and (2) the phase of the diurnal cycle of retrieved surface heat fluxes closely match with that of observations.

7. Conclusions This study introduces a variational data assimilation (VDA) framework that couples a vegetation dynamics model (VDM) with the surface energy balance (SEB) equation based on the linkage between photosynthesis and transpiration. Transpiration from the SEB equation is used as the key input variable to the VDM. The data assimilation framework uses remotely sensed Fraction of Photosynthetically Active Radiation absorbed by vegetation (FPAR) observations to constrain the key unknown parameter in the VDM.

Latitude

A detailed analysis of the plant-specific parameters showed that the specific leaf area (cg) is the key unknown parameter of the VDM and is therefore the best candidate for estimation. Minimization of misfits between spaceborne FPAR observations Days 152−181 Days 182−212 Days 213−243 Days 244−273 and model estimates provide site and period-specific values 17 for cg. The other unknowns of the VDA model are the neutral 16 heat flux transfer coefficient CHN and bare soil and canopy 15 evaporative fractions EFs and EFc, which are estimated by −2 −1.5 −1 assimilating LST into the heat Longitude diffusion equation. 0 20 40 60 80 100 120 140 160 180 200 [Wm−2]

Figure 12. Maps of average daytime sensible heat flux (Wm22).

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The developed VDA scheme is applied to the Gourma site in

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Days 152−181

10.1002/2013WR014573

Days 182−212

Days 213−243

Days 244−273

Days 182−212

Days 213−243

Days 244−273

500 400 300

[Wm−2]

200 100 0 −100 −200 10 15 Hour of day

b 700

Days 152−181

600 500

[Wm−2]

400 300 200 100 0 −100 −200 10 15 Hour of day Figure 13. Monthly mean diurnal cycles of estimated surface energy balance components at (top) Bamba and (bottom) Agoufou. Thick lines and open circles indicate retrieved and measured heat fluxes, respectively. Colors show different components of the surface energy balance, net radiation (black), latent heat (blue), sensible heat (red), and ground heat (green).

Mali. The results show that the remotely sensed FPAR observations can constrain the key unknown parameter of the VDM (i.e., cg) and consequently predict LAI dynamics well. Remotely sensed FPAR observations give the VDM the ability to simulate LAI dynamics over large-scale areas, which would not be possible from the VDM alone. Assimilating FPAR observations into the VDM also retrieves specific leaf area values over large-scale domains. Specific leaf area has an important role in plant growth. Field campaigns and manual sampling are usually needed to measure cg. These in situ approaches can provide point estimates, but cannot necessarily be scaled to map large regions. This study provides a pathway to using remotely sensed information to infer this important parameter. It enables the estimation of cg values over large domains from remotely sensed FPAR observations. The other retrieved parameter, neutral bulk heat transfer coefficient (CHN), indicates a pronounced northsouth gradient in periods 3 and 4 in which the monsoon rainfalls induce rapid vegetation growth with a pronounced north-south gradient. A relationship is deduced between the mapped CHN and LAI values that augments the sparse ground sampling-based results reported in the literature. This relationship reveals how CHN changes with variations in LAI, and therefore may be used in the future to parameterize CHN as a function of LAI and not as a monthly constant parameter. The retrieved daily EFs maps are compared with the AMSR-E/VUA-derived soil moisture, the main factor controlling EFs. The spatial patterns of EFs correspond with those of the AMSR-E/VUA-derived soil moisture for days with sufficient LST measurements.

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Finally, in a comparison with ground-based measurements of surface energy balance components, we show that the estimated latent and sensible heat fluxes (now as maps over large scales) are in agreement with the in situ observations in terms of both magnitude and phase. To further assess the capability of the developed VDA system, future studies should apply it over different sites with various hydrological conditions.

Acknowledgment This study has been made possible by the National Aeronautics and Space Administration (NASA) grant NEWS/042-0000-0164 to the Massachusetts Institute of Technology.

