an approach to soil-vegetation-atmosphere-transfer models...

M

AG RI CULTURAL AND

FOREST METEOROLOGY

ELSEVIER Agricultural and Forest Meteorology 83 (1997) 49-74

An approach to couple vegetation functioning and soil-vegetation-atmosphere-transfer models for semiarid grasslands during the HAPEX-Sahel

D. Lo Seen a'*, Á.[Chehbouni b, E. Njoku a, S. Saatchi a,

E. Mougin ', B.,Monteny 15f-W.

a Jet Propulsion Laborarory, 4800, Oak Groue Driue, Pasadena, CA 91109-8099, US4 ORSTOM- Laboratoire d'hydrologie, 911, avenue Agropolis, BP 5054,34032 Montpellier Cedex, France

CESBIO/ CNES, 18, auenue Edouard Belin, 3105 Toulouse Cedex, France

Received 18 September 1995; revised 7 March 1996; accepted 27 March 1996

Abstract

This paper presents a model which has been developed to simulate the major land surface processes occurring in and and semiarid grasslands. The model is composed of a hydrological submodel which describes the water and energy budgets, and a vegetation growth submodel which groups the processes associated with biomass production. Emphasis has been placed on develop- ing a realistic representation of the interaction between these subprocesses taking account of the different time scales involved. The hydrological submodel couples the energy balance of the soil/canopy with the soil moisture and thermal dynamics. It interacts with the vegetation growth submodel by exchanging information needed to account for the influence of plant water status and canopy temperature on photosynthesis, and the influence of the vegetation canopy on the boundary layer within which transport processes are taking place. The model has been tested with meteorological, biomass and energy flux measurements made on a grassland site during the HAPEX-Sahel experiment, Niger, in 1992. Model simulations of biomass over the growing season are all found to be within a 15% error margin allowed on biomass measurements. Hourly values of net radiation, as well as latent and sensible heat fluxes, are simulated with an RMSE of less than 50 W m-2. Given the relative simplicity of the model and the long period of uninterrupted simulation, these results are considered satisfactory. Overall, the results show that

* Corresponding author. Present address: CIRAD-Forêt, CIRAD/Maison de la Télédétection, 500 Rue J.F. Breton, 34093 Montpellier Cedex 5, France.

0168-1923/97/$17.00 Copyright O 1997 Elsevier Science B.V. All rights reserved. PII SO 168-1 923(96)02350-7

50 D. Lo Seen er al./Agricultural ancl Forest Meteorology 83 (1997) 49-74

the model behaves consistently at different stages of vegetation growth, and satisfactorily reproduces the interdependence of vegetation growth with the physical processes giving rise to the water and energy balances.

1. Introduction

Interconnected land surface processes control the energy, water and carbon transfers between soil, vegetation and the atmosphere. Several studies have put emphasis upon the necessity to correctly describe the land surface processes while investigating the interactions between land surface and regional climate (Wilson et al., 1987; Pielke and Avissar, 1990; Raupach, 1991 ). Soil-vegetation-atmosphere-transfer (SVAT) models have therefore been developed to simulate these mass and energy transfers for different land surfaces and vegetation types (e.g. forests, grasslands). But more than anywhere else, the need for an accurate description of the processes is crucial in arid and semiarid regions where neither the soil nor the vegetation dominates the exchange of heat and water with the atmosphere. Moreover, the land surface itself may change considerably during a year, like for example in the Sahel where the predominance of annual grasses makes the surface vary from bare soil during the dry season, to a sometimes luxuriant vegetated surface during the rainy season.

The model presented in this paper seeks to describe the major land surface processes occurring in.semiarid grasslands as typically found in the Sahel. Unlike other SVAT models which normally consider vegetation to be invariant in time, the model couples vegetation growth with the heat and moisture dynamics in the soil and the sparse canopy. From the point of view of the ecosystem modeling of primary productivity, the model uses an improved description of the water and energy budgets. The model simulates Sahelian grassland vegetation growth, evapotranspiration, sensible heat flux and the evolution of surface temperature and soil moisture during the growing season. It can be considered as a compromise between the need for a simplified representation of the processes, while retaining the main mechanisms which ensure a realistic simulation of these processes. After description of the land surface process model, the paper deals with the application of the model to a grassland site of the HAPEX-Sahel experiment, Niger, (Goutorbe et al., 1993; Prince et al., 1995) for which biomass, vegetation height and energy fluxes measurements have been made, and for which meteorological and precipitation data necessary to run the model have been recorded during the growing season of 1992.

2. Model description

The model can be schematically presented as two interacting submodels (see Fig. 1). The first submodel groups the hydrological processes such as soil water and thermal dynamics, coupled with the water and energy balances in a sparse canopy. The second submodel groups the main processes related to vegetation growth, such as photosynthesis, respiration and biomass production. The hydrological submodel runs with an hour

- SURFACE PROCESSES MODEL

Meteo. data (air temp., humidify, wind speed, in. solar radiation)

I Rainfalldata I

Soil fiermal and hydraulic properties

soil texture (%clay, %sand) I %C3/C4 l

e . OUTPUT

.Water and heat

.Soil-moisture

.Temperature of

fluxes

-ground -canopy

.Aerodynamic and radiative temperatures

. Biomass

. Net primary productivity

. Photosynthesis

. Respiration

I

Fig. I . Diagram showing the interaction between the vegetation growth submodel and the water and energy balance submodel, by the exchange of the necessary variables. The major input data needed, as well as the main processes and surface variables simulated, are also shown.

