A coupled model of land surface CO2 and energy fluxes using remote sensing data

Agricultural and Forest Meteorology 107 (2001) 131–152

A coupled model of land surface CO2 and energy fluxes using remote sensing data X. Zhan∗ , W.P. Kustas USDA/ARS Hydrology Laboratory, Beltsville, MD 20705-2350, USA Received 19 June 2000; received in revised form 19 October 2000; accepted 20 October 2000

Abstract Considering the coupling of plant transpiration with plant photosynthesis through stomatal opening, this paper develops a dual-source model that simulates the energy and CO2 fluxes between a vegetated land surface and the lower atmosphere. Two versions of the CO2 -energy coupled model (CECM) are presented. The version CECMSM uses daily surface soil moisture measurements or estimates along with meteorological variables and vegetation parameters as inputs. The other version CECMTr utilizes remotely sensed radiometric surface temperature instead of surface soil moisture estimates. The two versions of the model are evaluated by comparing their predictions of CO2 (Fc ), latent heat (LE) and sensible heat (H) fluxes and surface temperature (Tsf ) with three datasets collected from two large-scale field experiments (FIFE’87 and Monsoon’90), which were conducted over two different types of land surface. For the three datasets, the correlation coefficients between the predictions of H, LE and Tsf from both versions of CECM and their observations ranged from 0.77 to 0.97. The Fc predictions from CECMSM had a correlation of 0.96 and a 16% mean absolute percent difference (MAPD) with the observations. For both CECMSM and CECMTr the agreement with measured LE was generally better than H where MAPD values ranged from 15–35 to 20–55%, respectively. The values of some parameters in the stomatal conductance and leaf photosynthesis models obtained in the literature for general C3 plants in the temperate areas were found inappropriate for the C3 shrubs at the site of the Monsoon’90 experiment which have adapted to the semiarid environment. After these parameters were adjusted to give similar stomatal resistance from other work, the LE and H predictions from CECM were improved. © 2001 Elsevier Science B.V. All rights reserved. Keywords: CO2 -energy coupled model; Transpiration; Plant photosynthesis

1. Introduction There are at least two reasons for coupling the CO2 and energy exchanges between vegetated land surface and the atmosphere. First, the physiological process of plant CO2 uptake and the physical process of plant ∗ Corresponding author. Present address: Department of Geography, University of Maryland, 2181 LeFrak Hall, College Park, MD 20742, USA. Tel.: +1-301-405-4050; fax: +1-301-314-9299. E-mail address: [email protected] (X. Zhan).

transpiration are strongly coupled with each other through stomatal opening. Coupled simulation of both the CO2 and energy exchanges over a land surface would provide a very useful tool for better understanding the interaction of CO2 and energy fluxes between the land surface and the lower atmosphere (Norman, 1979; Collatz et al., 1991). Secondly, CO2 uptake of land surface vegetation is one of the most significant sinks in the global carbon cycle (Schimel et al., 1995). A significant change of the CO2 sink would affect or imply changes in atmospheric CO2 concentration and

0168-1923/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 ( 0 0 ) 0 0 2 2 9 - X

132

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Nomenclature An Ani Ani0 An5 Ca Cac Cii Cii Cli ea eac eli e∗ (T) Ex

f fc fd fg fpt3 fslt Fc Fcs g0

g1

net CO2 assimilation of the canopy (␮mol m−2 s−1 ) net CO2 assimilation of the ith type of leaves (␮mol m−2 s−1 ) net CO2 assimilation per unit area of the ith type of leaves (␮mol m−2 s−1 ) net CO2 assimilation of the 5th type of leaves(0) (␮mol m−2 s−1 ) CO2 concentration of the atmosphere (␮mol m−3 ) CO2 concentration within the canopy air space (␮mol m−3 ) CO2 concentration inside plant leaves (␮mol m−3 ) in Eq. (14) and (15) (␮mol mol−1 ) CO2 concentration at leaf surface (␮mol m−3 ) water vapor pressure at the reference height (Pa) water vapor pressure within the canopy air space (Pa) water vapor pressure at leaf surface (Pa) saturation vapor pressure at temperature T (Pa) activation energy for parameter x: Kci (65800), Koi (1400), Vcmaxi (68000), and Rdi (66405) (J mol−1 ) fraction of PAR absorbed by functional photosynthetic pigments (0.77) fraction of the surface covered by plant canopy diffusive PAR fraction in PAR0 fraction of green leaf area index in LAI fraction of C3 plant leaves in LAI fraction of sunlight leaf area index in total LAI CO2 flux of the surface (␮mol m−2 s−1 ) CO2 flux from the soil (␮mol m−2 s−1 ) a coefficient of the Ball stomatal conductance model, Eq. (10) (mol m−2 s−1 ) a coefficient of the Ball stomatal conductance model, Eq. (10)

gsti0

H Hc Hli Hl5

Hs i Ji

Jmaxi k0 kT Kci

Koi

LAI LAIi LAI∗ LE LEc LEli LEl5 LEs

stomatal conductance to latent and sensible heat transfer of the ith (m s−1 ) type of leaves for unit leaf area sensible heat flux density from the surface (W m−2 ) sensible heat flux density from the canopy (W m−2 ) sensible heat flux density from the ith type of leaves (W m−2 ) sensible heat flux density from the 5th type of leaves (dry leaves) (W m−2 ) sensible heat flux density from the soil (W m−2 ) number of the type of leaf (i = 1, 2, 3, 4, or 5) potential rate of the wholechain electron transport (␮mol m−2 s−1 ) maximum rate of the whole-chain electron transport (␮mol m−2 s−1 ) initial slope of photosynthetic CO2 response (0.7) (␮mol m−2 s−1 ) pseudo-first order rate constant with respect to Cii (␮mol m−2 s−1 ) Michaelis–Menten competitive inhibition constant for CO2 (Kci0 = 460) (␮mol mol−1 ) Michaelis–Menten competitive inhibition constant for O2 (Koi0 = 330) (␮mol mol−1 ) leaf area index of the surface leaf area index of the ith type of leaves sunlit leaf area index latent heat flux density from the surface (W m−2 ) latent heat flux density from the canopy (W m−2 ) latent heat flux density from the ith type of leaves (W m−2 ) latent heat flux density from the 5th type of leaves(0) (W m−2 ) latent heat flux density from the soil (W m−2 )

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

M

Oii

P PAR0 PARi

PARshd

PARslt

Q10

ra rac rlci

rli

rl5

rst rst10 rst20 rst30 rst40 rstci

gross photosynthetic rate determined by the rubisco and light-limited capacity (␮mol m−2 s−1 ) internal O2 concentration of the ith type of leaves (210) (mmol mol−1 ) air pressure (Pa) Photosynthetically active radiation above the canopy (␮mol m−2 s−1 ) Photosynthetically active radiation received by the ith type of leaves (␮mol m−2 s−1 ) photosynthetically active radiation received by shaded leaves ␮mol m−2 s−1 ) photosynthetically active radiation received by sunlit leaves ␮mol m−2 s−1 ) temperature coefficient (the relative increase of a parameter in response ◦ to 10 C temperature increase) aerodynamic resistance to latent and sensible heat transfer (s m−1 ) aerodynamic resistance to CO2 transfer (s m−1 ) leaf boundary layer resistance to CO2 transfer of the ith type of leaves (s m−1 ) leaf boundary layer resistance to latent and sensible heat transfer of the ith type of leaves (s m−1 ) leaf boundary layer resistance to latent and sensible heat transfer of dry leaves (s m−1 ) integrated stomatal resistance of the canopy (s m−1 ) integrated stomatal resistance of the C3 shaded green leaves (s m−1 ) integrated stomatal resistance of the C4 shaded green leaves (s m−1 ) integrated stomatal resistance of the C3 sunlit green leaves (s m−1 ) integrated stomatal resistance of the C4 sunlit green leaves (s m−1 ) stomatal resistance to CO2 transfer of the ith type of leaves (s m−1 )

rsti

rsti0

R Rdi Rd0

Rn Rnc Rnli Rnl1

Rnl2

Rnl3

Rnl4

Rnl5 Rns T0

Ta Tac Tc Tli Tl5

133

stomatal resistance to latent and sensible heat transfer of the ith type of leaves for unit ground area (s m−1 ) stomatal resistance to latent and sensible heat transfer of the ith type of leaves for unit leaf area (s m−1 ) universal gas constant (8.314) (J mol K−1 ) the dark respiration rate of the ith type of leaves (1.1) (␮mol m−2 s−1 ) a parameter in the model dark respiration rate of C4 leaves (0.8) (␮mol m−2 s−1 ) net radiation of the surface (W m−2 ) net radiation partitioned to the canopy per the unit ground area (W m−2 ) net radiation partitioned to the ith type of leaves per the unit ground area (W m−2 ) net radiation partitioned to the C3 shaded green leaves per the unit ground area (W m−2 ) net radiation partitioned to the C4 shaded green leaves per the unit ground area (W m−2 ) net radiation partitioned to the C3 sunlit green leaves per the unit ground area (W m−2 ) net radiation partitioned to the C4 sunlit green leaves per the unit ground area (W m−2 ) net radiation partitioned to the dry leaves per the unit ground area (W m−2 ) net radiation partitioned to the soil surface (W m−2 ) a reference value of Tli controlling the optimal leaf temperature for photosynthesis (◦ C) air temperature at the reference height (◦ C) air temperature at the canopy air space (◦ C) integrated leaf temperature of the canopy (◦ C) leaf temperature of the ith type of leaves (◦ C) leaf temperature of dry leaves (◦ C)