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References Ackerly, D. D., C. A. Knight, S. B. Weiss, K. Barton, and K. P. Starmer (2002), Leaf size, specific leaf area and microhabitat distribution of chaparral woody plants: Contrasting patterns in species level and community level analyses, Oecologia, 130, 449–457. Acock, B., D. A. Charles-Edwards, and S. Sawyer (1979), Growth response of a chrysanthemum crop to the environment. III: Effect of radiation and temperature on dry matter partitioning and photosynthesis, Ann. Bot., 44(3), 289–300. Alfieri, J. G., X. Xiao, D. Niyogi, R. A. P. Sr, F. Chen, and M. A. Lemone (2009), Satellite-based modeling of transpiration from the grasslands in southern great plains, usa, Global Planet. Change, 67(1-2), 78–86. Amthor, J. S. (1986), Evolution and applicability of a whole plant respiration model, J. Theor. Biol., 122(4), 473–490. Amthor, J. S. (1989), Respiration and Crop Productivity, Springer, N. Y. Anderson, M. C., J. M. Norman, G. R. Diak, W. P. Kustas, and J. R. Mecikalski (1997), A two-source time-integrated model for estimating surface fluxes using thermal infrared remote sensing, Remote Sens. Environ., 60(2), 195–216. Arora, V. K. (2002), Modelling vegetation as a dynamic component in soil-vegetation-atmosphere transfer schemes and hydrological models, Rev. Geophys., 40(2), 1006, doi:10.1029/2001RG000103. Atkin, O. K., D. Bruhn, V. M. Hurry, and M. G. Tjoelker (2005), The hot and the cold: Unravelling the variable response of plant respiration to temperature, Funct. Plant Biol., 32(2), 87–105, doi:10.1071/FP03176. Bastiaanssen, W. G. M., M. Menenti, R. A. Feddes, and A. A. M. Holtslag (1998a), A remote sensing surface energy balance algorithm for land (SEBAL): 1. Formulation, J. Hydrol., 212–213, 198–212. Bastiaanssen, W. G. M., H. Pelgrum, J. Wang, Y. Ma, J. F. Moreno, and G. J. Roerink (1998b), A remote sensing surface energy balance algorithm for land (SEBAL): 2. Validation, J. Hydrol., 212–213, 213–229. Bateni, S. M., and D. Entekhabi (2012a), Surface heat flux estimation with the ensemble Kalman smoother: Joint estimation of state and parameters, Water Resour. Res., 48, W08521, doi:10.1029/2011WR011542. Bateni, S. M., and D. Entekhabi (2012b), Relative efficiency of land surface energy balance components, Water Resour. Res., 48, W04510, doi: 10.1029/2011WR011357. Bateni, S. M., and S. Liang (2012), Estimating surface energy fluxes using a dual-source data assimilation approach adjoined to the heat diffusion equation, J. Geophys. Res., 117, D17118, doi:10.1029/2012JD017618. Bateni, S. M., D. S. Jeng, and S. M. M. Naeini (2012), Estimating soil thermal properties from sequences of land surface temperature using hybrid genetic algorithm-finite difference method, Eng. Appl. Artif. Intell., 25(7), 1425–1436, doi:10.1016/j.engappai.2012.02.017. Bateni, S. M., D. Entekhabi, and D. S. Jeng (2013a), Variational assimilation of land surface temperature and the estimation of surface energy balance components, J. Hydrol., 481, 143–156, doi:10.1016/j.jhydrol.2012.12.039. Bateni, S. M., D. Entekhabi, and F. Castelli (2013b), Mapping evaporation and estimation of surface control of evaporation using remotely sensed land surface temperature from a constellation of satellites, Water