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288 D. C. Goodrich et al. /Agricultural and Forest Meteorology 105 (2000) 181 -309 measurement periods. Due to limited availability of heat pulse velocity probes, sap flux measurements were not continuously made for the entire grow- ing season. The measurements alternated between the perennial Lewis Springs site and the ephemeral Escapule site (Schaeffer et al., 2000). To estimate C/W transpiration between, and outside the synoptic measurement periods, a model driven by more easily measured continuous variables is required. 4.2. Penman — Monteith (P —M) model for C/W transpiration The well -known P —M model (Monteith and Unsworth, 1990) was selected to model C/W transpi- ration throughout the riparian growing season. The P —M equation for evaporation is given by _ AA + pacpD/ra 1 �E A +y(1 +rclra) where XE is the evaporation (W m -2), A the slope of the saturation vapor pressure /temperature curve (kPa °C -1), A the available energy (Wm-2), Pa the density of moist air (kgm3), cp = 1013Jkg °C -1 the specific heat capacity of dry air under constant pressure, D the vapor pressure deficit (kPa), ra the aerodynamic resistance (s m -1), y the psychrometric constant (kPa °C -1), and r, the bulk canopy resistance (s m -1). In the above equation, A, pa, D, and y can be approximated by formulae described by Shuttleworth (1993), based on measurements of air temperature, Ta ( °C), relative humidity, RH ( %), and atmospheric pressure, P (kPa). These quantities were measured at the nearby mesquite site (Scott et al., 2000), and were found to reasonably approximate conditions in- side the C/W canopy. This assessment was based on comparisons to a limited set of measurements made from a 12.5 in tower inside the C/W canopy. Measure- ments from this tower were available in 1997 from DOY 190 to 290. For this period of time, the root mean square error (RMSE) and R2 between the vapor pressure deficit computed from measurements at the C/W tower and the mesquite tower were 0.26 kPa and 0.96, respectively. For air temperature, the RMSE was 1.21 °C, with R2 = 0.97 between the two towers. The available energy to the canopy is given by A = S J (1 — a) + Lnet — St (2) where SJ is the incoming solar radiation (W m -2), a the canopy albedo, Lnet the net long -wave radiation (W m -2), and St the temporary storage of energy into the tree itself (trunk and limbs) and the energy used in the photosynthesis process (W m -2). Because the bulk of the canopy is typically 10-20 in above the ground, soil heat flux contributions to the available energy for the canopy were considered negligible. The incom- ing solar radiation was measured over the mesquite site. Canopy albedo was estimated to be 0. 18, a value which has been measured over broadleaf oak trees (Bras, 1990). St was estimated to be 5% of the incom- ing solar radiation based on work by Moore and Fisch (1986) who found that St ranged between 0 and 10% of the net radiation available to a tropical forest. The net long -wave radiation contribution to the available energy was calculated from a formula provided by Shuttleworth (1993, p. 4.7). Because the P —M model only applies to tree transpiration, the net radiation was adjusted to account for the portion not intercepted by the leaves using a simple Beer's law relationship from Shuttleworth and Gurney (1990). This adjust- ment reduced the net radiation available to the canopy by 25 %. The aerodynamic resistance (ra) was assumed to be the sum of the turbulent resistance between the canopy and the atmosphere from turbulent eddies and the boundary layer resistance (Thom, 1975). Due to the relatively open nature of the cottonwood canopy, the turbulent canopy resistance is assumed negligible in comparison to the boundary layer resistance. Thus ra is assumed to equal the boundary layer resistance (rb). To estimate the boundary layer resistance, the model proposed by Choudhury and Monteith (1988) was used: 1 aatt w 3 /b = Lb (1 — exp( —watt)) U ( ) In this equation, L is the canopy projected leaf area index estimated to be 2.0 (Schaeffer et al., 2000). The quantity b was set equal to 0.0067ms -1/2. It is a scaling coefficient for leaf boundary layer resistance (Magnani et al., 1998). aatt is an attenuation coeffi- cient for wind speed inside the canopy, w = 0.05 in is a typical leaf width, and U the wind speed outside the canopy (measured at 10m above the ground at the mesquite site). The value for the wind attenuation