134

Ts Ts10 Tsf u Vcmaxi VT Vmax W05 W10 Wci Wji

x x0

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

surface soil temperature (◦ C) 10 cm soil temperature (◦ C) composite surface temperature (◦ C) wind speed above the canopy (m s−1 ) Maximum RuBP carboxylation rate (98) (␮mol m−2 s−1 ) temperature-dependent, substratesaturated canopy (␮mol m−2 s−1 ) temperature-dependent, substratesaturated canopy (39) (␮mol m−2 s−1 ) 0–5 cm layer soil water content (%) 0–10 cm layer soil water content (%) the RuBP-saturated carboxylation rate of the ith type of leaves (␮mol m−2 s−1 ) the carboxylation rate limited by RuBP regeneration of the ith type of leaves (␮mol m−2 s−1 ) one of the parameters (Kci , Koi , Vcmaxi , and Rdi ) initial value of x (Kci , Koi , Vcmaxi , and Rdi )

Greek symbols α relative humidity of the air within the top soil layer quantum efficiency(0.04) (mol m−1 ) αp a curvature parameter controlling the β1 transition between M and kT Cii (0.95) a curvature parameter controlling the β2 transition between VT and ␣p PARi (0.83) γ psychometric constant (Pa K−1 ) the CO2 compensation point of the Γ ∗i ith type of leaves (␮mol mol−1 ) θ a curvature parameter controlling the speed of transitions between Wci and Wji (◦ C) mean angle between the leaf normal θ ls ◦ and the sunlight(60 ) elevation angle of the sun θs ρcp volumetric heat capacity of air (J m−3 K−1 ) the global climate (Sellers et al., 1996a). CO2 uptake of an agricultural crop or an ecosystem is a key factor of the crop production and of the ecosystem net primary productivity (Waring and Schlesinger,

1985). Coupled simulation of the CO2 and energy fluxes would provide useful information for studying the global climate, predicting crop production and estimating ecosystem net primary productivity. In the last three decades, important advances have been achieved in understanding and mathematically modeling the physiology of stomatal movement (Jarvis, 1976; Cowan, 1977, 1982; Ball et al., 1987), the physics of evapotranspiration (Monteith, 1965; Shuttleworth and Wallace, 1985), and the biochemistry of photosynthesis (Farquhar et al., 1980; Collatz et al., 1992). This makes it possible to construct coupled models of land surface CO2 and energy fluxes. What remains elusive in this research front now is to extend the biochemical, physiological and physical understanding from the leaf scale to the canopy, regional and global scales. Many coupled models that allow scaling of photosynthesis and transpiration from leaves up to canopies have appeared in the literature. Theoretical attempts exploring the feasibility for coupling the processes at the canopy scale include Norman (1979) and Su et al. (1996). The most recent coupled models can successfully predict the observed behaviors of the CO2 and water vapor exchanging processes at scales of leaves (e.g. Collatz et al., 1991; Leuning, 1995), and of canopies (e.g. Amthor et al., 1994; Leuning et al., 1995; Williams et al., 1996; Kustas et al., 2000), and even a framework for regional applications (Anderson et al., 2000). Sellers et al. (1996b) simulated the coupling of CO2 and energy fluxes in a revised land surface parameterization scheme (namely, SiB2) for atmospheric General Circulation Models (GCMs). Using SiB2, Sellers et al. (1996a) studied the radiative and physiological effects of doubled atmospheric CO2 on global climate. In the literature, two general approaches have been used for scaling up leaf process simulation to characterize canopy scale processes: one is the “big-leaf” model, and the other is the multilayer model (Raupach and Finningan, 1988). A multilayer model integrates the fluxes for each layer to give the total flux of the canopy (e.g. Collatz et al., 1991; Leuning et al., 1995; Williams et al., 1996; Su et al., 1996). This integration requires knowledge of the spatial distribution of the model parameters and the micrometeorological factors (such as leaf area, leaf orientation, irradiance, temperature, humidity, wind speed, CO2 concentration of each layer within the canopy). Obtaining the

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

knowledge of the canopy details may not be practical for applications in atmospheric GCMs, ecosystem modeling and global carbon cycle studies. The “big-leaf” models map properties of the whole canopy on to the “big-leaf” before calculating the canopy fluxes (e.g. Monteith, 1965; Sinclare et al., 1976; Sellers et al., 1992b, 1996b; Amthor, 1994; Amthor et al., 1994; Norman et al., 1995; Anderson et al., 2000). Comparing with the multilayer models, the “big-leaf” models are simpler and dependent on a smaller number of input data and parameters, and thus are suitable in regional and global scale climate and ecosystem studies (e.g. Dickinson, 1984; Sellers et al., 1996a). There are significant differences among the “bigleaf” models. The Penman–Monteith equation is the simplest and the earliest “big-leaf” model that treats the land surface as one layer and does not distinguish the soil beneath the plant canopy. The “Penman–Monteith” equation results from the elimination of surface temperature from the surface energy balance equation. It loses a direct link to the surface temperature which is a key boundary condition for many land surface–atmosphere models and a variable that can be measured by satellite remote sensing on a global basis. To consider the contribution of the soil layer to the fluxes over a land surface with sparse canopy cover, Shuttleworth and Wallace (1985) proposed a two-layer model which treats the plant canopy and the soil beneath the canopy as separate sources of the fluxes over the surface. Similar to the Penman–Monteith equation, the Shuttleworth–Wallace two-layer model does not use the surface temperature as input variable either. Remote sensing techniques provides a practical approach for scaling up the coupled models at the local canopy scale to estimate the spatial distributions of the land surface CO2 and energy fluxes at regional and/or global scales. At this front, Sellers et al. (1996a,b) has pioneered the application of remotely sensed global vegetation data in the SiB2 model coupled with an atmospheric general circulation model. Recently, technologies for remote sensing the state variables of the land surface-atmosphere interaction system, such as land surface temperature and surface soil moisture, are being developed (Schmugge and Jackson, 1994; Justice et al., 1998). In order to take the advantage of remote sensing techniques, Norman

135

et al. (1995) developed a dual-source model using the remotely sensed surface temperature as one of the primary input variables. Following the concept of this model, we attempt to examine the potential application of the remotely sensed information of the land surface–atmosphere interaction system state variables (surface temperature or soil moisture) in estimating not only the energy fluxes (as the Norman’s dual source model does), but also the CO2 fluxes of a land surface by using the coupled-simulation approach. In this paper, a CO2 -energy coupled model (CECM) is constructed to estimate the CO2 , water vapor and sensible heat fluxes over a vegetated land surface using primarily meteorological data. A simplified version of the model is developed using remotely sensed surface temperature. The model predictions of CO2 and energy fluxes are validated with the field observations from the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) and the Monsoon’90 field experiment. The framework and verification of the model are presented in the following sections.

2. Model development The CECM attempts to predict the CO2 flux, the latent heat flux (evapotranspiration), and the sensible heat flux over a vegetated land surface. These fluxes are defined as the rates of CO2 , water vapor and sensible heat exchanges between the land surface and the lower atmosphere, respectively. A schematic diagram of the CO2 , water vapor and sensible heat exchange system is shown in Fig. 1. Symbols in Fig. 1 and other places of this paper are listed in the Nomenclature. In the mass and energy exchange system of Fig. 1, for the daytime cases, CO2 transfers from both of the reference height in the lower atmosphere and the soil layer beneath the plant canopy to the air space of the plant canopy. CO2 is then absorbed through the stomates into the photosynthetic sites inside the plant leaves. At the reference height in the lower atmosphere, the CO2 flux Fc is to be estimated. Water vapor evaporates from both the insides of plant stomates and the soil surface into the air space of the canopy, and is then transferred to the reference height in the lower atmosphere where a latent heat flux rate LE is to be estimated. Similarly, sensible heat is convected or conducted from both the

136

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Fig. 1. A schematic diagram of the CO2 , latent heat and sensible heat exchange system between land surface and the lower atmosphere.