Resour. Res., 49, 950–968, doi:10.1002/wrcr.20071. Bouriaud, K., K. Soudani, and N. Breda (2003), Leaf area index from litter collection: Impact of specific leaf area variability within a beech stand, Can. J. Remote Sens., 29(3), 371–380, doi:10.5589/m03-010. Cammalleri, C., M. C. Anderson, G. Ciraolo, G. DUrso, W. P. Kustas, G. L. Loggia, and M. Minacapilli (2010), The impact of in-canopy wind profile formulations on heat flux estimation in an open orchard using the remote sensing-based two-source model, Hydrol. Earth Syst. Sci., 14(12), 2643–2659, doi:10.5194/hess-14-2643-2010. Campbell, G. S. (1985), Soil Physics With Basic Transport Models for Soil-Plant Systems, Elsevier Sci., N. Y. Caparrini, F., F. Castelli, and D. Entekhabi (2004), Variational estimation of soil and vegetation turbulent transfer and heat flux parameters from sequences of multisensor imagery, Water Resour. Res., 40, W12515, doi:10.1029/2004WR003358. Carlson, T. N. (2007), An overview of the ‘‘triangle method’’ for estimating surface evapotranspiration and soil moisture from satellite imagery, Sensors, 7(8), 1612–1629, doi:10.3390/s7081612. Cayrol, P., A. Chehbouni, L. Kergoat, G. Dedieu, P. Mordelet, and Y. Nouvellon (2000a), Grassland modeling and monitoring with spot-4 vegetation instrument during the 1997–1999 salsa experiment, Agric. For. Meteorol., 105, 91–115, doi:10.1016/S01681923(00)00191-X. Cayrol, P., L. Kergoat, S. Moulin, G. Dedieu, and A. Chehbouni (2000b), Calibrating a coupled SVAT-vegetation growth model with remotely sensed reflectance and surface temperature-a case study for the HAPEX-Sahel grassland sites, J. Appl. Meteorol., 39, 2452–2472, doi: 10.1175/1520-0450(2000)0392.0.CO;2. Cervarolo, G., G. Mendicino, and A. Senatore (2010), A coupled ecohydrological-three-dimensional unsaturated flow model describing energy, H2O and CO2 fluxes, Ecohydrology, 3(2), 205–225, doi:10.1002/eco.111. Chen, D. X., and M. B. Coughenour (2004), Photosynthesis, transpiration, and primary productivity: Scaling up from leaves to canopies and regions using process models and remotely sensed data, Global Biogeochem. Cycles, 18, GB4033, doi:10.1029/2002GB001979. Chen, S. X. (2008), Thermal conductivity of sands, Heat Mass Transfer, 44, 1241–1246. Cunningham, S. A., B. Summerhayes, and M. Westoby (1999), Evolutionary divergences in leaf structure and chemistry, comparing rainfall and soil nutrient gradients, Ecology, 69(4), 569–588. Damour, G., T. Simonneau, H. Cochard, and L. Urban (2010), An overview of models of stomatal conductance at the leaf level, Plant Cell Environ., 33(9), 1419–1438, doi:10.1111/j.1365-3040.2010.02181.x. Detling, J. K., W. J. Parton, and H. W. Hunt (1979), A simulation model of Bouteloua gracilis biomass dynamics on the north American shortgrass prairie, Oecologia, 38(2), 167–191. Diaz, S., et al. (2004), The plant traits that derive ecosystems: Evidence from three continents, J. Veg. Sci., 15(3), 295–304, doi:10.1111/ j.1654-1103.2004.tb02266.x. Eagleson, P. S. (2002), Ecohydrology: Darwinian Expression of Vegetation Form and Function, Cambridge Univ. Press, N. Y. Field, C., and H. A. Mooney (1983), Leaf age and seasonal effects on light, water, and nitrogen use efficiency in a California shrub, Oecologia, 56(2-3), 348–355.