52 D. Lo Seen et al./Agricultural and Foresr Meteorology 83 (1997) 49-74

time step, whereas the vegetation growth submodel has a daily time step. The interaction between the two submodels, and the manner in which the difference in time steps is dealt with, are described later in this section. The notation used in this paper is listed in Appendix A.

2.1. Energy balance equations

The Sahelian grassland considered here, like most arid and semiarid vegetation, is typically sparse vegetation in which sensible and latent heat originate both from the canopy and the soil in comparable amounts. This energy partitioning gradually changes throughout the growing season as the vegetation grows, along with the recharge and depletion of soil moisture in the system following rain events. The model uses the one-dimensional two-layer approach proposed by Shuttleworth and Wallace (1985), which considers the soil and the vegetation as separate sources (or sinks) of latent and sensible heat. The approach has already been evaluated for sparse crops (e.g. Ham and Heilman, 1991) and sparse natural vegetation (e.g. Nichols, 1992). As the herbaceous vegetation present is exclusively composed of annuals, a model simulation carried out for the growing season should also account for the transition between bare soil (before the first rains, usuaIly in June) and fully grown vegetation (occurring around September). The general two-layer model is briefly presented here, knowing that it can be simplified to represent both the case of bare soil and that of closed canopy.

The net radiation available above the canopy is partitioned between the soil and the canopy, such that:

R , = R , , + R,,c

R, , , - AE, - H, - G = O

R , , - AE, - H , = O

(1)

(2)

(3)

An energy budget written separately for the soil and the canopy gives:

and

The model assumes the existence of a mean air-flow at a ‘source level’ within the canopy. Energy exchanges are then considered to occur between the soil surface, the canopy, the within-canopy source level and an above-canopy reference level. Fig. 2 shows the network of resistances across which differences in vapor pressure and temperature give the fluxes of latent (Eqs. (4)-(6)) and sensible heat (Eqs. (714911, by analogy to Ohm’s law.

PCp ( eo- ea) AE=- Y raa

( 4)

b s k? 9 % n 7 \ >

e, Mean canopy flow 2 -.

k

w2 8 T2 a

source height - - - - E c E" P 21 2 2 3

F B 8

Fig. 2. Diagram showing the network of resisfances (from Shultleworlh and Wallace, 1985) between the soil surface, the within-canopy source level and the above-canopy reference level, across which differences in vapor pressure and temperature give latent and sensible heat fluxes. The surface and root layers are also shown with their corresponding temperature and moislure confent.

2

L 2 u A \o I u A

ul W

54 D. Lo Seen et aL/Agricubural and Forest Meteorology 83 (1997) 49-74

Substituting Eqs. (4)-(6) in the conservation of latent heat of the canopy air flow gives

and similarly, Eqs. (7)-(9) with the conservation of sensible heat give

raarasT , + r a a r a c T , + r a c r a s T ,

rac ras + ‘,aras f rac raa To = -

The way the foliage prevents the radiation from reaching the ground, is expressed by the quantity wf (the shielding factor used by Deardroff, 1978; Taconet et a1.,-1986; Ben Mehrez, 1990). Assuming no heat storage in the canopy, radiative budgets written for shortwave and longwave radiation can be arranged such that R , , and Rn,s are expressed in terms of incoming atmospheric and shortwave radiation, the shielding factor, and the temperature, emissivity and albedo of the canopy and the soil.

D. Lo Seen et al./Agricultural and Forest Meteorology 83 (1997) 49-74 55

The incoming shortwave radiation is usually measured whereas the atmospheric radiation, when not measured, can be estimated by (Brutsaert, 1975):

Thus, if the different resistances are known, the latent, sensible and net radiation heat fluxes of the soil and the canopy can all be written in terms of q, r, and the measured Ta and e,.

2.2. Ground temperature and soil moisture time-dependent equations

The evolution of ground temperature and soil moisture are described following the force-restore method proposed in Deardroff (1978). The method was originally proposed by Bhumralkar (1975) for the computation of ground surface temperature, where the forcing by the ground heat flux is modified by the restore term which depends on the deep soil temperature T2 (Eq. (15) and Eq. (16)). The soil moisture is treated similarly (Eq. (17) and Eq. (18)) as proposed by Deardroff (1978) and modified by Noilhan and Planton (1989).

8% Cl c2

at Pwd, - = -(P - E , ) - 7‘ ws - we,) when O < w, 5 wfc

aw, P - E , - E , -=

at Pw d2 when O < w2 5 wfc

2.3. Determination of T, and T,

The system is solved for the two unknowns q, and T,, by first writing an energy budget separately for the canopy (Eq. (3)) and the soil (Eq. (2)), then by forwarding the soil heat flux G obtained in terms of q, and T, (by replacing Eq. (61, Eq. (9) and Eq. (13) into Eq. (211, as the forcing term in the soil surface temperature time dependent equation (Eq. (15)). Integration in time is done using the Crank-Nicolson method after linearization of the non-linear terms (Eq. (19) and Eq. (20)).