(1)

aerodynamic resistance of the air between the reference height and the canopy air space to latent heat and sensible heat transfer and CO2 transfer; ρcp the volumetric heat capacity of air; γ the psychometric constant. An , LEc , and Hc are, respectively, the net CO2 assimilation, the latent heat loss and the sensible heat loss by all leaves within the canopy. Fcs , LEs and Hs are the CO2 , latent heat and sensible heat fluxes from the soil surface beneath the plant canopy, respectively. Vegetation over a land surface may include both C3 and C4 plants, and a leaf within a plant canopy may be either dry (dead) or green, and either illuminated or shaded. Thus, the leaves within the canopy are classified into the following five types: 1, C3 shaded green leaves; 2, C4 shaded green leaves; 3, C3 sunlit green leaves; 4, C4 sunlit green leaves; and 5, dead dry leaves. The canopy fluxes, An , LEc , and Hc in Eqs. (1)–(3), are then, respectively, given as

(2)

An =

plant bodies and the soil surface into the canopy air space, and is then transferred to the reference height where a sensible heat flux rate H is to be estimated. To obtain the estimates of all Fc , LE and H, the above processes of CO2 , water vapor and sensible heat transfer need to be simulated at the same time. 2.1. Formulation of the surface fluxes In Fig. 1, Fc , LE and H are the transfer rates of CO2 , latent heat and sensible heat between the reference height in the lower atmosphere and the canopy air space. Each of them has two components: one is the flux between the canopy and the canopy air space, and the other is the flux between the soil and the canopy air space. Thus, the values of Fc , LE and H are computed as follows: Fc =

Ca − Cac = An − Fcs , rac

ρca eac − ea = LEc + LEs , LE = γ ra H = ρcp

Tac − Ta = Hc + Hs , ra

(3)

where Ca , Cac , ea , eac , Ta and Tac are, respectively, CO2 concentration, water vapor pressure and air temperature at the reference height and the canopy air space. The symbols ra and rac are, respectively, the

5 X Ani ,

(4)

i=1

LEc =

5 X LEli ,

(5)

i=1

Hc =

5 X Hli , i=1

(6)

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

where Ani , LEli and Hli are the net photosynthesis, latent heat loss and sensible heat loss of the leaves in type i (i = 1, 2, 3, 4, 5). 2.2. Estimation of the leaf scale fluxes The leaf scale fluxes Ani , LEli and Hli in Eqs. (4)–(6) for the four types of green leaves can be expressed with the following equations according to the analogue of Ohm’s law: Cac − Cii = Ani0 LAIi (7) Ani = rlci + rstci LEli = Hli =

ρcp e∗ (Tli ) − eac , γ rsti + rli Tli − Tac , rli

(8) (9)

where Cii is the intercellular CO2 concentration inside the leaves, Tli the temperature of the leaves, e∗ (Tli ) the saturation water vapor pressure at Tli , rli and rsti the leaf boundary layer aerodynamic resistance and the stomatal resistance of the leaves to latent heat and sensible heat transfer, respectively; rlci and rstci the corresponding resistance to CO2 transfer. Ani0 is the net photosynthetic rate of unit leaf area. LAIi is the leaf area index. The last subscript i represents leaf type. In the above equations, the resistance ra , rs , rli can be estimated from wind speed and vegetation parameters with equations introduced in Norman et al. (1995). The resistance rac , rlci and rstci for CO2 can be converted, respectively, from ra , rli and rsti with coefficients derived by Louwerse and Zweerde (1977). The stomatal resistance rsti for the unit ground area in the above equations is computed as the stomatal resistance for the unit leaf area divided by the corresponding leaf area index. The stomatal resistance for unit leaf area, denoted as rsti0 , can be estimated by inverting the stomatal conductance model proposed by Ball (1988). The Ball model of stomatal conductance is given as gsti0 = g0 + g1

Ani0 eli , Cli e∗ (Tli )

(10)

where g0 and g1 are coefficients determined by a series of laboratory measurements separately for C3 and C4

137

plants in Ball (1988). For general C3 plant leaves, g0 = 0.01 mol m−2 s−1 and g1 = 9.0. For general C4 plant leaves, g0 = 0.08 mol m−2 s−1 and g1 = 3.0. Since the units of rsti0 are s m−1 and the units of stomatal conductance gsti0 are mol m−2 s−1 , rsti is computed as rsti0 =

P , gsti0 RTac 1

(11)

where P is the air pressure in Pa, R = 8.314 J mol K−1 the universal gas constant. Tac in Eq. (11) is in K; eli and Cli in Eq. (10) are, respectively, the water vapor pressure and CO2 concentration at the leaf surface, and are determined with the following equations: eli =

rli e∗ (Tli ) + rsti eac , rsti + rli

(12)

Cli =

rlci Cii + rstci Cac . rstci + rlci

(13)

For C3 plant leaves, the net photosynthesis Ani0 in Eq. (10) is estimated with the following equation adopted from Collatz et al. (1991), which is a modified version of the biochemical model of C3 plant photosynthesis proposed by Farquhar et al. (1980):   1 − Γ∗i 1 Ani0 = Cii 2θ   q 2 × (Wci + Wji ) − (Wci + Wji ) − 4θ Wci Wji −Rdi ,

(14)

where G∗i is the CO2 compensation point in the absence of “dark respiration”. Wci is the rate of carboxylation when ribulose bisphosphate (RuBP) is saturated, and Wji is the carboxylation rate limited by RuBP regeneration. Rdi is the dark respiration rate of leaves in type i, and q = 0.95 is a parameter controlling the speed of the transition between Wci and Wji . Values of G∗i , Wci , Wji , and Rdi are dependent on the conditions of Cii , Tli , and the Photosynthetically Active Radiation (PARi ) received by the ith type of leaves. The equations for computing the values of Γ ∗i , Wci , Wji , and Rdi under various conditions of Cii , Tli , and PARi are listed in Appendix A. For C4 plant leaves, the biochemistry of photosynthesis is different from that for C3 plants. Following Farquhar’s approach to consider the biochemistry of plant photosynthesis, Collatz et al. (1992) analyzed

138

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

the limiting factors in the C4 photosynthetic pathway and obtained a model with some biochemical details for C4 plant photosynthesis. The model is given by Ani0 = 

1 2β1

2.3. Estimation of the soil surface fluxes The CO2 flux, Fcs , from the soil surface beneath the plant canopy is computed with an empirical equation in Norman et al. (1992), which is given as

 q 2 × (M + kT Cii ) − (M + kT Cii ) − 4β1 MkT Cii

Fcs = (0.135 + 0.054LAI)W10

−Rdi ,

where LAI is the leaf area index of the canopy, W10 is the 0–10 cm surface layer volumetric soil water content in percent and Ts10 is the 10 cm soil temperature in ◦ C. In this work, W10 and Ts10 in Eq. (18) are not available and are replaced with the 0–5 cm soil moisture W05 and the soil surface moisture Ts , respectively. When W05 is not available, W10 in Eq. (18) is held to be half of the field capacity. The sensible heat flux from the soil surface is expressed as

(15)

where M is the gross photosynthetic rate determined by the rubisco and light-limited capacity, kT Cii the gross photosynthetic rate limited by CO2 concentration, kT the temperature-dependent pseudo-first order rate constant with respect to Cii . b1 = 0.93 is a curvature parameter that gives a gradual transition between M and the CO2 limited rate. Rdi is the temperature-dependent rate of C4 leaf respiration. The equations for computing the values of M, kT and Rdi under various conditions of Cii , Tli , and PARi are listed in Appendix A. If the net radiation of the leaves in type i is known as Rnli , then the energy balance equation of the leaves is LEli + Hli = Rnli .

(16)

Eqs. (7)–(9), (11)–(13), (14) or (15), and (16) are independent on each other. When the environmental conditions of the leaves (i.e. Cac , eac , Tac , Rnli , PARi , wind speed, and vegetation parameters for computing the aerodynamic resistance) are given, they include only eight unknown variables, namely, Ani0 , LEli , Hli , rsti , Cli , eli , Tli and Cii . Using Newton’s solution method, an appropriate numerical solution of the eight unknowns can be obtained, usually in less than ten iterations. The dead dry leaves (the 5th type of leaves) are assumed to have no transpiration and nor photosynthesis. Thus, if the net radiation of the leaves is Rnl5 , the CO2 , latent heat and sensible heat fluxes between these leaves and the air space of the canopy are, respectively, An5 = 0, LEl5 = 0 and Hl5 = ρcp

Tl5 − Tac = Rnl5 , rl5

(17)

where Tl5 is the temperature of the dry leaves and rl5 is the aerodynamic resistance of the leaf boundary layer.