C 2014. American Geophysical Union. All Rights Reserved. V

18

Water Resources Research

10.1002/2013WR014573

Garnier, E., G. Laurent, A. Bellmann, S. Debain, P. Berthelier, B. Ducout, C. Roumet, and M. L. Navas (2001), Consistency of species ranking based on functional leaf traits, New Phytologist, 152(1), 69–83, doi:10.1046/j.0028-646x.2001.00239.x. Gentine, P., D. Entekhabi, and A. Chehbouni (2007), Analysis of evaporative fraction diurnal behavior, Agric. For. Meteorol., 143(1-2), 13–29, doi:10.1016/j.agrformet.2006.11.002. Gillies, R. R., T. N. Carlson, J. Cui, W. P. Kustas, and K. S. Humes (1997), A verification of the triangle method for obtaining surface soil water content and energy fluxes from remote measurements of the normalized difference vegetation index (NDVI) and surface radiant temperature, Int. J. Remote Sens., 18(15), 3145–3166, doi:10.1080/014311697217026. Goff, B. F. (1985), Dynamics of canopy structure and soil surface cover in a semi-arid grassland, MS thesis, Univ. of Ariz., Tucson. Gruhier, C., et al. (2009), Soil moisture active and passive microwave products: Intercomparison and evaluation over a Sahelian site, Hydrol. Earth Syst. Sci. Discuss., 6, 5303–5339, doi:10.5194/hessd-6-5303-2009. Hillel, D. (1998), Environmental Soil Physics, Academic, San Diego, Calif. Hipps, L. E., G. Asrar, and E. T. Kanemasu (1983), Assessing the interception of photosynthetically active radiation in winter wheat, Agric. Meteorol., 28(3), 253–259, doi:10.1016/0002-1571(83)90030-4. Hirota, T., J. W. Pomeroy, R. J. Granger, and C. P. Maule (2002), An extension of the force-restore method to estimating soil temperature at depth and evaluation for frozen soils under snow, J. Geophys. Res., 107(D24), 4767, doi:10.1029/2001JD001280. Hobbie, S. E. (2000), Interactions between litter lignin and soil nitrogen availability during litter decomposition in a Hawaiian Montane forest, Ecosystems, 3(5), 484–494, doi:10.1007/s100210000042. Hu, Z., and S. Islam (1995), Prediction of ground surface temperature and soil moisture content by the force-restore method, Water Resour. Res., 31(10), 2531–2539, doi:10.1029/95WR01650. Jarlan, L., G. Balsmo, S. Lafont, A. Beljaars, J. C. Calvet, and E. Mougin (2008b), Analysis of leaf area index in the ECMWF land surface model and impact on latent heat and carbon fluxes: Application to West Africa, J. Geophys. Res., 113, D24117, doi:10.1029/ 2007JD009370. Jing, X., W. Qiang, J. H. Wang, and X. Y. Song (2011), A study on the relationship between dynamic change of vegetation coverage and precipitation in Beijing’s mountainous areas during the last 20 years, Math. Comput. Modell., 54(3-4), 1079–1085, doi:10.1016/ j.mcm.2010.11.038. Jonckheere, I., S. Flecks, K. Nackaerts, B. Muys, P. Coppin, M. Weiss, and F. Baret (2004), Review of methods for in situ leaf area index determination: Part I. Theories, sensors and hemispherical photography, Agric. For. Meteorol., 121, 19–35, doi:10.1016/ j.agrformet.2003.08.027. Jung, M., M. Reichstein, and A. Bondeau (2009), Towards global empirical upscaling of fluxnet eddy covariance observations: Validation of a model tree ensemble approach using a biosphere model, Biogeosciences, 6, 2001–2013, doi:10.5194/bg-6-2001-2009. Jung, M., et al. (2011), Global patterns of land-atmosphere fluxes of carbon dioxide, latent heat, and sensible heat derived from eddy covariance, satellite, and meteorological observations, Biogeosciences, 116(G3), 2005–2012, doi:10.1029/2010JG001566. Kiniry, J. R., C. R. Tischler, and G. A. VanEsbroeck (1999), Radiation use efficiency and leaf CO2 exchange for diverse C4 grasses, Biomass Bioenergy, 17(2), 95–112. Korner, C. (1989), The nutritional status of plants from high altitudes—A worldwide