(19) \

[ q 1 + ~ q 4 = [qq4 + 4[qq3[qr+~f -

Once T, and T, are obtained for a given time step, the soil moisture can also be

. . , ,

56 D. Lo Seen et al./Agricultural und Forest Meteorology 83 (1997) 49-74

calculated using Eq. (17) and Eq. (18). The two component temperatures then allow the calculation of the aerodynamic temperature To using Eq. (111, as well as the total outgoing longwave radiation, which in turn is used to estimate the radiative temperature Tr by considering an average surface emissivity of 0.97.

2.4. Resistances

The Shuttleworth and Wallace (1985) approach adopted here involves the use of five resistances. For the present study, except when more appropriate formulations are available in the literature, the resistance formulations used generally follow those found in Shuttleworth and Gumey (1990). Each resistance formulation is briefly described in the following:

2.4.1. Resistance rac Assuming the eddy diffusivity and wind speed attenuation are the same inside the

canopy, and that energy is exchanged by molecular diffusion through a laminar layer around the leaves, the bulk boundary layer resistance to heat and water vapor in the canopy, is computed according to Choudhury and Monteith (1988).

1 (21)

2.4.2. Resistance ros The aerodynamic resistance between ground surface and within canopy source height

is estimated using the approach proposed in Shuttleworth and Gurney (1990), where the eddy diffusion coefficient, which is assumed to decrease exponentially in the canopy, is integrated between height = O and height = z, + d. The dependence of this resistance on plant density is accounted for by relating the roughness length of the canopy z, and the zero plane displacement height d to the leaf area index (Eq. (421, Eq. (431, in Shuttleworth and Gumey, 1990).

h r, =

where,

and


2.4.3. Resistance raa The aerodynamic resistance between within canopy source height and above canopy

reference height is estimated with the method proposed by Mahrt and Ek (1984) which takes into account the influence of atmospheric stability.

1 raa = -

Cq ua

The exchange coefficient Cq depends on atmospheric stability which can be expressed in terms of a Richardson number Ri (unstable case: Ri < O, stable case: Ri > O):

For the unstable case, Cq is given by: r 1 2

with

while for the stable case, C, is given by: 2

k 1

cq=[ln[zrd-:+zo) 1 (1 + 15Ri) ( l +5Ri) '12

As the Richardson number depends on the ground surface temperature q, the aerodynamic resistance needs to be computed using an iterative procedure.

2.4.4. Resistance rsc The bulk stomatal resistance of the canopy is expressed as the proáuct of a minimum

stomatal resistance rSmin and different factorstwhich are always 2 1, and which vary in time. As in Noilhan and Planton (1989), the factors considered here are a solar radiation factor f i , a water stress factor f2, a factor related to the pressure deficit of the atmosphere f 3 , and an air temperature dependence factor f4.

rsc = zfl(R: )f2( w 2 ) f 3 ( e * ( T ) - ea)f4(k - Ta) (30)

58 D. Lo Seen er al./Agricultural and Forest Meteorology 83 (1997) 49-74

with

I 1 when wz ’ Wfc

when wfc z w2 z wwp ( Wfc - ww,)

fZ(W2) = ( wz - wwp) I when wz < wwp I %

and

1

1 - O.O016( Tc - T,)’ ar, - T,) =

(32)

(33)

(34)

2.4.5. Resistance rss Evaporation from a soil surface is the result of complex processes occumng inside a

porous medium and at its interface with air. Numerous empirical formulations based on in situ data have been proposed to relate the soil surface resistance to the near surface soil moisture content. (See Mahfouf and Noilhan, 1991, for a comparative study of different formulations.) It is clear that the relationships proposed depend on the soil textures used in the different studies, as well as on the thickness of the soil surface over which the moisture content is averaged (Kondo et al., 1990). The formulation used in the present study assumes a simple linear relationship between r,, and the surface soil moisture as in Camillo and Gumey (1986):

‘

r,, = 414O( wsat - w,) - 805 (35)

2.5. Vegetation growth model

The model used to simulate herbaceous vegetation growth in the Sahelian site under study is taken from Mougin et al. (1995). The total standing aboveground biomass present in a given day during the growing season is the sum of green biomass BG and dead biomass B,, both expressed in kilogram dry matter per hectare (kg DM ha-’). The amount of green biomass changes in time according to the balance between gross photosynthesis P g , the incremental term and respiration R, and senescence S, the


decremental terms (Eq. (36)). Similarly, dead biomass increases with the senescing of green material, and decreases due to litter production L (Eq. (37)).

At the beginning of the season, when the surface soil moisture is above wilting point for 5 consecutive days, vegetation growth is made to start with an initial green biomass BG(0). Thenceforth, the values of BG and B,, are calculated with a daily time step using Eq. (36) and Eq. (37). Gross photosynthesis Pg is given by the product of intercepted photosynthetically active radiation (PAR), a conversion factor cg which can be considered as a growth efficiency in optimal temperature conditions and in the absence of water limitation, and two terms which account for the influence of water availability and temperature on vegetation growth.