× exp[0.069(Ts10 − 25)],

Hs = ρcp

Ts − Tac , rs

(18)

(19)

where rs is the aerodynamic resistance of the boundary layer at the soil surface beneath the canopy and is computed with the equation introduced in Norman et al. (1995). For estimating the latent heat flux LEs from the soil surface beneath the canopy, the following equation is adopted from Camillo and Gurney (1986): LEs =

ρcp αe∗ (Ts ) − eac , γ rs + rss

(20)

where α is the relative humidity of the air within the top soil layer and is computed from the top layer soil moisture with the equations used in Camillo and Gurney (1986); rss is the resistance of the surface soil layer to water vapor transfer. There are a number of equations in the literature for calculating rss from surface soil water content (Mauhfleau and Noilhan, 1991). The preliminary results of a study on rss formulations indicates that the exponential function introduced by Sellers et al. (1992b) provides reliable simulation of soil evaporation and has been used in validation studies of a regional energy balance model using remotely sensed soil moisture (Kustas et al., 1998, 1999). The soil surface energy balance equation is given as LEs + Hs = Rns − G,

(21)

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

where Rns is net radiation of the soil surface, G is the soil heat flux and can be computed as 30% of Rns (see Choudhury et al., 1987). When Rns is obtained as a portion of Rn , Eqs. (19)–(21) are combined to solve for the value of soil temperature Ts . Using Tac as the initial value of Ts , an appropriate numerical solution of Ts can be obtained within two to six iterations. With the solution of soil temperature Ts , values of LEs and Hs are obtained from Eqs. (20) and (21). 2.4. Calculation of leaf scale environmental variables The environmental variables for leaves within the canopy need to be estimated from their values measured or estimated at the reference height above the canopy. These variables include Photosynthetically active radiation (PAR), net radiation, and wind speed. According to Norman (1982), if the PAR measurement above the canopy is PAR0 and the fraction of diffusive PAR is fd , then the PAR received by shaded leaves (leaf types 1 and 2) is PARshd = fd PAR0 exp(−0.5LAI0.7 ) +0.07(1 − fd )PAR0 (1.1 − 0.1LAI) × exp(−sin θs ),

(22)

where θ s is elevation angle of the sun and calculated from the time of day, the day of year and the latitude of observational site with the equation used in (Campbell (1977), p. 55). The PAR received by the sunlit leaves (leaf types 3 and 4) is PARslt = (1 − fd )PAR0

cos θls + PARshd , sin θs

(23)

where θ ls is the mean angle between the leaf normal and the sunlight, which is 60◦ for a canopy with spherical leaf angle distribution (Norman, 1982). The method for partitioning total net radiation (Rn ), which is either measured or estimated, into net radiation for canopy leaves (Rnc ) and net radiation for soil surface (Rns ) is associated with Beer’s Law approximation for extinction of radiation within the canopy, that is (Norman et al., 1995)

139

The constant of 0.45 is obtained with the assumptions of random leaf positioning and spherical leaf angle distribution. A more physically-based approach of net radiation partitioning for sparse-clumped canopies has been recently proposed by Kustas et al. (2000) and will be implemented in future applications. Within the canopy, Rnc is partitioned to the different types of leaves according to their fractions in the total LAI. For example, if the fraction of C3 plants in the surface vegetation is fpt3 , the fraction of green leaves is fg and the fraction of sunlit leaves is fslt , then values of the net radiation partitioned to the four types of green leaves are, respectively Rnl1 = Rnc fpt3 fg (1 − fslt ),

(26)

Rnl2 = Rnc (1 − fpt3 )fg (1 − fslt ),

(27)

Rnl3 = Rnc fpt3 fg fslt ,

(28)

Rnl4 = Rnc (1 − fpt3 )fg fslt ,

(29)

where the fraction of sunlit leaves is the ratio of the sunlit leaf area index to LAI. Assuming random leaf positioning and spherical leaf angle distribution, the sunlit leaf area index is computed as (Campbell, 1977, p. 129)    −0.5LAI (30) sin θs . LAI∗ = 2 1 − exp sin θs For the dead dry leaves, the net radiation is Rnl5 = Rnc (1 − fg ).

(31)

The aerodynamic resistance of leaf boundary layer and of the soil surface boundary layer from the wind speed conditions for the leaves within the canopy and the soil surface are computed with the method used by Norman et al. (1995, see their Appendix C). 2.5. Aggregation of the simulated variables at the leaf scale

Rns = Rn exp(−0.45LAI),

(24)

The surface temperature Tsf is needed for stability correction to the aerodynamic resistance. Tsf is computed from the soil temperature Ts and the canopy temperature Tc with the following equation, which is introduced by Norman et al. (1995):

Rnc = Rn − Rns .

(25)

Tsf4 = fc Tc4 + (1 − fc )Ts4

(32)

140

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

where fc is the fractional coverage of canopy over the surface. The composite canopy temperature Tc is computed from the simulated temperatures of the leaves of the five types using the leaf area fractions as their weighing factor, that is Tc = fg {(1 − fslt )[fpt3 Tl1 + (1 − fpt3 )Tl2 ] +fslt [fpt3 Tl3 + (1 − fpt3 )Tl4 ]} + (1 − fg )Tl5 (33) Similarly, a composite stomatal resistance for all leaves within the canopy is computed as rst =

1/fg LAI . ((fpt3 /rst10 ) + (1 − fpt3 /rst20 ))(1 − fslt ) +((fpt3 /rst30 ) + (1 − fpt3 /rst40 ))fslt (34)

2.6. Model solution and implementation The equations described in the above sections compose the framework of CECM. Since the number of the unknowns in the above equations is consistent with the number of independent equations, an appropriate numerical solution of these equations can be obtained by assembling these equations with the following procedure: 1. Calculate the leaf environmental variables from the given data of θ s (from day of year, time of day and latitude), Rn , PAR0 , LAI, fpt3 , fc and fg with Eqs. (22)–(31). 2. Initialize Tc , Ts , Tac , Cac and eac with Ta , Ca and ea . 3. Start the iteration for solutions of the canopy scale variables by computing the aerodynamic resistance (ra , rli and rs ) from wind speed (u) and the surface temperature Tsf in Eq. (32). 4. Run the four sub-iterations for solutions of the leaf scale variables for the four types of green leaves with Eqs. (7)–(16) using Newton’s numerical solution method. 5. Calculate the variables of dry leaves using Eq. (17). 6. Calculate Tc with Eq. (33). 7. Run the sub-iteration for solving Ts with Eq. (21) using Newton’s numerical solution method.

8. Calculate of the soil surface fluxes using Eqs. (18)–(20). 9. Recalculate Tac , eac and Cac with the above solutions of the fluxes for all leaves and the soil surface using Eqs. (1)–(6). 10. Repeat steps (3)–(9) using the recalculated values of Tc , Ts , Tac , eac and Cac until the recalculated values of Tac , eac and Cac do not change significantly from their previous values. 11. Summarize and output the simulation results. This procedure is implemented with a FORTRAN program. Using the values of the meteorological forcing variables, the program outputs the corresponding values of CO2 flux, latent heat flux, sensible heat flux, composite surface temperature, canopy temperature, soil temperature, and integrated stomatal resistance. For most of the daytime cases, the above solutions procedure converges and finishes with only about three to six iterations. However, for some cases where the meteorological conditions reaches extremes (e.g. wind speed is very small, or in the early mornings the energy fluxes are not large enough to observe precisely), the above procedure may not converge and results in no solution. 2.7. Model formulation for using remotely sensed surface temperature When remotely sensed radiometric surface temperature Trad is available, Trad can be used to replace Tsf in Eq. (32). After the value of Tc is obtained from Eq. (33) and the simulations for the leaf scale variables, Ts can be solved from Eq. (32). This approach avoids solving the soil surface energy balance equation to obtain values of Ts which requires the availability of surface soil water content measurement or estimate. For solutions of the model using Eq. (32) to solve for Ts , the previous procedure needs only a change to step (7) and (8). After step (6), Tc is known, then in step (7) Ts is solved from Eq. (32) rather than Eq. (21). In step (8), Fcs and Hs are still calculated with Eqs. (18) and (19) while LEs is solved with Eq. (21) rather than Eq. (20). For convenience, the model requiring surface soil moisture estimates or observations and Eq. (21) to solve for Ts will be referred as CECMSM and the model using Eq. (31) to solve for Ts as CECMTr hereafter.

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152 Table 1 Model parameters and their values used for the test datesets Parameter

Units

Values for the test

F16 WG1 WG5

FIFE’87 Monsoon’90 Monsoon’90

Kansas Arizona Arizona

Tallgrass prairie Semiarid rangeland shrubs Semiarid rangeland grasses

3. Observational data Three datasets, namely, F16, WG1 and WG5, are used to validate the two versions of CECM described in the above section. These datasets were obtained from the two interdisciplinary large-scale field experiments, FIFE’87 and Monsoon’90, respectively. A description of the experimental sites and the surface types are listed in Table 1. 3.1. The F16 dataset The data of the F16 dataset were collected at one (No. 16, latitude 39◦ 030 N, longitude 96◦ 320 W and height 445 m above sea level) of the tallgrass prairie sites near Manhattan, Kansas during the First International Satellite Land Surface Climatology Project (ISLSCP) Experiment (FIFE) conducted in 1987 (see Sellers et al., 1988, 1992a,b). Data used in this work were collected on various days in the season from June to August and October of 1987. Vegetation variation of the prairie is mainly determined by whether the site was burned and grazed. The prairie at this site was burned annually in early spring. The experimental area was not grazed in 1986 and 1987. The vegetation at this site was about 80% C4 grass species (see Table 1 in Kim and Verma, 1990). The leaf area index (LAI), canopy height, green leaf area percentage and leaf width were measured at different stages of the season. Results of these measurements were listed in Sellers et al. (1992b). The roughness parameters (z0 and d0 ) for computing the aerodynamic resistance ra were estimated using one-tenth and two-third of the canopy height, respectively (Brutsaert, 1982). The soil at the site is predominantly Dwight silty clay loam. Daily gravimetric sampling of the 0–5 cm soil layer were collected to monitor the soil water content. The soil property parameters were listed in Sellers et al. (1992b). The fluxes of CO2 , water vapor and sensible heat were measured with eddy correlation