comparison, Oecologia, 81(3), 379–391. Kubota, A., and M. Sugita (1994), Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux. Part I: Parameterization of radiometric scalar roughness, Boundary Layer Meteorol., 69(4), 397–416, doi:10.1007/BF00718127. Kustas, W. P., K. S. Humes, J. M. Norman, and M. S. Moran (1996), Single- and dual-source modeling of surface energy fluxes with radiometric surface temperature, J. Appl. Meteorol., 35(1), 110–121, doi:10.1175/1520-0450(1996)0352.0.CO;2. Lebel, T., et al. (2009), AMMA-CATCH studies in the Sahelian region of West-Africa: An overview, J. Hydrol., 375(1-2), 3–13, doi:10.1016/ j.jhydrol.2009.03.020. Lee, J. H., and E. Heuvelink (2003), Simulation of leaf area development based on dry matter partitioning and specific leaf area for cut chrysanthemum, Ann. Bot., 91(3), 319–327, doi:10.1093/aob/mcg015. Lemon, M. A., F. Chen, J. G. Alfieri, M. Tewari, B. Geerts, Q. M. R. L. Grossman, and R. L. Coulter (2007), Influence of land cover and soil moisture on the horizontal distribution of sensible and latent heat fluxes in southeast Kansas during IHOP-2002 and CASES-97, J. Hydrometeorol., 8, 68–87, doi:10.1175/JHM554.1. Li, Y., D. A. Johnson, Y. Su, J. Cui, and T. Zhang (2005), Specific leaf area and leaf dry matter content of plants growing in sand dunes, Bot. Bull. Acad. Sin., 46, 127–134. Mallick, K., A. J. Jarvis, J. B. Fisher, K. P. Tu, E. Boegh, and D. Niyogi (2013), Latent heat flux and canopy conductance based on Penman-Monteith, Priestly-Taylor equation, and Bouchets complementary hypothesis, J. Hydrometeorol., 14, 419–442, doi:10.1175/JHM-D-12-0117.1. Mallick, K., et al. (2014), A surface temperature initiated closure (STIC) for surface energy balance fluxes, Remote Sens. Environ., 141, 243– 261, doi:10.1016/j.rse.2013.10.022. Marrero, T., and E. Mason (1972), Gaseous diffusion coefficients, J. Phys. Chem. Ref. Data, 1(1), 3–118, doi:10.1063/1.3253094. Mcdowell, N. G., C. D. Allen, and L. Marshall (2010), Growth, carbon-isotope discrimination, and drought-associated mortality across a pinus ponderosa elevational transect, Global Change Biol., 16(1), 399–415, doi:10.1111/j.1365-2486.2009.01994.x. Monica, M. C. A., M. H. Costa, and Y. E. Shimabukuro (2005), Fraction of photosynthetically active radiation absorbed by Amazon tropical forest: A comparison of field measurements, modeling, and remote sensing, J. Geophys. Res., 110, G01008, doi:10.1029/ 2004JG000005. Montaldo, N., R. Rondena, J. D. Albertson, and M. Mancini (2005), Parsimonious modeling of vegetation dynamics for ecohydrologic studies of water-limited ecosystems, Water Resour. Res., 41, W10461, doi:10.1029/2005WR004094. Montaldo, N., J. D. Albertson, and M. Mancini (2008), Vegetation dynamics and soil water balance in a water-limited Mediterranean ecosystem on Sardinia, Italy, Hydrol. Earth Syst. Sci. Discuss., 12, 1257–1271, doi:10.5194/hess-12-1257-2008. Monteith, J. L. (1988), Does transpiration limit the growth of vegetation or vice versa?, J. Hydrol., 100(1-3), 57–68, doi:10.1016/00221694(88)90181-3. Mooney, H. A., and E. L. Dunn (1970), Convergent evolution of Mediterranean-climate evergreen sclerophyllous shrubs, Evolution, 24(2), 292–303. Mougin, E., et al. (2009), The AMMA-CATCH Gourma observatory site in Mali: Relating climatic variations to changes in vegetation, surface hydrology, fluxes and natural resources, J. Hydrology, 375(1-2), 14–33, doi:10.1016/j.jhydrol.2009.06.045. Nielsen, S. L., S. Enriquez, C. M. Duarte, and K. Sand-Jensen (1996), Scaling maximum growth rates across photosynthetic organisms, Funct. Ecol., 10(2), 167–175. Niinemets, U. (2001), Global-scale climatic controls of leaf dry mass per area, density, and thickness in trees and shrubs, Ecology, 82(2), 453–469.

