Water vapor flux density

A. If the average water vapor flux density of the leaves is 1 mmol m-2 s-1, what is the transpiration rate of the tree in m3 s-1 ... 

The mass difference between layers was divided by the cross-sectional area of the snow sample and the duration of the experiment, and the measured water vapor flux fm was obtained. The measured mass flux Mm was calculated from the density change divided by the duration of the experiment. 

The water vapor flux seems to affect significantly the growth rate of depth hoar snow. It seemed that water vapor transportation also caused a density change in snow. The initial and final density of each layer is illustrated in Figure 6. Before and after the experiment, the lost mass was only 0.5 %. The density of layer I (warmest) decreased. 

Figure 5 Re-expressed relationships between the water vapor flux and the growth rate seen in Figure 4. Previous result reported in Kamata et al (1999) was also shown to examine the density dependence.

The moisture flux g (kg/(m, s)) in the bentonite has a liquid and a vapor component. The liquid flux g, is proportional to the gradient of the pore water pressure P with a hydraulic conductivity k(S) that is a function of the degree of water saturation S. The flux is inversely proportional to the viscosity rj(T). The water vapor flux g, is proportional to the gradient of the water vapor density in the gas phases in the pores with a vapor conductivity factor D,(5) that is a decreasing function of S. The heat flux q (W/m ) has a conductive part with a thermal conductivity. /i(S). There is also a negligible convective part. We have... 

Figure 8. The high frequency nature of the vertical velocity (W), water vapor (q ), and CO2 densities (C ) at 2 meters above a soybean canopy during a 3 minute period. The illustration also shows instantaneous water vapor (W q ) and carbon dioxide (W C ) fluxes and the mean quantities for the 15 minute period from which these traces were taken. Data courtesy of Center for Agricultural Meteorology and Climatology, University of Nebraska, Lincoln, Nebraska, and Environmental Sciences Division, Lawrence Livermore National Laboratory, Livermore, California.

We will represent the flux density of water vapor diffusing out of a leaf by the transpiration rate. If we multiply this amount of water leaving per unit time and per unit leaf area, Jw> by the energy necessary to evaporate a unit amount of water at the temperature of the leaf, //vap, we obtain the heat flux density accompanying transpiration, jJji... 

How much of the heat load on a leaf is dissipated by the evaporation of water during transpiration For an exposed leaf of a typical mesophyte during the daytime, can be about 4 mmol m-2 s-1 (Chapter 8, Section 8.2F). In Chapter 2 (Section 2.1A), we noted that water has a high heat of vaporization, e.g., 44.0 kJ mol-1 at 25°C (values at various temperatures are given in Appendix I). By Equation 7.22, the heat flux density out of the leaf by transpiration then is... 

Equation 8.2 shows how the net flux density of substance depends on its diffusion coefficient, Dj, and on the difference in its concentration, Ac] 1, across a distance Sbl of the air. The net flux density Jj is toward regions of lower Cj, which requires the negative sign associated with the concentration gradient and otherwise is incorporated into the definition of Acyin Equation 8.2. We will specifically consider the diffusion of water vapor and C02 toward lower concentrations in this chapter. Also, we will assume that the same boundary layer thickness (Sbl) derived for heat transfer (Eqs. 7.10-7.16) applies for mass transfer, an example of the similarity principle. Outside Sbl is a region of air turbulence, where we will assume that the concentrations of gases are the same as in the bulk atmosphere (an assumption that we will remove in Chapter 9, Section 9.IB). Equation 8.2 indicates that Jj equals Acbl multiplied by a conductance, gbl, or divided by a resistance, rbl. 

As we can see from relations such as Equation 8.2 (J = gjAcj = ACjlrj), the conductances or the resistances of the various parts of the pathway determine the drop in concentration across each component when the flux density is constant. Here we will apply this condition to a consideration of water vapor concentration and mole fraction in a leaf, and we will also consider water vapor partial pressures. In addition we will discuss the important effect of temperature on the water vapor content of air (also considered in Chapter 2, Section 2.4C). 

The rate of water vapor diffusion per unit leaf area, Jw> equals the difference in water vapor concentration multiplied by the conductance across which Acm occurs (// = g/Ac - Eq. 8.2). In the steady state (Chapter 3, Section 3.2B), when the flux density of water vapor and the conductance of each component are constant with time, this relation holds both for the overall pathway and for any individual segment of it. Because some water evaporates from the cell walls of mesophyll cells along the pathway within the leaf, is actually not spatially constant in the intercellular airspaces. For simplicity, however, we generally assume that Jm, is unchanging from the mesophyll cell walls out to the turbulent air outside a leaf. When water vapor moves out only across the lower epidermis of the leaf and when cuticular transpiration is negligible, we obtain the following relations in the... 

Based on quantities in Figure 8-7, we can readily calculate the flux density of water vapor moving out of the lower side of a leaf. Specifically, j w is equal to SwalAc tal or g alAA al, for example... 

Generally, 70 to 75% of the water vaporized on land is transpired by plants. This water comes from the soil (soil also affects the C02 fluxes for vegetation). Therefore, after we consider gas fluxes within a plant community, we will examine some of the hydraulic properties of soil. For instance, water in the soil is removed from larger pores before from smaller ones. This removal decreases the soil conductivity for subsequent water movement, and a greater drop in water potential from the bulk soil up to a root is therefore necessary for a particular water flux density. 

During the daytime, a transpiring and photosynthesizing plant community as a whole can have a net vertical flux density of CO2 (/coz) downward toward it and a net vertical flux density of water vapor (71W) upward away from it into the turbulent air above the canopy. These flux densities are expressed per unit area of the ground or, equivalently, per unit area of the (horizontal) plant canopy. Each of the flux densities depends on the appropriate gradient. The vertical flux density of water vapor, for example, depends on the rate of change of water vapor concentration in the turbulent air, c, with respect to distance, z, above the vegetation ... 

The flux density of water vapor just above the canopy, which includes transpiration from the leaves plus evaporation from the soil, is often termed evapotranspiration. For fairly dense vegetation and a moist soil, evapotrans-piration is appreciable, usually amounting to 60 to 90% of the flux density of water vapor from an exposed water surface (such as a lake) at the ambient air temperature. The daily evapotranspiration from a forest is often equivalent to a layer of water 3 to 5 mm thick, which averages 2 to 3 mmol m-2 s-1 over a day. At noon on a sunny day with a moderate wind, Jw above a plant canopy can be 7 mmol m-2 s-1. Using Equation 9.4 (Ac v = 7wr ) and our value for of 30 s m-1, we note that over the first 30 m of the turbulent air... 

This volumetric water flux density directed upward at the soil surface equals (1 x 10-8 m3 m-2 s 1)(l mol/18 x 10-6 m3), or 0.6 x 10-3 mol mT s-1 (= 0.6 mmol m-2 s-1). When discussing water vapor movement in the previous section, we indicated that Jm> emanating from a moist shaded soil is usually 0.2 to 1.0 mmol m-2 s-1, so our calculated flux density is consistent with the range of measured values. The calculation also indicates that a fairly large gradient in hydrostatic pressure can exist near the soil surface. 

Most of the basic conditions and parameters of the simulation are the same as in Table 5 those which are different are given in Table 6. The map of the cell is presented in Fig. 29. Application of a pressure gradient changes the distribution of water vapor concentration at the cathode dramatically. Due to the pressure gradient water accumulates in front of the Red channel. This leads to a significant flux of water into this channel (cf. Fig. 30). Under current density 0.4 A cm-2 the flux of water is about 0.1 A cm-2 (cf. Fig. 30). The Red channel, therefore, collects water. 

---