141

sensors mounted at a certain height above the ground. This height was changed at different time periods of the experimental season. Wind speed was measured at 2.25 m above the ground all the time. Photosynthetically active radiation, net radiation and downward solar radiation were measured with quantum sensors and radiometers located at 2.0 m above ground. Details about the instrumentation and procedure for these measurements can be found in Kim and Verma (1990). Since radiometric surface temperatures corresponding to the flux measurements were not available, this dataset can be used for validating CECMSM only. 3.2. The WG1 and WG5 datasets from Monsoon’90 The WG1 and WG5 datasets were collected in the Walnut Gulch Experimental Watershed near Tucson, Arizona during the Monsoon’90 large-scale field experiment (see Kustas et al., 1991). The basin is about 1500 m above sea level with gently hilly topography dissected by ephemeral channels. Data were obtained in June 1990 during the dry season and late July and early August during the wet season or so-called “monsoon” season where up to two-thirds of the annual precipitation occurs between July and the end of September. The Trad data were collected at two sites, one located at the Lucky Hills subwatershed (WG1) and the other at the Kendall subwatershed (WG5). During the main field campaign, continuous measurements of canopy and soil temperatures were made with two Everest Interscience Radiometers (Model 1000) at each site, one pointed at the soil and the other at the vegetation. Instruments were positioned 1–2 m above the surface. Nichols (1992) deployed this same measurement design at the semiarid sites in Nevada. The composite temperatures for the area surrounding the sites were estimated by using periodic observations with similar nadir viewing instruments mounted on yoke-type backpacks that collected data in both field campaigns. Details of these measurements are given by Moran et al. (1994). Regression equations were obtained using the canopy and soil temperatures as independent variables and the yoke measurements as the dependent variable. This allowed the estimation of composite temperatures with the continuous infrared observations. Both sites are heterogeneous having a wide range in vegetation cover, height and architecture. The Lucky Hills site had about 26% vegetation

142

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Table 2 Measures of model performance: RMSD, MAPD and MBD Name

Description

RMSD

RMSD of model prediction Pt to observation Ot

MAPD

Mean absolute percent difference of Pt to Ot

MBD

Mean bias difference of Pt to Ot

Mathematical definition " n #1/2 1X (Pt − Ot )2 n t=1 Pn |Pt − Ot | Pn 100 × t=1 t=1 Ot n

1X (Pt − Ot ) n t=1

cover and LAI of around 0.4 with the average vegetation height being around 0.26 m. At the Kendall site, there was about 40% vegetation cover and a LAI = 0.8 with the average vegetation height being about 0.1 m. Vegetation at Site 1 is dominated by shrubs that are C3 plants. At Site 5 the vegetation is predominantly grasses which are mostly C4 plants. The value of C3 plant percentage is estimated as 90% for Site 1 and 10% for Site 5. For more details about the vegetation and LAI estimates, see Weltz et al. (1994) and Daughtry et al. (1991), respectively. For computing the aerodynamic resistance ra , the roughness parameters (z0 and d0 ) were estimated as one tenth and one third of the mean vegetation height, respectively, for both WG1 and WG5 as for F16 described previously. The surface energy balance was determined by eddy correlation, Bowen ratio and variance (Tillman, 1972) techniques with measurements of net radiation and soil heat flux, and are described by Kustas et al. (1994) and Stannard et al. (1994). The flux and meteorological data were averaged over an hour. The meteorological measurements were made at a nominal height of 4 m above the ground surface. Three gravimetric samples of the 0–5 cm soil layer were collected at each site on a daily basis. These samples were converted to volumetric soil moisture using in situ bulk density measurements. Variation coefficient of the measured water content was less than 6% (Amer et al., 1994). 4. Results and discussion The two versions of CECM are verified by comparing their predictions of CO2 flux Fc , latent heat flux LE, sensible heat flux H, and surface tempera-

ture Tsf with the corresponding observational values. Performance of the model in predicting Fc , H and LE is evaluated using the following statistical measures: root mean square difference (RMSD), mean bias difference (MBD) and mean absolute percent difference (MAPD). Behavior of the model in predicting surface temperature Tsf is evaluated with RMSD and MBD. Definitions of RMSD, MAPD and MBD are listed in Table 2. Values of RMSD, MBD and MAPD of the CECMSM predictions of Fc , H and LE for the F16 dataset are listed in Table 3. They are all relatively small. The values the values of CO2 and energy fluxes predicted by CECMSM are plotted against their corresponding observational values from the F16 dataset in Figs. 2 and 3, respectively. In these figures, the scatter of the model predictions of Fc , H and LE from their observations are generally small. The values of the correlation coefficient r between the model predictions and the field observations shown in the figures are all close to 1.0 with the number of observations (n) being larger than 100. These results indicate that CECMSM performed reasonably well for the F16 dataset. However, Figs. 2 and 3 also show that CECMSM systematically overestimated the CO2 flux Fc and the water vapor flux LE, and underestimated the sensible heat flux H. The value of MBD Table 3 RMSD and MAPD of the CO2 and energy flux predictions by CECMSM for the FIFE’87 dataset (F16) Flux (␮mol m−2 s−1 )

Fc H (W m−2 ) LE (W m−2 )

RMSD 2.7 26 42

MBD 1.6 −6 31

MAPD (%) 25 27 15

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

143

Fig. 2. Predictions of carbon dioxide flux by CECMSM compared with their observational values from the F16 dataset.

in Table 3 reflects bias of model predictions from their observations. One of the reasons for the biases shown in Table 3 is the values of LAI used for the F16 dataset. There are indications (John M. Norman, personal communication) that the LAI values adopted from Sellers et al. (1992b) might overestimate the actual leaf area index. When smaller LAI values (i.e. 70% of original values) were used in the model runs, the biases were significantly reduced. Another reason for the bias in the Fc predictions is caused by the model estimation of the CO2 flux Fcs from the soil. In Eq. (18), both W10 and Ts10 are replaced with W05 and Ts , respectively, which contributes to the inaccuracy of the Fcs estimates. If W05 is 0.10 m3 /m3 lower than the actual values of W10 and Ts overestimates Ts10 by 10◦ C, then replacing W10 and Ts10 in Eq. (18), respectively, with W05 and Ts results in the computed Fcs increasing by 2.4 ␮mol m−2 s−1 . This is 32% higher than the Fcs value estimated when LAI = 2.0, W10 = 0.20 and Ts10 = 25◦ C. This means that the

use of Eq. (18) for estimating Fcs with W05 and Ts probably requires different coefficients. The WG1 and WG5 datasets include measurements of both surface soil moisture and radiometric surface temperature. Thus, they can be used to test both CECMSM and CECMTr . Comparisons of sensible heat and latent heat fluxes predicted by CECMSM and CECMTr versus their field measurements from WG1 and WG5 are illustrated in Figs. 4–7, respectively. The statistics of model performance are listed in Table 4. From these figures and Table 4, one can make several general conclusions. First, both CECMSM and CECMTr yield significant correlation coefficients with field measurements of H and LE greater than 0.75 for n > 100. For the WG5 dataset, values of RMSD for the H and LE predictions by both CECMSM and CECMTr are between 40 and 50 W m−2 . The values of MAPD shown in Table 4 for the WG5 dataset are all less than 30% which is similar to the uncertainty observed in hourly energy flux measurements in FIFE

144

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Fig. 3. Predictions of (a) sensible heat and (b) latent heat fluxes by CECMSM compared with their observational values from the F16 dataset.

Fig. 4. Predictions of (a) sensible heat and (b) latent heat fluxes by CECMSM compared with their observational values from the WG1 dataset.

(Nie et al., 1992) and the Monsoon’90 experiment. Secondly, both CECMSM and CECMTr systematically underestimate LE and overestimate H for the WG1 site (Figs. 4 and 5). This is also quantified in Table 4 where the values of MBD for H and LE for the WG1 site are significant.

Performance of CECMSM and CECMTr in predicting surface temperature, canopy temperature and soil temperature is examined with the observations of these temperatures from the Monsoon’90 datasets. Table 5 lists the values of RMSD and MBD of the model predictions from their observational values.

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

145

Fig. 5. Predictions of (a) sensible heat and (b) latent heat fluxes by CECMTr compared with their observational values from the WG1 dataset.

Fig. 6. Predictions of (a) sensible heat and (b) latent heat fluxes by CECMSM compared with their observational values from the WG5 dataset.