BATENI ET AL.

C 2014. American Geophysical Union. All Rights Reserved. V

19

Water Resources Research

10.1002/2013WR014573

Norman, J. M., W. P. Kustas, and K. Humes (1995), A two-source approach for estimation of soil and vegetation energy fluxes from observations of directional radiometric surface temperature, Agric. For. Meteorol., 77, 263–293. Nouvellon, Y., S. Rambal, D. L. Seen, M. S. Moran, J. P. Lhomme, A. Begue, A. G. Chehbouni, and Y. Keer (2000), Modeling of daily fluxes of water and carbon from shortgrass steppes, Agric. For. Meteorol., 100(2-3), 137–153, doi:10.1016/S0168-1923(99)00140-9. Owe, M., R. de Jeu, and J. Walker (2001), A methodology for surface soil moisture and vegetation optical depth retrieval using the microwave polarization difference index, IEEE Trans. Geosci. Remote Sens., 39(8), 1643–1654, doi:10.1109/36.942542. Owe, M., R. de Jeu, and T. Holmes (2008), Multi-sensor historical climatology of satellite-derived global land surface moisture, J. Geophys. Res., 113, F01002, doi:10.1029/2007JF000769. Peters-Lidard, C. D., S. V. Kumar, D. M. Mocko, and Y. Tian (2011), Estimating evapotranspiration with land data assimilation systems, hydrological processes, Hydrol. Processes, 25(26), 3979–3992, doi:10.1002/hyp.8387. Prentice, I. C., and S. P. Harrison (2009), Ecosystem effects of CO2 concentration: Evidence from past climates, Clim. Past, 5, 297–307, doi: 10.5194/cp-5-297-2009. Qualls, R. J., and W. Brutsaert (1996), Effect of vegetation density on the parameterization of scalar roughness to estimate spatially distributed sensible heat fluxes, Water Resour. Res., 32(3), 645–652, doi:10.1029/95WR03097. Reddy, V. R., B. Acock, D. N. Baker, and M. Acock (1989), Seasonal leaf area-leaf weight relationship in the cotton canopy, Agron. J., 81(1), 1–4. Rogers, R. R., and M. K. Yau (1989), A Short Course in Cloud Physics, Butterworth-Heinemann. Rosnay, P. D., C. Gruhier, F. Timouk, F. Baup, E. Mougin, P. Hiernaux, L. Kergoat, and V. LeDantec (2009), Multi-scale soil moisture measurements at the Gourma meso-scale site in Mali, J. Hydrol., 375(1-2), 241–252, doi:10.1016/j.jhydrol.2009.01.015. Roujean, J. L., and F. M. Breon (1995), Estimating par absorbed by vegetation from bidirectional reflectance measurements, Remote Sens. Environ., 51(3), 375–384, doi:10.1016/0034-4257(94)00114-3. Samain, O., L. Kergoat, P. Hiernaux, F. Guichard, E. Mougin, F. Timouk, and F. Lavenu (2008), Analysis of the in-situ and modis albedo variability at multiple time scales in the Sahel, J. Geophys. Res., 113, D14119, doi:10.1029/2007JD009174. Sandholt, I., K. Rasmussen, and J. Andersen (2002), A simple interpretation of the surface temperature/vegetation index space for assessment of surface miosture status, Remote Sens. Environ., 79(2-3), 213–224, doi:10.1016/S0034-4257(01)00274-7. Segal, M., R. Avissar, M. C. McCumber, and R. A. Pielke (1988), Evaluation of vegetation effects on the generation and modification of mesoscale circulations, J. Atmos. Sci., 45(16), 2268–2293, doi:10.1175/1520-0469(1988)0452.0.CO;2. Sellers, P. J., S. O. Los, C. J. Tucker, C. O. Justice, D. A. Dazlich, G. J. Collatz, and D. A. Randall (1996), A revised land surface parameterization (SiB2) for atmospheric GCMS. Part II. The generation of global fields of terrestrial biophysical parameters from satellite data, J. Climatol., 9(4), 706–737, doi:10.1175/1520-0442(1996)0092.0.CO;2. Shu, Y., S. Stisen, and K. H. Sandholt (2011), Estimation of regional evapotranspiration over the north China plain using geostationary satellite data, Int. J. Appl. Earth Obs. Geoinf., 13(2), 192–206, doi:10.1016/j.jag.2010.11.002. Shuttleworth, W. J., and J. Wallace (1985), Evaporation from sparse crops: An energy combination theory, Q. J. R. Meteorol. Soc., 111, 1143– 1162. Sinclair, T. R., C. B. Tanner, and J. M. Bennett (1984), Water-use efficiency in crop production, Bioscience, 34(1), 36–40, doi:10.2307/1309424. Sini, F., G. Boni, F. Caparrini, and D. Entekhabi (2008), Estimation of large-scale evaporation fields based on assimilation of remotely sensed land temperature, Water Resour. Res., 44, W06410, doi:10.1029/2006WR005574. Stull, R. B. (1994), An Introduction to Boundary Layer Meteorology, Kluwer Acad, Netherlands. Su, Z. (2002), The surface energy balance system (SEBS) for estimation of turbulent heat fluxes, Hydrol. Earth Syst. Sci., 6, 85–100, doi: 10.5194/hess-6-85-2002. Sugita, M., and