Pg = PAR.&, .&J- (F , ) . f (T , ) ( 3 8 )

with 1 .64rS,, + r,

f(FP) =

1.64rsmin( 1 + [ + r ,

and

f( c) = 1 - 0.0389( Topt - c)

( 3 9 )

Total respiration R , is written as the sum of photorespiration R, , and dark respiration which can be further identified as being composed of construction respiration R, and maintenance respiration R,. Photorespiration is estimated as a constant fraction p r of gross photosynthesis for C3 grasses, and is neglected for C4. Construction respiration is proportional to gross photosynthesis, and maintenance respiration, to green biomass.

R , = R, + R , i- R , (41)

R , = p r . Pg ( 4 2 )

R c = ( l - Y G ) ( l - p r ) P , ( 4 3 ) R , = mYG BG ( 44)

Throughout the growing season before pea$ biomass, senescence is roughly estimated as a constant fraction of the green biomass (a constant senescence rate SI, except when the vegetation suffers a severe stress, in which case the senescence rate follows a Q10-type relationship with plant water potential F,. At seed maturation, the senescence rate is made to increase drastically to simulate the fapid drying of the vegetation after peak biomass.

,

60 D. Lo Seen et al./Agricultural and Forest Meteorology 83 (1997) 49-74

The standing dry vegetation eventually reaches the litter pool under the mechanical effects of rain, wind, animals, etc. The modeling of litter production and decomposition, which would have been useful in the study of N cycling, is not included here. A constant value is used for litter production in order to simulate the decrease of total standing biomass at the beginning of the dry season. The growth and distribution of the root system is also not modeled implicitly; it is assumed that the rooting system is well developed enough not to limit the extraction of the water needed by the vegetation at any time during the growing season.

2.6. Coupling the vegetation growth submodel with the water and energy balance submodel

Closely related to the amount of latent heat coming from the canopy (transpiration) is the amount of CO, absorbed by the vegetation in an inverse pathway of the water flow through the stomates. In general, and especially in the arid and semiarid grasslands, vegetation growth depends on the water status of the plants. On the other hand, the water and energy balance depends on how the vegetation influences the boundary layer in which the transport processes are taking place. Here, the coupling of the vegetation growth model with the water and energy balance model is performed simply by exchanging the necessary variables between the models (see Fig. 1). As the vegetation growth model runs with a daily time step and the water and energy balance model with an hourly time step, the LAI and h needed for the calculation of the resistances every hour are considered constant throughout a given day. Conversely, TC and Fp used in the vegetation growth model are computed from hourly values; the daily canopy temperature is taken as the average of hourly temperatures, whereas the daily equivalent vegetation water potential is iteratively estimated from the cumulated daily transpiration, as being the potential necessary to extract from the soil (with soil moisture W) enough water to balance daily transpiration (Camillo and Schmugge, 1983):

a,

"

with

, , i , '

3. Application of the model

The one-dimensional model presented above has been tested using meteorological data and flux measurements acquired during the HAPEX-Sahel experiment, Niger, in 1992 (Prince et al., 1995). The objective was to determine whether the vegetation


growth and the water and energy balance submodels interact satisfactorily throughout the growing season, and whether simulations of energy fluxes as well as biomass compare well with measurements. This would then constitute a partial validation of the model, allowing a certain degree of confidence in the simulations obtained for other important variables which could not be monitored during the experiment. The energy fluxes were estimated using the energy budget/Bowen ratio method based on air temperature and vapor pressure measurements made at two different heights. A complete description of the instrumental setup and the data acquisition procedure can be found in Monteny et al. (1996). The fluxes and meteorological data (air temperature, air humidity, wind speed and incoming radiation) used are hourly values computed from 20-min averages of acquisitions made every 10 s. Rainfall data used are daily totals obtained with the nearest rain gauge of the EPSAT network (Lebel et al., 1992). As hourly values are needed in the model, the daily total is arbitrarily distributed aver 3 h during late evening. The consequence of this bias on the simulations is not known but is suspected to be important only when rain intensity is high; significant run-off may then occur and is not accounted for in the equations, as it may happen that soil saturation is not reached when the same amount of precipitation is distributed over a longer period of time.

b

3.1. The site during the growing season

Simulation is made to start before the first rains (beginning of June) and runs uninterrupted throughout the growing season until the vegetation has dried out (Novem- ber). The rainy period itself lasted around 3 months and for that particular site it brought a total of about 418 mm. Vegetative growth occurred after DOY 220, and peak biomass was reached around DOY 280. During that period, rainfall was well distributed leaving no significant interval of prolonged drought (Fig. 3(a)). However, periods of more than 5 consecutive days without significant rainfall were not uncommon, such that situations of water stress as well as water abundance have both been encountered during the season. Aboveground biomass measurements made regularly (approximately every 10 days) during the growing season showed that +e vegetation growth stages were not critically affected by any severe climatic event. In Fig. 3(b) simulated biomass is compared to measured biomass. The average amount of C3 vegetation with respect to that of C4 for the grassland site was estimated to be of the order of 35%. This value was used in the simulations. The simulation results for biomass are all found to be well within a(n optimistic) 15% error allowed on the biomas,s measurements and are therefore quite satisfactory.

