HEAT AND MASS TRANSFER BETWEEN SOIL AND ATMOSPHERE IN HANNO NEW RESIDENT TOWN

 

Pham Hong SON

Researcher, Hydroscience and Geotechnology Lab., Saitama University, Japan

Kuniaki SATO

Member of IAHR, Prof. Dr. Hydroscience and Geotechnology Lab.,Saitama University, Japan

KUNIO FUJII

Researcher, Dr., Wind Engineering Institute, Japan

 

 

ABSTRACT

This study concerns with an integrated simulation of coupled heat and mass transfer between bare soil and atmosphere. A model is constructed in one dimension from ground water table up to upper atmospheric boundary layer. Numerical solutions of momentum, heat and mass transport equations are available for prediction of physical processes occurring in atmospheric boundary layer and in porous bodies. The processes in the atmosphere and in the porous bodies are linking each other by a statement of heat and mass conservation. The water mass in the soil is treated as a two-phase mixture of liquid water and vapour. The simulated results are supported by the observation data recorded by a meteorological station placed in the experimental field in Hanno new resident town, Saitama prefecture. A good agreement indicates that the model is reliable for predicting a water budget dynamics in a zone near surface land and atmosphere.

 

Keywords: : Heat Transfer, Mass Transfer, Coupling Heat and Mass, Evaporation

 

1. Introduction

It is widely recognised that urbanisation may modify natural hydrological and thermal cycles. Worrying about possible negative impacts on the local environment, a study has been carried out to investigate heat and mass transfer in the Hanno area where a large-scale land development is under way. Under the plan, a total 137.7 ha of natural forest will be removed and a new resident city is to be build with 30% area for resident complex, 26% for public facilities and remaining for transportation and green area.

As part of outputs from water budged in the area, the evaporation from bare soil is observationally and numerically investigated herein. Modern metropolitan today accompanies not only with high building and large area of pavement but also with large underground facilities such as tunnels, shopping mails, etc. Therefore, it is necessary to consider the effects of the development on heat and water cycles in both atmospheric and soil zones near the land surface.

SALSA (Soil Atmosphere Linking Simulation Algorithm) (Berge¹⁾ 1990) is one of energetic models considering soil-surface-atmosphere as unique system. Following this algorithm, the heat and mass transfer between bare soil and atmosphere in Hanno test site of Housing Urban Development Co., Japan was simulated. The results provide useful information for estimating water balance in this area.

 

2. Methodology of modelling

The model is constructed basing on three main parts: surface, atmospheric and soil with a statement of mass and energy conservation. Using measured meteorological data and surface condition, the model estimates the heat and mass transfer between soil and atmosphere through the soil surface. After that, the physical processes occurring in atmospheric boundary layer and porous media are simulated. Only the main methodology of the model is described herein.

 

2.1 Atmospheric modelling

The equations describing the momentum, temperature and moisture in vertical direction are simplified in the following forms: (Berge¹⁾ 1990)

; ; (1)

; (2)

where u, v are two components of horizontal velocity, u_g, v_g are corresponding geostrophic velocities, f is Coriolis parameter, r is air density, q is moisture mixing ratio (kg water/kg dry air), H is the sensible heat flux, E is vapour flux (kgm^-2s^-1), q is potential temperature, C_p is specific heat of air and t is shear stress

Momentum, sensible heat and vapour flux transport can be written using eddy diffusivities K_M,H,V as follows:

; ; ; , (3)

where the subscripts M,H and V denote the moment, heat and vapour, respectively. The constant vertical fluxes are given by

. (4)

The length scales l_M,H,V are estimated from similarity functions f_M,H,V by the equation

(5)

in which stability parameter z=z/L, L is Monin-Obukhov length scale, k is Karman constant, a and C are empirical coefficients equal 4´10^-4 and 0.2, respectively. The above system is closed by the turbulent kinematic energy e (TKE) equation (Tennekes & Lumley²⁾ 1972)

(6)

where T is air temperature (K)

For the roughness sublayer, the logarithmic friction laws are imposed for velocity and potential temperature

 

2.2 Heat and WATER transfer in the soil

The problem of unsaturated flow induced by evaporation and integrated coupling of heat and mass has been discussed in many studies (Philip & de Vries³⁾, Milly⁴⁾, Fukuhara⁵⁾ et al. The equation used for describing the heat transfer in capillary porous bodies is simplified in the form:

(7)

where T_s is soil temperature, J_v (kg m^-2s^-1) is vapour flux, H_v (Jkg^-1) is latent heat of water vaporisation, C_s (Jm^-3K^-1) is soil capacity and l (Wm^-1K^-1) is soil conductivity.