W. Brutsaert (1990), Regional surface fluxes from remotely sensed skin temperature and lower boundary layer measurements, Water Resources Res., 26(12), 2937–2944, doi:10.1029/WR026i012p02937. Tang, R., Z. L. Li, and B. Tang (2010), An application of the TS-VI triangle method with enhanced edges determination for evapotranspiration for evpotranspiration estimation from modis data in arid and semi-arid regions: Implementation and validation, Remote Sens. Environ., 114(3), 540–551, doi:10.1016/j.rse.2009.10.012. Timmermans, W. J., P. K. William, M. C. Anderson, and A. N. French (2007), An intercomparison of the surface energy balance algorithm for land (SEBAL) and two-source energy balance (TSEB) modeling schemes, Remote Sens. Environ., 108(4), 369–384, doi:10.1016/ j.rse.2006.11.028. Timouk, F., L. Kergoat, E. Mougin, C. R. Lloyd, E. Ceschia, J.-M. Cohard, P. de Rosnay, P. Hiernaux, V. Demarez, and C. M. Taylor (2009), Response of surface energy balance to water regime and vegetation development in a Sahelian landscape, J. Hydrol., 375(1-2), 178–189, doi:10.1016/j.jhydrol.2009.04.022. Vile, D., et al. (2005), Specific leaf area and dry matter content estimate thickness in laminar leaves, Ann. Bot., 96(6), 1129–1136, doi: 10.1093/aob/mci264. Wang, J., P. M. Rich, and K. P. Price (2003), Temporal responses of NDVI to precipitation and temperature in the central great plains, USA, Int. J. Remote Sens., 24(11), 2345–2364, doi:10.1080/01431160210154812. Warren, C. R., M. Tausz, and M. A. Adams (2005), Does rainfall explain variation in leaf morphology and physiology among populations of red ironbark (Eucalyptus sideroxylon subsp. tricarpa) grown in a common garden?, Tree Physiol., 25(11), 1369–1378. Weiher, E., A. van der Werf, K. Thompson, M. Roderick, E. Garnier, and O. Eriksson (1999), Challenging theophrastus: A common core list of plant traits for functional ecology, J. Veg. Sci., 10(5), 609–620, doi:10.2307/3237076. Westoby, M. (1998), A leaf-height-seed (lhs) plant ecology strategy scheme, Plant Soil, 199, 213–227. White, J. W., and R. C. Montes (2005), Variation in parameters related to leaf thickness in common bean (Phaseolus vulgaris l.), Field Crop Res., 91(1), 7–21, doi:10.1016/j.fcr.2004.05.001. Wilson, P. J., K. Thompson, and J. G. Hodgson (1999), Specific leaf area and leaf dry matter content as alternative predictors of plant strategies, New Phytol., 143, 155–162. Witkowski, E. T. F., and B. B. Lamont (1991), Leaf specific mass confounds leaf density and thickness, Oecologia, 88, 486–493. Wright, I. J., and M. Westoby (1999), Differences in seedling growth behaviour among species: Trait correlations and shifts along nutrient compared to rainfall gradients, J. Ecol., 87(1), 85–97, doi:10.1046/j.1365-2745.1999.00330.x. Wright, I. J., et al. (2004), The worldwide leaf economics spectrum, Nature, 428, 821–827, doi:10.1038/nature02403. Xia, Y., et al. (2012a), Continental-scale water and energy flux analysis and validation for the North American Land Data Assimilation System Project Phase 2 (NLDAS-2): 1. Intercomparison and application of model products, J. Geophys. Res., 117, D03109, doi:10.1029/ 2011JD016048. Xia, Y., et al. (2012b), Continental-scale water and energy flux analysis and validation for North American Land Data Assimilation System Project Phase 2 (NLDAS-2): 2. Validation of model-simulated streamflow, J. Geophys. Res., 117, D03110, doi:10.1029/2011JD016051.

BATENI ET AL.

C 2014. American Geophysical Union. All Rights Reserved. V

20

Water Resources Research

10.1002/2013WR014573

Xu, T., S. M. Bateni, S. Liang, D. Entekhabi, and K. Mao (2014a), Estimation of surface turbulent heat fluxes via variational assimilation of sequences of land surface temperatures from geostationary operational environmental satellites, J. Geophys. Res. Atmos., doi:10.1002/ 2014JD021814, in press. Xu, T., S. M. Bateni, and S. Liang (2014b), Estimating turbulent heat fluxes with a weak-constraint data assimilation scheme: A case study (HiWATER-MUSOEXE), IEEE Geosci. Remote Sens. Lett., 12(1), 68–72, doi:10.1109/LGRS.2014.2326180. Zhang, X., M. Coldberg, D. Tarpley, M. A. Friedl, J. Morisette, F. Kogen, and Y. Yu (2010), Drought-induced vegetation stress in southwestern north America, Environ. Res. Lett., 5(2), 024008, doi:10.1088/1748-9326/5/2/024008.

BATENI ET AL.

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