A Parameterization of Bowen Ratio with Respect to Soil Moisture Availability

The Bowen ratio (B) is impacted by 5 environmental elements: soil moisture availability, m, the ratio of resist-ances between atmosphere and soil pores, ra/rd, atmospheric relative humidity, h, atmospheric stability, ΔT, and environment temperature. These impacts have been investigated over diverse surfaces, including bare soil, free water surface, and vegetation covered land, using an analytical approach. It was concluded that: (a) B is not a continuous function. The singularity exists at the condition αhcb=h, occurring preferably in the following conditions: weak turbulence, stable stratified stability, dry soil, and humid air, where hcb, defined by Eq.(11) is a critical variable. The existence of a singularity makes the dependence of B on the five variables very complicated. The value of B approaches being inversely proportional to m under the conditions m≥mfc (the soil capacity) and / or ra/rd→0. The proportional coefficient changes with season and latitude with relatively high values in winter and over the poles; (b) B is nearly independent of ra/rd during the day. The impact of m on B is much larger as compared to that of ra/rd on B, (c) when h increases, the absolute value of B also increases; (d) over bare soil, when the absolute surface net radiation increases, the absolute value of B will increase. The impact of RN on B is larger at night than during the day, and (e) over plant canopy, the singularity and the dependcies of B on m, ra , and h are modified as compared to that over bare soil. Also (i) during the daytime unstable condition, m exerts an even stronger impact on B, at night, however, B changes are weak in response to the change in m; (ii) the value of B is much more sensitive in response to the changes of turbulent intensity; (iii) the B response to the variation of h over a vegetation covered area is weaker; and (iv) the singularity exists at the condition hcp=h instead of αhcb=h as over bare soil, where hcp is defined by Eq.(49). The formulas derived over bare soil also hold the same when applied to free water bodies as long as they are visualized as a special soil in which the volumetric fraction of soil pore is equal to one and are fully filled with water. Finally, the above discussions, are used to briefly study the impact on the thermally induced mesoscale circulations.

A parameterization of Bowen ratio with respect to soil moisture availability

The Bowen ratio (B) is impacted by 5 environmental elements: soil moisture availabillity,m, the ratio of resistances between atmosphere and soil pores,r _a/r_D, atmospheric relative humidity,h, atmospheric stability, δT, and environment temperature. These impacts have been investigated over diverse surfaces, including bare soil, free water surface, and vegetation covered land, using an analytical approach. It was concluded that: (a)B is not a continuous function. The singularity exists at the condition ah_cb = h, occurring preferably in the following conditions: weak turbulence, stable stratified stability, dry soil, and humid air, where h_cb, defined by Eq.(11) is a critical variable. The existence of a singularity makes the dependence ofB on the five variables very complicated. The value ofB approaches being inversely proportional tom under the conditionsm ≥ m_fc (the soil capacity) and / orr _a/r_D→ 0. The proportional coefficient changes with season and latitude with relatively high values in winter and over the poles; (b)B is nearly independent of-during the day. The impact ofm onB is much larger as compared to that ofr _a/r_D onB; (c) whenh increases, the absolute value ofB also increases; (d) over bare soil, when the absolute surface net radiation increases, the absolute value ofB will increase. The impact of R_N onB is larger at night than during the day, and (e) over plant canopy, the singularity and the dependcies ofB on m,r_a, andh are modified as compared to that over bare soil. Also (i) during the daytime unstable condition,m exerts an even stronger impact onB; at night, however,B changes are weak in response to the change inm; (ii) the value ofB is much more sensitive in response to the changes of turbulent intensity; (iii) theB response to the variation ofh over a vegetation covered area is weaker; and (iv) the singularity exists at the condition h_cp = h instead of αh_cb =h as over bare soil, where h_cp is defined by Eq.(49). The formulas derived over bare soil also hold the same when applied to free water bodies as long as they are visualized as a special soil in which the volumetric fraction of soil pore is equal to one and are fully filled with water. Finally, the above discussions are used to briefly study the impact on the thermally induced mesoscale circulations.