From this table, one observes that CECMTr generally yield smaller values of RMSD and MBD for canopy temperature and significantly smaller values of RMSD and MBD for soil surface temperature compared to

CECMSM . The likely reason for generally smaller differences with CECMTr is that this version of the model directly uses the radiometric surface temperature measurement and has a means of constraining the

146

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Fig. 7. Predictions of (a) sensible heat and (b) latent heat fluxes by CECMTr compared with their observational values from the WG5 dataset.

magnitude of canopy and soil surface temperatures. In addition, the radiometric surface temperature CECMTr used as an input was measured on an hourly basis while the surface soil moisture data used by CECMSM

as an input were daily values. Surface soil water content varies diurnally as does soil evaporation (Steinberger et al., 1989). Therefore, the lack of considering this diurnal variation of surface soil water content may have contributed to the different performance of CECMSM from that of CECMTr . CECMTr performed better than CECMSM not only in predicting Tsf , Tc and Ts but also in predicting H and LE (see Table 4). From the results in Table 5, one can conclude that CECMSM and CECMTr performed better in predicting Tsf , Tc and Ts for the WG5 dataset than for the WG1 dataset. Summarizing the above results, both CECMSM and CECMTr provide reasonably good predictions of Fc , H and LE and/or surface, canopy and soil temperatures for the F16 and WG5 sites, but not for the WG1 site. For the latter site, both CECMSM and CECMTr significantly underestimate LE, overestimate H and, consequently, overestimate canopy temperature. The difference between the WG1 site and the F16 and WG5 sites is that WG1 contained predominately C3 shrubs while F16 and WG5 contained mainly C4 grasses. In both CECMSM and CECMTr , a distinction between C3 and C4 plants is made by adjusting the coefficients in the stomatal conductance model and using different leaf photosynthesis model. The parameters in the models of stomatal conductance and photosynthesis for C3 plants employed by CECMSM and CECMTr were taken from Ball (1988) and Long (1991) which are representative of temperate vegetation, and hence, probably not appropriate for the C3 shrubs adapted to the semiarid environment. Comparing the predictions of stomatal resistance by CECMSM and CECMTr with the estimates of stomatal resistance by Flerchinger et al. (1998), it is found that CECMSM and CECMTr overestimated stomatal resistance significantly for the WG1 dataset. There are two likely causes for the overestimation of the stomatal resistance: 1) the values of the coefficient g1 used in the stomatal conductance model, Eq. (10); 2) the values for the optimal leaf temperature of leaf photosynthesis assumed in the leaf photosynthesis model for C3 plants (cf. Eq. (14)). If the value of g1 in Eq. (10) is too small, then the stomatal conductance predicted by Eq. (10) is too small and the resulting stomatal resistance in Eq. (11) is too large. The original value of g1 = 9.0, determined for general C3 plants in temperate climate by Ball (1988), may be too low for the C3 shrubs in the semiarid environments. To obtain a

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

147

Table 4 RMSD, MBD and MAPD of the energy flux predictions by the initial runs of CECM for the Monsoon’90 datasets RMSD (W m−2 )

Dataset

CECMSM

MBD (W m−2 ) CECMTr

CECMSM

MAPD (%) CECMTr

CECMSM

CECMTr

Sensible heat flux H WG1 70 WG5 39

50 39

48 1

22 5

54 28

34 26

Latent heat flux LE WG1 61 WG5 49

50 39

−48 −4

−22 −5

35 21

25 16

model, Eq. (14). The original value of T0 of 25◦ C is also for general C3 plants in temperate climate (Long, 1991). Considering that the C3 shrubs at the WG1 site were adapted to the semiarid area in Arizona so that their optimal leaf temperature of photosynthesis may be around 30◦ C, the value of T0 was changed to 35◦ C. After the adjustment to the parameters of stomatal conductance model and photosynthesis model for C3 plant leaves, the biases of the predictions of H and LE by both CECMSM and CECMTr are significantly reduced for the WG1 dataset. The values of RMSD for the H and LE predictions by CECMSM are reduced from 70 and 61 W m−2 (see Table 4) to 40 W m−2 (see Table 6), respectively. The corresponding values of MAPD are reduced from 54 and 35 to 29 and 21%, respectively. The values of RMSD and MAPD in Table 6 of the predictions of H and LE by CECMTr are also improved significantly. Since the percentage of C3 plants at the WG5 site is only 10%, the parameter adjustment does not change the performance of both CECMSM and CECMTr for this site (compare Table 4 with Table 6).

Table 5 RMSD and MBD of the temperature predictions by the initial runs of CECM for the Monsoon’90 datasets Dataset

RMSD (◦ C) CECMSM

MBD (◦ C) CECMTr

CECMSM

CECMTr

Composite surface temperature WG1 6.3 0.0 WG5 3.9 0.0

4.8 2.1

0.0 0.0

Canopy temperature WG1 4.0 WG5 2.8

3.9 2.3

3.5 0.9

3.6 0.8

Surface soil temperature WG1 5.8 WG5 4.6

4.4 1.1

2.5 2.7

−3.9 −0.4

similar average of stomatal resistance predictions by Eq. (11) to that by Flerchinger et al. (1998) for the WG1 dataset, the g1 -value had to be changed to 15.0 along with an increase in the T0 -value in Eq. (A.5). T0 regulates the optimal leaf temperature of photosynthesis of C3 plants through the C3 plant photosynthesis

Table 6 RMSD, MBD and MAPD of the energy flux predictions by CECM with parameters modified for the C3 plants in the Monsoon’90 datasets Dataset

RMSD (W m−2 ) CECMSM

MBD (W m−2 )

MAPD (%)

CECMTr

CECMSM

CECMTr

CECMSM

CECMTr

Sensible heat flux H WG1 40 WG5 40

38 38

1 −6

−19 −3

29 27

27 24

Latent heat flux LE WG1 40 WG5 51

38 38

0 3

19 3

21 22

20 15

148

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

Table 7 RMSD and MBD of the temperature predictions by CECM with parameters modified for the C3 plants in the Monsoon’90 datasets Dataset

RMSD (◦ C) CECMSM

MBD 0◦ C) CECMTr

CECMSM

CECMTr

Composite surface temperature WG1 5.6 0.0 WG5 3.8 0.0

3.8 1.9

0.0 0.0

Canopy temperature WG1 2.0 WG5 2.9

1.8 2.3

1.3 0.5

1.4 0.4

Surface soil temperature WG1 5.7 WG5 4.6

3.6 1.0

1.8 2.5

−3.3 −0.2

The values of RMSD, MBD and MAPD for the predictions of the surface temperature, canopy temperature and soil temperature by CECMSM and CECMTr after the adjustment to the model parameters for C3 vegetation are listed in Table 7 for both of the two Monsoon’90 datasets (WG1 and WG5). In comparison to Table 5, the parameter adjustments do not change the performance of the two model versions in predicting the temperatures for the WG5 site, however, there is a reduction in the bias especially in the canopy temperature predictions for the WG1 site. This is in agreement with the improved energy flux predictions using the modified parameters for WG1 (Table 6).

5. Conclusions In this study, CECM using either surface soil moisture (CECMSM ) or radiometric surface temperature (CECMTr ) along with meteorological observations to estimate land surface energy and CO2 fluxes was developed and tested with data from subhumid and semiarid environments. The model gives reasonably accurate predictions of surface CO2 flux, latent heat flux, sensible heat flux and surface temperature when compared to observations from the FIFE’87 and Monsoon’90 experiments. When reliable radiometric surface temperature measurements were available representing the flux measurement source areas, CECMTr generally gave better results than CECMSM . However, surface temperature observations are not routinely available from satellites

due to clouds and frequency of satellite coverage. The exception to this would be GOES, but it has relatively coarse pixel resolution of around 4–8 km that makes it difficult to specify model parameters at this pixel size. This may limit the application of CECMTr to periodical calibration of CECM. However, if simplifications to CECMTr can be made similar to (Anderson et al. (1997); 2000), then it may be possible to compute the fluxes at regional scales operationally with GOES data. The surface soil moisture data needed by CECMSM are not operationally available. Current technology has shown the potential using passive microwave remote sensing to retrieve surface soil moisture (Schmugge and Jackson, 1994), but the resolution of passive microwave is one to two orders of magnitude larger than GOES. On the other hand, the soil moisture data used in the above analysis represent daily values. Thus, the model can use daily values of soil moisture to simulate hourly surface energy fluxes. If daily surface soil moisture becomes operationally available from satellite observations, then CECMSM has the potential of simulating the fluxes with routine weather data. When comparing these results to less complex two-source models in the literature (e.g. Norman et al., 1995), there is no real improvement in the predicted fluxes. However, the CECM has some advantages. First, CECM applies the CO2 constraints to the water vapor transport across the plant stomates according to the physics and the physiology, which may make the model predictions more reliable for various surfaces. Secondly, the model can directly output net CO2 assimilation rate that is useful for estimating land surface biomes, ecosystem primary productivity and agricultural crop yields. More observational data sets over different landscapes are needed to test and compare the output of CECM with simpler two-source model predictions in order to determine the complexity required to obtain reliable surface fluxes at larger scales.

