Carbon-water-energy relations for selected river basins

Adv. SpaceRes. Vol. 26, No. 7, pp. 1091-1099,200O 0 2000 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/00 $20.00 t 0.00 PII: SO273-1177(99)01124-2

Pergamon www.eIsevier.nI/locate/asr

CARBON-WATER-ENERGY

RELATIONS FOR SELECTED RIVER

BASINS Bhaskar J. Choudhury Hydrological Sciences Branch Laboratory for Hydrospheric Processes NASA Goddard Space Flight Center Gregbelt, MD 20771, USA

ABSTRACT Total evaporation couples water and energy balance equations, while transpiration, which is the major component of total evaporation over most of the global land surface, is strongly determined by the rate of carbon assimilation. A model combining the rate of carbon assimilation with water and energy balance equations has been developed, and run using satellite and ancillary data for 48-month period (January 1987 to December 1990) over global land surface. Relations between net carbon accumulation by terrestrial plant communities, evaporation, and net radiation are presented for 15 largest river basins of the world, and evaluated against those derived from field measurements. 0 2000 COSPAR. Published by Elsevier Science Ltd.

INTRODUCTION Total evaporation couples water and energy balance equations (Brutsaert, 1982), while transpiration, which is the major component of total evaporation over most of the land surface, is determined strongly by the rate of carbon assimilation (Monteith, 1988). Consequently, it is desirable to consider carbon assimilation in doing energy and water balance calculations. A biophysical process-based model, combining the rate of carbon assimilation with water and energy balance equations, described previously (Choudhury and DiGirolamo, 1998) has been run using spatially representative meteorologic and surface data for 48-month period (1987-1990) over the global land surface. The essential aspects of the model and the data used in the calculations are presented below, while full details can be found in Choudhury and DiGirolamo (1998). Then, relations between evaporation, net radiation, net carbon accumulation and photosynthetically active radiation absorbed by vegetation for 15 largest river basins of the world (namely, Amazon, Congo, Mississippi, Ob, Parana, Nile, Yenisey, Lena, Niger, Amur, Changjiang, Mackenzie, Volga, Zambeze, and St. Lawrence) are presented and discussed.

MODEL DESCRIPTION Water Balance Eauation Daily change of root-zone available soil moisture has been calculated from the following equation:

w(i+l> = w(j) + pQ>+ s,(i) - I(i)

1091

- Q,(j) - D(j) - E,(j) _ T(j)

(1)

B. J. Choudhury

1092

where j is day number, W (i) is root zone available water at the beginning of day j, P (i) is precipitation, Sin (i) is snowmelt, I (i) is interception, Q, (i) is surface runoff, D (i) is drainage out of the root-zone, E, (j) is soil evaporation, and T (j) is transpiration for day j. All fluxes are expressed as daily totals in units of mm. An analogous equation is used to calculate daily change of water equivalent of snow due to precipitation, interception, melt, and evaporation. Comuonents of Water Balance Interception has been calculated using the Horton’s model adopted for partial canopy cover: I=f*min(P,aP+b)

(2)

where f is fractional vegetation cover, and a and b are parameters dependent on vegetation type and rainfall intensity. The day index (‘j) appearing in Eq. (1) is implicit in Eq. (2) and in all following equations. Surface runoff has been calculated from the following equation (Schaake et al., 1996): Qs=I-12/(II+8)

(3)

where II is the daily total flux of water at the soil surface and 6 is the root-zone moisture deficit ( 6 = W, - W ). The maximum available water being W,, independent of time. Drainage out of the root-zone is calculated according to unit gravitational gradient, i.e., drainage is equal to soil hydraulic conductivity. Soil evaporation has been calculated to occur in two stages; the energy limited and exfiltration limited rates (Ritchie, 1972). The energy limited rate (Esl) is given by the Priestley and Taylor (1972) equation for evaporation ( E, ), adjusted for fractional exposed soil ( 1 - f ): Es1 =Eo(

1 -f)

(4)

The exfiltration limited rate ( E,, ) is calculated using Philip’s equation: Es2 = s [ tos5 - (t-l)Oe5 ] where s is the desorptivity and t is time (day number). The exfiltration limited rate is not allowed to exceed energy limited rate, and soil evaporation does not occur when snow water equivalent is greater than zero. The Penman-Monteith equation, adjusted for fractional vegetation cover, is used to calculate transpiration under well-watered conditions ( T, ): Tu=Epf where E, is given by, { A Rni + p cp D’ / re } Ep = _______________________-_____________ (7) h I A+y(rc+rH)/re 1

where h is latent heat of vaporization, A is the slope of saturated vapor pressure with respect to air temperature, y is psychrometer constant, Rni is isothermal net radiation (i.e., surface temperature being equal to the air temperature), p is the density and cp is the specific heat at constant pressure of air, D’ is the vapor pressure deficit, re is the effective resistance for heat transfer, given by, where rR is the radiative transfer resistance, given by