The water in the soil is treated here as a two-phase mixture of liquid water and water vapour. The liquid water equation is given in the form

(8)

where p is potential pressure (Pa), K is hydraulic conductivity (kgm^-1Pa^-1s^-1), r₁ is ground water density, g is gravity acceleration and q_w is volumetric water content.

The water vapour transfer is expressed by

(9)

where r_v is vapour density (kgm^-3), q_v is volumetric vapour content, D is diffusion coefficient of vapour m²s^-1. Among alternative available options, Van Genuchten's ⁶⁾(1980) equation for hydraulic conductivity, the approaches of Philip and de Vries³⁾ (1957) for r_v and of Cary⁷⁾ (1963) for D are applied herein. Detailed of the analyses are given in Berge¹⁾ 1990.

 

3. Observation Field Site

The field site where the measurement system is stationed locates in the Hanno new resident town, Saitama prefecture (35^o53'N, 138^o36'E) (see figure 1). The geology of the site consists of an alluvium above a basement in the Mesozoic and Paleozoic era, and the upper layer is covered with the talus, river deposits and unconsolidated gravel. The topography of the project site is mountainous, and the gradient of slope in valleys is steep in 30-40^o. The permeability of the site is small because the formation of mountain is composed of weakly cemented gravel.

 

 

Fig.1 Location of observation field and system of measurement

 

The meteorological properties: air temperatures at two height positions (0.5 and 1.0m), humidity, solar radiation, ground heat flux, albedo, precipitation, atmospheric pressure, wind speed and its direction, are recorded for every hour. Addition to the meteorological observation, the soil samples at each 5cm from surface down to 1m underground on Aug. 12, 1997 also taken to identify the soil hydraulic properties, its structure and water content in laboratory. Also on this day the thermal sensors were installed to record the soil temperature at corresponding depth. The net radiation is showed in figure 2.

 

 

Fig.2 Net radiation observed at the experimental field in Hanno in 1997.

 

4. Simulation Results

 

4.1 Simulation Condition

The simulation is carried out for a domain from ground water table up to 1500 m in atmospheric boundary layer with assumption that the domain is considered horizontally homogeneous. The ground table is supposed to be at 1.5m below the ground surface. At this boundary, the zero gradients of soil temperature and water content are imposed during total simulation period. The porous body is divided into 25 layers by nonuniform mesh. The grid size is smallest (0.2cm) at layer nearest to the surface and gradually increases to 30cm in ground water table layer.

For the atmospheric computational domain, total 20 grid points are used with smallest size 0.75m at the surface and 350 m for the top layer. At the top layer, the zero gradients of potential temperature and mixing ratio are enforced. Here u=u_g, v=v_g, t_x=t_y=0, H=0, E=0, also are specified.

The simulation is performed under condition in the field during the period Aug. 6-12, 1997 starting at 0.00 o'clock on Aug. 6. Time step is 1s during computational period and an implicit Crank-Nicholson differencing scheme is used in time. The net radiation and water vapour pressure are inputted during the calculation.

 

4.2 Results

For each time step, the surface subroutine is called first to estimate the surface heat fluxes and the surface soil temperature by solving the heat balance equation. After that the system of heat, liquid water and water vapour transfer equations in porous body is solved. Identification of soil properties of taken sample shows that the soil in the experiment site has similar structure and parameters in the zone from surface down to 0.7m. In lower zone the soil structure becomes more complicated with mixed gravel. The average value of the soil properties in near ground zone is used herein because the most important events are apparently occurred in this layer.