Daily transpiration is obtained by summing hourly values of latent heat flux from the canopy (AE,) converted into millimeters per day. Fig. 3(c) shows how daily transpiration evolves over the season. It roughly follows the amount of green vegetation, and as expected from the formulations of resistances usèd, is further modulated both by climatic factors and the availability of water from the soil reserve. By the end of the season, transpiration reaches high values of more than 1.5 mm day-' for fully grown vegetation.

62 D. Lo Seen et al./Agricultural and Forest Meteorology 83 (1997) 49-74

150 200 250 300 350 DOY

2ooo: _ _ Green 0 : _.___ Dead

2 15001 m

f

x Y

i 1000;

E üi 500 -

o : . I , , f ,,-,,-.,-.;\, , , , , , :

150 200 250 300 350 DOY

Fig. 3. (a) Rainfall measured at a grassland site in the Central Est Supersite during the HAPEX-Sahel experiment, Niger, in 1992. (b) Simulated live and dead biomass, compared to biomass measured about every 10 days during the 1992 growing season (crosses represent biomass measurement&$) Simulated daily banspiration throughout the season.

t

3.2. Canopy structural variables

In the vegetation growth submodel, the main variables which express the change in the amount of vegetation present at the site throughout the season are the green biomass B,, and the standing dead biomass B,. These do not convey much information about the structure of the canopy, and the variables used in the resistance formulations which describe the canopy are only the L A I and h, the height of the vegetation. As the way a given amount of biomass is displayed in a plant is essentially species dependent, it is not readily acceptable to derive LAI and h from biomass directly. However, it can be assumed that for a given site containing a variety of species of herbaceous vegetation, an average value of Lkl and h can still be estimated from biomass. Here, an estimate of M is obtained from green biomass by using an average value of the specific leaf area SLAG equal to 70 cm2 g-' DM (0.0007 ha kg-' DM), whereas the empirical relationship used to estimate h is obtained by fitting a second order polynomial to measurements of vegetation height and biomass made during the season.


150 200 250 300 350 DOY

150 200 250 300 350 DOY

Fig. 4. Canopy structural variables derived from simulated green biomass: (a) leaf area index; (b) vegetation height (crosses represent measurements).

The empirical relationships used to estimate LAI and h are shown in Eq. (47) and Eq. (481,

LAI= SLAG.BG (47)

h = ao + a,BG + a,B; (48) with ao = 5.0, a , = 0.072, a2 = -0.000024, h in cm and BG in kg DM ha-'.The evolution of LAI and h during the season are shown in Fig. 4(a) and (b). Eq. (46) is found to underestimate the vegetation height for low values of biomass. The bias could have been corrected by weighting the data points in favor of the low values, but this would also suggest an abnormally high value of the height at vegetation emergence. Also, when the height is computed using the polynomial, it is arbitrarily prevented from decreasing from one day to another, even when green biomass actually decreases.

3.3. Comparison of energy fluxes simulations with measurements

The observation period during which energy fluxes were continuously measured started on DOY 202 (July 20, 1992) and lasted for more than 2 months, covering stages of vegetation installation, vegetative growth and fully grown vegetation. One week in the middle of the growing season is chosen to show more closely the different input data used by the model and the main variables and processes simulated, as compared to measurements. Fig. 5 shows the meteorological data used by the model during that particular week which can be considered a typical week of the rainy season, with 2 or 3 rainy days and enough soil moisture in the soot layer to sustain vegetation growth. The biomass present was about 350 kg DM ha-', the height of the vegetation, about 25 cm and the LAI was estimated to be of the orcler of 0.25 (see Fig. 4). Days 242 and 243 received, respectively, 14 and 15.4 mm of rainfall. DOY 243 was also generally cloudy during the day as shown in Fig. 5(c). The main vqriables simulated by the model on an hourly basis, namely the temperatures and soil moistures, are shown in Fig. 6. The difference between soil temperature and canopy temperature is quite important during the day, and is found to be of the order of up to more than 10°C, as shown in Fig. 6(a). The canopy temperature, however, is not greater than air temperature by more than a

. . , . , . , . . I . . , , . . .

I . . .... "" . . . .

~ .' . . . r.3

.. . .

242 244 246 248 250 240 250 242 244 246 DOY DOY

1200 40 h 2 1000 -

O v \ z 800 e 30

C L1

600 L

- - - a .-

U

400 c E 20 L 5 .-

.= 200 O - O 10 242 244 246 240 250 242 244 246 248 250

DOY DOY

Fig. 5. Hydrological submodel main input parameters used for 1 week in the middle of the growing season (DOY 242-249): (a) relative humidity of the air; (b) wind speed; (cl incoming shortwave radiation; (d) air temperature.

I . .... "..

Fig. 6. Simulated temperatures and soil moistures for 1 week in the middle of the growing season (DOY 242-249): (a) soil surface temperature q, canopy temperature T, and the temperature of the deeper soil layer T,; (b) radiative temperature T, and aerodynamic temperature To; (c) surface soil moisture w, and root layer soil moisture w2.