‘e

-l = rB‘l + rR-l

(8)

Carbon-Water-Energy

1093

Relations

(3 is the Stefan-Boltzman constant, E is the longwave emissivity and T, is the air temperature, the aerodynamic resistance for heat transfer, given by

and rJ_Jis

lY,=h(Z/ZH)/(kU*)

(10)

where z is the effective height where friction velocity ( u* ) is determined, zJ_Jis the roughness height for heat transfer and k is von Karman’s constant, and rc is the daytime mean canopy stomata1 resistance, which has been calculated from daytime mean rate of carbon assimilation by the canopy ( A, ) as:

(11)

r,=y/A, where y is the slope relating leaf stomatal conductance (which is the inverse of resistance) assimilation rate. A, has been calculated from the following equation: Ac=(Am/K)Zn[(Am+eqalKS)/{

Am+eqalKS(

l-f)]]

to the

(12)

where A, is the maximum leaf assimilation rate, K is the extinction coefficient of photosynthetically active radiation ( PAR ) within the canopy, eq is the quantum efficiency, al is PAR absorptance of leaf and S is daytime mean PAR incident on the canopy. Eq. (11) establishes a strong physiological link between transpiration and carbon assimilation (Tanner and Sinclair, 1983; Lloyd and Farquhar, 1994). Thus, calculations of gross and net primary productivity are integral part of the model. Soil water stress affects A, and so also transpiration. Unstressed assimilation or transpiration occurs until the relative water content ( W / W, ) remains above 0.4, below which the rates are decrease linearly with (W/W,). Enernv Balance Eauation Net radiation (R,), sensible (H) and soil heat (G) fluxes have been calculated following Budyko (1974) and Mintz and Walker (1993). The following equation is used to calculate G ( W m-* ) for month J: G = 48.5 ( T, (J+l) - T, (J-l) ) /At

(13)

where T, (J+l) and T, (J-l) are, respectively, the mean monthly air temperature of month (J+l) and (J-l) and At is the number of days in the two months. Now, R, and H are obtained by solving the following simultaneous equations:

where E is total evaporation,

R,=R,i-H(rH/rR)

(14)

R,=RE+H+G

(15)

and rH and rR are defined above (Eqs. 9 and 10).

Net Primarv Productivitv The daily net carbon accumulation by plants ( C ) (or net primary productivity for a year) is given by the difference of daily total gross assimilation ( A,,, ) and respiration ( R ) (Amthor, 1989):

C =(Ag,t-W

(16)

where A,,, is obtained by integrating A, (Eq. 12) over the day. As a first approximation, R has been taken to be a constant fraction of Ag,t; the fraction varying with vegetation type (Kira, 1975; Monteith, 1981;

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B. J. Choudhury

McCree, 1988; Bunce, 1989). The effect of soil water stress on A, t is considered as discussed above for transpiration. Model Parameters All model parameters have been prescribed as average values determined from published field measurements; none of the parameters has been determined through calibration. Thus, for example, the maximum available water in the root-zone has been prescribed to be 200 mm, and the interception parameters (a and b) have been prescribed to be, respectively, 0.15 (-) and 1.O (mm) for deciduous forests, 0.2 (-) and 1.5 (mm) for coniferous forests, and 0.07 (-) and 0.7 (mm) for crops and grasses in temperate regions. The values of other model parameters can be found in Choudhury and DiGirolamo (1998). Land use and land cover data of Matthews (1983) have been used to provide the spatial distribution of vegetation-type dependent parameters over the global land surface. Data for Running the Model The data used to run the model are derived from satellite observations, four dimensional data assimilation (4DDA) and ground measurements for 48-month period (1987-1990). Surface albedo, solar and photosynthetically active radiation and fractional cloud cover are derived from data produced under the International Satellite Cloud Climatology Project (Whitlock et al., 1995). Air temperature and vapor pressure have been derived from Tiros Operational Vertical Sounder (TOVS) observations (Susskind et al., 1997; Choudhury, 1997). Friction velocity and surface air pressure are derived from 4DDA (Schubert et al., 1995). Precipitation data are based on guage measurements and satellite observations as produced under the Global Precipitation Climatology Project (WCRP, 1996) and International Satellite Land Surface Climatology Project (Meeson et al., 1995). Fractional vegetation cover has been derived from visible and near-infrared reflectances observed by the Advanced Very Hugh Resolution Radiometer (AVHRR) corrected for sensor degradation and atmospheric effects (Choudhury and DiGirolamo, 1998). These data have varied spatial resolution; highest resolution being that for fractional vegetation cover (0.25O x 0.25O latitude x longitude cell). Uncertainties in some of these data sets are can be found in Choudhury (1997). All data are mean monthly values; precipitation data have been disaggregated to daily values (Meeson et al., 1995). RESULTS AND DISCUSSION The calculated mean and the range of monthly total evaporation for the Amazon, Mississippi, Volga, and Ob river basins are compared in Figure 1 with the evaporation estimated using the atmospheric water budget method (Kuznetsova, 1990; Matsuyama, 1992; Roads et al., 1994), and some statistics for quantitative evaluation of this comparison are given in Table 1. These basins cover a wide range of vegetation and climatic conditions (tropical humid, temperate, and boreal). While the atmospheric water budget estimates have their own uncertainties, these estimates provide an independent assessment of evaporation. It is evident from the comparison that the present calculations are providing a reasonable depiction of seasonal variation and annual total evaporation.