Acknowledgements The cooperation and assistance of the USDA-ARS Southwest Watershed Research Center in Tucson, Arizona and on site personnel who maintain the Walnut Gulch Experimental Watershed during the Monsoon’90 experiment are gratefully acknowl-

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

edged. Processing of the yoke data for Monsoon’90 was performed by T.R. Clarke and M.S. Moran from the USDA-ARS US Water Conservation Lab, Phoenix, Arizona. The continuous measurements of soil and vegetation temperatures for Monsoon’90 were collected and processed by W.D. Nichols from the USGS-Water Resources Division, Carson City, Nevada. The authors also acknowledge D.I. Stannard from the US Geological Survey, Denver, CO, and J.H. Blanford, affiliated with the University of Arizona during Monsoon’90, who were mainly responsible for the Monsoon’90 surface flux data. Funding from NASA Interdisciplinary Research Program in Earth Sciences (NASA Reference Number IDP-88-086) and funds from USDA-ARS Beltsville Area Office provided the necessary financial support to conduct the Monsoon’90 field study. The authors are especially indebted to S.B. Verma and his coworkers at University of Nebraska-Lincoln who provided us with the dataset collected at site 16 of the FIFE experiment in 1987. The authors are also indebted to many individuals who participated in the planning and implementation of the FIFE experiment, among them: F.G. Hall (NASA), P.J. Sellers (NASA) and R.E. Murphy (NASA). Finally, the authors are indebted to the helpful comments from G.N. Flerchinger on an earlier version of this manuscript.

Appendix A. Equations for computing the parameters in the biochemical models of net photosynthesis of C3 and of C4 leaves According to Farquhar et al. (1980), the value of Γ ∗i in Eq. (14) is given by Γ∗i =

0.105Kci Oii . Koi

(A.1)

where Oii is the concentration O2 at the carboxylation sites inside the ith type of leaves, Kci and Koi are the Michaelis–Menten constants for CO2 and O2 , respectively. By the competitive Michaelis–Menten kinetics, the RuBP-saturated rate of carboxylation, Wci in Eq. (14), is Wci =

Vcmaxi Cii Cii + Kci (1 + Oii /Koi )

(A.2)

149

where Vcmaxi is the maximum RuBP carboxylation rate that is limited by the Rubisco activity, Cii is the concentration of CO2 at the carboxylation sites inside the leaves of group i. The RuBP regeneration-limited carboxylation rate Wji in Eq. (14), is represented by the rate of electron transport and is given by (Farquhar et al., 1980) Wji =

Ji 4.5 + 10.5(G∗i /Cii )

(A.3)

where Ji is the potential rate of whole-chain electron transport. The constants, 4.5 and 10.5 result from the stoichiometry of the whole electron transport chain (Farquhar and Caemmerer, 1982). Ji is dependent on the absorbed photosynthetically active radiation (PAR) as follows (Long, 1991): Ji =

Jmaxi fPARi fPARi + 2.1Jmaxi

(A.4)

where Jmaxi is the maximum rate of whole-chain electron transport, f is the fraction of PAR absorbed by functional photosynthetic pigments, PARi is the PAR received by the ith group of leaves. In Farquhar et al. (1980), the overall net photosynthetic rate Ani = min(Wci , Wji ) − Rdi . When the leaf environment changes and the limitation to photosynthetic rate switches from Wci to Wji or Wji to Wci , the variation curve of Ani versus some environmental variables (say, PAR) may display an interrupt change. To avoid this interrupt change, Collatz et al. (1991) proposed a quadrate equation to solve for Ani from Wci and Wji values and the result is Eq. (14). The parameters Kci , Koi , Vcmaxi in the above equations and Rdi in Eq. (14) are dependent on leaf temperature. The following equation adopted by Long (1991) is used to describe the dependency of parameter x on leaf temperature Tli :    0.5 Tli − T0 Ex Tli , (A.5) x = x0 exp T0 RTli T0 where x is one of the parameters (Kci , Koi , Vcmaxi , and Rdi ), x0 is the value of x when Tli = T0 , T0 is a reference value of Tli which regulates the optimal leaf temperature of photosynthesis, Ex is the activation energy for the parameter x, R again is the universal gas constant. Tli and T0 in Eq. (A.5) are in K. Following the similar idea for the development of Eq. (14), Collatz et al. (1992) computes the gross

150

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

photosynthetic rate determined by the rubisco and light-limited capacity, M, as follows: M=

1  (VT + αp PARi ) 2β2  q − (VT + αp PARi )2 − 4β2 VT αp PARi

(A.6)

where VT is the temperature-dependent, substratesaturated rubisco capacity, α p = 0.04 mol m−1 is the quantum efficiency, β2 = 0.83 is similar to β 1 being a curvature parameter. The temperature dependence of VT is given as (T −25)/10

Vmax Q10 li VT = (1 + e0.3(13−Tli ) )(1 + e0.3(Tli )−36 )

(A.7)

where Vmax is the maximum substrate-saturated rubisco capacity, Q10 = 2.0 is a temperature parameter which is the proportional increase in the value of a parameter for a 10◦ C increase in temperature. The temperature dependencies of kT and of Rdi in Eq. (15) are given as follows: (T −25)/10

kT = k0 Q10 li

(A.8)

(T −25)/10

Rdi

Rd0 Q10 li = 1 + e1.3(Tli −55)

(A.9)

where k0 and Rd0 are model parameters which are given in Collatz et al. (1992). References Amer, S.A., Reefer, T.O., Weltz, M.A., Goodrich, D.C., Bach, L.B., 1994. Soil moisture sensors for continuous monitoring. Water Resources Bull. 30, 69–83. Amthor, J.S., 1994. Scaling CO2 -photosynthesis relationships from the leaf to the canopy. Photosynthesis Res. 39, 321–350. Amthor, J.S., Goulden, M.L., Munger, J.W., Wofsy, S.C., 1994. Testing a mechanistic model of forest-canopy mass and energy exchange using eddy correlation: carbon dioxide and ozone update by mixed oak–maple stand. Aust. J. Plant Physiol. 21, 623–651. Anderson, M.C., Norman, J.M., Diak, G.R., Kustas, W.P., Mecikalski, J.R., 1997. A two-source time-integrated model for estimating surface fluxes from thermal infrared satellite observations. Remote Sens. Environ. 60, 195–216. Anderson, M.C., Norman, J.M., Meyers, T.P., Diak, G.R., 2000. An Analytical model for estimating canopy transpiration and carbon assimilation fluxes based on canopy light-use efficiency. Agric. For. Meteorol. 101, 265–289.

Ball, J.T., 1988. An Analysis of Stomatal Conductance. Ph.D. dissertation, Stanford University, Stanford, CA, 89 pp. Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Progress in Photosynthesis Research, Vol. IV, pp. 221–224. Brutsaert, W., 1982. Evaporation into The Atmosphere. D. Reidel, Dordrecht, 299 pp. Camillo, P.J., Gurney, R.J., 1986. A resistance parameter for bare-soil evaporation models. Soil Sci. 141 (2), 95–105. Campbell, G.S., 1977. An Introduction to Environmental Biophysics. Springer, New York, 159 pp. Choudhury, B.J., Idso, S.B., Reginato, R.J., 1987. Analysis of an empirical model for soil heat flux under a growing wheat crop for estimating evaporation by an infrared-temperature based energy balance equation. Agric. For. Meteorol. 39, 283–297. Collatz, G.J., Grivet, C., Ball, J.T., Berry, J.A., 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agric. For. Meteorol. 54, 107–136. Collatz, G.J., Ribas-Carbo, M., Berry, J.A., 1992. Coupled photosynthesis-stomatal conductance model for leaves of C4 plants. Aust. J. Plant Physiol. 19, 519–538. Cowan, I.R., 1977. Stomatal behaviour and environment. Adv. Bot. Res. 4, 117–228. Cowan, I.R., 1982. Regulation and water use in relation to carbon gain in higher plants. In: O.L. Lange, P.S. Nobel, C.B. Osmond (Eds.), Encyclopedia of Plant Physiology, New Series 12B, Springer, Berlin, pp. 589–613. Daughtry, C.S.T., Weltz, M.A., Perry, E.M., Dulaney, W.P., 1991. Direct and indirect estimates of leaf area index. In: AMS Preprints of the 10th Conference on Biometeorology and Aerobiology and Special Session on Hydrometeorology, Salt Lake City, UT, 10–13 September 1991, pp. 230–233. Dickinson, R.E., 1984. Modeling evapotranspiration for three-dimensional global climate models. In: J.E. Hanson, T. Takahashi (Eds.), Climate Processes and Climate Variability. Am. Geophys. Union, pp. 58–72. Farquhar, G.D., von Caemmerer, S., 1982. Modeling of photosynthetic responses to environmental conditions. In: O.L. Lange et al. (Eds.), Encyclopedia of Plant Physiology (New Series), Vol. 12B. Physiological Plant Ecology, Springer, New York, pp. 549–587. Farquhar, G.D., von Caemmerer, S., Berry, J.A., 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149, 78–90. Flerchinger, G.N., Kustas, W.P., Weltz, M.A., 1998. Simulating surface energy fluxes and radiometric surface temperatures for two arid vegetation communities using the SHAW model. J. Appl. Meteorol. 37, 449–460. Jarvis, P.G., 1976. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. R. Soc. Lond. Ser. B — Biol. Sci. 273, 593– 610. Justice, C.O., Vermote, E., Townshend, J.R.G., Defries, R., Roy, D.P., Hall, D.K., Salomonson, V.V., Privette, J.L., Riggs, G., Strahler, A., Lucht, W., Myneni, R.B., Knyazikhin, Y., Running,