E

Ts- TC-- T2-.-

50 h

Y e 40 a e

f

v

c

30

20

3

242 244 246 248 250 DOY

us- GIZ-.-

(.> ] 0.40 ' ' ' ' ' " ' . " ' ' '

Tr- To--

(b) " ' " " ~ " ' ' '

h u v 2 40 a - e

30 E I-

20

I 0 1 242 244 246 248 250

DOY

--.-.-._.-._._.

242 244 246 248 250 DOY

LE (simulated- measured 0)

400 6oo>

h N < 200 3 v

O

t 1 -200 i

242 244 246 248 250 DOY

Rn fsimulated- measured 0) 800

600

;; 400 E \ z 200

O y - - - - - - -

- 2 o o t . . . I . . . I . , . I . . . 1 242 244 246 248 250

DOY

H (simulated- measured O) ' ' ' ' ' ' I " ' I " 600

'

400

h N < 200 3 v

O

.- c ? ,a 0.1

e

.- C

+

0.0 242 244 246 248 250

DOY

Fig. 7. Simulatea heat fluxes compared to fluxes measured with the Bowen ratio method, for 1 week in the middle of the growing season (DOY 242-249): (a) latent heat flux; (b) sensible heat flux; (c) net radiation flux; (d) hourly simulated transpiration.

L __


few degrees, thus avoiding the higher temperature ranges which may become inhibitory for some vital plant processes. The deep ground temperature, as expected, remains fairly stable (about 29°C) over such a short time period. Fig. 6(b) shows the difference between radiative surface temperature T, and aerodynamic temperature To, and gives an indication of the overestimation which would be obtained when expressing sensible heat flux in terms of T, instead of To over sparsely vegetated areas (Chehbouni et al., 1996). The evolution of soil moisture in the surface layer and the root layer are shown in Fig. 6(c). The rain events of DOY 242 and 243 have brought the surface soil moisture up to saturation level during the night, and by noon the following day, the soil surface has already dried completely. For the non-rainy days, moisture from the root layer diffuses upwards during the night such that the surface soil moisture nearly reaches the root layer soil moisture in the morning. The soil surface then quickly dries up during the first hours of daylight, and around 10:00-11:00, the soil is completely dry again. The deeper root layer shows much less moisture variation and acts mainly as the storage which provides moisture to the vegetation in replacement of water lost by transpiration. The soil moisture conditions of the surface indicates that during the day.the latent heat flux is mainly composed of transpiration except for the first hours of the day when evaporation from the soil is also important. This can be seen in Fig. 7(a) and (d), where the differences between the simulated latent heat flux and transpiration occur mainly in the

600 " " ' " * . ' I ' ' ' 600 " ' ' ' ' ' ' ' ' " ' ~

/ (b) /

/ n

: (a> /

N 400- . / E ,. \ \

3 3

w 200

. . / n 7 400- . f '.. Y

P 200 - .- z -I , z o - /

u u u O

- c - - z

YI - w 0 - , , , ,

rmse 47.27 W/m2 . rmse 47.82 W/m2 . -200 -200 . . . I . . . , . ' I ' ' '

200 400 600 -200 o 200 400 600 -200 o LE measured (W/m2) H measured (W/m2)

, rmse 48.56 W/m2

- 2 0 0 . . I , . . # . . . * . ' S . . .

-200 O 200 400 600 800 Rn measured (W/m2)

Fig. 8. Scattergrams showing comparison of measured and simulated daytime (8:00-18:00) hourly heat fluxes during the observation period: (a) latent heat flux; (b) sensible heat flux; (c) net radiation flux.

68 D. Lo Seen et al./Agriculrural and Forest Meteorology 83 (1997) 49-74

6 0 0 - E \ 5 400- U c -

200- .- YI

C = 0 -

morning. Fig. 7(d) is also to be paired with Fig. 3(c), to illustrate how the transpiration observed during that week compares with the evolution of daily transpiration over the season. Fig. 7(a)-(c) shows the comparison between simulated and measured energy fluxes. A fairly good agreement is obtained in general, but differences of more than 50 W m-' are quite common, especially for latent and sensible heat fluxes.

In order to assess more objectively the performance of the model over the season, measured and simulated hourly energy fluxes are compared for the whole observation period. Flux values derived from measured Bowen ratios which are either missing or inexplicably too high or too low (> 600 W m-' or < O W m-' for day-time latent and sensible heat flux values) have been replaced by time interpolated values, and when several erroneous hourly fluxes are obtained during 1 same day, all the flux data for that day are rejected. Out of 70 days of observation, only 5 days of data have been removed in that way, suggesting that the error screening used in the present study has not been very severe. Fig. 8 shows the scattergrams obtained for (a) latent heat, (b) sensible heat and (c) net radiation with day-time (8:OO to 18:OO) values only (when night-time values are included, better RMSE are artificially obtained due to the high percentage of near-zero values). The RMSE computed for the three cases give values which are all of the same order of magnitude (about 50 W m-'1. These values are satisfactory even though they are slightly higher than the standard error tolerance normally associated

,

6001 " ' a " ' " ' I " ' 1 6001 ' ' ' ' " I : " I " ' I

/ , rmse 23.22 W/m2 rmse 25.68 W/m2

-200 . . . t . . . t , . , 1 . . . -200 . . . I , , , . I , , '

200 400 600 -200 o 200 400 600 -200 o LE measured (W/m2) H measured (W/m2)

800 ' ' ' ' ' ' " ' " " ' " ' ' ' I / t (cl / ,

/ rmse 29.83 W/m2

-200 . . . , . . . t . . . I . . . I . . -200 O 200 400 600 800

Rn measured (W/m2)

Fig. 9. Scattergrams showing comparison of measured and simulated daily averages of daytime (8:00-18:00) heat fluxes during the observation period: (a) latent heat flux; (b) sensible heat flux; (c) net radiation flux.