Table 1. Sample Statistics for Evaluating the Comparison of the Present Monthly Values of Total Evaporation with the Atmospheric Water Budget Estimates. The Statistics given are: Explained Variance (r2), Intercept (a; mm mo-l) and Slope (b) for Linear Least Square Regression, Mean Absolute Error (MAE, mm mo-l) and Per Cent Difference of Annual Evaporation (%) Basin

r2

a

b

MAE

%

Amazon Mississippi Ob Volga

0.00 0.87 0.88 0.93

84 -6 !;

0.03 1.07 0.94 1.11

15 11 12 8

9 7 27 2

All 4 Basins

0.86

5

0.89

12

2

Carbon-Water-Energy Relations

1095

160 140 120 100 60 60 40 20 0 120 100 60 60 40 20 0 -20 DeC

JUI

Time

Jlllle

D8C

Time

Fig. 1. Mean and range of monthly total evaporation calculated from the biophysical derived from the atmospheric water budget analysis for four river basins.

model and those

Assuming that long-term average evaporation would not exceed either precipitation or net radiation, one can stipulate from dimensional analysis of long-term average water and energy balance equations that evaporative fraction @ (ratio of evaporation and water equivalent of net radiation) might be related to a dryness index A (ratio of precipitation and water equivalent of net radiation) as (Turc, 1954; Choudhury, 1998): @=A/(

1 +Aa)lla

(17)

where a is a parameter, which varies with the spatial scale or variabilities of precipitation and net radiation. The value of a was found to be 2.5-2.7 for spatial scales of micrometeorologic observations (c, 1 km), while it is about 1.7-2.0 for river basins (c.100 km). The annual values of cf, and A for the 15 river basins are shown in Figure 2, together with Eq. (17) for a = 2. Relationship between the annual net primary productivity (NPP) and total evaporation (E), and photosynthetically active radiation absorbed by vegetation during the growing season (APAR) for the river basins are shown in Figures 3 and 4, respectively. The water use efficiency (i.e., the ratio of NPP and E) is calculated to be about 11 t (carbon) ha-t produced per meter of evaporation at the high end of the NPP, while it is about 8 t (carbon) ha-l produced per meter of evaporation

1096 1.4

4-

1.2

-____. 3a ri ”

1 .o

5

0.8

R,

[l + @z,*p %

hE=R,

_5 i? F

0.6

G f

0.4

s

W

0.2

0.0

T 0.0

0.2

0.4

DRYNESS

1.0

0.8

0.6

INDEX

1.4

1.2

1.6

( = 1P+,,)

Fig. 2. Relationship between evaporative fraction and dryness index. 16

II

’

14 -.

4

I

,

t

Y = -1.7 + 13.2 x

12 -_ i 2, ‘; m f s %

10 --

8 --

0 c 6 --

0

! 0

I

0.2

I

0.4

I

I

0.8

0.6

TOTAL NAPORATION

I

1.0

1.2

(m yf I)

Fig. 3. Relationship between annual net primary productivity

and total evaporation for 15 river basins

1097

Carbon-Water-Energy Relations

8

8

0

1

3

2

ABSORBED PAR (GJ mm2yr-l)

Fig. 4. Relationship radiation.