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152 S.W., Nemani, R.R., Wan, Z.M., Huete, A.R., van Leeuwen, W., Wolfe, R.E., Giglio, L., Muller, J.P., Lewis, P., Barnsley, M.J., 1998. The moderate imaging spectroradiometer (MODIS): land remote sensing for global research summary. IEEE Trans. Geosci. Remote Sens. 36, 1228–1249. Kim, J., Verma, S.B., 1990. Carbon dioxide exchange in a temperate grassland ecosystem. Boundary-Layer Meteorol. 52, 135–149. Kustas, W.P., Goodrich, D.C., Moran, M.S., et al., 1991. An interdisciplinary field study of the energy and water fluxes in the atmosphere–biosphere system over semiarid rangelands: description and some preliminary results. Bull. Am. Meteorol. Soc. 72, 1683–1705. Kustas, W.P., Blanford, J.H., Stannard, D.I., Daughtry, C.S.T., Nichols, W.D., Weltz, M.A., 1994. Local energy flux estimates for unstable conditions using variance data in semiarid rangelands. Water Resources Res. 30, 1351–1361. Kustas, W.P., Zhan, X., Schmugge, T.J., 1998. Combining optical and microwave remote sensing for mapping energy fluxes in a semiarid watershed. Remote Sens. Environ. 64, 116–131. Kustas, W.P., Zhan, X., Jackson, T.J., 1999. Mapping surface energy flux partitioning at large scales with optical and microwave remote sensing data from Washita’92. Water Resources Res. 35, 265–277. Kustas, W.P., Norman, J.M., Schmugge, T.J., Anderson, M.C., 2000. In: Quattochi, D.A., Luvall, J.C. (Eds.), Mapping surface energy fluxes with radiometric temperature. Remote Sensing in Land Surface Processes, in press. Leuning, R., 1995. A critical appraisal of a combined stomatal –photosynthesis model for C3 plants. Plant, Cell Environ. 18, 339–355. Leuning, R., Kelliher, F.M., de Pury, D.G.G., Schulze, E.D., 1995. Leaf nitrogen, photosynthesis, conductance and transpiration: scaling from leaf to canopies. Plant, Cell Environ. 18, 1183– 1200. Long, S.P., 1991. Modification of the responses of photosynthetic productivity to rising temperature by atmospheric CO2 concentrations: has its importance been underestimated? Plant, Cell Environ. 14, 729–739. Louwerse, W., Zweerde, W.V.D., 1977. Photosynthesis, transpiration and leaf morphology of Phaseolus vulgaris and Zea mays grown at different irradiances in artificial and sunlight. Photosynthetica 11, 11–21. Mauhfleau, J.F., Noilhan, J., 1991. Comparative study of various formulations of evaporation from bare soil using in situ data. J. Appl. Meteorol. 30, 1354–1365. Monteith, J.L., 1965. Evaporation and environment. Symp. Soc. Exp. Biol. 19, 205–234. Moran, M.S., Clarke, T.R., Kustas, W.P., Weltz, M.A., Amer, S.A., 1994. Evaluation of hydrologic parameters in semiarid rangeland using remotely sensed spectral data. Water Resources Res. 30, 1287–1297. Nichols, W.D., 1992. Energy budgets and resistance to energy transport in partially vegetated rangeland. Agric. For. Meteorol. 60, 221–247. Nie, D., Kanemasu, E.T., Fritschen, L.J., Weaver, H.L., Smith, E.A., Verma, S.B., Field, R.T., Kustas, W.P., Stewart, J.B.,

151

1992. An intercomparison of surface energy flux measurement systems used during FIFE 1987. J. Geophys. Res. 97 (D17), 18715–18724. Norman, J.M., 1979. Modeling the complete crop canopy. In: B.J. Hartfield, J.F. Gerber (Eds.), Modification of The Aerial Environment of Plants. American Society of Agricultural Engineering, St. Joseph, MI, 538 pp. Norman, J.M., 1982. Simulation of microclimates. In: Biometeorology in Integrated Pest Management. Academic Press, New York, pp. 65–99. Norman, J.M., Garcia, R., Verma, S.B., 1992. Soil surface CO2 fluxes and the carbon budget of a grassland. J. Geophys. Res. 97 (D17), 18845–18853. Norman, J.M., Kustas, W.P., Humes, K.S., 1995. A two-source approach for estimating soil and vegetation energy fluxes from observations of directional radiometric surface temperature. Agric. For. Meteorol. 77, 263–293. Raupach, M.R., Finningan, J.J., 1988. Single-layer models of evaporation from plant canopies are incorrect but useful, whereas multilayer models are correct but useless. Discussion Aust. J. Plant Physiol. 15, 705–716. Schimel, D., Enting I.G., Heimann, M., Wigley T.M.L., Raynaud, D., Alves, D., Siegenthaler, U., 1995. CO2 and the carbon cycle. In: Climate Change 1994 (Intergovernmental Panel on Climate Change). University of Cambridge Press, Cambridge, pp. 35–72. Schmugge, T.J., Jackson, T.J., 1994. Mapping surface soil moisture with microwave radiometers. Meteorol. Atmos. Phys. 54, 213– 223. Sellers, P.J., Hall, F.G., Asrar, G., Strebel, D.E., Murphy, R.E., 1988. The first ISLSCP field experiment (FIFE). Bull. Am. Meteorol. Soc. 69, 22–27. Sellers, P.J., Hall, F.G., Asrar, G., Strebel, D.E., Murphy, R.E., 1992a. An overview of the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE). J. Geophys. Res. 97 (D17), 18345–18372. Sellers, P.J., Heiser, M.D., Hall, F.G., 1992b. Relations between surface conductance and spectral vegetation indices at intermediate (100 m to 15 km) length scales. J. Geophys. Res. 97, 19033–19059. Sellers, P.J., Bounoua, L., Collatz, G.J., Randal, D.A., Dazlich, D.A., Los, S.O., Berry, J.A., Fung, I., Tucker, C.J., Field, C.B., Jensen, T.G., 1996a. Comparison of radiative and physiological effects of doubled atmospheric CO2 on climate. Science 271, 1402–1406. Sellers, P.J., Randall, D.A., Collatz, G.J., Berry, J.A., Field, C.B., Dazlich, D.A., Zhang, C., Collelo, G.D., Bounoua, L., 1996b. A revised land surface parameterization (SiB2) for atmospheric GCMs. Part I. Model formulation. J. Climate 9, 676–705. Sinclare, T.R., Murphy, C.E., Knoerr, K.R., 1976. Development and evaluation of simplified models for simulating canopy photosynthesis and transpiration. J. Appl. Ecol. 13, 813–830. Shuttleworth, W.J., Wallace, J.S., 1985. Evaporation from sparse crops — an energy combination theory. Q. J. R. Meteorol. Soc. 111, 839–855. Stannard, D.I., Blanford, J.H., Kustas, W.P., Nichols, W.D., Amer, S.A., Schmugge, T.J., Weltz, M.A., 1994. Interpretation of

152

X. Zhan, W.P. Kustas / Agricultural and Forest Meteorology 107 (2001) 131–152

surface flux measurements in heterogeneous terrain during the Monsoon’90 experiment. Water Resources Res. 30, 1227–1239. Steinberger, Y., Loboda, I., Garner, W., 1989. The influence of autumn dewfall on spatial and temporal distribution of nematodes in the desert ecosystem. J. Arid Environ. 16, 177–184. Su, H.B., Paw, U.K.T., Shaw, R.H., 1996. Development of a coupled leaf and canopy model for simulation of plant–atmosphere interaction. J. Appl. Meteorol. 35, 733–748. Tillman, J.E., 1972. The indirect determination of stability, heat and momentum fluxes in the atmospheric boundary layer from simple scalar variables during dry conditions. J. Appl. Meteorol. 11, 783–792.

Waring, R.H., Schlesinger, W.H., 1985. Forest Ecosystems: Concepts and Management. Academic Press, Orlando. Weltz, M.A., Ritchie, J.C., Fox, H.D., 1994. Comparison of laser and field measurements of vegetation height and canopy cover. Water Resources Res. 30, 1311–1320. Williams, M., Rastetter, E.B., Fernandes, D.N., Goulden, M.L., Wofsy, S.C., Shaver, G.R., Melillo, J.M., Munger, J.W., Fan, S.M., Nadelhoffer, K.J., 1996. Modelling the soil–plant–atmosphere continuum in a Quercus-Acer stand at Harvard Forest: the regulation of stomatal conductance by light, nitrogen and soil/plant hydraulic properties. Plant, Cell Environ. 19, 911–927.