D. Lo Seen ef al./Agricultural andForest Meteorology 83 (1997) 49-74 69

with energy fluxes measured using the Bowen ratio method. It has been shown that HAPEX-Sahel hourly sensible heat flux and latent heat flux measurements have confidence limits of +15% and +20%, respectively (Lloyd et al., 1996). When measured and simulated daily average fluxes are plotted (Fig. 9) better RMSE values are obtained, but it becomes also more evident that the model somewhat underestimates net radiation and sensible heat in favor of latent heat flux (in both cases, a line fitted to the data points lies about 35 W m-2 below the 1:l line). This tendency could be minimized or reversed by an appropriate calibration of resistances like rss and r,,, as well as relationships between soil thermal characteristics (heat capacity and thermal conductivity) and soil moisture. Unfortunately, the measurements necessary to carry out such calibrations have not been made at the time of the experiment. However, even with a better calibrated model, it is not certain that the accuracy of the simulations can be significantly increased. Given the relative simplicity of the 1-D model and the long period of uninterrupted simulation which characterizes this experiment, the model can be considered able to satisfactorily and realistically simulate the main processes occurring in a semiarid grassland.

4. Discussion and perspective

A model describing the major land surface processes occurring in semiarid grasslands has been presented in this paper. The model couples the water and energy balance of a sparsely vegetated surface with the vegetation growth and soil moisture and thermal dynamics. This coupling ensured a consistency between root uptake, transpiration and photosynthesis, as well as between 'rapid' (temperature, moisture content) and 'gradual' (amount of vegetation) changes in the state of the surface. Model simulations of biomass over the growing season are found to be within a 15% error margin allowed on biomass measurements. Hourly values of net radiation, as well as latent and sensible heat fluxes are simulated with an RMSE of less than 50 W m-2. Given the relative simplicity of the model and the long period of uninterrupted simulation, these results are considered satisfactory. However, additional field measurements would be beneficial to calibrate resistance formulations, and relationships between soil thermal properties and soil moisture, in order to correct a slight underestimation ( - 35 W m-2) of sensible heat flux in favor of latent heat flux.

The evolution of the state of the surface during the growing season is described in the model using variables that include soil moisture, leaf area index, vegetation height and temperature of the soil and canopy, which' are variables commonly used as inputs in radiative transfer modeling. This would enable the land surface process model to be used with radiative transfer models to study the sensitivity of remote sensing observations to varying surface conditions and associated processes. Ongoing research based on this modeling approach is directed towards the incorporation of remote sensing data in controling simulations of land surface processes. Through such studies, the surface variables and parameters by which the land surface process model may be controlled using remote sensing data can be objectively identified.

70

Acknowledgements

D. Lo Seen er al./Agriculrural and Forest Meteorology 83 (1997) 49-74

This work was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Field data supplied by contributors to the HAPEX-Sahel experiment database are gratefully acknowledged. DL was at JPL as a National Research Council Resident Research Associate.

Appendix A. Notation

A S . Variables

BCì* B D

Cl* c2

Aboveground standing herbaceous biomass, green and dry (kg DM ha-') Coefficient used in the surface soil moisture time dependent equation (C,(dimensionless) = 0.082 ( w , , , / ~ , ) ~ ~ ~ ~ ~ ; C,(dimensionless) = 3.9w2/(w,,, - w; + O.OOl), value estimated for sand, as in Noilhan and Planton, 1989)

AE, AE,, AE, Latent heat flux above the canopy, from the canopy and from the ground (W m-2)

G Ground heat flux (W m-2) H , H,, H, Sensible heat flux above the canopy, from the canopy and from the

ground (W m-') L Litter production (kg DM ha-' day- '1 LAI Leaf area index (m2 m-2) P Mass of precipitation reaching the soil surface per unit area and unit

time (kg m-' s-I) PAR Photosynthetically active radiation (W m-')

Gross photosynthesis (kg DM ha-' day- ') R,, R , , , R , , Net radiation flux into the canopy + ground, into the canopy and into

the ground (W m-2) R,, R,, R,, R , Construction and maintenance respiration, photorespiration and total

respiration (kg DM ha-' day-') Longwave radiation flux at the top of the canopy (W m-2) Shortwave radiation flux at the top of the canopy (W m-2) Senescence (kg DM ha- ' day- I) Air temperature at above canopy reference height (K) Temperature of the canopy (K) Daily average temperature of the canopy (K) Temperature of the ground surface (K) Air temperature at within canopy source height (K) Mean temperature of soil layer of depth d, (K) Daily transpiration (kg m-2 day- I)

Soil temperature at time step t (K) Zero plane displacement height for canopy (m)

I pg

Ri, R,1

r, S

T T, T,

T2 .;'

Tì-* T,', T,' d

E

r,

. .