between annual net primary productivity

and absorbed photosynthetically

active

at the low end of the NPP. The average water use efficiency for these river basins is about 10 t (carbon) ha-l produced per meter of evaporation (which is equivalent to 2 g (dry matter) rnT2 per millimeter of evaporation), and this value of the efficiency agrees well with the previous estimate of the mean value for different types of vegetation, continental and global averages (Choudhury, 1994). The intercept of NPP vs. E is considered to be approximately equal to soil evaporation (Fischer, 1979), and, based on this interpretation, average annual soil evaporation for the river basins appears to be about 129 mm. Annual soil evaporation calculated from the model varied among the basins, e.g., 88 mm for the Amazon, 101 mm for the Ob, 113 mm for the Lena, 159 mm for the Mississippi, 162 mm for the Congo, and 179 mm for the Nile. A relationship similar to that shown in Figure 3 was obtained when annual NPP was plotted against annual transpiration. The transpiration efficiency (ratio of NPP and transpiration) was found to be about 18 t (carbon) ha-l produced per meter of transpiration. The transpiration efficiency of crops averages to be about 19 t (carbon) ha-l produced per meter of transpiration (standard deviation of 6 t ha-l m-l , n=17) assuming 45% of the dry matter is carbon (Tanner and Sinclair, 1983; Gregory et al., 1992). It is clear from Figure 4 that APAR is a significant determinant of NPP, and, in fact, many studies of NPP assume that the radiation use efficiency (which the slope of NPP vs. APAR) is a conservative quantity to determine NPP. Field observations give the efficiency value of about 1 and 1.5 kg (carbon) per GJ APAR for, respectively, C, and C4 crops, while the efficiency for woody vegetation appears to be about 0.5 kg (carbon) per GJ APAR (Ruimy et al., 1994). The radiation use efficiency values for some river basins are given in Table 2. It appears that while transpiration efficiency of these river basins is comparable to that for agricultural crops, the radiation use efficiency is much lower than that for crops.

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B. J. Choudhury

Table 2. The Radiation (1987- 1990 average)

Use Efficiency

(RUE; kg (carbon) per GJ APAR) of Selected River Basins

Basin

RUE

Amazon Congo Lena Mackenzie Mississippi Niger Ob Zambeze

0.44 0.49 0.49 0.45 0.47 0.46 0.46 0.41

SUMMARY A biophysical model to calculate evaporation using satellite and ancillary data was presented, and was used to obtain evaporation from 15 largest river basins of the world for four years (1987-1990). The model additionally provided net radiation and sensible heat flux, complementing evaporation, and net primary productivity. The dryness index (i.e., ratio of precipitation and water equivalent of net radiation) was shown to be a significant determinant of the evaporative fraction (i.e., ratio of evaporation and water equivalent of net radiation). The water use efficiency based on total evaporation and transpiration were found to be, respectively, 10 and 18 t (carbon) ha-l per meter of evaporation (the former is equivalent to about 2 g (dry matter) me2 produced per millimeter of evaporation). The radiation use efficiency was found to be about 0.5 kg (carbon) per GJ APAR. ACKNOWLEDGEMENTS Great appreciation is extended to Drs. Shashi Gupta and Joel Susskind for providing substantial amount of meteorologic data used in this study. Dr. T. Oki provided digital templates for the river basins. Data processing assistance was provided by Nick DiGirolamo. REFERENCES Amthor, J. S., Respiration and Crop Productivity, 204 pp. Springer-Verlag, New York, NY (1989). Brutsaert, W., Evaporation into the Atmosphere, Reidel Publication, Boston, MA (1982). Budyko, M., Climate and Life, Academic Press, 508 pp. New York, NY (1974). Bunce, J. A., Growth rate, photosynthesis and respiration in relation to leaf area index, Annals of Botany, 63,459-463 (1989). Choudhury, B. J., Synergism of multispectral satellite observations for estimating regional land surface evaporation, Remote Sensing of Environment, 49,264-274 (1994). Choudhury, B. J., Global pattern of potential evaporation calculated from the Penman-Monteith equation using satellite and assimilated data, Remote Sensing of Environment, 61, 64-81 (1997). Choudhury, B. J., Evaluation of an empirical equation for annual evaporation using field observations and results from a biophysical model, Journal ofHydrology, (submitted) (1998). Choudhury, B. J. and N. E. DiGirolamo, A biophysical process-based estimate of global land surface evaporation using satellite and ancillary data. I. Model description and comparison with observations, Journal ofHydrology, 205, 164-185 (1998). Fischer, R. A., Growth and water limitation to dryland wheat yield in Australia: a physiological framework, Journal of the Australian Institute of Agricultural Science, 45,83-94 (1979). Gregory, P. J., D. Tennant and R. K. Belford, Root and shoot growth, and water and light use efficiency of barley and wheat crops grown on a shallow duplex soil in a Mediterranean-type climate, Australian Journal of Agricultural Research, 43, 555-573 (1992). Kira, T., Primary production of forests, in Photosynthesis and Productivity in DifSerent Environments, edited by J. P. Cooper, pp. 5-40, Cambridge University Press, New York, NY (1975).

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