Figure 3 showed the simulated profiles of soil temperature, water content and water mass flux from ground water table up to the surface on Aug. 12 (Julian day 225) at 5:00, 13:00 and 21:00 o'clock. On this day, the net radiation at noon was very strong (see figure 2). As a result, the variation of heat and water mass can be clearly observed on upper part of porous domain (0-0.5m deep). They are little being effected on lowered layer. This effect can be seen in the figure 4, the plots of soil temperature, water content and water mass flux at 0.2, 5.0, 15.0 and 40.0 cm underground vs. time.

 

 

Fig.3 Simulated profiles of soil temperature, water content and mass flux in soil below ground on Aug. 12, 1997

 

 

Fig. 4 Time dependence of simulated soil temperature, water content and mass flux at several depths

 

The absent of precipitation in the concerned period causes the surface to be drying, especially for the last two days when the input of net radiation is very strong. It can be found that during daytime, the development of drying zone in the near ground surface accelerates the temperature while thermally induced mass flow plays an important part in moisture deficit by evaporation. The variation of mass flux during the night is not the same with that in the night. In addition to the capillary flow, the thermally induced flow caused by a sharp gradient of temperature strongly contributes to recharging of water in near ground zone.

The profiles of simulated air potential temperature and mixing ratio on Aug. 12 at 5:00, 13:00 and 21:00 o'clock are showed in the figure 5. Their variation at 1.0m, 20m and 380m during the simulated period are plotted in the figure 6. It is clearly that the diurnal air temperature in the layer lower than 500 m is strongly changes while in the layer higher than 500 m weak effect is observed. As a result of evaporation from the surface, the moisture available on the subsurface layer increases at noon. This vapour is convected upward due to buoyancy effect caused by heating of the soil surface and momentum transfer in the atmosphere. The simulated results provide understanding of the heat and water mass variation in lower atmospheric layer and soil.

 

 

Fig.5 Simulated profile of air potential temperature, and mixing ratio on Aug. 12. 1997

 

 

Fig.6 Time dependence of simulated air potential temperature and mixing ratio

 

5. Conclusion

The reasonable obtained results indicate that the model successfully describes the physical heat and mass transfer in the computational domain from ground water table up to the upper boundary layer. The model therefore can be used as a predicting tool for estimation of evaporation from bare soil.

The simulation process has shown that an accuracy of the model depends on a set of location characteristics: soil structure, its conductivity and surface roughness.

Coupling between the dependent variables in porous bodies is strong and is non-linear that requires appropriate numerical method for solving the set of differential equations. Particular attention should be given to capillary force resulting in saturation and thermal induced effects, molecular diffusion due to local vapour pressure and gravity.

 

Acknowledgement

The authors would like to express their appreciation to the Housing Urban Development Corporation, Japan for providing the research data.

 

References

1.      H.F.M. ten Berge Heat and water transfer in bare topsoil and the lower atmosphere, Centre for agricultural Publishing and documentation (Pudoc) Wageningen, the Netherlands, 1990.

2.      Tennekes, H. & Lumley, 1972. A first course in turbulence. MIT Press, Cambridge, Massachusetts.

3.      Philip & de Vries, 1957, Moisture movement in porous materials under temperature gradients. Transactions of the American Geophysical Union 38: 222-231.

4.      Milly, Unsaturated flow induced by evaporation and transpiration, in H.J. Morel-Seytoux (ed.) Unsaturated flow in Hydrologic modelling. Theory and practice, 221-240, 1989.

5.      Fukuhara, T., G.F. Pinder & Sato K. An approach to fully coupled heat and moisture transfer analysis in saturated unsaturated porous media during surface evaporation, Proc. of Japan Society for civil engineers (JSCE) Vol. 423/II-14 pp 111-120.

6.      Rawls W.J. & Brakensiek D.L., 1989. Estimation of soil water retention and hydraulic properties. in H.J. Morel-Seytoux (ed.) Unsaturated flow in Hydrologic modelling. Theory and practice, 275-300, 1989.

7.      Cary, J.W., 1979. Soil heat tranducers and water vapor flow, Soil Science Society of America Journal 43: 835-839.