D. Lo Seen et al./Agricultural and Foresr Meteorology 83 (1997) 49-74 71

Vapor pressure at above canopy reference height (mbar) Vapor pressure at within canopy source height (mbar) Saturated vapor pressure at temperature T (mbar) Vegetation height (m) Richardson's number (dimensionless) Aerodynamic resistance between within canopy source heig..t and above canopy reference height (s m-I) Bulk boundary layer resistance of the canopy (s m-'> Aerodynamic resistance between ground surface and within canopy source height (s m-') Bulk stomatal resistance of the canopy (s m- I ) Surface resistance of the ground (s m-I) Wind speed at reference level zref (m s-I) Wind speed at top of the canopy (m s- ' Friction velocity (m s-') Characteristic leaf width (m) Volumetric soil moisture content of ground surface and mean soil moisture content of root layer (dimensionless) Surface soil moisture when gravity balances capillarity forces; it is equivalent to T2 in the restore t e m of the soil moisture time dependent equation; it depends on soil type, wsat and w2 (dimensionless) Roughness length of canopy (m) Roughness length of substrate (m) Daily average soil water content (dimensionless) Bulk canopy water potential and soil water potential in the root zone (bar) Daily equivalent bulk canopy water potential (bar) Efficiency of interception of PAR by the canopy, estimated from B, as in Mougin et al. (1994): ì?,(dimensionless) = 0.2 Log$ + BG/180) Ground surface albedo, estimated from soil moisture content as in Ben Mehrez (1990): a,(dimensionless) = 0.28 - 0.21( ws/wsat> Shortwave radiation shielding factor of ground by the canopy, estimated from LAI as in Kanemasu et al. (1977): uf(dimensionless) = 1 - exp( - 0.4 X LAI) Heat capacity of soil, estimated from soil moisture content as in DeVries (1963): p,cs (J K-' m-3) = 4.18 lo6 (0.3 + w), where w = w, or w2 Thermal conductivity o$ soil, estimated from soil moisture content as in DeVries (1963) and Ben Mehrez (1990): A, (W m-' K-') = 0.06 + O . ~ ( W ) ' / ~ , where w = ws or w2

A.2. Constants

cP C I ? C2

Specific heat of air at constant pressure (- 1012 J kg-' K- '1 Constants used in the ground temperature time-dependent equation (cI = 27r1l2, c2 = 27r, dimensionless)

8

D. Lo Seen et al./AgriculturaI and Forest Meteorology 83 (1997) 49-74

Acceleration due to gravity (9.81 m s-’1 von Kármán’s constant (0.4, dimensionless) Psychrometric ‘constant’ ( - 0.66 mbar K- ’ ) Latent heat of vaporization (- 2.45 lo6 J kg- ‘1 Density of air (- 1.2 kg m-3> Density of water ( - 1000 kg m-3) Stefan-Boltzmann constant (5.6705 lo-* W m-’ K-4> l-day period (86 400 s)

o-

A.3. Parameters

m Pr

SLAG S

Exponent in power function relating soil ‘matric’ potential to soil moisture content (3.79, derived from soil texture (clay = 6%, sand = 85%), Cosby et al., 1984) Initial aboveground biomass (30 kg DM ha-’) Percentage by mass of C3 species present (35%) Normalization depth for surface layer (10 cm), thickness of root layer (60 cm) Maintenance coefficient (0.02 day-’ ) Fraction of gross photosynthesis used as photorespiration (0.4 day- ’ for C3 species, negligible for C4 species) Minimum and maximum stomatal resistance (100, 5000 s m-’> Resistance of the mesophyll (183 s m-’, estimated from %C3) Total resistance to water flow in the plant and at the soil-root

interface, normalized to units used (1.03 bar kg-’ m2 day) Specific leaf area (0.0007 ha kg-’ DM) Senescence rate (0.003 day- ’ ) Canopy temperature at maximum photosynthesis (38°C) Soil moisture at saturation (0.3821, estimated from soil texture (clay = 6%, sand = 85%), Cosby et al., 1984) Volumetric soil moisture content at wilting point (at 16 bar) and at field capacity (at 0.1 bar) (0.0363, 0.1388) Fraction of the total mass of carbon used, incorporated into new structural tissues (0.75) Wind speed and eddy diffusivity attenuation constant in the canopy (2.5, dimensionless) Canopy albedo (0.22) Canopy emissivity and ground surface emissivity (0.98, 0.96) Growth efficiency in optimal conditions of water availability and temperature (3.6 g DM W-‘ day-’ or 4.17 g DM MJ-’) Canopy water potential corresponding to 50% stomatal closure (15 bar) Soil water potential at saturation (-0.00216 bar, estimated from soil texture (clay = 6%, sand = 85%), Cosby et al.; 1984)

D. Lo Seen et al./Agrìcultural and Forest Meteorology 83 (1997) 49-74 73

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